EARTHQUAKE ENGINEERING HANDBOOK
New Directions in Civil Engineering Series Editor
W. F. CHEN Hawaii University Published Titles Advanced Analysis of Steel Frames: Theory, Software, and Applications W.F. Chen and Shouji Toma Analysis and Software of Cylindrical Members W.F. Chen and Shouji Toma Artificial Intelligence and Expert Systems for Engineers C.S. Krishnamoorthy and S. Rajeev Cold Weather Concreting Boris A. Krylov Concrete Beams with Openings: Analysis and Design M.A. Mansur and Kiang-Hwee Tan Concrete Buildings: Analysis for Safe Construction W.F. Chen and K.H. Mosallam Flexural-Torsional Buckling of Structures N.S. Trahair Flood Frequency Analysis Ramachandro A. Rao and Khaled Hamed Fracture Processes of Concrete Jan G.M. van Mier Fracture and Size Effect in Concrete and Other Quasibrittle Materials Zdenek P. Bazant and Jaime Planas Introduction to Environmental Geotechnology Hsai-Yang Fang Limit Analysis and Concrete Plasticity M.P. Nielsen LRFD Steel Design Using Advanced Analysis W.F. Chen and Seung-Eock Kim Response Spectrum Method in Seismic Analysis and Design of Structures Ajaya Kumar Gupta Simulation-Based Reliability Assessment for Structural Engineers Pavel Marek, Milan Gustar, and Thalia Anagnos Stability Design of Steel Frames W.F. Chen and E.M. Lui Stability and Ductility of Steel Structures under Cyclic Loading Yuhshi Fukumoto and George C. Lee The Finite Strip Method Y.K. Cheung and L.G. Tham Theory of Adaptive Structures: Incorporating Intelligence into Engineered Products Senol Utku Unified Theory of Reinforced Concrete Thomas T.C. Hsu Water Treatment Processes: Simple Options S. Vigneswaran and C. Visvanathan ˆ
ˆ
Forthcoming Titles Earthquake Engineering Handbook W.F. Chen and Charles Scawthorn Transportation Systems Planning: Methods and Applications Konstandinos Goulias
EARTHQUAKE ENGINEERING HANDBOOK EDITED BY
Wai-Fah Chen Charles Scawthorn
CRC PR E S S Boca Raton London New York Washington, D.C.
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Library of Congress Cataloging-in-Publication Data Earthquake engineering handbook / edited by Wai-Fah Chen, Charles Scawthorn. p. cm.—(New directions in civil engineering) Includes bibliographical references and index. ISBN 0-8493-0068-1 (alk. paper) 1. Earthquake engineering—Handbooks, manuals, etc. I. Chen, Wai-Fah, 1936- II. Scawthorn, Charles, III. Series. TA654.6 .E374 2002 624.1'762—dc21
2002073647
This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and information, but the authors and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage or retrieval system, without prior permission in writing from the publisher. All rights reserved. Authorization to photocopy items for internal or personal use, or the personal or internal use of specific clients, may be granted by CRC Press LLC, provided that $1.50 per page photocopied is paid directly to Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923 USA The fee code for users of the Transactional Reporting Service is ISBN 0-8493-0068-1/03/$0.00+$1.50. The fee is subject to change without notice. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. The consent of CRC Press LLC does not extend to copying for general distribution, for promotion, for creating new works, or for resale. Specific permission must be obtained in writing from CRC Press LLC for such copying. Direct all inquiries to CRC Press LLC, 2000 N.W. Corporate Blvd., Boca Raton, Florida 33431. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation, without intent to infringe.
Visit the CRC Press Web site at www.crcpress.com © 2003 by CRC Press LLC Information contained in this work has been obtained from sources believed to be reliable. ICBO®, NCSEA, or their memberships shall not be responsible for any errors, omissions, or damages arising out of this information. This work is published with the understanding that ICBO and NCSEA, as copublishers, are supplying information but are not attempting to render engineering or other professional services. If such services are required, the assistance of an appropriate professional should be sought. No claim to original U.S. Government works International Standard Book Number 0-8493-0068-1 Library of Congress Card Number 2002073647 Printed in the United States of America 1 2 3 4 5 6 7 8 9 0 Printed on acid-free paper
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Foreword
The International Conference of Building Officials® (ICBO®) is proud to join CRC Press to co-publish the Earthquake Engineering Handbook. Known internationally for its development and publication of the Uniform Building Code™ (UBC™), ICBO’s reputation as a leader in seismic codes traces its origin back to 1927 with its release of the nation’s first complete model building code. The Earthquake Engineering Handbook is not only timely, reflecting the most recent research in earthquake engineering, but also comprehensive, covering more than 30 topics. Written by a panel of internationally known experts, the Handbook provides applications and practical information to help solve real-world problems faced by civil, structural, geotechnical, and environmental engineers. The Handbook also serves as an excellent resource for researchers and students wishing to extend their knowledge of earthquake engineering. Editors Wai-Fah Chen, and Charles Scawthorn have done a masterful job of assembling a “blue ribbon” panel of authors from both academic and professional engineering communities. The result is a book that more than lives up to the reputation of the long and outstanding line of engineering handbooks from CRC Press. The Earthquake Engineering Handbook does not just review standard practices, but also brings readers quickly up to date on new approaches and innovative techniques. CRC Press and ICBO would like to thank the National Council of Structural Engineers Associations (NCSEA) for co-sponsoring this Handbook. NCSEA was founded for the purpose of improving the level of standard practice for the structural engineering profession throughout the United States and to represent the profession on a national level. Mark A. Johnson Director of Publications and Product Development, ICBO
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Preface
The Handbook of Earthquake Engineering is a comprehensive reference and resource work covering the spectrum of disciplines required for mitigation of earthquake effects and design of earthquake-resistant structures. It has been written with the practitioner in mind. The focus is on a graduate engineer with a need for a single reference source to keep abreast of new techniques and practices, as well as review standard practices. Earthquake engineering requires first of all knowledge of the geologic causes of, and expected shaking, liquefaction, and other effects that result from, a strong earthquake. It also requires a good understanding of the impacts these natural effects have on humankind, ranging from our buildings and other structures to the entire built and even social environment. In this regard, earthquakes are an almost unique natural phenomenon, in that they affect virtually everything within a region — even to furnishings within a building, and underground structures. To this end, the Handbook is divided into five parts. Initially, Part I reviews the basic problem of earthquakes from a historical perspective, provides an overview of the framework within which earthquake risk is managed and an introduction to dynamics, since earthquakes are most fundamentally a dynamic process and problem. Part II of the Handbook addresses the geoscience aspects, covering geology, tectonics, liquefaction and tsunamis, focusing especially on earthquake strong ground motion. Parts III and IV cover the broad spectrum of structures, from buildings built of steel, concrete, wood and masonry, to special structures such as bridges and equipment, to the variety of infrastructure called lifelines — that is, the water, power, transportation and other systems and components without which modern urban society cannot function. Earthquake structural engineering in the last decade has also seen a burst of new technology intended to avoid rather than resist the forces of earthquakes. These topics, base isolation and structural control, are also included. Because earthquakes affect not only the built but also the social environment, in all its aspects, Part V addresses special topics that the earthquake engineer must be cognizant of, if not indeed be expert in. An important aspect of this is the social and economic impacts of earthquakes, which in recent years have assumed increasing importance. We wish to thank all the authors for their contributions and also to acknowledge the support of CRC Press. Wai-Fah Chen Charles Scawthorn
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Editors
Wai-Fah Chen is presently Dean of the College of Engineering at the University of Hawaii. He was a George E. Goodwin Distinguished Professor of Civil Engineering and Head of the Department of Structural Engineering at Purdue University from 1976 to 1999. He received his B.S. in civil engineering from the National ChengKung University, Taiwan, in 1959, M.S. in structural engineering from Lehigh University, Pennsylvania, in 1963, and Ph.D. in solid mechanics from Brown University, Rhode Island, in 1966. He received the Distinguished Alumnus Award from the National Cheng-Kung University in 1988 and the Distinguished Engineering Alumnus Medal from Brown University in 1999. Dr. Chen’s research interests cover several areas, including constitutive modeling of engineering materials, soil and concrete plasticity, structural connections, and structural stability. He is the recipient of several national engineering awards, including the Raymond Reese Research Prize and the Shortridge Hardesty Award, both from the American Society of Civil Engineers, and the T. R. Higgins Lectureship Award from the American Institute of Steel Construction. In 1995, he was elected to the U.S. National Academy of Engineering. In 1997, he was awarded Honorary Membership by the American Society of Civil Engineers. In 1998, he was elected to the Academia Sinica (National Academy of Science) in Taiwan. A widely respected author, Dr. Chen authored and coauthored more than 20 engineering books and 500 technical papers. His books include several classical works such as Limit Analysis and Soil Plasticity (Elsevier, 1975), the two-volume Theory of Beam-Columns (McGraw-Hill, 1976–77), Plasticity in Reinforced Concrete (McGraw-Hill, 1982), and the two-volume Constitutive Equations for Engineering Materials (Elsevier, 1994). He currently serves on the editorial boards of more than 10 technical journals. He has been listed in more than 20 Who’s Who publications. Dr. Chen is the editor-in-chief for the popular 1995 Civil Engineering Handbook, the 1997 Handbook of Structural Engineering, and the 1999 Bridge Engineering Handbook. He currently serves as the consulting editor for McGraw-Hill’s Encyclopedia of Science and Technology. He has been a longtime member of the Executive Committee of the Structural Stability Research Council and the Specification Committee of the American Institute of Steel Construction. He has been a consultant for Exxon Production Research on offshore structures, for Skidmore, Owings, and Merrill in Chicago on tall steel buildings, and for the World Bank on the Chinese University Development Projects, among many others. Dr. Chen has taught at Lehigh University, Purdue University, and the University of Hawaii.
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Charles Scawthorn is a Senior Vice President with an international risk consulting firm. He received his Bachelor of Engineering from The Cooper Union for the Advancement of Science and Art, New York; M.S. in structural engineering from Lehigh University, Bethlehem, Pennsylvania; and Doctor of Engineering in seismic risk analysis from Kyoto University, Kyoto, Japan. In more than 30 years of practice, Dr. Scawthorn has designed and analyzed buildings and industrial structures and engaged in planning projects and research in the United States and internationally. These projects have included structural design of high-rise buildings, offshore platforms, and critical facilities such as LNG plants and data processing and emergency operating centers. These activities have progressed from the assessment of individual structure risk to that of complex systems risk and the development of integrated risk reduction programs. Dr. Scawthorn has assessed organizational and community risk due to earthquake and other hazards for the Federal Emergency Management Agency (FEMA), the Office of Emergency Services, and other agencies in the United States, and for national governments and the World Bank internationally. These projects have ranged from analysis of portfolio risks for multinational corporations and insurance companies, and regional loss assessments for government, to analysis of enterprise-wide risk for multinationals, and design of national insurance programs. These projects have ranged across the United States, Mid-East, Far East, and Europe. Under funding from the National Science Foundation, the U.S. Geological Survey, FEMA and the insurance industry, Dr. Scawthorn has developed innovative approaches for the analysis of fires following earthquakes, optimizing urban land use with respect to natural hazards risk, and seismically reinforcing low-strength masonry buildings. Much of his decision-oriented and emergency management work on the spread and mitigation of fires following earthquakes has been performed in conjunction with fire departments in California, particularly San Francisco. He has been a principal in the development of techniques for the rapid assessment of seismic vulnerability, is the original author of the EQEHAZARDTM software for seismic risk assessment, and was technical lead on the development of a national Flood Loss Estimation Model for HAZUS, for the National Institute of Building Sciences and FEMA. Dr. Scawthorn has investigated natural disasters in the United States, Canada, Mexico, Japan, Turkey, and the former Soviet Union. Dr. Scawthorn is a Fellow of the American Society of Civil Engineers and a member of various other professional organizations. He has served on the Scientific Advisory Committee of the National Center for Earthquake Engineering Research, received the Applied Technology Council’s Award of Excellence for Extraordinary Achievement in Seismic Evaluation of Buildings, and is on the Editorial Board of Engineering Structures and the Natural Hazards Review (ASCE). He is the author of over 100 technical papers as well as a contributor to the McGraw-Hill Yearbook of Science and Technology.
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Contributors
Jorma K. Arros
Lian Duan
James J. Johnson
ABS Consulting Oakland, California
California Department of Transportation Sacramento, California
James J. Johnson and Associates Alamo, California
Donald B. Ballantyne ABS Consulting Seattle, Washington
Horst G. Brandes
Eser Durukal ˇ ¸ University Bogacizi Kandilli Observatory Istanbul, Turkey
Department of Civil Engineering University of Hawaii Honolulu, Hawaii
ImageCat, Inc. Long Beach, California
Gilles J. Bureau
Mustafa Erdik
Consulting Engineer Piedmont, California
ˇ ¸ University Bogacizi Kandilli Observatory Istanbul, Turkey
Kenneth W. Campbell ABS Consulting and EQECAT, Inc. Portland, Oregon
Kuo-Chun Chang Department of Civil Engineering National Taiwan University Taiwan, China
Wai-Fah Chen University of Hawaii Honolulu, Hawaii
J. Daniel Dolan Brooks Forest Product Research Center Department of Wood Science and Forest Products Virginia Polytechnic Institute and State University Blacksburg, Virginia
© 2003 by CRC Press LLC
Ronald T. Eguchi
Ronald O. Hamburger Simpson Gumpertz & Heger, Inc. San Francisco, California
Mahmoud Khater ABS Consulting Oakland, California
Richard E. Klingner Department of Civil Engineering The University of Texas Austin, Texas
Howard Kunreuther Wharton School University of Pennsylvania Philadelphia, Pennsylvania
David L. McCormick ABS Consulting Oakland, California
Susumu Iai Port and Airport Research Institute Yokosuka, Japan
Hirokazu Iemura Graduate School of Civil Engineering Department of Civil Engineering Systems Kyoto University Kyoto, Japan
Gayle S. Johnson Han-Padron Associates Oakland, California
Y. L. Mo Department of Civil and Environmental Engineering University of Houston Houston, Texas
Niaz A. Nazir DeSimone Consulting Engineers San Francisco, California
Michael J. O’Rourke Department of Civil Engineering Rensselaer Polytechnic Institute Troy, New York
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Keith A. Porter
Hope A. Seligson
Yeong-Bin Yang
Civil Engineering Department California Institute of Technology Pasadena, California
ABS Consulting Irvine, California
Department of Civil Engineering National Taiwan University Taiwan, China
Mulyo Harris Pradono Structural Dynamics Laboratory Department of Civil Engineering Systems Kyoto University Kyoto, Japan
Richard Roth, Jr. Consulting Casualty Actuary Huntington Beach, California
Charles Scawthorn Consulting Engineer Berkeley, California
Anschel J. Schiff Stanford University Stanford, California
© 2003 by CRC Press LLC
Guna Selvaduray Materials Engineering Department San Jose State University San Jose, California
Kimberly I. Shoaf School of Public Health University of California at Los Angeles Los Angeles, California
Costas Synolakis Department of Civil Engineering University of Southern California Los Angeles, California
Paul C. Thenhaus ABS Consulting Evergreen, Colorado
Jong-Dar Yau Department of Architecture and Building Technology Tamkang University Taiwan, China
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Contents
SECTION I
1
Earthquakes: A Historical Perspective 1.1 1.2
2
Jorma K. Arros Introduction Single-Degree-of-Freedom System Multidegree-of-Freedom Systems
SECTION II
5
Charles Scawthorn
Introduction Overview of Earthquake Risk Identifying the Assets at Risk Earthquake Hazard Earthquake Damage and Loss Mitigation Alternatives Earthquake Risk Management Decision-Making Earthquake Risk Management Program Summary
Dynamics of Structures 3.1 3.2 3.3
4
Charles Scawthorn
Introduction Review of Historical Earthquakes
Earthquake Risk Management: An Overview 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9
3
Fundamentals
Geoscience Aspects
Earthquakes: Seismogenesis, Measurement, and Distribution Charles Scawthorn 4.1 4.2 4.3 4.4 4.5
Introduction Causes of Earthquakes and Faulting Measurement of Earthquakes Global Distribution of Earthquakes Characterization of Seismicity
Engineering Models of Strong Ground Motion 5.1 5.2
Introduction The Attenuation Relation
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Kenneth W. Campbell
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5.3 5.4 5.5 5.6 5.7
Model Parameters Statistical Methods Theoretical Methods Engineering Models Engineering Evaluation
6
Simulation Modeling of Strong Ground Motion
7
Geotechnical and Foundation Aspects Horst G. Brandes
8
Seismic Hazard Analysis
6.1 6.2 6.3 6.4 6.5 6.6
7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8
8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 8.10 8.11 8.12 8.13 8.14 8.15 8.16 8.17 8.18
Mustafa Erdik and Eser Durukal Introduction Earthquake Source Models Time Domain Characteristics of Strong Ground Motion Frequency Domain Characteristics of Strong Ground Motion Radiation Pattern and Directivity Simulation of Strong Ground Motion
Introduction Seismic Hazards Strong Ground Motion Dynamic Soil Behavior Liquefaction Seismic Analysis of Slopes and Dams Earthquake-Resistant Design of Retaining Walls Soil Remediation Techniques for Mitigation of Seismic Hazards Paul C. Thenhaus and Kenneth W. Campbell Introduction Probabilistic Seismic Hazard Methodology Constituent Models of the Probabilistic Seismic Hazard Methodology Definition of Seismic Sources Earthquake Frequency Assessments Maximum Magnitude Assessments Ground Motion Attenuation Relationships Accounting for Uncertainties Typical Engineering Products of PSHA PSHA Disaggregation PSHA Case Study The Owen Fracture Zone–Murray Ridge Complex Makran Subduction Zone Southwestern India and Southern Pakistan Southeastern Arabian Peninsula and Northern Arabian Sea Ground Motion Models Soil Amplification Factors Results
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8.19 Conclusions 8.20 PSHA Computer Codes
9
10
Tsunami and Seiche 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9
Costas Synolakis Introduction Tsunamis vs. Wind Waves Tectonic Tsunami Sources Initial Waves Generated by Submarine Landslides Exact Solutions of the Shallow-Water (SW) Equations Numerical Solutions for Calculating Tsunami Inundation Harbor and Basin Oscillations Tsunami Forces Producing Inundation Maps
Soil–Structure Interaction 10.1 10.2 10.3 10.4 10.5
James J. Johnson Soil–Structure Interaction: Statement of the Problem Specification of the Free-Field Ground Motion Modeling of the Soil Soil–Structure Interaction Analysis Soil–Structure Interaction Response
SECTION III
11
Structural Aspects
Building Code Provisions for Seismic Resistance 11.1 11.2 11.3 11.4
Ronald O. Hamburger
Introduction Historical Development 2000 NEHRP Recommended Provisions Performance-Based Design Codes
12
Seismic Design of Steel Structures
13
Reinforced Concrete Structures
Ronald O. Hamburger and Niaz A. Nazir 12.1 Introduction 12.2 Historic Development and Performance of Steel Structures 12.3 Steel Making and Steel Material 12.4 Structural Systems 12.5 Unbraced Frames Appendix A: Design Procedure for a Typical Reduced Beam Section-Type Connection
13.1 Introduction 13.2 Basic Concepts
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Y. L. Mo
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13.3
14
Seismic Behavior 13.4 Analytical Models 13.5 Seismic Design 13.6 Seismic Retrofit
Precast and Tilt-Up Buildings 14.1 14.2 14.3 14.4 14.5
15
Wood Structures 15.1 15.2 15.3 15.4 15.5 15.6 15.7 15.8
16
J. Daniel Dolan Introduction Wood As a Material Seismic Performance of Wood Buildings Design Considerations Resistance Determination Diaphragms Shear Walls Connections
Seismic Behavior, Design, and Retrofitting of Masonry 16.1 16.2 16.3 16.4 16.5 16.6 16.7
17
Charles Scawthorn and David L. McCormick Introduction Precast and Tilt-Up Buildings Performance of Precast and Tilt-Up Buildings in Earthquakes Code Provisions for Precast and Tilt-Up Buildings Seismic Evaluation and Rehabilitation of Tilt-Up Buildings
Richard E. Klingner Introduction Masonry in the United States Performance of Masonry in U.S. Earthquakes Fundamental Basis for Seismic Design of Masonry in the United States Masonry Design Codes Used in the United States Analysis Approaches for Modern U.S. Masonry Seismic Retrofitting of Historical Masonry in the United States
Base Isolation 17.1 17.2 17.3 17.4 17.5 17.6 17.7 17.8 17.9
Yeong-Bin Yang, Kuo-Chun Chang, and Jong-Dar Yau Introduction Philosophy behind Seismic Isolation Systems Basic Requirements of Seismic Isolation Systems Design Criteria for Isolation Devices Design of High Damping Rubber Bearings Design of Lead Rubber Bearings Design of Friction Pendulum Systems Design Examples Concluding Remarks
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18
Bridges 18.1 18.2 18.3 18.4 18.5 18.6 18.7 18.8
19
Structural Control 19.1 19.2 19.3 19.4 19.5
20
Hirokazu Iemura and Mulyo Harris Pradono Introduction Structural Control Concepts Structural Control Hardware and Software Examples of the Application of Semiactive Control Concluding Remarks
Equipment and Systems 20.1 20.2 20.3 20.4 20.5 20.6 20.7
21
Lian Duan and Wai-Fah Chen Introduction Earthquake Damages to Bridges Seismic Design Philosophies Seismic Conceptual Design Seismic Performance Criteria Seismic Design Approaches Seismic Analysis and Modeling Seismic Detailing Requirements
Gayle S. Johnson Introduction Importance of Equipment Seismic Functionality Historical Performance Design Practices Code Provisions Assessment of Existing Facilities Nonstructural Damage
Seismic Vulnerability 21.1 21.2 21.3 21.4 21.5 21.6 21.7 21.8
Keith A. Porter Introduction Method 1: Statistical Approach Method 2: Expert Opinion Analytical Methods: General Validation of Vulnerability Functions Catalog of Vulnerability Functions Uses of Vulnerability Functions Closing Remarks
SECTION IV
22
Infrastructure Aspects
Lifeline Seismic Risk
Ronald T. Eguchi 22.1 Introduction 22.2 Brief History of Lifeline Earthquake Engineering in the United States
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22.3 22.4 22.5 22.6 22.7
23
Buried Pipelines 23.1 23.2 23.3 23.4 23.5 23.6 23.7 23.8 23.9 23.10
24
Donald B. Ballantyne Introduction Performance Objectives Analysis Overview Hazards Pipe Vulnerability and Damage Algorithms System Component Vulnerability System Assessment Mitigation Alternatives Summary and Conclusions
Electrical Power Systems 25.1 25.2 25.3 25.4 25.5 25.6 25.7 25.8 25.9
26
Michael J. O’Rourke Introduction Pipeline Performance in Past Earthquakes PGD Hazard Quantification Wave Propagation Hazard Quantification Pipe Failure Modes and Failure Criterion Pipeline Response to Faulting Pipeline Response to Longitudinal PGD Pipeline Response to Transverse PGD Pipeline Response to Wave Propagation Countermeasures to Mitigate Seismic Damage
Water and Wastewater Systems 24.1 24.2 24.3 24.4 24.5 24.6 24.7 24.8 24.9
25
Nonlinearity of Earthquakes Indirect Economic Losses Cost-Effective Mitigation Strategies Federal and Industry Lifeline Initiatives Lifeline Seismic Risk
Anschel J. Schiff Introduction Historical Response of Electrical Power Systems to Earthquakes Code Provision, Standards and Guidelines for Electrical Systems Earthquake Preparedness Earthquake Hazard and System Vulnerability Evaluation Earthquake Preparedness — Disaster-Response Planning Earthquake Preparedness — Earthquake Mitigation Earthquake Preparedness — Mitigation Closing Remarks
Dams and Appurtenant Facilities 26.1 Introduction 26.2 Dams and Earthquakes
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Gilles J. Bureau
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26.3 26.4 26.5 26.6 26.7
27
Seismic Vulnerability of Existing Dams Seismic Evaluation of Dams Seismic Upgrade of Existing Dams Seismic Design of New Dams Seismic Instrumentation of Dams
Port Structures 27.1 27.2 27.3 27.4 27.5 27.6 27.7
Susumu Iai Introduction Seismic Response of Port Structures Current Seismic Provisions for Port Structures Seismic Performance-Based Design Seismic Performance Evaluation and Analysis Methods for Analysis of Retaining/Earth Structures Analysis Methods for Open Pile/Frame Structures
SECTION V
28
Human Impacts of Earthquakes 28.1 28.2 28.3 28.4 28.5 28.6 28.7 28.8
29
Hope A. Seligson and Kimberley I. Shoaf Introduction Casualties in Historic Earthquakes A Standardized Earthquake Injury Classification Scheme Casualty Estimation Methodology Casualty Mitigation and Prevention Public Health Impacts Shelter Requirements Closing Remarks
Fire Following Earthquakes 29.1 29.2 29.3 29.4 29.5
30
Special Topics
Charles Scawthorn Introduction Fires following Selected Earthquakes Analysis Mitigation Conclusion
Hazardous Materials: Earthquake-Caused Incidents and Mitigation Approaches Guna Selvaduray 30.1 30.2 30.3 30.4 30.5
Introduction and Significance of Earthquake-Caused Hazardous Materials Incidents The Loma Prieta Earthquake The Northridge Earthquake The Hanshin-Awaji Earthquake Earthquake-Caused HAZMAT Incidents at Educational Institutions and Laboratories
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30.6 30.7 30.8 30.9 30.10
31
Loss Estimation 31.1 31.2 31.3 31.4 31.5 31.6 31.7 31.8 31.9
32
Damage and Corrective Actions at Japanese Petroleum Facilities Lessons Learned Mitigation Approaches Problem Areas That Must Be Addressed Conclusions Mahmoud Khater, Charles Scawthorn and James J. Johnson Introduction and Overview Why Do We Need Loss Estimation? History of Loss Estimation Loss Modeling The Hazard Module Seismic Vulnerability Models Damage and Loss Estimation HAZUS® Earthquake Loss Estimation Software Applications of Loss Estimation
Insurance and Financial Risk Transfer
Charles Scawthorn, Howard Kunreuther,
and Richard Roth, Jr. 32.1 Introduction 32.2 Insurance and the Insurance Industry 32.3 Earthquake Insurance 32.4 Earthquake Insurance Risk Assessment 32.5 Government Earthquake Insurance Pools 32.6 Alternative Risk Transfer 32.7 Summary
33
Emergency Planning
34
Developing an Earthquake Mitigation Program
Charles Scawthorn 33.1 Introduction 33.2 Planning for Emergencies 33.3 Writing the Emergency Plan 33.4 The Emergency Operations Center (EOC) 33.5 Training and Maintenance of the Emergency Plan 33.6 Summary: Developing an Emergency Plan Appendix A Appendix B
34.1 34.2 34.3 34.4 34.5
Introduction Overview of an Earthquake Mitigation Program Phase 0: Pre-Program Activities Phase 1: Assessing the Problem Phase 2: Developing the Program
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Charles Scawthorn
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34.6 Phase 3: Implementing the Program 34.7 Maintaining the Program
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I Fundamentals
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1 Earthquakes: A Historical Perspective 1.1
Introduction Global Earthquake Impacts
1.2
Review of Historical Earthquakes Pre-Twentieth Century Events · Early Twentieth Century Events · Mid-Century Events · First Turning Point · Second Turning Point
Charles Scawthorn Consulting Engineer Berkeley, CA
Defining Terms References Further Reading
Let us look at the facts. – Terence Adelphoe, l. 796
1.1 Introduction Earthquakes are a major problem for mankind, killing thousands each year. A review of Table 1.1 shows, for example, that an average of almost 17,000 persons per year were killed in the twentieth century.1 Earthquakes are also multifaceted, sometimes causing death and destruction in a wide variety of ways, from building collapse to conflagrations, tsunamis, and landslides. This chapter therefore reviews selected earthquakes and the damage they have caused, to inculcate in the reader the magnitude and complexity of the problem earthquakes pose for mankind. To do this, we first review in this introduction some basic statistics on damage. Section 1.2, the heart of this chapter, then reviews selected earthquakes, chosen for their particular damaging effects, or because the earthquake led to a significant advance in mitigation. This review is focused. It is relatively brief on earlier earthquakes, which are mentioned largely for historical interest or because you should be aware of them as portents for future events; however, the review is lengthier on selected recent events, especially U.S. events, because these provide the best record on the performance of modern structures. Table 1.2 shows selected U.S. earthquakes. Based on this review, the next section then extracts important lessons, following which we conclude with a brief history of the response to earthquakes.
1
The average is still more than 10,000 if the single largest event (Tangshan, 1976) is omitted.
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TABLE 1.1
Selected Earthquakes Since 1900 (Fatalities Greater than 1,000)a
Year
Day-Month
Location
Latitude
Longitude
Deaths
M
1902
19-Apr 16-Dec 19-Apr 28-Apr 04-Apr 08-Sep 31-Jan 16-Mar 18-Apr 17-Aug 14-Jan 21-Oct 28-Dec 23-Jan 09-Aug 13-Jan 21-Jan 30-Jul 13-Feb 16-Dec
Guatemala Turkestan Turkey Turkey India, Kangra Italy, Calabria Colombia Taiwan, Kagi San Francisco, CA Chile, Santiago Jamaica, Kingston Central Asia Italy, Messina Iran Turkey, Marmara Sea Italy, Avezzano Indonesia, Bali China China, Canton China, Gansu
14N 40.8N 39.1N 39.1N 33.0N 39.4N 1N 23.6N 38N 33S 18.2N 38N 38N 33.4N 40.5N 42N 8.0S 28.0N 23.5N 35.8N
91W 72.6E 42.4E 42.5E 76.0E 16.4E 81.5W 120.5E 123W 72W 76.7W 69E 15.5E 49.1E 27E 13.5E 115.4E 104.0E 117.0E 105.7E
2,000 4,500 1,700 2,200 19,000 2,500 1,000 1,300 2,000+ 20,000 1,600 12,000 70,000 5,500 1,950 29,980 15,000 1,800 10,000 200,000
7.5 6.4
24-Mar 25-May 01-Sep 16-Mar 07-Mar 22-May 01-May 06-May 23-Jul 31-Mar 25-Dec 02-Mar 25-Aug 15-Jan 20-Apr 30-May 16-Jul 25-Jan 26-Dec 10-Nov 26-Nov 20-Dec
China Iran Japan, Kanto China, Yunnan Japan, Tango China, nr Xining Iran Iran Italy Nicaragua China, Gansu Japan, Sanriku China India, Bihar-Nepal Formosa Pakistan, Quetta Taiwan Chile, Chillan Turkey, Erzincan Romania Turkey Turkey, Erbaa
31.3N 35.3N 35.0N 25.5N 35.8N 36.8N 38N 38.0N 41.1N 13.2N 39.7N 39.0N 32.0N 26.6N 24.0N 29.6N 24.4N 36.2S 39.6N 45.8N 40.5N 40.9N
100.8E 59.2E 139.5E 100.3E 134.8E 102.8E 58E 44.5E 15.4E 85.7W 97.0E 143.0E 103.7E 86.8E 121.0E 66.5E 120.7E 72.2W 38E 26.8E 34.0E 36.5E
5,000 2,200 143,000 5,000 3,020 200,000 3,300 2,500 1,430 2,400 70,000 2,990 10,000 10,700 3,280 30,000 2,700 28,000 30,000 1,000 4,000 3,000
7.3 5.7 8.3 7.1 7.9 8.3 7.4 7.2 6.5 5.6 7.6 8.9 7.4 8.4 7.1 7.5 6.5 8.3 8 7.3 7.6 7.3
10-Sep 26-Nov 15-Jan
Japan, Tottori Turkey Argentina, San Juan
35.6N 41.0N 31.6S
134.2E 33.7E 68.5W
1,190 4,000 5,000
7.4 7.6 7.8
01-Feb 07-Dec 12-Jan 27-Nov 31-May 10-Nov
Turkey Japan, Tonankai Japan, Mikawa Iran Turkey Peru, Ancash
41.4N 33.7N 34.8N 25.0N 39.5N 8.3S
32.7E 136.2E 137.0E 60.5E 41.5E 77.8W
2,800 1,000 1,900 4,000 1,300 1,400
7.4 8.3 7.1 8.2 6 7.3
20-Dec
Japan, Tonankai
32.5N
134.5E
1,330
8.4
1903 1905 1906
1907 1908 1909 1912 1915 1917 1918 1920 1923
1925 1927 1929 1930 1931 1932 1933 1934 1935
1939 1940 1942
1943 1944
1945 1946
© 2003 by CRC Press LLC
6.3 8.6 7.9 8.9 7.1 8.3 8.6 6.5 8.1 7.5 7.3 7.8 7.5 6.5 7.3 8.6
Comments/Damage ($ millions)
Conflagration Conflagration Conflagration Deaths possibly 100,000
Major fractures, landslides
$2800, conflagration
Large fractures
Deaths possibly 60,000 $100
Some reports of 1,000 killed
Deaths possibly 8,000 Deaths possibly 5,000
Landslides, great destruction
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TABLE 1.1 (CONTINUED) Selected Earthquakes Since 1900 (Fatalities Greater than 1,000)a Year
Day-Month
1948
28-Jun 05-Oct 05-Aug 15-Aug
1949 1950 1954 1957
1960 1962 1963 1966 1968 1969 1970
1972 1974 1975 1976
1977 1978 1980 1981 1982 1983 1985 1986 1987 1988 1990 1991 1992 1993 1995 1997
Location
Latitude
Longitude
Deaths
M
Japan, Fukui Turkmenistan Ecuador, Ambato India, Assam; Tibet
36.1N 38.0N 1.2S 28.7N
136.2E 58.3E 78.5E 96.6E
5,390 110,000 6,000 1,530
7.3 7.3 6.8 8.7
09-Sep 27-Jun 02-Jul 13-Dec 29-Feb 22-May 01-Sep 26-Jul
Algeria, Orleansvl. USSR (Russia) Iran Iran Morocco, Agadir Chile Iran, Qazvin Yugoslavia, Skopje
36N 56.3N 36.2N 34.4N 30N 39.5S 35.6N 42.1N
1.6E 116.5E 52.7E 47.6E 9W 74.5W 49.9E 21.4E
1,250 1,200 1,200 1,130 10,000 4,000 12,230 1,100
6.8 7.4 7.3 5.9 9.5 7.3 6
19-Aug 31-Aug 25-Jul 04-Jan 28-Mar 31-May 10-Apr 23-Dec 10-May 28-Dec 04-Feb 06-Sep 04-Feb 06-May 25-Jun 27-Jul
Turkey, Varto Iran Eastern China Yunnan, China Turkey, Gediz Peru Iran, southern Nicaragua China Pakistan China Turkey Guatemala Italy, northeastern New Guinea China, Tangshan
39.2N 34.0N 21.6N 24.1N 39.2N 9.2S 28.4N 12.4N 28.2N 35.0N 40.6N 38.5N 15.3N 46.4N 4.6S 39.6N
41.7E 59.0E 111.9E 102.5E 29.5E 78.8W 52.8E 86.1W 104.0E 72.8E 122.5E 40.7E 89.1W 13.3E 140.1E 118.0E
2,520 12,000 3,000 10,000 1,100 66,000 5,054 5,000 20,000 5,300 10,000 2,300 23,000 1,000 422 255,000
7.1 7.3 5.9 7.5 7.3 7.8 7.1 6.2 6.8 6.2 7.4 6.7 7.5 6.5 7.1 8
16-Aug 24-Nov 04-Mar 16-Sep 10-Oct 23-Nov 11-Jun 28-Jul 13-Dec 30-Oct 19-Sep 10-Oct 06-Mar 20-Aug 07-Dec 20-Jun 16-Jul 19-Oct 12-Dec
Philippines Iran-USSR border Romania Iran, Tabas Algeria, El Asnam Italy, southern Iran, southern Iran, southern W. Arabian Peninsula Turkey Mexico, Michoacan El Salvador Colombia-Ecuador Nepal-India border Armenia, Spitak Iran, western Philippines, Luzon India, northern Indonesia, Flores
6.3N 39.1N 45.8N 33.2N 36.1N 40.9N 29.9N 30.0N 14.7N 40.3N 18.2N 13.8N 0.2N 26.8N 41.0N 37.0N 15.7N 30.8N 8.5S
124.0E 44.0E 26.8E 57.4E 1.4E 15.3E 57.7E 57.8E 44.4E 42.2E 102.5W 89.2W 77.8W 86.6E 44.2E 49.4E 121.2E 78.8E 121.9E
8,000 5,000 1,500 15,000 3,500 3,000 3,000 1,500 2,800 1,342 9,500 1,000 1,000 1,450 25,000 40,000 1,621 2,000 2,500
7.9 7.3 7.2 7.8 7.7 7.2 6.9 7.3 6 6.9 8.1 5.5 7 6.6 7 7.7 7.8 7 7.5
29-Sep 16-Jan 27-May 10-May
India, southern Japan, Kobe Sakhalin Island Iran, northern
18.1N 34.6N 52.6N 33.9N
76.5E 135E 142.8E 59.7E
9,748 6,000 1,989 1,560
6.3 6.9 7.5 7.5
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Comments/Damage ($ millions) Conflagration Large landslides Great topographical changes
Deaths possibly 15,000 Deaths possibly 5,000 Shallow depth just under city Deaths possibly 20,000
Great rockslide; $500 Managua
$6,000 West Irian Deaths possibly 655,000; $2,000 Mindanao
$11
Deaths possibly 30,000
$16,200 Deaths possibly 50,000 Landslides, subsidence Tsunami wave height 25 m $100,000, conflagration 4,460 injured; 60,000 homeless
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TABLE 1.1 (CONTINUED) Selected Earthquakes Since 1900 (Fatalities Greater than 1,000)a Year
Day-Month
1998
04-Feb 30-May 17-Jul 25-Jan 17-Aug 20-Sep 26-Jan
1999
2001
Location
Latitude
Longitude
Deaths
M
Afghanistan Afghanistan Papua New Guinea Colombia Turkey Taiwan
37.1N 37.1N 2.96S 4.46N 40.7N 23.7N
70.1E 70.1E 141.9E 75.82W 30.0E 121.0E
2,323 4,000 2,183 1,185 17,118 2,297
6.1 6.9 7.1 6.3 7.4 7.6
India, Bhuj
23.3 N
70.3 E
19,988
7.7
Total Events = 108
Comments/Damage ($ millions) Also Tajikistan Also Tajikistan Tsunami 50,000 injured; $7,000 8,700 injured; 600,000 homeless 166,812 injured; 600,000 homeless
Total Deaths = 1,762,802
a
Magnitude scale varies. Source: National Earthquake Information Center, Golden, CO, http://neic.usgs.gov/neis/eqlists/eqsmajr.html.
TABLE 1.2
Selected U.S. Earthquakesa
Year
Month
Day
1755 1774 1791
11 2 5
18 21 16
1811 1812
12 1 2 10
16 23 7 5
36N 36.6N 36.6N
6 6 1 10 4 10 3 9 2 4 5 5 9 4 10 6 11 3 12 10 5 9 4 8 7 12 3 7 8 8 3 4 2 3
10 0 9 8 3 21 26 1 24 19 16 31 4 18 3 29 4 11 31 19 19 5 13 21 21 16 9 10 18 30 28 29 9 28
38N 37.5N 35N 37N 19N 37.5N 36.5N 32.9N 31.5N 38.5N 14N
122W 123W 119W 122W 156W 122W 118W 80W 117W 123W 143W
60N 38N 40.5N 34.3N 34.5N 33.6N 31.8N 46.6N 32.7N 44.7N 47.1N 19.7N 35N 39.3N 51.3N 58.6N 44.8N 41.8N 61N 47.4N 34.4N 42.1N
142W 123W 118W 120W 121W 118W 116W 112W 116W 74.7W 123W 156W 119W 118W 176W 137W 111W 112W 148W 122W 118W 113W
1817 1836 1838 1857 1865 1868 1872 1886 1892
1897 1899 1906 1915 1925 1927 1933 1934 1935 1940 1944 1949 1951 1952 1954 1957 1958 1959 1962 1964 1965 1971 1975
Latitude
Longitude
M
MMI
Fatalities
Damage US $ (millions)
8 7 8
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90W 89.6W 89.6W
8.6 8.4 8.7
8.3
6.8 8.5 7.7
5.8 8.3 8.3 7.8 6.2 7.5 6.3 7.1 6.2 7.1 5.6 7 6.9 7.7 7 8.6 7.9 7.7 5.8 8.3 6.5 6.7 6.2
12 12 8 10 10 7 9 10 10 10 9 10 9
81 3 50 60
5
2,000
400
13
8
115
40
10
2 9
8
8
19 6 2 25
11 10
13
60
8 11
9 10
3 5
7 11 8
131 7 65
2 540 13 553 1
Locale Massachusetts, Nr Cape Ann Eastern Virginia (MMI from Sta) Connecticut, E. Haddam (MMI from Sta) Missouri, New Madrid Missouri, New Madrid Missouri, New Madrid Massachusetts, Woburn (MMI from Sta) California California California, Central California, San Jose, Santa Cruz Hawaii California, Hayward California, Owens Valley South Carolina, Charleston California, San Diego County California, Vacaville, Winters Guam, Agana Virignia, Giles County (Mb from Sta) Alaska, Cape Yakataga California, San Francisco (fire) Nevada, Pleasant Valley California, Santa Barbara California, Lompoc California, Long Beach California, Baja, Imperial Valley Montana, Helena California, southeast of El Centro New York, Massena Washington, Olympia Hawaii California, Kern County Nevada, Dixie Valley Alaska Alaska, Lituyabay (landslide) Montana, Hebgen Lake Utah Alaska Washington, Seattle California, San Fernando Idaho, Pocatello Valley
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Earthquakes: A Historical Perspective
TABLE 1.2 (CONTINUED) Selected U.S. Earthquakesa
Year
Month
Day
Latitude
1975
8 11 1 5 7 11 5 10 11 4 7 10 11 6 10 2
1 29 24 25 27 8 2 28 16 24 8 1 24 26 18 28
39.4N 19.3N 37.8N 37.6N 38.2N 41.2N 36.2N 43.9N 19.5N 37.3N 34N 34.1N 33.2N 19.4N 37.1N 34.1N
122W 155W 122W 119W 83.9W 124W 120W 114W 155W 122W 117W 118W 116W 155W 122W 118W
6.1 7.2 5.9 6.4 5.2 7 6.5 7.3 6.6 6.2 6.1 6 6.3 6.1 7.1 5.5
4 4 6 6 6 3 9 1 1 2 10
23 25 28 28 29 25 21 16 17 3 6
34N 40.4N 34.2N 34.2N 36.7N 45N 42.3N 40.3N 34.2N 42.8N 65.2N
116W 124W 117W 116W 116W 123W 122W 76W 119W 111W 149W
6.3 7.1 6.7 7.6 5.6 5.6 5.9 4.6 6.8 6 6.4
1980
1983
1984 1986 1987 1989 1990 1992
1993 1994
1995
Longitude
M
MMI
Fatalities
9 7 7
2 1
7 8
5 2
8 7 7 8 6 6 9 7 7 8 8 9 7 7 5 9 7
8 2 62
Damage US $ (millions) 6 4 4 2 1 3 31 13 7 8 5 358
6,000 13 66
3
92
2 57
30,000
Locale California, Oroville Reservoir Hawaii California, Livermore California, Mammoth Lakes Kentucky, Maysville California, northern coast California, central, Coalinga Idaho, Borah Peak Hawaii, Kapapala California, Morgan Hill California, Palm Springs California, Whittier California, Superstition Hills Hawaii California, Loma Prieta California, southern, Claremont, Covina California, Joshua Tree California, Humboldt, Ferndale California, Big Bear California, Landers, Yucca Valley California-Nevada border T.S. Washington-Oregon Oregon, Klamath Falls Pennsylvania (felt Canada) California, Northridge Wyoming, Afton Alaska (oil pipeline damaged)
a
Magnitude scale varies. Source: National Earthquake Information Center (1996). Database of Significant Earthquakes Contained in Seismicity Catalogs, Golden, CO.
1.1.1 Global Earthquake Impacts Globally, earthquakes have caused massive death and destruction up to the present day. Table 1.1 provides a list of selected twentieth century earthquakes with fatalities of approximately 1,000 or more, and Table 1.3 provides a list of earthquakes with fatalities of approximately 50,000 or more prior to the twentieth century. All the earthquakes are in the Trans-Alpide belt or the circum-Pacific Ring of Fire (Figure 1.1), and the great loss of life is almost invariably due to low-strength masonry buildings and dwellings. Exceptions to this rule are few in number but include the 1923 Kanto (Japan) earthquake, where most of the approximately 140,000 fatalities were due to fire; the 1970 Peru earthquake, where large landslides destroyed whole towns; the 1988 Armenian event, where 25,000 were killed in Spitak and Leninakan, mostly due to poor quality, precast construction; and the 1999 Marmara (Turkey) earthquakes, where 17,000 were killed in a rapidly urbanizing area where many mid-rise, soft story, reinforced concrete buildings collapsed, due largely to inadequate code enforcement [Scawthorn, 2000]. The absolute trend for earthquake fatalities is not decreasing, as indicated in Figure 1.2, although if population increase is taken into account, some relative decrease is occurring. Economic and insured losses for all sources, as indicated in Figure 1.3, are increasing. The 1995 Kobe (Japan) earthquake, with unprecedented losses of $100 billion,2 may only be a harbinger of even greater losses if an earthquake strikes Tokyo, Los Angeles, San Francisco, or some other large urban region. To understand how these losses occur and how they might be reduced, it is valuable to review some important earthquakes from previous centuries as well as very recent earthquakes. 2 The largest previous loss due to any natural hazard was in the 1994 Northridge earthquake, estimated at about $40 billion.
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TABLE 1.3
Selected Pre-Twentieth Century Earthquakes (Fatalities Greater than 50,000)
Year
Month
Day
Location
Deaths
856 893 1138 1268 1290 1556 1667 1693 1727 1755 1783
12 3 8
22 23 9
Iran, Damghan Iran, Ardabil Syria, Aleppo Asia Minor, Silicia China, Chihli China, Shansi Caucasia, Shemakha Italy, Sicily Iran, Tabriz Portugal, Lisbon Italy, Calabria
200,000 150,000 230,000 60,000 100,000 830,000 80,000 60,000 77,000 70,000 50,000
9 1 11 1 11 11 2
23 11 18 1 4
M
Comments
8.7
Great tsunami, fires
Source: National Earthquake Information Center, Golden, CO, http://neic.usgs.gov/neis/eqlists/eqsmosde.html.
Earthquakes of 20th Century Number of Deaths 100,000 - 255,000
(5)
50,000 - 100,000
(3)
20,000 - 50,000
(9)
10,000 - 20,000 (14) 5,000 - 10,000 (14) 2,000 - 5,000 (31) 1,000 - 2,000 (32) 1,000 or less (1)
FIGURE 1.1 Selected earthquakes since 1900 (fatalities greater than 1000).
1.2 Review of Historical Earthquakes This section presents a review of selected historical earthquakes. The review is divided into several parts: pre-twentieth century, early and mid-twentieth century, and two periods termed first and second turning points, respectively. Magnitudes (M, see Chapter 4) are indicated but, especially for the earlier events, are necessarily estimated rather than measured, and are therefore quite approximate; later events are indicated on the moment magnitude scale (Mw) where possible. Similarly, seismic intensity maps are provided when available, in most cases using the Modified Mercalli Intensity scale (MMI, see Chapter 4). © 2003 by CRC Press LLC
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Earthquakes: A Historical Perspective
10,000,000 1,000,000 100,000 10,000 1,000 100 10 1
1
2
3
4
5
6
7
8
9
10
FIGURE 1.2 Twentieth century global earthquake fatalities, by decade.
US$ 160bn 80 70 60 50 40 30 20 10 0 1950
1955
1960
1965
1970
1975
1980
1985
1990
1995
2000
Economic losses (2000 values) of which insured losses (2000 values) Trend of economic losses Trend of insured losses (Amounts in US$ bn)
FIGURE 1.3 Trend of worldwide economic and insured losses. (From Munich Reinsurance.)
1.2.1 Pre-Twentieth Century Events As Table 1.3 indicates, truly catastrophic earthquakes have occurred for many centuries. Herein we review very briefly only a few of these events, selected for their historical importance. 1.2.1.1 1755: November 1, Lisbon, Portugal (M9) The earthquake began at 9:30 on November 1, 1755, and was centered in the Atlantic Ocean, about 200 km WSW of Cape St. Vincent.3 Lisbon, the Portuguese capital, was the largest and most important of the cities damaged; however, severe shaking also was felt in France, Switzerland, and Northern Italy, and in North Africa shaking was felt with heavy loss of life in Fez and Mequinez. A devastating fire following the earthquake raged for five days and destroyed a large part of Lisbon. 3
The following discussions are largely drawn from Kozak and James [n.d.].
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FIGURE 1.4 Lisbon, Portugal, ruins of Praca de Patriarcal (Patriarchal Square) (copper engraving, Paris, 1757), Le Bas series, Bibliothèque Nationale. Colleção de algunas ruinas de Lisboa, 1755. Drawings executed by Messrs Paris et Pedegache. Paris: Jacques-Phillippe Le Bas, 1757. (From the Kozak Collection of Images of Historical Earthquakes, National Information Service for Earthquake Engineering, University of California, Berkeley. With permission.)
A very strong tsunami caused heavy destruction along the coasts of Portugal, southwestern Spain, and western Morocco. About 30 min after the quake, a large wave swamped the area near Bugie Tower on the mouth of the Tagus. The area between Junqueria and Alcantara in the western part of the city was the most heavily damaged by a total of three waves with maximum height estimated at 6 m, each dragging people and debris out to sea and leaving exposed large stretches of the river bottom. In Setubal, 30 km south of Lisbon, the water reached the first floor of buildings. The destruction was greatest in Algarve, southern Portugal, where the tsunami dismantled some coastal fortresses and, in the lower levels, razed houses. In some places, the waves crested at more than 30 m. The tsunami reached, with less intensity, the coasts of France, Great Britain, Ireland, Belgium, and Holland. In Madeira and in the Azores, damage was extensive and many ships were in danger of being wrecked. The tsunami crossed the Atlantic Ocean, reaching the Antilles in the afternoon. Reports from Antigua, Martinique, and Barbados note that the sea first rose more than a meter, followed by large waves. The oscillation of suspended objects at great distances from the epicenter indicates an enormous area of perceptibility. The observation of seiches as far away as Finland suggests a magnitude approaching 9.0. Between the earthquake and the fires and tsunami that followed (which were probably more damaging than the actual earthquake), approximately 10,000 to 15,000 people died (population: 275,000) [Kendrick, 1956]. As Kozak and James [n.d.] note, most depictions of damaged Lisbon are fanciful; Figure 1.4, however, is an accurate depiction of a portion of central Lisbon following the earthquake. The 1755 Lisbon earthquake was felt across broad parts of Europe. It occurred at the height of the Enlightenment and on the eve of the Industrial Revolution. Its massive death and destruction of one of the largest and most beautiful cities in Europe shook thinkers such as Voltaire, whose inherent optimism was deeply shaken by the event, as can be seen in his poem, Poeme sur le desastre de Lisbonne: Did Lisbon, which is no more, have more vices Than London and Paris immersed in their pleasures? Lisbon is destroyed, and they dance in Paris! Rousseau disagreed with Voltaire’s change in philosophy, taking a more pragmatic view: …it was not Nature that collected twenty thousand houses on the site … if the inhabitants of this big city had been more equally dispersed and more lightly housed, the damage would have been much less. [Quoted in Goldberg, 1989] From a scientific viewpoint, changes were made in building construction in Lisbon following the earthquake, such as the gaiola (an internal wooden cage for masonry buildings), as well as in the planning of reconstructed Lisbon; however, while the gaiola survived to the 1920s in Portugal, it was little publicized and not utilized elsewhere [Tobriner, 1984]. Together with the 1783 Calabrian earthquakes, the Lisbon earthquake strengthened nascent European efforts at construction of seismological instruments [Dewey and Byerly, 1969]. 1.2.1.2 1755: November 18, Cape Ann, MA (M7) The heaviest damage due to this earthquake occurred in the region around Cape Ann and Boston. At Boston, much of the damage was confined to an area of infilled land near the wharfs. There, about 100 © 2003 by CRC Press LLC
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1-9
chimneys were leveled with the roofs of houses, and many others (1200 to 1500) were shattered and partly thrown down. Stone fences were thrown down throughout the countryside, particularly on a line extending from Boston to Montreal. New springs formed, and old springs dried up. Water and fine sand issued from ground cracks at Pembroke. This earthquake was felt from Lake George, NY, to a point at sea 200 miles east of Cape Ann, and from Chesapeake Bay to the Annapolis River, Nova Scotia, about 300,000 mi2 [Stover and Coffman, 1993]. Due to the proximity in dates, and observations of a tsunami in the eastern Atlantic caused by the Lisbon earthquake, effects at distance between the two events are sometimes confused. 1.2.1.3 1811–1812: New Madrid, MO, Sequence The 1811–1812 sequence of earthquakes centered around New Madrid, on the Mississippi River in the central United States, south of St. Louis and north of Memphis, are of note due to their being some of the largest magnitude earthquakes ever recorded in North America, and definitely the largest earthquakes east of the Rockies. Between 1811 and 1812, four catastrophic earthquakes, with magnitude estimates greater than 7.0, occurred during a 3-month period. Nuttli [1973] determined a 7.2 mb body-wave magnitude for the 2:15 a.m., December 16, 1811 event; and Street [1982] used the spatial attenuation of intensities for all four events to show magnitudes of 7.0 for the 8:15 a.m., December 16, 1811 event; 7.1 for the January 23, 1812 event; and 7.3 for the February 7, 1812 event. Hundreds of aftershocks followed over a period of several years. The total energy released by the principal shocks and their larger-magnitude aftershocks is estimated to be equivalent to that of an mb = 7.5 (or MS = 8.0) earthquake, approximately equivalent to the 1906 San Francisco earthquake. The largest earthquakes to have occurred since then were on January 4, 1843 and October 31, 1895, with magnitude estimates of 6.0 and 6.2, respectively, and considerable uncertainty exists as to the likelihood of large earthquakes in this region. Figure 1.5 shows MMI observations for the December 16, 1811 event, in which it can be seen that extremely violent shaking occurred in the Mississippi Valley, and the event was felt from Connecticut to Illinois to South Carolina. In 1811–1812, however, these areas were quite sparsely populated, with very few significant structures of any kind. If such events were to occur today, considering the enormous development in the central United States, including, for example, the massive navigational improvements constructed over the last 100 years along the Mississippi and tributary rivers, the potential loss of life, damage, and economic disruption would be catastrophic. No comprehensive loss estimates have been performed for a repeat of the 1811–1812 sequence; however, losses have been estimated for impacts to lifelines and ensuing economic impacts [Applied Technology Council, 1991], and for annualized losses to buildings (structures only) [Federal Emergency Management Agency, 2000], from which it can be approximately estimated that a repeat of the 1811–1812 events today would cause economic losses in the range of $50 to $100 billion. Fuller [1912] provides detailed information on topographical and geological effects, and Hopper [1985] provides estimates of intensity if similar events were to occur today. 1.2.1.4 1857: January 9, Fort Tejon, CA (M7) This earthquake occurred on the San Andreas fault, which ruptured from near Parkfield (in the Cholame Valley) almost to Wrightwood (a distance of about 300 km) (Figure 1.6). Horizontal displacement of as much as 9 m was observed on the Carrizo Plain. A comparison of this shock to the San Francisco earthquake, which occurred on the San Andreas fault on April 18, 1906, shows that the fault break in 1906 was longer but that the maximum and average displacements in 1857 were larger. Property loss was heavy in the sparsely populated area, and one person was killed in the collapse of an adobe house at Gorman. Strong shaking lasted from 1 to 3 min. Instances of seiching, fissuring, sandblows, and hydrologic changes were reported from Sacramento to the Colorado River delta. Sandblows occurred at Santa Barbara and in the flood plain of the Santa Clara River. The shock was felt from Marysville south to San Diego and east to Las Vegas, NV. Several slight to moderate foreshocks preceded the main shock by 1 to 9 h. Many aftershocks occurred, and two (January 9 and 16) were large enough to have been widely felt [Stover and Coffman, 1993]. © 2003 by CRC Press LLC
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F
F
F NF NF NF NF
NF 4
5
5
F
F
5
NF
6
4
7−8
6 5−6
7 6−7 8
8
5−6
5 5
6 6 7 7 6−7
6 6
NF
F 5 F NF 6
NF
5 6
5
5
5
7 5
7
NF
5
5
7 6 7 7−8 11 8 11
6
NF
6−7 4 6 7
5 7
5−6
4
4
5−6 F 6−7 6 5−6 5−6
5
6 4 5
6 5−6
F
NF DEC. 16, 1811 (02:15 A.M.) 0
KM
300
FIGURE 1.5 Isoseismal map of the December 16, 1811 earthquake. The arabic numbers give the Modified Mercalli Intensities at each data point. (From Nuttli, O.W. 1979. “Seismicity of the Central United States,” in Geology in the Siting of Nuclear Power Plants, Hatheway, A.W. and McClure, C.R., Eds., Geological Society of America, Rev. Eng. Geol, 4, 67–94. With permission.)
1.2.1.5 1886: Charleston, SC The largest and by far the most destructive earthquake in the southeast United States occurred on August 31, 1886, with epicenter about 15 miles northwest of Charleston, SC (32.9 N, 80.0 W). The first shock was at 21:51, with magnitude of 7.6 [Johnston, 1991], and the second about 8 min later. The earthquake was felt over 2.5 million mi2 (from Cuba to New York, and Bermuda to the Mississippi), equivalent to a © 2003 by CRC Press LLC
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Earthquakes: A Historical Perspective
124°
122°
120°
118°
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FIGURE 1.6 Modified Mercalli Intensity map, 1857 Fort Tejon, CA, earthquake. (From Stover, C.W. and Coffman, J.L. 1993. Seismicity of the United States, 1568–1989 (revised). U.S. Geological Survey Professional Paper 1527, Government Printing Office, Washington, D.C.)
radius of more than 800 mi; the strongly shaken portion extended to 100 mi. Approximately 110 persons lost their lives and 90% of the brick structures in Charleston were damaged [Dutton, 1889]. Damaging secondary effects were fires, ruptured water and sewage lines, damaged wells, flooding from a cracked dam in Langley, SC, and in the highest intensity area bent railroad tracks, throwing one train off the tracks. Dollar damage estimates in 1886 dollars were about $5.5 million. Four decades later, Freeman [1932] made a careful study of the damage, concluding that “taking the city as a whole, the ratio of earthquake damage to sound value was small in Charleston, and probably averaged little if any more than 10%.” The bending of rails and lateral displacement of tracks due to ground displacements were very evident in the epicentral region, though not at Charleston. There were severe bends of the track in places and sudden and sharp depressions of the roadbed. At one place, there was a sharp S-curve. At a number of locations, the effect on culverts and other structures demonstrated strong vertical force in action at the © 2003 by CRC Press LLC
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FIGURE 1.7 Effects in the epicentral area of the 1886 Charleston, SC, earthquake. (From Algermissen, S.T. 1983. An Introduction to the Seismicity of the United States, Earthquake Engineering Research Institute, Berkeley, CA. With permission.)
time of the earthquake. Figure 1.7 is a map of effects in the epicentral area, while Figure 1.8 shows damage in central Charleston, bent rails due to ground movement, and large sand boils, indicating liquefaction, in the surrounding hinterland. This and the 1755 Cape Ann, MA, earthquakes demonstrate the potential for large, damaging earthquakes in the eastern United States.
1.2.2 Early Twentieth Century Events 1.2.2.1 1906: April 18, San Francisco (Mw 7.9) This earthquake is the most devastating in the history of California, and one of the most important in the history of earthquake engineering. The region of destructive intensity extended over a distance of © 2003 by CRC Press LLC
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FIGURE 1.8 (A) Damage in central Charleston, (B) bent rails due to ground movement, and (C) large sand boils indicating liquefaction. (From Peters, K.E. and Herrmann, R.B., Eds. n.d. First-Hand Observations of the Charleston Earthquake of August 31, 1886 and Other Earthquake Materials, South Carolina Geological Survey Bulletin 41.)
600 km. The total felt area included most of California and parts of western Nevada and southern Oregon (Figure 1.9). This earthquake caused the most lengthy fault rupture observed in the contiguous United States, i.e., from San Juan Bautista to Point Arena, where it passes out to sea, with additional displacement observed farther north at Shelter Cove in Humbolt County, indicating a potential total length of rupture of 430 km. Fault displacements were predominantly right lateral strike-slip, with the largest horizontal displacement — 6.4 m — occurring near Point Reyes Station in Marin County (Figure 1.10). The surface of the ground was torn and heaved into furrow-like ridges. Roads crossing the fault were impassable, and pipelines were broken. On or near the San Andreas fault, some buildings were destroyed but other buildings, close to or even intersected by the fault, sustained nil to only light damage (Figure 1.11). South of San Francisco, the concrete block gravity-arch dam of the Crystal Springs Reservoir (dam only 100 to 200 yards from the fault, reservoir on the fault) was virtually undamaged by the event, and the San Andreas earthen dam, whose abutment was intersected by the fault rupture, was also virtually undamaged, although surrounding structures sustained significant damage or were destroyed [Lawson et al., 1908]. The earthquake and resulting fires caused an estimated 3000 deaths and $524 million in property loss. One pipeline that carried water from San Andreas Lake to San Francisco was broken, shutting off the water supply to the city. However, distorted ground within the city resulted in hundreds of breaks in water mains, which were the actual source of lack of water supply for firefighting (Figure 1.12). Fires that ignited in San Francisco soon after the onset of the earthquake burned for three days because of the lack of water to control them (Figure 1.13). Damage in San Francisco was devastating, with 28,000 buildings destroyed, although 80% of the damage was due to the fire, rather than the shaking (Figure 1.14). Fires also intensified the loss at Fort Bragg and Santa Rosa. Damage was severe at Stanford University, south of San Francisco (Figure 1.15). Although Santa Rosa lies about 30 km from the San Andreas fault, © 2003 by CRC Press LLC
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FIGURE 1.9 MMI map of 1906 San Francisco earthquake. (From Stover, C.W. and Coffman, J.L. 1993. Seismicity of the United States, 1568–1989 (revised). U.S. Geological Survey Professional Paper 1527, U.S. Government Printing Office, Washington, D.C.)
damage to property was severe and 50 people were killed. The earthquake also was severe in the Los Banos area of the western San Joaquin Valley, where the MMI was IX more than 48 km from the fault zone. The maximum intensity of XI was based on geologic effects, but the highest intensity based on damage was IX. Several foreshocks probably occurred, and many aftershocks were reported, some of which were severe [Stover and Coffman, 1993]. © 2003 by CRC Press LLC
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FIGURE 1.10 Fence about 1 km northwest of Woodville on the E.R. Strain farm. This fence was offset 2.6 m by the main fault. Note the swerve in the fence as it approaches the fault-trace. The total displacement of the straight portions of the fence is about 3.3 m. (From National Geophysical Data Center, wysiwyg://122/http:/ /www.ngdc.noaa.gov/seg/hazard/slideset/earthquakes/2/ 2_slides.html.)
FIGURE 1.11 At W.D. Skinner’s farm near Olema, a fence south of this barn was offset 4.7 m. The barn, beneath which the fault-trace passed, remained attached to the foundation on the southwest side, but was broken from it on the northwest side and dragged 4.8 m. The fault-trace at this location also showed vertical offset, most likely caused by local soil conditions. The maximum vertical displacement of the faulting was 1.2 m. (Photo: G.K. Gilbert, U.S. Geological Survey. From National Geophysical Data Center, wysiwyg://122/http:/ /www.ngdc.noaa.gov/seg/hazard/slideset/earthquakes/2/ 2_slides.html.)
FIGURE 1.12 Union Street, San Francisco, not more than a quarter of a block in length between Pierce and Steiner Streets, had been filled to equalize the street grade, and the sides of the streets were not supported. During the earthquake, the north sidewalk was shifted about 3.0 m to the north and depressed about 3.0 m below its original level. The south sidewalk was depressed a few centimeters and shifted to the north as much as 1 m. The paving and cable conduit in this area incurred more severe damage than at any other point in the city. (From National Geophysical Data Center, wysiwyg://122/ http://www.ngdc.noaa.gov/seg/hazard/slideset/earthquakes/2/2_slides.html.)
The devastation in San Francisco was so enormous, and so largely due to fire (Figure 1.16), however, that some of the lessons of the event were lost. Studies on the effects of the earthquake and fire on structures and structural materials [USGS, 1907] focused as much on the fire as on the earthquake. A detailed review of a number of engineered buildings found that many had not been badly damaged by the earthquake and even, if well-fireproofed, had survived the fire in reasonable shape. Enough buildings © 2003 by CRC Press LLC
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FIGURE 1.13 This row of two-story buildings tilted away from the street when the ground beneath the foundations slumped. Such ground failures contributed to the shaking intensity and to the subsequent building damage. This photo was taken before fire destroyed the entire block. Note billowing smoke in the sky. (Photo: NOAA/ NGDC, wysiwyg://122/http://www.ngdc.noaa.gov/seg/ hazard/slideset/earthquakes/2/2_slides.html.)
(A)
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FIGURE 1.14 (A) Collapsed San Francisco City Hall; (B) the “damn’dest finest ruins,” this view looks east toward Market Street in San Francisco. Wooden buildings, one to three stories high, with brick or stone-work fronts, were closely interspersed with two- to eight-story brick buildings. Mingled with these were modern office buildings. Here the fire burned fiercely. In its aftermath, the streets were heaped with rubble to a depth of a meter or more and were nearly impassible. Because of the heat of the fire, much of the damage due directly to the shock was concealed or obliterated in this part of the city. (Photo: Eric Swenson, U.S. Geological Survey.) (C) One of the camps set up for earthquake victims is depicted. Similar camps were established on the hills, parks, and open spaces of the city. Five days after the earthquake rains brought indescribable suffering to the tens of thousands of people camped in the open. Few people had waterproof covering initially. The downpour aggravated the unsanitary conditions of the camps and added numbers of pneumonia cases to the already crowded regular and temporary hospitals of the city. Eventually tents such as these were provided to the 300,000 homeless. (Photo: Eric Swenson, U.S. Geological Survey. From National Geophysical Data Center, wysiwyg://122/http://www.ngdc.noaa.gov/seg/hazard/slideset/earthquakes/2/ 2_slides.html.) © 2003 by CRC Press LLC
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FIGURE 1.15 Memorial Church as seen from the inner quadrangle at Stanford University, Palo Alto. The stone tower of the church fell and destroyed the parts of the roof immediately around the tower. The gable on the north end of the church was thrown outward into the quadrangle. (Photo: W.C. Mendenhall, U.S. Geological Survey, wysiwyg://122/http://www.ngdc.noaa.gov/seg/hazard/slideset/earthquakes/2/2_slides.html.)
Principal distribution mains. Salt-water system. Old shore line. Boundary line of burned district. Principal earthquake breaks in streets. Districts covered largely by brick structures. Cisterns in service.
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FIGURE 1.16 Map of San Francisco showing district burned in 1907. (From U.S. Geological Survey. 1907. The San Francisco Earthquake and Fire of April 18, 1906 and Their Effects on Structures and Structural Materials. Bulletin 324, Washington, D.C.)
of various construction types were present that the study drew clear lessons from the event: that wellengineered steel and reinforced concrete buildings could survive shaking of this intensity with little damage. It was also noted that “great earthquakes are followed by … an interval of 50 or 100 years during which no earthquakes occur” [USGS, 1907] (which turned out to be true; see below). As a result, for many years the event was more popularly known as “the Fire,” and earthquake provisions were not especially emphasized in building codes in California until after the 1925 Santa Barbara and 1933 Long Beach events (see Section 1.2.2.3). © 2003 by CRC Press LLC
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FIGURE 1.17 San Francisco Bay area seismicity, showing pattern of seismicity leading up to 1906 earthquake, subsequent quiescence, and initial stages of new cycle. (From U.S. Geological Survey. 1907. The San Francisco Earthquake and Fire of April 18, 1906 and Their Effects on Structures and Structural Materials. Bulletin 324, Washington, D.C.)
The San Francisco earthquake resulted in the largest urban fire in history, only exceeded in peacetime by the 1923 Tokyo earthquake and fire (see below). It was the largest insurance loss in history up to that time; and it resulted in the first modern study and documentation of earthquake effects [Lawson et al., 1908] and in the publication and dissemination of Reid’s theory of elastic rebound [Reid et al., 1910]. This theory was vital to the understanding of earthquakes, as it clearly and simply explained that an earthquake was the sudden reaction of the Earth’s overly strained crust “snapping back” along the fault. Coupled with advances in the study of the Earth’s structure, observations from the 1906 and other large earthquakes in the early to mid-twentieth century increasingly provided an understanding of earthquake sources, finally unified by the theory of plate tectonics in the 1960s. An outcome of this is the ability to understand the earthquake cycle, as shown in Figure 1.17, from which it can be seen that the 1906 earthquake was the final (and by far largest) release of strain energy stored in the Earth’s crust due to plate motion (in the case of California and the 1906 earthquake, the North American and Pacific plates; see Chapter 4). That is, as the plates move past each other, the Earth’s crust is deformed, storing strain energy, not unlike a spring as it is stretched. As the plates are deformed, there are internal localized failures (i.e., small to intermediate earthquakes) and partial slippages (i.e., earthquakes), until finally the entire fault, strained to the breaking point, ruptures along its entire length, and snaps back the several meters the plates had displaced during the previous several hundred years. The previous cycle in the San Francisco Bay area is seen in Figure 1.17 to have begun with the 1838 earthquake,4 with an increasing rate of seismicity until 1906. From 1906 to the 1979 M5.7 Coyote Lake earthquake, there were relatively few earthquakes, and then an increasing number, with the 1989 Loma Prieta event (discussed below) being the analog of the 1838 event. The implications of this for the San Francisco Bay area are, of course, ominous. Another result of the 1906 earthquake was the founding of the Seismological Society of America. However, given the magnitude of the event and resulting damage, it would seem that a more comprehensive
4 Note that historic records in the San Francisco Bay area, although incomplete, date from the founding of the Mission Dolores in San Francisco in 1776.
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program of investigation into seismology and earthquake engineering would have emerged from the 1906 event. However, as Maher5 observes [Carder, 1965]: The great San Francisco earthquake of Apr. 18, 1906, resulted in a temporary impetus in earthquake investigation. However, after the excitement had died down, interest in research on earthquakes declined, partly because of activity by pressure groups who considered that the dissemination of information about earthquakes was detrimental to business. The existence of “pressure groups” is confirmed by Branner [1913].6 1.2.2.2 1923: September 1, Kanto, Japan (M 7.9) The M7.9 Kanto earthquake occurred at 11:58 a.m., September 1, 1923, with epicenter beneath Sagami Bay (Figure 1.18). The Tokyo region (actually, Mt. Fuji) is the junction of four tectonic plates (Philippine Sea, Pacific, Eurasian, and North American), and the subduction of the Pacific plate beneath the Eurasian plate was the seismogenesis of the event. Figure 1.18 shows contours of shaking damage percentage for Japanese wooden houses, contours of uplift and subsidence, locations of tsunami, and other effects in the most severely affected region [Hamada et al., 1992]. Seismic intensity on the Japan Meteorological Agency scale (JMA, see Chapter 4) is also indicated on the figure. Damage was heaviest in the Yokohama and Tokyo urbanized areas, although the shore of Sagami Bay and parts of the Boso peninsula also sustained heavy damage, a 3- to 6-m tsunami, and major geologic effects, with maximum crustal uplift of 2 m. The death toll in Kanagawa and Tokyo prefectures was 97,000, including about 60,000 in Tokyo city. The total number of dead and missing reached about 143,000, with 104,000 people listed as injured. About 128,000 houses and buildings were destroyed, another 126,000 heavily damaged, and as many as 447,000 lost to fire (Figures 1.19 and 1.20). Fire accounted for the majority of houses destroyed in Tokyo, and about 50% of houses lost in Kanagawa prefecture could be attributed to fire [Hamada et al., 1992]. The conflagration as a result of this fire is the largest peacetime conflagration in history, with combined fire and earthquake fatalities exceeding those of the incendiary attacks on Tokyo in World War II, and also probably exceeding the immediate fatalities in either of the atomic bombings of Hiroshima or Nagasaki. The conflagration was initially a mass fire (Figure 1.21), although self-generated winds resulted in large vortices or “firestorm” conditions in several locations, most notably at the Military Clothing Depot in Honjo Ward, where many refugees had gathered. Most of them carried clothing, bedrolls, and other flammables rescued from their homes, which served as a ready fuel source, and the engulfing flames suffocated an estimated 40,000 people. The enormous conflagration was due to hot, dry, windy conditions (although there had been some rain recently), combined with the time of the earthquake, just before noon, when the population was preparing its lunch. Coal or charcoal cooking stoves were in use throughout Tokyo and Yokohama for the noontime meal, and fires sprang up everywhere within moments of the quake. Firespread was very rapid, due to high winds as well as lack of water for firefighting because of broken water mains [ASCE, 1929].
5
Thomas J. Maher was a captain of the U.S. Coast and Geodetic Survey, and inspector-in-charge of the Survey's San Francisco field station from 1928 to 1936. He retired in 1946, and died in June 1964. 6 “… Another and more serious obstacle is the attitude of many persons, organizations, and commercial interests toward earthquakes in general. The idea back of this false position — for it is a false one — is that earthquakes are detrimental to the good repute of the West Coast, and that they are likely to keep away business and capital, and therefore the less said about them the better. This theory has led to the deliberate suppression of news about earthquakes, and even of the simple mention of them. Shortly after the earthquake of April 1906, there was a general disposition that almost amounted to concerted action for the purpose of suppressing all mention of that catastrophe. When efforts were made by a few geologists to interest people and enterprises in the collection of information in regard to it, we were advised and even urged over and over again to gather no such information, and above all not to publish it. ‘Forget it,’ ‘the less said, the sooner mended,’ and ‘there hasn't been any earthquake,’ were the sentiments we heard on all sides…” © 2003 by CRC Press LLC
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FIGURE 1.18 Map of distribution of damage, 1923 Kanto earthquake. (From Hamada, M., Wakamatsu, K., and Yasuda, S. 1992. “Liquefaction-Induced Ground Deformation during the 1923 Kanto Earthquake,” in Case Studies of Liquefaction and Lifeline Performance during Past Earthquakes, Vol. I, Japanese Case Studies, Hamada, M. and O’Rourke, T.D., Eds., Technical report NCEER-92–0001, February, National Center for Earthquake Engineering Research, State University of New York, Buffalo. With permission.)
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FIGURE 1.19 Tokyo (Ginza) ruins. (From Home Office. 1926. The Great Earthquake of 1923 in Japan, Bureau of Social Affairs, Home Office, Tokyo. With permission.)
FIGURE 1.20 Tokyo (Ginza) ruins. (From Home Office. 1926. The Great Earthquake of 1923 in Japan, Bureau of Social Affairs, Home Office, Tokyo. With permission.)
FIGURE 1.21 1923 Kanto earthquake conflagration, banks of Sumida River (aerial photo). (From Home Office. 1926. The Great Earthquake of 1923 in Japan, Bureau of Social Affairs, Home Office, Tokyo. With permission.)
As Cameron and James note: The Great Kanto earthquake ushered in the modern age of earthquake engineering …, [as exemplified in] … the World Engineering Congress of 1929 … [where] an early base isolation technique … by Riuitchi Oka …, promoting the use of “spherical rockers” at the base of columns … . Also of note was a paper by Kenzaburo Mashima, entitled “Earthquakes and Building Construction,” in which flexible construction was strongly endorsed. … Mashima also concluded that masonry structures were the most dangerous during an earthquake, followed by reinforced concrete buildings. He gave steel and wood structures the highest marks for seismic resistance. … Strongly in favor of rigid construction was Dr. Taichu Naito, Professor of Architecture at Waseda University in Tokyo. Naito noted three important elements in seismic resistant design: structural rigidity, a rational distribution of lateral force, and the reduction of the natural period of elastic oscillation to one smaller than the probable period of an earthquake … immediate changes in building codes followed the 1923 earthquake and were in effect in the rebuilding of Tokyo and Yokohama, including mandated maximum height and added bracing for wood buildings; increased requirements for masonry buildings, including parapet bracing; addition of brackets or braces to increase rigidity for connections between columns and girders in steel buildings; and improved detailing for reinforced concrete structures [Cameron and James, n.d., paraphrased]. © 2003 by CRC Press LLC
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FIGURE 1.22 MMI isoseismal map, 1933 Long Beach earthquake. (From Stover, C.W. and Coffman, J.L. 1993. Seismicity of the United States, 1568–1989 (revised). U.S. Geological Survey Professional Paper 1527, U.S. Government Printing Office, Washington, D.C.)
1.2.2.3 1925: Santa Barbara; 1933: Long Beach Earthquakes The M6.2 Santa Barbara earthquake occurred on June 29, 1925 and caused $8 million damage and 13 fatalities from an offshore shock in the Santa Barbara Channel, on an extension of the Mesa Fault or the Santa Ynez system. On State Street, the principal business thoroughfare, few buildings escaped damage; several collapsed. The shock occurred at 6:42 a.m., before many people had reported for work and when streets were uncrowded, reducing death and injury. The M6.3 Long Beach earthquake of March 10, 1933 had its epicenter offshore, southeast of Long Beach, on the Newport-Inglewood fault, and caused $40 million property damage and 115 lives lost (Figure 1.22). The major damage occurred in the thickly settled district from Long Beach to the industrial section south of Los Angeles, where unfavorable geological conditions (made land, water-soaked alluvium) combined with much poor structural work to increase the damage. At Long Beach, buildings collapsed, tanks fell through roofs, and houses displaced on foundations. School buildings were among those structures most generally and severely damaged (Figure 1.23), and it was clear that a large number of children would have been killed and injured had the earthquake occurred during school hours. These two earthquakes are discussed not so much for the size or peculiarities of damage, but due to advances in engineering and building code requirements instituted following these two events (see Chapter 11, this volume, for a more detailed discussion of this aspect): © 2003 by CRC Press LLC
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FIGURE 1.23 Walls crumbled at Alexander Hamilton Jr. High School on State Street, Long Beach. Great loss of life would have occurred if the shock had taken place during school hours.
• Following the 1925 event, the first modern code containing seismic provisions was published: the first edition of the Uniform Building Code, published by the Pacific Coast Building Officials in 1927 (see Chapter 11, this volume). Its seismic requirements were not mandatory and appeared in an appendix. • As a result of the 1925 event [SEAOC, 1980] and the efforts by a number of parties,7 a Seismological Field Survey was created in 1932 within the the U.S. Coast and Geodetic Survey (USC&GS), with offices in San Francisco. A strong motion accelerometer designed in 1931 by McComb and Parkhurst of the USC&GS, and Wenner of the National Bureau of Standards [Cloud, in Carder, 1965], modeled after the Wood-Anderson instrument [EERI, 1997], was deployed in 1932. During the 1933 Long Beach earthquake the first-ever recordings of earthquake strong ground motions were thus made (actually three recordings of the main shock, at Long Beach, Vernon, and Los Angeles [Maher, in Carder, 1965]). “This was a milestone, as it was the first time any such records had been made anywhere in the world” [EERI, 1997]. Following the 1933 Long Beach earthquake, which caused extensive damage to unreinforced masonry buildings and, in particular, several public schools, the State of California adopted regulations: • Further construction of unreinforced masonry buildings was prohibited. • The Riley Act was required that all building in California be provided with a lateral strength equal to 3% of the weight of the structure, making seismic design mandatory. • The Field Act established and charged the Office of the State Architect with responsibility for the regulation of public school construction. Schools had been especially damaged in the 1933 event. The Office of the State Architect established rigorous standards for structural design, plan review, and inspection of construction that would affect structural engineering practice throughout California and eventually find its way into the building code requirements applicable to all forms of construction.
1.2.3 Mid-Century Events 1.2.3.1 July 21, 1952: Kern County, CA (M7.7) This earthquake was the largest in the conterminous United States since the San Francisco shock of 1906 (Figure 1.24) and received considerable study by the earthquake community. Jenkins and Oakeshott [1955] edited a volume focused on the geology, seismology, and structural damage specific to the event, and the Bulletin of the Seismological Society of America published a special issue on data collected by
7
Sources vary. Housner [EERI, 1997] gives John Freeman full credit, indicating Freeman literally had to lobby President Herbert Hoover and his Secretary of Commerce, while Maher [in Carder, 1965] cites efforts by a citizens’ group, including Levison (president of Firemans Fund Insurance Company), Dewell (a practicing structural engineer in San Francisco), Baily Willis, and others. © 2003 by CRC Press LLC
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FIGURE 1.24 Modified Mercalli Intensity map, 1952 Kern County earthquake. (From Stover, C.W. and Coffman, J.L. 1993. Seismicity of the United States, 1568–1989 (revised). U.S. Geological Survey Professional Paper 1527, U.S. Government Printing Office, Washington, D.C.)
the Pacific Fire Rating Bureau [Steinbrugge and Moran, 1954]. It claimed 12 lives and caused property damage estimated at $60 million. It was unusual in that an aftershock (August 22, M5.8) actually caused more damage in Bakersfield than the main shock, although the damage was to structures already somewhat damaged by the main shock. The generally moderate damage in Bakersfield was confined mainly to isolated parapet failure. Cracks formed in many brick buildings, and older school buildings were damaged somewhat. In contrast, however, the Kern General Hospital was damaged heavily. Multistory steel and concrete structures sustained minor damage, which commonly was confined to the first story. MMI XI was assigned to a small area on the Southern Pacific Railroad southeast of Bealville. There, the earthquake cracked reinforced-concrete tunnels having walls 46 cm thick, shortened the distance between portals of two tunnels about 2.5 m, and bent the rails into S-shaped curves. Reports of long-period wave effects from the earthquake were widespread. Water splashed from swimming pools as far distant as the Los Angeles area, where damage to tall buildings was nonstructural but extensive. Water also splashed in pressure tanks on tops of buildings in San Francisco [Stover and Coffman,1993]. The 1952 Kern County earthquake was investigated by a new generation of structural engineers and earth scientists, who moved over the next several years to create the first edition of the Structural Engineers Association of California’s Recommended Lateral Force Requirements, or “Blue Book,” which
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FIGURE 1.25 1960 Chile Mw 9.5 earthquake. The ship in the photo was wrecked by the tsunami on Isla Mocha (north of Valdivia). Note the raised beach and landslides. Large landslides and massive flows of earthen debris and rock occurred on the island. The tsunami runup on Isla Mocha was 25 m (more than 82 ft). (From NOAA/ NGDC, http://www.ngdc.noaa.gov/seg/hazard/slideset/ tsunamis.)
FIGURE 1.26 1960 Chile Mw 9.5 earthquake. The fishing village of Queule (north of Valdivia and south of Lebu) before and after the catastrophe of May 1960. The bottom photo was taken after the land subsidence and after the tsunami. The town was destroyed. The houses, together with the remains of fishing boats and uprooted trees, were washed as much as 2 km inland by a tsunami 4.5 m high. The sinking of the land also brought about a permanent rise of the sea. The meandering creek bed in the foreground has been changed into an estuary. The trees that dot the river bank in the top photo are the only ones that remain in the bottom photo. Also the linear feature next to the solitary tree in the bottom photo can be found in the top photo marked with smaller trees that later disappeared in the wave. (From NOAA/NGDC, http://www.ngdc.noaa.gov/seg/hazard/slideset/tsunamis/.)
was the first uniform code for seismic areas in the United States [SEAOC, 1980]. This was a critical development, as the Blue Book became the model for seismic requirements and building codes around the world. 1.2.3.2 1960: May 22, Chile (Mw 9.5) On May 22, 1960, a Mw 9.5 earthquake, the largest earthquake ever instrumentally recorded, occurred in southern Chile. The series of earthquakes that followed ravaged southern Chile and ruptured over a period of days a 1000-km section of the fault, one of the longest ruptures ever reported. The number of fatalities associated with both the tsunami and the earthquake has been estimated between 490 and 5,700. Reportedly there were 3,000 injured, and initially there were 717 missing. The Chilean government estimated 2,000,000 people were left homeless and 58,622 houses were completely destroyed. Damage (including tsunami damage) was more than U.S. $500 million. The main shock set up a series of seismic sea waves (tsunamis) that not only was destructive along the coast of Chile (Figures 1.25 and 1.26), but that also caused numerous casualties and extensive property damage in © 2003 by CRC Press LLC
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FIGURE 1.27 MMI map, 1964 Alaska earthquake. (From NOAA/NGDC, http://www.ngdc.noaa.gov/seg/hazard/ slideset/earthquakes/7/7_slides.html.)
Hawaii and Japan, and that was noticeable along shorelines throughout the Pacific Ocean area. There were several other geologic phenomena besides tsunamis associated with this event. Subsidence caused by the earthquake produced local flooding and permanently altered the shorelines of much of the area in Chile impacted by the earthquake. Landslides were common on Chilean hillsides. The Puyehue volcano erupted 47 h after the main shock [NOAA/NGDC, n.d.].
1.2.4 First Turning Point This section briefly describes salient points from selected earthquakes between 1964 and 1971, a period that ended with a major change in the thinking of earthquake engineers and that, within a few years, led to a National Earthquake Hazards Reduction Program in the United States, and heightened activity in other countries. 1.2.4.1 1964: March 28, Alaska (Mw 8.3) This great earthquake and ensuing tsunami took 125 lives (tsunami 110, earthquake 15), and caused about $311 million in property loss. Earthquake effects were heavy in many towns, including Anchorage, Chitina, Glennallen, Homer, Hope, Kasilof, Kenai, Kodiak, Moose Pass, Portage, Seldovia, Seward, Sterling, Valdez, Wasilla, and Whittier (Figure 1.27). Anchorage, about 120 km northwest of the epicenter, sustained the most severe damage to property. About 30 blocks of dwellings and commercial buildings were damaged or destroyed in the downtown area. The J.C. Penney Company building was damaged beyond repair (Figure 1.28); the Four Seasons apartment building, a new six-story structure, collapsed (Figure 1.29); and many other multistory © 2003 by CRC Press LLC
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FIGURE 1.28 This slide shows the five-story J.C. Penney building at 5th Avenue and Downing Street in Anchorage, where two people died and one was injured. Concrete facing fell on automobiles in front of the building. Although the building was approximately square, the arrangement of effective shear-resisting elements was quite asymmetrical, consisting principally of the south and west walls that were constructed of poured concrete for the full building height. The north and east sides of the building faced the street. The north side of the building had no shear wall but was covered by a facade composed of 4-inch (10.2-cm) thick precast, nonstructural reinforced concrete panels. The east wall, also covered with the precast panels, had poured-concrete shear walls between columns in the two northerly bays and in the bottom three stories of the two southerly bays. The rotational displacement induced by the earthquake apparently caused failure of this east wall shear-resistant element, the building became more susceptible to rotational distortion, and the south and west shear walls failed. (From NOAA/NGDC, http:// www.ngdc.noaa.gov/seg/hazard/slideset/earthquakes/7/7_slides.html.)
FIGURE 1.29 The Four Seasons Apartments in Anchorage was a six-story, lift-slab reinforced concrete building that crashed to the ground during the earthquake. The building was structurally complete but unoccupied at the time of the earthquake. The main shear-resistant structural elements of the building, a poured-in-place, reinforced-concrete stairwell and a combined elevator core and stairwell, fractured at the first floor and toppled over, and came to rest on top of the rubble of all six floors and the roof. The concrete stairwell is in the center of the picture. (From NOAA/ NGDC, http://www.ngdc.noaa.gov/seg/hazard/slideset/earthquakes/7/7_slides.html.)
buildings were damaged heavily. The schools in Anchorage were heavily damaged. The Government Hill Grade School, sitting astride a huge landslide, was almost a total loss. Anchorage High School and Denali Grade School were damaged severely. Duration of the shock was estimated at 3 min. Landslides in Anchorage caused heavy damage. Huge slides occurred in the downtown business section (Figure 1.30), at Government Hill, and especially at Turnagain Heights (Figure 1.31), where an area of about 130 acres was devasted by displacements that broke the ground into many deranged blocks that were collapsed and tilted at all angles. This slide destroyed about 75 private homes. Water mains and gas, sewer, telephone, and electrical systems were disrupted throughout the area. The earthquake was accompanied by vertical displacement over an area of about 52,000 km2. The major area of uplift trended northeast from southern Kodiak Island to Prince William Sound and trended © 2003 by CRC Press LLC
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FIGURE 1.30 This view of damage to Fourth Avenue buildings in downtown Anchorage shows the damage resulting from the slide in this area. Before the earthquake, the sidewalk in front of the stores on the left, which are in the graben, was at the level of the street on the right, which was not involved in the subsidence. The graben subsided 11 feet (3.3 m) in response to 14 feet (4.2 m) of horizontal movement of the slide block during the earthquake. Lateral spreading produced a fan-shaped slide 1800 feet (545.5 m) across that covered about 36 acres (14.6 ha) and moved a maximum of 17 feet (5.1 m). Movement on the landslide began after about 1 to 2 min of ground shaking and stopped when the shaking stopped. (From NOAA/NGDC, http://www.ngdc.noaa.gov/seg/hazard/slideset/earthquakes/7/7_slides.html.)
FIGURE 1.31 The Turnagain Heights landslide in Anchorage. Seventy-five homes twisted, slumped, or collapsed when liquefaction of subsoils caused parts of the suburban bluff to move as much as 2000 feet (606 m) downward toward the bay, forming a complex system of ridges and depressions. The slide developed because of a loss in strength of the soils, particularly of lenses of sand, that underlay the slide. The motion involved the subsidence of large blocks of soil, the lateral displacement of clay in a 25-foot (7.6-m) thick zone, and the simultaneous lateral translation of the slide debris on liquefied sands and silts. (From NOAA/NGDC, http://www.ngdc.noaa.gov/seg/hazard/slideset/ earthquakes/7/7_slides.html.)
east–west to the east of the sound. Vertical displacements ranged from about 11.5 m of uplift to 2.3 m of subsidence relative to sea level. Off the southwest end of Montague Island, there was absolute vertical displacement of about 13 to 15 m. Uplift also occurred along the extreme southeast coast of Kodiak Island, Sitkalidak Island, and over part or all of Sitkinak Island. The zone of subsidence covered about 285,000 km2, including the north and west parts of Prince William Sound, the west part of the Chugach Mountains, most of Kenai Peninsula, and almost all the Kodiak Island group. This shock generated a tsunami that devastated many towns along the Gulf of Alaska (Figure 1.32), and left serious damage at Alberni and Port Alberni, Canada, along the West Coast of the United States (15 killed), and in Hawaii. The maximum wave height recorded was 67 m at Valdez Inlet. Seiche action in rivers, lakes, bayous, and protected harbors and waterways along the Gulf Coast of Louisiana and Texas caused minor damage. It was also recorded on tide gages in Cuba and Puerto Rico. This great earthquake was felt over a large area of Alaska and in parts of western Yukon Territory and British Columbia, Canada [Stover and Coffman, 1993]. © 2003 by CRC Press LLC
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FIGURE 1.32 This photo was taken at Seward at the north end of Resurrection Bay, showing an overturned ship, a demolished Texaco chemical truck, and a torn-up dock strewn with logs and scrap metal after the tsunamis. The waves left a shambles of houses and boats in the lagoon area, some still looking relatively undamaged and some almost completely battered. The total damage to port and harbor facilities at Seward was estimated at more than $15,000. Most of this damage was the result of the tsunamis. Eleven persons lost their lives due to the sea waves at Seward. (From NOAA/NGDC, http://www.ngdc.noaa.gov/seg/hazard/slideset/earthquakes/7/ 7_slides.html.)
The Alaska earthquake had two significant influences: (1) its truly remarkable size, area affected, and geologic effects greatly stimulated the earth sciences in the United States, and led to a major documentation of the event [U.S. Coast and Geodetic Survey, 1967]; and (2) the impacts on modern structures, such as the J.C. Penney and Four Seasons Apartment buildings, alarmed structural engineers and started a thought process that would lead to major building code changes within a decade. 1.2.4.2 1964: June 16, Niigata, Japan (M7.5) The city of Niigata, on the Japan Sea coast of the island of Honshu, Japan, was struck by a M7.5 earthquake at 1:25 p.m, June 16, 1964, resulting in widespread damage (Figure 1.33) (see Chapter 4 for an explanation of the JMA intensity scale). Many buildings, bridges, quay walls, and lifeline systems suffered severe damage, and it was fortunate that only 26 persons were killed. The real significance of this event was the technical investigation and identification of the cause of some remarkable building failures, which were caused by liquefaction. Being a natural phenomenon, liquefaction had occurred in most larger earthquakes since time immemorial (see Figure 1.8, for example), but had not been specifically identified and investigated. At the Kawagishi-cho apartments in Niigata city, liquefaction occurred, resulting in the overturning collapse of the buildings (Figure 1.34). Note the quality of the construction; even though overturned, these buildings remained intact. Koizumi [1965] identified liquefaction and its cause and, combined with the major examples of liquefaction observed in Alaska earlier the same year, this led to a major research effort into the analysis and mitigation of liquefaction over the next several decades. 1.2.4.3 1971: February 9, San Fernando, CA (M6.5) This destructive earthquake occurred in a sparsely populated area of the San Gabriel Mountains, near San Fernando, killing 65, injuring more than 2000, and causing property damage estimated at $505 million [NOAA, 1973] (Figure 1.35). The earthquake created a zone of discontinuous surface faulting, named the San Fernando fault zone, which partly follows the boundary between the San Gabriel Mountains and the San Fernando-Tujunga Valleys and partly transects the northern salient of the San Fernando Valley. This latter zone of tectonic ruptures was associated with some of the heaviest property damage sustained in the region. Within the entire length of the surface faulting, which extended roughly east–west for about 15 km, the maximum vertical offset measured on a single scarp was about 1 m, the maximum lateral offset about 1 m, and the maximum shortening (thrust component) about 0.9 m.
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FIGURE 1.33 Japan Meteorological Agency intensity map of 1964 Niigata, Japan, earthquake. (From Japan Meteorological Agency. With permission.)
FIGURE 1.34 1964 Niigata earthquake, overturning of apartment buildings, Kawagishi-cho, Niigata. (From NOAA/NGDC, available online at http://www.ngdc.noaa.gov/seg/hazard/slideset/ earthquakes/.) © 2003 by CRC Press LLC
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FIGURE 1.35 Modified Mercalli Intensity map of 1971 San Fernando earthquake. (From NOAA/NGDC, available online at http://neic.usgs.gov/neis/eqlists/USA/1971_02_09_iso.html.)
The most spectacular damage included the destruction of major structures at the Olive View and the Veterans’ Administration Hospitals, and the collapse of freeway overpasses (Figure 1.36). The newly built earthquake-resistant buildings at the Olive View Hospital in Sylmar were destroyed; four five-story wings pulled away from the main building and three stair towers toppled (Figure 1.37). Although newly built and complying with the building code, the building’s columns lacked confinement due to widely spaced lateral ties. Older, unreinforced masonry buildings collapsed at the Veterans’ Administration Hospital at San Fernando, killing 49 people (Figure 1.38). Many older buildings in the Alhambra, Beverly Hills, Burbank, and Glendale areas were damaged beyond repair, and thousands of houses and chimneys were damaged in the region (Figure 1.39). A large number of one-story commercial buildings, termed tilt-ups, were found to have a common design flaw, involving the roof-wall connection putting the wood ledger in cross-grain bending, which is discussed in Chapter 14 of this volume. Public utilities and facilities of all kinds were damaged, both above and below ground. Severe ground fracturing and landslides were responsible for extensive damage in areas where faulting was not observed. The most damaging landslide occurred in the Upper Lake area of Van Norman Lakes, where highway overpasses, railroads, pipelines, and almost all structures in the path of the slide were damaged severely. Several overpasses collapsed. Two dams were damaged severely (Lower Van Norman Dam and Pacoima Dam) (Figure 1.40), and three others sustained minor damage. Lower Van Norman Dam came very close to overtopping, which would have resulted in a sudden release of the impounded water and probable mass casualties for the 80,000 people living below the dam [Stover and Coffman, 1993]. The impact of the San Fernando earthquake on engineers was out of all proportion to the number killed, or even the monetary costs. Engineers were shocked to observe that modern structures, such as Olive View Hospital, Van Norman Dam, highway bridges, and tilt-up buildings, were failing under a moderate-sized earthquake. Of note also was the recording during the event of about 100 strong ground motion records, which effectively doubled the number of new records then in existence! © 2003 by CRC Press LLC
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FIGURE 1.36 The I-5 (Golden State) and I-210 (Foothills) Freeway Exchange. There was damage to both roadway and structures on the completed portion of this freeway, from its intersection with Route 5 to the Maclay Street separation. Throughout this section, the freeway appeared to settle on a somewhat uniform grade line. The settling was especially noticeable at the bridges, where it varied from 6 to 24 inches. Pavement was buckled and broken for several hundred feet on each side of the damaged structures. Structural damage varied, from minor damage to wing walls and slope paving, to rotation and settlement of abutments, splaying and cracking of columns, displacement of wing walls, and contortion of the sides of fills. Street sections beneath the various undercrossings suffered damage to curbs, sidewalks, slope paving, and roadway sections. (Photo: E.V. Leyendecker, U.S. Geological Survey. From NOAA/NGDC, available online at http://www.ngdc.noaa.gov/seg/hazard/slideset/earthquakes/20/20_slides.html.)
(A)
(B)
FIGURE 1.37 Damage sustained in the 1971 San Fernando, California, earthquake. (A) This building, known as the Medical Treatment and Care Building (in the Olive View Hospital complex) was completed in 1970 at a cost of $25 million. The four towers containing the stairs and day-room areas were built to be structurally separated four inches from the main building. The three towers that failed were supported by concrete columns. When these columns failed, the towers overturned. Note that the base of the tower in this photo has fallen in the basement. After the shock, the building leaned as much as 2 feet in a northerly direction with nearly all of this drift in the first story. Note also the broken columns on the first floor. The first story nearly collapsed, and the building was ultimately demolished. The structure was located in a band that incurred heavy damage during the 1971 earthquake. (Photo: E.V. Leyendecker, U.S. Geological Survey.) (B) Close-up of first-story column failure at Olive View Hospital. The column was located at the west end of Wing B on the first story of the five-story hospital. This is a typical first-story tied corner column, and the damage is characteristic of column damage found on the first floor in all wings of the hospital. These corner columns were square with a corner notch out, giving the appearance of a thick L-shaped column. Note the broken ties, the spacing of the ties, and the bent rebar. The building was laterally displaced about 2 feet to the north in the earthquake. (Photo: E.V. Leyendecker, U.S. Geological Survey. From NOAA/NGDC, available online at http://www.ngdc.noaa.gov/seg/hazard/slideset/earthquakes/20/20_slides.html.) Shown as Color Figure 1.37. © 2003 by CRC Press LLC
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FIGURE 1.38 Aerial view of the damage to the San Fernando Veterans’ Administration Hospital and complex. This complex was located in the band of accentuated damage found along the base of the San Gabriel Mountains. The collapsed structure was built in 1926, before earthquake building codes were in effect. Fortyseven of the 65 deaths attributed to the earthquake occurred as a result of the collapse of this structure. (Photo: E.V. Leyendecker, U.S. Geological Survey. From N OA A / N G D C , a v a i l a b l e o n l i n e a t h t t p : / / www.ngdc.noaa.gov/seg/hazard/slideset/earthquakes/20/ 20_slides.html.)
FIGURE 1.39 A home in Crestview Park on Almetz Street. More than 700 dwellings were evacuated and declared unsafe after the San Fernando earthquake. (Photo: E.V. Leyendecker, U.S. Geological Survey. From N OA A / N G D C , a v a i l a b l e o n l i n e a t h t t p : / / www.ngdc.noaa.gov/seg/hazard/slideset/earthquakes/20/ 20_slides.html.)
FIGURE 1.40 Van Norman Dam (Lower San Fernando Dam). For a length of about 1800 feet, the embankment (including the parapet wall, dam crest, most of the upstream slope, and a portion of the downstream slope) slid into the reservoir. A loss of about 30 feet of dam height resulted when as much as 800,000 cubic yards of dam embankment was displaced into the reservoir. This material slid when liquefaction of the hydraulic fill on the upstream side of the embankment occurred. The dam was about half full at the time. Eighty-thousand people living downstream of the dam were immediately ordered to evacuate, and steps were taken to lower the water level in the reservoir as rapidly as possible. The Los Angeles Dam was constructed to replace the Van Norman Reservoir. (Photo: E.V. Leyendecker, U.S. Geological Survey. From NOAA/NGDC, available online at http:// www.ngdc.noaa.gov/seg/hazard/slideset/earthquakes/20/ 20_slides.html.)
1.2.4.4 New Directions The 1971 San Fernando earthquake, coming within a few years of the 1964 Alaska, 1964 Niigata (Japan), 1967 Caracas (Venezuela), and 1968 Tokachi-oki (Japan) earthquakes (the latter two events are not discussed here), brought a realization among geotechnical and structural engineers that major changes were needed in the building codes, as well as that other earthquake mitigation measures were required to deal with existing structures. During the 1970s: • The Uniform Building Code was revised in the 1973 and 1976 editions to increase lateral force requirements, correct the defective detail for roof-wall connections in tilt-up and similar buildings, © 2003 by CRC Press LLC
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• •
•
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and require adequate lateral spacing in reinforced concrete columns (see Hamburger, Chapter 11, this volume). A major reshaping of building code earthquake provisions was undertaken [Applied Technology Council, 1978]. Investigation of liquefaction, which was the root of the failure of the Lower Van Norman Dam, had begun following the 1964 events, and practical engineering tools soon emerged to analyze the potential for liquefaction (see Brandes, Chapter 7, this volume). The failures of power, water, and other infrastructure led to the birth of lifeline earthquake engineering (see Eguchi, Chapter 22, this volume) to address seismic vulnerabilities in urban infrastructure. The United States instituted a national dam-safety program (see Bureau, Chapter 26, this volume). In 1977, the National Earthquake Hazards Reduction Act of 1977, Public Law 95–124, was passed, culminating thinking that had begun prior to the 1964 Alaska earthquake and evolved into a series of studies and high-level reports [see EERI, 1999; also available online at http://quake.wr.usgs.gov/ research/history/wallace-VI.html] leading to the passage of the NEHRP.
1.2.5 Second Turning Point 1.2.5.1 1985: September 19, Michoacan, Mexico (M7.9) The earthquake occurred in the state of Michoacan, Mexico, on Thursday, September 19, 1985 at 7:18 a.m. local time. The epicenter was approximately 40 miles west of El Infiernillo Dam on the Balsas River, near the town of Lazaro Cardenas on the Pacific coast. The next day, an aftershock of magnitude 7.5 struck approximately 70 miles to the southwest, 15 miles north of Zihuatenejo, in the state of Guerrero, at 7:37 p.m. local time. At least 9,500 people were killed, about 30,000 were injured, more than 100,000 people were left homeless, and severe damage was caused in parts of Mexico City and in several states of central Mexico. It is widely rumored in Mexico that the death toll from this earthquake may have been as high as 35,000. It is estimated that the quake seriously affected an area of approximately 825,000 km2, caused between U.S. $3 and $4 billion of damage, and was felt by almost 20 million people. Four hundred twelve buildings collapsed and another 3,124 were seriously damaged in Mexico City. About 60% of the buildings were destroyed at Ciudad Guzman, Jalisco. Damage also occurred in the states of Colima, Guerrero, Mexico, Michoacan, Morelos, parts of Veracruz, and in other areas of Jalisco. This event was extremely remarkable and received wide attention because the epicenter was about 400 km from central Mexico City, where the greatest loss of life occurred. Earthquakes do not usually cause significant damage at this distance, and the major damage in Mexico City was due to an unfortunate combination of circumstances: 1. It was a large, distant event, resulting in higher frequencies being largely attenuated, with peak ground accelerations (PGA) of only 0.03 to 0.04 g on firm soils in Mexico City (CU station, see Figure 1.41), but with lower frequencies (longer periods) still having significant energy when the seismic waves reached Mexico City. 2. The Valle de Mexico has unusual geology. It is an enclosed basin, surrounded by active volcanoes, in which all drainage is trapped (a shallow lake still existed at the time of the Spanish Conquest, ca. 1500). There are three zones: (1) a foothill zone consisting of firm volcanic deposits mostly west of downtown; (2) a lake zone consisting of ash from the volcanoes which has fallen on the basin for thousands of years and slowly settled (pluviated) in the central lake of the basin, formed by the runoff trapped in the basin. The center of the basin is therefore a very deep, soft deposit of saturated ash; and (3) intermediate between these two zones is a transition zone. The soft ashwater deposits in the lake zone are very soft, but elastic over a large strain range, with a natural period of about 2 sec. 3. The oldest part of the city, and many of the high rises, are in the Lake zone. Settlement of buildings built in this zone is extreme, if not properly founded. A rule-of-thumb is that the natural period © 2003 by CRC Press LLC
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C = V/W
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FIGURE 1.41 Response spectra (5% damped), Mexico City CU (firm) and SCT (soft) stations, September 19, 1985 Michoacan earthquake.
of buildings, T, = 0.1N, where N is the number of stories, i.e., a 10-story building normally has a period of about 1 sec, a 20-story building 2 sec, etc.8 4. The long period motion from the large distant event therefore tuned in, i.e., matched the period (of about 2 sec) on the deep, soft deposits of the Lake zone, resulting in resonance of the input ground motion, with unusually strong amplification; PGA of 0.18 g was recorded at the SCT station near the edge of the Transition-Lake zones (see Figure 1.41). 5. On the soft soils the amplified ground motions with response spectra (for an explanation of response spectra, see Chapter 4) tuned in on buildings with periods of about 1.0 to 1.5 sec (i.e., 10- to 15-story buildings). As these buildings were damaged and weakened, their period softened, i.e., became longer, and thus moved toward the peak amplification region at 2 sec in the already amplified response spectra, resulting in a double resonance. As buildings in the 10- to 15-story range weakened, they were being more strongly loaded to collapse. As they weakened, taller buildings (longer periods) were moving into the downhill side of Figure 1.41, and thus shedding load. The result was that damage was highly selective and occurred most in buildings in the 10- to 15-story range. Figure 1.42 shows results of a survey by teachers and students at the Autonomous University of Mexico [UNAM, 1985], in which it can be seen that 9- to 12-story buildings were found to be most heavily damaged. The damage was truly devastating. Figure 1.43 shows the Pino Suarez 23-story building,9 the tallest building to collapse for any reason prior to September 11, 2001. In all three 23-story towers, the columns were welded box columns that buckled at the fourth floor, leading to a story mechanism and collapse [Osteraas and Krawinkler, 1989] of one of the 23-story towers onto the southern 16-story tower, both towers finally collapsing into the street. Figure 1.43A shows the elevation of the complex: three central 8 Specific building data for Mexico City buildings indicated the relationship was T = 0.12 + 0.086N [Scawthorn et al., 1986). 9 The Pino Suarez complex consisted of a 2-story, reinforced concrete base building supporting three 21-story and two 14-story, steel-framed towers (one 14-story at the north and one at the south end of the row of towers). The buildings are sometimes referred to as being 21 stories tall [e.g., Osteraas and Krawinkler, 1989], when in fact they were 23 stories above the ground (21 stories + 2-story base).
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DAMAGED BLDGS (%)
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FIGURE 1.42
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Damage survey. (From Scawthorn, C. et al. 1986, after UNAM, 1985. With permission.)
23-story towers with two 16-story towers each at each end, all steel framed; Figure 1.43B shows the collapsed towers; Figure 1.43B shows the remaining towers, with the southernmost one with cladding removed, exposing the steel framing; Figures 1.43C and D show the buckled box column (note the welded C-section around the buckle, placed following the earthquake to stabilize the buildings). In both remaining 23-story towers, the pattern of buckled columns at the fourth floor was remarkably consistent. Figure 1.44 shows the collapse of the 14-story reinforced concrete Nuevo Leon building in the Tlatelolco complex. As can be seen in Figure 1.44A, the building had an unusual X-bracing scheme in the transverse direction. Inspection indicated (1) columns sheared in the longitudinal direction at the sky-lobbies, and (2) failed X-bracing connections in the transverse direction. Figure 1.45 shows examples of other damage in this event. Figure 1.46 shows the Hotel Regis, which partially collapsed in the earthquake. An immediate ignition quickly engulfed the building and trapped occupants, and spread over the next 24 hours to all other buildings in the block, including several important government buildings. The Mexico City event was perhaps the first earthquake, with the exception of the 1967 Caracas, Venezuela, event (not discussed here), to cause the collapse of numerous major modern high-rise buildings. This was largely due to it being the first earthquake (Caracas excepted) to strongly shake major, modern high-rise buildings. 1.2.5.2 1988: December 7, Armenia (M7.0) On December 7, 1988, at 11:41 a.m. local time, a M7.0 earthquake struck northwest Armenia, at the time a Soviet republic with 3.5 million people. Armenia occupies approximately 30,000 km2 in the southern Caucasus Mountains, generally considered the boundary between Europe and Asia (Figure 1.47). The event caused catastrophic damage that resulted in 25,000 deaths and $16 billion loss in a 400-km2 epicentral region occupied by approximately 700,000 people. Damage and several deaths also occurred in the Kars region of Turkey, 80 km southwest of the earthquake’s epicenter. The Armenian earthquake was a disaster of modern concrete buildings designed and constructed in the 1970s, not of old, unreinforced stone masonry buildings, the predominant type of construction.
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FIGURE 1.43 Pino Suarez collapse, September 19, 1985 Mexico City earthquake. (A) Collapsed 23-story and 16story Pino Suarez towers. (Photo: E.V. Leyendecker. NOAA/NGDC.) (B) Elevation of two remaining 23-story and one remaining 16-story tower, showing framing. (C) Buckled box column, Pino Suarez tower. (D) Close-up of buckled box column, Pino Suarez tower. (Photos B, C, D: C. Scawthorn.) Shown as Color Figure 1.43.
Faced with a housing shortage and a wave of urbanization in the 1970s, Soviet urban planners relaxed standards for new multistory buildings and raised the height limit from five stories to nine. Failure of these new buildings claimed the most lives. When these buildings collapsed, they fell straight down, either crushing occupants in the compact piles of rubble or suffocating them. In Spitak, there were no undamaged buildings because of the strong epicentral shaking and the shallow (15 km) depth (Figure 1.48). In Leninakan (now called Gyumri), approximately 80% of the building stock was damaged, with many schools, hospitals, apartment buildings, and factories collapsing (Figure 1.49). The predominant building type (unreinforced stone masonry bearing-wall construction) performed poorly overall, although most low-rise unreinforced masonry buildings performed well. Nine-story precast, nonductile concrete frame buildings performed poorly, with less than 12 of the more than 50 buildings remaining standing after the earthquake. In contrast, a group of nine-story buildings having precast concrete wall and floor panels performed well. Of two lift-slab buildings, a 10-story collapsed and a 16-story (the tallest) exhibited severe torsion effects and heavy damage to the first floor.
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FIGURE 1.44 Nuevo Leon collapse, Tlatelolco complex, September 19, 1985 Mexico City earthquake. (A) Overview of the collapse site. Building still standing is virtually identical to collapsed structure. (B) Overview of the wreckage. (C) Search and rescue workers in the wreckage. (Photos: C. Scawthorn.) Shown as Color Figure 1.44.
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FIGURE 1.45 Examples of Mexico City building damage, September 19, 1985 earthquake. Parts (A), (B), (D), and (G) shown as Color Figure 1.45.
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FIGURE 1.46 Hotel Regis, Mexico City building damage, September 19, 1985 earthquake. (A) Before earthquake; (B) afterward.
Both the 1985 Mexico City and 1988 Armenia events were now raising serious questions about the safety of high-rise buildings. 1.2.5.3 1989: October 17, Loma Prieta (Mw 7.1) At 5:04 p.m., Tuesday, October 17, 1989, an Mw 7.1 earthquake struck the San Francisco Bay area. The 20-second earthquake was centered about 60 miles south of San Francisco on the San Andreas fault, was largely strike-slip motion, and was felt from Eureka to Los Angeles and east as far as Fallon, NV. It was felt in high-rise buildings in San Diego. Maximum intensity was IX in parts of Oakland and San Francisco (Figure 1.50), numerous landslides occurred in the epicentral area, liquefaction occurred in some areas of Oakland and San Francisco, and a small tsunami with maximum wave height (peak-to-trough) of 40 cm was recorded at Monterey. Among the most catastrophic seismic-induced events were: • The collapse of the double-deck elevated Cypress Street section of Interstate 880 in Oakland (Figure 1.51) • The collapse of a section of the roadbed of the San Francisco-Oakland Bay Bridge (Figure 1.52) • Multiple building collapses in San Francisco’s Marina district, as well as a major fire (see Chapter 29) (Figure 1.53) • The collapse of several structures in the town of Santa Cruz at the Pacific Garden Mall and in other areas around the epicentral region Ground motions were amplified in soft, water-saturated soils around the Bay’s margin, resulting in much of the dramatic damage in parts of San Francisco and Oakland. Fatalities were 62 people, a remarkably low number given the time and size of the earthquake. This was attributed to low traffic and many people having gone home early to watch the third game of the World Series between the San Francisco Giants and the Oakland Athletics. Most casualties were caused by the collapse of the Cypress Street section, which had much lighter traffic than usual for a rush hour, although the fall of a parapet from one building accounted for eight deaths of persons not even in the building (Figure 1.54). The earthquake received extraordinary media attention due to the disruption of the World Series, with national media already focused on the Bay area. Many people across the United States were seeing damage live on TV, such as the collapsed Cypress Street elevated highway, before people only a few blocks away from the damage were aware of it. Damage was estimated at $5.6 billion. Areas outside of Santa Cruz, including the towns of Watsonville, Hollister, and Los Gatos, also suffered heavy damage. At least 3,700 people were reported injured and more than 12,000 were displaced. More than 18,000 homes were damaged and 963 were destroyed. More than 2,500 other buildings were damaged and 147 were destroyed. © 2003 by CRC Press LLC
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FIGURE 1.47
Intensity map of December 7, 1988 Armenia earthquake. (Courtesy EQE International)
FIGURE 1.48 Damage in Spitak, December 7, 1988 Armenia earthquake. (Courtesy EQE International)
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FIGURE 1.49
Damage in Leninakan, December 7, 1988 Armenia earthquake. (Courtesy EQE International)
km 0 10 20 Santa Rosa
Vallejo 38°N
Stockton San Francisco X - Extreme Damage
Beverley Oakland
IX - Heavy Damage VIII - Moderate Damage VII - Light Damage VI - Minimal Damage
Half Menlo Park Sunnydale Moon San Jose Bay
V - Strongly Felt
Morgan Hill
II-IV - Lightly to Moderately Felt 37°N
I - Not Felt Undefined (White) 123°W
Santa Clara Hollister 122°W
FIGURE 1.50 Predictive intensity map, October 17, 1989 Loma Prieta earthquake. (http://quake.wr.usgs.gov/ research/strongmotion/intensity/1989.html.)
Downtown San Francisco was effectively closed for 3 days due to curtailment of electric power and gas service while the safety of those systems was restored. Restoration of the San Francisco Bay area following the earthquake was varied. The Bay Bridge was restored to service in 30 days and, surprisingly, impacts on commuter patterns during the disruption were much less than anticipated, due to BART (the regional subway system) and an emergency ferry system providing service. On the other hand, the Cypress Street elevated highway was a key link in the East Bay highway network; opposition over rebuilding the highway along the same route delayed rebuilding for 10 years, while an alternative route was found and the highway rebuilt. Chinatown in San Francisco had major business losses compared to prior to the earthquake, due to the loss of the Embarcadero Freeway. This elevated highway was very similar to the Cypress and sustained similar but not as severe damage (there was no collapse of the Embarcadero Freeway). However, the Embarcadero Freeway had always had significant public opposition due to its route along the waterfront, and opponents seized the © 2003 by CRC Press LLC
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FIGURE 1.51 Collapse of Cypress Street double-deck elevated highway, Oakland, October 17, 1989 Loma Prieta earthquake. Various views. (Courtesy EQE International) Part (B) shown as Color Figure 1.51.
opportunity and the Freeway was demolished (and replaced by a gracious surface roadway). The freeway provided quick access to Chinatown, however, and when this access was lost, tourism and local patronage in Chinatown was slow to recover. Similarly, the pedestrian mall in Santa Cruz sustained significant and steady business drop-off, due to a lengthy decision-making process regarding rebuilding. 1.2.5.4 1994: January 17, Northridge (Mw 6.7) At 4:31 a.m., Pacific Standard Time, Monday, January 17, a moderate but very damaging earthquake with a moment magnitude of 6.7 struck the densely populated San Fernando Valley in northern Los Angeles. This event was similar in magnitude, time of year, time of day, and epicentral location to the 1971 San Fernando earthquake, and affected largely the same area. Thousands of aftershocks, many in the magnitude 4.0 to 5.0 range, occurred during the next few weeks, further damaging already affected structures. The earthquake was felt throughout much of southern California and as far away as Turlock, CA; Las Vegas, NV; Richfield, UT; and Ensenada, Mexico. The maximum recorded acceleration exceeded 1.0 g at several sites in the area, with the largest value of 1.8 g recorded at Tarzana, about 7 km south of the epicenter, with corresponding MMI of IX (Figures 1.55 and 1.56). A maximum uplift of about 15 cm occurred in the Santa Susana Mountains; many rockslides occurred in mountain areas, blocking some roads; ground cracks were observed at Granada Hills and in Potrero Canyon; and liquefaction occurred at Simi Valley and in some other parts of the Los Angeles basin. In all, these geologic effects were a contributing but not major source of damage. © 2003 by CRC Press LLC
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FIGURE 1.52 Collapse of portion of the east span of the San Francisco Oakland Bay Bridge, October 17, 1989 Loma Prieta earthquake. (A) Collapsed span. (Courtesy EQE International) (B) Close-up of collapsed span; note beam seat at lower left. (C) Close-up of beam seat, showing amount of movement. (Photos B, C: C. Scawthorn) Shown as Color Figure 1.52.
Damage to several major freeways serving Los Angeles choked the traffic system in the days following the earthquake. Major freeway damage occurred up to 32 km from the epicenter (Figure 1.57). Collapses and other severe damage forced closure of portions of 11 major roads to downtown Los Angeles. The death toll was 57, and more than 1,500 people were seriously injured. A few days after the earthquake, 9,000 homes and businesses were still without electricity; 20,000 were without gas; and more than 48,500 had little or no water. Fires caused additional damage in the San Fernando Valley and at Malibu and Venice (Figure 1.58). About 12,500 structures were moderately to severely damaged, leaving thousands of people temporarily homeless (Figure 1.59). Of the 66,546 buildings inspected, 6% were severely damaged (red tagged) and 17% were moderately damaged (yellow tagged). Commercial buildings, especially parking structures and tilt-ups, sustained major damage in a number of cases (Figure 1.60). A surprising find was the cracking of connections in welded steel moment-resistant frames (see Chapter 12). Total direct damage, business interruption, and other losses that could be documented amounted to U.S. $24 billion. Further, amounts that could not be documented were also estimated to arrive at a final estimated economic loss of U.S. $44 billion [EQE, 1997], making this the most expensive natural catastrophe in history up to that time. Significantly, insurance claims were finally10 totaled at $15 billion, leading to insurers foregoing future earthquake underwriting in California for a period. Northridge, following within a little more than 5 years of the Loma Prieta earthquake, marked a turning point in the United States. Given the magnitude of the losses, it was clear that a larger earthquake
10
It took several years for all accounting to be completed (see Chapter 32, this volume, or Scawthorn [1995]).
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FIGURE 1.53 Collapse of buildings in the Marina district of San Francisco, October 17, 1989 Loma Prieta earthquake. Shown as Color Figure 1.53.
FIGURE 1.54 Collapse of parapet at building on Bluxome Street, San Francisco. Eight people died under the brick falling from the parapet. Shown as Color Figure 1.54.
could be a severe catastrophe. Caltrans was funded to retrofit all bridges in California by 2000 (and very nearly did so); many utilities accelerated programs initiated following Loma Prieta; the federal government significantly funded research on mitigation, including a multimillion dollar research effort into steel connections; several universities (Stanford and the University of California at Berkeley) accelerated their retrofit programs, and numerous local governments and private enterprises did likewise. © 2003 by CRC Press LLC
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FIGURE 1.55 Trinet Shake Map: instrumental intensity map, January 17, 1994 Northridge earthquake. Rather than using the traditional method of postcard responses from postmasters, this map is generated from instrumental data. (Courtesy U.S. Geological Survey)
1.2.5.5 1995: January 17, Hanshin (Kobe), Japan (Mw 6.8) The earthquake occurred at 5:46 a.m. with moment magnitude of 6.9, about 20 km southwest of downtown Kobe, between the northeast tip of Awaji Island and the island of Honshu. The fault rupture was 30 to 50 km in length, bilateral strike-slip, and ran directly through central Kobe, which contributed to the high level of destruction. Total fatalities were 6,427 people confirmed killed, with 36,896 injured, and extensive damage (VII JMA) in the Kobe area and on Awaji-shima. Over 90% of the casualties occurred along the southern coast of Honshu between Kobe and Nishinomiya. At least 28 people were killed by a landslide at Nishinomiya. About 310,000 people were evacuated to temporary shelters. Over 200,000 buildings were damaged or destroyed. Numerous fires, gas and water main breaks, and power outages occurred in the epicentral area. The earthquake was felt along a coastal strip extending from © 2003 by CRC Press LLC
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FIGURE 1.56 Community Intensity map, January 17, 1994 Northridge earthquake. Rather than using the traditional method of postcard responses from postmasters, this map is generated from citizen voluntary intensity observation data, via the Web. Citizens in California have quickly become familiar with this system and, for a major event, thousands of contributed data will be received and a map generated within an hour or less. (Courtesy U.S. Geological Survey)
FIGURE 1.57 Collapse of freeways, northern Los Angeles County, January 17, 1994 Northridge earthquake (M 6.7). (Courtesy EQE International) Shown as Color Figure 1.57. © 2003 by CRC Press LLC
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FIGURE 1.58 Gas flare and burned home, Balboa Boulevard, January 17, 1994 Northridge earthquake. (Courtesy EQE International)
FIGURE 1.59 Collapsed residential apartment buildings, January 17, 1994 Northridge earthquake. (Courtesy EQE International) Shown as Color Figure 1.59.
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FIGURE 1.60 Collapse of parking structures, January 17, 1994 Northridge earthquake. (Courtesy EQE International) Shown as Color Figure 1.60.
Suma Ward, Kobe, to Nishinomiya, and in the Ichinomiya area on Awaji-shima (VII JMA); at Hikone, Kyoto, and Toyooka (V JMA); at Nara, Okayama, Osaka, and Wakayama (IV JMA); at Iwakuni (V). The earthquake was also felt at Takamatsu, Shikoku (IV JMA). Right-lateral surface faulting was observed for 9 km with horizontal displacement of 1.2 to 1.5 m in the northern part of Awaji-shima (Figure 1.61). The number of buildings destroyed by the earthquake exceeded 100,000, or approximately one in five buildings in the strongly shaken area. An additional 80,000 buildings were badly damaged. The large numbers of damaged traditional-style Japanese residences and small, traditional commercial buildings of three stories or less account for a great deal of the damage. In sections where these buildings were © 2003 by CRC Press LLC
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17 January 1995 Hyogoken Nanbu Earthquake, M=6.9 135°E 163
35°N
Epicenter (JMA) active fault Kansai Committee JR Osaka Gas JMA aftershock zone (Kyoto U.)
195
Kyoto 263
113
323 601 229
270
481
Nojima Fault
561 819 833 616
Kobe
251 792 >318 >775 Nishinomiya 266
Osaka
245 145 113 220
240
Osaka Bay Awaji Island
149 0
20km
+ 200
FIGURE 1.61 Mainshock epicenter (JMA), aftershock zone, and peak ground motions (cm/s/s) of the 1995 Kobe earthquake, superimposed on a map of active faults, January 17, 1995 Hanshin earthquake. (From EERI [Earthquake Engineering Research Institute]. 1995. The Hyogo-Ken Nanbu Earthquake: Great Hanshin Earthquake Disaster, January 17, 1995. Preliminary Reconnaissance Report. Comartin, C.D., Greene, M., and Tubbesing, S.K., Tech. Eds. Earthquake Engineering Research Institute Report 95–04, sponsored by the Earthquake Engineering Research Institute, Oakland, CA, with support from the National Science Foundation and Federal Emergency Management Agency.)
concentrated, entire blocks of collapsed buildings were common. Several thousand buildings were also destroyed by the fires following the earthquake. Most of the heavily damaged wood-frame buildings were traditional one- or two-story residential or small commercial buildings of Shinkabe or Okabe construction. These buildings normally have very heavy mud and tile roofs (which are effective in preventing typhoon damage), supported by post-andbeam construction. Foundations are often stone or concrete blocks, and the wood framing is not well attached to the foundations. The Shinkabe construction has mud walls reinforced with a bamboo lattice. Okabe construction has thin-spaced wood sheathing that spans between the wood posts and is attached with limited nailing. The exterior plaster is not reinforced with wire mesh or well attached to the wood framing, so it falls off in sheets when cracked. In new (post-1981) construction, nominal diagonal bracing is required to resist lateral loads. Traditional wood-frame construction had the most widespread damage throughout the region, resulting in the largest number of casualties. Collapses led to the rupture of many gas lines. Failures in these buildings were typically caused by large inertial loads from the heavy roofs that exceeded the lateral earthquake load-resisting capacity of the supporting walls. The relatively weak bottom stories created by the open fronts typically collapsed. Unlike most U.S. homes, Japanese homes typically have few if any substantive interior partitions to help resist the earthquake loads. In this respect, the bottom stories are similar to the U.S. homes that are supported on unbraced cripple walls. In older homes, many framing members had been weakened by wood rot. Soil failures exacerbated the damage, because the foundations have virtually no strength to resist settlement, and connections between the residences and their foundations were weak (Figure 1.62). Mid-rise commercial buildings, generally 6 to 12 stories high, make up a substantial portion of the buildings in the Kobe business district. The highest concentration of damaged mid-rise buildings was © 2003 by CRC Press LLC
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FIGURE 1.62 Japanese house collapses, January 17, 1995 Hanshin earthquake. (Courtesy EQE International) Shown as Color Figure 1.62.
observed in the Sannomiya area of Kobe’s central business district. In this area, most of the commercial buildings had some structural damage, and a large number of buildings collapsed on virtually every block. Most collapses were toward the north, which was evidently the result of a long-period velocity pulse perpendicular to the fault. This effect has also been observed in other earthquakes. Failures of major commercial and residential buildings were noted as far away as Ashiya, Nishinomiya, and Takarazuka. In general, many newer structures performed quite well and withstood the earthquake with little or no damage. In the heavily damaged central sections of downtown Kobe, approximately 60% of the buildings had significant structural damage, and about 20% completely or partially collapsed. One survey of a 120,000-m2 area in downtown Kobe (the Sannomiya area) found that 21 of 116 buildings, or 18%, were visibly destroyed. Another report indicated that 22% of office buildings in a portion of the Kobe city center were unusable, while an additional 66% needed more than 6 months for complete restoration. City inspectors declared approximately 50% of the multifamily dwellings in Kobe unsafe to enter or unfit for habitation, leaving more than 300,000 people homeless (Figure 1.63). At the Ashiyama seaside town, 21 of 52 mid- and high-rise condominium structures built between 1975 and 1979 had severe damage to the structural steel framing. This innovative and unconventional structural system consisted of macro-steel moment frames in which the column and girder members were large steel trusses. Girders were typically located at every fifth floor. Housing units consisted of precast concrete assemblies that had been brought to the site by barge. Damage observed included the brittle fracture of square, tubular columns up to 50 cm wide with 5-cm-thick walls, and fracturing of steel wide-flange diagonal bracing elements. Residual horizontal offsets in column elements were observed to be as large as 2 cm in some cases. In general, it appeared that the brittle fractures had occurred in framing elements subjected to high combined tensile and shear stresses. In one of the units, six of the eight main steel columns forming the lateral-load-resisting system had fractured (Figure 1.64). Two limited-access highways service the Kobe-Osaka transportation corridor, the Hanshin and Wangan expressways. Built in the mid- to late 1960s, the Hanshin Expressway is the main through road and is almost entirely elevated for more than 40 km. Much of the roadway is supported by single, large reinforced concrete piers spaced every 32 m, many of which failed in shear or bending over a 20-km length. Similar failures of the roadway occurred at many locations, including complete toppling of large reinforced concrete pillars supporting a 500-m section. It was observed that the road deck changed from steel to a heavier concrete section at the location where this collapse occurred. These failures not only closed the Hanshin Expressway for an indefinite period, but severely impeded traffic on Route 43, a street-level highway beneath the expressway (Figure 1.65). Elevated railroad structures and railway stations were particularly hard hit. Three main lines (JR West, Hankyu, and Hanshin) run through the Kobe-Osaka transportation corridor, generally on elevated structures and embankments. All the lines had elevated structure and embankment failures, overpass collapses, distorted rails, and other severe damage. A large number of cars were damaged, and some fell © 2003 by CRC Press LLC
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FIGURE 1.63 Japanese commercial building collapses, January 17, 1995 Hanshin earthquake. (Courtesy EQE International)
onto city streets. Several stations and several kilometers of reinforced concrete elevated structures were destroyed, and numerous spans collapsed. The Rokkomichi Station (built in 1972) of the JR West line was virtually destroyed (Figure 1.66). The Shinkansen (Bullet Train) was constructed ca. 1964. Most of its path in the Kobe area is through two long tunnels under Rokko Mountain. No information on the tunnels’ performance was immediately available. At the east portal of the tunnel, the line is carried on an elevated viaduct built in 1968. For a length of 3 km, this viaduct was severely damaged, with a number of the longer spans collapsing. In general, these collapses were caused by shear failure of the supporting concrete columns (Figure 1.66C). Damage to underground facilities, such as mines, tunnels, or subways, is rare in earthquakes. An unusual example of severe damage to this type of facility occurred in the Kobe subway system, a twotrack line running under central Kobe, which was generally built by cut-and-cover methods in the mid1960s. The double track is typically carried through a concrete tube 9 m wide by 6.4 m high, which widens to 17 m at the stations. The tube typically has about 5 m of overburden, which is supported by 0.4-m-thick walls and roof slabs. The walls and roof slab are supported midspan (between the tracks) by a series of 5-m tall, 1-m long, 0.4-m wide reinforced concrete columns, which failed in shear due to displacements imposed by ground strain. The Port of Kobe, one of the largest container facilities in the world, sustained major damage during the earthquake. In effect, the port was practically destroyed. The total direct damage to the port easily exceeded U.S. $11 billion. The port complex, constructed on three man-made islands — Maya Container © 2003 by CRC Press LLC
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FIGURE 1.64 Ashiyahama Steel Buildings and column failures, January 17, 1995 Hanshin earthquake. (Photos: C. Scawthorn)
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FIGURE 1.65 Hanshin Expressway collapse, January 17, 1995 Hanshin earthquake. (Photo (B): C. Scawthorn) Shown as Color Figure 1.65.
Terminal, Port Island (with an area of 10 km2), and Rokko Island (with an area of 6 km2) — accounts for approximately 30% (2.7 million containers per year) of Japan’s container shipping. At the time of the earthquake, the three facilities included 27 active container berths and various other wharves, ferry terminals, roll-on facilities, and warehousing. In addition, the older parts of the port contain numerous other facilities, such as an extensive shipyard. Also, at the time of the earthquake, several new islands © 2003 by CRC Press LLC
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FIGURE 1.66
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Railroad and subway damage, January 17, 1995 Hanshin earthquake. (Courtesy EQE International)
were under development, and new berths were under construction to the east of Rokko Island (Figure 1.67). Numerous fires broke out, exacerbated by loss of water supply throughout the affected region (Figure 1.68) (see Chapter 29). 1.2.5.6 1999: August 17, Turkey (Mw 7.4) Similar to the San Andreas fault being the North American-Pacific plate boundary, Turkey lies on a major boundary between the African and Eurasian plates. The North Anatolian Fault Zone (NAFZ) is the most prominent active fault in Turkey and has been the source of numerous large earthquakes throughout history, including a number of major earthquakes in the twentieth century [Ambraseys and Finkel, 1995] (Figure 1.69). The Mw 7.4 Marmara (also known as Kocaeli) earthquake occurred at 3:10 a.m. local time, August 17, 1999, on the east–west trending north strand of the NAFZ, about 100 km southeast of Istanbul. The 125-km-long fault and high damage area follows or is close to the south shore of Izmit Bay (Figure 1.70), and has predominantly 2.2 m right lateral displacement, from Adapazari in the east to Yalova in the west. Significant vertical fault scarps of as much as 2 m occur at several locations (Figure 1.71). Peak ground accelerations of approximately 0.4 g were recorded near the fault, and liquefaction and subsidence were observed on the shores of Izmit Bay and Lake Sapanca. Figure 1.72 presents the response spectra for the north–south (NS) component of the YPT record, recorded at the Yarimca petrochemical complex on the north shore of Izmit Bay, approximately 4 km from the fault trace. Substantial geotechnical effects occurred due to the earthquake, especially along the south shores of Izmit Bay and Lake Sapanca, where settlement and slumping were observed at numerous locations (Figure 1.73). In Adapazari, significant settlement and liquefaction were observed, resulting in very major damage to buildings (Figure 1.74). Adapazari (at the eastern terminus of faulting) is a soft soil site that exhibited © 2003 by CRC Press LLC
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FIGURE 1.67 Figure 1.67.
Port damage, January 17, 1995 Hanshin earthquake. (Courtesy EQE International) Shown as Color
FIGURE 1.68
Fires, January 17, 1995 Hanshin earthquake. Shown as Color Figure 1.68.
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Location of August 17, 1999 Turkish Earthquake 1992 1967 1957 1944
1951
1943
1942
1939
Black Sea Istanbul
7.3
Izmit
7.3 n Fault lla Anato Nor th Ankara 100km
7.1
7.1 7.0 1999 Epicenter
0
7.9
TURKEY
6.8
Historical earthquake epicenter and magnitude 1957 Extent of surface rupture Direction of relative motion on fault
FIGURE 1.69 turkey/.)
Progressive North Anatolian Fault rupture in adjacent earthquakes. (From quake.wr.usgs.gov/study/
29°
30°
BOGAZIC UNIVERSITY KANDILLI OBSERVATORY and EARTHQUAKE RESEARCH INSTITUTE SEISMOLOGY LABORATORY
31°
BLACK SEA
Istanbul 41°
41° Düzce Adapazan Hendek
Izmit
MARMARA SEA Yalova
Gölcük
Akyazi
Gernlik 17.08.1999 Izmit Earthquake (Mw = 7.4) Bursa Bileclk
5<M<6 Aftershocks 4<M<5 Aftershocks 40°
40° 29°
FIGURE 1.70
30°
31°
Aftershock pattern, August 17, 1999 Marmara earthquake. (From www.koeri.boun.edu.tr/.)
FIGURE 1.71 Vertical fault scarp near Golcuk, August 17, 1999 Marmara earthquake. Note lack of damage to house literally on the fault. (Photo: C. Scawthorn) Shown as Color Figure 1.71.
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STATION YPT-NS RESPONSE SPECTRA 1,000
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FIGURE 1.72 YPT 5% damped response spectra, August 17, 1999 Marmara earthquake. (From http://geophysics.gg.utk.edu/izmit/earthquake.htm.)
FIGURE 1.73 Subsidence, south shore of Izmit Bay, east of Golchuk, August 17, 1999 Marmara earthquake. Note crane and buildings in water, indicating subsided quay or pier. (Photo: C. Scawthorn) Shown as Color Figure 1.73.
(A)
(B)
FIGURE 1.74 Adapazari, August 17, 1999 Marmara earthquake. (A) Overturned building, due to foundation failure brought on by liquefaction. (B) Main street of Adapazari, showing damage to numerous buildings, due to soft soil amplified ground motion and liquefaction. (Photos: C. Scawthorn) Shown as Color Figure 1.74.
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FIGURE 1.75 August 17, 1999 Marmara earthquake. Complex of four-story reinforced concrete frames east of Golchuk, all of which collapsed due to soft stories. (Photos: C. Scawthorn) Parts (B) and (C) shown as Color Figure 1.75.
liquefaction and settlement. The name Adapazari derives from ad meaning island, and pazari meaning bazaar; originally the site was an island in a shallow lake, where a regional bazaar was held. As time went on, traders congregated longer and longer, and eventually the city developed and the lake was filled in. Although the north shore of Izmit Bay is bounded by steep mountains, and there is hilly terrain elsewhere, no landsliding was observed. Several million persons live in the Izmit region, which has experienced rapid growth and heavy industrialization in the last two decades. The predominant building type is mid-rise nonductile reinforced concrete (RC) frames with hollow clay tile infill and soft stories. Thousands of these collapsed in a “pancake” mode, resulting in a death toll of approximately 17,000, with estimates of population requiring short- to long-term shelter ranging from 200,000 to 600,000. Figure 1.75 illustrates collapse of this type of building, thousands of which collapsed throughout the region. Steel buildings fared much better than the nonductile RC frames shown. Lifeline damage was moderate to major, as follows: • Electric: Power failed within minutes of the earthquake, but was generally restored to most areas within several days. Substations did not appear to be damaged, nor transmission lines or towers, except where the lines crossed the fault. • Telephone: Service continued with only minor disruptions, and cell service was reportedly uninterrupted. © 2003 by CRC Press LLC
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• Gas: There is no domestic underground gas piping in the area. It is unknown as of this writing if there are bulk transmission lines in the area. • Rail: Rail lines were buckled at fault crossings, but repairs were quickly effected, and rail service restored within several days. • Highways: Roads and highways were generally undamaged except for several highway bridges intersected by traces of the fault. Where this put the bridge in tension, spans were pulled off their beam seats, and the spans collapsed. The main motorway connecting Istanbul and Ankara passes along the north shore of Izmit Bay and close to Adapazari; in general, it was undamaged. • Water: The main source of water is the recently constructed Izmit Water Project, built and operated by Thames Water. It is the largest privatized water project in the world as of this writing, and replaces a variety of low-quality sources for the various municipalities in the area. The water treatment plant is 440 million liter/day capacity (110 mgd) and sustained minor but manageable damage. Downstream of the plant, water is conveyed to retail customers via a 2.2-m spiral-welded steel pipe, which crosses the fault trace with approximately a 2-m right lateral offset at that location. The pipe was uncovered and found to need repairs, but service was largely unaffected. A number of ignitions occurred in building collapses, but these were generally confined to the building of origin, due to the prevalent nonflammable building materials. The most dramatic fire was at the Tupras oil refinery, where it appears that two separate fires initiated during the earthquake and burned for several days (see Chapter 20). The Mw 7.4 Kocaeli earthquake was a devastating catastrophe and great human tragedy for the Turkish people. The earthquake should have come as no surprise, because the long history of earthquakes and clear pattern of sequential segmented rupturing of the NAFZ was well known. Rapid development of the Marmara region led to unregulated building, resulting in inadequate lateral force systems in buildings. Almost the only building type is nonductile RC frames with hollow clay tile infill which, combined with soft stories, results in a pancake type of collapse. As a result, approximately 17,000 fatalities occurred. The Izmit Bay area is heavily industrialized and accounts for perhaps 10% of Turkey’s gross domestic product. Combined with other economic problems, the earthquake exacerbated an already severe burden on the national economy. Considering the entire spectrum of the built environment, the damage resulting from the event, while substantial, was generally within the resources of Turkey to manage and tolerate. The exception to this was the dismal performance of the RC frames, virtually ubiquitous in the region. The collapse of thousands of these buildings transformed this earthquake from a damaging event to a catastrophe. Within the spectrum of the built environment, only this aspect was a spike. Design and construction of RC frames to withstand strong earthquake motions are possible, and the principles were well understood by Turkish engineers. Unfortunately, the rapid development of the region overtaxed the ability of the society to assure that these principles were followed. The result was inadequate buildings, when there need not have been, and a tragic catastrophe. A review of Figure 1.69 indicates that Istanbul is now threatened by a similar catastrophe, in the form of a seismic gap in the Sea of Marmara. 1.2.5.7 1999: September 21, Taiwan (Mw 7.5) This earthquake came only a month after the Marmara earthquake, and caused at least 2,297 people killed, 8,700 injured, 600,000 people left homeless, and about 82,000 housing units damaged by the earthquake and larger aftershocks. Damage was estimated at U.S. $14 billion. Major geologic effects were observed; half of a village was lost by subsidence into the Ta-an Hsi and landslides blocked the Chingshui Hsi, creating a large lake. Surface faulting occurred along 75 km of the Chelungpu Fault. Many high-rise building collapses occurred due to inherent weaknesses of soft first stories. In sharp contrast to Turkey’s quick recovery of its electrical distribution system, Taiwan’s system was slow to recover, in large part because it was highly dependent on a single junction station 10 km from the epicenter that suffered landslide and shaking damage. Although Taiwan has very high-tech factories, they were significantly disrupted due to prolonged disruption to the power grid. The Shih-kang Dam failed because it straddled one of the faults that ruptured and released its water, 40% of the Taichung County’s supply. © 2003 by CRC Press LLC
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1.2.5.8 2001: January 26, Bhuj (Mw 7.7) At least 20,005 people were killed, 166,836 injured, approximately 339,000 buildings destroyed, and 783,000 damaged in the Bhuj-Ahmadabad-Rajkot area and other parts of Gujarat. Many bridges and roads were damaged in Gujarat. This earthquake was felt throughout northern India and much of Pakistan, and also felt in Bangladesh and western Nepal. The earthquake occurred along an approximately east–west trending thrust fault at shallow depth. The stress that caused this earthquake is due to the Indian plate pushing northward into the Eurasian plate. 1.2.5.9 Newer Directions The 1994 Northridge earthquake, coming within a few years of the 1989 Loma Prieta event, brought a realization among government and private sector leaders that what the earthquake community had been saying for decades had indeed to be heard and acted upon. During the 1990s: • Infrastructure systems in California and the Pacific Northwest conducted major projects to reduce their vulnerability. • Selected cities similarly conducted major projects to reduce their vulnerability. • Many large corporations similarly conducted major projects to reduce their vulnerability. • The insurance industry moved from a paper-based PML methodology to modern, probabilistic risk assessment and management of their book of business (see Chapter 32). • The federal government moved ahead with an assessment of the seismic vulnerability of all of its buildings, and developed HAZUS, a sophisticated earthquake loss-estimation methodology and free software code, for use by the general public. The federal government quickly responded to the new problem of cracked steel column connections, and funded a major study into this problem in a timely manner. • Major efforts were put into the writing of new modern building codes (see Chapter 11). Most of these were U.S. developments. Following the 1995 Hanshin (Kobe) earthquake, Japan quickly moved ahead on a parallel track to strengthen key infrastructure and reduce major vulnerabilities. Japan also liberalized earthquake insurance. However, Japan’s earthquake risk problem is enormous, and it will be a number of years before it can significantly reduce its earthquake risk, due to its existing housing stock and pattern of land development. Still, Japan’s leaders were also listening and acting. However, most of these developments were in the advanced industrialized nations. The 1985 Mexico City and 1988 Armenia events, as well as others not reviewed here (e.g., 1990 Iran, with 40,000 killed; 1990 Philippines, 1,600 killed; 1993 India, 10,000 killed, etc., see Table 1.1), started responsible persons also thinking and acting. When the 1999 Marmara earthquake occurred, it served as a springboard for a new initiative by the World Bank to introduce natural hazards catastrophe insurance into developing nations, as both a method for fiscal responsibility and to bring into play the benefits of the market mechanism for mitigation. With World Bank assistance, Turkey initiated the TCIP program (see Chapter 32), which appears to have been well designed and launched. Other nations are expected to follow suit.
Defining Terms Attenuation — The rate at which earthquake ground motion decreases with distance. Earthquake cycle — Concept that seismicity follows a cyclical pattern, with repetitions of similar events every several hundred to thousands of years, depending on the region. Clearly demonstrated by repeated similar events where record is long, such as on the Nankai trough, offshore Japan. Epicenter — The projection on the surface of the Earth directly above the hypocenter. Fault — A zone of the Earth’s crust within which the two sides have moved. Faults may be hundreds of miles long, from 1 to more than 100 miles deep, and not readily apparent on the ground surface.
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Hypocenter — The location of initial radiation of seismic waves (i.e., the first location of dynamic rupture).
Intensity — A metric of the effect, or the strength, of an earthquake hazard at a specific location, commonly measured on qualitative scales such as MMI, MSK, and JMA. Lateral-force-resisting system — A structural system for resisting horizontal forces, due for example to earthquake or wind (as opposed to the vertical-force-resisting system, which provides support against gravity). Liquefaction — A process resulting in a soil’s loss of shear strength, due to a transient excess of pore water pressure. Magnitude — A unique measure of an individual earthquake’s release of strain energy, measured on a variety of scales, of which the moment magnitude Mw (derived from seismic moment) is preferred. Meizoseismal — The area of strong shaking and damage. Near-field — Within one source dimension of the epicenter, where source dimension refers to the length or width of faulting, whichever is less. Normal fault — A fault that exhibits dip-slip motion, where the two sides are in tension and move away from each other. Peak ground acceleration (PGA) — The maximum amplitude of recorded acceleration (also termed the ZPA, or zero period acceleration). PML — Probable maximum loss. Pounding — The collision of adjacent buildings during an earthquake due to insufficient lateral clearance. Response spectrum — A plot of maximum amplitudes (acceleration, velocity, or displacement) of a single-degree-of-freedom oscillator (SDOF), as the natural period of the SDOF is varied across a spectrum of engineering interest (typically, for natural periods from 0.03 to 3.0 or more seconds, or frequencies of 0.3 to 30 or more hertz). Ring of Fire — A zone of major global seismicity due to the interaction (collision and subduction) of the Pacific plate with several other plates. Sand boils or mud volcanoes — Ejecta of solids (i.e., sand, silt) carried to the surface by water, due to liquefaction. Seismic gap — A portion of a fault or seismogenic zone that can be deduced to be likely to rupture in the near term, based on patterns of seismicity and geological evidence. Seismic hazards — The phenomenon or expectation (or both) of an earthquake-related agent of damage, such as fault rupture, vibratory ground motion (i.e., shaking), inundation (e.g., tsunami, seiche, dam failure), various kinds of permanent ground failure (e.g., liquefaction), fire, or hazardous materials release. Seismic moment — The moment generated by the forces generated on an earthquake fault during slip. Seismic risk — The product of the hazard and the vulnerability (i.e., the expected damage or loss, or the full probability distribution). Soft story — A story of a building signifiantly less stiff than adjacent stories, i.e., lateral stiffness is 70% or less than that in the story above, or less than 80% of the average stiffness of the three stories above. Spectrum amplification factor — The ratio of a response spectral parameter to the ground motion parameter (where parameter indicates acceleration, velocity, or displacement). Subduction — Refers to the plunging of a tectonic plate (e.g., the Pacific) beneath another (e.g., the North American) down into the mantle, due to convergent motion. Tectonic — Relating to, causing, or resulting from structural deformation of the Earth’s crust (from Greek tektonikos, from tektn, builder).
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Theory of elastic rebound — Concept that the Earth’s crust is deformed by plate movements, thus storing strain energy, until energy is released by fault rupture, resulting in an earthquake (formulated by H.F. Reid, 1910). Thrust fault — Low-angle reverse faulting. Blind thrust faults are faults at depth occurring under anticlinal folds. They have only subtle surface expression. Trans-Alpide belt — A zone of major global seismicity, extending from the Mediterranean through the Middle East, the Himalayas, and the Indonesian archipelago, resulting from the collision of several major tectonic plates. Transform or strike-slip fault — A fault where relative fault motion occurs in the horizontal plane, parallel to the strike of the fault.
References Algermissen, S.T. 1983. An Introduction to the Seismicity of the United States, Earthquake Engineering Research Institute, Berkeley, CA. Ambraseys, N.N. and Finkel, C.F. 1995. The Seismicity of Turkey and Adjacent Areas, A Historical Review, 1500–1800, EREN, Istanbul. ASCE (American Society of Civil Engineers). 1929. “Report of Special Committee on Effects of Earthquakes on Engineering Structures.” Unpublished manuscript, American Society of Civil Engineers, New York. Applied Technology Council. 1978. Tentative Provisions for the Development of Seismic Regulations for Buildings (ATC-3–06). Report funded by National Science Foundation and National Bureau of Standards. Applied Technology Council, Redwood City, CA. Applied Technology Council. 1991. Seismic Vulnerability and Impact of Disruption of Lifelines in the Conterminous United States (ATC-25). Report prepared by Applied Technology Council, Redwood City, CA, for the Federal Emergency Management Agency, Washington, D.C. (available from FEMA as FEMA 224). Branner, J.C. 1913. “Earthquakes and structural engineering,” Bull. Seismol. Soc. Am., 3(1), 1–5. Full article available online at: http://www.sfmuseum.org/1906/branner.html. Cameron, C. and James, C. n.d. The 1923 Great Kanto Earthquake and Fire, National Information Service for Earthquake Engineering, University of California, Berkeley, http://nisee.berkeley.edu/kanto/ yokohama.html. Carder, D.S., Ed. 1965. Earthquake Investigations in the Western United States, 1931–1964, U.S. Coast and Geodetic Survey. Publication 41–2, U.S. Department of Commerce, Coast and Geodetic Survey; U.S. Government Printing Office, Washington, D.C. Dewey, J. and Byerly, P. 1969. “The Early History of Seismometry (to 1900): Seismoscopes in Eighteenth Century Europe,” Bull. Seismol. Soc. Am., 59(1), 183–227, available online at http://neic.usgs.gov/ neis/seismology/part04.html. Dutton, C.E. 1889. “The Charleston Earthquake of August 31, 1886,” U.S. Geological Survey Ninth Annual Report, 1887–1888, U.S. Geological Survey, Washington, D.C., 203–528. EERI (Earthquake Engineering Research Institute). 1995. The Hyogo-Ken Nanbu Earthquake: Great Hanshin Earthquake Disaster, January 17, 1995. Preliminary Reconnaissance Report. Comartin, C.D., Greene, M., and Tubbesing, S.K., Tech. Eds. Earthquake Engineering Research Institute Report 95–04, sponsored by the Earthquake Engineering Research Institute, Oakland, CA, with support from the National Science Foundation and Federal Emergency Management Agency. EERI (Earthquake Engineering Research Institute). 1997. “George Housner, Connections, the EERI Oral History Series,” Stanley Scott, interviewer. Earthquake Engineering Research Institute, Oakland, CA.
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EERI (Earthquake Engineering Research Institute). 1999. “Robert E. Wallace, Connections, The EERI Oral History Series,” Stanley Scott, interviewer. Earthquake Engineering Research Institute, Oakland, CA (also available as U.S. Geological Survey Open-File Report 96–260, Robert E. Wallace: Earthquakes, Minerals and Me, online at http://quake.wr.usgs.gov/research/history/wallaceVI.html). EQE. 1995. The Northridge Earthquake of January 17, 1994: Report of Data Collection and Analysis, Part A: Damage and Inventory Data. Prepared by EQE International, Inc. and the Geographic Information Systems Group of the Governor’s Office of Emergency Services of the State of California, Sacramento. EQE. 1997. The Northridge Earthquake of January 17, 1994: Report of Data Collection and Analysis, Part B: Analysis and Trends. Prepared by EQE International, Inc. and the Geographic Information Systems Group of the Governor’s Office of Emergency Services of the State of California, Sacramento. Federal Emergency Management Agency. 2000. HAZUS® 99 Estimated Annualized Earthquake Losses for the United States (FEMA 366), Federal Emergency Management Agency, Washington, D.C. Freeman, J.H. 1932. Earthquake Damage and Earthquake Insurance. McGraw-Hill, New York. Fuller, M.L. 1912. The New Madrid Earthquake, Bulletin 494, U.S. Geological Survey, Washington, D.C. Goldberg, R. 1989. “Voltaire, Rousseau, and the Lisbon Earthquake,” Eighteenth Century Life, 13(2), 1–20. Hamada, M., Wakamatsu, K., and Yasuda, S. 1992. “Liquefaction-Induced Ground Deformation during the 1923 Kanto Earthquake,” in Case Studies of Liquefaction and Lifeline Performance during Past Earthquakes, Vol. I, Japanese Case Studies, Hamada, M. and O’Rourke, T.D., Eds., Tech. Rep. NCEER-92–0001, February, National Center for Earthquake Engineering Research, State University of New York, Buffalo. Home Office. 1926. The Great Earthquake of 1923 in Japan. Bureau of Social Affairs, Home Office, Tokyo. Hopper, M.G. 1985. Estimation of Earthquake Effects Associated with Large Earthquakes in the New Madrid Seismic Zones, U.S. Geological Survey Open-File Report 85-457, Denver, CO. Jenkins, O.P. and Oakeshott, G.B. 1955. “Earthquakes in Kern County, California during 1952.” Bulletin 171, California Division of Mines, San Francisco. Johnston, A.C. 1991. “The Stable Continental Region Earthquake Data Base,” in Methods for Measuring Maximum Earthquakes in the Eastern United States, Coppersmith, K.J., Johnston, A.C., Kanter, L.R., Youngs, R.R., and Metzger, A.G., Eds., EPRI Report RP-2556–12, Electric Power Research Institute, Palo Alto, CA. Kendrick, T.D. 1956. The Lisbon Earthquake. Methuen, London. Koizumi, Y. 1965. “Change of Density of Stand Layer Due to Niigate Earthquake,” Tsuchi to Kiso, 13(2). Kozak, J.T. and James, C.D. n.d. “Historical Depictions of the 1755 Lisbon Earthquake.” Available online at http://nisee.berkeley.edu/lisbon/. Lawson, A.C. et al. 1908. The California Earthquake of April 18, 1906. Report of the State Earthquake Investigation Commission (two volumes and atlas), Vol. I, Carnegie Institution, Washington, D.C. (reprinted 1969). NEIC (National Earthquake Information Center). 1996. Database of Significant Earthquakes Contained in Seismicity Catalogs. National Earthquake Information Center, Golden, CO. NOAA (National Oceanic and Atmospheric Administration). 1973. San Fernando, California, Earthquake of February 9, 1971, Vol. I, Parts A and B: Effect on Buildings; Vol. II: Utilities, Transportation, and Sociological Aspects; and Vol. III: Geological and Geophysical Studies, Murphy, L.M., Ed., U.S. Department of Commerce, Washington, D.C. NOAA/NGDC (National Oceanic and Atmospheric Administration and National Geophysical Data Center). n.d. http://www.ngdc.noaa.gov/seg/hazard/slideset/tsunamis/. Nuttli, O.W. 1973. “The Mississippi Valley Earthquakes of 1811 and 1812: Intensities, Ground Motion and Magnitude,” Bull. Seismol. Soc. Am., 63, 227–248. Nuttli, O.W. 1979. “Seismicity of the Central United States,” in Geology in the Siting of Nuclear Power Plants, Hatheway, A.W. and McClure, C.R., Eds., Geological Society of America, Rev. Eng. Geol., 4, 67–94. © 2003 by CRC Press LLC
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Osteraas, J. and Krawinkler, H. 1989. “The Mexico Earthquake of September 19, 1985: Behavior of Steel Buildings,” Earthquake Spectra, 5(1), 51–88. Peters, K.E. and Herrmann, R.B., Eds. n.d. First-Hand Observations of the Charleston Earthquake of August 31, 1886 and Other Earthquake Materials, South Carolina Geological Survey Bulletin 41. Reid, H.F. et al. 1910. The California Earthquake of April 18, 1906. Report of the State Earthquake Investigation Commission (two volumes and atlas), Vol. II: The Mechanics of the Earthquake, Carnegie Institution, Washington, D.C. (reprinted 1969). Reitherman, R.K. n.d. “Frank Lloyd Wright’s Imperial Hotel: A Seismic Re-Evaluation.” National Information Service for Earthquake Engineering, University of California, Berkeley, http://nisee.berkeley.edu/kanto/kanto.html. Scawthorn, C. 1995. “Insurance Estimation: Performance in the Northridge Earthquake,” Contingencies, the magazine of the American Institute of Actuaries, Washington, D.C. Scawthorn, C., Ed. 2000. The Marmara, Turkey Earthquake of August 17, 1999. Reconnaissance Report. MCEER Tech. Rep. MCEER-00–0001, Multidisciplinary Center for Earthquake Engineering Research, State University of New York, Buffalo. Scawthorn, C., Celebi, M., and Prince, J. 1986. “Performance Characteristics of Structures, 1985 Mexico City Earthquake,” in The 1985 Mexico City Earthquakes, Factors Involved and Lessons Learned. American Society of Civil Engineers, New York. SEAOC (Structural Engineers Association of California). 1980. History of Earthquake Codes in California, Recommended Lateral Force Requirements, Structural Engineers Association of California, San Francisco. Steinbrugge, K.V. and Moran, D.F. 1954. “An Engineering Study of the Southern California Earthquake of July 21, 1952 and its Aftershocks,” Bull. Seismol. Soc. Am., 44(2B). Stover, C.W. and Coffman, J.L. 1993. Seismicity of the United States, 1568–1989 (revised). U.S. Geological Survey Professional Paper 1527, U.S. Government Printing Office, Washington, D.C. Street, R. 1982. “A Contribution to the Documentation of the 1811–1812 Mississippi Valley Earthquake Sequence,” Earthquake Notes, 53(2). Tobriner, S. 1984. “A History of Reinforced Masonry Construction Designed to Resist Earthquakes: 1755–1907,” Earthquake Spectra, 1(1), 125–149. UNAM. 1985. Efectos de los sismos de Sept. de 1985 en las constructiones de la Ciudad de Mexico. Aspectos Estructurales, Segundo informe del Instituto de lng. de la Universidad Nacional Auton. de Mexico, Noviembre. U.S. Coast and Geodetic Survey. 1967. The Prince William Sound, Alaska, Earthquake of 1964 and Aftershocks (three volumes), Environmental Sciences Services Administration, U.S. Government Printing Office, Washington, D.C. USGS (U.S. Geological Survey). 1907. The San Francisco Earthquake and Fire of April 18, 1906 and Their Effects on Structures and Structural Materials, Bulletin 324, U.S. Geological Survey, Washington, D.C. Wald, D.J., Quitoriano, V., Dengler, L.A., and Dewey, J.W. 1999. “Utilization of the Internet for Rapid Community Intensity Maps,” Seismol. Res. Lett., available online at: http://pasadena.wr.usgs.gov/ shake/pubs/ciim/ciimweb.html.
Further Reading There is a vast literature on historical earthquakes, due to observers feeling the importance of recording the natural event and its human consequences, which goes back to Biblical times and expanded enormously with the advent of modern science. Several repositories that can be searched for reports and data on historical events can be accessed via: National Information Service For Earthquake Engineering: (http://nisee.ce.berkeley.edu/) National Earthquake Information Center (USGS): http://neic.usgs.gov/ MCEER: (http://mceer.buffalo.edu/) EQNET: http://www.eqnet.org/ © 2003 by CRC Press LLC
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Listed here are a few references for selected important events or to provide an overview for major regions of the globe: Ambraseys, N.N. and Melville, C.P. 1982. History of Persian Earthquakes, Cambridge University Press, Cambridge. Ambraseys, N.N. and Melville, C.P. 1994. In Seismicity of Egypt, Arabia and the Red Sea: A Historical Review, Adams, R.D., Ed., Cambridge University Press, Cambridge. Ambraseys, N.N. and Finkel, C.E. 1995. The Seismicity of Turkey and Adjacent Areas, A Historical Review, 1500–1800, EREN, Istanbul. American Society of Civil Engineers. 1929. “Report of Special Committee on Effects of Earthquakes on Engineering Structures,” American Society of Civil Engineers, New York (unpublished manuscript, on the 1923 Tokyo earthquake). Atlas of Isoseismal Maps, Central and Eastern Europe. 1978. Geophysical Institute of the Czechoslavak Academy of Sciences, Prague. Bapat, A. et al. 1983. Catalogue of Earthquakes in India and Neighborhood from Historical Period up to 1979. Indian Society of Earthquake Technology, Roorkee. Benfer, N.A. and Coffman, J.L., Eds. 1973. The San Fernando, California, Earthquake of February 9, 1971, National Oceanic and Atmospheric Administration, Washington, D.C. Bureau of Social Affairs. 1926. The Great Earthquake of 1923 in Japan, Home Office, Tokyo. Cassaro, M. and Martinez Romero, E. 1987. The Mexico Earthquakes: 1985, Factors Involved and Lessons Learned, American Society of Civil Engineers, New York. Chen, Y. 1988. The Great Tangshan Earthquake of 1976: An Anatomy of Disaster, Pergamon Press, Oxford. Chien, K. 1989. The Great China Earthquake, Foreign Languages Press, Beijing. Chung, R., Ed. 1996. The January 17, 1995 Hyogoken-Nanbu (Kobe) Earthquake, Performance of Structures, Lifelines and Fire Protection Systems, NIST Special Publication 901, National Institute of Standards and Technology, Gaithersburg, MD. CNR. 1993. Historical Investigations of European Earthquakes 1, Materials of the CEC Project Review of Historical Seismicity in Europe, Stucchi, M., Ed., Istituto di Ricerca sul Rischio Sismico, Milan, Italy. CNR. 1994. Historical Investigations of European Earthquakes 2, Materials of the CEC Project Review of Historical Seismicity in Europe, Albini P. and Moroni, A., Eds., Istituto di Ricerca sul Rischio Sismico, Milan, Italy. Coffman, J.L., von Hake, C.A., and Stover, C.W. 1980. Earthquake History of the United States, NOAA Publ. 41–1, U.S. Department of Commerce, Washington, D.C. Downes, G.L. 1995. Atlas of Isoseismal Maps of New Zealand Earthquakes, Institute of Geological and Nuclear Sciences, Lower Hutt. Dutton, C.E., Ed. 1889. “The Charleston Earthquake of August 31, 1886,” U.S. Geological Survey, Ninth Annual Report 1887–1888, U.S. Geological Survey, Washington, D.C. EQE Engineering. 1990. Earthquakes of the 1980s, EQE, San Francisco. Freeman, J.R. 1932. Earthquake Damage and Earthquake Insurance. McGraw-Hill, New York. Fuller, M.L. 1912. The New Madrid Earthquake. U.S. Geological Survey Bulletin 494, Department of the Interior, U.S. Government Printing Office, Washington, D.C. Gilbert, G.K. et al. 1907. The San Francisco Earthquake and Fire of April 18, 1906 and Their Effects on Structures and Structural Materials. U.S. Geological Survey Bulletin 324, Washington, D.C. Imperial Earthquake Investigation Committee. n.d.. Sinsai Yobo Tyosakwai Hokoku (Earthquake Disaster Report). Reports No. 100 E (6 vols., in Japanese, detailed report on the 1923 Tokyo earthquake), Tokyo. Lawson, A.C. and Reid, H.F. 1908–1910. The California Earthquake of April 18, 1906. Report of the State Earthquake Investigation Commission, California. State Earthquake Investigation Commission, Carnegie Institution of Washington, Washington, D.C. Lee, W.H.K., Meyers, H., and Shimazaki, K. 1988. Historical Seismograms and Earthquakes of the World, Academic Press, New York. © 2003 by CRC Press LLC
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Lomnitz, C. 1974. Global Tectonics and Earthquake Risk, Elsevier, New York. Nuttli, O.W., Bollinger, G.A., and Herrmann, R.B. 1986. The 1886 Charleston, South Carolina, Earthquake: A 1986 Perspective. U.S. Geological Survey Circular 985, Washington, D.C. Office of the Engineer. 1949. The Fukui Earthquake, Hokuriku Region, Japan, 28 June 1948. General Headquarters, Far East Command, U.S. Army. Postpischl, D., Ed. 1985. Catalogo dei Terremoti Italiani Dall’anno 1000 al 1980 (in Italian). Consiglio Nazionale delle Ricerche, Progetto Finalizzato Geodinamica, Bergamo. Richter, C.F. 1958. Elementary Seismology, W.H. Freeman, San Francisco. Scawthorn, C., Ed. 2000. The Marmara, Turkey Earthquake of August 17, 1999: Reconnaissance Report. Tech. Rep. MCEER-00–0001, Multidisciplinary Center for Earthquake Engineering Research, State University of New York, Buffalo. Steinbrugge, K.V. 1982. Earthquakes, Volcanoes, and Tsunamis: An Anatomy of Hazards, Skandia America Group, New York. Usami, T. 1981. Nihon Higai Jishin Soran (List of Damaging Japanese Earthquakes) (in Japanese), University of Tokyo Press, Tokyo. U.S. Geological Survey. The Loma Prieta, California, Earthquake of October 17, 1989. Series of U.S. Geological Survey Professional Papers 1550 to 1553 (numerous subvolumes, a trove of detailed information on the 1989 event, T. Holzer, USGS coordinator). Wakamatsu, K. 1991. Maps for Historic Liquefaction Sites in Japan, Tokai University Press, Tokyo. Woo, G., Wood, R., and Muir, R. 1984. “British Seismicity and Seismic Hazard,” in Proc. Eighth World Conf. Earthquake Eng., Vol. 1, pp. 39–44, Earthquake Engineering Research Institute, Oakland, CA. Wood, F.J., Ed. 1966–1969. The Prince William Sound, Alaska, Earthquake of 1964 and Aftershocks, U.S. Coast and Geodetic Survey, Washington, D.C. Woods, M.C. and Seiple, W.R. 1995. The Northridge, California, Earthquake of 17 January 1994, Special Publication 116, Department of Conservation, Division of Mines and Geology, Sacramento, CA.
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2 Earthquake Risk Management: An Overview 2.1 2.2 2.3 2.4 2.5
Introduction Overview of Earthquake Risk Identifying the Assets at Risk Earthquake Hazard Earthquake Damage and Loss
2.6 2.7
Mitigation Alternatives Earthquake Risk Management Decision-Making
Infrastructure · Loss
Maximization (Benefit–Cost) or Minimization (Total Cost) · Maximin and Maximax · Minimum Regret · Minimum Uncertainty · Satisficing · Next Steps
Charles Scawthorn Consulting Engineer Berkeley, CA
2.8 Earthquake Risk Management Program 2.9 Summary Defining Terms References Further Reading
2.1 Introduction Earthquakes represent a risk in many parts of the world, particularly western North and South America, Japan, China, the Philippines, New Zealand, and the lands surrounding the Mediterranean, to name only some of the higher seismic risk regions. This is well known. What to do about earthquake risk, however, and how, is not so clear. To address these questions, this chapter provides an overview of the earthquake risk management process, as a sort of road map for reducing earthquake risk. That is, the reduction of earthquake risk involves the use of knowledge, methods, and data from disparate fields, including the geosciences, engineering, emergency planning and disaster response, insurance, and economics. These are the tools that engineers, planners, and other professionals have for the job of reducing, or managing, earthquake risk. This chapter provides an overview on how to use these tools — that is, on assessing the risk of earthquakes, determining mitigation alternatives, making a decision about what to do, and doing it. While each succeeding chapter in this handbook provides detail on one or another of the tools, it is this chapter that provides the framework within which these tools are employed.
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2.2 Overview of Earthquake Risk The first step in understanding earthquake risk is to dissect the earthquake risk or loss process into its constituent steps (see Figure 2.2). Earthquake risk begins with the occurrence of the earthquake, which results in a number of earthquake hazards. The most fundamental of these hazards is faulting, that is, the surface expression of the differential movement of blocks of the Earth’s crust. Faulting can be a simple “mole-track” lateral movement, or a major vertical scarp, or may not even be visible. In most cases, faulting is typically a long narrow feature, and therefore affects a relatively small fraction of the total affected structures and persons. Affecting a much greater number of structures and persons is shaking, which is typically the primary hazard due to earthquakes. Depending on the earthquake, liquefaction, other forms of ground failure, tsunamis, or other types of hazards may be significant agents of damage. For various reasons, many buildings, portions of the infrastructure, and other structures cannot fully resist these hazards, and sustain some degree of damage. Primary damage can vary from minor cracking to total collapse. Some building types are more vulnerable than others, but even when a building sustains no structural damage, the contents of the building may be severely damaged. For certain occupancies, such as hospitals or emergency services dispatch centers, this damage to contents (laboratories, specialized machinery, communication equipment, etc.) can be very important. Additionally, these various kinds of primary damage can lead to other secondary forms of hazard and damage, such as releases of hazardous materials, major fires, or flooding. Damage results in loss. Primary loss can take many forms — life loss or injury is the primary concern, but financial loss and loss of function are also of major concern. The likelihood of sustaining a loss is termed risk. Primary losses lead to secondary forms of loss, such as loss of revenues resulting from business interruption and loss of market share and/or reputation.
2.3 Identifying the Assets at Risk Earthquake risk management starts by defining the problem — what is at risk? As a general rule of thumb, anything that is potentially subject to an earthquake hazard is at risk from earthquakes. It is of value to catalog the types of assets potentially at risk, as a sort of checklist. Table 2.1 provides a sample catalog of the typical assets that are at risk from earthquakes — it focuses not only on the assets at risk, but also the threats that earthquakes pose to these assets and, generally but not exhaustively, the mitigation alternatives available for countering each of these threats. In general, three types of things of value (assets) are at risk: • People can be killed or injured by earthquake effects in a number of ways — most commonly by building collapse, but also by tsunami, fire, landslide, etc. • Money can be lost, both in a relatively direct manner, such as having to pay to repair or rebuild a building, and in less direct but no less real ways, such as loss of employment when the factory is damaged, or due to short- to long-term shifts in economic conditions caused by earthquake damage. • Function can be impaired or lost, which eventually translates to human injury or financial loss. Examples of functional impairment include 911 services not being able to function, and business interruption due to damage to a factory or store. In summary, if one is attempting to manage earthquake risk, the starting point is to define what one might possibly lose due to an earthquake. In general, for an individual person or a large corporation, losses can occur in all three asset classes (people, money, function). For example, an engineer may examine the earthquake safety of a school building. The benefit of strengthening the building will be not only fewer deaths or injuries, but also reduced repair costs for the building and contents, and continued maintenance of function (i.e., another building does not have to be found and school can stay in session).
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TABLE 2.1
Assets at Risk
Asset: Loss
Earthquake Threat
Mitigation Alternatives
People: death and injury
Building damage/collapse, via fault rupture, shaking, ground failure, etc.
Investigate site for potential faulting Strengthen the building Base isolate the building Provide supplemental damping Provide ground or foundation improvements, if ground failure is the issue Replace the building (i.e., move, or new construction) Inventory all contents and brace or otherwise reduce damage Modify building motions via base isolation, supplemental damping etc. Identify and review critical equipment for continuity of functionality during and after and earthquake (e.g., check for relay chatter, backup power, water, fuel, etc.) Assure equipment will not be damaged (i.e., brace, etc.) Provide redundant equipment Develop emergency plans and procedures for equipment malfunction Identify and review neighborhood for earthquake hazards (e.g., tsunami, landslide) and threats (e.g., nearby hazardous operations, such as a chemical process plant) Develop Emergency plans and procedures, including possible warning mechanisms Build protective barriers Acquire protective equipment and training (e.g., fire brigades) Modify offsite threat (e.g., earthmoving, for a landslide; or buy out nearby hazardous operation; or move) Same as above, plus Emergency plans and procedures to minimize damage (e.g., recovery of inventory, quick shut-down of broken sprinklers) Earthquake insurance Contingency planning for loss/replacement or recovery of facilities (e.g., backup sites or suppliers, rapid recovery via pre-arranged inspection and repair contractors) Financial planning for loss of revenue Earthquake/loss of profits insurance Planning for alternative production/transportation to maintain market share
Building contents damage
Equipment malfunction
Offsite threats
Property: financial loss
Same as above Inventory
Function: business interruption, revenue, market share
Same as above plus loss of infrastructure (e.g., transportation), loss of vendors
2.4 Earthquake Hazard Hazard and risk can be expressed and measured in a variety of ways. Prior to the invention of modern scientific instruments, earthquakes were measured qualitatively by their effect or intensity, which varied from point to point. With the deployment of seismometers, instrumental quantification of the entire earthquake event — the unique size or magnitude of the event — became possible. A number of different scales for magnitude and intensity have been developed, which are sometimes confused.1 In the United States, intensity is measured qualitatively using the Modified Mercalli Intensity (MMI) scale, while engineers and scientists quantify seismic intensity in terms of peak ground acceleration (PGA) and other measures. PGA is often expressed in terms of a fraction of the acceleration of gravity (g), such 1 Earthquake magnitude and intensity are analogous to a lightbulb and the light it emits. A particular lightbulb has only one energy level, or wattage (e.g., 100 watts, analogous to an earthquake’s magnitude). Near the lightbulb, the light intensity is very bright (perhaps 100 foot-candles, analogous to MMI IX), while farther away the intensity decreases (e.g., 10 foot-candles, MMI V). A particular earthquake has only one magnitude value, whereas it has many intensity values.
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Trinet Rapid Instrumental Intensity Map for Northridge JAN 17 1994 04:30:55 PST M6.7 N34.213 W118.5357 (site corrected)
34° 30'N BLUE AREA MMI < V
RED AREA MMI > IX
34° 00'N km 0
10
20
119° 00'W
30
118° 30'W
118° 00'W
FIGURE 2.1 MMI shaking intensities, 1994 Northridge earthquake. (Courtesy Trinet)
as 0.5 g or 50% of the acceleration of gravity. Figure 2.1 shows the MMI distribution for the 1994 Northridge, California earthquake, for example. The identification and determination of earthquake hazards for a site or community are critical elements in the earthquake risk management process. Earthquake hazard is a quantification of the various ground effects at a specific site produced by earthquakes, and the likelihood that these effects will exceed certain levels. More typically, it is a representation of how strongly the ground will shake and how often it is likely to do so. Earthquake hazards are site specific, that is, they are different at each individual site, depending on the site’s location and the properties of the ground beneath the site. Earthquake shaking is usually very strong on or very close to the fault, and decreases or attenuates with distance from the fault. This attenuation depends on the magnitude of the earthquake, and the geology of the region. Soils, especially soft soils such as old filled-in marshes, can greatly increase or amplify the ground motion. The effect of soils is a primary factor in the intensity of the shaking so that, even though shaking generally attenuates with distance from the fault, shaking can still be very strong at a large distance, if a building is on poor soils.
2.5 Earthquake Damage and Loss As noted above, many buildings, elements of the infrastructure, and structures other than buildings cannot fully resist earthquake effects. This section provides a summary overview of the kinds of damage and loss that earthquakes can cause. Subsequent chapters provide more detailed information on the earthquake performance of specific types of structures. Buildings can fail or be damaged in any of several ways in an earthquake: • Exterior walls fall away — this is the primary deficiency of unreinforced masonry (URM) and older tilt-up buildings, and can result in partial or even total collapse of the roof system, posing a significant life hazard and, typically, a major financial loss. • Concrete columns can shear — dropping the building in a “pancake” mode of collapse. This mode of failure poses a great life safety hazard and is common in older reinforced concrete frame buildings. © 2003 by CRC Press LLC
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• Certain kinds of steel beam-column connections can crack — this problem has only recently emerged and was observed in significant numbers following the 1994 Northridge, California earthquake, and is the subject of current research. None of the buildings that sustained this damage collapsed, and the hazard to life safety is still unclear, but the financial consequences can be significant. • Wood-frame buildings, for example, can slide off their foundations — this is the primary mode of failure for older wood single-family dwellings with a crawl space beneath the first floor. The crawl space can collapse when the so-called cripple walls supporting the first floor fall over. This failure mode usually does not result in great loss of life, but can result in major or total financial loss of the building. These are only the more common modes of building failure, and can all occur in a partial manner or to a lesser degree — in such cases, the building will require inspection, perhaps vacating, and structural and/or nonstructural repairs. As a rule of thumb, certain eras of building types have higher vulnerability: • Masonry buildings may be unreinforced2 and have a high likelihood of exterior wall and parapet collapse in even moderate shaking. • Multistory concrete frames from the 1920s to 1970s often rely on their columns for seismic resistance (termed moment frames). However, the columns often do not have the shearing resistance we now understand is needed, so that this era of unreinforced concrete buildings has the potential for a pancake type of collapse, with great life loss. • Steel moment frame buildings of the 1970s and 1980s rely on the beam–column connection for seismic resistance and, as noted above, certain kinds of these connections have been observed to crack in recent earthquakes. • Pre-1991 tilt-up buildings (a common commercial and factory building in California) may have a particularly weak wall–roof connection, which has resulted in many instances of damage. Because this weakness was observed in the 1971 San Fernando earthquake, newer tilt-ups may have better connections, and many of the older buildings have been retrofitted. From the above, it can be seen that, in earthquake terms, one or two decades may make a building seismically “old.” Nonstructural damage and repairs, from an occupancy viewpoint, can be as significant as structural damage. Tumbled and broken furniture or equipment, fallen ceilings, cracked floors, broken water, sprinkler, or gas lines, broken windows, extensive cracking of nonstructural interior walls, broken heating or air conditioning equipment, spilled noxious materials, and other types of nonstructural damage can all result in major costs, extended vacancies, and loss of productive use of the building. For certain occupancies, such as hospitals or emergency service dispatch centers, this nonstructural damage can be catastrophic, since these facilities are most needed following an earthquake. However, even nonessential occupancies, such as small businesses, can suffer severe financial hardships as a result of this type of disruption.
2.5.1 Infrastructure When buildings sustain significant damage, infrastructure in the same neighborhood is typically also heavily impacted. Examples include: • Freeway collapse, such as the I-880 Cypress Structure in the 1989 Loma Prieta earthquake, the collapsed bridges and interchanges on the various Los Angeles area freeways in the 1994 Northridge earthquake, and the collapsed Hanshin Expressway in the 1995 Kobe earthquake. • Underground piping breaks, especially in areas of poor soil. The combination of broken gas and water lines both provides the fuel for fires and takes away the firefighter’s best weapon. More noxious materials, such as sewage or crude or refined oil, may also be spilled, causing major occupancy and clean-up problems. 2
Except more modern masonry buildings in high seismic areas.
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• Water and wastewater treatment plants can also be damaged, resulting in prolonged periods of boil-water orders and spilling of raw sewage into bays or rivers. • Electric power and telecommunications may suffer widespread short-term outages but, except in the hardest hit areas, have typically performed reasonably well and been restored within a few days. For certain types of businesses or services, however, even a few days disruption of these vital services can be a major problem. These various kinds of primary damage can lead to other secondary forms of damage, such as releases of hazardous materials, major fires, or flooding. Major fires occur and spread due to the many ignitions occurring in an earthquake. These numerous ignitions, combined with delayed response by the fire department (since communications have been impaired), and lack of water for firefighting (due to damaged infrastructure), can lead to a catastrophic situation.
2.5.2 Loss Damage results in loss. Primary loss can take many forms: • Life loss or injury is the primary concern. With the exception of a rare heart attack, earthquakes do not kill people — rather, falling buildings or other structures injure and kill people.3 Thus, if building collapses, major releases of hazardous materials, and/or fires can be prevented, numbers of lives lost and serious injuries may be at levels which are as low as reasonably possible. • Major damage to property can occur, even if life loss or damage are minimal. The cost to repair or replace damaged buildings, contents, equipment, and other infrastructure is a direct financial loss. Additional losses are incurred as a result of disruption of use. • Loss of function can also be a major loss. If schools are closed for an extended period of time, for example, the postponement of education is clearly a loss. Loss of hospitals, city offices, emergency communications, and other important public functions are other clear examples. • Primary losses lead to other forms of loss, such as loss of revenues resulting from business interruption, loss of market share and/or reputation. These forms of loss can impact both the public and private sectors. • In the private sector, business interruption (BI) is a serious matter that some companies insure against. Recent earthquakes in California, for example, have seen a number of small- and mediumsized businesses fail, due to BI following earthquakes. These failed businesses and reduced activity of the rest of the business community result in reductions in sales, property, and other taxes, adversely affecting a local government’s finances. • The public sector can have BI analogous to the private sector. Besides the obvious disruption to public services, many local governments rely on revenue from ports, airports, or other special facilities. If these are disrupted, finances are strained. • If disruption to a community is prolonged, permanent loss of businesses or factories, with their jobs, may occur. This is analogous to loss of market share in the private sector. If the jurisdiction relies on revenue from a special facility, and the operation of that facility is disrupted for a prolonged period, that facility’s customers may be forced to go elsewhere and may never return. A prime example of this was the 1995 Kobe earthquake in Japan, where the world’s largest container port permanently lost several major shipping lines to other ports it had been in competition with prior to the earthquake. The overall disruption of the Port of Kobe in that case was less than a year, but the customers are lost for many years, if not forever.
3
Earthquake-related natural hazards, such as tsunami or landslides, have killed hundreds or thousands of people.
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2.6 Mitigation Alternatives The previous section described the nature and variety of damages and loss that can result from earthquakes. However, damage and loss can be reduced, or mitigated, in a number of ways. Figure 2.3 is a modified form of Figure 2.2, and indicates how, at each step of the earthquake risk process, mitigation of damage and loss is possible. That is, just as Figure 2.2 lays out the chain of causation of earthquake damage, Figure 2.3 shows that breaking that chain anywhere reduces or eliminates the loss — and that typically the earlier (higher) in the process the chain is broken, the more effective is the mitigation. Each of the mitigation approaches indicated in the spectrum of earthquake mitigation alternatives is a proven technology: • Hazards such as faulting and shaking can be mapped. In many cases faults have been mapped in detail, with improved and more detailed mapping going on all the time. For example, the California Geological Survey over the last two decades has mapped the most active faults in California (Figure 2.4). Shaking intensity maps are also readily available, even through the Internet (Figure 2.1). This type of mapping identifies the existence of the specific hazard. If that hazard is poor soil, where liquefaction or ground failure might occur, then ground remediation may be required. Recent decades have seen the development of a variety of new methods for soil improvement and liquefaction mitigation, including soil mixing, stone columns, soil wicks, and chemical and pressure grouting, to name only a few. • Primary damage mitigation is the purview of design professionals, who have developed a large toolkit for bracing, strengthening, or otherwise improving the earthquake performance of buildings and other structures, nonstructural elements, equipment, and contents. These techniques are discussed in subsequent chapters. • Secondary damage is typically due to the interaction of several problems, and can be a very complex issue. It is therefore best mitigated prior to the earthquake, through better handling of materials and improving of infrastructure. Since this cannot be done everywhere, it must also be mitigated HAZARD
EARTHQUAKE OCCURS
PRIMARY HAZARDS: Faulting, Shaking, Liquefaction, Landsliding, Tsunami…
PRIMARY DAMAGE: DAMAGE OR VULNERABILITY
Building / Structural Nonstructural / Equipment
SECONDARY HAZARD / DAMAGE: Fire, Hazmat, Flooding…
PRIMARY LOSS: Life / Injury, Repair Costs, Function, Communications/Control…
LOSS or RISK
SECONDARY LOSS: Business / Operations Interruption Market Share, Reputation…
FIGURE 2.2 Earthquake loss process.
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EARTHQUAKE OCCURS
RESULT
MITIGATION
Hazard mapping; ground remediation; tsunami walls…
Bracing and strengthening, reduction of mass, base isolation, structural control…
Improved storage/infrastructure, better emergency response…
PRIMARY HAZARDS: Faulting, Shaking, Liquefaction, Landsliding, Tsunami…
Demand (hazard) eliminated or reduced
PRIMARY DAMAGE:
Capacity (strength…) increased
Building / Structural Nonstructural / Equipment
SECONDARY HAZARD / DAMAGE: Fire, Hazmat, Flooding…
Secondary demands eliminated or reduced
PRIMARY LOSS: Life / Injury, Repair Costs, Function, Communications/Control… Improved emergency planning and response; insurance…
SECONDARY LOSS:
Loss avoided or shared
Business / Operations Interruption Market Share, Reputation…
FIGURE 2.3 Mitigation of earthquake damage.
Fault Trace
Special Studies Fault Zone
FIGURE 2.4 Typical special studies fault zone map. (Courtesy California Geological Survey) © 2003 by CRC Press LLC
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via improved emergency response, that is, via analysis of the problem, acquisition of the necessary equipment, and ongoing training and exercises. • Loss is mitigated via damage control, that is, via improved emergency planning and response. Since the damage has not been prevented, coping with the damage so as to minimize loss is necessary. The other dimension of loss mitigation at this stage is financial, that is, earthquake insurance. Earthquake insurance can be effective in selected circumstances, but it does nothing for life loss or injury, and typically only partially offsets primary financial loss. The farther down in the damage process one goes, the more difficult is mitigation. Secondary losses, such as business interruption, often cannot be fully mitigated.
2.7 Earthquake Risk Management Decision-Making The previous sections have provided an overview of earthquake risk, its components of hazard, damage, and loss, and a glimpse of the broad spectrum of mitigation alternatives that a community or organization has available for dealing with earthquakes. The fundamental problem of earthquake risk management is not to find a solution, but rather to find which solution is best. The answer to this key problem varies with each community or organization’s particular circumstances, and is arrived at by following the decision-making process shown in Figure 2.5. Estimate the Risk
PROBLEM Define Define Problem Problem Estimate Estimate Baseline Baseline Risk Risk
Internal Internal Policy Policy External External Constraints Constraints
Determine Determine Further Further Action Action Needed Needed Y
N Stop Stop
Select Select Basis Basis for for Analysis Analysis Identify Identify Alternatives Alternatives
Examine Mitigation Alternatives
Alternatives Eliminated
Screen Screen Alternatives Alternatives Choose Choose Decision Decision Method Method Describe Describe Alternatives Alternatives
Values Values Uncertainties Uncertainties
Collect Collect and and Organize Organize Data Data Apply Apply Decision Decision Method Method Communicate Communicate Results Results Make Make Decision Decision
Make Decision
ACTION FIGURE 2.5 Earthquake risk management decision process. © 2003 by CRC Press LLC
Further Further Analysis Analysis
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Although the figure may appear dauntingly complex, the process consists of two basic steps. 1. Estimate the risk by: • Defining the problem — that is, what are the assets at risk? What do we wish for them? The assets at risk are often the same as, what is the community or organization responsible for? What we wish is usually no significant life safety risk, and an acceptable maximum financial loss. • Quantifying the baseline risk — that is, what is the likely and probable maximum number of lives to be lost and financial loss, considering potential earthquakes and the assets at risk, under present conditions? Simply determining the baseline risk is a significant task performed by specialists, and is described in some detail in later chapters. • Determining if further action is needed — in some cases, the current risk may be acceptable, or obviously dealt with in a simple manner. Otherwise, mitigation alternatives need to be developed, and decisions made between alternatives, in order to reduce the existing risk to a level that is acceptable. 2. Examine mitigation alternatives by: • Selecting the basis for analysis — this refers to the basic constraints on the ability of a community or organization to mitigate the risk. For example, mandated retrofitting of residential buildings may not be politically feasible — the public may vote out whoever attempts to enact mandated retrofitting. In such a case, the basis for analysis would be voluntary retrofitting, and the alternatives consist of distributing information, financial incentives, and other more palatable measures. • Identifying alternatives — this consists of identifying as broad a spectrum of mitigation alternatives as possible, given the constraints. The previous section indicated how each link in the chain of causation of earthquake loss offers opportunities for mitigation, often multiple opportunities. The goal at this stage is creative thinking, to develop as many possible alternatives as possible. • Screening alternatives — having brainstormed a broad range of alternatives, some can be eliminated for obvious reasons. • Choosing a decision method — this consists of purposefully developing a framework and criteria for making a decision, and is a very important step in the earthquake risk management process, as the basis for the decision will be closely examined. There are many different methods and criteria for deciding between alternatives, including simple scoring methods, benefit–cost analysis, and multiattribute utility theory. The decision as to whether that risk is acceptable or not should be based on two fundamental criteria: • What loss would be tolerable, should it occur? • How easy (i.e., at what cost) would it be to reduce the loss? The decisions being considered here are financial in nature and, in general, significant risk of structural collapse4 should not be tolerated today. In that sense, some aspects of the decision-making may be easy, for example, if the baseline risk assessment indicates that collapse is likely or there is other significant risk to life-safety, then that risk must be reduced. What we discuss here is, given that life-safety has been addressed, then to what additional extent should earthquake risk be reduced, that is, what makes operational and financial sense? There are a variety of various methods available for making that decision (see AIChE 1995), which we summarize in this section.
2.7.1
Maximization (Benefit–Cost) or Minimization (Total Cost )
The most common decision-making method is maximization, which forms the core of the well-known benefit–cost method. In this method, the decision-maker quantifies and seeks to maximize the net benefits 4
Or other risks to life-safety, such as major releases of hazardous materials in an earthquake.
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Cost
Total Cost = CL + CM
Least total cost
C (satisficed)
A CM =Cost of mitigation
B
CL = Expected loss
Mitigation (increasing effectiveness)
FIGURE 2.6 Typical cost of mitigation curve.
(i.e., benefit minus cost associated with the alternative, where the benefit in this case is the reduced loss) with each alternative. The corollary of this is the minimization of the total cost, where the total cost is the expected loss plus the cost of mitigation. This is shown in Figure 2.6, where point A is the least total cost (note that point A does not necessarily correspond to point B, the crossing of the expected loss curve with the mitigation cost curve). In order to apply these rules, each alternative must be associated with a single value that represents benefits. When uncertainty is ignored, applying the maximization rule is straightforward and expresses the decision-maker’s simple desire for more of a good thing. When considering uncertainty, the usual procedure for applying the maximization rule is to determine the likelihood of the possible outcomes of an alternative, and compute an expected value for each alternative. The expected value is the weighted sum of values for each possible outcome, with the weights determined by the likelihood (probability) of these outcomes.
2.7.2 Maximin and Maximax Another common decision rule is the maximin rule (maximize the minimum). It can be applied in situations where multiple outcomes are possible, but there are likelihoods that are not characterized. Using this rule the decision-maker takes each decision and associates it with the value resulting from the worst possible outcome that could occur under that alternative. The alternative that provides for the highest value under its worst possible outcome is selected. The maximin rule is truly a pessimist’s rule, for it ensures that the decision-maker avoids choosing alternatives that could lead to the worst possible outcomes, even if these alternatives could yield attractive outcomes as well. On the contrary, the optimist’s rule is the maximax rule (maximize the maximum). Using this rule, the decision-maker selects the alternative whose return under the most favorable circumstances is the greatest. In this case, the decisionmaker is “going for broke” by ignoring all possible downsides to each alternative, and focusing only on the possible benefits [AIChE, 1995].
2.7.3 Minimum Regret A decision-maker may be criticized long after a decision has been made by others who operate with perfect hindsight. Perfect hindsight may reveal that a different alternative than the one chosen would have led to a better outcome under the circumstances that occurred subsequent to the decision. For example, a plant manager chooses to delay seismic retrofit due to its high cost and a judgment that there is an extremely small chance of a major earthquake in the next 5 years. An earthquake occurs soon after this decision, which causes a 30-day interruption of operations. Even though the decision was in fact a wise one, given the decision-maker’s understanding of the costs and risks, the plant manager is criticized © 2003 by CRC Press LLC
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for not choosing the alternative that would have yielded the best outcome. The regret rule chooses to minimize the risk to the decision-maker of being adversely confronted in hindsight. For each possible future scenario, the decision-maker assesses the difference in value between each alternative and the best alternative given that the scenario was to occur. This difference is referred to as the regret. Regret represents the cost of not having perfect foresight and selecting the best decision. This rule then applies a minimax rule, selecting the decision in which the maximum regret is the least.
2.7.4 Minimum Uncertainty Most decision-makers are risk-averse: they prefer to avoid choosing alternatives for which the outcomes are uncertain. When outcomes are presented to a decision-maker in terms of the probability for each of the possible values that could result, another decision rule, called minimum uncertainty, can be employed. Minimum uncertainty may also be referred to as minimum risk, where risk refers not to physical or financial risks specifically but to aversion to uncertainty as described above. With outcomes quantified by a probability distribution, extremely risk-averse decision-makers may wish to select an alternative that gives them the most certainty about future rewards by minimizing the variance on possible outcomes. Alternatively, some decision-makers choose to account for only those outcomes associated with the most likely future event. A minimum uncertainty rule can lead the decision-maker to reject attractive but uncertain alternatives, and instead choose a safer alternative with smaller potential rewards.
2.7.5 Satisficing Not all decision rules yield a single best alternative. Many organizations are concerned with meeting many, sometimes contradictory, goals. Satisficing is a decision rule that is used to find one or more alternatives that can satisfy all (or most) of the organization’s goals rather than determining the best alternative. When using a satisficing decision rule, a minimum level of achievement on each of several goals is set. For example, in a safety decision the goals may be to “reduce the risk of death below 10–7 per year” and “spend less than $100,000.” All alternatives that meet these goals would be considered satisfactory. An example of satisficing is shown in Figure 2.6, at point C, which is not the least cost, but a point where the marginal cost of mitigation is a set ratio to the expected loss. Since many total cost curves are rather flat, a near-minimum total cost can be achieved at a cost of mitigation far below the cost of mitigation corresponding to the true minimum point A.
2.7.6 Next Steps Any of the above methods can be employed in decision-making. After a decision has been made, the next steps in the process are: Describing alternatives, which consists of examining each alternative, including its impact on the baseline risk, using the same methods as were used in determining the baseline risk, but this time in the light of the mitigation alternative. Collecting and organizing the data, which refers to assembling the various alternatives, their costs and impacts on baseline risk. An important element in the various data is values, and the confidence (or uncertainty) associated with each alternative. Applying the decision method, to prioritize, or determine the most appropriate alternative(s). Communicating the results to decision-makers for their action. The elements of communication here are the basis, logic and range of alternatives examined, and the sensitivity of the findings to key assumptions and parameters. Different stakeholders (such as tenants, owners, parents, rate-payers, and others) will be interested in different aspects of the decision, so that their interests need to be identified and addressed.
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Making the decision, which is not always as easy as it sounds, so that questions may arise, and further analyses may be required. Eventually however, a set of alternatives will emerge. Implementing the plan, which is discussed below, and more fully later in this handbook.
2.8 Earthquake Risk Management Program Given that a decision to implement a set of alternatives has been made, the last step in earthquake risk management is implementing the alternatives. This consists of developing a program, which typically will consist of one or more of the following steps (shown in Figure 2.7): • Funding — there are a wide variety of ways to pay for earthquake risk mitigation, depending on the community or organization, including (for the public sector) from general revenues, special assessments, bonds, user’s fees, and/or grants from state or federal programs, to name a few. In the private sector, analogous sources of expensing, one-time charges, loans or bonds, and/or public subsidy exist.
Decide on Mitigation Alternatives
Obtain Funding
Program Management Dedicate staff, find/retain specialists, consultants and/or schedule the work, communicate with neighbors, and affected parties
Implement CIP/Other Projects Multi-year implementation
Residual Risk Emergency Plan
Risk Transfer Insurance, capital markets...
Develop as interim solution, and for ongoing residual risk
After the Earthquake Maintain emergency plan, have backup sites ready, engineers on-call…
FIGURE 2.7 Earthquake risk mitigation program.
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• Project management — putting the plan into action involves dedicating staff for managing the program, bringing in specialists, consultants and/or contractors, scheduling the work, communicating with neighbors and affected parties, and following up to assure goals are being met. • Implementing the plan – performing the various projects. Major strengthening and other large projects will usually be done as part of the capital improvement plan (CIP), while contents bracing and smaller projects may be done as part of maintenance, or out of general revenues. • Risk transference is a more general term for what is usually thought of as insurance, and which really can only transfer parts of the financial risk to third parties. Recent innovations in the capital markets have added new dimensions to this kind of mitigation alternative, which may make it more viable than ordinary insurance previously was. • What happens after the earthquake is a consideration that should always be borne in mind. That is, a community or organization should always have an emergency response plan in place, which considers all assets at risk and accounts for unknowns. The basis for this plan should be the residual risk, that is, the portion of the baseline risk that the implemented mitigation alternatives cannot feasibly reduce. Understanding, preparing for, and clearly communicating this residual risk, that is, the loss that has been deemed acceptable, is necessary to avoid surprises and unnecessary recriminations following the earthquake. It also should form the basis for a considered recovery plan.
2.9 Summary This chapter has provided an overview of the earthquake risk problem and a guide to the management of this problem. In summary, earthquake risk management consists of a series of rational steps aimed at 1. 2. 3. 4. 5.
Identifying what is at risk — that is, what assets could be lost due to an earthquake Assessing how the earthquake places these assets at risk Determining which alternatives might reduce this risk Deciding among these alternatives, which are the best for the specific situation Implementing — that is, putting these alternatives into practice
Defining Terms Attenuation — The rate at which earthquake ground motion decreases with distance. Damage — Physical disruption, such as cracking in walls, overturning of cabinets, etc., often used synonymously with loss.
Hazard — The potential for or occurrence of natural phenomena, such as ground shaking, liquefaction, tsunami, etc., which might lead to loss.
Intensity — A metric of the effect, or the strength, of an earthquake hazard at a specific location, commonly measured on qualitative scales such as MMI, MSK, and JMA.
Loss — The human or financial consequences of damage, such as human injury or cost of repairs. Mitigation — Literally the moderating of a force or intensity of something that causes suffering; used in earthquake engineering as synonymous with reducing earthquake risk. Risk — The potential for loss. Risk can be expressed in absolute terms such as the risk of collapse, or in probabilistic terms, such as “the risk per year is $1,000.” Satisficing — A decision rule that is used to find one or more alternatives that can satisfy all (or most) of the organization’s goals rather than determining the best alternative.
References AIChE, 1995. Tools for Making Acute Decisions, with Chemical Process Safety Applications, Center for Chemical Process Safety of the American Institute of Chemical Engineers, New York. © 2003 by CRC Press LLC
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Richter, C.F., 1957. Elementary Seismology, W.H. Freeman, San Francisco. Seismic Safety Commission, 1999. Earthquake Risk Management — A Toolkit for Decision-Makers, SSC report 99–04, California Seismic Safety Commission, Sacramento. (Available in PDF format at www.seismic.ca.gov.)
Further Reading There is a wide variety of information and resources readily available on various aspects of earthquake risk management. The reader is referred to the following key publications: Seismic Safety Commission, Earthquake Risk Management – A Toolkit for Decision-Makers, SSC report 99–04, California Seismic Safety Commission, Sacramento, 1999. This is an integrated group of three documents meant to assist local governments in developing a successful earthquake risk reduction program. It can be downloaded over the Web in PDF format at www.seismic.ca.gov. California Governor’s Office of Emergency Services (OES), Emergency Planning Guidance for Local Government. This document addresses emergency planning at the city and county level. It has evolved from the insight and experience gathered from past disasters and the cooperation between OES staff and local government emergency managers. Additionally, there is a wealth of information available on the Internet: Site
URL
Applied Technology Council (ATC)
www.atcouncil.org
Assn. Bay Area Governments (ABAG)
www.abag.org
California Division of Mines and Geology (CDMG)
http://www.consrv.ca.gov/cgs/
California Seismic Safety Commission (CSSC)
www.seismic.ca.gov
Consortium of Universities for Research in Earthquake Engineering (CUREE) Disaster Research Center (DRC)
www.curee.org
Earthquake Engineering Research Center (EERC)
© 2003 by CRC Press LLC
www.udel.edu/DRC/
www.eerc.berkeley.edu/eea
Features Information about the council’s mission and organization; recent news releases; newsletters; recent reports, briefs, and training manuals; databases; seminars and workshops; and other ATC products. Maps of seismicity for San Francisco Bay area; information on building vulnerability. CDMG has primary responsibility for work in the geosciences in California, including hazard mapping, earthquake scenarios, a strong motion instrumentation program, and policy implementation. Provides information about the commission, its publications, pending legislation relevant to seismic hazards in California, and a table of significant California earthquakes. CUREE is a consortium of U.S. universities for coordination of work on earthquake research problems. DRC is the first social science research center in the world devoted to the study of disasters. Earthquake Engineering Abstracts; covers the world literature in earthquake engineering since 1971. Contents include selected technical reports, conference papers, monographs, and journal articles. Most materials are available for loan from the PEER library (University of California at Berkeley).
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Site
URL
Earthquake Engineering Research Institute (EERI)
www.eeri.org
EQNET
www.EQNET.org
Federal Emergency Management Agency (FEMA) Global Seismic Hazard Assessment Program (GSHAP)
www.fema.gov
Japan NDRPI
http://www.bosai.go.jp/
Mexico National Seismological Service
http://www.ssn.unam.mx/SSN/ Sismos/region_sismica_mx.html
Multidisciplinary Center for Earthquake Engineering Research (MCEER)
mceer.buffalo.edu/
Natural Hazards Research and Applications Information Center (NHRAIC)
www.colorado.edu/hazards/litbase/ litindex
Pacific Earthquake Engineering Research (PEER) Center
peer.berkeley.edu
Southern California Earthquake Center (SCEC)
www.scec.org
Structural Engineers Association of California (SEAOC)
www.seaoc.org
© 2003 by CRC Press LLC
http://seismo.ethz.ch/GSHAP/ index.html
Features N\EERI is the de facto U.S. national society for earthquake engineering — contains useful information and links. Excellent database of earthquake information sources on the Web. Many free publications of high caliber, useful information. A collection of seismotectonic models and hazard maps, for various portions of the globe. The project terminated in 1999. National Disaster Prevention Research Institute, maintains realtime seismic net (Kyoshin) and other data (English and Japanese). Maps and other information on seismic hazards in Mexico (in Spanish). MCEER bibliographies; literature and research guides, and list of FEMA and NEHRP guidelines and handbooks for earthquake resistant construction and design. The latter category includes: Seismic Safety of Lifelines, Seismic Safety of Existing Buildings, and Seismic Safety of New Buildings. An excellent on-line index that provides bibliographic access only to that collection of NHRAIC at the University of Colorado at Boulder. While HazLit is not a full-text database, and the Hazards Center Library does not loan its holdings to the general public, this is an excellent resource. PEER is a consortium of earthquake engineering research universities in the western United States — the Web site has their reports, much useful information. SCEC is a Science and Technology Center of the National Science Foundation. Home Page contains background information about SCEC and links to its many member academic institutions. Both the SCEC newsletter and SCEC publications list are available from this site. Also, check out the Earthquake Hazard Analysis Map — a map of probable future Southern California earthquakes. SEAOC’s site is useful for keeping up with research specific to structural engineering, especially buildings, and with the practice.
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Site
URL
Swiss Seismological Service
http://seismo.ethz.ch/
Turkey, Disaster Management and Implementation and Research Center Turkey, Kandilli Observatory and Earthquake Research Institute
http://www.metu.edu.tr/home/ wwwdmc/main-e.html http://www.koeri.boun.edu.tr/ geophy/anasayfa/eanafr.html
University of Washington Earthquake page
www.geophys.washington.edu/ seismosurfing
U.S. Geological Survey Earthquake Information
quake.wr.usgs.gov
© 2003 by CRC Press LLC
Features Excellent source of information on earthquakes and other hazards, including Global Seismic Hazard Assessment Program (GSHAP) Abundant information on Turkish earthquakes, at Middle East Technical University (METU) Observatory with abundant information on Turkish earthquakes, at Bogazici University. Excellent general site, with directory to many other sites related to earthquakes. Excellent source of information on many aspects of earthquakes.
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3 Dynamics of Structures 3.1 3.2
Introduction Single-Degree-of-Freedom System Equation of Motion · Solution of the Equation of Motion · Evaluation of Damping in SDOF Systems · Response to Impulsive Loads · Approximate Analysis of Impulsive-Load Response · Duhamel Integral · Response to Periodic Loading
3.3
Jorma K. Arros ABS Consulting Oakland, CA
Multidegree-of-Freedom Systems Equations of Motion · Vibration Mode Shapes and Frequencies · Modal Equations of Motion · Earthquake Response Analysis · Nonlinear Analysis
Defining Terms References
3.1 Introduction The essence of earthquake effects on structures is the dynamic nature of earthquake loading. This section provides an overview of the dynamics of structures, as a foundation for succeeding sections. Mechanics as a branch of physics is subdivided into statics and dynamics. Statics studies systems in static equilibrium, i.e., in a state where the system internal forces counterbalance external forces acting on the system. Static refers to the fact that the state of the system and the applied forces do not vary in time; they are time-independent. Dynamics is the study of systems subject to time-varying applied forces. As a consequence of the time variability of the applied forces, the system’s internal forces and its state (defined in terms of displacement and deformation) also vary with time — the system’s response involves motion. While a static problem has a single time-independent solution, the solution of a dynamic problem involves a description of the system’s state at every time point within the period of study. The appearance of inertia effects associated with mass in motion is another key distinction of dynamic problems. Structural dynamics can be considered as the study of a body or structure in dynamic equilibrium. The mathematical expression of this equilibrium is the equation of motion. While the static equilibrium equation expresses the balance between the structure’s internal forces and externally applied forces, the equation of motion expresses the equilibrium of internal and external force terms (which are exactly the same as in the static equilibrium equation) and the mass inertia and damping effects. As the inertia term involves the second derivative and the damping term the first derivative of the displacement with respect to time, the equation of motion is a second-order differential equation with constant coefficients. Theory
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for this type of differential equation is well established in mathematics and provides ready tools, both analytic and numerical, for solution of structural dynamics problems. This chapter begins the discussion with the dynamics of a single-degree-of-freedom (SDOF) system in Section 3.2. Dynamics of multidegree-of-freedom (MDOF) systems is discussed in Section 3.3. Typical aspects of dynamic analysis specific to earthquakes are discussed in Section 3.3.4, while dynamic analysis of nonlinear systems is reviewed briefly in Section 3.3.5. The discussion of dynamics in this chapter specifically addresses response of structures to seismic ground motion.
3.2 Single-Degree-of-Freedom System This section examines the single-degree-of-freedom (SDOF) system sketched in Figure 3.1. The SDOF system consists of a rigid block with mass m, elastic weightless spring with stiffness k, and a viscous damper c. The mass block of the SDOF system can move only in translation along a single line, with the displacement from the initial, static equilibrium position, denoted as variable u, completely defining its position. Time-varying load p(t) acts on the mass block, causing the dynamic response.
3.2.1 Equation of Motion The equation of motion is derived by expressing the equilibrium of all forces acting on the mass. As shown in Figure 3.1, the forces acting in the direction of the displacement degree of freedom include the applied load p(t) and three forces resulting from the motion: inertia f1, damping fD , and the elastic spring force fS. The equilibrium of these forces is written as: f1 + f D + fS = p (t )
(3.1)
Each of the forces represented on the left side of this equation is a function of the displacement u, or of its derivatives as follows. Per d’Alembert’s principle, the inertia force is: f1 = mu˙˙
(3.2)
f D = cu˙
(3.3)
fS = ku
(3.4)
Viscous damping force:
Spring force:
FIGURE 3.1 Single-degree-of-freedom system and a free body diagram of the mass block.
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By substituting Equations 3.2, 3.3, and 3.4 in Equation 3.1, the equation of motion of the SDOF system is written as: mu˙˙ + cu˙ + ku = p (t )
(3.5)
3.2.1.1 Equation of Motion for Support Excitation Loading Instead of the time-varying applied force, dynamic loading to a system may be caused by motion of its support points. The motion forced by an earthquake on a building foundation, illustrated in Figure 3.2, is an example of such a loading. The horizontal ground motion relative to the fixed reference axis is indicated by the displacement ug. As in Equation 3.1, equilibrium of forces for this system may be written: f1 + f D + fS = p (t )
(3.6)
where the damping and elastic forces may be expressed as in Equations 3.3 and 3.4, except that the expressions are now in terms of the relative displacement ur , i.e., displacement relative to a frame of reference attached to the support points that are moving relative to the reference axis. The inertia force in this case is given by: f1 = mu˙˙t
(3.7)
where ut represents the total displacement of the mass from the reference axis and is equal to the sum of the relative displacement and the ground motion: ut = ur + u g
(3.8)
Substituting for the inertia, damping, and elastic forces in Equation 3.6 yields: mu˙˙t + cu˙ r + kur = 0
(3.9)
Substituting Equation 3.8 in Equation 3.9 yields: mu˙˙r + cu˙ r + kur = −mu˙˙g (t ) ≡ peff (t )
FIGURE 3.2 (a) Support point excitation and (b) the free body diagram of the mass.
© 2003 by CRC Press LLC
(3.10)
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In this equation, peff (t) denotes the effective support excitation loading. By comparing Equations 3.5 and 3.10, it can be concluded that the relative motion of the system, ur(t), excited by support point motion üg(t), will be the same as the total motion of a fixed base system, u(t), acted upon by a force equal to peff (t) = –müg(t).
3.2.2 Solution of the Equation of Motion To determine the response, u(t), of the SDOF system, the equation of motion is solved using either analytical or numerical methods. The choice of method may depend on the following considerations: • Whether the problem is linear or nonlinear — nonlinear problems typically call for numerical solutions. • Type of loading function, certain types of loading being more tractable analytically than others. For example, representation of an actual earthquake acceleration history analytically is not practical, and a numerical solution is called for. • Level of accuracy of the solution desired. Analytical solutions are typically in terms of exact closedform formulas or in terms of infinite series, such as Fourier series, that achieve any level of desired accuracy by inclusion of an adequate number of the series terms. Solutions derived using numerical methods are typically approximate, but often adequate for practical problems. In some cases solution in the frequency domain, instead of the time domain, is preferred. Conceptually this approach consists of: 1. Transforming the loading function p(t) (or –müg[t] ≡ peff [t]) to the frequency domain via the Fourier transformation 2. Obtaining the Fourier transformation of the response 3. Performing the inverse Fourier transform (i.e., back to the time domain) to obtain the response u(t) Fourier analysis became quite practical with the advent of the fast Fourier transform (FFT) several decades ago. The analytical solution of the equation of motion is discussed in Section 3.2.2, numerical time history analysis procedures are discussed in Section 3.3.4.2, and solution in the frequency domain is introduced in Section 3.2.7.1 As for any linear differential equation, the complete, general solution is the sum of complementary solution uc(t) and the particular solution up(t), i.e., u (t ) = uc (t ) + u p (t )
(3.11)
Since the equation of motion is a second-order differential equation, the complementary solution has two constants of integration that are evaluated based on the initial conditions, i.e., u(0) and u· (0). The complementary solution is the solution of the homogeneous equation, i.e., the equation of motion with the right-hand side set equal to zero: mu˙˙ (t ) + cu˙ (t ) + ku (t ) = 0
(3.12)
Motions that satisfy Equation 3.12, with no forcing function, are referred to as free vibrations. The solution of Equation 3.12, as of any linear homogeneous ordinary differential equation with constant coefficients, is of the form: u (t ) = Ce st
(3.13)
Substituting this into Equation 3.12, and after dividing by Cest, leads to the characteristic equation: ms 2 + cs + k = 0 © 2003 by CRC Press LLC
(3.14)
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Using the notation: ω2 =
k m
(3.15)
s is solved: 2
s=−
c c 2 ± −ω 2m 2m
(3.16)
It is evident from Equation 3.16 that the nature of the solution will depend on the damping value c. If c > 2mω, s will be real valued, but if c < 2mω, s will be a complex number. How this affects the response will be explored in the following sections. 3.2.2.1 Undamped Free Vibrations If the system is undamped, i.e., if c = 0, s becomes, by Equation 3.16: s = ±iω
(3.17)
u (t ) = C1e iωt + C 2e − iωt
(3.18)
and the response given by Equation 3.13 is:
As both of the terms on the right-hand side, irrespective of the values C1 and C2, are solutions to Equation 3.12 and the equation is linear, the sum is also a solution. As we are looking for the general solution, both terms are included. By utilizing Euler’s equation: e ± iωt = cos ωt ± i sin ωt
(3.19)
u (t ) = A sin ωt + B cos ωt
(3.20)
The result may be written in the form:
This type of motion is called a simple harmonic motion. The quantity ω is the natural angular velocity of the undamped system (sometimes also referred to as the natural angular frequency) and is related to natural frequency f as: ω 2π
(3.21)
2π 1 = ω f
(3.22)
f = The reciprocal of f is called the natural period T: T=
Constants A and B are determined based on the initial conditions: the displacement u(0) = B and · velocity u(0) = Aωt at time t = 0, resulting in: u (t ) = Figure 3.3 illustrates this solution. © 2003 by CRC Press LLC
u˙ (0) sin ωt + u (0) cos ωt ω
(3.23)
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FIGURE 3.3 Undamped free vibration.
By utilizing the relationships of the trigonometric sine and cosine functions, the motion u(t) of Equation 3.23 can be recast into: u (t ) = R cos (ωt − θ)
(3.24)
The response is given by the real part, or horizontal projection, of the two rotating vectors. Thus, the amplitude of motion is given by the resultant:
[u (0)]
2
R=
u˙ (0) + ω
2
(3.25)
and the phase angle by: θ = tan −1
u˙ (0) ωu(0)
(3.26)
3.2.2.2 Damped Free Vibrations If the oscillator is damped, i.e., c > 0, three different types of motion are possible, depending on whether the value of the term under the square root in the expression for s (Equation 3.16): 2
s=−
c c 2 ± −ω 2m 2m
(3.16)
is zero, negative, or positive, as discussed in the following. 3.2.2.2.1 Critical Damping The value of c that makes the value of the term under the square root in Equation 3.16 equal to zero is called the critical damping, cc, i.e.,
c c = 2 mω
(3.27)
At critical damping, the value of s in Equation 3.16 becomes: s=−
© 2003 by CRC Press LLC
cc = −ω 2m
(3.28)
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so that the response is given by: u (t ) = (C1 + C 2t ) e − ωt
(3.29)
which is easily verified by substituting in Equation 3.12. By imposing the initial conditions the response is written as:
[
]
u (t ) = u (0) (1 + ωt ) + u˙ (0) t e − ωt
(3.30)
It is readily observed from Equation 3.30 that the critically damped response does not involve oscillations about the zero deflection point and the displacement returns to zero in accordance with the exponential decay term. Critical damping is the smallest amount of damping that keeps a SDOF system from oscillating during free response. 3.2.2.2.2 Underdamped Systems If the damping is less than critical, i.e., c < 2mω, it is customary to express the damping as a ratio to the critical damping value: ξ=
c c = c c 2 mω
(3.31)
where ξ is called the damping ratio. Substituting Equation 3.31 into Equation 3.16 leads to: s = −ξω ±
(ξω)2 − ω 2
(3.32)
By using the notation ω D = ω 1 − ξ 2 Equation 3.32 can be rewritten as: s = −ξω ± iω D
(3.33)
ωD is called the damped vibration frequency. Note that for typical structures damping ratios rarely exceed about 10% (ξ < 0.10), and ωD differs very little from the undamped natural frequency. By substituting to Equation 3.13, the response is written as:
(
u (t ) = e − ξωt C1e iωDt + C 2e − iωDt
)
(3.34)
By using Euler’s equation, the response can be written in the form: u(t ) = e −ξωt (A sin ω Dt + B cos ω Dt )
(3.35)
The second term in Equation 3.35 is of the same form as the simple harmonic motion of the undamped oscillator, Equation 3.20, except now at the damped, slightly lower frequency. The first term in Equation 3.35 indicates exponential attenuation of the oscillations. Constants of integration A and B are again · determined based on the initial conditions u(0) and u(0) as before. 3.2.2.3 Harmonic Loading The particular solution is a solution that satisfies the equation of motion with the loading included on the right-hand side of the equation, Equation 3.5: mu˙˙ (t ) + cu˙ (t ) + ku (t ) = p (t ) © 2003 by CRC Press LLC
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The particular solution is particular to the loading function. As the first case, the response of the SDOF system to a harmonic forcing function is studied. The equation of motion is written as: mu˙˙ (t ) + cu˙ (t ) + ku (t ) = p0 sin ω pt
(3.36)
where p0 is the amplitude and ωp the angular velocity of the loading. 3.2.2.3.1 Non-Damped SDOF System Again, damping is first assumed to be zero, i.e., the equation of motion is written as: mu˙˙ (t ) + ku (t ) = p0 sin ω pt
(3.37)
The complementary solution of this equation is the free-vibration response of Equation 3.20. In this case, the particular solution can be found by “guessing” that the solution is in the form of harmonic motion, i.e., u p (t ) = C sinω pt
(3.38)
By substituting this “trial” solution in Equation 3.37, C is solved as: C=
p0 1 k 1− ω ω p
(
)
(3.39)
2
and the particular solution is: u p (t ) =
p0 1 sin ω p t k 1− ω ω 2 p
(
(3.40)
)
The general solution is the combination of the complementary solution, Equation 3.20, and the particular solution, Equation 3.40: u (t ) = uc (t ) + u p (t ) = A sin ωt + B cos ωt +
p0 1 k 1− ω ω p
(
)
2
sin ω pt
(3.41)
Again, constants A and B are solved based on initial conditions. For the specific case of a system that · is initially at rest, i.e., u(0) = 0 and u(0) = 0, the constants are readily solved as: A=−
p0 ω p ω k
(
1
1− ωp ω
)
2
(3.42)
B=0 and the expression for the response becomes: u (t ) =
p0 1 k 1− ω ω p
(
)
2
(sin ω t − ω p
p
ω sin ωt
)
(3.43)
Note that the first term on the right-hand side of Equation 3.43, p0 /k, is the displacement, ust , which force p0 would cause if applied statically. The rest of the right-hand side of Equation 3.43 is termed the © 2003 by CRC Press LLC
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response ratio, R(t), and expresses the momentary ratio of the total displacement to the static displacement, i.e., R(t ) =
u (t ) u (t ) = ust p0 k
(3.44)
3.2.2.3.2 Damped SDOF System Next, the response of a SDOF system with damping is considered. The equation of motion, Equation 3.36, is: mu˙˙ (t ) + cu˙ (t ) + ku (t ) = p0 sin ω pt
(3.36)
Dividing by m, and using notation of Equation 3.31, i.e., c/m = 2ξω, leads to: u˙˙ (t ) + 2ξωu˙ (t ) + ω 2u (t ) =
p0 sin ω pt m
(3.45)
The complementary solution of this equation is the damped free-vibration response given by Equation 3.35 (assuming that the structure is less than critically damped, as is the case for all practical structures): uc (t ) = e −ξω t ( A sin ω Dt + B cos ω Dt )
(3.46)
The particular solution can be found by substituting in Equation 3.45 the following “trial” solution: u p (t ) = C1 sin ω pt + C 2 cos ω pt
(3.47)
(or, alternatively, up (t) = C3 sin (ωp t – θ). Note that, in general, the response of a damped system is not in phase with the loading.) Coefficients C1 and C2 (or, alternatively, C3 and θ) can be solved readily by equating (1) those terms that multiply sin ωpt and (2) those terms that multiply cos ωpt. The general solution is the combination of the complementary solution, Equation 3.35, and the particular solution, Equation 3.47. After denoting ωp/ω = α, the general solution is written as: u (t ) = e −ξωt ( A sin ω Dt + B cos ω Dt ) +
[(
)
p0 1 1 − α 2 sin ω pt − 2ξα cos ω pt k 1 − α 2 2 + (2ξα )2
(
)
]
(3.48)
As before, the constants A and B could be evaluated based on the initial conditions. However, as the complementary solution is attenuated by the exponential function e−ξωt, and therefore typically diminishes quickly, the exact determination of the complementary solution is often not called for. Also, consistent with the fact that it typically diminishes quickly, the complementary solution is often referred to as the transient response. The second term in Equation 3.48 does not diminish with time and is referred to as the steady-state response. The steady-state response involves harmonic motion at a frequency equal to that of the applied loading but out of phase with it as indicated by the presence of both the sin ωpt and cos ωp t terms. By manipulation of the trigonometric terms, the steady-state response of Equation 3.48 can be cast to the following alternative form, directly indicating magnitude R and phase angle θ:
(
u (t ) = R sin ω pt − θ © 2003 by CRC Press LLC
)
(3.49)
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where R=
−1/ 2 2 p0 2 1 − α 2 + (2 ξα ) k
(
)
θ = tan −1
2 ξα 1 − α2
(3.50)
(3.51)
The ratio of the response amplitude, R, to the static displacement, p0/k, caused by the static application of force p0 is the dynamic amplification factor, D: D≡
(
)
2 2 = 1 − α 2 + (2αξ) p0 k
R
−1/ 2
(3.52)
Figure 3.4 shows plots of the dynamic amplification factor as a function of ωp/ω for various levels of damping. 3.2.2.3.3 Response at Resonance The condition where the frequency of harmonic loading is equal to the undamped natural frequency of an oscillator, i.e., α = 1, is called resonance. We readily observe from Figure 3.4 that the peak steadystate response occurs near the resonance frequency for lightly damped systems and at slightly decreasing frequency ratios with increasing damping. Based on Equations 3.43 and 3.44, the response ratio of an undamped system grows to infinity when the frequency ratio α = 1. Equation 3.52 indicates that for a damped system at resonance, the dynamic amplification factor is inversely proportional to the damping ratio: Dα =1 =
FIGURE 3.4
1 2ξ
Dynamic amplification factor for harmonic force at varying damping levels.
© 2003 by CRC Press LLC
(3.53)
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As indicated above, Dα = 1 of Equation 3.53 is not exactly the maximum value of the amplification factor, but is close to it. The actual maximum value can be easily determined by using basic differential calculus. The frequency ratio that maximizes D is found by setting the first differential of the expression in Equation 3.52 with respect to α equal to zero, resulting in: α peak = 1 − 2 ξ 2
(3.54)
and the corresponding peak response is: Dmax =
1
(3.55)
2 ξ 1 − ξ2
For typical levels of damping, the difference between Equation 3.55 and the simpler Equation 3.53 is negligible.
3.2.3 Evaluation of Damping in SDOF Systems Typically, mass and stiffness properties of structures can be determined adequately for engineering purposes based on measurements and standard analysis procedures. In many respects, determination of the damping in a structure is a more complicated phenomenon, and the typical assumed viscous damping is often a crude representation of the energy dissipation mechanisms that are responsible for the decay of dynamic response. Damping is inherent in the free vibration of any material, the level of damping depending on the material — that is, damping is a material property. The elements of a building are constructed of a multitude of materials and connected to each other in various ways. For small amplitude oscillations with low level elastic strains prevailing, the material damping is an essential component of the overall building damping. With increasing oscillation amplitude, phenomena such as small inelastic (hysteretic) deformations in the connections and concrete cracking start occurring. This introduces additional damping, while the overall building response may still be linear. Eventually, when amplitudes are large enough, significant material nonlinear, inelastic response occurs within the main structural elements, with associated energy dissipation resulting in additional damping. Thus, the level of damping increases with increasing response amplitude. Table 3.1 shows typically recommended damping values for different types of construction. The significance of the approximations inherent in damping modeling depends on the type of problem at hand. In general, the level of damping in very short duration dynamic phenomena, e.g., blast and impact problems, has small influence on the response. On the other hand, as illustrated by the discussion above of the steady-state response to harmonic loading, damping may be very essential in “controlling” response at frequencies close to resonance. TABLE 3.1
Typical Recommended Modal Damping Ratiosa Structure Type
Stress Level 1b
Stress Level 2b
Welded and friction-bolted steel structures Bearing-bolted steel structures Prestressed concrete structures Reinforced concrete structures
0.02 0.04 0.02 0.04
0.04 0.07 0.05 0.07
a
Fraction of critical damping. At stress level 1, member forces are generally less than about one half ultimate strength for concrete and less than about one half yield capacity for steel. At stress level 2, a majority of the primary load-resisting member forces are more than about half ultimate strength for concrete and more than half yield capacity for steel. Damping values higher than stress level 2 values are generally appropriate for structures responding well into their nonlinear range.
b
© 2003 by CRC Press LLC
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Where proper estimation of damping is important, experimental methods may be useful in determining the damping ratio. Three simple methods to estimate damping based on measurements are introduced in the following. 3.2.3.1 Free-Vibration Amplitude Decay Consider the damped SDOF response expressed by Equation 3.35: u(t ) = e −ξωt (A sin ω Dt + B cos ω Dt )
(3.35)
It is evident that rate of decay of the oscillatory response reflects the level of damping, suggesting that if the decay rate can be measured, the level of damping can be determined. Recognizing that for low to moderate damping levels, ωD ≈ ω, and consequently TD ≈ T, the ratio from one peak value to the next, un/un+1 (or any two response values one period apart), are related as: un / un+1 = e ξωT = e
ξ
2π T T
= e 2 πξ
(3.56)
from which the damping ratio can be solved as: ξ=
ln(un / un+1) 2π
(3.57)
and if the peaks are measured m cycles apart, i.e., un and un+m, an estimate of the damping ratio can be computed from: ξ=
ln(un / un+m ) 2mπ
(3.58)
The vibrations can be initiated by any convenient method, and only the relative displacement amplitudes need be measured. 3.2.3.2 Amplification at Resonance Measurement of amplification at resonance is based on determination of steady-state harmonic response amplification at (essentially) resonance and requires application of harmonic excitations to the structure at selected frequencies. The method is based on the relationship expressed by Equation 3.53, i.e., 1 2ξ
(3.53)
1 2Dα =1
(3.59)
Dα =1 = From this, the damping ratio can be solved as: ξ=
As was pointed out in Section 3.2.2.3.3, Dα = 1 is not exactly the maximum amplification factor, which is easier to determine by measurement, since the maximum amplification factor is related to the damping factor as: Dmax =
© 2003 by CRC Press LLC
1 2ξ 1 − ξ 2
(3.60)
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FIGURE 3.5 Frequency-response curve for a moderately damped system.
at a frequency defined by Equation 3.54, i.e., ω p = ω 1 − 2ξ 2 For low and moderate damping levels, the square root expression in Equation 3.60 is essentially unity, and the damping ratio can be expressed as: ξ=
1 2Dmax
(3.61)
The method requires that the frequency-response curve, i.e., the plot of D = D(ωp), for the structure be constructed by applying a harmonic load at closely spaced frequencies extending up to the resonance frequency. A typical frequency-response curve for a moderately damped structure is shown in Figure 3.5. 3.2.3.3 Half-Power (Bandwidth) Method Examination of Equation 3.52 and Figure 3.5 readily reveals that damping affects not only the height of the peak of the D vs. α curve, but also the width of the peak. The half-power bandwidth method of estimating damping value is based on a particular relationship between the width of the peak of the D vs. α curve. Specifically, by using the relationship of Equation 3.52, it can be shown that the difference between the two frequencies on either side of the peak of the curve, α1 and α2, at which the response amplitude is reduced to 1 2 times the peak value, is related to the damping ratio as:
ξ≅
© 2003 by CRC Press LLC
1
2
(α
2
− α1
)
(3.62)
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To illustrate the use of this method of estimating the damping ratio, a horizontal line is shown across the curve at 1 2 times the resonant-response value. According to Equation 3.62, the difference between the frequencies at which this line intersects the response curve is equal to twice the damping ratio.
(
)
3.2.4 Response to Impulsive Loads Impulsive or shock loads, consisting of a single short duration pulse, are of great importance in the design of certain structures. Unlike for longer duration loading, damping usually has little influence on the response to impulsive load as the maximum response is reached in a very short time. In the following, response to impulsive loading is illustrated by four example cases: (1) sine wave impulse, (2) rectangular impulse, (3) decaying triangular impulse, and (4) increasing triangular impulse. In each case, the solution is divided into two phases: (1) the interval during which the load acts and (2) the following free vibration. 3.2.4.1 Sine-Wave Impulse During phase I, for 0 ≤ t ≤ t1, the structure is subjected to harmonic loading, starting from rest (Figure 3.6), and the undamped response, including the transient as well as the steady-state term, is given by Equation 3.43: u (t ) =
(
p0 1 sin ω pt − α sin ωt k 1 − α2
)
(3.63)
During phase II, for t = t – t1 ≥ 0, the free-vibration motion depends on the displacement u(t1) and velocity u· (t1) at the end of phase I, and may be expressed as follows (see Equation 3.23): u (t ) =
u˙ (t1 ) ω
sin ωt + u (t1 ) cos ωt
(3.64)
umax can be found using the standard approach of differential calculus, i.e., as the value of u at the point where the first derivative of u(t), i.e., velocity u· (t) is equal to zero. The computations reveal that if the ratio of the loading and system natural frequency, α = ωp/ω, is less than 1, umax will occur during phase I, i.e., while the impulsive load is acting. If α >1, umax will occur during free vibration in phase II with the amplification factor, D, given by: D≡
umax πt = 2 sin 1 p0 k T
3.2.4.2 Rectangular Impulse In the case of the rectangular impulse shown in Figure 3.7, response is again divided into the loading phase and the subsequent free-vibration phase. In phase I, the particular solution for a step loading, with 0 ≤ t ≤ t1, is simply:
up =
p0 k
(3.65)
The general solution with the integration constants set to satisfy the at-rest initial conditions is easily found to be: u (t ) =
p0 (1 − cos ωt ) k
(3.66)
In phase II, the free vibration, with t = t – t1 ≥ 0, is again given by Equation 3.64: u (t ) = © 2003 by CRC Press LLC
u˙ (t1 ) ω
sin ωt + u (t1 ) cos ωt
(3.67)
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FIGURE 3.6 Half sine-wave impulse.
FIGURE 3.7 Rectangular impulse.
The maximum response umax can again be found using the approach outlined above for the sine-wave impulse case, and the amplification factor is as follows: For t1 1 ≤ T 2 u πt D ≡ max = 2 sin 1 p0 k T © 2003 by CRC Press LLC
(3.68)
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and for t1 1 > T 2 D=2
(3.69)
3.2.4.3 Decaying Triangular Impulse Response to the decaying triangular impulse shown in Figure 3.8 is solved again in two steps using the same approach for the rectangular impulse above. For phase I, the decreasing triangular loading is p0(1 − t/t1), and the particular solution to this loading is: u p (t ) =
p0 t 1− k t1
(3.70)
With zero initial conditions, the general solution is: u (t ) =
p0 sin ωt t − cos ωt − + 1 k ωt1 t1
(3.71)
For phase II, Equation 3.71 and its first derivative at the end of phase I (t = t1) gives: p0 sin ωt1 − cos ωt1 k ωt1
(3.72)
p0ω cos ωt1 1 + sin ωt1 − ωt1 k ωt1
(3.73)
u (t1 ) = u˙ (t1 ) =
which can be substituted into Equation 3.67 to obtain the free-vibration response in phase II.
FIGURE 3.8 Decaying triangular impulse.
© 2003 by CRC Press LLC
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The maximum response is found again from the zero-velocity condition. For very short duration loading (t1/T < 0.4), the maximum response occurs during the free vibrations of phase II; otherwise it occurs during the loading interval (phase I). For phase I, during the application of the loading, for 0 ≤ t ≤ t1, with zero initial conditions, the general solution is: u (t ) =
p0 t sinωt − k t1 ωt1
(3.74)
During application of loading in phase I, for t = t – t1 ≥ 0, is again given by Equation 3.64, which after determining u(t1) and u· (t1) at the end of phase I and substitution becomes: u (t ) =
p0 k
1 sin ωt1 1 − cos ωt1 ) sin ωt + 1 − cos ωt ( ωt1 ωt1
(3.75)
Figure 3.10 shows the dynamic amplification factor D as a function of t1/T for the four idealized impulsive load shapes.
3.2.5 Approximate Analysis of Impulsive-Load Response For a short duration impulsive loading, with duration significantly less than the natural period, i.e., t1 << T, an approximate expression for the response may be derived based on the equation of motion, Equation 3.5, and the free-vibration response, Equation 3.67. Rearranging the terms of the equation of motion and integrating from time zero to t1, and noting that:
∫
t1
˙˙ = m∆u˙ mudt
(3.76)
0
the following results: m ∆u˙ =
∫ [ p (t ) − cu˙ (t ) − ku (t )]dt t1
(3.77)
0
where ∆u˙ represents the change of velocity from time zero to t1. The velocity u˙ (t1) and displacement u(t1) developed over the period from time zero to t1 are very small, the damping and elastic energy terms in Equation 3.77 can be ignored1 and Equation 3.77 rewritten as: m ∆u˙ =
1 m
∫
t1
0
p (t ) dt
(3.78)
The response after the termination of the loading is a free vibration expressed by Equation 3.67: u (t ) =
1
u˙ (t1 ) ω
sin ωt + u (t1 ) cos ωt
(3.79)
Note that as the left-hand side and the integrated impulse term are of the order of t1, while the integrated term associated with damping is of the order of t12 and the elastic energy term of the order of t13, the latter two terms become negligible when t1 approaches zero. © 2003 by CRC Press LLC
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FIGURE 3.9 Triangular impulse.
FIGURE 3.10 Dynamic amplification factor for four types of impulse loads as a function of t1 /T.
– where t = t – t1. · ) = ∆u, · and t ≅ –t, the following approximate relationship As u(t1) is negligibly small and velocity u(t 1 may be used: u (t ) ≅
© 2003 by CRC Press LLC
1 mω
∫
t1
0
p (t ) dt sin ωt
(3.80)
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Dynamics of Structures
FIGURE 3.11
Arbitrary periodic loading.
3.2.6 Duhamel Integral In the following, an expression for the response to an arbitrary dynamic loading is developed based on Equation 3.80. The concept is to first derive, based on Equation 3.80, the differential response due to a differential impulse, acting over an infinitesimal time interval and then, based on an assumption of linearity, obtain the total response as the summation (integral) of the differential responses. For the differential time interval dτ, the response is (for t > τ): du (t ) =
p (τ) dτ sin ω (t − τ) mω
(3.81)
du(t) represents the differential response contribution of the impulse p(τ)dτ to the total response, which is obtained by integrating Equation 3.81 as: 1 mω
u (t ) =
t
∫ p (τ) sin ω (t − τ) dτ
(3.82)
0
Equation 3.82, known as the Duhamel integral, can be used to obtain the response of an undamped2 SDOF system to any dynamic loading p(t).
3.2.7 Response to Periodic Loading The following two points are key to the powerful concise representation of SDOF system response to periodic loading, and the extension to response analysis in the frequency domain: 1. The expression of the periodic loading as a Fourier series. 2. Based on linearity of the equation of motion, the superposition principle can be utilized to construct the total response as the sum of the responses for each of the terms of the Fourier series. The Fourier series expression of the periodic function p(t), such as shown in Figure 3.11, is: p (t ) = a0 +
∞
∑
an cos
n=1
2πn t+ Tp
∞
∑ b sin 2Tπn n
n=1
(3.84)
p
2 For a damped system, the derivation is identical except that the free-vibration response initiated by the differential load impulse decays exponentially. The Duhamel integral for a damped SDOF system is:
u (t ) = © 2003 by CRC Press LLC
1 mω D
t
∫ p ( τ) e 0
− ξω(t − τ )
sin ω D (t − τ) dτ
(3.83)
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where Tp is the period of the load function and: a0 =
1 Tp
an =
2 Tp
∫
Tp
bn =
2 Tp
∫
Tp
0
0
∫
Tp
0
p (t ) dt
(3.85)
p (t ) cos
2πn t Tp
(3.86)
p (t ) sin
2πn t Tp
(3.87)
The response to the loading of Equation 3.84 is the sum of the responses for each of the terms. The SDOF response to the type of harmonic (and the constant) terms of Equation 3.84 has been discussed in the previous sections. The steady-state response to the constant load component (which is equal to the average load) is the static deflection, i.e., u0 =
a0 k
(3.88)
The steady-state response of an undamped SDOF structure for each term of the series is written, by analogy with Equation 3.40, as follows: Sine terms: un (t ) =
1 bn sin nω pt k 1 − αn2
(3.89)
where αn =
nω p nω p = ω ω
(3.90)
Cosine terms: un (t ) =
1 an cos nω pt k 1 − αn2
(3.91)
The total response of the undamped system is then expressed as the sum of all the individual responses above: u (t ) =
1 a0 + k
∞
∑ 1 −1α (a cos nω t + b sin nω t ) 2
n=1
n
p
n
p
(3.92)
n
The response of a damped SDOF system subject to the periodic loading of Equation 3.84 is obtained by using the damped-harmonic-response expressions of the form of Equation 3.48 in lieu of the undamped-response expressions, Equations 3.89 and 3.91 above. As a precursor for response analysis in the frequency domain (in the next section), Equations 3.84 through 3.87 are written in exponential form by utilizing Euler’s equation: e ix = cos x + i sin x © 2003 by CRC Press LLC
(3.93)
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and the following two corollary equations:
(
sin x = − 1 2 i e − ix − e − ix cos x =
1
2
(e
− ix
+ e − ix
)
(3.94)
)
(3.95)
where i is the imaginary unit ( i = – 1 ) . The exponential expression of p(t) is: ∞
∑c
p (t ) =
(
exp inω pt
n
n=−∞
)
(3.96)
)
(3.97)
where cn =
1 Tp
∫
Tp
0
(
p (t ) exp −inω pt dt
Note that while cn is complex, in the series of Equation 3.96 all the terms with n ≠ 0 can be arranged in complex conjugate pairs such that the imaginary parts cancel and the sum is real. To examine the response in a case where the loading is expressed in the exponential form of Equation 3.96, first consider the response to a single complex term (n = 1) of Equation 3.96:
( )
mu˙˙ (t ) + cu˙ (t ) + ku (t ) = exp iω pt
(3.98)
The steady-state solution can be written in the form:
( ) ( )
u (t ) = H ω p exp iω pt
(3.99)
where H(ωp) is found by substituting to Equation 3.98 as:
( )
H ωp =
1 2 −ω p m + iω pc + k
(3.100)
Denoting the frequency ratio by α and the damping ratio by ξ, this becomes:
( ) k ( −α
H ωp =
2
1 + 2iαξ + 1
(3.101)
)
and for any arbitrary frequency nωp:
( ) k ( −n α
H nω p =
2
2
1 + 2inαξ + 1
)
(3.102)
By superposition, the total steady-state response is written as: u (t ) =
∞
∑ H (nω )c exp (inω t ) p
n
p
(3.103)
n=−∞
Note that H(nωp) and H(−nωp) are complex conjugates, as are, consequently, each (+n) and (−n) term of the summation, and hence the sum is real.
© 2003 by CRC Press LLC
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3.2.7.1 Response Analysis through the Frequency Domain The concepts of the periodic loading and response outlined above can be further extended by generalizing the Fourier series to Fourier integrals that are not limited to periodic functions.3 When the loading period is extended to infinity the frequency increment becomes an infinitesimal dωp and the discrete frequencies become a continuous function. Thus in the limit, the Fourier series expression for p(t), Equation 3.96, becomes the following Fourier integral: p (t ) =
1 2π
∫
∞
ω p =− ∞
( ) ( )
c ω p exp iω pt dω p
(3.104)
where the harmonic-amplitude function, c(ωp), is given by:
( ) ∫
c ωp =
∞
t =−∞
(
)
p (t ) exp −iω pt dt
(3.105)
Equations 3.104 and 3.105 are known as a Fourier transform pair and Equation 3.104 can be considered as an extension of the finite sum of Equation 3.96 to an infinite integral that represents the loading as an infinite sum of harmonic components. Analogous to Equation 3.103, the response u(t) can be written (omitting some details) as: u (t ) =
1 2π
∫
∞
ω p =− ∞
( )( ) ( )
H ω p c ω p exp iω pt dω p
(3.106)
Equation 3.106 can be considered as the basic equation for the analysis of response through the frequency domain. 3.2.7.1.1 Numerical Analysis in the Frequency Domain For practical problems, the integrals of Equations 3.105 and 3.106 are evaluated numerically. The key elements in this process are the concept of discrete Fourier transform (DFT) and the fast Fourier transform (FFT) numerical technique used for evaluating the DFTs. The DFT converts the integrals of Equations 3.105 and 3.106 back to finite series and thereby invokes the periodicity assumption. However, the period can be taken sufficiently long, and the number of terms in the series sufficiently high, as to not pose an unwanted limitation on the accuracy of the solution of the practical problem. The selected load period, Tp , defines the lowest frequency that can be captured in the analysis, i.e., ω p = ∆ω p =
2π Tp
(3.107)
The load period is divided into N equal time increments ∆t = Tp/N, and the load is defined for the discrete times tm = m∆t and frequencies ωpn = n∆ωp. The exponential term in Equation 3.104 can be written:
(
)
(
)
nm exp iω pnt m = exp in∆ω pm∆t = exp 2πi N
3
(3.108)
For the Fourier integral to exist, the only condition for the loading function is that the following integral must ∞ be finite:
∫
−∞
© 2003 by CRC Press LLC
p (t ) dt
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Dynamics of Structures
and Equation 3.104 is discretized as: p (t m ) =
∆ω p 2π
N −1
∑ c (ω ) exp 2πi nm N pn
(3.109)
n=0
where the highest frequency to be included is set at (N − 1) ∆ωp . The discrete expression for the amplitude function c(ωpn) is obtained as:
( )
N −1
c ω pn = ∆t
∑ p (t m=0
m
) exp −2πi nm N
(3.110)
Equations 3.109 and 3.110 are the DFT pair corresponding to the continuous integral transforms of Equations 3.104 and 3.105. 3.2.7.1.2 Fast Fourier Transform Analysis In the current practice of frequency domain analysis, the sums in the DFT equations are computed utilizing the powerful FFT technique. The details of this method are beyond the scope of this discussion, and the reader is referred to the many texts on this topic [e.g., Newland, 1975; Clough and Penzien, 1975].
3.3 Multidegree-of-Freedom Systems A structure can be modeled and its response analyzed using a SDOF model if the mass is essentially concentrated at a single point that can move, translate, or rotate only in one direction, or if the system is constrained in such a way as to permit only a single mode of displacement. In general, the mass of a larger building or structure is distributed throughout the structure and can move in many ways. A realistic description of the dynamic response of such systems generally requires the use of a number of independent displacement coordinates, and modeling of the system as a multidegree-of-freedom (MDOF) system. Dynamic analysis of such MDOF systems is discussed in the following sections.
3.3.1 Equations of Motion The MDOF analysis procedure is illustrated by examining the dynamic response of the idealized twostory building shown in Figure 3.12. The mass of the structure is assumed to be concentrated at the floor levels, which are further assumed to be rigid and displace in one translational direction only. Thus, the dynamic behavior of this structure is completely defined by the two-story displacements u1(t) and u2(t). The equation of motion of any story can be derived from the expression of dynamic equilibrium of all of the forces acting on the story mass, including the inertia, damping, and elastic forces that result from the motion, and the externally applied force. The equations of equilibrium for the two stories can be written as follows (using notation analogous to the SDOF case): FI1 + FD1 + FS1 = P1 (t )
(3.111)
FI2 + FD2 + FS2 = P2 (t )
(3.112)
FI + FD + FS = P (t )
(3.113)
or equivalently in vector form:
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Two-degree-of-freedom system.
The inertia forces are given simply as the product of the story mass and the story acceleration, which may be represented in matrix form as: FI M1 FI = 1 = FI2 0
0 u˙˙1 M 2 u˙˙2
(3.114)
or simply:
FI = Mu˙˙
(3.115)
in which FI is the inertia force vector, ü is the acceleration vector, and M is the mass matrix. It is important to note in Equation 3.114 that the inertia force corresponding to any degree of freedom depends only on the acceleration in that degree of freedom. Such mass description is referred to as lumped mass and the mass matrix is diagonal. In general, the mass matrix for a MDOF system is not necessarily diagonal. For example, if the mass matrix is developed using the consistent mass matrix finite element formulation, the mass matrix will not be diagonal and inertia coupling will be introduced between the displacement coordinates. In some cases, the lack of mass coupling is desirable, and the lumped mass representation is used in many practical analyses. The elastic forces in Equations 3.111 and 3.112 are expressed as:
FS = Ku
(3.116)
where Fs is the elastic force vector, u is the displacement vector, and K is the stiffness matrix of the structure. The stiffness matrix K is generally not diagonal. The off-diagonal terms indicate that elastic forces for a given coordinate depend on displacements of the other coordinates; there is stiffness coupling between the coordinates. In practical applications, the stiffness matrix is most commonly constructed using computer programs based on the finite element method. Conceptually, the damping forces in Equations 3.111 and 3.112 can be expressed as:
FD = Cu˙
(3.117)
In the practical methods developed for MDOF analysis, individual elements of the damping matrix are not computed based on “local” damping properties in the vicinity of the associated degrees of freedom. Instead, damping is usually expressed in terms of damping ratios as discussed in Sections 3.2.2.2.2 and 3.2.3.1.
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FIGURE 3.13
Two-degree-of-freedom system with base excitation.
Substituting Equations 3.115 through 3.117 to Equation 3.113, the equations of dynamic equilibrium may be written in matrix form as:
()
Mu˙˙ + Cu˙ + Ku = P t
(3.118)
Equation 3.118 represents the equations of motion of an arbitrary structural system having any number of degrees of freedom. The similarity of this matrix equation to the corresponding SDOF equation (Equation 3.5) is noteworthy. 3.3.1.1 Equation of Motion for Support Excitation Loading Figure 3.13 illustrates the case where the dynamic loading is due to support excitation. The horizontal ground motion relative to the fixed reference axis is indicated by the displacement ug. Instead of Equation 3.115, the inertia force for this case is given by:
FI = Mu˙˙ t
(3.119)
i.e., for each mass point, the inertia force is the product of the mass and the total, absolute acceleration, which can be written as: u˙˙ t = u˙˙ + u˙˙ g
(3.120)
In the above example each mass point has only one translational degree of freedom and each of the two elements of vector üg is simply üg(t), that is, the ground acceleration time history. In a more general case each mass point has more than one degree of freedom, e.g., all three translations and three rotations. In the general case the ground acceleration vector is written as: ) u˙˙ g = I u˙˙g
(3.121)
) where I defines the direction of the support excitation and consists of ones for those degrees of freedom in the direction of excitation, and zeros otherwise. After moving the ground motion acceleration terms to the right-hand side, the equation of motion for support excitation becomes: ) Mu˙˙ + Cu˙ + Ku = −MI u˙˙g (t ) © 2003 by CRC Press LLC
(3.122)
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On the left-hand side, the acceleration u˙˙ , velocity u˙ , and displacement u are relative to the fixed base. ) Therefore, the term Mü does not represent the full inertial loading on the mass points [ M (u˙˙ + I u˙˙g ) does], while Cü and Ku do represent the full damping and elastic forces acting on the mass points. It is worth noting that the solution of Equation 3.122 for the relative displacement vector is the) same as the solution of Equation 3.118, in this case for total displacement vector, for P (t ) = Peff (t ) = − MI u˙˙g (t ). This is illustrated in Figure 3.13. Note that the “effective” inertia force acts at every mass point.
3.3.2 Vibration Mode Shapes and Frequencies As for an SDOF system, the first step in finding the solution of the MDOF system equation of motion is to study undamped free vibrations, i.e., damping and applied loads of Equation 3.118 set to zero: Mu˙˙ + Ku = 0
(3.123)
Postulating that a solution can be found as harmonic motion with all the degrees of freedom moving in phase, the displacement vector is written as: u = ϕ sinωt
(3.124)
where ϕ represents the amplitude vector of the vibratory motion and ω is the circular frequency. By differentiating Equation 3.124 twice with respect to time, the acceleration vector is: u˙˙ = −ω 2ϕ sin ωt
(3.125)
Substituting Equations 3.124 and 3.125 into Equation 3.123 and canceling the sin ωt term leads to: −ω 2Mϕ + Kϕ = 0
(3.126)
(K − ω M) ϕ = 0
(3.127)
or rearranging: 2
Equation 3.127 is a form of an eigenvalue problem. An eigenvalue problem associated with square matrices of dimension n typically has n solutions, each consisting of an eigenvalue ωi2 and the eigenvector ϕi , referred to as a mode shape in structural dynamics. Before proceeding to discuss the response of the MDOF system, the properties of the mass and stiffness matrices are briefly explored in the following section. 3.3.2.1 On Properties of Mass and Stiffness Matrix The mass and stiffness matrices of a MDOF system have characteristics that have a strong bearing on the mathematical analysis of the dynamic response of these systems. Some of these characteristics are identified in the following, but a detailed discussion of these aspects is beyond the scope of this summary presentation. 1. Both stiffness and mass matrices for linear elastic systems are symmetric. 2. Mass matrices are positive definite and stiffness matrices are positive semidefinite, i.e., ϕT Mϕ > 0 for every ϕ ≠ 0
(3.128)
ϕT Kϕ ≥ 0 for every ϕ ≠ 0
(3.129)
and
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Another important property of the eigensolutions is the orthogonality of the eigenvectors with respect to both the mass and stiffness matrices M and K. This orthogonality property is expressed mathematically by the following two equations: T
(3.130)
T
(3.131)
ϕ i Mϕ j = 0 and ϕ i Kϕ j = 0
Furthermore, the n orthogonal eigenvectors are linearly independent, and consequently any and all vectors of the n-space can be constructed as a linear combination of these eigenvectors, i.e., any displacement vector u can be expressed as: u (t ) =
N
∑ ϕ η (t ) = Φη(t ) i
i
(3.132)
i =1
where Φ is a matrix containing the vectors ϕi (i 1, … n) as its columns and η can be considered a generalized coordinate vector.
3.3.3 Modal Equations of Motion A solution of Equation 3.127:
(K − ω M) ϕ = 0 2
(3.133)
is termed a natural mode of vibration and is defined by an eigenvalue ωi, termed the natural angular frequency, and the corresponding eigenvector ϕi, termed the natural mode shape. It is readily observed from Equation 3.133 that any eigenvector multiplied by a constant is also an eigenvector, hence the magnitude of the eigenvector is not unique. However, it is customary to normalize the model shape vectors with respect to the mass matrix such that: T
ϕ i Mϕ i = 1
(3.134)
When the eigenvectors are arranged to a square matrix, with the vectors as the columns of the matrix, the following relationships are written based on Equation 3.134 and the orthogonality properties: ΦT MΦ = I
(3.135)
ΦT KΦ = Ω
(3.136)
where Ω is a diagonal matrix with the ωi values as the diagonal entries. Next we express the equations of motion of the multidegree system in terms of the modal coordinates. By differentiating Equation 3.132, the velocity and acceleration vectors are written as:
© 2003 by CRC Press LLC
u˙ = Φη˙ (t )
(3.137)
˙˙ (t ) u˙˙ = Φη
(3.138)
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Substituting into Equation 3.118 results in: ˙˙ + CΦη˙ + KΦη = P (t ) MΦη
(3.139)
Multiplying Equation 3.139 with ΦT from the left results in: ˙˙ + ΦT CΦη˙ + ΦT KΦη = ΦT P (t ) ΦT MΦη
(3.140)
Based on the orthogonality conditions of Equations 3.130 and 3.131, the first and third terms of the left-hand side are diagonal matrices. If we further assume that same type of orthogonality conditions also applies to the damping matrix, i.e., that: T
ϕ i Cϕ j = 0
(3.141)
the normal coordinate equation of motion may be written more conveniently by introducing the following symbols for the generalized coordinate properties of each mode i: ˙˙ i + ϕ i Cϕ i η˙ i + ϕ i Kϕ i ηi = ϕ i P (t ) ϕ i Mϕ i η
(3.142)
˙˙ i + Ci* η˙ i + K i* ηi = Pi* (t ) M i* η
(3.143)
T
T
T
T
T
Generalized mass: M i* = ϕ i Mϕ i
(3.144)
T
(3.145)
Generalized stiffness: K i* = ϕ i Kϕ i
T
(3.146)
Generalized loading: Pi* (t ) = ϕ i P (t )
(3.147)
Generalized damping: Ci* = ϕ i Cϕ i
T
Thus, by expressing the equations of motion, Equation 3.118, in terms of the modal coordinates, the system of n coupled equations have been decoupled to n independent equations of motion that can be written as: ˙˙ i + 2ξi ω i η˙ i + ω i2 ηi = η
Pi* (t ) M i*
i = 1,..., n
(3.148)
These n independent equations of motion are of exactly the same form as the SDOF equation of motion discussed above. Each of the equations in Equation 3.148 can be solved for the modal coordinate ηi(t) using methods discussed in Section 3.2.2. The modal coordinates can then be combined to obtain the displacement vector u per Equation 3.132. The method of solving the MDOF equation of motion by transforming the problem to the modal coordinate system, solving the uncoupled equations, and finally superposing the modal contributions is referred to as the modal superposition method. 3.3.3.1 Rayleigh Proportional Damping An assumption was made above that the damping matrix C has similar orthogonality properties as the mass and stiffness matrices. If the damping matrix is represented as Rayleigh proportional damping, i.e., as a linear combination of the mass and stiffness matrices: C = a0M + a1K © 2003 by CRC Press LLC
(3.149)
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FIGURE 3.14
Rayleigh damping.
then the damping matrix does possess the same orthogonality properties as the mass and stiffness matrices, i.e., T
ϕ i Cϕ j = 0
(3.150)
Using notations of Equations 3.144 through 3.146, damping of the ith mode is expressed as: Ci* = a0 M i* + a1K i* = a0 M i* + a1ω i2 M i*
(3.151)
and as for the SDOF system, the damping ratio for mode i is written as: ξi =
Ci* 2M i*ω i
(3.152)
Substituting Equation 3.151 in Equation 3.152, the damping ratio becomes: ξi =
a0 1 a1 + ω 2 ωi 2 i
(3.153)
Equation 3.153 indicates that the contribution from the mass related damping term is inversely proportional to frequency, while the contribution from the stiffness related term is proportional to frequency. Figure 3.14 shows the Rayleigh damping variation with natural frequency. The coefficients a0 and a1 can be determined from specified damping ratios at two independent modes k and l. Expressing Equation 3.153 for these two modes will lead to the following equations: ξk =
a0 1 a1 + ω 2 ωk 2 k
(3.154)
ξl =
a0 1 a1 + ω 2 ωl 2 l
(3.155)
2ω kω l ωk + ωl
(3.156)
a0 and a1 can be solved as: a0 = ξ
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a1 = ξ
2 ωk + ωl
(3.157)
Note that at frequencies between ωk and ωl, damping is less than ξ. In practical problems, the parameters ξ, ωk, and ωl should be set such that all the modes with significant contribution to the response are assigned reasonable damping ratio values. Especially when used in nonlinear analysis for systems where motions resembling rigid-body motion may occur, mass proportional damping is to be used with caution, as unreasonably high damping may result.
3.3.4 Earthquake Response Analysis In the case where the loading is earthquake ground motion, the right-hand side of the equation is written as in Equation 3.122: ) Peff (t ) = −MI u˙˙g (t )
(3.158)
) where I defines the direction of the support excitation and consists of ones for those degrees of freedom in the direction of excitation, and zeros otherwise. Substituting Equation 3.158 for P(t) in Equation 3.140, the generalized effective earthquake load vector is written as: ) Peff* (t ) = − ΦMI u˙˙g (t )
(3.159)
) Peff* , i (t ) = −ϕTi MI u˙˙g (t )
(3.160)
which for mode i gives:
By defining a participation factor for mode i for earthquake excitation in the direction defined by the ) vector I as: ) βi = ϕTi MI the equation of motion for mode i of a multidegree system becomes: ˙˙ i + 2ξi ω i η˙ i + ω i2 ηi = − βi* u˙˙g (t ) η Mi The response of the ith mode can be expressed in terms of the Duhamel integral: ηi (t ) =
βi 1 M i* ω i
t
∫ u˙˙ (τ)e 0
− ξ i ω i (t − τ )
g
sin ω i (t − τ) dτ
(3.161)
By denoting the integral as Ui(t): U i (t ) =
1 ωi
t
∫ u˙˙ (τ)e 0
− ξ i ω i (t − τ )
g
sin ω i (t − τ) dτ
(3.162)
The ith modal coordinate response can be written as: ηi (t ) =
© 2003 by CRC Press LLC
βi U (t ) M i* i
(3.163)
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The complete displacement of the structure at time t is then obtained by superposing the contribution of all modes evaluated at this time by Equation 3.132 as: u (t ) =
N
∑ ϕ η (t ) = Φη(t ) i
i
(3.132)
i =1
Typically, the modes with the lowest natural frequencies contribute most to the overall response, (1) as the participation factors of these modes for earthquake excitation are high in comparison to those of the higher modes, and (2) due to the presence of ωi in the denominator of the Duhamel integral (Equation 3.161). Therefore, an adequate approximation of the response is often obtained by including only a number of the lowest modes in the summation of Equation 3.132. The method of MDOF earthquake response analysis outlined above, culminating in superposition of modal responses, is referred to as the modal superposition method. While the time integration of modal responses was formulated above in terms of analytic functions, the time integration could be, and in practice usually is, performed using numerical time integration methods that are discussed in Section 3.3.4.2. 3.3.4.1 Response Spectrum Analysis The response spectrum method allows an approximate determination of the maximum response of an MDOF system without performing a time history analysis, e.g., without employing the modal superposition method of the previous section or the direct time history analysis discussed in Section 3.3.4.2. Response spectrum analysis consists of three steps: 1. Modal analysis, i.e., determination of the natural modes of vibration and the associated frequencies as outlined in Section 3.3.3 2. Determination of the maximum response in each mode, “modal response,” included in the analysis; this involves determination of maximum value of the modal coordinate, ηimax, over the duration of the earthquake loading for each mode 3. Combination of the modal responses to obtain approximate maximum response The maximum modal response for mode i, ηimax , can be expressed (see Equation 3.163) in terms of the displacement response spectrum, Sd (ωi)(see Chapter 4): ηimax =
βi S (ω ) M i* d i
(3.164)
The (relative) displacement vector uimax associated with the maximum peak response of mode i, i.e., ηimax, is: u imax = ϕ i ηimax = ϕ i
βi S (ω ) M i* d i
(3.165)
Maximum values of response quantities such as relative displacement, element forces, and reaction forces due to response in mode i can readily be determined based on the deformation defined by uimax. In general, the maximum response uimax does not occur at the same point in time for all the modes i = 1, …, n, and any combination of the modal maxima can only be an approximation of the actual maximum response. A relatively simple and practical method, supported to an extent by probabilistic considerations, for computing approximate total maximum response quantities is the square-root-ofthe-sum-of-the-squares (SRSS) procedure. If qimax is the maximum value of a response quantity, e.g., an element shear force, due to mode i, an approximate total maximum of this quantity due to responses in all modes included in the analysis, i = 1, …, N, is computed as:
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N
∑q
qmax =
2 imax
(3.166)
i =1
Several other schemes of combining modal responses have been developed, for example, the complete quadratic combination (CQC) rule (see Chopra [2001] for details), some of them particularly to predict total response more accurately than the SRSS procedure in situations where the system has closely spaced modes (i.e., some of the natural frequencies are very close to each other). A key benefit of the response spectrum method is the ability to obtain a generally good approximation of the earthquake response of a multidegree structure without having to perform a full-time history analysis. The method is a standard feature in various structural analysis software packages. Response spectra for design purposes are specified in the design codes and response spectra for major earthquakes are customarily computed from accelerogram records and made available for public use. 3.3.4.2 Numerical Time Integration The Duhamel integral is a useful conceptual tool and can be used to obtain a closed-form solution of the equation of motion in cases where the integrand has an analytic integral function. In cases where an analytic integral function cannot be developed, the integral can be evaluated numerically based on approximation of the definite integral by a summation utilizing any of the classical summation rules, e.g., the trapezoidal or Simpson’s rules. In practice, however, step-by-step numerical integration schemes derived by expressing the relationships between displacement and its time derivatives, velocity, and acceleration, utilizing approximate discretized (with respect to time) expressions, and substituting these to the equation of motion, are most commonly used. The Newmark family of time integration methods illustrates these numerical schemes. The Newmark family contains as special cases many widely used methods. The method is based on the following formulas: Mu˙˙ t + ∆t + Cu˙ t + ∆t + Kut + ∆t = Pt + ∆t u t + ∆t = u t + u˙ t ∆t +
(3.167)
∆t 2 (1 − 2β)u˙˙ t + 2βu˙˙ t +∆t 2
[
[
u˙ t + ∆t = u˙ t + ∆t (1 − γ ) u˙˙ t + γu˙˙ t + ∆t
]
]
(3.168) (3.169)
where u t , u˙ t , and u˙˙ t are approximations of u (t ), u˙ (t ), and u˙˙ (t ), respectively. Equations 3.167, 3.168, and 3.169 can be thought of as three equations for three unknowns, u t + ∆t , u˙ t + ∆t , and u˙˙ t + ∆t , assuming that u t , u˙ t , and u˙˙ t are known from the previous step. By solving u˙˙ t +∆t from Equation 3.168 in terms of u t +∆t , then substituting for u˙˙ t +∆t in Equation 3.169, expressions are obtained for u˙˙ t +∆t and u˙ t +∆t in terms of u t +∆t as: u˙˙ t + ∆t =
1 1 1 − ut ) − u u˙ t − − 1 u˙˙ t 2 ( t + ∆t β∆t β∆t 2β
u˙ t + ∆t = u˙ t + ∆t (1 − γ )u˙˙ t + γ∆tu˙˙ t + ∆t
(3.170)
(3.171)
When these expressions are substituted in Equation 3.167, the resulting equation can be written as: K *u t + ∆t = Pt*+ ∆t
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(3.172)
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where K* =
γ 1 M+ C +K β∆t 2 β∆t
(3.173)
and 1 1 1 Pt*+ ∆t = Pt + ∆t + M u + u˙ t + − 1 u˙˙ t + 2 t β∆t 2β β∆t γ C ut β∆t
γ ∆t γ + − 1 u˙ t + − 2 u˙˙ 2 β t β
(3.174)
The response can be solved step by step using the above equations starting from the initial conditions u 0 , u˙ 0 , and u˙˙ 0 and over the period of time of interest. Convergence to the true solution requires that a
sufficiently short time step, ∆t, be used. The specific choice of values for the parameters β and γ affect the accuracy and stability of the algorithm. A method is called unstable for a given time step size if the solution, ut , grows out of bounds at some point even if the true solution, u(t), does not. It can be shown that when: γ ≥ 0.50
(3.175)
the method defined by Equations 3.170 through 3.174 is stable provided that the time step is less than the threshold value that can be expressed in the form: ∆t ≤ αTmin
(3.176)
where Tmin is the period of the highest natural mode of the system (and α is a coefficient that depends on β and γ as well as on damping). The constraint imposed by Equation 3.176 may lead to a far shorter time step than required to adequately resolve the low modes that dominate the response, and thereby potentially cause an unreasonable computational burden. A method that is stable only when a condition for the time step, of the type of Equation 3.176, is satisfied is conditionally stable and a method that is stable regardless of time step size is unconditionally stable. If, in addition to the condition of Equation 3.175, coefficient β satisfies the condition: β ≥ 0.25 ( γ + 0.5)
2
(3.177)
the method is unconditionally stable. As in most seismic analyses of building structures, the low modes dominate the response, high modes contributing negligibly to element forces, the number of modes necessary to be included in the analysis to achieve reasonable accuracy is typically much less than the total number of degrees of freedom (i.e., total number of equations). Therefore, it is highly desirable not to be subject to the time step restriction of Equation 3.176, which typically would force a much shorter time step than necessary to accurately integrate the dominant low modes. Table 3.2 provides the β and γ values, and the stability conditions for three widely used methods of the Newmark family. In this table, the average acceleration and linear acceleration methods are indicated as implicit. The term implicit refers to the fact that the equation of motion, Equation 3.167 (and consequently Equation 3.172), is written at time t + ∆t and as the matrix K* multiplying the unknown vector ut + ∆t is nondiagonal (as it includes the generally nondiagonal K, as well as C, which is nondiagonal © 2003 by CRC Press LLC
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TABLE 3.2 Properties of Selected Numerical Time Integration Algorithms of the Newmark Family
∆t Method
Type
β
γ
TMIN
Average acceleration Linear acceleration Central difference
Implicit Implicit Explicit
1/4 1/6 0
1/2 1/2 1/2
∞ 0.5513 0.3183
if coeffcient a1 of Rayleigh damping [Equation 3.149] is positive), obtaining ut + ∆t involves solution of coupled equations. In Table 3.1 the central difference method is indicated as explicit. This refers to the fact that (1) when Equation 3.167 (and subsequently Equation 3.172) is written for time step t, and (2) with the indicated values of β = 0 and γ =1/2, üt and u· t become, using Equations 3.170 and 3.171: u˙˙ t =
u t + ∆t − 2u t + u t − ∆t ∆t 2
(3.178)
u t + ∆t − u t − ∆t 2∆t
(3.179)
u˙ t =
and (3) M (and C if present) is diagonal, the matrix K* multiplying the unknown vector ut + ∆t is diagonal (the nondiagonal K only multiplying the known ut [see Equation 3.180 below]), and consequently the equations are uncoupled, leading to fast solution for each time step: 1 2 1 1 1 C u = Pt − K − 2 M u t − 2 M − C u 2 M+ ∆t ∆t 2∆t t + ∆t 2∆t t − ∆t ∆t
(3.180)
When time integration is used for nonlinear problems with the stiffness matrix varying over time, the reduction in the amount of computations, in comparison to implicit methods, is significant. Countering the benefit of simple fast solution per time step is the requirement for short time step imposed by conditional stability. Problems for which use of explicit methods are particularly beneficial, or in many cases mandatory, are nonlinear problems that involve one or more of the following characteristics: 1. Large deformations 2. Large rotations 3. Contact/impact with or without sliding These types of problems often require the use of very short time steps in any case to achieve reasonable accuracy and, therefore, the condition for short time step imposed by the stability condition is not a burden. As is typical of numerical methods, the numerical time integration algorithms are approximate. However, like any generally acceptable numerical algorithm, a properly implemented time integration scheme is convergent, i.e., the computed solution approaches the exact value when time step size approaches zero (i.e., ut → u(t) when ∆t → 0). For the time integration algorithms introduced above, the errors in the computed response can be categorized as period elongation and amplitude decay. Figure 3.15 illustrates these errors for a case where a free vibration response is integrated numerically. Typically, the implicit methods elongate the period while the explicit central difference method reduces the period relative to the exact value. Typically, all the methods except the Newmark constant average acceleration method (i.e., β = 1/4 and γ = 1/2) cause amplitude decay that can be thought of as numerical damping, which adds to any damping included explicitly in the model, e.g., through Rayleigh damping. © 2003 by CRC Press LLC
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FIGURE 3.15 Amplitude decay and period elongation.
By shortening the time step, these errors can be limited to any desired level. For the Newmark family of implicit methods, it is generally recommended that time step be limited to: ∆t ≈ 0.05Tcut −off
(3.181)
where Tcut-off is the period of the highest mode required to be resolved with a reasonable level of accuracy in order to capture the response adequately. With the central difference method, any time step that satisfies the stability condition typically results in adequate accuracy of the computed response for most practical problems.
3.3.5 Nonlinear Analysis Linear analysis implies that the properties of the system — stiffness, damping, and mass — are not dependent on the response variables of displacement, velocity or acceleration, or time — that is, the properties of the system are constant with time. Consequently, the coefficients (matrices for MDOF) multiplying the unknown displacement, velocity, or acceleration (vectors for MDOF) are constant. As the level of loading and response increase, at some point the assumption of system properties remaining constant is no longer valid. For example, the stiffness properties may change as a result of material strains growing large enough to cause yielding or other nonlinear behavior, changes in stiffness due to change in geometry resulting from large deformation or rotation, or contact/impact to neighboring structures as displacements increase. The superposition principle, which is inherent both in the Duhamel integral and in the mode superposition method of MDOF systems, is not valid for nonlinear systems. The existence of the orthogonal natural modes of vibration of an MDOF system, which allow decoupling of the equations of motion in the mode superposition method, is tied to the linearity assumption. Consequently, the only method generally suitable for analysis of nonlinear response is a direct step-by-step time integration. (Direct refers to the fact the numerical algorithm is applied “directly” to the “original” matrix equation of motion of an MDOF system, not to a system converted to modal coordinates.) The concept in the step-by-step integration is that the response is solved. To enable the proper consideration of the changing properties during the solution of a nonlinear problem, the solution is performed in small incremental steps adjusting the properties at the beginning of each step based on the deformation and stress in the beginning of each step. The length of the step is selected such that adequate accuracy in tracking the time-varying load, capturing the dynamic aspects of the response, and capturing the changes in properties is achieved. (In static nonlinear analysis, the stepby-step incremental procedure is also required to allow incorporation of the change in properties with the increasing load, in this case without reference to time and without the damping and inertia effects.) © 2003 by CRC Press LLC
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FIGURE 3.16
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Nonlinear internal force–displacement relationship and tangent stiffness.
In the dynamic analysis of building structures, the mass matrix is generally assumed to be constant. In many nonlinear building time-history analyses, it is convenient and in most cases adequate to model damping with the Rayleigh proportional damping, Equation 3.149:
C = αM + βK
(3.149)
where the stiffness matrix K is the original elastic stiffness matrix. It is important to note that nonlinear modeling may introduce damping mechanisms in addition to the damping effected through the C matrix. For example, elements with material descriptions including plasticity, as well as nonlinear link, cable, and contact elements may introduce hysteretic deformation behavior that results in energy dissipation. Care has to be exercised not to overestimate damping by “double counting” the energy dissipation through the combined effect of nonlinear element behavior and damping with the global damping matrix C. To introduce the nonlinear effects due to material nonlinear behavior, geometric nonlinearity, and contact/impact, we first denote the structure internal force vector by fint, which for a linear elastic system can be written as:
f int = Ku
(3.182)
Assume that the displacements increase to a point beyond which response is nonlinear. Beyond this point, the change in the internal force vector, ∆f int, due to a small additional displacement increment, ∆u, can be written as:
∆f int = K T ∆u
(3.183)
where KT is the tangent stiffness matrix. (The superscript T denotes tangent, not transpose, of the matrix K.) The elements of the matrix are defined by:
kijT =
∂fi int ∂u j
(3.184)
Figure 3.16 illustrates nonlinear internal force and tangent stiffness. Denoting the value of f int at time t by f int t , and the change in displacement vector u from time t to time t + ∆t by ∆ut + ∆t, the value of f int at t + ∆t can be written as: int ftint + KtT ∆u t + ∆t + ∆t = ft
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(3.185)
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where KTt is the tangent stiffness matrix at time t, and ∆ut + ∆t “updates” ut to ut + ∆t , i.e., u t + ∆t = u t + ∆u t + ∆t
(3.186)
Substitution of the term ftint for the elastic nodal force vector Kut + ∆t in Equation 3.167 leads to: +∆t Mu˙˙ t + ∆t + Cu˙ t + ∆t + ftint + ∆t = Pt + ∆t
(3.187)
Direct time integration algorithms, such as those represented by the Newmark family, can be readily adopted for use in nonlinear analysis. Using the Newmark Equations 3.170 and 3.171 for üt + ∆t and u· t + ∆t , respectively, and substituting expression 3.185 for ftint leads to: +∆t * ˜ ∆u K t t + ∆t = Pt + ∆t
(3.188)
where, when parameters β and γ are assigned values 1/4 and 1/2, respectively (i.e., the constant average acceleration method is used): ˜ = 4 M + 2 C + KT K t t ∆t 2 ∆t
(3.189)
4 Pt*+ ∆t = Pt + ∆t − ftint + M u˙ t + u˙˙ t + Cu˙ t ∆t
(3.190)
Once ∆ut + ∆t is solved from Equation 3.188, ut + ∆t is computed from Equation 3.186. Because the tangent stiffness was evaluated at ut (not at ut + ∆t) the solution is approximate. Often iterations are required to achieve sufficient accuracy. One widely used iteration procedure is the modified Newton iteration, which is formulated by replacing Equation 3.186 with: u (t k+)∆t = u t(k+−∆1t) + ∆u t(k+)∆t
(3.191)
u t(0+)∆t = u t
(3.192)
and
where k is the iteration counter. This results in slight modification of Equation 3.188, which is now written for the unknown ∆u(t k+)∆t : ˜ ∆u (k ) = P * K t t + ∆t t + ∆t
(3.193)
˜ is unchanged, while the right-hand side P * is modified to: The coefficient matrix K t t +∆t
4 4 Pt*+ ∆t = Pt + ∆t − ftint(k −1) − M 2 u (t k+−∆1t) − u t − u˙ t − u˙˙ t − ∆t ∆t
(
)
2 C u (t k+−∆1t) − u t − u˙ t ∆ t
(
)
(3.194)
For each iteration, acceleration and velocity are computed from the following equations (Equations k) 3.170 and 3.171 with u (t +∆ , Equation 3.191, substituted for ut + ∆t , and β and γ equal to 1/4 and 1/2, t respectively): © 2003 by CRC Press LLC
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u˙˙ (t k+)∆t =
(
)
4 4 u (t k+−∆1t) + ∆u t(k+)∆t − u t − u˙ t − u˙˙ t 2 ∆t ∆t
u˙ (t k+)∆t =
(
)
2 u (k −1) + ∆u t(k+)∆t − u t − u˙ t ∆t t + ∆t
(3.195)
(3.196)
Defining Terms Angular velocity — A measure of rotational speed, for which the typical unit is radians/second. Characteristic equation — The polynomial equation resulting from substitution of an exponential trial solution to a differential equation.
Complementary solution — Solution of the homogeneous differential equation; includes the coefficients of integration that are defined based on initial conditions.
Conditional stability — A numerical time integration method is conditionally stable if it is stable only for a time step size shorter than some threshold value; otherwise it is unconditionally stable.
Convergence — A numerical time integration method is convergent if the computed solution approaches the exact value when time step size approaches zero (i.e., ut → u(t) when ∆t → 0). Critical damping — The lowest level of damping at which the free response will not involve oscillations across the zero displacement condition. Damping — Energy dissipation mechanism that leads to decay of the response; often modeled by linear viscous dashpot. Damping ratio — Ratio of damping to critical damping. Diagonal — Property of a matrix, where only the diagonal terms (i.e., terms in which row and column numbers are equal) are non-zero. Direct method — A numerical time integration method that operates directly on the “original” MDOF equations of motion, i.e., not on the “transformed” uncoupled modal equations of motion. Discrete Fourier transform — A discretized approximation of the Fourier transform integral. Duhamel integral — An analytic integral expression that yields the response of an SDOF system to an arbitrary loading function. Dynamic amplification factor — Ratio of the maximum displacement response amplitude to the static displacement. Eigenvalue problem — In MDOF dynamics context, a set of n simultaneous homogeneous linear equations for n unknowns that only has a solution for certain values (the eigenvalues) of a parameter. The solution of an eigenproblem consists of the eigenvalue and the associated eigenvector. Elastic spring — A spring that follows the same force-displacement curve for loading and unloading. Explicit — In an explicit time integration method, only the diagonal mass matrix multiplies the unknown displacement vector to be solved for the next time step; does not involve solution of coupled equations. Fast Fourier transform — A numerical technique for computation of the Fourier transform; utilizes the discrete Fourier transform in the process. Fourier series — A representation of a periodic function as a (generally infinite) series of sine and cosine terms. Fourier transform — A generalization of Fourier series to nonperiodic functions, the infinite series becoming infinite integral expressions. Free vibrations — Vibration of a system with no loading applied, after the system has been set in motion by some means. General solution — The complete solution of a differential equation, consisting of the complementary solution and the particular solution. Homogeneous equation — The version of a differential equation with the right-hand side, i.e., the loading term, set to zero. © 2003 by CRC Press LLC
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Implicit — In an implicit time integration method, the (nondiagonal) stiffness matrix multiplies the unknown (displacement or acceleration) vector to be solved for the next time step; involves solution of coupled equations. Impulsive load — A short duration (relative to natural period) loading consisting of a single “spike.” Inertia — The tendency of mass to maintain its momentum (both linear and angular momentum). Linear — In a linear system, multiplication of the input, e.g., applied force, by a constant results in the response being multiplied by the same constant. L(·) is linear if L(u) = f ⇒ L(αu) = αf. Linearly independent — Vectors ϕi are linearly independent if n
∑ α ϕ = 0 implies that every α = 0. i
i
i
i =1
Lumped mass — A discretized representation, in a diagonal mass matrix, of the generally continuous distributed mass inertia (translational and/or rotational) of a MDOF system with no inertia coupling between degrees of freedom. Mode shape — Often referred to as a natural mode of vibration, is an eigenvector (see eigenvalue problem) of the eigenvalue problem of structural dynamics. Multiple degree of freedom (MDOF) — System with multiple mass points; description of motion requiring use of multiple displacement variables. Natural angular frequency — Synonym for natural angular velocity. Natural angular velocity — The angular velocity obtained as a solution of the characteristic equation of an undamped system. Natural frequency — Number of cycles per second, obtained by dividing natural angular frequency by 2π. Natural period — The inverse of natural frequency. Nonlinear — A system is nonlinear if it is not linear. Numerical damping — Associated with most numerical time integration methods and causes amplitude decay in the computed free vibration response of an undamped system. ϕj = 0. Orthogonal — Vectors ϕi and ϕj are orthogonal with respect to matrix M if ϕiT Mϕ Particular solution — Solution of the differential equation with the loading term on the right-hand side of the equation. Periodic loading — A loading history function with a particular pattern repeating at constant intervals, i.e., P(t + ∆) = P(t), where ∆ is the period. ϕj > 0 for every ϕ ≠ 0. Positive definite — Matrix M is positive definite if ϕT Mϕ ϕj ≥ 0 for every ϕ ≠ 0. Positive semidefinite — Matrix K is positive semidefinite if ϕT Kϕ Rayleigh proportional damping — Rayleigh proportional damping is of the form C = a0 M + a1 K. Resonance — The condition where the frequency of the harmonic loading is equal to the undamped natural frequency of the system. Response ratio — The momentary ratio of the total displacement to the static displacement. Response spectrum — A representation of the maximum value of a response parameter, such as acceleration or displacement, over the duration of earthquake loading as a function of frequency ω for a given earthquake and damping level. For an acceleration response spectral ordinate Sa (ω) is the maximum acceleration experienced by the mass of the SDOF system that has a natural frequency of ω during the earthquake loading. Response spectrum method — An approximate method of earthquake response analysis based on modal superposition and response spectrum concepts. Simple harmonic motion — Undamped motion described by a sine or cosine function with oscillations at the natural frequency. Single-degree-of-freedom (SDOF) — System with a single mass point whose motion can be described with a single displacement variable.
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Solution in the frequency domain — Refers to solution of the equation of motion by performing a Fourier transform of the loading, finding the Fourier transform of the solution, and obtaining the solution (i.e., the displacement function) through the inverse Fourier transform. In practice the computations are implemented using the fast Fourier transform algorithm. Stability — A numerical time integration method is unstable if at some time point the computed response grows without bounds even if the exact solution does not; otherwise it is stable. Steady-state response — The particular solution of a damped system to periodic loading. Tangent stiffness — A “local” approximate linearized stiffness at a given deformation state during nonlinear response. Transient response — The complementary solution for a damped system that decays exponentially and is typically relevant only in the “beginning” of the response.
References Bathe, K.-J. 1982. Finite Element Procedures in Engineering Analysis, Prentice-Hall, New York. Biggs, J.M. 1964. Introduction to Structural Dynamics, McGraw-Hill, New York. Chopra, A.N. 2001. Dynamics of Structures, 2nd ed., Prentice-Hall, New York. Clough, R.W. and Penzien, J. 1975. Dynamics of Structures, McGraw-Hill, New York. Harris, C.M. 1988. Shock and Vibration Handbook, McGraw-Hill, New York. Hughes, T.J.R. 1987. The Finite Element Method, Linear Static and Dynamic Finite Element Analysis, Prentice-Hall, New York. Meirovitch, L. 1975. Elements of Vibration Analysis, McGraw-Hill, New York. Newland, D.E. 1975. An Introduction to Random Vibrations and Spectral Analysis, Longman, New York. Wiegel, R.L. 1970. Earthquake Engineering, Prentice-Hall, New York.
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II Geoscience Aspects
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4 Earthquakes: Seismogenesis, Measurement, and Distribution 4.1 4.2 4.3
Introduction Causes of Earthquakes and Faulting Measurement of Earthquakes Magnitude · Intensity · Time History · Elastic Response Spectra · Inelastic Response Spectra · Response Spectrum Intensity and Other Measures · Engineering Intensity Scale
4.4
Global Distribution of Earthquakes Global Overview · Pacific Rim · Trans-Alpide Belt · Other Areas
Charles Scawthorn Consulting Engineer Berkeley, CA
4.5 Characterization of Seismicity Defining Terms References Further Reading
4.1 Introduction This chapter provides a basic understanding of earthquakes, by first discussing the causes of earthquakes, then defining commonly used terms, explaining how earthquakes are measured, discussing the global distribution of seismicity, and finally explaining how seismicity can be characterized. Earthquakes are naturally occurring, broad-banded vibratory ground motions, resulting from a number of causes including tectonic ground motions, volcanism, landslides, rockbursts, and man-made explosions. Of these various causes, tectonic-related earthquakes are the largest and most important. These are caused by the fracture and sliding of rock along faults within the Earth’s crust. A fault is a zone of the Earth’s crust within which the two sides have moved — faults may be hundreds of miles long, from 1 to over 100 miles deep, and not readily apparent on the ground surface. Earthquakes initiate a number of phenomena or agents, termed seismic hazards, which can cause significant damage to the built environment — these include fault rupture, vibratory ground motion (i.e., shaking), inundation (e.g., tsunami, seiche, dam failure), various kinds of permanent ground failure (e.g., liquefaction, landsliding), fire, and/or hazardous materials release. In an earthquake event, any particular hazard can dominate, and historically each has caused major damage and great loss of life in particular earthquakes.
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For most earthquakes, shaking is the dominant and most widespread agent of damage. Shaking near the actual earthquake rupture lasts only during the time when the fault ruptures, a process that takes seconds or at most a few minutes. The seismic waves generated by the rupture propagate long after the movement on the fault has stopped, however, spanning the globe in about 20 min. Typically earthquake ground motions are powerful enough to cause damage only in the near-field (i.e., within a few tens of kilometers from the causative fault). In a few instances, long period motions have caused significant damage at great distances, to selected lightly damped structures. A prime example of this was the 1985 Mexico City earthquake, where numerous collapses of mid- and high-rise buildings were due to a M8.1 earthquake occurring at a distance of approximately 400 km from Mexico City.
4.2 Causes of Earthquakes and Faulting In a global sense, tectonic earthquakes result from motion between a number of large plates comprising the Earth’s crust or lithosphere (about 15 large plates, in total, see Figure 4.1). These plates are driven by the convective motion of the material in the Earth’s mantle, which in turn is driven by heat generated at the Earth’s core. Relative plate motion at the fault interface is constrained by friction and/or asperities (areas of interlocking due to protrusions in the fault surfaces). However, strain energy accumulates in the plates, eventually overcomes any resistance, and causes slip between the two sides of the fault. This sudden slip, termed elastic rebound by Reid [1910] based on his studies of regional deformation following the 1906 San Francisco earthquake, releases large amounts of energy, which constitutes or is the earthquake. The location of initial radiation of seismic waves (i.e., the first location of dynamic rupture) is termed the hypocenter, while the projection on the surface of the Earth directly above the hypocenter is termed the epicenter. Other terminology includes near-field1 (within one source dimension of the epicenter, where source dimension refers to the width or length of faulting, whichever is shorter), far-field (beyond near-field), and meizoseismal (the area of strong shaking and damage). Energy is radiated over a broad spectrum of frequencies through the Earth, in body waves and surface waves [Bolt, 1993]. Body waves are of two types: P waves (transmitting energy via push–pull motion), and slower S waves (transmitting energy via shear action at right angles to the direction of motion). Surface waves are also of two types: horizontally oscillating Love waves (analogous to S body waves) and vertically oscillating Rayleigh waves.
A FIGURE 4.1 (A) Global tectonic plate boundaries. (Courtesy United States Geological Survey) (B) plate boundaries and motions. (Courtesy P.D. Lowman, National Aeronautic and Space Administration) (C) Global seismicity 1975–1995. (Courtesy United States Geological Survey) Part C shown as Color Figure 4.1. 1 Not to be confused with near-source as used in the 1997 Uniform Building Code, which can be as much as 15 km, depending on type of faulting.
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B
60'
30'
0' -30'
-60'
-30'
0'
30'
60'
90'
120'
150'
C FIGURE 4.1 (CONTINUED)
© 2003 by CRC Press LLC
180'
-150' -120'
-90'
-60'
-30'
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Auxiliary plane Fault plane “Beach ball” Strike Slip
Normal
Reverse
Oblique Reverse
A FIGURE 4.2
B
(A) Types of faulting; (B) focal mechanisms. (Courtesy United States Geological Survey)
While the accumulation of strain energy within the plate can cause motion (and consequent release of energy) at faults at any location, earthquakes occur with greatest frequency at the boundaries of the tectonic plates. The boundary of the Pacific plate is the source of nearly half of the world’s great earthquakes. Stretching 40,000 km (24,000 mi) around the circumference of the Pacific Ocean, it includes Japan, the west coast of North America, and other highly populated areas, and is aptly termed the Ring of Fire. The interiors of plates, such as ocean basins and continental shields, are areas of low seismicity but are not inactive — the largest earthquakes known to have occurred in North America, for example, occurred in 1811–1812 in the New Madrid area, far from a plate boundary. Tectonic plates move relatively slowly (5 cm per year is relatively fast) and irregularly, with relatively frequent small and only occasional large earthquakes. Forces may build up for decades or centuries at plate interfaces until a large movement occurs all at once. These sudden, violent motions produce the shaking that is felt as an earthquake. The shaking can cause direct damage to buildings, roads, bridges, and other man-made structures, as well as trigger landslides, fires, tidal waves (tsunamis), and other damaging phenomena. Faults are the physical expression of the boundaries between adjacent tectonic plates and thus may be hundreds of miles long. In addition, there may be thousands of shorter faults parallel to or branching out from a main fault zone. Generally, the longer a fault the larger the earthquake it can generate. Beyond the main tectonic plates, there are many smaller subplates, “platelets,” and simple blocks of crust that occasionally move and shift due to the “jostling” of their neighbors and/or the major plates. The existence of these many subplates means that smaller but still damaging earthquakes are possible almost anywhere, although often with less likelihood. Faults are typically classified according to their sense of motion (Figure 4.2). Basic terms include transform or strike slip (relative fault motion occurs in the horizontal plane, parallel to the strike of the fault), dip-slip (motion at right angles to the strike, up- or down-slip), normal (dip-slip motion, two sides in tension move away from each other), reverse (dip-slip, two sides in compression move towards each other), and thrust (low-angle reverse faulting). Generally, earthquakes will be concentrated in the vicinity of faults. Faults that are moving more rapidly than others will tend to have higher rates of seismicity, and larger faults are more likely than others to produce a large event. Many faults are identified on regional geological maps, and useful information on fault location and displacement history is available from local and national geological surveys in areas of high seismicity. Considering this information, areas of an expected large earthquake © 2003 by CRC Press LLC
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4-5
Subduction Zone Back Arc Mountain Belt Outer Rise
Shallow Trench Accretionary Wedge
Young Plate
Great Interplate Earthquakes
Shallow dipping Wadati-Benioff Zone
Shallow Upper-plate Interplate Earthquakes Bending-related Intraplate Earthquakes
FIGURE 4.3 Schematic diagram of subduction zone, typical of the west coast of South America, the U.S. Pacific Northwest, or Japan.
in the near future (usually measured in years or decades) can be, and have been, identified. However, earthquakes continue to occur on “unknown” or “inactive” faults. An important development has been the growing recognition of blind thrust faults, which emerged as a result of several earthquakes in the 1980s, none of which were accompanied by surface faulting [Stein and Yeats, 1989]. Blind thrust faults are faults at depth occurring under anticlinal folds — since they have only subtle surface expression, their seismogenic potential can only be evaluated by indirect means [Greenwood, 1995]. Blind thrust faults are particularly worrisome because they are hidden, are associated with folded topography in general, including areas of lower and infrequent seismicity, and therefore result in a situation where the potential for an earthquake exists in any area of anticlinal geology, even if there are few or no earthquakes in the historic record. Recent major earthquakes of this type have included the 1980 MW 7.3 El Asnam (Algeria), 1988 MW 6.8 Spitak (Armenia), and 1994 MW 6.7 Northridge (California) events. Focal mechanism refers to the direction of slip in an earthquake, and the orientation of the fault on which it occurs. Focal mechanisms are determined from seismograms, and typically displayed on maps as a black and white “beach ball” symbol. This symbol is the projection on a horizontal plane of the lower half of an imaginary, spherical shell (focal sphere) surrounding the earthquake source [USGS, n.d.]. A line is scribed where the fault plane intersects the shell. The beach ball depicts the stress-field orientation at the time of rupture such that the black quadrants contain the tension axis (T), which reflects the minimum compressive stress direction, and the white quadrants contain the pressure axis (P), which reflects the maximum compressive stress direction. For mechanisms calculated from firstmotion directions (as well as some other methods), more than one focal mechanism solution may fit the data equally well, so that there is an ambiguity in identifying the fault plane on which slip occurred from the orthogonal, mathematically equivalent, auxiliary plane. The ambiguity may sometimes be resolved by comparing the two fault-plane orientations to the alignment of small earthquakes and aftershocks. The first three examples describe fault motion that is purely horizontal (strike slip) or vertical (normal or reverse). The oblique-reverse mechanism illustrates that slip may also have components of horizontal and vertical motion. Subduction refers to the plunging of one plate (e.g., the Pacific) beneath another, into the mantle, due to convergent motion, as shown in Figure 4.3. Subduction zones are typically characterized by © 2003 by CRC Press LLC
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volcanism, as a portion of the plate (melting in the lower mantle) re-emerges as volcanic lava. Four types of earthquakes are associated with subduction zones: 1. 2. 3. 4.
Shallow crustal events, in the accretionary wedge Intraplate events, due to plate bending Large interplate events, associated with slippage of one plate past the other Deep Benioff zone events
Subduction occurs along the west coast of South America at the boundary of the Nazca and South American plate, in Central America (boundary of the Cocos and Caribbean plates), in Taiwan and Japan (boundary of the Philippine and Eurasian plates), and in the North American Pacific Northwest (boundary of the Juan de Fuca and North American plates), among other places. Probabilistic methods can be usefully employed to quantify the likelihood of an earthquake’s occurrence. However, at present the earthquake generating process is not understood well enough to reliably predict the times, sizes, and locations of earthquakes with precision. In general, therefore, communities must be prepared for an earthquake to occur at any time.
4.3 Measurement of Earthquakes Earthquakes are complex multidimensional phenomena, the scientific analysis of which requires measurement. Prior to the invention of modern scientific instruments, earthquakes were qualitatively measured by their effect or intensity, which differed from point to point. With the deployment of seismometers, an instrumental quantification of the entire earthquake event — the unique magnitude of the event — became possible. These are still the two most widely used measures of an earthquake, and a number of different scales for each have been developed, which are sometimes confused.2 Engineering design, however, requires measurement of earthquake phenomena in units such as force or displacement. This section defines and discusses each of these measures.
4.3.1 Magnitude An individual earthquake is a unique release of strain energy — quantification of this energy has formed the basis for measuring the earthquake event. Richter [1935] was the first to define earthquake magnitude, as: M L = log A – log Ao
(4.1)
where ML is local magnitude (which Richter only defined for Southern California), A is the maximum trace amplitude in microns recorded on a standard Wood–Anderson short-period torsion seismometer,3 at a site 100 km from the epicenter, log Ao is a standard value as a function of distance, for instruments located at distances other than 100 km and less than 600 km. Subsequently, a number of other magnitudes have been defined, the most important of which are surface wave magnitude MS , body wave magnitude mb , and moment magnitude MW . Due to the fact that ML was only locally defined for California (i.e., for events within about 600 km of the observing stations), surface wave magnitude MS was defined analogously to ML , using teleseismic observations of surface waves of 20-sec period [Richter, 1935]. Magnitude, which is defined on the basis of the amplitude
2 Earthquake magnitude and intensity are analogous to a lightbulb and the light it emits. A particular lightbulb has only one energy level, or wattage (e.g., 100 watts, analogous to an earthquake’s magnitude). Near the lightbulb, the light intensity is very bright (perhaps 100 foot-candles, analogous to MMI IX), while farther away the intensity decreases (e.g., 10 foot-candles, MMI V). A particular earthquake has only one magnitude value, whereas it has many intensity values. 3 The instrument has a natural period of 0.8 sec, critical damping ration 0.8, magnification 2,800.
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of ground displacements, can be related to the total energy in the expanding wave front generated by an earthquake, and thus to the total energy release — an empirical relation by Richter is: log 10 E s = 11.8 + 1.5 M s
(4.2)
where ES is the total energy in ergs.4 Note that 101.5 = 31.6, so that an increase of one magnitude unit is equivalent to 31.6 times more energy release, two magnitude units increase is equivalent to 1000 times more energy, etc. Subsequently, due to the observation that deep-focus earthquakes commonly do not register measurable surface waves with periods near 20 sec, a body wave magnitude mb was defined [Gutenberg and Richter, 1956], which can be related to MS [Darragh et al., 1994]: mb = 2.5 + 0.63 M S
(4.3)
Body wave magnitudes are more commonly used in eastern North America, due to the deeper earthquakes there. A number of other magnitude scales have been developed, most of which tend to saturate — that is, asymptote to an upper bound due to larger earthquakes radiating significant amounts of energy at periods longer than used for determining the magnitude (e.g., for MS , defined by measuring 20-sec surface waves, saturation occurs at about MS > 7.5). More recently, seismic moment has been employed to define a moment magnitude MW [Hanks and Kanamori, 1979; also denoted as boldface M] which is finding increased and widespread use: log M 0 = 1.5 M W + 16.0
(4.4)
where seismic moment M0 (dyne-cm) is defined as [Lomnitz, 1974]: M 0 = µAu
(4.5)
where µ is the material shear modulus, A is the area of fault plane rupture, and u is the mean relative displacement between the two sides of the fault (the averaged fault slip). Comparatively, MW and MS are numerically almost identical up to magnitude 7.5. Figure 4.4 indicates the relationship between moment magnitude and various magnitude scales. For lay communications, it is sometimes customary to speak of great earthquakes, large earthquakes, etc. There is no standard definition for these, but the following is an approximate categorization: Earthquake Magnitude*
Micro Not felt
Small <5
Moderate 5 ~ 6.5
Large 6.5 ~ 8
Great >8
* Not specifically defined.
From the foregoing discussion, it can be seen that magnitude and energy are related to fault rupture length and slip. Slemmons [1977] and Bonilla et al. [1984] have determined statistical relations between these parameters for worldwide and regional data sets, aggregated and segregated by type of faulting (normal, reverse, strike-slip). Bonilla et al.’s worldwide results for all types of faults are: M S = 6.04 + 0.708 log 10 L
s = .306
(4.6)
log 10 L = −2.77 + 0.619 M S
s = .286
(4.7)
4 Richter [1958] gives 11.4 for the constant term, rather than 11.8, which is based on subsequent work — the uncertainty in the data makes this difference inconsequential.
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W
MS
~
M
9
M
MJMA
8
mB ML
MAGNITUDE
7
mb
6
5
S
M
L
M
4
3
2 2
3
4
5
6
7
8
9
10
MOMENT MAGNITUDE
FIGURE 4.4 Relationship between moment magnitude and various magnitude scales. (From Campbell, K.W. (1985). Earthquake Spectra, 1, 759–804. With permission.)
M S = 6.95 + 0.723 log 10 d
s = .323
(4.8)
log 10 d = −3.58 + 0.550 M S
s = .282
(4.9)
which indicates for example that, for MS = 7, the average fault rupture length is about 36 km (and the average displacement is about 1.86 m), and s indicates standard deviation. Conversely, a fault of 100 km length is capable of about a MS = 7.55 event. More recently, Wells and Coppersmith [1994] have performed an extensive analysis of a dataset of 421 earthquakes — their results are presented in Table 4.1.
4.3.2 Intensity In general, seismic intensity is a metric of the effect, or the strength, of an earthquake hazard at a specific location. While the term can be generically applied to engineering measures such as peak ground acceleration, it is usually reserved for qualitative measures of location-specific earthquake effects, based on observed human behavior and structural damage. Numerous intensity scales developed in pre-instrumental times — the most common in use today are the Modified Mercalli Intensity (MMI) [Wood and Neumann, 1931], Rossi–Forel (R–F), Medvedev–Sponheur–Karnik [MSK-64, 1981], European Macroseismic Scale [EMS-98, 1998], and Japan Meteorological Agency (JMA) [Kanai, 1983] scales. 5 Note that L = g(M ) should not be inverted to solve for M = f(L), as a regression for y = f(x) is different than S S a regression for x = g(y).
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M = a + b * log(SRL)
log(SRL) = a + b * M
M = a + b * log(RLD)
log(RLD) = a + b * M
M = a + b * log(RW)
log(RW) = a + b * M
M = a + b * log(RA)
log(RA) = a + b * M
Slip Typeb SS R N All SS R N All SS R N All SS R N All SS R N All SS R N All SS R N All SS R N All
43 19 15 77 43 19 15 77 93 50 24 167 93 50 24 167 87 43 23 153 87 43 23 153 83 43 22 148 83 43 22 148
a (sa)
b (sb)
Standard Deviation s
5.16(0.13) 5.00(0.22) 4.86(0.34) 5.08(0.10) –3.55(0.37) –2.86(0.55) –2.01(0.65) –3.22(0.27) 4.33(0.06) 4.49(0.11) 4.34(0.23) 4.38(0.06) –2.57(0.12) –2.42(0.21) –1.88(0.37) –2.44(0.11) 3.80(0.17) 4.37(0.16) 4.04(0.29) 4.06(0.11) –0.76(0.12) –1.61(0.20) –1.14(0.28) –1.01(0.10) 3.98(0.07) 4.33(0.12) 3.93(0.23) 4.07(0.06) –3.42(0.18) –3.99(0.36) –2.87(0.50) –3.49(0.16)
1.12(0.08) 1.22(0.16) 1.32(0.26) 1.16(0.07) 0.74(0.05) 0.63(0.08) 0.50(0.10) 0.69(0.04) 1.49(0.05) 1.49(0.09) 1.54(0.18) 1.49(0.04) 0.62(0.02) 0.58(0.03) 0.50(0.06) 0.59(0.02) 2.59(0.18) 1.95(0.15) 2.11(0.28) 2.25(0.12) 0.27(0.02) 0.41(0.03) 0.35(0.05) 0.32(0.02) 1.02(0.03) 0.90(0.05) 1.02(0.10) 0.98(0.03) 0.90(0.03) 0.98(0.06) 0.82(0.08) 0.91(0.03)
0.28 0.28 0.34 0.28 0.23 0.20 0.21 0.22 0.24 0.26 0.31 0.26 0.15 0.16 0.17 0.16 0.45 0.32 0.31 0.41 0.14 0.15 0.12 0.15 0.23 0.25 0.25 0.24 0.22 0.26 0.22 0.24
Coefficients and Standard Errors
Correlation Coefficient r
Magnitude Range
Length/Width Range (km)
0.91 0.88 0.81 0.89 0.91 0.88 0.81 0.89 0.96 0.93 0.88 0.94 0.96 0.93 0.88 0.94 0.84 0.90 0.86 0.84 0.84 0.90 0.86 0.84 0.96 0.94 0.92 0.95 0.96 0.94 0.92 0.95
5.6 to 8.1 5.4 to 7.4 5.2 to 7.3 5.2 to 8.1 5.6 to 8.1 5.4 to 7.4 5.2 to 7.3 5.2 to 8.1 4.8 to 8.1 4.8 to 7.6 5.2 to 7.3 4.8 to 8.1 4.8 to 8.1 4.8 to 7.6 5.2 to 7.3 4.8 to 8.1 4.8 to 8.1 4.8 to 7.6 5.2 to 7.3 4.8 to 8.1 4.8 to 8.1 4.8 to 7.6 5.2 to 7.3 4.8 to 8.1 4.8 to 7.9 4.8 to 7.6 5.2 to 7.3 4.8 to 7.9 4.8 to 7.9 4.8 to 7.6 5.2 to 7.3 4.8 to 7.9
1.3 to 432 3.3 to 85 2.5 to 41 1.3 to 432 1.3 to 432 3.3 to 85 2.5 to 41 1.3 to 432 1.5 to 350 1.1 to 80 3.8 to 63 1.1 to 350 1.5 to 350 1.1 to 80 3.8 to 63 1.1 to 350 1.5 to 350 1.1 to 80 3.8 to 63 1.1 to 350 1.5 to 350 1.1 to 80 3.8 to 63 1.1 to 350 3 to 5,184 2.2 to 2,400 19 to 900 2.2 to 5,184 3 to 5,184 2.2 to 2,400 19 to 900 2.2 to 5,184
a
SRL — surface rupture length (km); RLD — subsurface rupture length (km); RW — downdip rupture width (km): RA — rupture area (km2). SS — strike slip; R — reverse; N — normal. Source: From Wells, D.L. and Coopersmith, K.J. (1994). “Empirical Relationships Among Magnitude, Rupture Length, Rupture Width, Rupture Area and Surface Displacements,” Bull. Seismol. Soc. Am., 84(4), 974–1002. With permission. b
4-9
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0068_C04_fm Page 9 Tuesday, August 13, 2002 8:21 AM
Equationa
Number of Events
Earthquakes: Seismogenesis, Measurement, and Distribution
TABLE 4.1A Regressions of Rupture Length, Rupture Width, Rupture Area, and Moment Magnitude
Equationa M = a + b * log(MD)
log(MD) = a + b * M
M = a + b * log(AD)
log(AD) = a + b * M
SS {Rc N All SS {R N All SS {R N All SS {R N All
43 21 16 80 43 21 16 80 29 15 12 56 29 15 12 56
a(sa)
b(sb)
Standard Deviation s
6.81(0.05) 6.52(0.11) 6.61(0.09) 6.69(0.04) –7.03(0.55) –1.84(1.14) –5.90(1.18) –5.46(0.51) 7.04(0.05) 6.64(0.16) 6.78(0.12) 6.93(0.05) –6.32(0.61) –0.74(1.40) –4.45(1.59) –4.80(0.57)
0.78(0.06) 0.44(0.26) 0.71(0.15) 0.74(0.07) 1.03(0.08) 0.29(0.17) 0.89(0.18) 0.82(0.08) 0.89(0.09) 0.13(0.36) 0.65(0.25) 0.82(0.10) 0.90(0.09) 0.08(0.21) 0.63(0.24) 0.69(0.08)
0.29 0.52 0.34 0.40 0.34 0.42 0.38 0.42 0.28 0.50 0.33 0.39 0.28 0.38 0.33 0.36
Coefficients and Standard Errors
Correlation Coefficient r
Magnitude Range
Displacement Range (km)
0.90 0.36 0.80 0.78 0.90 0.36 0.80 0.78 0.89 0.10 0.64 0.75 0.89 0.10 0.64 0.75
5.6 to 8.1 5.4 to 7.4 5.2 to 7.3 5.2 to 8.1 5.6 to 8.1 5.4 to 7.4 5.2 to 7.3 5.2 to 8.1 5.6 to 8.1 5.8 to 7.4 6.0 to 7.3 5.6 to 8.1 5.6 to 8.1 5.8 to 7.4 6.0 to 7.3 5.6 to 8.1
0.01 to 14.6 0.11 to 6.5} 0.06 to 6.1 0.01 to 14.6 0.01 to 14.6 0.11 to 6.5} 0.06 to 6.1 0.01 to 14.6 0.05 to 8.0 0.06 to 1.5} 0.08 to 2.1 0.05 to 8.0 0.05 to 8.0 0.06 to 1.5} 0.08 to 2.1 0.05 to 8.0
MD — maximum displacement (m); AD — average displacement (M). SS — strike slip; R — reverse; N — normal. c Regressions for reverse-slip relationships shown in italics and brackets are not significant at a 95% probability level. Source: From Wells, D.L. and Coopersmith, K.J. (1994). “Empirical Relationships Among Magnitude, Rupture Length, Rupture Width, Rupture Area and Surface Displacements,” Bull. Seismol. Soc. Am., 84(4), 974–1002. With permission. b
© 2003 by CRC Press LLC
Earthquake Engineering Handbook
a
Slip Typeb
Number of Events
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TABLE 4.1B Regressions of Displacement and Moment Magnitude
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4-11
MMI is a scale defining the level of shaking at specific sites on a scale of I to XII (MMI is expressed in Roman numerals, to denote its approximate nature). For example, moderate shaking that causes few instances of fallen plaster or cracks in chimneys constitutes MMI VI. It is difficult to find a reliable relationship between magnitude, which is a description of the earthquake’s total energy level, and intensity, which is a subjective description of the level of shaking of the earthquake at specific sites, because shaking severity can vary with building type, design and construction practices, soil type, and distance from the event. More recently, the European Seismological Commission has completed a detailed study to define the EMS–98. As the Commission states: … the basis for establishing the EMS was the … MSK scale, which preceded it … one of a family of intensity scales which originated with the widely used simple ten degree scale by Rossi and Forel; this was revised by Mercalli, subsequently expanded by Cancani to twelve degrees, and then defined in a very full way by Sieberg as the Mercalli–Cancani–Sieberg (MCS) scale. It is this scale which forms the starting point not only for the MSK/EM–98 scale, but also for the numerous versions of the “Modified Mercalli” scale. Most of these twelve-degree scales are roughly equivalent to one another in actual values. They vary in the degree of sophistication employed in the formulation. The major difference between the EMS–98 and other intensity scales is in the detail with which different terms used are defined at the outset, in particular, building types, damage grades, and quantities, and these are now considered individually. Also, the EMS is the first intensity scale to be illustrated. Drawings show graphically precisely what is meant by the different damage grades, and example photographs … can be used in the field for comparison with actual cases of damaged structures. The use of these illustrations is intended to improve the standardization between individual practitioners in the use of the scale [European Seismological Commission, 1998]. As the Commission notes, the use of illustrations and photographs to more clearly and precisely identify seismic intensity is a significant improvement. Figure 4.5 shows an example of this use of damage photographs. Note that MMI X is the maximum considered physically possible due to “mere” shaking, and that MMI XI and XII are considered due more to permanent ground deformations and other geologic effects than to shaking. Other intensity scales are defined analogously (see Table 4.2, which also contains an approximate conversion from MMI to acceleration a [peak ground amplitude, PGA, in cm/sec2 or gals]). The conversion is due to Richter [1935] (other conversions are also available: Trifunac and Brady, 1975; Murphy and O’Brien, 1977): log a = MMI 3 −1 2
(4.10)
which indicates, for example, that MMI VII is approximately equivalent to a PGA of 68 gals. Intensity maps are produced as a result of detailed investigation of the type of effects tabulated in Table 4.3, as shown in Figure 4.6 for the 1994 MW 6.7 Northridge earthquake. Correlations have been developed between the area of various MMI intensities and earthquake magnitude, which are of value for seismological and planning purposes. Figure 4.7, for example, correlates Afelt vs. MW . For pre-instrumental historical earthquakes, Afelt can be estimated from newspapers and other reports, which then can be used to estimate the event magnitude, thus supplementing the seismicity catalog. This technique has been especially useful in regions with a long historical record [Woo and Muirwood, 1984; Ambrayses and Melville, 1982].
4.3.3 Time History Sensitive strong motion seismometers have been available since the 1930s, and record actual ground motions specific to their location, as shown in Figure 4.8. Typically, the ground motion records, termed seismographs or time histories, have recorded acceleration (these records are termed accelerograms), © 2003 by CRC Press LLC
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Earthquake Engineering Handbook
TYPE OF STRUCTURE
RC frame
EARTHQUAKE/SITE
Spitak, Armenia 1988 / Leninakan
GRADE OF DAMAGE
1
2
3
4
5 X
Comment: This is obviously very heavy structural damage and near-total collapse, and therefore damage grade 5. Note: This RC frame structure incorporating a certain level of earthquake resistant design was adversely affected by the insufficient coupling between beams and columns. This building type is a typical example where one should assign a low vulnerability class, in this case B, which represents an exceptionally low class for this type of structure. FIGURE 4.5
Example illustration from EMS-98.
for many years in analog form on photographic film and, more recently, digitally. Analog records required considerable effort for correction due to instrumental drift, before they could be used. Time histories theoretically contain complete information about the motion at the instrumental location, recording three traces or orthogonal records (two horizontal and one vertical). Time histories (i.e., the earthquake motion at the site) can differ dramatically in duration, frequency content, and amplitude. The maximum amplitude of recorded acceleration is termed the peak ground acceleration (PGA) (also termed the ZPA, or zero period acceleration) — peak ground velocity (PGV) and peak ground displacement (PGD) are the maximum respective amplitudes of velocity and displacement. Acceleration is normally recorded, with velocity and displacement being determined by integration — however, actual velocity and displacement meters are also deployed, to a lesser extent. Acceleration can be expressed in units of cm/sec2 (termed gals), but is often also expressed in terms of the fraction or percent of the acceleration of gravity (980.66 gals, termed 1 g). Velocity is expressed in cm/sec (termed kine). Recent earthquakes (1994 Northridge, MW 6.7 and 1995 Hanshin or Kobe, MW 6.9) have recorded PGAs of about 0.8 g and PGVs of about 100 kine — almost 2 g was recorded in the 1992 Cape Mendocino earthquake.6
6
While almost 2 g was recorded in the Cape Mendocino event, the portion of the record was a very narrow spike and, while considered genuine, is not considered to be a significant acceleration for structures. © 2003 by CRC Press LLC
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Earthquakes: Seismogenesis, Measurement, and Distribution
TABLE 4.2
Comparison of Modified Mercalli (MMI) and Other Intensity Scales
a gals
MMI Modified Mercalli
R–F Rossi–Forel
MSK Medvedev–Sponheur–Karnik
0.7 1.5 3 7 15 32 68 147 316 681 (1468)* (3162)*
I II III IV V VI VII VIII IX X XI XII
I I–II III IV–V V–VI VI–VII VIII– VIII+ to IX– IX+ X — —
I II III IV V VI VII VIII IX X XI XII
JMA Japan Meteorological Agency 0 I II II–III III IV IV–V V V–VI VI VII
* Note: a values provided for reference only. MMI > X are due more to geologic effects.
TABLE 4.3 I II III IV
V
VI VII
VIII
IX
X
XI XII
Modified Mercalli Intensity Scale of 1931
Not felt, except by a very few under especially favorable circumstances. Felt only by a few persons at rest, especially on upper floors of buildings. Delicately suspended objects may swing. Felt quite noticeably indoors, especially on upper floors of buildings, but many people do not recognize it as an earthquake. Standing motor cars may rock slightly. Vibration like passing truck. Duration estimated. During the day felt indoors by many, outdoors by few. At night some awakened. Dishes, windows, and doors disturbed; walls make creaking sound. Sensation like heavy truck striking building. Standing motorcars rock noticeably. Felt by nearly everyone; many awakened. Some dishes, windows, etc., broken; a few instances of cracked plaster; unstable objects overturned. Disturbance of trees, poles, and other tall objects sometimes noticed. Pendulum clocks may stop. Felt by all; many frightened and run outdoors. Some heavy furniture moved; a few instances of fallen plaster or damaged chimneys. Damage slight. Everybody runs outdoors. Damage negligible in buildings of good design and construction slight to moderate in well-built ordinary structures; considerable in poorly built or badly designed structures. Some chimneys broken. Noticed by persons driving motor cars. Damage slight in specially designed structures; considerable in ordinary substantial buildings, with partial collapse; great in poorly built structures. Panel walls thrown out of frame structures. Fall of chimneys, factory stacks, columns, monuments, walls. Heavy furniture overturned. Sand and mud ejected in small amounts. Changes in well water. Persons driving motor cars disturbed. Damage considerable in specially designed structures; well-designed frame structures thrown out of plumb; great in substantial buildings, with partial collapse. Buildings shifted off foundations. Ground cracked conspicuously. Underground pipes broken. Some well-built wooden structures destroyed; most masonry and frame structures destroyed with foundations; ground badly cracked. Rails bent. Landslides considerable from river banks and steep slopes. Shifted sand and mud. Water splashed over banks. Few, if any (masonry), structures remain standing. Bridges destroyed. Broad fissures in ground. Underground pipelines completely out of service. Earth slumps and land slips in soft ground. Rails bent greatly. Damage total. Waves seen on ground surfaces. Lines of sight and level distorted. Objects thrown upward into the air.
Source: After Wood, H. O. and Neumann, F. (1931). Bull. Seismol. Soc. Am., 21, 277–283.
4.3.4 Elastic Response Spectra If a single-degree-of-freedom (SDOF) mass is subjected to a time history of ground (i.e., base) motion similar to that shown in Figure 4.8, the mass or elastic structural response can be readily calculated as a function of time, generating a structural response time history, as shown in Figure 4.9 for several oscillators with differing natural periods. The response time history can be calculated by direct integration of equation (1) in the time domain, or by solution of the Duhamel integral [Clough and Penzien, 1975]. © 2003 by CRC Press LLC
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Earthquake Engineering Handbook
FIGURE 4.6 MMI maps, 1994 MW 6.7 Northridge earthquake (From Dewey, J.W. et al. (1995). In The Northridge, California Earthquake of 17 January 1994, Woods, M.C. and Seiple, W.R., eds., California Department of Conservation, Division of Mines and Geology, Special Publ. 116, 39–46. With permission.)
FIGURE 4.7 Log afelt (km2) vs. MW . (From Hanks, T.C. and Johnston, A.C. (1992). Bull. Seismol. Soc. Am., 82, 1–23. With permission.)
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4-15
FIGURE 4.8 Typical earthquake accelerograms. (From Darragh, R.B., Huang, M.J., and Shakal, A.F., Proc. Fifth U.S. Conf. Earthquake Eng., 3, 99–108, 1994.)
However, this is time-consuming, and the elastic response is more typically calculated in the frequency domain: v (t ) =
1 2π
∫
∞
ϖ =− ∞
Η (ϖ) c (ϖ) exp (iϖt ) dϖ
(4.11)
where ν(t) is the elastic structural displacement response time history, ϖ is frequency Η (ϖ) = c (ϖ) =
1 is the complex frequency response function − ϖ 2m + ic + k
∫
∞
ϖ =− ∞
p (t ) exp (−iϖt ) dt
is the Fourier transform of the input motion (i.e., the Fourier transform of the ground motion time history), which takes advantage of computational efficiency using the fast Fourier transform [Clough and Penzien, 1975].
For design purposes, it is often sufficient to know only the maximum amplitude of the response time history. If the natural period of the SDOF is varied across a spectrum of engineering interest (typically, for natural periods from .03 to 3 or more seconds, or frequencies of 0.3 to 30+ Hz), then the plot of these maximum amplitudes is termed a response spectrum. Figure 4.9 illustrates this process, resulting in Sd , the displacement response spectrum, while Figure 4.10 shows (a) Sd , the displacement response spectrum, (b) Sv , the velocity response spectrum (also denoted PSV, the pseudo spectral velocity, pseudo to emphasize that this spectrum is not exactly the same as the relative velocity response spectrum [Hudson, 1979]), and (c) Sa , the acceleration response spectrum. Note that: Sv =
2π S = ϖSd T d
(4.12)
and 2
Sa =
© 2003 by CRC Press LLC
2π 2π Sv = ϖSv = Sd = ϖ 2 Sd T T
(4.13)
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GROUND ACCELERATION, üg (t)
Earthquake Engineering Handbook
EL CENTR0, SOOE COMPONENT, MAY 18, 1940
−0.4g 0 −0.4g
0
10
20
30
TIME, sec 10 Umax = 2.48 in. 0
DEFORMATION, u, in.
T = 0.5 sec ξ = 0.02
T = 1 sec ξ = 0.02
−10 10 0 Umax = 6.61 in. −10 10
0
T = 2 sec ξ = 0.02
Umax = 8.84 in. −10
0
10
20
30
TIME, sec 20 DEFORMATION (OR DISPLACEMENT) RESPONSE SPECTRUM ξ = 2 PERCENT
Sd, in.
15 10 5 0 0
1
2
3
NATURAL VIBRATION PERIOD, T, sec
FIGURE 4.9 Computation of deformation (or displacement) response spectrum. (From Chopra, A.K., Dynamics of Structures: A Primer, Earthquake Engineering Research Institute, Oakland, CA, 1981. With permission.)
Response spectra form the basis for much modern earthquake engineering structural analysis and design. They are readily calculated if the ground motion is known. For design purposes, however, response spectra must be estimated — this process is discussed in another chapter. Response spectra may be plotted in any of several ways, as shown in Figure 4.10 with arithmetic axes, and in Figure 4.11, where the velocity response spectrum is plotted on tripartite logarithmic axes, which equally enables reading of displacement and acceleration response. Response spectra are most normally presented for 5% of critical damping. While actual response spectra are irregular in shape, they generally have a concave-down arch or trapezoidal shape, when plotted on tripartite log paper. Newmark observed that response spectra tend to be characterized by three regions: (1) a region of constant acceleration, in the high-frequency portion © 2003 by CRC Press LLC
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Earthquakes: Seismogenesis, Measurement, and Distribution
20
Sd, in.
15
10
(a)
5
0 50
Sv, in./sec
40 30 (b) 20 10 0 1.5
Sa, g
1.0 (c) 0.5
0 0
1
2
3
NATURAL VIBRATION PERIOD, T, sec FIGURE 4.10 Response spectra. (From Chopra, A.K., Dynamics of Structures: A Primer, Earthquake Engineering Research Institute, Oakland, CA, 1981. With permission.)
of the spectra; (2) constant displacement, at low frequencies; and (3) constant velocity, at intermediate frequencies, as shown in Figure 4.12. If a spectrum amplification factor is defined as the ratio of the spectral parameter to the ground motion parameter (where parameter indicates acceleration, velocity, or displacement), then response spectra can be estimated from the data in Table 4.4, provided estimates of the ground motion parameters are available. An example spectrum using these data is given in Figure 4.12. A standardized response spectrum is provided in the Uniform Building Code [IBC, 1997]. The spectrum is a smoothed average of normalized 5% damped spectra obtained from actual ground motion records grouped by subsurface soil conditions at the location of the recording instrument, and is applicable for earthquakes characteristic of those that occur in California [SEAOC, 1988]. This normalized shape may be employed to determine a response spectrum appropriate for the soil conditions. Note that © 2003 by CRC Press LLC
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Earthquake Engineering Handbook
400
n. ,i d
S
40
20
0
100 80
1 8 0
0 10 80
6 4
40
40
60
60
60
40
2
20
.8
1
10 8
20
20
.6
6
.4
4
10 8
1
.1 .0 .0 8 .0 6 4
2
.2
10 8
.8
6
.6
4
.0 .0 1 .0 08 .0 06 04
.0
.2 .1 8 .0 6
.0
.0 .0 01 0 .0 08 .0 006 00 4
.0
1 .0 8 0 .0 6 0 04 .0 .0
.4
2
02
4
.0 2 .0
1 .8
6
2
.4
4
2
200
40
20
,g Sa
100 80
0 80 00 6 0
200
1 8 00 60 0
400
1 .8 .6 .4
02 .0
.2
.2
.1
.04 .06 .08 .1
.2
.4
.6 .8 1
2
4
6
8 10
20
.1
FIGURE 4.11 Response spectra, tri-partite plot (El Centro S 0º E component). (From Chopra, A.K. (1981). Dynamics of Structures: A Primer, Earthquake Engineering Research Institute, Oakland, CA. With permission.)
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Earthquakes: Seismogenesis, Measurement, and Distribution
500 ,g
50
O N AT I 5
ER EL C AC 1
2
5 0.
5
2 1
0.
5
2
0.
20
05
2
0.
1
0. 0.
0.
1
10
5
00
0.
01
0.
0.
02
01
0.
~ 8 Hz
0.
5
02
05
0.
VELOCITY, cm/sec
10
MAXIMUM GROUND MOTION
cm T,
A 50
20
10
EN EM
20
AC
D
50
PL
100
0
IS
V
10
D
200
2
00
0.
2 1 0.1
A = 0.5 x 2.71 = 1.35 g V = 61 x 2.30 = 140 cm/sec D = 45 x 2.01 = 90 cm ~ 33 Hz
0.2
0.5
1
2
5
10
20
50
100
FREQUENCY, Hz FIGURE 4.12 Idealized elastic design spectrum, horizontal motion (ZPA = 0.5g, 5% damping, one sigma cumulative probability). (After Newmark, N.M. and Hall, W.J. (1982). Earthquake Spectra and Design, Earthquake Engineering Research Institute, Oakland, CA. With permission.)
the maximum amplification factor is 2.5, over a period range approximately 0.15 sec to 0.4 ~ 0.9 sec, depending on the soil conditions (Figure 4.13).
4.3.5 Inelastic Response Spectra While the foregoing discussion has been for elastic response spectra, most structures are not expected, or even designed, to remain elastic under strong ground motions. Rather, structures are expected to enter the inelastic region — the extent to which they behave inelastically can be defined by the ductility factor, µ: µ=
um uy
(4.14)
where um is the actual displacement of the mass under actual ground motions and uy is the displacement at yield (i.e., that displacement which defines the extreme of elastic behavior). Inelastic response spectra can be calculated in the time domain by direct integration, analogous to elastic response spectra but with the structural stiffness as a nonlinear function of displacement, k = k(u). If elastoplastic behavior is assumed, then elastic response spectra can be readily modified to reflect inelastic behavior [Newmark and Hall, 1982], on the basis that at low frequencies (<0.3 Hz) displacements are the same, at high frequencies (>33 Hz) accelerations are equal, and at intermediate frequencies the absorbed energy is preserved. Actual construction of inelastic response spectra on this basis is shown in Figure 4.14, where DVAAo is the elastic spectrum, which is reduced to D′ and V′ by the ratio of 1/µ for frequencies less than 2 Hz, and by the ratio of 1/(2 µ – 1)1/2 between 2 and 8 Hz. Above 33 Hz there is no reduction. The result is the inelastic acceleration spectrum (D′V′A′Ao), while A″Ao ′ is the inelastic displacement spectrum. A specific example, for ZPA = 0.16 g, damping = 5% of critical, and µ = 3, is shown in Figure 4.15.
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TABLE 4.4
Spectrum Amplification Factors for Horizontal Elastic Response One Sigma (84.1%)
Damping, % Critical 0.5 1 2 3 5 7 10 20
Median (50%)
A
V
D
A
V
D
5.10 4.38 3.66 3.24 2.71 2.36 1.99 1.26
3.84 3.38 2.92 2.64 2.30 2.08 1.84 1.37
3.04 2.73 2.42 2.24 2.01 1.85 1.69 1.38
3.68 3.21 2.74 2.46 2.12 1.89 1.64 1.17
2.59 2.31 2.03 1.86 1.65 1.51 1.37 1.08
2.01 1.82 1.63 1.52 1.39 1.29 1.20 1.01
Source: Newmark, N.M. and Hall, W.J. (1982). Earthquake Spectra and Design, Earthquake Engineering Research Institute, Oakland, CA. With permission.
SPECTRAL ACCELERATION EFFECTIVE PEAK GROUND ACCELERATION
4 SOFT TO MEDIUM CLAY AND SANDS (SOIL TYPE 3) 3 DEEP COHESIONLESS OR STIFF CLAY SOILS (SOIL TYPE 2) ROCK AND STIFF SOILS (SOIL TYPE 1)
2
1
0 0
0.5
1.0
1.5
2.0
2.5
3
PERIOD, T (Seconds)
FIGURE 4.13
Normalized response spectra shapes. (From IBC, Uniform Building Code, 1994.)
4.3.6 Response Spectrum Intensity and Other Measures While the elastic response spectrum cannot directly define damage to a structure (which is essentially inelastic deformation) it captures in one curve the amount of elastic deformation for a wide variety of structural periods, and therefore may be a good overall measure of ground motion intensity. On this basis, Housner defined a response spectrum intensity as the integral of the elastic response spectrum velocity over the period range 0.1 to 2.5 sec: 2.5
SI (h ) =
∫
T = 0.1
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Sv (h, T ) dT
(4.15)
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0.3 Hz
2 Hz
8 Hz
Elastic Spectrum Inelastic Spectrum
Inelastic Displacement Spectrum
V
Elastic Spectrum for Acceleration and Displacement
A'' rv
D
A V' ra
rd
D'
A'
Ao'
Inelastic Acceleration Spectrum
Reduction Factors µ rd = rv = 1/µ
ra =
1 2 µ −1
Ao = ZPA 33 Hz
FIGURE 4.14 Inelastic response spectra for earthquakes. (After Newmark, N.M. and Hall, W.J. (1982). Earthquake Spectra and Design, Earthquake Engineering Research Institute, Oakland, CA. With permission.)
where h = damping (as a percentage of ccrit). A number of other measures exist, including Fourier amplitude spectrum [Clough and Penzien, 1975] and Arias intensity [Arias, 1970]: τ
π 2 IA = a (t ) dt g
∫
(4.16)
0
4.3.7 Engineering Intensity Scale Blume [1970] defined a measure of earthquake intensity, the engineering intensity scale (EIS), which has been relatively underutilized but is worth noting as it attempts to combine the engineering benefits of response spectra with the simplicity of qualitative intensity scales, such as MMI. The EIS is simply a 10 × 9 matrix which characterizes a 5% damped elastic response spectrum, Figure 4.16. Nine period bands (0.01–0.1, –0.2, –0.4, –0.6, –1.0, –2.0, –4.0, –7.0, –10.0 sec), and ten Sv levels (0.01–0.1, –1.0, –4.0, –10.0, –30.0, –60.0, –100, –300, –1000 kine) are defined. As can be seen, since the response spectrum for the example ground motion in period band II (0.1–0.2 sec) is predominantly in Sv level 5 (10–30 kine), it is assigned EIS 5 (X is assigned where the response spectrum does not cross a period band). In this manner, a nine-digit EIS can be assigned to a ground motion (in the example, it is X56,777,76X), which can be reduced to three digits (5,7,6) by averaging, or even to one digit (6, for this example). Numerically, single-digit EIS values tend to be a unit or so lower than the equivalent MMI intensity value.
4.4 Global Distribution of Earthquakes This section discusses and characterizes the nature and distribution of global seismicity.
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20
50
10
ELASTIC RESPONSE
2
,g N
AT I
EL ER
1
C AC
5 0.
1 0.
1
ACCELERATION FOR µ = 3
5
0.
2
0.
5
0. 1
2
05 0.
05
0. 0. 02
02
0.
01
01
0.
0.
PL
00
IS
2 1
i T, n.
0.5
1
2
5
10
20
00
EN
1 05
0.2
00
EM
00
0.1 0.1
0.
2
AC
00
0. 0. 00
0.
0.2
5
5
D
00
0.
0.5
0.
1
0.
VELOCITY, in./sec
O
5
20 5 2
MAXIMUM GROUND MOTIONS
10
10
DISPLACEMENT FOR µ = 3
20
50
FREQUENCY, Hz FIGURE 4.15 Example inelastic response spectra. (After Newmark, N.M. and Hall, W.J. (1982). Earthquake Spectra and Design, Earthquake Engineering Research Institute, Oakland, CA. With permission.)
4.4.1 Global Overview It is evident that some parts of the globe experience more and larger earthquakes than others. The two major regions of seismicity are the circum-Pacific Ring of Fire, and the Trans-Alpide belt, extending from the western Mediterranean through the Middle East and the northern India subcontinent to Indonesia. The Pacific plate is created at its South Pacific extensional boundary — its motion is generally northwestward, resulting in relative strike-slip motion in California and New Zealand (with, however, a compressive component), and major compression and subduction in Alaska, the Aleutians, Kuriles, and northern Japan. Subduction also occurs along the west coast of South America at the boundary of the Nazca and South American plates, in Central America (boundary of the Cocos and Caribbean plates), in Taiwan and Japan (boundary of the Philippine and Eurasian plates), and in the North American Pacific Northwest (boundary of the Juan de Fuca and North American plates). Seismicity in the Trans-Alpide seismic belt is basically due to the relative motions of the African and Australia plates colliding and subducting with the Eurasian plate. Pacheco and Sykes [1992] compiled a catalog of all large shallow earthquakes for the period 1900 to 1989, which they showed to be complete and uniform for the period, for events Ms > 7.0. For the more than 800 events, approximately 85% of seismic moment release occurs at subduction zones, and more than 95% is produced by shallow, plate-boundary earthquakes. It is interesting to note that the great Chile earthquake of 1960, which ruptured over 800 km of plate boundary, accounted for 30% of the total moment released in the period 1900 to 1989. Table 4.5 presents the events with seismic moment larger
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1000.0 Band:
I
II
III
IV
V
VI
VII VIII IX 9
9
e lut bso , S ag A n o ud atio Pse celer c 8 A .1 g 0
300.0
Pseudo Relative Response Velocity, Sv – CM/SEC.
8 100.0 7 60.0 6 *30.0 5
7
7
R
7
7 D elativ is e 1 pla
7
6 El Centro, 1940 N/S Component
6
6
.0 ceme cm nt, S
d
X 5
00
1g
.0 5 0
10.0 4
X
4 10.0 c
m
4.0
g
01
0.0
3
3 1.0
1.0
cm
2
2
1g
00
0.0
0.1 0.1
1
1
0.01 0.01 Damping 5%
cm
0.1
0.2 0.4 0.6 1.0 Period In Seconds
2.0
4.0
7.010.0
FIGURE 4.16 Engineering intensity scale matrix with example. (From Blume, J.A., Bull. Seismol. Soc. Am., 60, 217–229, 1970. With permission.)
than 50 · 1020 dyne cm, and also (Table 4.5B) selected other events of interest, such as the 1906 San Francisco and 1923 Tokyo events.
4.4.2 Pacific Rim This section discusses seismicity around the Pacific Rim. While several large nations (e.g., the United States, Canada, China) border on the Pacific Rim but also extend into other tectonic regimes, they will be discussed in this section, since much of their seismicity is in their regions bordering on the Pacific Rim. This discussion begins at the north of the Pacific Rim, and traverses it in a clockwise fashion.
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TABLE 4.5A Shallow Earthquakes 1900–1989, Mo > 50 · 1020 dyne cm Yr
M
D
hrmn
lat
lon
Mo*
1960 1964 1957 1952 1950 1923 1906 1918 1922 1965 1957 1950 1906 1963 1917 1923 1963 1906 1905 1952 1938 1964 1905 1919 1938 1963
May Mar Mar Nov Aug Feb Jan Sep Nov Feb Mar Aug Jan Oct Jun Feb Oct Aug Jul Nov Feb Mar Jul Apr Nov Oct
22 28 9 4 15 3 31 7 11 4 9 15 31 13 26 3 13 17 9 4 1 28 23 30 10 13
1911 336 1422 1658 1409 1601 1536 1716 432 501 1422 1409 1536 517 549 1601 517 40 940 1658 1904 336 246 717 2018 517
–38.2 61.1 51.63 52.75 28.7 54 1 45.5 –28.5 51.3 51.63 28.7 1 44.9 –15.5 54 44.9 –33 49 52.75 –5.05 61.1 49 –19 55.48 44.9
–73.5 –147.6 –175.4 159.5 96.6 161 –81.3 151.5 –70 178.6 –175.4 96.6 –81.3 149.6 –173 161 149.6 –72 99 159.5 131.5 –147.6 97 –172.5 –158.4 149.6
Mw
Region
2700 9.55 South Chile 750 9.18 Central Alaska 400 9.00 Central Aleutians 350 8.96 Kamchatka 210 8.81 Tibet 200 8.80 Kamchatka 140 8.70 Colombia–Ecuador 140 8.70 South Kurils 140 8.70 Central Chile 140 8.70 Central Aleutians 100 8.60 Central Aleutians 95 8.59 Tibet 80 8.54 Colombia-Ecuador 75 8.52 South Kurils 70 8.50 Tonga Islands 70 8.50 Kamchatka 67 8.48 South Kurils 66 8.48 Central Chile 55 8.43 Altai 54.85 8.43 Kamchatka 52 8.41 Banda Sea 51 8.41 Central Alaska 50 8.40 Altai 50 8.40 Tonga Islands 50 8.40 Eastern Aleutians 50 8.40 South Kurils 8997 = Sum Mo All Large Shallow Earthquakes 1900–1989 30% = Chile EQ%
* Mo in 1020 dyne-cm. Source: Pacheco, J.F. and Sykes, L.R. (1992). Bull. Seismol. Soc. Am., 82, 1306–1349. With permission.
TABLE 4.5B Selected Earthquakes 1900–1989 Yr
M
D
hrmn
lat
long
Mo*
Mw
Region
1906 1906 1906 1906 1906 1923 1927 1933 1944 1946 1948 1949 1949 1952 1960 1964 1968 1976 1976 1977 1985 1985 1989
Jan Apr Aug Nov Dec Sep Mar Mar Dec Dec Jun Feb Dec Mar May Mar May Jul Nov Nov Apr Sep Oct
31 18 30 19 22 1 7 2 7 20 28 23 29 4 22 28 16 27 24 23 9 19 18
1536 1312 238 718 1821 258 927 1730 435 1919 713 1608 303 122 1911 336 48 1942 1222 926 156 1317 4
1 38 –21 –22 43.3 35.4 35.6 39.25 33.75 33.1 36.1 41 18 42.5 –38.2 61.1 40.9 39.57 39.32 –31.03 –34.13 18.14 37.04
–81.3 –123 –70 109 85 139.2 135.1 144.5 136 135.8 136.2 83.5 121 143 –73.5 –147.6 143.4 118 43.73 –67.76 –71.62 –102.7 –121.9
21 9.3 0.44 0.62 0.62 7.6 0.46 43 15 15 0.33 1.23 0.87 17 2700 750 28 1.2 0.75 1.9 0.5 8.3 0.34
8.15 7.91 7.03 7.13 7.13 7.85 7.04 8.36 8.05 8.05 6.95 7.33 7.23 8.09 9.55 9.18 8.23 7.32 7.18 7.45 7.07 7.88 6.95
Colombia–Ecuador San Andreas Northern Chile Australia Tien Shan Sagami Trough Inland Japan Japan Nankaido Nankaido Inland Japan Tien Shan Manila Japan South Chile Central Alaska Japan Shansi Iran-Turkey Argentina Central Chile Mexico San Andreas
* Mo in 1020 dyne-cm. Source: Pacheco, J.F. and Sykes, L.R. (1992). Bull. Seismol. Soc. Am., 82, 1306–1349. With permission.
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17
0°
70
°
180
° -17 0° -160° -150°
° -140
0°
-13
°
70
°
60
60
°
°
50
50
° 17 0
0°
°
-13
°
180
-140
° -170°
-300
FIGURE 4.17
-160° -150
-70 -33 Depth (km)
-150°
0
Aleutian and Alaska seismicity. (Courtesy United States Geological Survey)
The predominant seismicity in the Kuriles and Kamchatka (north of Japan) and the Aleutians and Alaska is due to subduction of the Pacific plate beneath the North American plate. The predominant seismicity along the western boundary of North America is due to transform faults (i.e., strike-slip) as the Pacific plate displaces northwestward relative to the North American plate, although the smaller Juan de Fuca plate offshore from Washington and Oregon, and the still smaller Gorda plate offshore from northern California, are driven into subduction beneath North America by the Pacific plate. Further south, the Cocos plate is similarly subducting beneath Mexico and Central America due to the Pacific plate, while the Nazca plate lies offshore and is subducted beneath South America. The Pacific plate is created along an extensional boundary in the South Pacific. In the southwest Pacific, New Zealand is longitudinally bisected by the transverse-compressive Alpine fault, where the Pacific plate adjoins the Indo-Australian plate and between which are several smaller plates (Caroline, Fiji). A major feature is the Philippine plate, which is generally subducting beneath all three of the Pacific, Indo-Australian, and Eurasian plates. Lastly, the Japanese archipelago is an island arc formed by (south of Mount Fuji) the subduction of the Philippine plate beneath the Eurasian plate, and (north of Mount Fuji) the subduction of the Pacific plate beneath the North American plate (it may seem strange, but Tokyo and northern Japan lie on the North American plate). Each of these regions is discussed further in the next subsections. 4.4.2.1 Kurile and Aleutian Island Chains The Kurile and Aleutian island chains (Figure 4.17) are typical Pacific active arcs, with relatively high seismicity at shallow depth (due to subduction) following the concave sides of the Kurile and Aleutian Trenches. Near the east end of the Aleutian arc there is a higher activity in the vicinity of the Kenai Peninsula. Right-lateral strike-slip motion occurs along the Fairweather and Queen Charlotte transform faults as the Pacific plate moves northward relative to the North American plate. In southern Alaska, the Pacific sea-floor underthrusts the Alaska peninsula and the Aleutian Islands, but the direction of convergence becomes more oblique to the arc and the trench in the central and western Aleutians. Three
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Seismicity database used to determine Canadian seismic hazard
Magnitude 2.7 - 3.9
5.0 - 6.4
4.0 - 4.9
≥ 6.5
FIGURE 4.18 Canada seismicity 1990–2000. (From Global Seismic Hazard Assessment Program, http:// seismo.ethz.ch/gshap/northam/report.html.)
great earthquakes (1957, 1964, and 1965) have recently ruptured most of the Aleutian zone, although several seismic gaps remain: • At the western end of the Aleutian arc • Between the 1957 and 1964 rupture zones • Between the rupture zones of the 1964 and 1958 earthquakes in southern Alaska This region is near Yakutat Bay, the site of several large events that occurred around the turn of the century. 4.4.2.2 Canada Earthquakes in Canada of M ≥ 7 have occurred south of Newfoundland, in the St. Lawrence Valley below Quebec City, in the Queen Charlotte Islands, along the coast of Vancouver Island, and in the Canadian Arctic (Figure 4.18). Important earthquakes in Canada since 1899 are the 1929 M7.2 Grand Banks event, St. Lawrence event of 1925, 1933 M7.3 Baffin Bay event, Vancouver Island events of 1918 and 1946, Queen Charlotte Islands event of 1949, and two events in Alaska in 1899 and 1958 near British Columbia. Earthquakes in eastern Canada include six M6± Charlevoix earthquakes since 1663. Most Canadian seismicity is on the west coast, along a narrow band near the coastline, with epicenters along a series of faults connected by ridges. The system forms a link between the San Andreas rift zone and the eastern end of the Aleutian arc. The Queen Charlotte earthquake of M8 occurred at the north end of one of these transform faults. © 2003 by CRC Press LLC
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2 12
3 3 WAS H
2
2
3
3 2 4 4
OREG
3
MAINE
MONT
IDANO
N. DAK
MINN
2 3
WISC
S. DAK
NY
WYO 2 4 2
NEBR
NEV
2
ILL
3
UTAH
CA
LIF
2
COLO
KANS
MO
3
W. VA VA N. C TENNS
N. MEX
2
MISS TEX
2
IND
ARK
ARIZ 1
2
OHIO
KY
ONLA
3
22
PA
IOWA
3 2
12
MARY
MICH
ALA
S. C GA
4
LA FLA LEGEND INTENSITY V-V1 (except california) INTENSITY VII INTENSITY VIII INTENSITY IX INTENSITY X-XII
0
200 km
FIGURE 4.19 U.S. seismicity. (From Algermissen, S.T. (1983). An Introduction to the Seismicity of the United States, Earthquake Engineering Research Institute, Oakland, CA; after Coffman, J.L., von Hake, C.A., and Stover, C.W. (1980). Earthquake History of the United States, U.S. Department of Commerce, NOAA, Publ. 41–1, Washington, D.C. With permission.)
North of the Queen Charlotte Islands the earthquake zone becomes wider. The 1958 and 1899 events were along the coast, although the Denali fault curves inland from British Columbia and the Yukon to central Alaska. There have been several earthquakes with epicenters near the mouth of the Mackenzie River. There have been strong earthquakes near Vancouver Island (1918 M7, 1957 M6). The earthquakes along the Strait of Georgia and Puget Sound are large enough to cause damage. The 1946 earthquake at the north end of the Strait of Georgia had magnitude 7.3. No large subduction zone earthquakes have occurred along the west coast of Canada historically. The geologic record indicates that great earthquakes have occurred off Vancouver Island, with a recurrence interval of several hundred years, while the last great Cascadia subduction zone earthquake occurred about 300 years ago, in 1700 [Satake et al., 1996]. Seismicity within the Canadian Shield falls into three groups: to the southeast in the region of the St. Lawrence River, to the northeast in Baffin Bay, and to the northwest in the region of the mouth of the Mackenzie River. A great earthquake in 1663 was violent near Three Rivers, comparable to the 1811–1812 New Madrid earthquakes. The Baffin Bay earthquake of 1933 (M7.3) is the best example of a strong earthquake in the Canadian Arctic. Along the St. Lawrence river there are few events near Sept Isles, a concentration of events near La Malbaie, an absence of earthquakes near Trois-Rivieres, then an increase again towards Cornwall. 4.4.2.3 United States The San Andreas fault system in California and the Aleutian Trench off the coast of Alaska are part of the boundary between the North American and Pacific tectonic plates, and are associated with most U.S. seismicity (Figure 4.19 and Table 4.6). There are many other smaller fault zones throughout the western United States that are also helping to release the stress that is built up as the tectonic plates move past one another, Figure 4.20.
© 2003 by CRC Press LLC
Yr
M
D
Lat.
Long.
M
MMI
Deaths
1976 1920 1923 1908 1932 1970 1990 1927 1915 1935 1939 1939 1978 1988 1976 1974 1948 1905 1917 1968 1962 1907 1960 1980 1934 1918 1933 1975
7 12 9 2 12 5 6 5 1 5 12 1 9 12 2 5 10 4 1 8 9 10 2 10 1 2 8 2
27 16 1 0 25 31 20 22 13 30 26 25 16 7 4 10 5 4 21 31 1 21 29 10 15 13 25 4
39.5 N 36.5 N 35.3 N 38.2 N 39.2 N 9.1 S 37 N 37.6 N 41.9 N 29.5 N 39.5 N 36.2 S 33.4 N 41 N 15.3 N 28.2 N 37.9 N 33 N 8S 33.9 N 35.6 N 38.5 N 30.4 N 36.1 N 26.5 N 23.5 N 32 N 40.6 N
118 E 106 E 140 E 15.6 E 96.5 E 78.8 W 49.4 E 103 E 13.6 E 66.8 E 38.5 E 72.2 W 57.5 E 44.2 E 89.2 W 104 E 58.6 E 76 E 115 E 59 E 49.9 E 67.9 E 9.6 W 1.4 E 86.5 E 117 E 104 E 123 E
8 8.5 8.2 7.5 7.6 7.8 7.7 8 7 7.5 7.9 8.3 7.4 6.8 7.5 6.8 7.2 8.6 — 7.3 7.3 7.8 5.9 7.7 8.4 7.3 7.4 7.4
X — — — — IX VII — XI X XII — — X IX — — — — — — IX — — — — — X
255,000a 200,000 142,807 75,000 70,000 67,000 50,000 40,912 35,000 30,000 30,000 28,000 25,000 25,000 22,400 20,000 19,800 19,000 15,000 15,000 12,225 12,000 12,000 11,000 10,700 10,000 10,000 10,000
Damage (USD millions) $2,000 $2,800
$500
$100 $11 $16,200 $6,000
Locale China: NE: Tangshan China: Gansu and Shanxi Japan: Toyko, Yokohama, Tsunami Italy: Sicily China: Gansu Province Peru Iran: Manjil China: Gansu Province Italy: Abruzzi, Avezzano Pakistan: Quetta Turkey: Erzincan Chile: Chillan Iran: Tabas CIS: Armenia Guatemala: Tsunami China: Yunnan and Sichuan CIS: Turkmenistan: Aschabad India: Kangra Indonesia; Bali, Tsunami Iran Iran: NW CIS: Uzbekistan: SE Morocco: Agadir Algeria: Elasnam Nepal-India China: Guandong Province China: Sichuan Province China: NE: Yingtao
The number may be as large as 655,000. Source: NEIC. (1996). “Database of Significant Earthquakes,” in Seismicity Catalogs, National Earthquake Information Center, Golden, CO. With permission.
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a
4-28
TABLE 4.6
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126° 42°
124°
122°
120°
118°
116°
114°
40°
38°
IF PAC
SAN FRANCISCO
IC
OC
EA N
36°
CA NE LI VA FO DA RN IA
EXPLANATION Magnitudes 1.5+ 3.0+ 4.0+ 5.0+ 6.0+
34°
0
100
200 KILOMETERS
32°
FIGURE 4.20 Seismicity for California and Nevada, 1980–1986 M > 1.5. (From Jennings, C.W. (1994). Fault Activity Map for California and Adjacent Areas, California Department of Conservation, Sacramento. With permission.)
While California has had numerous destructive earthquakes, there is also clear evidence that the potential exists for great earthquakes in the Pacific Northwest [Atwater et al., 1995]. On February 28, 2001 the MW 6.8 Nisqually struck the Puget Sound area, a very similar earthquake to the MW 6.5 1965 event. Fortunately, the Nisqually event was relatively deep (~50 km), and caused relatively few casualties, although still about $1 billion in damage. On the east coast of the United States, the cause of earthquakes is less well understood. There is no plate boundary and very few locations of active faults are known so that it is more difficult to assess where earthquakes are most likely to occur. Several significant historical earthquakes have occurred, such as in Charleston, South Carolina, in 1886 and New Madrid, Missouri, in 1811 and 1812, indicating that there is potential for very large and destructive earthquakes [Wheeler, 1994; Harland and Lindbergh, 1988]. However, most earthquakes in the eastern United States are smaller magnitude events. Because of regional geologic differences, eastern and central U.S. earthquakes are felt at much greater distances than those in the western United States, sometimes up to a thousand miles away [Hopper, 1985].
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120 °W 30°N
50°W 110°W
100°W
90°W
80°W
70°W
60°W
30°
N
20°
N
20°N 10°
N
10°N 50°W
120 °W
60°W 110°W
100°W
90°W
80°W
70°W
FIGURE 4.21 Mexico and Central America seismicity. (From Global Seismic Hazard Assessment Program, North Andes, http://seismo.ethz.ch/gshap/northam/report.html., 1998. With permission.)
4.4.2.4 Mexico and Central America Mexico and Central America have suffered numerous catastrophic earthquakes, including the 1985 Mexico City (MW 8.1, 10,000+ deaths), the 1986 El Salvador earthquake (MS 5.4, 1500 deaths), the 1972 Nicaragua earthquake (MS 6.2, 11,000 deaths), and the 1976 Guatemala earthquake (MS 7.5, 23,000 deaths) [Shedlock, n.d.]. Seismicity in Mexico is concentrated along the Pacific/Cocos/Caribbean/North American plate boundaries, off the south and west coasts and Baja California (Figure 4.21). The historical catalog for Mexico begins in 1475 [Zúñiga et al., 1997]. The largest earthquakes (M > 7.5) in Mexico have occurred along the North American/Cocos (and the small Rivera) plate boundaries. The plate interface(s) dip shallowly and the large earthquakes occur at depths >30 km [Dewey and Suárez, 1991]. The Pacific/North American plate boundary is an en echelon transform fault boundary with smaller, less frequent earthquakes [Shedlock, n.d.]. Seismicity in Central America is similarly concentrated along the North American/South American/Caribbean/Cocos/Nazca (and associated smaller) plate boundaries. The historical catalog for the region begins in 1516 [Shedlock, n.d.]. The Cocos/Caribbean plate interface is steeply dipping beneath Central America from Guatemala to northern Costa Rica, with interface earthquakes as large as M8 and as deep as 200 km [Dewey and Suárez, 1991]. The interface shallows towards the Cocos/ Nazca/Caribbean triple junction, with deep-to-intermediate earthquakes disappearing altogether. The most destructive earthquakes in much of Central America have been shallow, moderate (M5 to 6.5), intraplate, strike-slip earthquakes [Dewey and Suárez, 1991]. 4.4.2.5 South America Seismicity in South America can be divided into three major zones: 1. Along almost the entire west coast of South America, subduction of the Nazca plate beneath the South American plate, which is responsible for the great majority of seismicity in South America 2. In the north (i.e., mostly Venezuela), where a major transform boundary exists between the Caribbean and South American plates 3. At the very south, where the Antarctic plate is probably subducting beneath the South American plate © 2003 by CRC Press LLC
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90°W
80°W
70°W
60°W
50°W
40°W
30°W
10°N
10°N
0°
0°
10°S
10°S
20°S
20°S
30°S
40°S
50°S 60°S
30°S
40°S
50°S 6 70°W 60°W 50°W 40°W 30 0°S °W 90°W 80°W
FIGURE 4.22 South America seismicity. (From Global Seismic Hazard Assessment Program, North Andes, http://seismo.ethz.ch/gshap/northam/report.html., 1998. With permission.)
Of these three zones, the GSHAP project report on the North Andes seismic hazard zonation [GSHAP North Andes, 1998] provides an excellent summary of the tectonics of the more seismic portions of northern and western South America: The northwestern region of South America is characterized by two contrasting provinces from the geologic and geographic point of view: a relatively stable, low topography, region known as the South American platform, involving central and southern Venezuela, and eastern Colombia, Ecuador, Peru, and Bolivia; and a second region to the west, active and deformed, associated to the mountain chain of the Andes. The Andes extends as a single chain along the continental margin from Central Chile to Southern Bolivia where the Altiplano is developed up to central Peru. From there north to Ecuador the Andes becomes again a single chain and in Colombia it splits in three chains, the easternmost continuing into Venezuela. Tectonics of the region has been interpreted in terms of the convergence of the Caribbean, Nazca and South American plates. Interaction of these plates results in the deformation of the continental margin forming the belt of folded mountains that now constitute the ranges of the Andes. Relative motion between the Caribbean and South American plates at a rate of 14 mm/year in an ESE direction [Freymuller et al., 1993] is absorbed mainly along an extended transform system conformed by the Boconó, Morón and El Pilar Faults in Venezuela and the Caribbean Deformed Belt in the coastal margin in Colombia. Subduction of the oceanic Nazca plate under the South America plate in the Northern Andes takes place along the Colombia–Ecuador–Peru trench. These two plates converge in a N80°E direction at a rate of 78 mm/year [de Mets et al. 1990] giving rise to numerous great earthquakes along the margin. The subducted plate geometry inferred from the intermediate and deep seismicity indicates variations along strike associated to segmentation and buckling of subduction [Pennington, 1981; Jordan et al., 1983; Norabuena et al., 1994]. © 2003 by CRC Press LLC
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TABLE 4.7
Major Earthquakes in Chile, 1851–2001
Date 1851 1851 1859 1868 1869 1869 1871 1871 1877 1879 1880 1906 1918 1922 1923 1927 1928 1939 1943 1949 1953 1960 1966 1971 1985
Apr May Oct Aug Aug Aug Mar Oct May Feb Aug Aug Dec Nov Jun Nov Dec Jun Apr Dec May May Dec Jul Mar
02 26 05 13 19 24 25 05 09 02 15 16 18 10 04 21 01 24 06 07 06 22 28 08 03
Epicenter Region
Magnitude
Casabalanca Caldera Copiapo Arica Iquique Pisagua Valparaiso Iquique Pisagua Estrecho Magallanes Illapel Valparaiso Copiapo Huasco Caldera Aisen Talca Chillan Illapel Punta Arenas Chillan Valdiva Taltal Valparaiso San Antonio
7.0–7.5 7.0–7.5 7.5–7.7 8.5 7.0 –7.5 7.0–7.5 8.0–8.5 7.0–7.5 7.5–8. 8.6 >7.5 8.4
8.4 8.3 8.3 7.5 7.5 8.3 7.5 7.9 7.8
Source: Wyllie, L.A., Ed. (1986). “The Chile Earthquake of March 3, 1985,” Earthquake Spectra, 2.
The changes in geometry of subduction correlate to the presence and absence of the volcanic arc. Zones of subhorizontal subduction exists with the absence of volcanism, while normal angle subducting plate geometry is present with active volcanic arc. Besides activity associated to plate boundaries, convergent tectonics originates active internal deformation in the Andean block evidenced by neotectonic activity and seismicity concentrations along the interandean valleys and coastal fault systems. The relative motion between Caribbean, Nazca and South American plates is accommodated along the margins defining the regions where the major earthquakes occur. Nevertheless, the Andes represents a zone of wide spread deformation where the remaining convergence is adjusted. The Andes defines a zone of compression characterized by reverse faulting on the foothills (e.g., Subandean, Colombian Llanos foothills) roughly perpendicular to the vectors of plate convergence, strike slip faults (e.g., Oca Fault, Pallatanga Fault) and some normal faults on the high cordillera (e.g., Cordillera Blanca Fault). Seismicity clearly defines the deformation front of the previously mentioned zones. Seismicity for South America is shown in Figure 4.22. South of the area discussed above, the Peru–Chile Trench continues, with the deepest zone located about 120 km west of Valparaiso, and with the Pacific plate dipping about 20° to the east beneath the South American plate. In this region, Chile has experienced 25 major earthquakes in the last 150 years, including major damaging events in 1906, 1960, and 1985 (Table 4.7). 4.4.2.6 New Zealand New Zealand’s seismicity is due to a major plate boundary (Pacific with Indian–Australian plates), which transitions from transform to thrust from the South to the North Island [Scholz, 1990]. The large Alpine transform fault bisects South Island, and then transitions offshore in a splayed manner, into the Hukurangi Trough, becoming, further north, east of North Island, the Kermadec Trough. However, at the
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TABLE 4.8
Selected New Zealand Faults
Fault/Area Alpine Wellington Wairarapa Hope
Rate of Movement (mm/year)
Periodicity of Large Earthquakes
2.5–4.5
250–400 years 600 years
15–25
Last Big Quake No movement in last 100 years 300–500 years ago 1855 magnitude 8–8.2 1888 magnitude 7–7.3
north of South Island, major strands from the splayed Alpine fault (e.g., Wairau, Awatere, Clarence, Kekerengu, and Hope-Kaikoura) cross Cook Strait, becoming on North Island the Owhariu, Wellington, and East and West Wairarapa faults. The Wellington fault is particularly significant since it literally runs through parts of the city of Wellington, New Zealand’s capital. Table 4.8 presents data on selected larger New Zealand faults. 4.4.2.7 Philippines The Philippine archipelago is largely situated on the Philippine plate which itself is caught between the much larger Pacific and Eurasian plates. To the east, the Philippine plate is subducting beneath the northwestward moving Pacific plate at about 7 cm per year, while to the west the Eurasian plate is subducting beneath the Philippine plate along the western sides of Luzon and Mindanao Islands at about 3 cm per year. The result is high seismicity and volcanism associated with the following oceanic trenches: Philippine, East Luzon, Manila, Negros, Sulu, Cotabata, and Davao, and the following collisional and fault zones: Palawan-Mindanao, Zamboanga-Mindanao, Philippine Fault zone, Digdig Fault, and many other active faults, for example, Lubang, Tablas, Casiguran, and Mindanao (Figure 4.23). 4.4.2.8 Japan Japan is an island archipelago with a long history of damaging earthquakes [Usami, 1981], due to the interaction of four tectonic plates (Pacific, Eurasian, North American, and Philippine), which all converge at Mt. Fuji, near Tokyo. Tectonically, the Japanese archipelago has two long structural lines: 1. The Fossa Magna, located across the main island of Honshu in a nearly N–S direction at about 138°E, which separates Japan into northeast and southwest sectors 2. The Median Tectonic Line, which runs through southwest Japan (Kyushu, Shikoku, and Honshu) oriented WSW–ENE at about 33–35°N, and divides southwest Japan into an inner (north) and outer zone Great events occur frequently offshore the Pacific Coast, due to the subduction of the Philippine plate (south and west of Mt. Fuji) and the Pacific plate (north and east of Mt. Fuji). Although they are very large earthquakes and occasionally devastating, such as in 1923, these events are usually less damaging than smaller (approximate M7) crustal events onshore, such as the 1995 Hanshin event. Figure 4.24 indicates the pattern of Japanese seismicity, which is seen to be higher in the north of Japan. Since about 1600, Japan has sustained about 70 great damaging earthquakes — that is, on average once every 5 years there has been a large damaging earthquake in Japan. In modern times these include the 1891 Nobi, 1896 and 1933 Sanriku Tsunami, 1923 Kanto, 1927 Kito Tango, 1943 Tottori, 1944 Tonankai, 1945 Mikawa, 1946 Nankai, 1948 Fukui, 1964 Niigata, 1968 Tokachi-oki, 1993 Nansei Hokkaido-oki, and 1995 Hanshin (Kobe) events. The Nobi earthquake of 1891 was the first event in which modern structures suffered damage. This experience led to the recognition that structures should be designed to be able to resist horizontal loads in order to be earthquake resistant, and was the birth of modern earthquake engineering in Japan. The Great Kanto earthquake of 1923 (M7.9, about 140,000 fatalities) was a great subduction earthquake, and destroyed many buildings in Tokyo and Yokohama, although the conflagration that followed destroyed many more. The lesson was recognized that earthquake damage to structures depends on the vibration © 2003 by CRC Press LLC
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116°
118°
120°
122°
124°
126°
128°E
Legend 20°N
gh Tr ou
Zone of collision
East Luzo n Trench
R A N FAULT
IG U CA S
DIGDIG FAULT
Nor th L HIN A SE
Probable active fault 18°
16°
14°
LU
BA
14°
PH
a Manil
SOU
TH C
16°
Fault zone: fault, active
on uz
Trench
A
18°
20°
Subduction
S FA ULT TAB IA Negros Tr e nc h
gh
h renc ne T
nT ro u
SEA
12°
ippi
E ON TZ UL FA
10°
Phil
NE PI IP IL PH
12°
INE
PP
ILI
NO F AULT
10°
nc
0 50 100
Trench Davao
T UL FA
C o t a b o Tr e at
6°
O NA DA
IN
h nc re T u
l
Su
8°
M
Pa la
wa
SULU SEA
h
CELEBES SEA
200
6°
Km 4°
116°
118°
120°
122°
124°
126°
128° 4°
FIGURE 4.23 Philippine archipelago tectonic features. (From Saxena, S., Sharpe, B., and Acacio, A. (1991). Geoscience and Geotechnical, Philippines Earthquake Reconnaissance Report, A. Schiff, Tech. Ed., Earthquake Spectra, 7A (Suppl.). With permission.)
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130
135
140
145
42
42
40
40
38
38
36
36 Kobe
34
34
32
32
30
0
km
1000
Japan Islands
28 130
135
Magnitude FIGURE 4.24
30
28
140
5
145
6
7
8
Japan seismicity, 1960–1965.
characteristics of both the structure and its subgrade. The 1964 Niigata earthquake was the first earthquake to emphasize the importance of liquefaction, and Japan thereafter engaged in state-of-the-art earthquake engineering which, however, did not prevent major damage in the 1995 MW 6.9 Hanshin (Kobe) earthquake, which caused approximately 6,000 fatalities and severely damaged some modern structures as well as many structures built prior to the last major updating of the Japanese seismic codes (ca. 1981). Today, central Japan is still an area of major seismic risk, particularly Tokyo, which has sustained a number of damaging earthquakes in history.
4.4.3 Trans-Alpide Belt The Trans-Alpide belt includes the Mediterranean, which has very significant seismicity in North Africa, Italy, Greece, and Turkey due to the African plate’s motion relative to the Eurasian plate; the Caucasus (e.g., Armenia) and the Middle East (Iran, Afghanistan), due to the Arabian plate being forced northeastward into the Eurasian plate by the African plate; and the Indian subcontinent (Pakistan, northern India), and the subduction boundary along the southwestern side of Sumatra and Java, which are all part of the Indian-Australian plate. Seismicity also extends northward through Burma and into western China. 4.4.3.1 Europe, the Mediterranean, and the Middle East Northwestern Europe seismicity is in general rather low, the highest seismic activity being associated with active tectonic processes in the Alps, Iceland, and locally at intermediate depths in the Vrançea area (Romania) (Figure 4.25). The strongest earthquakes reach magnitudes MW = 6.2 – 6.5 in the upper crust in the Alps (e.g., Basel, 1356 and Friuli, 1976) and exceed MW = 7 relatively frequently in the Vrançea area (e.g., 1940, 1977, and 1986). Other concentrations of earthquake foci are connected with the ongoing tectonics of tertiary and quaternary graben structures, e.g., the Upper Rhine graben with its northwest extension towards the Lower Rhine embayment (e.g., Düren, 1756 and Roermond, 1992, both MW 5.4), © 2003 by CRC Press LLC
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-30°
0°
30°
0 -33 -71 -151
60°
60°
-301
-501
30° -30°
FIGURE 4.25
30° 0°
30°
-800 Depth (km)
European seismicity 1975–1995. (Courtesy United States Geologic Survey)
and the transpressive neotectonics of the Pannonian basin and its surrounding orogeny. Scattered seismic activity in western France and Great Britain is not well understood and hard to relate to known neotectonic elements. The seismic activity of Fennoscandia, with concentration mainly in some coastal regions of Norway and Sweden, has been interpreted partly as a result of deglaciation, partly of tectonic origin, i.e., push from the mid-Atlantic ridge. The mid-Atlantic ridge zone crossing Iceland creates a narrow belt of relatively high seismic activity. There are nearly aseismic areas in Ireland, the North German basin, and the East European platform, i.e., the area northeast of the mountainous parts surrounding the Pannonian basin and the Bohemian massif [Gottfried, 1999]. Southern Europe and North Africa are seismically active regions due to the transpressive Eurasia–African plate boundary. The Ibero-Maghreb region (Portugal, Spain, Algeria, Morocco, and Tunisia) is located at the westernmost segment of the Eurasia–Africa plate boundary, forming a subcontinental-sized tectonic domain where strain is distributed over a wide area and no single plate boundary can be outlined. Several strong and damaging earthquakes have taken place in this region, for example, Lisbon, 1755; Andalusia, 1884; Agadir, 1960; and El Asnam, 1980 [Jiminez, n.d.]. The Italian peninsula is an area of high seismicity — the Council for National Research has compiled a catalog of over 37,000 earthquakes from 1000 AD to 1980 [Postpischl, 1985; Table 4.9]. The Italian peninsula and associated regions are currently interpreted as a rigid microplate bordered on the eastern, northern, and western margins by a mobile mountain belt that includes the Albanides, the Dinarides, the Alps, and the Apennines. No plate convergence can explain the recent tectonic evolution of the Apennines, which appears to have been entirely controlled by passive subduction processes. In the southern Apennines, passive subduction processes and consequent arc migration ended around 0.65 Ma; due to the persisting Adria-Europe convergence, extensional processes have developed since then, with a generation of young normal faults superimposed on the inactive contractional structures [Slejko, n.d.]. © 2003 by CRC Press LLC
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TABLE 4.9
Selected 20th Century Italian Earthquakes
Date 9 Aug 1905 28 Dec 1908 13 Jan 1915 23 Jul 1930 13 Apr 1938 16 Mar 1941 6 May 1976 23 Nov 1980
Lat.
Long.
M
Region
38.8 38.17 42 41.05 39.2 38.3 46.27 40.76
16.1 15.6 13.6 15.42 15.2 12.2 13.25 15.3
7.3 7.2 6.6 6.5 7.1 6.9 6.5 6.9
Calabrian coast Messina Avezzano Apulia Tyrrhenian Sea Western Sicily Friuli Irpinia
48°
46°
44°
42°
40°
38°
36° 6°
8°
10°
12°
14°
16°
18°
20°
22°
FIGURE 4.26 Seismicity in Italy and associate regions. (From Slejko D., Seismic Hazard Assessment for the Adria Region, http://seismo.ethz.ch/gshap/adria/report.html. With permission.)
Seismicity in the Adriatic Sea appears to be very low (Figure 4.26), while interplate margin seismicity in the Apennines expresses both compressional and extensional earthquakes, and strike-slip mechanisms are located where the lateral continuity of the arcs is broken. The Po plain is a sort of gap in the seismicity distribution; strike-slip and reverse fault mechanisms become prevalent on the borders of the Adria indentation in the western Alps. The southern Alps are mainly characterized by thrust mechanisms, and the maximum compression is expected to be oriented N–S in the Friuli region, with a gradual transition to transcurrent characteristics both westward, for example, the 1936 Belluno earthquake [Peruzza et al., 1989] and eastward, for example, the 1997 Bovec earthquake, associated to the Idrija line. A decrease in the activity is located in northern Dalmatia, where the seismicity vanishes. Again along the Dinarides, from Slovenia to the island of Cephalonia, mainly thrust and strike-slip mechanisms have © 2003 by CRC Press LLC
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20°E
30°E
40°E
50°E
EURASIAN PLATE
ADRIATIC PLATE
AEGEAN PLATE
40°N
TURKISH PLATE CASPIAN PLATE VAN PLATE
IONIAN PLATE
IRAN PLATE LEVANTINE PLATE ARABIAN PLATE
30°N
AFRICAN PLATE
FIGURE 4.27 Tectonics of Middle East. (From Erdik, M. et al., Assessment of Earthquake Hazard in Turkey and Neighboring Regions, http://seismo.ethz.ch/gshap/turkey/papergshap71.htm (n.d.); Dewey, J.F. et al. (1973). “Plate Tectonics and the Evolution of the Alpine System,” Geol. Soc. Am. Bull., 84, 3137–3180. With permission.)
been observed. Seismicity is typical of subduction zones in the Aegean and the Calabrian Arc [Slejko, n.d.]. The Tyrrhenian Sea to the west of southern Italy is an actively spreading back-arc basin, and overlies a classic Benioff zone dipping steeply towards the northwest down to a depth of 500 km [Anderson and Jackson, 1987a]. However, the active tectonics of the Calabrian toe of Italy involves rapid, relatively aseismic, uplift in the form of a great crustal fold [Valensise, 1992]. The crustal tectonics in this region involves extension across the center of the uplift. This is a particularly unusual and potentially unstable tectonic configuration that seems likely to give rise to renewed low-angle subduction zone overthrusting in the future. The bulk of Anatolia, the Aegean Sea, and Cyprus are located on the Anatolian or Turkish plate (Figure 4.27). The northern boundary of the Anatolian plate is the Anatolian trough and the rightlateral, strike-slip North Anatolian fault (NAF). The southern boundary of the Anatolian plate is formed by the Hellenic arc, south of Cyprus and the East Anatolian fault (EAF), which joins the NAF at Karliova. The EAF, located between the Gulf of Iskenderun and Karliova, is a left-lateral, strikeslip fault. The southwestward motion of the Anatolian plate, relative to Africa, is taken up by the subduction along the Hellenic Trench. In western Anatolia, the east-west trending grabens account for most of the seismic events of this region. The area encompassing Turkey, from the Aegean region in the west to the Caucasus in the east is comprised of many major seismically active regions. The Aegean region, the Caucasus, the NAF Zone, and the EAF Zone are the most well known among these, where numerous damaging earthquakes have occurred [Erdik et al., n.d.]. Seismicity in the eastern Mediterranean is mainly associated with the northward movement of the Arabian plate (Figure 4.28). Israel and the surrounding area have a very long record of historic seismicity. The record extends to Biblical times — the famous “walls of Jericho” are attributed to earthquake (Ben-Menaheim, 1979 notes that the walls of Jericho were actually destroyed about 17 times between 2100 BC and 3100 BC, although he allows for destruction due to erosion, flood, and war, as well as © 2003 by CRC Press LLC
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earthquake). Several records of Middle Eastern seismicity exist, of which the most complete and reliable appears to be Ben-Menaheim [1979], who lists 270 seismic events with assigned magnitudes that have occurred since 92 BC within 1800 km of Jerusalem. The list is believed to be complete for the Dead Sea fault zone for events greater than ML 6.4 over the past 43 centuries. Selected events from that list for the Dead Sea fault system are indicated in Table 4.10. This area is dominated by the Dead Sea Fault Zone, a nearly 1000-km-long system of faults extending northward from the Gulf of Elat through the Arava, Dead Sea, and Jordan valleys, and on into Lebanon (Figure 4.28a). This “rift” system was formed during the middle Cenozoic by the breakup of the previously continuous Afro-Arabian continent. It is interpreted to be a leaky transform fault connecting the Red Sea spreading center with the Zagros-Taurus zone of plate convergence. An important element in this interpretation is the 105 to 110 km of left-lateral strike-slip movement along the transform, that is inferred to have taken place during two different stages: one, in the Miocene, of about 65 km, and another during the Plio-Pleistocene, of about 40 km. The breakup of the Afro-Arabian continent created two separate plates along the transform: the Sinai plate on its west and the Arabian plate on its east. 4.4.3.2 India The Indian plate boundary is characterized by a continental collision segment along the Himalayas in the north, a complex to an oblique subduction along the Burma–Andaman arc in the east and transverse fault systems such as the Chaman fault in the northwest. Most of the seismicity in the Himalayan region is concentrated along shallow north dipping planes, which indicate underthrusting of the Indian plate beneath the Eurasian plate (Figure 4.29). In addition to four great earthquakes of M > 8 in 1897, 1905, 1934, and 1950, another 10 earthquakes exceeding magnitude 7.5 have occurred in the Himalayan belt during the past 100 years. The Burma–Andaman arc marks the eastern margin of the Indian plate, along which an oblique convergence between the Indian and the Burmese plate has been suggested. The Sumatran fault system in the southeast, the western Andaman fault (WAF) and the Sagaing fault further east, are the features supporting major right-lateral movements in this region. The distribution of earthquakes in the Burmese arc region suggests the presence of a subducted Indian lithosphere slab beneath the Burmese plate. The tectonics of the Shillong plateau, which experienced a M 8.7 event in 1897, is distinctly different from that of the regions to its north, south, and west. The Hindukush and Pamir knot region are characterized by the junction of several tectonic features. This plate boundary region experiences high levels of seismicity varying from shallow to intermediate-depth earthquakes. The other prominent tectonic features in the northwestern India region are the transverse fault systems known as the Chaman fault, the Kirthar and Sulaiman ranges (SR). The Indian shield region is marked by several rift zones and shear/thrust zones. Although considered to be a stable continental region (SCR), this region has experienced many earthquakes of magnitude M > 6.0 since the 18th century, some of which were disastrous. Among them are the Mahabaleshwar (1764), Kutch (1819), Damooh Hill (near Jabalpur, 1846), Mount Abu (1848), Coimbatore (1900), Son-Valley (1927), Satpura (1938), and Jabalpur (May, 1997) earthquakes. The seismicity in the shield region is quite diffused except for a few localized alignments. 4.4.3.3 Indonesia Located at the junction of the colliding Indo-Australian and Eurasian plates, Indonesia is one of the more active seismic regions (Figure 4.30). Seismic zones follow the Sunda, Banda, and Andaman island arcs, where earthquakes extend to 650 km down the subduction zones beneath the islands and most of the shallow seismicity is well offshore. Tsunamis are a major hazard in this area. The tectonics of the eastern Sunda arc are complex and still poorly understood. The lack of great thrust earthquakes at shallow depths may be related to the dipping slab as it bends around the eastern Banda Sea and to the interference of the Australian continental shelf, Christmas Island ridge, and other features of the subduction process. At the Sunda Strait (between Sumatra and Java) the arc undergoes a sharp bend from a northwest strike, and the direction of relative plate motion becomes increasingly oblique. The maximum depth of earthquakes changes abruptly from 600 km east of the Sunda Strait © 2003 by CRC Press LLC
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(a) FIGURE 4.28 (a) Dead Sea fault zone; (b) Seismicity of the Middle East 1975–1995. (Part (b) courtesy United States Geological Survey)
to about 200 km on the west side. Great shallow events that are thought to involve thrust faulting are recorded historically, as well as large inland shocks (stike-slip) associated with the Semangko fault (on Sumatra). Major earthquakes in Sumatra have been confined to the highlands along the west coast of the island. Particularly destructive earthquakes occurred in 1892 (near Padang) and in 1893 (Bengkulu). In 1936 an earthquake (M7.2) occurred west of Medan, causing minor damage. A 1935 M8.1 earthquake west of Padang is the largest earthquake recorded in Sumatra. Most major earthquakes have occurred in the Sunda Strait region and to the south of Java. A small number of shallow earthquakes of M6 or less and intermediate depth earthquakes of M7 have occurred on land, but the main earthquake activity is located between the south Java coast and the axes of the Java Trench. The largest earthquake on Java (M8.1) occurred in the south of West Java in 1903. Two M7 © 2003 by CRC Press LLC
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(b) FIGURE 4.28 (CONTINUED) TABLE 4.10 Selected Earthquakes: Israeli and Vicinity Year
Lat.
Long.
M
Comment
1927 1837 1759 1546 1202 746 658 362 31 BC
32 33 33 32 32.5 32 32.5 31.3 32
35.5 35.5 35.5 35.5 35.5 35.5 35.5 35.5 35.6
6.25 6.4 6.5 7 6.8 7.3 6.6 6.4 7
500 killed Tsunami in Sea of Galilee Tsunami in Sea of Galilee Tsunami in Dead Sea Felt in Syria, Egypt Felt in Syria, Egypt Tsunami in Dead Sea
earthquakes have occurred in the Sunda Strait. There is some drop in activity in Central Java, but several destructive earthquakes have occurred in this region [Bhatia et al., n.d.].
4.4.4 Other Areas 4.4.4.1 China Yunnan–Sichuan is perhaps the most seismically active region of China (Figure 4.29). There have been 32 earthquakes with MS > 7 since the beginning of documented history in the region 1500 years ago, with two events with MS > 8. Earthquakes in this region are characterized by shallow strike-slip faulting © 2003 by CRC Press LLC
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60°
70°
80°
90°
100°
110°
120°
50°
50°
40°
40°
30°
30°
20°
20°
60°
70°
80°
90°
100°
110°
120°
FIGURE 4.29 Seismicity of Central Asia 1977–1997. (Courtesy United States Geological Survey)
90°
100° 110° 120° 130° 140° 150° 160° 170° 180° 190°
20°
20°
10°
10°
0°
0°
-10°
-10°
-20°
-20°
-30°
-30°
-40°
-40°
-50°
-50°
-60°
-60° 90°
FIGURE 4.30
100° 110° 120° 130° 140° 150° 160° 170° 180° 190°
Seismicity of the Indo-Australian plate, 1977–1997. (Courtesy United States Geological Survey)
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(focal depths between 10 and 15 km). Earthquakes in the western Sichuan–eastern Yunnan subregion occur mainly in the northwestern-trending Xianshuihe and the north-trending Xiaojiang fault systems. The Xianshuihe fault is a 450-km long left-lateral strike-slip fault with a Holocene slip rate of 13 mm/ year. Nine earthquakes with MS > 7 have occurred along this fault zone. The latest one, the 1973 Luhuo earthquake (MS 7.9) was associated with 90 km of surface rupture and a maximum left-lateral displacement of 6 m. To the south, the Xianshuihe fault, which curves into the north–south-trending Xiaojiang fault, also is a source of strong earthquakes. For example, the 1833 Songming earthquake (MS 8) occurred along this fault. Earthquakes are widely distributed in the western Yunnan seismic subregion. Both major active faults with lengths of several hundred kilometers (i.e., the Red River and Jingsha Jiang faults), and short faults with different orientations host occurrences of strong earthquakes in the western Yunnan subregion. The frequency of occurrence of earthquakes in this subregion is the highest within China. This very active seismic subregion is part of the Assam–Yunnan–Myanmar earthquake region resulting from the penetration of the Indian plate into the Eurasian plate. The North China basin is an extensional region of high seismic hazard. Strike-slip and normal faults are the predominant active structures in the North China region, probably caused, in part, by southeastward extrusion of southeastern Asia with respect to Eurasia. There have been 6 earthquakes of MS > 8, and 16 earthquakes of MS > 7 in this region during the past 2000 years. These large earthquakes generally have occurred along major active faults that bound large basins. Although earthquake recurrence intervals along any individual fault are relatively long (usually in the range of several thousand years), the composite recurrence interval for the whole region is on the order of a few decades. The region is densely populated, and is the cultural and economic center of China. Five earthquakes with MS > 7 occurred in this region within the decade between 1966 and 1976. The 1976 Tangshan earthquake is a tragic example of the seismic hazard in this region (at least 255,000 people were killed) [Zhang, n.d.]. 4.4.4.2 Australia Australia is located entirely on the Indo-Australian plate, away from a plate boundary, so that seismicity is entirely intraplate, and the causes are not well known (Figure 4.30). In the last 100 years there have been 20 earthquakes of M6 or more, 7 of which have ruptured the crust. From a seismicity aspect, Australia can be divided into three regions. In western Australia stress patterns appear to produce several separate zones of seismic activity, each a few hundred kilometers long. In addition to these zones there is considerable activity offshore which does not follow any well-defined lineations. Most of Australia’s largest earthquakes have occurred in this state or offshore, with the largest known, of M7.4, occurring there in 1906. The next two largest, Meeberie in 1941 and Meckering in 1968, also occurred here. The Central Region extends from the Victoria/South Australia border to the Simpson Desert. Most of the earthquakes arising here can be explained by postulating a regional stress field resulting predominately from a north–south pressure axis. The Beachport (1897), Warooka (1902), and Adelaide (1954) earthquakes occurred here. In the Simpson Desert, an earthquake of M6.25 occurred in 1975. The earthquakes in the eastern region tend to be associated with the Tasman geosyncline, with no major lineations of events in the region. Activity appears to be the result of regional stresses in the crust. The cause of the stress pattern is unknown, but it appears to result from a predominant north–south compression. The most active area is the Dalton/Gunning zone about 50 km north of Canberra and several damaging earthquakes have taken place there in the last 50 years. The Gayndah (1935), Roberson (1961), and Picton (1973) earthquakes caused the most damage. The most damaging earthquake in the last 200 years was the moderate M5.6 earthquake near Newcastle, New South Wales on 28 December 1989, which resulted in 13 deaths and AUS$1.2 billion damage. A similar sized earthquake near Adelaide, South Australia in 1954 caused $100 million damage, but there were no deaths. The largest known continental Australia earthquake was a M7.2 event in 1906 off the central west coast of Western Australia, which was felt over one third of the continent.
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4.4.4.3 Caribbean Seismicity in the Caribbean is concentrated along the Caribbean/South American/North American (and associated smaller) plate boundaries (Figure 4.21). The Caribbean plate is overriding the North and South American plates on the east. On the west, the Cocos plate is subducting beneath the Caribbean plate. The north and south boundaries of the Caribbean plate are complicated, multiple transform faults. The historical catalog for the region begins in 1532. Seismicity recorded in the Caribbean region is concentrated along the Antilles arc, from Hispaniola to Trinidad, where the Caribbean plate is overriding the North and South American plates. Most of the large and moderate earthquakes have been shallow intraplate earthquakes near the plate boundaries, although some researchers have interpreted a few large earthquakes as plate interface events. The island of Puerto Rico is surrounded by potentially strong seismic sources whose historical record dates back to 1520 and which have caused widespread damage [Asencio, 1980]. The island lies along the active border between the Caribbean and North American plates, with the Caribbean plate moving easterly relative to the North American plate and the border dominated by left-lateral strike-slip highly oblique subduction along the Puerto Rico Trench north of Puerto Rico. Relative movement between these plates is estimated to be between 20 and 40 mm per year [Sykes et al., 1982]. Two major northwesttrending fault systems, the Great Southern and the Great Northern Puerto Rico fault zones, extend obliquely across the island. Offshore features include faults associated with the Muertos Trough, the Anegada Passage, and Mona Canyon. The northern margin of the Caribbean plate is characterized by several small microplates, or “platelets,” and a large part of the Puerto Rico–Virgin Islands platform is termed the Puerto Rico platelet [McCann et al., 1987]. The margins of this platelet include the Puerto Rico Trench on the north, the Mona Canyon faults on the west, the Great Southern Puerto Rico fault zone on the southwest, the Muertos Trough on the south, and the Anegada Trough on the southeast. The Puerto Rico Trench is over 8 km deep and is the deepest part of the Atlantic Ocean. The Benioff zone defining the subducted plate dips steeply (about 60° to the south) to a depth of about 150 km [McCann et al., 1987]. The western margin of the Puerto Rico platelet lies within the Mona Canyon (or Mona Passage), which is a north–south-trending canyon that joins the Puerto Rico Trench on the north. The West Mona Canyon fault is a major discontinuity that appears to truncate the Great Southern Puerto Rico fault zone to the west of Puerto Rico. The largest earthquakes that occurred in the Puerto Rico region during the 20th century occurred in the vicinity of the Mona Canyon (1918, M7.5; 1943, M7.8). The Muertos Trough, an east–west-trending bathymetric low located about 80 km south of Puerto Rico, delineates the southern margin of the Puerto Rico platelet. West of Puerto Rico and south of Hispaniola, the submarine topographic scarp that defines the northern margin of the Muertos Trough appears to be tectonically active. A great earthquake occurred in 1751 that caused damage along the south coast of Hispaniola. In 1984 there was a strong (M6 to 7) earthquake in the area having a focal mechanism that indicates northward underthrusting of the Caribbean plate beneath Hispaniola [Byrne et al., 1985]. The Anegada Trough (or Anegada Passage) forms the southeastern margin of the Puerto Rico platelet by connecting the Muertos Trough on the south and the Puerto Rico Trench on the north. Microseismicity is associated with the Anegada Trough, and a strong earthquake in 1867 (M7.5) probably ruptured a fault along the southern margin of the trough.
4.5 Characterization of Seismicity The previous section described the global distribution of seismicity, in qualitative terms. This section describes how that seismicity may be mathematically characterized, in terms of magnitude-frequency and other relations. The term magnitude-frequency relation was first characterized by Gutenberg and Richter [1954] as: log N (m ) = aN − bN m
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where N(m) = the number of earthquake events equal to or greater than magnitude m occurring on a seismic source per unit time, and aN and bN are regional constants (10aN = the total number of earthquakes with magnitude >0, and bN is the rate of seismicity; bN is typically 1 ± 0.3). Gutenberg and Richter’s examination of the seismicity record for many portions of the Earth indicated this relation was valid, for selected magnitude ranges. That is, while this relation appears as a straight line when plotted on semilog paper, the data is only linear for a selected middle range of magnitudes, typically falling below the line for both the smaller and larger magnitudes, as shown in Figure 4.31a for Japan earthquake data for the period 1885 to 1990. The fall-off for smaller magnitudes is usually attributed to lack of instrumental sensitivity. That is, some of the smaller events are not detected. Typically, some improved instruments, better able to detect distant small earthquakes, are introduced during any observation period — this can be seen in Figure 4.31b, where there are relatively few detected earthquakes in the early decades of the record. The fall-off for larger magnitudes is usually attributed to two reasons: the observation period is shorter than the return period of the largest earthquakes; and there is some physical limit to the size of earthquakes, so that the Gutenberg–Richter relation cannot be indefinitely extrapolated to larger and larger magnitudes. The Gutenberg–Richter relation can be normalized to:
[
]
F (m ) = 1. − exp − BM (m − M 0 )
(4.18)
where F(m) is the cumulative distribution function (CDF) of magnitude, BM is a regional constant, and M0 is a small enough magnitude such that lesser events can be ignored. Combining this with a Poisson distribution to model large earthquake occurrence [Esteva, 1976] leads to the CDF of earthquake magnitude per unit time:
[
{
}]
F (m ) = exp − exp − aM (m − µM )
(4.19)
which has the form of a Gumbel [1958] extreme value type I (largest values) distribution (denoted EXI,L), which is an unbounded distribution (i.e., the variate can assume any value). The parameters aM and µM can be evaluated by a least squares regression on historical seismicity data, although the probability of very large earthquakes tends to be overestimated. Several attempts have been made to account for this [e.g., Cornell and Merz, 1972]. Yegulalp and Kuo [1974] have used Gumbel’s type III (largest value, denoted EXIII,L) to successfully account for this deficiency. This distribution, w −m k F (m ) = exp − w −u
(4.20)
has the advantage that w is the largest possible value of the variate (i.e., earthquake magnitude), thus permitting (when w, u, and k are estimated by regression on historical data) an estimate of the source’s largest possible magnitude. It can be shown [Yegulalp and Kuo, 1974] that estimators of w, u, and k can be obtained by satisfying Kuhn–Tucker conditions although, if the data is too incomplete, the EXIII,L parameters approach those of the EXI,L: u → µM
k ( w − u) → a M
Determination of these parameters requires careful analysis of historical seismicity data, which is highly complex and something of an art [Donovan and Bornstein, 1978], and the merging of the resulting statistics with estimates of maximum magnitude and seismicity made on the basis of geological evidence (i.e., as discussed above, maximum magnitude can be estimated from fault length, fault displacement © 2003 by CRC Press LLC
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No. Events > M
10,000
Data
log N = a - b M 5.5 < M < 7.5
100
JMA Data 1885-1990
Magnitude, M 1 4
5
6
7
8
9
(a) 700
600
JMA Data 1885-1990 No. Events, by Decade
500
400
300
200
100
0 1895
1905
1915
1925
1935
1945
1955
1965
1975
1985
(b) FIGURE 4.31 (a) Plot of seismicity data for Japan, 1885–1990, from Japan Meteorological Agency catalog — note actual data falls below Gutenberg–Richter relation at smaller and larger magnitudes; (b) number of events by decade, for Japan, 1885–1990. (From Japan Meteorological Agency catalog.)
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Seismic Segmentation Segmentation Segments Attenuation Fault Relationship Recurrence Sources Model Model
Status of Total Fault Activity Length
Dip
Maximum Recurrence Recurrence Magnitude Data Rate
Unnamed Unsegmented 0.2
Oquirrh Mtns
Campbell
Model A
Wasatch
0.4
0.333
East Coshe
Exponential 0.3
West Valley
Cominston
65°
5000 0.04
Ogden
0.5
.3333 0.28
SLC Provo
Segmented
Active
37 km
1.0
1.0 45°
Nephi
0.8
0.5
Levon
Hansel Valley
Model B
Sadigh
Bear Lake
0.6
Backgnd
0.333
N/A
Characteristic 0.7
N/A
Active 1.0
N/A
N/A
7.0 0.15 7.25 0.7 7.5 0.15 6.0 0.3 6.25 0.5 6.5 0.2
Fault 1.0
2500 0.48 2000 0.16
Segment 1.0 N/A
1667 0.04 8.5 0.333 9.3 0.334 9.8 0.333
Joyer-Fumal 0.333
FIGURE 4.32 Hazard model logic tree. Parameter values are shown above the branches and assessed probabilities are shown in parentheses. (From Schwartz, D.P. (1988). In Earthquake Engineering and Soil Dynamics II — Recent Advances in Ground-Motion Evaluation, J.L.van Thun, Ed., Geotechnical Spec. Publ. No. 20., American Society of Civil Engineers, New York; after Youngs, R.R. and Coppersmith, K.J. (1987). Bull. Seismol. Soc. Am., 75, 939–964. With permission.)
data, time since last event, and other evidence, and seismicity can be estimated from fault slippage rates combined with time since last event; see Schwartz [1988] for an excellent discussion of these aspects). In a full probabilistic seismic hazard analysis, many of these aspects are treated fully or partially probabilistically, including the attenuation, magnitude–frequency relation, upper and lower bound magnitudes for each source zone, geographical bounds of source zones, fault rupture length, and many other aspects. The full treatment requires complex specialized computer codes, which incorporate uncertainty via use of multiple alternative source zonations, attenuation relations and other parameters [EPRI, 1986; Bernreuter et al., 1989] often using a logic tree format (Figure 4.32). A number of codes have been developed using the public domain FRISK (fault risk) code first developed by McGuire [1978]. Several topics are worth noting briefly here. 1. While analysis of the seismicity of a number of regions indicates that the Gutenberg–Richter relation log N(M) = a − b M is a good overall model for the magnitude–frequency or probability of occurrence relation, studies of late Quaternary faults during the 1980s indicated that the exponential model is not appropriate for expressing earthquake recurrence on individual faults or fault segments [Schwartz, 1988]. Rather, it was found that many individual faults tend to generate essentially the same size or characteristic earthquake [Schwartz and Coppersmith, 1987], having a relatively narrow range of magnitudes at or near the maximum that can be produced by the geometry, mechanical properties, and state of stress of the fault. This implies that, relative to the Gutenberg–Richter magnitude–frequency relation, faults exhibiting characteristic earthquake behavior will have relatively less seismicity (i.e., higher b value) at low and moderate magnitudes, and more near the characteristic earthquake magnitude (i.e., lower b value). 2. Most probabilistic seismic hazard analysis models assume the Gutenberg–Richter exponential distribution of earthquake magnitude and that earthquakes follow a Poisson process, occurring on a seismic source zone randomly in time and space. This implies that the time between © 2003 by CRC Press LLC
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earthquake occurrences is exponentially distributed, and that the time of occurrence of the next earthquake is independent of the elapsed time since the prior earthquake.7 The CDF for the exponential distribution is: F (t ) = 1 − exp (− λt )
(4.21)
Note that this forms the basis for many modern building codes, in that the probabilistic seismic hazard analysis results are selected such that the seismic hazard parameter (e.g., PGA) has a “10% probability of exceedance in 50 years” [IBC, 1994] — that is, if t = 50 years and F (t) = 0.1 (i.e., only 10% probability that the event has occurred in t years), then λ = .0021 per year, or 1 per 475 years. A number of more sophisticated models of earthquake occurrence have been investigated, including time-predictable models [Anagnos and Kiremidjian, 1984], renewal models [Nishenko and Buland, 1987; Kameda and Takagi, 1981], and time-dependent models [Ellsworth et al., 1999; USGS, 1999]. The latter have formed the basis for state-of-the-art estimation of seismic hazard for the San Francisco Bay area by the U.S. Geological Survey, but can only be used when sufficient data is available. 3. As was seen from the data for Japan, historic seismicity observations vary with event size — large magnitude events will have been noted and recorded for perhaps the full length of the historic record, while small magnitude events will only have been recorded with the advent of instruments, with quality of the instrumental record usually improving in more recent times. Thus, in analyzing any historic seismicity record, the issue of completeness is important, and should be analyzed. Stepp [1972] has developed a method assuming the earthquake sequence can be modeled as a Poisson distribution. If k1, k2, k3, … kn are the number of events per unit time interval, then: λ=
1 n
n
∑k
i
i =1
and its variance is σ2 = λ/n where n = the number of unit time intervals. Taking the unit time interval to be 1 year gives as the standard deviation of the estimate of the mean, where T is the sample length (in years). That is, this provides a test for stationarity of the observational quality — if the data for a magnitude interval (say 5.6 < M < 6.5, to test for quality of observation for events in this magnitude range) is plotted as log(σλ) vs. log(T), then the portion of the record with slope T–1/2 can be considered homogeneous (Figure 4.33), and used with data for other magnitude ranges (but for different observational periods) similarly tested for homogeneity, to develop estimates of magnitude–frequency parameters. A more recent method is also provided by Habermann [1987]. Construction of response spectra for design purposes is usually performed in one of two ways: 1. Using probabilistic seismic hazard analysis to obtain an estimate of the PGA, and using this to scale a normalized response spectral shape, or, alternatively, estimating PGA and PSV (also perhaps PSD) and using these to fit a normalized response spectral shape, for each portion of the spectra. Since probabilistic response spectra are a composite of the contributions of varying earthquake magnitudes at varying distances, the ground motions of which attenuate differently at different periods, this method has the drawback that the resulting spectra have varying (and unknown) probabilities of exceedance at different periods. Because of this drawback, this method is declining in favor, but still offers the advantage of economy of effort. 2. An alternative method results in the development of uniform hazard spectra [Anderson and Trifunac, 1977], and consists of performing the probabilistic seismic hazard analysis for a number of different periods, with attenuation equations appropriate for each period (e.g., those of Boore, 7
For this aspect, the Poisson model is often termed a memoryless model.
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1.0
V
Τ
MMI VI complete this range only
σλ = λ
/
VI
0.1
Intensity IV
VII -1/2
Slope = T
V VI
VIII
VII VIII
0.01 5
10
100 Time (Years)
FIGURE 4.33 Standard deviation of the estimate of the mean of the annual number of events as a function of sample length and intensity class. (After Stepp, J.C. (1972). Proc. First Conf. Microzonation, Seattle. With permission.)
Joyner, and Fumal). This method is currently preferred, as the additional effort is not prohibitive, and the resulting response spectra have the attribute that the probability of exceedance is independent of frequency.
Defining Terms Attenuation — The rate at which earthquake ground motion decreases with distance. Benioff zone — A narrow zone, defined by earthquake foci, that is tens of kms. thick dipping from the surface under the Earth’s crust to depths of 700 km (also termed Wadati-Benioff zone).
Body waves — Vibrational waves transmitted through the body of the Earth; are of two types: P waves (transmitting energy via dilatational or push–pull motion), and slower S waves (transmitting energy via shear action at right angles to the direction of motion). Characteristic earthquake — A relatively narrow range of magnitudes at or near the maximum that can be produced by the geometry, mechanical properties, and state of stress of a fault [Schwartz and Coppersmith, 1987]. © 2003 by CRC Press LLC
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Completeness — Homogeneity of the seismicity record. Corner frequency, fo — The frequency above which earthquake radiation spectra vary with ϖ-3 below fo , the spectra are proportional to seismic moment. Cripple wall — A carpenter’s term indicating a wood frame wall of less than full height, usually built without bracing. Critical damping — The value of damping such that free vibration of a structure will cease after one cycle (ccrit = 2 mω). Damping represents the force or energy lost in the process of material deformation (damping coefficient c = force per velocity). Dip-slip — Motion at right angles to the strike, up- or down-slip. Dip — The angle between a plane, such as a fault, and the Earth’s surface. Ductile detailing — Special requirements such as, for reinforced concrete and masonry, close spacing of lateral reinforcement to attain confinement of a concrete core, appropriate relative dimensioning of beams and columns, 135° hooks on lateral reinforcement, hooks on main beam reinforcement within the column, etc.). Ductile frames — Frames required to furnish satisfactory load-carrying performance under large deflections (i.e., ductility). In reinforced concrete and masonry this is achieved by ductile detailing. Ductility factor — The ratio of the total displacement (elastic plus inelastic) to the elastic (i.e., yield) displacement. Epicenter — The projection on the surface of the Earth directly above the hypocenter. Far-field (beyond near-field), also termed teleseismic fault — A zone of the Earth’s crust within which the two sides have moved; faults may be hundreds of miles long, from 1 to over 100 miles deep, and not readily apparent on the ground surface. Focal mechanism — Refers to the direction of slip in an earthquake, and the orientation of the fault on which it occurs. Fragility — The probability of a specific level of damage given a specified level of hazard. Hypocenter — The location of initial radiation of seismic waves (i.e., the first location of dynamic rupture). Intensity — A metric of the effect, or the strength, of an earthquake hazard at a specific location, commonly measured on qualitative scales such as MMI, MSK, and JMA. Lateral-force-resisting system — A structural system for resisting horizontal forces, due for example to earthquake or wind (as opposed to the vertical force resisting system, which provides support against gravity). Liquefaction — A process resulting in a soil’s loss of shear strength, due to a transient excess of pore water pressure. Magnitude–frequency relation — The probability of occurrence of a selected magnitude — the commonest is log10 n(m) = a – bm [Gutenberg and Richter, 1954]. Magnitude — A unique measure of an individual earthquake’s release of strain energy, measured on a variety of scales, of which the moment magnitude MW (derived from seismic moment) is preferred. Meizoseismal — The area of strong shaking and damage. Near-field — Within one source dimension of the epicenter, where source dimension refers to the length or width of faulting, whichever is less. Nonductile frames — Frames lacking ducility or energy absorption capacity due to lack of ductile detailing — ultimate load is sustained over a smaller deflection (relative to ductile frames), and for fewer cycles. Normal fault — A fault that exhibits dip-slip motion, where the two sides are in tension and move away from each other. Peak ground acceleration (PGA) — The maximum amplitude of recorded acceleration (also termed the ZPA, or zero period acceleration).
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Pounding — The collision of adjacent buildings during an earthquake due to insufficient lateral clearance.
Response spectrum — A plot of maximum amplitudes (acceleration, velocity, or displacement) of a single-degree-of-freedom oscillator (SDOF), as the natural period of the SDOF is varied across a spectrum of engineering interest (typically, for natural periods from 0.03 to 3 or more sec, or frequencies of 0.3 to 30+ Hz). Reverse fault — A fault that exhibits dip-slip motion, where the two sides are in compression and move away towards each other. Ring of Fire — A zone of major global seismicity due to the interaction (collision and subduction) of the Pacific plate with several other plates. Sand boils or mud volcanoes — Ejecta of solids (i.e., sand, silt) carried to the surface by water, due to liquefaction. Seismic gap — A portion of a fault or seismogenic zone that can be deduced to be likely to rupture in the near term, based on patterns of seismicity and geological evidence. Seismic hazards — The phenomena and/or expectation of an earthquake-related agent of damage, such as fault rupture, vibratory ground motion (i.e., shaking), inundation (e.g., tsunami, seiche, dam failure), various kinds of permanent ground failure (e.g., liquefaction), fire, or hazardous materials release. Seismic moment — The moment generated by the forces generated on an earthquake fault during slip. Seismic risk — The product of the hazard and the vulnerability (i.e., the expected damage or loss, or the full probability distribution). Seismotectonic model — A mathematical model representing the seismicity, attenuation, and related environment. Soft story — A story of a building signifiantly less stiff than adjacent stories (that is, the lateral stiffness is 70% or less than that in the story above, or less than 80% of the average stiffness of the three stories above [BSSC, 1994]). Spectrum amplification factor — The ratio of a response spectral parameter to the ground motion parameter (where parameter indicates acceleration, velocity, or displacement). Strike — The intersection of a fault and the surface of the Earth, usually measured from north (e.g., the fault strike is N 60οW). Subduction — Refers to the plunging of a tectonic plate (e.g., the Pacific) beneath another (e.g., the North American) down into the mantle, due to convergent motion. Surface waves — Vibrational waves transmitted within the surficial layer of the Earth; are of two types, horizontally oscillating Love waves, analogous to S body waves, and vertically oscillating Rayleigh waves. Tectonic — Relating to, causing, or resulting from structural deformation of the Earth’s crust (from Greek tektonikos, from tektn or builder). Thrust fault — Low-angle reverse faulting (blind thrust faults are faults at depth occurring under anticlinal folds — they have only subtle surface expression). Trans-Alpide belt — A zone of major global seismicity, extending from the Mediterranean through the Middle East, Himalayas, and Indonesian archipelago, resulting from the collision of several major tectonic plates. Transform or strike-slip fault — A fault where relative fault motion occurs in the horizontal plane, parallel to the strike of the fault. Uniform hazard spectra — Response spectra with the attribute that the probability of exceedance is independent of frequency. Vulnerability — The expected damage given a specified value of a hazard parameter.
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References ACI (American Concrete Institute). (1995). Building Code Requirements for Structural Concrete (ACI 318–95) and Commentary (ACI 318R-95), American Concrete Institute, Farmington Hills, MI. Algermissen, S.T. (1983). An Introduction to the Seismicity of the United States, Earthquake Engineering Research Institute, Oakland, CA. Ambrayses, N.N. and Finkel, C.F. (n.d.). The Seismicity of Turkey and Adjacent Areas, A Historical Review, 1500–1800, EREN, Istanbul. Ambrayses, N.N. and Melville, C.P. (1982). A History of Persian Earthquakes, Cambridge University Press, Cambridge. Anagnos, T. and Kiremidjian, A.S. (1984). “Temporal Dependence in Earthquake Occurrence,” Proc. Eighth World Conf. Earthquake Eng., 1, 255–262, Earthquake Engineering Research Institute, Oakland, CA. Anderson, J. et al. (1952). “Lateral Forces of Earthquake and Wind,” Trans. Am. Soc. Civil Eng., 117. Anderson, J.G. and Trifunac, M.D. (1977). “Uniform Risk Absolute Acceleration Spectra,” Advances in Civil Engineering through Engineering Mechanics: Proc. Second Annual Engineering Mechanics Division Specialty Conference, Raleigh, NC, May 23–25, American Society of Civil Engineers, New York, pp. 332–335. Anderson, H. and Jackson, J. (1987). “Active Tectonics of the Adriatic Region,” Geophys. J. R. Astron. Soc., 91, 937–983. Arias, A. (1970). “A Measure of Earthquake Intensity,” in Seismic Design of Nuclear Power Plants, R. Hansen, Ed., MIT Press, Boston. Asencio, E. 1980. “Western Puerto Rico Seismicity,” U.S. Geological Survey Open-File Report 80–192, Menlo Park, CA. ATC 3–06. (1978). Tentative Provisions for the Development of Seismic Regulations for Buildings, Applied Technology Council, Redwood City, CA. Atkinson, G.M. (1995). “Attenuation and Source Parameters of Earthquakes in the Cascadia Region,” Bull. Seismol. Soc. Am., 85, 1327–1342. Atwater, B.F. et al. (1995). “Summary of Coastal Geologic Evidence for Past Great Earthquakes at the Cascadia Subduction Zone,” Earthquake Spectra, 11, 1–18. Bartlett, S.F. and Youd, T.L. (1992). Empirical Analysis of Horizontal Ground Displacement Generated by Liquefaction-Induced Lateral Spread, Tech. Rep. NCEER-92–0021, National Center for Earthquake Engineering Research, Buffalo, NY. Ben-Menaheim, A. 1979. “Earthquake Catalogue for the Middle East (92 BC–1980 AD),” Boll. Geofis. Teor. Appl., 21, 245–313. Bernreuter, D.L. et al. (1989). Seismic Hazard Characterization of 69 Nuclear Power Plant Sites East of the Rocky Mountains, NUREG/CR-5250, U.S. Nuclear Regulatory Commission, Washington, D.C. Bhatia, S.C., Kumar M.R., and Gupta H.K. (n.d.). A Probabilistic Seismic Hazard Map of India and Adjoining Regions, http://seismo.ethz.ch/gshap/ict/india.html. Blume, J.A. (1970). “An Engineering Intensity Scale for Earthquakes and Other Ground Motions,” Bull. Seismol. Soc. Am., 60, 217–229. Bolt, B.A. (1973). “Duration of Strong Ground Motion,” Proc. Fifth World Conf. on Earthquake Engineering, vol. 1, International Association of Earthquake Engineering, Tokyo, pp. 1304–1313. Bolt, B.A. (1993). Earthquakes, W.H. Freeman, New York. Bonilla, M.G. et al. (1984) “Statistical Relations among Earthquake Magnitude, Surface Rupture Length, and Surface Fault Displacement,” Bull. Seismol. Soc. Am., 74, 2379–2411. Boore, D.M. and Atkinson, G.M. (1987). “Stochastic Prediction of Ground Motion and Spectral Response Parameters at Hard-Rock Sites in Eastern North America,” Bull. Seismol. Soc. Am., 77, 440–487. Boore, D.M. and Joyner, W.B. (1991). “Estimation of Ground Motion at Deep-Soil Sites in Eastern North America,” Bull. Seismol. Soc. Am., 81, 2167–2185.
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Ellsworth, W.L. et al. (1999). A Physically-Based Earthquake Recurrence Model for Estimation of Long-Term Earthquake Probabilities, Workshop on Earthquake Recurrence: State of the Art and Directions for the Future, Istituto Nazionale de Geofisica, Rome, February. Erdik, M. et al. (n.d.). “Assessment of Earthquake Hazard in Turkey and Neighboring Regions,” (http:// seismo.ethz.ch/gshap/turkey/papergshap71.htm). Esteva, L. (1976) “Seismicity,” in Lomnitz, C. and Rosenblueth, E., Eds., Seismic Risk and Engineering Decisions, Elsevier, New York. European Seismological Commission. 1998. European Macroseismic Scale 1998, EMS-98, Grunthal, G. ed., Subcommission on Engineering Seismology, Working Group Macroseismic Scales, GeoForschungsZentrum, Potsdam, Germany (http: www.gfz-potsdam.de/pb1/pg2/ems_new/ INDEX.HTM). Evernden, J.F. (1991). “Computer Programs and Data Bases Useful for Prediction of Ground Motion Resulting from Earthquakes in California and the Conterminous United States,” U.S. Geological Survey Open-File Report 91–338, Menlo Park, CA. Freymueller, J., Kellogg, J., and Vega, V. (1993). “Plate Motions in the North Andean Region,” J. Geophys. Res., 98, 21853–21863. Gottfried, G. (1999). “Seismic Hazard Assessment for Central, North and Northwest Europe: GSHAP Region 3,” Ann. Geofis., 42, 999–1011. Greenwood, R.B. (1995). “Characterizing Blind Thrust Fault Sources — An Overview,” in Woods, M.C. and Seiple, W.R., Eds., The Northridge California Earthquake of 17 January 1994, Special Publ. 116, California Department of Conservation, Division of Mines and Geology, Sacramento, pp. 279–287. Grünthal, G. (n.d.). Compilation of the GSHAP Regional Seismic Hazard for Europe, Africa and the Middle East (http://seismo.ethz.ch/GSHAP/eu-af-me/euraf.html). GSHAP North Andes. (1998). Global Seismic Hazard Assessment Program, North Andean Region Final Report. Index Final Report, Observatorio de San Calixto, Bolivia Instituto de Investigaciones en Geociencias, Minería y Química (INGEOMINAS), Colombia Escuela Politécnica de Quito (EPN), Ecuador Instituto Geofísico del Perú (IGP), Fundación Venezolana de Investigaciones Sismológica (FUNVISIS),Venezuela Geoforschungs Zentrum (GFZ), Germany Institute of Geophysics, ETH, Switzerland Istituto Nazionale di Geofisica (ING) (http://seismo.ethz.ch/gshap/piloto/ report.html). Gumbel, E.J. (1958). Statistics of Extremes, Columbia University Press, New York. Gutenberg, B. and Richter, C.F. (1954). Seismicity of the Earth and Associated Phenomena, Princeton University Press, Princeton, NJ. Gutenberg, B. and Richter, C.F. (1956). “Magnitude and Energy of Earthquakes,” Ann. Geofis., 9, 1–15. Habermann, R.E. (1987). “Man-made Changes of Seismicity Rates,” Bull. Seismol. Soc. Am., 77, 141–159. Hamada, M. and O’Rourke, T.D., eds. (1992). Case Studies of Liquefaction and Lifeline Performance During Past Earthquakes, Volume 1: Japanese Case Studies, National Center for Earthquake Engineering Research, State University of New York, Buffalo, February. Hanks, T.C. and Johnston, A.C. (1992). “Common Features of the Excitation and Propagation of Strong Ground Motion for North American Earthquakes,” Bull. Seismol. Soc. Am., 82, 1–23. Hanks, T.C. and Kanamori, H. (1979). “A Moment Magnitude Scale,” J. Geophys. Res., 84, 2348–2350. Hanks, T.C. and McGuire, R.K. (1981). “The Character of High Frequency Strong Ground Motion,” Bull. Seismol. Soc. Am., 71, 2071–2095. Harlan, M.R. and Lindbergh, C. (1988). “An Earthquake Vulnerability Analysis of the Charleston, South Carolina,” Area Rep. No. CE-88–1, Department of Civil Engineering, The Citadel, Charleston, SC. Hausmann, M.R. (1990). Engineering Principals of Ground Modification, McGraw-Hill, New York. Hopper, M.G. (1985). “Estimation of Earthquake Effects Associated with Large Earthquakes in the New Madrid Seismic Zone,” U.S. Geological Society Open-File Report 85–457, Washington, D.C. Housner, G. (1984). “Historical View of Earthquake Engineering,” Proc. Eighth World Conf. on Earthquake Engineering, pp. 25–39, as quoted by S. Otani [1995]. Housner, G.W. (1963). “The Dynamic Behaviour of Water Tanks,” Bull. Seismol. Soc. Am., 53, 381–387. © 2003 by CRC Press LLC
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Hudson, D.E. (1979). Reading and Interpreting Strong Motion Accelerograms, Earthquake Engineering Research Institute, Oakland, CA. IAEE (International Association for Earthquake Engineering). (1992). Earthquake Resistant Regulations: A World List-1992, rev. ed. Prepared by the International Association for Earthquake Engineering, Tokyo, distributed by Gakujutsu Bunken Fukyu-Kai (Association for Science Documents Information) Oh-Okayama, 2–12–1, Meguroku, Tokyo, 152. Jasperse, B.H. and Ryan, C.R. (1992). Stabilization and Fixation Using Soil Mixing: Grouting, Soil Improvement and Geosynthetics, ASCE Geotechnical Spec. Publ. No. 30, American Society of Civil Engineers, New York, pp. 1273–1284. Jennings, C.W. (1994). Fault Activity Map of California and Adjacent Areas, Department of Conservation, Division of Mines and Geology, Sacramento, CA. Jiménez, M.J. (n.d.). Seismic Hazard Assessment in the Ibero-Maghreb Region (part of GSHAP) http:// seismo.ethz.ch/gshap/iberomag/report.html. Jordan, T.E. et al. (1983). “Andean Tectonics Related to Geometry of Subducted Nazca Plate,” Geol. Soc. Am. Bull., 94, 341–361. Joyner, W.B. and Boore, D.M. (1988). “Measurements, Characterization and Prediction of Strong Ground Motion,” in Earthquake Engineering and Soil Dynamics, vol. II, Recent Advances in Ground-Motion Evaluation, J.L. van Thun, Ed., Geotechnical Spec. Publ. No. 20, American Society of Civil Engineers, New York. Kameda, H. and Takagi, H. (1981). “Seismic Hazard Estimation Based on Non-Poisson Earthquake Occurrences,” Mem. Fac. Eng., Kyoto University, 43. Kanai, K. (1983). Engineering Seismology, University of Tokyo Press, Tokyo. Kawashima, K. and Aizawa, K. (1989). “Bracketed and Normalized Duration of Earthquake Ground Acceleration,” Earthquake Eng. Struct. Dyn., 18, 1041–1051. Lawson, A.C. and Reid, H.F. (1908–1910). The California Earthquake of April 18, 1906. Report of the State Earthquake Investigation Commission, California, State Earthquake Investigation Commission, Carnegie Institution of Washington, Washington, D.C. Lomnitz, C. (1974). Global Tectonics and Earthquake Risk, Elsevier, New York. McCann, W.R., Joyce, J., and Lithgow, C. (1987). “The Puerto Rico Platelet at the Northwestern Edge of the Caribbean Plate” [abstr.] EOS, 68, 1483. McGuire, R.K. (1978). “FRISK: Computer Program for Seismic Risk Analysis Using Faults as Earthquake Sources,” U.S. Geological Society Open-File Report 78–1007, Menlo Park, CA. McGuire, R.K., ed. (1993). Practice of Earthquake Hazard Assessment, International Association of Seismology and Physics of the Earth’s Interior, Denver, CO. McGuire, R.K. and Barnhard, T.P. (1979). “The Usefulness of Ground Motion Duration in Predicting the Severity of Seismic Shaking,” Proc. 2nd U.S. Natl. Conf. on Earthquake Engineering, Earthquake Engineering Research Institute, Oakland, CA. Meeting on Updating of MSK-64. (1981). Report on the Ad-hoc Panel Meeting of Experts on Updating of the MSK-64 Seismic Intensity Scale, Jena, 10–14 March 1980, Gerlands Beitr. Geophys., 90, 261–268. Midorikawa, S. (1991). “Attenuation of Peak Ground Acceleration and Velocity from Large Subduction Earthquakes,” Proc. Fourth International Conference on Seismic Zonation, vol. 2, Stanford University, August 25–29, pp. 179–186. Mitchell, J.K. (1981). “Soil Improvement: State-of-the-Art,” Proc. 10th Int. Conf. Soil Mech. and Found. Eng., vol. 4, Stockholm, pp. 509–565. Mohraz, B. (1976). “A Study of Earthquake Response Spectra for Different Geological Conditions,” Bull. Seismol. Soc. Am., 66, 915–935. Murphy, J.R. and O’Brien, L.J. (1977). “The Correlation of Peak Ground Acceleration Amplitude with Seismic Intensity and Other Physical Parameters,” Bull. Seismol. Soc. Am., 67, 877–915. National Academy of Sciences. (1988). Probabilistic Seismic Hazard Analysis, National Academy Press, Washington, D.C. © 2003 by CRC Press LLC
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NEIC. (1996). “Database of Significant Earthquakes,” in Seismicity Catalogs, 2 CD-ROMS available from National Earthquake Information Center, Golden, CO. Newmark, N.M. (1965). “Effects of Earthquakes on Dams and Embankments,” Geotechnique, 15, 129–160. Newmark, N.M. (1973). A Study of Vertical and Horizontal Earthquake Spectra, Dir. of Licensing, U.S. Atomic Energy Commission, Washington, D.C. Newmark, N.M. and Hall, W.J. (1982). Earthquake Spectra and Design, Earthquake Engineering Research Institute, Oakland, CA. Nishenko, S.P. and Buland, R. (1987). “A Generic Recurrence Interval Distribution for Earthquake Forecasting,” Bull. Seismol. Soc. Am., 77, 1382–1399. Norabuena, E.O., Snoke, J.A., and James, D.E. (1994). “Structure of the Subducted Nazca Plate beneath Perú,” J. Geophys. Res., 99, 9215–9226. NRC (National Research Council). (1985). Liquefaction of Soils During Earthquakes, National Academy Press, Washington, D.C. O’Rourke, T.D. and Hamada, M., Eds. (1992). Case Studies of Liquefaction and Lifeline Performance during Past Earthquakes, vol. 2, United States Case Studies, National Center for Earthquake Engineering Research, State University of New York, Buffalo, February. O’Rourke, T.D., Pease, J.W., and Stewart, H.E. (1992). “Lifeline Performance and Ground Deformation during the Earthquake,” in O’Rourke, T., Ed., USGS, Loma Prieta, California, Earthquake of October 17, 1989: Marina District, U.S. Government Printing Office, Washington, D.C. Ohsaki, Y. (1966). “Niigata Earthquakes, 1964 Building Damage and Condition, Soils and Foundations,” Jpn. Soc. Soil Mech. Found. Eng., 6, 14–37. Otani, S. (1995). “A Brief History of Japanese Seismic Design Requirements,” Concrete Int., 17, 46–53. Pacheco, J.F. and Sykes, L.R. (1992). “Seismic Moment Catalog of Large, Shallow Earthquakes. 1900–1989,” Bull. Seismol. Soc. Am., 82, 1306–1349. Paz, M., Ed. (1994). International Handbook of Earthquake Engineering: Codes, Programs, and Examples, Chapman & Hall, New York. Peng, M.H., Elghadamsi, F., and Mohraz, B. (1989). “A Simplified Procedure for Constructing Probabilistic Response Spectra,” Earthquake Spectra, 5, 393–408. Pennington, W. (1981). “Subduction of the Eastern Panama Basin and Seismotectonics of Northwestern South America,” J. Geophys. Res., 86, 10753–10770. Postpischl, D., Ed. 1985. Catalogo del Terremoti Italiani Dall’anno 1000 al 1980. Quaderni della Ricerca Scientifica, 1 14 2b, CNR-PFG, Bologna. Prevost, J.H. (1981). “DYNA-FLOW: A Nonlinear Transient Finite Element Analysis Program,” Rep. No. 81-SM-1, Department of Civil Engineering, Princeton University, Princeton, NJ. Reid, H.F. (1910). The Mechanics of the Earthquake, the California Earthquake of April 18, 1906, Report of the State Investigation Committee, vol. 2, Carnegie Institution of Washington, Washington, D.C. Reiter, L. (1990). Earthquake Hazard Analysis, Issues and Insights, Columbia University Press, New York. Richter, C.F (1935). An Instrumental Earthquake Scale, Bull. Seismol. Soc. Am., 25, 1–32. Richter, C.F. (1958). Elementary Seismology, W.H. Freeman, San Francisco. Satake, K. et al. (1996). “Time and Size of a Giant Earthquake in Cascadia Inferred from Japanese Tsunami Records of January 1700,” Nature, 379, 246–249. Saxena, S., Sharpe, B., and Acacio, A. (1991). Geoscience and Geotechnical, Philippines Earthquake Reconnaissance Report, A. Schiff, Tech. Ed., Earthquake Spectra, 7A (Suppl.). Schnabel, P.B., Lysmer, J., and Seed, H.B. (1972). SHAKE: A Computer Program for Earthquake Response Analysis of Horizontally Layered Sites, Rept. No. EERC-72–12, Earthquake Engineering Research Center, University of California, Berkeley. Scholz, C.H. (1990). The Mechanics of Earthquakes and Faulting, Cambridge University Press, New York. Schwartz, D.P. (1988). “Geologic Characterization of Seismic Sources: Moving into the 1990s,” in Earthquake Engineering and Soil Dynamics, vol. 2, Recent Advances in Ground-Motion Evaluation, J.L. van Thun, Ed., Geotechnical Spec. Publ. No. 20, American Society of Civil Engineers, New York.
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Schwartz, D.P. and Coppersmith, K.J. (1984). “Fault Behavior and Characteristic Earthquakes: Examples from the Wasatch and San Andreas Faults,” J. Geophys. Res., 89, 5681–5698. SEAOC. (1980). Recommended Lateral Force Requirements and Commentary, Seismology Committee, Structural Engineers of California, San Francisco. Seed, H.B. and Wilson, S.D. (1967). “The Turnagain Heights Landslide, Anchorage, Alaska,” J. Soil Mech. Found. Div., 93, 325–353. Seed, H.B. and Idriss, I.M. (1982). Ground Motions and Soil Liquefaction during Earthquakes, Earthquake Engineering Research Institute, Oakland, CA. Shedlock, K. (n.d.). Seismic Hazard Map of North and Central America and the Caribbean, GSHAP (http://seismo.ethz.ch/gshap/northam/report.html). Slejko, D. (n.d.). Seismic Hazard Assessment for the Adria Region, GSHAP (http://seismo.ethz.ch/gshap/ adria/report.html). Slemmons, D.B. (1977). “State-of-the-Art for Assessing Earthquake Hazards in the United States,” Report 6: Faults and Earthquake Magnitude, U.S. Army Corps of Engineers, Waterways Experiment Station, Misc. Paper s-73–1. Somerville, P. (1989). “Strong Ground Motion Attenuation in the Puget Sound-Portland Region,” Proceedings of Conference XLVIII: 3rd Annual Workshop on Earthquake Hazards in the Puget Sound, Portland Area, March 28–30, Portland, OR, Hays-Walter, W., Ed., U.S. Geological Survey, Reston, VA, pp. 50–51. Stein, R.S. and Yeats, R.S. (1989). “Hidden Earthquakes,” Sci. Am., June. Stepp, J.C. (1972). “Analysis of Completeness of the Earthquake Sample in the Puget Sound Area and its Effect on Statistical Estimates of Earthquake Hazard,” Proc. First Conf. Microzonation, Seattle, October, National Science Foundation, Washington, D.C., pp. 897–909. Structural Engineers Association of California. (1988). Recommended Lateral Force Requirements and Tentative Commentary, Structural Engineers Association of California, San Francisco. Sykes, L.R., McCann, W.R., and Kafka, A.L. (1982). “Motion of Caribbean Plate during Last Seven Million Years and Implications for Earlier Cenozoic Movements,” J. Geophys. Res., 87, 10656–10676. Toro, G.R. and McGuire, R.K. (1987). “An Investigation into Earthquake Ground Motion Characteristics in Eastern North America,” Bull. Seismol. Soc. Am., 77, 468–489. Trifunac, M.D. and Brady, A.G. (1975). “A Study on the Duration of Strong Earthquake Ground Motion,” Bull. Seismol. Soc. Am., 65, 581–626. Trifunac, M.D. and Brady, A.G. (1975). “On the Correlation of Seismic Intensity Scales with the Peaks of Recorded Strong Ground Motion,” Bull. Seismol. Soc. Am., 65, 139–162. Trifunac, M.D. and Novikova, E.I. (1995). State of the Art Review on Strong Motion Duration, Proc. 10th European Conf. on Earthquake Engineering, European Association of Earthquake Engineering, pp. 131–140. Uniform Building Code. (1997). 1997 Uniform Building Code, International Conference of Building Officials, Whittier, CA. U.S. Army. (1992). Seismic Design for Buildings, Army: TM 5–809–10; Navy: NAVFAC P-355; USAF: AFM88–3, Chapter 13, Depts. of the Army, Navy, and Air Force, Washington, D.C. Available from the National Technical Information Service (NTIS), Military Publications Division, Washington, D.C. USGS. (1999). “Earthquake Probabilities in the San Francisco Bay Region: 2000 to 2030 — A Summary of Findings,” Working Group on California Earthquake Probabilities, U.S. Geological Survey OpenFile Report 99–517, Menlo Park, CA. USGS. (n.d.). http://quake.wr.usgs.gov/recenteqs/beachball.html. Usami, T. (1981). Nihon Higai Jishin Soran (List of Damaging Japanese Earthquakes, in Japanese), University of Tokyo Press, Tokyo. Valensise, G. and Pantosti, D. (1991). “A 125 Kyr-long Geological Record of Seismic Source Repeatability: the Messina Straits (Southern Italy) and the 1908 Earthquake (MS 7.5),” Terra Nova, 4.
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Wald, D.J., Burdick, L.J., and Somerville, P.G. (1988). “Simulation of Acceleration Time Histories Close to Large Earthquakes,” in Earthquake Engineering and Soil Dynamics, vol. 2, Recent Advances in Ground-Motion Evaluation, J.L. van Thun, Ed., Geotechnical Spec. Publ. No. 20, American Society of Civil Engineers, New York. Wells, D.L. and Coppersmith, K.J. (1994). “Empirical Relationships among Magnitude, Rupture Length, Rupture Width, Rupture Area and Surface Displacement,” Bull. Seismol. Soc. Am., 84, 974–1002. Wheeler, R.L. et al. (1994). “Elements of Infrastructure and Seismic Hazard in the Central United States,” U.S. Geological Survey Prof. Paper 1538-M, Washington, DC. Woo, G. and Muirwood, R. (1984). “British Seismicity and Seismic Hazard,” Proc. of the Eighth World Conference on Earthquake Engineering, vol. 1, pp. 39–44. Wood, H.O. and Neumann, F. (1931). “Modified Mercalli Intensity Scale of 1931,” Bull. Seismol. Soc. Am., 21, 277–283. Wyllie, L.A., Ed. (1986). “The Chile Earthquake of March 3, 1985,” Earthquake Spectra, 2, 249–513. Yamazaki, F. (1993). “Comparative Study of Attenuation Characteristics of Ground Motion in Europe, North America and Japan,” Bull. Earthquake Resistant Structure Research Center, no. 26, University of Tokyo, pp. 39–56. Yegulalp, T.M. and Kuo, J.T. (1974). “Statistical Prediction of the Occurrence of Maximum Magnitude Earthquakes,” Bull. Seismol. Soc. Am., 64, 393–414. Youngs, R.R. and Coppersmith, K.J. (1987). “Implication of Fault Slip Rates and Earthquake Recurrence Models to Probabilistic Seismic Hazard Estimates,” Bull. Seismol. Soc. Am., 75, 939–964. Youngs, R. R. and Coppersmith, K J. (1989). “Attenuation Relationships for Evaluation of Seismic Hazards from Large Subduction Zone Earthquakes,” Proc. Conference XLVIII: 3rd Annual Workshop on Earthquake Hazards in the Puget Sound, Portland Area; March 28–30, Portland, OR, Hays-Walter, W., ed., U. S. Geological Society, Reston, VA, pp. 42–49. Zhang, P. (n.d.) Global Seismic Hazard Assessment Program (GSHAP) in Continental Asia (http:// seismo.ethz.ch/gshap/eastasia/eastasia.html).
Further Reading There is a wealth of good references on earthquakes. The reader is referred to Earthquakes by B.A. Bolt (1993, Freeman, San Francisco) for an excellent and readable introduction to the subject; The Mechanics of Earthquakes and Faulting by C.A. Scholz (1990, Cambridge University Press, New York) for an erudite treatment of seismogenesis; The Geology of Earthquakes by R.S. Yeats, K. Sieh, and C.R. Allen (1997, Oxford University Press, New York) for an exhaustive review of faulting around the world; Modern Global Seismology by T. Lay and T.C. Wallace (1995, Academic Press, New York) for a readable theoretical text on seismology (a very rare thing); and to the study by the Working Group on California Earthquake Probabilities (USGS OF99–517, 1999) for a state-of-the-art review of seismicity characterization for seismic hazard estimation (see also the GSHAP documents discussed below). Richter’s classic Elementary Seismology (1958, Freeman, San Francisco) remains of enormous value, as does Earthquake Engineering, edited by R.L. Wiegel (1970, Prentice-Hall, Englewood Cliffs, NJ). Ambraseys’ various studies on Persian, Turkish, and other earthquakes are of interest to anyone working in the Trans-Alpide belt. Lastly, the GSHAP project (Global Seismic Hazard Assessment Project) documents, freely available on the Web at http://seismo.ethz.ch/GSHAP/, are a generous resource and contribution on tectonics and seismicity around the world, for which this author is indebted.
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5 Engineering Models of Strong Ground Motion 5.1 5.2 5.3
Introduction The Attenuation Relation Model Parameters Ground Motion Parameters · Earthquake Magnitude · Source-to-Site Distance · Faulting Mechanism · Local Site Conditions · Stress Drop · Source Directivity and Radiation Pattern · Hanging-Wall and Footwall Effects · Tectonic Environment · Instrument Location
5.4
Statistical Methods Regression Analysis · Standard Deviation · Predicted Value
5.5
Theoretical Methods Source Spectrum · Stress Drop · Crustal Attenuation · Site Response · Peak Ground-Motion Parameters
5.6
Engineering Models Western North America · Eastern North America · Europe · Japan · Worldwide Subduction Environments · Worldwide Extensional Environments · Hanging-Wall and Footwall Effects · Rupture Directivity Effects
Kenneth W. Campbell ABS Consulting and EQECAT, Inc. Portland, Oregon
5.7 Engineering Evaluation Defining Terms References Further Reading Appendix–Notation
5.1 Introduction There are two basic methods used to estimate strong ground motion in engineering practice. In the first method, known as deterministic seismic hazard analysis or DSHA, ground motion is estimated from a given set of seismological parameters, such as earthquake magnitude and the distance from the earthquake rupture zone to the site of interest. In the second method, referred to as probabilistic seismic hazard analysis or PSHA, ground motion is estimated statistically using all possible earthquake locations and magnitudes together with their expected probabilities of occurring. Both of these methods have one thing in common: they need a means of estimating strong ground motion from the specified seismological parameters. This estimation is usually done using a ground motion relation, or what is commonly referred to in engineering as an attenuation relation. Only engineering models that directly predict ground-motion amplitude or that predict the modulation of this amplitude from such effects as fault geometry and source directivity are discussed in this chapter. Duration is an important aspect of strong ground motion, especially for the inelastic response
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of structures, but much less attention has been paid to predicting duration and, therefore, no consensus engineering models are available. Generally speaking, the inelastic behavior of structures is included in structural design through the use of time histories and structural ductility factors, which are the topics of other chapters in this book. Although it is not the intent of this chapter to provide a history of engineering models, it is important to mention some of the pioneers whose early and continued efforts led to their widespread acceptance in engineering and engineering seismology, particularly for use in the then-fledgling field of PSHA. Some of these pioneers (listed alphabetically) include Neville Donovan, Luis Esteva, George Housner, Ed Idriss, Bill Joyner, Kiyoshi Kanai, Robin McGuire, H. Bolton Seed, and Mihailo Trifunac. Many others, including the author, have followed in the footsteps of these pioneers, and this body of work forms the basis for the contemporary engineering models discussed in this chapter. A more complete review can be found in the references provided in the section entitled Further Reading.
5.2 The Attenuation Relation In its most basic form, an attenuation relation can be described by the expression: Y = c 1e c 2 M R − c 3 e − c 4R e c 5 F e c 6Se
(5.1)
or by its more common logarithmic form: ln Y = c 1 + c 2 M − c 3 ln R − c 4 R + c 5 F + c 6 S + ε
(5.2)
where the distance term R is given by one of the alternative expressions: r + c 7 exp (c 8 M ) R= 2 r + c 7 + exp (c 8 M )
[
or
]
2
(5.3)
In the above equations, Y is the strong-motion parameter of interest, M is magnitude, F is the faulting mechanism of the earthquake, S is a description of the local site conditions beneath the site, ε is a random error term with a mean of zero and a standard deviation of σln Y (the standard error of estimate of ln Y), and r is a measure of the shortest distance from the site to the source of the earthquake. In the more complicated forms of Equations 5.1 to 5.3, the coefficients c3, c6, and c7 are defined in terms of M and R. Many of these coefficients also have been found to be dependent on the tectonic environment of the regions in which the earthquakes occurred. Figure 5.1 shows an attenuation relation for peak ground acceleration (PGA) and the database on which it was based. A selected set of attenuation relations that are commonly used for engineering evaluation and design throughout the world are presented later. Many of the mathematical expressions in Equations 5.1 to 5.3 have their roots in earthquake seismology [Lay and Wallace, 1995]. For example, the expressions Y ∝ e c2M and ln Y ∝ c2M are consistent with the original definition of earthquake magnitude [Richter, 1935]. The expressions Y ∝ R –c3 and ln Y ∝ –c3 ln R are consistent with the geometric attenuation of the seismic wave front as it propagates away from the earthquake source. Some attenuation relations assume c3 = 1, which is the theoretical value for spherical spreading of the wave front from a point source in a homogeneous whole space. If unconstrained, c3 typically will be greater than 1. Sometimes c3 is varied as a function of distance to accommodate differences in the geometric attenuation of different wave types, such as direct waves or surface waves, and to account for the critical reflection off the base of the crust or other strong crustal reflectors. The expressions Y ∝ e –c4R and ln Y ∝ –c4R are consistent with the anelastic attenuation that results from material damping and scattering as the seismic waves propagate through the crust. The relationship
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Uncorrected PGA Corrected PGA
Horizontal Acceleration (g)
1
M 7.5
0.1 M 5.5
Strike Slip Faults Holocene Soil
0.01
1
10
100
Distance to Seismogenic Rupture (km) 8.0 Corrected Additional Uncorrected
Moment Magnitude
7.5 7.0 6.5 6.0 5.5 5.0 4.5 0
10
20
30
40
50
60
Distance to Seismogenic Rupture (km) FIGURE 5.1 Example PGA attenuation relation (top) and its associated database (bottom). Uncorrected recordings are analog or digital acceleration time histories that have not been processed and, therefore, can provide only estimates of PGA. Corrected recordings are acceleration times histories that have been processed to derive velocity and displacement time histories, response spectra, and Fourier amplitude spectra. (From Campbell, K.W. and Bozorgnia, Y. 1999. “Vertical Ground Motion: Characteristics, Relationship with Horizontal Component, and Building-Code Implications,” in Proc. SMIP99 Seminar on Utilization of Strong-Motion Data, M. Huang, Ed., Sept. 15, San Francisco, pp. 23–49. California Strong Motion Instrumentation Program, Sacramento. With permission.)
between Y and the remaining parameters have been established over the years from both empirical and theoretical ground-motion modeling. The mathematical relationships defined in Equation 5.3 are used to incorporate the widely held belief that ground motion at short period or high frequency should become less dependent on magnitude (or saturate) close to the causative fault. Schnabel and Seed [1973] first modeled this behavior using simple geometrical considerations. Since then, similar results have been obtained using empirical models [Campbell, 1981] and theoretical finite-source models [Anderson, 2000]. Now, most modelers consider this an accepted behavior of near-fault ground motion.
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The remainder of this chapter describes in some detail the strong-motion and seismological parameters that appear in Equations 5.1 to 5.3. The discussion specifically addresses issues regarding the use of attenuation relations to predict strong ground motion for engineering evaluation and design. Particular emphasis is placed on the prediction of peak time-domain and peak frequency-domain parameters, because these parameters are those most commonly used by engineers. This is followed by a selected compilation of recently published attenuation relations.
5.3 Model Parameters 5.3.1 Ground Motion Parameters A complete description of ground motion requires defining its amplitude as a function of time by means of a time history or equivalently in the frequency domain by means of a Fourier spectrum. However, for most engineering applications such a complex description of ground motion is not necessary. Instead, simple time-domain and frequency-domain parameters are used to define strong ground motion. Historically, PGA and peak ground velocity (PGV) have been the most common time-domain parameters used in engineering. They represent the maximum absolute amplitude of ground motion measured from a recorded or synthetic acceleration or velocity time history. As seismic design procedures became more sophisticated, engineers began to incorporate natural period and natural frequency in the design of a structure through the use of a response spectrum [Gupta, 1993]. The most common response-spectral parameters are pseudoacceleration (which has been variously denoted PSSA, PSA, or SA) and pseudovelocity (which has been variously denoted PSRV, PSV, or SV). The terms PSA and PSV are used throughout this chapter to represent pseudoacceleration and pseudovelocity, noting that Gupta [1993] prefers the use of SA and SV, because these latter terms have also been used to define absolute acceleration and relative velocity, which are similar but not equal to PSA and PSV. PSA and PSV are related to relative displacement (SD) by the expression: 2
2π 2π PSA = PSV = SD Tn Tn
(5.4)
where Tn is the undamped natural period of a single-degree-of-freedom (SDOF) oscillator. It has been common practice in the past to estimate a design response spectrum from PGA or from a combination of PGA, PGV, and peak ground displacement [Campbell, 2000a; Newmark and Hall, 1982]. Even in modern U.S. building codes, the design response spectrum is defined in terms of only two natural periods, 0.2 and 1 sec [Leyendecker et al., 2000]. Such procedures are typically used in building codes and other seismic regulations where a simple prescribed method for estimating a simple response spectrum is required. For more important structures, it is common practice to develop response spectra directly from attenuation relations, rather than use code-prescribed response spectra.
5.3.2 Earthquake Magnitude Earthquake magnitude is used to define the “size” of an earthquake. There are many different scales that can be used to define magnitude. The magnitude scales that have commonly been used in the development of attenuation relations throughout the world are moment magnitude (denoted M or MW), surface-wave magnitude MS , short-period body-wave magnitude mb, local magnitude ML, Lg magnitude (denoted mLg or mN), and JMA magnitude MJ. These magnitude scales are compared in Figure 5.2. Seismological network operators typically use one of the above magnitude scales as a definition of magnitude in their region. However, even the use of the same magnitude scale can lead to different
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W
MS MJMA
M
~
M
9
8
mB ML
MAGNITUDE
7
mb
6
5
S
M
L
M
4
3
2 2
3
4
5
6
7
8
9
10
MOMENT MAGNITUDE
FIGURE 5.2 Comparison of magnitude scales. (From Heaton, T.H., Tajima, F., and Mori, A.W. 1986. “Estimating Ground Motions Using Recorded Accelerograms,” Surv. Geophys., 8, 25–83. With permission.)
regional estimates of magnitude due to differences in the way it is locally defined and calculated. The definition of all peak time-domain magnitude scales can be given by the equation [Lay and Wallace, 1995]:
(
)
M = log ( A T ) + f R, hhypo + C s + Cr
(5.5)
where A is the amplitude of the seismic phase on which the magnitude scale is based measured on a seismometer, T is the period of the signal, f(R, hhypo ) is a correction for the distance from the earthquake source to the seismometer and the hypocentral depth hhypo, Cs is a correction for the siting of the seismometer, and Cr is a correction for the earthquake source region. There is an increasing tendency to adopt MW as the worldwide standard for quantifying magnitude because of its strong physical and seismological basis [Bolt, 1993]. By definition, MW is related to seismic moment M0 , a measure of the seismic energy radiated by an earthquake, by the formula [Hanks and Kanamori, 1979; Kanamori, 1978]: MW =
2 log M 0 − 10.7 3
where M 0 = µA f D = 2 µES ∆σ
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where
µ = Af = D = ∆σ = Es =
shear modulus of the crust in the source region rupture area average displacement on the rupture plane stress drop radiated seismic energy
The definition based on Af D allows M0 to be derived from geological faulting parameters that can be easily observed in the field for large surface-rupturing earthquakes. The definition based on Es /∆σ allows M0 to be derived from seismological measurements.
5.3.3 Source-to-Site Distance Source-to-site distance is used to characterize the decrease in ground motion as it propagates away from the earthquake source. Distance measures can be grouped into two broad classes depending on whether they treat the earthquake source as a single point or as a finite fault rupture. Point-source distance measures include epicentral distance repi and hypocentral distance rhypo . Hypocentral distance is the distance from the site to the hypocenter or focus of an earthquake, defined as the point within the Earth where the earthquake rupture begins. Epicentral distance is the distance from the site to the epicenter, defined as the point on the Earth’s surface directly above the hypocenter. The two measures are related to one another by the expression: 2 2 rhypo = repi + hhypo
(5.7)
where hhypo is the depth of the hypocenter, measured from the Earth’s surface. Generally speaking, repi and rhypo are poor measures of distance for earthquakes with large rupture areas. They are primarily used for characterizing distances for small earthquakes that can be reasonably represented by a point source. Experience has shown that attenuation relations that use point-source measures should not be used to estimate ground motions close to large earthquakes unless there is absolutely no other alternative available. There are three finite-source distance measures that are commonly used in practice: rjb or the closest horizontal distance to the vertical projection of the rupture plane, introduced by Joyner and Boore [1981]; rrup or the closest distance to the rupture plane, introduced by Schnabel and Seed [1973]; and rseis or the closest distance to the seismogenic part of the rupture plane, introduced by Campbell [1987, 2000b]. The measure rseis assumes that fault rupture within the near-surface sediments or shallow fault gouge is nonseismogenic, which was later proposed and demonstrated seismologically by Marone and Scholz [1988]. These distance measures are compared in Figure 5.3. Although rjb is reasonably easy to estimate for a future (design) earthquake, rrup and rseis are not as easily determined, particularly when the earthquake is not expected to rupture the entire seismogenic width of the crust. In such cases, the average depth to the top of the inferred rupture plane, drup , or to the seismogenic part of this rupture plane, dseis, can be calculated from the equation [Campbell, 2000c]:
[
]
1 H + H bot − W sin (δ) di = 2 top H i
for di ≤ H i
(5.8)
otherwise
where the subscript i = rup or seis is the distance measure of interest, Hbot is the depth to the bottom of the seismogenic part of the crust, Htop is the depth to the top of the fault, Hseis is the depth to the top of the seismogenic part of the fault, δ is the angle between the Earth’s surface and a line extending
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Vertical Faults rjb rrup rseis
Seismogenic Depth
rhypo
Hypocenter
Dipping Faults rjb = 0
rjb
rrup rseis rhypo
Seismogenic Depth
Hypocenter
rseis & rrup
rhypo
Hypocenter
FIGURE 5.3 Comparison of distance measures. (From Abrahamson, N.A. and Shedlock, K.M. 1997. “Overview,” Seismol. Res. Lett., 68, 9–23. With permission.)
down-dip perpendicular to the strike of the fault (dip angle); and W is the down-dip width of the fault rupture. The rupture plane width can be calculated from the expression [Wells and Coppersmith, 1994]: log W = −1.01 + 0.32 MW
(5.9)
where W is in km and the standard deviation of log W is 0.15. Campbell [1997] recommends using Hseis ≥ 3 km even when the fault ruptures to the Earth’s surface. This recommendation is based on (1) observations of aftershock distributions and background seismicity, (2) slip distributions from earthquake modeling studies, and (3) an independent assessment of seismogenic rupture by Marone and Scholz [1988]. Representative values of drup and dseis for various values of δ are given in Table 5.1.
5.3.4 Faulting Mechanism The faulting mechanism, also referred to as the type or style of faulting, characterizes the direction of slip on the fault plane, seismologically known as the rake angle [Lay and Wallace, 1995]. Rake angle © 2003 by CRC Press LLC
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TABLE 5.1
Representative Values for the Average Depth to the Top of Fault Rupture
MW
W (km)
δ = 30°
δ = 45°
δ = 90°
δ = 30°
δ = 45°
δ = 90°
5.00 5.25 5.50 5.75 6.00 6.25 6.50 6.75 7.00 7.25 7.50 7.75 8.00
3.9 4.7 5.6 6.8 8.1 9.8 11.7 14.1 17.0 20.4 24.5 29.5 35.5
6.5 6.3 6.1 5.8 5.5 5.1 4.6 4.0 3.3 2.4 1.4 0.1 0.0
6.1 5.8 5.5 5.1 4.6 4.0 3.3 2.5 1.5 0.3 0.0 0.0 0.0
5.6 5.2 4.7 4.1 3.4 2.6 1.6 0.4 0.0 0.0 0.0 0.0 0.0
6.5 6.3 6.1 5.8 5.5 5.1 4.6 4.0 3.3 3.0 3.0 3.0 3.0
6.1 5.8 5.5 5.1 4.6 4.0 3.3 3.0 3.0 3.0 3.0 3.0 3.0
5.6 5.2 4.7 4.1 3.4 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0
drup (km)
dseis (km)
Note: Assumes Htop = 0, Hbot = 15 km, and Hseis = 3 km. Source: Adapted from Campbell, K.W. 2000c. “Erratum: Empirical Near-Source Attenuation Relationships for Horizontal and Vertical Components of Peak Ground Acceleration, Peak Ground Velocity, and Pseudo-Absolute Acceleration Response Spectra,” Seismol. Res. Lett., 71, 353–355. With permission.
is a continuous variable representing the angle between the direction of slip on the fault plane and the strike or the orientation of the fault on the Earth’s surface. Rake angle has not been used directly in an attenuation relation to define faulting mechanism. Instead, the faulting mechanism has been classified in terms of two or more categories. These categories include strike slip, reverse slip, and normal slip (Chapter 4). The values of rake angle corresponding to these faulting mechanisms are 0° for left-lateral strike-slip faulting, 180° for right-lateral strike-slip faulting, 90° for reverse faulting, and 270° for normal faulting [Lay and Wallace, 1995]. Thrust faulting is a special case of reverse faulting in which the dip angle of the rupture plane is less than 45°. A combination of strike-slip with either reverse-slip or normal-slip is known as oblique faulting and will have a rake angle that falls between those given here. Campbell [1981] empirically demonstrated that reverse and thrust faulting causes higher ground motion than strike-slip or normal faulting. Many subsequent studies have proven this effect to be universal. It has been common practice in the past to put strike-slip and normal-faulting events into a single category. However, a recent study by Spudich et al. [1999] suggests that normal-faulting events, or strike-slip events in an extensional stress regime, may have lower ground motions than other types of shallow crustal earthquakes. There has been a great deal of interest in blind thrust faults after observing unusually large ground motions during the 1987 Whittier-Narrows, CA earthquake, the 1988 Saguenay, Canada earthquake, and the 1994 Northridge, CA earthquake. Whether similarly high ground motions can be expected from all future blind-thrust earthquakes is speculative at present. However, it cannot be ruled out, considering the current limited observational database. The higher ground motions observed during the previously mentioned earthquakes have been found to correspond to higher-than-average stress drop. More theoretical and empirical studies will be needed before there is a clear understanding why these earthquakes produced such high stress drops and how such events can be predicted in the future.
5.3.5 Local Site Conditions Local site conditions describe the materials that lie directly beneath the site from the surface to basement rock. They are usually defined in terms of surface or near-surface geology, shear-wave velocity, and the depth of sediments beneath the site. The latter two descriptions are preferred because they represent parameters that can be related directly to the dynamic response of the materials beneath the site as the
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TABLE 5.2
Definition of Building-Code Site Classes 30-m Velocity, VS30 (m/sec)
Site Class A B BC C CD D DE E
Soil Profile Name Hard rock Rock BC boundary Very dense soil and soft rock CD boundary Stiff soil DE boundary Soft soil
Range
Average
>1,500 760–1500 555–1000 360–760 270–555 180–360 90–270 <180
1890 1130 760 560 360 270 180 150
Source: Adapted from Wills, C.J. et al. 2000. “A Site-Conditions Map for California Based on Geology and Shear-Wave Velocity,” Bull. Seismol. Soc. Am., 90, S187–S208. With permission.
ground motion propagates from below see (Chapter 6). A general description of the different site classes used in recently published attenuation relations is presented later and in the Appendix. Traditionally, local site conditions have been classified simply as soil or rock. Many attenuation relations continue to use this simple classification. Campbell [1981] proposed that site conditions should be subdivided into shallow soil, soft soil, Holocene or firm soil, and Pleistocene or very firm soil, and that rock should be further subdivided into soft or primarily sedimentary rock and hard or primarily crystalline rock. Although this more refined geological classification has not been utilized in most attenuation relations, Campbell and Bozorgnia [in press] clearly demonstrated the importance of this classification scheme in the prediction of near-source ground motion. Park and Elrick [1998] and Wills and Silva [1998] have also shown that a more refined geological classification is warranted based on measurements of shear-wave velocity in various geologic units in California. There are typically two methods for classifying a site in terms of shear-wave velocity, VS . The first is the average value of VS in the top 30 m (100 ft) of a site profile, referred to as 30-m velocity. The second is the average value of VS over a depth equal to a quarter-wavelength of the period or frequency of interest, referred to by Boore and Joyner [1991] as effective velocity. Modern U.S. building codes [BSSC, 1998; ICBO, 1997; ICC, 2000] have all adopted the 30-m velocity, designated VS30 in this chapter, as the primary basis for classifying a site for purposes of incorporating local site conditions in the estimation of design ground motion. These building codes define five site classes in terms of a range of 30-m velocities, designated A through E. Wills et al. [2000] extended this classification in California to include intermediate values. Typical values (usually the midpoint of the ranges) are given in Table 5.2. For the site classes defined by inequalities, typical values for Soft Soil are from Borcherdt [1994] and those for Hard Rock, considered to be an older sedimentary rock in eastern North America, are from Savy and coworkers [1987]. The value of 30-m velocity is determined from the formula: n
VS 30 =
n
∑ ∑d di
i =1
i
VSi
(5.10)
i =1
where di is the thickness and VSi is the shear-wave velocity of soil layer i. Progressively deeper soil layers are incorporated until the summation in the numerator equals 30 m (100 ft). Boore and coworkers [1993] were the first to use site categories based on VS30 in the development of an attenuation relation. In 1994, these same authors were the first to use VS30 directly as a parameter in an attenuation relation [Boore et al., 1994]. Because of its adoption in the building codes, 30-m velocity has become the preferred site parameter in engineering analysis. According to Boore and Joyner [1997], VS30 = 310 m/sec and VS30 = 620 m/sec are reasonable estimates of 30-m velocity for generic soil and generic rock sites in western North America. © 2003 by CRC Press LLC
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Joyner and coworkers [1981] proposed a VS-based site parameter that is related to the nonresonant amplification produced as a result of the energy conservation of seismic waves propagating vertically upward through a site profile of gradually changing velocity. This parameter, later referred to as effective velocity [Boore and Joyner, 1991], is defined as the average velocity from the surface to a depth corresponding to a quarter-wavelength of the period or frequency of interest. Effective velocity can be calculated from Equation 5.10 by summing to a depth corresponding to a quarter-wavelength rather than 30 m. This depth is given by the expression [Boore, in press]: D1/ 4 ( f ) =
n
∑d
i
(5.11)
i =1
where T = 1/f is the period of interest. Progressively deeper soil layers are used in the above summation until the equality n
∑d
i
VSi = T 4
i =1
is met. Effective velocity should be a better site parameter than 30-m velocity because it takes the period of the wave into account. Joyner and coworkers [Joyner and Fumal, 1984; Joyner and Boore, 1988] are the only investigators to include effective velocity as a parameter in an empirical attenuation relation. Effective velocity has found widespread use in the calculation of site amplification using the stochastic method discussed later. The two attenuation relations for the eastern United States presented later were developed using the stochastic method. Sediment or basin depth is the depth to the basement-rock horizon beneath the site. Basement rock is a geological term that is used to describe the more resistant, generally crystalline rock that lies beneath layers or irregular deposits of younger, relatively deformed sedimentary rock. It was introduced as a site parameter by Trifunac and Lee [1979] and later used by Campbell [1987, 2000b] to quantify the response of long-period ground motion. Both of these investigators have continued to use this parameter in their subsequent studies but it has not generally been used by others. Recently its importance has been recognized by several seismologists. For example, based on empirical and theoretical considerations, Joyner [2000] found that sediment depth appeared to be a reasonable proxy for modeling the effects of traveling surface waves generated at the edge of a sedimentary basin. Lee and Anderson [2000] and Field and the SCEC Phase III Working Group [2000] found that sediment depth could be used to approximately model the three-dimensional response of the Los Angeles basin. Rodriguez-Marek and coworkers [2001] found that depth to bedrock, defined as VS ≥ 760 m/sec, was an important parameter in estimating seismic site response from the 1989 Loma Prieta and 1994 Northridge, CA earthquakes.
5.3.6 Stress Drop Stress drop or, more correctly, dynamic stress drop, is the amount of stress that is relieved at the rupture front during an earthquake. Theoretical studies have shown that higher stress drop results in higher ground motion. It has been shown theoretically [Boore and Atkinson, 1987; Boore, in press] and implied empirically [Campbell and Bozorgnia, in press] that stress drop has a larger effect on short-period ground motion. No attenuation relation explicitly includes stress drop as a parameter. However, stress drop is one of the parameters that must be included in the calculation of ground motion using the stochastic method. High stress drops are the likely cause of the relatively high ground motions observed during some recent blind-thrust earthquakes. On the other hand, low stress drops may be the cause of the relatively low short-period ground motions observed during the 1999 Chi-Chi, Taiwan (MW 7.6) [Tsai and Huang, 2000; Boore, 2001] and Kocaeli, Turkey (MW 7.4) earthquakes [Anderson, 2000]. The observation of © 2003 by CRC Press LLC
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FIGURE 5.4 Radiation pattern showing the variability of compressional and horizontal shear-wave amplitude for a fault rupture propagating from left to right. The diagrams on the left are for a rupture propagation velocity of 0.5 times the shear-wave velocity and those on the right are for a rupture propagation velocity of 0.9 times the shearwave velocity. (From Lay, T. and Wallace, T.C. 1995. Modern Global Seismology, Academic Press, San Diego. With permission.)
relatively low ground motions during the Chi-Chi earthquake is particularly significant, because it was a large thrust earthquake, which had been expected from previous empirical and theoretical studies to have relatively large ground motions. The relatively low stress drops implied for the Taiwan and Turkey earthquakes may have been caused by the large total slip on the causative faults [Anderson, in press] or because they ruptured the Earth’s surface [Somerville, 2000]. More study will be needed to better understand the phenomena that may have contributed to these low ground motions. If these earthquakes are found to be typical of similar large earthquakes worldwide, then the implication is that the current attenuation relations overpredict short-period ground motions from large earthquakes, an attribute suggested from observations of precarious rocks near great earthquakes on the San Andreas fault [Brune, 1999].
5.3.7 Source Directivity and Radiation Pattern Radiation pattern is the geographic asymmetry of the ground motion caused by the faulting process. It is closely related to the faulting mechanism of the earthquake. The radiation pattern can be perturbed by source directivity, which causes an increase or decrease in the ground motion as a result of the propagation of the rupture, analogous to the Doppler effect in sound. Ground-motion amplitudes in the forward direction of rupture propagation will be increased, while those in the backward direction will be decreased due to source directivity. This effect is particularly important during unilateral faulting. The general concept of radiation pattern and source directivity is shown schematically in Figure 5.4. Source directivity has its largest positive effect on the long-period horizontal ground-motion component that is oriented perpendicular or normal to the rupture plane (the fault-normal component). A schematic showing the radiation pattern for a vertical strike-slip fault and its effect on the fault-normal and fault-parallel components of near-fault ground displacements is shown in Figure 5.5. © 2003 by CRC Press LLC
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FIGURE 5.5 Radiation pattern for a vertical strike-slip fault showing its effect on the fault-normal and fault-parallel components of near-fault ground displacement. (From Somerville, P.G., Smith, N.F., Graves, R.W., and Abrahamson, N.A. 1997. “Modification of Empirical Strong Ground Motion Attenuation Relations to Include the Amplitude and Duration Effects of Rupture Directivity,” Seismol. Res. Lett., 68, 199–222. With permission.)
Rupture directivity is a well-known seismological principle [Lay and Wallace, 1995]. It has been observed or proposed as a factor in controlling the azimuthal dependence of strong ground motion during the 1979 Imperial Valley earthquake [Singh, 1985], the 1980 Livermore earthquakes [Boatwright and Boore, 1982], the 1989 Loma Prieta earthquake [Campbell, 1998], the 1992 Landers earthquake [Campbell and Bozorgnia, 1994], and the 1999 Chi-Chi, Taiwan and Kocaeli, Turkey earthquakes [Somerville, 2000]. Except to a limited extent [Campbell, 1987, 2000b], source directivity has not been used directly in the development of an attenuation relation. Somerville and coworkers [1997] and Abrahamson [2000] developed a simple engineering model, presented later, for estimating the effects of source directivity and radiation pattern on the prediction of the fault-normal and fault-parallel components of PGA and PSA. Somerville and coworkers [1997] provide a list of near-source time histories that they believe contain significant directivity and other near-source effects that can be used for engineering evaluation and design. Somerville [2000] suggests that the empirical models proposed by Somerville et al. [1997] and Abrahamson [2000] are likely to be too simplistic. He has found that the near-fault directivity effects observed in recent earthquakes, including the 1999 Chi-Chi, Taiwan and Kocaeli, Turkey events, appear to manifest themselves as narrow-band pulses whose period increases with increasing magnitude. This increase in period can actually lead to lower values of PSA at mid-periods (Tn ≈ 1 sec) for MW > 7 1/4 . This latter observation is inconsistent with the assumption made in the current engineering model that spectral amplitudes must increase monotonically with period. The directivity pulse model needs more development before it is ready to be used in engineering. Until then, the simple engineering model suggested by Somerville et al. [1997] and Abrahamson [2000] will remain the state of the art.
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5.3.8 Hanging-Wall and Footwall Effects Generally speaking, the hanging wall is that portion of the crust that lies above the rupture plane of a dipping fault and the footwall is that portion of the crust that lies below this plane. The exact definitions of these two crustal regimes differ depending on the application. Somerville and Abrahamson [1995, 2000], Abrahamson and Somerville [1996], and Abrahamson and Silva [1997] found that sites located on the hanging wall of a reverse or thrust fault generally exhibit higher-than-average ground motion. Somerville and Abrahamson [1995] found that sites located on the footwall generally have lower-thanaverage ground motion. The hanging-wall effect is probably caused by a combination of radiation pattern, source directivity, and the entrapment of seismic waves within the hanging-wall wedge of the crust (that portion between the rupture plane and the Earth’s surface). These authors present a simple engineering model, presented later, that can be used to estimate the effects of the hanging wall and footwall on the prediction of strong ground motion. Theoretical ground-motion modeling has consistently shown that higher ground motions can be expected on the hanging wall of reverse and thrust faults and lower ground motions can be expected on the footwall of such faults [Anderson, in press; Brune 2001]. This is consistent with the observation of shattered rock on the hanging wall of thrust faults in southern California, and the lack of shattered rock and the presence of precariously balanced rocks on the footwall of two thrust faults in this same region [Brune, 2001].
5.3.9 Tectonic Environment The tectonic environment has a significant impact on the amplitude and attenuation of strong ground motion. It has traditionally been classified into four basic types for the purpose of estimating strong ground motion: (1) shallow-crustal earthquakes in active tectonic regions, (2) shallow-crustal earthquakes in stable tectonic regions, (3) intermediate-depth earthquakes (also known as WadatiBenioff or intraslab earthquakes) within subducting plates, and (4) earthquakes along the interface of two subducting plates. The shallow-crustal environment can be further divided into compressional and extensional stress regimes. A detailed discussion of the different tectonic environments and their global distribution is provided in Moores and Twiss [1995]. A shallow crustal environment refers to the seismogenic part of the Earth’s crust that varies anywhere from 10 to 30 km in thickness, depending on the region. An active tectonic environment is one in which large earthquakes are frequent, and tectonic deformation is relatively large and is usually located in the vicinity of tectonic plate margins. Earthquake stress drops are relatively low and anelastic attenuation is relatively high in these regions. A stable tectonic environment is one in which large earthquakes are infrequent and tectonic deformation is relatively small and is usually located away from plate margins in areas of very old continental crust. Stress drops are relatively high and anelastic attenuation is relatively low in these regions. Johnston [1994] presents a series of maps that show the geographic distribution of active and stable continental tectonic regions worldwide. A global version of this map is presented in Figure 5.6. A compressional stress regime is one in which the crust is shortening or being squeezed together. An extensional stress regime is one in which the crust is lengthening or being pulled apart. Zoback [1992] presents a global stress map that shows the geographic distribution of compressional and extensional stress regimes worldwide (Figure 5.7). A subduction zone is a region where one tectonic plate (usually oceanic crust) thrusts beneath or is subducted by another tectonic plate (usually continental crust). Subduction interface earthquakes, some of which are the largest known to have occurred in the world, occur along the seismogenic boundary of the subducting and overriding plates (see Chapter 4 for a global map of subduction zones). Depending on the age of the subducting plate, this interface can occur at depths ranging from 20 to 50 km. Socalled Wadati-Benioff earthquakes occur within the subducting plate below the subduction interface zone as it descends into the Earth’s mantle, first by being pushed from above and then by being pulled from below.
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FIGURE 5.6 Geographic distribution of active and stable continental tectonic regions worldwide. (From Johnston, A.C. 1994. “Seismotectonic Interpretations and Conclusions from the Stable Continental Region Seismicity Database,” in The Earthquake of Stable Continental Regions, Vol. 1, Assessment of Large Earthquake Potential, Electric Power Research Institute, Palo Alto, CA, pp. 1–103. With permission.)
5.3.10 Instrument Location Engineering estimates of ground motion are intended to provide estimates of strong ground motion on level ground in the free field unaffected by any man-made or natural structures. This means that the strong-motion recordings that are used to develop an attenuation relation should not be located on or near a large structure, in an area of strong topographic relief, or below the ground surface. All of these situations have been shown to significantly modify free-field ground motion in some situations [Campbell, 1986, 1987; Stewart, 2000]. It is agreed that nonfree-field recordings should be excluded from an empirical analysis. However, not everyone agrees on which recordings these should be. Furthermore, because the majority of the available strong-motion recordings were obtained in or near some sort of structure, it is impossible to restrict the database to “true” freefield recordings without reducing their number to a point where a regression analysis may not be statistically meaningful. Stewart [2000] evaluated the conditions for which recordings obtained at the foundation of a structure can provide a reasonably unbiased estimate of free-field ground motion with minimal uncertainty. He found that variations between foundation and free-field spectral acceleration correlate well with dimensionless parameters that strongly influence kinematic and inertial soil–structure interaction phenomena, such as embedment ratio, dimensionless frequency (the product of wave frequency and foundation radius normalized by soil shear-wave velocity), and structure-to-soil stiffness ratio. Stewart found that lowfrequency components of PSA recorded on shallow foundations provide reasonable estimates of freefield ground motion. However, PGA and PGV were both found to be diminished or deamplified under these conditions. Stewart’s findings should provide better and more quantitative criteria for identifying free-field recordings in the future.
5.4 Statistical Methods 5.4.1 Regression Analysis Whether developed from empirical observations or theoretical data, all attenuation relations are derived from a statistical fitting procedure known as regression analysis [Draper and Smith, 1981]. A regression © 2003 by CRC Press LLC
5-15
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Engineering Models of Strong Ground Motion FIGURE 5.7 A generalized stress map showing compressional stress regimes (thick, inward pointing arrows), extensional stress regimes (thick, outward-pointing arrows), and intermediate stress regimes (thick, inward-pointing arrows and thin, outward-pointing arrows). Shading indicates topographic relief. (From Zoback, M.L. 1992. “First- and SecondOrder Patterns of Stress in the Lithosphere: The World Stress Map Project,” J. Geophys. Res., 97, 11,703–11,728. With permission.)
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analysis is used to determine the best estimate of the coefficients c1 through c8 in Equations 5.2 and 5.3 using statistical fitting procedures such as minimum least squares or maximum likelihood. Traditionally, there have been three methods for performing a regression analysis for the purpose of developing an attenuation relation: (1) weighted nonlinear least-squares regression, introduced by Campbell [1981]; (2) two-step regression, introduced and later refined by Joyner and Boore [1981, 1994]; and (3) randomeffects regression, introduced by Brillinger and Preisler [1984] and later refined by Abrahamson and Youngs [1992]. Each of these methods has its strengths and weaknesses but they all have the same intended purpose — to mitigate the bias introduced by the uneven distribution of recordings with respect to magnitude, distance, and other seismological parameters. The advantage of the latter two methods is that they provide a direct estimate of the intra- and inter-earthquake components of randomness.
5.4.2 Standard Deviation The difference between a ground-motion observation and its predicted value is known as a residual. The standard deviation of the residuals is the standard error of estimate of the regression and represents a measure of aleatory or random variability in the ground-motion parameter. The standard deviation of ln Y is calculated from the expression:
σ lnY =
1 n− p
n
∑ (ln Y − ln Y ) i
i
2
(5.12)
i =1
where n is the number of observations, p is the number of regression coefficients, i is the index of the recording, ln Yi is the observed value, and lnYi is the predicted value. Plots of the residuals vs. one or more seismological parameters such as magnitude or distance are used to identify unwanted biases in the attenuation relation by revealing trends in the residuals. Any statistically significant trend identified visually or from a formal statistical hypothesis test [Draper and Smith, 1981] can indicate epistemic or modeling uncertainty, such as a problem with the functional form of the relation or the need to include another seismological parameter in the model [Campbell, 1985]. Figure 5.8 gives an example of residual plots that do not indicate a significant trend with magnitude or distance and, therefore, indicate an unbiased model. It is often convenient to segregate σlnY into its intra- or within-earthquake and its inter- or betweenearthquake components, traditionally designated σ and τ. Specific algorithms for determining σ and τ are given by Abrahamson and Youngs [1992] and Joyner and Boore [1993, 1994] for the random-effects and two-step regression procedures. If the regression analysis is performed on the geometric mean (average of the logarithms) of the two horizontal components of a strong-motion parameter and the variability between these components is desired, an additional component-to-component standard deviation term is needed. The predicted value of strong ground motion that includes component-to-component variability is what Joyner and Boore [1993, 1994] refer to as the random horizontal component. Referring to these thr ee standar d deviations as σintra, σinter , and σcomp , the total standar d deviation of lnY is given by the expression: 2 2 σ lnY = σ inter + σ intra + σ 2comp
(5.13)
The standard deviation of lnY has been found to be a function of magnitude [e.g., Youngs et al., 1995] and the amplitude of ground motion [Donovan and Bornstein, 1978; Campbell and Bozorgnia, 1994]. However, these dependencies are not always taken into account when determining the value of σlnY . These dependencies can be significant and will always result in lower values of σlnY for larger magnitudes and higher amplitudes. Lower estimates of standard deviation will always lead to a significant reduction in the higher percentile estimates of ground motion computed using a DSHA and in the longer returnperiod and higher percentile estimates of ground motion computed using a PSHA. © 2003 by CRC Press LLC
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5 All Faults All Soils
4
Normalized Residual
3 2 1 0 -1 -2 -3 -4 -5 4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
Moment Magnitude 5 All Faults All Soils
4
Normalized Residual
3 2 1 0 -1 -2 -3 -4 -5 0.0
10.0
20.0
30.0
40.0
50.0
60.0
Distance to Seismogenic Rupture (km) FIGURE 5.8 Residuals from a regression analysis of strong-motion data plotted against magnitude (top) and distance (bottom). (From Campbell, K.W. and Bozorgnia, Y. 1999. “Vertical Ground Motion: Characteristics, Relationship with Horizontal Component, and Building-Code Implications,” in Proc. SMIP99 Seminar on Utilization of Strong-Motion Data, M. Huang, Ed., Sept. 15, San Francisco, pp. 23–49. California Strong Motion Instrumentation Program, Sacramento. With permission.)
5.4.3 Predicted Value Because the predicted value of ground motion from Equation 5.2 is the logarithm of Y, it represents the mean of lnY or equivalently the 50th percentile or median value of Y. The median is the value of Y that is exceeded by 50% of the observations. The 100(1 − α)-percentile estimate of the mean of n0 future observations of lnY is statistically defined by the expression [Draper and Smith, 1981]:
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ln Y1−α = ln Y + t v (α )
σ ln2 Y + σ ln2 Y n0
(5.14)
where tv(α) is the Student’s t-statistic for a given exceedance probability α and v = n – p degrees of freedom (this statistic is widely available in statistics books), and σ lnY is the standard error of the mean value of ln Y excluding random error (an indicator of epistemic uncertainty). The 100(1 − α)percentile estimate of a single future observation of ln Y, the most common application of Equation 5.14, is calculated by letting n0 = 1. It is common to calculate the 100(1 − α)-percentile estimate of a single future value of lnY by setting σ lnY = 0 and replacing the t-statistic with the standard normal variable z. These assumptions reduce Equation 5.14 to its more simplified and common form: ln Y1−α = ln Y + z α σ lnY
(5.15)
where zα is the standard normal variable for an exceedance probability of α (this variable is widely available in statistics books). Although statistically incorrect, results using Equation 5.15 are not significantly different from those using Equation 5.14, except when the predicted value is based on an extrapolation of the regression equation or on very few recordings. In the first case, the value of σ lnY should not be ignored, and in the second, the z-statistic is inappropriate. The most common application of Equation 5.15 in DSHA is to estimate either the median value of Y (α = 0.5), by setting zα = 0, or the 84th-percentile value of Y (α = 0.16), by setting zα = 1. The 84thpercentile value is often used as a conservative estimate of ground motion to use in the design of critical facilities, such as nuclear power plants and major dams. Equation 5.15 is assumed to be a continuous distribution of Y when used in PSHA, although it is usually truncated at zα = 2 or 3 (i.e., at ±2 to 3 standard deviations) to avoid unrealistic predicted values. In both DSHA and PSHA, it is typical to include epistemic uncertainty in the predicted ground motion by using more than one attenuation relation to estimate Y in lieu of formally defining σ lnY .
5.5 Theoretical Methods Theoretical methods are used to develop attenuation relations in areas where there are an insufficient number of strong-motion recordings. The most common of these is the stochastic method [Boore, in press; see also Chapter 6). There have been some attempts to use more complicated kinematic and dynamic models to develop attenuation relations [e.g., Somerville et al., 2001] but this field is still evolving. Because of its popularity, the stochastic method is summarized below in the context of its use in developing engineering estimates of strong ground motion. Two of the attenuation relations presented later [Atkinson and Boore, 1995, 1997; Toro et al., 1997] were developed using the stochastic method. In the stochastic method, the Fourier amplitude spectrum (FAS) of the average horizontal component of ground acceleration is described by the general relation: A ( f ) = Src ( f ) Attn ( f , R) Amp ( f )
(5.16)
where Src (f ) describes the earthquake source, Attn (f ) describes the attenuation caused by wave propagation through the crust, and Amp(f) describes the response of the materials beneath the site.
5.5.1 Source Spectrum The equivalent acceleration source spectrum, arbitrarily defined at a reference distance of 1 km, is given by the equation:
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2 ℜ V FS Src ( f ) = (2 π f ) M0S ( f ) 3 4 πρβ
(5.17)
where R = 0.55 is the average shear-wave radiation pattern, V = 1 2 is the partition of the radiated energy into two orthogonal horizontal components, FS = 2 is the amplification due to the free surface, β is the shear-wave velocity of the crust in the source region, ρ is the density of the crust in the source region, M0 is seismic moment, and S(f) is the source displacement spectrum, known simply as the source spectrum. The simplest representation of the source spectrum is the one-corner, point-source model [Brune 1970, 1971]: S( f ) =
1
1+( f f0)
(5.18)
2
where f0 is corner frequency (the inflection point in the source spectrum). Joyner [1984] argued on theoretical grounds that the source spectrum should have two corner frequencies, if the width of faulting is limited by the finiteness of the seismogenic crust. Since then, others have developed twocorner source models based on both empirical and theoretical considerations. All of these models are based on the addition or multiplication of two one-corner source spectra, similar to Equation 5.18, with each defined by a separate corner frequency, fa and fb, and combined using a relative weighting factor. Atkinson and Boore [1998] give a comparison of the near-source acceleration source spectra estimated from several of these one-corner and two-corner models. This comparison is shown in Figure 5.9. There are two attenuation relations presented later that are based on the stochastic method. One uses a one-corner source spectrum and the other a two-corner source spectrum. The one-corner source spectrum used in the Toro and coworkers’ [1997] attenuation relation is given by Equation 5.18, in which the corner frequency is related to magnitude by the expression [Atkinson and Boore, 1998]: 2.609 + 0.5 M W f0 = 2.446 + 0.5 M W
for the Midcontinent region for the Gulf Coast region
(5.19)
assuming ∆σ = 120 bar, hhypo = 10 km, and β = 3.76 m/sec for the Midcontinent region and 2.58 km/ sec for the Gulf Coast region [EPRI, 1993]. According to Atkinson and Boore [1998], the two-corner source spectrum used in the Atkinson and Boore [1995, 1997] attenuation relations is given by the expression: S( f ) =
1− w
1+( f fa )
2
+
w
1+( f fb )
2
(5.20)
where
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2.41 − 0.533 M W log f a = 2.678 − 0.5 M W
for M W ≥ 4.0 for M W < 4.0
(5.21)
1.43 − 0.188 M W log f b = 2.678 − 0.5 M W
for M W ≥ 4.0 for M W < 4.0
(5.22)
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104
Fourier Acceleration Spectrum (cm/s)
103
M = 7.5
102
M = 4.5
101
AB95 AB98-Ca H96 Fea96 (no site amp) BC92 J97
100
10−1 10−2
10−1
10−0
101
102
freq (Hz)
FIGURE 5.9 Fourier amplitude spectra of acceleration for a reference distance of 1 km, based on several source spectral models. (From Atkinson, G.M. and Boore, D.M. 1998. “Evaluation of Models for Earthquake Source Spectra in Eastern North America,” Bull. Seismol. Soc. Am., 88, 917–934. With permission.)
2.52 − 0.637 M W log w = 0
for M W ≥ 4.0 for M W < 4.0
(5.23)
The differences in ground motion between the one-corner and two-corner source spectra can be significant. For example, the two-corner spectrum has been shown to produce PSA values in the midperiod range that are substantially smaller than those predicted by the one-corner model [Atkinson and Boore, 1995, 1997].
5.5.2 Stress Drop Stress drop is implicitly included in theoretical attenuation relations developed from the stochastic method by virtue of its relationship to the corner frequency of the earthquake source spectrum [Brune 1970, 1971]: f 0 = 4.9 × 106 β ( ∆σ M 0 )
1/ 3
(5.24)
where β has units of km/sec, ∆σ units of bars, and M0 units of dyne-cm. As originally defined by Brune [1970, 1971], stress drop is the parameter that controls the highfrequency part of the source spectrum. Therefore, it is more closely related to dynamic stress drop than to static stress drop. In fact, it should not be confused with static stress drop, which is a measure of the average displacement on the fault [Lay and Wallace, 1995]. To avoid potential confusion, some
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seismologists prefer to call the Brune stress drop the “stress parameter” [Atkinson and Beresnev, 1997]. The term stress drop is retained here to be consistent with Brune’s original terminology.
5.5.3 Crustal Attenuation Crustal attenuation is defined as the multiplication of two terms: Attn ( f , R) = G ( R) D ( f )
(5.25)
where G(R) describes the geometric attenuation of ground motion and D (f ) describes the diminution of ground motion with distance from the source, or crustal damping. Geometric attenuation is modeled using the distance parameter R−n, where R is either rhypo or rrup, and n varies with distance according to the dominant wave type (e.g., direct or surface waves) and whether arrivals of critical reflections off the Moho (the top of the Earth’s mantle) or other strong crustal reflectors are included. Spherical spreading from a point source corresponds to n = 1. In the Toro and coworkers’ [1997] attenuation relation presented later, geometric attenuation is given by the general expression: G ( R) =
n
∑ i =1
G ( R)
1/ 2
2 i
(5.26)
where Gi is the geometric attenuation of an individual ground-motion ray in a layered crust determined from geometrical optics and n is the total number of arrivals within the ergodic window [Ou and Herrmann, 1990]. In the Atkinson and Boore [1995, 1997] attenuation relation presented later, geometric attenuation is given by the three-part expression: 1 R G ( R) = 1 70 (1 70) 130 R
for R < 70 km for 70 ≤ R < 130 km for R ≥ 130 km
(5.27)
Crustal damping is modeled by the expression: −π f R D ( f ) = exp Q ( f )β
(5.28)
where Q (f ), the quality factor, is a measure of anelastic attenuation and scattering within the crust, which is usually defined by the power law: Q ( f ) = Q0 f
η
(5.29)
where Q0 and η vary according to the tectonic environment [e.g., Singh and Herrmann, 1983].
5.5.4 Site Response Site response, often called amplification, is calculated from the equation: Amp ( f ) =
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ρβ exp (− πκ 0 f ) ρs ( f )β s ( f )
(5.30)
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where β and ρ are the shear-wave velocity and density of the crust beneath the site. The effective velocity βs (f ), effective density ρs (f ), and site damping factor κ0 are calculated from the expressions [Boore, in press]: βs ( f ) =
n1
n1
∑ ∑v i =1
ρs ( f ) =
di
di
i =1
n1
n1
∑
∑d
ρi di
(5.32)
i
i =1
i =1
n2
κ0 =
(5.31)
si
∑v Q di
si
i =1
(5.33) si
where n1 is the number of distinct velocity layers to a depth corresponding to a quarter-wavelength, and n2 is the number of these layers above the crust. The depth to a quarter-wavelength is calculated from Equation 5.11, substituting n with n1. Estimates of κ0 can also be obtained from recordings [Anderson and Hough, 1984; Hough et al., 1988] or inferred from empirical ground-motion models [Boore et al., 1992; Schneider et al., 1993; Silva and Darragh, 1995].
5.5.5 Peak Ground-Motion Parameters The pseudoacceleration response of a SDOF oscillator with natural frequency fn = 1/Tn and fraction of critical damping ξc is calculated from Equation 5.16 as: A ( f , fn) = A ( f ) I ( f , fn)
(5.34)
where I(f, fn ) is given by [Silva and Lee, 1987; Liu and Pezeshk, 1999]: I ( f , fn) =
f n2
(
f2−f2 n
) + (2ξ ff ) 2
c
n
2
1/ 2
(5.35)
The expected value of PGA or PSA is calculated from A(f) or A(f, fn) using random vibration theory (RVT). In RVT, the peak of a random function is calculated from its root-mean-square (RMS) value according to the relationship [Cartwright and Longuet-Higgins, 1956]: Y = YRMS f ( N )
(5.36)
where the peak factor f (N) ≈ 2 ln N + γ Euler 2 ln N , when N (the number of cycles in the time domain) is large, and γEule r = 0.55726 (Euler’s constant). From Parseval’s theorem, the RMS acceleration is defined by the integral:
YRMS
1 = DRMS
∞
∫ Y(f )
−∞
2
df
1/ 2
(5.37)
where Y (f ) = A (f ) or A(f, fn), depending on whether Y is PGA or PSA, and DRMS is the equivalent RMS duration. One of the critical elements of this relation is the appropriate selection of DRMS. This is particularly critical for SDOF oscillators with long periods where, for small earthquakes, the natural © 2003 by CRC Press LLC
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period can be longer than the duration of the ground motion. This issue is addressed by Boore and Joyner [1984] and Liu and Pezeshk [1999]. The expression proposed by Liu and Pezeshk [1999] is given by: γ2 DRMS = DS + D0 2 γ +k
(5.38)
γ = DS Tn
(5.39)
D0 = Tn 2πξ c
(5.40)
m12 k = 2π 1 − m0m 2
(5.41)
where
mi =
2π DS
∞
∫ f G ( f )df i
(5.42)
0
and DS is the duration of the source often assumed to be 1/f0 + 0.05R [Herrmann, 1985], mi is the ith spectral moment of the power spectral density function of the random process, and G(f) is the one-sided power spectral density function. Boore [1996] distributes a set of computer programs that can be used to evaluate the stochastic method using a point-source representation of the earthquake source. These programs can be used to estimate peak parameters using RVT or to simulate ground-motion time histories. Beresnev and Atkinson [1998] distribute a computer program that can be used to evaluate the stochastic method assuming the earthquake is a finite rather than a point source.
5.6 Engineering Models There are a large number of attenuation relations that have been and can be used to develop engineering estimates of strong ground motion throughout the world. It is impossible to list all of them. Instead, this section presents several attenuation relations that have been published since about 1990. These attenuation relations were chosen to represent a selection of those commonly used to estimate acceleration response spectra for engineering evaluation and design. Attenuation relations used in the United States, Europe, and Japan, and in extensional and subduction tectonic environments worldwide, are presented. For practical purposes and for emphasis on engineering, the discussion is restricted to attenuation relations and other related engineering models used to incorporate hanging-wall, footwall, and source directivity effects that provide estimates of PGA and PSA. These relations must all be easily available, so they all have been published in internationally recognized journals. This excludes models that predict PGA only or some measure of seismic intensity, such as Modified Mercalli Intensity (MMI), Japan Meteorological Agency (JMA) intensity, or Medvedev-Sponheuer Karnik (MSK) intensity. The selected attenuation relations are listed in Table 5.3 and are organized according to the country or region of origin and the tectonic environment. All of the ground-motion and seismological parameters used in the attenuation relations are presented in terms of a consistent set of symbols and functional forms that may not conform to those used in the original reference. This is intended to aid in the presentation and use of the models. The constants in the relations were adjusted to give a consistent set of units for the predicted strong-motion parameters, © 2003 by CRC Press LLC
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TABLE 5.3
List of Selected Attenuation Relations
Region
Tectonic Environment
Western North America
Shallow active crust
Eastern North America
Shallow stable crust
Europe
Shallow active crust Shallow stable crust All types undivided Shallow extended crust Subduction interface Subduction intraslab Subduction undivided
Japan Worldwide
Attenuation Relation Abrahamson and Silva [1997] Boore et al. [1997] Campbell and Bozorgnia [in press] Sadigh et al. [1993, 1997] Atkinson and Boore [1995, 1997] Toro et al. [1997] Campbell [in press] Ambraseys et al. [1996] Dahle et al. [1990] Molas and Yamazaki [1995, 1996] Spudich et al. [1999] Youngs et al. [1997] Youngs et al. [1997] Crouse [1991a, 1991b]
in this case fraction of g for acceleration and cm/sec for velocity. Pseudovelocity was converted to pseudoacceleration if the original relation was given in terms of PSV. Logarithms are consistently defined in terms of the natural logarithm in the attenuation relations. All other equations were left in terms of the common logarithm if that is how they were defined originally. Some of the model’s functional forms were modified in order to simplify or generalize them so that a single table of regression coefficients could be used. Although this means that the attenuation relations depart from their original mathematical forms, the modifications provide a consistent framework for understanding and applying these relations in an informed and unambiguous manner. The strongmotion parameters are defined as either the largest horizontal component or the geometric mean (hereafter referred to simply as the average) of the two horizontal components, with no attempt to convert between the two. If such a conversion is necessary, the largest horizontal component can be estimated approximately from the average horizontal component by multiplying by 1.15 [Campbell, 1981; Ansary et al., 1995]. All engineering models have limitations that result from the availability of recordings, the criteria used to select the recordings, the theoretical assumptions used to develop the models, and the seismological parameters used to define the source, path, and site effects. It is dangerous to assume that an engineering model can be extrapolated beyond the data, the theoretical assumptions, or the geographic region of applicability, and still provide a reliable estimate of ground motion. In fact, some of these models come with specific caveats regarding their use. When such caveats are given, they have been noted. The notation used to define the parameters in the engineering models is defined in the Appendix so that it need not be repeated after each model. Two specific parameters, site class and faulting mechanism, generically designated S and F, pose a particular challenge, because each model defines these parameters somewhat differently. Different site classes used in the attenuation relations are denoted by different subscripts. An approximate correspondence among values of VS30, the related site classes, and the site parameters used in the attenuation relations given in Table 5.3 is listed in Table 5.4. The faulting mechanism parameter is generally set to 0, 0.5, or 1, depending on the particular faulting mechanism category but each model defines these categories differently in terms of the rake angle λ. Instead of defining different faulting mechanism parameters for each model, the values of F and the corresponding range of λ for the attenuation relations given in Table 5.3 are listed in Table 5.5.
5.6.1 Western North America North American attenuation relations for shallow crustal earthquakes are segregated into active tectonic areas of western North America (WNA) and stable tectonic areas of eastern North America (ENA). The division between these two regions has traditionally been taken as 105°W longitude. A somewhat more detailed definition of this boundary has been proposed by Frankel and coworkers [1996, 2000]. It is often © 2003 by CRC Press LLC
Attenuation Relation Abrahamson and Silva [1997] Boore et al. [1997] Campbell and Bozorgnia [in press]
Sadigh et al. [1997] Ambraseys et al. [1996]
Dahle et al. [1990] Molas and Yamazaki [1995, 1996]
Crouse [1991a, 1991b] Youngs et al. [1997] Spudich et al. [1999] Atkinson and Boore [1995, 1997] Toro et al. [1997] Campbell [in press]
Site Parameter
Code Class E
Code Class D
Firm Soil
Generic Soil
Very Firm Soil
Soft Rock
ENA Deep Stiff Soil
Code Class C
Generic Rock
Firm Rock
Code Class B
ENA Hard Rock
SSoil SRock VS30 SFS SVFS SSR SFR SSoil SRock SD SC SB SB S4 S3 S2 S1 SSoil SSoil SRock SSoil SRock SDeep SENA SENA SENA
— — 150 — — — — — — — — — — 1 0 0 0 — — — — — — — — —
— — 270 — — — — — — 1 0 0 — 0 1 0 0 — — — — — — — — —
— — 298 1 0 0 0 — — — — — — — — — — — — — — — — — — —
1 0 310 0 0.25 0 0 1 0 — — — — 0 0.5 0.5 0 1 1 0 1 0 — — — —
— — 368 0 1 0 0 — — — — — — 0 0 1 0 — — — — — — — — —
— — 421 0 0 1 0 — — — — — — — — — — — — — — — — — — —
— — 500 — — — — — — — — — — — — — — — — — — — 1 0 — —
— — 560 — — — — — — 0 1 0 — — — — — — — — — — — — — —
0 1 620 0 0 0.5 0.5 0 1 — — — — 0 0 0 1 — 0 1 0 1 — — — —
— — 830 0 0 0 1 — — — — — — — — — — — — — — — — — — —
— — 1130 — — — — — — 0 0 1 1 — — — — — — — — — — — — —
— — 2800 — — — — — — — — — — — — — — — — — — — 0 1 1 1
Note: Approximate values of 30-m velocity for each site class in m/sec are listed under the entries for Boore et al. [1997]. Blank entries refer to parameters that are not used for that attenuation relation.
5-25
© 2003 by CRC Press LLC
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Site Categories and Related Site Parameters for Selected Attenuation Relations
Engineering Models of Strong Ground Motion
TABLE 5.4
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Earthquake Engineering Handbook
TABLE 5.5 Relations
Faulting Mechanism Categories and Related Rake Angles for Selected Attenuation
Attenuation Relation Abrahamson and Silva [1997]
Boore et al. [1997]
Campbell and Bozorgnia [in press]
Sadigh et al. [1993, 1997]
Spudich et al. [1999]
Category
F
Rake Angle (λ)
Strike slip Normal Reverse-oblique Reverse Strike slip Normal Unknown Reverse Strike slip Normal Reverse (FRV =1) Thrust (FTH =1) Strike slip Normal Reverse Strike slip Normal
0 0 0.5 1.0 — — — — 0 0 1.0 1.0 0 0 1.0 — —
0–30°, 150–210°, 330–360° 210−330° 30−60°, 120−150° 60° to 120° 0–30°, 150–210°, 330–360° 210−330° Unknown or random 30–150° 0–22.5°, 177.5–202.5°, 337.5–360° 202.5–337.5° 22.5–157.5° (δ > 45°) 22.5–157.5° (δ ≤ 45°) 0–45°, 135–225°, 315–360° 225–315° 45–135° 0–45°, 135–225°, 315–360° 225–315°
Note: Unless otherwise indicated, an unknown or random faulting mechanism is given by F = 0.5, FRV = 0.25, and FTH = 0.25.
assumed that the WNA attenuation relations, some of which use a limited number of recordings outside of North America, can be used to estimate ground motions in similar tectonic environments worldwide. This has been confirmed to a limited extent by comparing these relations with those from Italy [Sabetta and Pugliese, 1996] and from active tectonic regions in Europe [Ambraseys et al., 1996]. Nonetheless, caution should be used when using these relations in areas outside of WNA. Four attenuation relations commonly used to develop engineering estimates of strong ground motion in WNA are presented [Abrahamson and Silva, 1997; Boore et al., 1997; Campbell and Bozorgnia, in press; Sadigh et al., 1993, 1997]. All of these relations are empirically based, meaning that they were developed from a regression analysis of strong-motion recordings. The Campbell and Bozorgnia attenuation relation, published in an abbreviated and slightly different form in Campbell and Bozorgnia [2000], is included although it is relatively new, because the authors recommend that it supersede that of Campbell [1997, 2000c, 2001] and is being used in place of this latter relation in the 2002 update of the seismic hazard maps produced by the U.S. Geological Survey. This is noteworthy because many engineering studies use the same attenuation relations used by the U.S. Geological Survey in order to be consistent with the hazard defined in these maps. 5.6.1.1 The Abrahamson and Silva Model The attenuation relation of Abrahamson and Silva [1997] can be represented by the expression:
(
)
(
)
ln Y = f1 MW , rrup + f 2 ( MW ) F + f3 MW , rrup HW + f 4 (S, ARock )
(5.43)
where Y is the average horizontal or vertical component of PGA or PSA and
(
f 1 M W , rrup
© 2003 by CRC Press LLC
)
c + c ( M W 1 2 = c 1 + c 7 ( M W
− 6.4) + c 3 (8.5 − M W )
c4
− 6.4) + c 3 (8.5 − M W )
c4
[
]
for M W ≤ 6.4
[
]
for M W > 6.4
+ c 5 + c 6 ( M W − 6.4) ln R + c 5 + c 6 ( M W − 6.4) ln R
(5.44)
0068_C05_fm Page 27 Thursday, August 1, 2002 7:59 AM
5-27
Engineering Models of Strong Ground Motion
2 R = rrup + c 82
(5.45)
c 9 (c − c ) ( MW − 5.8) f 2 ( M W ) = c 9 + 10 9 0.6 c 10
(
)
for M W ≤ 5.8 for 5.8 < M W < 6.4 for M W ≥ 6.4
( )
f 3 M W , rrup = f HW ( M W ) f HW rrup 0 f HW ( M W ) = M W − 5.5 1
( )
f HW rrup
for M W ≤ 5.5 for 5.5 < M W < 6.5 for M W ≥ 6.5
0 r −4 c rup 11 4 = c 11 rrup − 18 c11 1 − 7 0
[
(5.46)
(5.47)
(5.48)
for rrup ≤ 4 km for 4 < rrup ≤ 8 km for 8 < rrup ≤ 18 km
(5.49)
for 18 < rrup ≤ 25 km for rrup > 25 km
]
f 4 ( S, A Rock ) = c 12 + c 13 ln ( A Rock + c 14 ) SSoil
(5.50)
The parameter Arock is the value of the average horizontal or vertical component of PGA for generic rock. The indicator variable HW quantifies the effect of the hanging wall. The standard deviation of lnY is separated into its inter- and intra-earthquake components. However, to be consistent with engineering convention, only the total value is reported by the authors. The total standard deviation is defined as a function of magnitude according to the expression: c 15 σ lnY ( M W ) = c15 − c 16 ( M W − 5) c − 2c 16 15
for M W ≤ 5.0 for 5.0 < M W < 7.0 for M W ≥ 7.0
(5.51)
The period-independent regression coefficients in the above equations are c2 = 0.512, c4 = 2, c6 = 0.17, c7 = −0.144, and c14 = 0.03 for the average horizontal component of ground motion, and c2 = 0.909, c4 = 3, c6 = 0.06, c7 = 0.275, and c14 = 0.3 for the vertical component of ground motion. The remaining regression coefficients are listed in Tables 5.6 and 5.7. The relation predicts ground motion for generic rock, equivalent to the condition SRock = 1, when SSoil = 0. When SSoil = 1, it predicts ground motion for generic soil (see Table 5.4). The expression for local site conditions accounts for the nonlinear behavior of soil by linking soil amplification to the amplitude of PGA on rock. The relation includes soils up to 20 m thick in the definition of rock. This thickness is greater than that used in most other relations, making the generic rock classification softer than that defined by Boore and Joyner [1997]. One of the authors [Walt Silva, personal communication, 2001] recommends using a 30-m velocity of 290 m/sec for generic soil and 510 m/sec for generic rock when using this attenuation relation. Nonetheless, it is generally assumed that the rock classification used in this relation is approximately the same as that used in other relations when making engineering estimates of ground motion in WNA (Table 5.4). Faulting mechanism is defined as reverse, reverse-oblique, and © 2003 by CRC Press LLC
0068_C05_fm Page 28 Thursday, August 1, 2002 7:59 AM
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Earthquake Engineering Handbook
TABLE 5.6
Coefficients for Abrahamson and Silva Attenuation Relation: Horizontal Component
Tn (s)
c1
c3
c5
c8
c9
c10
c11
c12
c13
c15
c16
PGA 0.02 0.03 0.04 0.05 0.06 0.075 0.09 0.10 0.12 0.15 0.17 0.20 0.24 0.30 0.36 0.40 0.46 0.50 0.60 0.75 0.85 1.00 1.50 2.00 3.00 4.00 5.00
1.640 1.640 1.690 1.780 1.870 1.940 2.037 2.100 2.160 2.272 2.407 2.430 2.406 2.293 2.114 1.955 1.860 1.717 1.615 1.428 1.160 1.020 0.828 0.260 –0.150 –0.690 –1.130 –1.460
0.0000 0.0000 0.0143 0.0245 0.0280 0.0300 0.0300 0.0300 0.0280 0.0180 0.0050 –0.0040 –0.0138 –0.0238 –0.0360 –0.0460 –0.0518 –0.0594 –0.0635 –0.0740 –0.0862 –0.0927 –0.1020 –0.1200 –0.1400 –0.1726 –0.1956 –0.2150
–1.1450 –1.1450 –1.1450 –1.1450 –1.1450 –1.1450 –1.1450 –1.1450 –1.1450 –1.1450 –1.1450 –1.1350 –1.1150 –1.0790 –1.0350 –1.0052 –0.9880 –0.9652 –0.9515 –0.9218 –0.8852 –0.8648 –0.8383 –0.7721 –0.7250 –0.7250 –0.7250 –0.7250
5.60 5.60 5.60 5.60 5.60 5.60 5.58 5.54 5.50 5.39 5.27 5.19 5.10 4.97 4.80 4.62 4.52 4.38 4.30 4.12 3.90 3.81 3.70 3.55 3.50 3.50 3.50 3.50
0.610 0.610 0.610 0.610 0.610 0.610 0.610 0.610 0.610 0.610 0.610 0.610 0.610 0.610 0.610 0.610 0.610 0.592 0.581 0.557 0.528 0.512 0.490 0.438 0.400 0.400 0.400 0.400
0.260 0.260 0.260 0.260 0.260 0.260 0.260 0.260 0.260 0.260 0.260 0.260 0.260 0.232 0.198 0.170 0.154 0.132 0.119 0.091 0.057 0.038 0.013 –0.049 –0.094 –0.156 –0.200 –0.200
0.370 0.370 0.370 0.370 0.370 0.370 0.370 0.370 0.370 0.370 0.370 0.370 0.370 0.370 0.370 0.370 0.370 0.370 0.370 0.370 0.331 0.309 0.281 0.210 0.160 0.089 0.039 0.000
–0.417 –0.417 –0.470 –0.555 –0.620 –0.665 –0.628 –0.609 –0.598 –0.591 –0.577 –0.522 –0.445 –0.350 –0.219 –0.123 –0.065 0.020 0.085 0.194 0.320 0.370 0.423 0.600 0.610 0.630 0.640 0.664
–0.230 –0.230 –0.230 –0.251 –0.267 –0.280 –0.280 –0.280 –0.280 –0.280 –0.280 –0.265 –0.245 –0.223 –0.195 –0.173 –0.160 –0.136 –0.121 –0.089 –0.050 –0.028 0.000 0.040 0.040 0.040 0.040 0.040
0.70 0.70 0.70 0.71 0.71 0.72 0.73 0.74 0.74 0.75 0.75 0.76 0.77 0.77 0.78 0.79 0.79 0.80 0.80 0.81 0.81 0.82 0.83 0.84 0.85 0.87 0.88 0.89
0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.135 0.132 0.130 0.127 0.123 0.121 0.118 0.110 0.105 0.097 0.092 0.087
Source: Adapted from Abrahamson, N.A. and Silva, W.J. 1997. “Empirical Response Spectral Attenuation Relations for Shallow Crustal Earthquakes,” Seismol. Res. Lett., 68, 94–127.
other than reverse and reverse-oblique (i.e., strike slip and normal) without specifically defining these categories in terms of rake angle. As a result, it is somewhat ambiguous how the faulting mechanism parameter F should be determined for a specific fault. Some guidance can be obtained from the relationship between F and λ used in other models (Table 5.5). 5.6.1.2 The Boore et al. Model The attenuation relation of Boore et al. [1997] can be represented by the expression:
(
)
ln Y = f 1 M W , r jb + f 2 (VS 30 )
(5.52)
where Y is the average horizontal component of PGA or PSA and
(
)
f 1 M W , r jb = c 1 + c 2 ( M W − 6) + c 3 ( M W − 6) + c 4 ln R
(5.53)
R = r jb2 + c 52
(5.54)
c 1U c 1 = c 1S c 1R © 2003 by CRC Press LLC
2
for unspecified faulting for strike-slip faulting for reverse faulting
(5.55)
0068_C05_fm Page 29 Thursday, August 1, 2002 7:59 AM
5-29
Engineering Models of Strong Ground Motion
TABLE 5.7
Coefficients for Abrahamson and Silva Attenuation Relation: Vertical Component
Tn (s)
c1
c3
c5
c8
c9
c10
c11
c12
c13
c15
c16
PGA 0.02 0.03 0.04 0.05 0.06 0.075 0.09 0.10 0.12 0.15 0.17 0.20 0.24 0.30 0.36 0.40 0.46 0.50 0.60 0.75 0.85 1.00 1.50 2.00 3.00 4.00 5.00
1.642 1.642 2.100 2.420 2.620 2.710 2.750 2.730 2.700 2.480 2.170 1.960 1.648 1.312 0.878 0.617 0.478 0.271 0.145 –0.087 –0.344 –0.469 –0.602 –0.966 –1.224 –1.581 –1.857 –2.053
0.0000 0.0000 0.0000 0.0000 –0.0002 –0.0004 –0.0007 –0.0009 –0.0010 –0.0015 –0.0022 –0.0025 –0.0030 –0.0035 –0.0042 –0.0047 –0.0050 –0.0056 –0.0060 –0.0068 –0.0083 –0.0097 –0.0115 –0.0180 –0.0240 –0.0431 –0.0565 –0.0670
–1.2520 –1.2520 –1.3168 –1.3700 –1.3700 –1.3700 –1.3700 –1.3700 –1.3700 –1.2986 –1.2113 –1.1623 –1.0987 –1.0274 –0.9400 –0.9004 –0.8776 –0.8472 –0.8291 –0.7896 –0.7488 –0.7451 –0.7404 –0.7285 –0.7200 –0.7200 –0.7200 –0.7200
6.00 6.00 6.00 6.00 6.00 6.00 6.00 6.00 6.00 6.00 6.00 5.72 5.35 4.93 4.42 4.01 3.77 3.45 3.26 2.85 2.50 2.50 2.50 2.50 2.50 2.50 2.50 2.50
0.390 0.390 0.432 0.469 0.496 0.518 0.545 0.567 0.580 0.580 0.580 0.580 0.580 0.580 0.580 0.571 0.539 0.497 0.471 0.416 0.348 0.309 0.260 0.260 0.260 0.260 0.260 0.260
–0.050 –0.050 –0.050 –0.050 –0.050 –0.050 –0.050 –0.050 –0.050 –0.017 0.024 0.047 0.076 0.109 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.058 –0.008 –0.100 –0.100 –0.100
0.630 0.630 0.630 0.630 0.630 0.630 0.630 0.630 0.630 0.630 0.630 0.604 0.571 0.533 0.488 0.450 0.428 0.400 0.383 0.345 0.299 0.273 0.240 0.240 0.240 0.240 0.240 0.240
–0.140 –0.140 –0.140 –0.140 –0.140 –0.140 –0.129 –0.119 –0.114 –0.104 –0.093 –0.087 –0.078 –0.069 –0.057 –0.048 –0.043 –0.035 –0.031 –0.022 –0.010 –0.004 0.004 0.025 0.040 0.040 0.040 0.040
–0.220 –0.220 –0.220 –0.220 –0.220 –0.220 –0.220 –0.220 –0.220 –0.220 –0.220 –0.220 –0.220 –0.220 –0.220 –0.220 –0.220 –0.220 –0.220 –0.220 –0.220 –0.220 –0.220 –0.220 –0.220 –0.220 –0.220 –0.220
0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.74 0.72 0.70 0.69 0.69 0.69 0.69 0.69 0.69 0.69 0.69 0.69 0.69 0.69 0.69 0.69 0.72 0.75 0.78
0.085 0.085 0.085 0.085 0.085 0.085 0.085 0.085 0.085 0.075 0.063 0.056 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.050
Source: Adapted from Abrahamson, N.A. and Silva, W.J. 1997. “Empirical Response Spectral Attenuation Relations for Shallow Crustal Earthquakes,” Seismol. Res. Lett., 68, 94–127.
f 2 (VS 30 ) = c 6 ln (VS 30 c 7 )
(5.56)
The standard deviation of lnY is separated into its inter- and intra-earthquake components. Furthermore, the authors report the total standard deviation, which includes the randomness between the two horizontal components of ground motion, or what constitutes the random rather than the average horizontal component. To be consistent with standard engineering convention, the total standard deviation excluding the component-to-component randomness is reported here. The regression coefficients and the total standard deviation are listed in Table 5.8. The relation is considered valid for MW = 5.5 to 7.5 and rrup ≤ 80 km. The relation accounts for site response through the 30-m velocity VS30. Some typical values for VS30 are provided in Tables 5.2 and 5.4 [see also Wills and Silva, 1998]. This parameter must be set to some value in order for the prediction to be valid. Boore and Joyner [1997] recommend using VS30 = 310 m/sec and 620 m/sec for generic soil and generic rock, respectively. The relationship between the faulting categories and the rake angle λ is given in Table 5.5. 5.6.1.3 The Campbell and Bozorgnia Model The attenuation relation of Campbell and Bozorgnia [in press] can be represented by the expression: ln Y = c 1 + f 1 ( M W ) + c 4 ln f 2 ( M W , rseis , S) + f 3 ( F ) + f 4 ( S) + f 5 ( HW , M W , rseis )
© 2003 by CRC Press LLC
(5.57)
0068_C05_fm Page 30 Thursday, August 1, 2002 7:59 AM
5-30
TABLE 5.8
Earthquake Engineering Handbook
Coefficients for Boore et al. Attenuation Relation
Tn (s)
c1U
c1S
c1R
c2
c3
c4
c5
c6
c7
σIn Y
PGA 0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.22 0.24 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00
–0.242 1.059 1.130 1.174 1.200 1.208 1.204 1.192 1.173 1.151 1.122 1.089 1.019 0.941 0.861 0.780 0.700 0.619 0.540 0.462 0.385 0.311 0.239 0.169 0.102 0.036 –0.025 –0.176 –0.314 –0.440 –0.555 –0.661 –0.760 –0.851 –0.933 –1.010 –1.080 –1.208 –1.315 –1.407 –1.483 –1.550 –1.605 –1.652 –1.689 –1.720 –1.743
–0.313 1.006 1.072 1.109 1.128 1.135 1.128 1.112 1.090 1.063 1.032 0.999 0.925 0.847 0.764 0.681 0.598 0.518 0.439 0.361 0.286 0.212 0.140 0.073 0.005 –0.058 –0.122 –0.268 –0.401 –0.523 –0.634 –0.737 –0.829 –0.915 –0.993 –1.066 –1.133 –1.249 –1.345 –1.428 –1.495 –1.552 –1.598 –1.634 –1.663 –1.685 –1.699
–0.117 1.087 1.164 1.215 1.246 1.261 1.264 1.257 1.242 1.222 1.198 1.170 1.104 1.033 0.958 0.881 0.803 0.725 0.648 0.570 0.495 0.423 0.352 0.282 0.217 0.151 0.087 –0.063 –0.203 –0.331 –0.452 –0.562 –0.666 –0.761 –0.848 –0.932 –1.009 –1.145 –1.265 –1.370 –1.460 –1.538 –1.608 –1.668 –1.718 –1.763 –1.801
0.527 0.753 0.732 0.721 0.711 0.707 0.702 0.702 0.702 0.705 0.709 0.711 0.721 0.732 0.744 0.758 0.769 0.783 0.794 0.806 0.820 0.831 0.840 0.852 0.863 0.873 0.884 0.907 0.928 0.946 0.962 0.979 0.992 1.006 1.018 1.027 1.036 1.052 1.064 1.073 1.080 1.085 1.087 1.089 1.087 1.087 1.085
0.000 –0.226 –0.230 –0.233 –0.233 –0.230 –0.228 –0.226 –0.221 –0.216 –0.212 –0.207 –0.198 –0.189 –0.180 –0.168 –0.161 –0.152 –0.143 –0.136 –0.127 –0.120 –0.113 –0.108 –0.101 –0.097 –0.090 –0.078 –0.069 –0.060 –0.053 –0.046 –0.041 –0.037 –0.035 –0.032 –0.032 –0.030 –0.032 –0.035 –0.039 –0.044 –0.051 –0.058 –0.067 –0.074 –0.085
–0.778 –0.934 –0.937 –0.939 –0.939 –0.938 –0.937 –0.935 –0.933 –0.930 –0.927 –0.924 –0.918 –0.912 –0.906 –0.899 –0.893 –0.888 –0.882 –0.877 –0.872 –0.867 –0.862 –0.858 –0.854 –0.850 –0.846 –0.837 –0.830 –0.823 –0.818 –0.813 –0.809 –0.805 –0.802 –0.800 –0.798 –0.795 –0.794 –0.793 –0.794 –0.796 –0.798 –0.801 –0.804 –0.808 –0.812
5.57 6.27 6.65 6.91 7.08 7.18 7.23 7.24 7.21 7.16 7.10 7.02 6.83 6.62 6.39 6.17 5.94 5.72 5.50 5.30 5.10 4.91 4.74 4.57 4.41 4.26 4.13 3.82 3.57 3.36 3.20 3.07 2.98 2.92 2.89 2.88 2.90 2.99 3.14 3.36 3.62 3.92 4.26 4.62 5.01 5.42 5.85
–0.371 –0.212 –0.211 –0.215 –0.221 –0.228 –0.238 –0.248 –0.258 –0.270 –0.281 –0.292 –0.315 –0.338 –0.360 –0.381 –0.401 –0.420 –0.438 –0.456 –0.472 –0.487 –0.502 –0.516 –0.529 –0.541 –0.553 –0.579 –0.602 –0.622 –0.639 –0.653 –0.666 –0.676 –0.685 –0.692 –0.698 –0.706 –0.710 –0.711 –0.709 –0.704 –0.697 –0.689 –0.679 –0.667 –0.655
1396 1112 1291 1452 1596 1718 1820 1910 1977 2037 2080 2118 2158 2178 2173 2158 2133 2104 2070 2032 1995 1954 1919 1884 1849 1816 1782 1710 1644 1592 1545 1507 1476 1452 1432 1416 1406 1396 1400 1416 1442 1479 1524 1581 1644 1714 1795
0.468 0.440 0.437 0.437 0.435 0.435 0.435 0.436 0.436 0.435 0.435 0.435 0.438 0.439 0.439 0.441 0.443 0.445 0.449 0.450 0.453 0.454 0.458 0.460 0.463 0.464 0.469 0.474 0.480 0.485 0.492 0.497 0.502 0.505 0.511 0.515 0.520 0.528 0.533 0.540 0.545 0.550 0.554 0.558 0.561 0.565 0.566
Source: Adapted from Boore, D.M., Joyner, W.B., and Fumal, T.E. 1997. “Equations for Estimating Horizontal Response Spectra and Peak Acceleration from Western North American Earthquakes: A Summary of Recent Work,” Seismol. Res. Lett., 68, 128–153.
© 2003 by CRC Press LLC
0068_C05_fm Page 31 Tuesday, August 13, 2002 9:16 AM
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Engineering Models of Strong Ground Motion
where Y is the average horizontal or vertical component of PGA or PSA and f 1 ( M W ) = c 2 M W + c 3 (8.5 − MW )
2
[
(5.58)
]
2 2 2 f 2 ( M W , rseis , S) = rseis + g ( S) exp c 8 M W + c 9 (8.5 − M W )
2
(5.59a)
g ( S) = c 5 + c 6 ( SVFS + SSR ) + c 7 SFR
(5.59b)
f 3 ( F ) = (c 10 FRV + c 11 FTH ) F
(5.60)
f 4 ( S) = c 12 SVFS + c 13 SSR + c 14 SFR
(5.61)
f5 ( HW , MW , rseis ) = HW f HW ( MW ) f HW (rseis )
(5.62a)
0 HW = (SVFS + SSR + SFR ) 5 − rjb 5
(
0 f HW ( MW ) = MW − 5.5 1 c (r 8) f HW (rseis ) = 15 seis c15
)
for rjb ≥ 5 km for rjb < 5 km
(5.62b)
for MW < 5.5 for 5.5 ≤ MW ≤ 6.5 for MW > 5.5
(5.62c)
for rseis < 8 km for rseis ≥ 8 km
(5.62d)
The parameter HW quantifies the effect of the hanging wall and will always evaluate to zero for firm soil and for a horizontal distance of 5 km or greater from the rupture plane. This distinguishes it from the hanging-wall factor of Abrahamson and Silva [1997]. The standard deviation of lnY is defined as a function of magnitude according to the expression: c − 0.07 MW σ lnY = 16 c16 − 0.518
for MW < 7.4 for MW ≥ 7.4
(5.63a)
or as a function of PGA according to the expression:
σ lnY
c17 + 0.351 = c17 − 0.132 ln (PGA ) c + 0.183 17
for PGA ≤ 0.07 g for 0.07 g < PGA < 0.25 g for PGA ≥ 0.25 g
(5.63b)
where PGA is either uncorrected PGA or corrected PGA, depending on the application (see footnote to Table 5.9). The regression coefficients are listed in Tables 5.9 and 5.10. The relation is considered valid for MW ≥ 4.7 and rseis ≤ 60 km. The relation predicts ground motion for firm soil, equivalent to the condition SFS = 1, unless one of the site parameters in g (S) and f4 (S) is set to one, in which case it predicts ground motion for either very firm soil, soft rock, or firm rock. Further guidance on evaluating the relation for various site conditions is given tin Table 5.4. The relationship between the faulting mechanism parameters FRV (reverse © 2003 by CRC Press LLC
0068_C05_fm Page 32 Tuesday, August 13, 2002 9:16 AM
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Earthquake Engineering Handbook
faulting with dip greater than 45°) and FTH (thrust faulting with dip less than or equal to 45°) and the rake angle λ is given in Table 5.5. Sediment depth D was evaluated and found to be important, but it was not included as a parameter, since it is rarely used in engineering practice. If desired, sediment depth can be included in an estimate of ground motion by using the attenuation relation developed by Campbell [1997, 2000c, 2001]. 5.6.1.4 The Sadigh et al. Model The attenuation relation of Sadigh et al. [1993, 1997] can be represented by the expression:
(
ln Y = c1F + f MW , rrup
)
(5.64)
where Y is the average horizontal or vertical component of PGA or PSA and
(
)
(
)
f MW , rrup = c 2 + c 3 MW + c 4 (8.5 − MW ) + c 5 ln R + c 6 ln rrup + 2
(5.65)
R = rrup + c 7 exp (c 8 MW )
(5.66)
2.5
σ lnY
c 9 = c10 − c11MW c 12
for MW ≤ c13 for c13 < MW < c14 for MW ≥ c14
(5.67)
The relation can be used to estimate ground motion for generic soil, equivalent to the condition SSoil = 1, or generic rock, equivalent to the condition SRock = 1 (Table 5.4). The regression coefficients for generic rock are listed in Tables 5.11 and 5.12 and those for generic soil in Table 5.13. No regression coefficients are given for the vertical component of ground motion for soil. The relation is considered valid for MW = 4.0 to 8.0 and rrup ≤ 100 km. The authors say that they define rock as a deposit with less than a meter of soil. However, one of the authors [Bob Youngs, personal communication, 2001] says that this goal was not actually achieved and that the rock and soil categories are generally consistent with those of Abrahamson and Silva [1997]. Youngs therefore recommends using VS30 = 290 m/sec and 510 m/sec to represent generic soil and generic rock in the Sadigh et al. attenuation relations. Nonetheless, it is generally assumed that the rock classification used in this relation is approximately the same as that used in other relations when making engineering estimates of ground motion in WNA (Table 5.4). The relationship between the faulting mechanism parameter F and the rake angle λ is given in Table 5.5.
5.6.2 Eastern North America As discussed previously, the stable tectonic area of eastern North America (ENA) has traditionally been taken as the region east of 105°W longitude, while a somewhat more detailed definition of this area has been proposed by Frankel and coworkers [1996, 2000]. Because ENA is tectonically stable, earthquakes in this region are typically associated with higher stress drops and lower attenuation rates, resulting in higher ground motion at short periods and large distances, than in WNA. Like for the WNA attenuation relations, it is often assumed that the ENA attenuation relations can be used to estimate ground motion in similar tectonic environments worldwide. Nonetheless, caution should be used when using these relations in regions outside of ENA. Three attenuation relations commonly used to develop engineering estimates of strong ground motion in ENA are presented [Atkinson and Boore, 1995, 1997; Toro et al., 1997; Campbell, in press]. Because of the limited number of strong-motion recordings in the region, none of these relations were developed using the empirical method. The Atkinson and Boore and the Toro et al. models were developed using the stochastic method, meaning that they were developed from a regression © 2003 by CRC Press LLC
Tn (s)
c1
c2
c3
c4
c5
c6
c7
c8
c9
c10
c11
c12
c13
c14
c15
c16
c17
Unc PGA Cor PGA 0.05 0.075 0.10 0.15 0.20 0.30 0.40 0.50 0.75 1.0 1.5 2.0 3.0 4.0
–2.896 –4.033 –3.740 –3.076 –2.661 –2.270 –2.771 –2.999 –3.511 –3.556 –3.709 –3.867 –4.093 –4.311 –4.817 –5.211
0.812 0.812 0.812 0.812 0.812 0.812 0.812 0.812 0.812 0.812 0.812 0.812 0.812 0.812 0.812 0.812
0.000 0.036 0.036 0.050 0.060 0.041 0.030 0.007 –0.015 –0.035 –0.071 –0.101 –0.150 –0.180 –0.193 –0.202
–1.318 –1.061 –1.121 –1.252 –1.308 –1.324 –1.153 –1.080 –0.964 –0.964 –0.964 –0.964 –0.964 –0.964 –0.964 –0.964
0.187 0.041 0.058 0.121 0.166 0.212 0.098 0.059 0.024 0.023 0.021 0.019 0.019 0.019 0.019 0.019
–0.029 –0.005 –0.004 –0.005 –0.009 –0.033 –0.014 –0.007 –0.002 –0.002 –0.002 0 0 0 0 0
–0.064 –0.018 –0.028 –0.051 –0.068 –0.081 –0.038 –0.022 –0.005 –0.004 –0.002 0 0 0 0 0
0.616 0.766 0.724 0.648 0.621 0.613 0.704 0.752 0.842 0.842 0.842 0.842 0.842 0.842 0.842 0.842
0 0.034 0.032 0.040 0.046 0.031 0.026 0.007 –0.016 –0.036 –0.074 –0.105 –0.155 –0.187 –0.200 –0.209
0.179 0.343 0.302 0.243 0.224 0.318 0.296 0.359 0.379 0.406 0.347 0.329 0.217 0.060 –0.079 –0.061
0.307 0.351 0.362 0.333 0.313 0.344 0.342 0.385 0.438 0.479 0.419 0.338 0.188 0.064 0.021 0.057
–0.062 –0.123 –0.140 –0.150 –0.146 –0.176 –0.148 –0.162 –0.078 –0.122 –0.108 –0.073 –0.079 –0.124 –0.154 –0.054
–0.195 –0.138 –0.158 –0.196 –0.253 –0.267 –0.183 –0.157 –0.129 –0.130 –0.124 –0.072 –0.056 –0.116 –0.117 –0.261
–0.320 –0.289 –0.205 –0.208 –0.258 –0.284 –0.359 –0.585 –0.557 –0.701 –0.796 –0.858 –0.954 –0.916 –0.873 –0.889
0.370 0.370 0.370 0.370 0.370 0.370 0.370 0.370 0.370 0.370 0.331 0.281 0.210 0.160 0.089 0.039
0.964 0.920 0.940 0.952 0.958 0.974 0.981 0.984 0.987 0.990 1.021 1.021 1.021 1.021 1.021 1.021
0.263 0.219 0.239 0.251 0.257 0.273 0.280 0.283 0.286 0.289 0.320 0.320 0.320 0.320 0.320 0.320
Note: Uncorrected PGA is to be used only when an estimate of PGA is required. Corrected PGA is to be used when an estimate of PGA compatible with PSA is required. Source: Adapted from Campbell, K.W. and Bozorgnia, Y., in press. “Updated Near-Source Ground Motion (Attenuation) Relations for the Horizontal and Vertical Components of Peak Ground Acceleration and Acceleration Response Spectra,” Bull. Seismol. Soc. Am.
5-33
© 2003 by CRC Press LLC
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Coefficients for Campbell and Bozorgnia Attenuation Relation: Horizontal Component
Engineering Models of Strong Ground Motion
TABLE 5.9
c1
c2
c3
c4
c5
c6
c7
c8
c9
c10
c11
c12
c13
c14
c15
c17
c17
Unc PGA Cor PGA 0.05 0.075 0.10 0.15 0.20 0.30 0.40 0.50 0.75 1.0 1.5 2.0 3.0 4.0
–2.807 –3.108 –1.918 –1.504 –1.672 –2.323 –2.998 –3.721 –4.536 –4.651 –4.903 –4.950 –5.073 –5.292 –5.748 –6.042
0.756 0.756 0.756 0.756 0.756 0.756 0.756 0.756 0.756 0.756 0.756 0.756 0.756 0.756 0.756 0.756
0 0 0 0 0 0 0 0.007 –0.015 –0.035 –0.071 –0.101 –0.150 –0.180 –0.193 –0.202
–1.391 –1.287 –1.517 –1.551 –1.473 –1.280 –1.131 –1.028 –0.812 –0.812 –0.812 –0.812 –0.812 –0.812 –0.812 –0.812
0.191 0.142 0.309 0.343 0.282 0.171 0.089 0.050 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012
0.044 0.046 0.069 0.083 0.062 0.045 0.028 0.010 0 0 0 0 0 0 0 0
–0.014 –0.040 –0.023 0.000 0.001 0.008 0.004 0.004 0 0 0 0 0 0 0 0
0.544 0.587 0.498 0.487 0.513 0.591 0.668 0.736 0.931 0.931 0.931 0.931 0.931 0.931 0.931 0.931
0 0 0 0 0 0 0 0.007 –0.018 –0.043 –0.087 –0.124 –0.184 –0.222 –0.238 –0.248
0.091 0.253 0.058 0.135 0.168 0.223 0.234 0.249 0.299 0.243 0.295 0.266 0.171 0.114 0.179 0.237
0.223 0.173 0.100 0.182 0.210 0.238 0.256 0.328 0.317 0.354 0.418 0.315 0.211 0.115 0.159 0.134
–0.096 –0.135 –0.195 –0.224 –0.198 –0.170 –0.098 –0.026 –0.017 –0.020 0.078 0.043 –0.038 0.033 –0.010 –0.059
–0.212 –0.138 –0.274 –0.303 –0.275 –0.175 –0.041 0.082 0.022 0.092 0.091 0.101 –0.018 –0.022 –0.047 –0.267
–0.199 –0.256 –0.219 –0.263 –0.252 –0.270 –0.311 –0.265 –0.257 –0.293 –0.349 –0.481 –0.518 –0.503 –0.539 –0.606
0.630 0.630 0.630 0.630 0.630 0.630 0.571 0.488 0.428 0.383 0.299 0.240 0.240 0.240 0.240 0.240
1.003 0.975 1.031 1.031 1.031 1.031 1.031 1.031 1.031 1.031 1.031 1.031 1.031 1.031 1.031 1.031
0.320 0.274 0.330 0.330 0.330 0.330 0.330 0.330 0.330 0.330 0.330 0.330 0.330 0.330 0.330 0.330
Note: Uncorrected PGA is to be used only when an estimate of PGA is required. Corrected PGA is to be used when an estimate of PGA compatible with PSA is required. Source: Adapted from Campbell, K.W. and Bozorgnia, Y. in press. “Updated Near-Source Ground Motion (Attenuation) Relations for the Horizontal and Vertical Components of Peak Ground Acceleration and Acceleration Response Spectra,” Bull. Seismol. Soc. Am.
© 2003 by CRC Press LLC
Earthquake Engineering Handbook
Tn (s)
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TABLE 5.10 Coefficients for Campbell and Bozorgnia Attenuation Relation: Vertical Component
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Engineering Models of Strong Ground Motion
analysis o f seismolo gical-base d est imates of strong g round mot ion. The Campbell model was developed using the h ybrid empirical me thod, in which attenuation relations in WNA were modified for use in EN A using se ismolo gical est imates of ground mot ion in WNA and ENA. Because o f its use o f empirical att enuation relations in WNA, this latt er model inherently incorporates finitefault ing effects. It should b e noted that the re are two additional attenuation relations [Frankel et al., 1996; Somerville et al., 2001] that ha ve not b een publishe d in an international jour nal but which are being use d in the 2002 updat e of the se ismic hazar d maps p roduced by the U.S. Geolo gical Survey (the F rankel et al. relation was also use d in the 1996 v ersion of these hazar d maps). This is noteworthy because man y engineering st udies a dopt the att enuation relations use d by the U.S. Geolo gical Survey in order to be consist ent with the hazar d defined in these maps . The three selected attenuation relations provide ground-motion estimates for a very hard rock, typically referred to as ENA hard rock [Boore and Joyner, 1997; see also Table 5.4]. ENA hard rock, with a 30-m velocity of around 2800 m/sec, is not a typical site condition encountered in engineering investigations, even in ENA, so some adjustment must be made for local site conditions. Atkinson and Boore [1995, 1997] provide a site term to use with their attenuation relation but this term corresponds to a very firm soil or soft rock and is calculated using the stochastic method assuming linear soil response. As a result, this site term may not be appropriate for the larger ground motions of engineering interest. One simple approach is to assume that ENA hard rock represents building-code Site Class A and use the site factors in the U.S. building codes to approximate the effect of local soil conditions for other site classes. One of the problems with this approach is that these soil factors are given only for spectral accelerations averaged over short periods (Tn = 0.1 to 0.5 sec) or long periods (Tn = 0.5 to 2.0 sec), so one would have to use judgment in order to use these factors for individual periods. Another problem is that Site Class A is usually associated with a 30-m velocity of around 1890 m/sec [Savy et al., 1987], which is much less than that for ENA hard rock. Boore [in press] suggests that nonlinear soil effects should be taken into account using a nonlinear site-response analysis. Additional guidance on incorporating site effects is provided by Savy and coworkers [1987], EPRI [1993], and Hwang and coworkers [1997]. 5.6.2.1
The Atkinson and Boore Model
The attenuation relation of Atkinson and Boore [1995, 1997] can be represented by the expression:
(
)
ln Y = f 1 M W , rhypo + f 2 ( S)
(5.68)
where Y is the average horizontal component of PGA, PGV, or PSA and
(
)
f 1 M W , rhypo = c 1 + c 2 ( M W − 6) + c 3 ( M W − 6) − ln rhypo + c 4 rhypo
(5.69)
f 2 ( S) = c 5 SDeep
(5.70)
2
The regression coefficients and the recommended values of the standard deviation of ln Y [taken from Atkinson, 1995] are listed in Table 5.14. The regression coefficient c5 was theoretically developed using Equation 5.30, so caution should be used when applying this coefficient to very high ground-motion amplitudes where nonlinear soil behavior may be expected. The relation is considered valid for MW = 4.0 to 7.25 and rhypo = 10 to 500 km. The attenuation relations were developed as an approximation to the simulated ground-motion values for use with PSHA. The relations overestimate the simulated values for MW ≤ 5.5 and rhypo > 30 km. This bias is not an issue for most seismic hazard studies. However, a more accurate estimate of ground motion can be obtained from the tables provided in the appendices of Atkinson and Boore [1995, 1997]. The relation can be used to estimate ground motion for ENA hard rock, equivalent to the condition SENA = 1, or ENA deep stiff soil, equivalent to setting SDeep = 1 (see also Table 5.4). A deep stiff soil is defined as a very stiff site with soil depth > 60 m and VS30 ≈ 500 m/sec. This is similar to the average 30-m velocity for building-code Site Class C (Tables 5.2 and 5.4) but its site-response characteristics are © 2003 by CRC Press LLC
Tn (s)
c1
c2
c3
c4
c5
c6
0.182 0.182 0.182 0.182 0.182 0.182 0.182 0.182 0.182 0.182 0.182 0.182 0.182 0.182 0.182 0.182 0.182 0.182 0.182 0.182 0.182 0.182
–0.624 –0.090 0.110 0.212 0.275 0.348 0.307 0.285 0.239 0.153 0.060 –0.057 –0.298 –0.588 –1.208 –1.705 –2.407 –2.945 –3.700 –4.230 –4.714 –5.530
1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
0 0.006 0.006 0.006 0.006 0.005 0.004 0.002 0 –0.004 –0.011 –0.017 –0.028 –0.040 –0.050 –0.055 –0.065 –0.070 –0.080 –0.100 –0.100 –0.110
–2.100 –2.128 –2.128 –2.140 –2.148 –2.162 –2.144 –2.130 –2.110 –2.080 –2.053 –2.028 –1.990 –1.945 –1.865 –1.800 –1.725 –1.670 –1.610 –1.570 –1.540 –1.510
0 –0.082 –0.082 –0.052 –0.041 –0.014 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
c7
c8
c9
c10
c11
c12
c13
c14
3.6564 3.6564 3.6564 3.6564 3.6564 3.6564 3.6564 3.6564 3.6564 3.6564 3.6564 3.6564 3.6564 3.6564 3.6564 3.6564 3.6564 3.6564 3.6564 3.6564 3.6564 3.6564
0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1.39 1.39 1.40 1.40 1.41 1.41 1.42 1.42 1.42 1.43 1.44 1.45 1.48 1.50 1.52 1.53 1.53 1.53 1.53 1.53 1.53 1.53
0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14
0.38 0.38 0.39 0.39 0.40 0.40 0.41 0.41 0.41 0.42 0.43 0.44 0.47 0.49 0.51 0.52 0.52 0.52 0.52 0.52 0.52 0.52
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
7.21 7.21 7.21 7.21 7.21 7.21 7.21 7.21 7.21 7.21 7.21 7.21 7.21 7.21 7.21 7.21 7.21 7.21 7.21 7.21 7.21 7.21
MW ≤ 6.5
© 2003 by CRC Press LLC
Earthquake Engineering Handbook
PGA 0.05 0.07 0.09 0.10 0.12 0.14 0.15 0.17 0.20 0.24 0.30 0.40 0.50 0.75 1.0 1.5 2.0 3.0 4.0 5.0 7.5
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TABLE 5.11 Coefficients for Sadigh et al. Rock Attenuation Relation: Horizontal Component
0.182 0.182 0.182 0.182 0.182 0.182 0.182 0.182 0.182 0.182 0.182 0.182 0.182 0.182 0.182 0.182 0.182 0.182 0.182 0.182 0.182 0.182
–1.274 –0.740 –0.540 –0.438 –0.375 –0.302 –0.343 –0.365 –0.411 –0.497 –0.590 –0.707 –0.948 –1.238 –1.858 –2.355 –3.057 –3.595 –4.350 –4.880 –5.364 –6.180
1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1
0 0.006 0.006 0.006 0.006 0.005 0.004 0.002 0 –0.004 –0.011 –0.017 –0.028 –0.040 –0.050 –0.055 –0.065 –0.070 –0.080 –0.100 –0.100 –0.110
–2.100 –2.128 –2.128 –2.140 –2.148 –2.162 –2.144 –2.130 –2.110 –2.080 –2.053 –2.028 –1.990 –1.945 –1.865 –1.800 –1.725 –1.670 –1.610 –1.570 –1.540 –1.510
0 –0.082 –0.082 –0.052 –0.041 –0.014 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0.6160 0.6160 0.6160 0.6160 0.6160 0.6160 0.6160 0.6160 0.6160 0.6160 0.6160 0.6160 0.6160 0.6160 0.6160 0.6160 0.6160 0.6160 0.6160 0.6160 0.6160 0.6160
0.524 0.524 0.524 0.524 0.524 0.524 0.524 0.524 0.524 0.524 0.524 0.524 0.524 0.524 0.524 0.524 0.524 0.524 0.524 0.524 0.524 0.524
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1.39 1.39 1.40 1.40 1.41 1.41 1.42 1.42 1.42 1.43 1.44 1.45 1.48 1.50 1.52 1.53 1.53 1.53 1.53 1.53 1.53 1.53
0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14
0.38 0.38 0.39 0.39 0.40 0.40 0.41 0.41 0.41 0.42 0.43 0.44 0.47 0.49 0.51 0.52 0.52 0.52 0.52 0.52 0.52 0.52
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
7.21 7.21 7.21 7.21 7.21 7.21 7.21 7.21 7.21 7.21 7.21 7.21 7.21 7.21 7.21 7.21 7.21 7.21 7.21 7.21 7.21 7.21
© 2003 by CRC Press LLC
Earthquake Engineering Handbook
Source: Adapted from Sadigh, K. et al. 1993. “Specification of Long-Period Ground Motions: Updated Attenuation Relationships for Rock Site Conditions and Adjustment Factors for Near-Fault Effects,” in Proc. ATC-17-1 Seminar on Seismic Isolation, Passive Energy Dissipation, and Active Control, Vol. I, March 11–12, San Francisco, pp. 11–23, Applied Technology Council, Redwood City, CA; and Sadigh, K. et al. 1997. “Attenuation Relationships for Shallow Crustal Earthquakes Based on California Strong Motion Data,” Seismol. Res. Lett., 68, 180–189.
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MW > 6.5 PGA 0.05 0.07 0.09 0.10 0.12 0.14 0.15 0.17 0.20 0.24 0.30 0.40 0.50 0.75 1.0 1.5 2.0 3.0 4.0 5.0 7.5
Tn (s)
c1
c2
c3
c4
c5
c6
c7
c8
c9
c10
c11
c12
c13
c14
3.5701 3.5701 3.5701 3.5701 3.5701 3.5701 3.5701 3.5701 3.5701 3.5701 3.5701 3.5701 3.5701 3.5701 3.5701 3.5701 3.5701 3.5701 3.5701 3.5701 3.5701 3.5701
0.228 0.228 0.228 0.228 0.228 0.228 0.228 0.228 0.228 0.228 0.228 0.228 0.228 0.228 0.228 0.228 0.228 0.228 0.228 0.228 0.228 0.228
0.68 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75
3.08 2.91 2.91 2.91 2.91 2.91 2.91 2.91 2.91 2.91 2.91 2.91 2.91 2.91 2.91 2.91 2.91 2.91 2.91 2.91 2.91 2.91
0.40 0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.36
0.48 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57
6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0
6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5
MW ≤ 6.5 0.0953 0.0953 0.0953 0.0953 0.0953 0.0953 0.0953 0.0953 0.0953 0.0953 0.0953 0.0953 0.0953 0.0953 0.0953 0.0953 0.0953 0.0953 0.0953 0.0953 0.0953 0.0953
–0.4300 0.3379 0.5041 0.6095 0.6896 0.6718 0.6252 0.5535 0.3813 0.2524 0.0122 –0.3005 –0.6678 –1.1392 –1.7656 –2.2748 –3.2062 –3.8818 –4.2618 –4.5719 –4.8167 –5.0364
© 2003 by CRC Press LLC
1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
0 0 0 0 0 –0.00330 –0.00468 –0.00707 –0.00909 –0.01000 –0.01462 –0.02061 –0.02734 –0.03558 –0.04619 –0.05442 –0.06939 –0.08000 –0.08554 –0.08946 –0.09251 –0.09500
–2.300 –2.450 –2.450 –2.450 –2.450 –2.420 –2.400 –2.380 –2.333 –2.300 –2.241 –2.164 –2.077 –1.971 –1.835 –1.729 –1.536 –1.400 –1.400 –1.400 –1.400 –1.400
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Earthquake Engineering Handbook
PGA 0.04 0.05 0.06 0.07 0.09 0.10 0.12 0.14 0.15 0.17 0.20 0.24 0.30 0.40 0.50 0.75 1.0 1.5 2.0 2.5 3.0
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5-38
TABLE 5.12 Coefficients for Sadigh et al. Rock Attenuation Relation: Vertical Component
–1.0800 –0.3121 –0.1459 –0.0405 0.03956 0.0218 –0.0248 –0.0965 –0.2687 –0.3976 –0.6378 –0.9505 –1.3178 –1.7893 –2.4157 –2.9248 –3.8562 –4.5318 –4.9118 –5.2219 –5.4667 –5.6864
1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1
0 0 0 0 0 –0.00330 –0.00468 –0.00707 –0.00909 –0.01000 –0.01462 –0.02061 –0.02734 –0.03558 –0.04619 –0.05442 –0.06939 –0.08000 –0.08554 –0.08946 –0.09251 –0.09500
–2.300 –2.450 –2.450 –2.450 –2.450 –2.420 –2.400 –2.380 –2.333 –2.300 –2.241 –2.164 –2.077 –1.971 –1.835 –1.729 –1.536 –1.400 –1.400 –1.400 –1.400 –1.400
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0.7030 0.7030 0.7030 0.7030 0.7030 0.7030 0.7030 0.7030 0.7030 0.7030 0.7030 0.7030 0.7030 0.7030 0.7030 0.7030 0.7030 0.7030 0.7030 0.7030 0.7030 0.7030
0.478 0.478 0.478 0.478 0.478 0.478 0.478 0.478 0.478 0.478 0.478 0.478 0.478 0.478 0.478 0.478 0.478 0.478 0.478 0.478 0.478 0.478
0.68 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75
3.08 2.91 2.91 2.91 2.91 2.91 2.91 2.91 2.91 2.91 2.91 2.91 2.91 2.91 2.91 2.91 2.91 2.91 2.91 2.91 2.91 2.91
0.40 0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.36
0.48 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57
6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0
6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5
Source: Adapted from Sadigh, K. et al. 1993. “Specification of Long-Period Ground Motions: Updated Attenuation Relationships for Rock Site Conditions and Adjustment Factors for Near-Fault Effects,” in Proc. ATC-17-1 Seminar on Seismic Isolation, Passive Energy Dissipation, and Active Control, Vol. I, March 11–12, San Francisco, pp. 11–23, Applied Technology Council, Redwood City, CA.
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0.0953 0.0953 0.0953 0.0953 0.0953 0.0953 0.0953 0.0953 0.0953 0.0953 0.0953 0.0953 0.0953 0.0953 0.0953 0.0953 0.0953 0.0953 0.0953 0.0953 0.0953 0.0953
Engineering Models of Strong Ground Motion
MW > 6.5 PGA 0.04 0.05 0.06 0.07 0.09 0.10 0.12 0.14 0.15 0.17 0.20 0.24 0.30 0.40 0.50 0.75 1.0 1.5 2.0 2.5 3.0
Tn (s)
c1
c2
c3
c4
c5
c6
c7
c8
c9
c10
c11
c12
c13
c14
2.1863 2.1863 2.1863 2.1863 2.1863 2.1863 2.1863 2.1863 2.1863 2.1863 2.1863 2.1863 2.1863
0.320 0.320 0.320 0.320 0.320 0.320 0.320 0.320 0.320 0.320 0.320 0.320 0.320
0 0 0 0 0 0 0 0 0 0 0 0 0
1.520 1.540 1.540 1.565 1.580 1.595 1.610 1.635 1.660 1.690 1.700 1.710 1.710
0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16
0.40 0.42 0.42 0.45 0.46 0.48 0.49 0.52 0.54 0.57 0.58 0.59 0.59
0 0 0 0 0 0 0 0 0 0 0 0 0
7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0
0.5882 0.5882 0.5882 0.5882 0.5882 0.5882 0.5882 0.5882 0.5882 0.5882 0.5882 0.5882 0.5882
0 0 0 0 0 0 0 0 0 0 0 0 0
1.520 1.540 1.540 1.565 1.580 1.595 1.610 1.635 1.660 1.690 1.700 1.710 1.710
0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16
0.40 0.42 0.42 0.45 0.46 0.48 0.49 0.52 0.54 0.57 0.58 0.59 0.59
0 0 0 0 0 0 0 0 0 0 0 0 0
7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0
MW ≤ 6.5 PGA 0.075 0.10 0.20 0.30 0.40 0.50 0.75 1.0 1.5 2.0 3.0 4.0
0.2500 0.2500 0.2500 0.2500 0.2500 0.2254 0.2291 0.2292 0.1910 0.1480 0.0973 0.0396 –0.0133
–2.1700 –1.7128 –1.5305 –1.2513 –1.2153 –1.2449 –1.3206 –1.4690 –1.6035 –1.8465 –2.0699 –2.4501 –2.7974
1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
0 0.005 0.005 –0.004 –0.014 –0.024 –0.033 –0.051 –0.065 –0.090 –0.108 –0.139 –0.160
–1.700 –1.700 –1.700 –1.700 –1.700 –1.700 –1.700 –1.700 –1.700 –1.700 –1.700 –1.700 –1.700
0 0 0 0 0 0 0 0 0 0 0 0 0
MW > 6.5 0.2500 0.2500 0.2500 0.2500 0.2500 0.2254 0.2291 0.2292 0.1910 0.1480 0.0973 0.0396 –0.0133
–2.1700 –1.7128 –1.5305 –1.2513 –1.2153 –1.2449 –1.3206 –1.4690 –1.6035 –1.8465 –2.0699 –2.4501 –2.7974
1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
0 0.005 0.005 –0.004 –0.014 –0.024 –0.033 –0.051 –0.065 –0.090 –0.108 –0.139 –0.160
–1.700 –1.700 –1.700 –1.700 –1.700 –1.700 –1.700 –1.700 –1.700 –1.700 –1.700 –1.700 –1.700
0 0 0 0 0 0 0 0 0 0 0 0 0
0.3825 0.3825 0.3825 0.3825 0.3825 0.3825 0.3825 0.3825 0.3825 0.3825 0.3825 0.3825 0.3825
Source: Adapted from Sadigh, K. et al. 1997. “Attenuation Relationships for Shallow Crustal Earthquakes Based on California Strong Motion Data,” Seismol. Res. Lett., 68, 180–189.
© 2003 by CRC Press LLC
Earthquake Engineering Handbook
PGA 0.075 0.10 0.20 0.30 0.40 0.50 0.75 1.0 1.5 2.0 3.0 4.0
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TABLE 5.13 Coefficients for Sadigh et al. Soil Attenuation Relation
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Engineering Models of Strong Ground Motion
TABLE 5.14 Coefficients for Atkinson and Boore Attenuation Relation σln Y Tn (s)
c1
c2
c3
c4
c5
MW
mLg
PGA PGV 0.050 0.077 0.10 0.13 0.20 0.31 0.50 0.77 1.00 1.25 2.00
1.841 4.697 2.762 2.463 2.301 2.140 1.749 1.265 0.620 –0.094 –0.508 –0.900 –1.660
0.686 0.972 0.755 0.797 0.829 0.864 0.963 1.094 1.267 1.391 1.428 1.462 1.460
–0.123 –0.0859 –0.110 –0.113 –0.121 –0.129 –0.148 –0.165 –0.147 –0.118 –0.094 –0.071 –0.039
–0.00311 0 –0.00520 –0.00352 –0.00279 –0.00207 –0.00105 –0.00024 0 0 0 0 0
— — –0.069 — 0.345 — 0.553 — 0.668 — 0.622 — 0.622
— — — — 0.622 — 0.599 — 0.553 — 0.553 — —
— — — — 0.668 — 0.714 — 0.783 — 0.990 — —
Source: Adapted from Atkinson, G.M. and Boore, D.M. 1995. “New Ground Motion Relations for Eastern North America,” Bull. Seismol. Soc. Am., 85, 17–30; and Atkinson, G.M. and Boore, D.M. 1997. “Some Comparisons between Recent Ground Motion Relations,” Seismol. Res. Lett., 68, 24–40.
likely to be different, because of the difference in the bedrock properties between ENA and WNA, the source region for deriving the site-response characteristic of Site Class C used in the building codes. If an estimate of ground motion for a given value of the magnitude measure mLg (mN in Canada) is required, MW can be estimated from mLg, using the relation: −0.39 + 0.98 m Lg MW = 2 2.715 – 0.277 m Lg + 0.127 m Lg
for m Lg ≤ 6.0 for m Lg > 6.0
(5.71)
The use of hypocentral distance as the distance measure means that the relation is not strictly valid for large earthquakes with extended rupture zones. Boore [in press] suggests using rhypo as an estimate of the closest distance to fault rupture rrup in such cases. Guidance on incorporating local soil effects is given in Section 5.6.2. 5.6.2.2 The Toro et al. Model The attenuation relation of Toro et al. [1997] can be represented by the expression: ln Y = c 1 + c 2 ( M − 6) + c 3 ( M − 6) + c 4 ln R + c 5 f ( R) + c 6 R 2
(5.72)
where Y is the average horizontal component of PGA or PSA, M = MW or mLg and 0 f ( R) = ln ( R 100)
for R ≤ 100 km for R > 100 km
R = r jb2 + c 72
(5.73)
(5.74)
Because the relations were developed from ground motions calculated using the stochastic method, the standard deviation of lnY is theoretically rather than empirically defined from median estimates of parametric uncertainty, according to the equation:
( )
σ lnY = σ ln2 Y ( M ) + σ ln2 Y r jb
(5.75)
where σlnY (M) and σln Y(rjb) are computed by linear interpolation of the values given in Table 5.15. © 2003 by CRC Press LLC
σln Y (M) Tn (s)
c1
c2
c3
c4
c5
2.20 4.00 3.68 2.37 1.73 1.07 0.09 –0.74
0.81 0.79 0.80 0.81 0.84 1.05 1.42 1.86
0 0 0 0 0 –0.10 –0.20 –0.31
–1.27 –1.57 –1.46 –1.10 –0.98 –0.93 –0.90 –0.92
–0.11 0.26 0.31 –0.08 –0.32 –0.37 –0.41 –0.46
c6
c7
MW 5.0 mLg 5.0
σln Y (rrup)
MW 5.5 mLg 6.0
MW 8.0 mLg 7.5
<5 km
>20 km
0.55 0.62 0.62 0.59 0.60 0.63 0.63 0.61
0.59 0.63 0.63 0.61 0.64 0.68 0.64 0.62
0.50 0.50 0.50 0.50 0.56 0.64 0.67 0.66
0.54 0.62 0.57 0.50 0.45 0.45 0.45 0.45
0.20 0.35 0.29 0.17 0.12 0.12 0.12 0.12
0.58 0.57 0.57 0.54 0.54 0.58 0.62 0.63
0.58 0.58 0.58 0.57 0.63 0.70 0.81 0.81
0.44 0.44 0.44 0.44 0.51 0.59 0.61 0.61
0.54 0.62 0.57 0.50 0.45 0.45 0.45 0.45
0.20 0.35 0.29 0.17 0.12 0.12 0.12 0.12
Midcontinent Region, MW –0.0021 –0.0008 –0.0013 –0.0040 –0.0042 –0.0033 –0.0023 –0.0017
9.3 11.1 10.5 8.3 7.5 7.1 6.8 6.9
Midcontinent Region, mLg PGA 0.029 0.040 0.10 0.20 0.40 1.00 2.00
2.07 3.87 3.54 2.36 1.60 0.90 –0.12 –0.97
1.20 1.19 1.19 1.23 1.24 1.70 2.05 2.52
© 2003 by CRC Press LLC
0 0 0 0 0 –0.26 –0.34 –0.47
–1.28 –1.58 –1.46 –1.12 –0.98 –0.94 –0.90 –0.93
–0.05 0.32 0.38 –0.07 –0.24 –0.29 –0.31 –0.33
–0.0018 –0.0005 –0.0010 –0.0043 –0.0039 –0.0030 –0.0019 –0.0012
9.3 11.1 10.5 8.5 7.5 7.2 6.8 7.0
Earthquake Engineering Handbook
PGA 0.029 0.040 0.10 0.20 0.40 1.00 2.00
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TABLE 5.15 Coefficients for Toro et al. Attenuation Relation
0.92 0.91 0.91 1.00 0.92 1.06 1.31 1.72
0 0 0 0 0 –0.08 –0.15 –0.26
–1.49 –1.89 –1.96 –1.87 –1.34 –0.99 –0.79 –0.74
0.12 –0.09 0.00 0.65 0.61 0.28 0.03 –0.03
–0.0014 –0.0008 –0.0004 –0.0002 –0.0017 –0.0036 –0.0034 –0.0025
10.9 11.9 12.9 14.1 11.4 8.9 7.2 6.6
0.55 0.62 0.62 0.59 0.60 0.63 0.63 0.61
0.59 0.63 0.63 0.61 0.64 0.68 0.64 0.62
0.50 0.50 0.50 0.50 0.56 0.64 0.67 0.66
0.48 0.68 0.63 0.53 0.50 0.50 0.51 0.54
0.30 0.47 0.47 0.38 0.33 0.34 0.39 0.39
0.58 0.57 0.57 0.54 0.54 0.58 0.62 0.63
0.58 0.58 0.58 0.57 0.63 0.70 0.81 0.81
0.44 0.44 0.44 0.44 0.51 0.59 0.61 0.61
0.48 0.68 0.63 0.53 0.50 0.50 0.51 0.54
0.30 0.47 0.47 0.38 0.33 0.34 0.39 0.39
Gulf Coast Region, mLg PGA 0.029 0.040 0.10 0.20 0.40 1.00 2.00
2.80 4.68 5.08 4.65 3.00 1.49 0.06 –1.01
1.31 1.30 1.29 1.30 1.31 1.74 1.97 2.38
0 0 0 0 0 –0.26 –0.32 –0.42
–1.49 –1.89 –1.97 –1.78 –1.35 –1.00 –0.80 –0.75
0.19 –0.01 0.07 0.63 0.68 0.36 0.12 0.08
–0.0017 –0.0005 –0.0000 –0.0000 –0.0014 –0.0032 –0.0030 –0.0032
10.9 11.9 12.9 13.8 11.4 9.0 7.3 6.8
Source: Adapted from Toro, G.R., Abrahamson, N.A., and Schneider, J.F. 1997. “Model of Strong Ground Motions from Earthquakes in Central and Eastern North America: Best Estimates and Uncertainties,” Seismol. Res. Lett., 68, 41–57.
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2.91 4.81 5.19 5.08 3.10 1.64 0.24 –0.81
Engineering Models of Strong Ground Motion
Gulf Coast Region, MW PGA 0.029 0.040 0.10 0.20 0.40 1.00 2.00
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Earthquake Engineering Handbook
The regression coefficients are listed in Table 5.15. There are two sets of regression coefficients, one for the Midcontinent region and one for the Gulf Coast region. The Gulf Coast region represents the lowlands that border the Gulf of Mexico and includes Louisiana, the southeastern coast of Texas, and the southern areas of Alabama and Mississippi [EPRI, 1993]. The Midcontinent region covers the remaining part of ENA. The authors provide no guidelines regarding the limitations of the relation. However, some guidance can be obtained in EPRI [1993], the resource document for the relation, which states that the relation was developed using the stochastic method for MW = 4.5 to 8.0 and rjb = 1 to 500 km. The relation predicts ground motion for ENA hard rock, equivalent to the condition SENA = 1 (Table 5.4). The authors recommend that nonlinear soil effects should be modeled using the site factors given in EPRI [1993], which were developed for sites of various soil thickness using dynamic site-response analysis. Additional guidance on incorporating local soil effects is given in Section 5.6.2. 5.6.2.3 The Campbell Model The attenuation relation of Campbell [in press] can be represented by the expression:
[ (
)] ( )
ln Y = c 1 + c 2 M W + c 3 (8.5 − M W ) + c 4 ln f 1 M W , rrup + f 2 rrup + (c 9 + c 10 M W ) rrup 2
(5.76)
where Y is the average horizontal component of PGA or PSA and
(
)
[
]
2 f 1 M W , rrup = rrup + c 5 exp (c 6 M W )
( )
f 2 rrup
0 = c7 ln rrup − ln 70 c 7 ln rrup − ln 70 + c 8 ln rrup − ln 130
( (
) ) (
2
(5.77)
for rrup ≤ 70 km
)
for 70 < rrup ≤ 130 km
(5.78)
for rrup > 130 km
The standard deviation of lnY is defined as a function of magnitude according to the expression: c + c M σ lnY = 11 12 W c 13
for M W < 7.16 for M W ≥ 7.16
(5.79)
The regression coefficients are listed in Table 5.16. The relation is considered valid for MW ≥ 5.0 and rrup ≥ 0 but it should be noted that the empirical database in WNA is restricted to earthquakes up to magnitude 7.5. The author believes that it can be extrapolated to larger magnitudes because of its physically based functional form and to large distances, beyond the 100-km limit of the WNA database, because of its seismologically constrained attenuation rate. The relation can be used to estimate ground motion for ENA hard rock, equivalent to the condition SENA = 1 (Table 5.4). Guidance on incorporating local soil effects is given in Section 5.6.2.
5.6.3 Europe There are many attenuation relations that have been developed for specific countries in Europe. The two presented in this section [Ambraseys et al., 1996; Dahle et al., 1990] were chosen because they represent the two major tectonic environments of the European continent as a whole rather than any one specific country. Like North America, Europe can be divided into a shallow active tectonic region and a shallow stable tectonic region. The attenuation characteristics of these two regions are similar to their counterparts in North America. As a result, it is common to use the attenuation relations for WNA and ENA together with European relations to develop engineering estimates of ground motion in Europe. Johnston [1994, 1996] and references therein show the geographic distribution of these two tectonic environments throughout Europe and the rest of the world (Figure 5.6). Both of the selected relations were developed using the empirical method, meaning that they are based on regression analysis of strong-motion recordings. © 2003 by CRC Press LLC
c1
c2
c3
c4
c5
c6
c7
c8
c9
c10
c11
c12
c13
0.01 0.02 0.03 0.05 0.075 0.10 0.15 0.20 0.30 0.50 0.75 1.0 1.5 2.0 3.0 4.0
0.0305 1.3535 1.1860 0.3736 –0.0395 –0.1475 –0.1901 –0.4328 –0.6906 –0.5907 –0.5429 –0.6104 –0.9666 –1.4306 –2.2331 –2.7975
0.633 0.630 0.622 0.616 0.615 0.613 0.616 0.617 0.609 0.534 0.480 0.451 0.441 0.459 0.492 0.507
–0.0427 –0.0404 –0.0362 –0.0353 –0.0353 –0.0353 –0.0478 –0.0586 –0.0786 –0.1379 –0.1806 –0.2090 –0.2405 –0.2552 –0.2646 –0.2738
–1.591 –1.787 –1.691 –1.469 –1.383 –1.369 –1.368 –1.320 –1.280 –1.216 –1.184 –1.158 –1.135 –1.124 –1.121 –1.119
0.683 1.020 0.922 0.630 0.491 0.484 0.461 0.399 0.349 0.318 0.304 0.299 0.304 0.310 0.310 0.294
0.416 0.363 0.376 0.423 0.463 0.467 0.478 0.493 0.502 0.503 0.504 0.503 0.500 0.499 0.499 0.506
1.140 0.851 0.759 0.771 0.955 1.096 1.239 1.250 1.241 1.166 1.110 1.067 1.029 1.015 1.014 1.018
–0.873 –0.715 –0.922 –1.239 –1.349 –1.284 –1.079 –0.928 –0.753 –0.606 –0.526 –0.482 –0.438 –0.417 –0.393 –0.386
–0.00428 –0.00388 –0.00367 –0.00378 –0.00421 –0.00454 –0.00473 –0.00460 –0.00414 –0.00341 –0.00288 –0.00255 –0.00213 –0.00187 –0.00154 –0.00135
0.000483 0.000497 0.000501 0.000500 0.000486 0.000460 0.000393 0.000337 0.000263 0.000194 0.000160 0.000141 0.000119 0.000103 0.000084 0.000074
1.030 1.030 1.030 1.042 1.052 1.059 1.068 1.077 1.081 1.098 1.105 1.110 1.099 1.093 1.090 1.092
–0.0860 –0.0860 –0.0860 –0.0838 –0.0838 –0.0838 –0.0838 –0.0838 –0.0838 –0.0824 –0.0806 –0.0793 –0.0771 –0.0758 –0.0737 –0.0722
0.414 0.414 0.414 0.443 0.453 0.460 0.469 0.478 0.482 0.508 0.528 0.543 0.547 0.551 0.562 0.575
Source: Adapted from Campbell, K.W. in press. “Prediction of Strong Ground Motion Using the Hybrid Empirical Method: Example Application to Eastern North America,” Bull. Seismol. Soc. Am.
© 2003 by CRC Press LLC
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Tn (s)
Engineering Models of Strong Ground Motion
TABLE 5.16 Coefficients for Campbell Attenuation Relation
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Earthquake Engineering Handbook
5.6.3.1 The Ambraseys et al. Model The attenuation relation of Ambraseys et al. [1996] for the active tectonic region of Europe can be represented by the expression:
(
)
ln Y = f 1 M S , r jb + f 2 ( S)
(5.80)
where Y is the largest horizontal component of PGA or PSA and f 1 M S , r jb = c 1 + c 2 M S + c 3 ln R
(
)
(5.81)
R = r jb2 + c 42
(5.82)
f 2 ( S) = c 5 SC + c 6 SD
(5.83)
The regression coefficients and the standard deviation of lnY are listed in Table 5.17. The relation is considered valid for MS = 4.0 to 7.5 and rjb ≤ 200 km. The relation predicts ground motion for buildingcode Site Class B, equivalent to the condition SB = 1, unless SC or SD = 1, in which case it predicts ground motion for Site Classes B or C, respectively (see Tables 5.2 and 5.4). When an estimate of ground motion for a specified value of MW is required, it can be calculated from the expression [Ambraseys et al., 1996]:
(
)
M S = −48.443 + 3.487 ( log M 0 ) − 0.05266 ( log M 0 ) − 0.0036 hhypo − 30 p 2
(5.84)
where seismic moment Mo is related to MW by Equation 5.6 and p is 0 for hhypo ≤ 30 km and 1 for hhypo > 30 km. This equation, which was developed from European earthquakes, is very similar to one developed by Ekstrom and Dziewonski [1988] from a database of worldwide earthquakes. 5.6.3.2 The Dahle et al. Model The attenuation relation of Dahle et al. [1990] for the stable tectonic region of Europe can be represented by the expression: ln Y = c 1 + c 2 M S + ln R + c 3rhypo
(5.85)
where Y is the largest horizontal component of PGA or PSA and 1 rhypo R= (1 100) 100 rhypo
(
)
for rhypo ≤ 100 km 5/ 6
for rhypo > 100 km
(5.86)
The regression coefficients and total standard deviation are listed in Table 5.18. The authors give no guidelines for the use of the relation. However, the database contains recordings with MS = 3.0 to 6.9 and rhypo = 6 to 1300 km. The standard deviation of ln Y was separated into its intra- and inter-earthquake components. The total standard deviation is reported here to be consistent with engineering convention. One of the authors [Hilmar Bungum, personal communication, 2000] says that the relation can be used to estimate ground motion for building-code Site Class B, equivalent to the condition SB = 1 (see Tables 5.2 and 5.4). The tectonic environment represented by the attenuation relation is described as an “intraplate” region, another term for a stable tectonic region. The region is defined as an area that is tectonically stable and geologically more uniform than a plate margin area. In order to obtain enough strong-motion recordings for an analysis, the criterion for what qualified as intraplate was somewhat relaxed. Strong-motion © 2003 by CRC Press LLC
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Engineering Models of Strong Ground Motion
TABLE 5.17 Coefficients for Ambraseys et al. Attenuation Relation Tn (s)
c1
c2
c3
c4
c5
c6
σln Y
PGA 0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.22 0.24 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00
–3.408 –1.934 –1.980 –2.003 –2.003 –2.164 –2.257 –2.418 –2.487 –2.602 –2.740 –2.786 –2.947 –3.155 –3.224 –3.362 –3.569 –3.753 –3.799 –3.891 –4.191 –4.467 –4.582 –4.720 –4.858 –4.997 –5.181 –5.480 –5.733 –5.941 –6.148 –6.332 –6.585 –6.747 –6.977 –7.138 –7.299 –7.599 –7.783 –7.898 –8.105 –8.312 –8.474 –8.612 –8.727 –8.750 –8.727
0.612 0.504 0.509 0.532 0.548 0.562 0.569 0.580 0.594 0.617 0.640 0.654 0.679 0.709 0.732 0.751 0.778 0.804 0.808 0.815 0.838 0.868 0.884 0.905 0.923 0.944 0.967 0.999 1.009 1.038 1.066 1.098 1.117 1.133 1.156 1.158 1.170 1.181 1.181 1.184 1.202 1.207 1.197 1.190 1.184 1.170 1.158
–0.922 –0.954 –0.945 –0.960 –0.981 –0.955 –0.938 –0.907 –0.896 –0.901 –0.907 –0.922 –0.911 –0.916 –0.942 –0.946 –0.933 –0.932 –0.939 –0.936 –0.900 –0.888 –0.897 –0.908 –0.911 –0.920 –0.913 –0.911 –0.881 –0.901 –0.914 –0.942 –0.925 –0.920 –0.920 –0.892 –0.885 –0.857 –0.851 –0.848 –0.839 –0.817 –0.781 –0.759 –0.730 –0.724 –0.728
3.5 4.5 4.5 4.7 5.3 4.9 4.7 4.4 4.3 4.0 3.9 4.2 4.1 3.9 4.3 4.4 4.2 4.2 4.4 4.5 3.9 3.6 3.7 3.9 3.7 3.5 3.3 3.1 2.5 2.8 3.1 3.5 3.7 3.9 4.0 4.0 4.3 4.0 3.6 3.6 3.4 3.0 2.5 2.5 2.4 2.8 3.2
0.269 0.180 0.226 0.256 0.302 0.313 0.329 0.350 0.322 0.297 0.306 0.311 0.276 0.286 0.309 0.309 0.306 0.288 0.272 0.286 0.304 0.320 0.338 0.352 0.343 0.345 0.338 0.309 0.286 0.281 0.267 0.260 0.292 0.286 0.286 0.279 0.295 0.283 0.295 0.265 0.251 0.251 0.249 0.242 0.239 0.237 0.233
0.286 0.062 0.083 0.120 0.157 0.177 0.196 0.233 0.235 0.246 0.299 0.327 0.329 0.357 0.375 0.364 0.341 0.371 0.375 0.368 0.378 0.396 0.414 0.431 0.440 0.454 0.463 0.467 0.488 0.495 0.493 0.488 0.502 0.502 0.518 0.500 0.504 0.474 0.493 0.461 0.454 0.470 0.474 0.474 0.470 0.447 0.419
0.576 0.622 0.622 0.622 0.622 0.622 0.622 0.622 0.622 0.622 0.645 0.622 0.645 0.645 0.645 0.668 0.691 0.714 0.714 0.714 0.714 0.714 0.737 0.737 0.737 0.737 0.737 0.737 0.737 0.737 0.760 0.737 0.737 0.737 0.737 0.737 0.737 0.737 0.714 0.714 0.714 0.714 0.714 0.714 0.737 0.737 0.737
Source: Adapted from Ambraseys, N.N., Simpson, K.A., and Bommer, J.J. 1996. “Prediction of Horizontal Response Spectra in Europe,” Earthquake Eng. Struct. Dyn., 25, 371–400.
recordings from ENA, Europe, China, and Australia were used, making this relation more worldwide than strictly European. The largest amount of data comes from mainshock and aftershock recordings of the 1976 Tangshan, China earthquake, the 1976 Friuli, Italy earthquake, and the 1988 Saguenay, Canada earthquake. Some of the recordings do not belong to a genuine intraplate environment. This caveat applies particularly to the Italian data and to a few recordings from southern Europe that come from an area that has been characterized as a complex collision zone, where the inferred attenuation rate has © 2003 by CRC Press LLC
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TABLE 5.18 Coefficients for Dahle et al. Attenuation Relation Tn (s)
c1
c2
c3
σln Y
PGA 0.025 0.10 0.20 0.50 1.0 2.0 4.0
–3.7541 –3.7541 –2.6626 –4.2777 –6.4780 –8.0022 –9.3383 –9.3385
0.849 0.849 0.769 1.025 1.247 1.330 1.386 1.181
–0.00418 –0.00418 –0.00454 –0.00412 –0.00173 –0.00108 –0.00046 0
0.83 0.83 0.90 0.95 1.01 0.86 0.81 1.01
Source: Adapted from Dahle, A., Bungum, H., and Dvamme, L.G. 1990. “Attenuation Models Inferred from Intraplate Earthquake Recordings,” Earthquake Eng. Struct. Dyn., 19, 1125–1141.
been shown to be somewhat stronger than that for a truly stable tectonic environment, such as northwestern Europe. The authors later applied a stricter criterion for selecting intraplate recordings that they believe is more appropriate to the stable tectonic environment of northwestern Europe [Dahle et al., 1991]. However, this latter relation incorporates only a limited number of periods for defining PSA and is difficult to use in engineering practice. The use of hypocentral distance as the distance measure implies that the attenuation relation is not strictly valid for large earthquakes with extended rupture zones. In such cases, Boore [in press] suggests using rhypo as an estimate of rrup . If an estimate of ground-motion in terms of MW is required, MS can be estimated from MW using Equation 5.84 or a similar relation developed by Ekstrom and Dziewonski [1988].
5.6.4 Japan Japan represents a unique tectonic environment where four large crustal plates converge to form an archipelago (see Chapter 4). As a result of this unique tectonic environment, the strong-motion recordings in Japan come from a mixture of shallow crustal earthquakes, subduction interface earthquakes, and subduction intraslab or Wadati-Benioff earthquakes. Japanese scientists and engineers do not generally distinguish between these different tectonic environments, other than to include some measure of depth in their relations. An exception is the attenuation relations for PGA and PGV developed by Si and Midorikawa [2000]. These authors, using Japanese recordings, and Youngs et al. [1997] and Atkinson and Boore [2001], using worldwide recordings, have found that the amplitudes and attenuation rates of ground motion vary significantly in these tectonic environments. As a result, some engineers also use attenuation relations derived from shallow crustal earthquakes in WNA and from subduction earthquakes worldwide to estimate the ground motion from similar tectonic environments in Japan. There are many attenuation relations that have been developed specifically for Japan but very few of these predict PSA, because PGV is the principal parameter used in the Japanese building codes. One exception is the attenuation relation developed by Molas and Yamazaki [1995, 1996], which can be represented by the expression:
(
)
ln Y = f 1 M J , rrup , hrup + f 2 ( S)
(5.87)
where Y is the largest horizontal component of PGA, PGV, or PSA and
(
© 2003 by CRC Press LLC
)
f 1 M J , rrup , hrup = c 1 + c 2 M J − ln rrup + c 3rrup + c 4hrup
(5.88)
f 2 ( S) = c 5 S1 + c 6 S2 + c 7 S3 + c 8 S4
(5.89)
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TABLE 5.19 Coefficients for Molas and Yamazaki Attenuation Relation Tn (s)
c1
c2
c3
c4
c5
c6
c7
c8
σln Y
0.10 0.15 0.20 0.30 0.40 0.50 0.75 1.0 1.5 2.0 3.0 4.0 PGA PGV
–5.272 –5.108 –5.297 –6.085 –6.897 –7.570 –9.255 –10.556 –12.046 –12.893 –13.633 –13.593 –6.414 –4.073
0.976 0.999 1.052 1.186 1.312 1.400 1.628 1.785 1.930 1.985 1.976 1.858 1.098 1.446
–0.00366 –0.00364 –0.00338 –0.00320 –0.00313 –0.00302 –0.00286 –0.00262 –0.00246 –0.00226 –0.00210 –0.00163 –0.00332 –0.00299
0.00834 0.00822 0.00735 0.00661 0.00566 0.00511 0.00371 0.00283 0.00168 0.00122 0.00111 0.00122 0.00716 0.00511
0 0.092 –0.120 –0.281 –0.304 –0.362 –0.472 –0.465 –0.403 –0.373 –0.385 –0.350 –0.127 –0.334
–0.035 –0.085 –0.081 –0.046 –0.115 –0.177 –0.150 –0.115 –0.035 –0.028 0 0 –0.069 –0.076
0 0 0.074 0.219 0.276 0.373 0.403 0.350 0.230 0.207 0.177 0.166 0.127 0.251
0.051 –0.127 –0.138 0.228 0.691 0.808 0.532 0.557 0.626 0.488 0.477 0.454 0.253 0.525
0.672 0.686 0.677 0.654 0.633 0.612 0.606 0.587 0.569 0.557 0.541 0.539 0.636 0.592
Source: Adapted from Molas, G.L. and Yamazaki, F. 1995. “Attenuation of Earthquake Ground Motion in Japan Including Deep Focus Events,” Bull. Seismol. Soc. Am., 85, 1343–1358; and Molas, G.L. and Yamazaki, F. 1996. “Attenuation of Response Spectra in Japan Using New JMA Records,” Bull. Earthquake Resistant Struct. Res. Center, 29, 115–128.
TABLE 5.20 Site Classes Used in Japan Site Parameter
Site Class
S1
Type 1 (rock)
S2
Type 2 (hard soil)
S3
Type 3 (medium soil)
S4
Type 4 (soft soil)
Geological Description Tertiary or older rock (defined as bedrock) or diluvium with thickness < 10 m Diluvium with thickness > 10 m or alluvium with thickness < 10 m Alluvium with thickness < 25 m, including soft layer with thickness < 5 m Other than above, usually soft alluvium or reclaimed land
Site Period (s) TS < 0.2 0.2 ≤ TS < 0.4 0.4 ≤ TS < 0.6 TS ≥ 0.6
Source: Adapted from Molas, G.L. and Yamazaki, F. 1995. “Attenuation of Earthquake Ground Motion in Japan Including Deep Focus Events,” Bull. Seismol. Soc. Am., 85, 1343–1358; and Molas, G.L. and Yamazaki, F. 1996. “Attenuation of Response Spectra in Japan Using New JMA Records,” Bull. Earthquake Resistant Struct. Res. Center, 29, 115–128.
The regression coefficients and the total standard deviation are listed in Table 5.19. The authors do not give any guidelines for use of the relation. However, the database contains recordings with MJ = 4.0 to 7.8, rrup = 8 to 1000 km, and hrup ≤ 200 km. The standard deviation of lnY was separated into its intraand inter-earthquake components. Consistent with engineering convention, the total standard deviation is reported here. The definition of the site parameters S1 through S4 is given in Table 5.20. Additional guidance on their use is given in Table 5.4. One limitation in the use of the relation is that the predicted strong-motion parameter goes to infinity as rrup approaches zero. Because by definition rrup can be zero when the earthquake ruptures the Earth’s surface, the authors admit that their attenuation relation is not valid for small rupture distances. This limitation can be mitigated to some extent by replacing rrup by rhypo at short distances as recommended by Boore [in press] when estimating ground motion using the stochastic method. The relation combines earthquakes from shallow crustal earthquakes, subduction interface earthquakes, and subduction intraslab or Wadati-Benioff earthquakes. The only way to distinguish between these different tectonic environments is through the depth parameter hrup. The functional form itself does not allow for differences in amplitude between shallow crustal earthquakes and shallow subduction interface earthquakes or in the rate of attenuation between shallow crustal earthquakes, subduction interface, or subduction intraslab earthquakes. Youngs et al. [1997], Si and Midorikawa [2000], and Atkinson and Boore [2001] have found these differences to be important. © 2003 by CRC Press LLC
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TABLE 5.21 Coefficients for Crouse Attenuation Relation Tn (s)
c1
c2
c3
c4
c5
c6
σln Y
0.1 0.2 0.4 0.6 0.8 1.0 1.5 2.0 3.0 4.0 PGA PGA
0.512 0.999 –1.104 –1.680 –3.007 –3.620 –5.889 –6.731 –7.819 –8.637 4.612 –0.528
1.12 1.09 1.18 1.41 1.50 1.56 1.50 1.50 1.59 1.67 0.657 1.76
–1.93 –1.92 –1.69 –1.93 –1.83 –1.83 –1.45 –1.38 –1.41 –1.46 –2.09 –2.73
0.00566 0.00531 0.00357 0.00257 0.00215 0.00114 –0.00084 –0.00220 –0.00367 –0.00439 0.00397 0.00916
1.58 1.58 1.58 1.58 1.58 1.58 1.58 1.58 1.58 1.58 63.70 1.58
0.608 0.608 0.608 0.608 0.608 0.608 0.608 0.608 0.608 0.608 0.128 0.608
0.738 0.675 0.637 0.691 0.705 0.748 0.736 0.719 0.804 0.810 0.631 0.773
Note: First value of PGA is for use as the short-period asymptote of PSA; second value of PGA is for use with applications requiring PGA only [e.g., liquefaction analysis]. Source: Adapted from Crouse, C.B. 1991a. “Ground-Motion Attenuation Equations for Earthquakes on the Cascadia Subduction Zone,” Earthquake Spectra, 7, 201–235; and Crouse, C.B. 1991b. “Erratum: Ground-Motion Attenuation Equations for Earthquakes on the Cascadia Subduction Zone,” Earthquake Spectra, 7, 506.
5.6.5 Worldwide Subduction Environments Some types of strong-motion recordings are so rare that they must be collected from similar tectonic environments located throughout the world in order to obtain enough recordings for a meaningful empirical analysis. Great earthquakes on subduction zones are one such type of event. Major subduction zones occur along the Pacific Rim within a narrow region known as the “Ring of Fire” [Moores and Twiss, 1995; see also Chapter 4). There have been few attenuation relations that have been developed specifically for subduction zone environments. The two presented here [Crouse, 1991a, 1991b; Youngs et al., 1997] are the ones most commonly used to develop engineering estimates of strong ground motion from subduction zone earthquakes outside of Japan. It should be noted that at the time this volume was being published, Atkinson and Boore [2001] were developing a new attenuation relation for subduction zone environments. A preliminary version of this model is being used together with that from Youngs et al. [1997] to estimate ground motions from intraslab earthquakes on the Cascadia subduction zone in the 2002 update of the seismic hazard maps produced by the U.S. Geological Survey. 5.6.5.1
The Crouse Model
The attenuation relation of Crouse [1991a, 1991b] can be represented by the expression: ln Y = c 1 + c 2 M W + c 3 ln R + c 4hhypo
(5.90)
where Y is the average horizontal component of PGA or PSA and R = rcer + c 5 exp (c 6 M W ) The regression coefficients and the standard deviation of ln Y are listed in Table 5.21. The author does not give any guidance regarding use of the relation. However, the database contains recordings with MW = 4.8 to 7.8, repi = 8 to 866 km, and hhypo = 0 to 238 km. There are two sets of regression coefficients for PGA. According to the author [C.B. Crouse, personal communication, 2000], one set is based on the same database that was used to derive the regression coefficients for PSA and should be used to calculate the short-period asymptote of the pseudoacceleration response spectrum. The second set is based on a larger database and should be used only when an estimate of PGA is needed.
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The relation predicts ground motion for generic soil, equivalent to the condition SSoil = 1 (Table 5.4). Because the recording sites are located throughout the world, they will not necessarily have an average shear-wave velocity consistent with that of typical WNA generic soil sites. Nonetheless, this assumption is usually made when using the relation to develop engineering estimates of strong ground motion in the Pacific Northwest for earthquakes on the Cascadia subduction zone. The distance measure rcer is defined as the distance to the center of energy release on the fault. For all earthquakes less than magnitude 7.5, this point was assumed to be at the hypocenter of the earthquake. For most of the larger events, the center of energy release was assumed to be at the centroid of the rupture plane defined by the aftershocks. If special studies of source characteristics and aftershock distributions were available, the center of energy release was selected as a point on the fault plane that corresponded to the location of the greatest amount of energy release. This latter definition is not easily applied in practice, because one does not generally know in advance where the maximum energy release will be. Because rcer is essentially a point-source measure of distance, caution should be used when calculating ground motion at short distances to the rupture plane of large earthquakes. This distance measure can be close to zero or as large as a few hundred kilometers, depending on the size of the rupture plane, the location of the site, and where on the fault plane the center of energy release is located. For most engineering applications, rcer should be conservatively equated to the closest distance to the rupture surface rrup, otherwise the ground motion predicted from the relation could be underestimated [C.B. Crouse, personal communication, 2000]. The relation does not distinguish between subduction interface and subduction intraslab (WadatiBenioff) earthquakes. It does, however, include hypocentral depth as a parameter, which does account to some extent for the higher ground motions that other investigators [Youngs et al., 1997; Si and Midorikawa, 2000, Atkinson and Boore, 2001] have found for intraslab earthquakes. 5.6.5.2 The Youngs et al. Model The attenuation relation of Youngs et al. [1997] can be represented by the expression:
(
)
ln Y = f 1 M W , rrup , hhypo + f 2 ( zT )
(5.91)
where Y is the average horizontal component of PGA or PSA and
(
)
f 1 M W , rrup , hhypo = c 1 + c 2 M W + c 3 (10 − M W ) + c 4 ln R + c 5hhypo 2
R = rrup + c 7 exp (c 8 M W ) f 2 ( ZT ) = c 6 z T
(5.92)
(5.93)
The parameter zT is 0 for subduction interface earthquakes and 1 for subduction intraslab or WadatiBenioff earthquakes. The standard deviation of lnY was separated into its intra- and inter-earthquake components. Consistent with engineering convention, only the total standard deviation is reported here. This total standard deviation is given as a function of magnitude by the expression: c + c M σ lnY = 9 10 W c11
for M W ≤ 8.0 for M W > 8.0
(5.94)
The regression coefficients are listed in Table 5.22. The relation is considered to be valid for MW ≥ 5.0 and rrup = 10 to 500 km. Although no depth criteria are given, the deepest earthquake in the database has a hypocentral depth of 229 km. Differences in ground motion between generic soil, equivalent to the condition SSoil = 1, and generic rock, equivalent to the condition SRock = 1 (Table 5.4), are taken into © 2003 by CRC Press LLC
Tn (s)
c1
c2
c3
c4
c5
c6
c7
c8
c9
c10
c11
0.3846 0.3846 0.3846 0.3846 0.3846 0.3846 0.3846 0.3846 0.3846 0.3846 0.3846 0.3846
1.7818 1.7818 1.7818 1.7818 1.7818 1.7818 1.7818 1.7818 1.7818 1.7818 1.7818 1.7818
0.554 0.554 0.554 0.554 0.554 0.554 0.554 0.554 0.554 0.554 0.554 0.554
1.45 1.45 1.45 1.45 1.45 1.45 1.45 1.45 1.45 1.50 1.55 1.65
–0.1 –0.1 –0.1 –0.1 –0.1 –0.1 –0.1 –0.1 –0.1 –0.1 –0.1 –0.1
0.650 0.650 0.650 0.650 0.650 0.650 0.650 0.650 0.650 0.700 0.750 0.850
0.3648 0.3648 0.3648 0.3648 0.3648 0.3648 0.3648 0.3648 0.3648 0.3648 0.3648 0.3648 0.3648
1.097 1.097 1.097 1.097 1.097 1.097 1.097 1.097 1.097 1.097 1.097 1.097 1.097
0.617 0.617 0.617 0.617 0.617 0.617 0.617 0.617 0.617 0.617 0.617 0.617 0.617
1.45 1.45 1.45 1.45 1.45 1.45 1.45 1.45 1.45 1.50 1.55 1.65 1.65
–0.1 –0.1 –0.1 –0.1 –0.1 –0.1 –0.1 –0.1 –0.1 –0.1 –0.1 –0.1 –0.1
0.650 0.650 0.650 0.650 0.650 0.650 0.650 0.650 0.650 0.700 0.750 0.850 0.850
Generic Rock PGA 0.075 0.1 0.2 0.3 0.4 0.5 0.75 1.0 1.5 2.0 3.0
0.2418 1.5168 1.4298 0.9638 0.4878 0.1268 –0.1582 –0.9072 –1.4942 –2.3922 –3.0862 –4.2692
1.414 1.414 1.414 1.414 1.414 1.414 1.414 1.414 1.414 1.414 1.414 1.414
0 0 –0.0011 –0.0027 –0.0036 –0.0043 –0.0048 –0.0057 –0.0064 –0.0073 –0.0080 –0.0089
–2.552 –2.707 –2.655 –2.528 –2.454 –2.401 –2.360 –2.286 –2.234 –2.160 –2.107 –2.033
0.00617 0.00617 0.00617 0.00617 0.00617 0.00617 0.00617 0.00617 0.00617 0.00617 0.00617 0.00617 Generic Soil
–0.6687 1.7313 1.8473 0.8803 0.1243 –0.5247 –1.1067 –2.3727 –3.5387 –5.7697 –7.1017 –7.3407 –8.2867
1.438 1.438 1.438 1.438 1.438 1.438 1.438 1.438 1.438 1.438 1.438 1.438 1.438
0 –0.0019 –0.0019 –0.0019 –0.0020 –0.0020 –0.0035 –0.0048 –0.0066 –0.0114 –0.0164 –0.0221 –0.0235
–2.329 –2.697 –2.697 –2.464 –2.327 –2.230 –2.140 –1.952 –1.785 –1.470 –1.290 –1.347 –1.272
0.00648 0.00648 0.00648 0.00648 0.00648 0.00648 0.00648 0.00648 0.00648 0.00648 0.00648 0.00648 0.00648
Source: Adapted from Youngs, R.R., Chiou, S.J., Silva, W.J., and Humphrey, J.R. 1997. “Strong Ground Motion Attenuation Relationships for Subduction Zone Earthquakes,” Seismol. Res. Lett., 68, 58–73.
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Earthquake Engineering Handbook
PGA 0.075 0.1 0.2 0.3 0.4 0.5 0.75 1.0 1.5 2.0 3.0 4.0
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TABLE 5.22 Coefficients for Youngs et al. Attenuation Relation
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account with different sets of regression coefficients. Because the recording sites are located throughout the world, they will not necessarily have an average shear-wave velocity consistent with that of typical WNA generic rock and soil sites. Nonetheless, this assumption is usually made when using the relation to develop engineering estimates of strong ground motion in the Pacific Northwest for earthquakes on the Cascadia subduction zone.
5.6.6 Worldwide Extensional Environments Extensional environments are those where the crust is being pulled apart. The Basin and Range province, which is located between the Sierra Nevada Mountains in eastern California and the Wasatch Mountains in central Utah, represents an example of a shallow extensional tectonic environment. Much of Western Europe, including parts of Italy and Greece, is another example of such an environment. The world stress map developed by Zoback [1992] shows other regions of the world where extensional tectonic environments exist (Figure 5.7). There have been several attempts to evaluate worldwide strong-motion recordings from shallow extensional regions, most with equivocal results [e.g., Westaway and Smith, 1989]. The most recent and systematic analysis is that provided by Spudich et al. [1999]. The Spudich et al. [1999] attenuation relation can be represented by the expression:
(
)
ln Y = f 1 M W , r jb + f 2 ( S)
(5.95)
where Y is the average horizontal component of PGA or PSA and
(
)
f 1 M W , r jb = c 1 + c 2 ( M W − 6) + c 3 ( M W − 6) + c 4 ln R
(5.96)
R = r jb2 + c 52
(5.97)
f 2 ( S) = c 6 SSoil
(5.98)
2
The regression coefficients and the total standard deviation of ln Y are listed in Table 5.23. The relation is considered to be valid for MW = 5.0 to 7.7 and rjb ≤ 100 km. The standard deviation of ln Y is separated into its intra- and inter-earthquake components. The authors report the total standard deviation for the horizontal component of ground motion both with and without including the randomness between the two horizontal components. To be consistent with engineering convention, only the total standard deviation excluding the component-to-component randomness is reported here. The relation predicts ground motion for generic rock, equivalent to the condition SRock = 1. It is evaluated for generic soil by setting SSoil = 1 (Table 5.4). Because the recordings are located throughout the world, they will not necessarily have an average shear-wave velocity consistent with that of typical WNA generic rock and soil sites. Nonetheless, this assumption is usually made when using this attenuation relation to develop engineering estimates of strong ground motion in extensional regions in WNA. Selected strong-motion recordings were not limited to extensional regions dominated by normal faulting. In addition to recordings from eastern California, the Basin and Range province (Nevada, Idaho, and Utah), Italy, and Greece, where large normal faults dominate the landscape, the authors also included recordings from extensional regions with predominately strike-slip faulting. These latter regions include the Imperial Valley of California, Baja California, Central America, New Zealand, and Turkey. Thus, there is a large degree of crossover between this database and that used by other investigators who have
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TABLE 5.23 Coefficients for Spudich et al. Attenuation Relation Tn (s)
c1
c2
c3
c4
c5
c6
σln Y
PGA 0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.22 0.24 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0
0.688 2.189 2.119 2.055 1.996 1.942 1.892 1.846 1.801 1.758 1.718 1.680 1.608 1.539 1.478 1.420 1.364 1.311 1.260 1.212 1.165 1.120 1.079 1.037 0.997 0.959 0.920 0.830 0.745 0.665 0.588 0.515 0.446 0.378 0.314 0.251 0.190 0.074 –0.033 –0.137 –0.236 –0.330 –0.420 –0.508 –0.591 –0.673 –0.751
0.527 0.753 0.732 0.721 0.711 0.707 0.702 0.702 0.702 0.705 0.709 0.711 0.721 0.732 0.744 0.758 0.769 0.783 0.794 0.806 0.820 0.831 0.840 0.852 0.863 0.873 0.884 0.907 0.928 0.946 0.962 0.979 0.992 1.006 1.018 1.027 1.036 1.052 1.064 1.073 1.080 1.085 1.087 1.089 1.087 1.087 1.085
0 –0.226 –0.230 –0.233 –0.233 –0.230 –0.228 –0.226 –0.221 –0.216 –0.212 –0.207 –0.198 –0.189 –0.180 –0.168 –0.161 –0.152 –0.143 –0.136 –0.127 –0.120 –0.113 –0.108 –0.101 –0.097 –0.090 –0.078 –0.069 –0.060 –0.053 –0.046 –0.041 –0.037 –0.035 –0.032 –0.032 –0.030 –0.032 –0.035 –0.039 –0.044 –0.051 –0.058 –0.067 –0.074 –0.085
–1.052 –1.250 –1.207 –1.173 –1.145 –1.122 –1.103 –1.088 –1.075 –1.064 –1.055 –1.047 –1.036 –1.029 –1.024 –1.021 –1.020 –1.019 –1.020 –1.021 –1.023 –1.025 –1.027 –1.030 –1.032 –1.035 –1.038 –1.044 –1.051 –1.057 –1.062 –1.067 –1.071 –1.075 –1.078 –1.081 –1.083 –1.085 –1.086 –1.085 –1.083 –1.079 –1.075 –1.070 –1.063 –1.056 –1.049
7.27 9.99 9.84 9.69 9.54 9.39 9.25 9.12 8.99 8.86 8.74 8.63 8.41 8.22 8.04 7.87 7.72 7.58 7.45 7.33 7.22 7.11 7.02 6.93 6.85 6.77 6.70 6.55 6.42 6.32 6.23 6.17 6.11 6.07 6.04 6.02 6.01 6.01 6.03 6.07 6.13 6.21 6.29 6.39 6.49 6.60 6.71
0.258 0.147 0.147 0.150 0.154 0.159 0.166 0.173 0.180 0.187 0.196 0.203 0.219 0.235 0.249 0.265 0.279 0.290 0.304 0.315 0.327 0.338 0.348 0.357 0.366 0.375 0.382 0.401 0.417 0.431 0.442 0.454 0.461 0.467 0.474 0.479 0.484 0.490 0.493 0.493 0.490 0.488 0.484 0.477 0.470 0.463 0.454
0.468 0.630 0.610 0.591 0.580 0.568 0.558 0.551 0.546 0.542 0.539 0.536 0.532 0.531 0.531 0.532 0.534 0.534 0.536 0.539 0.543 0.545 0.548 0.550 0.555 0.556 0.559 0.566 0.574 0.579 0.585 0.592 0.598 0.602 0.607 0.615 0.620 0.628 0.640 0.650 0.658 0.669 0.679 0.689 0.699 0.708 0.718
Source: Adapted from Spudich, P., Joyner, W.B., Lindh, A.G., Boore, D.M., Margaris, B.M., and Fletcher, J.B. 1999. “SEA99: A Revised Ground Motion Prediction Relation for Use in Extensional Tectonic Regimes,” Bull. Seismol. Soc. Am., 89, 1156–1170.
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developed attenuation relations that include shallow strike-slip earthquakes in many of these same extensional environments. One of the interesting consequences of including both normal-faulting and strike-slip earthquakes in the relation is that the authors were able to evaluate possible differences in ground motion between these two types of events. The results of their analysis indicated that there was no statistically significant difference between ground motions from normal-faulting and strike-slip earthquakes in extensional regimes. This conclusion is similar to assumptions made for non-extensional regimes by other investigators. The authors compared their extensional recordings with predictions from the Boore et al. [1997] attenuation relation evaluated for strike-slip faulting. They concluded that extensional rock ground motion is on average 20% lower than the strike-slip ground motion predicted from the Boore et al. model. Extensional soil recordings are generally less than 10% lower than ground motion predicted from the Boore et al. model. An evaluation of the extensional relation by the authors found that it overpredicts the extensional rock recordings, whereas it provides a reasonably unbiased estimate of the extensional soil recordings. The authors concluded from this that their assumption of VS30 = 620 m/sec for the extensional rock sites (Table 5.4) is probably too low. Lower stress drops have been proposed by some investigators as a possible reason why ground motion in an extensional environment should be lower than in a compressional environment [e.g., McGarr, 1984]. If this were the case for the Spudich et al. [1999] relation, the differences between the extensional recordings and the Boore et al. [1997] empirical predictions should decrease rather than increase with period as the authors have found [e.g., see Boore, in press]. This suggests an alternative hypothesis that the differences between the Boore et al. and Spudich et al. ground-motion predictions may be due, at least in part, to systematic differences in crustal properties or local site conditions between WNA and non-WNA recordings rather than to lower stress drops.
5.6.7 Hanging-Wall and Footwall Effects Abrahamson and Somerville [1996] were the first to empirically quantify the effects of the hanging wall and footwall on strong ground motion using recordings from the 1994 Northridge, California earthquake. Somerville and Abrahamson [1995] extended this study to other earthquakes and proposed several empirical models for including these effects in the prediction of strong ground motion. The database used for this analysis was a preliminary version of that used subsequently by Abrahamson and Silva [1997]. However, the subset of data used to evaluate the hanging-wall and footwall effects was much smaller, consisting of only 24 recordings on the hanging wall and 19 recordings on the footwall from 9 earthquakes with MW > 6.0. The majority of the recordings came from the Northridge earthquake. Abrahamson and Silva [1997] later added a magnitude component to the hanging-wall effect to cause it to smoothly decrease to zero at MW = 5.5. Later still, Somerville and Abrahamson [2000] developed a somewhat more complicated model for the hanging-wall effect after removing the effects attributable to the type of faulting. An engineering model that can be used to account for hanging-wall and footwall effects, based on the work of the above authors, can be represented by the expression:
[ ( )
( )
ln YHW , FW = ln Y + f 1 ( M W ) f 2 rrup FW + f 3 rrup HW
]
(5.99)
where Y is the average horizontal or vertical component of PGA or PSA excluding the hanging-wall or footwall effects, YHF,FW is the value of Y including these effects, and 0 f 1 ( M W ) = M W − 5.5 1
© 2003 by CRC Press LLC
for M W ≤ 5.5 for 5.5 < M W < 6.5 for M W ≥ 6.5
(5.100)
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( )
f 2 rrup
( )
f 3 rrup
0 c 2 2 = c 2 c 2 2 0
0 r −6 c rup 1 6 = c 1 rrup − 25 c 1 1 − 25 0
(
for rrup ≤ 6 km for 6 < rrup ≤ 12 km for 12 < rrup ≤ 25 km for 25 < rrup ≤ 50 km for rrup > 50 km for rrup ≤ 4 km
)
π r −4 cos rup + π + 1 4
(
π r − 18 cos rup 7
(5.101)
)
+ 1
for 4 < rrup ≤ 8 km for 8 < rrup ≤ 18 km
(5.102)
for 18 < rrup ≤ 25 km for rrup > 25 km
TABLE 5.24 Coefficients for the Engineering Model of Hanging-Wall and Footwall Effects Horizontal Component
Vertical Component
Tn (s)
c1
c2
c1
c2
PGA 0.10 0.17 0.20 0.30 0.40 0.50 0.60 0.75 1.0 2.0 3.0 4.0 5.0 6.0
–0.29 –0.29 — –0.29 –0.35 –0.41 –0.48 — –0.59 –0.64 –0.64 –0.64 –0.64 — —
0.370 0.370 0.370 0.370 0.370 0.370 0.370 0.370 0.332 0.282 0.161 0.090 0.040 0 0
— — — — — — — — — — — — — — —
0.630 0.630 0.630 0.594 0.505 0.442 0.393 0.352 0.303 0.240 0.240 0.240 0.240 0.240 0.240
Note: Coefficients at other periods can be found by linear interpolation of ln Tn . Source: Data from Somerville and Abrahamson [1995]; Somerville and Abrahamson [2002]; and Abrahamson and Silva [1997].
The regression coefficients are listed in Table 5.24. The definition of the hanging wall and footwall to be used with the model is schematically shown in Figure 5.10. Somerville and Abrahamson [1995, 2000] suggest that the hanging-wall and footwall effects are primarily geometrical effects that result from the use of rrup as the distance measure. A similar geometrical effect is expected from the distance measure rseis used by Campbell [1997] and Campbell and Bozorgnia [in press]. According to Somerville and Abrahamson, the rjb distance measure used by Boore et al. [1997] implicitly accounts for the difference in ground motion over the hanging wall and footwall and, in their opinion, should not be corrected for these geometrical effects. The hanging-wall and footwall effects given by Equations 5.99 to 5.102 and by
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22.5°
FIGURE 5.10 Definition of hanging wall and footwall in the engineering model used to incorporate hanging-wall and footwall effects in the estimation of strong ground motion. (From Somerville, P. and Abrahamson, N. 1995. “Ground Motion Prediction for Thrust Earthquakes,” in Proc. SMIP95 Seminar on Seismological and Engineering Implications of Recent Strong-Motion Data, May 16, San Francisco, pp. 11–23. California Strong Motion Instrumentation Program, Sacramento.)
Abrahamson and Silva [1997] can theoretically be applied to any attenuation relation that uses rrup or rseis as the distance measure. Because they are geometrical effects, they should theoretically be valid for both reverse-faulting and normal-faulting earthquakes. However, there is insufficient data to test this hypothesis for normal-faulting events. The model predicts that sites located on the hanging wall at distances of 8 to 18 km can have an increase in ground motion of up to 45% for the horizontal component of ground motion and 88% for the vertical component of ground motion. Sites on the footwall at distances of 12 to 25 km can have a decrease in ground motion of up to 47%. Although these results are largely driven by recordings from the Northridge earthquake, similar effects were observed during the 1999 MW = 7.6 Chi-Chi, Taiwan earthquake [Loh, 1999; Tsai and Huang, 2000], where some sites on the hanging wall had PGA values ranging from 0.5 to 1 g and PGV values ranging from 100 to 300 cm/sec. The largest values of PGV were recorded near the surface trace of the fault, where they may also have been impacted by source directivity. Abrahamson and Silva [1997] and Somerville and Abrahamson [2000] recommend against incorporating footwall effects in the engineering estimation of strong ground motion because, in their opinion, these effects are not as credible as the hanging-wall effects. However, the apparent footwall effects observed during the 1999 Chi-Chi earthquake, if proven to be valid, will add to their credibility. © 2003 by CRC Press LLC
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5.6.8 Rupture Directivity Effects Somerville and coworkers [1997] and Abrahamson [2000] developed a general empirical model that can be used to account for rupture directivity effects in the engineering estimation of strong ground motion. Somerville and coworkers [1997] found that rupture directivity effects cause spatial variations in the radiation pattern as well as differences between the fault-normal and fault-parallel components of horizontal ground motion. A schematic view of the radiation pattern for a vertical strike-slip fault and its effect on near-source ground displacement is shown in Figure 5.5. These effects are significant at periods of 0.6 sec and greater and generally increase in size with increasing period. Abrahamson [2000] found that there were several aspects of the spatial component of the Somerville et al. [1997] rupture directivity model that needed to be modified in order to make the model more generally applicable in engineering practice, such as for use in PSHA. He proposed three modifications of the model based on these findings. The first recommendation was to apply a distance and magnitude taper to the model to smoothly reduce the effect of the directivity effects to zero at large distances and small magnitudes. The second recommendation was to change the rate at which the dependence of the directivity effect for strike-slip faulting increases with azimuth and to cap this effect based on both empirical observations and numerical simulations. The last recommendation was to reduce the standard deviation of the predicted value of PSA to account for the reduced variability by including the directivity effect. An engineering model that can be used to account for source directivity effects, taking into account the modifications suggested by Abrahamson [2000], can be represented by the expression:
( )
(
ln YDir = ln Y + f 1 ( DR, ξ) T rrup T ( M W ) + f 2 rrup , M W , ξ
)
(5.103)
where Y is the average horizontal component of PGA or PSA excluding directivity effects, YDir is the value of Y including these effects, and for strike-slip faulting: c + 1.88 c 2 ( s L) cos (θ) f 1 ( DR, ξ) = 1 c 1 + 0.75 c 2
for ( S L) cos (θ) ≤ 0.4 for ( S L) cos (θ) > 0.4
(5.104)
and for dip-slip faulting: f 1 ( DR, ξ) = c 1 + c 2 (d W ) cos φ
(5.105)
and
[ [
(
)
(
)
] ]
1 2 (cos 2ξ) c 3 + c 4 ln rrup + 1 + c 5 ( M W − 6) 1 f 2 rrup , M W , ξ = − (cos 2ξ) c 3 + c 4 ln rrup + 1 + c 5 ( M W − 6) 2 0
(
)
( )
T rrup
© 2003 by CRC Press LLC
1 = 1 − rrup − 30 30 0
(
)
for fault - normal for fault - parallel
(5.106)
for ξ ≥ 45°
for rrup ≤ 30 km for 30 < rrup < 60 km for rrup ≥ 60 km
(5.107)
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1 T ( M W ) = 1 − (6.5 − M W ) 0.5 0
for M W ≥ 6.5 for 6.0 < M W < 6.5 for M W ≤ 6.0
(5.108)
The standard deviation of the predicted strong-motion parameter when directivity effects are taken into account can be calculated from the expression: σ ln Y, Dir = σ ln Y − 0.05 c 2 1.333
(5.109)
where σlnY, Dir is the standard deviation of ln YDir, and σln Y is the standard deviation of lnY. In the above equations, the length and width ratio DR = s/L and d/W are defined as the fraction of fault rupture length L and fault rupture width W that ruptures towards the site for strike-slip faults and dip-slip faults, respectively; and ξ = θ and φ are the azimuth or zenith angle between the fault rupture plane and the ray path to the site for strike-slip and dip-slip faults, respectively. These parameters are defined schematically in Figure 5.11. The regression coefficients are listed in Table 5.25. Note that in this table the values of c1 and c2 depend on the faulting mechanism, where dip slip is a generic term for both reverse, thrust, and normal faulting.
FIGURE 5.11 Definition of fault-rupture directivity parameters used in the engineering model used to incorporate rupture directivity effects in the estimation of strong ground motion. (From Somerville, P.G., Smith, N.F., Graves, R.W., and Abrahamson, N.A. 1997. “Modification of Empirical Strong Ground Motion Attenuation Relations to Include the Amplitude and Duration Effects of Rupture Directivity,” Seismol. Res. Lett., 68, 199–222. With permission.)
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TABLE 5.25 Coefficients for the Engineering Model of Rupture Directivity Effects Strike Slip Tn (s) 0.6 0.7 0.75 0.8 0.9 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 6.0
Dip Slip
c1
c2
c1
c2
c3
c4
c5
0 — –0.084 — — –0.192 –0.344 –0.452 — –0.605 — –0.713 — –0.797 —
0 — 0.185 — — 0.423 0.759 0.998 — 1.333 — 1.571 — 1.757 —
0 — –0.045 — — –0.104 –0.186 –0.245 — –0.327 — –0.386 — –0.431 —
0 — 0.008 — — 0.178 0.318 0.418 — 0.559 — 0.659 — 0.737 —
0.027 0.050 0.061 0.070 0.088 0.104 0.164 0.207 0.280 0.353 0.415 0.456 0.462 0.450 0.424
–0.0069 –0.0127 –0.0155 –0.0178 –0.0220 –0.0255 –0.0490 –0.0613 –0.0816 –0.1007 –0.1172 –0.1282 –0.1307 –0.1269 –0.1223
0 0 0 0 0 0 0.034 0.059 0.078 0.093 0.106 0.118 0.128 0.137 0.152
Source: Adapted from Somerville, P.G., Smith, N.F., Graves, R.W., and Abrahamson, N.A. 1997. “Modification of Empirical Strong Ground Motion Attenuation Relations to Include the Amplitude and Duration Effects of Rupture Directivity,” Seismol. Res. Lett., 68, 199–222; and Abrahamson, N.A. 2000. “Effects of Rupture Directivity on Probabilistic Seismic Hazard Analysis,” in Proc. 6th International Conference on Seismic Zonation, Nov. 12–15, Palm Springs, CA, Proc. CD-ROM, Earthquake Engineering Research Institute, Oakland, CA.
According to the relation, maximum directivity conditions for strike-slip faulting occur when (s/L) cosθ = 1 and can result in an increase of up to 68% in the average horizontal component of PSA at a period of 5 sec. Minimum directivity conditions occur when (s/L) cosθ = 0 and can result in a similar reduction in PSA. These effects are only about ±36% for dip-slip faulting. Maximum fault-normal and fault-parallel effects occur at large magnitudes and long periods when θ = φ = 0. These effects can result in an increase of up to 107% in the fault-normal component of PSA and a similar decrease in the faultparallel component. Because the spatial and fault-normal effects are cumulative, the total maximum directivity effects can approach a factor of 3.5.
5.7 Engineering Evaluation The most common use of an engineering ground-motion model is the development of a response spectrum to use in structural evaluation and design. This section presents and compares acceleration response spectra predicted from the engineering models presented in the previous sections of this chapter for a hypothetical structure located 10 km from the causative fault of an earthquake of magnitude 7.0. Using the notation given in the Appendix, this corresponds to MW = 7 and rjb = 10 km, except over the hanging wall of a reverse or thrust fault, for which by definition rjb = 0. In each case, the short-period asymptote of the response spectrum is estimated by using PGA to predict PSA at Tn = 0.03 sec in active tectonic regions and at Tn = 0.01 sec in stable tectonic regions. For consistency, all of the models are evaluated for the average horizontal component of ground motion. The specific values of magnitude and distance are selected not only for their engineering importance (they represent typical design earthquakes in high-seismicity areas) but also because MW = 7 conveniently evaluates to MS = MJ = mLg = 7. The relationship between rjb and the other distance measures used in the engineering models depends on the geometry and depth of the earthquake rupture plane and on the location of the site with respect to this rupture plane (Figure 5.3). The fault-rupture geometry and site locations for each hypothetical © 2003 by CRC Press LLC
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TABLE 5.26 Seismological Parameters Used in the Evaluation of the Engineering Models Faulting Scenario
F
FRV
FTH
HW
FW
ZT
rjb
rrup
rseis
rhypo
rcer
hhypo
Strike slip Unknown Reverse/thrust Reverse (hanging wall) Reverse (footwall) Subduction interface Subduction intraslab
0 0.5 1 1 1 — —
0 0.25 0.5 0.5 0.5 — —
0 0.25 0.5 0.5 0.5 — —
0 0 0 1 0 — —
0 0 0 0 1 — —
— — — — — 0 1
10.0 10.0 10.0 0 10.0 10.0 10.0
10.0 10.0 10.0 10.0 10.0 18.0 51.0
10.0 10.0 10.4 10.0 10.9 — —
— 10.0 — — — — —
— — — — — 18.0 51.0
— 10.0 — — — 15.0 50.0
TABLE 5.27 Site Parameters Used in the Evaluation of the Engineering Models Attenuation Relation
Generic Rock
Generic Soil
Firm/Hard Rock
Abrahamson and Silva [1997] Boore et al. [1997] Campbell and Bozorgnia [in press]
SSoil =0 (rock) VS30 = 620 SVFS = 0, SSR = 0.5, SHR = 0.5 Rock —
— — — — —
—
—
— VS30 = 760 SVFS = 0, SSR = 0, SFR = 1 — SDeep = 0 (VS30 = 2800) ENA hard rock (VS30 = 2800) SC = 0, SD = 0 (Site Class B) Site Class B —
Sadigh et al. [1993, 1997] Atkinson and Boore [1995, 1997] Toro et al. [1997] Ambraseys et al. [1996] Dahle et al. [1990] Molas and Yamazaki [1995, 1996] Crouse [1991a, 1991b] Youngs et al. [1997] Spudich et al. [1999]
SC = 1, SD = 0 (Site Class C) — S1 = 0, S2 = 0, S3 = 0, S4 = 0 — — SSoil = 0 (rock)
— — S1 = 1, S2 = 0.5, S3 = 0.5, S4 = 0 Soil Soil —
— — —
Note: For those attenuation relations that represent only one site condition or whose reference site condition is not represented by a specific site parameter, the name of the reference site class or the approximate value of the 30-m velocity is given in parentheses. Blank cells indicate that the attenuation relation was not used to evaluate that site condition.
faulting scenario is kept simple to avoid unnecessary complication, although it should be noted that actual scenarios can be much more difficult to evaluate. The definition of the faulting scenarios and the seismological parameters that were used to evaluate the different engineering models are listed in Table 5.26. The values of the site parameters that were used to evaluate each of these models are listed in Table 5.27. Predictions of response spectra for shallow active tectonic regions in WNA, Japan, and worldwide extensional regions are done for generic rock (nominally VS30 = 620 m/sec). Most engineering estimates of ground motion are done for this site condition so that soil effects can be treated in a site-specific manner using dynamic site-response analyses or building-code site factors. No adjustment is made to account for possible variations in VS30 between different definitions of generic rock, which is also typical of engineering evaluations. Predictions for shallow stable tectonic regions in ENA are done for ENA hard rock (nominally VS30 = 2800 m/sec). Those in Europe are done for building-code Site Class B, the reference site condition for the Dahle et al. [1990] attenuation relation. Site Class B has a maximum 30-m velocity of only 1500 m/sec (Table 5.2) but it is the closest site condition to ENA hard rock that is available for evaluating the attenuation relation for the European stable tectonic region. Where predicted spectra for nominal hard rock in WNA are compared to those for ENA hard rock, WNA firm rock (nominally VS30 = 760 m/sec) is used for this comparison. This latter value for the 30-m velocity is used by Frankel © 2003 by CRC Press LLC
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WNA - Faulting Mechanism
WNA - Generic Rock
(b)
Horizontal Spectral Acceleration (g)
Horizontal Spectral Acceleration (g)
(a) 1.0
0.1
Abrahamson & Silva (1997) Boore et al. (1997) Campbell & Bozorgnia (2002) Sadigh et al. (1993, 1997)
0.0 0.01
0.1
1
1.0
0.1
Strike Slip Reverse or Thrust Hanging Wall Footwall
0.0 0.01
10
WNA - Directivity
ENA - Very Hard Rock
10
(d)
Horizontal Spectral Acceleration (g)
Horizontal Spectral Acceleration (g)
1
Period (sec)
(c) 1.0
0.1
No Directivity Spatial Directivity Fault Normal (FN) Fault Parallel (FP)
0.0 0.01
0.1
Period (sec)
0.1
1
Period (sec)
10
1.0
0.1
Atkinson & Boore (1995, 1997) Toro et al. (1997) Campbell (2002)
0.0 0.01
0.1
1
10
Period (sec)
FIGURE 5.12 Predicted horizontal acceleration response spectra for shallow active and stable tectonic regions of North America for MW = 7.0 and a nominal surface distance (rjb) of 10 km (0 km over the hanging wall) showing differences among: (a) the four selected attenuation relations for generic rock in WNA; (b) the effects of faulting mechanism and fault geometry for generic rock in WNA; (c) the effects of rupture directivity for generic rock in WNA; and (d) the three selected attenuation relations for very hard rock in ENA (see Tables 5.26 and 5.27 for a description of the seismological and site parameters used in the evaluations).
et al. [1996, 2000] to develop the seismic hazard maps adopted for use with the 1997 NEHRP and 2000 International Building Codes [BSSC, 1998; ICC, 2000]. Because the Crouse [1991a, 1991b] relation is valid only for generic soil, predicted spectra for the subduction zone environments both worldwide and in Japan are calculated for this site condition (nominally VS30 = 310 m/sec).
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Figure 5.12 compares the predicted response spectra for North American active (WNA) and stable (ENA) tectonic regions. Except for those plots where individual attenuation relations are identified, the spectra for WNA and ENA represent the geometric mean of the individual estimates from the relations for each of these regions. The WNA comparisons also show differences due to faulting mechanism, hanging-wall, footwall, and source directivity effects. Directivity effects are evaluated for (s/L) cosθ = 1 and for the fault-normal (FN) and fault-parallel (FP) horizontal component. Unless otherwise noted, all evaluations are for an unknown or random faulting mechanism and for average directivity effects. The large difference in the spectral accelerations at long periods in the ENA comparison clearly shows the large difference between the one-corner source spectrum used by Toro and coworkers [1997] and the two-corner source spectrum used by Atkinson and Boore [1995, 1997]. Figure 5.13 compares the predicted response spectra for worldwide active and stable tectonic regions and for worldwide subduction interface and intraslab (Wadati-Benioff) earthquakes. Comparisons for active tectonic regions include WNA, Europe, Japan, and worldwide extensional environments. Note that the predicted response spectrum for the extensional regime is not that much less than the predicted response spectra for the other regions. This difference would even be less if an adjustment was made for the bias noted by Spudich and coworkers[1999] for their extensional rock predictions. Comparisons for stable tectonic regions include ENA and Europe, with WNA hard rock included to show the significant difference in spectral shape between ENA and WNA. The large differences in these latter spectra are due to two factors: (1) differences in the tectonic regime in which the European stable tectonic region is intermediate to the ENA stable tectonic and WNA active tectonic regions [Dahle et al., 1990], and (2) differences in local site conditions in which 30-m velocity is approximately 2800 m/sec for ENA, 1130 m/sec for Europe, and 760 m/sec for WNA. Comparisons for subduction zones include Japan and worldwide interface and intraslab events. Note that in the latter comparison, the Crouse [1991a, 1991b] and Molas and Yamazaki [1995, 1996] attenuation relations include hypocentral depth as the only parameter to distinguish between interface and intraslab events, which leads them to predict smaller intraslab estimates than the Youngs et al. [1997] relation. The large variability in the subduction zone spectra demonstrates the large degree of uncertainty associated with the estimation of ground motion in subduction zone environments. There is one last item — vertical response spectra — that should be mentioned. Vertical ground motion has largely been ignored by engineers because current practice dictates that (1) it is usually so small as to not add significantly to the combined vertical and horizontal seismic design loads, (2) the structure is already designed for a vertical load of 1 g and should not need strengthening in that direction, and (3) its peak is usually out of phase with the peak in the horizontal ground motion. This thinking came from an often-quoted engineering “rule of thumb” that vertical motion can be assumed to be two thirds that of the horizontal motion [e.g., Newmark and Hall, 1982]. None of these conditions is appropriate at near-source distances from large earthquakes in many cases. The recent plethora of nearsource ground motion recordings has shown that vertical response spectra can have short-period amplitudes that exceed the average horizontal amplitudes by a factor of two or more, especially for sites on soil, and that this difference strongly increases with decreasing distance [Campbell and Bozorgnia, in press]. Figure 5.14 compares the vertical and average horizontal response spectra predicted from those WNA attenuation relations that provide estimates for both [Abrahamson and Silva, 1997; Campbell, 1997, 2000c, 2001; Sadigh et al., 1993]. The comparison is made using the same magnitude and distance as that used in the comparison of the horizontal spectra. These spectra represent generic rock, for which the vertical-to-horizontal (V/H) spectral ratio is minimal. Figure 5.15 shows the large difference in V/H spectral ratio that can be expected for soil (approximately building-code Site Class D) for distances ranging from 3 to 60 km. This figure clearly shows that the largest V/H ratios occur at periods of 0.05 to 0.15 sec but that this ratio decreases rapidly with period, reaching values less than one half at periods exceeding 0.3 sec. Therefore, the two thirds “rule of thumb” is not appropriate for longer periods either, where it is much less than commonly assumed.
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Shallow Active Regions
Shallow Stable Regions (b) Horizontal Spectral Acceleration (g)
Horizontal Spectral Acceleration (g)
(a) 1.0
0.1
WNA (Generic Rock) Europe (Class C) Japan (Type 1) Extensional (Generic Rock)
0.0 0.01
0.1
1
1.0
0.1
WNA (Firm Rock) ENA (Very Hard Rock) Europe (Class B)
0.0 0.01
10
Period (sec)
10
Subduction Intraslab - Soil (d) Horizontal Spectral Acceleration (g)
(c) Horizontal Spectral Acceleration (g)
1
Period (sec)
Subduction Interface - Soil
1.0
0.1
Crouse (1991a,b) Youngs et al. (1997) Japan (Types 2 & 3)
0.0 0.01
0.1
0.1
1
Period (sec)
10
1.0
0.1
Crouse (1991a,b) Youngs et al. (1997) Japan (Types 2 & 3)
0.0 0.01
0.1
1
10
Period (sec)
FIGURE 5.13 Predicted horizontal acceleration response spectra for MW = 7.0 and a nominal surface distance (rjb) of 10 km showing differences among: (a) four worldwide shallow active tectonic regions for generic rock or its equivalent; (b) two worldwide stable tectonic regions together with the active tectonic region of WNA (for comparison) for the hardest rock available in each region; (c) the three selected subduction interface relations for generic soil or its equivalent; and (d) the three selected subduction intraslab (Wadati-Benioff zone) relations for generic soil or its equivalent (see Tables 5.26 and 5.27 for a description of the seismological and site parameters used in the evaluations).
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WNA Models - Generic Rock
Spectral Acceleration (g)
1.0
0.1
Average Horizontal Vertical
0.0 0.01
0.1
1
10
Period (sec) FIGURE 5.14 Predicted horizontal and vertical acceleration response spectra for shallow active tectonic regions in WNA for MW = 7.0 and a nominal surface distance (rjb) of 10 km (see Tables 5.26 and 5.27 for a description of the seismological and site parameters used in the evaluations).
1.8 STRIKE SLIP, M 6.5 R = 3 km R = 10 km R = 20 km R = 60 km R = 3 km R = 10 km R = 20 km R = 60 km
1.6
V/H Ratio
1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.01
0.1
1
10
Period (sec) FIGURE 5.15 The effect of distance on the vertical-to-horizontal response spectral ratio for recordings on firm soil. Symbols represent the ratio for PGA. (From Campbell, K.W. and Bozorgnia, Y. 1999. “Vertical Ground Motion: Characteristics, Relationship with Horizontal Component, and Building-Code Implications,” in Proc. SMIP99 Seminar on Utilization of Strong-Motion Data, M. Huang, Ed., Sept. 15, San Francisco, pp. 23–49. California Strong Motion Instrumentation Program, Sacramento, CA).
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Defining Terms Aleatory variability — Uncertainty due to randomness in the phenomena, as differentiated from epistemic uncertainty.
Anelastic attenuation — The diminution of ground motion with distance from the source due to material damping and scattering of waves from inhomogeneities in the crust.
Attenuation relation — An equation or tabulation used to estimate a strong-motion parameter from one or more seismological parameters; also known as a ground motion relation. Basement rock — The more resistant, generally crystalline rock that lies beneath layers or irregular deposits of younger, relatively deformed sedimentary rock. Critical reflection — The incidence angle below which the ground-motion ray is completely reflected off a layer of higher wave velocity. Epicenter — The point on the Earth’s surface directly above the hypocenter. Epistemic uncertainty — Uncertainty due to lack of knowledge (e.g., omission of a key parameter due to not recognizing its importance in a phenomenon, uncertainty in a parameter or model). Faulting mechanism — The type or style of faulting defined by the direction of slip on the fault rupture plane; usually referred to by such terms as strike slip, reverse, thrust, normal, or oblique. Focus — See hypocenter. Footwall — That portion of the crust that lies below the fault or fault rupture plane. Fourier spectrum — A complete frequency-domain description of the ground motion time history a(t) given by F (ω ) =
S
∫ a(t )exp (−iωt )dt , 0
where S is the duration of ground motion and ω is circular frequency.
Fourier amplitude spectrum — The amplitude of the Fourier spectrum given by F (ω ) =
2
a(t ) cos ωt dt + 0
∫
S
a (t ) sin ωt dt 0
∫
S
2
1/ 2
.
Frequency — The reciprocal of period, i.e., the number of cycles of oscillation per unit of time (e.g., 1 sec). Usually measured in terms of hertz (1 Hz = 1 cycle per second).
Geometric attenuation — The diminution of ground motion with distance from the source as the area of the wave front expands.
Ground motion — The vibration of the ground in the time or frequency domain measured by a seismometer that records acceleration, velocity, or displacement, or an estimate of this vibration or a ground-motion parameter that characterizes this vibration. Hanging wall — That portion of the crust that lies above the fault or fault rupture plane. Hypocenter — The point within the Earth where the earthquake rupture begins (see also focus). Local site conditions — A qualitative or quantitative description of the material properties of the soil and sedimentary rock layers above basement rock. Magnitude — An instrumental or seismological measure of an earthquake’s size proportional to the logarithm of the amplitude or energy of ground motion. Natural frequency — The reciprocal of natural period. Natural period — The period of an oscillator or structure during free (i.e., unforced) vibration. Period — The duration of time (e.g., number of seconds) required to complete one oscillation.
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Radiation pattern — A geometric description of the amplitude of ground motion and the sense of initial motion at the source which for shear waves has a low-order symmetry that can be used to infer the faulting mechanism. Rake angle — The angle between the direction of slip on the fault rupture plane and the fault strike. Response spectrum — A plot of undamped natural period or frequency vs. the maximum response of a viscously damped single-degree-of-freedom (SDOF) oscillator subjected to a specified ground motion time history at its base. Seismogenic — That part of the Earth’s crust that is capable of generating ground motion at periods of engineering interest, usually 10 sec or less. Seismometer — An instrument used to record ground motion. Seismological parameter — A parameter used to characterize a seismological property of the earthquake source, the propagation medium, or the response of the materials beneath the site. Shear-wave velocity — The speed at which shear waves travel through a material; shear waves are waves whose amplitude is perpendicular to the direction of propagation and are the most potentially damaging to man-made structures. Source directivity — The azimuthal perturbation of the radiation pattern due to rupture propagation on the fault in which the amplitude increases in the direction of rupture and decreases in the opposite direction. Stress drop — The amount of stress released at the rupture front during an earthquake. Strike — The orientation of a fault on the Earth’s surface, usually measured clockwise from north. Strong ground motion — Ground motion having the potential to cause measurable damage to a structure’s architectural or structural components; usually associated with a PGA of 0.05 g or greater. Strong-motion parameter — A parameter characterizing the amplitude of strong ground motion in the time domain (time-domain parameter) or the frequency domain (frequency-domain parameter). Time history — A data set, usually composed of one vertical and two orthogonal horizontal components, describing a strong-motion parameter (such as ground acceleration) as a function of time. Tectonic environment — The type of tectonic deformation that occurs in a region, usually described by such terms as active, stable, compressional, extensional, or subduction.
References Abrahamson, N.A. 2000. “Effects of Rupture Directivity on Probabilistic Seismic Hazard Analysis,” in Proc. 6th International Conference on Seismic Zonation, Nov. 12–15, Palm Springs, CA, Proc. CD-ROM, Earthquake Engineering Research Institute, Oakland. Abrahamson, N.A. and Shedlock, K.M. 1997. “Overview,” Seismol. Res. Lett., 68, 9–23. Abrahamson, N.A. and Silva, W.J. 1997. “Empirical Response Spectral Attenuation Relations for Shallow Crustal Earthquakes,” Seismol. Res. Lett., 68, 94–127. Abrahamson, N.A. and Somerville, P.C. 1996. “Effects of the Hanging Wall and Footwall on Ground Motions Recorded during the Northridge Earthquake,” Bull. Seismol. Soc. Am., 86, S93–S99. Abrahamson, N.A. and Youngs, R.R. 1992. “A Stable Algorithm for Regression Analyses Using the Random Effects Model,” Bull. Seismol. Soc. Am., 82, 505–510. Ambraseys, N.N., Simpson, K.A., and Bommer, J.J. 1996. “Prediction of Horizontal Response Spectra in Europe,” Earthquake Eng. Struct. Dyn., 25, 371–400. Anderson, J.G. 2000. “Expected Shape of Regressions for Ground Motion Parameters on Rock,” Bull. Seismol. Soc. Am., 90, S43–S52. Anderson, J.G., in press. “Strong Motion Seismology,” in International Handbook of Earthquake and Engineering Seismology, W.H.K. Lee, H. Kanamori, P.C. Jennings, and C. Kisslinger, Eds., Chapter 57, Academic Press, London. © 2003 by CRC Press LLC
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Anderson, J.G. and Hough, S.E. 1984. “A Model for the Shape of the Fourier Amplitude Spectrum of Acceleration at high Frequencies,” Bull. Seismol. Soc. Am., 74, 1969–1993. Ansary, M.A., Yamazaki, F., and Katayama, T. 1995. “Statistical Analysis of Peaks and Directivity of Earthquake Ground Motion,” Earthquake Eng. Struct. Dyn., 24, 1527–1539. Atkinson, G.M. 1995. “Optimal Choice of Magnitude Scales for Seismic Hazard Analysis,” Seismol. Res. Lett., 66, 51–55. Atkinson, G.M. and Beresnev, I. 1997. “Don’t Call it Stress Drop,” Seismol. Res. Lett., 68, 3–4. Atkinson, G.M. and Boore, D.M. 1995. “New Ground Motion Relations for Eastern North America,” Bull. Seismol. Soc. Am., 85, 17–30. Atkinson, G.M. and Boore, D.M. 1997. “Some Comparisons between Recent Ground Motion Relations,” Seismol. Res. Lett., 68, 24–40. Atkinson, G.M. and Boore, D.M. 1998. “Evaluation of Models for Earthquake Source Spectra in Eastern North America,” Bull. Seismol. Soc. Am., 88, 917–934. Atkinson, G.M. and Boore, D.M. 2001. “Empirical Ground Motion Relations for Subduction Zone Earthquakes (Abstract),” Seismol. Res. Lett., 72, 271. Beresnev, I.A. and Atkinson, G.M. 1998. “FINSIM — a FORTRAN Program for Simulating Stochastic Acceleration Time Histories from Finite Faults,” Seismol. Res. Lett., 69, 27–32. Boatwright, J.A. and Boore, D.M. 1982. “Analysis of the Ground Accelerations Radiated by the 1980 Livermore Valley Earthquakes for Directivity and Dynamic Source Characteristics,” Bull. Seismol. Soc. Am., 72, 1843–1865. Bolt, B.A. 1993. Earthquakes and Geological Discovery, Scientific American Library, New York. Boore, D.M 1996. “SMSIM — Fortran Programs for Simulating Ground Motions from Earthquakes: Version 1.0,” U.S. Geological Survey, Open-File Rept. 96-80-A and 96-80-B. Boore, D.M. 2001. “Comparisons of Ground Motions from the 1999 Chi-Chi Earthquake with Empirical Predictions Largely Based on Data from California,” Bull. Seismol. Soc. Am., 91, 1212–1217. Boore, D.M., in press. “Prediction of Ground Motion Using the Stochastic Method,” Pure Appl. Geophys. Boore, D.M. and Atkinson, G.M. 1987. “Stochastic Prediction of Ground Motion and Spectral Response Parameters at Hard-Rock Sites in Eastern North America,” Bull. Seismol. Soc. Am., 77, 440–467. Boore, D.M. and Joyner, W.B. 1984. “A Note on the Use of Random Vibration Theory to Predict Peak Amplitudes of Transient Signals,” Bull. Seismol. Soc. Am., 74, 2035–2039. Boore, D.M. and Joyner, W.B. 1991. “Estimation of Ground Motion at Deep-Soil Sites in Eastern North America,” Bull. Seismol. Soc. Am., 81, 2167–2185. Boore, D.M. and Joyner, W.B. 1997. “Site Amplification for Generic Rock Sites,” Bull. Seismol. Soc. Am., 87, 327–341. Boore, D.M., Joyner, W.B., and Fumal, T.E. 1993. “Estimation of Response Spectra and Peak Accelerations from Western North American Earthquakes: An Interim Report,” U.S. Geological Survey, Open-File Rept. 93-509. Boore, D.M., Joyner, W.B., and Fumal, T.E. 1994. “Estimation of Response Spectra and Peak Accelerations from Western North American Earthquakes: An Interim Report, Part 2,” U.S. Geological Survey, Open-File Rept. 94-127. Boore, D.M., Joyner, W.B., and Fumal, T.E. 1997. “Equations for Estimating Horizontal Response Spectra and Peak Acceleration from Western North American Earthquakes: A Summary of Recent Work,” Seismol. Res. Lett., 68, 128–153. Boore, D.M., Joyner, W.B., and Wennerberg, L. 1992. “Fitting the Stochastic ω−2 Source Model to Observed Response Spectra in Western North America: Trade-Offs between ∆σ and κ,” Bull. Seismol. Soc. Am., 82, 1956–1963. Borcherdt, R.D. 1994. “Estimates of Site-Dependent Response Spectra for Design (Methodology and Justification),” Earthquake Spectra, 10, 617–653.
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Brillinger, D.R. and Preisler, H.K. 1984. “An Exploratory Analysis of the Joyner-Boore Attenuation Data,” Bull. Seismol. Soc. Am., 74, 1441–1450. Brune, J. 1970. “Tectonic Stress and the Spectra of Seismic Shear Waves,” J. Geophys. Res., 75, 4997–5009. Brune, J. 1971. “Correction: Tectonic Stress and the Spectra of Seismic Shear Waves,” J. Geophys. Res., 76, 5002. Brune, J.N. 1999. “Precarious Rocks Along the Mojave Section of the San Andreas Fault, California: Constraints on Ground Motion from Great Earthquakes,” Seismol. Res. Lett., 70, 29–33. Brune, J.N. 2001. “Shattered Rock and Precarious Rock Evidence for Strong Asymmetry in Ground Motions during Thrust Faulting,” Bull. Seismol. Soc. Am., 91, 441–447. BSSC (Building Seismic Safety Council). 1998. NEHRP Recommended Provisions for Seismic Regulations for New Buildings and Other Structures, 1997 ed., Rept. FEMA-302, Federal Emergency Management Agency, Washington, D.C. Campbell, K.W. 1981. “Near-Source Attenuation of Peak Horizontal Acceleration,” Bull. Seismol. Soc. Am., 71, 2039–2070. Campbell, K.W. 1985. “Strong Motion Attenuation Relations: A Ten-Year Perspective,” Earthquake Spectra, 1, 759–804. Campbell, K.W. 1986. “Empirical Prediction of Free-Field Ground Motion Using Statistical Regression Models,” in Proc. Soil Structure Interaction Workshop, NUREG/CP-0054, U.S. Nuclear Regulatory Commission, Washington, D.C., pp. 72–115. Campbell, K.W. 1987. “Predicting Strong Ground Motion in Utah,” in Assessment of Regional Earthquake Hazards and Risk Along the Wasatch Front, Utah, Vol. II, P.L. Gori and W.W. Hays, Eds., U.S. Geological Survey, Open-File Rept. 87-585, pp. L1–L90. Campbell, K.W. 1997. “Empirical Near-Source Attenuation Relationships for Horizontal and Vertical Components of Peak Ground Acceleration, Peak Ground Velocity, and Pseudo-Absolute Acceleration Response Spectra,” Seismol. Res. Lett., 68, 154–179. Campbell, K.W. 1998. “Empirical Analysis of Peak Horizontal Acceleration, Peak Horizontal Velocity, and Modified Mercalli Intensity,” in The Loma Prieta, California, Earthquake of October 17, 1989 — Earth Structures and Engineering Characterization of Ground Motion, T.L. Holzer, Ed., U.S. Geological Survey, Professional paper 1552-D, pp. D47–D68. Campbell, K.W. 2000a. “Seismology, Engineering,” in Encyclopedia of Physical Science and Technology, 3rd ed., R.A. Meyers, Ed., Academic Press, San Diego. Campbell, K.W. 2000b. “Predicting Strong Ground Motion in Utah,” in Assessment of Regional Earthquake Hazards and Risk Along the Wasatch Front, Utah, P.L. Gori and W.W. Hays, Eds., U.S. Geological Survey, Professional Paper 1500-L, pp. L1–L31. Campbell, K.W. 2000c. “Erratum: Empirical Near-Source Attenuation Relationships for Horizontal and Vertical Components of Peak Ground Acceleration, Peak Ground Velocity, and PseudoAbsolute Acceleration Response Spectra,” Seismol. Res. Lett., 71, 353–355. Campbell, K.W. 2001. “Erratum: Empirical Near-Source Attenuation Relationships for Horizontal and Vertical Components of Peak Ground Acceleration, Peak Ground Velocity, and PseudoAbsolute Acceleration Response Spectra,” Seismol. Res. Lett., 72, 474. Campbell, K.W., in press. “Prediction of Strong Ground Motion Using the Hybrid Empirical Method: Example Application to Eastern North America,” Bull. Seismol. Soc. Am. Campbell, K.W. and Bozorgnia, Y. 1994. “Empirical Analysis of Strong Ground Motion from the 1992 Landers, California, Earthquake,” Bull. Seismol. Soc. Am., 84, 573–588. Campbell, K.W. and Bozorgnia, Y. 1999. “Vertical Ground Motion: Characteristics, Relationship with Horizontal Component, and Building-Code Implications,” in Proc. SMIP99 Seminar on Utilization of Strong-Motion Data, M. Huang, Ed., Sept. 15, San Francisco, pp. 23–49, California Strong Motion Instrumentation Program, Sacramento.
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Campbell, K.W. and Bozorgnia, Y. 2000. “New Empirical Models for Predicting Near-Source Horizontal, Vertical, and V/H Response Spectra: Implications for Design,” in Proc. 6th International Conference on Seismic Zonation, Nov. 12–15, Palm Springs, CA, Proc. CD-ROM, Earthquake Engineering Research Institute, Oakland, CA. Campbell, K.W. and Bozorgnia, Y., in press. “Updated Near-Source Ground Motion (Attenuation) Relations for the Horizontal and Vertical Components of Peak Ground Acceleration and Acceleration Response Spectra,” Bull. Seismol. Soc. Am. Cartwright, D.E. and Longuet-Higgins, M.S. 1956. “The Statistical Distribution of the Maxima of a Random Function,” Proc. R. Soc. London, Ser. A, 237, 212–232. Crouse, C.B. 1991a. “Ground-Motion Attenuation Equations for Earthquakes on the Cascadia Subduction Zone,” Earthquake Spectra, 7, 201–235. Crouse, C.B. 1991b. “Erratum: Ground-Motion Attenuation Equations for Earthquakes on the Cascadia Subduction Zone,” Earthquake Spectra, 7, 506. Dahle, A., Bungum, H., and Dvamme, L.G. 1990. “Attenuation Models Inferred from Intraplate Earthquake Recordings,” Earthquake Eng. Struct. Dyn., 19, 1125–1141. Dahle, A., Bungum, H., and Dvamme, L.G. 1991. “Empirically Derived PSV Spectral Attenuation Models for Intraplate Conditions,” European Earthquake Eng., 3, 42–52. Donovan, N.C. and Bornstein, A.E. 1978. “Uncertainties in Seismic Risk Procedures,” J. Geotech. Eng. Div. ASCE, 104, 869–887. Draper, N.R. and Smith, H. 1981. Applied Regression Analysis, 2nd ed., John Wiley & Sons, New York. Ekstrom, G. and Dziewonski, A.M. 1988. “Evidence of Bias in Estimation of Earthquake Size,” Nature, 332, 319–322. EPRI (Electric Power Research Institute). 1993. “Methods and Guidelines for Estimating Earthquake Ground Motion in Eastern North America,” in Guidelines for Determining Design Basis Ground Motions, Vol. 1, Rept. EPRI TR-102293, Electric Power Research Institute, Palo Alto, CA. Field, E.H. 2000. “A Modified Ground-Motion Attenuation Relationship for Southern California that Accounts for Detailed Site Classification and a Basin-Depth Effect,” Bull. Seismol. Soc. Am., 90, S209–S221. Field, E.H. and the SCEC Phase III Working Group. 2000. “Accounting for Site Effects in Probabilistic Seismic Hazard Analysis of Southern California: Overview of the SCEC Phase III Report,” Bull. Seismol. Soc. Am., 90, S1–S31. Frankel, A., Mueller, C., Barnhard, T., Perkins, D., Leyendecker, E., Dickman, N., Hanson, S., and Hopper, M. 1996. “National Seismic Hazard Maps: Documentation June 1996,” U.S. Geological Survey, Open-File Rept. 96-532. Frankel, A.D., Mueller, C.S., Barnhard, T.P., Leyendecker, E.V., Wesson, R.L., Harmsen, S.C., Klein, F.W., Perkins, D.M., Dickman, N.C., Hanson, S.L., and Hopper, M.G. 2000. “USGS National Seismic Hazard Maps,” Earthquake Spectra, 16, 1–19. Gupta, A.K. 1993. Response Spectrum Method in Seismic Analysis and Design, CRC Press, Boca Raton, FL. Hanks, T.C. and Kanamori, H. 1979. “A Moment-Magnitude Scale,” J. Geophys. Res., 84, 2348–2350. Heaton, T.H., Tajima, F., and Mori, A.W. 1986. “Estimating Ground Motions Using Recorded Accelerograms,” Surv. Geophys., 8, 25–83. Herrmann, R.B. 1985. “An Extension of Random Vibration Theory Estimates of Strong Ground Motion to Large Distances,” Bull. Seismol. Soc. Am., 75, 1447–1453. Hough, S.E., Anderson, J.G., Brune, J., Vernon, F., III, Berger, J., Fletcher, J., Haar, L., Hanks, T., and Baker, L. 1988. “Attenuation Near Anza, California,” Bull. Seismol. Soc. Am., 78, 672–691. Hwang, H.H.M., Huijie, L., and Huo, J.R. 1997. “Site Coefficients for Design of Buildings in Eastern North America,” Soil Dyn. Earthquake Eng., 16, 29–40. ICBO (International Council of Building Officials). 1997. Uniform Building Code, International Council of Building Officials, Whittier, CA. ICC (International Code Council). 2000. International Building Code, International Code Council, Falls Church, VA. © 2003 by CRC Press LLC
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Johnston, A.C. 1994. “Seismotectonic Interpretations and Conclusions from the Stable Continental Region Seismicity Database,” in The Earthquakes of Stable Continental Regions, Vol. 1, Assessment of Large Earthquake Potential, Electric Power Research Institute, Palo Alto, CA, pp. 1–103. Johnston, A.C. 1996. “Seismic Moment Assessment of Earthquakes in Stable Continental Regions. I. Instrumental Seismicity,” Geophys. J. Int., 124, 381–414. Joyner, W.B. 1984. “A Scaling Law for the Spectra of Large Earthquakes,” Bull. Seismol. Soc. Am., 74, 1167–1188. Joyner, W.B. 2000. “Strong Motion from Surface Waves in Deep Sedimentary Basins,” Bull. Seismol. Soc. Am., 90, S95–S112. Joyner, W.B. and Boore, D.M. 1981. “Peak Horizontal Acceleration and Velocity from Strong-Motion Records Including Records from the 1979 Imperial Valley, California, Earthquake,” Bull. Seismol. Soc. Am., 71, 2011–2038. Joyner, W.B. and Boore, D.M. 1988. “Measurement, Characterization, and Prediction of Strong Ground Motion,” in Proc. Conference on Earthquake Engineering and Soil Dynamics II—Recent Advances in Ground-Motion Evaluation, J.L. von Thun, Ed., June 27–30, 1988, Park City, UT, Geotech. Spec. Pub. No. 20, pp.43–102, American Society of Civil Engineers, New York. Joyner, W.B. and Boore, D.M. 1993. “Methods for Regression Analysis of Strong-Motion Data,” Bull. Seismol. Soc. Am., 83, 469–487. Joyner, W.B. and Boore, D.M. 1994. “Errata: Methods for Regression Analysis of Strong-Motion Data,” Bull. Seismol. Soc. Am., 84, 955–956. Joyner, W.B. and Fumal, T.E. 1984. “Use of Measured Shear-Wave Velocity for Predicting Geologic Site Effects on Strong Ground Motion,” in Proc. 8th World Conference on Earthquake Engineering, Vol. 2, July 21–28, San Francisco, pp. 777–783, Prentice-Hall, Englewood Cliffs, NJ. Joyner, W.B., Warrick, R.E., and Fumal, T.E. 1981. “The Effect of Quaternary Alluvium on Strong Ground Motion in the Coyote Lake, California, Earthquake of 1979,” Bull. Seismol. Soc. Am., 71, 1333–1349. Kanamori, H. 1978. “Quantification of Earthquakes,” Nature, 271, 411–414. Lay, T. and Wallace, T.C. 1995. Modern Global Seismology, Academic Press, San Diego. Lee, Y. and Anderson, J.G. 2000. “Potential for Improving Ground-Motion Relations in Southern California by Incorporating Various Site Parameters,” Bull. Seismol. Soc. Am., 90, S170–S186. Leyendecker, E.V., Hunt, J.R., Frankel, A.D., and Rukstales, K.S. 2000. “Development of Maximum Considered Earthquake Ground Motion Maps,” Earthquake Spectra, 16, 21–40. Liu, L. and Pezeshk, S. 1999. “An Improvement on the Estimation of Pseudoresponse Spectral Velocity Using RVT Method,” Bull. Seismol. Soc. Am., 89, 1384–1389. Loh, C.H. 1999. “Interpretation of Structural Damage in 921 Chi-Chi Earthquake,” in Proc. International Workshop on Chi-Chi, Taiwan Earthquake of September 21, 1999, Dec. 14–17, Tai-Chung, Taiwan, ROC. Marone, C. and Scholz, C.H. 1988. “The Depth of Seismic Faulting and the Upper Transition from Stable to Unstable Slip Regimes,” Geophys. Res. Lett., 15, 621–624. McGarr, A. 1984. “Scaling of Ground Motion Parameters, State of Stress, and Focal Depth,” J. Geophys. Res., 89, 6969–6979. Molas, G.L. and Yamazaki, F. 1995. “Attenuation of Earthquake Ground Motion in Japan Including Deep Focus Events,” Bull. Seismol. Soc. Am., 85, 1343–1358. Molas, G.L. and Yamazaki, F. 1996. “Attenuation of Response Spectra in Japan Using New JMA Records,” Bull. Earthquake Resistant Struct. Res. Center, 29, 115–128. Moores, E.M. and Twiss, R.J. 1995. Tectonics, W.H. Freeman and Company, New York. Newmark, N.M. and Hall, W.J. 1982. Earthquake Spectra and Design, Earthquake Engineering Research Institute, Berkeley, CA. Ou, G.B. and Herrmann, R.B. 1990. “A Statistical Model for Ground Motion Produced by Earthquakes at Local and Regional Distances, Bull. Seismol. Soc. Am., 80, 1397–1417.
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Park, S. and Elrick, S. 1988. “Predictions of Shear-Wave Velocities in Southern California Using Surface Geology,” Bull. Seismol. Soc. Am., 88, 677–685. Richter, C.F. 1935. “An Instrumental Earthquake Magnitude Scale,” Bull. Seismol. Soc. Am., 25, 1–32. Rodriguez-Marek, A., Bray, J.D., and Abrahamson, N.A. 2001. “An Empirical Geotechnical Seismic Site Response Procedure,” Earthquake Spectra, 17, 65–87. Sabetta, F. and Pugliese, A. 1996. “Estimation of Response Spectra and Simulation of Nonstationary Earthquake Ground Motions,” Bull. Seismol. Soc. Am., 86, 337–352. Sadigh, K., Chang, C.Y., Abrahamson, N.A., Chiou, S.J., and Power, M.S. 1993. “Specification of LongPeriod Ground Motions: Updated Attenuation Relationships for Rock Site Conditions and Adjustment Factors for Near-Fault Effects,” in Proc. ATC-17-1 Seminar on Seismic Isolation, Passive Energy Dissipation, and Active Control, Vol. I, March 11–12, San Francisco, pp. 11–23, Applied Technology Council, Redwood City, CA. Sadigh, K., Chang, C.Y., Egan, J.A., Makdisi, F., and Youngs, R.R. 1997. “Attenuation Relationships for Shallow Crustal Earthquakes Based on California Strong Motion Data,” Seismol. Res. Lett., 68, 180–189. Savy, J.B., Bernreuter, D.L., and Chen, J.C. 1987. “A Methodology to Correct for Effect of the Local Site Characteristics in Seismic Hazard Analyses,” in Ground Motion and Engineering Seismology, A.S. Cakmak, Ed., Developments in Geotechnical Engineering, Vol. 44, pp. 243–255, Elsevier, Amsterdam. Schnabel, P.B. and Seed, H.B. 1973. “Accelerations in Rock for Earthquakes in the Western United States,” Bull. Seismol. Soc. Am., 63, 501–516. Schneider, J.F., Silva, W.J., and Stark, C.L. 1993. “Ground Motion Model for the 1989 M 6.9 Loma Prieta Earthquake Including Effects of Source, Path and Site,” Earthquake Spectra, 9, 251–287. Si, H. and Midorikawa, S. 2000. “New Attenuation Relations for Peak Ground Acceleration and Velocity Considering Effects of Fault Type and Site Condition,” in Proc. 12th World Conference on Earthquake Engineering, Jan. 30–Feb. 4, Auckland, Proc. CD-ROM, Paper 532, New Zealand Society of Earthquake Engineering, Silverstream, New Zealand. Silva, W. and Darragh, R.B. 1995. Engineering Characterization of Strong Ground Motion Recorded at Rock Sites, Rept. EPRI TR-102262, Electric Power Research Institute, Palo Alto, CA. Silva, W.J. and Lee, K. 1987. “WES RASCAL Code for Synthesizing Earthquake Ground Motions,” in State-of-the-Art for Assessing Earthquake Hazards in the United States, Paper S-73-1, Rept. 24, Department of the Army, U.S. Army Corps of Engineers, Vicksburg, MS. Singh, J.P. 1985. “Earthquake Ground Motions: Implications for Designing Structures and Reconciling Structural Damage,” Earthquake Spectra, 1, 239–270. Singh, S. and Herrmann, R.B. 1983. “Regionalization of Crustal Coda Q in the Continental United States,” J. Geophys. Res., 88, 527–538. Somerville, P. 2000. “New Developments in Seismic Hazard Estimation,” in Proc. 6th International Conference on Seismic Zonation, Nov. 12–15, Palm Springs, CA, Proc. CD-ROM, Earthquake Engineering Research Institute, Oakland, CA. Somerville, P. and Abrahamson, N. 1995. “Ground Motion Prediction for Thrust Earthquakes,” in Proc. SMIP95 Seminar on Seismological and Engineering Implications of Recent Strong-Motion Data, May 16, San Francisco, pp. 11–23, California Strong Motion Instrumentation Program, Sacramento, CA. Somerville, P. and Abrahamson, N. 2000. “Prediction of Ground Motions for Thrust Earthquakes,” Data utilization report CSMIP/00-01, California Strong Motion Instrumentation Program, Sacramento, CA. Somerville, P.G., Smith, N.F., Graves, R.W., and Abrahamson, N.A. 1997. “Modification of Empirical Strong Ground Motion Attenuation Relations to Include the Amplitude and Duration Effects of Rupture Directivity,” Seismol. Res. Lett., 68, 199–222.
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Somerville, P., Collins, N., Abrahamson, N., Graves, R., and Saikia, C. 2001. “Ground Motion Attenuation Relations for the Central and Eastern United States, U.S. Geological Survey, Award 99HQGR0098, Final Report. Spudich, P., Joyner, W.B., Lindh, A.G., Boore, D.M., Margaris, B.M., and Fletcher, J.B. 1999. “SEA99: A Revised Ground Motion Prediction Relation for Use in Extensional Tectonic Regimes,” Bull. Seismol. Soc. Am., 89, 1156–1170. Stewart, J.P. 2000. “Variations between Foundation-Level and Free-Field Earthquake Ground Motions,” Earthquake Spectra, 16, 511–532. Toro, G.R., Abrahamson, N.A., and Schneider, J.F. 1997. “Model of Strong Ground Motions from Earthquakes in Central and Eastern North America: Best Estimates and Uncertainties,” Seismol. Res. Lett., 68, 41–57. Trifunac, M.D. and Lee, V.W. 1979. Dependence of Pseudo-Relative Velocity Spectra of Strong Motion Acceleration on the Depth of Sedimentary Deposits, Rept. CE79-02, Dept. of Civil Engineering, University of Southern California, Los Angeles. Tsai, Y.B. and Huang, M.W. 1999. Strong Ground Motion Characteristics of the Chi-Chi, Taiwan Earthquake of September 21, 1999, Institute of Geophysics, National Central University, Chung-Li, Taiwan, ROC. Tsai, Y.B. and Huang, M.W. 2000. “Strong Ground Motion Characteristics of the Chi-Chi, Taiwan Earthquake of September 21, 1999,” Earthquake Eng. Eng. Seismol., 2, 1–21. Wells, D.L. and Coppersmith, K.J. 1994. “New Empirical Relationships among Magnitude, Rupture Length, Rupture Width, Rupture Area, and Surface Displacement,” Bull. Seismol. Soc. Am., 84, 974–1002. Westaway, R. and Smith, R.B. 1989. “Strong Ground Motion in Normal-Faulting Earthquakes,” Geophys. J., 96, 529–559. Wills, C.J. and Silva, W. 1998. “Shear-Wave Velocity Characteristics of Geologic Units in California,” Earthquake Spectra, 14, 533–556. Wills, C.J., Petersen, M., Bryant, W.A., Reichle, M., Saucedo, G.J., Tan, S., Taylor, G, and Treiman, J. 2000. “A Site-Conditions Map for California Based on Geology and Shear-Wave Velocity,” Bull. Seismol. Soc. Am., 90, S187–S208. Youngs, R.R., Abrahamson, N.A., Makdisi, F., and Sadigh, K. 1995. “Magnitude Dependent Dispersion in Peak Ground Acceleration,” Bull. Seismol. Soc. Am., 85, 1161–1176. Youngs, R.R., Chiou, S.J., Silva, W.J., and Humphrey, J.R. 1997. “Strong Ground Motion Attenuation Relationships for Subduction Zone Earthquakes,” Seismol. Res. Lett., 68, 58–73. Zoback, M.L. 1992. “First- and Second-Order Patterns of Stress in the Lithosphere: The World Stress Map Project,” J. Geophys. Res., 97, 11,703–11,728.
Further Reading There have been many reviews and discussions of attenuation relations and their use in engineering. A recent comprehensive review is provided in “Earthquake Ground Motion Estimation Using Strong-Motion Records: A Review of Equations for the Estimation of Peak Ground Acceleration and Response Spectral Ordinates,” by J. Douglas in the journal Earth-Science Reviews. On the related but broader topic of engineering seismology, there are several good summaries including “Strong Motion Seismology,” by John Anderson in the International Handbook of Earthquake Engineering and Seismology; “Seismology, Engineering,” by Kenneth Campbell in the Encyclopedia of Physical Science and Technology, 3rd ed.; and Engineering Seismology, by Kiyoshi Kanai. Recent advances in the prediction of strong ground motion are published in several earthquake engineering and seismology journals, including the Bulletin of the Seismological Society of America and Seismological Research Letters, both published by the Seismological Society of America; Earthquake Spectra, published by the Earthquake Engineering Research Institute; Earthquake Engineering and
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Structural Dynamics, published by John Wiley & Sons; and Soil Dynamics and Earthquake Engineering, published by Elsevier Science Publishers. Other useful reviews include: Abrahamson, N.A. and Shedlock, K.M. 1997. “Overview,” Seismol. Res. Lett., 68, 9–23. Ambraseys, N.N. and Bommer, J.J. 1995. “Attenuation Relations for Use in Europe: An Overview,” in Proc. 5th SECED Conference on European Seismic Design Practice, E.A. Elnashai, Ed., October 26–27, Chester, United Kingdom, pp. 67–74, A.A. Balkema, Rotterdam. Boore, D.M. 1987. “The Prediction of Strong Ground Motion,” in Strong Ground Motion Seismology, M.O. Erdik and M.N. Toksoz, Eds., D. Reidel, Dordrecht, the Netherlands, pp. 109–141. Boore, D.M. and Joyner, W.B. 1982. “The Empirical Prediction of Ground Motion,” Bull. Seismol. Soc. Am., 72, S43–S60. Campbell, K.W. 1985. “Strong Motion Attenuation Relations: A Ten-Year Perspective,” Earthquake Spectra, 1, 759–804. Iai, S. and Brady, A.G. 1993. Proceedings of the International Workshop on Strong Motion Data, Dec. 13–17, Menlo Park, CA, Vols. 1 and 2, The Port and Harbour Research Institute, Kanagawa, Japan. Idriss, I.M. 1979. “Characteristics of Earthquake Ground Motions,” in Proc. ASCE Specialty Conference on Earthquake Engineering and Soil Dynamics, Vol. III, June 19–21, Pasadena, CA., pp. 1154–1261, American Society of Civil Engineers, New York. Idriss, I.M. 1993. Procedures for Selecting Earthquake Ground Motions at Rock Sites, Rept. NIST GCR 93625, National Institute of Standards and Technology, Gaithersburg, MD. Idriss, I.M. 1995. “An Overview of Earthquake Ground Motions Pertinent to Seismic Zonation,” in Proc. 5th International Conference on Seismic Zonation, Vol. III, Oct. 17–19, Nice, France, pp. 2111–2126, Ouest Editions, Presses Academiques, Nantes Cedex, France. Joyner, W.B. and Boore, D.M. 1988. “Measurement, Characterization, and Prediction of Strong Ground Motion,” in Proc. Conference on Earthquake Engineering and Soil Dynamics II—Recent Advances in Ground-Motion Evaluation, J.L. von Thun, Ed., June 27–30, Park City, UT, Geotech. Spec. Pub. No. 20, pp.43–102, American Society of Civil Engineers, New York. Joyner, W.B. and Boore, D.M. 1990. “Empirical Methods of Ground Motion Estimation,” in Proc. POLA Seismic Workshop on Seismic Engineering, R.C. Wittkop and G.R. Martin, Eds., March 21–23, San Pedro, CA, pp. 273–308, Port of Los Angeles. Joyner, W.B. and Boore, D.M. 1996. “Recent Developments in Strong Motion Attenuation Relationships,” in Proc. 28th Joint Meeting of the U.S.–Japan Cooperative Program in Natural Resource Panel on Wind and Seismic Effects, N.J. Raufaste, Ed., May 14–17, Gaithersburg, MD, pp. 101–116, National Institute of Standards and Technology, Gaithersburg, MD. Seed, H.B. and Idriss, I.M. 1982. Ground Motions and Soil Liquefaction during Earthquakes, Earthquake Engineering Research Institute, Berkeley, CA. Somerville, P. 1999. “Recent Advances in Strong Ground Motion Prediction,” in Proc. 8th Canadian Conference on Earthquake Engineering, June 13–16, Vancouver, Canada, pp. 7–28, Canadian Association for Earthquake Engineering, Vancouver. Somerville, P. 2000. “New Developments in Seismic Hazard Estimation,” in Proc. 6th International Conference on Seismic Zonation, Nov. 12–15, Palm Springs, CA, Proc. CD-ROM, Earthquake Engineering Research Institute, Oakland, CA.
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Appendix–Notation Ground Motion Parameters PGA PGV PSA Y YDir YHW,FW σlnY σlnY,Dir
Peak ground acceleration (g) Peak ground velocity (cm/sec) Acceleration response of a single-degree-of-freedom system (g, 5% damping) Peak ground motion (generic) Peak ground motion (generic) including rupture directivity effects Peak ground motion (generic) including hanging-wall or footwall effects Standard deviation of lnY Standard deviation of lnYDir (i.e., when directivity effects are included)
Magnitude Parameters (see Figure 5.2) mLg mN M M MJ MS MW
Lg-wave magnitude used in eastern United States (equivalent to mN in Canada) Lg-wave magnitude used in eastern Canada (equivalent to mLg in eastern United States) Moment magnitude (equivalent to MW) Earthquake magnitude (generic) Japan Meteorological Agency (JMA) magnitude used in Japan Surface-wave magnitude Moment magnitude (equivalent to M)
Distance Parameters (see Figure 5.3) rcer repi rhypo rjb rrup rseis R
Distance to center of energy release on the rupture plane (km) Epicentral distance (km) Hypocentral distance (km) Closest distance to the surface projection of the rupture plane (km) Closest distance to the rupture plane (km) Closest distance to the seismogenic part of the rupture plane (km) Distance to the earthquake source (generic)
Depth Parameters drup dseis hhypo hrup Hbot Htop Hseis
Average depth to top of the rupture plane (km) Average depth to top of the seismogenic part of the rupture plane (km) Hypocentral depth (also focal depth) (km) Depth to the point on the fault rupture plane that corresponds to rrup (km) Depth to the bottom of the seismogenic part of the fault (km) Depth to the top of the fault (km) Depth to the top of the seismogenic part of the fault (km)
Faulting Mechanism Parameters (see Table 5.5) F FRV FTH λ
Indicator variable for the type or style of faulting Indicator variable for reverse faulting (δ > 45°) in Campbell and Bozorgnia model Indicator variable for thrust faulting (δ ≤ 45°) in Campbell and Bozorgnia model Rake angle (direction of slip vector on the fault plane): 0° for pure left-lateral strike-slip faulting 90° for pure reverse faulting 180° for pure right-lateral strike-slip faulting 270° for pure normal faulting
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Site Parameters (see Tables 5.2 and 5.4) D S1 S2 S3 S4 SA SB SC SD SE SENA SFS SVFS SSR SFR SDeep SSoil SRock VS30 VS
Depth to basement rock (also referred to as sediment depth or basin depth) (km) Indicator variable for Type 1 ground condition (rock) in Japan Indicator variable for Type 2 ground condition (hard soil) in Japan Indicator variable for Type 3 ground condition (medium soil) in Japan Indicator variable for Type 4 ground condition (soft soil) in Japan Indicator variable for hard rock in building code site class Indicator variable for rock in building code site class Indicator variable for very dense soil and soft rock in building code site class Indicator variable for stiff soil in building code site class Indicator variable for soft soil in building code site class Indicator variable for very hard rock in eastern North America Indicator variable for firm soil in Campbell and Bozorgnia site class Indicator variable for very firm soil in Campbell and Bozorgnia site class Indicator variable for soft rock in Campbell and Bozorgnia site class Indicator variable for firm rock in Campbell and Bozorgnia site class Indicator variable for deep stiff soil in eastern North America Indicator variable for generic soil in western North America Indicator variable for generic rock in western North America Average value of VS in the top 30 m (100 ft) of a site profile Shear-wave velocity (generic)
Hanging-Wall and Footwall Parameters FW HW
Indicator variable for a site located on the footwall of rupture plane Indicator variable for a site located on the hanging wall of the rupture plane
Source Directivity Parameters d DR L s φ θ
Effective rupture width for estimating directivity effects for dip-slip faults Fraction of fault rupture length (s/L) or width (d/W) rupturing towards a site Length of the fault rupture plane Effective rupture length for estimating directivity effects for strike-slip faults Zenith angle between fault rupture plane and ray path to a site for dip-slip faults Azimuth angle between rupture plane and ray path to a site for strike-slip faults
Miscellaneous Parameters f fn g T Tn W zT δ π
Wave frequency (1/T, Hz) Natural frequency of a single-degree-of-freedom system (1/Tn , Hz) Fraction of gravity (980.6550 cm/sec2) Period (1/f, sec) Natural period of a single-degree-of-freedom system (1/fn , sec) Down-dip width of the fault rupture plane (km) Indicator variable for subduction interface and intraslab events Angle of the fault plane with respect to the Earth’s surface (dip angle) Archimedes number (3.141593)
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6 Simulation Modeling of Strong Ground Motion 6.1 6.2
Introduction Earthquake Source Models Seismic Moment and Stress Parameters · Brune’s Source Model for Near-Field Ground Motion · Models for Far-Field Strong Ground Motion · Complex Source Models (Asperities and Barriers)
6.3
Time Domain Characteristics of Strong Ground Motion Modeling of RMS Acceleration · Duration of the Strong Ground Motion · Time Domain Envelope of the Strong Ground Motion
6.4
Frequency Domain Characteristics of Strong Ground Motion
6.5 6.6
Radiation Pattern and Directivity Simulation of Strong Ground Motion
Theoretical Model of the Fourier Amplitude Spectrum
Mustafa Erdik ˘ Bogaziçi University Istanbul, Turkey
Eser Durukal ˘ Bogaziçi University Istanbul, Turkey
Stochastic Simulations · Deterministic Simulation Models · Empirical Green’s Function Method · Hybrid Simulation Methods
Defining Terms References Further Reading
6.1 Introduction The introduction of performance-based earthquake-resistant design for buildings and other civil engineering structures has increased the need for simulating realistic ground motions. Combined with recent developments in software tools and structural modeling techniques for time domain transient nonlinear dynamic analysis, the use of simulated time histories of ground motion has gained major importance. Although the use of recorded ground motion under conditions similar to the design earthquake is appealing, there may never be an adequate suite of such data in terms of tectonic structure, earthquake size, local geology, and near-fault conditions. The variability of ground acceleration traces induced by the source, propagation path, and site characteristics is illustrated in Figure 6.1, where a collection of representative horizontal acceleration time histories is plotted with the same amplitude and time scales. A number of methods have been developed and are in use for the adjustment of selected recorded time histories to provide conformity to site conditions (so-called accelerogram scaling) and other spectrum matching techniques [e.g., Gasparini and Vanmarcke, 1976; Abrahamson, 1998] that aim to
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FIGURE 6.1 Variability of earthquake ground acceleration traces. (From Chopra, A.K., 2000, Dynamics of Structures: Theory and Applications to Earthquake Engineering, 2nd ed., Prentice-Hall, Englewood Cliffs, NJ. Reprinted by permission of Pearson Education, Inc., Upper Saddle River, NJ.)
generate time histories of ground motion whose response spectra match the design response spectrum. Methods that rely on the description of site- or region-specific ground motion time histories in terms of statistically significant parameters, rather than seismological constraints, are also used for the so-called statistical simulation of strong ground motion. For such methods autoregressive moving average (ARMA) processes have been generally used [e.g., Deodatis and Shinozuka, 1988; Ellis and Cakmak, 1991]. These methods do not generally involve rigorous considerations of the physics of the earthquakes and will not be included in the scope of this chapter. There are several approaches to the modeling and simulation of strong ground motion taking into account the physics of the source and propagation process. Each approach accommodates, to varying degrees, the seismic wave radiation from a fault rupture, propagation through the crust, and modifications by local site conditions. Three main approaches are used for modeling earthquake strong ground © 2003 by CRC Press LLC
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motion, stochastic simulation, kinematic modeling, and dynamic modeling. A fourth approach, which can be called hybrid modeling, involves a combination of the main approaches. This chapter first reviews the elements of the earthquake source physics important to the modeling of strong ground motion. The time and frequency domain characteristics of the ground motion relevant to the scope of this chapter are reviewed, and the theoretical shape of the Fourier amplitude spectrum (FAS) of the ground acceleration, both for the near field and in general, is covered. Stochastic simulation of strong ground motion with physical constraints for point sources and finite fault ruptures is discussed, with appropriate examples. Kinematic modeling of the strong ground motion involving Green’s function summation techniques is then covered, with explanations suitable for the objectives of this handbook. Lastly, an approach to hybrid strong motion modeling is elaborated, with a specific example.
6.2 Earthquake Source Models The elastic rebound theory proposed by Reid in 1911 constitutes the essential foundation of the earthquake source process used in the modeling of strong ground motion. Sudden fault rupture that results from the accumulation of strains in the crust is the cause of the radiation of seismic waves and, consequently, of ground motion. The development and propagation of the dislocation front on the fault surface, and the time for completion of the slip, are essential for an explanation of the ground motion. Seismic moment, various stress parameters, rupture velocity, and slip-time functions are considered as the main parameters necessary for description of the source and for the simulation of ground motion. This section discusses seismic moment and stress parameters since they are basic to this chapter. Other source parameters will be covered under the appropriate sections. The second and third subsections encompass Brune’s source model as it relates to the near-fault ground motion, and other models developed for modeling far-field ground motion. It has been shown repeatedly that a strong motion acceleration time history is highly influenced by the complexity of the source rupture due to fault heterogeneities. An introductory subsection on complex source models and the basic elements of heterogeneous fault rupture (asperities and barriers) are also included.
6.2.1 Seismic Moment and Stress Parameters A shear dislocation mathematically models an earthquake fault across a given surface in an elastic medium. The concept of seismic moment, M0 , introduced by Aki [1966], stems from the equivalence of elastic dislocation and a double-force couple and constitutes a good physical measure of the earthquake: M0 = µ A D
(6.1)
where µ is the shear modulus (Lamé’s constant) of the medium, D is the average total dislocation (i.e., mean fault offset or slip), and A is the area of the dislocation surface (i.e., fault rupture surface). Various researchers suggest that the average total dislocation (slip) is about three quarters of the maximum slip. For crustal rocks µ = 3.3 × 1011 dyne/cm2 (33 GPa). A mechanically oriented model for the explanation of the seismic moment is provided in Figure 6.2. Seismic moment (M0) is measured in N-m or dyn-cm (1 N-m = 107 dyn-cm). Seismic moment can be assessed either from the earthquake records or by observation of the fault rupture dimensions. The moment magnitude MW scale is based on the seismic moment [Kanamori, 1977], where M0 is expressed in N-m: MW = (2 3) log M 0 − 10.73
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FIGURE 6.2
Earthquake Engineering Handbook
A mechanical model for the explanation of seismic moment.
Fault rupture is caused by stress in the earth. In the simplest model of fault rupture, the relative slip on both sides of the dislocation surface is due to the level of the acting shear stress exceeding the available friction stress. Stresses are measured in bar, dyn/cm2, and N/m2 (Pa). The related conversions are: 1 bar = 106 dyn/cm2, 1 Pa = 10 dyn/cm2, and 1 Mpa = 106 Pa. The stress drop, ∆σ, is defined as the difference between the initial state of the shear stress σo (i.e., before the earthquake) and the final state of the shear stress σ1 (i.e., after the earthquake): ∆σ = σ 0 − σ1
(6.3)
Owing to the friction there will always be some σ1 remaining after the earthquake. Under ideal cases, if σ1 = 0 then the stress drop is total. The average stress σm is defined as the mean value of the shear stresses acting before and after the earthquake: σ m = (σ 0 + σ1 ) 2
(6.4)
The total energy, E, released by the fracture will be simply: E = σ m D A = (σ m µ ) M 0
(6.5)
The effective stress σ is the difference between the initial static stress and frictional stress, σf , in existence during the rupture process: σ = σ0 − σ f
(6.6)
The effective stress is considered as the available stress to drive the slip motion on the fault. In general, by assuming σf as the dynamic frictional stress, the effective stress and the stress drop are used interchangeably. Brune [1970] defines the fractional stress drop, ε, as the ratio between the stress drop and the effective stress: ε = ∆σ σ © 2003 by CRC Press LLC
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In earthquakes with variation of slip on the dislocation surface, all of these stresses vary spatially as a function of asperities and other irregularities. On the basis of the geological observations of the crust after the earthquake, the “static stress drop” is what can be observed [Kanamori and Anderson, 1975]. Typical values of the static stress drop, controlled by the dimensions of the entire rupture, are between 10 and 100 bar (1 bar = 105 Pa). The terms stress drop and the static stress drop are generally used interchangeably. Kanamori and Anderson [1975] indicate a constant static stress drop of about 30 bar (3 Mpa) for interplate earthquakes and about 100 bar (10 Mpa) for intraplate earthquakes of moderate and large magnitudes (magnitude >5). Constancy in static stress drop is also inherent in the definition of moment magnitude MW [Kanamori, 1977]. For a uniform shear rupture, the static stress drop can be given as [Aki, 1972]: ∆σ = C µ ( D Lc )
(6.8)
where Lc is the characteristic dimension (length) of the rupture surface and C is a constant with a value around unity that depends on the rupture surface geometry. Using the definition of seismic moment (Equation 6.1) it can be shown that: M 0 = C1 ∆σ Lc
(6.9)
where C1 is another constant that depends on the rupture surface geometry. For a circular fault of radius a, the relationship between the static stress drop and the average dislocation (fault offset) is given by [Keilis Borok, 1957; Kanamori and Anderson, 1975]: ∆σ = (7 π 16) µ ( D a)
(6.10)
Using the definition of seismic moment: ∆σ = (7 16) M 0 a −3
(6.11)
Corresponding relationships for a strike-slip fault of length L and width W are: ∆σ = (2 π) µ ( D W ) = (2 π) M 0 L−1W −2
(6.12)
As can be seen, the estimation of stress drop is very sensitive to variations in the fault radius (dimension). Since the fault size can only be assessed from the rupture duration and rupture velocity, estimated values of stress drop lack precision. For a circular fault, the dislocation radius can be related to seismic moment and stress drop as: a = (7 16)
1/3
(M0
∆σ)
1/3
(6.13)
Aki [1987] states that for a wide range of rupture models the relationship between the stress drop and the slip velocity is given by: ∆σ = K (µ β) ( D τr )
(6.14)
where K is a scaling factor that varies between 0.5 and 1, D is the average slip on the fault, τr is the rise time, β is the shear-wave propagation velocity, and (V = D/τr) is the slip velocity.
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The original concept of the static stress drop was related to a measure of fault slip relative to the fault size; however, it is not an easily quantified physical parameter. It may be prudent to call it a stress parameter that controls the strength of high frequency radiation.
6.2.2 Brune’s Source Model for Near-Field Ground Motion To model near-field ground motion Brune [1970] considered a tangential stress pulse applied instantaneously to an interior of a dislocation surface (Figure 6.3). The fault propagation effects are neglected. This stress pulse generates a shear wave along the direction normal to the dislocation surface (i.e., fault surface). If x represents the perpendicular distance from the fault surface and H(t) is the Heaviside unitstep function and β is the shear-wave propagation velocity, the initial time function for shear stress pulse can be written as: σ ( x , t ) = σH (t – x β)
(6.15)
where σ is the effective shear stress (Figure 6.3). Ground displacement close to the fault center parallel to the fault surface, u, can be obtained through integration: σ = µ(δu δx ) at x = 0
u = (σ µ ) β t for 0 < t < T
(6.16) (6.17)
where µ is the Lamé’s constant and T is the time required for the waves to propagate across the fault surface. The initial particle velocity parallel to the fault is: v = (σ µ ) β
(6.18)
FIGURE 6.3 Brune dislocation model for S waves. (From Brune, J.N., 1970, J. Geophys. Res., 75, 4997–5009. Published by the American Geophysical Union.)
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For σ = 100 bar (1 × 108 dyn/cm2), µ = 3 × 1011 dyn/cm2 and β = 3 km/sec the initial velocity takes a value of v = 1 m/sec, which is in line with peak ground velocities experienced in large earthquakes around the world. Brune [1970] has estimated the maximum ground acceleration as 2 g, by assuming a stress drop of σ = 100 bar and by considering the contribution of the band of frequencies between 0 and 10 Hz. This value is also in line with the peak ground accelerations measured in earthquakes. Brune [1970] indicates that the near-field ground displacement parallel to the fault (Equation 6.17) increases linearly with time until the effects of the boundaries of dislocation reach the observation point, and then decrease gradually to zero. This effect is modeled by the following exponential factor: v ( x = 0, t ) = (σ µ ) β exp (−t τ)
[(
(6.19)
)]
u ( x = 0, t ) = (σ µ ) β τ 1− exp (−t τ)
(6.20)
where τ is the order of a/β, a being the appropriate fault dimension (dislocation surface) which, in reality, governs the speed of rise in dislocation displacement to its final value. For a large t, u(x = 0,t) tends to a constant level (final dislocation) given by: umax = (σ µ ) β τ
(6.21)
The solutions of a static shear crack model with uniform stress drop on the fault plane can generally be given as [Keilis-Borok, 1957]: D=ξσ a µ
(6.22)
where D is the average final dislocation, a is the critical dimension of the fault (radius for a circular fault), and ξ is a nondimensional constant, equal to 1.37 for a circular fault. Considering Equations 6.21 and 6.22: τ av = ξ (a β)
(6.23)
The FAS of the near-field S-wave displacement, UNF (ω), and acceleration, ANF (ω), can be computed from Equation 6.20:
(
U NF (ω ) = (σ µ ) β ω −1 ω 2 + τ −2
(
ANF (ω ) = (σ µ ) β ω ω 2 + τ −2
)
)
−1/ 2
−1/ 2
(6.24) (6.25)
The acceleration spectrum given by Equation 6.25 has a constant amplitude of (σβ/µ) in high frequency regions and diminishes by (σµτ/β)ω in low frequency regions. The transition frequency (ωc , corner frequency) between these two regions is given by 1/τ: ω c = 2πfc = 1 τ
(
ANF (ω ) = (σ µ ) β ω ω 2 + ω c2
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(6.26)
)
−1/ 2
(6.27)
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FIGURE 6.4 Brune near-fault S-wave acceleration Fourier amplitude spectrum. (From Brune, J.N., 1970, J. Geophys. Res., 75, 4997–5009. Published by the American Geophysical Union.)
Figure 6.4 provides a plot of Brune’s near-field spectrum in log-log coordinates. As can be seen, the theoretical spectrum has a flat high frequency amplitude that cannot represent the high frequency decay observed in empirical spectra. The dashed line in the high frequency region of Figure 6.4 illustrates the effect of high frequency diminution. The important difference is that Brune’s spectrum has only one corner frequency, whereas a high frequency corner frequency (ωh = 2πfh) is generally evident from the empirical spectra. The high frequency decay can be considered to be a manifestation of site effects, attenuation or source properties, such as decay time of stress drop or size of the asperities. This high frequency diminution of the spectral amplitudes can be accounted for with the inclusion of a high frequency filter in Equation 6.27 [Trifunac, 1976]:
(
ANF (ω ) = (σ µ ) β ω ω 2 + ω c2
)
-1/2
(
ω 2 ω 2 + ω 2 h h
)
−1/ 2
(6.28)
For California earthquakes of magnitude between 5.5 and 7.2, the cut-off frequency fh is nearly constant at about 4 to 5 Hz [Aki, 1987]. For near-field California earthquakes Hanks [1982b] locates fh at frequencies in the vicinity of 15 Hz. It should be noted that in earthquakes, rupture is far from being uniform and is controlled by successive irregular breaking of several asperities with stopping and restarting phases. These complexities are reflected in the near-field acceleration time domain traces and their Fourier amplitude spectra. Thus, only the overall features of the source process are reflected in the model given by Equation 6.28.
6.2.3 Models for Far-Field Strong Ground Motion Far-field shear wave displacement, u(r, t), from a point shear dislocation in a homogeneous elastic half space (with no energy loss and no surface effects) is given by [Aki and Richards, 1980]:
[
(
u (r , t ) = ( RµA) 4 πρβ3r
)] d'(t − r β)
(6.29)
where R is the scaling factor for the angular radiation pattern, ρ is the density of the medium, r is the hypocentral distance, d'(t) is the time derivative of the average dislocation on the rupture surface (source time function). By defining the source time function, d(t), as:
[
]
d (t ) = D 1 − (1 + t τ) exp (t τ)
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(6.30)
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and by using the definition of the seismic moment (Equation 6.1), Beresnev and Atkinson [1997] have shown that the FAS of the far-field shear wave displacement (Equation 6.24) becomes:
[
(
U (r ,ω ) = ( RM 0 ) 4πρβ3r
)] 1 + (ω ωc ) 2
−1
(6.31)
where |U(r,ω)| is the FAS of the far-field shear wave displacement and ωc (or fc) is the corner frequency equal to: ω c = 2πfc = 1 τ
(6.32)
where τ is the time parameter that controls the rise time (rate of growth in the dislocation). If the source rise time (τr) can be defined as the time during which the fault slip reaches a certain fraction (δ) of the average total fault slip (D), the corner frequency can be related to the rise time as: f c = C3 τ r
(6.33)
where C3 is a constant that varies depending on the fraction δ (C3 = 0.27 in Bresenev and Atkinson, 1997; C3 = 1 in Boore, 1983). As can be seen, the low frequency asymptotic limit of |U(r,ω)| is proportional to the seismic moment, M0. This property is used for the estimation of seismic moment and consequently, moment magnitude, from records of ground motion. If the slip at every point on the dislocation surface continues uniformly until the rupture reaches and stops at its boundary, it can be shown that the corner frequency can be expressed as: fc = C 4 (β Lc )
(6.34)
where C4 is a constant of proportionality. Brune [1970] gives C4 = 0.37 for a circular rupture surface where Lc is equal to its radius a. For a rectangular fault of length L and width W, Savage [1966] gives C4 = 0.60, where Lc = (LW)1/2. Through use of Equations 6.13 and 6.34 it can be shown that: f c = C5 β ( ∆ σ M 0 )
1/3
(6.35)
where C5 is a constant of proportionality. Equations 6.34 and 6.35 are commonly known as the spectral scaling law. 6.2.3.1 Brune’s Model Brune [1970], by use of physical arguments, has obtained the following far-field average shear wave displacement function: u (r , t ) = (σβ µ )(a r ) t ' exp (−ω c t ')
(6.36)
where r is the epicentral distance, a is the dimension of the equivalent circular dislocation surface (radius of the circular fault), a/r accounts for the geometric spreading, ωc is the corner frequency, and t' is: t '= t − r β
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(6.37)
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It should be noted that the effect of the radiation pattern is not taken into account in Equation 6.36. The Fourier amplitude spectra of the far-field shear wave displacement, U(r,ω), and acceleration, AFF (r,ω), become:
[ (
)]
(6.38)
[ (
)]
(6.39)
U (r ,ω ) = (σβ µ )(a r ) 1 ω 2 + ω c2
A (r ,ω ) = (σβ µ )(a r ) ω 2 ω 2 + ω c2
A(r, ω), given by Equation 6.39, is similar to ANF (ω), given by Equation 6.25. The main difference is in the decay rate for frequencies less than the corner frequency and in the inclusion of a geometric attenuation factor. The low frequency limit of Equation 6.38 leads to the constant:
(
U (r ,0) = (σβ µ )(a r ) 1 ω c2
)
(6.40)
It can be shown [e.g., Keilis-Borok, 1957; Brune, 1976] that the low frequency limit of the FAS of the far-field shear wave displacement from a double-couple point source, Ω(ω = 0), can be written in terms of the seismic moment, M0 , as:
(
Ω (ω = 0) = U (r , 0) = M 0 4πρr β3
)
−1
(6.41)
Combining Equations 6.41 and 6.38 and with the inclusion of R, the scaling factor for the angular radiation pattern, the FAS of the far-field shear wave displacement can be expressed similarly to Equation 6.31:
(
U (r ,ω ) = RM 0 4πρrβ3
)
[
1 + (ω ω c )
−1
2
]
−1
(6.42)
Using the definition of M0 it can be shown [Brune, 1970] that the corner frequency becomes: ω c = (7 π 4)
1/ 2
(β a) = 2.34 (β a)
(6.43)
Following Brune [1976], the expression for the far-field shear wave RMS acceleration spectrum AFF (r,ω) can be given as:
[ (
A (r , ω ) = R (σβ µ )(a r ) ω 2 ω 2 + (2.34 β a)
)] = R (σβ µ)(a r )[ω (ω
2
2
2
+ ω c2
)]
(6.44)
where R is the scaling factor for the RMS radiation pattern. Figure 6.5 provides a plot of the Brune’s far-field spectrum in log-log coordinates. As can be seen for frequencies less than ωc, the spectral amplitudes decay by ω2. The spectral amplitudes asymptote to a constant level equal to R(σβ/µ)(a/r). The effects of high frequency diminution, not accounted for by Equation 6.44, are indicated by a dashed line in the high frequency regions. Using Equation 6.42 the FAS of the far-field shear wave acceleration can be given as:
(
A (r ,ω ) = RM 0 4πρr β3
)
−1
[
ω 2 1 + (ω ω c )
2
]
−1
(6.45)
Brune [1970, 1976] has shown that if the stress drop is a fraction, ε, of the effective stress ∆σ = ε σ, the low frequency spectral amplitudes of U (r,ω) will be scaled by ε. In frequencies around ωc the spectral amplitudes will decay by ω–1. In high frequencies this decay will be proportional to ω–2, as is the case for ε = 1.
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FIGURE 6.5 Brune far-field S-wave acceleration Fourier amplitude spectrum. (Brune, J.N., 1970, J. Geophys. Res., 75, 4997–5009. Published by the American Geophysical Union.)
6.2.3.2 Haskell’s Model Haskell’s model [Haskell, 1964] considers the propagation of slip to be a ramp-type slip d(t) (i.e., source time function) along a rectangular fault of length L and width W with constant rupture velocity vr . The propagation is along the L direction with instant and constant slip along the W direction. Rupture starts at a point (hypocenter) and when the rupture front reaches to a point on the fault, slip starts and continues until a final offset is reached. The time that it takes to reach the level of final offset is called the rise time. For large magnitude earthquakes rise times may vary from a few seconds to about 10 sec and are much shorter than the total duration of rupture. Fractures that propagate from one end of the fault to the other are called unilateral and those that propagate from the middle to both ends are called bilateral fractures. The Fourier transform of the P-wave displacements, Up(ω), is given by [Udias, 1999]:
[
)]
(
U p (ω ) = W L ω D (ω )(sin cX ) exp − exp (i π 2) (ω r α ) − X − π 2
(6.47)
sin c X = sin X X
[
(6.46)
]
X = − (ωL) (2α ) (α v r − cos φ)
(6.48)
where α is the P-wave propagation velocity, r is the hypocentral distance of the point of observation, and φ is the angle between L direction and the line connecting the hypocenter with the point of observation. D(ω) is the Fourier transform of d(t). For a “ramp-type” source time function:
( )
d (t ) = D t τ r
for 0 < t < τ r
(6.49)
d (t ) = D
for t > τ r
(6.50)
and
where τ r is the rise time that d(t) attains its maximum value D at each point of the fault plane. The Fourier transform of the source time function is given by:
[ ( )][1 − exp (−i ω τ )]
D (ω ) = D ω 2 τ r
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r
(6.51)
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As can be seen from Equations 6.46 and 6.51, Up(ω) is proportional to (L W D), or to seismic moment (M0 = µ L W D), for low frequencies, and decreases as 1/ω2 for high frequencies. If Up(ω) is plotted with respect to log ω, the low frequency flat part can be seen to be separated from the high frequency part decreasing with ω–2 by the corner frequency, ωc . For a particular case of φ = π/2, ωc becomes [Udias, 1999]: ω c = 2 vr L
(6.52)
Shearer [1999] treats the far-field displacement pulse in Haskell’s model as the convolution of two boxcar functions, one with width equal to the rise time, τr , and the other with width equal to the apparent rupture duration time, τd . The resulting far-field displacement pulse will be trapezoid with an area equal to the seismic moment M0 , after corrections for radiation pattern and properties of the medium. Shearer [1999] gives the far-field FAS of this displacement pulse as: U (ω ) = G M 0 sin c (ω τ r 2) sin c (ω τ d 2)
(6.53)
where G is a scaling term that accounts for the radiation pattern and properties of the medium. The plot of log(U(ω)) vs. log(ω) is provided in Figure 6.6 [Shearer, 1999]. The spectrum is divided into three parts by the corner frequencies equal to 2/τr and 2/τd , in the following manner: • A low frequency flat portion proportional to (G M0) for ω < 2/τd • A mid-frequency portion decreasing with ω–1 for 2/τd < ω < 2/τr • A high frequency portion decreasing with ω–1 for 2/τr < ω This spectral model is called the omega-square source model. In empirical spectra observed in most earthquakes, it is not easy to separate the mid-frequency portion, and only one corner frequency can be distinguished.
FIGURE 6.6 Far-field displacement Fourier amplitude spectrum based on Haskell-type source spectrum. (From Shearer, M.P., 1999, Introduction to Seismology, Cambridge University Press, Cambridge. With permission.)
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6-13
FIGURE 6.7 Source parameters and slip distribution in the August 17, 1999 Kocaeli (MW = 7.4) earthquake. (After Yagi, Y. and M. Kikuchi, 2000, http://www.eic.eri.u-tokyo.ac.jp/yuji/PDF/turkey.pdf.)
6.2.4 Complex Source Models (Asperities and Barriers) Brune’s and Haskell’s simple source models assume that the main fault rupture parameters (rupture velocity, rise time, and stress parameters) are homogeneous and coherent over the plane of the dislocation. Recorded strong ground motion (accelerograms), however, indicate that the faulting process is highly heterogeneous, having many complex arrivals and a high frequency content, which cannot be explained by these simple source models. This observation has necessitated the development of complex source models that can account for the variability of stress and fault parameters. Two models have been proposed for this purpose: • The asperity model [Kanamori and Stewart, 1978; Lay et al., 1982; Rudnicki and Kanamori, 1981] • The barrier model [Das and Aki, 1977] Patches on the fault plane with higher slips are called asperities. Asperities are highly stressed regions surrounded by weak or zero stress zones. The fault plane is then composed of patches of high stress and low or zero stress, which leads to a nonuniform stress drop during an earthquake event. During the failure of these asperities, high frequency P waves are radiated. Inversion results of the 1999 Kocaeli, Turkey earthquake indicate two regions with higher slip, which can be called asperities (Figure 6.7). Barriers are identified as those portions of the fault plane that do not rupture. When a rupture propagating over the fault plane reaches these barriers, it is forced to stop suddenly, radiating high frequency stopping phases. Aftershocks tend to occur in the regions of the fault plane corresponding to barriers and are considered as failures of unbroken barriers. This implies that a barrier can become the asperity of a future earthquake on the same fault.
6.3 Time Domain Characteristics of Strong Ground Motion Peak ground acceleration (PGA), velocity (PGV), and displacement (PGD) are the most common and easily recognizable time domain parameters of strong ground motion. For the sake of completeness, these © 2003 by CRC Press LLC
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displacement (cm)
velocity (cm/s)
acceleration (cm/s2)
Sakarya East-West 400 300 200 100 0 -100 -200 -300 -400 0 90 80 70 60 50 40 30 20 10 0 -10 -20 -30 0 240 220 200 180 160 140 120 100 80 60 40 20 0
0
4
8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80
4
8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80
4
8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80
time (s)
FIGURE 6.8. Corrected acceleration, velocity and displacement traces from Sakaraya near-field station during the August 17, 1999 Kocaeli (MW = 7.4) earthquake.
parameters are indicated in Figure 6.8 where time history traces of acceleration, velocity, and displacement of the Sakarya record obtained in the August 17, 1999 Kocaeli (MW = 7.4) earthquake are illustrated. This is a near-fault record from a major strike-slip earthquake, as evidenced by the pulse-like velocity and permanent displacement. This section addresses the modeling of root-mean-square (RMS) acceleration, the duration of the strong ground motion, and the time domain envelope functions.
6.3.1 Modeling of RMS Acceleration Hanks [1979] and McGuire and Hanks [1980] have obtained an estimate of the RMS value of the ground acceleration associated with far-field shear waves through an operation of Parseval’s theorem on the Brune [1970] source model. Hanks and McGuire [1981] provide this estimate as follows:
][ (
[
arms = 2 R (2π) 2 106 ∆ σ ρr 2/3
)] [(Qβ) (πf )]
1/ 2
c
(6.54)
for cases where the anelastic attenuation of the FAS is of the form:
[
]
exp (− πfr ) (Qβ)
(6.55)
In these expressions R is the radiation pattern factor, ∆σ is the stress drop, ρ is density, β is the shear wave propagation velocity, r is the hypocentral distance, Q is the so-called quality factor, and fc is the corner frequency. © 2003 by CRC Press LLC
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Defining fmax = [(Qβ)/(πr)] and assuming 2R = 0.85, Equation 6.54 can be rewritten as:
[
][
][
arms = 2 R (2π) 2 106 ∆ σ (ρr ) f max fc
]
1/ 2
(6.56)
The duration of motion used in the estimates of arms is taken equal to the reciprocal of corner frequency fc . For a fixed value of stress drop equal to 100 bar, Hanks and McGuire [1981] obtained a good fit between the estimated and empirical arms values. For constant stress drop earthquakes the source dependence of arms depends only on (fc)–1/2 or on the square root of the source duration. It can also be shown that under a constant stress drop assumption, arms depends on the one sixth power of moment magnitude. On the basis of a study of several hundred strong ground motion records in California, Hanks and McGuire [1981] found that strong ground motion can be modeled by finite duration, band-limited Gaussian white noise. For a fixed value of ∆σ = 100 bar, the peak ground acceleration (PGA, amax) is given by the following expression with considerable accuracy (less than 50%):
[
]
amax = arms 2 ln (2 f max fc )
1/ 2
(6.57)
Aki [1987] has also developed a model for the estimation of the RMS value of the ground acceleration. Since the local effective stress determines the level of the FAS and the power spectrum of the ground acceleration, for a circular dislocation surface the level of the acceleration power spectrum P0 observed at a distance (r) from the dislocation can be given as [Aki, 1987]: P0 = c W V v r4 ( ∆ σ µ ) (βr ) 2
−2
(6.58)
where W is the fault width, V is the velocity of the rupture front, and vr is the velocity of rupture spreading within a circular crack. If the acceleration is band limited within fc and fmax , the RMS acceleration arms becomes [Aki and Richards, 1980]:
[
]
arms = P0 2 ( f max − fc )
1/ 2
(6.59)
or, approximately,
[
arms = P0 2 f max
]
1/ 2
(6.60)
Since for California earthquakes of magnitude between 5.5 and 7.2, the cut-off frequency fmax is nearly constant at about 4 to 5 Hz [Aki, 1987], the RMS acceleration amplitudes are mainly controlled by the stress drop.
6.3.2 Duration of the Strong Ground Motion Duration of strong ground motion is an important parameter playing a direct role in the destructiveness of an earthquake, and is a function of fault parameters (i.e., size of the rupturing part of the fault, rupture velocity), path from source to station, local site effects (soft soil, basin effects), and directivity. A number of definitions exist in the literature for the duration of the strongest part of shaking [Bommer and Martinez-Pereira, 2000]. Perhaps the most widely used definitions of strong ground motion duration are the (1) bracketed duration and (2) significant duration. The bracketed duration is the interval between the two points in time where the acceleration amplitude first and last exceeds a prescribed level such as 0.03 g [Ambraseys and Sarma, 1967] or 0.05 g [Bolt, 1969]. Significant duration is defined as the time required to build up from 5 to 95% of the integral of (∫ a2 dt) for the total duration of the record, where
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FIGURE 6.9 Bracketed duration and significant duration illustrated for the Sakarya record of the August 17, 1999 Kocaeli (MW = 7.4) earthquake.
a is the acceleration [Trifunac and Brady, 1975]. Arias [1970] showed that this integral is a measure of the energy in the ground motion acceleration. Dobry, Idriss, and Ng [1978] have provided an empirical correlation of magnitude with significant duration, Ts , of strong ground motion: log (Ts ) = 0.423 M − 1.83
(6.61)
The correlation is valid for rock sites in the western United States, and for magnitude ranges 4.5 < M < 7.6. Duration on soil sites may be up to twice the value for rock sites. Bracketed duration and significant duration are shown in Figure 6.9 using the August 17, 1999 Kocaeli, Turkey earthquake Sakarya accelerogram in the form of a Husid [1969] plot. The definition of significant duration is based on energy. For records at large distances from an earthquake source, the bracketed duration will have a smaller value than the significant duration. Boore [2000] defines the duration of the strong ground motion, Td , by: Td = Ts + Tp
(6.62)
where the first term (Ts) denotes the source duration and the second term (Tp ) denotes the path duration. The source duration is given as: Ts = 1 fa [for western North America, Boore, 2000]
(6.63)
Ts = 1 (2 fa ) [for eastern North America, Atkinson and Boore, 1995]
(6.64)
where fa is the first corner frequency of a two-corner frequency source spectra model. Tp is the path duration dependent on the epicentral distance (r). Tp = 0.05 r [for western United States, Boore, 2000] © 2003 by CRC Press LLC
(6.65)
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The following definition of path duration is used for the northeastern United States [Atkinson and Boore, 1995]: Tp = 0
for r < 10 km
Tp = 0.16 (r − 10)
for 10 km < r < 70 km
Tp = 9.6 − 0.03 (r − 70)
for 70 km < r < 130 km
(6.66)
6.3.3 Time Domain Envelope of the Strong Ground Motion The Gaussian white noise time series of duration Tw is windowed using the shape (coda) function, w(t), of Saragoni and Hart [1974], as described in Boore [1983]: w (t ) = an t b exp (−ct ) H (t )
(6.67)
where H(t) is the Heaviside (unit step) function, a is the normalizing factor, and b and c are the shape parameters. Saragoni and Hart [1974] showed that this window is a good representation of the averaged envelope of squared ground motion acceleration, with b and c given as;
] [1 + ε (ln (ε) − 1)]
[
b = − ε ln ( η)
c = b (ε Tw )
(6.68) (6.69)
where ε and η are constants and Tw is the specified duration. The use of the following normalizing factor (an) gives a shape function w(t) with a maximum value of unity:
[
an = exp (1) ε Tw
]
b
(6.70)
Boore [1983, 2000] uses ε = 0.2 and η = 0.05.
6.4 Frequency Domain Characteristics of Strong Ground Motion In the frequency domain, the Fourier amplitude and phase spectrum, power spectrum, and several definitions of response spectra are used in the quantification of strong ground motion. Among these, modeling of the FAS is of prime importance for simulation. Both empirical and theoretical models of Fourier amplitude spectra exist. Trifunac and Lee [1989] provide empirical models for scaling Fourier amplitude spectra in terms of earthquake magnitude, source-to-site distance, site intensity, and recording site conditions. These models are based on the regression of the empirical amplitudes at specific frequencies. This section presents a theoretical model for the FAS of ground motion, involving the elements of source, propagation path attenuation, high frequency diminution, and site amplification, as illustrated in Figure 6.10.
6.4.1 Theoretical Model of the Fourier Amplitude Spectrum The FAS of free field horizontal acceleration at an epicentral distance (r) caused by the propagation of shear waves from an earthquake with a point source slip model is given by Boore [1983], Atkinson and Boore [1998], and Atkinson and Silva [2000]: A ( f , r ) = C0 M 0 S ( f ) Y ( f , r ) P ( f ) Z ( f ) © 2003 by CRC Press LLC
(6.71)
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Elements of the Fourier amplitude spectrum of the earthquake ground motion modeling.
where C0 is the frequency independent scaling factor, M0 is the seismic moment, S(f ) is the source spectrum, Y(f,r) is the attenuation factor, P(f ) is the high frequency decay factor, and Z(f ) is the scaling factor that accounts for the site effects. For the ideal cases where Y(f,r), P(f ), and Z(f ) are not considered, A(f,r) is given by: A ( f , r ) = C0 M 0 S( f )
(6.72)
Equation 6.72 has the same form and is essentially identical to the FAS of the far-field shear wave acceleration given in Equations 6.39, 6.44, and 6.45. The frequency independent scaling factor C0 is expressed as:
(
C0 = ( R P F ) 4 πρβ3
)
(6.73)
where R = 0.55 is the scaling parameter to account for the average radiation parameter, P = 0.707 is the scaling parameter for partition into two horizontal parameters, and F = 2 is the scaling parameter to account for free surface amplification. Density and the shear wave propagation velocity of the medium in the vicinity of the source are indicated, respectively, by ρ(g/cm3) and β(km/sec). Boore [2000] suggests the use of ρ = 2.8 g/cm3 and β = 3.5 km/sec for western North America, and ρ = 2.8 g/cm3 and β = 3.6 km/sec for eastern North America. S(f ) is called the source spectrum, and accounts for the spectral model of the radiated waves from the source. It consists of two parts: the spectral shape and the scaling law (the relationship between the seismic moment and the corner frequency). One of the simplest and most commonly used source spectra with a single corner frequency, fc , is called the omega-squared spectrum, similar to the Brune’s spectral shape given by Equation 6.42. S ( f ) = ( 2π f )
2
(1 + ( f f ) ) 2
(6.74)
c
A generalized form of source spectrum that provides a better fit to the empirical spectral shapes has been proposed by Atkinson and Silva [2000] and Atkinson and Boore [1995]. This spectrum can account for the sag in spectral amplitudes observed at intermediate frequencies in the western United States.
[
(
)] [
(
S ( f ) = Sa ( f ) + Sb ( f ) = (2πf ) 2 (1 − e ) 1 + ( f fa ) 2 + (2πf ) 2 e 1 + ( f fb ) 2
)]
(6.75)
where fa and fb are called, respectively, the low frequency corner frequency and the high frequency corner frequency. For e = 1, the spectra model given in Equation 6.75 converges to Equation 6.74 and becomes identical with the single frequency model, for fa = fc .
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The corner frequency and the seismic moment are related [Brune 1970; also compare with Equation 6.35] by the so-called spectral scaling law: fc = 4.9 × 106 β ( ∆ σ M 0 )
1/3
(6.76)
where ∆σ is in bars (1 bar = 105 Pa) and M0 is the seismic moment in dyn–cm and β is in km/sec. A number of studies have shown that choosing a constant value for ∆σ, depending on the tectonic region, leads to predictions in good agreement with the empirical data [Boore, 1987]. Thus, for constant ∆σ, the source-spectral scaling is only a function of seismic moment. The most important parameter affecting the source is the stress drop, also called the stress parameter. For the central and eastern United States, Frankel [1996] has chosen 150 bar for the stress parameter. As has been shown in Brune [1970] the C M0 S(f ) part of A(f, r) given in Equation 6.72 will behave as M0 fc2 for high frequencies. Similarly, through the use of Equation 6.76:
[
] [
] [
]
A( f , r ) = C M 0 S ( f ) α M 0 fc α M 10/3 ∆σ 2/3 for f > fc
(6.77)
Thus, the FAS of the ground acceleration at near source conditions, at frequencies above the corner frequency, will be proportional to M01/3 ∆σ2/3. The stress drop generally varies between 50 and 150 bar. Assuming a constant stress drop, the corner frequency can be related directly to the seismic moment, Mo, or moment magnitude, MW . log fa = 2.62 − 0.5 MW
[∆σ = 150 bar, Atkinson and Boore, 1998; Frankel, 1996]
(6.78)
log fa = 2.18 − 0.5 MW
(6.79)
log fb = 2.41 − 0.48 MW
(6.80)
log e = 0.605 − 0.255 MW
[For western United States, ∆σ =
80 bar, Atkinson and Silva, 2000]
(6.81)
log fa = 2.41 − 0.533 MW
(6.82)
log fb = 1.43 − 0.188 MW
(6.83)
log e = 2.52 − 0.637 MW
[For middle and eastern United States, Atkinson and Boore, 1995]
(6.84)
The seismic moment M0 and the moment magnitude MW are related with the expression given in Equation 6.2. For eastern North America, region-specific source models (the barrier model) have also been developed [Papageorgiou, 1988], where Y (f, r) is called the attenuation factor: Y ( f , r ) = YG (r )YA ( f , r )
(6.85)
YG (r) is the geometric attenuation factor due to geometric spreading of the seismic energy and YA(r) is the anelastic attenuation.
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At epicentral distances (r) less than about 100 km, empirical evidence indicates a geometric attenuation by (1/r). Atkinson and Silva [2000] state that the geometric attenuation is proportional to (1/r) at epicentral distances less than 40 km but to (1/r)1/2 at epicentral distances greater than 40 km. The functional form of the geometric attenuation term developed by Atkinson and Boore [1995] is shown below: YG (r ) = 1 r YG (r ) = 1 70 1/ 2 YG (r ) = (1 70)(130 r )
for r < 70 km for 70 km < r < 130 km for r > 130 km
(6.86)
YA(f,r) is the anelastic attenuation (or whole-path attenuation) factor given by the following expression:
[
]
YA ( f , r ) = exp (− π f r ) (Q β)
(6.87)
where Q is the so-called quality factor and, in its simplest definition, can be taken as a constant (Q = Q0). Several researchers have shown that Q has a region-specific and frequency-dependent behavior: Q ( f ) = 180 f 0.45 [For western United States, Atkinson and Silva, 2000]
(6.88)
Q ( f ) = 150 f 0.60 [For western North America, Silva and Green, 1989]
(6.89)
Q ( f ) = 680 f 0.36 [For northeastern United States, Atkinson and Boore, 1995]
(6.90)
Q ( f ) = 500 f 0.65 [For eastern North America, Silva and Green, 1989]
(6.91)
Boore [2000] has used a trilinear functional form for Q(f ) in the log Q – log f space. P(f ) serves as the high frequency diminution factor in Equation 6.71, which accounts for the decay of spectral amplitudes at high frequencies, believed to be caused by the weathering in the upper layers of the medium. Boore [1983] assigns a fourth-order Butterworth filter for P(f ):
[
P2 ( f ) = 1 + ( f fm )
]
8 −1/ 2
(6.92)
Anderson and Hough [1984] model P(f ) by the spectral decay factor κ as: P1 ( f ) = exp (− π κ f )
(6.93)
Boore [2000] combines P1(f ) and P2(f ) for the following definition for P(f ): P ( f ) = P1 ( f ) P2 ( f )
(6.94)
The cut-off frequency filter (fm) may vary between 50 Hz [in the northeastern United States; Atkinson and Boore, 1998] and 100 Hz [in the western United States; Frankel, 1996]. The kappa parameter controls the diminution of high frequencies at close to moderate distances controlling peak ground accelerations. The following values have been indicated for the kappa operator:
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κ = 0.01 sec ( very hard rock) to 0.04 sec (firm_ordinary rock) [Boore and Joyner, 1997] κ = 0.066 sec (alluvium) to 0.04 sec (rock ) [ Anderson and Hough, 1984] As an example we will use the FAS model of ground acceleration proposed by Anderson and Hough [1984]:
[
(
A ( f ) = C0 S ( f ) P1 ( f ) = C0 (2πf ) 2 1 + ( f fc )
2
)]exp (−πκf )
(6.95)
to match the spectrum of a record, and to obtain the spectral decay factor (κ) and corner frequency (fc) values through a linear-square fit to the recorded lin-log acceleration spectra following Andrews [1986). Fourier amplitude spectra of the record at Yarimca (August 17, 1999 Kocaeli earthquake) and theoretical spectra are shown together in Figure 6.11, using data recorded at station Yarimca during the Kocaeli earthquake, together with the best fitting values of κ and fc . The match between the recorded and theoretical spectra is remarkable. Z(f ) represents the scaling factor accounting for site effects. Geologic conditions in the upper crust and the general soil conditions in the site vicinity modify the FAS of the ground motion as a function of frequency by factors as high as 3. Although site response analysis methods are well developed, the necessity of obtaining detailed geotechnical information limits their general utilization. In the quarter wavelength approximation method [Joyner et al., 1981], the amplification at a specific frequency (or wavelength) (Aq (f )) is given by the square root of the ratio between the seismic impedance (ρ β) at the site averaged over a depth equal to one quarter of the wavelength and the seismic impedance at the source:
[
]
Aq ( f ) = (ρoβo ) (ρsβs )
1/ 2
(6.96)
where the subscripts o and s indicate site and source media, respectively. The square-root impedance amplification is a first-order approach to complete amplification analysis using rigorous wave propagation theory. Boore and Joyner [1997] provide amplification values as a function of frequency for the assessment of Z(f ) in terms of typical soil profiles associated with NEHRP [1997] site classes. Amplifications for generic very hard rock (v30 = 2900 m/sec), generic rock (v30 = 620 m/sec), generic soil (v30 = 310 m/sec), NEHRP C class (v30 = 520 m/sec), and NEHRP D class (v30 = 255 m/sec) sites are provided in Figure 6.12. The combined effect of site amplification Z(f ) and near-surface attenuation of high frequencies P1(f ), can be seen in Figure 6.13 using κ = 0.003 sec for very hard rock sites and κ = 0.035 sec for other site types.
6.5 Radiation Pattern and Directivity The amplitude and polarity of a seismic wave radiated from an earthquake source changes with the orientation of the source and the receiver. This dependence is termed the radiation pattern. There is a difference in radiation patterns of P and S waves for a point source (Figure 6.14). The effect of an extended fault on the radiation patterns of P and S waves can be seen in the same figure as well. The radiation patterns corresponding to different fault types, such as strike-slip, normal, and reverse are given in Figure 6.15. Imagine a rupture propagating at a certain velocity along a fault plane. Stations located in the direction of rupture propagation experience shorter duration ground motions than stations located in the direction opposite to the direction of rupture. This is called directivity, and is analogous to the Doppler effect in sound. Associated ground motion amplitudes are larger for stations in the forward directivity region
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acceleration (cm/s**2)
August 17, 1999, Kocaeli, Turkey Earthquake Station Yarimca, EW 300 200 100 0 -100 -200 -300 0
2
4
6
8
10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40
time (s)
FIGURE 6.11 Comparison of the empirical and theoretical Fourier amplitude spectra for the Yarimca EW record of the August 17, 1999 Kocaeli (MW = 7.4) earthquake.
than the stations in the backward directivity region, due to conservation of energy. Directivity was observed in the 1979 Imperial Valley earthquake (Figure 6.16). This earthquake was associated with a unilateral rupture propagating in a northwesterly direction and was recorded by a series of accelerographs in the vicinity of the fault. Higher amplitude velocities, with a shorter duration, can be observed in Figure 6.16 as compared to velocities recorded at stations BCR and CXO close to the epicenter. At high period ranges, forward directivity effects at near-fault locations result in high amplitude velocity pulses. The fault normal component of the ground velocity will generally consist of a full-cycle velocity pulse, which upon integration will not create a permanent displacement. However, the fault parallel components will generally have a half-cycle velocity pulse, which creates a permanent absolute displacement equal to the fault offset. These effects can be clearly seen in the acceleration, velocity, and displacement time history traces of the Sakarya record of the August 17, 1999 Kocaeli earthquake, given in Figure 6.8. The station is located about 3 km from the fault trace. The rise time of the displacement is about 3 sec. © 2003 by CRC Press LLC
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5 generic very hard rock, V(30m) = 2900 m/s generic rock, V(30m) = 620m/s NEHRP class C, V(30m) = 520m/s generic soil, V(30m) = 310m/s NEHRP class D, V(30m) = 255m/s
4
Amplification
3
2
1 10−2
10−1
100 frequency, Hz
101
102
FIGURE 6.12 Site amplification factors for various site classes. (After Boore, D.M. and W.B. Joyner, 1997, Bull. Seismol. Soc. Am., 87, 327–341.)
Amplification*e(pi*kappa*f)
3 generic very hard rock, V(30m)=2900 m/s generic rock, V(30m)=620 m/s NEHRP class C, V(30m)=520 m/s generic soil, V(30m)=310 m/s NEHRP class D, V(30m)=255 m/s
2
kappa=0.003 s for very hard rock kappa=0.003 s for others
1 10-2
10-1
100
101
frequency, Hz
FIGURE 6.13 Combined effect of site amplification and κ diminution. (After Boore, D.M. and W.B. Joyner, 1997, Bull. Seismol. Soc. Am., 87, 327–341.)
Theoretically the change in the duration as a result of directivity can be expressed by: t d = L (1 v r − 1 v ) for stations in the forward directivity region, with td L vr v
= apparent rupture duration = the length of the fault propagation takes place on = rupture velocity = vp or vs for P or S waves, respectively
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(6.97)
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FIGURE 6.14 Radiation patterns for P and S waves for a point source. (From Das, S., 1997, Proc. Adv. Stu. Course Seis. Risk., SERINA, ITSAK, pp. 72–100.)
For stations in the backward directivity region td is given by: t d = L (1 v r + 1 v )
(6.98)
The directivity effect of a propagating rupture was effectively demonstrated by Bouchon [1987] using the discrete wave number method. The following parameters were used in the simulations: a unilaterally rupturing, strike-slip fault plane of length 30 km and width 10 km in a homogeneous half space, a ramp-type slip function with a rise time of 0.5 sec, a rupture velocity of 2.2 km/sec, P-wave velocity of 6 km/sec, S-wave velocity of 3.5 km/sec and medium density of 2.8 g/cm3. The simulations were performed for a grid with a total size of 100 km × 50 km consisting of about 1300 sites. In Figure 6.17 snapshots of displacements between 2 and 26 sec are presented at each 4-sec interval for fault parallel, fault perpendicular, and vertical directions. The inset figure in Figure 6.17 shows the source-mediumreceiver configuration used in the model. The rupture starts at the left edge of the fault and propagates to the right. As can be seen, the displacements build up as time progresses and reach their static levels. General observations regarding Figure 6.17 are: displacements have lower-frequency contents and a simpler shape in the fault parallel region than the fault perpendicular displacements, large amplitude and higher-frequency displacements in the fault normal direction exist for a longer distance from the fault trace, and there is an increased radiation of energy in the direction of fault rupture. The same exercise was carried out with the inclusion of a 1.5-km deep sedimentary layer in the model. The fault extends from the base of the sediments to a depth of 10 km. The same half-space parameters were used as before. The results are shown in Figure 6.18. A pronounced effect of directivity can be observed for © 2003 by CRC Press LLC
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FIGURE 6.15 Radiation patterns (focal spheres) for different fault geometries. (From Shearer, M.P., 1999, Introduction to Seismology, Cambridge University Press, Cambridge. With permission.)
sites in the forward directivity region both for fault parallel and fault normal directions. In the fault normal direction, in particular, large amplitude ground displacements are quite striking. This increase in amplitude occurs because the rupture velocity is higher than the S-wave velocity in the sedimentary layer. Luco and Anderson [1985] have studied the near-fault ground motions using a simple theoretical model. The fault is modeled by a finite width, infinitely long, vertical strike-slip dislocation. The fault, buried in a homogeneous half space, extends from a depth of zu = 2 km to zd = 10 km (as illustrated in the inset figures of Figures 6.19, 6.20, and 6.21). The P- and S-wave propagation velocities of the medium are 6 km/sec and 3.464 km/sec. A step-type dislocation of amplitude 100 cm propagates horizontally with a rupture velocity of 3.184 km/sec along the fault. The rupture front is vertical. Fault parallel, fault normal, and vertical acceleration, velocity and displacement time histories at any observation point along the fault for various distances to the surface projection of the fault are shown in Figures 6.19, 6.20, and 6.21. As can be seen, the peak amplitudes occur at distances (about 2 km) comparable to the depth of the top of the fault. Figure 6.20 shows prominent velocity pulses in the fault normal direction. The durations of the acceleration and velocity pulses increase, especially for fault normal components, with distance from the fault. Fault normal displacement and velocities stay approximately constant for fault © 2003 by CRC Press LLC
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FIGURE 6.16 Low-pass filtered ground velocities recorded during the October 15, 1979 Imperial Valley earthquake. The rupture propagated from south to north. (From Archuleta, R.J., 1984, J. Geophys. Res., 86, 4559–4585. Published by the American Geophysical Union.)
distances less than the vertical distance to the top of the fault. The pulse amplitudes are sensitive to the location of the top of the fault relative to the observation point, and inclusion of softer layers at the top of the half-space can lead to substantial amplification factors ranging from 2 to 8 [Bouchon, 1987]. Fault rupture directivity essentially results in spatial variations of ground motion in the vicinity of faults. For design purposes, the variation of the average horizontal response spectra and the difference between the fault normal and fault parallel components of the response spectra in near-fault conditions becomes an important consideration. Somerville et al. [1997] have presented a procedure for the modification of response spectra of near-fault strong ground motion to account for the rupture directivity. The modifications are based on an empirical analysis of limited near-fault data. The modification factor for the spatial variation of average horizontal response spectral acceleration is provided in Figure 6.22 for strike-slip and dip-slip faulting. Definitions of the rupture directivity parameters of X and θ for strike-slip faults and Y and φ for dip-slip faults are indicated in the inset figures. Figure 6.23 provides an empirical model of the ratio of the fault-normal spectral component amplitudes to average spectral amplitudes. Models of this ratio are given for different magnitudes and epicentral distances against period, and for different magnitudes and periods against distance. As can be seen, forward directivity caused larger spectral amplitudes at periods larger than 0.6 sec and the ratio of the fault spectral amplitudes to the average spectral amplitudes can be as high as 1.6 at periods in the vicinity of 6 sec, under favorable forward directivity conditions.
6.6 Simulation of Strong Ground Motion Two types of modeling exist in seismology: forward modeling and inverse modeling. Forward modeling deals with the estimation of ground motion at the ground surface by modeling the earthquake faulting process, the earth medium between the earthquake source and the station, and local site effects near the station, such as modeling of topography, basin structure, and soft soil conditions. Inverse modeling, on the other hand, uses recorded ground motion data and tries to model the earthquake source processes. For engineering purposes, estimation of ground motion at a location, whether it is the future site of an important engineering facility or the site of a future earthquake, is important. Therefore, forward modeling is used on many occasions for strong ground motion estimation, using the results of inverse modeling as input, if available. In the following paragraphs we will deal with forward modeling only. © 2003 by CRC Press LLC
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FIGURE 6.17 Snapshots of ground displacement emanating from the fault rupture shown in the inset figure. Homogeneous half-space. (After Bouchon, M., 1987, in Strong Ground Motion Seismology, M. Erdik and M.N. Toksoz, Eds., NATO ASI Series, D. Reidel, Dordrecht. 185–207.)
Earthquake ground motion is caused by seismic waves, generated by the sudden rupture of a fault, propagating through the earth medium. Therefore, the problem of modeling of strong ground motion consists of modeling of the seismic sources and of the propagation of seismic waves radiated from the source through the earth medium. In most simulation applications, modeling of the source and the earth medium is treated as one integral step. The effect of local site conditions is then reflected in a separate step. © 2003 by CRC Press LLC
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FIGURE 6.18 Snapshots of ground displacement emanating from the fault rupture shown in the inset figure. Homogeneous half-space overlain by a sedimentary layer. (After Bouchon, M., 1987, in Strong Ground Motion Seismology, M. Erdik and M.N. Toksoz, Eds., NATO ASI Series, D. Reidel, Dordrecht. 185–207.)
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FIGURE 6.19 Simulated acceleration time histories associated with the rupture of an infinite strike-slip fault. (After Luco, J.E. and J.G. Anderson, 1985, Strong Ground Motion Simulation and Earthquake Engineering Applications: A Technological Assessment, EERI Publication No. 85-02, 16.1–16.20. Earthquake Engineering Research Institute, Oakland, CA.)
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FIGURE 6.20 Simulated velocity time histories associated with the rupture of an infinite strike-slip fault. (After Luco, J.E. and J.G. Anderson, 1985, Strong Ground Motion Simulation and Earthquake Engineering Applications: A Technological Assessment, EERI Publication No. 85-02, 16.1–16.20. Earthquake Engineering Research Institute, Oakland, CA.)
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FIGURE 6.21 Simulated displacement time histories associated with the rupture of an infinite strike-slip fault. (After Luco, J.E. and J.G. Anderson, 1985, Strong Ground Motion Simulation and Earthquake Engineering Applications: A Technological Assessment, EERI Publication No. 85-02, 16.1–16.20. Earthquake Engineering Research Institute, Oakland, CA.) © 2003 by CRC Press LLC
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FIGURE 6.22 Modification factor for the directivity-related spatial variation of average horizontal response spectral acceleration. (From Somerville, P.G. et al., 1997, Seismol. Res. Lett., 68, 199–222.)
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FIGURE 6.23 Ratio of the fault-normal spectral component amplitudes to average spectral amplitudes. (From Somerville, P.G. et al., 1997, Seismol. Res. Lett., 68, 199–222.)
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There are two types of source models: kinematic and dynamic. In kinematic source models the slip over the rupturing portion of a fault, as a function of fault plane coordinates and of time, is known or given a priori (that is, it is not a function of the causative stresses). In dynamic source models, on the other hand, slip over the rupturing segment of a fault is a function of tectonic stresses acting on the region. In kinematic source models, the final slip distribution over the fault plane, as well as the location and time-specific evolution of slip over it, can be taken from inverse problem solutions, which use recorded data, or can be found by source models such as Haskell’s model. In dynamic source models, shear dislocation or slip is the result of a stress drop in a tectonic region [Kostrov and Das, 1989; Scholz, 1989; Madariaga, 1976]. Slip, its amount, direction, the way the rupture travels over the fault plane (i.e., its velocity and direction) are controlled by surrounding forces in the region, as well as by the material properties of the earth material adjacent to the fault plane. The rupture of a fault takes between a fraction of a second for small earthquakes and several minutes for major events. During the slippage of the fault, waves are generated, varying from frequencies near zero, corresponding to the permanent ground deformation, up to very high frequencies. With the deployment of numerous accelerometers in the near field of causative faults, there has been a definite increase in near-field strong motion data. This has led to an awareness of the existence and importance of coherent, long-period velocity pulses in these regions. The 1994 Northridge and 1995 Kobe earthquake strong motion records reconfirmed the severity of the previously noted long-period pulses associated with severe damage. Passing of the rupture front, or so-called source directivity, causes these large, coherent velocity pulses. Given this, and the needs of the earthquake engineering community, there is a growing trend towards simulation techniques that incorporate broadband ground motions of longer periods, directivity effects, and higher frequencies. For simulation of deterministic ground motion, empirical [e.g., Hartzell, 1978], semi-empirical [e.g., Irikura, 1983; Somerville, 1991], stochastic [e.g., Boore, 1983; Silva et al., 1990], and hybrid methods have been proposed and utilized.
6.6.1 Stochastic Simulations As noted above, high frequency accelerations are highly incoherent, and are the result of irregularities of the rupture front, heterogeneity of co-seismic slip distribution, fault geometry irregularity, propagation transfer, rupture bifurcation, and sudden changes in rupture velocity and slip amplitude. These details are unknown and unpredictable and probably impossible to model in a deterministic manner. Therefore, in strong ground motion simulations the incoherence of ground accelerations is accounted for using stochastic methods. Stochastic approaches to the simulation of strong ground motion filter and window the white-noise time series according to seismologically determined average spectra and duration [Boore, 1983]. This is a widely used and easily applicable method for simulation of higher-frequency motions; however, it lacks low frequency information. In a recent study by Tumarkin and Archuleta [1997], there are efforts towards incorporating the rupture directivity effect into the stochastic method by adjusting the corner frequency, and towards increased low frequency content by the use of a new filter. In this subsection stochastic simulations for point source and finite fault ruptures are presented, with appropriate examples. 6.6.1.1 Stochastic Simulations for Point Source Earthquakes This is essentially an engineering approach to the simulation of strong ground motion. Ground acceleration is modeled as a filtered Gaussian white noise modulated by a deterministic envelope function [Safak, 1988]. The filter parameters are determined by either matching the empirical properties of the spectrum of the strong ground motion [e.g., Trifunac and Lee, 1988], theoretical spectral shapes [i.e., the Kanai-Tajimi spectrum; Housner and Jennings, 1964], or are determined on the basis of reliable physical characteristics of the earthquake source and propagation media [e.g., Hanks and McGuire, 1981; Boore, 1983]. The FAS model used in the latter stochastic simulations is essentially an S-wave ground motion spectrum based on the far-field model of Brune [1970]. It has been found to satisfy the main © 2003 by CRC Press LLC
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parameters of high frequency ground motion for earthquakes within a wide magnitude range [McGuire and Hanks, 1980]. The stochastic simulation of strong ground motions, which relies on seismic source physics, has found substantial applications in earthquake engineering, with successful comparisons of predicted and recorded data. Boore [1983] developed a so-called band-limited white noise model for stochastic simulation of strong ground motion with seismological constraints. In the time-domain procedure, elaborated in Boore [1983], a Gaussian white noise is windowed with a shaping function having a prescribed duration. The window is chosen such that the mean level of the spectrum of the windowed white noise is unity. The windowed time series is transformed into the frequency domain (using the fast Fourier transform; see Brigham, 1988). Its FAS is scaled to the square root of the mean squared absolute spectrum and multiplied by the site-specific shape of the theoretical FAS of the free field acceleration of the horizontal ground motion at the site, A(f,r), given by Equation 6.71. Transformation back into the time domain results in the simulated (synthetic) time history of the horizontal component of the ground motion. For the vertical component of the FAS, Av(f,r), Atkinson and Boore [1995] suggest the following amplitude modulation of the FAS of the horizontal acceleration:
(
Av ( f , r ) = A ( f , r ) 100.0519 f 0.117
)
(6.99)
Boore’s [1983] stochastic simulation methodology has been adopted by Papageorgiou et al. [2000] for application in eastern North America with incorporation of region-specific parameters and a barrier model for the source function. Silva and Lee [1987] employ a similar simulation methodology, using the empirical phase spectrum from an earthquake record instead of Boore’s random phase to generate the synthetic time history. The empirical phase spectrum contains information on the distribution of the energy in the time domain as determined by the source, propagation path, and site conditions. As such it will be ideal to choose a record that satisfies the criteria for magnitude source location and the observation point of the design earthquake. Wong and Trifunac [1978] have employed the dispersive properties of earthquake waves propagating through low velocity layers of the crust to model the phase characteristics of the simulated ground motion. Higher order modes of Love and Rayleigh-wave group velocity dispersion curves are used. Related computer codes for this purpose, such as SMSIM [Boore, 2000], SGMS-ENA [Papageorgiou et al., 2000], and RASCAL [Silva and Lee, 1987], are available to the public. Peak ground motion parameters, such as peak ground acceleration (PGA) and spectral amplitudes, can also be calculated using random vibration theory (RVT). Random vibration theory relates peak parameters in the time domain to RMS parameters [Cartwright and Longuet-Higgins, 1956]. The RMS parameters are calculated using Parseval’s theorem, which relates the total energy in the frequency domain to the total energy in the time domain [Vanmarcke and Lai, 1980]. Using random process theory the relation between the root-mean-square (arms) and the peak motion (amax) of a stochastic acceleration time series can be given as [Boore, 1987]:
[
]
amax arms = 2 ln (N )
1/ 2
(6.100)
where N is the number of extrema in the time series. N can be estimated in terms of the characteristic frequency, fch , and the duration Td : N = 2 fch Td
(6.101)
Since Td is related to the spectral model, amax can be computed from estimated values of fch and arms [Boore, 1987]:
(
)
fch = 1 (2 π) (m2 m0 ) © 2003 by CRC Press LLC
1/ 2
(6.102)
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arms = (m0 Td )
1/ 2
(6.103)
The spectral moments m0 and m2 can be obtained through Parseval’s theorem. The k-th spectral moment (mk) is given by the following expression: mk = 2 (2 π)
k
∞
∫ f 0
k
2 A( f ) df
(6.104)
A substantial number of studies have shown that the use of an omega-squared [Brune 1970] pointsource spectrum with a stochastic ground motion model successfully predicts the ground acceleration for earthquakes in California and elsewhere. However, strong ground motions simulated on the basis of this approach are not intended to be design (or scenario) earthquake-specific triaxial time histories that include near-fault and directivity effects but, rather, a representative motion encompassing general characteristics of source and the propagation path. The procedure also cannot faithfully simulate the low frequency (displacement) components of the ground motion. Software developed originally by Dr. Erdal Safak of the U.S. Geological Survey (Golden, Colorado) with modifications by the authors of this chapter will be used to provide some examples for the simulation of strong ground motion from point sources. The software is written in the MATLAB (http://www.mathworks.com) language and follows, almost exactly, the time-domain procedure developed by Boore [1983] and coded in Boore [2000]. For the example simulations the spectral constants are taken as: Soil density = 2.8 g/cm3 Shear wave velocity = 3.6 km/sec Partition factor for energy = 0.707 Factor for radiation pattern = 0.55 Factor for free surface amplification = 2 For geometric spreading a simple r –1 model is assumed. A single corner frequency ω2-model is used for the spectral shape (Section 6.4.1, Equation 6.74). The frequency-dependent Q model for the wholepath attenuation, plotted in Figure 6.24, is identical to the model used by Boore [2000] for the western United States. Source duration is taken equal to the inverse of the corner frequency and the path duration is modeled as 5% of the epicentral distance. An exponential time windowing function identical to that covered in Section 6.3.3 is used with parameters of: • Effective duration as a fraction of simulation duration for the time window = 1 • Parameter specifying the location of peak (in percent of time window) = 0.2 • Parameter specifying amplitude (in percent of peak) at time window = 0.05 As an illustration, the shape of the exponential time window is plotted in Figure 6.25 for a moment magnitude of MW = 7.6 at an epicentral distance of 100 km. The high frequency diminution function (Section 6.4.1) is modeled by a fourth-order Butterworth filter with a cut-off frequency of fm = 50 Hz and a spectral decay factor κ = 0.035 [Anderson and Hough, 1984]. The diminution function used is plotted in Figure 6.26 as a function of frequency. The local site amplification function used in the simulations is plotted vs. frequency in Figure 6.27. One of the simulations of ground acceleration for a MW = 7.6 earthquake at 20 km epicentral distance is provided in Figure 6.28, together with the match of the averaged Fourier amplitude spectra of 20 simulations with the target spectra. The integrated (and polynomial base-line corrected) velocity and displacement traces of this simulation are provided in Figure 6.29. An example simulation and the match of simulated and target spectra are provided in Figure 6.30 for the same earthquake (MW = 7.6) but at an epicentral distance of 100 km. © 2003 by CRC Press LLC
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FIGURE 6.24
An example of frequency-dependent Q-model for the whole path attenuation.
FIGURE 6.25
Exponential time window shape for a MW = 7.6 earthquake at 100-km epicentral distance.
6-37
FIGURE 6.26 Shape of the high frequency diminution factor modeled by a fourth-order Butterworth filter with a cut-off frequency of 50 Hz and a spectral decay factor κ = 0.035.
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FIGURE 6.27
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Frequency-dependent variation of the amplification factor.
For illustration purposes, simulated accelerations and spectral comparisons at an epicentral distance of 10 km for magnitudes of MW = 4, 5, 6, and 7 are provided in Figures 6.31(a) to (d). 6.6.1.2 Stochastic Simulations for Finite Fault Rupture Earthquakes Beresnev and Atkinson [1997] have developed a procedure (FINSIM) for the stochastic simulation of strong ground motion from finite fault ruptures. The fault rupture plane is modeled with an array of subfaults. The radiation from each subfault is modeled as a point source with a ω2-spectrum, similar to Boore [1983]. The fault rupture initiates at the hypocenter and spreads uniformly along the fault plane with a constant rupture velocity triggering radiation from subfaults in succession. Simulations from each subfault, properly lagged and summed at the observation point, provide the simulation of ground motion from the modeled finite fault rupture. The size of the subfaults controls the overall spectral shape at medium frequencies. Optimal subfault size (∆l) is given as [Beresnev and Atkinson, 1999]: log ( ∆1) = −2.0 + 0.4 MW
(6.105)
The total number of subfaults is controlled by the constraint that the total seismic moment of the subfaults must be equal to the target seismic moment. To provide an example for stochastic simulation of strong ground motion from finite fault ruptures, the accelerations recorded by near-field stations during the August 17, 1999 (MW = 7.4) Kocaeli (Turkey) earthquake will be simulated using the code FINSIM developed by Beresnev and Atkinson [1997]. An isometric view of the fault rupture plane, location of the epicenter, and the recording stations at Yarimca, Izmit, and Adapazari are indicated in Figure 6.32. The geometry of the fault rupture plane and the relative distribution of slip have been adopted from the slip model developed by Yagi and Kikuchi [1999] for the Kocaeli earthquake (Figure 6.7). The fault dislocation is modeled as an 110-km long, 20-km deep, vertical plane with subfaults of size 5 × 5 km. Rupture velocity is 2.7 km/sec. The distribution of the relative slip values used as input for the simulation and the absolute slip values used by the program are indicated in Figure 6.33. For the whole-path attenuation a crustal Q model of Q(f ) = 180 f 0.45 is adopted, as reported by Atkinson and Silva [2000] for the western United States (Equation 6.88). For site amplification, frequencydependent amplification function values provided by Boore and Joyner [1997] using the NEHRP site class for each station are used (Section 6.4.1, Figures 6.12 and 6.13). As for the near surface attenuation, kappa (κ) values of 0.07, 0.05, and 0.03 are employed for the Yarimca, Izmit, and Sakarya stations, respectively. The factor that controls the strength of subfault radiation (sfact) is 1.5 for simulations in Izmit and Sakarya stations, and 2.0 in Yarimca. A Saragoni and Hart [1974]-based envelope function is used for radiation from subfaults, similar to Boore [1983]. © 2003 by CRC Press LLC
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FIGURE 6.28 A stochastic simulation of horizontal ground acceleration and the comparison of average simulated and theoretical Fourier amplitude spectra (MW = 7.6 earthquake at 20-km epicentral distance); accelerations are given in cm/sec2.
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FIGURE 6.29 A stochastic simulation of horizontal ground acceleration, velocity and displacement time histories. Polynomial base-line adjustment is used after integration (MW = 7.6 earthquake at 20-km epicentral distance).
Simulated accelerations for the Yarımca, Izmit, and Sakarya stations are presented in Figure 6.34. Spectral accelerations averaged over five simulations can be seen in Figure 6.35. For comparison, we also show empirical spectral accelerations (from the August 17, 1999 earthquake) in the same figure. Using this model, it was possible to get a very satisfactory fit of spectral accelerations with the recorded data (Figure 6.35). Peak accelerations are somewhat lower than the recorded ones. Simulated peak horizontal accelerations are 226 cm/sec2, 186 cm/sec2, and 334 cm/sec2 for Yarimca, Izmit, and Sakarya stations, respectively. The code FINSIM inherently cannot account for the differences in the ground motion as a result of polarity. Calculated peak accelerations are to be considered horizontal accelerations. Therefore it is believed that the calculated accelerations are satisfactory. Respective velocities calculated from the accelerations using a polynomial baseline correction are 28 cm/sec, 21 cm/sec, and 25 cm/sec for the Yarimca, Izmit, and Sakarya stations. © 2003 by CRC Press LLC
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FIGURE 6.30 A stochastic simulation of horizontal ground acceleration and the comparison of average simulated and theoretical Fourier amplitude spectra (MW = 7.6 earthquake at 100-km epicentral distance); accelerations are given in cm/sec2.
© 2003 by CRC Press LLC
Earthquake Engineering Handbook
FIGURE 6.31 Stochastic simulations of horizontal ground acceleration and comparisons of average simulated and theoretical Fourier amplitude spectra. (a) MW = 4; (b) MW = 5; (c) MW = 6; (d) MW = 7 at 10 km epicentral distance; accelerations are given in cm/sec2.
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(a)
FIGURE 6.31 (CONTINUED)
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(b)
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FIGURE 6.31 (CONTINUED)
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(c)
FIGURE 6.31 (CONTINUED)
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(d)
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FIGURE 6.32 Fault rupture geometry, hypocenter, and the location of the recording stations in the August 17, 1999 Kocaeli (MW = 7.4) earthquake.
6.6.2 Deterministic Simulation Models A number of different methods have been used for the deterministic simulation of strong ground motion, including the three-dimensional finite difference method, discrete wave-number method, indirect boundary element method, modal summation method, ray theory, 2.5-D discrete wave number-boundary integral equation method, 2.5-D pseudo-spectral method, and the 2.5-D finite difference method. Essentially, all of these deterministic methods convolve the source function with synthetic Green’s functions to produce the motion at ground surface. The first theoretical treatment of the simulation of ground motion was presented by Lamb [1904]. He calculated the seismogram considering propagation of waves caused by an arbitrary point source in a semi-infinite isotropic elastic solid. His solution was consistent with the case of long-period waves, and insensitive to the small scale inhomogeneities in the earth media. With the introduction of the force-dislocation equivalence theorem, which stated that the displacement field due to shear dislocation on an infinitesimal surface element is the same as the one obtained by a double-couple applied at the element without any dislocation, it was possible to analytically express the displacement field through the earth medium, provided that the displacement discontinuity on the fault plane is known. The displacement field then was the space-time convolution of the source function with the so-called Green’s function — that is, the earth’s response to a double-couple or, in seismological terms, to a point source. Rupture propagation was modeled by introducing a time delay. Knopoff and Gilbert [1959] introduced the propagating unit step function, and Haskell [1964] the propagating ramp function with a rise time. Recorded near-field displacements during the 1966 Parkfield, California earthquake were synthesized successfully by Aki [1968] and Haskell [1969] for an infinite earth medium. The problem of propagating waves through horizontal earth layers was approached by Thomson [1950] and Haskell [1953], who developed a matrix formalism. Dunkin’s [1965] matrix formulation of wave propagation through layered media avoided numerical difficulties in the modal calculations. Chouet [1987] introduced a method for computation of synthetics for an arbitrary seismic source embedded in a stratified medium. Bouchon and Aki [1977] presented the discrete wave-number representation of seismic wave fields. Bouchon [1979] introduced the discrete wave number representation of elastic wave fields in three space dimensions. Haskell introduced the first source model, as a ramp-type kinematic source function described by the amount of final slip and rise time. The slip modeled as a ramp function propagates unilaterally along a rectangular fault at a constant rupture velocity [Haskell, 1964, 1966]. Dynamic source models [Brune, 1970; Madariaga, 1976] were based on describing the faulting using the stress changes on the fault plane. Stochastic source models exist as well [AIJ, 1993]; however, they lack a physical basis in quantifying the randomness. In the barrier model of Papageorgiou and Aki [1983], the fault plane is covered by circular cracks of equal diameter separated by unbroken barriers. Individual circular cracks rupture randomly, yielding a random Fourier phase spectrum. Deodatis et al. [1990a, 1990b], using the spectral representation method, analytically derived the frequency-wave number spectra in an elastic homogeneous half-space for a point source. A seismic source in a layered half-space described by Haskell’s model was introduced in the formulation by Theoharis © 2003 by CRC Press LLC
0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0
0.0 2.0 0.0 0.0
0.0 0.0 0.0 0.0
1.0 2.0 1.0 0.0
3.0 3.0 2.0 0.0
4.0 4.0 3.0 0.0
3.0 6.0 4.0 2.0
3.0 7.0 6.0 3.0
3.0 5.0 6.0 3.0
3.0 3.0 3.0 2.0
4.0 2.0 0.0 0.0
4.0 2.0 0.0 0.0
4.0 2.0 0.0 0.0
5.0 3.0 0.0 0.0
5.0 3.0 0.0 0.0
4.0 3.0 0.0 0.0
3.0 2.0 0.0 0.0
2.0 2.0 0.0 0.0
0.0 0.0 0.0 2.0
0.0 0.0 0.0 0.0
5.4 2.3 0.0 0.0
5.4 2.3 0.0 0.0
5.4 2.3 0.0 0.0
6.1 3.8 0.0 0.0
6.1 3.8 0.0 0.0
5.4 3.8 0.0 0.0
3.8 2.3 0.0 0.0
2.3 2.3 0.0 0.0
0.0 0.0 0.0 2.3
0.0 0.0 0.0 0.0
Absolute Slip Values (in m) over the Fault Plane Computed by Finsim 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0
0.0 2.3 0.0 0.0
0.0 0.0 0.0 0.0
1.5 2.3 1.5 0.0
3.8 3.8 2.3 0.0
5.4 5.4 3.8 0.0
3.8 7.7 5.4 2.3
3.8 8.4 7.7 3.8
3.8 6.1 7.7 3.8
3.8 3.8 3.8 2.3
FIGURE 6.33 Distribution of relative slip values on the dislocation surface and the absolute slips computed by the FINSIM routine. (After Yagi, Y. and M. Kikuchi, 2000, http://wwweic.eri.u-tokyo.ac.jp/yuji/PDF/turkey.pdf.)
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Relative Slip Values over the Fault Plane Provided as Input (after Yagi and Kikuchi, 2000)
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Yarimca velocity (cm/sec)
400 300 200 100 0 -100 -200 -300 -400 0
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5
10
15
20
25
30
35
40
45
50
Yarimca
30 20 10 0 -10 -20 -30
0
5
10
15
time (sec)
Izmit velocity (cm/sec)
400 300 200 100 0 -100 -200 -300 -400 0
25
30
35
40
45
50
Izmit
30 20 10 0
-10 -20
5
10
15
20
25
30
35
40
45
50
-30 0
5
10
15
time (sec) 400 300 200 100 0 -100 -200 -300 -400 0
20
time (sec)
Sakarya velocity (cm/sec)
acceleration (cm/sec**2) acceleration (cm/sec**2) acceleration (cm/sec**2)
6-48
5
10
15
20
25
30
35
40
45
50
20
25
30
time (sec)
35
40
45
50
Sakarya
30 20 10 0 -10 -20 -30
time (sec)
0
5
10
15
20
25
30
35
40
45
50
time (sec)
FIGURE 6.34 Simulated accelerations and velocities at stations Yarimca, Izmit and Sakarya for Kocaeli earthquake using code FINSIM.
[1991], Theoharis and Deodatis [1994], and Deodatis and Theoharis [1994]. They have used a discrete wave number approach in conjunction with a propagator-based formalism based on the work of Bouchon [1979], Dunkin [1965], and Chouet [1987]. Deodatis and Zhang [1993a, 1993b] used the barrier model as the source function. Zhang [1995] introduced the random medium and the random boundary formulation into layered half-space modeling. The finite difference method first used by Madariaga [1976] to study earthquake rupture is an efficient way of studying wave propagation in heterogeneous elastic media. The method has been used successfully in the simulation of ground motion for past earthquakes [Olsen et al., 1997], for estimation of ground motion due to a future event, as well as for basin modeling [Olsen, 2000; Graves et al., 1998; Graves, 1996].
6.6.3 Empirical Green’s Function Method The general concept of the empirical Green’s function method [Hartzell, 1978] is to account for realistic path and site effects by using observed records of so-called subevent small earthquakes originating within the rupture area of the simulated large earthquake, which can individually represent heterogeneities, asperities, etc. For the validity of this approach, all subevents must have focal mechanisms similar to that of the simulated main event. That is, empirical Green’s function methods use micro earthquakes as point dislocation Green’s functions, assuming that the focal mechanisms and propagation paths of the small and large earthquakes are identical. The method is valid up to the corner frequency of small earthquakes used in the simulation of large earthquakes, and depends on the availability of micro earthquake data. Since the method utilizes real recordings associated with a subsection of a fault, small event data already contain all the information about the physical processes involved in the problem, such as source effects, seismic energy radiation, anelastic wave propagation, scattering by random heterogeneities, the effect of the Earth’s surface, and local site effects. The main shock or a future large event expected on the fault is found by moment scaling of small events, correction for radiation pattern, introducing a lag time for modeling of rupture propagation along the fault, and possibly a correction for site conditions if the original data are from sites with different site conditions. A schematic presentation of the method can © 2003 by CRC Press LLC
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Yarimca average response spectrum over 5 trials 1.000
spectral acceleration (cm/sec2)
500
100
50
Yarimca simulated Yarimca EW, recorded Yarimca NS, recorded 10 0.1
1
10
100
freq (Hz)
Izmit average response spectrum over 5 trials 1.000
spectral acceleration (cm/sec2)
500
100
50
Izmit, simulated Izmit EW, recorded Izmit NS, recorded 10 0.1
1
10
100
freq (Hz)
Sakarya average response spectrum over 5 trials
spectral acceleration (cm/sec2)
1.000
500
100
50
Sakarya, simulated Sakarya EW, recorded 10 0.1
1
10
freq (Hz)
FIGURE 6.35
Comparison of simulated and recorded acceleration response spectra.
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OBSERVED SUBEVENTS WAVEFORMS
SIMULATED MAIN EVENT 100
10 0 −10 0 −10 0 −10 0 −10 0 −10
50 0 −50 −100
STATION
PATHS OBSERVED SUBEVENTS
FAULT SURFACE OF THE SIMULATED EVENT
FIGURE 6.36 A schematic simulation of empirical Green’s function method. (From Tumarkin, A.G. and R.J. Archuleta, 1994, Proc. Int. School Earthquake Source. Mech., Special Issue, 37, 159–188. With permission.)
be seen in Figure 6.36 and in Figure 6.37, where the simulation of a large earthquake is modeled as a rupture of properly scaled and lagged subevents. The choice of method to sum the subevent records to obtain the prediction is the most challenging part of this approach [Hartzell, 1978; Irikura, 1983; Joyner and Boore, 1986]. Usually, the empirical Green’s function method considers a single observed subevent in order to simulate the ground motions for an anticipated main event. This subevent is replicated many times to obtain a distribution of similar subevents covering the expected rupture area of the main event. Using only one initial record allows the predictions to have a strong dependence on the characteristics of the input record. Consequently, there is a large variation in results, simply due to the choice of the subevent [Dan et al., 1990]. Hadley and Helmberger [1980] found very good fit with the observed data in the 1966 Parkfield earthquake, using the empirical Green’s function method. Hutchings [1991] demonstrated the empirical Green’s function method of Hutchings and Wu [1990] by “predicting” actual recorded ground motion from the Loma Prieta earthquake. Hutchings’ method has also been applied to predict the 1988, M = 6.0, Saguenay earthquake (Hutchings et al., 1997a), an M = 7.25 earthquake along the Sanyi-Tungshih-Puli seismic zone [Hutchings et al., 1997b], and an M = 7.2 earthquake along the Gulf of Corinth, Greece [Hutchings et al., 1997c]. The limitation of the empirical Green’s function method is that it cannot account for nonlinear soil effects, and ground motions are estimated at prescribed locations where the smaller event data are recorded.
6.6.4 Hybrid Simulation Methods Deterministic theoretical predictions of ground motion can be achieved by convolution of the Green’s function and the slip function. Green’s functions can be calculated through empirical and synthetic means. Although certain predictions can be made for the total slip and the mode of faulting, no prediction can be made regarding the rupture characteristics. This necessitates the consideration of different rupture models. Such deterministic predictions cannot be extended into the frequency regions above about 1 Hz, © 2003 by CRC Press LLC
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FIGURE 6.37 A schematic simulation of empirical Green’s function method. (From Rosset, P. and J.J. Wagner, 2000, Proc. European Conf. Global Change Catastrophe Risk Management: Earthquake Risks in Europe, International Institute for Applied Systems Analysis, Laxenburg, Austria. With permission.) © 2003 by CRC Press LLC
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since high frequency ground motions are controlled by the heterogeneities in the fault rupture, which cannot be accounted for a priori in a deterministic manner. This requires either the use of stochastic source models or the stochastic treatment of the high frequency component of the ground motion. Thus, hybrid procedures are developed for simulation of strong ground motion, which address the low and high frequency components of the ground motion separately and then combine the two motions. Several hybrid techniques have been proposed. They are common in the deterministic simulation of ground motion in the low frequency region up to 1–2 Hz at most, and differ in simulation and incorporation of the high frequency components of strong ground motion. Wald et al. [1997] combine the finite-fault methodology of Hartzell and Heaton [1983] for long-period deterministic simulation ground motion with actual acceleration recordings, after filtering out the short periods from the synthetics and the long periods from actual recordings. Papageorgiou et al. [1997] simulate the low frequency part by the discrete wave number method of Bouchon [1979], use an empirical Green’s function method for simulation of intermediate and high frequencies, and superpose the two. Irikura and Kamae [1996] calculate low frequency motions for point sources numerically, find corresponding high frequency motions following Boore [1983], combine the two and determine ground motions due to a large earthquake by summing these hybrid Green’s functions following the empirical Green’s function method. Hutchings et al. [1997] synthesized strong ground motion along the Sanyi-Tungshih-Puli seismic zone by combining synthetic Green’s functions computed by Kennett’s reflectivity code [Kennett, 1983] with empirical Green’s functions. Wenzel [2001, private communication] employs a combination of the threedimensional finite difference method with empirical Green’s functions. In the hybrid broadband simulation procedure adopted by Somerville et al. [2000], the source is represented by an empirical source time function. For simulations of ground motion for frequencies below 1 Hz, a theoretically rigorous representation of radiation pattern, rupture directivity, and wave propagation effects are incorporated in Green’s function computations. At higher frequencies, stochastic simulation techniques that include source radiation pattern and scattering in the path and site are utilized. In a recent paper Erdik and Durukal [2001] applied a hybrid method to simulate strong ground motion for a container port facility near the Sapanca segment of the North Anatolian Fault (Figure 6.38). Low frequency ground motion (DC 1 Hz) calculated with the help of the discrete wave number method was combined with stochastically simulated high frequency components using a methodology proposed by Boore [1983]. The basic tenets of the simulation procedure were chosen to: 1. Preserve the deterministic displacement shape 2. Satisfy the corresponding theoretical FAS 3. Yield a coda shape in conformance with applicable empirical findings An additional goal was that the peak ground acceleration (PGA) and the pseudo spectral relative velocity (PSRV) values should compare favorably with those obtained from empirical attenuation relationships for conformity. The essential elements of the procedure were: 1. Assessment of the source parameters of the design basis earthquake motion associated with the corresponding return period for specific conditions of site and seismicity. 2. Deterministic assessment of the low frequency (DC t. 1 Hz) ground motion, at the outcrop of a reference soil layer, due to rupture of seismic faults. 3. Use of a Boore [1983]-type stochastic simulation method to complement the deterministic low frequency ground motion with high frequency (1 to 50 Hz) components. 4. Combination of the two parts of ground motion to yield a site-specific simulation for a frequency range of DC 50 Hz. 5. Site response analysis, if required, to include the local wave propagation effects in the soil media above the reference soil layer. The August 17, 1999 Kocaeli, Turkey earthquake provided a unique opportunity to test the simulation results, which were carried out before that date. Tectonics of the area, location of strong motion stations, and the location of the container port facility are presented in Figure 6.38. © 2003 by CRC Press LLC
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FIGURE 6.38 Geometry of the fault rupture, properties of the medium, and the dislocation surface used in the hybrid simulation.
The properties of the medium, dislocation surface, and the rupture patterns assumed for the simulation of low frequency ground motion are indicated in the inset figures. The design basis simulation is controlled by a bilateral rupture of the 70 × 15 km Sapanca segment. A Haskell-type ramp function is considered as the slip function with a rupture velocity of 2.8 km/sec, 1 sec rise time, 1.5 m final strike slip, and 0.05 m final dip slip. Figure 6.39 provides the simulated low frequency (<1 Hz) fault parallel, fault normal, and vertical velocity and displacements. The final broadband hybrid simulations, which involved the combination of low (deterministic) and high frequency (stochastic) simulations at the competent soil outcrop, are given in Figure 6.40. The 80-m deep soft soil layers at the top of the competent soil media necessitated the use of a nonlinear site response analysis to obtain the free-field ground motions, which are indicated in Figure 6.41. These simulations were performed prior to the August 17, 1999 Kocaeli earthquake, which essentially hit the same region and site with the same design earthquake level. Considering that the simulations represent a “blind test,” the comparison of the recorded accelerations, velocities, and displacements, as well as of spectral accelerations, provide a remarkable fit to the simulations [Erdik and Durukal, 2001]. © 2003 by CRC Press LLC
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(a) FIGURE 6.39
Simulated low-frequency ground motion on competent soil (bilateral rupture on Sapanca segment).
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(b) FIGURE 6.39 (CONTINUED)
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(a) FIGURE 6.40 Hybrid simulation of broad-band strong ground motion on competent soil (bilateral rupture on Sapanca segment).
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(b) FIGURE 6.40 (CONTINUED)
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FIGURE 6.41 Horizontal surface acceleration, velocity, and displacement traces obtained on the basis of nonlinear site-response analysis. Input motion is the hybrid simulated ground motion given in Figure 6.40.
Defining Terms Acceleration time history — A paired data set or series of acceleration values versus time. Accelerogram — A record showing acceleration as a function of time. Accelerometer — An instrument for measuring acceleration as a function of time. Amplification — Modification of the input bedrock ground motion by the overlying unconsolidated materials.
Amplitude (wave) — The maximum height of a wave crest or depth of a trough. Arias intensity — A ground motion parameter derived from an accelerogram and proportional to the integral over time of the acceleration squared.
Asperities (fault) — Roughness on the fault surface subject to slip. Attenuation — Decrease in amplitude and change in frequency content of the seismic waves with distance, because of geometric spreading, energy absorption, and scattering.
Bar — Unit of pressure equal to 1 atmosphere, or 100 kilopascal. © 2003 by CRC Press LLC
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Barrier — A portion of the fault surface unusually resistant to slip. Body wave — Waves that propagate in the interior of a body (P and S waves). Corner frequency — Frequency where the high and low frequency trends of a spectrum intersect. Crust — The Earth’s outermost layer. Directivity — An effect of a propagating fault rupture whereby earthquake ground motion in the direction of propagation is more severe than that in other directions from the earthquake source.
Elastic dislocation theory — In seismology, a theoretical description of how an elastic Earth responds to fault slip, as represented by a distribution of displacement discontinuities.
Elastic rebound theory — The theory of earthquake generation proposing that faults remain locked while strain energy slowly accumulates, and then slip suddenly, radiating seismic waves. Originally proposed by H. Reid [1911]. Epicenter — The point on the Earth’s surface vertically above the hypocenter. Fault — A fracture or fracture zone along which displacement has occurred parallel to the fracture. Fault plane — The plane that coincides with the rupture surface of a fault. Fmax — The frequency above which little seismic energy is observed at most strong-motion stations. Focus — see Hypocenter. Fourier amplitude spectrum (FAS) — The relative amplitude at different component frequencies that are derived from a time history by Fourier analysis. Fourier transform — The mathematical operation that converts a time function into a function of frequency, and vice versa. Frequency — Number of cycles occurring per unit time. Gaussian distribution — Normal distribution in statistics. Gaussian noise spectrum — The spectrum of a time history whose sample values are generated by random selection from a normal or Gaussian statistical population that has a specified mean and standard deviation. Geometrical attenuation — That component of attenuation of seismic-wave amplitudes due to the radial spreading of seismic energy with distance from a given source. Green’s function — Green’s function characterizes the response of the Earth to a point source earthquake. Through a summation process it is used as a building block to simulate ground motion from a more general source. Half space — A mathematical model bounded only by one plane surface. Hypocenter — The point within the Earth that marks the origin of the elastic waves of an earthquake (also termed the focus). Love waves — Seismic surface waves with only horizontal shear motion transverse to the direction of propagation. Moment magnitude — Magnitude, MW , of an earthquake determined from the seismic moment. Near-field motion — Ground motion recorded in the vicinity of a fault. P wave — Body wave in which the direction of the particle motion is the same as the direction of wave propagation. Period (wave) — The time interval between successive crests in a sinusoidal wave train; the period is the inverse of the frequency of a cyclic event. PGA — Peak ground acceleration. Phase — The angle of lag or lead (or the displacement) of a harmonic wave with respect to a reference. Power spectrum — A graph of power spectral density versus frequency. Q — An index of the dissipative nature of the earth’s transmission path on propagating seismic waves. Also called quality factor. Rayleigh wave — Seismic surface wave with ground motion only in a vertical plane containing the direction of propagation of the waves. Response spectrum — The peak response of a series of simple harmonic oscillators of different natural period, when subjected to a particular input motion. © 2003 by CRC Press LLC
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Root mean square — Square root of the mean squared value of a variable. Rupture front — The instantaneous boundary between the slipping and locked parts of a fault during an earthquake. Rupture velocity — The velocity at which the fault rupture propagates along the fault length. S wave (shear wave) — Body wave in which the particle motion is at right angles to the direction of wave propagation. Seismic moment — A measurement of earthquake size related to the double couple forces across the area of the fault slip. Slip model — A kinematic model that describes the amount, distribution, and timing of slip associated with an earthquake. Slip rate — The rate of movement of the two sides of a fault slipping relative to one another, as determined from geodetic measurements, from offset man-made structures, or from offset geologic features whose age can be estimated. Source — The released forces that generate seismic waves, also called the earthquake source. Source function — The ground motion generated at the fault during rupture. Stochastic — Adjective denoting processes having random characteristics. Stress drop — Initial shear stress acting across a fault plane minus the residual shear stress across the same fault plane after occurrence of slippage. Strike-slip fault — A fault in which movement is principally horizontal. Strong motion — Ground motion of sufficient amplitude and duration to be potentially damaging to man-made structures. Surface faulting — Displacement that reaches the Earth’s surface during slip along a fault. Synthetic acceleration time history — An acceleration time history that is not recorded during an actual earthquake but is developed, using analytical and theoretical methods, to be representative of an acceleration time history that could be recorded during an earthquake. Wave length — Distance between two consecutive wave fronts. White noise — Random energy containing all frequency components in equal proportions.
References Abrahamson, N.A., 1998, “Non-stationary Spectral Matching Program RSPMATCH,” PG&E Internal Report, San Francisco, CA. AIJ (Architectural Institute of Japan), 1993, Earthquake Motions and Ground Conditions, AIJ, Maruzen Company Ltd, Tokyo. Aki, K., 1966, “Generation and Propagation of G Waves from Niigata Earthquake of June 16, 1964. Estimation of Earthquake Movement, Released Energy and Stress-Strain Drop from G Wave Spectrum,” Bull. Earthquake Res. Inst., 44, 23–86. Aki, K., 1968, “Seismic Displacements Near a Fault,” J. Geophys. Res., 73, 5359–5376. Aki, K., 1972, “Earthquake Mechanisms,” Tectonophysics, 13, 423–446. Aki, K., 1987, “Strong Motion Seismology,” in Strong Ground Motion Seismology, M. Erdik and M.N. Toksoz, Eds., NATO ASI Series, D. Reidel, Dordrecht. Aki, K. and P.G. Richards, 1980, Quantitative Seismology: Theory and Methods, W.H. Freeman, New York. Ambraseys, N.N. and Sarma, S.K., 1967, “The Response of Earth Dams to Strong Earthquakes,” Geotechnique, 17, 181–283. Anderson, J.G. and S.E. Hough, 1984, “A Model for the Shape of the Fourier Amplitude Spectrum of Acceleration at High Frequencies,” Bull. Seismol. Soc. Am., 74, no. 5, 1969–1993. Archuleta, R.J., 1984, “A Faulting Model for the 1979 Imperial Valley Earthquake,” J. Geophys. Res., 86, 4559–4585. Arias, A., 1970, “A Measure of Earthquake Intensity,” in Seismic Design for Nuclear Power Plants, R. Hanson, Ed., Massachusetts Institute of Technology Press, Cambridge, MA.
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Atkinson, G.M., 1993, “Earthquake Source Spectra in Eastern North America,” Bull. Seismol. Soc. Am., 83, 1778 –1796. Atkinson, G.M., 1995, “Attenuation and Source Parameters of Earthquakes in the Cascadia Region,” Bull. Seismol. Soc. Am., 85, 1327–1342. Atkinson, G.M. and D.M. Boore, 1995, “Ground Motion Relations for Eastern North America,” Bull. Seismol. Soc. Am., 85, 17–30. Atkinson, G.M. and D.M. Boore, 1998, “Evaluation of Models for Earthquake Source Spectra in Eastern North America,” Bull. Seismol. Soc. Am., 88, 917–934. Atkinson, G.M. and W. Silva, 2000, “Stochastic Modeling of California Ground Motions,” Bull. Seismol. Soc. Am., 90, 255–274. Benioff, H., 1955, “Mechanism and Strain Characteristics of the White Wolf Fault as Indicated by the Aftershock Sequence,” Calif. Div. Mines Bull., 171, 199–202. Beresnev, I.A. and G. Atkinson, 1999, “Generic Finite-Fault Model for Ground Motion Prediction in Eastern North America,” Bull. Seismol. Soc. Am., 89, 608–625. Beresnev, I. and G. Atkinson, 1997, “Modeling Finite Fault Radiation from the ωn Spectrum,” Bull. Seismol. Soc. Am., 87, 67–84. Bolt, B., 1969, “Duration of Strong Motion,” Proceedings of the Fourth World Conference on Earthquake Engineering, pp. 1304–1315, Chilean Association on Seismology and Earthquake Engineering, Santiago, Chile. Bommer, J.J. and A. Martinez-Pereira, 2000, “Strong Motion Parameters: Definition, Usefulness and Predictability,” Proceedings of the Twelfth World Conference on Earthquake Engineering, p. 206, Auckland, New Zealand, February. Boore, D.M., 1977, “The Motion of the Ground in Earthquakes,” Sci. Am., Dec. Boore, D.M., 1983, “Stochastic Simulation of High-Frequency Ground Motions Based on Seismological Models of the Radiated Spectra,” Bull. Seismol. Soc. Am., 73, 1865–1894. Boore, D.M., 1984, “Use of Seismoscope Records to Determine Ml and Peak Velocities,” Bull. Seismol. Soc. Am., 74, 315–324. Boore, D.M., 1986a, “Short-period P- and S-Wave Radiation from Large Earthquakes: Implications for Spectral Scaling Relations,” Bull. Seismol. Soc. Am., 76, 43–64. Boore, D.M., 1986b, “The Effect of Finite Bandwidth on Seismic Scaling Relationships,” in Earthquake Source Mechanics, S. Das, J. Boatright, and C. Scholz, Eds., Geophysical Monograph 37, American Geophysical Union, Washington, D.C., 275–283. Boore, D.M., 1987, “The Prediction of Strong Ground Motion,” in Strong Ground Motion Seismology, M. Erdik and M.N. Toksoz, Eds., NATO ASI Series, D. Reidel, Dordrecht. Boore, D.M., 1996, “SMSIM–Fortran Programs for Simulating Ground Motions from Earthquakes: Version 1.0,” U.S. Geological Survey Open-File Report, 96–80-A and 96–80-B, 73. Boore, D.M., 2000, SMSIM–Fortran Programs for Simulating Ground Motions From Earthquakes: Version 2.0 — A Revision of OFR 96–80-A, U.S. Geological Survey Open File Report OF 00–509. Boore, D.M., 2001, “Prediction of Ground Motion Using the Stochastic Method,” Pure Appl. Geophys., in press. Boore, D.M. and G.M. Atkinson, 1987, “Stochastic Prediction of Ground Motion and Spectral Response Parameters at Hard-Rock Sites in Eastern North America,” Bull. Seismol. Soc. Am., 77, 440–467. Boore, D.M. and J. Boatwright, 1984, “Average Body-Wave Radiation Coefficients,” Bull. Seismol. Soc. Am., 74, 1615–1621. Boore, D.M. and W.B. Joyner, 1984, “A Note on the Use of Random Vibration Theory to Predict Peak Amplitudes of Transient Signals,” Bull. Seismol. Soc. Am., 74, 2035–2039. Boore, D.M. and W.B. Joyner, 1991, “Estimation of Ground Motion at Deep-Soil Sites in Eastern North America,” Bull. Seismol. Soc. Am., 81, 2167–2185. Boore, D.M. and W.B. Joyner, 1997, “Site Amplification for Generic Soil Sites,” Bull. Seismol. Soc. Am., 87, 327–341.
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Boore, D.M., W.B. Joyner, and L. Wennerberg, 1992, “Fitting the Stochastic ω–2 Source Model to Observed Response Spectra in Western North America: Trade-off ’s between ∆σ and κ,” Bull. Seismol. Soc. Am., 82, 1956–1963. Bouchon, M., 1979, “Discrete Wave Number Representation of Elastic Wave Fields in Three-Space Dimensions,” J. Geophys. Res., 84, 3609–3614. Bouchon, M., 1987, “Numerical Simulation of Earthquake Ground Motion,” in Strong Ground Motion Seismology, M. Edik and M.N. Toksoz, Eds., NATO ASI Series, D. Reidel, Dordrecht, 185–207. Bouchon, M. and K. Aki, 1977, “Discrete Wave Number Representation of Seismic Source Wave Fields,” Bull. Seismol. Soc. Am., 67, 259–277. Brigham, E., 1986, The Fast Fourier Transform and Its Applications, Prentice-Hall, New York. Brune, J.N., 1970, “Tectonic Stress and the Spectra of Seismic Shear Waves from Earthquakes,” J. Geophys. Res., 75, 4997–5009. Brune, J.N., 1971, “Correction,” J. Geophys. Res., 76, 5002. Brune, J.N., 1976, “The Physics of Earthquake Strong Motion,” in Seismic Risk and Engineering Decisions, C. Lomnitz and E. Rosenblueth, Eds., Elsevier, Amsterdam. Brune, J.N. and A. Anooshehpoor, 1997, Strong Ground Motion Expected from Large Normal Fault Earthquakes Based on Evidence from Precarious Rocks and Source Modeling, Basin and Range Province Seismic Hazards Summit: Program and Abstracts, Reno, NV, p. 36. Cartwright, D.E. and M.S. Longuet-Higgins, 1956, “The Statistical Distribution of the Maxima of a Random Function,” Proc. R. Soc. London Ser. A (Math. Phys. Sci.), 237, 212–232. Chopra, A.K., 2000, Dynamics of Structures: Theory and Applications to Earthquake Engineering, 2nd ed., Prentice-Hall, Englewood Cliffs, NJ. Chouet, B., 1987, “Representation of an Extended Seismic Source in a Propagator Based Formalism,” Bull. Seismol. Soc. Am., 77, 14–27. Converse, A.M., 1992, “BAP — Basic Strong-Motion Accelerogram Processing Software,” Version 1.0, U.S. Geological Survey Open-File Report, 92-296A. Dan, K., T. Watanabe, K. Tanaka, and R. Sato, 1990, “Stability of Earthquake Ground Motion Synthesized by Using Different Small-Event Records as Empirical Green’s Functions,” Bull. Seismol. Soc. Am., 80, 1433–1455. Das, S., 1997, “Far Field Radiation from an Earthquake Source,” Proc. of the Advanced Study Course on Seismic Risk, SERINA, ITSAK, pp. 72–100. Das, S. and K. Aki, 1977, “Fault Plane with Barriers: A Versatile Earthquake Model,” J. Geophys. Res., 82, 5648–5670. Deodatis, G. and M. Shinozuka, 1988, “Autoregressive Model for Non-stationary Stochastic Processes,” J. Eng. Mech., 114, 1995–2012. Deodatis, G. and A.P. Theoharis, 1994, “Seismic Ground Motion in a Layered Half-Space due to a Haskell Type Source. II. Applications,” Soil Dyn. Earthquake Eng., 13, 293–301. Deodatis, G. and R. Zhang, 1993, Seismic Ground Motion Generation Using a Specific Barrier Model Description of the Seismic Source, Final technical report, Department of Civil Engineering and Operations Research, Princeton University, Princeton, NJ. Deodatis, G., M. Shinozuka, and A. Pagageorgiou, 1990a, “Stochastic Wave Representation of Seismic Ground Motion. I. F-K spectra,” J. Eng. Mech., 116, 2363–2379. Deodatis, G., M. Shinozuka, and A. Pagageorgiou, 1990b, “Stochastic Wave Representation of Seismic Ground Motion. I. Simulation,” J. Eng. Mech., 116, 2381–2399. Dobry, R., I.M. Idriss, and E. Ng, 1978, “Duration Characteristics of Horizontal Components of StrongMotion Earthquake Records,” Bull. Seismol. Soc. Am., 68, 1487–1520. Dunkin, J.W., 1965, “Computation of Modal Solutions in Layered, Elastic Media at High Frequencies,” Bull. Seismol. Soc. Am., 55, 335–356. Ellis, G.W. and A.S. Cakmak, 1991, “Time Series Modelling of Strong Ground Motion from Multiple Event Earthquakes,” Soil Dyn. Earthquake Eng., 10, 42–54.
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Erdik, M. and E. Durukal, 2001, “A Hybrid Procedure for the Assessment of Design Basis Earthquake Ground Motion for Near-Fault Conditions,” Soil Dyn. Earthquake Eng., 21, no. 5, 431–443. Frankel, A., C. Mueller, T. Barnhard, D. Perkins, E. Leyendecker, N. Dickman, S. Hanson, and M. Hopper, 1996, “National Seismic Hazard Maps: Documentation June 1996,” U.S. Geological Survey OpenFile Report, 96-532, p. 69. Gasparini, D.A. and E.H. Vanmarcke, 1976, Simulated Earthquake Motions Compatible with Prescribed Response Spectra, Department of Civil Engineering, Research Report R76–4, Masschusetts Institute of Technology, Cambridge, MA. Graves, R.W., 1996, “Simulating Realistic Earthquake Ground Motions in Regions of Deep Sedimentary Basins”, Proceedings of the 11th World Conference on Earthquake Engineering, Acapulco, Mexico, Pergamon, Elsevier Science, Oxford. Graves, R.W., A. Pitarka, and P.G. Somerville, 1998, “Ground Motion Amplification in the Santa Monica Area: Effects of Shallow Basin Edge Structure,” Bull. Seismol. Soc. Am., 88, 1224–1242. Gutenberg, B., 1955, “Magnitude Determination for Larger Kern County Shocks, 1952: Effects of Station Azimuth and Calculation Methods,” Calif. Div. Mines Bull., 171, 171–175. Hadley, D. and D.V. Helmberger, 1980, “Simulation of Strong Ground Motions,” Bull. Seismol. Soc. Am., 70, 617–630 Hanks, T.C., 1982a, “The Dynamic Characteristics of Faulting Inferred from Recordings of Strong Ground Motion,” U.S. Geological Survey Open-File Report 82–591. Hanks, T.C., 1982b, “Fmax,” Bull. Seismol. Soc. Am., 72, 1867–1879. Hanks, T.C. and H. Kanamori, 1979, “A Moment Magnitude Scale,” J. Geophys. Res., 84, 2348–2350. Hanks, T.C. and R.K. McGuire, 1981, “The Character of High-Frequency Strong Ground Motion,” Bull. Seismol. Soc. Am., 71, 2071–2095. Hao, H., 1989, Effects of Spatial Variation of Ground Motions on Large Multiply-Supported Structures, Report No: UCB/EERC-89/06, Earthquake Engineering Research Center, University of California, Berkeley, CA. Hartzell, S.H., 1978, “Earthquake Aftershocks as Green’s Functions,” Geophys. Res. Lett., 5, 1–4. Hartzell, S.H. and T.H. Heaton, 1983, “Inversion of Strong Ground Motion and Teleseismic Waveform Data for the Fault Rupture History of the 1979 Imperial Valley, California Earthquake,” Bull. Seismol. Soc. Am., 73, 1553–1583. Haskell, N.A., 1953, “The Dispersion of Surface Waves on Multilayered Media,” Bull. Seismol. Soc. Am., 43, 17–34. Haskell, N.A., 1964, “Total Energy and Spectral Density of Elastic Wave Radiation from Propagating Faults,” Bull. Seismol. Soc. Am., 54, 1811–1844. Haskell, N.A., 1966, “Total Energy and Energy Spectral Density of Elastic Wave Radiation from Propagating Faults. II. A Statistical Source Model,” Bull. Seismol. Soc. Am., 56, 125–140. Haskell, N.A., 1969, “Elastic Displacements in the Near Field of a Propagating Fault,” Bull. Seismol. Soc. Am., 59, 865–906. Herrmann, R.B., 1996, Computer Programs in Seismology, Department of Earth and Atmospheric Sciences, St. Louis University, St. Louis, MO. Housner, G.W. and P.C. Jennings, 1964, “Generation of Artificial Earthquakes,” ASCE J. Eng. Mech. Div., 90, 113–150. Husid, R.L., 1969, “Analisis De Terremotos: Analisis General,” Rev. IDIEM, 8, no. 1, 21–42. Hutchings, L., 1988, “Modeling Strong Earthquake Ground Motion with an Earthquake Simulation Program EMPSYN That Utilizes Empirical Green’s Functions,” UCRL-ID-105890, Lawrence Livermore National Laboratory, Livermore, CA, p. 122. Hutchings, L., 1991, “‘Prediction’ of Strong Ground Motion for the 1989 Loma Prieta Earthquake Using Empirical Green’s Functions,” Bull. Seismol. Soc. Am., 81, 88–121. Hutchings, L. and F. Wu, 1990, “Empirical Green’s Functions from Small Earthquakes — A Waveform Study of Locally Recorded Aftershocks of the San Fernando Earthquake,” J. Geophys.
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Hutchings, L., S. Japre, P. Kasameyer, and W. Foxall, 1997a, “Validation of a Ground Motion Synthesis and Prediction Methodology for the 1988, M = 6.0, Saguenay Earthquake,” NCEER Workshop on Ground Motion Methodologies for the Eastern United States, Memphis, TN, October 16–17. Hutchings, L., F.T. Wu, S. Jarpe, P. Kasameyer, and W. Foxall, 1997b, Strong Ground Motion Synthesis Along the Sanyi-Tungshih-Puli Seismic Zone Using Empirical Green’s Functions, 1997 Central Weather Bureau 100th Anniversary International Conference on Weather Analysis and Forecasting, March 3–5. Hutchings, L., G.N. Stavrakakis, E. Ioannidou, F.T. Wu, S. Jarpe, and P. Kasameyer, 1997c, “Strong Ground Motion Synthesis for a M = 7.2 Earthquake in the Gulf of Corinth, Greece Using Empirical Green’s Functions,” 29th IASPEI General Assembly, Thessaloniki, Greece, August 18–26. Irikura, K., 1983, “Semiempirical Estimation of Strong Ground Motions during Large Earthquakes,” Bull. Disast. Res. Inst., Kyoto University, 33, 63–104. Irikura, K. and K. Kamae, 1996, Estimation of Strong Ground Motion Using Hybrid Green’s Function, Fundamental Research for the Mitigation of Urban Disasters by Near-Field Earthquakes, Graduate School of Civil Engineering, Kyoto University, p. 5. Joyner, W.B., 1984, “A Scaling Law for the Spectra of Large Earthquakes,” Bull. Seismol. Soc. Am., 74, 1167–1186. Joyner, W.B. and D.M. Boore, 1986, “On Simulating Large Earthquake by Green’s-Function Addition of Smaller Earthquakes,” in Earthquake Source Mechanics, Maurice Ewing, Ser., S. Das et al., Eds., American Geophysical Union, Washington, D.C., 6, 269–274. Joyner, W.B. and D.M. Boore, 1988, “Measurement, Characterization and Prediction of Strong Ground Motion, Earthquake Engineering and Soil Dynamics, II. Proc. Am. Soc. Civil Eng. Geotech. Eng. Div. Specialty of, June 27–30, Park City, UT, pp. 43–102. Joyner, W.B., R.E. Warrick, and T. Fumal, 1981, “The Effect of Quaternary Alluvium on Strong Ground Motion in the Coyote Lake, California, Earthquake of 1979,” Bull. Seismol. Soc. Am., 71, 1333–1349. Kanamori, H., 1977, “The Energy Release in Great Earthquakes,” J. Geophys. Res., 82, 2921–2987. Kanamori, H. and D.L. Anderson, 1975, “Theoretical Basis of Some Empirical Relations in Seismology,” Bull. Seismol. Soc. Am., 65, 1073–1095. Kanamori, H. and G.S. Stewart, 1978, “Seismological Aspects of the Guatemala Earthquake of February 4, 1976,” J. Geophys. Res., 83, 3427–3434. Kanamori, H., P.C. Jennings, D. Helmberger, R. Clayton, K. Singh, L. Astiz, and E. Mena, 1983, “Estimation of Ground Motions in Mexico City,” Proc. Ninth World Conf. Earth. Eng., vol. 8, Japan Association of Earthquake Disaster Prevention, Tokyo, pp. 43–49. Keilis-Borok, V.I., 1957, “Investigation of the Mechanisms of Earthquakes,” Sov. Res.Geophys., 4. Kennett, B.L.N., 1983, Seismic Wave Propagation in Stratified Media, Cambridge University Press, Cambridge. Knopoff, L. and F. Gilbert, 1959, “Radiation from a Strike-slip Fault,” Bull. Seismol. Soc. Am., 49, 163–176. Kostrov, B. and S. Das, 1989, Principles of Earthquake Source Mechanics, Cambridge University Press, New York. Lamb, H., 1904, “On the Propagation Tremors at the Surface of an Elastic Solid,” Philos. Trans. R. Soc. London, A203, 1–42. Lay, T., H. Kanamori, and L. Ruff, 1982, “The Asperity Model and the Nature of Large Subduction Zone Earthquakes,” Earthquake Prediction Res., 1, 3–71 Liu, L. and S. Pezeshk, 1999, “An Improvement on the Estimation of Pseudo Response Spectral Velocity Using RVT Method,” Bull. Seismol. Soc. Am., 89, 1384–1389. Luco, J.E. and J.G. Anderson, 1985, Strong Ground Motion Simulation and Earthquake Engineering Applications, A Technological Assessment, EERI Publication No: 85–02, 16.1–16.20, Earthquake Engineering Research Institute, Oakland, CA. Madariaga, R., 1976, “Dynamics of an Expanding Circular Fault,” Bull. Seismol. Soc. Am., 66, 639–667. McGuire, R.K. and T.C. Hanks, 1980, “RMS Acceleration and Spectral Amplitudes of Strong Ground Motion during the San Fernando, California, Earthquake,” Bull. Seismol. Soc. Am., 70, 1907–1919. © 2003 by CRC Press LLC
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McGuire, R.K., G.R. Toro, and W.J. Silva, 1988, “Engineering Model of Earthquake Ground Motion for Eastern North America,” EPRI Final Report NP-6074, prepared by Risk Engineering, Inc. for the Electric Power Research Institute, Palo Alto, CA. Olsen, K.B., 2000, “Site Amplification in the Los Angeles Basin from Three-Dimensional Modeling of Ground Motion,” Bull. Seismol. Soc. Am., 90, no. 63, S77–S94. Olsen, K.B., R. Madariaga, and R.J. Archuleta, 1997, “Three-Dimensional Dynamic Simulation of the 1992 Landers Earthquake,” Science, 278, 834–838. Olson, J.A., 1986, “Seismicity of the San Andreas Fault Zone in the San Francisco Peninsula Area: California,” Bull. R. Soc. NZ, 24, 87–97. Papageorgiou, A.S. and K. Aki, 1983, “A Specific Barrier Model for the Quantitative Description of Inhomogeneous Faulting and the Prediction of Strong Ground Motion. I. Description of the Model,” Bull. Seismol. Soc. Am., 73, 693–722. Papageorgiou, A.S., B. Zhang, and G. Dong, 1997, “Estimation of Strong Ground Motion from the Great 1964 Prince William Sound Earthquake,” Seismol. Res. Lett., 68, 325. Papageorgiou, A., B. Halldorsson, and G. Dong, 2000, Strong Ground Motion Simulation Code for Eastern North America SGMS-ENA: User Manual, Version 1.0, Department of Civil, Structural and Environmental Engineering, State University of New York at Buffalo. Press, W.H., S.A. Teukolsky, W.T. Vetterling, and B.P. Lannery, 1992, Numerical Recipes in FORTRAN: The Art of Scientific Computing, Cambridge University Press, Cambridge. Reid, H.F., 1911, The Elastic-Rebound Theory of Earthquake, University of California Publications in the Geological Sciences, vol. 6, University of California, Berkeley, pp. 413–444. Rosset, P. and J.J. Wagner, 2000, “Deterministic Approach to Assess Seismic Hazard: Contribution for an Integrated Assessment of Risk in the Alpine Context,” Proceedings of the EuroConference on Global Change and Catastrophe Risk Management: Earthquake Risks in Europe, International Institute for Applied Systems Analysis, Laxenburg, Austria, 6–9 July 2000. (http://www.iiasa.ac.at/Research/ RMS/july2000/Papers/rosset0821.pdf). Rudnicki, J.W. and H. Kanamori, 1981, “Effect of Fault Interaction on Moment, Stress Drop and Strain Energy Release,” J. Geophys. Res., 86, 1785–1793. Safak, E., 1988, “Analytical Approach to Calculation of Response Spectra from Seismological Models of Ground Motion,” Earthquake Eng. Struc. Dyn, 16, 121–134. Saragoni, G.R. and G.C. Hart, 1974, “Simulation of Artificial Earthquakes,” Earthquake Eng. Struct. Dyn., 2, 249–267. Savage, J.C., 1966, “Radiation from a Realistic Model of Faulting,” Bull. Seismol. Soc. Am., 56, 577–592. Scholz, C., 1989, The Mechanics of Earthquakes and Faulting, Cambridge University Press, New York. Shearer, M.P., 1999, Introduction to Seismology, Cambridge University Press, Cambridge. Silva, W.J. and R.K. Green, 1989, “Magnitude and Distance Scaling of Response Spectral Shapes for Rock Sites with Applications to North American Tectonic Environment,” EarthquakeSpectra, 5, 591–624 Silva, W.J., R. Darragh, C. Stark, I. Wong, J.C. Stepp, J.F. Schneider, and S.-J. Chiou, 1990, “A Methodology to Estimate Design Response Spectra in the Near-source Region of Large Earthquakes Using the Band-Limited-White-Noise Ground Motion Model,” Proc. 4th U.S. Natl. Conf. Earth. Eng., vol. 1, pp. 487–494. Silva, W.J. and K. Lee, 1987, “WES RASCAL Code for Synthesizing Earthquake Ground Motions,” Stateof-the-Art for Assessing Earthquake Hazards in the United States, Report 24, U.S. Army Engineers Waterways Experiment Station, Misc., S-73–1. Somerville, P.G., M.K. Sen, and B. Cohee, 1991, “Simulation of Strong Ground Motions Recorded During the 1985 Michoacan, Mexico and Valparasio, Chile Earthquakes,” Bull. Seismol. Soc. Am., 81, 1–27. Somerville, P.G., N.F. Smith, R.W. Graves, and N.A. Abrahamson, 1997, “Modification of Empirical Strong Motion Attenuation Relations to Include the Amplitude and Duration Effects of Rupture Directivity,” Seismol. Res. Lett., 68, 199–222. Somerville, P., R. Graves, and N. Collins, 2000, Ground Motions for Site Response Estimates: 1906 Earthquake, Report no. 2000/05, Pacific Earthquake Engineering Research Center, Berkeley. © 2003 by CRC Press LLC
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Spudich, P., J.B. Fletcher, M. Hellweg, J. Boatwright, C. Sullivan, W.B. Joyner, T.C. Hanks, D.M. Boore, A. MsGarr, L.M. Baker, and A.G. Lindh, 1997a, “SEA96: A New Predictive Relation for Earthquake Ground Motions in Extensional Tectonic Regimes,” Seismol. Res. Lett., 68, 190–196. Spudich, P., J.B. Fletcher, M. Hellweg, J. Boatwright, C. Sullivan, W.B. Joyner, T.C. Hanks, D.M. Boore, A. MsGarr, L.M. Baker, and A.G. Lindh, 1997b, Earthquake Ground Motions in Extensional Regimes, Basin and Range Province Seismic Hazards Summit: Program and Abstracts, Reno, NV, p. 32. Theoharis, A.P., 1991, “Wave Representation of Seismic Ground Motion,” Ph.D. thesis, Department of Civil Engineering and Operations Research, Princeton University, Princeton, NJ. Theoharis, A. and G. Deodatis, 1994, “Seismic Ground Motion in a Layered Half-Space due to a HaskellType Source. I. Theory,” Soil Dyn. Earthquake Eng., 13, no. 4, 281–292. Thomson, W.T., 1950, “Transmission of Elastic Waves through a Stratified Earth Medium,” J. Appl. Phys., 21, 89–93. Todorovska, M.I. and M.D. Trifunac, 1997, “Amplitudes, Polarity and Time of Peaks of Strong Ground Motion during the 1994 Northridge, California Earthquake,” Soil Dyn. Earthquake Eng., 16, 235–256. Toro, G.R., 1985, “Stochastic Model Estimates of Strong Ground Motion,” Section 3 of Seismic Hazard Methodology for Nuclear Facilities in the Eastern United States, Report prepared for EPRI, Project Number P101–29, Electric Power Research Institute, Palo Alto, CA. Trifunac, M.D., 1976, “Preliminary Empirical Model for Scaling Fourier Amplitude Spectra of Strong Ground Acceleration in Terms of Earthquake Magnitude, Source to Station Distance and Recording Site Conditions,” Bull. Seismol. Soc. Am., 66, 1342. Trifunac, M.D. and A.G. Brady, 1975, “A Study on the Duration of Strong Earthquake Ground Motion,” Bull. Seismol. Soc. Am., 65, 581–626. Trifunac, M.D. and V.W. Lee, 1989, “Empirical Models for Scaling Fourier Amplitude Spectra of Strong Ground Acceleration in Terms of Earthquake Magnitude, Source to Station Distance, Site Intensity and Recording Site Conditions,” J. Soil Dyn. Earthquake Eng., 8, no. 3, 110–125. Tumarkin, A. and R. Archuleta, 1997, “Stochastic Ground Motion Modeling Revisited,” Seismol. Res.Lett., 68, 312. Tumarkin, A.G. and R.J. Archuleta, 1994, “Empirical Ground-Motion Prediction,” Ann. Geofis., Special Issue, Proc. of the International School on Earthquake Source Mechanics, September 1–7, Erice, Sicily, vol. 37, pp. 159–186. Udias, A., 1999, Principles of Seismology, Cambridge University Press, Cambridge. Uhrhammer, R.A. and E.R. Collins, 1990, “Synthesis of Wood-Anderson Seismograms from Broadband Digital Records,” Bull. Seismol. Soc. Am., 80, 702–716. Vanmarcke, E.H. and S.P. Lai, 1980, “Strong-Motion Duration and RMS Amplitude of Earthquake Records,” Bull. Seismol. Soc. Am., 70, no. 4, 1293–1307. Wald, D.J, T.H. Heaton, and K.W. Hudnut, “Estimation of Uniformly Spaced, Near-Source, Broadband Ground Motions for the 1994 Northridge Earthquake from Forward and Inverse Modeling,” CURE Proceedings, Los Angeles, CA, 1997. Wong, H.L. and M.D. Trifunac, 1978, “Synthesizing Realistic Ground Motion Accelerograms,” Report No: CE 78–07, Department of Civil Engineering, University of Southern California, Los Angeles, CA. Yagi, Y. and M. Kikuchi, 2000, “Source Rupture Process of the Kocaeli, Turkey Earthquake of August 17, 1999, Obtained from the Joint Inversion of Near-Field Data and Teleseimic Data” (online: http://wwweic.eri.u-tokyo.ac.jp/yuji/PDF/turkey.pdf). Zhang, L., 1995, “Seismic Waves in an Imperfect Earth Medium,” Ph.D. thesis, Department of Civil Engineering and Operations Research, Princeton University, Princeton, NJ.
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Further Reading For further reading, the following journals, conference and workshop proceedings, and texts are recommended, all of which can be found in university libraries: Applied Technology Council, ATC-15, 1994. Proceedings of Seminar on New Developments in Earthquake Ground Motion Estimation and Implications for Earthquake Resistant Design. Scholl, R. and J.L. King, Eds., 1985. Strong Ground Motion Simulation and Earthquake Engineering Applications: A Technological Assessment, EERI 1985–2002, Earthquake Engineering Research Institute, Oakland, CA. Bolt, B., Ed., 1987. Seismic Strong Motion Synthetics, Academic Press, New York. Erdik, M. and M.N. Toksoz, Eds., 1987. Strong Ground Motion Seismology, NATO ASI Series, D. Reidel, Dordrecht. Proceedings of International Conference on Earthquake Engineering (various years, organized by International Association for Earthquake Engineering, Tokyo, Japan). Proceedings of U.S. National Conference on Earthquake Engineering (various years, organized by Earthquake Engineering Research Institute, Oakland, CA). Proceedings of European Conference on Earthquake Engineering (various years, organized by European Association for Earthquake Engineering) Bulletin of Seismological Society of America, El Cerrito, CA. Earthquake Engineering and Structural Dynamics, Wiley (International Journal) Soil Dynamics and Earthquake Engineering, Elsevier (International Journal)
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7 Geotechnical and Foundation Aspects 7.1 7.2 7.3
Introduction Seismic Hazards Strong Ground Motion Characterization of Strong Ground Motion · Site-Specific Soil and Topographic Effects · Design Ground Motions
7.4 7.5
Dynamic Soil Behavior Liquefaction General Concepts · Magnitude Scaling Factors and Other Corrections · Liquefaction Settlement · Shear Strength of Liquefied Soil
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Horst G. Brandes University of Hawaii, Honolulu
Seismic Analysis of Slopes and Dams Earthquake-Resistant Design of Retaining Walls Soil Remediation Techniques for Mitigation of Seismic Hazards Defining Terms References Further Reading
7.1 Introduction Most earthquakes involve a sudden release of energy as rock masses in the Earth’s crust fracture due to tectonic faulting. Some are also associated with volcanic processes, landslides, large explosions, or even ground loading from the filling of large reservoirs. Following an earthquake, energy propagates outward from the source in the form of elastic seismic waves . The duration, amplitude, and frequency characteristics of these waves are a function of the type and magnitude of the earthquake, the distance from the epicenter , and the type and distribution of geologic materials through which the waves travel. Structures located along the way are subject to shaking and may experience damage or even fail catastrophically. Whereas the broad field of earthquake engineering deals with all of these aspects, the perspective of geotechnical engineers is often more site-specific, dealing with issues relating to the propagation of seismic waves through soil and rock layers close to the ground surface, the effects that shaking has on ground displacements and stresses, as well as on civil engineering structures such as dams, slopes, retaining walls, foundations, and lifelines. A proper understanding of geotechnical earthquake engineering principles is necessary for rational and sound earthquake-resistant design. The focus of this chapter is on geotechnical aspects. The reader is directed to the rest of this volume for additional topics on earthquake engineering. Geologists, seismologists, and geophysical scientists have addressed earthquakes in earnest for at least 100 years, although they have been concerned primarily with low-intensity seismic effects. Geotechnical earthquake engineering is a comparatively younger discipline. Significant progress has only been made
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FIGURE 7.1 National Strong Motion Program recording stations as of April 10, 2002. (Courtesy National Strong Motion Program, U.S. Geological Survey)
in the past 30 to 40 years, especially after the 1971 San Fernando earthquake, when large numbers of strong motion sensors were installed to record high-magnitude earthquakes of the type that can cause damage to civil engineering structures. Understanding of the effects of strong ground shaking is now advancing rapidly because of the placement of large networks of digital sensors in seismically active regions of the world, including the United States, Japan, Taiwan, Europe, and elsewhere. Data sets from earthquakes outside the United States are becoming increasingly more accessible. The U.S. Geological Survey (USGS) operates the National Strong Motion Program (http:// nsmp.wr.usgs.gov), which oversees a network of more than 900 instruments located at approximately 628 permanent stations throughout North America, Hawaii, and the Caribbean (Figure 7.1). Records of strong motion can be obtained from the USGS for selected earthquakes dating back as far as 1933. Strong motion records are also available from other government agencies, such as the California Geological Survey (http://docinet3.consrv.ca.gov/csmip/) and the National Oceanic and Atmospheric Administration (http://www.ngdc.noaa.gov/seg/hazard/strong.html). Various universities and research institutions also maintain strong motion databases, including the University of California at Berkeley (http://peer.berkeley.edu/smcat/), the University of Washington (http://www.geophys.washington.edu/SEIS/ PNSN/SMO/), the Lamont-Doherty Observatory (http://www.Ideo.columbia.edu/nceer/nceer.html), and the University of California at Santa Barbara (http://db.cosmos-eq.org/), among others. A number of recent earthquakes have provided an unprecedented wealth of new data that are currently the focus of intense study. This has already resulted in a better understanding of how local soil conditions affect ground motions, liquefaction, and the dynamic behavior of structures. Additional developments are certain to follow in the years to come [Finn, 2000].
7.2 Seismic Hazards Earthquakes can be tremendously deadly and expensive, with large economic and social effects. Earthquake engineering is concerned with correctly identifying and minimizing seismic hazards and risk © 2003 by CRC Press LLC
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FIGURE 7.2 Building that collapsed during the 1999 Turkey (Kocaeli) earthquake due to liquefaction of the subsurface with little or no damage to the structure itself. (Courtesy J. P. Bardet)
FIGURE 7.3 Building heavily damaged during the 1999 Taiwan (Chi-Chi) earthquake. Intense shaking caused the failure of load-bearing columns in the lower floors. (Courtesy J. P. Bardet)
through increased public awareness, sensitive land development policies, and implementation of technically sound seismic building codes. Past earthquakes have shown that the effects of strong ground shaking are diverse but can broadly be divided into two classes depending on whether they lead to permanent ground displacements or not. Damage to constructed structures can occur in either case. The distinction between the two types of distress is illustrated in Figures 7.2 and 7.3. The first image shows a building that collapsed during the 1999 Turkey (Kocaeli) earthquake due to liquefaction of the subsurface, with © 2003 by CRC Press LLC
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FIGURE 7.4 Ground cracks that developed during the July 1990 Philippines earthquake. (Courtesy EQE International)
little or no damage to the structure itself. In contrast, Figure 7.3 shows a building that was heavily damaged due to the collapse of a portion of the two lower floors during the 1999 Taiwan (Chi-Chi) earthquake. In this case, there was no evidence of large residual ground displacements. Intense shaking caused the failure of load-bearing columns in the lower floors. Among the hazards associated with permanent ground displacements are the development of ground cracks, surface faults, liquefaction-induced settlements and lateral spreads, ground heave, slope and rock failures, and settling and failure of earth structures. Ground cracks can range from small fractures to long and deep depressions that in some cases can extend over long distances (Figure 7.4). Where these cracks transect roads, railroads, dams, or populated centers, they can cause widespread damage (Figures 7.5 and 7.6). If water fills these surface fractures, the resulting lateral pressures can lead to failures of slopes, embankments, and retaining structures. Faulting involves the vertical offset of the ground surface, which in some cases can be on the order of several meters (Figures 7.7 to 7.9). The formation of ground cracks and faults as a result of earthquakes is difficult to predict because their distribution and extent is highly dependent on geologic and soil nonconformities, which are inherently random. No reliable design procedures exist that account for these types of failures. Liquefaction, i.e., the temporary loss of soil strength and fluidization that occurs in certain saturated granular soils due to seismic shaking, represents a significant hazard in coastal areas and other locations with a high water table. The reduction in bearing capacity that accompanies the process of liquefaction can lead to the sinking of buildings, bridges, and other heavy structures, often with little or no damage to the structure itself (Figure 7.2). Liquefied beds can sometimes be detected by the presence of surface sand boils, formed as mixtures of soil and water squeeze out of the ground, with the soil residue deposited nearby (Figure 7.10). Significantly more hazardous are flow failures that involve the lateral displacement of fluidized, or nearly fluidized, soil under the effect of gravity. Such lateral spreading can take place at ground © 2003 by CRC Press LLC
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FIGURE 7.5 Ground cracking transecting roadway, 1991 Costa Rica earthquake. (Courtesy EQE International)
FIGURE 7.6 Cracks up to 6 m deep developed on the upstream face of Fatehgadh Dam during the 2001 India (Bhuj) earthquake. (Courtesy J. P. Bardet)
inclinations of as little as 0.1% and can result in deformations ranging from a few millimeters to tens of meters [Bardet et al., 1999]. They can cause damage to dams (Figure 7.11), harbor structures (Figure 7.12), buildings (Figure 7.13), estuarine and river embankments (Figure 7.14), bridges, utilities, roadways, and airport runways. Liquefied deposits that do not undergo significant lateral displacements can still settle a considerable amount due to subsequent consolidation, and therefore can cause damage as well. The engineering treatment of liquefaction has progressed significantly over the past 10 years and © 2003 by CRC Press LLC
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FIGURE 7.7 Failure of the Shihkang Dam during the 1999 Taiwan (Chi-Chi) earthquake due to tectonic uplifting and compression associated with a large fault transecting the structure. (Courtesy J. P. Bardet)
FIGURE 7.8 Fault intersecting running track at local school in Wu Feng, with an offset of approximately 1.7 m, due to the 1999 Taiwan (Chi-Chi) earthquake. (Courtesy J. P. Bardet)
can now be considered a subdiscipline in its own right [Seed et al., 2001]. It is addressed in building codes and is currently the subject of extensive research. Earthquakes can cause the failure of soil and rock slopes, particularly those that are marginally stable to begin with. The most common type of landslides triggered by seismic events include rock falls, soil slides, and rock slides on relatively steep slopes that are covered with disaggregated soil and rock [Wieczorek, 1996]. The debris from such failures can cut off roads and streams, and it can damage buildings, bridges, and other structures (Figures 7.15 and 7.16). Water that is impounded behind streams that are blocked by debris can break through suddenly and cause additional destruction. Loss of life due to landslides is a common occurrence. Of special concern © 2003 by CRC Press LLC
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FIGURE 7.9 Fault rupture across road led to a lateral offset of 4 m during the 1999 Turkey (Duzce) earthquake. (Courtesy J. P. Bardet)
FIGURE 7.10 Sand boils showing vents and sand and silt deposits from spouting associated with liquefied beds, 1976 Guatemala earthquake. (U.S. Geological Survey photo, courtesy National Oceanic and Atmospheric Administration-National Geophysical Data Center) © 2003 by CRC Press LLC
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FIGURE 7.11 Liquefaction failure of Lower San Fernando Dam during the 1971 San Fernando earthquake. Analysis of this particular failure led to significant advances in the understanding of liquefaction phenomena. (K. Steinbrugge Collection, courtesy Earthquake Engineering Research Center, University of California, Berkeley)
FIGURE 7.12 Lateral spreading and sand boils in fill material retained by pier structure, 1995 Japan (Kobe) earthquake. (Kobe Geotechnical Collection, courtesy Earthquake Engineering Research Center, University of California, Berkeley)
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FIGURE 7.13 Subsidence and lateral spreading due to liquefaction lead to the collapse of buildings along the shoreline in the fishing village of Guzelyali during the 1999 Turkey (Kocaeli) earthquake. (J.C. Borrero photo, courtesy National Oceanic and Atmospheric Administration-National Geophysical Data Center)
FIGURE 7.14 This sidewalk slipped into the water due to the combined effects of lateral spreading, subsidence, and a tsunami that resulted from the 1999 Turkey (Kocaeli) earthquake. (J.C. Borrero photo, courtesy National Oceanic and Atmospheric Administration-National Geophysical Data Center)
are slope failures that progress quickly, where the displaced material moves at speeds in excess of 5 m/sec. This is approximately the velocity at which a person can run [Cruden and Varnes, 1996]. A tragic example is the Huascaran Mountain landslide that occurred as a result of the 1970 (M 7.7) Peru earthquake. It buried the town of Yungay and part of the town of Ranrahirca, with a loss of life exceeding 18,000. In many earthquakes, landslides are the principal cause of death and destruction, and therefore constitute the greatest hazard. It is not uncommon for a single earthquake to trigger thousands of landslides, although most are usually small and take place in remote areas. The stability of slopes under seismic conditions can be analyzed by a number of techniques, ranging from pseudostatic to fully dynamic © 2003 by CRC Press LLC
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FIGURE 7.15 A large landslide triggered during the 1999 Taiwan (Chi-Chi) earthquake altered the path of the Taichai River, forcing it onto adjacent agricultural land. (Courtesy J. P. Bardet)
FIGURE 7.16 Numerous rock slides occurred along roads cut into mountain sides, involving both colluvium and bedrock, during the Southern Peru earthquake of 2001. (Courtesy Joseph Wartman, Drexel University)
numerical methods. Somewhat more problematic but equally important is estimating the runoff distance of the waste debris. Retaining walls and earth structures are susceptible to failure either due to liquefaction of fill material or due to severe shaking leading to dynamic lateral pressures that exceed the capacity of the soil-retaining structure system (Figures 7.12, 7.17, and 7.18). If located in seismically active areas, harbor structures such as gravity quay walls, sheet pile bulkheads, and pile and caisson piers must be designed for seismic loading, especially if their failure carries unacceptable risk of loss of life or dire economic consequences. Design principles for retaining walls and earth fill dams are described in this chapter. Lifelines consist of infrastructure systems whose purpose is to deliver electric power, water, sewage, gas, oil, telephone, and digital data. Many of these utilities are installed below ground and can be damaged © 2003 by CRC Press LLC
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FIGURE 7.17 Extensional cracks up to 12 cm wide developed in this retaining spillway wall of the Austrian Dam in the Santa Cruz Mountains of California as a result of the 1989 Loma Prieta earthquake. (G.R. Fisher photo, courtesy U.S. Geological Survey)
FIGURE 7.18 Extensive damage occurred to the Kobe waterfront due to widespread ground failure associated with liquefaction-related phenomena during the 1995 Japan (Kobe) earthquake. (R. Hutchinson photo, courtesy National Oceanic and Atmospheric Administration-National Geophysical Data Center)
by ground movement. In addition to utilities, lifelines also include transportation systems such as roads, railroads, airports, and harbors. In a modern city, lifelines constitute complex systems that are crucial for safety and economic reasons. Their interruption due to earthquakes can be devastating. Much recent research is focusing on ways to minimize hazards to lifelines from earthquakes. Another significant hazard associated with certain earthquakes is the generation of tsunamis, which are long water waves that form when the seafloor displaces suddenly. Tsunamis are a concern primarily in the Pacific Ocean due to the large number of earthquakes that occur along its rim. However, not all earthquakes lead to tsunamis. It appears that only those that involve dip-slip faulting or seabed mass wasting lead to tsunamis. History includes numerous examples of destructive events. For example, in © 2003 by CRC Press LLC
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1960 an M 9.5 earthquake in Chile generated a large tsunami that resulted in the deaths of 231 people in Hawaii, Japan, the Phillipines, and the west coast of the United States. More recently, the 1998 Papua New Guinea M 7.0 earthquake caused a massive underwater slump that led to a large tsunami, which destroyed several villages and killed more than 2000 people in the Sissano area [Tappin et al., 1999; Geist, 2000]. Maximum wave heights were estimated at 15 m [Geist, 2000].
7.3 Strong Ground Motion 7.3.1 Characterization of Strong Ground Motion Seismic waves result in complex ground displacements that vary from one location to the next. Seismometers are instruments that allow recording of the time-history of this motion. Of interest to engineers are devices that are designed to record the type of strong ground motions that can cause damage in an earthquake. Modern instruments use sets of accelerometers to measure components of acceleration in three orthogonal directions, two in the horizontal direction and one in the vertical (Figure 7.19). Although analog systems that record data on photographic film are still in widespread use, they are rapidly being replaced and supplemented with digital systems that collect data electronically at rates of tens or hundreds of measurements per second. These devices convert the analog transducer data into digital data and store the information on solid-state memory. Some instruments can be accessed remotely and the data downloaded through telemetry. Seismometers remain in standby mode until they are triggered by motion above a certain threshold. The raw digital data obtained by strong motion recorders must be corrected for various type of error, including the instrument’s intrinsic dynamic response, background noise, and baseline errors associated with the level of motion necessary for triggering the instrument. Software is available from the USGS to correct digitized records of strong motion earthquakes. The computer program BAP (Basic Strong Motion Accelerogram Processing Software) can be used to apply linear baseline corrections, instrument corrections, and to filter high and low frequency components from the record. It is described in more detail and is available on the Internet for download at http://nsmp.wr.usgs.gov/processing.html. An acceleration time series can be integrated numerically to obtain the corresponding velocity and displacement time series (Figure 7.20). Time histories, such as those in Figures 7.19 and 7.20, represent the complete record of motion at the instrument site. From a geotechnical point of view, the duration, frequency content, and amplitude of the motions are important. A number of parameters have been proposed to express these characteristics; the most commonly used is peak ground acceleration (PGA), which represents the largest recorded acceleration. It can be determined directly from the accelerogram and is typically expressed in fractions of gravity g, where 1 g is equal to 9.81 m/sec2. The focus is usually on peak horizontal accelerations (PHA) (sometimes the average of the two orthogonal PHAs), due to their role in determining lateral inertial forces in structures. However, peak vertical horizontal accelerations (PVA) may be of importance when considering the effects of earthquakes on light structures, whose weight may be insufficient to resist vertical dynamic loads from strong shaking. For practical purposes, the PVA has often been taken to be two thirds of the PHA [Newark and Hall, 1982]. For example, the records in Figure 7.19 indicate a PHA of 0.358 g and a PVA of 0.229 g, for a ratio of 0.64. However, recent research has shown that this ratio approaches unity close to the earthquake fault (see Chapter 5, this volume). As a general rule of thumb, acceleration levels must approach 0.1 g to produce damage in the weakest of constructions, whereas accelerations in excess of 0.5 g are deemed to be very dangerous to many structures [Arnold and Reitherman, 1982]. Of course, duration and frequency are of importance as well. Peak horizontal accelerations have been correlated to earthquake intensity through the Modified Mercalli Intensity Scale, which rates the effects of an earthquake on humans, structures, and the ground at specific locations (Figure 7.21; see also Chapter 4 of this volume). Peak horizontal velocity (PHV) and peak horizontal displacement (PHD) are sometimes reported. They each reflect different sensitivities to the frequency components of the motion. In some cases, accelerations and velocities refer not to peak values but to some other level of motion. For example, © 2003 by CRC Press LLC
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FIGURE 7.19 Accelerogram of recorded motions along three mutually perpendicular directions, obtained during the 1999 Turkey (Kocaeli) earthquake (M 7.4).
terms such as effective, sustained maximum, and effective design accelerations or velocities are occasionally used [Kramer, 1996]. Earthquake-induced ground motions contain a broad range of frequencies. The dynamic response of compliant structures is highly dependent on the frequency characteristics of these motions, which can be expressed conveniently with reference to a linear single-degree-of-freedom (SDOF) system, as shown in Figure 7.22. Displacement of the ground is noted by ug(t), and the relative displacement between the © 2003 by CRC Press LLC
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FIGURE 7.20 Velocity and displacement time histories corresponding to the 180˚ accelerogram in Figure 7.19.
FIGURE 7.21 MMI scale. (From Trifunac, M.D. and A.G. Brady. 1975. “On the Correlation of Seismic Intensity with Peaks of Recorded Strong Ground Motion,” Bull. Seismol. Soc. Am., 65, 139–162. With permission.) © 2003 by CRC Press LLC
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ug(t) c
u(t) m
k
FIGURE 7.22 Single-degree-of-freedom system.
ground and the mass m by u(t). Hence the total, i.e., absolute, displacement of the mass becomes uT(t) = u(t) + ug(t). The response of the SDOF system is given by the following equation of motion:
(
)
m u˙˙ (t ) + u˙˙g (t ) + cu˙ (t ) + ku (t ) = 0
(7.1)
where c is the viscous damping coefficient of the dashpot and k is the spring stiffness. The first term on the left-hand side represents the inertial force, the second term the damping force, and the third term the elastic force. Equation 7.1 can be rewritten as:
(
)
2 ηωu˙ (t ) + ω 2u (t ) = − u˙˙ (t ) + u˙˙g (t )
(7.2)
where ω is the resonant natural frequency of the system, ω = k / m = 2π / T , T is the resonant period, and η is the damping ratio expressed as a fraction of the critical damping, η = c/ccr = c/(2m ω). The ground acceleration u g(t ) would be given by site-specific acceleration time histories, such as the ones in Figure 7.19. Solution of Equation 7.2, which for the case of complex ground motions ug(t ) must be accomplished numerically, yields the relative displacement history u (t ). Notice that the displacement is a function of time t, resonant frequency ω, and damping ratio η. The response spectrum is a plot of the maximum computed displacement as a function of natural frequency of the SDOF system: Sd (ω, η) = max u (t , ω, η)
(7.3)
Spectra are determined for a given level of damping, typically 5%. In a similar fashion, velocity u˙ (t ) and acceleration u˙˙ (t) spectra can be determined by numerical differentiation of the displacement u(t). However, in practice it is more common to make use of pseudovelocity (Sv or PSV) and pseudoacceleration (Sa or PSA) spectra, which are computed directly from Sd by noting that the three quantities are related: Sv = ω Sd
(7.4)
Sa = ω 2Sd
(7.5)
Sv and Sd , which are different in magnitude from the spectra based on u˙ (t) and u˙˙ (t), are more meaningful quantities. Sv can be related to the peak value of strain energy stored in the system during a given earthquake, and Sd can be related to the base shear coefficient used in building codes to estimate base shear forces in structures. Sd , Sv , and Sa spectra are shown in Figure 7.23 for the 180° accelerograph in Figure 7.19. The three spectra illustrate how displacement, velocity, and acceleration are each associated with different frequency ranges. Peak displacements occur at comparatively high periods (or low frequencies), whereas peak accelerations are found at low periods (or high frequencies). Stiff structures with a low resonant period are most sensitive to the low period components of the ground motion, therefore consideration of the acceleration spectrum is of critical importance. On the other hand, flexible structures with a high resonant © 2003 by CRC Press LLC
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150
Sd (cm)
5% Damping 100 50 0 0
10
5
15
20
Period (s)
Sv or PSV (cm/s)
160 5% Damping 120 80 40 0 0
5
10
15
20
Period (s)
1.2
Sa or PSA (g)
5% Damping 0.8 0.4 0.0 0
5
10
15
20
Period (s)
FIGURE 7.23 Response spectra for 180° accelerograph in Figure 7.19.
period are more sensitive to the high-period components of the motion, which are better reflected in the displacement spectrum. Because Sd , Sv , and Sa are related, they are sometimes combined in a tripartite plot that uses four logarithmic scales to display displacement, velocity, acceleration, and either period or frequency (Figure 7.24). Linear response spectra are widely used in earthquake engineering as a practical means of characterizing strong ground motions. However, it should be remembered that most structures behave inelastically when subjected to strong ground motions. Inelastic response spectra can be determined to account for nonlinearities in the force-displacement relationship [Newark and Hall, 1982]. The extent to which a particular structure behaves inelastically can be defined by a ductility factor µ: µ=
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up uy
(7.6)
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10 0, 00 0
10
00
,0
,0
00
10
2
S
PS A
10
00
00
10
(c m /s
2
)
10
1
10
10
PSV (sec)
0
10
0
10
) m (c
d
1
10
0
1
0.
0.
1
10
1
0.
01
01
0.
10
0.
00
01
0.
1
00
00
1
0. 1
10
0
10
1
10
2
10
ω (rad/sec)
FIGURE 7.24 Tripartite plot of response spectral displacement, velocity, and acceleration for the record in Figure 7.23.
where u p is the peak displacement of the mass for a given ground excitation and uy is the displacement of the mass necessary to yield inelastic response. Inelastic response spectra can be calculated in the time domain by assuming that the stiffness term in Equation 7.1 is a function of displacement. When compared to the elastic case, inelastic spectral accelerations decrease with ductility. This topic is covered in Chapter 4 of this volume, as well as in Chopra [2001]. The duration of strong ground motion, and in particular the number of load reversals, has a strong influence on the damage that a particular earthquake can cause. A moderate earthquake of long duration can result in equal or larger destruction than a short, intense one. Structures that are loaded beyond a cyclically stable range may fail after a given number of load reversals. The same is true for foundation elements that may lose their support upon repeated load reversals due to reduction in soil stiffness and strength. Also, pore pressures in saturated, loose granular soils can accumulate with load cycles and lead to liquefaction after a given number of load reversals. Duration of the strong motion component of a seismic event can be determined from an accelerogram using one of a number of criteria [Kramer, 1996]. The most straightforward approach is to measure the time between the first and last exceedance of some threshold acceleration, typically 0.05 g. This is referred to as the bracketed duration [Bolt, 1969].
7.3.2 Site-Specific Soil and Topographic Effects In general, ground motions decrease with distance from the earthquake’s epicenter. Ground motion attenuation is a function of the type and magnitude of the earthquake, distance from the source, and the geology through which seismic waves travel. Attenuation relationships are crucial for determining earthquake hazard assessments and for establishing seismic design criteria for engineered structures. © 2003 by CRC Press LLC
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Attenuation is usually expressed in terms of peak ground acceleration (PGA), peak ground velocity (PGV), or spectral ground acceleration (PSA), at 5% damping. For example, the 1996 U.S. National Seismic Hazard maps prepared by the USGS display PGA and PSA at periods of 0.2, 0.3, and 1.0 sec, with a 10%, 5%, and 2% probability of exceedance in 50 years (http://geohazards.cr.usgs.gov/eq/). A number of attenuation relationships have been developed over the years and new data from recent earthquakes will undoubtedly lead to refinements in the future. These expressions require input parameters that describe earthquake magnitude, type of faulting, distance, and local soil or rock characteristics. Specific ground motion attenuation relationships are associated with particular tectonic environments and are derived empirically by statistical means from large numbers of earthquakes or synthetically by assuming a particular seismological model. Relationships have been developed for shallow crustal earthquakes in active tectonic regions such as western North America, for shallow earthquakes in stable continental regions such as central and eastern North America, and for earthquakes in subduction zones such as Alaska [Abrahamson and Shedlock, 1997]. A detailed description of current ground motion attenuation relationships in use in North America can be found in a 1997 special issue of Seismological Research Letters (Vol. 68, No. 1) and in Chapter 5. Site-specific conditions are usually included only in crude terms through broad classifications such as rock/stiff soil, deep soil, and soft soil. A notable exception is the model of Boore et al. [1997], which takes into account the average shear wave velocity to a depth of 30 m. Attenuation relationships have also been developed for use in Japan and elsewhere [Molas and Yamazaki, 1995, 1996; Shabestari and Yamazaki, 1998]. It has long been recognized that soils whose stiffness differs from that of the underlying bedrock can affect the amplitude, frequency, and duration content of surface strong motions. In particular, thick soft soil deposits have been observed to cause amplification of ground motions. Important evidence was collected during the 1985 Michoacan (Mexico) earthquake (M8.1) and during the 1989 Loma Prieta earthquake (MW 7.1). The center of Mexico City is partially located on soft lake clays that extend down 50 m or more. Further to the west, the clay deposits thin out and are gradually replaced by granular and rock materials of volcanic origin. Figure 7.25 illustrates how spectral accelerations at the SCT site, overlying approximately 38 m of clay, are significantly larger than at the UNAM site, which was located on basaltic rock and hard soil. The frequency content is also distinctly different. Whereas spectral energy is concentrated around a period of 2 sec at the SCT site, the UNAM spectrum is much broader. Severe damage to buildings occurred where the clay thickness exceeded 40 m and where the natural period of the soil deposit matched that of the structure [Stone et al., 1987]. Amplification of ground motions at
5% Damping
Sa (g)
SCT
UNAM
T (s) FIGURE 7.25 Spectral accelerations at SCT site (soft soil) vs. UNAM site (rock), 1985 Mexico earthquake. (From Romo, M.P. and H.B. Seed. 1986. “Analytical Modeling of Dynamic Soil Response in the Mexico Earthquake of September 19, 1985,” in Proc. ASCE International Conference on the Mexico Earthquakes 1985, Mexico City, American Society of Civil Engineers, New York. With permission.)
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sites with thick soil deposits was also observed during the 1989 Loma Prieta (M7.1) earthquake. In general, seismic shaking decreased with distance from the epicenter, located in the Santa Cruz Mountains, but areas underlain by substantial deposits of alluvium and bay mud clearly suffered the worst damage. For example, local site conditions at the northern section of the Cypress viaduct, consisting of engineered fill and soft to medium stiff bay mud, strongly amplified peak ground surface accelerations, and especially the long-period components, causing the collapse of the bridge in that area. On the other hand, the southern section was not founded on bay mud and did not collapse [Seed et al., 1990]. Based in large part on extensive measurements taken during the 1985 Michoacan and the 1989 Loma Prieta earthquakes, Idriss [1990] has proposed an approximate relationship between peak accelerations on rock sites vs. peak accelerations on soil sites (Figure 7.26). Seed et al. [1976] considered the effects of different soil types on average spectral acceleration (Figure 7.27). It is clear from Figure 7.27 that the presence of soil also affects the frequency content of ground motions. In particular, soft and deep deposits result in a shift towards higher periods with significant energy at values of 1 sec and higher. Such periods may be similar to those of large structures and therefore they can induce dangerous inertial forces. A simple analytical model can be used to illustrate some of the important aspects of wave propagation through surface soil layers. Assume a uniform deposit, consisting of a viscoelastic soil of thickness H, located above a rigid bedrock (Figure 7.28). The equation of motion describing harmonic shear waves traveling upward from the bedrock can be solved to obtain the horizontal soil displacement through a soil layer having a shear velocity Vs [Kramer, 1996]: u ( z , t ) = A cos
ω i ωt ze Vs
(7.7)
This equation represents a standing wave with amplitude A cos(ω/Vs ). The ratio of maximum displacement at the ground surface to maximum displacement at the soil–bedrock interface is given, for small damping ratios η, by: A=
1 cos (ωH Vs ) + ( ηωH Vs ) 2
(7.8)
2
Acceleration - soil sites (g)
0.6
0.5
0.4
0.3
0.2
0.1
0.0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
Acceleration - rock sites (g) FIGURE 7.26 Peak accelerations on rock sites vs. peak accelerations on soil sites. (From Idriss, I.M. 1990. H. Bolton Seed Memorial Symposium, BiTech Publishers. With permission.)
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Soft to medium clay and sand (15 records) Deep cohesionless soils, >250ft (30 records)
Stiff soils, <200ft (31 records)
Rock (28 records)
FIGURE 7.27 Effect of soil type on average spectral acceleration at 5% damping. (From Seed, H.B., C. Ugas et al. 1976. “Site-Dependent Spectra for Earthquake-Resistant Design,” Bull. Seismol. Soc. Am., 66, 221–243. With permission.)
Ground surface
Soil Deposit with shear wave velocity Vs
H
z
Rigid Bedrock
FIGURE 7.28 Simple model for vertical wave propagation.
Note that amplification is a function of the frequency of the motion and the damping of the soil. Amplification maxima occur at the following frequency values: ωn =
Vs π + n π H 2
(7.9)
where n = 0, 1, 2,… These are the natural or resonant frequencies of the soil deposit. For an undamped soil, they result in infinite amplification. At finite damping values, amplification decreases with increasing frequency and the maximum occurs at the lowest natural frequency, i.e., at n = 0. This is known as the fundamental frequency, ω0 = πVs /(2H). The characteristic site period corresponding to this frequency is T0 = 4H/Vs. For example, assuming that Vs = 450 m/sec, H = 150 m, and η = 5%, the characteristic site period becomes T0 = 1.34 sec, and the – amplification factor A = 12.7 (Figure 7.29). This means that ground motion with a concentration of energy near this period will result in resonance and more than a tenfold amplification of horizontal ground displacement. If we use the rule of thumb that the fundamental period of a building with N floors is approximately N/10, then buildings with 13 or 14 floors would be in resonance and would face the potential of severe damage if not properly designed and built. For level stratified deposits with approximately horizontal soil layers, shear velocities can be averaged as a first approximation. Similar methods of analysis © 2003 by CRC Press LLC
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Amplification factor
15 η=0 10 η = 5% 5 0 0
5
10
15 Natural frequency, ω
20
25
30
FIGURE 7.29 Site amplification as a function of frequency and soil damping for VS = 450 m/sec and H = 150 m.
for one-dimensional wave propagation are presented by Kramer [1996] for uniform and for layered soil on elastic rock. The assumptions made in these types of analysis are quite simplistic. Most soils do not behave elastically and their properties can vary significantly over short distances. Propagation of seismic waves through soil layers invariably involves some level of material nonlinearity. At all but the smallest levels of strain, stiffness decreases and damping increases with strain. This effect appears to become more pronounced the lower the plasticity of the soil [Vucetic and Dorby, 1991]. Nonlinear, site-specific ground response analysis requires a numerical approach where the variation of stiffness and damping with shear strain is described explicitly. Such information is usually determined from cyclic stress-strain tests conducted on representative soil samples. Ground motions are computed using either an equivalent-linear model or a more rigorous nonlinear model. In the former, a single solution step is used to predict strain by selecting stiffness and damping values according to an initially assumed level of strain. Upon computation of the resulting strains, the stiffness and damping corresponding to the computed strain are checked against the assumed values and updated. The analysis is repeated until convergence is achieved. The second formulation involves solution of the equations of motion by nonlinear incremental stress-strain methods. This approach is potentially more accurate and versatile but often requires more extensive material characterization, depending on the particular constitutive model selected. The computer code SHAKE91 is the most widely used program for computing the one-dimensional seismic response of horizontally layered soil deposits. It uses the equivalent-linear method. A number of other programs are available that allow for nonlinear dynamic analysis, as well as consideration of excess pore pressures and the presence of structural elements. Many of the more recent codes, such as PLAXIS, SASSI 2000, and QUAKE/W, are based on the finite element method.
7.3.3 Design ground motions The development of design ground motions ideally involves site-specific analysis of the type described previously. However, a suite of bedrock motions must be considered that corresponds to probable seismic events ranging from moderate earthquakes with a high probability of occurrence to large earthquakes that occur only rarely. Seismicity at a particular location can be described in probabilistic terms, accounting for variations in earthquake magnitude, type, size, and distance. A common requirement is that design ground motions be based on parameters that have a 10% probability of exceedance in 50 years. Because most seismic events concentrate energy in a relatively narrow frequency band, it is important that multiple earthquakes with contrasting spectra be considered so that the computed ground motions cover a broad range of frequencies. In developing an appropriate set of design ground motions, it is also important to keep in mind the dynamic characteristics of the structure, acceptable levels of damage, the consequences of failure, and overall uncertainties [Finn, 2001]. Design ground motions are usually expressed in terms of smooth response spectra that ignore the small peaks and valleys resulting from any one single seismic record. Methods of probabilistic seismic hazard analysis are presented in greater detail in Chapter 8. It is not always possible or desirable to generate design ground motions using site-specific analysis. For noncritical structures, and as permitted by local ordinances, design ground motion parameters may © 2003 by CRC Press LLC
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be obtained from applicable building codes. In the United States, building codes are the jurisdiction of states, which may further delegate adoption and administration of specific provisions to local entities. Fortunately, most jurisdictions have modeled their provisions on the Unified Building Code (UBC), the Building Officials Code Administrators (BOCA) National Code, or the Standard Building Code (SBC), which have now been merged into the International Building Code (IBC) [ICC, 2000]. The seismic provisions contained in the three earlier model codes share similar formats, particularly in versions after 1994, although specific aspects may vary from location to location. The new International Building Code was developed in 2000, under the guidance of the International Code Council (ICC), with the intention of replacing the UBC, BOCA, and SBC codes. Seismic provisions in the IBC code incorporate the recommendations from the National Earthquake Hazards Reduction Program (NEHRP), developed by the Building Seismic Safety Council (BSSC). However, the IBC has not yet been widely adopted. At present, a patchwork of different codes exist across the United States. Nonetheless, the seismic provisions of the UBC and the NEHRP (BSSC, 1997) are the most common ones in use at present. In both cases, an allowance is made for site-specific soil conditions in selecting appropriate design accelerations or spectra. Most countries in seismically active regions have also adopted seismic codes (see Chapter 11). For example, Japan’s seismic design requirements are contained in its Building Standard Law, most recently revised in 2000 [Otani, 2000]. In the UBC, earthquake-resistant design of buildings is accomplished by estimating a static design base shear force that must be accommodated, or by analyzing the dynamic response of the structure subjected to a smoothed response spectra or a site-specific ground motion time history. The design base shear force, V, is given by: V=
1.25 ZIW S RwT 2/3
(7.10)
where Z I Rw W T S
= = = = = =
the seismic zone factor the importance factor the structural ductility factor the seismic dead load the fundamental period of the structure the soil coefficient
A further description of the parameters in Equation 7.10 can be found in the 1997 edition of the UBC [ICBO, 1997] and in Chapter 11 of this volume. Of special interest from a geotechnical perspective is the soil coefficient S, which expresses the site-specific soil conditions. It can be determined from Table 7.1. This static approach to design should be used with caution because it does not reflect the influence of soil characteristics on ground motion intensity, frequency, and duration, hence its use is limited by the UBC to very simple structures. A more comprehensive design can be carried out using one of the TABLE 7.1
UBC Soil Type Parameter S
Type S1
S2 S3 S4
Description
S
A soil profile with either: a. A rock-like material characterized by a shear wave velocity greater than 2500 ft/sec or by other suitable means of classification OR b. Medium dense to dense or medium stiff to stiff soil conditions, where the soil depth is less than 200 ft A soil profile with predominantly medium dense to dense or medium stiff to stiff soil conditions, where the soil depth exceeds 200 ft or more A soil profile containing more than 20 ft of soft to medium stiff clay, but not more than 40 ft of soft clay A soil profile containing more than 40 ft of soft clay characterized by a shear wave velocity less than 500 ft/sec
1.0
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1.2
1.5 2.0
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FIGURE 7.30 Normalized spectral shapes for various types of soil and rock. (From Uniform Building Code. 1994. Used by permission of the International Conference of Building Officials.)
normalized spectral shapes in Figure 7.30, which were derived from the work of Seed et al. [1976] and others. One of the spectral curves in Figure 7.30 is chosen for analysis of the structure in question, depending on the prevailing soil conditions at the site. The design spectral curve is obtained by multiplying the ordinates in Figure 7.30 by the effective peak ground acceleration (EPA), defined as EPA = Sa /2.5, where Sa is the average spectral acceleration over the period interval from 0.1 to 0.5 sec. The EPA can also be assumed as the value of the factor Z in Equation 7.10, expressed as a function of gravity. When site-specific ground motion histories are to be used instead of a normalized response spectra, due consideration must be given to selecting a representative set of ground motions as discussed earlier. Design ground motions in either case must correspond to a 10% probability of exceedance in a 50-year period. When soil conditions are of type S4, the UBC requires that a site-specific analysis be conducted for flexible structures whose resonant period is larger than 0.7 sec. The UBC site classification system in Table 7.1 is of a qualitative nature. The NEHRP provisions, on the other hand, allow for a more sound and detailed method of characterizing sites for purposes of estimating amplification of seismic motions. The main index parameter is the average shear velocity, Vs, in the upper 30 m (100 ft) of deposit. The motivation for using Vs can be seen by referring to the resonant period of a soil deposit of thickness H, i.e., T0 = 4H/Vs . Shear velocity is a convenient parameter because it is inversely proportional to site period and therefore can be used to compare the ground motion amplification potential of different soil types of similar thickness. The NEHRP site classification scheme is shown in Table 7.2. Because shear wave velocity measurements may not always be available, alternative indexes are also provided that correspond approximately to the velocity ranges indicated. The average – standard penetration resistance, N, can be used for cohesionless soils, and the average undrained shear – strength, Su , for clayey soils. Spectral response shapes can be constructed for any of the soil types in Table 7.2 for various levels of shaking. Maximum considered earthquake spectral response accelerations at 5% damping are calculated for short period motions centered at 0.2 sec, SMS, and for longer period motions centered at 1 sec, SM1:
© 2003 by CRC Press LLC
SMS = Fa SS
(7.11)
SM1 = Fv S1
(7.12)
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TABLE 7.2 Site Class A B C D E
F
NEHRP and IBC 2000 Site Classifications
Description – Hard rock with measured shear wave velocity: Vs > 5000 ft/sec (1500 m/sec) – – Rock with: 2500 ft/sec Vs ≤ 5000 ft/sec (760 m/sec < Vs ≤ 1500 m/sec) – – Very dense soil and soft rock with 1200 ft/sec < Vs ≤ 2500 ft/sec (360 m/sec < Vs ≤ 760 m/sec) or with – – either N > 50 or Su > 2000 psf (100 kPa) – – – Stiff soil with 600 ft/sec ≤ Vs ≤ 1200 ft/sec (180 m/sec ≤ Vs ≤ 360 m/sec) or with either 15 ≤ N ≤ 50 or – – 1000 psf ≤ Su ≤ 2000 psf (50 kPa ≤ Su ≤ 100 kPa) – – – a. A soil profile with Vs < 600 ft/sec (180 m/sec) or with either N < 15 or Su < 1000 psf (50 kPa) OR b. Any soil profile with more than 10 ft (3 m) of soft clay defined as soil with PI > 20, w ≥ 40%, and Su < 500 psf (25 kPa) Soil requiring site-specific evaluations: 1. Soils vulnerable to potential failure or collapse under seismic loading such as liquefiable soils, quick and highly sensitive clays, collapsible weakly cemented soils 2. Peats and/or highly organic clays (H > 10 ft [3 m] of peat and/or highly organic clay where H = thickness of soil) 3. Very high plasticity clays (H > 25 ft [8 m] with PI > 75) 4. Very thick soft/medium stiff clays (H > 120 ft [36 m]) Exception: When the soil properties are not known in sufficient detail to determine the Site Class, Site Class D shall be used. Site Classes E or F need not be assumed unless the authority having jurisdiction determines that Site Classes E or F could be present at the site or in the event that Site Classes E or F are established by geotechnical data.
The site coefficients Fa and Fv are obtained from Table 7.3 for various combinations of soil types and maximum earthquake spectral accelerations. These maximum accelerations are based on a probabilistic seismic hazard analysis with a 10% probability of exceedance in 50 years. SS and S1 can be obtained from NEHRP maps prepared by the USGS (http://geohazards.cr.usgs.gov/eq/html/nehrp.html). The maximum spectral accelerations are scaled for design purposes as follows: 2 SDS = SMS 3
(7.13)
2 SD1 = SM1 3
(7.14)
The design response spectrum is prepared as indicated in Figure 7.31 with: T0 = 0.2 TS =
SD1 SDS
SD1 SDS
(7.15)
(7.16)
For periods less than or equal to To , the design spectral acceleration, Sa , is given by: Sa = 0.6
SDS T + 0.4SDS To
(7.17)
For periods greater than TS , Sa varies inversely with period: Sa = © 2003 by CRC Press LLC
SD1 ST
(7.18)
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TABLE 7.3A Fa as a Function of Site Class and Short-Period Earthquake Spectral Acceleration Mapped Maximum Considered Earthquake Spectral Response Acceleration at Short Periods Site Class
Ss ≤ 0.25
Ss = 0.50
Ss = 0.75
Ss = 1.00
Ss ≥ 1.25
0.8 1.0 1.2 1.6 2.5
0.8 1.0 1.2 1.4 1.7
0.8 1.0 1.1 1.2 1.2
0.8 1.0 1.0 1.1 0.9
0.8 1.0 1.0 1.0
a
a
a
a
a
A B C D E F
a
a
Note: Use straight line interpolation for intermediate values of Ss . Site-specific geotechnical investigation and dynamic site response analysis shall be performed.
TABLE 7.3B Fv as a Function of Site Class and 1-Second Earthquake Spectral Acceleration Mapped Maximum Considered Earthquake Spectral Response Acceleration at 1-Second Periods Site Class
S1 ≤ 0.1
S1 = 0.2
S1 = 0.3
S1 = 0.4
S1 ≥ 0.50
0.8 1.0 1.7 2.4 3.5
0.8 1.0 1.6 2.0 3.2
0.8 1.0 1.5 1.8 2.8
0.8 1.0 1.4 1.6 2.4
0.8 1.0 1.3 1.5
a
a
a
a
a
A B C D E F
Note: Use straight line interpolation for intermediate values of S1. Site-specific geotechnical investigation and dynamic site response analysis shall be performed.
Spectral Acceleration Sa
a
a
SDS
Sa=SD1/T SD1
To
Ts
1.0
Period T (s) FIGURE 7.31 NEHRP design response spectra. (From BSSC. 1997. NEHRP Recommended Provisions for Seismic Regulations for New Building and Other Structures, Part 1, Provisions, FEMA 302. Used by permission of the Building Seismic Safety Council.)
Note that a site-specific procedure for determining ground motion accelerations must be conducted for all levels of shaking where site conditions of type F are encountered, as well as for very large shaking intensities at sites of type E (Table 7.3). In general, where a site-specific approach is used, maximum considered earthquake ground motions must represent a 2% probability of exceedance within a 50-year period. © 2003 by CRC Press LLC
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x z
φ1
φ
φ2
ground motion (A)
(B)
FIGURE 7.32 Vertical propagation of horizontal shear wave arriving at a triangular surface wedge. (Modified from Faccioli, E. 1991. “Seismic Amplification in the Presence of Geologic and Topographic Irregularities,” in Proc. Second International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, St. Louis, MO.)
For the NEHRP static equivalent lateral earth procedure, the base shear force V is calculated as follows: V = CsW
(7.19)
where W includes the dead load and certain other loads, and Cs is the seismic response coefficient that need not exceed: SD1 T (R I )
(7.20)
Cs = 0.1SD1I
(7.21)
Cs =
but should be at least:
For buildings and structures located on sites of types E and F, the minimum value for Cs is: Cs =
0.5S1 RI
(7.22)
In this expression, R is a response modification factor (different from the one used by the UBC), I is an occupancy factor, and T is the fundamental period of the structure. These parameters are discussed in greater detail in the NEHRP provisions. The discussion thus far has focused on sites with a level ground underlain by horizontal soil deposits of laterally uniform thickness. Evidence suggests that where surface topography is not level or where large sedimentary basins are encountered ground motions can be complex and significantly different from what can be expected from conventional one-dimensional attenuation and soil propagation models. The effect of surface topography can be illustrated with reference to the simple case of upward traveling SH waves, i.e., shear waves whose motion is perpendicular to the direction of travel, arriving at a triangular surface wedge of infinite extent (Figure 7.32). Aki [1988] showed that for this case ground motions can be amplified by a factor of 2π/φ, where the angle φ is measured in degrees. This result can be used for a first-order estimate of ground motion amplification at ridges and deamplification at troughs relative to a horizontal topography. Higher levels of ground motions at crests relative to nearby troughs has indeed been inferred from damage patterns in a number of recent earthquakes [Finn, 1991, 2001]. Sediment deposits in basins are typically thickest near the center and thin out towards the flanks. In addition to vertically propagating seismic waves, such basins may trap body waves that propagate along © 2003 by CRC Press LLC
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the surface and increase the intensity and duration of the shaking. Records collected in basins often reveal significant energy at periods above 1 sec. This implies wave lengths much longer than 30 m. Their amplitude cannot be characterized by the site classification scheme in Table 7.3. Instead, long-period motion depends on much deeper and larger geologic features, which in many cases are not horizontally layered. These long-period waves can become trapped in basins that are hundreds of meters thick if they enter at incidence angles less than critical [Graves, 1993]. The trapped waves propagate across the basin and can lead to complex interference patterns as they combine with vertically propagating shear waves and various reflections, particularly near the edges of the basin. Proper modeling in that case requires that a two- or three-dimensional analysis be conducted [Graves et al., 1998]. The damaging effects from long-period waves in sedimentary basins were observed during the 1977 Caracas earthquake, the 1985 Michoacan earthquake, the 1994 Northridge earthquake, and the 1995 Kobe earthquake [Somerville, 1998]. Many large cities in the United States, such as Los Angeles, Seattle, Portland, and Tucson, are located on sedimentary basins and are susceptible to this effect. Strong ground motions at locations near the earthquake source are strongly influenced by the geometry of the fault [Somerville, 1998]. Two important effects occur in the near-fault region. When earthquakes are caused by dipping faults, two sites located on opposite sides but at the same distance from the fault may experience significantly different motions. Specifically, larger short-period ground motions may occur on the hanging-wall side of the fault compared to the foot-wall side [Abrahamson and Somerville, 1996]. For earthquakes caused by vertical or dipping faults, the direction of rupture propagation in the near field can cause substantial differences in the level of shaking for different orientations relative to the fault’s strike. This has been corroborated by damage patterns in many recent earthquakes but particularly following the 1995 Kobe earthquake [Finn et al., 1996] and the 1994 Northridge earthquake [Somerville et al., 1996]. Sites close to the earthquake source typically reveal strike-normal peak velocities substantially larger than strike-parallel velocities. The effect is most evident at periods longer than about 0.5 sec [Somerville and Graves, 1996]. Obviously, directivity effects must be taken into account in the design of buildings and other large structures located close to potential earthquake sources. Site-specific effects are the focus of intense current research efforts. For example, Seed et al. [1997] and Rodriguez-Marek et al. [1999] have proposed alternate, more intricate soil classification systems that may aid in the design of ground motions, although they are not yet widely used by practicing engineers. Near-field site issues are being addressed by seismologists and engineers but have not yet been incorporated in current building codes. In the future, ground motion maps will likely include the effects described previously as more data are collected and analyzed, especially now that extensive networks of ground motion recorders have been installed or are being contemplated worldwide.
7.4 Dynamic Soil Behavior The behavior of soils under cyclic loading plays a crucial role in determining the extent and distribution of ground displacements, which in turn are directly related to the potential for causing earthquake damage. Of importance are the stress-strain and strength response of soil under cyclic conditions. In general, different levels of induced strain require consideration of different types of material models. If the focus is on propagation of seismic waves, it is often sufficient to consider small strain, elastic behavior. On the other hand, if the level of cyclic loading is substantial, it becomes necessary to consider inelastic, permanent deformations, as well as cyclically induced changes in strength. The cyclic stress-strain and strength properties of soils can be determined directly or empirically from any of a number of field or laboratory tests (Table 7.4). The reader is referred to Kramer [1996] for further information. At relatively low levels of strain, the shear response of a typical soil subjected to cyclic load reversals of constant amplitude is as shown for any of the stress-strain loops in Figure 7.33A. The hysteretic nature of the response implies that even at low strains the behavior is nonlinear, albeit reversible, and involves energy dissipation. For many applications, it is adequate to simplify this type of behavior in terms of two equivalent parameters that characterize the stiffness and damping aspects of the soil. The equivalentlinear shear modulus, G, is a function of the cyclic strain amplitude, γc , and is described in terms of a © 2003 by CRC Press LLC
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Test Methods for Determining Dynamic Properties of Soils
Conditions
Test
Parameters
Field – Low strain
Seismic reflection Seismic refraction Suspension logging Spectral analysis of surface waves Seismic cross-hole test Seismic down-hole or up-hole test Piezocone Standard penetration test Cone penetration test Dilatometer test Resonant column Piezoelectric bender element test Cyclic triaxial test Cyclic direct simple shear test Cyclic torsional shear test Shaking table tests Centrifuge tests
Vp, thickness of major soil units Vs, Vp , thickness of major soil units V s, V p VR, wave length, Vs Vs, Vp , damping ratio Vs, Vp , thickness of major soil units Vs , thickness of major soil units Density, stiffness, strength Density, stiffness, strength, soil type, pore pressure Stiffness Stress-strain, strength Vs Stress-strain, strength, pore pressure Stress-strain, strength, pore pressure Stress-strain, strength, pore pressure Forces and displacements, pore pressure Forces and displacements, pore pressure
Field – High strain
Lab – Low strain Lab – High strain
Note: Vs = shear wave velocity, Vp = compressional wave velocity, VR = Rayleigh wave phase velocity.
backbone curve (Figure 7.33A and B). Energy dissipation is given in terms of the equivalent damping ratio, η, which can be expressed as: η=
1 ED 1 ED = 4π E So 2π Gγ s2
(7.23)
where ESo is the strain energy stored in the soil at a cyclic strain of γc , and ED is the energy dissipated within the hysteretic loop. The equivalent damping ratio is also a function of strain level, γc , as indicated in Figure 7.33C. The maximum value of the shear modulus, Gmax , represents the tangent stiffness at very low strain (less than about 10 –4 %). It is generally difficult to measure from the stress-strain response of laboratory specimens, which typically involve relatively large levels of strain but instead is obtained from shear wave velocity measurements conducted either in the field or in laboratory samples: Gmax = ρVs2
(7.24)
where ρ is the density of the soil. Alternatively, Gmax can be obtained empirically from any of a number of in situ field tests, which are conveniently summarized in Kramer [1996]. Some guidelines are provided in the section on liquefaction settlement. The equivalent-linear model is appealing because it incorporates material nonlinearity, yet it only requires two relatively simple material constants. It is easily implemented and commonly used for ground response analysis. Nonetheless, it is important to realize that the model represents an approximation to soil behavior. It assumes that no permanent displacements accumulate with multiple cycles of loading and that no failure occurs. True cyclic soil behavior for load reversals of constant amplitude is closer to that shown in Figure 7.34. It involves open hysteretic loops with irreversible energy dissipation and permanent strain accumulation. This type of behavior can be accounted for but it requires a point-wise description of the backbone curve and a set of rules for unloading and reloading behavior [Kramer, 1996]. A hierarchy of nonlinear cyclic models can be considered, ranging from simple Masing-type models with simple loading-unloading rules, to more sophisticated models that can account for changes in the shape of the backbone curve due to volume changes, i.e., hardening or softening, and for mechanisms of pore pressure generation that lead to changes in effective stress during cyclic loading. Although quite powerful, sophisticated nonlinear cyclic models are typically limited in terms of soil types and loading conditions for which they provide reasonable predictions. © 2003 by CRC Press LLC
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τ
(A)
Gmax G τc
Backbone curve
ESo
γc
ED
γ
(C)
(B)
G Gmax
η
log γ
log γc
FIGURE 7.33 (A) Typical response of soil subjected to cyclic load reversals; (B) modulus reduction curve; and (C) damping curve.
τ
γ
FIGURE 7.34 Approximate true behavior of soil subjected to load reversals of constant amplitude.
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Cyclic strength ratio, τcyc/Su
1.2
Single amplitude failure strain: εf >5%
1.0
εf ≤3%
0.8 0.6 0.4 0.2 0
1
3
10
100
300
1,000
3,000
10,000
Number of cycles to failure, N FIGURE 7.35 Cyclic strength ratio variation with number of cycles to reach failure strain for different soils. (From Lee, K.L. and J.A. Focht. 1976. “Strength of Clay Subjected to Cyclic Loading,” Mar. Geotechnol., 1(3), 165–188. Used by permission of Taylor and Francis, Inc.)
The most thorough approach to modeling the cyclic behavior of soils involves the use of general elastoplastic constitutive models that account for three-dimensional stress and strain components, the effect of initial stress conditions, general stress paths, hardening or softening behavior, and generation and dissipation of excess pore pressures under monotonic and cyclic loading conditions. They are often framed in terms of critical state concepts. Even though they are potentially very accurate and general in nature, they have not found widespread use in standard practice because they typically require a large number of material parameters, many of which are difficult to determine. However, comprehensive soil models can provide a compatible link between pre-failure and failure deformation mechanics. It is useful to consider the strength of fine-grained cohesive soils separately from that of noncohesive granular soils that may be susceptible to liquefaction. Failure associated with the phenomenon of liquefaction is discussed in the next section. For all practical purposes, cyclic loading due to ground shaking can be assumed to occur under undrained conditions in most soils, except perhaps in coarse gravels. Failure is usually defined in terms of a critical level of deformation, beyond which the ability of a particular structure to provide its intended service is compromised. This may involve either cyclic or unidirectional displacements that exceed acceptable thresholds. The maximum shear stress associated with this level of straining is referred to as the cyclic strength. It is a function of the average shear stress, as well as the amount of shear stress induced in each cycle of loading. Cyclic shear strength is usually expressed in terms of the cyclic strength ratio, τcyc /Su , where Su is the undrained shear strength under monotonic loading conditions. If the average shear stress is zero, no unidirectional shearing occurs and the strength ratio associated with a particular level of failure shear strain (typically taken in the 3 to 5% range) decreases with the number of load cycles (Figure 7.35). Note that at cyclic stress levels below a given value, the failure shear strain is never reached and the soil is said to remain stable. As is evident from Figure 7.35, this cutoff stress ratio varies with soil type. It generally increases with plasticity. If the average shear stress is not zero, as is the case along potential failure surfaces associated with slopes, retaining structures, and most types of foundations, the cyclic shear strain and the average shear strain will depend on both the average level of shear stress and the cyclic shear stress. For example, a potential failure plane with an average static shear stress level that is close to the maximum shear stress that can be mobilized requires only a small amount of cyclic loading to reach unacceptable levels of shear strain, whereas one that is subjected to a low level of average shear stress will require more intensive cyclic loading to reach the same level of failure shear strain. After earthquake shaking ceases, it is necessary to make sure that critical structures remain stable over the long term. Any changes in available shear strength must be evaluated. The large-strain, residual © 2003 by CRC Press LLC
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100
Liquid Limit (%)
80
Safe
60
40 Liquid Limit = 35% 0.9 x Liquid Limit
20
Test
0 0
20
40
60
80
100
Water Content (%)
FIGURE 7.36 Modified Chinese Criteria for liquefaction assessment of fine-grained soils. (Modified from Finn, W.D.L., R.H. Ledbetter et al. 1994. Liquefaction in Silty Soils: Design and Analysis, Geotechnical Publication No. 44, American Society of Civil Engineers, pp. 51–76.)
strength of saturated soil depends on void ratio and fabric. If shaking does not induce changes in either of these two, undrained strength before and after shaking is essentially the same. Although stiffness may be affected by the development of excess pore pressures, volume changes that follow the shaking determine changes in strength; that is, of course, if no disturbance of the soil structure occurs. Soil destructuring is of little importance in most insensitive soils strained to low or modest strain levels but it becomes increasingly more important as cyclic strain amplitude increases and it is certainly a major concern in sensitive soils [Thiers and Seed, 1978].
7.5 Liquefaction 7.5.1 General Concepts The phenomenon of liquefaction is generally associated with cohesionless soils. It results from seismic shaking that is of a sufficient intensity and duration. It occurs most commonly in loose, saturated, granular soils that are uniformly graded and that contain few fines. Although sands are especially susceptible, liquefaction is also known to develop in some silts and gravels. Two necessary conditions for liquefaction to occur are the presence of soils of sufficiently low density that will tend to undergo volume reduction upon shaking, and a state of full or near full saturation. Under these conditions, cohesionless soils will tend to densify when subjected to cyclic shear stresses from ground vibrations but will be temporarily prevented from doing so at depth due to restricted drainage. As a result, excess pore pressures accumulate, effective stresses decrease, and soils lose strength and may become liquefied [Seed and Idriss, 1982]. Because the capacity of soils to bear foundation loads is directly related to their strength, liquefaction poses a serious hazard to constructed structures and must be assessed in seismic areas where susceptible deposits exist. It should be noted that liquefaction herein refers to loss of strength and stiffness due to the cyclic pore pressure-generation mechanism just described, and not due to strength loss and stiffness changes that occur in sensitive soils upon monotonic shearing or remolding. This latter mechanism presents a danger in its own right but is not normally seismically related. Not all granular soils are prone to liquefaction. As a general rule of thumb, cohesionless deposits with depth-corrected standard penetration values (N1)60 > 30, depth-corrected normalized cone penetration resistance values qc1N > 175, or stress-corrected shear wave velocity VS1 > 230 m/sec (755 ft/sec) are considered of sufficient density to pose little risk of liquefying. The potential for fine-grained soils to liquefy can be evaluated with reference to the Modified Chinese Criteria [Finn et al., 1994] shown in Figure 7.36. According to these criteria, soils may liquefy if the clay fraction is less than 15% (using the © 2003 by CRC Press LLC
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Liquid Limit < 32
Liquid Limit ≥ 32
Clay content < 10%
Susceptible
May be susceptible (conduct additional testing)
Clay content ≥ 10%
May be susceptible (conduct additional testing)
Not susceptible
FIGURE 7.37 Liquefaction criteria for fine-grained soils. (Modified from Andrews, D.C.A. and G.R. Martin. 2000. “Criteria for Liquefaction of Silty Soils,” in Proc. 12th World Conference on Earthquake Engineering, Auckland, New Zealand.)
Chinese definition of clay size as less than 0.005 mm), the liquid limit is less than 35%, and the water content is larger than 0.9 times the liquid limit. These criteria are somewhat controversial and they do not represent a consensus among practicing engineers [NCEER, 1997]. Establishing more precise and reliable measures for identifying which finer-grained soils are potentially susceptible to liquefaction is an area of ongoing research [Seed et al., 2001]. For example, Andrews and Martin [2000] have reevaluated a large number of field liquefaction case histories and have proposed an adaptation of the Modified Chinese Criteria for U.S. use (Figure 7.37). Evaluation of the liquefaction resistance of soil deposits has evolved over the years into a commonly accepted, simplified empirical procedure, originally developed by Seed and Idriss [1971]. This simplified procedure represents the standard of practice in North America and in many other countries. It is reviewed periodically by groups of experts who make recommendations for changes according to data collected from new earthquakes and new developments in liquefaction hazard assessment. The latest consensus statement is contained in a 1996 NCEER workshop report [NCEER, 1997; Youd and Idriss, 2001], upon which much of the following discussion is based. The potential for liquefaction is assessed with the aid of liquefaction charts, which are based on observations of whether liquefaction did or did not occur at specific sites during numerous past earthquakes. These charts can be used to determine what combinations of shaking intensity and soil resistance are likely to result in liquefaction. Cyclic resistance ratio (CRR) curves represent limiting conditions that determine whether liquefaction will occur. The intensity of earthquake shaking is expressed in terms of the average effective cyclic stress ratio (CSR). Seed and Idriss [1971] proposed the following expression for CSR: CSR =
τ av σ a = 0.65 max vo rd σ ′vo g σ ′vo
(7.25)
where τav is the equivalent shear stress amplitude, amax is the peak horizontal acceleration at ground surface generated by the earthquake, g is the acceleration of gravity, σvo and σ′vo are the total and effective vertical overburden stresses, respectively, and rd is a nonlinear stress reduction coefficient that varies with depth and may be approximated as follows:
© 2003 by CRC Press LLC
rd = 1.000 − 0.00765 z
z ≤ 9.15 m
(7.26a)
rd = 1.174 − 0.02670 z
9.15m < z ≤ 23m
(7.26b)
rd = 0.744 − 0.00800 z
23m < z ≤ 30m
(7.26c)
rd = 0.500
z > 30m
(7.26d)
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FIGURE 7.38 Liquefaction resistance based on SPT. (From Seed, H.B., K. Tokimatsu et al. 1985. “The Influence of STP Procedures in Soil Liquefaction Resistance Evaluations,” J. Geotech. Eng. ASCE, 111(12), 1425–1445. With permission.)
These expressions represent mean values that are suitable for routine engineering practice. However, the variance in rd at any given depth is considerable, and the reliability of these expressions has not been sufficiently verified at depths below about 15 m. In fact, Cetin and Seed [2000] have suggested that the above equations overestimate the true value of rd at depths between 3 and 10 m. They propose a new empirical method for determining rd . However, their approach has not yet been widely adopted in practice. In any case, the best method of estimating the in situ CSR is to conduct a site-specific analysis for a particular earthquake of interest, if feasible. In the simplified procedure, soil resistance to liquefaction is evaluated using any of a number of in situ tests, including the standard penetration test (SPT), the cone penetration test (CPT), shear wave velocity measurements (Vs), and the Becker penetration test. 7.5.1.1 SPT Liquefaction Assessment Chart Liquefaction resistance based on SPT results can be determined with reference to Figure 7.38. This figure was originally developed by Seed and coworkers [1985] and is continually updated with observations
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TABLE 7.5
SPT Corrections
Correction Factor Energy ratio
a
Borehole diameter
Rod length
Sampling method a
Variable
Term
Value
Donut hammer Safety hammer Automatic-trip donut-type hammer 65–115 mm 150 mm 200 mm 3–4 m 4–6 m 6–10 m 10–30 m >30 m Standard sampler Sampler without liner
CE
0.5–1.0 0.7–1.2 0.9–1.3 1.0 1.05 1.15 0.75 0.85 0.95 1.0 <1.0 1.0 1.1–1.3
CB
CR
CS
The preferred method is to measure the energy ratio repeatedly at each site.
following new earthquakes. Combinations of corrected blow count (N1)60 and CSR that plot above the appropriate CRR curve indicate a high probability of liquefaction, whereas those plotting below suggest a low probability of liquefaction. Individual CRR curves are shown for various amounts of fines. The CRR curve for a fines content of less than 5% is referred to as the ”simplified base curve.” The SPT chart is for an earthquake of magnitude 7.5. Corrections for earthquakes of different magnitude, as well as for high overburden pressures and sloping ground surface, are discussed later. The raw measured penetration number, Nm , is corrected to a standard set of conditions so that field values can be compared in a meaningful way. Nm is adjusted to correspond to 60% of the maximum potential free fall energy of a U.S. safety hammer operated by rope and pulley. A correction factor, CE , is applied to the penetration number for other combinations of hammers and hammer release modes. Although values are suggested for use below, it is preferable to directly measure the energy ratio at each site where the SPT is used. Adherence to ASTM D-1686 procedures during field testing should yield consistent energy ratios. In granular soils, N is also affected by the effective overburden pressure σ ′vo , therefore it is corrected to a standard stress of 95.6 kN/m2 (1 ton/ft2) through the use of the factor CN. Corrections to N values are also made for borehole diameter (CB), rod length (CR ), and sampling method (CS):
(N1 )60 = CN N mCECBCRCS
(7.27)
(N1)60 represents the corrected standard penetration value to be used with the SPT liquefaction chart. Values of CE, CB , CR, and CS recommended by the NCEER committee [NCEER, 1997] are listed in Table 7.5. A number of different expressions exist for the overburden correction factor CN. One of the most common ones is given by Liao and Whitman [1986]: CN =
Pa σ ′vo
(7.28)
where Pa equals 1 U.S. ton/ft2, or 96 kPa, and is given in the same units as the overburden stress σ′vo . Values of CN should not exceed about 2.0 for very shallow deposits. 7.5.1.2 CPT Liquefaction Assessment Chart Resistance of soil deposits to liquefaction can also be determined from tip resistance measured during a cone penetration test (CPT). As opposed to the SPT, the CPT provides continuous profiles of penetration resistance. This represents a distinct advantage for interpreting the stratigraphy of soil deposits because the location of soil boundaries and the presence of thin soil layers can be detected much more accurately. © 2003 by CRC Press LLC
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FIGURE 7.39 Liquefaction criteria based on CPT data. (From Robertson, P.K. and C.E. Wride. 1997. “Cyclic Liquefaction and its Evaluation Based on the SPT and CPT,” in Proc. NCEER Workshop on Evaluation of Liquefaction Resistance of Soils, Salt Lake City, NV. Used by permission of the Multidisciplinary Center for Earthquake Engineering Research, Buffalo, NY.)
CPT results are generally more consistent and repeatable than those from any of the other tests used for liquefaction assessment. In addition, the CPT test is conducted under much lower rates of penetration than the SPT, therefore it is inherently more suitable for providing empirical estimates of soil behavior parameters, including those associated with seismic response. However, CPT criteria for evaluating liquefaction resistance are not yet as widely accepted as those associated with the SPT. The reason is that the database upon which the liquefaction criteria in the corresponding CPT chart (Figure 7.39) are based is not nearly as extensive as it is for the SPT chart. There is no doubt that as new field performance data become available and the correlations in Figure 7.39 are revised, the CPT approach will find a wider acceptance in engineering practice The CPT liquefaction assessment chart in Figure 7.39, developed by Robertson and Wride [1997], is used to determine the CRR for a magnitude 7.5 earthquake and for clean sands with less than 5% of fines. The dashed curves show approximate cyclic shear strain potential, γe , to emphasize that shear strain and the potential for ground deformation increase as the resistance to penetration decreases. The raw cone penetration resistance, qc , is corrected for overburden stress and normalized to qc1N , as follows: qc1N = CQ
qc Pa
P CQ = a σ ′vo
(7.29)
n
(7.30)
where Pa equals 1 U.S. ton/ft2, or 96 kPa, and is given in the same units as the overburden stress σ ′vo . A maximum value of 2.0 is applied to the normalizing factor CQ at shallow depths. The exponent n has a value that depends on soil type and ranges from about 0.5 for clean sands to about 1.0 for clayey-type soils. More details on this parameter and the influence of soil type on qc1N are given in Robertson and © 2003 by CRC Press LLC
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Wride [1997]. An additional correction to cone penetration resistance for the presence of thin layers of sand or stiff clay, bounded on either side by softer soil, is discussed by Robertson and Fear [1995]. 7.5.1.3 Shear Wave Velocity Liquefaction Assessment Chart Shear wave velocity Vs can be used as an index to liquefaction resistance because both Vs and CRR reflect, albeit in different proportions, a soil deposit’s void ratio, effective confining stress, stress history, and geologic age [Youd and Idriss, 2001]. Although shear velocity can be determined with great accuracy in the field by various downhole, crosshole, seismic CPT, and surface wave spectral analysis techniques, it reflects small strain behavior, whereas liquefaction involves large strain phenomena. Shear wave velocity measurements should be conducted in conjunction with a limited number of borings when assessing liquefaction resistance so that soil intervals that would appear to classify as liquefiable by the Vs criteria do not include nonliquefiable, soft, clay-rich soils [NCEER, 1997]. Similarly, weakly cemented soils may be susceptible to liquefaction even though they classify as nonliquefiable based on measured values of Vs . Shear wave velocity is normalized in a similar manner to the SPT and CPT procedures described above: P VS1 = VS a σ ′vo
0.25
(7.31)
where again Pa equals 1 U.S. ton/ft2, or 96 kPa, and is given in the same units as the overburden stress σ′vo . The liquefaction chart in Figure 7.40 should only be used for Holocene-age uncemented soils. A dashed CRR curve is shown for values of Vs less than 100 m/sec to indicate that essentially no field performance data exists at lower velocities to substantiate the indicated trend. 7.5.1.4 Becker Penetration Test Gravelly soils can be susceptible to liquefaction. However, SPT, CPT, and Vs measurements are unreliable in these types of soils. The reason is that as the size of individual soil particles approaches that of the penetrometer, resistance to penetration is tied to the properties and arrangement of individual particles in the zone of deformation. This can increase the resistance to penetration in unpredictable ways. The obvious solution appears to be the use of larger penetrometers. The Becker Penetrometer Test (BPT) constitutes a type of test that makes use of this concept. It consists of a 168-mm-wide double-walled casing that is driven into the ground by a diesel pile hammer. The Becker penetration resistance is defined as the number of blows required to advance the casing a distance of 300 mm. Very few tests have been conducted at sites where liquefaction has been observed to occur and no liquefaction charts equivalent to those in Figures 7.38 and 7.39 have been developed. Instead, the BPT has been correlated to the SPT at a number of locations where both types of tests have been conducted side by side [Harder and Seed, 1986]. Using the correlations in Figure 7.41, the BPT value is converted to an equivalent SPT blow count, which in turn is used to estimate liquefaction resistance. There are a number of concerns about the BPT that have not been addressed adequately. Due to the high driving energy that is possible with this device, the test is appealing for use in very deep deposits. However, friction along the casing becomes difficult to evaluate properly in deposits deeper than about 30 m. In this case, the correlation of Harder and Seed [1986] in Figure 7.41, which incorporates friction intrinsically, may not be appropriate [Sy and Campanella, 1994]. Also, this correlation should not be used for sites with thick, dense deposits overlying loose sands or gravels because it has not been verified for these conditions [NCEER, 1997].
7.5.2 Magnitude Scaling Factors and Other Corrections The CRR curves in the SPT, CPT, and Vs charts correspond to an earthquake of magnitude 7.5. Seed and Idriss [1982] suggested the use of magnitude scaling factors (MSF) for earthquakes of magnitude other than 7.5. These factors are used to shift the CRR base curve vertically according to: CRRcor = CRR 7.5 × MSF © 2003 by CRC Press LLC
(7.32)
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FIGURE 7.40 Liquefaction criteria based on shear wave velocity for Holocene uncemented sands. (From Andrus, R.D. and K.H. Stokoe. 1997. “Liquefaction Resistance Based on Shear Wave Velocity,” in Proc. NCEER Workshop on Evaluation of Liquefaction Resistance of Soils, Salt Lake City, NV. Used by permission of the Multidisciplinary Center for Earthquake Engineering Research, Buffalo, NY.)
The range of MSF values recommended by the NCEER committee is shown in Figure 7.42. The chart-based empirical approach to liquefaction assessment has become widely used in engineering practice. It was originally intended for relatively shallow and level deposits. In order to expand the range of conditions for which the approach can be applied, correction factors were developed by Seed [1983] for large static overburden stresses and for large shear stresses on potential failure planes, specifically for use in conjunction with liquefaction assessment of embankment dams. When applicable, these factors are used as follows: CRRcor = CRR 7.5× MSF × K σ × K α
(7.33)
Very few liquefaction observations have been made where large initial overburden or shear stresses played a role. Therefore, these factors have been developed primarily from the results of extensive laboratory testing. The liquefaction resistance of a soil increases with increasing confining pressure. Cyclic triaxial compression tests show that the resistance to liquefaction, as measured by the CSR, decreases nonlinearly with increasing confining pressure. To account for this effect at overburden pressures larger than 100 kPa (depths larger than about 10 to 15 m), Seed [1983] recommended the use of the factor Kσ. The NCEER committee [1997] reviewed the Seed factors and recommended that the values shown in Figure 7.43 be used instead. They also reviewed data from a number of studies that considered the effect of soil type and density but no consensus was reached on what to recommend for engineering practice. The NCEER © 2003 by CRC Press LLC
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FIGURE 7.41 Correlation between BPT and SPT blow counts. (From Harder, L.F. and H.B. Seed. 1986. “Determination of Penetration Resistance for Coarse-Grained Soils Using the Becker Hammer Drill,” Earthquake Engineering Research Center, University of California, Berkeley. With permission.)
FIGURE 7.42 Range of MSF values. (From Youd, T.L. and S.K. Noble. 1997. “Magnitude Scaling Factors,” in Proc. NCEER Workshop on Evaluation of Liquefaction Resistance of Soils, Salt Lake City, NV. Used by permission of the Multidisciplinary Center for Earthquake Engineering Research, Buffalo, NY.)
committee is considering three correction curves, with the curve shown in Figure 7.43 corresponding to a medium-dense sand [Finn, 2001]. In any case, caution must be exercised when using these factors at depths exceeding 15 m because of the lack of field data to substantiate the reported values. Where a sloping ground surface exists, potential failure surfaces are subjected to gravitational shear stresses prior to earthquake shaking. The effect of such an initial static shear stress, τst , on subsequent liquefaction resistance can be considered by normalizing such a stress by the effective vertical stress, i.e., © 2003 by CRC Press LLC
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FIGURE 7.43 Correction for effective confining pressure for clean and silty sands and gravels. (From Harder, L.F. and R. Boulanger. 1997. “Application of Ksigma and Kalpha Correction Factors,” in Proc. NCEER Workshop on Evaluation of Liquefaction Resistance of Soils, Salt Lake City, NV. Used by permission of the Multidisciplinary Center for Earthquake Engineering Research, Buffalo, NY.)
2.0 σ'vo ≤ 300 kPa 1.5 Dr≈55-70% Kα
1.0
Dr≈45-50%
0.5
Dr≈35%
0.0 0.0
0.1
0.2 τ α= s σ'vo
0.3
0.4
FIGURE 7.44 Effect of initial static shear stress on liquefaction potential. (From Harder, L.F. and R. Boulanger. 1997. “Application of Ksigma and Kalpha Correction Factors,” in Proc. NCEER Workshop on Evaluation of Liquefaction Resistance of Soils, Salt Lake City, NV. Used by permission of the Multidisciplinary Center for Earthquake Engineering Research, Buffalo, NY. With permission.)
α = τst /σ′vo . This alpha ratio is zero for a level ground surface. In general, its has been found that the presence of a static shear stress on the potential failure surface tends to increase the cyclic resistance, in terms of the CSR necessary to trigger liquefaction, as long as the soil is relatively dense and the confining pressure is low. On the other hand, loose soils and some soils under high confining pressure have a lower liquefaction resistance when an initial static shear stress is present [Harder and Boulanger, 1997; NCEER 1997]. Harder and Boulanger have recommended tentative α vs. Kα curves (Figure 7.44), which, however, were not endorsed by the NCEER committee for use in practice due to their uncertainty. Liquefaction analysis for sloping ground conditions is a complex problem that requires further research. © 2003 by CRC Press LLC
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It has been observed that liquefaction resistance of soil deposits increases with age [Youd and Hoose, 1977; Youd and Perkins, 1978; Seed, 1979b]. Young Holocene sediments are more prone to liquefaction than older Holocene sediments. Pleistocene and earlier deposits are even more resistant. However, this trend has not been quantified due to a lack of data and an incomplete understanding of the effects of age on liquefaction resistance. The liquefaction assessment procedures described above should only be used for Holocene deposits that are not more than a few thousand years old. In some cases, it may be possible to balance the effect of a decreasing value of Kσ with depth with a parallel increase in liquefaction resistance that could be expected due to increasing age with depth. Such an approach should only be used with great care and certainly would only be reasonable for natural deposits where age effects increase uniformly with depth [Youd and Idriss, 2001].
7.5.3 Liquefaction Settlement Loose sand deposits that are prone to liquefaction during an earthquake are also susceptible to settlement, which has proven to be very damaging to structures, pavements, and lifelines. Recent earthquakes in Japan, Turkey, Taiwan, and elsewhere have resulted in surface settlements of tens of centimeters at some locations. However, estimating settlement resulting from seismic shaking is a difficult proposition and errors of 50% or more can be expected when making predictions [Kramer, 1996]. Although detailed ground response analysis can be conducted to estimate settlements, and this may be necessary for dams or other instances where the ground surface is nonlevel, a simplified procedure may be sufficient in many cases [Tokimatsu and Seed, 1987]. Liquefaction settlement in dry sands is a function of the density of the soil, the number of strain cycles and the magnitude of the cyclic shear strain induced by seismic shaking [Silver and Seed, 1971]. An effective shear strain, γeff , can be calculated from the average cyclic shear stress, τav , as follows: γ eff =
τ av Geff Gmax Gmax
(7.34)
where G max is the small-strain shear modulus and G eff the effective shear modulus at the induced strain level. The average cyclic shear stress is given by Equation 7.25; therefore, the above expressions can be rewritten as: G σ a γ eff eff = 0.65 max vo rd g Gmax Gmax
(7.35)
G max can be determined from shear wave velocity measurements or other suitable small-strain laboratory or field procedures. It can also be approximated by the relationship given by Seed and Idriss [1970]: Gmax = 1, 000 × ( K 2 )max × (σ m′ )
1/3
(7.36)
where σ′m is the mean principal stress in units of psf. The parameter (K2)max is a function of void ratio or relative density (Table 7.6) and can also be obtained from corrected SPT values:
(K 2 )max = 20[(N1 )60 ]
1/3
(7.37)
Equations (7.36) and (7.37), along with the appropriate maximum acceleration, amax, are evaluated to determine the term on the left-hand side of Equation (7.35). This quantity is used in Figure 7.45 to determine the effective shear strain γeff , which in turn is used with Figure 7.46 to obtain the associated volumetric strain. A soil profile is divided into an appropriate number of layers of approximately uniform relative density, or corrected SPT number, and the volumetric strain is computed using the above approach. Figure 7.46 corresponds to an earthquake of magnitude 7.5 © 2003 by CRC Press LLC
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TABLE 7.6
(K2) max Values for Estimating Maximum Shear Modulus
DR (%) 30 40 45 60 75 90
(K2) max
Void ratio, e
(K2) max
34 40 43 52 59 70
0.4 0.5 0.6 0.7 0.8 0.9
70 60 51 44 39 34
Source: Modified from Seed, H.B. and I.M. Idriss. 1970. “Soil Moduli and Damping Factors for Dynamic Response Analysis,” Earthquake Engineering Research Center, University of California, Berkeley. 10−2
σ′m = 0.1 tsf 0.2 0.5
12
Shear Strain, γeff
10−3
10−4
10−5 10−5
10−4 γeff (Geff/Gmax)
10−3
FIGURE 7.45 Induced strain in sand deposits. (From Tokimatsu, K. and H.B. Seed. 1987. “Evaluation of Settlements in Sand Due to Earthquake Shaking,” J. Geotech. Eng. ASCE, 113(8), 861–878. Used by permission of the American Society of Civil Engineers.)
with approximately 15 representative cycles. For earthquakes with magnitudes other than 7.5, the volumetric strain can be obtained from the volumetric strain scaling factor rm : rm =
(ε c )M (εc )M =7.5
(7.38)
Values for r m are listed in Table 7.7. Since the relationships in Figure 7.46 are based on unidirectional simple shear conditions, whereas actual earthquakes subject soil deposits to multidirectional shaking, it is necessary to double the volumetric strains obtained from Figure 7.46. Settlement is calculated by multiplying the volumetric strain by the layer thickness. The total settlement then is the sum of the settlements for each of the layers. Finally, the total settlement is doubled to account for the effects of multidirectional shaking. © 2003 by CRC Press LLC
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Cyclic Shear Strain, γxy − percent −3
10−2
Volumetric Strain Due to Compaction, εc − percent
10 10−3
10−2
N1 ≈ 40 ≈ 30 ≈ 20 ≈ 15 ≈ 10
10−1
1
15 Cycles
≈5
10−1
1
10
FIGURE 7.46 Relationship between volumetric strain, shear strain, and penetration resistance for dry sands. (From Tokimatsu, K. and H.B. Seed. 1987. “Evaluation of Settlements in Sand Due to Earthquake Shaking,” J. Geotech. Eng. ASCE, 113(8), 861–878. Used by permission of the American Society of Civil Engineers.)
For the case of saturated sands, Tokimatsu and Seed [1987] provide the chart in Figure 7.47 to estimate the corresponding volumetric strain of each soil layer. Again, this strain is adjusted for earthquakes of magnitude other than 7.5 by using the factors in Table 7.7 and the settlements are calculated as described for the case of dry sand.
7.5.4 Shear Strength of Liquefied Soil Where the ground surface is inclined, as in the case of natural or embankment slopes, post-liquefaction lateral displacements are a potential concern. The amount of lateral deformation following a period of shaking is a function of the difference between the post-liquefaction steady-state shear strength, Ssu , and the shear stress necessary to reestablish equilibrium. The larger this difference, the larger the expected liquefaction flow. The residual shear strength corresponds to a limiting state of constant shear stress, constant confining pressure, and constant volume [Castro and Poulos, 1977]. It can be determined through laboratory procedures or field correlations. It is a function primarily of the volume change tendency of the soil. The laboratory procedure consists of consolidating a representative specimen to its in situ stress state, as close as possible, and shearing it under undrained conditions along an appropriate stress path. The resulting steady-state shear strength then must be corrected for disturbance due to sampling and handling. Poulos et al. [1985] have suggested a rational procedure for carrying out such a correction that involves additional testing of reconstituted specimens. Conversely, Seed [1986] analyzed a number of flow slides and back-calculated the post-liquefaction shear strength in each case. He suggested a relationship between shear strength and SPT penetration number (Figure 7.48). Seed and Harder [1990] and Stark and Mesri [1992] have further proposed that corrections be applied to the penetration number for soils with more than 10% fines to obtain an equivalent clean sand SPT value for use in Figure 7.48:
(N1 )60−cs = (N1 )60 + N corr where the correction factor N corr is obtained from Table 7.8. © 2003 by CRC Press LLC
(7.39)
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0.6
Volumetric strain (%) 0.5
10 5 4 3
2
1
0.5
0.2
0.4
0.1
τav σ'vo 0.3
0.2
0.1
0.0
0
10
20
30
40
50
(N1)60
FIGURE 7.47 Relationship between cyclic stress ratio and volumetric strain for saturated clean sands. (From Tokimatsu, K. and H.B. Seed. 1987. “Evaluation of Settlements in Sand Due to Earthquake Shaking,” J. Geotech. Eng. ASCE, 113(8), 861–878. Used by permission of the American Society of Civil Engineers.) TABLE 7.7
Scaling Factors for Equation 7.38
Earthquake Magnitude (M)
Volumetric Strain Scaling Factor (rm)
5.25 6 6.75 7.5 8.5
0.4 0.6 0.85 1.0 1.25
Source: Adapted from Tokimatsu, K. and H.B. Seed. 1987. “Evaluation of Settlements in Sand Due to Earthquake Shaking,” J. Geotech. Eng. ASCE, 113(8), 861–878.
7.6 Seismic Analysis of Slopes and Dams Seismic shaking can induce destabilizing dynamic forces in earth embankments, natural and constructed slopes, and retained fills. The result may be unacceptable levels of deformation and even outright failure. A series of analysis methods exist to evaluate the effects of earthquake motions, ranging from a simple pseudostatic approach to comprehensive stress-strain dynamic finite element methods that account for nonlinear material behavior and strength reduction due to liquefaction or strain softening. In the pseudostatic method inertial forces induced by earthquake shaking are represented in terms of pseudostatic accelerations, ah and av , and associated inertial forces, Fh and Fv: Fh = © 2003 by CRC Press LLC
ah W = kh W g
Fv =
av W = kvW g
(7.40)
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FIGURE 7.48 Residual shear strength as a function of SPT penetration number. (From Seed, R.B. and L.F. Harder. 1990. “SPT-Based Analysis of Cyclic Pore Pressure Generation and Undrained Residual Strength,” H. Bolton Seed Memorial Symposium. Used by permission of BiTech Publishers.) TABLE 7.8 Correction of SPT Resistance for Estimating Residual Undrained Shear Strength for Various Fine Contents According to the Procedures of Seed–Harder and Stark–Mesri Fines Content (%)
Ncor r [Seed and Harder, 1990]
Ncor r [Stark and Mesri, 1992]
0 1 — — 2 — — 4 5
0 2.5 4 5 6 6.5 7 7 7
0 10 15 20 25 30 35 50 75 Data from Kramer [1996].
where ah and av are the horizontal and vertical accelerations, respectively, associated with a particular level of earthquake shaking, and kh and kv are nondimensional pseudostatic earthquake coefficients. W is the weight of the failed mass. These forces can be incorporated into any limit equilibrium analysis procedure to determine an equivalent overall factor of safety. For example, in terms of the Ordinary Method of Slices (Figure 7.49), the factor of safety is expressed as: M
resisting force FS = = driving force © 2003 by CRC Press LLC
∑ cb + [(W − F )cos α − F sin α]tan φ v
n
h
(W − Fv ) sin α + Fh cos α
(7.41)
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Slice n M number of slices Fv β
Fh
e
W b
α
c, φ rfac u es r u l fai
FIGURE 7.49 Ordinary Method of Slices for slope stability analysis with pseudostatic seismic forces.
TABLE 7.9
Typical Values of Kh and FS for Use in Stability Calculations
kh
FS
0.10 0.15 0.05–0.15
>1.0 >1.0
0.15–0.25 0.15 1/3 to 1/2 PGA 1/2 PGA
>1.0 >1.15 >1.0 >1.0
Comments Major earthquake Great earthquake Standard of practice; somewhat larger for critical conditions Standard of practice With a 20% strength reduction With a 20% strength reduction
Source U.S. Army Corps of Engineers [1982] State of California Japan Seed [1979a] Marcuson and Franklin [1983] Hynes-Griffin and Franklin [1984]
Source: Adapted from Abramson, L.W., T.S. Lee et al. 2002. Slope Stability and Stabilization Methods. New York, John Wiley & Sons.
where c and φ are the Mohr-Coulomb strength parameters along the failure surface and the summation is carried out over all M slices. Compared to the nonseismic case, F h clearly results in a reduction of the FS. On the other hand, the effect of F v is less pronounced because it appears with the same sign in both the numerator and the denominator. As a result, it is common to neglect F v altogether. Most modern commercial limit equilibrium slope stability programs allow for this type of pseudostatic analysis. The difficulty arises in selecting appropriate values of kh and FS. Because kh represents the inertial shaking effects, it is reasonable to assume that it should be related in some fashion to the peak horizontal acceleration amax (PHA). In general, slope deposits are compliant to various degrees and amax only occurs over a very short period of time. Therefore, in practice kh is taken as a fraction of the maximum acceleration. Considerable judgment is required in selecting appropriate values of kh. A number of suggestions can be found in the literature [Seed, 1979a; U.S. Army Corps of Engineers, 1982; Marcuson and Franklin, 1983; Hynes-Griffin and Franklin, 1984; Abramson et al., 2002] and some of these are listed in Table 7.9. The value of kh is often prescribed in local codes. Although easy to conduct, the pseudostatic approach is quite simplistic. It attempts to represent complex dynamic behavior in terms of static forces. Stability is expressed in terms of an overall factor of safety. The implicit assumption is that the soil is rigid-perfectly plastic and unchanging. This does not represent an appropriate approach in cases where significant excess pore pressures may accumulate or where strength degradation due to seismic loading is in excess of approximately 15% [Kramer, 1996]. Displacements associated with time-varying inertial forces can be estimated, to a first degree, with the procedure proposed by Newmark [1965], which represents an extension of the pseudostatic approach. An analogy is made between failure along a given sliding surface in a slope and a block initially resting on an inclined surface (Figure 7.50). The block is subjected to horizontal inertial forces kh(t)W that © 2003 by CRC Press LLC
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A
kh(t)W
kh(t)W
W B
W
ay
C
t
FIGURE 7.50 Newmark sliding block method.
correspond to seismic motions propagating through the slope deposit. Displacement is initiated when the sum of the downslope static and inertial forces equals the strength developed at the interface between the block and the inclined plane. This condition occurs when the factor of safety is 1.0 and corresponds to a yield coefficient ky and a yield acceleration ay = kyg. When the block is subjected to an interval with acceleration larger than ay , it will begin to move relative to the plane (Figure 7.50). The corresponding velocities and displacements can be obtained through integration of the acceleration record in excess of ay . The assumption is that the sliding mass constitutes a rigid body. This assumption is only appropriate for slopes where soils are very stiff or where the motion is of low frequency. Where this is not the case careful consideration must be given in selecting an appropriate accelerogram. This may be done by carrying out a site response analysis and determining acceleration series at various points along the potential failure surface. An average horizontal equivalent acceleration (HEA) can be developed for use with the Newark sliding block method. With reference to Figure 7.50, this would be computed as: HEA (t ) =
m Aa A (t ) + mB aB (t ) + mC aC (t ) m A + mB + mC
(7.42)
where m represents the mass of soil in each slice above the point where the acceleration response a(t) is given. Conversely, a dynamic finite element analysis can be conducted to calculate average accelerations over finite lengths of the potential failure surface based on integration of the time-dependent stresses. These acceleration time series can in turn be used as input for the sliding block analysis. A number of computer programs are available that can carry out such an analysis, including QUAD-4 [Idriss et al., 1973] and FLUSH [Lysmer et al., 1975]. Makdisi and Seed [1978] developed a simplified procedure to estimate permanent horizontal displacements of earth dams and embankments. These are determined with the aid of the charts in Figure 7.51. The analysis is based on the dynamic response of embankments subjected to a range of ground motions representing earthquakes of various magnitudes. Makdisi and Seed calculated the distribution of average maximum acceleration with depth below the crest of the embankment (Figure 7.51A and B). Displacements were estimated by comparing the acceleration at depth to the corresponding yield acceleration by means of a Newmark-type sliding block analysis. The yield acceleration was taken as 80% of the undrained shear strength of the soil. Results of the sliding block analysis are summarized in Figure 7.51C, from which the horizontal displacement can be calculated for any failure surface extending a distance y below the crest. To is the fundamental period of the dam, which can be obtained by means of an approximate shear beam analysis [Gazetas, 1982] or other two-dimensional dynamic response modeling approach. Although widely used, it is important to note that the Makdisi-Seed procedure is based on a limited set © 2003 by CRC Press LLC
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of case studies and, strictly speaking, should only be applied to dams and embankment slopes with seismic motions corresponding to earthquake magnitudes in the range of 6.5 to 8.5 where the PGA at the base of the embankment is at least 0.2 g. A number of equivalent-linear procedures have been suggested to estimate approximate permanent displacements in dams and slopes [Lee, 1974; Serff et al., 1976]. Their most appealing quality is that they retain the simplicity of linear material behavior. They work well, provided that pore pressures remain relatively low and that seismic motions do not induce excessive levels of material nonlinearity [Finn, 2001]. However, it is likely that in the future more reliance will be placed on stress-based finite element and other similar numerical procedures that directly incorporate inelastic soil behavior. A sufficient number of two- and three-dimensional analyses have been conducted using constitutive models ranging from simple hysteretic to complex elasto-plastic models to validate this approach [Prevost et al., 1985; Finn, 1988; Griffiths and Prevost, 1988; Marcuson et al., 1992]. Computer codes such as TARA-3 [Finn et al., 1986], PLAXIS [Brinkgreve and Vermeer, 1988], and QUAKE/W [Quake/W, 2001] have been developed to carry out these types of analysis.
7.7 Earthquake-Resistant Design of Retaining Walls Soil pressures that act on retaining structures during earthquake shaking include both static and dynamic components. Dynamic forces vary as the shaking proceeds and reflect not only the type of wall and soil retained but also complex structure-interaction effects that in general are difficult to analyze. For example, motion components that are close to the natural period of the soil-structure system can induce very large transient pressures. Also, phase differences along the length of the retaining structure may induce significant shear forces and bending moments. In practice, however, most walls are designed using simplified pseudostatic methods similar to those described previously for natural and constructed slopes. The approach is to determine all static forces, along with pseudostatic seismic forces, and proceed with conventional stability checks for overturning, sliding, bearing capacity, and overall stability. Seismic effects are usually considered using the Mononobe–Okabe method [Mononobe and Matsuo, 1929; Okabe, 1929], which represents an extension of the Coulomb theory. The forces acting on active and passive wedges of cohesionless soil are shown in Figure 7.52. The pseudostatic forces are given in terms of the wedge weight W and the seismic coefficients kh and kv described earlier. For the active case (Figure 7.52A), the total lateral force on the wall corresponds to the maximum value of Pae exerted by any wedge with critical failure surface of inclination η. This force can be expressed as: Pae =
1 γH 2 (1 − kv )K ae 2
(7.43)
where K ae =
(
cos 2 φ − θ − β
) ( )
)
1/ 2 − − δ + φ φ α β sin sin ( ) cos 2 θ cos β cos δ + θ + β 1 + cos δ + θ + β cos (α − θ)
(
)
(
2
(7.44)
and k β = tan −1 h 1 − kv
© 2003 by CRC Press LLC
(7.45)
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Y
H
(A) 0
F.E. Method 0.2 “Shear Slice” (range for all data) 0.4 y/h 0.6
Average of all data
0.8
10 0
0.2
(B)
0.4 0.6 kmax/ümax
0.8
1.0
10
M~8
1
M~8 7
U/kmax g To − seconds
M~7
6 0.1
M~6 0.01
0.001 (a)
(b)
0.0001 0
(C)
0.2
0.4
0.6 ky/kmax
0.8
1.0 0
0.2
0.4
0.6 ky/kmax
0.8
1.0
FIGURE 7.51 Simplified procedure to estimate permanent horizontal displacements of earth dams and embankments. (From Makdisi, F.I. and H.B. Seed. 1978. “Simplified Procedure for Estimating Dam and Embankment Earthquake-Induced Deformations,” J. Geotech. Eng. ASCE, 104(GT7), 849–867. Used by permission of the American Society of Civil Engineers.) © 2003 by CRC Press LLC
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A
C
α
C
α A
Fv
Fv
γ, φ c=0 Fh
θ
θ Fh W
φ
W
Ppe R
δ Pae
R
φ
δ
γ, φ c=0 η
η B
B (A) Active
(B) Passive
FIGURE 7.52 Mononobe–Okabe method. Forces acting on active (A) and passive (B) wedges of cohesionless soil.
Note that if φ – α – β < 0, Equation 7.44 cannot be evaluated. This means that equilibrium is not satisfied. For stability under seismic conditions it is therefore necessary that α ≤ φ – β . The location of the combined wall force Pae can be obtained by separating Pae into static and dynamic components: Pae = Pa + ∆ Pae
(7.46)
The static force Pa acts at a height of H/3 above the base of the wall. According to Seed and Whitman [1970], the dynamic component Pae acts at an approximate elevation of 0.6H above the base. Hence, the location of Pae can be calculated as: z=
Pa ( H 3) + ∆Pae (0.6 H ) Pae
(7.47)
The critical failure surface for seismic conditions is flatter than for the static case. An expression for the angle δ can be found in Kramer [1996]. The Mononobe–Okabe method for estimating Pae can also be applied to c-ϕ backfill soil [Prakash and Saran, 1966]. For the passive case (Figure 7.52B), the total lateral force on the wall is given by: Ppe =
1 γ H 2 (1 − kv )K pe 2
(7.48)
where K pe =
(
cos 2 φ + θ − β
) ( )
)
1/ 2 sin (δ + φ) sin φ + α − β 2 cos θ cos β cos δ − θ + β 1 − cos δ − θ + β cos (α − θ)
(
)
(
2
(7.49)
The Mononobe–Okabe method is subject to the limitations of the Coulomb theory and to the same uncertainties associated in selecting appropriate coefficients kh and kv as was discussed earlier. This method should not be used for soils that may liquefy or otherwise may lose strength due to the shaking. Wood [1973] showed that where the principal energy of the input motions approaches the fundamental frequency of the unrestrained backfill ( fo = Vs /4H), dynamic amplification becomes an important factor, which is not considered in any of the analysis procedures described in this section. © 2003 by CRC Press LLC
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Elastic soil
H L
Unyielding wall
1.2
ν = 0.5 ν = 0.4
1.0
0.8
ν = 0.3
0.8
ν = 0.5
ν = 0.2 Fp 0.6
0.6
0.4
Fm 0.4
0.2
0.2
ν = 0.4
ν = 0.3 ν = 0.2
0
0 0
2
4
6
8
10
0
L/H
2
4
6
8
10
L/H
Dimensionless thrust factor for various geometries and soil Poisson’s ratio values.
Dimensionless moment factor for various geometries and soil Poisson’s ratio values.
FIGURE 7.53 Dynamic loads on rigid retaining walls. (Modified from Wood, J. 1973. “Earthquake-Induced Soil Pressures on Structures,” Report EERL 73-05, California Institute of Technology, Pasadena, p. 311.)
Very large gravity walls and other retaining structures that are restrained may not yield sufficiently to reach active or passive plastic equilibrium states. Wood [1973] presents a method to calculate dynamic lateral forces and overturning moments for a rigid wall by assuming that the backfill soil behaves in a homogeneous, linearly elastic fashion, and that the seismic excitation is due to a uniform, constant, horizontal acceleration throughout the backfill. Wood actually considered two rigid walls separated by a distance L of sufficient magnitude to avoid interaction between the two of them (Figure 7.53). The dynamic force and moment are calculated as:
© 2003 by CRC Press LLC
∆Poe = γ H 2
ah F g p
(7.50)
∆M oe = γ H 3
ah F g m
(7.51)
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where ah is the amplitude of the motion. The dimensionless factors F p and F m are shown in Figure 7.53. The point of application of ∆Poe, above the base of the wall, is given by: z=
∆M oe ≈ 0.63H ∆Poe
(7.52)
The previous methods assume that the backfill is not immersed in water. Although walls are typically built with provisions for proper drainage, this is not possible for retaining structures where water is found on either side, as is the case for many harbor and other shore-front structures. Extensive damage to such structures was observed during recent earthquakes in Turkey, Taiwan, and Japan and in many cases were attributed to dynamic water effects. Water influences the inertial forces in the backfill and may result in substantial hydrodynamic pressures. Also, a loose, saturated granular backfill may liquefy and cause undesirable settlements. If the permeability of the soil is sufficiently small (typically less than about 10–3 cm/sec), the solid and fluid fractions are likely to move in unison, whereas if the permeability is very large, the fluid will tend to move independently of the solid structure. In the former case, the inertial forces are dependent on the total unit weight of the soil, whereas in the latter case they will be a function of the submerged unit weight. If the type of backfill is such that water is restrained by the soil skeleton, the Monotobe–Okabe method can be modified to give the active total soil force on the wall by replacing the soil unit weight in Equation 7.43 according to: γ = γ b (1 − ru )
(7.53)
where r u is the pore pressure ratio, defined as the pore pressure divided by the effective confining pressure, and γb is the submerged unit weight. The seismic coefficient given in Equation 7.45 now becomes: γ sat kh β = tan −1 γ b (1 − ru ) (1 − kv )
(7.54)
where γsat is the saturated unit weight of the soil. In addition to the hydrostatic water pressure in the absence of shaking, an additional equivalent hydrostatic term must be considered which is calculated using an equivalent fluid unit weight: γ w −eq = γ w + ru γ b
(7.55)
If the backfill is partially submerged to a height λH above the base of the wall (λ < 1.0), it is necessary to use an average soil unit weight:
(
)
γ = λ2 γ sat + 1 − λ2 γ d
(7.56)
where γd is the dry unit weight of the soil. The additional equivalent hydrostatic term calculated with the equivalent fluid unit weight in Equation 7.55 also must be included for partially submerged backfill. Permanent displacements of yielding walls are often a greater concern than outright failure because excessive deformations can severely limit their intended function. Richards and Elms [1979] use Newmark’s sliding block method to estimate permanent lateral displacement of gravity walls. Consider a gravity wall acted upon by a Monotobe–Okabe lateral force Pae during seismic shaking, as shown in Figure 7.54. Lateral displacement will be initiated on the verge of active failure, at which point plastic equilibrium dictates that:
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θ khW
Pae δ
W
FIGURE 7.54 Forces acting on gravity wall during seismic shaking.
φb
N = W + Pae sin (δ + θ)
(7.57)
T = khW + Pae cos (δ + θ)
(7.58)
T = N tan φb
(7.59)
where φb is the friction angle between the base and the foundation soil. These expressions can be combined to obtain: kh =
ay g
= tan φb −
Pae cos (δ + θ) − Pae sin (δ + θ) tan φb W
(7.60)
The term ay represents the yield acceleration, beyond which lateral displacement occurs. Using the results of Newmark [1965] and Franklin and Chang [1977], Richards and Elms developed the following relationship to estimate permanent lateral displacement: d perm = 0.087
v p2 a3p a3y
(7.61)
In this equation vp is the peak velocity and ap the peak acceleration at the wall location. This type of analysis should not be used indiscriminately because it is rather simplistic and ignores several effects that may play an important role in some cases. Only accelerations in the direction normal to the length of the wall are considered. Neither vertical nor horizontal acceleration components in the direction of the length of the wall are accounted for. Also, the backfill and the wall are assumed to act as one and no amplification of input motions occurs in the retained soil. Only lateral sliding displacements are estimated but not tilting or vertical settlements. Whitman and Liao [1985] considered some of these effects and estimated errors associated with them. Kramer [1996] presents procedures for the design of various types of retaining structures that are based on the pseudostatic methods described in this section. A more rigorous approach to the design and analysis of retaining structures is possible by means of the finite element method. In fact, the finite element method is quickly becoming the method of choice for the design of all but the simplest of retaining structures. © 2003 by CRC Press LLC
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7.8 Soil Remediation Techniques for Mitigation of Seismic Hazards If seismic hazards are deemed to be unacceptably high because of poor soil conditions, it is often possible to achieve improved seismic performance through the use of one or more soil remediation techniques. Poor performance is the result of (1) inadequate strength, (2) low stiffness, or (3) insufficient drainage. Many remediation techniques have evolved over the years, mostly through trial and error, aimed at improving at least one of these properties. When selecting one or more mitigation methods, it is important to consider the effectiveness of the remediation approach for the particular situation at hand, cost, environmental consequences, regulatory requirements, and technical feasibility. Also, careful assessment of the degree of ground improvement achieved is essential. The subject of soil remediation is quite extensive and a number of excellent sources and case studies are available in the literature [Hausmann, 1990; Hryciw, 1995; Mitchell et al., 1995; Schaefer, 1997]. The purpose of this section is to highlight the most promising techniques for improving seismic performance. Excavation and replacement may be a cost-effective solution for sufficiently shallow deposits. Placing a structure at depth may bypass undesirable surface soils, although costs and construction difficulties increase rapidly with depth and with excavation below the water table, particularly in high-permeability soils. Surrounding deposits that have not been modified may still cause problems as lifelines and other connecting structures may be damaged during an earthquake. Compaction can be accomplished using a variety of techniques that are aimed at increasing the density of soil, thereby resulting in improved stiffness, strength, and liquefaction resistance. Vibrocompaction is most effective for clean, loose cohesionless soils with less than about 15% silt and less than about 3% clay content. It is achieved by vibration of the head of the vibration probe as it is withdrawn. Because compaction occurs only within a short range of the probe, the procedure must be repeated at regular spacings on the order of 5 to 10 ft. Of course, the spacing depends on the size of the probe and the soil type. During the past few years, larger and more powerful vibrators have been introduced, which allow larger spacings and deeper penetration (in some cases, up to 120 ft). When compaction is achieved by horizontal motion of the vibrator, it is referred to as vibroflotation. Vibratory techniques also exist that induce vertical vibration, such as Terra-Probe, Vibro-Wing, and Tri-Star or Y-Probe methods [Hryciw, 1995]. Wightman [1991] presents an overview of this technique. Dynamic compaction involves dropping a heavy weight from a large distance. The high energy upon impact is provided by heavy steel or concrete units (6 to 35 tons) that freefall from distances up to 100 ft or more. It often represents an alternative to vibrocompaction, especially for uncontrolled fills, municipal solid waste deposits, coal mine spoils, and other loose soils. Soils with significant amounts of fines (20% or more) can in some cases be densified quite effectively. The depth of improvement is related to the tamper weight and drop height but may reach up to 30 ft or more. A good reference on dynamic compaction is the FHWA publication by Lukas [1986], which was updated in 1996 as FHWA Geotechnical Engineering Circular No. 1. Blast densification is another high-energy ground improvement technique that achieves densification by destroying existing soil structure and forcing soil grains into a tighter configuration as a result of shock waves produced by the blast. Charges are placed in predrilled or jetted holes. The size of the charge must be selected carefully so that it is sufficiently large to be effective but not too intense to cause excessive vibrations that may cause damage to nearby structures. Liquefaction may develop and may have to be controlled by proper drainage means. Because of the potential of undesirable effects in surrounding areas, blast densification has not seen the same degree of use as the previous techniques. However, it has been shown effective in densifying soils to depths of approximately 130 ft [Narin van Court and Mitchell, 1995]. Compaction piles achieve densification by displacing the soil as the piles are driven into the ground. Because they typically densify the soil to distances on the order of a only few pile diameters, they must be placed close together to be effective. Improvements have been noted to depths of about 60 ft [Marcuson et al., 1991]. Grouting involves the injection of various grouting agents into the soil. Compaction grouting has been shown to be effective for mitigation of liquefaction potential [Graf, 1992; Boulanger and Hayden, 1995]. The technique consists of injecting a soil-cement grout of sufficient plasticity and friction under pressure, © 2003 by CRC Press LLC
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which displaces and densifies soil in a controlled fashion. Although the technique is widely used for a number of purposes, there is little in terms of a rational design methodology. Instead, the method has progressed based almost entirely on trial and error and a few empirical observations. Research is now under way to establish optimum grout characteristics, injection pressures, and effective pumping rates vs. soil characteristics [Schaefer, 1997]. Advances have been made recently in terms of equipment and monitoring, and particularly in terms of evaluating the degree of improvement through seismic testing. Whereas compaction grouting results in discrete bulbs of grout in the soil, permeation grouting uses low viscosity grouts that are able to penetrate into individual voids with minimal disturbance to the soil structure. The types of grouts used range from high-slump cements to various gels of very low viscosity, depending primarily on the void characteristics of the soil [Graf, 1992]. In jet grouting, a high-pressure fluid is used to erode soil in a predrilled hole and replace it with an engineered soil-grout mix to form a solid element sometimes referred to as soilcrete or grout column. The dimensions of the grouted cavities are controlled by the injection pressure, the type and operation of the injection nozzle, and the erosion susceptibility of the soil. Jet grouting is most successful in cohesionless soils and can be performed as deep as predrilled holes can be provided. This technique has been used successfully as a liquefaction countermeasure [Hayden, 1994]. Another soil improvement technique that can be used to mix underperforming soil with grouts and admixtures is to use large rotary augers to churn up soil and blend in cementitous agents that result in increased stiffness and strength. Soil-mixing can be used to provide support for overlaying structures or to reduce liquefaction hazards [Schaefer, 1997]. Vibrostone columns have been used to improve soils prone to liquefaction since the 1970s [Dobson, 1987]. Construction is accomplished by introducing a vibratory probe into the ground, which displaces the soil laterally through vibratory motion and therefore induces densification in the surrounding volume. The void that is created is backfilled with stone. The resulting column and surrounding soil provide for higher stiffness and strength. Also, the damaging effects of liquefaction are reduced because the stone columns provide a relief path for excess pore pressures to dissipate. A review of the performance of vibrostone columns for reduction of soil liquefaction is presented by Baez [1995]. Wick drains can also be used to dissipate excess pore pressures generated during earthquake shaking. They consist of either properly graded sand and gravel drains or of prefabricated geosynthetic materials. Figure 7.55 illustrates the general soil particle size ranges for applicability of various stabilization techniques. An excellent review of liquefaction remediation techniques is presented in PHRI [1997].
Defining Terms Amplification — Increase in ground motion due to the presence of soil deposits, usually expressed in terms of the ratio of ground surface to bedrock motion.
Attenuation — Rate of seismic ground motion decrease with distance. Backbone curve — Nonlinear stress-strain relationship for a soil that is loaded monotonically. Bracketed duration — Time between the first and last exceedance of a given threshold acceleration during a seismic event.
Cyclic resistance ratio — Cyclic stress ratio above which liquefaction is triggered. Cyclic strength — Shear stress during cyclic loading at which the resulting deformations are considered excessive.
Cyclic stress ratio — Ratio of earthquake-induced equivalent shear stress amplitude to effective overburden stress.
Damping curve — Relationship between viscous damping coefficient and shear strain for nonlinear soils.
Epicenter — Projection on the surface of the Earth directly above the location where the initial seismic disturbance occurred. Equivalent damping ratio — Ratio between the dissipated and stored energies within a hysteretic loop at a given shear strain. © 2003 by CRC Press LLC
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Gravel
Sand
Silt
Clay
Vibro-compaction Blasting Particulate Grout Chemical Grout Displacement Grout Pre-compression Dynamic Deep Compaction Electro-osmosis Reinforcement (tension, compression, shear) Thermal Treatment Admixtures
10
1.0
0.1
0.01 Particle Size (mm)
0.00 1
0.0001
FIGURE 7.55 Applicable grain size ranges for different stabilization methods. (Modified from Mitchell, J.K. 1981. “Soil Improvement: State-of-the-Art,” in Proc. Tenth International Conference on Soil Mechanics and Foundation Engineering, Stockholm, American Society of Civil Engineers, New York.)
Equivalent-linear soil model — A stress-strain model that uses elastic shear modulus and damping ratio parameters that are functions of shear strain. These parameters are updated iteratively during each incremental step until they match the target values corresponding to the level of strain in the soil. Flow failures — Soil failure due to liquefaction involving large lateral displacements that occur when the static shear stress along a potential failure plane is larger than the shear strength of the liquefied soil. Intensity — Strength of shaking from a particular earthquake at a given location. Lateral spreading — Small to moderate lateral displacements associated with liquefaction that occur due to seismic shaking when the static shear stress is less than the shear strength of the liquefied soil. Liquefaction — A process in which the soil loses shear strength and approaches the state of a liquid due to a transient accumulation of excess pore pressures. Magnitude — A measure of the energy released at the source of the earthquake. Magnitude scaling factors — Factors to be applied to the cyclic resistance ratio obtained from the standard penetration test, cone penetration test, and shear wave velocity liquefaction charts for earthquakes of magnitude other than 7.5. Modulus reduction curve — Relationship expressing the rate at which the maximum shear modulus of soil decreases with shear strain due to nonlinear effects. Near-field — Within a distance equal to the dimension of the fault section involved in the earthquake. Nonlinear cyclic model: — A stress-strain model that is truly nonelastic and that models the nonlinearity through an explicit relationship involving nonelastic material parameters. Peak ground acceleration (PGA) — Maximum recorded acceleration amplitude. © 2003 by CRC Press LLC
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Pseudostatic approach — Stability analysis procedure in which inertial forces caused by earthquake shaking are approximated by equivalent static forces that are a function of peak ground motion acceleration and soil weight. Residual shear strength — Soil shear strength after seismic shaking has stopped. Response spectrum — A plot of maximum acceleration, velocity, or displacement for a single-degreeof-freedom oscillator as a function of system period, for a given input motion and system damping (typically 5%). Sand boils — Sand and silt mounds deposited by spouting from crater-like vents as excess pore pressure dissipates from buried deposits that have liquefied. Seismic hazards — Possible types of damage from earthquake shaking. Seismic waves — Waves originating from an earthquake event and traveling through geologic media, including compressional p-waves, shear S-waves, surface Love waves, and long-period Rayleigh waves. Site-specific ground response analysis — Ground motion analysis that involves site-specific material distributions, dynamic soil response, and boundary conditions. It is usually carried out using a numerical approach. Strong motion — Seismic shaking that is of sufficient intensity to have a significant effect on engineering structures. Tsunami — Large tidal wave that follows from the sudden displacement of the seafloor or a submarine landslide, usually caused by an offshore earthquake. Yield acceleration — Acceleration corresponding to a pseudostatic safety factor equal to 1, above which permanent deformations accumulate.
References Abrahamson, N.A. and K.M. Shedlock. 1997. “Overview,” Seismol. Res. Lett., 68(1), 9–23. Abrahamson, N.A. and P.G. Somerville. 1996. “Effects of the Hanging Wall and Footwall on Ground Motions Recorded during the Northridge Earthquake,” Bull. Seismol. Soc. Am., 86, S93–S99. Abramson, L.W., T.S. Lee, et al. 2002. Slope Stability and Stabilization Methods, John Wiley & Sons, New York. Aki, K. 1988. “Local Site Effects on Strong Ground Motion,” in Earthquake Engineering and Soil Dynamics, Vol, II, Recent Advances in Ground Motion Evaluation, Geotechnical Special Publication No. 20, American Society of Civil Engineers, New York. Andrews, D.C.A. and G.R. Martin. 2000. “Criteria for Liquefaction of Silty Soils,” in Proc. 12th World Conference on Earthquake Engineering, Auckland, New Zealand. Andrus, R.D. and K.H. Stokoe. 1997. “Liquefaction Resistance Based on Shear Wave Velocity,” in Proc. NCEER Workshop on Evaluation of Liquefaction Resistance of Soils, Salt Lake City, NV, Multidisciplinary Center for Earthquake Engineering Research, Buffalo, NY. Arnold, C. and R. Reitherman. 1982. Building Configuration and Seismic Design. John Wiley & Sons, New York. Baez, J.I. 1995. “A Design Model for the Reduction of Soil Liquefaction by Vibro-Stone Columns,” University of Southern California, Los Angeles, p. 207. Bardet, J.-P., N. Mace, et al. 1999. “Liquefaction-Induced Ground Deformation and Failure,” University of California, Department of Civil Engineering, p. 125. Bolt, B.A. 1969. “Duration of Strong Motion,” in Proc. 4th World Conference on Earthquake Engineering, Santiago, Chile. Boore, D.M., W. Joyner, et al. 1997. “Empirical Near-Source Attenuation Relationships for Horizontal and Vertical Components of Peak Ground Acceleration, Peak Ground Velocity, and Pseudo-Absolute Acceleration Response Spectra,” Seismol. Res. Lett., 68(1), 154–179. Boulanger, R.W. and R.F. Hayden. 1995. “Aspects of Compaction Grouting of Liquefiable Soils,” ASCE J. Geotech. Eng., 12(121), 844–855. © 2003 by CRC Press LLC
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Brinkgreve, R.B.J. and P.A. Vermeer. 1988. “PLAXIS, Finite Element Code for Soil and Rock Analysis, Version 7, Balkema, Rotterdam. BSSC (Building Seismic Safety Council). 1997. NEHRP Recomme nded Provisions for Seismic Regulat ions for New Building s and Othe r Structures, National Institute of Building Sciences, p. 335. Castro, G. and S.J. Poulos. 1977. “Factors Affecting Liquefaction and Cyclic Mobility,” J. Geotech. Eng. Div. ASCE, 106(GT6), 501–506. Cetin, K.O. and R.B. Seed. 2000. “Nonlinear Shear Mass Participation Factor (Rd) for Cyclic Shear Stress Ratio Evaluation,” University of California, Berkeley. Chopra, A.K. 2001. Dynamic s of Structures, Theory and Applicat ions to Earthquak e Engineering. PrenticeHall, Upper Saddle River, NJ. Cruden, D.M. and D.J. Varnes. 1996. “Landslide Types and Processes,” in Landslides, Investigation and Mitigation, Transportation Research Board Special Report 247, pp. 36–75, A.K. Turner and R.L. Schuster, Eds., National Academy Press, Washington, D.C. Dobson, T. 1987. Case Histories of the Vibro Systems to Minimiz e the Risk of Liquefaction, Geotechnical Special Publication No. 12, American Society of Civil Engineers, New York, pp. 167–183. Faccioli, E. 1991. “Seismic Amplification in the Presence of Geologic and Topographic Irregularities,” in Proc. Second International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, St. Louis, MO. Finn, W.D.L. 1988. “Dynamic Analysis in Geotechnical Engineering,” in Earthquak e Engineering and Soil Dynamic s, Vol. II: Recent Advances in Ground-Motion Evaluat ion, Geotechnical Special Publication 20, American Society of Civil Engineers, New York. Finn, W.D.L. 1991. “Geotechnical Engineering Aspects of Microzonation,” in Proc. Fourth International Conference on Microzonation, Earthquake Engineering Research Institute, Stanford University, Palo Alto. Finn, W.D.L. 2000. “State-of-the-Art of Geotechnical Earthquake Engineering Practice,” Soil Dyn. Earthquake Eng., 20, 1–15. Finn, W.D.L. 2001. “Earthquake Engineering,” in Geotechnical and G eoenvironmental E ngineering Handbook, R.K. Rowe, Ed., Kluwer Academic, Boston, pp. 615–659. Finn, W.D.L., P.M. Byrne, et al. 1996. “Some Geotechnical Aspects of the Hyogo-ken-Nanbu (Kobe) Earthquake of January 17, 1995,” Can. J. Civil Eng., 23(3), 778–796. Finn, W.D.L., R.H. Ledbetter, et al. 1994. Liquefaction in Silty Soils: Design and Analysis, Geotechnical Publication No. 44, American Society of Civil Engineers, New York, pp. 51–76. Finn, W.D.L., M. Yogendrakumar, et al. 1986. “TARA-3: A Problem for Non-Linear Static and Dynamic Effective Stress Analysis,” Soil Dynamics Group, University of British Columbia, Vancouver. Franklin, A.G. and F.K. Chang. 1977. “Permanent Displacements of Earth Embankments by Newmark Sliding Block Analysis,” U.S. Army Corps of Engineers, Waterways Experiment Station, Vicksburg, MS. Gazetas, G. 1982. “Shear Vibrations of Vertically Inhomogeneous Earth Dams,” Int. J. Num. Analyt. Meth. Geomech., 6(1), 219–241. Geist, E.L. 2000. “Origin of the 17 July 1998 Papua New Guinea Tsunami: Earthquake or Landslide?” Seismol. Res. Lett., 71(3), 344–351. Graf, E.D. 1992. Earthquak e Support Grouting in Sands , Geotechnical Special Publication No. 30, American Society of Civil Engineers, New York, pp. 265–274. Graves, R.W. 1993. “Modeling Three-Dimensional Site Response Effects in the Marina District Basin, San Francisco, California,” Bull. Seismol. Soc. Am., 83: 1042–1063. Graves, R.W., A. Pitarka et al. 1998. “Ground Motion Amplification in the Santa Monica Area: Effects of Shallow Basin Edge Structure,” Bull. Seismol. Soc. Am., 88(5), 1224–1242. Griffiths, D.V. and J.H. Prevost. 1988. “Two- and Three-Dimensional Finite Element Analysis of the Long Valley Dam,” National Center for Earthquake Engineering Research, University of New York, Buffalo.
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Harder, L.F. and R. Boulanger. 1997. “Application of Ksigma and Kalpha Correction Factors,” in Proc. NCEER Workshop on Evaluation of Liquefaction Resistance of Soils, Salt Lake City, NV, Multidisciplinary Center for Earthquake Engineering Research, Buffalo, NY. Harder, L.F. and H.B. Seed. 1986. “Determination of Penetration Resistance for Coarse-Grained Soils Using the Becker Hammer Drill,” Earthquake Engineering Research Center, University of California, Berkeley. Hausmann, M.R. 1990. Engineering Principles of Ground Modification. McGraw-Hill, New York. Hayden, R.F. 1994. “Utilization of Liquefaction Countermeasures in North America,” in Proc. Fifth U.S. National Conference on Earthquake Engineering, Chicago. Hryciw, R.D., Ed. 1995. Soil Improvement for Earthquake Hazard Mitigation, Geotechnical Special Publication No. 49, American Society of Civil Engineers, New York. Hynes-Griffin, M.E. and A.G. Franklin. 1984. “Rationalizing the Seismic Coefficient Method,” U.S. Army Corps of Engineers, Waterways Experiment Station 21, Vicksburg, MS. ICBO (International Conference of Building Officials). 1997. Uniform Building Code, International Conference of Building Officials, Whittier, CA. ICC (International Code Council). 2000. International Building Code, International Code Council, Falls Church, VA. Idriss, I.M. 1990. “Response of Soft Soil Sites during Earthquakes,” H. Bolton Seed Memorial Symposium, BiTech Publishers. Idriss, I.M., J. Lysmer, et al. 1973. “QUAD-4: A Computer Program for Evaluating the Seismic Response of Soil Structures by Variable Damping Finite Element Procedures,” Earthquake Engineering Research Center, University of California, Berkeley. Kramer, S.L. 1996. Geotechnical Earthquake Engineering, Prentice-Hall, Upper Saddle River, NJ. Lee, K.L. 1974. “Seismic Permanent Deformations in Earth Dams,” School of Engineering and Applied Science, University of California, Los Angeles. Lee, K.L. and J.A. Focht. 1976. “Strength of Clay Subjected to Cyclic Loading,” Mar. Geotechnol., 1(3), 165–188. Liao, S.S.C. and R.V. Whitman. 1986. “Overburden Correction Factors for SPT in Sand,” J. Geotech. Eng. ASCE, 112(3), 373–377. Lukas, R.G. 1986. Dynamic Compaction for Highway Construction, Vol. 1. Design and Construction Guidelines, Federal Highway Administration. Lysmer, J., T. Udaka, et al. 1975. “FLUSH: A Computer Program for Approximate 3-D Analysis of SoilStructure Interaction Problems,” Earthquake Engineering Research Center, University of California, Berkeley. Makdisi, F.I. and H.B. Seed. 1978. “Simplified Procedure for Estimating Dam and Embankment Earthquake-Induced Deformations,” J. Geotech. Eng. ASCE, 104(GT7), 849–867. Marcuson, W.F. and A.G. Franklin. 1983. Seismic Design, Analysis and Remedial Measures to Improve the Stability of Existing Earth Dams, Corps of Engineers Approach, Seismic Design of Embankments and Caverns, American Society of Civil Engineers, New York. Marcuson, W.F., P.F. Hadala, et al. 1991. Seismic Rehabilitation of Earth Dams, Geotechnical Publication No. 35, American Society of Civil Engineers, New York, pp. 430–466. Marcuson, W.F., M.E. Hynes, et al. 1992. “Seismic Stability and Permanent Deformation Analysis: The Last Twenty Five Years,” in ASCE Specialty Conference on Stability and Performance of Slopes and Embankments, Vol. II, Geotechnical Special Publication No. 31, American Society of Civil Engineers, New York. Mitchell, J.K. 1981. “Soil Improvement: State-of-the-Art,” in Proc. Tenth International Conference on Soil Mechanics and Foundation Engineering, Stockholm, American Society of Civil Engineers, New York. Mitchell, J.K., C.D.P. Baxter, et al. 1995. “Performance of Improved Ground During Earthquakes,” in Soil Improvement for Earthquake Mitigation, American Society of Civil Engineers, New York.
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Molas, G.L. and F. Yamazaki. 1995. “Attenuation of Earthquake Ground Motion in Japan Including Deep Focus Events,” Bull. Seismol. Soc. Am., 85(5), 1343–1358. Molas, G.L. and F. Yamazaki. 1996. “Attenuation of Response Spectra in Japan Using New JMA Records,” Bull. Earthquake Resistant Structure Research Center, Institute of Industrial Science, University of Tokyo (29), 115–28. Mononobe, N. and H. Matsuo. 1929. “On the Determination of Earth Pressures During Earthquakes,” in Proc. World Engineering Conference. Narin van Court, W.A. and J.K. Mitchell. 1995. New Insights into Explosive Compaction of Loose, Saturated, Cohesionless Soils, Special Geotechnical Publication No. 49, American Society of Civil Engineers, New York, pp. 51–65. NCEER (National Center for Earthquake Engineering Research). 1992. Case Studies of Liquefaction and Lifeline Performance during Past Earthquakes. Vol. 1, Japanese Case Studies; Vol. 2, United States Case Studies, National Center for Earthquake Engineering Research, State University of New York, Buffalo. NCEER (National Center for Earthquake Engineering Research). 1997. Proceedings of the NCEER Workshop on Evaluation of Liquefaction Resistance of Soils, Summary Report, T.L. Youd and I. Idriss, Eds., National Center for Earthquake Engineering Research, State University of New York, Buffalo. Newmark, N.M. 1965. “Effects of Earthquakes on Dams and Embankments,” Geotechnique, 15(2), 139–160. Newmark, N.M. and W.J. Hall. 1982. Earthquake Spectra and Design, Earthquake Engineering Research Institute, University of California, Berkeley, p. 103. Okabe, S. 1929. “General Theory of Earth Pressures,” J. Jpn. Soc. Civil Eng., 12(1). O’Rourke, T.D. 1992. The Loma Prieta, California, Earthquake of October 17, 1989: Marina District, United States Geological Service, Government Printing Office, Washington, D.C. Otani, S. 2000. “New Seismic Design Provisions in Japan,” Pacific Earthquake Engineering Research Center, University of California, Berkeley, pp. 3–14. PHRI (Port and Harbor Research Institute). 1997. Handbook on Liquefaction Remediation of Reclaimed Land, Port and Harbour Research Institute, Japan, Brookfield, VT. Poulos, S.J., G. Castro, et al. 1985. “Liquefaction Evaluation Procedure,” J. Geotech. Eng. ASCE, 111(6), 772–792. Prakash, S. and S. Saran. 1966. “Static and Dynamic Earth Pressure Behind Retaining Walls,” in Proc. Third Symposium on Earthquake Engineering, Roorkee, India. Prevost, J.H., A.M. Abdel-Ghaffar, et al. 1985. “Nonlinear Dynamic Analysis of Earth Dams: A Comparative Study,” J. Geotech. Eng. ASCE, 111(2), 882–897. Quake/W. 2001. “Quake/W for Finite Element Dynamic Earthquake Analysis: Users’ Guide,” GEO-SLOPE International Ltd., Calgary. Richards, R. and D.G. Elms. 1979. “Seismic Behavior of Gravity Retaining Walls,” J. Geotech. Eng. ASCE, 105(GT4), 449–464. Robertson, P.K. and C.E. Fear. 1995. “Liquefaction of Sand and its Evaluation,” in Proc. 1st International Conference on Earthquake Geotechnical Engineering, Tokyo. Robertson, P.K. and C.E. Wride. 1997. “Cyclic Liquefaction and its Evaluation Based on the SPT and CPT,” in Proc. NCEER Workshop on Evaluation of Liquefaction Resistance of Soils, Salt Lake City, NV, Multidisciplinary Center for Earthquake Engineering Research, Buffalo, NY. Rodriguez-Marek, A., J.D. Bray, et al. 1999. “Characterization of Site Response, General Site Categories,” Pacific Earthquake Engineering Research Center, University of California, Berkeley, p. 134. Romo, M.P. and H.B. Seed. 1986. “Analytical Modeling of Dynamic Soil Response in the Mexico Earthquake of September 19, 1985,” in Proc. ASCE International Conference on the Mexico Earthquakes 1985, Mexico City, American Society of Civil Engineers, New York. Schaefer, V.R., Ed. 1997. Ground Improvement, Ground Reinforcement, Ground Treatment, Geotechnical Special Publication No. 69, American Society of Civil Engineers, New York.
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Seed, H.B. 1979a. “Considerations in the Earthquake-Resistant Design of Earth and Rockfill Dams,” Geotechnique, 29(3), 215–263. Seed, H.B. 1979b. “Soil Liquefaction and Cyclic Mobility for Level Ground During Earthquakes,” J. Geotech. Eng. ASCE, 105(GT2), 201–255. Seed, H.B. 1983. “Earthquake Resistant Design of Earth Dams,” in Proc. Symposium on Seismic Design of Earth Dams and Caverns, New York. Seed, H.B. 1986. “Design Problems in Soil Liquefaction,” J. Geotech. Eng. ASCE, 113(8), 827–845. Seed, R.B. and L.F. Harder. 1990. “SPT-Based Analysis of Cyclic Pore Pressure Generation and Undrained Residual Strength,” H. Bolton Seed Memorial Symposium, BiTech Publishers. Seed, H.B. and I.M. Idriss. 1970. “Soil Moduli and Damping Factors for Dynamic Response Analysis,” Earthquake Engineering Research Center, University of California, Berkeley. Seed, H.B. and I.M. Idriss. 1971. “Simplified Procedure for Evaluating Soil Liquefaction Potential,” J. Soil Mech. Found. Div. ASCE, 97(SM9), 1249–1273. Seed, H.B. and I.M. Idriss. 1982. Ground Motions and Soil L iquefaction during Earthquak es, Monogr. 5, Earthquake Engineering Research Institute, University of California, Berkeley. Seed, H.B. and R.V. Whitman. 1970. “Design of Earth Retaining Structures for Dynamic Loads,” in Proc. ASCE Specialty Conference on Lateral Stresses in the Ground and Design of Earth Retaining Structures, American Society of Civil Engineers, New York. Seed, R.B., K.O. Cetin, et al. 2001. “Recent Advances in Soil Liquefaction Engineering and Seismic Site Response Evaluation,” in Proc. Fourth International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, University of Missouri, Rolla. Seed, R.B., S.W. Chang, et al. 1997. “Site-Dependent Seismic Response Including Recent Strong Motion Data,” Special Session on Earthquake Geotechnical Engineering, Proc. XIV Internat ional Conference on Soil Mechanics and Foundat ion Engineering, Balkema, Hamburg. Seed, R.B., S.E. Dickenson, et al. 1990. “Preliminary Report on the Principal Geotechnical Aspects of the October 17, 1989 Loma Prieta Earthquake,” Earthquake Engineering Research Center, University of California, Berkeley, p. 137. Seed, H.B., K. Tokimatsu et al. 1985. “The Influence of STP Procedures in Soil Liquefaction Resistance Evaluations,” J. Geotech. Eng. ASCE, 111(12), 1425–1445. Seed, H.B., C. Ugas, et al. 1976. “Site-Dependent Spectra for Earthquake-Resistant Design,” Bull. Seismol. Soc. Am., 66, 221–243. Serff, N., H.B. Seed, et al. 1976. “Earthquake-Induced Deformations of Earth Dams,” Earthquake Engineering Research Center, University of California, Berkeley, p. 140. Shabestari, K.T. and F. Yamazaki. 1998. “Attenuation Relationship of JMA Seismic Intensity Using JMA Records,” in Proc. Tenth Japan Earthquake Engineering Symposium, Kobe, Japan. Silver, M.L. and H.B. Seed. 1971. “Volume Changes in Sands during Cyclic Loading,” J. Soil Mech. Found. Div. ASCE, 97(9), 1171–1182. Somerville, P. 1998. “Emerging Art: Earthquake Ground Motion,” in Geotechnical E arthquak e Engineering and Soil D ynamic s, Vol. III, Geotechnical Special Publication No. 75, American Society of Civil Engineers, New York. Somerville, P.G. and R.W. Graves. 1996. “Strong Ground Motions of the Kobe, Japan Earthquake of January 17, 1995, and Development of a Model of Forward Rupture Directivity Applicable in California,” in Proc. Western Regional Technical Seminar on Earthquake Engineering for Dams, Association of State Dam Officials, Sacramento. Somerville, P.G., C.K. Saikia, et al. 1996. “Implications of the Northridge Earthquake for Strong Ground Motions from Thrust Faults,” Bull. Seismol. Soc. Am., 86, S115–S125. Stark, T.D. and G. Mesri. 1992. “Undrained Shear Strength of Sands for Stability Analysis,” J. Geotech. Eng. ASCE, 118(11), 1727–1747. Stone, W.C., F.Y. Yokel, et al. 1987. Engineering Aspects of the September 19, 1985 Mexico Earthquak e, NBS Building Science Series, 165, National Bureau of Science, Washington, D.C., p. 207.
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Sy, A. and R.G. Campanella. 1994. “Becker and Standard Penetration Tests (BPT-SPT) Correlations with Consideration of Casing Friction,” Can. Geotech. J., 31, 343–356. Tappin, D.R., T. Matsumoto et al. 1999. “Offshore Surveys Identify Sediment Slump as Likely Cause of Devastating Papua New Guinea Tsunami 1998,” Eos, 80(30), 329. Thiers, G.R. and H.B. Seed. 1978. Strength and S tress-Strain Char acteristics of Clays Subjected to Seismic Loading C onditions, ASTM Special Technical Publication 450, American Society for Testing and Materials, pp. 3–56. Tokimatsu, K. and H.B. Seed. 1987. “Evaluation of Settlements in Sand Due to Earthquake Shaking,” J. Geotech. Eng. ASCE, 113(8), 861–878. Trifunac, M.D. and A.G. Brady. 1975. “On the Correlation of Seismic Intensity with Peaks of Recorded Strong Ground Motion,” Bull. Seismol. Soc. Am., 65, 139–162. U.S. Army Corps of Engineers. 1982. Slope Stability Manual, Department of the Army, Office of the Chief of Engineers, Washington, D.C. Vucetic, M. and R. Dorby. 1991. “Effect of Soil Plasticity on Cyclic Response,” J. Geotech. Eng. ASCE, 117(1), 89–107. Whitman, R.V. and S. Liao. 1985. “Seismic Design of Retaining Walls,” U.S. Army Corps of Engineers, Waterways Experiment Station, Vicksburg, MS. Wieczorek, G.F. 1996. “Landslide Triggering Mechanisms,” in Landslides, Investigation and Mitigation, A.K. Turner and R.L. Schuster, Eds., Transportation Research Board Special Report 247, National Academy Press, Washington, D.C., pp. 76–90. Wightman, A. 1991. “Ground Improvement by Vibrocompaction,” Geotech. News, 9(2), 39–41. Wood, J. 1973. “Earthquake-Induced Soil Pressures on Structures,” Report EERL 73-05, California Institute of Technology, Pasadena, p. 311. Youd, T.L. and S.N. Hoose. 1977. “Liquefaction Susceptibility and Geologic Setting,” in Proc. 6th World Conference on Earthquak e Engineering, Prentice-Hall, Englewood Cliffs, NJ. Youd, T.L. and I.M. Idriss. 2001. “Liquefaction Resistance of Soils: Summary Report from the 1996 NCEER and 1998 NCEER/NSF Workshops on Evaluation of Liquefaction Resistance of Soils,” J. Geotech. Eng. ASCE, 127(4), 297–313. Youd, T.L. and S.K. Noble. 1997. “Magnitude Scaling Factors,” in Proc. NCEER Workshop on Evaluation of Liquefaction Resistance of Soils, Salt Lake City, NV, Multidisciplinary Center for Earthquake Engineering Research, Buffalo, NY. Youd, T.L. and D.M. Perkins. 1978. “Mapping of Liquefaction-Induced Ground Failure Potential,” J. Geotech. Eng. Div. ASCE, 104(GT4), 433–446.
Further Reading Kramer’s book [Kramer, 1996] provides a detailed explanation of earthquake effects on geotechnical engineering parameters, as does Finn’s article on the state of the art of geotechnical earthquake engineering practice [Finn, 2001]. A series of U.S. and Japanese case studies of liquefaction effects on lifeline performance during earthquakes contains a wealth of information on lifeline performance during earthquakes [NCEER, 1992]. Another case study of interest is a USGS professional paper on the Marina district of San Francisco in the 1989 Loma Prieta earthquake [O’Rourke, 1992]. An excellent review of liquefaction remediation techniques is presented in a handbook on liquefaction remediation of reclaimed land [PHRI, 1997].
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8 Seismic Hazard Analysis 8.1 8.2 8.3
Introduction Probabilistic Seismic Hazard Methodology Constituent Models of the Probabilistic Seismic Hazard Methodology Seismic Sources · Earthquake Recurrence Frequency · Ground Motion Attenuation · Ground Motion Probability
8.4
Definition of Seismic Sources
8.5
Earthquake Frequency Assessments
Area Sources · Fault Sources Historical Frequency Assessments · Geologic Earthquake Frequency Assessments · Conservation of Seismic Moment on Segmented Faults · Time-Dependent Probability Modeling
8.6
Maximum Magnitude Assessments Area Source Determinations · Individual Fault Determinations · Mixed Source Determinations
8.7
Ground Motion Attenuation Relationships Impact on Seismic Source Definition · Reference Site Class
8.8 Accounting for Uncertainties 8.9 Typical Engineering Products of PSHA 8.10 PSHA Disaggregation Scaling Empirical Earthquake Spectra
8.11 PSHA Case Study Tectonic Setting · Regional Seismicity · Great Earthquakes · Earthquake Source Characterization
8.12 The Owen Fracture Zone–Murray Ridge Complex Maximum Magnitude · Earthquake Recurrence Frequencies
8.13 Makran Subduction Zone Maximum Magnitude · Earthquake Recurrence Frequencies
8.14 Southwestern India and Southern Pakistan Maximum Magnitude · Earthquake Recurrence Frequencies
8.15 Southeastern Arabian Peninsula and Northern Arabian Sea Maximum Magnitude · Earthquake Recurrence Frequencies
8.16 Ground Motion Models Stable Continental Interior Earthquakes · Stable Oceanic Interior Earthquakes · Transform Plate Boundary Earthquakes · Subduction Zone Earthquakes
Paul C. Thenhaus ABS Consulting Evergreen, CO
Kenneth W. Campbell ABS Consulting and EQECAT Inc. Portland, OR © 2003 by CRC Press LLC
8.17 Soil Amplification Factors 8.18 Results 8.19 Conclusions 8.20 PSHA Computer Codes Defining Terms References Further Reading
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8.1 Introduction Seismic hazard is a broad term used in a general sense to refer to the potentially damaging phenomena associated with earthquakes, such as ground shaking, liquefaction, landslides, and tsunami. In the specific sense, seismic hazard is the likelihood, or probability, of experiencing a specified intensity of any damaging phenomenon at a particular site, or over a region, in some period of interest. It is the latter, specific sense, that is the subject of this chapter. The methodology for assessing the probability of seismic hazards grew out of an engineering need for better designs in the context of structural reliability [Cornell, 1968, 1969], since such assessments are frequently made for the purpose of guiding decisions related to mitigating risk. However, the probabilistic method has also proven to be a compelling, structured framework for the explicit quantification of scientific uncertainties involved in the hazard estimation process. Uncertainty is inherent in the estimation of earthquake occurrence and the associated hazards of damaging ground motion, permanent ground displacements, and, in some cases, seiche and tsunami. Scientific knowledge for the accurate quantification of these hazards is always limited. The balance of the hazard assessment is comprised of informed technical judgment. Prior to the widespread use of probabilistic seismic hazard analysis (PSHA) for assessing earthquake hazards, deterministic methods dominated such assessments. Deterministic methods consider the effect at a site of either a single scenario earthquake, or a relatively small number of individual earthquakes. Difficulties surrounded the selection of a representative earthquake on which the hazard assessment would be based. These difficulties often involved the identification of an earthquake that satisfied a codified or regulatory definition. The probabilistic methodology reduces the need for such earthquake definitions, which typically are ambiguous at best. The probabilistic methodology quantifies the hazard at a site from all earthquakes of all possible magnitudes, at all significant distances from the site of interest, as a probability by taking into account their frequency of occurrence. Deterministic earthquake scenarios, therefore, are a subset of the probabilistic methodology. In principle, PSHA can address any natural hazard associated with earthquakes, including ground shaking, fault rupture, landslide, liquefaction, seiche, or tsunami. However, most interest is in the probabilistic estimation of ground-shaking hazard, since it causes the largest economic losses in most earthquakes. The presentation here, therefore, is restricted to the estimation of the earthquake ground motion hazard. Figure 8.1 illustrates elements of the probabilistic ground motion hazard methodology in the context of a complete program for establishing engineering seismic design criteria for a site of significant engineering importance. The process begins with the characterization of earthquake occurrence using two sources of data: observed seismicity (historical and instrumental) and geologic. The occurrence information is combined with data on the transmission of seismic shaking (termed attenuation, see Chapter 5) to form the seismotectonic model. Since uncertainty is inherent in the earthquake process, the parameters of the seismotectonic model are systematically varied via logic trees, Monte Carlo simulation, and other techniques, to provide the probabilistic seismic hazard model’s results. The results may be disaggregated (also known as deaggregation) to identify specific contributory parameters to the overall results. The results must also consider the site-specific soil properties. The final results, presented in many different ways depending on the user’s needs, are termed seismic design criteria, if the end use is the design of an engineering structure. Each of these aspects is discussed further below.
8.2 Probabilistic Seismic Hazard Methodology PSHA can be summarized as the solution of the following expression of the total probability theorem: λ[X ≥ x] ≈
M Max
∑ ν ∫ ∫ P [ X ≥ x M , R] f i
Sources i
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Mo
R|M
M
(m) f R|M (r m) dr dm
(8.1)
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FIGURE 8.1 Flowchart showing the elements of the probabilistic hazard methodology in the context of a seismic design criteria methodology.
where λ[X ≥ x ] is the annual frequency that ground motion at a site exceeds the chosen level X = x ; νi is the annual rate of occurrence of earthquakes on seismic source i, having magnitudes between Mo and MMax; Mo is the minimum magnitude of engineering significance; MMax is the maximum magnitude assumed to occur on the source; P[X ≥ x |M,R] denotes the conditional probability that the chosen ground motion level is exceeded for a given magnitude and distance; fM(m) is the probability density function of earthquake magnitude; fR|M(r |m ) is the probability density function of distance from the earthquake source to the site of interest. In application, this expression is solved for each seismic source i of a seismotectonic model. Once the annual exceedance rate λ[X ≥ x ] is known, the probability that an observed ground motion parameter X will be greater than or equal to the value x in the next t years (the exposure period) is easily computed from the equation:
(
)
P [ X ≥ x ] = 1 − exp −tλ [ X ≥ x ]
(8.2)
where the “return period” of x is defined as: RX ( x ) =
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1 −t = λ [ X ≥ x ] ln 1 − P [ X ≥ x ]
(
)
(8.3)
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Probability values commonly used and cited in PSHA are ground motions that have a 10% probability of being exceeded in a 50-year exposure period of engineering interest. From Equation 8.3, this gives a return period of: RX ( x ) =
−50 = 475 years ln (1 − 0.1)
(8.4)
Thus, these specific ground motions, which have a 10% probability of being exceeded during 50 years, are commonly termed to have an average 475-year return period. It is informative to note that setting the exposure period equal to the return period in Equations 8.2 and 8.3 results in a 63% probability that the ground motions will be exceeded in t years under the Poisson assumption used to develop these relationships.
8.3 Constituent Models of the Probabilistic Seismic Hazard Methodology Figure 8.2 schematically illustrates the constituent models of the probabilistic approach to estimating earthquake ground motion hazard. These are models of: 1. 2. 3. 4.
Seismic sources Earthquake recurrence frequency Ground motion attenuation Ground motion occurrence probability at a site
These models are introduced here and discussed in more detail in the following sections of this chapter.
8.3.1 Seismic Sources PSHA requires that the distribution of earthquakes be defined in space with each epicenter having a defined distance from the site of interest. This has been traditionally accomplished through the geographic delineation of seismic source zones and seismically active faults. Definitions of these sources are based on interpretations of available geological, geophysical, and seismological data with respect to earthquake mechanisms and source structures that are likely to be common within specific geographic regions (Figure 8.3). Seismic source delineation is generally premised on geoscience knowledge that relates earthquakes to geological structure. However, where causative earthquake faults and structure are not known with certainty, seismic source interpretations are not unique [Thenhaus, 1983, 1986] and the geographic distribution of earthquakes largely guides the definition of sources [Electric Power Research Institute, 1986]. Methods of seismicity smoothing have recently been introduced to avoid arbitrary decisions regarding placement of area-source boundaries [Frankel et al., 1995, 1996, 2000] and to better represent the fractal geometry of distributed seismicity as a self-organized critical-state process [Woo, 1996].
8.3.2 Earthquake Recurrence Frequency Determining the earthquake recurrence frequency of the defined seismic sources is an important explicit task in PSHA, whereas it is either implicit or is disregarded in deterministic seismic hazard analysis. Earthquake recurrence frequency is based largely on statistical analyses of the historical record of earthquakes for all but the most tectonically active areas of the world where detailed paleoseismic studies of active faults have been performed. Paleoseismology is the geological study of prehistoric earthquakes [McCalpin, 1996; Yeats et al., 1997] and aids the analysis of large-earthquake occurrence frequency. Earthquake frequency estimates in PSHA typically assume independence of earthquake events, or Poisson arrival times. However, time-dependent treatments of earthquake recurrence estimates are the basis for © 2003 by CRC Press LLC
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8-5
FIGURE 8.2 Elements of PSHA shown in relation to constructing a uniform hazard spectrum. (From EERI, Earthquake Spectra, 5, 675–699, 1989. With permission.)
earthquake forecasting in areas, such as the San Francisco Bay area, where a good historical and paleoseismic record of past earthquakes is available.
8.3.3 Ground Motion Attenuation Empirical ground motion attenuation relationships are widely used to establish the amplitude of earthquake ground motion at a site of interest (see Chapter 5). In engineering applications, the ground motion parameters of interest are typically peak ground acceleration (PGA), response spectral acceleration (PSA), response spectral velocity (PSV), and spectral displacement (SD). Proper implementation of most modern ground motion attenuation relationships requires that the seismic sources are characterized by the details of a fault-rupture model including depth to the top and bottom of the earthquake rupture zone, fault dip, and the style of fault slip (i.e., strike-slip, normal, or reverse). These faultrupture parameters are a product of the tectonic environment of the region in which the analysis is being performed.
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45°N 44°N 43°N 42°N 41°N 40°N 39°N 38°N 37°N 36°N 35°N 34°N
0
33°N
150 300 Kilometers
32°N 18°E 20°E 22°E 24°E 26°E 28°E 30°E 32°E 34°E 36°E 38°E 40°E 42°E 44°E 46°E 48°E 50°E 52°E
FIGURE 8.3 Seismic source zones overlaid on major faults and tectonic features, for Turkey. (From Erdik, M. et al., 1999, Assessment of Earthquake Hazards in Turkey and Neighboring Regions, contribution to Global Seismic Hazard Assessment Program, available at http://seismo.ethz.ch/gshap/turkey/papergshap71.htm.)
8.3.4 Ground Motion Probability The estimation of the probability of exceeding some amplitude of shaking at a site in some period of interest requires that a probability distribution of the ground motion amplitudes be assumed. The Poisson model serves as a reasonable assumption in most engineering applications except in rare cases where a single earthquake source may dominate the hazard at a site and the earthquake occurrence model for the source can be considered time-dependent, or non-Poissonian [Cornell and Winterstein, 1988]. Poisson models have traditionally been used throughout seismic hazard assessment. However, timedependent earthquake occurrence estimates have been used for earthquake forecasting in the San Francisco Bay area of California [Working Group on California Earthquake Probabilities, 1999] as well as elsewhere in California [Working Group on California Earthquake Probabilities, 1995]. Time-dependent probability models are discussed later in this chapter.
8.4 Definition of Seismic Sources The fundamental assumptions of a defined earthquake source is that (1) earthquake occurrence is uniformly distributed for given magnitude within the source, and (2) earthquake occurrence is only considered between a minimum earthquake magnitude of engineering interest (Mmin) and a maximum magnitude (Mmax) that is representative of the entire source [Reiter, 1990]. The seismic sources are shown as map representations of lines (fault sources), and area source zones that are defined on the basis of a number of different types of geological, geophysical, and seismological data (Figure 8.3). These data are summarized in Table 8.1 along with their indicated usefulness in the definition of types of seismic sources. The defined geographic distribution of seismic sources and the specification of all source characteristics required for the seismic hazard analysis is termed the seismotectonic model. The seismotectonic model provides a complete description of earthquake occurrence in time and space to an outer distance of an engineering interest, and to a depth sufficient to encompass the seismogenic thickness of brittle crust beneath the site. Depending on the seismotectonic regime and the application for the results, the maximum distance and depth considered may be several hundred kilometers and a hundred kilometers, respectively. The entire model is summarized in an input file format appropriate to the PSHA computer code being used. © 2003 by CRC Press LLC
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TABLE 8.1
General Data Types and Their Applications in Identifying and Characterizing Seismic Source Zones Zone Type Faults Data Type
Area Sources
Location
Activity
Length
Dip
X X X X
X X X X X X X X X
X X X
X
Depth
Style
Area
X X X X
X X
Depth
Geological/Remote Sensing Detailed mapping Geomorphic data Quaternary surface rupture Fault trenching data Geochronology Paleoliquefaction data Borehole data Aerial photography Low sun-angle photography Satellite imagery Regional structure Balanced cross section
X X X X X X X
X X
X X X X X
X
X X
X X
X
X X X X X
X
X X X
X X X
X
X
X
X X X
X X
Geophysical Regional potential field data Local potential field data High resolution reflection data Standard reflection data Deep crustal reflection data Tectonic geodetic/strain data Regional stress data
X X X X X X
X X X
X
X X
X
X
X
Seismological Reflected crustal phase data Historical earthquake data Teleseismic earthquake data Regional network seismicity data Local network seismicity data Focal mechanism data
X X X X
X X
X X
X X X
X X
X X X
X X
X
8.4.1 Area Sources Area seismic sources define regions of the Earth’s crust that are assumed to have uniform seismicity characteristics that are distinct from neighboring zones, and are exclusive of active faults that are individually defined. The central and eastern United States (CEUS) region is often cited as a leading example of a region where seismic hazard is defined through the use of area seismic source zones [Thenhaus, 1983; Reiter, 1990; Coppersmith, 1991; Coppersmith et al., 1993]. This region is located interior to the North American tectonic plate where earthquake occurrence is much less frequent than in the western United States, the historical and instrumental seismicity generally does not correlate well with geologic structures observable at the surface, evidence of prehistoric earthquakes that is preserved in the geologic record is difficult to find, and strain-rates of crustal deformation are exceedingly low. With the exception of a few areas, such as the New Madrid Seismic Zone, the result of these characteristics is a seismotectonic environment in which the identification of geologic structures that are responsible for earthquakes is ambiguous and not unique. Interpretations of the regional distribution of seismicity largely guide the definition of area seismic sources in this region [Thenhaus, 1983; EPRI, 1986]. Analogous regions of the world are areas that are located large distances from active plate boundary zones (Figure 8.4). Such regions are referred to as “stable continental interior regions” [Johnston et al., 1994]. Stable continental interiors, as the name implies, are some of the least active areas worldwide with regard to earthquake © 2003 by CRC Press LLC
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Earthquake Engineering Handbook
Active Volcanoes, Plate Tectonics, and the “Ring of Fire” Eurasian Plate
North American Plate CASCADE RANGE San Andreas Fault
Aleutian Trench
“Ring of Fire”
Mid-Atlantic Ridge
Hawaiian "Hot Spot"
Eurasian Plate
Arabian Plate
Cocos Plate
Java Trench
East Pacific Rise
Nazca Plate
Indo- Australian Plate
South American Plate
African Plate
Pacific Plate
USGS
Antarctic Plate
FIGURE 8.4 Plate tectonic setting of the world (from the U.S. Geological Survey). Primary tectonic plates are labeled by name. Heavy black lines indicate plate boundaries. “Ring of Fire” is a colloquialism referring to the earthquakes and volcanoes that occur along the northern boundary of the Pacific tectonic plate, extending from Japan through North America.
activity and are generally comprised of areas of very old continental crust in which the most active geologic process operating today is that of erosion. An alternative to defining uncertain area source boundaries within regions of low seismicity is that of seismicity smoothing. Woo [1996] formalized a kernel-estimation method of seismicity smoothing, noting that the practice of seismic source zonation “should not be merely routine when applied to areas where such correlations [between geological structure and seismicity] are tenuous.” Woo [1996] argued that use of “Euclidean zones” (standard area sources) unrealistically impose a uniform spatial distribution of epicenters in PSHA that conflicts with the clustering habit and inter-event correlation of recorded seismicity [Kagan and Knopoff, 1980; Korvin, 1992]. Woo goes on to say that the power-law of the Gutenberg–Richter relationship can be explained by the theory of self-organized criticality where, over geologic time periods, regional build-up of crustal stress is marginally balanced by the stress released during earthquakes. Some of this stress is manifested in aseismic deformation and folding. However, the regional fault network is self-organized to the extent that earthquakes occur as a critical chain reaction. As Woo [1996] notes, “if the process were supercritical, it would run away, but if the process were subcritical, it would terminate rapidly.” Noteworthy in this regard was the documented regional increase in seismicity throughout the western United States following the magnitude 7.3 Landers, California earthquake [Hill et al., 1993]. This was the first time that such a large regional influence has been scientifically documented from the occurrence of a single earthquake. Frankel et al. [1996, 1998, 2000; http://earthquakes.usgs.gov/hazards/] applied seismicity smoothing in recent updates of the U.S. national seismic hazard maps that have been produced over the last 24 years by the U.S. Geological Survey under the auspices of the National Earthquake Hazards Reduction Program (NEHRP). This model separates the CEUS into two broad areas of different estimated maximum potential earthquakes. The mid-continent region of the central United States is defined as an area in which the maximum earthquake is judged to be magnitude MW 6.5. The region of the Appalachian Mountains eastward, and the Gulf Coast area of the southern United States, are areas of rifted continental crust © 2003 by CRC Press LLC
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CEUS maximum-magnitude zones
50¡
240¡
250¡
260¡
270¡
290¡
280¡
50¡
6.5
40¡
40¡ 7.5 7.5 6.5
30¡
30¡
7.2 7.5
290¡
240¡
250¡
260¡
270¡
280¡
FIGURE 8.5 Maximum magnitude zones for the central and eastern U.S. used by Frankel et al., 1996. Magnitudes are in terms of the moment magnitude (MW) scale.
(areas of past episodes of extension and faulting) and defined as areas capable of sustaining earthquakes as large as MW 7.5 (Figure 8.5). Earthquake frequency throughout these broad regions was determined on a 0.1° grid of points using the common Gutenberg–Richter relationship of occurrence frequencies (see Chapter 4): log N (m) = a − bm
(8.5)
where N(m) = the number of earthquake events equal to or greater than magnitude m occurring on a seismic source per unit time, and a and b are regional constants (10a = the total number of earthquakes with magnitude > 0, and b is the rate of seismicity; b is typically 1 ± 0.3). The a-value of this relationship was determined for the regional grid of points that have been smoothed over a distance of 50 km using a Gaussian smoothing function [Frankel, 1995; Frankel et al., 1996]. Thus, area sources of this model are only used to characterize regions of uniform maximum magnitude, not uniform earthquake frequency. While seismicity smoothing frees the PSHA analyst of subjective judgment in locating area source boundaries, subjective judgment is not eliminated by these methodologies, and is still required in choosing reasonable smoothing parameters and inter-event correlation distances based on the available seismicity data [Frankel and Safak, 1998]. These choices have a large impact on the estimated ground motion amplitudes [Perkins and Algermissen, 1987].
8.4.2 Fault Sources Line sources are defined in PSHA ground motion analyses as map-view representations of three-dimensional fault planes for the purpose of explicit representation of faults that are considered capable of earthquake rupture. By far, these types of sources are primarily defined in active tectonic regions that are generally located in proximity to the boundaries of the world’s tectonic plates (Figure 8.4). However, strain from plate–boundary tectonic processes are transmitted large distances through the Earth’s crust. Earthquake faults can, therefore, be located large distances from these plate boundaries, albeit at greatly diminished rates of activity and geographic concentration. Faults exhibit a wide range of offset styles that depend on the prevailing tectonic stress regime, be it compression or extension, and the threedimensional geometry (i.e., strike and dip) of the individual fault within that stress regime (see Chapter 4). Many modern ground motion attenuation relationships (see Chapter 5) are specific to the © 2003 by CRC Press LLC
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style of faulting and require specification of the three-dimensional geometry of the defined fault through the Earth’s crust so that source-to-site distances are accurately calculated. The definition of earthquake faults need not be restricted to faults that are observable at the surface. Blind-faults (faults that do not break the surface), such as ruptured in the 1983 Coalinga and 1994 Northridge, California earthquakes [Wentworth and Zoback, 1990], can and should be included in a PSHA seismotectonic model, with appropriate specification of the depth to the top and bottom of the earthquake rupture zone.
8.5 Earthquake Frequency Assessments There are two fundamental approaches to assess earthquake recurrence frequency of the defined seismic sources in PSHA. These are historical and geological frequency assessments. Historical frequency assessments are based on statistical analyses of the historical catalog of earthquakes that have occurred within a region. Geological frequency assessments are generally based either on a prehistoric record of earthquake occurrence on faults (termed paleoseismicity ), which is compiled through detailed field geologic investigations, or on physical estimates of seismic moment either on individual faults or distributed throughout broad regions. Moment-based recurrence frequency estimates require some knowledge of the average long-term rate at which faults are slipping, or the rate at which tectonic deformation is occurring over a region.
8.5.1 Historical Frequency Assessments Historical catalogs of earthquakes are heterogeneous; that is, the data typically: • Are nonuniform with respect to time periods of complete reporting for earthquakes of various magnitudes • Are nonuniform with respect to magnitude measures used to quantify earthquake size • Contain a nonuniform mix of mainshock and aftershock earthquake events • Contain duplicate earthquake entries • May contain man-made events (such as blasts) that are not a product of the natural tectonic environment of a region Significant scrutiny (“clean-up”) of these catalogs is therefore required prior to performing statistical analyses to determine representative estimates of earthquake recurrence frequency. This is not to denigrate the value of historic earthquake catalogs — without such catalogs, the earthquake record would only extend back to a few decades ago. With historic catalogs, the record extends back hundreds, in some cases thousands, of years. Recent diligent efforts to research historic earthquakes are a significant contribution to PSHA [see, for example, Lee et al., 1988; Downes, 1995; Stucchi, 1993; Usami, 1981; Ambraseys and Finkel, n.d.; and Ambraseys and Melville, 1982]. An initial project earthquake catalog typically contains subcatalogs from various international and local seismological reporting agencies, resulting in duplicate earthquake entries. Prioritization and ranking of the various data contributed to the catalog are required to select the most reliable entries in terms of earthquake location, time of occurrence, and magnitude. Conversion of multiple magnitude measures to a single, representative magnitude for all earthquakes in a catalog is performed using empirical correlation relationships either available in seismological research literature (see Chapter 4) or developed directly from the various magnitude measures in the catalog itself, providing that sufficient data are available for obtaining statistical regression conversion relationships. Dependent events are removed from the catalog based on magnitude–time–distance parameters appropriate for characterizing aftershock earthquake sequences [see, for example, Reasenberg and Jones, 1989]. Removal of dependent events assures that the Poisson assumption of the PSHA is not violated in terms of earthquake recurrence. © 2003 by CRC Press LLC
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1.0 Intensity IV V VI VII VIII
V
VI
0.1
σλ =
λ / λ
MMI VI complete this range only
VII
Slope - T1/2
VIII
0.01 5
10
Time (Years)
100
FIGURE 8.6 Completeness time plots in terms of earthquake epicenter intensity following the method of Stepp [1973]. Each symbol refers to a different earthquake intensity class.
Most commonly, the statistical procedures proposed by Stepp [1972] are used to assess completeness times of the reported magnitudes, which assume the earthquake sequence in a catalog can be modeled as a Poisson distribution. If k1, k2, k3 … kn are the number of events per unit time interval, then: λ=
1 n
∑
n i =1
ki
(8.6)
and its variance is σ2 = λ/n, where n equals the number of unit time intervals. If unit time is one year, σλ = λ1/2/T1/2 as the standard deviation of the estimate of the mean where T is the sample length in years. This test, then, is for stationarity of observational quality. If data for a magnitude interval are plotted as log (σλ) vs. log (T), then the portion of the line with slope T–1/2 can be considered homogeneous (Figure 8.6) and used with data for other magnitude ranges (but for different observational periods) similarly tested for homogeneity to develop estimates of recurrence frequency. Over large regions, Gutenberg and Richter [1954] found that the average recurrence frequency of earthquakes follows an exponential distribution related to magnitude (Equation 8.5). In its cumulative form, the Gutenberg–Richter relation of recurrence frequencies is unbounded at the upper magnitude. In PSHA, this relationship imposes the unrealistic assumption that the maximum potential earthquake for any region under consideration is unbounded and unrelated to the seismotectonic setting. The © 2003 by CRC Press LLC
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truncated exponential recurrence relationship [Cornell and Vanmarcke, 1969] is therefore commonly used in practice:
( )
N (m) = N m
0
( (
))
( (
exp −β m − m0 − exp −β mu − m0
( (
1 − exp −β m − m u
0
))
))
for m ≤ mu
(8.7)
where m0 is an arbitrary reference magnitude; mu is an upper-bound magnitude where n(m) = 0 for m > mu; and β = b · ln10. In this form, earthquake frequency approaches zero for some chosen maximum earthquake of a region. Other magnitude-frequency relations are discussed in Chapter 4.
8.5.2 Geologic Earthquake Frequency Assessments Characterizing earthquake recurrence frequency on individual faults, as opposed to regionally distributed area sources, is a more challenging proposition. Many earthquake faults have recurrence frequencies for significant earthquakes of hundreds to thousands of years. It is largely fortuitous, then, if even one large-earthquake interoccurrence interval is represented in the historical record. This lack of empirical earthquake data precludes robust assessments of earthquake frequency by statistical treatments of historical earthquake data. Other means are required for determining earthquake frequency on seismically active faults. Significant efforts have been made in the past 25 years to characterize the rate at which faults slip in many seismically active regions of the world [McCalpin, 1996]. Fault slip-rate can be related to earthquake occurrence frequency through the use of seismic moment [Molnar, 1979; Anderson, 1979]. Seismic moment, Mo , is the most physically meaningful way to describe the size of an earthquake in terms of static fault parameters. It is defined as: Mo = µ Af D
(8.8)
where m is the rigidity or shear modulus of the fault, usually taken to be 3 × 1011 dyne/cm2; Af is the rupture area on the fault plane undergoing slip during the earthquake; and D is the average displacement over the slip surface. The seismic moment is translated to earthquake magnitude according to an expression of the form:
( )
log M o M = c M
(8.9)
Based on both theoretical considerations and empirical observations, c and d are rationalized as 1.5 and 16.1, respectively [Molnar, 1979; Anderson, 1979]. Actually, to be consistent with the definition of moment magnitude, d should be set equal to 16.05 [Kanamori, 1978; Hanks and Kanamori, 1979]. The total seismic moment rate is the rate of seismic energy release along a fault. According to Brune [1968], the slip rate of a fault can be related to the seismic moment rate M 0T as follows: M oT = µA f S
(8.10)
where S is the average slip rate (per unit time) along the fault. The seismic moment rate, therefore, provides an important link between geologic and seismicity data. While the Gutenberg–Richter relationship describes the regional occurrence frequency of earthquakes, it has been found to be nonrepresentative of large earthquake occurrence on individual faults [Schwartz and Coppersmith, 1984; Wesnousky, 1994]. Physically, this can be attributed to the breakdown of the power law of the Gutenberg–Richter relationship between large and small earthquakes because they are not self-similar processes [Scholz, 1990]. Geologic investigations of faults of the San Andreas system of western California and of the Wasatch fault in central Utah have indicated that surface-rupturing © 2003 by CRC Press LLC
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Annual Number of Earthquakes, N (m)
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FIGURE 8.7 Comparison of the exponential (solid line) and characteristic recurrence (dashed line) frequency curves. (From Youngs, R.R. and Coppersmith, K.J., Bull. Seismol. Soc. Am., 75, 939–964, 1985.)
10 1 –1
10 10
–2
10
–3
10
–4
10
–5
4
5 6 7 Magnitude, m
8
earthquakes tend to occur within a relatively narrow range of magnitudes at an increased frequency over that which would be estimated from the Gutenberg–Richter relationship. These have been termed characteristic earthquakes. The characteristic recurrence frequency distribution reconciles the exponential rate of small- and moderate-magnitude earthquakes with the larger characteristic earthquakes on individual faults (Figure 8.7). The summed rate of earthquakes over many faults in a region reverts to the truncated exponential distribution [Youngs and Coppersmith, 1985] and is therefore consistent with the regional empirical Gutenberg–Richter relationship. The characteristic recurrence frequency distribution can be separated into a noncharacteristic Gutenberg–Richter relationship for small and moderate earthquakes, and a characteristic frequency part for large earthquake occurrence. The cumulative rate of noncharacteristic, exponentially distributed earthquakes, Ne , is estimated from the seismic moment and seismic moment rate as follows: − β m −0.25 1−e ( u )
N e= M oT Mo e
− β ( mu −0.25)
(
−c/2 b b10 − c / 2 b10 1 − 10 + c −b c
)
(8.11)
The cumulative rate of characteristic earthquakes, Nc , is related to the cumulative rate of noncharacteristic earthquakes by the expression: Nc =
− β m −m −1.5 β Ne e ( u 0 )
(
− β m −m −0.5 2 1−e ( u 0 )
)
(8.12)
Similar to the truncated exponential recurrence model, frequency estimates from the characteristic recurrence model approach zero at the defined maximum magnitude for the source. Figure 8.7 compares the truncated exponential and characteristic frequency distributions. If a fault can be considered truly characteristic, then only a single earthquake of specified magnitude is expected to occur on the fault. Such a model was used by Frankel et al. [1996, 2000] and the Working Group on California Earthquake Probabilities [1995, 1999] for large faults in California that have been well characterized paleoseismically. In this case, the frequency of the characteristic event, which is assumed to rupture an entire fault segment or series of segments, is given by the expression: N char =
© 2003 by CRC Press LLC
M 0T M 0 ( M char )
(8.13)
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where Mchar is the magnitude of the characteristic event. This is referred to as the characteristic earthquake or maximum-magnitude model. This expression becomes somewhat more complex if the characteristic event is assumed to have a truncated Gaussian magnitude distribution (to account for inherent randomness in the magnitude of the event) as was assumed by the Working Group on California Earthquake Probabilities [1999]. To conserve the mean seismic moment rate, N char must be reduced when the truncated Gaussian distribution is used. This reduction is a function of both the standard deviation and the truncation limit. The Working Group on California Earthquake Probabilities [1999] used a standard deviation of 0.12 and a truncation limit of ±2 standard deviations. In this case, N char would have to be multiplied by 0.94 to conserve the mean seismic moment rate. The cumulative truncated Gaussian magnitude distribution is given by the equation:
N char
m M + zσ νchar Fchar f M (m) dm − f M (m) dm 0 0 = M + zσ f M (m) dm − 1 2 0
∫
∫
(8.14)
∫
where N char is the annual number of events with magnitude greater than or equal to m, νchar is the mean rate of characteristic events on the fault (equal to the inverse of the recurrence time), F char is the reduction factor needed to conserve the mean seismic moment rate [see Field et al., 1999], M is the characteristic magnitude on the fault (referred to as Mchar above), z is the truncation limit, σ is the standard deviation, and fM(m) is the Gaussian (normal) probability density function, given by: f M (m) =
1 σM
1 m − M 2 exp − 2π 2 σ M
(8.15)
The above integrals are widely available in statistics books. In the case of the application by the Working Group on California Earthquake Probabilities [1999], F char = 0.94, σM = 0.12, and z = 2. The truncated exponential distribution can also be characterized in terms of seismic moment rate so that it can be used in conjunction with slip rate. This distribution is given by Equation 8.14, in which N 0 is given by the expression [Shedlock et al., 1980; Campbell, 1983]: N 0 = N 0′
10 − b(m0 −m0′ ) − 10 − b(mu −m0′ ) 1 − 10 − b(mu −m0′ )
(8.16)
where N 0′ =
M 0T (c − b)
[ b[1 − 10 − b(m −m′ ) ] u
0
]
M 0 (mu )10 − b(mu −m0′ ) − M 0 (m0′ )
−1
(8.17)
and m0′ ≤ m0 is the magnitude corresponding to a physical lower limit below which earthquakes are not expected to occur or do not contribute to the observed slip on the fault, M0( m0′ ) is the seismic moment of this lower limit magnitude, and M0(m u) is the seismic moment of the upper bound magnitude m u. The physical lower limit magnitude should not be confused with the lower-bound magnitude m 0 , the lower limit of engineering significance. If there is no physical limit to the smallest earthquake that can occur on a fault, or if mu >> m0′ , then Equation 8.17 can be simplified considerably, resulting in the relationship [Campbell, 1983]: N 0′ =
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M 0T (c − b)10bmu bM 0 (mu )
for mu >> m0′
(8.18)
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which can be used with the truncated exponential distribution above or as an estimate of the a-value in the Gutenberg–Richter relationship given in Equation 8.5. Petersen et al. [1996] used an incremental version of the above relationship to estimate the a-value for characteristic faults in California.
8.5.3 Conservation of Seismic Moment on Segmented Faults The maximum magnitude and characteristic earthquake recurrence models are conceptually linked to the idea that large fault zones rupture in a segmented manner and rarely break their entire length in a single earthquake. The segmented nature of the mechanics of faulting was revealed through intense paleoseismic investigations of the San Andreas and Wasatch fault zones in the western United States [Schwartz and Coppersmith, 1984]. Relatively small displacements observed in natural exposures or excavations of the fault zones were not laterally continuous. Larger displacements, however, were continuous over longer lengths and crossed structural discontinuities within the fault zone. The logical confinement of ruptures between identifiable structural discontinuities, or rupture barriers, within fault zones led to the concept of segmented fault rupture [King and Nabelek, 1985; Schwartz, 1988]. This concept has proven very useful in explaining the extent of recent earthquake ruptures [e.g., Crone et al., 1985], in defining paleoseismic ruptures [e.g., Machette et al., 1992], and in relating the development of geologic structure to repeated earthquake rupture of fault zones [Cowie and Scholz, 1992]. Although fault segmentation has proven a very useful tool in earthquake hazards assessment, it is important to recognize that segment boundaries do not repeatedly arrest all earthquake ruptures and that their position is not necessarily constant in geologic time and space [Wheeler and Krystinik, 1992]. Nonetheless, a basic tenet of fault segmentation is that, in a relative sense, smaller earthquakes tend to be confined to single segment ruptures, whereas larger earthquakes tend to be characterized by multisegment ruptures. Specific lengths of segment ruptures depend on the tectonic environment of the region and the style of faulting that is present. Repeated faulting of all styles, over geologic time, will produce recognizable geologic structures at segment boundaries. Detailed documentation of fault slip rates along faults of the San Andreas system in southern California has shown that slip rate is not constant along all segments of a single fault zone [Working Group on California Earthquake Probabilities, 1995, 1999]. Slip rate typically varies among the various segments and could be due to any number of physical changes that may occur along the fault. A difficulty in PSHA, therefore, is accounting for the varying slip-rate values between different segments of individual faults. The various slip rates could be completely accommodated in the PSHA by a series of fault sources specific to each segment with each segment’s earthquake rate governed by the segment slip rate. This would be an unrealistic model, however, both in terms of the resulting distribution of probabilistic ground motion and the representation of large historical earthquake ruptures that have been documented to rupture more than one segment on some faults. The Working Group on California Earthquake Probabilities [1995, 1999] developed a “cascade” model of earthquake recurrence frequency to satisfactorily account for varying slip rates and fault depths on a single fault zone in a PSHA. The 1995 cascade model assumes that large earthquakes break multiple, contiguous segments of a fault at a frequency that is governed by the lowest-slipping segment. Once the moment rate (Equation 8.17) of the slowest-slipping segment is depleted in the production of these large earthquakes, it drops from any further considerations regarding multisegment ruptures and the slip rates of the remaining segments are reduced by the rate of the slowest-slipping segment. A new set of multisegment ruptures are thereby defined, and the procedure repeats until only single-segment ruptures of the highest-slipping segments are left to rupture in single earthquakes at a rate that is determined from the residual slip when all multisegment ruptures have been exhausted. This novel modeling approach maintains the slip-rate and seismic-moment budget on each defined fault segment. In the 1999 model, each possible cascade on a fault zone was assigned a relative weight by a panel of experts and the final weights adjusted to achieve a moment-balanced model.
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8.5.4 Time-Dependent Probability Modeling
© 2003 by CRC Press LLC
T1
T1
T2
T2
u
u
CUM. COSEISMIC SLIP
FIGURE 8.8 Three types of earthquake occurrence models. Upper row of figures shows stress patterns of increase and decrease through multiple earthquake cycles. Lower row of figures shows corresponding patterns of fault slip through the earthquake cycles. (a) Perfectly periodic model of constant stress increase to a certain level (T1), and constant stress drop back to a certain level during the earthquake (T2). (b) Time-predictable model illustrating stress buildup to a certain level and nonuniform stress drops. (c) Slip-predictable model showing nonuniform stress buildups and stressdrops to a certain level. (From Scholz, D.H., 1990, The Mechanics of Earthquake Faulting, Cambridge University Press, Cambridge. With permission.)
STRESS
Use of the previously described magnitude-frequency models in most seismic hazard applications assumes that the occurrence of an earthquake is independent of all other earthquakes, both spatially and temporally. That is, that earthquake occurrence follows a Poisson process, which can be characterized by a mean annual rate and a variance equal to this mean rate. These applications are therefore time-independent. Time-dependent occurrence models, on the other hand, assume that the probability of a future earthquake increases with the elapsed time since the last earthquake. Faults that are early in their seismic cycle are less likely to have an earthquake than the Poisson model would predict and faults late in their seismic cycle are more likely to have an earthquake. Such models are called renewal models. The consequences of time-dependent probability on seismic hazard have been investigated only to a limited extent in the literature [Cramer et al., 2000], but it has found widespread use in engineering practice and in loss modeling. It has also found professional acceptance in assessing short-term probabilities of large earthquakes on the San Andreas and related faults in California [Working Group on California Earthquake Probabilities, 1988, 1990, 1995, 1999], which has greatly impacted hazard mitigation policy in the San Francisco and Los Angeles areas. Following the great 1906 San Francisco earthquake, Reid [1910] proposed the elastic rebound theory in which earthquakes occur whenever stress builds to a certain level on a fault (Figure 8.8). The earthquake relieves this stored stress and the earthquake cycle begins anew. With the assumption of constant stress increase, the recurrence time in this model is perfectly periodic. Based on a long earthquake history in the vicinity of Kyoto, Japan and measured coastal uplifts during earthquakes, Shimazaki and Nakata [1980] proposed two other alternative forms of recurrence. The first is a time-predictable model that predicts earthquakes will occur when stress accumulation on the fault reaches a critical level, but that the stress drop and magnitude of the earthquakes vary among the seismic cycles (Figure 8.8). Thus, the time to the next earthquake can be predicted from the slip in the previous earthquake assuming a constant fault-slip rate. The second is a slip-predictable model in which earthquake failure on the fault resets the stress on the fault to some constant level irrespective of the earthquake’s magnitude (Figure 8.8). Thus, slip in the next earthquake can be predicted from the time since the previous earthquake. The motivation for time-dependent probability models arose from the identification by seismologists of “seismic gaps” along segments of major plate boundaries of the circum-Pacific region [see for example, Sykes, 1971]. Seismic gaps were identified as unbroken sections of major plate boundaries that were bounded on each end by ruptures from previous earthquakes. The implication from such observations was that the unbroken sections had an increased likelihood of rupturing in a future earthquake than those sections that had previously ruptured. Nishenko [1991] formalized the concept for 96 circumPacific plate boundary segments in terms of a conditional probability that a large earthquake would occur in future time windows of 5, 10, and 20 years, given that one had occurred at some known time in the past. A primary issue in such earthquake forecasts is the reliable quantification of large (characteristic) earthquake recurrence intervals. In that these large earthquakes are rare events in themselves, there is
(a)
t
u
(b) TIME
t
(c)
t
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insufficient available data on any individual rupture segment from which to obtain a robust statistical distribution of recurrence times. Nishenko and Buland [1987] found that normalized earthquake recurrence intervals for large earthquakes in the circum-Pacific region follow a lognormal distribution with a virtually constant intrinsic standard deviation of σD = 0.205 for historic recurrence data and 0.215 for combined historic and geologic recurrence data, when a normalizing function T/Tave was used. In this formulation, T is the recurrence interval of an individual earthquake sequence, and Tave is the observed average recurrence interval for the sequence. This distribution has since become a primary element of the renewal-type time-dependent earthquake models used by the Working Group on California Earthquake Probabilities [1988, 1990, 1995, 1999]. A finite value for the average intrinsic standard deviation (usually taken to be between 0.21 and 0.5) is a significant element of the model, because it introduces a degree of aperiodicity in the occurrence of characteristic earthquakes. The physical reality of a finite value for the intrinsic standard deviation is also significant because it may present a barrier to precise earthquake prediction since physical reasons for this value are currently unknown [Scholz, 1990]. In part, it might be due to stress interactions from other earthquakes in the region, as discussed later in this chapter. The probability that a large earthquake will occur on a fault at time τ in an interval (T, T + ∆T), assuming a probability density function for recurrence time fT(t), can be given by the integral: P (T ≤ τ ≤ T + ∆T ) =
∫
T + ∆T
T
fT (t ) dt
(8.19)
If the elapsed time since the previous earthquake on the fault Te is known, the conditional probability that the earthquake will occur in the next ∆T years is given by the ratio:
∫ )
(
P Te ≤ τ ≤ Te + ∆T τ > Te =
Te + ∆T
Te
∫
∞
T
fT (t ) dt
fT (t ) dt
(8.20)
It has been common to assume a lognormal probability density function for recurrence time [Nishenko and Buland, 1987; Working Group on California Earthquake Probabilities, 1988, 1990, 1995; Cramer et al., 2000], which is given by the equation: fT (t ) =
1 t σ lnT
2 1 t Tˆ exp − 2 σ lnT 2
(8.21)
where σlnT is the standard deviation of the logarithm of recurrence time and Tˆ is the median recurrence time, related to the mean by the expression: Tˆ = T exp
(
1 2
σ ln2 T
)
The standard deviation is composed of two parts, an intrinsic standard deviation σi and a parametric standard deviation σp , where σ lnT = σ i2 + σ 2p The intrinsic standard deviation represents aleatory or random variability, whereas the parametric standard deviation represents epistemic or modeling uncertainty. The latter standard deviation accounts for uncertainty in the median estimate of the recurrence interval, which comes from deriving it from events with uncertainty dates, such as paleoseismic estimates. Epistemic uncertainty can also be included by
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Monte Carlo simulation, rather than including it in σlnT [Working Group on California Earthquake Probabilities, 1995, 1999]. While the lognormal distribution has been the most common distribution used to describe the variability in recurrence intervals, several other distributions have been proposed and used. Most notable are the Weibul and time-predictable distributions [Cornell and Winterstein, 1988] and the Brownian passage time distribution [Working Group on California Earthquake Probabilities, 1999]. Other nonPoissonian distributions are reviewed by Cornell and Winterstein [1988]. Faults are not only affected by earthquakes that occur on them, but also by earthquakes that occur on nearby faults, through stress transfer [Stein, 1999]. The occurrence of a large earthquake modifies shear and normal stresses on other faults in the region, although these stress changes are small, being on the order of several bars or less. Considering that stress drops in earthquakes are on the order of 50 to 100 bars, the changes related to stress transfer are only a small fraction of the stress drops involved in fault rupture. Nonetheless, the frequency of earthquakes has been observed to increase in areas of increased stress transfer and decrease in areas of decreased stress transfer. For example, stress changes following the MW 6.9 Hyogo-ken Nanbu, Kobe, Japan earthquake is believed to have produced a tenfold probability decrease of a large earthquake in the next 30 years on the western segment of the Arima-Takatsuki Line (the fault that terminated the Kobe rupture on the north), where stress decreased [Toda et al., 1998]. On the other hand, it was estimated that there was a fivefold increase in probability on the eastern segment of the Arima-Takatsuki Line, where stress was increased (Figure 8.9). Incorporating such stress changes augments the physical bases of time-dependent earthquake probability estimates. The permanent probability gain caused by a stress increase is amplified by a transient gain that decays with time [Stein, 1999]. The opposite occurs for a stress decrease. The transient gain is an effect of rateand state-dependent friction [Dietrich, 1994], which describes behavior seen in laboratory experiments and in natural seismic phenomena, such as earthquake sequences, clustering, and aftershocks. The transient gain can be significant, but will decrease exponentially after the earthquake, according to Omori’s law, until it reaches the level of the static stress change. The rate increase can be converted to a probability gain using Equation 8.2. The seismicity rate equation is given by [Dietrich, 1994; Stein, 1999]: R (t ) =
− ∆σ f exp Aσ n
r −t − 1 exp t + 1 a
(8.22)
where R(t) is the seismicity rate as a function of time t, following a Coulomb stress change ∆σf , A is a constitutive parameter, σn is the total normal stress, ta is the aftershock duration (equal to ∆σ/ τ˙ , where τ˙ is the stressing rate on the fault), and r is the seismicity rate before the stress perturbation. To evaluate this equation, the Coulomb stress change is calculated and r, ta , and τ˙ are estimated from observations, allowing Aσn to be inferred. Using such a model, Parsons et al. [2000] estimated a 62 ± 15% probability of an earthquake capable of causing strong shaking in Istanbul in the next 30 years as a result of the 1999 MW 7.4 Izmit, Turkey earthquake. This can be compared to a probability of 49 ± 15% using only the renewal model. The Poisson model results in a 30-year probability of 20 ± 10%. The probability during the next decade is estimated to be 32 ± 12% compared to a renewal rate of 20 ± 9%. Large earthquakes can also have a significant quiescent affect on seismicity, called a stress shadow. Harris and Simpson [1998] evaluated the observed suppression of MW 6 earthquakes in the San Francisco Bay area after the 1906 MW 7.8 San Francisco earthquake, and found a set of stress and rate-and-state parameters that were consistent with the observed rate change. Applying these parameters to the Hayward fault, they found that the probability of a MW 6.8 earthquake during the period 2000 to 2030, such as occurred in 1868, is 15 to 25% lower if the effect of the 1906 stress shadow is included. Stress transfer following the great 1906 San Francisco earthquake is one of the models considered by the Working Group on California Earthquake Probabilities [1999] in their time-dependent probability estimates for the © 2003 by CRC Press LLC
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M ≥1.0 Aftershocks
Coulomb Stress Change (bars)
for Optimally Oriented Faults -0.5
0.0
0.5 for Major Strike-Slip Faults
FIGURE 8.9 Illustration of stress transfer following the 1995 Hyogo-ken Nanbu (Kobe), Japan earthquake and aftershocks greater than magnitude 2.0. Star indicates the epicenter of the.earthquake located on the northeast trend of the fault rupture. The Arima-Takatsuki Tectonic Line trends east-northeast at the northern end of the fault rupture. 63% of the aftershocks were found to occur where Culomb stress increased on optimally oriented faults by greater than 0.1 bar. (From Toda, S. et al., J. Geophys. Res., 103, 24,543–24,565, 1985. Also http://quake.usgs.gov/research/ deformation/modeling/ papers/kobe/fig6.jpg/.)
San Francisco Bay area. Figure 8.10 illustrates the regional, as well as fault-segment-specific, conditional probabilities of MW 6.7 earthquakes in the San Francisco Bay region made by the Working Group for a 30-year time window from 2000 to 2030. The Working Group estimated this probability to be 70 ± 10% with individual fault segments contributing anywhere from 4 to 32% of this overall probability. Also new in these assessments is the incorporation of a probability (i.e., 9%) that a future earthquake may occur off the major faults in the regions that were considered in the study.
8.6 Maximum Magnitude Assessments Assessment of the maximum magnitude earthquake for the defined seismic sources is an important, fundamental task in PSHA. For PSHAs addressing low-probability hazard (i.e., long return-period hazard), the maximum magnitude earthquakes may dominate the ground motion assessments [Bender, 1984]. In probabilistic analyses, the maximum earthquake is defined as the earthquake that is assessed as physically capable of occurring within, or on, a defined seismic source in the contemporary tectonic © 2003 by CRC Press LLC
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SAN FRANCISCO BAY REGION EARTHQUAKE PROBABILITY
70% odds (±10%) for one or more magnitude 6.7 or greater earthquakes from 2000 to 2030. This result incorporates 9% odds of quakes not on shown faults.
Expanding urban areas
21%
New odds of magnitude 6.7 or greater quakes before 2030 on the indicated fault
18%
Odds for faults that were not previously included in probability studies
Increasing quake odds along fault segments Individual fault probabilities are uncertain by 5 to 10%
FIGURE 8.10 Time-dependent earthquake probabilities in the San Francisco Bay area, California for a time window from 2000–2030. (From the Working Group on California Earthquake Probabilities, 1999, U.S. Geological Survey Open-File Rep. 99-517, http://Geopubs.wr.usgs.gov/fact sheet/fs152–99.)
stress regime. Another term defining such an event is maximum credible earthquake [California Division of Mines and Geology, 1975]. A number of diverse methods have been used to define such earthquakes, each dependent on the purpose of the hazard assessment, the amount and kinds of seismological and geological data that lend themselves to such assessment, and the variety of seismotectonic settings in which PSHAs have been performed [dePolo and Slemmons, 1990]. The assessment of maximum earthquake magnitude is possible mainly because empirical data indicate a correlation between earthquake magnitude and fault parameters of rupture length, rupture area, and displacement [Wells and Coppersmith, 1994; see Chapter 4]. However, the use of several techniques can result in more reliable estimates than any single technique by itself [Coppersmith, 1991]. Maximum magnitude assessments in PSHA are broadly divisible into those that characterize area sources and those that are specific to individual earthquake faults.
8.6.1 Area Source Determinations Area sources are generally employed due to the lack of recognizable earthquake faults and seismically active geologic structure. Empirical correlation equations between fault rupture parameters and earthquake size, therefore, have limited application to these source types. Maximum magnitudes for these sources are typically assessed from an extrapolation of the historical seismicity of the region, from
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compelling worldwide analogs of the regional tectonic setting, from regional paleoseismologic data and interpretations (if available), or simply from the judgments of experts. Lacking clear geological guides from which to estimate maximum earthquakes in regions of low seismicity, methods of estimating maximum magnitudes from historical earthquake data have been commonly used. Since large earthquakes in these regions have very long recurrence times, it is generally assumed that the largest historical earthquake is the minimum value for a maximum earthquake estimate. Nuttli [1979], for example, evaluated the largest earthquake of the 1811–1812 New Madrid earthquake sequence in the New Madrid Seismic Zone as mb 7.4 and expressed confidence that the sum of the energy of the three principal shocks of the sequence defines the maximum earthquake for this seismic source (mb 7.5). Elsewhere in the central United States region, magnitude increments of between 0.5 and 1.0 unit above the historically observed maximum earthquake were judged to approximate earthquakes with recurrence intervals of around 10,000 years in application to nuclear facility sites. Nuttli [1981] later extended this approach for normalized areas of 100,000 km2 and a time period of 1000 years in application to seismic zones of the central United States. Justification was based on the fact that these parameters provided maximum magnitude estimates in general agreement with the historical maximum earthquakes of both the New Madrid and Charleston seismic zones, which are considered to be essentially the maximum earthquakes in these zones. Such techniques assume that the addition of magnitude increments to historical maximum observations accounts, to some extent, for the relative shortness of the historical reporting period. For a b-value of 1.0 in the Gutenberg–Richter recurrence relationship (see Chapter 4), the addition of 1.0 magnitude unit to the historical maximum observation is equivalent to multiplying the length of the observation period by a factor 10. Justification is then required for expecting the maximum magnitude event within this period of time. A primary issue with this technique is the correct characterization of the form of recurrence–frequency relationship. Minor changes in the Gutenberg–Richter b-value imply greatly differing time periods of catalog compensation, and other forms of recurrence–frequency relationships may also be appropriate [Wesnousky et al., 1983; Wesnousky, 1994]. The technique of using worldwide tectonic analogs for assessing maximum magnitudes is premised on the acquisition of more complete data by substituting space for time. In many regions, the historical period of earthquake reporting is far too short to have probably sampled the largest possible earthquake. However, even if the occurrence of maximum earthquakes is random in time and space, the likelihood of having observed a maximum earthquake is greater over a collection of similar regions worldwide. This was the basis for a far-reaching study by the Electric Power Research Institute [Johnston et al., 1994] of stable continental interior earthquakes worldwide. From a regionalization of the world into areas of similar geologic and tectonic histories and a detailed examination of the historical earthquakes in each, this study was able to identify associations of maximum earthquakes with specific classes of continental crust. Very old continental crust that had not been disturbed by regional tectonism over the last billion years exhibited lower magnitude earthquakes than continental crust that had been disturbed over the last 0.5 billion years. Such analogies can provide strong arguments for maximum magnitude assessments in regions of sparse seismicity. Paleoseismologic data, such as paleoliquefaction, can be an insightful tool in assessing the maximum magnitudes of low-seismicity regions. Unlike tectonic analogs that substitute space for time, paleoseismological data extend the record of earthquakes into prehistoric time. Munson et al. [1992, 1994] documented widespread liquefaction features throughout southern Illinois and Indiana dating from a single earthquake 6100 ± 200 years ago. A second strong earthquake was documented as occurring 12,000 years ago. Historical earthquakes in this region up to magnitude 5.5 have no reports of accompanying liquefaction, and the prehistoric earthquakes therefore appear to be considerably larger than the historic earthquakes. Obermeier et al. [1993] evaluated the earthquake that occurred 6100 years ago as a magnitude 7.5 earthquake based on the physical dimensions and properties of the liquefaction features. Thus, although the source of the prehistoric earthquakes remains unknown, assessments of the seismic hazard in this region must assess significantly higher maximum magnitudes than have been observed historically. A similar example can be cited for the Pacific northwest region of the United States where no large © 2003 by CRC Press LLC
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earthquake has affected coastal Oregon and Washington historically. Yet, regional paleoseismological evidence suggests sudden, regional submergence of coastal marshes along the Oregon and Washington coasts [Atwater, 1987; 1992]. These phenomena have been ascribed to prehistoric great earthquakes (moment magnitude of 8 ~ 9) and their associated tsunamis that occurred 300 years ago, and earlier, along the Cascadia subduction zone. Recently, evidence from tsunami observations in Japan permitted precise dating of the last earthquake at 1700 and its magnitude at ~9 [Satake et al., 1996].
8.6.2 Individual Fault Determinations Guidelines for establishing maximum magnitudes for individual faults are significantly better than for establishing maximum magnitudes for area seismic sources. Estimates of maximum magnitudes on faults are typically computed from empirical correlation relationships between earthquake magnitude and rupture dimensions [e.g., Wells and Coppersmith, 1994]. The most common characteristic that is correlated with earthquake magnitude is fault rupture length. Extensive study has been made of this correlation over the past 30 years [Bonilla and Buchanan, 1970; Mark and Bonilla, 1977; Bonilla, 1980; Wells and Coppersmith, 1994; among many others; see Chapter 4] and the database of worldwide earthquake surface ruptures has grown rapidly [e.g., Wells and Coppersmith, 1994]. In addition, the formal statistical treatment of the data has improved over the years. Modern correlation relationships: 1. 2. 3. 4.
Quantify the scatter in the data in terms of the standard deviation Are sensitive to earthquake magnitude type Provide unique definition of fault-type categories Minimize the error in prediction by providing separate regression relationships for the various independent variables
Wells and Coppersmith’s [1994] relationships, presented in Chapter 4, are based on data from 244 historical continental earthquakes worldwide that produced surface rupture and had focal depths shallower than 40 km and magnitudes greater than 4.5. Two primary sources of uncertainty exist in employing magnitude-rupture length correlation equations in the assessment of earthquake magnitudes. One is the variability of the regression equation itself, which has been described in Wells and Coppersmith’s [1994] assessments in terms of the standard deviations of the regressions and which can be considered in the application of the relationships. The other is the uncertainty of establishing future rupture lengths. While the empirical correlation relationships provide a relatively complete assessment of past earthquake ruptures related to earthquake magnitude, their forward application in predicting future earthquake magnitude on a fault is ambiguous owing to the need to define the length of future fault ruptures. In applications of a few decades ago, rather arbitrary fractional lengths of known earthquake faults were used to determine maximum magnitudes, premised on the empirical observation that faults seldom rupture their entire lengths in single earthquakes, and commonly ruptured in less than half of their entire length [Albee and Smith, 1966]. However, the concept of fault segmentation also has proven to be a useful tool in the definition of future potential lengths of fault rupture. For example, in the cascade model of determining earthquake recurrence frequencies on singular faults with segment-specific slip rates, the magnitude of each earthquake cascade, whether a multi- or single-segment rupture, is defined by the individual cascade rupture dimension.
8.6.3 Mixed Source Determinations The previous discussions of earthquake recurrence frequency and maximum magnitude assessment in PSHA were organized around area and fault source determinations for simplicity of presentation. However, it is common practice to define a mixed-source type in which one or more earthquake faults are defined within the boundaries of a regional area source. Such mixed-source definitions require particular care in specifying earthquake frequencies and maximum magnitudes to avoid double counting of earthquake occurrences. The simplest manner of handling such sources is to define two separate sets of © 2003 by CRC Press LLC
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minimum and maximum magnitudes, one for the area source and one for the fault sources, respectively. Such a treatment typically defines the area source as a region of background seismicity in which smalland moderate-magnitude earthquakes are modeled as random events up to a maximum magnitude of about 6.5, with a recurrence frequency statistically determined from the catalog of earthquakes in the region. Above this magnitude, the larger earthquakes can be modeled in various ways as occurring on the defined earthquake faults with a recurrence frequency defined either from an extrapolation of the historical data, available paleoseismic data, or some combination of both. Maximum magnitudes may then be based on the physical parameters of the faults, as previously described. The magnitude break in area source/fault source modeling techniques for the mixed-source type is often rationalized around the threshold magnitude of surface faulting in the tectonic province of the site. In the Basin and Range province of the western United States, this threshold magnitude is around 6.75 [Bucknam and Anderson, 1979]. Care should be taken to evaluate the implied seismicity and seismic moment rates for mixed-source types to assure that the summed seismicity parameters are reasonable within the constraints of available seismotectonic data. This is of particular importance if the modeled magnitude range of the defined area source overlaps with those of the defined fault sources. Unrealistic regional magnitude-frequency relations could easily result from such a treatment of seismic sources.
8.7 Ground Motion Attenuation Relationships The ground motion attenuation relationships provide the means of estimating a strong-motion parameter of interest from parameters of the earthquake, such as magnitude, source-to-site distance, faulting mechanism, local site conditions, etc. [see Chapter 5]. This relationship is a particularly important element in PSHA for three reasons: 1. It dictates the detailed requirements of the seismic source definition. 2. It dictates the ground motion parameters that may be estimated. 3. It is a major contributor to uncertainty in the PSHA results [McGuire and Shedlock, 1981; Bender, 1984]. A wide variety of empirical ground motion attenuation relationships is available for application in PSHA [Campbell, 1985; see also Chapter 5] and research has shown ground motion attenuation to be regionally dependent. In large part, the choice of an appropriate relationship is governed by the regional tectonic setting of the site of interest, whether it is located within a stable continental region or an active tectonic region, or whether the site is in proximity to a subduction zone tectonic environment.
8.7.1 Impact on Seismic Source Definition A fundamental aspect of applying attenuation relationships within the PSHA methodology is the distance measure on which the chosen relationship is based. Two broad categories exist: • Those based on a measure of an earthquake’s distance from the site, whether measured as an epicentral or hypocentral distance • Those based on a distance from the earthquake fault rupture Epicentral distance is measured as an earthquake’s horizontal distance to a site irrespective of earthquake depth. Hypocentral distance is measured as the slant distance to the site, accounting for both the horizontal and vertical distances from the earthquake to the site. Such types of attenuation relationships do not require the specification of fault planes in the definition of seismic sources. Area source definitions completely satisfy the application requirements of these attenuation relationships and point-source models of earthquake rupture suffice in the PSHA model. If such relationships are used with explicit linear or planar fault sources, the rupture dimensions of earthquakes on these sources must be constrained to infinitely small rupture areas that approximate points. Otherwise, the distance measure may be applied inappropriately and the ground motion hazard may very likely be overestimated. © 2003 by CRC Press LLC
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Application of hypocentral distance measures requires that at least a top and bottom depth of the area source be defined in order to constrain the depths of the modeled earthquakes. Typically, these depth parameters are defined on the bases of either regional or local seismological network data and are a measure of the thickness of brittle crust in a region. Generally, this is referred to as the thickness of the seismogenic layer. In active tectonic regions, such as the western United States, the seismogenic layer generally ranges between 10 and 20 km deep, depending on the locality. In the stable continental region of the eastern United States, the seismogenic layer may range up to 40 km deep in some localities. Most modern attenuation relationships for active tectonic regions are based on various distance measures from the fault rupture zone (see Chapter 5). These relationships allow the specification of the top and bottom of seismogenic faulting (as in the seismogenic layer), can accommodate specific definitions of fault-dip (i.e., the inclination of the fault from horizontal), and require specification of the style of faulting for each defined source. A significant aspect of empirical attenuation relationships is the large scatter in the ground motion data on which the relationships are based, which results in large standard errors about the mean relationship. Campbell [1997] was able to significantly reduce the standard deviation of his relationships by segregating the strong motion database according to fault-rupture style (among other non-fault parameters, such as soil type) prior to regression analysis. His relationships, as well as others, therefore require explicit definition of fault-rupture style, consisting of normal or strikeslip, and reverse faulting. As attenuation relationships have evolved into these more precise definitions of the earthquake source, their application has challenged the PSHA analyst with more precise definitions of seismic sources.
8.7.2 Reference Site Class In addition to defining the earthquake source, application of ground motion attenuation relationships is specific to a soil or rock type on which the PSHA ground motion estimate is to be made. These ground types are referred to as the site class, and are defined in broad categories such as hard rock, soft rock, firm soil, and soft soil. In some cases, such as Campbell [1997], the site classes are unambiguously defined by soil shear-wave velocities. More commonly, the site classes are only qualitatively defined soil types. The choice of site class is important in PSHA since soil tends to amplify long-period motion and deamplify short-period motion over that of rock. Such site effects are embodied in the various site classes of modern spectral attenuation relationships (see Chapter 5). The site class that is chosen for application in PSHA, referred to as the reference site class, may depend on a number of factors, not the least of which is the purpose of the PSHA. Site-specific engineering PSHA evaluations are often performed to obtain a more precise measure of ground motion amplitude than can be found in regional hazard maps contained in building code documents. If seismic engineering for the site is to follow code procedures, then the site class for the PSHA must be consistent with the reference site class on which the codified procedures are based. If dynamic site response analyses are to be performed in order to produce synthetic time histories, either at the ground surface or at various depths (e.g., for pile design), then the reference site class for the PSHA depends on the geotechnical data that are available, the depth to which the geotechnical data extend, and the depth of bedrock at the site. The reference site class in such case may be either soil or rock.
8.8 Accounting for Uncertainties Development of a seismotectonic model and the many required input parameters to PSHA admits to a wide range of interpretations and uncertainties. Median probabilistic seismic hazard models consist of a single, best-estimate set of defined sources that are characterized by a single set of best-estimate seismicity and fault-rupture parameters [Bernreuter et al., 1989]. Development of such models is generally made with cognizance of diverse alternative choices, but individual modeling and parameter selections are made relative to the purpose of the hazard estimate and with respect to the representative nature of the individual selections. For example, the Algermissen et al. [1982] PSHA model for the United States © 2003 by CRC Press LLC
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was premised on a single set of seismic sources and input parameters but only following consideration of diverse views presented in a series of workshops held prior to developing the PSHA models [Thenhaus, 1983]. The Frankel et al. [1996] national PSHA model was similarly constructed following a series of regional workshops across the United States to sample professional opinion on PSHA input, but also contained a limited logic-tree approach to more explicitly represent critical uncertainties in the national seismic hazard estimates. Fully probabilistic seismic hazard models may employ a number of alternative seismic source interpretations with probability distributions defined for the various seismicity and fault-rupture parameters for each source of each model. Models similar to the fully probabilistic one are generally required to establish a mean seismic hazard result [Bernreuter et al., 1989]. In application to the seismic hazard of nuclear power plants in the eastern United States, Bernreuter et al. [1989] solicited 11 distinct PSHA models from individual experts with each model weighted by its creator as to credibility. Feedback was given to each of the experts on the ground motion consequences of their model so that each expert was comfortable with the results. However, little interaction among the experts was promoted. In an alternative approach, the Electric Power Research Institute [EPRI, 1986] performed a very structured PSHA that promoted much interaction and data exchange among experts of six Tectonic Evaluation Committees (TEC), each of which was composed of at least one geologist, geophysicist, and seismologist. Defined seismic sources by each TEC were thoroughly documented within a probabilistic framework as to their physical characteristics that may promote the generation of earthquakes and as to their spatial association with the cataloged earthquakes in the region. The result of this thorough probabilistic treatment was six highly detailed regional seismotectonic models of the eastern United States from which complete probabilistic descriptions of ground motion at the nuclear sites could be obtained. The EPRI [1986] PSHA stands as probably the most comprehensive PSHA performed to date. It should be pointed out that the Bernreuter et al. [1989] and EPRI [1986] PSHAs were designed to address very low levels of risk associated with projects in the nuclear industry. Such comprehensive investigations were developed to address annual risk levels at the power plant sites of 10–4 and lower. Most PSHA applications address common buildings and industrial facilities where annual levels of risk of 10–2 to 10–3 are generally acceptable as an industry or code standard. PSHA methodologies are therefore scaled back from those of the nuclear industry for appropriateness to the project objectives and for cost effectiveness. There are two types of variability that can be included in PSHA. These are aleatory and epistemic variabilities [SSHAC, 1997]. Aleatory variability is uncertainty in the data used in an analysis and generally accounts for randomness associated with the prediction of a parameter from a specific model, assuming that the model is correct. Specification of the standard deviation (σ) of a mean ground motion attenuation relationship is a representation of aleatory variability. Epistemic variability, or modeling uncertainty, accounts for incomplete knowledge in the predictive models and the variability in the interpretations of the data used to develop the models. Aleatory variability is included directly in the PSHA calculations by means of mathematical integration. Epistemic uncertainty, on the other hand, is included in the PSHA by explicitly including alternative hypotheses and models. This uncertainty can be accounted for through the evaluation of multiple individual seismotectonic models or through the formulation of a logic tree that includes multiple alternative hypotheses in a single model. The logic tree allows a formal characterization of uncertainty in the analysis by explicitly including alternative interpretations, models, and parameters that are weighted in the analysis according to their probability of being correct. Logic tree models may be exhaustively evaluated, or adequately sampled through Monte Carlo simulation, which is computationally a more efficient procedure. An example of a logic tree seismotectonic model is shown in Figure 8.11. Each alternative hypothesis, indicated by a branch of the logic tree, is given a subjective weight corresponding to its assessed likelihood of being correct. The proposed alternative hypotheses account for uncertainty in earthquake source zonation, maximum magnitude, earthquake recurrence rate, location and segmentation of seismogenic faults, style of faulting, distribution of seismicity between faults and area sources, and ground motion attenuation relationships. © 2003 by CRC Press LLC
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Seismic Segmentation Segmentation Segments Attenuation Fault Model Relationship Recurrence Sources Model
Status of Total Fault Activity Length
Dip
Maximum Recurrence Recurrence Magnitude Data Rate
Unnamed Unsegmented 0.2
Oquirrh Mtns
Campbell
Model A
Wasatch
0.4
0.333
East Coshe
Exponential 0.3
West Valley
Cominston
65°
5000 0.04
Ogden
0.5
.3333 0.28
SLC Provo
Segmented
Active
37 km
1.0
1.0 45°
Nephi
0.8
0.5
Levon
Hansel Valley
Model B
Sadigh
Bear Lake
0.6
Backgnd
0.333
N/A
Characteristic 0.7
N/A
Active 1.0
N/A
N/A
7.0 0.15 7.25 0.7 7.5 0.15 6.0 0.3 6.25 0.5 6.5 0.2
Fault 1.0
2500 0.48 2000 0.16
Segment 1.0 N/A
1667 0.04 8.5 0.333 9.3 0.334 9.8 0.333
Joyer-Fumal 0.333
FIGURE 8.11 Example logic tree characterization for seismic sources. (From Youngs, R.R. et al., 1987, “Probabilistic Analysis of Earthquake Ground Shaking along the Wasatch Front, Utah,” in P.L. Gori and W.W. Hays, Eds., Assessment of Regional Earthquake Hazards and Risk along the Wasatch Fault, Utah, U.S. Geological Survey Open File Rep. 87-585, pp. M1-M110.)
8.9 Typical Engineering Products of PSHA The fundamental engineering product of PSHA is an amplitude of some ground motion parameter that is associated with a particular return period. This probabilistic format of relating ground motion amplitude to a specific return period is now commonplace in a number of seismic design codes and recommended practices, including those of the National Earthquake Hazards Reduction Program (NEHRP), the International Building Code (IBC), the National Fire Protection Association (NFPA), the American Petroleum Institute (API), and the International Standards Organization (ISO), among others. Probabilistic results can be presented in a number of formats. Perhaps the most widely recognized product is that of a ground motion hazard map, such as produced by the U.S. Geological Survey under the National Earthquake Hazards Reduction Program for the United States (Figure 8.12) and one of the world that was recently produced under the auspices of the Global Seismic Hazard Assessment Program (GSHAP) [Giardini, 1999; Figure 8.13]. Such maps illustrate the regional differences in ground motion amplitude (typically peak ground acceleration, or PGA) at a constant return period (i.e., a constant probability of exceedance). These maps allow the rapid comparison of the seismic hazard for regions and the identification of the most hazardous regions, on a uniform basis. A common goal of hazard models is to rapidly estimate a hazard curve for a particular engineering site of interest. The hazard curve is a plot showing the change in ground motion amplitude relative to return period (Figure 8.14). Ground motion amplitude always increases with increasing return period in Poisson hazard models and, for a single fault, will asymptotically approach the mean ground motion amplitude of the maximum magnitude earthquake at the given source-to-site distance when attenuation variability is not included in the estimate. Another common product in engineering PSHA is the constant-probability, or uniform hazard, response spectrum (Figure 8.15). These curves illustrate ground motion amplitudes over a number of oscillator periods of engineering interest at a constant return period. Comparison of such curves at a constant return period, but for various site classes, illustrates the modification of ground motion amplitudes by various types of soil and rock. Soils tend to deamplify short-period motion, but amplify longperiod motion. Rock sites have the inverse effect. The probabilistic response spectrum is generally smooth © 2003 by CRC Press LLC
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Peak Acceleration (%g) with 10% Probability of Exceedance in 50 Years
50°
-120
°
site: NEHRP B-C boundary -110°
-100°
-90°
-80°
-70°
50°
40°
40°
30°
30°
Nov. 1996 -120
180 100 80 60 40 30 25 20 15 10 9 8 7 6 5 4 3 2 1 0
-70°
°
-110°
-100°
-90°
-80°
U.S. Geological Survey National Seismic Hazard Mapping Project
FIGURE 8.12 Four hundred seventy-five-year return period ground motion hazard map of the conterminous United States. (From Frankel, A., 1996, U.S. Geological Survey Open-File Rep. 96–532. With permission.)
FIGURE 8.13 Four hundred seventy-five-year return period ground motion hazard map of the world. (From Giardini, D. Ann. Geofis., 42, 1999. http://www.gfz-potsdam.de/pb5/pb53/project/gshap/final_result.html.)
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Peak Ground Acceleration - Site Class=C - Soft Rock
Return Period (years)
10 4
10 3
10 2 Mean 5th% 16th% 50th% 84th% 95th%
10 1 0.0
0.1
0.2
0.3
0.4
Horizontal Acceleration (g)
FIGURE 8.14 Example of a peak ground acceleration (PGA) hazard curve on a soft rock site class for a logic-tree seismotectonic model in a low seismicity region of Eurasia. Mean estimate and confidence intervals are shown by different line types in the legend of the figure.
and broader in shape than the response spectrum obtained from an actual earthquake recording, since the probabilistic spectrum is the result of the aggregated ground motion contributions from all magnitudes and distances of significance to a site, weighted by their frequency of occurrence. Median hazard models result in a single estimate of the uniform hazard spectrum (UHS). More fully probabilistic PSHA models can represent the spread of UHS results accounting for uncertainty (e.g., through a logic tree) and are often presented by percentile levels (Figure 8.16). Such a complete description of the seismic hazard allows explicit representation of various levels of conservatism that may be applied in seismic engineering design.
8.10 PSHA Disaggregation The PSHA methodology aggregates ground motion contributions from earthquake magnitudes and distances of significance to a site of engineering interest and, as such, the PSHA results are not representative of a single earthquake. However, engineering models and computer codes generally require empirical or synthetic earthquake acceleration time series as input to dynamic analyses. Specific magnitudes and distances are also often required in slope stability and liquefaction analyses. An issue, then, is the selection of representative earthquake time acceleration series given a probabilistic uniform hazard response spectrum. A procedure called disaggregation (or deaggregation) has been developed to examine the spatial and magnitude dependence of PSHA hazard results. Considerable attention has recently been focused on PSHA disaggregation in recent research literature [e.g., Stepp et al., 1993; Cramer et al., 1996; Chapman, 1995; McGuire, 1995; Bazzurro and Cornell, 1999; Harmsen et al., 1999]. © 2003 by CRC Press LLC
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5%-Damped Horizontal Acceleration (g)
1
0.1
Hard Rock Soft Rock Firm Soil Soft Soil 0.01 0.001
0.01
0.1
1
10
Period (sec)
FIGURE 8.15 Example median uniform hazard response spectra (UHS) for a moderate seismicity site for various site classes.
The PSHA results are disaggregated to determine the magnitudes and distances that contribute to the calculated exceedance frequencies (i.e., the hazard) at a given return period and at a structural period of engineering interest (typically, the fundamental period of a structure). In this process, the hazard for a given return period and at a specified ground motion period is partitioned into selected magnitude and distance bins and the relative contribution to the hazard of each bin is calculated by dividing the bin exceedance frequency by the total exceedance frequency of all bins. The bins with the largest relative contributions — the modes — identify those earthquakes that contribute the most to the total hazard. If there are no clear modes, the controlling or design earthquakes are typically defined by the mean magnitude and mean distance. These results are displayed as a histogram giving the percent contribution to the specified hazard of those earthquakes that are capable of causing ground motions equal to or greater than that corresponding to this hazard as a function of magnitude and distance. This histogram will be different for spectral accelerations of varying structural periods because of the difference in the way these spectral values scale with magnitude and distance. The relative frequencies specified by these histograms can be used to develop mean estimates of magnitude and distance, or to identify the modal contributions to the site hazard, in order to define a set of controlling or design earthquakes corresponding to specified structural periods and return periods. These design earthquakes can then be used as bases to select or construct input time histories for use in a dynamic site-response analysis or for groundfailure evaluation. Figures 8.17 and 8.18 illustrate disaggregation plots. Figure 8.17 is unimodal and the mode of the distribution is relatively clear from the plot. Figure 8.18, however, illustrates a relatively strong bimodal contribution to PSHA hazard at the specific return period and structural period at which the disaggregation was performed. In such cases, two or more design earthquakes might need to be specified in order to fully represent the spectral content of ground motion expected at the site. Note that using a mean magnitude and distance for this bimodal distribution would result in a large magnitude earthquake that has no physical association with a known active fault.
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FIGURE 8.16 Example uniform hazard response spectrum for a single site class showing confidence limits obtained from a fully probabilistic application of the PSHA methodology. Note that because of lognormal distributions in many parameters used in PSHA, the mean estimate is always higher than median estimate.
The expected (median) ground motion amplitude corresponding to the disaggregated mean or modal magnitude and distance can be calculated by substituting these values into the attenuation relationships that were used in the PSHA. The difference between the logarithm of the ground motion value corresponding to the PSHA hazard at the return period of interest and the logarithm of the ground motion value for the disaggregated mean magnitude and distance, divided by the logarithmic standard error of estimate of the attenuation relationship, is referred to as ε (epsilon) [McGuire, 1995]. ε is the number of standard deviations that the probabilistically derived ground motion amplitude deviates from the median ground motion amplitude for an event defined by the mean magnitude and distance. An ε of 1 indicates that the probabilistic value of ground motion corresponds to the one-standard-deviation value of the deterministic ground motion. The larger the absolute value of ε, the greater the contribution of ground-shaking variability to the calculated hazard. Very large absolute values of ε should be avoided, since they indicate that the hazard is potentially being overly dominated by variability in the attenuation relationship.
8.10.1 Scaling Empirical Earthquake Spectra As previously mentioned, a common application of the design earthquake parameters resulting from a PSHA disaggregation is the identification of suitable earthquake records to be used in dynamic engineering testing and design. The defined magnitude and distance parameters from the disaggregation serves as a guide in the selection of three-component (two horizontal and one vertical) empirical earthquake time series from appropriate recording stations of historical earthquakes. The design earthquake parameters are only a general guide, however, with other factors such as site class, earthquake mechanism (i.e., style of slip), and representative spectral shape also having a bearing on the record selection. All of these parameters cannot usually be completely satisfied in the record search, and prioritization of the search © 2003 by CRC Press LLC
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Percent Contribution to Exceedance
10.0 9.0 8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0
8.00
7.00
6.00
5.00
145
135
125
115
km)
105
nce (
95
Dista
85
75
65
55
45
35
15
25
5
0.0
e
ud
it gn Ma
FIGURE 8.17 PSHA disaggregation plot showing a typical unimodal distribution of earthquake magnitude and distance to ground motion exceedance frequency. The mode of this distribution is a magnitude 6.5 to 7.0 earthquake occurring at a distance of 5 to 10 km from the site.
criteria is required. Typically, the spectral amplitudes of the identified suitable records do not match the UHS (i.e., the target spectrum) within the period band of engineering interest, and scaling of the empirical records is required. The scaling is commonly performed on some average of the spectra of the two horizontal components of motion. There are a number of averaging methods that can be applied, including a simple mean, a geometric mean, and the square root of the sum of squares (SRSS), among others. The geometric mean is defined with respect to the two horizontal components as (H1*H2)1/2 and may be preferred as it is the averaging method consistent with that applied in empirical ground motion attenuation relationships that are used to establish the UHS. Once the mean spectrum of the two horizontal components of motion is established, it can be scaled to a best-fit criterion to the target spectrum within the period band of engineering interest (Figure 8.19). The best-fit criterion is defined as a fit where 50% of the empirical spectral amplitudes are both above and below the target spectrum within the engineering period band of interest. The scale factor to achieve the best-fit spectrum may then be applied to each horizontal component time series to obtain empirical motions that are representative of expected earthquake ground motions at the site for a return period of interest. If dynamic response analyses are to be performed on the soil column at the site, the above procedure can be performed for a reference site class representative of the input soil layer for the empirical time series.
8.11 PSHA Case Study This section presents an illustrative case study of a simple, median, peak ground acceleration (PGA) hazard assessment along the proposed offshore Oman India pipeline route. The proposed Oman India pipeline traverses approximately 1135 km of the northern Arabian Sea floor and adjacent continental shelves at water depths of over 3 km on its route from Ra’s al Jifan, Oman, to Rapar Gadhwali, India (Figure 8.20). Ground-shaking hazard was quantified in terms of PGA for return periods of 200, 500, and 1000 years using the PSHA computer program Seisrisk III [Bender and Perkins, 1987]. © 2003 by CRC Press LLC
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Percent Contribution to Exceedance
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6.00
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135
)
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115
ce
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tan
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Dis
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65
55
45
35
25
15
5
0.0
e
ud
it gn a M
FIGURE 8.18 PSHA disaggregation plot showing a bimodal distribution of earthquake magnitude and distance to ground motion exceedance frequency. The primary mode of this distribution is a magnitude 6.5 to 7.0 earthquake at 80 to 85 km from the site. The secondary mode is a magnitude 6.5 to 7.0 earthquake at 5 to 10 km from the site. This distribution is for a site near the eastern coast of Honshu, Japan that is in close proximity to a shallow active fault (secondary mode), although the Japan Trench subduction zone is the strongest contributor to the hazard (primary mode).
This summary is excerpted from the original publication [Campbell et al., 1996] and the reader is referred there for further discussions and a full citation of references on which the work is based. This PSHA was performed in 1995. On January 26, 2001, the MW 7.9, Bhuj (Gujarat, India) earthquake struck the Kutch region of northwestern India in the vicinity of the western terminus of the planned pipeline. This region was identified in the PSHA as one of high hazard. Thus, the case study serves as an example of the utility of PSHA in the engineering and planning of future development. The case study further illustrates that generally conservative results are obtained from time-independent, stationary models of seismicity if parameter estimates are made carefully and estimates of maximum magnitude earthquakes are realistic and not merely based on the maximum earthquake observed in a short reporting period [see McGuire and Barnhard, 1981]. © 2003 by CRC Press LLC
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5%-Damped Horizontal Acceleration (g)
1
0.1
0.01
200 Yr. UHS H1 H2 Mean
0.001 0.01
0.1
1
10
Period (sec)
FIGURE 8.19 Example scaled empirical earthquake spectra to a target, 200-year UHS. Solid bold line is the 200year return period target UHS. Heavy dashed line indicates the geometric mean of the two horizontal components. Light line styles are the H1 and H2 components. The geometric mean of the empirical spectra has been scaled to a best-fit criterion within the period band of 0.6 ± 0.5 seconds.
55°
60°
65°
70°
75°
PAKISTAN IRAN
MAGNITUDE id
ge
25°
y
R
Rapar Gadhwali
ur
ra
OMAN
M
Ra'as al Jifan
INDIA
ne
e
Oman - India
Owen
Fra ctu
re
Zo
20°
lin
pe
Pi
ARABIAN 0
8 to 8.2
(2)
7 to 7.9
(12)
6 to 6.9 (40) 5 to 5.9 (223) 4 to 4.9 (876) 3 to 3.9 (47) all others (89)
SEA 250
500
Kilometers
FIGURE 8.20 Location map of the Oman India pipeline route shown in relation to the regional distribution of earthquakes. © 2003 by CRC Press LLC
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20°
30°
40°
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60°
70°
80°
90°
40° 40°
30° 30°
20° 20°
10° 10°
0° 40°
50°
60°
70°
80°
FIGURE 8.21 Plate tectonic setting of the region surrounding the northern Arabian Sea showing regional tectonic features. (After Jacob, K.H. and R.L. Quittmeyer, Geodynamics of Pakistan, Geological Survey of Pakistan, pp. 305–317, 1979. With permission.)
8.11.1 Tectonic Setting Within the Arabian Sea basin, the Owen Fracture Zone and the Murray Ridge are two distinct structural geologic provinces of a transform plate boundary that accommodates slow, right-lateral differential motion between the Arabian and Indian plates (Figure 8.21). The northern tectonic boundaries of the Arabian and Indian plates are in continental collisional contact with the Eurasian plate, giving rise to the complex compressional tectonics of the Zagros and Himalayan Mountains. However, only in the Gulf of Oman is subduction currently occurring (i.e., where the ocean floor of the Arabian Sea is being thrust beneath the overriding Eurasian plate). Rupture along the contact between these two plates results in great thrust earthquakes, as demonstrated by an MS 8.2 earthquake and accompanying tsunami that occurred off the coast of Pakistan in 1945 (Figure 8.20).
8.11.2 Regional Seismicity The seismicity of the Arabian Sea and surrounding areas is dominated by earthquakes along the major tectonic plate boundaries (Figures 8.20 and 8.21). The primary sources of earthquake data used for the study were the Catalog of Middle East Earthquakes and the Catalog of Earthquakes for Peninsular India, 1839–1900. The Middle East catalog contains more than 22,000 earthquakes that occurred from 1900 to 1983. These catalogs were supplemented with several historic earthquake accounts of India. Seismicity between 1983 and 1992 was taken from the Preliminary Determination of Epicenters (PDE), published monthly by the U.S. Geological Survey. The regional earthquake catalogs were aggregated into a single catalog by removing duplicate entries through an automated winnowing procedure. The aggregated earthquake catalog used surface-wave magnitude (MS) to quantify earthquake size. MS was converted to moment magnitude (MW), the © 2003 by CRC Press LLC
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magnitude measure used in the strong-motion attenuation relationships described later, using relationships between magnitude measures given in Khattri et al. [1984], Hanks and Kanamori [1979], and Ekstrom and Dziewonski [1988]. The aggregated earthquake catalog was culled of aftershocks and the remaining earthquakes were analyzed for completeness by determining the time period over which events of various magnitudes were found to be completely reported. The analysis indicated that earthquakes of various magnitudes are completely reported for the following periods: MW 5.0 ± 0.2 for the past 20 years; MW 5.4 ± 0.2 for the last 30 years; MW 5.8 ± 0.2 for the last 60 years; and MW 6.0 for the last 80 years. Complete reporting times for larger earthquakes range from about 100 years for MW 6.2 to about 300 years, or the total period of the historic catalog, for great earthquakes (MW ≥ 8.0).
8.11.3 Great Earthquakes On June 16, 1819, a great (MS ≈ 8) earthquake occurred in the Rann of Kutch, India near the eastern terminus of the pipeline route. This earthquake was not on a plate boundary but, rather, was an intraplate earthquake similar to those that occurred in New Madrid, Missouri in 1811 and 1812. The Kutch earthquake was accompanied by surface rupture along a zone measuring 32 km by 16 km. The Kutch and New Madrid earthquakes are two examples of only a few historic intraplate earthquakes that have ruptured the ground surface. The Kutch earthquake caused damage over an extensive area. In the town of Bhuj nearly 7000 houses were “overthrown” with a reported 1140 casualties. The recent MW 7.9 Gujuarat earthquake that occurred on January 26, 2001 also devastated the city of Bhuj as well as the larger region of Gujuarat State in northwestern India [EERI, 2001]. Another great (MS 8.2) earthquake ruptured the plate interface zone of the Makran Subduction Zone on November 27, 1945. Historic accounts indicate a rumbling sound accompanied the earthquake at Karachi, Pakistan, but only a few windows were reported broken. A tsunami followed the earthquake and was most severe on the Makran coast, northwest of Karachi, where a telegraph office was reportedly washed to sea and a number of buildings were damaged. In the suburbs of Bombay, India, boats were reportedly smashed at their moorings. Two new islands had appeared in the Arabian Sea about 180 miles west of Karachi after the earthquake.
8.11.4 Earthquake Source Characterization The earthquake source characterization of the northern Arabian Sea and surrounding areas consisted of defining earthquake source zones and earthquake recurrence relationships that accurately modeled the occurrence of earthquakes in space and time within the study area. This model was developed to be consistent with the contemporary understanding of the tectonics and seismicity of the region as documented in the technical literature. The earthquake source zones are shown in Figure 8.22. Earthquake recurrence was modeled using the Gutenberg–Richter relationship, Equation 8.5. Earthquakes were modeled between a minimum magnitude of 5.0 and the magnitude of the largest earthquake judged capable of occurring within each of the earthquake source zones.
8.12 The Owen Fracture Zone–Murray Ridge Complex The tectonic model of the Owen Fracture Zone–Murray Ridge Complex (Figure 8.22) consists of linear representations of young faults that have been identified in a number of offshore seismic reflection and geophysical studies. South of latitude 20°N, the Owen Fracture Zone was modeled as a series of linear faults along the eastern side of a series of narrow, discontinuous ridges and troughs, consistent with interpretations of faulting in seismic reflection profiles. There are significant structural differences in the Owen Fracture Zone north of about 29°20'N. At this latitude, the narrow, linear trend of the southern and central segments of the Owen Fracture Zone merges with the broader structure of the Qalhat Seamount. © 2003 by CRC Press LLC
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70° Chama n
PAKISTAN IRAN
25°
ZN 4
Omach-Nai
ZN 5
Makran Subduction Zone
y
R
id
Rapar Gadhwali
ur (Qalhat Seamount)
e
in
Oman - India
l pe
Pi
Zo
lt
re Fra ctu
ARABIAN
ZN 6
SEA
ZN 1
Owen
Fa u Si
qu
alr ah
Central
South
INDIA
M
North
ne
Ra'as al Jifan
20°
ZN 3
ra
OMAN
ZN 2 ge
North South (Dalrymple Trough)
75°
FIGURE 8.22 Seismic sources used in assessing probabilistic peak ground acceleration (PGA) hazard along the Oman India pipeline. Faults are shown as bold lines. Area sources are ruled. Vertical ruled area of the Makron Subduction Zone interface thrust fault dips northward beneath Zone 5.
At the northern end of the Owen Fracture Zone, a low basement ridge defines a southwestern extension of the Qalhat Seamount, some 60 km northwest of the main plate boundary. Geophysical data suggest that this western margin of the Qalhat Seamount could be fault-bounded. Because this seamount is an integral part of the transform plate boundary, we modeled bounding faults along both the eastern and western flanks of this feature. Short, east-trending cross-faults were modeled between the east and west flanking faults, consistent with interpretations of geophysical data. Bathymetric and geophysical data indicate that most of the ridges and intervening troughs associated with the Murray Ridge are fault-bounded. Although the overall structure of the Murray Ridge is a bathymetric high, it is split by deep, fault-controlled troughs that are floored by very recent sediments. The Dalrymple Trough is a prime example of one of these troughs. The present floor of the Dalrymple Trough has down-dropped 800 m below the adjacent Arabian Sea floor. Based on these interpretations, we modeled all linear bathymetric ridges and intervening trough with bounding faults.
8.12.1 Maximum Magnitude Burr and Soloman [1978] provide a comprehensive account of the source parameters of all large earthquakes that had occurred on oceanic transforms up to the mid-1970s. Of the 36 earthquakes studied, 35 had M ≤ 7. The largest earthquakes that have occurred in the vicinity of the Owen Fracture Zone–Murray Ridge Complex are three MS 5.9 events that occurred from 1933 to 1935. Since 1964, the largest reported earthquake on this zone was MS 5.7. We adopted a maximum magnitude of 6.8 for all segments of the oceanic plate boundary a value only slightly smaller than that observed in association with oceanic transform earthquakes. Because a slip-rate model used to determine earthquake frequencies uses maximum magnitude as one of its parameters, an upper bound of 6.8 rather than 7.0 was chosen to give frequencies for moderate earthquakes that are consistent with those observed since 1964. A larger maximum magnitude allows too much of the seismic moment release along the transform boundary to be taken up by infrequent, large earthquakes, resulting in unreasonably long repeat times for magnitude 5 to 6 earthquakes.
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8.12.2 Earthquake Recurrence Frequencies A moment-based frequency model was used to estimate earthquake recurrence rates from tectonic slip rate, Mmax , b-value, crustal shear rigidity, and the seismogenic area of the fault. We used a slip rate of 1.75 mm/year for this analysis, which is the average rate determined from worldwide models of rigid plate interactions. Earthquake recurrence rates were calculated for each structural segment along the length of the oceanic transform plate boundary using the length of each structural segment, a crustal thickness of 8 km, and a shear rigidity of 3 ×1011 dyne/cm typical of crustal rock. A b-value of 0.9 was determined from a maximum likelihood fit of 39 earthquakes of M ≥ 4.8 that have occurred on, or in the vicinity of, the oceanic transform boundary. Except for the northern (Qalhat Seamount) segment of the Owen Fracture Zone, the calculated recurrence rates were distributed equally among all modeled faults that define each structural segment of the transform boundary. The recurrence rate for the eastern and western flanking faults of the northern Qalhat Seamount segment was distributed in such a way as to give twice as much seismicity to the easternbounding fault. This was done to account for both the greater degree of fault offset and the higher historic rate of earthquakes along the eastern margin of this portion of the plate boundary (Figure 8.20). A comparison of the earthquake recurrence rates determined from the assumed slip rate and the maximum likelihood fit of the 39 earthquakes that have been observed along the entire length of the Owen Frature Zone–Murray Ridge Complex indicates that the estimated annual frequency of earthquakes of 4.8 ≤ M ≤ 6.2 given by both procedures agrees to within ±10%.
8.13 Makran Subduction Zone The Makran Subduction Zone megathrust boundary between the Arabian and Eurasian plates dips gently northward beneath the coasts of Iran and Pakistan from its origin at a sediment-filled trench off the Makran continental slope [Jacob and Quittmeyer, 1979] (Figure 8.22). Earthquakes located approximately 400 km north of the trench at a depth of about 60 km have focal mechanisms indicative of extensional stresses in the subducting slab of Arabian Sea floor. Normal-faulting earthquakes in this “slab-bend” region of the subducting plate is a common feature of subduction zones throughout the world. They represent a transition region within the subducting slab from compression trenchward of this zone to extension in the deeper part of the slab, where it is being consumed within the Earth’s mantle. This region marks the maximum possible extent of the seismogenic portion of the plate interface beneath Pakistan and Iran. A cross-sectional plot of seismicity across the Makran region was used to identify the top of the downgoing slab as it penetrates the Earth’s mantle. This cross section indicates that the seismogenic portion of the plate interface extends some 200 to 300 km north from the oceanic trench offshore southern Pakistan and southeastern Iran to a depth of approximately 30 km. Based on this observation, we modeled the megathrust interface of the Makran Subduction Zone as a 250-km-wide, shallow (~7°) planar fault. Based on tectonic considerations, the Makran Subduction Zone was estimated to be approximately 1000 km long, representing that portion of the Arabian–Eurasian convergence zone between the Ornach-Nal fault on the east and the “Oman line” on the west. The convergence rate between the Arabian and Eurasian plates across the Makran Subduction Zone has been estimated to be about 5 cm/year from regional and worldwide geodynamic models of plate interactions. This convergence rate reflects the total deformation rate between the two plates, which is manifested in the subduction of the Arabian plate beneath the Eurasia plate. Some of this convergence is very likely accommodated aseismically along the interface, and in folding of the overriding southern edge of the Eurasian plate in the Makran Mountains of southern Pakistan and southeastern Iran. Geologic studies that might indicate how this overall convergence rate is partitioned between seismic and aseismic compressional deformation processes have not yet been performed.
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8.13.1 Maximum Magnitude The largest known earthquake on the Makran Subduction Zone was an MS 8.2 earthquake in 1945. However, there is no reason to believe that the entire plate interface cannot rupture in a single “megathrust” earthquake. Based on this hypothesis, we assigned a maximum magnitude of 9.2 to this zone, consistent with both empirical rupture area–magnitude relationships and the magnitude of the great 1964 Prince William Sound, Alaska earthquake that ruptured a similar length.
8.13.2 Earthquake Recurrence Frequencies Using seismic moment-based relationships between convergence rate, crustal shear rigidity, and the cross-sectional area of the converging plates, we estimated the recurrence rate of earthquakes for various magnitudes that would be expected to occur on the Makran Subduction Zone assuming that all 5 cm/year of the estimated convergence rate was released in earthquakes. The resulting recurrence rates were found to be significantly larger than those observed historically. Probable reasons for this inconsistency are that some of the convergence is released by earthquakes occurring within the overriding Eurasian plate and some is accommodated through aseismic deformation. Because of this inconsistency, we adopted area-normalized earthquake recurrence rates that were developed from the historical occurrence of earthquakes in this zone [Khattri et al., 1984]. These rates, which were defined in MS , were adjusted to correspond to MW using common empirical relationships between these two magnitudes’ measures. Khattri et al.’s [1984] recurrence frequencies were normalized to a 40-year time period, not the 1-year time period that is usually used to develop earthquake recurrence relationships. For consistency with other recurrence relationships developed in this study, we converted these rates to an annual rate. We partitioned these recurrence frequencies into two parts. Earthquakes of 7.6 ≤ M ≤ 9.2 were assumed to occur on the plate interface. Earthquakes of M < 7.6 were assumed to occur within the shallow crust of the overriding Eurasian plate. This partitioning results in an average recurrence interval of 200 years for earthquakes of similar size to the 1945 earthquake, an interval that is consistent with the observation that only one event of this size has occurred on this zone in 300 years for which the earthquake catalog is considered to be complete in this region. Using a range of magnitudes to model the occurrence of earthquakes on the plate interface was consistent with other seismological investigations that suggested the plate interface is a segmented thrust fault.
8.14 Southwestern India and Southern Pakistan The Ornach-Nal and Chaman faults accommodate left-lateral movement between the Eurasian and Indian plates in southern Pakistan (Figure 8.22). Earthquakes of M ≥ 6.4 on these faults were modeled as linear ruptures. Throughout a broader zone, mostly east of the Ornach-Nal and Chaman faults (ZN 4, Figure 8.22), earthquakes smaller than 6.4 were modeled as point sources uniformly distributed throughout the zone. The area source encompasses a region of diffuse seismicity related to a broader zone of deformation within southern Pakistan. Shallow earthquakes of M ≤ 7.6 occurring within the Eurasian plate were placed in a broad source zone in southern Pakistan and southeastern Iran that encompasses the Makran Mountains (ZN 5, Figure 8.22). The Makran Mountains form the leading edge of crustal deformation along the southern boundary of the Eurasian plate above the Makran Subduction Zone. Crustal faults of this zone characteristically trend east–west and have both thrust and strike-slip components of slip. Compressional deformation and seismicity are widespread and are not limited to a few major faults. We have modeled earthquakes of M ≥ 6.4 within this zone as linear ruptures on a series of uniformly spaced faults that follow the predominant east–west strike of the structural trend of the region. Smaller earthquakes are modeled as point sources distributed uniformly throughout the zone.
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We adopted the earthquake source zones proposed by Khattri et al. [1984] for our source zones in western India (ZN 1 to 3, Figure 8.22). These zones were developed based on the association of clusters of historic earthquake occurrences with ancient tectonic trends of the Indian subcontinent a common technique used throughout the world for developing seismic source zones in intraplate environments. Earthquakes of M < 6.4 were modeled as point sources uniformly distributed within the source zones. Larger-magnitude earthquakes in the Kutch and West Coast of India source zones (ZN 1 and 2) were modeled as linear ruptures on faults representing the major tectonic trends in these regions. In the Kutch zone, these modeled faults strike east-west following the Kutch Rift-Delhi Trend. Notably, the January 26, 2001 Bhuj (Gujarat, India) earthquake exhibited east-west-trending surface rupture along this same trend. In Zone 1 (Figure 8.22), we modeled a single north-trending fault to coincide with the Panvel Flexure-West Coast fault zone.
8.14.1 Maximum Magnitude The maximum magnitude associated with shallow seismicity in the Makran Mountains (ZN 5, Figure 8.22) was estimated to be about 7.6 (earthquakes larger than this were constrained to occur on the plate interface of the Makran Subduction Zone). This is about one-half magnitude higher than the largest observed crustal earthquake in this zone. It is, however, generally consistent with calculated maximum magnitudes for faults with lengths of up to 120 km that have been mapped in the Pakistani portion of this zone. Khattri and others [1984] assigned a maximum magnitude of 8 to both the Kutch and West Coast of India source zones (ZN 1 and 2, Figure 8.22) based on the historic occurrence of the 1819 Kutch earthquake (MS ~ 8) and the presence of Quaternary deformation along the older Panvel Flexure tectonic trends in the West Coast of India zone. They assigned a relatively small maximum magnitude of 6 to the Arravali source zone (ZN 3, Figure 8.22), consistent with its relatively small source dimensions and historical seismicity. We adopted these maximum magnitudes for this study.
8.14.2 Earthquake Recurrence Frequencies We adopted the area-normalized earthquake recurrence frequencies given in Khattri et al. [1984] for all of the source zones in this region (ZN 1 to 5, Figure 8.22). These rates were annualized and adjusted to MW as discussed previously for the Makran Subduction Zone. Earthquake recurrence rates for M ≥ 6.4 earthquakes in the Kutch and West Coast of India source zones (ZN 1 and 2) were uniformly distributed among the modeled faults in these zones in proportion to their total fault lengths.
8.15 Southeastern Arabian Peninsula and Northern Arabian Sea The Arabian Sea basin and eastern Arabian Peninsula were placed in a broad background zone of diffuse seismicity (ZN 6, Figure 8.22). This zone is characterized by the infrequent occurrence of small to moderate earthquakes. The total area of comparable background seismicity is quite large, extending beyond the study area westward across the entire Arabian Peninsula to the Red Sea Rift and the Lavant Transform plate boundaries. Earthquakes of M ≥ 6.4 within the study area were constrained to two faults on the Omani continental shelf that have been identified as being potentially active from offshore boreholes and geophysical investigations. We included the Siquirah fault (Figure 8.22) based on an interpretation of reflection profiles that suggests that it is a profound structural feature of the southeast Omani outer-continental shelf. The fault displaces sea-bottom reflectors, indicating recent movement, although no earthquake epicenters plot near the fault (Figure 8.20). The northward extend of the Siquirah fault was based on the interpretation that the entire coastline and linear continental slope of eastern Oman is possibly the result of strike-slip faulting. The lack of epicenters in the vicinity of the Siquirah fault might only indicate a recurrence interval of significant earthquakes that is longer than the historic period of observation. © 2003 by CRC Press LLC
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A second, shorter fault located east of the Siquirah fault (Figure 8.22) and near the base of the Oman continental slope bounds a narrow linear basement ridge. The ridge forms the eastern structural boundary of a sedimentary trough between the continental shelf and floor of the Oman basin. Consistent with our interpretation of similar features within the Murray Ridge, we modeled this basement ridge as being fault-bounded. We refer to this fault as the Oman Basin fault.
8.15.1 Maximum Magnitude We assigned a maximum magnitude of 6.4 to the background zone (ZN 6, Figure 8.22). This value is three quarters of a magnitude higher than that observed historically. We believe that the higher maximum magnitude unit was warranted because of the large degree of uncertainty associated with the extremely low level of seismicity in this region. We adopted a maximum magnitude of 7.6 for the Siquirah fault based on empirical rupture length–magnitude relationships and the assumption that one half of the total length of the fault could rupture in a single event. Similarly, we assigned a maximum magnitude of 7.2 to the much shorter Owen Basin fault based on the assumption that the entire length of that fault could rupture in a single event.
8.15.2 Earthquake Recurrence Frequencies Since only five historic earthquakes have occurred in this region, it was not possible to develop earthquake recurrence frequencies using a formal statistical procedure. Instead, we adopted the b-value that was determined from the maximum likelihood fit of 39 earthquakes that occurred within the Owen Fracture Zone–Murray Ridge Complex. We estimated the earthquake recurrence rate in this zone from the observation that three MS 4.1 to 5.0 earthquakes had occurred in this region within the last 22 years. Lacking available geologic or geodynamic data for the Siquirah and Owen Basin faults, we simply used the recurrence relationship developed for the background zone to model the cumulative occurrence of M ≥ 6.4 earthquakes on these faults. Based on this model, the calculated cumulative recurrence interval for earthquakes of M ≥ 6.4 is 400 years. This estimate is consistent with the lack of observed earthquakes along this portion of the Omani continental shelf within the last few hundred years.
8.16 Ground Motion Models PGA was estimated from attenuation relationships of the form: log(PGA) = b 1+ b 2M – b 3logR – b 4R + ε
(8.23)
where PGA is the mean horizontal component of peak ground acceleration (g), M is earthquake magnitude (MW), R is distance from the earthquake source to the site (km), ε is a random error term with a mean of zero and a standard deviation equal to the standard error of estimate of log (PGA), and b1 through b4 are parameters dependent on the tectonic environment. The attenuation relationships adopted for this study were chosen to represent as closely as possible the earthquake and propagation characteristics of the major tectonic environments encountered in the Arabian Sea and surrounding regions. Separate relationships were used to model the stable oceanic and continental interior regions of the Arabian and Indian plates; the oceanic and continental transform boundaries between the Eurasian, Arabian, and Indian plates; and the megathrust interface of the Makran Subduction Zone.
8.16.1 Stable Continental Interior Earthquakes Stable continental interior regions, such as the Arabian Peninsula (Oman) and the Indian subcontinent (southwestern India), are composed of very old, Precambrian crust, often referred to as stable continental interiors. These regions are known to occasionally produce earthquakes that have relatively high stress © 2003 by CRC Press LLC
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drops and relatively low anelastic attenuation. The best studied of these regions is the stable continental interior of eastern North America. Since these regions are characterized by relatively infrequent earthquakes, there are an insufficient number of strong-motion recordings with which to develop reliable empirical attenuation relationships. As a result, attenuation relationships developed for these regions have been based on intensity data (usually characterized in terms of the Modified Mercalli Intensity [MMI] scale) or, more recently, on simple seismological models of the earthquake source and propagation medium. One of the most recent and best-documented theoretical attenuation relationships for stable continental regions is that developed by the Electric Power Research Institute [EPRI, 1993] for eastern North America. Because of its thorough review and sound seismologic basis, this model was selected to represent the attenuation of PGA in the stable continental-interior regions of Oman and India. The model was developed to represent the attenuation characteristics of sites on hard rock using a median stress drop of 120 bars and an anelastic attenuation parameter (Q) consistent with observed earthquakes in eastern North America. The standard error of estimate (σln PGA) associated with the EPRI attenuation relationship, averaged over magnitude and distance, was estimated to be 0.7 for the near-source distances of most concern in this study.
8.16.2 Stable Oceanic Interior Earthquakes There are no attenuation relationships available for stable oceanic interior regions. However, the oceanic lithosphere is known to be an extremely efficient waveguide for high-frequency seismic energy. For example, the anelastic attenuation of high-frequency waves in the Ngendei region of the Southwest Pacific has been found to be consistent with Q of 450 for that part of the lithosphere above the Moho (6.65 km below mudline) and Q of 1000 for that part of the lithosphere below this depth. These values are consistent with Q observed in the stable continental-interior regions of eastern North America [EPRI, 1993]. Based on this similarity, the EPRI attenuation relationship was used to model the attenuation of PGA from earthquakes occurring in the intraplate regions of the Arabian Sea.
8.16.3 Transform Plate Boundary Earthquakes Transform plate boundary earthquakes, such as those typical of the strike-slip San Andreas fault system in western California, have lower average stress drops than intraplate earthquakes [EPRI, 1993]. However, unlike California, plate boundary earthquakes associated with the Owen Fracture Zone–Murray Ridge Complex and the Ornach-Nal and Chaman faults occur on a transform boundary between intraplate regions of low anelastic attenuation, similar to the craton of eastern North America. Therefore, the source characteristics of these plate-boundary earthquakes are expected to be similar to those in other plate boundary environments (e.g., the San Andreas fault system); whereas, the attenuation characteristics of these earthquakes are expected to be typical of the attenuation characteristics of an intraplate environment. The majority of strong-motion recordings from plate-boundary earthquakes are from California, where anelastic attenuation is much greater than in stable continental interiors. Therefore, attenuation relationships from these regions are not applicable for this region. Instead, we modified the EPRI attenuation relationship to predict the attenuation of PGA from plate-boundary earthquakes in the northern Arabian Sea and southern Pakistan regions. EPRI [1993] gives stress drops for earthquakes in interplate and intraplate tectonic environments that have been calculated from strong-motion and standard seismograph recordings. These calculations indicate a median stress drop of 120 bars for intraplate regions. On the other hand, the data for interplate strike-slip and normal faulting earthquakes, typical of the plate-boundary earthquakes in the northern Arabian Sea and southern Pakistan regions, were found to be consistent with a median stress drop of about 85 bars. Research has indicated PGA ∝ ∆σ0.8. Therefore, PGA predicted by the EPRI attenuation relationship was reduced by 25% for plate boundary earthquakes in the northern Arabian Sea and southern Pakistan regions. © 2003 by CRC Press LLC
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8.16.4 Subduction Zone Earthquakes Subduction-zone earthquakes, similar to those associated with the Makran Subduction Zone, have been found to have significantly different attenuation characteristics from either shallow crustal interplate or intraplate earthquakes. Therefore, it is important to model these earthquakes with an attenuation relationship appropriate for this tectonic environment. The attenuation relationship selected for this purpose was one developed from rock recordings of large subduction-zone earthquakes throughout the world. The standard error of estimate (σln PGA) associated with this relationship for the larger earthquakes of interest in this study is 0.55.
8.17 Soil Amplification Factors Estimates of PGA from the attenuation relationships described above are for hard rock. Therefore, it is necessary to multiply these estimates by an appropriate site amplification factor in order to account for the existing predominant soil conditions at mudline along the pipeline route. This adjustment was done using the amplitude-dependent amplification factors given in Borcherdt [1993]. The classification of the existing soils along the pipeline route was based on preliminary geotechnical and seismic data collected along the pipeline route. The soil amplification factors for each of the soil classifications given by Borcherdt [1993] were normalized to hard rock and the amplitude of PGA for the existing soil conditions are obtained by multiplying the estimate of PGA on hard rock by these normalized factors. The maximum value of PGA on soft soils was limited to 0.45 g based on site-response studies of Holocene Bay Mud in the San Francisco Bay area. If shear strains large enough to cause significant cyclic degradation (e.g., liquefaction) are induced in these deposits, then actual values of PGA for these soft soils may be further limited to values on the order of 0.2 to 0.25 g. Of course, for such large strains, ground failure will become an important issue.
8.18 Results Values of PGA on hard rock were calculated at 130 locations along the pipeline route for return periods of 200, 500, and 1000 years (Figure 8.23). However, much of the pipeline route is characterized by soft pelagic and detrital deposits that are subject to submarine turbidite flows if disturbed by strong ground shaking from earthquakes. A map showing 500-year values of PGA on hard rock and on the existing soil conditions at mudline (in parentheses) at selected locations along the pipeline route and Indus Canyon is given in Figure 8.24. The existing soil conditions at all of the selected sites were classified as soft soil. For all return periods, the highest values of PGA were obtained at the intersection of the pipeline route with the Owen Fracture Zone, where calculated values on hard rock (soft soil) were 0.35 g (0.40 g), 0.56 g (0.45 g), and 0.77 g (0.45 g) for return periods of 200, 500, and 1000 years, respectively. Intermediate values of PGA were calculated for the eastern pipeline terminus at the India coast and at the crossing of the southwest extension of the Qalhat Seamount, located approximately 60 km west of the Owen Fracture Zone, where values on hard rock (soft soil) ranging between 0.17 g (0.32 g) and 0.31 g (0.40 g) were calculated for a 200-year return period and values ranging between 0.45 g (0.45 g) and 0.57 g (0.45 g) were obtained for a 1000-year return period. The lowest values of PGA were calculated for the Arabian Sea Abyssal Plain, east of the Owen Fracture Zone, where estimates for hard rock (soft soil) ranged from 0.03 g (0.08) for a 200-year return period to 0.09 g (0.22 g) for a 1000-year return period.
8.19 Conclusions The computed ground-shaking hazard along the Oman India pipeline was found to be relatively high in the vicinity of the Owen Fracture Zone–Murray Ridge Complex and at the India coast in the Kutch region. These values are high enough to potentially trigger geologic hazards such as liquefaction, slope © 2003 by CRC Press LLC
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0.80 OMAN
0.70
Owen Fracture Zone
INDIA 200-yr
0.60
PGA (g)
Kutch Zone
SWExtension, Qalhat Seamount
0.50
500-yr 1,000-yr
0.40 Siquirah Fault
0.30 0.20
Indus Fan Crossing
0.10
68.56
68.18
67.79
67.37
66.93
66.43
65.88
65.23
64.64
64.02
63.40
62.78
62.16
61.63
61.26
60.73
60.22
59.72
0.00
Longitude (deg. E)
FIGURE 8.23 Longitudinal profile of PGA on hard rock along the pipeline route for three return periods.
60°
65°
IRAN
70°
PAKISTAN
25°
Rapar Gadhwali
OMAN
0.11 (0.25)
Ra'as al Jifan
INDIA
20°
0.10 (0.23)
Pi
pe
lin
e
0.07 (0.18) Oman - India 0.30 (0.39)
0.56 (0.45)
0.08 (0.20)
0.44 (0.45)
0.05 (0.13)
ARABIAN
SEA
FIGURE 8.24 Calculated PGA on hard rock and soft soil (in parentheses) with a return period of 500 years at selected locations along the pipeline route and at the Indus Canyon.
instability, and turbidity flows in areas that are susceptible to these hazards. Notably, liquefaction and ground failures were widespread throughout Western Gujuarat State in the 2001 Bhuj earthquake. Although the computed ground-shaking hazard elsewhere along the pipeline route was found to be relatively low, estimates of PGA are high enough offshore to also potentially trigger geologic hazards in areas that are highly susceptible to these hazards (e.g., unstable channel slopes).
8.20 PSHA Computer Codes There are a number of PSHA computer codes that are available to the analyst. A few are distributed free, or at low cost [McGuire, 1976, 1978; Bender and Perkins, 1987; U.S. Geological Survey (http://geohazards.cr.usgs.gov/eq/html/hazsoft.html)]. An excellent source for software is the National Information © 2003 by CRC Press LLC
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Service for Earthquake Engineering at the University of California, Berkeley (http://nisee.berkelye.edu/ software_and_data/eng_soft/index.html). Some codes are not necessarily user-friendly as they are primarily products of scientific/engineering research efforts and are not created for easy use with an end-user in mind. Several commercially available codes are available and are user-friendly in terms of the data input interface and overall ease of use. They also offer a wide variety of output enhancements in addition to the basic PSHA results. Prior to selection of a specific computer code for use in engineering applications, an analyst should have a clear understanding of his or her specific needs. Some codes are specific to area source modeling, while others are specific to the requirements of fault modeling. Some codes are appropriate for creating grids of PSHA values suitable for contouring in ground motion maps, while others are better adapted for site-specific analyses. Commercial codes often come with a variety of databases and built-in models, including ground motion attenuation relationships and seismotectonic models specific to certain regions, and generally have the flexibility of modeling both area and fault sources, as well as mixed sources. There is likely to be a suitable code available for any practical application required by the PSHA analyst.
Defining Terms Aleatory — Uncertainty in the data used in an analysis; generally accounts for randomness associated with the prediction of a parameter from a specific model, assuming that the model is correct. Specification of the standard deviation (σ) of a mean ground motion attenuation relationship is a representation of aleatory variability. Characteristic earthquake — Surface-rupturing earthquakes occurring on a known tectonic structure, within a relatively narrow range of magnitudes at an increased frequency over that which would be estimated from the Gutenberg–Richter relationship. Epistemic — Modeling uncertainty; accounts for incomplete knowledge in the predictive models and the variability in the interpretations of the data used to develop the models. Intensity — A metric of the effect, or the strength, of an earthquake hazard at a specific location, commonly measured on qualitative scales such as MMI, MSK, and JMA (see Chapter 4). Paleoseismicity — Prehistoric earthquakes — since there is no human record, these earthquakes are identified (i.e., location, magnitude, etc.) via geologic trenching and other evidence. Return period — The reciprocal of the annual probability of occurrence — earthquake probabilities of occurrence are commonly stated in terms of a return period, which misleads some people since they infer the earthquake occurs on a regular cycle equal to the return period. Seismic hazard — The likelihood or probability of experiencing a specified intensity of any damaging phenomenon, at a specific site, or over a region. Seismotectonic model — An analytical model combining models of earthquake sources, occurrence, and attenuation.
References Albee, A.L. and J.L. Smith, 1966, “Earthquake Characteristics and Fault Activity in Southern California,” in Engineering Geology in Southern California, R. Lung and T. Proctor, Eds., Association of Engineering Geologists, Sudbury, MA, pp. 9–34. Algermissen, S.T., D.M. Perkins, P.C. Thenhaus, S.L. Hanson, and B.L. Bender, 1982, Probabilistic Estimates of Maximum Acceleration and Velocity in Rock in the Contiguous United States, U.S. Geological Survey Open-File Rep. 82-1033. Ambraseys, N.N. and C.F. Finkel, The Seismicity of Turkey and Adjacent Areas, EREN, Istanbul. Ambraseys, N.N. and C.P. Melville, 1982, A History of Persian Earthquakes, Cambridge Earth Science Series, Cambridge, U.K. Anderson, J.G., 1979, “Estimating the Seismicity from Geological Structure for Seismic Risk Studies,” Bull. Seismol. Soc. Am., 69, 135–158. © 2003 by CRC Press LLC
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Atwater, B.F., 1987, “Evidence for Great Holocene Earthquakes along the Outer Coast of Washington State,” Science, 236, 942–944. Atwater, B.F., 1992, “Geologic Evidence for Earthquakes during the Past 2000 Years along the Copalis River, Southern Coastal Washington,” J. Geophys. Res., 97, 1901–1919. Bazzurro, P. and C.A. Cornell, 1999, “Disaggregation of Seismic Hazard,” Bull. Seismol. Soc. Am., 89, 501–520. Bender, B., 1984, “Incorporating Acceleration Variability into Seismic Hazard Analysis,” Bull. Seismol. Soc. Am., 74, 1451–1462. Bender, B. and D.M. Perkins, 1987, “Seisrisk III, A Computer Program for Seismic Hazard Estimation,” U.S. Geol. Survey Bull. 1772. Bernreuter, D.L., J.B. Savy, R.W. Mensing, and J.C. Chen, 1989, “Seismic Hazard Characterization of 69 Nuclear Plant Sites East of the Rocky Mountains,” Report prepared for the U.S. Nuclear Regulatory Commission, Lawrence Livermore National Laboratory, Report No. NUREG/CR-5250, Washington, D.C. Bonilla, M.G., 1980, Comment and Reply on “Estimating Maximum Expectable Magnitudes of Earthquakes from Fault Dimensions,” Geology, 8, 162–163. Bonilla, M.G. and J.M. Buchanan, 1970, “Interim Report on Worldwide Historic Surface Faulting,” U.S. Geol. Survey Bull. Open File Rep. Borcherdt, R.D., 1993, “On the Estimation of Site-Dependent Response Spectra,” Proceedings of the International Workshop on Strong Motion Data, Vol. 2, Menlo Park, CA, The Port Harbour Research Institute, Kanagawa, Japan. Brune, J.N., 1968, “Seismic Moment, Seismicity and Rate of Slip along Major Fault Zones,” J. Geophys. Res., 73, 777–784. Bucknam, R.C. and R.E. Anderson, 1979, “Estimation of Fault-Scarp Ages from a Scarp-Height-SlopeAngle Relationship,” Bull. Seismol. Soc. Am., 7, 11–14. Burr, N.C. and S.C. Soloman, 1978, “The Relationship of Source Parameters of Oceanic Transform Earthquakes to Plate Velocity and Transform Length,” J. Geophys. Res., 83, 1193–1204. California Division of Mines and Geology, 1975, “Recommended Guidelines for Determining the Maximum Credible Earthquake and the Maximum Probable Earthquakes,” California Division of Mines and Geology, Sacramento, CA, Note 43, p. 1. Campbell, K.W., 1983, “Bayesian Analysis of Extreme Earthquake Occurrences. II. Application to the San Jacinto Fault Zone of Southern California,” Bull. Seismol. Soc. Am., 73, 1099–1115. Campbell, K.W., 1985, “Strong Motion Attenuation Relations: A Ten-Year Perspective,” Earthquake Spectra, 1, 759–804. Campbell, K.W., 1997, “Empirical Near-Source Attenuation Relationships for Horizontal and Vertical Components of Peak Ground Acceleration, Peak Ground Velocity, and Pseudo-Absolute Acceleration Response Spectra,” Seismol. Res. Lett., 68, 154–179. Campbell, K.W., P.C. Thenhaus, J.E. Mullee, and R. Preston, 1996, “Seismic Hazard Evaluation of the Oman India Pipeline,” Proceedings of the Offshore Technology Conference, May 6–9, 1996, Houston, TX, OTC 8135, pp. 185–195. Chapman, M.C., 1995, “A Probabilistic Approach to Ground-Motion Selection for Engineering Design,” Bull. Seismol. Soc. Am., 85, 937–942. Coppersmith, K.J., 1991, “Seismic Source Characterization for Engineering Seismic Hazard Analysis,” in Proceedings of the Fourth International Conference on Siesmic Zonation, Vol. 1, Aug. 25–29, 1991, Stanford, CA, Earthquake Engineering Research Institute, Oakland, CA, pp. 3–60. Coppersmith, K.J., P.C. Thenhaus, J.E. Ebel, W.K. Wedge, J.H. Williams, and N.C. Hester, 1993, “Regional Seismotectonic Setting,” in Seismic Hazard Assessment in the Central and Eastern United States, Monograph 1: Hazard Assessment, S.T. Algermissen and G.A. Bollinger, Eds., Central United States Earthquake Consortium, Memphis, TN, pp. 35–80. Cornell, C.A., 1968, “Engineering Seismic Risk Analysis,” Bull. Seismol. Soc. Am., 58, 1583–1606.
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Cornell, C.A., 1969, “Bayesian Statistical Decision Theory and Reliability-Based Design,” Proceedings of the International Conference on Structural Safety and Reliability, A.M. Freudenthal, Ed., Smithsonian Institution, Washington, D.C., April 9–11, pp. 47–66. Cornell, C.A. and E.H. Vanmarcke, 1969, “The Major Influences on Seismic Risk,” in Proceedings of the Fourth World Conference of Earthquake Engineering, Vol. 1, Santiago, Chile, pp. 69–83. Cornell, C.A. and S.R. Winterstein, 1988, “Temporal and Magnitude Dependence in Earthquake Recurrence Models,” Bull. Seismol. Soc. Am., 78, 1522–1537. Cowie, P.A. and C.H. Scholz, 1992, “Growth of Faults by Accumulation of Seismic Slip,” J. Geophys. Res., 97, 11085–11095. Cramer, C.H. and M.D. Petersen, 1996, “Predominant Seismic Source Distance and Magnitude Maps for Los Angeles, Orange and Ventura Counties, California,” Bull. Seismol. Soc. Am., 86, 1645–1649. Cramer, C.H., M.D. Petersen, T. Cao, T.R. Toppozada, and M. Reichle, 2000, “A Time-Dependent SeismicHazard Model for California,” Bull. Seismol. Soc. Am., 90, 1–21. Crone, A.J., M.N. Machette, M.G. Bonilla, J.J. Lienkaemper, K.L. Pierce, W.E. Scott, and R.C. Bucknam, 1985, “Characteristics of Surface Faulting Accompanying the Borah Peak Earthquake, Central Idaho,” in R.S. Stein and R.C. Bucknam, Eds., Proceedings of Workshop XXVIII: The Borah Peak, Idaho Earthquake, Vol. A, October 3–6, 1984, U.S. Geol. Surv. Open-File Rep., pp. 43–58. dePolo, C.M. and D.B. Slemmons, 1990, “Estimation of Earthquake Size for Seismic Hazards,” in E.L. Krinitzsky and D.B. Slemmons, Eds., Nectonics in Earthquake Evaluation, Geological Society of America, Reviews in Engineering, Vol. 8, pp. 1–28. Dietrich, J.A., 1994, “A Constitutive Law for Rate of Earthquake Production and its Application to Earthquake Clustering,” J. Geophys. Res., 99, 2601–2618. Downes, G.L., 1995. Atlas of Isosiesmal Maps of New Zealand Earthquakes, Institute of Geological and Nuclear Sciences, Lower Hutt. Earthquake Engineering Research Institute (EERI), 1989, “The Basics of Seismic Risk Analysis,” Earthquake Spectra, 5, 675–699. Earthquake Engineering Research Institute (EERI), 2001, “Preliminary Observations on the Origin and Effects of the January 26, 2001 Bhuj (Gujarat, India) Earthquake,” EERI Newsletter Special Earthquake Rep., Vol. 35, no. 4, p. 16. Ekstrom, G. and A.M. Dziewonski, 1988, “Evidence of Bias in Estimations of Earthquake Size,” Nature, 332, 319. Electric Power Research Institute (EPRI), 1986, Seismic Hazard Methodology for the Central and Eastern United States, EPRI NP-4726, Electric Power Research Institute, Palo Alto, CA. Electric Power Research Institute (EPRI), 1993, “Methods and Guidelines for Estimating Earthquake Ground Motion in Eastern North America,” Guidelines for Determining Design Basis Ground Motions, Report No. EPRI TR-102293, Vol. 1, Electric Power Research Institute, Palo Alto, CA. Erdik, M. et al., 1999, Assessment of Earthquake Hazard in Turkey and Neighboring Regions (contribution to GSHAP, available at http://seismo.ethz.ch/gshap/turkey/papergshap71.htm). Field, E.H., D.D. Jackson, and J.F. Dolan, 1999, “A Mutually Consistent Seismic-Hazard Source Model for Southern California,” Bull. Seismol. Soc. Am., 89, 559–578. Frankel, A., 1995, “Mapping Seismic Hazard in the Central and Eastern United States,” Bull. Seismol. Soc. Am., 66, 8–21. Frankel, A., 1996, National Seismic Hazard Maps: Documentation June 1996, U.S. Geological Survey OpenFile Rep. 96-532. Frankel, A. and E. Safak, 1998, “Recent Trends and Future Prospects in Seismic Hazard Analysis, in P. Dakoulas, M. Yegian, and R. Holtz, Eds., Geotechnical Earthquake Engineering and Soil Dynamics III, Vol. 1, Geotechnical Special Publication No. 75, American Society of Civil Engineers, Reston, VA, pp. 91–115. Frankel, A., C. Mueller, T. Barnhard, D. Perkins, E.V. Leyendecker, N. Dickman, S. Hanson, and M. Hopper, 2000, “USGS National Seismic Hazard Maps,” Earthquake Spectra, 16, 1–19.
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Stepp, J.C., 1973, “Analysis of Completeness of the Earthquake Sample in the Puget Sound Area,” in S.T. Harding, Ed., “Contributions to Seismic Zoning,” Technical Report ERL 267-ESL 30, pp. 16–28, National Oceanic and Atmospheric Administration, Washington, D.C. Stepp, J.C., W.J. Silva, R.K. McGuire, and R.W. Sewell, 1993, “Determination of Earthquake Design Loads for a High Level Nuclear Waste Repository Facility,” in Proceedings of the Natural Phenomena Hazards Mitigation Conference, Vol. 2, pp. 651–657, October 19–22, Atlanta, GA. Stucchi, M., Ed., 1993, Historical Investigations of European Earthquakes, CNR – Istituto di Ricerca sul Rischio Sismico, Milano. Sykes, L.R., 1971, “Aftershock Zones of Great Earthquakes, Seismicity Gaps, and Earthquake Prediction for Alaska and the Aleutians,” J. Geophys. Res., 76, 8021–8041. Thenhaus, P.C., 1983, “Summary of Workshops Concerning Regional Seismic Source Zones of Parts of the Conterminous United States, Convened 1979–1980, Golden, Colorado,” U.S. Geol. Surv. Circular 898. Thenhaus, P.C., 1986, “Seismic Source Zones in Probabilistic Estimation of the Earthquake Ground Motion Hazard: A Classification with Key Issues,” Proceedings of Conference 34: Workshop on Probablistic Earthquake Hazards Assessments, pp. 53–71. Toda, S., R.S. Stein, P.A. Reasonberg, and J.H. Dietrich, 1998, “Stress Transferred by the Mw = 6.5 Kobe, Japan, Shock: Effects on Aftershocks and Earthquake Probabilities,” J. Geophys. Res., 103, 24,543–24,565. Usami, T., 1981, Nihon Higai Jishin Soran (List of Damaging Japanese Earthquakes), University of Tokyo Press (in Japanese). Wells, D.L. and K.J. Coppersmith, 1994, “New Empirical Relationships among Magnitude, Rupture Length, Rupture Width, Rupture Area, and Surface Displacement,” Bull. Seismol. Soc. Am., 84, 974–1002. Wentworth, C.M. and M.D. Zoback, 1990, “Structure of the Coalinga Area and Thrust Origin of the Earthquake,” in M.J. Rymer and W.L. Ellsworth, Eds., The Coalinga, California, Earthquake of May 2, 1983, U.S. Geological Survey Prof. Paper 1487, pp. 41–68. Wesnousky, S.G., 1994, “The Gutenberg–Richter or Characteristic Earthquake Distribution, Which Is it?,” Bull. Seismol. Soc. Am., 84, 1940–1959. Wesnousky, S.G., C. Scholz, K. Shimazaki, and T. Matsuda, 1983, “Earthquake Frequency Distribution and the Mechanics of Faulting,” J. Geophys. Res., 87, 6829–6852. Wheeler, R.L. and K.B. Krystinik, 1992, “Persistent and Nonpersistent Segmentation of the Wasatch Fault Zone, Utah: Statistical Analysis for Evaluation of Seismic Hazard,” in P.L. Gori and W.W. Hays, Eds., Assessment of Regional Earthquake Hazards and Risk along the Wasach Front, Utah, U.S. Geological Survey Prof. Paper. 1500-A-J, pp. B1–B47. Woo, G., 1996, “Kernel Estimation Methods for Seismic Hazard Area Source Modeling,” Bull. Seismol. Soc. Am., 86, 353–362. Working Group on California Earthquake Probabilities, 1988, Probabilities of Large Earthquakes Occurring in California on the San Andres Fault, U.S. Geological Survey Open-File Rep. 88-398. Working Group on California Earthquake Probabilities, 1990, “Probabilities of Large Earthquakes in the San Francisco Bay Region, California,” U.S. Geol. Surv. Circular 1053. Working Group on California Earthquake Probabilities, 1995, “Seismic Hazards in Southern California: Probable Earthquakes, 1994 to 2024,” Bull. Seismol. Soc. Am., 85, 379–439. Working Group on California Earthquake Probabilities, 1999, Earthquake Probabilities in the San Francisco Bay Region: 2000 to 2030 — A Summary of Findings, U.S. Geological Survey Open-File Rep. 99-517. Yeats, R.S., K. Sieh, and C.R. Allen, 1997, The Geology of Earthquakes, Oxford University Press, New York. Youngs, R.R. and K.J. Coppersmith, 1985, “Implications of Fault Slip Rates and Earthquake Recurrence Models to Probabilistic Seismic Hazard Estimates,” Bull. Seismol. Soc. Am., 75, 939–964.
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Youngs, R.R., Swan, F.H., Powers, M.S., Schwartz, D.P., and Green, R.K., 1987, “Probabilistic Analysis of Earthquake Ground Shaking along the Wasatch Front, Utah,” in P.L. Gori and W.W. Hays, Eds., Assessment of Regional Earthquake Hazards and Risk along the Wasatch Fault, Utah, U.S. Geological Survey Open File Report 87-585, pp. M1-M110.
Further Reading There is an extensive literature on seismic hazard analysis. Reiter’s book [1990] is a good introduction, as is Cornell’s classic paper [Cornell, 1968], which started the field, and Cornell and Vanmarcke [1969]. McGuire has made a number of contributions over the years [1995; many others] which are very instructive. McGuire [1993] is an excellent compendium of international seismic hazard assessment practice, as is the more recent GSHAP project and papers, available on-line at [http://seismo.ethz.ch/ gshap/]. McCalpin’s [1996] book is an excellent summary of the state of the art in the relatively new field of paleoseismology. Yeats et al.’s [1997] book provides an excellent overview of geology related to earthquakes and synopses of worldwide seismotectonic settings. Sholz’s [1990] book is highly instructive in the theory of fault rupture mechanics and earthquake generation, and provides an insightful synopsis of hazard analysis and earthquake prediction.
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9 Tsunami and Seiche 9.1 9.2 9.3 9.4 9.5
Introduction Tsunamis vs. Wind Waves Tectonic Tsunami Sources Initial Waves Generated by Submarine Landslides Exact Solutions of the Shallow-Water (SW) Equations Basic Equations and Solutions of the 1+1 or Two-Dimensional Equations · Linear 1+1 Theory · Exact Solutions of the LSW Boundary Value Problem · Nonlinear 1+1 Theory · The Solitary Wave Solutions · The Evolution of Solitary Waves · The Maximum Run-Up of Solitary Waves · The Validity of the Solitary Wave Solutions · The N-Wave Results · Evolution and Run-Up of N-Waves · 1+1 Wave Run-Up on Composite Beaches · Example of Calculation of the Run-Up of Solitary Waves on a Continental Shelf with a Beach · Example of Calculation of the Run-Up of Solitary Waves on a Composite Beach Fronted by a Seawall
9.6
Numerical Solutions for Calculating Tsunami Inundation The Splitting Technique · Boundary Conditions for Fixed Boundaries · The Finite-Difference Scheme · The Moving Boundary Condition · Verification of the Model
9.7
Harbor and Basin Oscillations Introduction · Calculating Basin Oscillations · Forced Oscillations in Basins of Simple Planform · The Sloshing of the Los Angeles Reservoir: a Case Study · Introduction to Harbor Resonance · Harbor Resonance for Harbors of Simple Geometry · Example of Analytical Harbor Resonance Computation · Numerical Modeling of Harbor Resonance
9.8
Tsunami Forces Forces on Piles · Impact Forces on Seawalls · Example of Impact Force Computation · Practical Design Considerations
9.9
Costas Synolakis University of Southern California Los Angeles, CA
Producing Inundation Maps The California Experience · Existing Analyses of Tsunami Hazards in California · Developing Inundation Maps for the State of California
Acknowledgments References
9.1 Introduction Tsunamis are long waves of small steepness generated by impulsive geophysical events of the seafloor and of the coastline, such as earthquakes and submarine or aerial landslides. Volcanic eruptions and asteroid impacts are less common but more spectacular triggers of tsunamis. The determination of the terminal
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effects of tsunamis as they strike shorelines and coastal structures is one of the quintessential problems in earthquake engineering. Tsunamis are notorious for exporting “death and destruction at distant coastlines,” for tsunamis sometimes travel across the world’s oceans without dissipating sufficient energy to render them harmless. In the past 10 years, 12 major tsunamis have struck coastlines around the Pacific Rim, causing more than 3000 deaths and an estimated U.S. $1 billion (2001 dollars) in damage. Fortuitously, these tsunamis have either struck less developed coastlines or developed coastlines at low season with few or no visitors along the coast. Within the contiguous 48 states of the United States, the most significant historic tsunami has been the 1964 Alaskan tsunami, which killed nine people in Crescent City, California and caused more than U.S. $30 million (1964 dollars) in damage. Before the 1995 Kobe, Japan and the 1999 Izmit, Turkey earthquakes, it had been estimated that tsunamis cause between 5 and 15% of the earthquake damage worldwide. Table 9.1 lists the major tsunamis of the past 100 years. The term tsunami, also known as seismic sea wave or tidal wave, comes from the Japanese term meaning harbor wave. In Japan, historical documentation of tsunamis goes back almost 1000 years and suggests that they attack Japan’s shores, on average, about once every decade. Since ancient times, harbors have been centers of commercial activity, and when even relatively small tsunamis enter a harbor they can trigger substantial harbor oscillations by bouncing off the harbor’s embankments and combining together to form larger waves. Alaska’s 1964 infamous Good Friday earthquake triggered large tsunamis that entered harbors throughout the region, including at Anchorage, Valdez, and Seward, and caused catastrophic destruction. Not only can these harbor waves reach substantial heights in a harbor, with amplification factors of 6 not entirely uncommon, but often the water motions persist for many hours. Most likely, in early Japan, harbors were where most people witnessed and recognized these giant waves as something out of the ordinary — thus seismic sea waves became known as great harbor waves. In Spanish, the word for tsunami is maremoto, meaning a trembling sea. Tidal wave is an exact translation from the Greek name for tsunami, well known to the ancient Greeks. The eruption of a volcano on Thera, around 1680 B.C., triggered a large tsunami that had until recently been considered the cause for the destruction of Minoan civilization on the island of Crete, about 60 miles south of Thera (see Figure 9.1). The disappearance of the Minoans was the event that created the myth of Atlantis described in Plato’s Timaeus (320 B.C.). Modern estimates from models such as shown in Figure 9.1 [Yalciner et al., 2002] suggest waves with run-up of 12 m close to Cnossos, Crete. It is now well established from different sources that the Minoan palaces were not abandoned until about 200 years after the eruption, so the tsunamis from Thera were one of the many fatal blows that the Minoans suffered before ultimately succumbing to the Dorians, who migrated from central Europe and the mainland of Greece. Although the initial manifestation of a tsunami more often than not resembles a fast ebbing tide, the term tidal wave is less commonly used, to avoid the association with tides, not only incorrect with regard to its origin (nothing to do with the tides), but also inappropriate in its descriptive character.
9.2 Tsunamis vs. Wind Waves Tsunamis are created by sudden movements or disturbances of the seafloor, submarine explosions, or impacts of large objects, such as landslides from the coastline or asteroids, or landslides that occur in or flow into the sea, also known as subaqueous slumps. These events trigger a series of fast-moving, long waves of initial low amplitude that radiate outward in a manner resembling the waves radiating when a pebble is dropped in the ocean. In contrast, most of the waves observed on beaches are generated by wind dragging or disturbing the surface of the sea. Tsunamis are generated by disturbing the seafloor, wind waves by disturbing the ocean surface. Another mechanism for triggering tsunamis is shaking of a closed basin, such as a reservoir, lake, or harbor. These tsunamis are also referred to as sloshing waves or seiches and sometimes they can be observed several hours after large earthquakes even at large distances. The 1755 Great Lisbon earthquake triggered sloshing at Loch Lomond in Scotland that persisted for several hours and caused the shoreline to advance repeatedly to elevations up to 1 m from the still water line. © 2003 by CRC Press LLC
Year
Date
Coordinates
Location
M
hmax
No. of Deaths
1891 1892 1894 1894 1894 1896 1897 1897 1899 1899 1902 1904 1906 1906 1906 1907 1907 1908 1913 1913 1914 1915 1915 1916 1917 1918 1918 1918 1918
29-Nov 16-May 22-Mar 27-Apr 10-Jul 15-June 15-Aug 21-Sep 10-Sep 30-Sep 26-Feb 25-Jun 31-Jan 17-Aug 17-Aug 14-Jan 23-Oct 28-Dec 22-Feb 11-Oct 12-Jan 26-May 7-Aug 1-Jan 1-May 15-Aug 7-Sep 11-Oct 8-Nov
48.1N 123.4W 14N 143.3E 42.3N 145.1E 38.7N 23E 40N 29E 39.6N 144.2E 38N 143.7E 6N 122E 60N 140W 3S 128.5E 14N 91W 52N 159E 1N 81.5W 51N 179E 33S 179E 77W 18N 38N 16E 15.5E 38N 41.75S 171.5E 7S 148E 31.1N 130.4E 2S 137E 38.5N 20.7E 4S 154E 16S 177W 5.5N 123E 45.5N 151.5E 18.5N 67.5W 44.6N 151.5E
Seattle, Washington Marianas Islands and Guam Nemuro, Japan Lokris, Greece Istanbul, Turkey Sanriku, Japan Tohoku District, Japan Sulu Sea, Philippines Yakutat Bay, Alaska Banda Sea, (Ambon) Indonesia El Salvador Near Petropavlosk, Kamchatka Equador–Colombia Aleutian Islands, Alaska Valparaiso, Central Chile Jamaica Calabria, Italy Messina, Italy Tasman Sea, New Zealand Near east end of New Guinea Sakurajima, Japan North coast of New Guinea Ionian Islands (near Ithaki) New Britain, Papua New Guinea Kermadec Islands–Fiji S. Mindanao, Philippine Islands Kuril Islands (near Ostrov Urup) Puerto Rico S. Kuril Islands
— 7.50 7.90 7.00 >7.00 7.60 7.70 8.70 8.60 7.80 — 8.10 8.60 8.30 8.60 6.50 5.90 7.2/7.5 6.80 7.90 6.2/7.1 7.90 6.70 7.75 8.00 8.30 — 7.50 7.80
2.1 4 4 3 >6 3 3.6 7 16/60 12/60 5 2 5 — 3.6/S 2.4 — 13 1.5 0.1 3 2.8 0.8/1.5 2.8 12 12 12.1 6 2
— — 1 — — 27,122 — 13 — 3,620 185 — 500–1,500 — — — — — — — 55 — — — — 6 47 42 —
9-3
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TABLE 9.1
Year
4-Dec 30-Apr 6-May 11-Nov 3-Feb 1-Sep 16-Sep 7-Mar 11 and 12 Sept 4-Nov 28-Dec 16-17 June 7-Mar 26-May 18-Nov 3-Oct 3-Jun 18-Jun 22-Jun 3-Mar 27-Oct 28 and 29 May 19-May 23-May 26-27-Dec 24-May 2-Aug 5-Dec 24-Aug 7-Dec
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Coordinates 26S 71W 21.5S 172.5E 5S 154E 28.5S 70W 53N 161E 35.6N 139E 11.5S 160E 35.7N 135E 44.5N 34.5E 34.5N 121.5W 54N 161E 16.3N 98W 51N 170W 51N 131W 44.5N 56.3W 10.5S 161.7E 19.5N 104W 19.5N 103.5W 19N 104.5W 39.2N 144.7E 58.6N 137.1W 42S 152.2E 1S 120E 36.7N 141.4E 39.8N 37.5E 10.5W 77E 44.1N 139.5E 8.5N 83W 15S 76W 33.7N 136E
Location Copiapo, Chile North of Vava’u, Tonga Bismarck Sea, New Guinea Atacuma, Chile East Kamchatka Kwanto, Japan Near Rennel, Solomon Islands SW Honshu Island, Japan Near Crimea, Black Sea Pt. Arguello-Lompoc, California Near Petropavlovska, Kamchatka Acapulco, Mexico Near Umnak, E. Aleutian Islands Queen Charlotte Islands, Canada Grand Banks, Newfoundland, Canada Guadalcanal, Solomon Islands Jalisco, Mexico Jalisco, Mexico Jalisco, Mexico Sanriku Coast, Japan Lituya Bay, Alaska Blanche Bay, New Britian Sulawesi, Indonesia Ibaraki, Japan Erzincan, Turkey Lima, Callao, Peru Northern part of Sea of Japan Panama–Costa Rica Near Lima, Peru Japan (Kumanonoda)
M 7.80 8.30 7.70 8.30 8.30 8.00 7.10 7.50 6.50 7.30 7.30 8.10 8.10 7.00 7.40 7.90 8.10 7.80 6.90 8.30 LS — 7.60 7.10 8.00 8.40 7.00 7.50 8.1/8.6 8.00
hmax 5 2.5 2.5/5.6 9 8 12–13 — 11.2/1.5/1.1 1 1.5–2 0.1/2 8/2.5 0.2/1 1.5 4.6 10/7.5 2.8/0.75 0.1/2 10/6 28–30 ≈150 5.9/≈2 3/2.3 0.8/1.5 15 2 3.5 0.22 2 10/7
No. of Deaths — — — >100 3 2,144 — 3,017/325 — — — — — — 51 50 — — 10 >3,000 — 500 17/8 — — 250 10/7 — — 9,984
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1918 1919 1919 1922 1923 1923 1926 1927 1927 1927 1927 1928 1929 1929 1929 1931 1932 1932 1932 1933 1936 1937 1938 1938 1939 1940 1940 1941 1942 1944
Date
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TABLE 9.1 (CONTINUED) Tsunamis in the Last 100 Years
14.1N 62.4E*2/25.4N 63E*3 52.75N 163.5W 49.8N 124.5W 19.3N 68.9W 33N 135.6E 35.5N 27.2E 21S 174W 18N 121E 19.2N 156.1W 42.2N 143.8E 9.5W 127E 52.8N 159.5E 38.1N 20.6E 18.2S 178.3E 34.3S 80.6W 3.4S 80.6W 36.2N 1.6E 36.7N 25.8E 51.3N 175.8W 58.6N 137.1W
Arabian Sea Aleutian Islands, Alaska E. Vancouver Island, British Columbia Dominican Republic Nankaido, Honshu, Japan Sea of Crete Tonga Island Philippine Islands Kona, Hawaii Tocachi-Oki, Japan East of Mindanao, Philippines Paramushir Island, Kuril Islands Kefallonia and Zakynthos, Ionian Islands Suva, Fiji Boso-Oki, Japan Peru–Ecuador Orleansville, Algeria Amorgos, South Aegian Sea Central Aleutian Islands Lituya Bay, Alaska
44.3N 148.5E 53.4N 159.8E 11.78S 80W 30.0N 10E 38.3S 72.6W 18.5S 168.3E 17.2N 99.6W 24.4N 122.1E 40.5N 29E 44.9N 149.6E
Iturap, USSR Kamchatka, USSR Ancon, Peru Agadir, Morocco The Great Chilean Earthquake S. Vanuatu (near Efate) S. Mexico (Acapulco) E. Taiwan–Ryukyu Islands Near Cinarcik, Marmara Sea S. Kuril Islands
8.30 7.40 7.30 8.10 8.10 7.10 7.80 7.20 6.90 8.10 7.20 8.20 7.20 6.75 7.50 7.30 6.75 7.50 7.9–8.3 — — 8.10 7.70 7.80 — 8.60 7 7.2 7.3 6.30 8.1
15.2 30–35 30 4.6 6.6 1.2 0.1/2 2 3.6 6.5 — 18–20 — 3 3 1/18/0.5 — 25 15–16 30 520 5 2 5.7 — 25 1.5 — 0.2 1 5
— 165/17 1 >100 1,997/1,405 — — 16/15 — 28/5/600/33 — — — 5/8 1 7 — — 2 — 0/5 — — — — 534/1,260/4/5 — 30 15 — —
9-5
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1958 1959 1961 1960 1960 1961 1962 1963 1963 1963
27-Nov 1-Apr 23-Jun 4-Aug 21-Dec 9-Feb 8-Sep 29-Dec 21-Aug 4-Mar 19-Mar 4-Nov 11-Aug 14-Sep 26-Nov 12-Dec 9-Sep 9-Jul 9-Mar 9 July at 20:00 10 July in morning 6-Nov 4-May 13-Jan 29-Feb 22-May 23-Jul 19-May 13-Feb 18-Sep 13-Oct
Tsunami and Seiche
1945 1946 1946 1946 1946 1948 1948 1949 1951 1952 1952 1952 1953 1953 1953 1953 1954 1956 1957 1958
Date
Coordinates
1963 1964 1965 1965 1965 1966 1966 1966 1967 1967 1967 1968 1968 1968 1968 1969 1969 1970 1970 1971 1971 1973 1973 1973 1974 1974 1974 1975 1975
20-Oct 28-Mar 24-Jan 4-Feb 6-Jul 17-Oct 28-Dec 31-Dec 11-Apr 12-Apr 3-Sep 1-Apr 16-May 3-Sep 14-Aug 11-Aug 22-Nov 31-May 1-Nov 14-Jul 26-Jul 28-Feb 17-Jun 24-Jun 31-Jan 1-Feb 3-Oct 10-Jun 29-Nov
44.5N 150.3E 61.1N 147.5W 2.4S 126E 51.3N 178.6E 38.4N 22.3E 10.7S 78.8W 25.5S 70.6W 11.8S 166.8E 3.4S 119.1E 5.5N 97.3E 10.6S 79.8W 32.3N 132.5E 40.7N 143.6E 41.7N 32.6E 0.2N 119.8E 42.7N 147.6E 57.7N 163.6E 9.2S 78.8W 4.9S 145.5E 5.5S 153.9E 4.9S 153.2E 50.5N 156.6E 43N 146E 43.3N 146.4E 7.4S 155.6E 7.4S 155.6E 12.3S 77.8W 42.8N 148.2E 19.3N 155W
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Location S. Kuril Islands The Great Alaskan Earthquake Ceram Island, Indonesia W. Aleutian Islands North Corinth Gulf, Greece Offshore Chimbote, N. Peru Taltal, N. Chile N. New Hebrides Islands (Vanuatu) Makassar Strait, Indonesia Malay Peninsula Offshore Chimbote, N. Peru Seikaido, Japan N. Honshu, Japan (near Tohoku) Amasra, Turkey N. Celebes, Banda Sea, Indonesia SE Hokkaido, Kuril Islands Bering Strait, Alaska Offshore Chimbote, N. Peru Bismarck Sea, New Guinea Bismarck Sea, New Guinea Bismarck Sea, New Guinea Kamchatka, Kuril Islands Kuril Islands and Hokkaido, Japan Kuril Islands and Hokkaido, Japan Solomon Islands Solomon Islands Callao, Peru Kuril Islands and Hokkaido, Japan S. Hilo, Hawaii
M
hmax
No. of Deaths
6.7/7.2 8.5 7.6 8.2 6.9 8 7.8 8.1 5.5 7.5 7 7.5 7.9–8 6.60 7.7–7.8 7.8 7.3 7.6/6.6 7 7.8–7.9 7.7–7.9 7.2–7.5 7.4 7.5 7 7.4 8.1 6.8–7.0 7.2
15 70/67.1 4 10 20/3 3 1 2 3 2 2 2.4–3 5 3 10 2.6/5 15 1.8 3 3 10/3.4 1.5 4.5/1.5 4.6 4.6 4.5 1.58 4.9/5.5 8/14.3
— 123/115 71 — — 125 3 — 58/13 14 — 1 52 — 200/392 — — — 3 2 — — — — — — — — 2/16
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Year
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TABLE 9.1 (CONTINUED) Tsunamis in the Last 100 Years
6.3N 124E 11S 118.4E 8.5S 123.5E 1.7S 135.9E 1.6N 79.3W 46.2N 122.2W 36.2N 1.35E 40.4N 139.1E 17.8N 101.6W 6.2S 149.1E
1990 1990 1992 1992 1992 1993 1994 1994 1994 1995 1995 1995 1996 1996 1996 1997 1998 1998 1999
25-Mar 4-Apr 25-Apr 2-Sep 12-Dec 12-Jul 15-Feb 2-Jun 3-Nov 14-May 15-Jun 9-Oct 1-Jan 17-Feb 21-Feb 21-Apr 17-Jul 6-Aug 17-Aug
9.9N 84.8W 40.4N 124.3W 11.76N 87.4W 8.5S 121.9E 42.8N 139.2E 5S 104.3E 10.5S 112.8E 59.5N 135.3W 8.3S 125.1E 38.4N 22.3E 18.9N 104.1W 0.7N 119.9E 0.9S 137E 9.6S 79.6W 12.6S 166.7E 2.9S 141.9E 25.1N 95.1E 40.7N 30E
Moro Gulf, Philippines Sunda Islands Lomblen Island, Indonesia W. Irian, Indonesia Colombia–Ecuador Mount Saint Helens, Washington El Asnam, Algeria Noshiro, Japan Acapulco, Mexico Whiterman Ra, New Britain, Papua New Guinea Puntarenas, Costa Rica Mindanao, Philippines Cape Mendocino, N. California Offshore Nicaragua Flores, Indonesia Japan Sea (offshore W. Hokkaido) Southern Sumatra, Indonesia East Java, Indonesia Skagway, Alaska Timor, Indonesia Aigiou, Greece Manzanillo, Mexico Sulawesi, Indonesia Irian Jaya, Indonesia Chimbote, Peru Santa Cruz Island, Vanuatu Aitape, Papua New Guinea Burma–India Kocaeli, Turkey
7.8 8 — 8.1 7.7 5.1 7.7 7.7 7.6 7.7 7 — 7.1 7.2–7.4 7.5 7.6 7 7.2 LS 6.9 6.3 7.3–7.6 7.6 8.1 6.6/7.5 7.9 7.1 7.2 7.8
5 15 10 2 5 225 — 14.5 1.2 0.1
8,000/4,000 189 539–540 100/15 500/600 57 — 103–104 — —
1 2.5 1.8 10 26 30.6–31.7 — 12 12 4 2 5–11 5/3.43 7.7 ≈5 0.2 15 — 2.9
— — — 168–170 2,080 330 7 ≈200 1 11 — 1 9/24 127/108 12/2 100/0 2,182/3,000 2 3–11
9-7
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16-Aug 19-Aug 18-Jul 12-Sep 12-Dec 18-May 10-Oct 26-May 21-Sep 16-Oct
Tsunami and Seiche
1976 1977 1979 1979 1979 1980 1980 1983 1985 1987
Year
Date
Coordinates
1999 2000 2000 2001
26-Nov 26-Jan 4-May 23-Jun
16.4N 168.2E 5.1N 120.2E 1.1S 123.6E 16.2S 73.6W
Location Pentacost Island, Vanuatu Islands Tawi-Tawi, Philippines Sulawesi, Indonesia Camana, Peru
M
hmax
7.3 0 7.5 8.4
5/6 20 5/6 4
No. of Deaths 3/5 0 0 23
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Earthquake Engineering Handbook
Note: LS = Land Slide. When multiple entries are provided they should be taken as indicative of the range of values along the target coastline, or that sources disagree on the correct value. Sometimes values refer to estimates of the wave height, otherwise to estimates of the maximum run-up or estimates of overland flow depths. Other than tsunamis in the last half of the twentieth century which have been properly surveyed, all other height estimates should be interpreted with extreme caution, for tsunami run-up varies substantially over the coast for any given event. The use of the table is only for indicating tsunami incidence around the world. Source: Data are from Soloviev and Go’s Catalogue of Tsunamis, the National Geophysical Database Center, the Novosibirsk Tsunami Laboratory of the Siberian Science Computing Center, and from Camfield [1980].
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TABLE 9.1 (CONTINUED) Tsunamis in the Last 100 Years
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FIGURE 9.1 The tsunami that started it all. Initial wave from the 1680 B.C. eruption of the Thera volcano in the Aegean. The tsunami has been blamed for destroying the Minoan civilization in Crete, but computations suggest that the wave disrupted but did not destroy the Minoans. Shown as Color Figure 9.1.
Both wind waves and tsunamis are characterized by a wavelength, the horizontal distance between crests or peaks; a period, the time it takes successive peaks to pass a fixed point; and a height, the vertical distance from the wave trough to its crest. Wind waves tend to have a wavelength up to 200 m (666 ft) and periods of about 0.5 to 30 sec [Prager, 1999]. In contrast, tectonic tsunamis near the source typically have a wavelength of hundreds of kilometers and periods of tens of minutes. Wind waves vary in height from tiny ripples on the sea surface to the rare rogue waves imaged in the motion picture, The Perfect Storm. © 2003 by CRC Press LLC
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Tsunamis, on the other hand, race across the open ocean as a series of long, low-crested waves, usually less than 1 m high. Their steepness is so small that a ship out at sea may not feel a tsunami pass beneath the hull [Prager, 1999]. In general, waves are considered deep-water waves if their wavelength L is relatively small compared to the water depth d through which they travel. Wind waves do not “feel” the seafloor until within tens of meters from the coastline, depending on the slope of the beach. In the open ocean, where depths average about 4 km (2.5 mi), most wind waves are deep-water waves, i.e., with a short wavelength relative to depth, d/L > 1.5. In contrast, shallow-water (SW) waves are those with a long wavelength relative to depth, d/L < 20. The depth and nature of the seafloor strongly influence how SW waves propagate or travel. Because tsunamis have such long wavelengths, even when traveling through very deep water, they are considered SW waves [Prager, 1999]. In wind-generated waves, the orbital motion of the water particles decreases with depth from the water surface. As energy is transferred through the motion of the water particles, the energy of wind waves traveling through deep water is concentrated near the surface. By contrast, the energy imparted to the water during tsunami formation sets the entire water column in motion. Orbital velocities do not decrease significantly with depth, and although the wave height at the surface is relatively small, the energy contained throughout the entire water column is substantial. Furthermore, the rate at which water waves lose energy is inversely proportional to their wavelength. So tsunamis not only contain a lot of energy, and move at high speeds, but they can also travel great distances with little energy loss. The speed or wave velocity or celerity c is calculated by dividing the wavelength L by its period T. The speed of deep-water waves does not depend on the depth, and the waves are dispersive, as each component frequency of a complex spectrum propagates at its own frequency-dependent speed. It is for this reason that complex sea states generated by storms far offshore manifest themselves in groups of waves of approximately similar period when they strike the coast. SW waves travel at a speed c = gd where d is the local depth, hence all frequencies in the spectrum of a tsunami travel at the same velocity. It is for this reason that tsunamis do not alter their shape substantially as they propagate over fairly constant depth. In typical ocean depths of 4 km, a tsunami travels at a speed of nearly 200 m/sec, or almost 700 km/h (437 mph) — the speed of jet aircraft. When tsunamis enter shallower water they slow down; at a depth of 30 m, an SW wave travels at only 59 km/h (36 mph). As they move toward the coast, tsunamis pass through varying depths and over complex seafloor topography. Changes in the depth and seafloor cause them to continuously evolve and change shape. A tsunami generated from an earthquake off Peru may look entirely different along the Peruvian coastline as compared to when it enters a bay in California, and still different when it strikes a beach in Hawaii. Both tsunamis and wind waves behave similarly as they approach a coastline; they refract and shoal. Shoaling is the process in which the wave front steepens and the wave height increases. The front of the wave enters shallower water and moves more slowly than the tail of the wave, since the depth is smaller, hence the steepness at the front. If the wave is sufficiently steep and the continental shelf long, it eventually breaks, as the wave in essence trips over itself. However, when refracting, the crest lengths of tsunamis often cause unexpected wave patterns in refraction compared to wind waves. During the 1992 Flores, Indonesia event, the tsunami struck Babi Island about 6 mi off Flores and concentrated its energy on the fishing villages built on the lee side of the island, which was sheltered from wind waves (see Figure 9.2). The tsunamis appear to have hit the island, traveled around its shoreline as a trapped wave, and inundated the backside [Yeh et al., 1992], as also described in Section 9.6. When tsunamis start advancing up on dry land, they can snap trees, destroy engineered structures, and carry boats far inland. During the 1994 Mindoro, Philippines event a 2-m tsunami carried a 6000-ton power-generating barge moored at the delta of the Baryan River 1 mi inland and left it there. When the water level recovered, there was not sufficient freeboard to tow the barge back to the delta [Imamura et al., 1995]. Not all tsunamis break at the shoreline; some just swiftly submerge the shore and generate swirling currents. Most tsunamis manifest themselves on the coastline as a leading depression wave, a particular kind of what are referred to in mathematics as N-waves or dipole waves. Numerous anecdotal stories relate how © 2003 by CRC Press LLC
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FIGURE 9.2 A view of Babi Island, off Flores, Indonesia (top of photo). The village on the back side of Babi was completely destroyed by the tsunami, which wrapped around the island, killing hundreds.
people set out to collect fish left stranded and flapping by a great retreat of the sea. In fact the great tsunami of All Saints Day, November 1, 1755, which destroyed Lisbon, Portugal and led the two French philosophers Voltaire and Rousseau to argue whether optimism had a place in human life (see Chapter 1), was preceded by a leading depression wave. So was the April Fool’s Day 1946 tsunami which, after destroying the Scotch Cap Lighthouse at Unimak Island, Alaska, killing five people (Figure 9.3), 2300 mi away and 5 h later hit Hilo, Hawaii, killing 159 people [Dudley and Lee, 1988]. So was the 1992 Nicaraguan tsunami and, conspicuously, all tsunamis of the past 10 years surveyed by the International Tsunami Survey Team (ITST) had at least several reports of leading depression N-waves. Tsunamis can also cause sediment erosion or sediment deposition, or they can rip apart coral reefs that lie in their path. Coastal regions that are low lying or are located between steep cliffs or bodies of water are particularly vulnerable to tsunami damage. The September 1, 1992 Nicaraguan tsunami deposited a vast sediment blanket over many lowlands along the affected areas. On June 3, 1994, an earthquake occurred in the Java trench in the Indian Ocean. The magnitude 7.2 quake triggered a large tsunami that struck the coast of southeast Java and rolled on to hit southwest Bali. Some 200 people were killed, 400 injured, and 1000 left homeless. Post-tsunami surveys found clues, such as trees with sand-encrusted bark and leaves, that indicated that run-up reached some 5 m in west Bali and up to 14 m in southeast Java. Several beaches were completely washed away, while rivers effectively blocked evacuation routes. Eyewitnesses near G-camp in Southeast Java, a surfing locale of renown, reported that within a 20-m section of a nearby coral reef, about a meter’s worth of surface growth had been shaved off [Synolakis et al., 1995], see Figure 9.4. The ITST found large pieces of the reef on a nearby beach. Some of the © 2003 by CRC Press LLC
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FIGURE 9.3 Scotch Cap, Unimak, Alaska. The lighthouse in the inset stood where the marker indicates. The wave rose 42 m past the structure on the headlands. The lighthouse was completely destroyed and five people perished.
eroded sand from the shore was deposited in broad offshore bars. The same tsunami was documented along the northwestern Australian coast. In one area a surge of water, some 3–4 m (10–13.3 ft) high, carried fish, crayfish, and rocks nearly 300 m (1000 ft) inland. The 1998 Papua New Guinea tsunami deposited a sediment layer that in some areas was 1 m (3.3 ft) high. Up until recently, earthquake-induced seafloor deformation was believed to be the primary cause of most tsunamis, even though numerous major landslides and associated waves were triggered in fjords and lakes of southern Alaska by the great 1964 Alaska earthquake (see summary and references in Plafker et al., 1967). It is now suspected that landslides play a much greater role in tsunami generation than previously believed. Landslide-generated tsunamis differ from the classic long waves, in that they are steeper and disperse rapidly, particularly in shallow water. There are several important differences between tsunamis triggered by mass movements and by earthquakes, also called tectonic tsunamis. Tectonic tsunamis tend to have longer wavelengths, longer periods, and a larger source area than those generated by mass movements of earth. However, whereas there is little question that the timing of the seafloor deformation is not important to first order in calculating tsunami evolution, there is also little question that the timing of mass movements is more important in the wave evolution; very slow movements will not generate large waves. Nonetheless, the characteristic time cannot be determined very accurately. When a potential tsunami-triggering earthquake occurs, sufficient information is often available to predict whether or not a massive wave will be created. However, mass movements often occur and trigger tsunamis unexpectedly and sometimes aseismically. The 1994 Skagway, Alaska tsunami was triggered by sediment instabilities at extreme low tides, without any detectable associated seismic event. Figure 9.5A shows the slabs that failed in retrograde fashion from C to B to A and triggered the tsunami. Figures 9.5B and C © 2003 by CRC Press LLC
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FIGURE 9.4 The aftermath of the 1994 East Java tsunami. There had been no damage from the earthquake and it had been hardly felt. Shown as Color Figure 9.4.
show stills from an animation of the tsunami as it attacks the nearby dock of the Pacific Arctic Railway Company. Notice how the dock is destroyed as the wave advances from north to south [Synolakis et al., 2002a]. Although still controversial, the 1998 Papua New Guinea tsunami that killed more than 2100 people, with waves ranging up to 12 m, was triggered by a submarine slump. Figure 9.6A shows a graphic of the wave as it attacks Sissano Lagoon on the north coast of Papua New Guinea. The aftermath is shown in Figure 9.6B. This event was documented extensively [Synolakis et al., 2002b] in Science, August 17, 2001, and the New York Times, April 23, 2002. There are at least four characteristics of mass movements that determine whether or not a tsunami will form, its length, width, thickness, and the inclination of the slope that fails and triggers the landslide. The effects on the generated waves of the geomechanical characteristics of the material that slides remain controversial, primarily due to lack of validated constitutive models and lack of knowledge as to the effect of the timing of the seafloor motions. None of these characteristics can yet be accurately predicted and the relevant information on geometric slide characteristics typically comes only after the event. The potential for tsunami-triggering mass movements often can only be assessed in the context of the surrounding geology, and this typically requires a multidisciplinary approach to modeling and bathymetric cruises. In some cases, information on submarine landslides can be obtained from the resultant breaks in underwater cables. The timing of communications cable breaks and the subsequent loss of communications can be used to document undersea mass movements and actually record the timing of the event. Observers during undersea debris flows have also reported seeing muddy seawater rolling toward the surface. In the absence of such information, it is nearly impossible to determine the exact timing.
9.3 Tectonic Tsunami Sources Although landslides, volcanoes, and asteroid impacts can all trigger tsunamis, by far the most common cause is submarine earthquakes. Even if the seafloor motion itself does not trigger tsunamis, the shaking may trigger coseismic landslides. Recent speculation suggests that up to one third of the tsunamis in the © 2003 by CRC Press LLC
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(A)
(B)
FIGURE 9.5 (A) The three slabs that slid during the 1994 Skagway, Alaska disaster, triggering the wave shown in (B) and (C).
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(C)
FIGURE 9.5 (CONTINUED)
past 10 years may have been cogenerated by quake-induced landslides. Not all earthquakes generate tsunamis. Looking at earthquake catalogs, one can deduce that in the past 30 years, there have been approximately one magnitude 8 or higher earthquake and about ten magnitude 7 submarine earthquakes per year, yet only 20 of them have reportedly created tsunamis. The pattern and extent of vertical ground deformation from an earthquake uniquely determines whether or not a tsunami is formed. Earthquake fault geometries constitute a ternary family featuring three fundamental end members: strike-slip, thrust, and normal faults. Strike-slip or transform faults involve horizontal motion of the Earth’s crust, while thrust and normal faults entail vertical motion. Submarine thrust or normal faults produce tsunamis as the seafloor lifts up or drops down, and either pushes the water up or pulls it down — triggering wave motion on the ocean surface. On the other hand, strike-slip motions, generally, do not generate sufficient vertical displacement on the seafloor, yet they may generate tsunamis through coseismic events. Most faults combine both strike-slip and thrust motions, but primarily only faults that have predominantly vertical displacement and create sufficiently large seafloor deformations appear to trigger tsunamis. Generally, the larger the magnitude of an earthquake, the larger the area that is deformed, as shown in Table 9.2. The deformed area usually contains an area of uplift and subsidence, whereas quite frequently there is more than one dipole shape of the wave. The deformation area refers to the horizontal extent of deformation, while slip length is a measure of vertical change. Strong earthquakes not only deform larger areas, but they do so by a greater amount of slip, thus producing disproportionally larger tsunamis than smaller events. In addition to an earthquake’s magnitude, the deeper the hypocenter or focus of an earthquake, the smaller the vertical deformation of the Earth’s surface. A deeper hypocenter allows the seismic energy to spread over a larger volume so that less energy reaches the ground surface. Earthquakes deeper than about 30 km (18.75 mi) rarely cause sufficient deformation to generate tsunamis. However, truly great megathrust earthquakes that occur deeper than 30 km, such as the 1960 Chilean event, can occasionally trigger tsunamis. To understand the process, refer to Figure 9.7, which shows a typical subduction zone © 2003 by CRC Press LLC
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(A)
(B)
FIGURE 9.6 (A) The aftermath of the Papua New Guinea disaster. Only the stilts from the houses remain. The bucket on the tree in the picture is a watermark that is used to indicate the flow depth during the tsunami. (B) Initial and final profiles of the Papua New Guinea wave. Part (A) shown as color Figure 9.6. © 2003 by CRC Press LLC
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TABLE 9.2
Estimates of Fault Parameters for Tsunamigenic Earthquakes
Mw
W (km)
L (km)
D (m)
S (m)
L/V (sec)
7 8 9 9.5
30 80 240 250
70 200 60 1000
0.6 2.7 9.0 27.0
0.16 0.70 2.30 7.00
23 70 200 330
Note: L, W, and D are the fault width, length, and displacement at the dislocation also known as fault slip, respectively, and V is the rupture velocity. S is the corresponding vertical seafloor displacement. Data from Synolakis et al. (1997a).
(Deep Water Tsunami) Vertical Displacement
Uz
No Coastal Movement
X Z
Ocean Rupture
Continental Shelf Coastline Interplate Thrust
X
FIGURE 9.7 Definition sketch of subduction zone generation of tsunamis.
event and the leading depression N-wave tsunami generated on the ocean surface. If the rupture is closer to shore then the subsidence takes place primarily onshore and the initial tsunami may manifest itself as a leading elevation wave. An earthquake whose epicenter lies inland will only generate a tsunami if it produces sufficient vertical deformation offshore on the seafloor. Therefore, only very strong inland thrust earthquakes, as compared to even moderate offshore earthquakes, are potential tsunami generators (unless of course they trigger a massive landslide into the sea). For example, the 1994 Northridge earthquake that shook Los Angeles violently resulted in vertical ground deformations of up to 2 m (6 ft), but did not produce a tsunami. Had the fault ruptured with the same ferocity about 60 km (40 mi) west offshore, it would have probably created a substantial tsunami inside Santa Monica Bay. The first piece of information required for modeling tsunamis is the size and distribution of seafloor deformation following an earthquake, and the amount of energy released. The amount of seafloor deformation can either be measured or predicted by another model. The most accurate means of determining seafloor deformation is to actually measure it by comparing the underwater topography (bathymetry) of the seafloor post-quake to pre-quake data. Unfortunately, this cannot be done quickly and is often impossible, as bathymetry at sufficiently high resolution rarely exists for most coastline areas of the United States and the world. Given the difficulties in actually determining the seafloor deformation that triggers a tsunami, earthquake engineers usually rely on predictions provided by seismologic models, referred to as source models. The input for a tsunami inundation model comes from an earthquake model. These computer simulations are based on models of elastic deformation on half-spaces and are applicable for all earthquakes whether submarine or not. In a sense, for each earthquake, seismologists estimate what the surface deformation would be in a material with the same elastic properties as the Earth’s interior, given an internal displacement of the size inferred from seismic records. Each earthquake event is modeled using what is referred to as the Harvard fault plane solution or CMT. The Harvard solution uses seismologic recordings, at different stations around the world and solves © 2003 by CRC Press LLC
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FIGURE 9.8 The estimated energy as a function of the seismic moment. The anomalous events 42, 24, and 36 are tsunami earthquakes, particularly efficient in generating tsunamis. (From Newman, A.V. and Okal, E.A. 1998. “Teleseismic Estimates of Radiated Seismic Energy: The E/M0 Discriminant for Tsunami Earthquakes,” J. Geophys. Res., 103, 26885-26898.)
the classic inverse problem in geophysics to determine the rupture characteristics of the source and its location. The CMT reveals, fairly accurately, the moment magnitude of the earthquake. If the seismic moment is M0 , then: M0 = µDA
(9.1)
where µ ≈ 5 − 7 × 10 dyn/cm is the rigidity, D is the slip, and Α is the area of the fault. D and Α both increase with the moment, as shown in Table 9.2 [Liu and Synolakis, 2003]. Α is estimated from the aftershock distribution and is usually assumed rectangular. Other earthquake characteristics important for estimating the patterns of ground deformation, such as the strike, dip, and slip angles, are also inverted from the CMT algorithm. A measure of the barrier interval (the heterogeneity of the fault plane) over the rupture velocity V is defined as the rise time, and this is quite an elusive parameter to determine accurately. Tsunami models use the energy released, the size of the deformed area, the mean displacement at the surface l < D, and the dip δ, strike φ, and slip λ angles, to infer a seafloor displacement pattern, using what are known as Okada’s [1985] formulas. These closed form solutions are based on Mansinha and Smylie [1971] and, straightforward as they may be, they are too long to be repeated here. Then, tsunami models assume that water motion occurs instantaneously; therefore, the initial tsunami wave is assumed to be of the same shape as the seafloor displacement. Whatever mass of fluid is displaced by the seafloor moving up or down causes an equivalent displacement of the water surface in the same direction. The instantaneous assumption is based on the fact that tsunamis propagate at speeds up to 220 m/sec (733 fps), while seismic waves cause rupture to propagate at typical speeds of 2 to 3 km/sec (1.25 to 1.9 mph). Certain earthquakes are quite efficient in generating tsunamis and may produce large tsunamis at moment magnitudes lower than otherwise expected. These anomalous events include tsunami earthquakes (Kanamori, 1972). Figure 9.8 suggests a method for uniquely identifying tsunami earthquakes as 11
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those with a deficiency of up to two orders of magnitude in the ratio of the estimated seismic energy EE to the seismic moment M0. The energy EE is estimated from the high frequencies in the P-wave part of the signal, while M0 is estimated from the longer frequencies in the surface wave part of the signal. This EE/M0 measure will eventually be part of TREMORS, a quick and potent algorithm used to estimate source characteristics based on a single broad band instrument. TREMORS is now in use in the tsunami warning centers in several countries. Once the initial wave conditions are established, tsunami models estimate the evolution of the tsunami from its source to the target coastline, based on the underlying seafloor bathymetry. When the simulated wave arrives at the coastline, tsunami models become inundation models and calculate the evolution of the tsunami as it moves inland. Tsunami models are really the synthesis of earthquake, wave, and flood inundation models. It should be stressed that the solutions used for tectonic tsunamis are most often based on idealized elastic dislocation theory applicable to a uniform half-space [Mansinha and Smylie, 1971]. In reality, nonuniform slip distributions arising from barriers (or asperities) can cause local ground displacements that can be up to two or three times the values predicted by the Okada [1985] formulas. Recent anecdotal evidence also suggests that sediment lenses within tens of meters from the ground surface can amplify the ground displacement up to a factor of two. Until more evolved ground deformation models predict the vertical displacement more accurately, caution is needed in interpreting results derived from initial conditions based on Okada [1985].
9.4 Initial Waves Generated by Submarine Landslides Modeling tsunamis generated by submarine landslides is not as well understood as waves generated by seismic displacements. Coseismic deformation of the seafloor occurs very rapidly relative to the propagation speeds of SW waves, allowing for simple specification of initial conditions by transferring the terminal deformation to the free surface. The idea that submarine landslides might generate long waves is not new. Gutenberg [1939] suggested that “submarine landslides are to be considered at least as one of the chief causes, if not indeed the major cause of tsunamis.” He supported his statements by referring to the work of Montessus de Ballore, who himself referred to earlier work by Verbeck. Gutenberg [1939] wrote that the large waves that drowned many people in Chile in Ceram in 1899 were probably triggered by coseismic landslides. He also referred to a report by Milne in the 1898 meeting of the British Association for the Advancement of Sciences. Milne suggested that tsunamis on Japan’s east coast were the result of submarine slides on the Tusacarora slope. Gutenberg finally refers to Forster’s 1890 work, which attributed underwater cable breaks in Greece to coseismic submarine slides. Recent work has also highlighted the possibility of substantial tsunamis generated by submarine slides and slumps. Hasegawa and Kanamori [1987] studied the 1929 Grand Banks “earthquake” and tsunami. Eissler and Kanamori [1987] studied the 1975 Kalapana earthquake and tsunami on the Island of Hawaii. While there is still continuing debate on the exact causative mechanism of the 1946 Aleutian tsunami [Kanamori, 1985; Okal, 1992; Pelayo and Wiens, 1992; Fryer et al., 2001; Okal et al., 2002a, 2002b), the working assumption is that the near-source damage was due to a submarine slump. Compared with the understanding of earthquake-induced initial tsunami waves, the understanding of landslide initial waves is marginal. A few empirical and computational methods exist to generate oneor two-dimensional surface waveforms generated by underwater mass movements. Wiegel [1955] discusses impulsively generated water waves, described as “the sudden movement of a submerged body for a short interval of time,” which “may be considered representative of a submarine landslide.” He states that the energy in the wave generated by a submerged falling block is on the order of 1% of the initial potential energy of the block. Wiegel’s [1955] study considered both vertically falling blocks and blocks sliding down an inclined plane. His data suggest that wave height increases with increasing slope, submerged weight, and decreasing depth of submergence. He also reported that wave period increases with decreasing slope. © 2003 by CRC Press LLC
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water level
Ds D0 Slide Scar h
FIGURE 9.9 Definition sketch for landslide waves.
Based on the work of Striem and Miloh [1975], Murty [1979] used the energy released by a moving block sliding from its initial position to its final position, tranferred that energy into a solitary wave and calculated the height of the wave. This approach was also used by McCulloch [1985] when discussing the tsunami hazard associated with landslides offshore of southern California. The formulation used by Murty equates the potential energy of a sliding mass with the energy contained in an initial wave, assumed to be a solitary wave. Murty’s equation takes the form: H=
[
]
( 2/3) 1/ 2 1 8 (3) µlh ( γ − 1) ( Do − Ds ) D
(9.2)
where H is the predicted wave height; Do, Ds , h, and l are defined in Figure 9.9; and µ is an empirical parameter to represent the energy transfer from the sliding mass to the water wave it generates. γ is the specific gravity and it is the ratio of the density of the slide to the local water density. Murty (1979) used an energy transfer of µ = 1% from the sliding mass into wave generation based on the experiments performed by Wiegel. McCulloch assumed values of D = Do = 700 m, Ds = 600 m, l = 2500 m, h = 50 m, µ = 0.01, and γ = 1.6 as representative of typical landslide parameters offshore of Southern California. The calculated wave using these values is 14 m, in accordance with values estimated by other methods. Due to an arithmetic error, McCulloch had calculated it as 0.14 m, leading to an underestimation of the tsunami hazards off Southern California [Borrero, 2002]. In principle, Murty’s formula should work well only when the run of the slide Do − D is known. In most cases, wave generation takes place almost immediately, and the energy transfer is far less efficient as the slide proceeds into deeper water. If Do is significantly larger than Ds , the formula overpredicts the wave height. Heinrich [1992] used a two-dimensional finite difference solution of the Navier–Stokes equations to model wave generation from landslides. He validated his use of the numerical scheme by comparing it to laboratory data and found generally good agreement. His simulations modeled a right triangular block sliding down a 45˚ incline and showed the largest discrepancy with model experiments just after initiation of movement of the sliding mass — where turbulence is greatest. Similar results have been obtained by Raichlen and Synolakis [2002] where flow separation is seen to occur. Jiang and LeBlond [1992] have proposed a model for wave generation where the “landslide is treated as the laminar flow of an incompressible viscous fluid.” They modeled their deforming slide as a parabola perched on an inclined plane. When released under gravity, the slide mass was allowed to freely deform moving down the incline. The solution was based on the two-layer 2 + 1-dimensional SW equations. For one particular case, with an initial slide 686 m (2286 ft) long and 24 m (80 ft) thick on a 4˚ slope, the waves traveling seaward had a maximum crest amplitude of 5 m with a shoreward propagating trough
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∆X
Z max Z min
X min Xg
D
T b
θ
FIGURE 9.10 Definition sketch for landslide-generated waves by moving bodies.
of the same magnitude. Jiang and LeBlond [1992] noted that the maximum depended on the density of the slide, with less dense slides transferring more energy than more dense slides, and calculated an energy transfer rate of µ = 15%. Watts [1997, 1998] also studied waves generated by underwater landslides. He presented scaling equations for slide-generated waves based on laboratory experiments. Watts’ analysis is the basis for the initial wave shapes used in this study and will be discussed in some detail here. Pelinovsky and Poplavsky [1996] and later Watts [1997] presented the force balance on a submerged solid block sliding along a plane inclined at angle θ, as shown in Figure 9.10, as: 1 ds ds ≈ (mb – mo ) g (sin θ – Cn cos θ) – Cd ρoωl cos θ sin θ (mb + Cmmo ) dt 2 dt 2 2
2
(9.3)
where s mb mo ρ0 ω l Cm , Cn, Cd
= = = = = = =
the instantaneous position of the center of mass the mass of the sliding block the mass of the displaced fluid the density of water the width of the block the length of the block along the incline coefficients of added mass, Coulombic friction, and fluid dynamic drag, respectively
Pelinofsky and Poplavsky [1996] argued that terminal velocity is reached when the block is no longer accelerating, hence d 2S/dt2 = 0, and derived that the terminal velocity ut is given by: 2 gL ut = ( γ − 1) (sin θ − Cn cos θ) Cd © 2003 by CRC Press LLC
(9.4)
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and
ao =
(γ − 1) g sin θ (γ + 1)
(9.5)
Setting Cm = 1, Cn = 0, and using experimentally derived values for the term Cd sin θ cos θ, Watts [1998] and Borrero [2002] derive, for a semielliptical sliding body, that: ut = 0.5 gbπ ( γ − 1) sin θ
(9.6)
where ao and ut are the initial acceleration and terminal velocities of the slides, respectively; b = l cos θ is the length parallel to the upper surface of the sliding block; and γ is the specific gravity of the block. These expressions are the basis for a curve fit based on Watts [1997, 1998], which describes a characteristic two-dimensional tsunami amplitude of a sliding ellipse down an inclined plane. This equation, as described in Watts and Borrero [2001], is: T b η2d ≈ so 0.0506 sin1.25 θ − 0.0328 sin 2.25 θ b d
(
)
1.25
(9.7)
where T is the thickness of the ellipse, d is the depth over the ellipse, b is the length of the ellipse along the inclined plane, and so is a characteristic “run” defined as ut2/a0. For rotational slumps, one additional parameter is needed, the radius of curvature R. Then: T b η2d ≈ soδφ0.39 0.1308 sin0.22 θ − b d
(
)
1.25
b R
0.63
(9.8)
Watts and Borrero (2001) report that this empirical formula is valid for T < 9.2L, L < R < 2L, d > 0.06L, θ < 30°, and ∆φ < 0.53. In the method of Watts, these equations describe a characteristic tsunami amplitude, not a particular wave height at any fixed point in space. To describe the wave shape explicitly, the value of η2d described above is used in expressions derived from alleged curve fits of laboratory and numerical data [Watts, 1997, 1998, 2000]. Values for the location of the maximum depression Zmin, the distance between the crest of the elevation wave and the trough of the depression wave ∆x, and the height of the maximum elevation wave Zmax and Zmin are given by Borrero (2002) as:
(
X min = 0.95 X g + 0.4338 so cos θ
© 2003 by CRC Press LLC
)
(9.9)
∆X = 0.5 t o gd = 0.5 λ
(9.10)
Z min = 2.1 η2d
(9.11)
0.2 d Z max = 0.64 η2d 0.8 + b sin θ
(9.12)
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These four equations describe the longitudinal wave shape. For the direction transverse to the slide motion, the width w of the landslide is used and a sech2 profile is fitted, and the following expression is derived for the three-dimensional waveform generated by a submarine landslide: η( x, y ) =
ω 3y sech 2 w + λ λ +w
2 2 ( X − Xmin ) X − Xmin − ∆X − 1.2 Zmin − Zmax λ λ + Z maxe −1.2 Z mine
(9.13)
Bohannon and Gardner [2002] use a modification of Murty’s formula. They suggest the energy contained in one cycle of a sinusoidal wave of height a and wavelength is given by ε = µρgwλa2, where again µ is the energy transfer coefficient of Murty. They assume the sliding mass to have volume equal to LTw, and derive the initial wave height for a mass dropping a distance ∆z as: H=
µ ( γ − 1) LT∆ z λ
(9.14)
In as yet unpublished work Synolakis and Uslu [2003] argue that Murty’s and Bohannon and Gardner’s formulations both need an arbitrary specification of the drop of the slide, and assume a value of the energy transfer coefficient. Generally, if one uses as the drop of the slide the entire height between the location of the slide and the nearest flat seafloor, the formulas predict unrealistic initial wave heights. Clearly, the energy transfer coefficient depends on the instantaneous depth. As the slide goes into deeper water, the transfer is less efficient. Based on analytical results, Synolakis and Uslu (2003) assume that the initial wave is generated within a horizontal motion of no longer than half the slide length. They propose that the energy transfer is similar to that of a wave maker for the first tens of seconds of motion, and 1/3 1/3 d g ( g a0 ) , where again that the initial wave is generated within a time t 0 = (1 / 4) λ − 1 ao = g sin θ λ + 1 They calculated the net energy in an isosceles N-wave with height H and sech-like transverse shape as ε=
3/ 2 2 3 πρgw (dH ) = (1 2) ρg LTw∆ z 5
with ∆ z = (1 2) aot 02 sinθ. Therefore, 1/3
L2T 2 ao H = 0.139 d g
2/9
(9.15)
Note that in the Synolakis and Uslu (2003) analysis, the height of the depression wave is equal to the height of the elevation wave, and does not rely on any assumptions on the transfer coeffiecient µ or any fitted empirical factors. The results computed using the four different landslide wave formulas are presented in Table 9.3. Given the present state of the art, it is clear that further progress will have to await validation of these formulas with numerical and laboratory experiments, currently under way, see Synolakis and Raichlen [2002].
© 2003 by CRC Press LLC
d = Ds (m) Munson–Nygren (New England) East Breaks Gulf of Mexico Seward (Alaska) Papua New Guinea Palos Verdes, CA
Skagway, Alaska
a b c d
45000 200000 70000 70000 150 150 3000 4500 5000 4000 4000 480 480 3000 610
Thickness h (m)
β (o)
Watts ηm
250 35 20 20 30 30 450 600 50 70 70 20 10 150 24
4 4 4 4 4 4 8.95 8.95 5 7.1 4.6 30 30 3 5.1
46 12 86 9 0.6 0.2 17 42 8 12 8 2 2 11 1.4
169 133 47 61 1.9 2.4 66 98 12 14 14 3 1.4 16 3
Murty b (µ = 1%) 174 35 68 11 5 3 64 143 13 27 27 2 0.7 87 6
Refers to Equation 9.14. Refers to Equation 9.2. Refers to Equation 9.15. Estimates derived using ∆z in the right-most column, which is calculated as in the Synolakis and Uslu formula (Equation 9.15).
© 2003 by CRC Press LLC
Synus with ∆z c (µ = 100%)
Modified Murty with ∆z d (µ = 1%)
Modified Bohannon with ∆z d (µ = 100%)
∆z
38 28 20 11 0.6 0.5 20 34 6 9 6 4 3 6 1.4
17 12 8 5 0.3 0.2 8 12 1.4 3 2.3 1.2 0.5 3 0.5
26 14 5 8 1.0 1.2 35 43 5 8 6 8 5 5 1.7
8 8 1 5 0 1 18 14 2 3 2 11 5 1 1
Earthquake Engineering Handbook
Santa Barbara, CA Kitimat, British Columbia
1900 1900 200 1350 80 160 1600 1250 350 350 350 200 100 300 119
L (m)
Bohannon & Gardner a (µ = 1%)
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TABLE 9.3
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9.5 Exact Solutions of the Shallow-Water (SW) Equations To calculate tsunami currents, forces, and run-up on coastal structures and inundation of coastlines one must calculate the evolution of the tsunami wave from the source region to its target. The evolution of waves on beaches is one of the classic problems of coastal engineering. Most practical engineering problems involve directional waveforms with frequency spectra ranging from short to extremely long waves, called infragravity waves, and a number of numerical methods now exist for evaluating their interaction with the coastline. In the last 10 years consensus is emerging that certain terminal effects, such as coastal flooding and inundation, are mainly affected by the infragravity waves. These waves can be described by a certain class of equations known as the shallow-water wave equations (SW), which are also the standard model for tsunamis or tidal waves. The SW equations are approximations of the Navier–Stokes equations (N-S), which describe most incompressible flows. While N-S equation solvers now exist, interest in the SW equations has been rekindled in the last two decades because comparisons with both large-scale laboratory data and field data have demonstrated a remarkable and surprising capability to model complex evolution phenomena, and in particular the maximum run-up. The maximum run-up is arguably the single most important parameter in the design of coastal structures such as seawalls and dikes and for evaluating the inundation potential of tsunamis. Exact solutions of the SW equations are useful in two respects: one for assessing directly the effects of different bathymetric and topographic features and of geometric parameters in the preliminary design of structures, and also for validating the complex numerical models used for final design, which often involve ad hoc assumptions. While elegant 2+1 solutions exist [Kanoglu and Synolakis, 1998], this section only presents certain common 1+1 propagation problems, such as sinusoidal, solitary, and N-waves. The waves evolve over constant depth and then over plane beaches and composite beaches. Even though most results derived for idealized waveforms often used tsunami engineering to describe the leading wave of a tsunami, the generalization to realistic spectral distributions is trivial with the closed-form integrals provided. It should be underscored again that exact solutions are very helpful in validating numerical solutions of the SW equations, and no modeling of any real tsunami should ever be undertaken with any code before comparing its predictions with the benchmark solutions described here. The SW equations describe the evolution of the water surface elevation and of the depth-averaged water particle velocity of waves with wavelengths large compared with the depth of propagation. The equations assume that the pressure distribution is hydrostatic everywhere, i.e., there is no variation with depth of any of the flow variables other than the hydrostatic pressure. One general form of the SW equations is: ht + (uh)x + (vh) y
=0
ut + uux + vu y + ghx = gdx
(9.16)
vt + uv x + vvy + ghy = gd y where h(x,y) is the undisturbed water depth, u and v are the depth-averaged water particle velocities in the cross-shore x and longshore y directions, respectively, η(x,y,t) is the wave amplitude measured with respect to the undisturbed water surface, and g is the acceleration of gravity. These equations are referred to as the 2+1 equations for the independent variables are the two space propagation directions x,y and the time t. The three equations (9.16) are coupled and nonlinear and they can be derived directly from the Navier–Stokes equations, if the viscous effects and vertical accelerations are neglected, or from a Hamiltonian approach [Liu, 1995]. A consequence of the approximations involved is that these equations are nondispersive, i.e., all waves propagate at a speed c = gh( x , y ) that only depends on the depth h(x,y). Note that the coriolis effect can be trivially added in Equation 9.16, when needed.
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t*= t*max
* t=0 H
y*
R
x* d
L
X*= X*1
INITIAL SHORELINE POSITION X*= 0
β X*= X*0
FIGURE 9.11 Definition sketch for shallow-water wave theory.
9.5.1 Basic Equations and Solutions of the 1+1 or Two-Dimensional Equations The so-called canonical problem of the SW equations is the calculation of a long wave climbing up a sloping beach coupled to a constant depth region. This topography consists of a plane sloping beach of angle β, as shown in Figure 9.11. The origin of the coordinate system is at the initial position of the shoreline and x˜ increases seaward. Dimensionless variables are introduced as follows: ˜ = ηd, u˜ = u gd , and t˜ = d g x˜ = xd, h˜0 = h0d, η
(9.17)
where η u h0 d
= = = =
the amplitude the depth-averaged horizontal velocity the undisturbed water depth the depth of the constant-depth region
The topography is described by h0(x) = x tan β when x ≤ cot β and h0(x) = 1 when x > cot β. Even though in engineering practice dimensionless variables are not preferred, here they have distinct advantages as everything scales simply with an offshore characteristic depth. Note that with this normalization (nondimensionalization) the dimensionless frequency ω is equal to the dimensionless wave number k. To see ˜ = ck ˜˜, and ω ˜ =ω ˜ g d , while k˜ = k d . For this reason, in analytical this, note that in dimensional terms, ω solutions ω and k are sometimes used interchangeably. In numerical solutions, dimensional variables are most often used. Consider a tsunami evolution problem described by the 1+1 nonlinear form of the SW (NSW) equations (9.16): ht + (uh)x
=0
ut + uux + ηx = 0
(9.18)
with h(x,t) = η(x,t) + h0(x). By examination, it is clear that nonlinear effects are small when the surface ηx and velocity gradients ux are small; however, the propagation distances in x over which these nonlinear effects manifest themselves to affect the results or how they are affected is not clear a priori.
9.5.2 Linear 1+1 Theory The NSW system (Equation 9.18) can be linearized by retaining the first-order terms only, resulting in the following set of equations. First, let h0(x,t) = h0(x). Then the NSW equations reduce to the linear set: © 2003 by CRC Press LLC
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ηt + (uh0 )x = 0 ut + ηx
=0
(9.19)
It is easy to eliminate u(x,t) and derive the following u(x,t)-independent equation in terms of η(x,t): ηtt − ( ηx h0 )x = 0
(9.20)
an equation referred to as the LSW equation. For constant depth h0(x,t) = d0, Equation 9.19 takes the form: ηtt − ηxx = 0
(9.21)
This is the classic one-dimensional wave equation, with solutions that can be written either as combinations of sine and cosine functions or of exponentials. The exponential functions are particularly useful as eigenfuctions in this problem, and thus one can write the entire solution for the amplitude η(x,t) = Ai e –iω(x+t) + Ar e iω(x–t) when h0(x) = 1. Ai is the amplitude of the incident wave and Ar is the amplitude of the reflected wave. Note the difference in sign in the arguments of the exponentials. The phase ω(x + t) indicates a wave moving towards the negative x direction, i.e., towards the beach, while the phase ω(x – t) indicates a wave moving in the positive x direction, i.e., offshore. (Recall that dimensionless variables are used, and since in this non-dimensionalization the dimensionless c = 1, and then ω = k.) When the depth is linearly and monotonically decreasing to zero, h0(x) = x tan β, i.e., for a sloping beach, Equation 9.20 becomes: ηtt − tan β ( xηx )x = 0
(9.22)
with the following finite-at-the-shoreline solution:
(
)
η( x , t ) = B (ω, β) J 0 2ω x cot β e − iωt −φ when h0 ( x ) = x tan β
(9.23)
J0 is the Bessel function of the first kind. Bessel functions are built into symbolic manipulator programs such as MATHEMATICA or MATLAB and exist in most FORTRAN subroutine libraries such as IMSL. Tables of Bessel functions can be found in Abramowitz and Stegun [1964]. B(ω,β) is referred to as the amplification factor, not to be confused with the arbitrary fudge factor sometimes used to match tsunami field data with numerical predictions from threshold-type models that interrupt the computation at the 10-m contour to avoid inundation calculations, the latter only euphemistically also called the amplification factor. Titov and Synolakis [1997] discuss these models and their limitations. These basic solutions can be combined to derive solutions specific to topographies that are combinations of a constant depth and a sloping beach. To this end, Keller and Keller (1964) presented a steadystate solution for the canonical model of Figure 9.11, simply by deriving interface conditions at x = cot β to match the inner and outer beach solutions, (x < cot β) and (x > cot β), respectively. The resulting equations allow simple algebraic solutions for the two unknowns, i.e., the amplitude of the reflected wave Ar and the shape of the transmitted wave ηt in terms of the incident wave height Ai. For an incident wave, Ai cos (kx − ωt), written for convenience as Ai cos[ω(x − t)] since ω = k, then the wave transmitted to the beach and the reflected wave moving offshore are given by: ηt ( x , t ) = 2 Ai B(ω, β) cos (ωx − ωt − 2 ω cot β + φ) © 2003 by CRC Press LLC
(9.24)
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where J (2ω cot β) φ (ω, β) = arctan 1 J 0 (2 ω cot β)
(9.25)
and J 02 (2 ω cot β) + J12 (2 ω cot β)
(9.26)
ηr ( x , t ) = Ai cos (ωx − ωt − 2 ω cot β + 2 φ)
(9.27)
B (ω, β) = 1 and
Note that the reflected tsunami amplitude is equal to the incident amplitude, but there is a phase shift φ that is both frequency ω and beach slope β dependent. Any combination of sinusoidal waves approaching the beach will reflect with a combined amplitude that will in general be different from the combined incident amplitude of the combination. This property cannot be underscored strongly enough, as many coastal engineers consider the reflected amplitude of spectra of long waves as equal to the incident amplitude, just relying on the monochromatic wave results. This is not true, and can lead to erroneous results when calculating run-up.
9.5.3 Exact Solutions of the LSW Boundary Value Problem Since the governing equation (9.20) is linear and homogeneous, then, as Stoker (1947) pointed out, standing wave solutions can be used to obtain traveling wave solutions by linear superposition. This is an important detail, often ignored; many have relied on numerical solutions to solve the problem above, which is easily solvable by old-fashioned integration. At least for the canonical problems and other simple topographies and for well-defined tsunami spectra, a numerical solution of the field equation is unnecessary. When a boundary condition for the wave amplitude η(x0,t) is specified, the solution follows directly from the Fourier transform of the equation. For example, when the incident wave at the constant depth region is known at some x = x1, and can be described by a Fourier integral of the form: η( x1 , t ) =
∫
∞
−∞
Φ (ω ) e − iωt
(9.28)
then the transmitted wave to the sloping beach is given by: η( x, t ) = 2
∫
∞
−∞
Φ (ω )
(
)
J 0 2ω x cot β e
− iω ( x0 +t )
J 0 (2ω cot β) − iJ1 (2 ω cot β)
dω
(9.29)
with the understanding that for all physical problems of engineering interest, one takes the real part of the integral. In other words, the real part is: η( x, t ) = 2
∫
∞
−∞
Φ (ω )
(
)
J 0 2ω x cot β cos (ωX 0 + ωt + φ) J (2 ω cot β) + J12 (2 ω cot β) 2 0
dω
(9.30)
This solution is only valid when x ≥ 0; when x < 0, Equation 9.20 does not reduce to Bessel’s equation. To obtain details of the wave motion in this case, one must solve the NSW (Equation 9.18). Notice that
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the integral (Equation 9.30) can be evaluated with standard numerical methods. However, the advantage of this form is that it allows calculation of the solution for many physically realistic tsunami waveforms simply by plugging in the Φ(ω) of the incoming wave, hopefully known at some offshore location x1.
9.5.4 Nonlinear 1+1 Theory To solve the nonlinear set (Equation 9.18) for the sloping beach case, h0(x) = x tan β, Carrier and Greenspan [1958] introduced the hodograph transformation, u = ψ σ , into Equation 9.18, and they σ derived the following equation:
(σψ )
σ σ
= σψ λλ
(9.31)
Notice the similarity with the linear form of the SW equation, (ηx h0)x = ηtt. Also, notice the conservation of difficulty. Instead of having to solve the coupled nonlinear set (Equation 9.18), one now has to solve a linear equation, but the transformation equations that relate the transformed variables with the physical variables: u=
ψσ σ
(9.32)
σ2 ψ λ u2 x = cotβ − + 4 2 16
(9.33)
ψ λ t = cotβ σ − σ 2
(9.34)
η=
ψ λ u2 − 4 2
(9.35)
are nonlinear, coupled, and implicit. Yet, a redeeming feature is that in the hodograph plane, i.e., in the (σ,λ) space the shoreline is always at σ = 0. This allows for direct analytical solutions and for much simpler numerical solutions, without the complications of the moving shoreline boundary. In general, it is quite difficult to specify initial or boundary data for the nonlinear problem in the physical space coordinates (x,t) without making restrictive assumptions; a boundary condition requires specification of the solution at (x0, ∀t), and an initial condition specification at (t0, ∀x), but, in practice, the wave approaching the beach is only known offshore for (x0 ≥ cot β, t < t0), where t0 is the time at which the wave reaches the x location X0. Even when boundary or initial conditions are available in the space, the process of deriving the equivalent conditions in the space is not trivial. These difficulties have restricted the use of this transformation to problems that can be reduced directly to those solved by Carrier and Greenspan [1958]. Synolakis [1986] revived the Carrier and Greenspan formalism by developing a method to specify a boundary condition including reflection. He used the solution of the equivalent linear problem, as given by the transform integral (Equation 9.30), at the seaward boundary of the beach, i.e., at x = x0 = cot β corresponding to σ = σ0 = 4. Then, Equation 9.35 implies that η(X 0 , t) = 1/4 ψλ (4, λ). Assuming that ψ(σ0, λ) → 0 as λ → ±∞, then Synolakis [1987] showed that the Carrier and Greenspan potential is given by: λ − iκx0 1−
2 Φ(κ ) J 0 (σ κx 0 2) e 16i dκ ψ ( σ, λ ) = − x 0 −∞ κ J 0 (2 κx 0 ) − iJ1 (2 κx 0 )
∫
© 2003 by CRC Press LLC
∞
(9.36)
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where the substitution κ = 2/x0 k˜ was used for simplification. Recall also that with the normalization used x0 = cot β. An astonishing feature of the NSW is that the predictions for the maximum run-up are identical to those of the LSW, when identical boundary conditions are specified at x = cot β. The maximum run-up according to LSW is the maximum value attained by the wave amplitude at the initial position of the shoreline, while the maximum run-up is given by the maximum value of the amplitude at the evolving shoreline η(xs,λ), where xs is the x coordinate of the shoreline tip and corresponds to σ = 0. Carrier [1966] and Synolakis [1987] have shown that the linear and nonlinear theory produce mathematically identical predictions. Carrier and Greenspan’s transformation of coordinates suggests a criterion for validity of the exact nonlinear theory solutions, based on the regularization of the Jacobian of the transformation from the (x, t) space to the (σ, λ) space. After some algebra, this criterion translates into:
(
J = c t σ2 − t λ
2
)
(9.37)
and for monochromatic waves: 2 Ai ω 2 cot 2 β ≤ 1
(9.38)
This criterion is often referred to as the breaking criterion and indicates whether solutions become multivalued, in analogy to physical wave breaking. As Meyer [1988] pointed out, it is only a criterion of validity of the Carrier and Greenspan transformation.
9.5.5 The Solitary Wave Solutions Solitary waves have long been used as a model for the leading wave of tsunamis. Solitary waves were first described by Scott-Russel [1833] as the great waves of translation, and consist of a single elevation wave. While capturing some of the basic physics of tsunamis, they do not model the physical manifestation of tsunamis in nature, which are invariably N-wave-like, with a leading depression wave followed by an elevation wave. A solitary wave centered offshore at x = x1 at t = 0 has the following surface profile: η( x ,0) = H sech 2 γ ( x − x1 )
(9.39)
where γ = 3H 4 . The function Φ(k) associated with this profile is derived in Synolakis [1986] and it is given by: 2 Φ (k ) = ω cosech (αω ) e iωx1 3
(9.40)
where α = π/(2γ). In the context of water-wave theory, the solitary wave (Equation 9.39) is an exact solution of the Korteweg–de Vries (KdV) equation, therefore a KdV solitary wave propagates over constant depth with no change in shape. The KdV theory is both dispersive and nonlinear, and solitary waves are the only waves with this unique property of unchanging shape. However, Equation 9.39 can be used as an initial condition for other wave theories, without, of course, the a priori expectation that the SW model will preserve the classic soliton properties, which include their ability to go through each other (interact in mathematical lingo) without any change in shape through nonlinear interactions. This having been said, since the LSW is nondispersive and linear, and hence all waves propagate over constant depth with no change in shape, in the range of wave steepness and amplitudes relevant for tsunamis, it is now well established that, at least for the 1+1 problem far from the shoreline, the LSW theory, which also preserves the wave shape for propagation over constant depth, is quite adequate [Liu et al., 1991], and useful when the engineering problem has simple geometry. © 2003 by CRC Press LLC
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9.9.6 The Evolution of Solitary Waves The derivation of the amplitude evolution for solitary waves is not as straightforward as often assumed. The wave is not of the form convenient for Green’s [1832] or Lamb’s [1932] style of evolution analysis, because the amplification factor (Equation 9.26) depends on the frequency ω, and there is a ω-dependent phase shift. It is therefore not obvious that linear superposition will produce a similar amplitude variation given this frequency-dependent phase shift. To describe the evolution of a solitary wave up a plane beach, Synolakis [1986, 1987] substituted Equation 9.40 into Equation 9.30 to obtain: η( x, t ) =
4 3
∫
∞
−∞
ω cosech (αω )
(
)
J 0 2 ω xx 0 e
− iω ( x0 − x1 +t )
J 0 (2 x 0ω ) − iJ1 (2x˜0ω )
dω
(9.41)
where, as earlier, α = π 3H . As per Synolakis [1988, 1989], this integral can be evaluated directly through contour integration. In the region where the wave evolves as it is climbing up a sloping beach, x is large, and Equation 9.41 becomes: η( x, t ) =
4π 2 x0 3α 2 x
1/ 4
∞
∑ (−1)
ne − ( π/α ) θ′n
n+1
(9.42)
n=1
θ′ = X 0 − X1 − t − 2 xx 0 The maximum of the power series is 1/4 ; therefore, the maximum local value of the wave amplitude ηmax is given explicitly by: ηmax x 0 = x H
1/ 4
1 = h0
1/ 4
(9.43)
This is an amplitude variation similar to Green’s law. The region over which Equation 9.43 applies is the region of gradual shoaling; the region of rapid shoaling is often identified with the Boussinesq result, i.e., ηmax ∼ h. The fact that both evolution laws may coexist was first identified by Shuto [1972]. Synolakis and Skjelbreia [1993] also present results that show that Green’s law-type evolution is valid over a wide range of slopes and for finite-amplitude waves, at least in the region of gradual shoaling. Figure 9.12 shows profiles of an H/d = 0.02 solitary wave climbing up a 1:19:85 beach and compares laboratory data with the analytical NSW predictions of Synolakis [1986, 1987].
9.5.7 The Maximum Run-Up of Solitary Waves The results of the previous section can now be readily applied to derive a result for the maximum runup of a solitary wave climbing up a sloping beach. Writing R(t) = η(0,t), i.e., R(t) is the free-surface elevation at the initial shoreline; in the LSW theory, the shoreline does not move beyond x = 0. The maximum value of R(t) is the maximum run-up R, arguably the most important parameter in the longwave run-up problem, and it is the maximum vertical excursion of the shoreline at the time instant of maximum run-up. According to Synolakis [1986], from Equation 9.41, it can be deduced that: R(t ) = 8 H
∞
∑ I (4γx n) + I (4γx n) n=1
© 2003 by CRC Press LLC
(−1)n+1ne −2γ ( x −x −t ) n 1
0
0
1
0
0
(9.44)
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0.04 (a) 0.02
η 0
0.02
2
0
2
4
6
8
10
12
14
16
18
20
0.04
η
(b) 0.02
0 0.02 2
0
2
4
6
8
10
12
14
16
18
20
0.04 (c) 0.02
η 0
0.02
2
0
2
4
6
8
10
12
14
16
18
20
0.04 (d) 0.02
η 0 0.02 2
0
2
4
6
8
10
12
14
16
18
20
χ 0.08 (e)
0.06
η
0.04 0.02 0 0.02
2
0
2
4
6
8
10
12
14
16
18
20
0.08 (f)
0.06
η
0.04 0.02 0 0.02
2
0
2
4
6
8
10
12
14
16
18
20
FIGURE 9.12 The climb of a H/d = 0.02 solitary wave up a 1:19.85 sloping beach. Normalized free surface profiles shown at different times.
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0.10 (g)
0.08 0.06
η
0.04 0.02 0 0.02
2
0
2
4
6
8
10
12
14
16
18
20
0.10 (h)
0.08 0.06
η
0.04 0.02 0 0.02
2
0
2
4
6
8
10
12
14
16
18
20
0.06 (i)
0.04
η
0.02 0 0.02 0.04
2
0
2
4
6
8
10
12
14
16
18
20
0.06 (k)
0.04
η
0.02 0 0.02 0.04
2
0
2
4
6
8
10
12
14
16
18
20
FIGURE 9.12 (CONTINUED)
The series can be simplified further by using the asymptotic form for large arguments of the modified Bessel functions. The resulting series is of the form
∑
∞
n=1
(−1)n+1n3/2χn
Its maximum value occurs at χ = 0.481 = e−0.732. This value defines the time tmax, when the wave reaches its maximum run-up. At tmax the maximum of the series smax = 0.15173. Defining as R the maximum value of R(t), and evaluating the term: 8 π 3 s max , then the following expression results for the maximum run-up: 5
R = 2.831 cotβ H 4
(9.45)
This result is formally correct when H >> 0.288 tan β — the assumption implied when using the asymptotic form of the Bessel functions. Equation 9.45 was first derived by Synolakis [1987] and has since been referred to as the run-up law. As will be apparent in later sections, this methodology to find the maximum run-up is quite powerful and it will allow calculation of the run-up of other waveforms such as N- or dipole waves, not to mention the run-up of waves evolving over piecewise linear bathymetries. © 2003 by CRC Press LLC
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THE MAXIMUM RUNUP OF SOLITARY WAVES CLIMBING UP A 19.85 BEACH
1 6 5 4 3
R/d
2
nonbreaking waves breaking waves asymptotic solution
0.1 6 5 4 3 2
0.01 0.001
2
3
4 5 6
0.01
2
3
4 5 6
0.1
2
3
4 5 6
1
H/d
FIGURE 9.13 Normalized solitary wave run-up on a 1:19.85 beach as a function of the normalized off-shore height.
Recent results suggest that the dependence of the run-up on the slope and on the offshore wave height in two-dimensional problems of idealized conditions is often quite similar to this one-dimensional power law. Maximum run-up data for breaking and nonbreaking solitary waves of different heights and propagating over a wide range of depths on a 1:20 laboratory beach are presented in Figure 9.13. The parameter H in the ordinate represents the maximum normalized wave height measured at a distance L from the toe of the beach, where L is one measure of the horizontal extent of the wave. Here L = (1/γ ) arccosh ( 1 / 0.05 ), where again γ = 3H / 4 . In essence this is the distance offshore from the toe of the beach to the crest of the wave, so that the wave height over the toe is 5% of the maximum wave height. Since Synolakis [1987], this measure is the standard referencing distance for specifying the height of a solitary wave at the toe of a sloping beach [Kobayashi et al., 1987; Briggs et al., 1993, 1994, 1995]. Thus, heights of longer solitary waves are defined from measurements further from the beach than those of shorter waves, assuring that all waves propagated through the same relative distance L between the measurement location and the toe of the beach. Figure 9.13 shows two distinct run-up regimes for breaking and nonbreaking waves. Breaking on the laboratory beach occurs first during the backwash when H > 0.044; breaking during run-up occurs when H > 0.055. The existence of these two different run-up regimes in single-wave run-up had never been observed before the original publication of Figure 9.13. One possible explanation is that most experimental investigations have dealt primarily with breaking solitary waves and, even when nonbreaking wave data were generated, they were grouped together with breaking wave data for the purpose of deriving empirical relationships. The asymptotic result (Equation 9.45) is valid for waves that do not break during run-up, suggesting that it is appropriate to use the qualifier “nonbreaking” for waves that do not break during run-up but may or may not break during rundown. The real usefulness of any asymptotic result is how well it identifies the scaling, i.e., if it can identify how the solution depends on the problem parameters; numerical solutions will invariably produce more accurate specific predictions, but they can rarely provide useful information about the problem scaling. To check if the run-up law (Equation 9.45) provides the correct scaling, Synolakis [1986, 1987] examined the classic laboratory data set of Hall and Watts [1953]. That study includes both breaking and nonbreaking wave data without identifying them as such, clearly because there was no realization of the differences. The empirical run-up relationships derived by Hall and Watts (1953) are not directly applicable when © 2003 by CRC Press LLC
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THE MAXIMUM RUNUP OF NONBREAKING WAVES CLIMBING DIFFERENT BEACHES
10
1
1:30 1:20 1:11.43 1:5.671 1:3.732 1:2.747 1:2.144 1:1 runup law
R/d
4
2
0.1 8 6 4
2
–0.01 2
0.01
4
6
8
2
4
6 8
0.1
2
4
6
1
8
10
5.4
2.831 cot β (H/d)
FIGURE 9.14 Normalized wave run-up on a single beach as a function of the run-up law.
determining the run-up of nonbreaking waves. To perform an a posteriori identification of those data, the breaking criterion H < 0.49 (cotβ)–10/9 was used; this criterion is discussed in the next section. Figure 9.14 presents all the nonbreaking solitary wave data from that and from two other studies. The asymptotic result does seem to model the existing laboratory data satisfactorily. Most importantly, it does seem to collapse all the nonbreaking Hall and Watts data into the same curve; not identifying the correct scaling led Hall and Watts to report their data in plots of R vs. H, individually for different beach slopes.
9.5.8 The Validity of the Solitary Wave Solutions Any change of variables is valid if the Jacobian remains regular; any solutions of the type shown in Equation 9.41 are valid for functions Φ(k) such that the Jacobian is never equal to zero, i.e., when Equation 9.37 is regular. The Jacobian becomes singular when the solution is multivalued, i.e., when the surface slope ∂η/∂x becomes infinite. In the (x,t) space, this point is often interpreted as the point of wave breaking. After elementary manipulations and asymptotic expansions as σ → 0, the Jacobian becomes: 1 J → cot 2 β 4 uλ − 2
(
© 2003 by CRC Press LLC
)
2
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The limiting H when uλ − 1 goes through zero is: 2 H < 0.8183 (cotβ)
−
10 9
(9.46)
This is a weaker restriction than that derived by Gjevik and Pedersen [1981], who determined that solitary-like waves do not break if H < 0.479(cotβ)–10/9. However, there are two basic differences between the two results. The Gjevik–Pedersen criterion suggests a limiting H for solitary wave breaking during the backwash. Equation 9.46 indicates when a wave first breaks during run-up. It is not surprising, therefore, that the former is a stronger criterion, since long waves that do not break during run-up may break during rundown. Also, the Gjevik–Pedersen result was derived by using the sinusoidal wave whose one cycle best fits the Boussinesq profile (Equation 9.39), while Equation 9.46 is based on the actual KdV profile. Equation 9.46 still remains — 10 years after it was derived — the only analytic criterion for determining the breaking of solitary waves on plane beaches. In terms of real tsunamis, Equation 9.46 provides an upper limit for checking whether the tsunami will break on any given beach or seawall. Tsunamis are N-waves that tend to be steeper than solitary waves and thus break at smaller heights.
9.5.9 The N-Wave Results Most tsunami eyewitness accounts suggest that tsunamis are N-wave-like, i.e., they are dipolar, which means they appear as a combination of a depression and an elevation wave, and frequently as a series of N-waves, sometimes known as double-N-waves [Tadepalli and Synolakis, 1994]. Up until recently, the solitary wave model was used exclusively to evaluate the run-up of tsunamis. The N-wave model was motivated by observations from earthquakes in Nicaragua (September 1, 1993); Flores, Indonesia (December 12, 1992); Okushiri, Japan (July 7, 1993); East Java, Indonesia (June 6, 1994); Kuril Islands, Russia (October 4, 1994); Mindoro, Philippines (November 14, 1994); Manzanillo, Mexico (October 9, 1995); Chimbote, Peru (March 3, 1996); Papua New Guinea (July 17, 1998); Vanuatu (November 26, 1999); and Caminade, Peru (June 20, 2001), all of which produced tsunami waves that caused nearby shorelines to first recede before advancing. The most specific description was during the October 9, 1995 Manzanillo, Mexico earthquake. One eyewitness saw the shoreline retreat beyond a rock outcrop, which was normally submerged in over 5 m depth and at a distance of about 400 m from the shoreline, suggesting a leading depression wave. A photograph of Manzanillo bay emptying, taken by the same eyewitness, is shown in Figure 9.15A. Figure 9.15B shows the 2 m (6.6 ft) tsunami climbing up the central square in La Manzanilla. Modeling tsunamis with solitary waves cannot possibly explain these observations, because a solitary wave is a leading elevation wave. Therefore, and to reflect the fact that tsunamigenic faulting in subduction zones is associated with both vertical uplift and subsidence of the sea bottom, Tadepalli and Synolakis [1994] conjectured that all tsunami waves at generation have an N-wave or dipole shape. Tadepalli and Synolakis [1994, 1996] proposed a general function as a unified model for near-shore, far-field, and landslide tsunamis, as follows:
[
]
η( x ,0) = ( x − x 2 ) ε Hsech 2 γ ( x − x1 )
(9.47)
Here γ = 3 H p0 4 , L = X1 – X2, p0 is a steepness parameter, and ε < 1 is a scaling parameter defining the crest amplitude, introduced only for reference to ensure that the wave height of the wave in Equation 9.47 is H. Note that X1 and X2 are analogous to Xmin and Xmin + ∆X in Figure 9.10. ε can be chosen to fit desired field-inferred surface profiles. H and the wavelength of the profile inferred from Equation 9.47 are vertical and horizontal measures of ground deformation, respectively. When a wave propagates with the trough first it is referred to as a leading depression N-wave or LDN. When the crest arrives first, it is a leading elevation wave or LEN. When the crest and trough heights are equal, these
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N-waves are referred to as isosceles; the latter can be described by Equation 9.47 by setting L = 0, or more directly with: η ( x , 0) =
[
]
[
]
3 3H sech 2 γ ( x − x1 ) tanh γ ( x − x1 ) 2
(9.48)
with γ=
3 2
3 H 4
The basic premise of the N-wave model is that the leading waves of tsunamis at generation are always N-wave-like. When tsunamis are generated near shore — typical distances from near-shore subduction zones to target coastline are of the order of 100 to 300 km — then the tsunami invariably manifests itself with a leading N-wave (refer to Figure 9.7). Even when generated far-field, the leading wave manifestation at the shoreline is always N-wave-like, because of the leading wave height and steepness, typically both of O(10–3) to O(10–4). Landslide tsunamis are always N-wave-like at generation, but are much steeper than corresponding tectonic tsunamis of the same height; hence, they disperse rapidly and are hardly detectable far-field. While the SW equations are useful when specifying initial conditions on the free surface, when considering the effects of an evolving seafloor, the derivation of the SW equations changes, and a forcing term appears on the right-hand side of the equations of conservation of momentum. The forced LSW takes the form: ηtt − ηxx = h0tt
(9.49)
Consider the following seafloor motion, which literally rips the seafloor by propagating an uplift and a subsidence in the positive x direction at constant speed equal to the speed of the generated tsunami waves:
[
]
h0 ( x , t ) = − (2ε H γ ) tanh γ ( x − t )
(9.50)
h0(x,t) is measured from horizontal data. Most submarine earthquakes are bipolar or multipolar, with regions of sudden uplift and subsidence. The ground deformation stops quickly after the rupture and does not propagate indefinitely as the definition of Equation 9.50 suggests. Also, in most cases of tectonic tsunamis, the seafloor motion is much faster than the speed of the tsunami waves; hence, the deformation can be considered instantaneous. Nonetheless, Equation 9.50 is sufficient to motivate the shape of the initial profile (Equation 9.47), which is one particular and exact solution of the nonhomogeneous problem (Equation 9.49). An earlier misconception in tsunami engineering had been that most tsunamis were solitary waves. This was based on a mathematical theory known as inverse scattering, which predicted that all waveforms with positive net volume would evolve into series of waves with at least one soliton at infinity. This had been a particularly useful theory because it allowed engineers in principle to ignore the evolution details, then difficult to calculate anyway. From estimates of the initial wave, engineers would calculate the height of the leading solitary wave that would involve far-field, taken to be infinity, and thus estimate the impact of the tsunami at distant shores. While mathematically sound, in the context of tsunami engineering the theory was abandoned when Tadepalli and Synolakis [1996] showed that LDN waves with initial heights of 0.0001 were practically unchanged after propagating over 2000 depths, suggesting that the wave propagation is essentially linear and nondispersive, i.e., no leading solitons emerge in the range of wave heights and steepness and propagation distances of geophysical interest. The fact that LDN waves are stable over transoceanic propagation distances explains why the waves that struck Hawaii after the Alaskan 1946 and Chilean 1960 events may have been LDN waves, as reported by eyewitnesses. © 2003 by CRC Press LLC
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FIGURE 9.15A Tenacatita Bay during the leading depression N-wave of the 1995 Manzanillo tsunami. Shown as Color Figure 9.15A.
9.5.10 Evolution and Run-Up of N-Waves Tadepalli and Synolakis [1996] show that N-waves evolve according to Green’s law (Equation 9.43), whether leading depression or leading elevation. Introducing φ = θ + 2X0, and performing tedious contour integrations, the maximum run-up of the generalized N-wave (Equation 9.47) is found, for LDN waves, to be: 5
R=4
1
3 πεQ ( L, γ ) cot β H 4 p04 .
(9.51)
This is valid for large 4x0γ, and for H < Hbr for LDN waves. This expression is valid for a wide range of L and it can be rewritten in terms of the maximum run-up of the Boussinesq solitary profile Rsol as 1 R = 3.3 εp 04 QRsol. It is reassuring that this expression is asymptotically close to the run-up law for solitary waves (Equation 9.45); in the asymptotic limit solitary waves profiles are almost identical to the N-waves (e.g., L = 30 and ε = 0.032). Another type of N-wave of this class exists, with leading elevation and depression waves of the same height and at a constant separation distance. Tadepalli and Synolakis [1996] refer to this wave as an isosceles N-wave with a surface profile given by Equation 9.48. This wave profile is an LDN and has a maximum wave amplitude H. Using contour integration to evaluate the maximum of RT = η(9,t), one can find that: 1
R Nwave = 3.86 (cot β) 2 H 5/ 4
(9.52)
Comparing the run-up of a solitary wave (Equation 9.45) with the run-up of an isosceles N-wave, RNwave = 1.364Rsol. Because of the symmetry of the profile, this is also the minimum rundown of an isosceles leading depression N-wave. Tadepalli and Synolakis [1996] show that the normalized maximum run-up of nonbreaking isosceles LEN is smaller than the run-up of isosceles LDN, and that both are higher than the run-up of a solitary wave with the same wave height; the latter is known as the N-wave effect. Comparing the time of maximum run-up for a solitary wave to that of an N-wave, one finds that:
(t max )solitary wave − (t max )N−wave = 0.γ201 = 0.232 H s
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(9.53)
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FIGURE 9.15B The 1995 Manzanillo tsunami advancing on la Manzanilla. By the time the bottom photo was taken, the wave had already advanced about 100 m. Eyewitnesses reported that the wave advanced as fast as people could run. Shown as Color Figure 9.15B.
Interestingly, a nonbreaking isosceles LEN reaches the shoreline earlier than a solitary wave of the same offshore wave height, and the time lag is larger for the smaller waves. The maximum run-up of LEN isosceles waves is given by: 1
5
R = 3.041 p04 cot β H 4
(9.54)
and the maximum run-up of isosceles LDN is given by: 1
5
R = 5.48 p04 cot β H 4 © 2003 by CRC Press LLC
(9.55)
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Nic. Profile N–wave
1 0.5
η
(m) 0 –0.5 1 0
20
40
60 x (km)
80
100
120
FIGURE 9.16 Comparison of the initial wave of the 1992 Nicaraguan profile as calculated using MOST and fitted with a leading depression N-wave.
The earlier stipulations regarding the interpretation of the Jacobian regularization condition not withstanding, Tadepalli and Synolakis [1996] also derived the breaking criteria for isosceles N-waves. The limiting values for the applicability of this theory for isosceles LENs and H– for isosceles LDNs are: H + = 0.1660 (cot β)
−10/9
, and H − = 0.1623 (cot β)
−10/9
(9.56)
Note that LDN and LEN waves break earlier than the equivalent solitary waves of the same offshore height. The two-dimensional character of the generation region limits the direct application of the N-wave and solitary wave models. However, N-wave theory does provide a conceptual framework for analysis and for explaining certain field observations qualitatively. In this regard, it is intriguing to perform simple calculations using the model to model the Nicaraguan topography. One segment of the Pacific coastline of Nicaragua is a 73-km (45-mi) long, almost uniform plane beach slope of cot β = 33.18, fronted by a 200-m (666-ft) deep continental shelf. This simplicity has allowed the use of two-dimensional numerical shoreline models coupled with three-dimensional offshore propagation models to calculate the run-up and inundation. Figure 9.16 shows a comparison between the numerically generated surface profile for the Nicaraguan tsunami with an N-wave, at the time when the wave reaches the toe of the beach, as calculated by Titov and Synolakis [1993]. The measured-average and numerically computed maximum run-up values were 6 ± 2 m (20 ± 6.6 ft), while the run-up laws predict 3.5 m (11.6 ft), a satisfactory result given the uncertainties in initial conditions and topographic resolution.
9.5.11 1+1 Wave Run-Up on Composite Beaches The methodology developed in the previous sections for wave run-up on a sloping beach can be generalized to study tsunami run-up over more generalized topography. A common practical problem is the determination of the run-up of a tsunami propagating over fairly complicated bathymetry before reaching the shoreline, such as a constant depth region fronting a steep continental shelf, which then slopes gently to the coastline, or a beach and then a seawall. Shaw [1974] studied several problems of this nature, while Goring [1978] studied wave transmission over a slope between two constant depth regions. Neu and Shaw [1987] examined the filtering action of a submerged seamount, a trench slope-shelf system and the effect of a continental slope-shelf system. All these studies used sinusoidal waves, and despite the physical interest of the problem, no analytical results appropriate for asymptotic analysis existed until Kanoglu [1996]. Most topographies of engineering interest can be approximated by piecewise linear segments allowing the use of LSW to determine approximate analytical results for the wave run-up of more complicated waveforms, in closed form. To motivate the problem, consider the continental slope and shelf topography studied by Neu and Shaw [1987], shown in Figure 9.17, which is also a definition sketch for this section.
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X 3
2
1
∇ h1 m1 h3
h2 m2 2
x1 x2
FIGURE 9.17 Definition sketch for wave run-up on a composite beach.
There are three regions, and two possible choices for the characteristic length scale for normalization of the variables. Here the depth h2 of the constant depth region three is used for non-dimensionalization. By inspection, the solution for the wave height η(x,t) in the three regions is given by:
(
)
η( x , t ) = BJ 0 2 ω h1 / m1 e − iωt when 0 < x < x1
(9.57)
2ω h2 2ω h2 − iωt η ( x , t ) = K1 J 0 when x1 < x < x 2 + K 2Y0 e m2 m2
(9.58)
and
{
η( x , t ) = η( x , t ) = Aie
− iωx / h3
+ Ar e
iωx / h3
}e
− iωt
when x 2 < x
(9.59)
Only the incident wave height Ai is known a priori. To determine B, K1, K2 , and Ar, matching conditions for the amplitude and surface slope at the two interface points x1 and x2 are used, and this results in a system of four equations in four unknowns, written in matrix form as: 2ω h 1 J0 m2 2 ω h1 J1 m2 J 2 ω h2 0 m2 2ω h 2 J1 m 2
2 ω h1 Y0 m2 2 ω h1 Y1 m2 2 ω h2 Y0 m2 2 ω h2 Y1 m2
0
0 iωx2
−e
h3
iωx2
ie
h3
2ω h1 J0 m1 2ω h1 J1 m1 0 0
0 K1 0 K iωx2 2 = − A Ar e h3 i − iωx2 h3 B e
(9.60)
In a similar fashion one can build equivalent matrices for any reasonable piecewise linear topography. © 2003 by CRC Press LLC
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In most engineering applications, the problem would be considered solved and numerical matrix inversion would provide solutions for the four unknowns. However, with numerical solutions it is not simple to visualize the parameter dependence of R on the individual slopes m1 and m2 and on the transition depth h1. Alternatively, the problem can be solved in analogy to geometric optics. When solving for the magnification of an optical system, individual refracting surfaces are represented by 2 × 2 matrices. Gerrard and Bunch [1987] developed a methodology for explicit evaluation of the focal length of an optical system with n refractive surfaces. Kanoglu [1996] and Kanoglu and Synolakis [1998] developed a formulation to determine the amplification of a tsunami evolving piecewise linear topography by representing the wave evolution over each segment by 2 × 2 matrices, as follows. Kanoglu (1996) associated each constant depth region of depth hr with the matrix: − iω x p hr Dpr = e iω x p − hr ie
iω x p h −ie r iω x p hr
e
(9.61)
He associated each linearly varying depth region with positive slope mr with the matrix:
( (
J 2ω h / m p r 0 S pr+ = J 2ω h / m p r 1
) )
( (
) )
Y0 2 ω hp / mr Y1 2 ω hp / mr
(9.62)
and each linearly varying depth region with negative slope (negative mr) with:
( (
) )
J 2ω h / | m | p r 0 S pr− = − J 2 ω h / | m | p r 1
( (
) )
Y0 2 ω hp / | mr | −Y1 2 ω hp / | mr |
(9.63)
The superscripts in the expressions for the Spr matrices are used to emphasize the differences between positively and negatively sloping regions; in the nomenclature henceforth they will be dropped, with the understanding that either Equation 9.62 or Equation 9.63 will be used, depending on the sign of mr . Notice also, that in Equations 9.61, 9.62, and 9.63 the first subscript p identifies the transition point and the second subscript r identifies region, i.e., if a region has two transition points, there are two associated 2 × 2 matrices. In any piecewise linear topography the shoreward and seaward matrices are special and are henceforth denoted by P11 and R. If the topographic feature of interest has n linear segments, then there are another (n − 2) intermediate segments. The associated matrices are either Spr or Dpr . For brevity they are both denoted as Qpr . If Kn = [Ai , Ar] is the incident wave vector, the transmitted wave vector towards the shore is K1 = [B,0] and it is given by: n− 2 P11K1 = Q j ( j +1) Q(−j1+1) ( j +1) R(n−1) n K n j =1
∏
(9.64)
Here again R(n–1)n is the most seaward matrix. This product allows direct and explicit calculation of the transmitted wave amplitude B and of the reflected wave amplitude Ar , because it only involves the inversion of a product of 2 × 2 matrices, which ultimately is a 2 × 2 matrix. Each topographic segment adds one Q matrix and one inverse matrix to the product, except in the left and the right boundaries, where the only unknowns are the amplification factor and the reflected wave height. © 2003 by CRC Press LLC
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9.5.12 Example of Calculation of the Run-Up of Solitary Waves on a Continental Shelf with a Beach Noting again that the governing equation is linear and homogeneous, solutions can be superposed, once the amplification factor B closest to the initial shoreline is known. For the topography of Figure 9.17, the amplification factor is determined from Equation 9.64, which in this case reduces to: B (ω, h1 , h2 , m1 , m2 ) = −
− 2m2 1 e πω h1 ϕ (ω ) + iχ (ω )
iω x2 h2
(9.65)
where ϕ(ω, h1, h2, m1, m2) + iχ(ω, h1, h2, m1, m2) is a complex function defined by: 2 ω h1 J0 m1 ϕ c (ω ) + iχ c (ω ) = 2 ω h1 J1 m1
+
2 ω h1 Y0 m2 2 ω h1 Y1 m2
2ω h 2 ω h2 2 J 0 − iJ 1 m2 m 2
2 ω h1 J0 m1
2 ω h1 J0 m2
2 ω h1 J1 m1
2 ω h1 J1 m2
(9.66)
2ω h 2 ω h2 2 Y 0 − iY1 m2 m2
Using the tools developed earlier, it is easy to find the amplitude at the shoreline for a solitary wave evolving over the topography of Figure 9.17, as: R (t ) = η(0, t ) = −
4 m2 3 π h1
cosech (αω ) iω ( xs − x2 −t ) e dω −∞ ϕ (ω ) + iχ (ω )
∫
∞
(9.67)
Conjecturing that ϕ + iχ does not have any poles in the upper half plane, and calculating the Laurent expansion, and again using asymptotic expansions, Kanoglu and Synolakis [1998] found that:
R (t ) =
3π
8
m1
∞
H
5/ 4
∑ (−1)
n+1 3/ 2
n e
−
h1 nπ − (1/m2 ) θ+ 2 α m1
(
h1 −1
)
(9.68)
n=1
Its maximum run-up is given by: R = 2.831 m1 H 5/ 4
(9.69)
Realizing that m1 = cot β, observe that it is identical to the run-up of solitary waves on single plane beaches (Equation 9.45). This implies that, at least for those solitary waves for which the asymptotic analysis is appropriate, the run-up depends only on the slope of the shoreward segment, and the effect of the seaward sloping segment is negligible. Similar results can be found for the run-up for any reasonable combination of n positively sloping segments. To better understand this result, refer to Figure 9.18, which shows the variation of the maximum run-up with the depth at the transition point between the two segments of the composite beach of Figure 9.17; the shoreward slope is kept constant and the seaward beach varies from 1:10 to 1:100. The figure also shows predictions from the numerical solution of the NSW of Titov and Synolakis (1995). © 2003 by CRC Press LLC
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m 1 = 1/10, Analytical solution m = 2 Analytical solution m = 2
1/1, 1/1,
1/20, 1/100
1/50,
1/100
0.100
(a) 0.080
R 0.060
H = 0.01
0.040 0.020 0.0
0.2
0.4
0.6
0.8
0.005
1.0
(b)
0.004
R H = 0.001
0.003
0.002 0.0
0.2
0.4
0.6
0.8
1.0
h1
FIGURE 9.18 Solitary wave run-up on a composite beach; comparison of analytical and numerical predictions.
Observe that, if the transition point is at one and a half offshore depths or deeper, i.e., h1 > 0.5, then the shoreward segment dominates the run-up, and the effect of the seaward segment is negligible, as predicted by Equation 9.69. As h1 → 0, the shoreward segment vanishes and the seaward segment dominates. Notice also that, as expected, as H increases the effect of the second region on maximum run-up also increases; smaller waves, being longer, do not feel the transition as much as shorter but higher waves. More extensive results can be found in Kanoglu (1996) for shoreward slopes of 1:10 to 1:20.
9.5.13 Example of Calculation of the Run-Up of Solitary Waves on a Composite Beach Fronted by a Seawall The results of the previous sections suggest that the run-up of most nonbreaking waves is dominated by the slope closest to the shoreline. Consider here another example to check this assertion with a more complex topography, consisting of three segments and a vertical wall. Laboratory data exist for this topography from a U.S. Army Corps of Engineers, Coastal Engineering Research Center experiment of wave run-up on a physical model of Revere Beach, Massachusetts. This beach profile and the laboratory are discussed in greater detail in Yeh et al. [1996]. The profile of the model is shown in Figure 9.19. It consists of three piecewise linear slopes of slopes 1:53, 1:150, and 1:13 from seaward to shoreward. At the shoreline there is a vertical wall. In the laboratory experiments to evaluate the overtopping of the seawall, the wavemaker was located at 23.22 m and tests were done at two depths, 18.6 and 21.3 cm. Proceeding as earlier, Equation 9.64 can be rewritten directly as: −1 −1 P11K = Q12Q22 Q23Q33 D34 A4
© 2003 by CRC Press LLC
(9.70)
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23.2m 15m
1 2 3
4.4m
4
5
2.9m
6
7
0.9m
8
9
10
WAVE GAGES
d=21.8 cm
d=18.8 cm 1/13 1/150 VERTICAL WALL
1/53 WAVE MAKER
FIGURE 9.19 Drawing of the laboratory set-up for the Revere Beach experiments showing locations of measurements. The seawall is on the right.
and now the amplification factor B can be evaluated easily. The amplitude at the shoreline is: R (t ) = η(0, t ) = − ( 4 3)
m1 π h0
cosech (αω ) e ( s ϕ (ω ) + iχ (ω ) −∞
∫
iω x − x3 −t )
∞
dω
(9.71)
Again, ϕ(ω) + iχ(ω) is a complicated but determinable expression from Equation 9.70 in terms of Bessel functions of zero and first order, quite easily using tools such as MATHEMATICA or MATLAB. Kanoglu and Synolakis [1998] conjectured again that ϕ(z) + iχ(z) is an entire function in the upper half plane, and derived the Laurent expansion and its asymptotic form as: R(t ) = 8 h0−1/4 H
∞
∑ (−1)
n+1
nχ n
(9.72)
n=1
where
χ=e
−
1 π x − x − 2t α s 3 m1
(
)
h0 − h1 +
1 m2
(
) m11 (
h1 − h2 +
h2 −1
)
This is a power series of the form ∑(–1)n+1 nχn and its maximum is equal to 1/4 . Therefore, the maximum run-up for solitary waves propagating up Revere Beach is given by the run-up law: R = 2 h0−1/ 4 H
(9.73)
The run-up law above suggests that the maximum run-up only depends on the depth at the seawall fronting the beach, and it does not depend on any of the three slopes in front of the seawall. The result can be generalized for N-waves, by substituting the correct transform Φ(ω) in Equation 9.72. Figure 9.20 presents comparisons of the predictions of Equation 9.73 with the laboratory experiments of Briggs et al. [1993], where appropriate, i.e., up to the limiting H where the waves broke in their physical manifestation. The run-up law (Equation 9.73) predicts the nonbreaking data surprisingly well. Note that no Jacobian regularization conditions as yet exist for wave evolution on composite beaches, and the Kanoglu–Synolakis theory should be applied with caution. © 2003 by CRC Press LLC
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1
Theory, R = 2 h –1/4 H w
0.1
R
0.01
0.01
d = 18.8 cm
Experiment Theory
d = 21.8 cm
Experiment Theory
0.1
1
H FIGURE 9.20 Wave run-up on Revere Beach. Comparison of analytical predictions and laboratory measurements.
9.6 Numerical Solutions for Calculating Tsunami Inundation Although analytical solutions are useful for first-order analysis and for determining upper limits for tsunami inundation for preliminary design, in most applications a numerical solution of the 2+1 evolution of the tsunami from generation to the shoreline is undertaken. Depending on the sophistication of the model, numerical solutions are capable of predicting coastal inundation, even for extreme events such as the 1993 Hokkaido-Nansei-Oki tsunami [Titov and Synolakis, 1997, 1998]. Although the existing numerical solutions cannot resolve the specific pattern of the breaking front, in those cases when tsunamis break, high-end numerical models adequately predict the overall wave behavior and give reliable predictions of run-up values over a wide range of wave parameters. Numerical solutions for wave inundation are notoriously unstable, as shoreline motions involve small water depths and large velocities. Whereas several models had been developed and published in the 1960s and 1970s attempting to calculate the shoreline one-plus-one or two-plus-one evolution of tsunamis generated by submarine earthquakes or mass movements, none was validated either by comparison with laboratory experiments or with field data. As early as 1990, in a U.S. National Science Foundation workshop in Catalina, California, the problem of understanding the 2+1 near-shore evolution and associated shoreline motions was identified as a priority, and the development of comprehensive largescale laboratory data described as essential for further progress [Liu et al., 1991]. To this end, a series of laboratory tests were undertaken by Briggs et al. [1993, 1994, 1995] in a large wave basin at the U.S. Army Corps of Engineers Coastal Engineering Research Center (CERC) in Vicksburg, Mississippi. The CERC water tank is 25 m wide, 30 m (100 ft) long, and 60 cm (2 ft) deep. Waves were realistically created in the tank by a horizontal wave generator with 60 different paddles, each 45 cm (0.5 ft) wide and moving independently. The tank and one of the models are shown in Figures 9.21A and 9.21B. These experiments provided run-up observations for validating numerical models and supplemented comparisons with analytical results, as per the previous section. By serendipity, several large tsunamis have occurred since 1992, in Nicaragua, Indonesia, Japan, Russia, Mexico, Peru, and Papua
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FIGURE 9.21A The 30-m wave basin at the Coastal Engineering Research Center, showing the directional spectrum generator and the conical island used in the experiments by Briggs et al. [1993, 1994].
FIGURE 9.21B Top view of a solitary wave attacking the conical island in the Coastal Engineering Research Center basin during the 1994 experiments. The wave is approaching from the top. Note the enhanced run-up on the back of the island, known as the Babi Island effect.
New Guinea, which provided additional field data for model validation. The two 1992 tsunamis identified serious deficiencies in the older modeling efforts, which used models that do not calculate run-up motions, as their predictions involved errors of factors of five to ten, when compared with field run-up observations. These older models would stop the wave evolution calculations at some threshold offshore depth, sometimes at the initial shoreline or even at the 5-m (16.7-ft) or 10-m (33.3-ft) depth contour to avoid the shoreline evolution computation. In essence, the early models treated the ocean as if it had vertical walls near the coastline, and predicted the height of the tsunamis as they hit these seawalls. Even casual observation of wind waves hitting a seawall or evolving on a natural beach would point out that this is unsatisfactory, as wave height can change dramatically when it comes ashore. The deficiencies of threshold models triggered rapid development of 2+1 numerical inundation models, i.e., models that include shoreline motions in the tsunami evolution calculations. Comparisons between field data and model predictions are referred to as model validation or verification and are a crucial part of any scientific modeling effort. Without comparison to real-world data there is no basis to accept the predictive capability of any model. To underline this process, the National Science Foundation of the United States organized a follow-up workshop to the 1990 Catalina workshop in Friday Harbor in 1995, as described in Yeh et al. [1996]. The three organizers provided modelers with well-described © 2003 by CRC Press LLC
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initial conditions for four benchmark problems, one of which was the seafloor deformation of the Hokkaido-Nansei-Oki tsunami of 1993. The modelers prepared predictions of the associated water motions and of the inundation computations and presented their results in the workshop. It was then that the actual laboratory or field data were shown to assess the relative effectiveness of different numerical models. A conspicuous characteristic of almost all models presented was their gradual evolution from threshold 1+1 propagation models to 1+1 inundation models, to threshold 2+1 models to 2+1 inundation models. This evolution, often extending over a 10-year period, allowed modelers to identify modeling nuances and artifacts and the community at large to understand what is important to first order. The Hokkaido-Nansei-Oki tsunami of 1993 that struck Okushiri island with extreme run-up heights of 30 m (100 ft) and currents of the order of 10 to18 m/sec (33.3 to 60 fps) was a disaster, but provided fortuitous high quality data. High-resolution seafloor bathymetry existed before the event and when coupled with bathymetric surveys following the event allowed meaningful identification of the seafloor deformation. The only two models that were proven capable of modeling the entire range of available data from the laboratory scale to the Hokkaido-Nansei-Oki event were those by Imamura et al. [1996], TUNAMI-N2, and Titov and Synolakis [1996, 1998], VTCS-3. Both are copyrighted by the developers. The latter has become the standard model of the National Oceanic and Atmospheric Administration for coastal inundation and is now known as MOST (Method of Splitting Tsunami). One conclusion of the successes of these modeling efforts has been that — at least for this event — the details of the timing of seafloor deformation may not be as important as some believed, and that what ultimately matters is the differences between initial and final water depth. Since publication of the successful modeling of the Hokkaido-Nansei-Oki tsunami, there is renewed focus on better understanding of the initial conditions [Titov and Synolakis, 1997]. Both TUNAMI-N2 and MOST use finite-difference (FD) algorithms to solve the NSW equation set (Equation 9.16). Whereas solution methods for coupled hyperbolic partial differential equations (PDEs) exist in some computational packages of MATLAB and MATHEMATICA, the substantial and nonstandard difficulty is with the prediction of tsunami inundation in what is referred to as the run-up computation. The tsunami wave evolution over dry land involves the interaction of three phases of matter [Liu et al., 1991]. In FD type numerical solutions, this involves introducing additional grid points as the tsunami front evolves on the beach and runs up, the removal of these grid points as the wave runs down, and the repetition of this cycle as the next tsunami wave in the tsunami train approaches the beach. Whereas it has been argued that finite-element (FE) algorithms are more naturally suited for this type of problem, in practice, FE methods have been proven cumbersome and less flexible than FD solutions. TUNAMI-N2 and MOST differ in two ways. TUNAMI-N2 uses a fixed computational grid, involves a friction factor and, although it lets the wave advance past the initial shoreline, its maximum run-up prediction is based on the maximum wave height at the shoreline. MOST uses a variable computational grid, no friction factors, and its run-up prediction is based on the elevation of the last wet grid point the wave encounters as it climbs up on the beach. The methodology of MOST will be described briefly here. MOST does not include bottom friction terms in the model. Although the bottom friction does affect the dynamic of the run-up process in the surf zone, there are several reasons for not using the friction terms in an FD model. The commonly used bottom friction model for SW approximation is the Chésy formula with different types of roughness coefficient [Packwood and Peregrine, 1981; Kobayashi and Greenwald, 1987; Liu et al., 1995]. This formula is an empirical relationship developed from steady channel flows and, possibly, it does not reflect the dynamic of the rapid run-up process adequately. Also, there is no consensus on a proper form of the roughness coefficient in the formula. A number of studies have been devoted to the designing of a proper roughness coefficient instead of the commonly used Manning’s coefficient [Fujima and Shuto, 1989]. However, several studies suggest that an unsteady flow during run-up is not very sensitive to changes in the roughness coefficient value [Packwood and Peregrine, 1981; Kobayashi and Greenwald, 1987; Zelt, 1991]. Any numerical algorithm of moving boundary for the wave run-up induces a numerical friction near the tip of the climbing wave, and this complicates the situation with the proper choice of the friction coefficient for a numerical model. The roughness coefficient at the present stage of the science appears to be a fairly arbitrary parameter, adjusted to fit any given © 2003 by CRC Press LLC
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experimental data set, but is very difficult to be determined a priori. In principle, this reduces dramatically the prediction ability of a numerical model. In practice, the choice of coefficient in TUNAMI-N2 has been well calibrated through its repeated use for prediction of past tsunami events, but then again its friction factor is applicable only to the numerical procedure in TUNAMI-N2. Since in any engineering problem the interest is the evaluation of the maximum run-up level for design purposes, and friction can only reduce it, it is recommended that if a computation is otherwise stable, no friction factor be used. A variety of boundary and initial conditions can be specified for these equations. To solve the problem of tsunami generation due to bottom displacement, one specifies the following initial conditions: d ( x , y , t ) = d0 ( x , y , t ), t ≤ t 0 , and d ( x , y , t ) = d0 ( x , y , t ), t > t 0
(9.74)
Usually, t0 is assumed to be small, so that the seafloor movement is an almost instantaneous vertical displacement, which can be directly translated into an initial condition, so that η(x,y,t = 0) = d(x,y,t0). This is an excellent approximation for tectonic tsunamis where the rupture velocity is substantially larger than the local tsunami speed over the deformation area. For landslide-generated tsunamis when the slide evolves at speeds of the same order as the local water-wave velocity, then one must solve the forced equivalent of the NSW (Equation 9.16), as for example in Equation 9.49. To avoid the additional complication of introducing an evolving seafloor in TUNAMI-N2 or MOST, the standard practice is to obtain an initial condition for the landslide tsunami from some other approximate model and to transfer this initial condition to the two codes.
9.6.1 The Splitting Technique For arbitrary topography and bottom displacements MOST uses an FD algorithm based on the splitting method, also known as the method of fractional steps of Yanenko [1971]. This method reduces the numerical solution of the two-dimensional (2+1) problem into consecutive solution of two locally onedimensional problems. This is achieved by splitting the governing system of Equation 9.16 into a pair of 1+1 systems, each containing only one space variable, as follows: ht + (uh)x = 0 ut + uuz + ghx = gdx vt + uv x = 0
ht + (vh) = 0 y vt + vv y + ghy = gd y ut + vu y = 0
(9.75)
The two systems of Equation 9.75 can then be solved sequentially at each time step using standard numerical methods. MOST uses an explicit FD scheme, although most often implicit numerical schemes are preferred when using the splitting method with elliptic and parabolic equations. Splitting gives a substantial reduction of the number of operations compared with implicit schemes applied directly to two-dimensional elliptic or parabolic equations. The NSW equations (Equation 9.16) form a hyperbolic quasi-linear system and explicit methods have proven most efficient. The main advantage is the potential of solving the characteristic form of the two 1+1 equations, which helps establish a well-posed boundary value problem (BVP) for the numerical method. The characteristic form of equations also allows for an efficient FD realization [Titov and Synolakis, 1995]. Each of the systems in Equation 9.75 is a hyperbolic quasi-linear system with all real and different eigenvalues and can be written in characteristic form as follows: pt + λ1 px = gdx qt + λ 2qx = gdx v ′ + λ 3v ′ = 0
© 2003 by CRC Press LLC
(9.76)
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where p = u + 2 gh q = u − 2 gh
(9.77)
v′ = v are the Riemann invariants of this system, and λ1 = u + gh λ 2 = u − gh
(9.78)
λ3 = u are the eigenvalues. We use an explicit FD method to solve Equation 9.75 along the x and y coordinates sequentially, every time step. The first two equations in Equation 9.75 constitute a one-dimensional NSW problem. At every time step, MOST solves a one-dimensional NSW propagation problem along each coordinate plus one more equation describing a nonlinear momentum flux in the direction normal to this coordinate. In summary, the overall procedure utilizing the splitting technique for the system (Equation 9.75) transformed into Equation 9.76. Suppose values un, v´n, hn for time instant t are given. The algorithm of computing values un+1, v´n+1, hn+1 for time t + dt consists of the following steps: 1. The primitive variables un, vn, hn are converted into the Riemann invariants pn, qn, v´n using the transformation in Equation 9.76. 2. pn+1/2, qn+1/2, v´n+1/2 are computed by solving numerically Equation 9.77 along the x coordinate. 3. pn+1/2, qn+1/2, v´n+1/2 are than converted back to the primitive variables un+1/2, vn+1/2, hn+1/2. 4. Steps 1 through 3 above are repeated for un+1/2, v´n+1/2, hn+1/2 along the y coordinate to compute the values un+1, v´n+1, hn+1. Note that Riemann invariants are different here, because u and v interchange with each other in Equation 9.78.
9.6.2 Boundary Conditions for Fixed Boundaries The splitting method requires solving the two 1+1 systems of Equation 9.75 every time step. Boundary conditions are established for each 1+1 problem using characteristic analysis, as follows. Equation 9.76 is a hyperbolic quasi-linear system with real and distinct eigenvalues (Equation 9.78), with three families of characteristic lines with slopes λ1, λ2, and λ3. λ1 > 0, λ2 < 0 everywhere the Froude number (u / gd ) is less than 1, while λ3 can be either positive or negative. A well-posed boundary value problem requires the number of boundary conditions for Riemann invariants to be equal to the number of outgoing characteristic lines for this boundary. Therefore, one or two boundary conditions are necessary on each boundary depending on the sign of λ3 on that boundary. The boundary conditions for a totally reflective left boundary are: p = −q v′ = 0
(9.79)
while the reflective conditions for the right boundary are: q = −p v′ = 0
© 2003 by CRC Press LLC
(9.80)
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Gustafsson and Kreiss [1979] used this characteristic approach to develop absorbing boundary conditions for time-dependent problems. A totally absorbing boundary allows waves to go through (absorb) but it does not allow any waves to reflect back into the computation region. In characteristic terms, the invariants on outgoing characteristics do not carry any disturbances back into the computational area. For the right boundary, the requirement of no wave motion on that characteristic implies that u = 0, v = 0, η = 0, therefore q = –2 gd , v′ = 0. In addition, MOST assumes that the water depth is constant outside the area of computation and equal to the depth at the right boundary dn, hence q is constant on that boundary. Therefore, appropriate conditions are: q = −2 gdn v′ = 0
(9.81)
while for the left boundary: p = 2 gdn v′ = 0
(9.82)
The run-up computations require a moving boundary condition to be used for the tip of the climbing tsunami wave. Titov and Synolakis [1995] developed a moving boundary condition for 1+1 NSW equations. The same basic approach can be used for the run-up boundary condition and will be discussed briefly in the next section.
9.6.3 The Finite-Difference Scheme We use the following explicit finite-difference scheme for each equation in the system shown in Equation 9.78. n ∆ n n ∆t pin 1 n n + λ ( ∆ + ∆ x ) pi − 2∆tλ i ∆ x x λ i pi = ∆t ∆xi −1 + ∆xi i − x ∆xi ∆ g ( ∆ − x + ∆ x ) din − 2∆tλni ∆ x x din ∆xi −1 + ∆xi ∆ xi
(9.83)
where fi n = f ( x i , t n ) ∆t fin = f ( xi , t n + ∆t ) − f ( xi , t n ) ∆ x f i n = f ( x i + ∆x , t n ) − f ( x i , t n ) ∆ − x fin = f ( xi , t n ) − f ( xi + ∆x , t n ) Note that this scheme allows for the spatial grid with a variable space step ∆xi . The condition of stability for the scheme is the Courant–Friedrichs–Lewy (CFL) criterion: ∆t ≤ min i
which always has to be satisfied. © 2003 by CRC Press LLC
∆x i ui + ghi
(9.84)
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FIGURE 9.22 Definition diagram for shoreline calculations.
The FD scheme (Equation 9.83) is used for the computation of the unknown variables p, q, and v´ in the interior grid points of the computational area. However, these equations cannot be used to compute boundary values. At those points, the boundary conditions determine only two among the three invariants. The other value on the boundary (the value of the Riemann invariant on the incoming characteristic) is computed by MOST by the upwind FD scheme: pbn+1 = pbn −
[ (
∆t n λ ∆ pn − g ∆ − x dbn ∆x b 1 − x b
) (
)]
(9.85)
where pb, db are the values of the variables on the boundary. During shoaling the wavelength of the tsunami becomes shorter. Therefore, calculations using a uniform grid throughout the computational domain suffer either loss of accuracy in the near-shore field or loss of efficiency through the use of a very fine grid. Neither approach produces consistent resolution. MOST uses a variable in each direction grid to keep consistent resolution [Titov and Synolakis, 1995], as in cylindrical two-dimensional domains, where the depth is changing predominantly along one direction. To model tsunami wave propagation in areas with complex bottom profiles containing complicated shoreline patterns and islands, an additional nested grid is often needed for the near-shore computations, when computer resources do not allow for large grids. The nested grid has finer grid spacing for an efficient computation of the shorter waves in the near-shore area.
9.6.4 The Moving Boundary Condition Calculation of the evolution on the dry bed involves moving boundary conditions. The Froude number may be greater than one near the shoreline point, implying that all characteristic families have the same inclination in this region. Hence, it is impossible to use the direct relationships between the Riemann invariants near the shoreline. MOST uses approximations of the boundary values from previous space nodes, as shown in the definition sketch in Figure 9.22. The shoreline algorithm uses a time-dependent space step ∆x(t) of the last node of the computational area. The objective is to maintain the shoreline boundary point, represented consecutively by (A), (B), or (C) on Figure 9.22 on the surface of the beach during the computation. The length of the last space step ∆x(t) is adjusted every time step, so that the shoreline point (A) is at the intersection of the beach with © 2003 by CRC Press LLC
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3000
amplitude (cm)
2500 2000 1500 1000 500 0 2000
4000
6000
8000
distance from north to south (m)
FIGURE 9.23 Comparison of MOST predictions with field measurements during the 1993 Hokkaido-Nansei-Oki tsunami. The heavy line, solid circles, and open circles are MOST predictions at 50, 150, and 450 m resolution, respectively. Vertical bars are threshold model-type predictions with calculations stopping at the 10-m contour. Stars are the field measurements.
the horizontal projection of the last “wet” point, for example, the n − 1 node in Figure 9.22. The value of the velocity on the shoreline node is equal to the velocity on the previous “wet” point. Additional grid points are introduced as needed, as follows. Referring to Figure 9.22, at the time interval between times t and ∆t, there are n grid points, n − 1 fixed grid points, and the instantaneous shoreline, points (A) or (B) in the computation. At time t + 2∆t, when the shoreline point (C) reaches beyond the next fixed grid point (the nth fixed node of the constant dry bed grid), this nth fixed point is introduced between the shoreline point (C) and the previous internal fixed node n − 1 and η(D) = η(C). Now, there are n + 1 grid points in the computational area and the process is repeated. During rundown, the number of dry grid points is reduced sequentially in an analogous manner.
9.6.5 Verification of the Model As an example of validating codes for use in tsunami engineering, Figure 9.23 shows the comparison among the computed values and with field measurements from the 1993 Hokaido-Nansei-Oki tsunami, at Okushiri Island, Japan. The model is seen to predict even extreme run-up values of 30 m (100 ft) adequately. This was an extremely difficult tsunami because there was overland flow over Aonae cape, as shown in Figure 9.24.
9.7 Harbor and Basin Oscillations 9.7.1 Introduction to Basin Oscillations The sloshing of basins, reservoirs, dams, and harbors is a classical problem of hydrodynamics. This sloshing occurs when a closed or open basin is excited either by ground motion or offshore waves, or by impulsive atmospheric disturbances, such as barometric fronts or pressure waves from volcanic eruptions. The resulting waves are also known as seiches.11 1Seiche is a word believed to originate from the Latin siccus, which means dry or exposed [Wilson, 1972], but it seems now to be out of favor in the English scientific literature.
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FIGURE 9.24 Computed results using MOST of the tsunami running over Aonae Cape during the 1993 HakkaidoNansei-Oki tsunami.
As these waves approach the boundaries of the basin, they reflect; when the boundaries are vertical, the reflection process is almost perfect, and the reflected waves have the same frequency as the incident ones with no phase shifts. As the excitation continues, interference sets up standing waves, which tend to grow; most of these waves are long and dissipation is often not important to first order. When the basin is closed, or when the harbor entrance is small, the resulting waves may grow, as there is no or little wave energy radiated offshore, respectively. The latter has led to the formulation of the classical “harbor paradox,” where closing the entrance of a harbor sometimes leads to amplification of the waves, contrary to lay intuition, which would have led one to expect that the narrower the entrance, the smaller the wave motion inside the harbor. Both from the engineering and the analytical points of view the problem is intriguing. Most large water bodies, but also harbors, have adjacent communities and/or constructed marine facilities. Largeamplitude wave motions within these water bodies can be rather disruptive, not to mention outright catastrophic, since the inundation associated with such large water motions can be extensive, and have been reported to last for several hours. It is well known that oscillations in Lake Erie excited by barometric pressure disturbances can last for more than a week beyond the forcing. There have been numerous anecdotal reports in the literary literature over the past 2000 years of unexplained and rapid rises in water level; often these unusual phenomena were associated with astronomical cycles, but as the understanding of tides grew, these associations proved inadequate. In Japan, where historic records exist for almost 1000 years, these motions were often associated with tsunamis. Tsunami is the Japanese word for what is referred to in English as a tidal wave. Interestingly, the exact transliteration of the word tsunami means harbor wave, a reflection perhaps of the fact that these waves were first observed in harbors. In more modern times, it is believed that the rhythmic oscillations occurring at the narrow end of Lac Léman off Geneva were first mentioned in a chronicle by Schulthaiss in 1549 and recorded in 1730 by deDuiller [Wilson, 1972]. The first scientific study was initiated by Forel through his observations of the oscillations of the same lake, in 1869. Forel noticed that the amplitude of the oscillation increases towards © 2003 by CRC Press LLC
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the western end of the lake, and that the oscillations may occur at all times of the year, and seem only to be affected by the “state of the atmosphere.” Chrystal [1905], in his seminal study of lake seiching, refers to Forel as the Faraday of seiching; Faraday first described capillary (surface-tension controlled) waves generated in small closed basins under continuous vertical excitations. Chrystal [1905] published a comprehensive study of basin seiching, including numerous observations. He quoted a description of seiching from the Scots Magazine of 1755 because, as he wrote, the “source is not easily accessible to everyone.” He correlated this phenomenon with the great Lisbon earthquake of 1755. Indeed, this description may still not be easily accessible, so it is provided below. On the 1st of November last, Loch Lomond, all of the sudden, and without the least gust of wind, rose against its banks with great rapidity, and immediately retiring, in about five minutes subsided as low, in appearance, as ever it used to be in the greatest drought of summer. In about five minutes after, it returned again, as high and with great rapidity as before. The agitation continued in the same manner from half an hour past nine till fifteen minutes after ten in the morning; the waters taking five minutes to subside and as many to rise again. From ten to eleven the agitation was not too great; and every rise is somewhat less than the immediately preceding one; by taking the same time, viz. five minutes to flow and five minutes to ebb, as before. About eleven the agitation ceased. The height of the waters was measured immediately after and was found to be 2 feet 6 inches (76cm) perpendicular. The same day, at the same hour, Loch Lung and Loch Keatrin were agitated in much the same manner; and we were informed from Inverness, that the agitation in Loch Ness was so violent as to threaten destruction to some houses built on the sides of it. The Great Lisbon earthquake occurred on the morning of November 1, 1755; Chrystal observed that both Loch Ness and Loch Lomond lie along an almost straight line with the center of the disturbance in Lisbon. Interestingly, the same event generated a rather large and destructive tsunami; our current understanding suggests that this earthquake was at least a magnitude 8 and was tsunamigenic, and a comparatively large portion of its energy was in the long wave part of the spectrum. These long waves do not attenuate rapidly, explaining perhaps why they had sufficient energy to excite the lakes in Scotland. More recently, the Great Alaskan earthquake of March 27, 1964 produced anecdotal reports of sloshing in different reservoirs operated by the Army Corps of Engineers, and coastal seiches along the coastlines of Texas and Louisiana [Korgen, 1995]. The observations of seiches in the nineteenth century led to the formulation of simple mathematical models based on the linear theory of long wave evolution. Some of the greatest names in hydrodynamics, including Green, Rayleigh, Stokes, and Lamb, have provided simple analytical results for simple geometries. In summary, all formulations to date either assume lakes with orthogonal cross sections or fairly long canal-shaped lakes, and with simple depth variation in the longitudinal direction, either uniformly sloping or constant or convex or concave parabolic, or with cylindrical symmetry. All these formulations allow for simple one-dimensional equations of motion, either in one rectilinear coordinate or in the radial direction. For simplicity with assigning the boundary condition, all studies have assumed that the lake walls are vertical beyond the initial shoreline, i.e., that there is a vertical boundary wall along the shoreline; this allows the imposition of no fluid motion past the boundary, an assumption which is perhaps adequate when the shoreline motions are small, but clearly not so, when the basin has gently sloping boundaries, which may produce large horizontal excursions. It is interesting that difficulties encountered in most of the nineteenth- and twentieth-century studies in matching the results for any other than the fundamental period — not to mention with the wave height — with observations, these difficulties led Chrystal [1905] to ask, “Is this an accident due to the position at which the limnograph2 was placed, or are these seiches unstable owing to irregularities of the lake bottom near one or more of the corresponding nodes?” 2
Limnograph is the name given to a tide-gage instrument, that is, an instrument that measures the water level variation, when deployed inside a lake. Typically these instruments only respond to slow variations such as tidal changes. © 2003 by CRC Press LLC
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It is perhaps worthwhile to speculate that these difficulties in interpretation may be due to the excitation of transverse modes in different lakes and basins. When the forcing source is an atmospheric disturbance and usually coming from the same direction, then the periods of oscillations observed in any given lake may be consistent from year to year, yet if they occur in the transverse direction they may not be accessible with the simple longitudinal-mode theories proposed earlier. Unless the direction of excitation is very close to the longitudinal direction, both transverse and longitudinal modes may be excited and any expectation of predicting the amplitude of the oscillation with a one-dimensional theory may not be well placed for closed basins, appropriate as it may be for harbors, where the excitation is often one dimensional. Sloping boundaries may dramatically complicate the interpretation; even the theory of long waves evolution and run-up over infinitely wide ocean beaches was only fully developed in the last 30 years, with consistent numerical results becoming available only in the last 10 years. These results suggest that the wave height off the beach may be dramatically underestimated if there is no shoreline-evolution computation, such as when imposing a vertical wall-type boundary condition, as in the early studies.
9.7.2
Calculating Basin Oscillations
In basin oscillation studies it is customary and appropriate to integrate the basic Navier–Stokes equations over the depth, but it is preferred to express the resulting LSW equations in terms of the volume flow rate per unit time per unit width of vertical cross section: qx =
∫ ud A, and q =∫ vd A y
A
(9.86)
A
where A is the cross-sectional area of the basin at the particular plane of integration. It is customary and not unrealistic for long waves to assume that the vertical accelerations of the free surface are small in comparison with the acceleration terms ∂u/∂t and ∂v/∂t. Convective terms of the form u(∂u/ ∂x) are also neglected in comparison to ∂u/∂t, similarly in the y direction. With all other restrictions above, the equation of conservation of mass can be written as: ∂qx ∂q y ∂η + + =0 ∂x ∂y ∂t
(9.87)
while Newton’s law becomes, in terms of qx , qy :
∂qx ∂t
+ g (h + η)
∂η = ∂x
τ xz
z=η z = −h (h + η) ∂patm − ρ ρ ∂x
(9.88)
and
∂q y ∂t
+ g (h + η)
∂η = ∂y
τ yz
z=η z = −h (h + η) ∂patm − ρ ρ ∂y
(9.89)
Now, it is convenient to approximate the bottom shear stress τxz | z=–h = Kqx where K is a bottom friction factor, and similarly τyz | z=–h = Kqy . At the free water surface, z = η, the shear stress can be incorporated in a forcing term of the form: Fx ( x , y , t ) = © 2003 by CRC Press LLC
τ xz z = − η (h + η) ∂patm – ρ ρ ∂x
(9.90)
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After substitution, what results is a set of three coupled equations: ∂qx ∂q y ∂η + + =0 ∂x ∂y ∂t
(9.91)
∂qx ∂η + Kqx + g (h + η) = Fx ( x , y , t ) ∂t ∂x
(9.92)
∂q y ∂t
+ Kq y + g (h + η)
∂η = Fy ( x , y , t ) ∂y
(9.93)
for the unknowns qx , qy , and η.
9.7.3
Forced Oscillations in Basins of Simple Planform
For calculating oscillations in narrow closed basins, where there is no y (width) dependence, qx can be trivially eliminated among the equations, resulting in the following: ∂F ∂2η ∂η ∂ +K −g =− x (h + η) ∂η ∂t 2 ∂t ∂x ∂x ∂x
(9.94)
and, in a long rectangular basin of uniform depth h = d, length L >> width and with vertical boundaries, the equation becomes: ∂F ∂2η ∂η 2 ∂ 2 η +K −c =− x 2 2 ∂t ∂t ∂x ∂x
(9.95)
an equation in the canonical form of a forced one-degree dynamic system, which can be solved by separation of variables. An equivalent equation can be trivially derived for the volume flow rate. c = gd is the wave velocity. The standard boundary condition is of the form qx(0,t) = qx(L,t) = 0, i.e., there is no flow at the two boundaries, which is equivalent to imposing a vertical wall at the shoreline. Then, the solution for the free oscillations (Fx(x,t) = 0) is the following: η( x , t ) = ae − Kt / 2 cos kx cos ( γt + )
(9.96)
qx (t ) = (aγ k ) e − Kt / 2 sin kx sin ( γt + )
(9.97)
and
The amplitude a and the phase difference ε are, of course, to be determined from initial conditions. Also, k = nπ/L, n = 1, 2, 3, … and γ = ω 1 − K ω 2 ; since ω = kc, then: ω = (nπ L) gd
(9.98)
Therefore, the periods of free oscillation — when damping is negligible — are: Tn =
© 2003 by CRC Press LLC
2L n gd
(9.99)
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The fundamental mode is when n = 1. Equation 9.99 apparently was first proposed by Merian [1828] and bears his name. As explained, the assumption is that the basin is one dimensional, with constant – depth and width. There have been attempts to account for variable depth by using the average depth d over the longitudinal axis, or the so-called deBoys approximation: Tn =
2 n
∫
L
0
dx
(9.100)
gh ( x )
to calculate the periods of oscillation, but neither of the two is known to produce satisfactory results; their effectiveness will be checked later, and another analytical method for obtaining the natural frequencies will be discussed. An interesting result regarding atmospheric excitation is given by Wilson [1972]. When Equation 9.95 is forced by a Gaussian-distributed pressure pulse of length l, and the equation solved using a Fourier series, the excitation produces resonance when the ratio of the length of the pulse to the basin length is l/L = 8/9. A number of other one-dimensional solutions for variable depth are presented in Lamb [1932] and summarized in Defant [1961]. By scrupulously choosing the depth variation h(x) in Equation 9.94, the latter may take the form of Bessel’s or Legendre’s equation. Then the natural frequencies can be calculated readily. Unfortunately, solutions only exist for basins with uniformly varying depths or with hyperbolic depth profiles. Even for the one-dimensional case of a trapezoidal bottom variation, no solution exists, and authors revert to numerical procedures [Gardarsson, 1997]. When bottom friction is negligible, the 2+1 LSW is:
g
∂ ∂ (hη) 1 ∂ 2 η ∂ ∂ (hη) +g = ∂y ∂y ∂x ∂x c ∂t 2
(9.101)
subject to the condition of no flux, h∂η/∂n = 0 at the boundaries. h(x,y) is the local depth, which may vary inside the basin. Equation 9.101 is valid for inviscid, incompressible, irrotational flows with long waves of small amplitude. For two-dimensional reservoirs, when the width W is of the same order as the length L, an analytic solution exists only for a basin of uniform depth h = d. Then, Equation 9.101 becomes: ∂2η ∂2η ∂2η = c2 2 + 2 2 ∂t ∂y ∂x
(9.102)
∂η ∂η ∂η ∂η x = 0, y , t ) = x = a, y , t ) = x , y = 0, t ) = ( ( ( (x =, y = b, t ) = 0 ∂x ∂x ∂y ∂y
(9.103)
with c = gd subject to
and initial conditions for η(x,y,t = 0) and ∂n/∂t(x,y,t = 0) specified by any well-behaved functions. Using standard separation of variables methods of engineering mathematics, it is trivial to show that the natural frequencies of Equation 9.102 are given by: ω nm = π g d n 2 (d a) + m 2 (d b) 2
2
(9.104)
for any initial conditions. The two lowest-frequency modes are the ones for n = 1, m = 0 and n = 0, m = 1 also sometimes referred to as fundamental modes, while n = m = 1 is the first coupled mode. The solution for η(x,y,t) in generic form is given by the eigenfunction expansion: © 2003 by CRC Press LLC
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η( x, y, t ) =
∞
∞
∑ ∑(A
nm
n=0 m=0
cos ω nmt + Bnm sin ω nmt ) cos
nπx mπy cos a b
(9.105)
with the understanding that both n and m cannot be simultaneously zero. Anm and Bnm are determined from the two initial conditions, by expanding η(x,y,t = 0) and ∂n/∂t(x,y,t = 0) in Fourier series in terms of the cosine eigenfunctions. If the width b of the basin is much smaller than the length, and it can be formally shown then the lengthwise motions dominate and the periods of motion are given by: T=
2a n gd
(9.106)
Raichlen [1966] notes that Equation 9.106 estimates the first mode of Loch Earn, Scotland, with a = 6.2 mi (10 km), d = 200 ft (61 m) as T = 13.65 min, with an observed period of 14.5 min. For Lake Baikal in Siberia, with a = 413 mi (660 km), d = 2230 ft (675 m), Raichlen calculated T = 4.52 h, with an observed period of T = 4.64 h. However, for Lac Léman in Geneva, Switzerland, with a = 43.5 mi (70 km) and d = 525 ft (159 m), T = 59 min, while the observed period is 83.5 min, a difference attributed to the complexity of the shape of the lake. While these formulas can be applied to calculate adequate first estimates of the natural frequencies of basins excited by strong ground motions, such as the Los Angeles Reservoir (LAR) during the 1994 Northridge earthquake, they cannot be used directly for harbors, which are in essence basins with openings.
9.7.4
The Sloshing of the Los Angeles Reservoir: A Case Study
The MW = 6.7 Northridge earthquake occurred on January 17, 1994 at 4:30 a.m. PST, with an epicenter about 1 mi south-southwest of Northridge, California at a focal depth of 12 mi [Hall et al., 1994]. Numerous national and international reconnaissance teams performed field surveys immediately following the earthquake and at least three preliminary reports have been published [EQE, 1994]. These preliminary reports did not refer to any run-up observations around any of the LA area dams or reservoirs. On January 18, 1994, the day following the event, the Los Angeles Times reported that a 30 ft (9 m) wave had overtopped the Los Angeles dam (LAD), but that there had been no structural damage. The LAR is located about 6 mi from the epicenter of the earthquake, inside the Van Norman complex of the Department of Water and Power (DWP). This site suffered substantial damage in the 1971 San Fernando earthquake, and the LAR was built to replace the Lower San Fernando dam; that older dam is now used as a debris basin. Lateral spreading, liquefaction, and ground settlement were observed in the entire area referred to as the Van Norman complex. Based on the intensity contour maps of Trifunac et al. [1994], peak horizontal and vertical accelerations were in excess of 0.60 and 0.80 g, respectively. Hall et al. [1994] reported that the dam settled 9 cm (3.54 in.), while DWP claims that the dam moved horizontally 7.5 cm (3 in.); both numbers are consistent with fairly impressive ground shaking. The LAR is trapezoidal-shaped in plan view; at the rim the trapezoid has 790 m (2600 ft) height and 1130 m (3700 ft) and 710 m (2325 ft) bases. The southeastern part of the reservoir is referred to as the Los Angeles Dam or LAD. The dam is 25 m (83 ft) high and it is built on bedrock. At the time of the earthquake, the water surface is believed to have been 7 m (23 ft) below the crest of the dam, which is at an elevation of 360 m (1200 ft) above sea level. The reservoir was rapidly emptied to check for cracks, starting the day after the event. The slope of the embankments ranges from 3.5 horizontal to 1 vertical, to 3:1. The area was surveyed on January 18, 1994 by two groups of faculty and students of Civil Engineering from the University of Southern California; the group headed by Synolakis surveyed the hydrodynamic © 2003 by CRC Press LLC
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aspects and, in particular, attempted to evaluate the 30-ft (9-m) high wave of the newspaper reports. They were unable to find eyewitnesses or the origin of the report. However, during a walk-around inspection of the embankments of the LAD, they located conspicuous chalk marks that bore no relationship to any of the visible cracks. East of the water-intake tower, they found a line of debris of fragments of bird nests. On closer inspection, it was noticed that underneath the catwalk there were numerous remains of bird nests. They speculated that during the ground shaking, parts of the bird nests fell in the reservoir and they were carried by the sloshing waves up the embankment. The fact that this debris line existed only east of the catwalk could provide a clue as to the predominant direction of sloshing in the reservoir. On the east side of the reservoir there is a narrow section with a crest 3.3 m (10 ft) lower than the rest of the reservoir. This section is an overflow and it leads to a storm channel; there were unconfirmed reports that there was some overtopping in this section, but the team learned of them long after the field survey took place. The measured data suggest that the sloshing may have reached 3.3 m (15 ft) vertical height above the still water level of January 17, 1994, the date of the earthquake. If this observation is correct, then the northeastern embankment (whose crest is lower) might have overtopped had the water level been higher at the time of the earthquake. Observations of significant run-up heights of this order are rare. The conventional paradigm suggests that dams over 22 m (75 ft) high do not overtop, unless there is a landslide or other impulsive catastrophic occurrence, although perhaps this dictum represents more wishful thinking than sound engineering judgment. While it may never be possible to reconstruct what happened in the LAR, Ruscher [1998] attempted to determine if the run-up distances measured on the embankment of the LAD were compatible with the sloshing expected from the ground motion measured at the site. The only method available then to address these questions for this particular study was a series of laboratory shaking tests using a scale model; inundation models have yet to be tested for shaking reservoirs with sloping boundaries where run-up is important. The laboratory experiments revealed sharply resonant water-surface motions highly dependent on the excitation parameters and on the water depth. Four distinct modes of sloshing were observed. In the laboratory, these modes are realized for fixed depths and amplitudes of excitation by varying the frequency. The different regimes of sloshing are shown in Figure 9.25A, while the resonance results are shown in Figure 9.25B. Note that Ruscher [1998] was able to find the correct scaling for the dimensionless frequency, maximum wave height, and maximum run-up. Let v*, η*, and R* refer to the dimensional frequency, wave height, and run-up, respectively. L is the longitudinal length of the reservoir, from rim to rim, S the displacement at the base, and d the undisturbed depth. Figure 9.25B suggests that the correct dimensionless variables are:
v =v*
Ld η* L R* L , η= , and R = g S d S d
(9.107)
These dimensionless variables allow extrapolation from the model results to the prototype. Note that the scaling may be forcing-direction dependent, in which case L changes.
9.7.5
Introduction to Harbor Resonance
In his classic introduction to the chapter on Harbor Resonance (HR) in Ippen’s Estuary and Coastal Hydrodynamics [1966], Fred Raichlen wrote: It has been found that the maximum wave amplitude at locations within a harbor can be greatly affected by a resonance phenomenon. For certain incident wave periods a particular harbor can act as an amplifier, thereby magnifying the oscillations within the harbor above those which one would expect. This phenomenon of resonant oscillations in harbors has been termed by various investigators as seiche, surging, or range action. © 2003 by CRC Press LLC
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Harbor oscillations occur when incident storm waves contain frequencies at directions of incidence that cause the harbor to amplify their amplitudes at select locations. Harbor and basin oscillations can also be excited by incident tsunamis. Except for large ports, most harbors have natural frequencies that are longer than most storm waves and shorter than most tsunami waves; however, the possibility needs to be carefully evaluated because the exposure is great. Even if harbor oscillation does not result in casualties, the loss of use of harbor facilities even for a few days can result in substantial monetary losses, as one can extrapolate from the losses in Kobe (1995). The 1964 Alaskan tsunami caused an estimated U.S. $1 million damage to the Port of Long Beach. Notably, most of the damage was in the Cerritos channel and was due to the tsunami-induced currents, not to overtopping. More recently the 1999 Marmara earthquake caused a small tsunami and possibly harbor oscillations that caused an oil tanker to break off its moorings, triggering a refinery fire that burned for days. It is for this reason that the Federal Emergency Management Agency (FEMA) is currently (2002) developing standards and guidelines for ports and marine terminals for tsunami attack. The engineering problem of interest is to determine whether oscillations will be triggered, given an incident tsunami wave. The problem is not as straightforward as would appear, for tsunamis are highly transient waves, and occasionally it is difficult to identify frequencies that are sustained long enough to cause oscillations. Typically HR is evaluated numerically using complex numerical codes such as MIKE21 or CGWAVE or the proprietary code of Lee [1969]. All HR codes calculate the amplification of individual sinusoids at given incident directions everywhere inside the harbor. In this case, the directional spectrum of the incident tsunami is determined and frequencies close to the known natural frequencies of the harbor are identified and then input in the HR codes to determine amplification factors at specific locations inside the harbor. One disadvantage is that nonlinear coupling between frequencies is not considered, as the importance of the coupling has not yet been established. Long wave codes such as MOST or TUNAMI-N2 have been used to calculate HR as well, but their relative advantages compared to traditional HR codes have not yet been described. Numerically this is not a simple undertaking, since HR codes have to be run for several hours to follow the wave as it reflects and re-reflects back and forth inside the harbor. Numerical errors mount, particularly if the harbor has sloping boundaries, or outside the harbor at the boundaries of the computation, and occasionally numerical overflows appear. Here, first, certain simple analytic results will be presented suitable for first-order analysis to determine if more in-depth studies are necessary.
9.7.6
Harbor Resonance for Harbors of Simple Geometry
Raichlen [1966] describes the classic problem of a rectangular harbor of constant depth with an opening α, width 2w, length l, and depth d. The harbor is open to an infinite sea and the problem of interest is to determine the wavelength of the incident wave that will produce resonance. The coordinate system is as shown in Figure 9.26, and it is centered at the mouth entrance. The engineering problem is formulated as a forced, single-degree-of-freedom damped oscillator. The objective is not only to determine the resonant frequency but also the amplification of waves incident at the resonant frequency inside the harbor. In the classic theory of harbor resonance, a harbor of simple geometry is assumed to act as a damper oscillator. In dynamics, a damped oscillator is described by an equation of motion of the form d2y/dt2 + 2ζωdy/dt + ω2y = F(t). It is customary in dynamics to define Q = 1/2ζ. Q is the dissipation factor and it is a measure of the damping of the system and, in a simple system, it is independent of the frequency. It is also known as the Q-factor and it is infinite for a system with no dissipation. For one-degree-offreedom systems, critical damping occurs when Q = 1/2 and a system is underdamped when Q > 1. In analogy with dynamics, we define the power amplification factor R , a parameter that represents the ratio of the amplitude of the wave at some reference location inside the harbor to the incident wave amplitude, by:
R2 =
© 2003 by CRC Press LLC
1
(1 − ω ω r )
2
+
2 1 ω ωr ) 2 ( Q
(9.108)
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Resonance mode
Corner mode
Uniform mode
Ripples mode
FIGURE 9.25A The four modes of oscillation of the Los Angeles Reservoir.
where ω is the frequency of the incident wave and ωr is the resonant frequency of the harbor. In structural dynamics, the square of the denominator of Equation 9.108 is also known as the normalized impedance and sometimes denoted by Z = 1 – (ω/ω – r)2 + i(1/Q) (ω/ωr), so that R2 = 1/|Z|2. Miles and Munk [1961] note that harbors are complicated multi-degree-of-freedom systems; hence, Equation 9.108 is not applicable, except near resonance, which is what is of interest anyway. At resonance R = Q. In real harbors, Q varies between 2 and 10. Raichlen [1966] notes that a good approximation of Equation 9.108 is: R r2 ω ≈ 1 + 4 Q 2 1 − 2 2 R ωr
(9.109)
when ω is very close to the resonant frequency ωr . A harbor dissipates energy both internally and through radiative losses at the harbor opening. Since the problem is linear, individual values of Q can be calculated and then their inverses added. Miles and Munk [1961] estimate the internal losses for a standing wave of amplitude a over depth h and conclude that the internal dissipation is negligible compared with the radiative losses. Hence, they continue on to estimate Q based on radiative losses only, by writing the mean potential and kinetic energies radiated from the mouth of the harbor as E = (1/4) ρg|η|2 per unit area. Then, the radiated energy over the harbor entrance is given by: dE = dt
∫
π/ 2
− π/ 2
2
ρgc η rdθ
(9.110)
while the energy within the harbor perimeter is: E=
© 2003 by CRC Press LLC
1 2
∫
harborarea
2
ρg η d S
(9.111)
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10
M1
M2
M3
M4
η1
5 0 .5
-10 -15 0.00
0.05
0.10
ν
0.15
0.20
0.25
0.00
0.05
0.10
ν
0.15
0.20
0.25
0.00
0.05
0.10
ν
0.15
0.20
0.25
10
η2
5 0 .5
-10 -15
25 20
R
15 10 5 0
d=20mm, S=4mm; d=20mm, S=8mm; d=20mm, S=16mm;
d=30mm, S=9mm; d=40mm, S=8mm;
FIGURE 9.25B Normalized heights at the center (top), corner (middle), and maximum run-up on the Los Angeles Reservoir as a function of the normalized frequency.
When the harbor has an opening of width α, with kα << 1, or, if it is fully open, with 2kw << 1, then Miles and Munk [1961] derive what is essentially a solution of Equation 9.102 for the wave amplitude η(x,y,t) and find that: 1 2 kr l + sin 2 kr l 1 − Q= π 2 kr w 1 − cos 2 kr l
(9.112)
1 πα cot (kr l ) = 2 kr w 0.478 − ln kr α sin 4w π
(9.113)
with
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HARBOR RESONANCE
Region II
2w
a
+∞
Region I
-∞ Coordinate system of a rectangular harbor coupled to open sea.
FIGURE 9.26 Definition sketch for harbor resonance studies. (After Raichlen, 1966.)
Notice that in the special case when krl << 1, then Equation 9.112 becomes simply: Q=4
l 1 – 2d π
(9.114)
Raichlen [1966] noted that these expressions are physically realistic. Miles and Munk [1961] noted that the harbor can be considered as a quarter resonator if the length is increased by an amount associated with the aspect ratio and the aperture ratio and calculated asymptotic expressions for increase in length ∆l, ∆l =
2w πα 2w 1 cosech 1.051 + log (l 2 w ) + 2 w log π π 4 w α
(9.115)
Then the fundamental — also termed lower or grave — resonant mode can be found directly from: λ r = 4 (l + ∆l )
(9.116)
Another important factor when determining the vulnerability of harbors to tsunami attack is the time it takes the harbor to adjust itself to the excitation, i.e., to reach steady state. Tsunamis are transient waves, rarely with more than three or four identifiable cycles. Landslide tsunamis may have more, as landslide waves are more dispersive than tectonic tsunamis. According to Miles and Munk [1961], it takes O (Q /π)cycles to fully excite the harbor. So a simple harbor with Q between 2 and 10 is likely to be excited by a tsunami. Note, while Q does not depend on the depth or the incident wave height, the amplification factor does. Hence, if the Q of a harbor is known, the analysis is simplified considerably. The Miles and Munk analysis leads to the classic analytic result that, as the relative opening of the harbor α/2w is decreased, the power amplification is increased, an observation known as the harbor paradox. LeMehaute and Wilson’s [1962] explanation is that the Miles and Munk analysis does not include fully the effects of dissipation at the entrance. No matter what the correct explanation for the paradox, the resonant frequency of a harbor is not greatly affected by dissipation, and the analysis is useful for identifying the resonant frequency. As Wilson [1962] noted: The non-accordance of the experimental results with the theory of Miles and Munk must necessarily imply that the latter loses some of its validity at certain ranges of the parameters involved particularly when 2w/l and α/2w become small. It must be presumed that friction, two-dimensional effects and nonlinear effects with the basin and entrance, which were neglected, account for this. The writer can provide his own testimony of the evident nonlinear effects in the flow through the entrance (α/2w = 0.07) of the Duncan Dock at Cape Town on occasions of surging. © 2003 by CRC Press LLC
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100 80
2d/ 0.02
Fundamental mode
second mode
40
c
30
0.05
2d
2d/= 0.02
20
6 5 4
5
0.05
0
0.
0.2
1.
0.
8
/= 1 2d 0.0 .02 0 .05 0 .1 0 2 0.
0.15
5
10
0.1
0
/= 2d 0.01 2 0.0 .05 0 1 0. 2 0.
1.
Amplification factor at resonance RR
60 50
0.3
10
3
8
2
0.1
0.4 0.5 0.6 0.8 1.0 6
54
0.15 0.2 0.3
1.5 3
0.4
2.0
0.5
1 π 2
1 0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
π
3.0
3.2
1.5 1.0
3.4
3 π 2
0.6 0.8
3.6
3.8
4.0
4.2
4.4
4.6
4.8
Relative harbor length at resonance ( k ) R
FIGURE 9.27 Amplification factor for forced oscillations in rectangular harbors.
Wilson [1962] further commented on Miles and Munk’s [1961] statements about reducing the effects of harbor resonance by mismatching the harbor to the incident wave spectrum, which is equivalent to altering Q. Clearly, as harbors are subject to tides, as Wilson notes, any adjustment of mean depth in practical amounts might do more than cause surging to be troublesome at some other state of tide. Therefore, the preferred solution is changing the shape, which of course is not practical once the harbor is built. An effective solution is the containment of the harbor basins by chains of basins suitably designed to have low Q, as in the design of Terminal Island in the Ports of LA/LB and at Cape Town. Raichlen [1966] provided the design curves shown in Figure 9.27, which shows the amplification factor for a symmetric rectangular harbor as a function of the relative harbor length at resonance.
9.7.7
Example of Analytical Harbor Resonance Computation
Consider the classic Raichlen problem of a rectangular harbor of width 2w = 500 ft, length l = 2000 ft, and a symmetric opening of width α = 200 ft connected to the open sea. The depth d = 30 ft is constant inside and outside the harbor. Find the first and second resonant periods and wave numbers, and the amplification factor for a tsunami wave of period T = 10 min. First, from Equation 9.115, calculate ∆l = 615 ft. Then, calculate the effective length of the quarter resonator l + ∆l = 2618 ft, so that Lr = 10,460 ft. Then, the shortest wave number at resonance is kr = 2π/Lr = 0.0006/ft. Since krα = 0.0006/ft × 200 ft = 0.12 << 1, therefore the Miles and Munk theory is applicable. For tsunamis, ωr /kr = gd , therefore the longest period at resonance is T = 337 sec = 5.6 min. Second, to find the second mode, add π radians to krl = 0.0006/ft × 2000 ft, or kr2l + π = 4.34. Then kr2 = 0.0022/ft, then Lr2 = 2π/kr2 = 2895 ft. Then T2 = 2π/(kr2 gd ) = 93 sec ≈ 1.55 min. Third, calculate the amplification factor at resonance, using Equation 9.112. Then Q = 5.58 for the first mode, and Q = 4.64 for the second mode. The wave number corresponding to a T = 10 min wave is ω = 2π/T = 0.01 Hz, k = ω/ gh = 0.01 Hz/80 fps = 0.0001/ft. Then from Equation 9.109, calculate the amplification R r /R = 4.99 for the first mode and 7.91 for the second mode, implying that the incident wave height will amplify 4.99 and 7.91 times less than it does at resonance. Since no frictional effects within the harbor have been considered, this amplification factor would not constitute cause for concern. © 2003 by CRC Press LLC
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Occasionally, the amplification of the second mode is larger than the amplification of the first mode, particularly for narrow harbors. Miles and Munk noted that turbulent dissipation in the entrance is higher in the fundamental mode, thereby decreasing further its amplification relative to the second mode.
9.7.8
Numerical Modeling of Harbor Resonance
Most modern harbors have individual basins of varying geometry and are protected by attached or detached breakwaters. While elegant methods exist [Lee, 1969] for matching incoming and outgoing waves at the connecting open boundaries of each basin and then deriving solutions for incoming periodic waves, frequently numerical codes for calculating the amplification factor of sinusoidal waves approaching from different directions offshore are used; practitioners often shy away from semianalytical methods, regardless of the substantial differences in computational costs. The standard practice is to use equations that combine the effects of diffraction and refraction as waves approach and then enter the harbor. The most commonly used is the so-called mild-slope equation (MSE), which is really the generalization of the wave equation (Equation 9.102) for variable depth. Just like Equation 9.102, it is a depth-averaged, elliptic, partial differential equation, which assumes that the rate of change of depth is small within a wavelength. The equation has been rederived by Berkhoff [1973] and most recently solved by Tsay and Liu [1983], Mei [1989], Chen and Houston [1987], and Xu and Pachang [1993]. It is the basis of the CGWAVE model developed by the University of Maine and the U.S. Army Corps of Engineers. As presented in Martin and Dalrymple [1994], the MSE for the steady-state ˜ (x,y) of the surface elevation is: evolution of the amplitude η
(
) (
)
˜ + Cg C ω 2 η ˜ =0 ∇ ⋅ CCg ∇η
(9.117)
This equation is derived from the Lagrangian for the velocity potential Φ(x,y,z,t), hence it is implicit that the wave motion is irrotational and of small amplitude. Then:
[
(
˜ ( x , y ) exp −i (π 2) ωt Φ (x, y, z , t ) = ( g ω) R η
)] [cosh (k (z + d)) / cosh (kd)]
(9.118)
d is once again the undisturbed water depth, C = ω/k is the phase velocity, and Cg = ∂ω/∂k = (1/2) C (1 + 2kd/sinh 2kd) is the group velocity. k(x,y) = 2π/L is the wave number, and in general ω 2 = gk tanh
kd. The physical water surface elevation is obtained after the solution of Equation 9.117 by η(x,y,t) = R ( η˜ (x,y) exp(iωt)). Here R implies taking the real part and is not related to the amplification factor used earlier. Lee et al. [1998] suggest the following boundary conditions for the mild slope equation, to account for the various types of boundaries one encounters in a harbor. For example, for a perfectly reflecting boundary: ∂Φ =0 ∂n
(9.119)
∂Φ iα ∂ 2 Φ = −iαj Φ − =0 ∂n 2 k ∂S
(9.120)
and for a partially absorbing boundary,
Equation 9.117 is only solved for the steady state of the wave system. Tsunamis are long waves, and then C = gd = Cg . Then, since C = ω/k, Equation 9.117 then — for constant depth — reduces to: ˜ + k 2η ˜ =0 ∇2η
(9.121)
which is the Helmholtz equation that Munk and Miles [1961] solved to derive the solution for Q and for the resonant frequency ωr . © 2003 by CRC Press LLC
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Note that even though Equation 9.117 could be significantly simplified for tsunamis, in practice this is not often possible. Landslide tsunami waves evolve rapidly and may produce a spectrum of waves with energies in intermediate frequencies. Equation 9.117 does not include the effects of dissipation due to bottom friction or wave breaking. Demirbelek and Pachang [1998] include dissipation and friction, and solve the modified MSE:
(
) ((
)
)
˜ + Cg C ω 2 + iωW + iCg ωγ η ˜ =0 ∇ ⋅ CCg ∇η
(9.122)
with the damping factor W per Dalrymple et al. [1984]: ak 2 2f W = (2 nω k ) b 3π (2 kd + sinh 2 kd ) sin hkd
(9.123)
a = H/2 is the amplitude of the incident sinusoidal wave; fb is a bottom friction factor determined empirically and specified as a free parameter; n is Manning’s dissipation coefficient; and γ is a breaking parameter. According to Demirbilek [1994] and Demirbilek et al. [1996]: γ=
χ Γ 2d 2 with χ = 0.15 and Γ = 0.4 1− d 4a 2
(9.124)
Solution details are provided in Demirbelek and Pachang [1998], where the FE formulation used is described extensively. The numerical procedure is non-trivial both in the generation of the FE grid and because Equation 9.122 is solved both inside the harbor and, typically, in a semicircular domain outside the harbor. The direction and frequency of the incident wave are specified, then CGWAVE calculates the wave field inside the harbor over several prototype hours to ensure that steady state is reached. Then the maximum wave height at each location in the harbor is the local amplification factor, since the incident wave height is unity. Because the problem is linear, it is expected that the amplification factor will not vary with the incident wave height.
9.8 Tsunami Forces Tsunamis can generate large on-shore currents and move large objects far inland. Historic examples from large tsunamis abound. The most notorious is the report of the USN Watery, the ship moved by the 1868 Arica, Chile tsunami 2 miles inland and then moved back to shore during the 1877 Arica tsunami, so that the ship could sail on. As a measure of what even small tsunamis can do, consider the 1994 Mindoro, Philippines tsunami. In an area where the vertical inundation heights did not exceed 3 m (10 ft), the tsunamis generated floated a 6000-ton generating barge, broke its mooring lines, and carried it 1 mile inland up the Baryan river. The barge is shown in Figure 9.28A at its final resting place. Figure 9.28B shows the fault trace on the surface near northeast Mindoro; this strike-slip fault did generate a tsunami. Impact forces can cause collapse of coastal structures. An excellent visualization of the process can be observed in detail in Discovery’s television documentary, Tidal Wave [1998]. The estimation of impact forces and currents is still an art and far less understood than hydrodynamic evolution and inundation computations. In what follows, different methods and formulas in the literature are described, although none has been truly validated by comparison with field data.
9.8.1
Forces on Piles
In principle, the calculation of wave forces on structures involves the integration of the pressure and the shear force over the exposed area of the structure during the wave motion. In the simplest case of
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(A)
(B)
FIGURE 9.28 (A) The 6000-ton power generating barge that was moved 1 mi inland by the 1994 Mindoro tsunami. (B) Surface expression of the strike-slip fault that triggered the 1994 Mindoro tsunami.
calculating the instantaneous wave force at time t over a cylinder of radius R, in the direction of the wave propagation, and assuming a pressure p(R, θ, z, t) and a tangential shear stress τrθ(R, θ, z, t), then the force is given by: FT (t ) =
∫
η p (t )+ hp
∫
2π
η p (t )+ hp
0
∫
0
© 2003 by CRC Press LLC
0
p (θ, z , t ) R cos θ dθ dz +
∫
2π
0
τ r θ (θ, z , t ) R sin θ d θ dz
(9.125)
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Here the ηp and hp are the local amplitude and undisturbed water depth at the pile, respectively, with the assumption that they do not vary significantly over the pile diameter, hence their dependence on r is not shown in their arguments. In practice, for all but the simplest steady flows, determining either the pressure or the tangential shear stresses through calculation of the velocity gradients is impossible at this state of knowledge, as it involves solution of the Navier–Stokes equation. The SW equations described earlier are depth-averaged approximations of the Navier–Stokes equations for inviscid flow, and there are no velocity gradients perpendicular to the cylinder. So the classic simplification is to consider a mass coefficient that incorporates some of the dynamic pressure effects and drag coefficient CD that incorporates all the effects of the viscous forces on the cylinder. In terms of these coefficients, the force on a cylinder is given by: FT (t ) =
∫
η p (t )+ hp
0
π C M ρR 2
dV dz + dt
∫
η p (t )+ hp
0
C DρRV V dz
(9.126)
Here V is the instantaneous horizontal velocity in the direction of wave motion, while dV/dt is the → instantaneous water particle acceleration. Clearly F is a vector in the same direction as the velocity vector → V , hence, again the force given by Equation 9.126 is in the direction of wave propagation. The absolute value is used to underscore that the force may change direction as the water particle velocity changes → → → direction. For example, V = u i + v j and V = u 2 + v 2 with u,v→ the horizontal particle velocities in x,y. → If the flow is primarily one dimensional and onshore, V = u i , and u is positive under the crest and negative below the crest, if x is pointing towards the pile, or, in other words, if x increases towards the pile. Dean and Harleman [1966] note that the expression (Equation 9.126) for the drag force was determined empirically for steady flows, yet it is used for wave flows. For convenience, the same formulation is used for strongly unsteady flows, such as the impact of bores and surges, but then the coefficients CD and CM have to be carefully chosen. The variation of CD with the Reynolds number Re = uD/υ is shown in Ippen [1966], as Figure 8.2, p. 344. In the range of 193 < Re < 5 × 105, then CD ≈ 1. Note that CD does depend on the roughness of the cylinder, although for tsunamis a usual assumption is that the pile is hydrodynamically smooth, given the wavelength of the tsunami wave train. Whether this is indeed a good assumption remains to be confirmed. There are a few cases where Equation 9.126 can be used directly to calculate tsunami forces. As an example, consider small amplitude wave theory. This theory is→ only valid for irrotational flows, which in analytical terms means that the flow is irrotational, i.e., ∇ V = 0, an assumption that is not correct when waves are breaking. Shallow-water wave theory (SW), as described by Equation 9.16, is also irrotational, in the sense that there are no velocity gradients perpendicular to the direction of wave propagation. However, recall that SW theory is valid for larger amplitudes, for L/d >> 1, while small amplitude theory applies to a/h << 1. In small amplitude theory, a velocity potential Φ(x,y,t) is postulated with u = ∂Φ/∂x and v = ∂Φ/∂y. In the shallow water limit of the small amplitude approximation, for a periodic tsunami wave amplitude of the form η(x,t) = a cos(kx − σt), the horizontal velocity no longer depends on the depth, and: u ( x , t ) = (aσ kh) cos (kx – σt )
(9.127)
and
(
)
du = − aσ 2 kh sin (kx − σt ) dt Therefore, assuming that the pile is located at x = 0, and using k = 2π/L and σ/k =
(
)
FT (t ) = −ρp πR 2akh C M a sin (σt ) + ρgC D a 2 R cos (σt ) cos (σt )
© 2003 by CRC Press LLC
(9.128) gh then: (9.129)
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with the understanding that Equation 9.129 is valid for small-amplitude long waves. Dean and Harleman [1966] note that the inertial force is inversely proportional to the period, while the drag force is independent of the period. Equation 9.129 is an adequate approximation for calculating forces on piles offshore for tectonic tsunamis generated far-field or for landslide tsunamis, i.e., for tsunami wave trains with more than one or two waves in the wave train. For tsunamis generated near-field, when there is not sufficient evolution distance for a wave train to fully emerge, these equations have to be used with caution, and it is preferred to use the methodology described in the next subsection. The total moment is formally calculated from: MT (t ) =
∫
η p (t )+ hp
0
zFT (t ) dz
i.e., it is the integral of the force over the height of the pile from the ocean floor to the free surface. To the same level of approximation as Equation 9.126, then: 1 1 MT (t ) = ρgC D Ra 2h cos (σt ) cos (σt ) − ρgC M πR 2akh 2 sin (σt ) 2 2
(9.130)
Note that consistent to the SW approximation, the moment is seen to equal the force times a moment arm of h/2, since SW implies that the force is uniform over the depth. Note also that the drag force does not depend on the period of the wave motion. The above methodology can also be used with results from SW theory, with the numerical predictions for the depth-averaged u,v substituted directly into Equation 9.126, with V2 = u2 + v2. 9.8.1.1 Limitations of This Analysis Proximity effects to adjacent piles and to seawalls need to be considered when the spacing of the piles S is such that S/(2R) < 2. If the drag coefficient for an isolated pile is C∞ then the ratio of the drag coefficient CD/C∞ needs to be considered. In this case, one refers to Figures 8.18 and 8.19 in Ippen [1966], which provides laboratory results for different angles of attack to the piles as a function of s/2R. In general, when S/2R > 3 then CD/C∞ = 0.26 for normal incidence, i.e., there is less drag on the second pile behind the first pile S/2R away as the wave attacks in the direction perpendicular to both piles. For other directions of incidence, CD/C∞ ≈ 1 for S/2R > 3. Proximity of the pile to a seawall may create lift forces on the pile, due to ground effects, in modern aero-speak. For example, if a tsunami approaches a long dock parallel to a steep coastline, then the piles closest to the steep beach face will experience the equivalent of a lift force. This is the case for docks in steep Alaskan fjords, where piles are almost parallel to the fjord walls and landslide-generated tsunamis as well as tectonic tsunamis may occur a few times every century. In this case, waves may approach the piles at an angle, as refraction does not have sufficient time to turn the wave crests parallel to the shoreline. The lift force may not always be pointing away from the wall; as Dean and Harleman [1966] point out, the boundary layer is asymmetric, probably remaining laminar between the pile and the wall, while being turbulent on the other side at least for critical Reynolds numbers. The lift force is calculated in the same manner as the drag force, with coefficients of lift CL varying from −0.2 to 0.4. For Re < 1.5 × 105 then CL ≈ 0.06 for S/2R > 0.3, where S is now the distance from the circumference of the pile to the wall. No data have been reported for S/2R > 2, so it is unlikely that ground effects are important when the pile is more than two diameters away from the wall. Again, these results have been obtained for submerged piles under steady conditions, so their extrapolation to tsunami calculations should be with caution. Calculating the x − y current distributions and magnitudes and their time variation is possible using the SW equations described in Section 9.5. However, harbor resonance effects, breakwaters, and seawalls with characteristic sizes smaller than the grid spacing are transparent to the numerical computations. For example, a typical grid size ∆x, ∆y ≈ 100 m (333 ft) will miss all coastal structures smaller than 100 m, unless the grid is positioned appropriately. This is not as simple as it sounds, for numerical grids © 2003 by CRC Press LLC
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are calculated so as to model the hydrodynamic evolution correctly by attempting to maintain a constant number of grid points per wavelength, as the wavelength changes. Sophisticated higher-order simulation methods for calculating currents and forces are now under development but they have so far only been used to calibrate parameters through laboratory experiments. Their computational complexity only permits their use close to the structure, with initialization from flow variables such as velocities and wave heights obtained from SW models. Generally, wave forces can be thought of as having two parts, an inertial component and another due to the dynamic effects of the moving flow. When the structure is not fully submerged, generally, the forces are calculated in the manner of classic analyses of drag forces in fluids. When there is impact on a seawall and a structure that causes full reflection of the wave, then the forces are calculated using impact force theory.
9.8.2
Impact Forces on Seawalls
Impact forces are calculated by different methods, depending on whether or not the breaking wave is forming a surge or a bore. Impact forces on the vertical front face of a structure have traditionally been estimated using the classic formula of Cross [1967]. In his classic work, he quotes from the account by Eaton et al. [1961] of the attack of the 1960 tsunami on Hilo. At first there was only the sound, a dull rumble like a distant train, that came from the darkness far out towards the mouth of the bay … As our eyes searched for the source of the ominous noise, a pale wall of tumbling water, the broken crest of the third wave was caught in the dim light thrown across the water by the lights of Hilo. Cross [1967] proposed that the force on a seawall b wide is given by 1 Fwall (t ) = ρgbη2 ( x = X w , t ) + C f (t ) ρbη( x = X w , t ) C 2 2 where ηw = η(x = Xw, t) is the water surface elevation on the wall located at some x = Xw , b is the width of the wall, C is the surge or bore velocity, and Cf = (1 + tan1.2θ) is a computed force coefficient. tanθ is the slope of the front face of the bore as it impacts the wall (see Figure 9.29). For practical applications, Cross suggested calculating η(x = Xw, t) as if the wall were not there, i.e., the bore would pass through the wall relatively unchanged. Therefore, Cf (t) could be a function of time, since the front slope of the wave may change as the wave evolves. Writing the depth at the seawall as hw , Ramsden and Raichlen [1990] wrote Cross’ equation as: Fwall (t )
2
η C 1 ηw + C (t ) w = (1 2) ρgbH 2 H f H gH
(9.131)
In Cross’ original formulation, Cf ≈ 1 for a gentle surge with θ = 0 and ranges to Cf ≈ 4.5 for θ = 70°, for a very steep bore. In other words, the impact force depends on the local depth at the seawall hw, the bore height H and the slope of the front face of the bore tanθ. As it turns out, the bore celerity depends exclusively on H/h. Figure 9.30 shows the variation of the bore slope, and normalized run-up as a function of the bore strength H/h.
9.8.3
Example of Impact Force Computation
One example of calculation of tsunami forces on seawalls is the case study performed by Ramsden [1993], who used the description by Eaton et al. [1961] of the May 23, 1960 tsunami impact on Hilo, Hawaii. Recall that the May 23, 1960 megathrust earthquake was the largest seismic event recorded in the past © 2003 by CRC Press LLC
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g
(a)
η(x,t)
θ(x,t)
z w
C(x) x u
SWL
h
dη/dx 1 H (b)
R(t) SWL h 3
FIGURE 9.29 Definition sketch for the forces on seawalls from bores. (After Ramsden, 1993.)
century, yet it did not generate the largest tsunami. The impact of the 1960 tsunami was dramatically different from that of the April 1, 1946 Aleutian tsunami, which was the largest tsunami of the past century in terms of height, underscoring how important source- and site-specific studies are for tsunami hazard assessment. Eaton writes that the two tide gages in Hilo harbor were “put out of action” by the leading depression wave before the highest wave, which was the third in the tsunami train, struck Hilo. Eaton and other observers from the United States Geological Survey situated themselves on the north end of Wailuku bridge and they measured wave heights with tape measures at “various reference points on the northernmost pier.” Their results are shown in the record in Figure 9.31, which is perhaps the only record available of a tsunami wave train with the signature of a bore. Eaton et al. [1961] wrote that the tsunami hit Hilo at 12:07 a.m. Hawaiian time (10:07 GMT) and the initial disturbance was reported as a leading elevation wave. The wave had traveled from Chile over 6600 mi (10,560 km) in about 15 h, for an average speed of 442 mph (707 km/h). The estimated arrival time had been 20 min earlier than observed, and Eaton speculated that part of the difference may be attributed to the slow propagation times over extreme shallow water near the bridge. It is also possible that a long leading depression wave of smaller height may have arrived but gone unnoticed because of its size. The crest of the first wave appears on the record as an elevation wave of height of about 1.2 m followed by a depression wave cresting at about −0.9 m. The second elevation wave crested 33 min later followed by −2.1 m depression 10 min later. The third elevation wave was a bore of approximate wave height of 6.1 m and crested about 20 min after the second wave. There were four other smaller waves measured behind the bore for the following 45 min. The entire phenomenon lasted for about 2 h after the first arrival. (In what follows, the calculations will be presented only in SI units.) The estimated time for the travel of the bore over the 2100 m separating the tip of the breakwater to the shoreline was about 2.5 min, giving an estimated speed of 12.7 m/sec. The local beach slope was estimated at tanβ = 0.015 or about 1:67. Assuming that the beach slope is fairly uniform, Ramsden [1993] then proceeded to calculate the force on a tall 3-m deep seawall at the shoreline from the Hw = 6.1-m high 1960 Hilo bore as follows (refer to the definition sketch shown in Figure 9.29). © 2003 by CRC Press LLC
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3.00 Experimental:
a)
Theoretical:
1.00
solitary waves undular bores turbulent bores: S=0.0 turbulent bores: S=0.02 Tanaka (1986)
IIdη/dxII
120° sharp crested wave 0.50 0.30
0.10
undular bores
strong turbulent bores
range of dry bed surge data
0.05 10 Theoretical: Su and Mirie (1980) moving hydraulic jump reflection Stoker (1957)
b) 7
R/2H
5
undular bores
strong turbulent bores
3
1 3 c)
Rg/c
2
1
range of dry bed surge data
0.7 0.5 strong turbulent bores
0.3 undular bores 0.1 0.1
0.3
0.5
1
3
5
10
30
H/k FIGURE 9.30 Experimental and theoretical maximum water surface slopes (a); run-up normalized by twice the incident wave height (b); and run-up normalized by twice the velocity head due to the wave celerity (c).
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14 12 10 8 6 4 2 0
Approx. mean Lower low water
-2 -4 -6
0h00m 10h00m
MAY 23
0h30m
1h00m 11h00m HOURS
1h30m
2h00m (Hawaiian Time) 12h00m (G.C.T.)
FIGURE 9.31 Measurements of the 1960 tsunami arriving at Hilo, Hawaii, from measurements made at the Wailuku River bridge (height in feet). (After Eckart et al., 1961.)
Given that the bore followed a −2.1-m depression wave, the estimated local depth hw at the tip of the seawall as the bore impinged was hw = 0.9 m, since the total depth was 3 m. The depth h where the estimate of H = 6.1 m was made has to be estimated so that the effective bore strength H/h can be calculated; recall what is known is only the depth at the seawall hw . Finding H/h is, in general, an iterative procedure and one uses Figure 9.30A. First, find the distance 3L from the seawall where the slope is calculated. Anticipating that this is a strong bore, first guess an effective frontal slope for the bore of dη/dx = 0.3. This implies that the effective horizontal length scale of the bore face L = H/(dη/dx) = 6.1 m/ 0.3 = 20.3 m. Therefore, the depth h is given by h = hw + 3L tanβ = 1.8 m. Therefore, given that H = 6.1 m then H/h = 3.4, and according to Figure 9.30A, the guess of dη/dx = 0.3 is adequate. Using Figure 9.32, the F/Fi ≈ 3.1, using the top of the envelope of data values in the figure. Then Fi = (1/2)ρg(2H + hw)2 ≈ 842 × 103 Nt/m, therefore F = (F/Fi) × Fi.= 2.6 × 106 Nt/m. Using Figure 9.30B, it is estimated that the expected run-up on the seawall is R/2H = 2.6; therefore, the expected run-up had the wall been that high is R = 32 m. The overturning moment can be estimated from Figure 9.33. For H/h = 3.4, the top of the data envelope suggests an M/Mi = 6.6; therefore, M = 23.1 × 106 Nt/m. If one uses the Cross [1967] equation with the maximum run-up as the maximum height on the wall of R = 32 m, then F = (1/2)ρgR2 + ρCfRc2, per unit width of the seawall. Given that dη/dx = tanθ = 0.3, then Cf = 1 + (tanθ)2 = 1.09. Using the estimate of c = g (H + hw ) = 8.25 m/sec, then F = 5.0 × 106 Nt + 2.4 × 106 Nt = 7.4 × 106 Nt/m. However if one uses the local speed of the bore C as obtained from Figure 9.34, then c/ gh = 3.3 for H/h = 3.4. Then F = (1/2) ρg (H + hw)2 + 2ρCf Hg (hw + H) = 240 × 103 + 3.3 × 836 × 103 Nt/m = 3 × 106 Nt/m. Also, note that if one used the height of the bore H and the depth ahead of the bore hw instead of the effective H/h, then H/hw = 6.8, and then F/Fi = 4.9, giving a force of 4.1 × 106 Nt/m, which is 57% higher than the force calculated from using the effective H/h. Clearly, extreme care is warranted in using the appropriate H/h in the force calculations. Ramsden [1993] points out that when b/H ≈ 1, then three-dimensional effects take over. Threedimensional effects are expected to reduce the overall force. On the other hand, when b << H, i.e., the © 2003 by CRC Press LLC
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30
10 7
F/F1
5 3
Experimental: solitary waves undular bores undular bores (first wave crest) turbulent bores: S=0.00 turbulent bores: S=0.02 Theoretical: Su and Mirie (1980). moving hydraulic jump reflection Stoker (1957)
1 0.7 0.5
undular bores
strong turbulent bores
0.3 FIGURE 9.32 Experimental and theoretical maximum force on the wall normalized by the hydrostatic force due to a run-up equal to twice the incident wave height.
100 70 50
M/M 1
30
10 7 5
Experimental: solitary waves undular bores undular bores (first wave crest) turbulent bores: S=0.00 Theoretical: Su and Mirie (1980). moving hydraulic jump reflection Stoker (1957)
3
1 0.7 0.5
undular bores
strong turbulent bores
0.3 FIGURE 9.33 Experimental and theoretical maximum moment on the wall normalized by the hydrostatic moment due to run-up equal to twice the incident wave height.
width of the wall is smaller than the effective crest length of the wave, the force would be primarily the drag force. When overtopping occurs, i.e., the wall height is smaller than the expected run-up R, the resulting forces may be significantly less. Since there are no established and validated formulas for overtopping, at least this theory provides a worst-case scenario for the forces on the wall. © 2003 by CRC Press LLC
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30 Experimental: solitary waves undular bores turbulent bores: S=0.00 turbulent bores: S=0.02 Theoretical: solitary wave: LonguetHiggins and Fenton (1974)
C/(gh) 1/2
10
moving hydraulic jump Stoker (1957)
7 5
strong turbulent bores 3 undular bores
1 01
0.3
0.5
1
3
5
10
30
H/h FIGURE 9.34 Experimental and theoretical wave celerities for all the experiments conducted during this study.
9.8.4
Practical Design Considerations
The Coastal Construction Manual (CCM) notes that flood loads include the following: • Hydrostatic forces, such as loads from standing or slowly moving water and buoyancy forces, denoted by fsta , Fbuoyancy • Forces from breaking waves, denoted by Fbrkw • Hydrodynamic forces from rapidly moving water, broken and breaking waves, tsunami run-up, denoted by FD, and in the cases of structures as Fdyn • Forces from debris impact, denoted by Fi In the worst-case scenario of natural catastrophes, tsunami flooding will be in addition to flooding from torrential rains. This is not as extreme as it sounds; there are suspicions that the 1994 Skagway, Alaska tsunami was generated by a submarine landslide, which was triggered by the additional sediment loading from the Skagway River in one of its more extreme flooding days. One has to check whether the design flood elevation (DFE), which may be different from the base flood elevation (BFE), includes the effects of tsunamis, and in most locales most likely it does not. The design flood depth is estimated from: ds = E sw − GS
© 2003 by CRC Press LLC
(9.132)
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where Esw is the 100-year still-water elevation above the datum, and GS the lowest eroded ground elevation, above datum, adjacent to the structure, excluding the effects of local scour [CCM, 1999]. The manual specifies that if the building site is near a flood zone, is steeply sloping, or adjacent to other buildings or obstructions that will accelerate flood velocities, then the upper bound of the design flood velocity should be taken, i.e., Vs = 2 gds
(9.133)
which is twice the SW velocity. The lateral hydrostatic load per unit width is calculated using: 1 1 fsta = ρgds2 = γds2 2 2
(9.134)
Waves and coastal flooding produce uplift forces on platforms, docks, and coastal structures on piles or stilts. The hydrostatic buoyancy force is calculated using Archimedes’ principle of buoyancy, i.e., that the buoyancy force is equal to the weight of the displaced fluid. When a “body” — in this case a structure — is tied to its foundation, the calculation of the buoyancy force is not as straightforward as the calculation of the buoyancy force on a floating body, which is simply the weight of the body. One would have to carefully calculate the submerged volume Vsubmerged of the structure and find its weight, i.e., Fbouyancy = ρg Vsubmerged = γ Vsubmerged
(9.135)
The CCM recommends that the breaking wave load be used as the design wave load, derived from storm wave statistics. For impact load on piles, CMM recommend Cd = 1.2 for nonbreaking waves, and then calculation of the drag force FD as follows: 1 FD = Cd ρV 2 A 2
(9.136)
where A is the submerged frontal area of the pile and A = 2Rds . In the case of tsunamis, if one follows the CCM recommendation and sets V2 = 4gds , i.e., V is equal to twice the critical flow speed, then: FD = 2Cd ρgds2 R
(9.137)
which is a very conservative estimate. For breaking waves, the CMM recommends that the breaking drag coefficient, Cdb = 1.75, be used with Hb = 0.78ds . The latter is the limiting wave height and is taken as the breaking wave height. For impact of breaking waves on vertical walls, CMM recommends for the wave force Fbrkw per unit width: Fbrkw = 1.1 C pρgds2 + 2.41 ρgds2
(9.138)
The manual cautions that the formula includes hydrostatic loading, and assumes that the vertical seawall causes full reflection or standing waves, and that the crest of the wave reaches a height of 1.2ds. Cp is the dynamic pressure coefficient and ranges from 1.6 for an “accessory structure with low hazard to human life” [CCM, 1999] to 2.8 for a coastal building to 3.2 for a high occupancy building or critical facility. The example of the calculation of forces for the Hilo bore underscores how difficult it is to use © 2003 by CRC Press LLC
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Equation 9.138 for a real tsunami, because the identification of ds is not obvious. It is recommended that the appropriate formulas in the earlier section are used whenever numerical simulation data exist for the particular locale for a design wave. To calculate the hydrodynamic load on a rectangular structure, CCM recommends using an equivalent depth ddyn = (1/2)CdV2/g for calculation of the forces, when the velocity V < 10 fps = 3.03 m/sec, which would normally translate to a limiting depth, ds = 5.7 ft. In other words, if the expected DSE or flow depth during a tsunami is smaller than this limiting ds = 5.7 ft, and, since for tsunamis it is CMMrecommended that V2 = 4gds , then ddyn = 2Cdds. The hydrodynamic force is given by: 1 2 Fdyn = ρgddyn = 2 Cd ρgds2 2
(9.139)
CD is the drag coefficient and depends on the relative ratio of width of the structure b to the DFE depth ds at the front of the structure. CCM also recommends b/ds < 12, Cd = 1.25, and for b/ds > 120, Cd = 2.0. The reason is that the larger the width of the structure, the larger the drag, not only because the frontal area increases, but also because of suction pressures smaller than hydrostatic on the back face. The wider the object, the smaller the back pressure. For velocities V > 10 fps, CCM recommends: 1 Fdyn = Cd ρV 2dsb 2
(9.140)
Debris loads are a significant hazard during tsunami attack. During the 1946 Alaskan tsunami, in the area most affected on Unimak and Senak Island, the tsunami carried logs from a nearby lumber plant and deposited them to elevations up to 42 m (140 ft). The debris line from tsunami-borne logs is still visible along the southern coastlines of Unimak and Senak. Logs and driftwood are omnipresent along the Pacific Northwest as well. In the densely populated beaches of Southern California parking lots front the first row of houses. Contrary to intuition, it does not take a large wave to float a vehicle and carry it inland. During the 1995 Manzanillo, Mexico tsunami, a 3-m (10-ft) tsunami carried recreational vehicles more than 100 m (333 ft) inland. Waterborne debris can become battering rams when they hit structures. At high speeds, large pieces of driftwood can resemble incoming missiles, at least as far as the initial impact to a wooden structure is concerned. Calculating debris impact loads involves guesswork as to the size of the object being carried by the flow and whether it is dragging along the beach face or the ocean floor. The CCM recommends for the impact load Fi, Fi = wV ( gt )
(9.141)
where w is the weight of the object impacting the structure, V is its velocity, and t is the duration of impact. As per the CCM, in the absence of any specific information as to the size of debris, consider w = 1000 lb, with V = gds for tsunamis. Clearly, large objects such as vehicles are not carried at the same speed as the tsunami current, so Equation 9.141 provides again a conservative estimate. In terms of the duration time t the CCM recommends a range of 0.7 to 1.1 sec for wood walls, 0.5 to 1.0 for wood piles, 0.2 to 0.4 for reinforced concrete walls, 0.3 to 0.6 for concrete piles, and 0.3 to 0.6 for reinforced concrete piles and concrete masonry walls and pipes. The values differ because of the differences in stiffness among the different materials. Heavier structures on shorter piles are stiffer, so it would be reasonable to use the low values in the ranges and use the upper values for lighter structures on longer piles.
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9.9 Producing Inundation Maps 9.9.1 The California Experience Inundation maps provide emergency managers in coastal communities necessary tools to plan and mitigate tsunami disasters. Inundation maps are not only useful in assessing the population and facilities at risk, but are also helpful in planning for emergency response. The preparation of inundation maps involves the assessment of the local geologic hazards, their interpretation in terms of tsunami initial conditions, and the calculation of the resulting potential coastal inundation. Inundation maps are now under preparation for most coastal areas of the Pacific states of the United States, most coastal areas of Japan, and several other vulnerable areas around the world. This section presents, as a case study, the preparation of tsunami inundation maps in California. Even using these state-of-the-art inundation prediction tools, California presents unique challenges in assessing tsunami hazards. First, there is an extremely short historic record of tsunamis in the state. Whereas in some areas in the Pacific 1000-year-long records exist, in California there are none known before the nineteenth century. Several tsunamis have been reported since 1800, but in most cases the information is not sufficient for reasonable inferences of the inundation. Second, most of the geologic work in the state has concentrated on identifying the risks associated with on-shore faults. Even at the time of writing (May 2002), there is scant and mostly unpublished information on offshore faults or landslide and slump scars suggestive of past submarine mass failures. Third, earlier estimates of tsunami hazards relied almost entirely on far-field sources and used pre-1980s inundation mapping technology. This created the impression among policy planners and the general public that the tsunami hazard was small. Fourth, near-shore seismic events may trigger tsunamis arriving within less than 20 min from generation, allowing little time for evacuation. Fifth, the coastal population density is the highest among the five Pacific states, and a tsunami arriving on the southern California beaches on a summer Sunday afternoon with tens of thousands of people on the beach poses nontrivial risks whose mitigation needs to be carefully planned for.
9.9.2
Existing Analyses of Tsunami Hazards in California
The most comprehensive calculation of tsunami hazards for California is the work of Houston and Garcia [1974] and of Houston [1980], both of which focused on the hazard in Southern California from farfield events. McCulloch [1985] also focused on the hazards in the Los Angeles region primarily from farfield events, but also considered several local events. Satake and Sommerville [1992] analyzed the Lompoc 1927 earthquake and the associated local hazards. In a seminal review, McCarthy et al. [1993] analyzed the historic records of tsunamis in California and predicted qualitatively the hazard over the entire State. Synolakis et al. [1997b] reviewed pre-1997 studies and observed that the earlier run-up estimates did not include inundation calculations. When performed with the new generation of inundation models, runup estimates were occasionally up to 100% higher than the earlier calculations suggested, depending on the near-shore topography. Borrero et al. [1999, 2001] studied near-shore tectonic, landslide, and slump sources in East Santa Barbara channel and produced run-up estimates ranging from 2 to 13 m. Locat et al. [2002] provide estimates for the leading wave heights for landslide-generated waves off Palos Verdes ranging from 10 to 40 m, depending on the initiation depth. The bathymetry off Palos Verdes is shown in Figure 9.35, with features suggestive even to non-marine geologists of landslide scarps. The current state of understanding is reviewed in Borrero [2002] and in Synolakis et al. [2002c]. Houston and Garcia [1974] used a combination FD solution and analytic solution of the LSW to calculate tsunami propagation, except in the Santa Monica and San Diego Bays, where they used an FE solution to resolve possible local resonance effects. They argued that the only reliable data for defining source characteristics at that time were from the 1964 Alaskan and the 1960 Chilean earthquakes. Based on these data, they approximated the initial ground deformation by a hypothetical uplift mass of ellipsoidal shape, about 600 mi long, with an aspect ratio of 1:5 and maximum vertical uplift of 8 to 10 m.
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FIGURE 9.35 The bathymetry in Santa Monica and San Pedro Bays. (After Bohannon and Gardner, 2002.) TABLE 9.4 Revised Predictions for Tsunami Hazards in Southern California Location
R100
R500
POLA/POLB Port Huaneme Santa Barbara
8 ft 11 ft 15 ft
15.0 ft 21.0 ft 33.0 ft
They then divided the Aleutian trench into segments and calculated the wave evolution from each segment, and repeated the procedure for tsunamis from the Peru-Chile trench to derive 100-year (R100) and 500-year (R500) tsunami run-up heights. Borrero [2002] and Synolakis et al. [2002c] have argued that the 100-year hazard in California is dominated by distant events, hence the Houston and Garcia analysis is probably adequate. Given the recent results on offshore landslide hazards, they argued that the 500-year hazard is dominated by local events and revised Houston and Garcia’s estimates. An example of the revised estimates is given in Table 9.4. McCulloch’s [1985] study was a seminal work on tsunami hazard potential in Southern California. McCulloch relied on Houston’s results for far-field tsunamis and then used seismological data to make predictions for near-shore events. McCulloch relied on several empirical formulas developed in Japan. These formulas had been extensively used before 1992; since then, high quality run-up data from the 1992 to 2001 events for many areas around the Pacific suggest that these formulas may only be applicable in Japan and that they can substantially underpredict the run-up elsewhere. McCulloch used the Japanese data to argue that a local seafloor earthquake having a magnitude 7.5 and a hypocentral depth of 4 km (2.5 mi) to 14 km (8.75 mi) could produce a tsunami accompanied by a run-up height of 4 m (13 ft) to 6 m (20 ft). In 1985, a 6-m tsunami may have appeared a marginal hazard, even though the tsunami height in the 1964 Alaskan tsunami in Crescent City, which killed 11 people, was about 6.2 m (20.6 ft), while the run-up height was 3.8 m (12.6 ft). The 1992 to 2001 postevent field surveys have shown that even a 4-m tsunami can cause extensive damage and flooding in flat coastlines, such as those in Santa Monica Bay or in Orange and San Diego Counties. Perhaps the most serious implication of McCulloch’s assessments is his conclusion that landslidegenerated waves would be small. As noted earlier, McCulloch’s calculation had an arithmetic error and his 0.014 m value should have been 14 m, consistent with newer estimates. Locat et al. [2002] provide estimates for the same slide ranging from 10 to 40 m. Homa Lee (private communication, 10/19/01) has suggested that a slide in this location may have happened in the past 500 years. McCarthy et al. [1993] performed a systematic analysis of all historic and possible tsunami hazards in California and they qualitatively calculated the tsunami hazard in California as high along the coast from Crescent City to Cape Mendocino, moderate south of the Cape to north of Monterey, high south of © 2003 by CRC Press LLC
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runup (m)
20 15 10 5 0
runup (m)
Monterey to Palos Verdes, and moderate south of Palos Verdes to San Diego. Synolakis et al. [1997b] revisited the McCarthy et al. estimates and identified the need for modeling from near-shore events. As an example, they considered a hypothetical fault rupture along the San Clemente fault. They found that results using the older pre-1980 methodology were as much as 50% lower than results using current inundation models. Borrero et al. [2001] studied tsunamis in East Santa Barbara Channel using the state-of-the-art inundation code used by NOAA-PMEL and known as MOST. They considered tsunamis generated from coseismic displacements from thrust faults underlying the Santa Barbara Channel. They also considered tsunamis generated by slope failures along the walls of the Santa Barbara Channel. Their results include predictions from the Gaviota mud flow [Edwards et al. 1993] and from the recently mapped Goleta slide [Greene et al., 2000]. Borrero et al. [2001] and Synolakis et al. [2002c] used a variety of publicly available maps and sources to develop a 250 m ≈ 9 arcsec computational grid including the Scripps Institute of Oceanography 3 arcsec grid of near-shore bathymetry. Examples of their work and of run-up distributions along the coast of Santa Barbara County are shown in Figure 9.36. Interestingly, their results are consistent with earlier reports of 9-m (30-ft) run-up for the 1812 tsunami [McCulloch, 1985] — revised “by reference to other earlier unpublished reports as 3–4 m (10–13.3 ft).” Unpublished results suggest that there is sedimentologic evidence also to associate the landslide with the 1812 event. Borrero et al.
20 15 10 5 0
Goleta slide, case 1
Goleta slide, case 2 -18m
60
Goleta case 1 50
-18m +6m
40
Goleta case 2
200m
400m +6m
30
200m
20
Santa Cruz Island
600m
10
1000m
0 0
20
40
60 Kilometers
FIGURE 9.36 Run-up estimates for two different locations of the Goleta slide.
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25 20 15 10 5 0 Los Angeles Harbor
Kilometers
40
-12m
30
+4m
20
10 wave gauge locations contours of initial surface
0 0
10
20
Kilometers
30
40 0
10
20
runup (m)
FIGURE 9.37 Run-up estimates from tsunamis triggered by the Palos Verdes debris avalanche.
[2001] found that purely tectonic sources could generate tsunamis with ≈ 2-m (6.7-ft) run-up, while combination of tectonic sources and submarine mass movements could generate extreme run-up of ≈ 20 m (66.67 ft) in one location. For the latter, they observed narrow run-up peaks and warned that, “A wave of this size anywhere along the populated shores of southern California would be devastating, and further mapping work is urgently needed to quantify this possibility.” Borrero [2002] also estimated the economic losses associated with a tsunami in San Pedro Bay, as shown in Figure 9.37. His results are shown in Figure 9.38, which also compares the relative economic impact from a tsunami and from flooding from a dam break.
9.9.4
Developing Inundation Maps for the State of California
In 1996, the Tsunami Hazard Mitigation Federal/State Working Group prepared a report to the United States Congress recommending the preparation of inundation maps for five states: Alaska, California, Hawaii, Oregon, and Washington. The report led to mobilization of significant federal resources for tsunami hazards mitigation, and to the establishment of the U.S. National Tsunami Hazard Mitigation Program (NTHMP), which provides resources in all five states for mitigating tsunami hazards. The NTHMP was the focus of a program review during the International Tsunami Symposium held on August 5 to 7, 2001 in Seattle, Washington [NOAA, 2001]. As early as 1997, the California’s Coastal Region Administrator of the Governor’s Office of Emergency Services (OES), through a series of workshops and publications, informed local governments and © 2003 by CRC Press LLC
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FIGURE 9.38 Socioeconomic impact from a possible rupture of the Palos Verdes debris avalanche and of a dam break around Long Beach, California.
emergency agencies of the plans to address tsunami hazards and presented the NTHMP. OES solicited input as to the levels of hazards to be represented on the maps, as the short length of the historic record did not permit a comprehensive probabilistic hazard assessment. It was then decided that the maps would include realistic worst-case scenarios to be identified further in the mapping process. In 1998, as funding became available for the state, OES contracted to the Tsunami Research Program of the University of Southern California the development of the first generation of inundation maps for the state. The State of California has the most densely populated coastlines of the five states in the NTHMP. The state had to utilize the same limited resources as the other four but assess offshore tsunami hazards over a much longer coastline. A comprehensive tsunami hazard evaluation involves both the probabilistic hazard assessment of different far-field and near-field, on-shore and offshore sources and the hydrodynamic computation of the tsunami evolution from the source to the target coastline. Given the level of funding, this was not feasible, and this presented another challenge for California. Given the quantitative agreement between model results and measurements for the 1964 tsunami of the work of Houston and Garcia [1974], it was decided to focus on near-shore tsunami hazards, which had not been modeled before 1999. If inundation predictions from near-shore events proved smaller than twice the far-field tsunami results of Houston and Garcia, then far-field sources would have to be considered as well. Early results suggested that for the areas studied, near-shore sources produced higher inundation heights that were twice the 100-year values of Houston and Garcia, hence only near-shore sources were considered. The State of California was also faced with the decision of choosing its mapping priorities. By considering the geographic distribution of population centers, the state opted to perform modeling of the Santa Barbara and San Francisco coastlines in year one, of Los Angeles and San Diego in year two, and of Monterey Bay in year three. The next decision was the resolution of the numerical grids to be used © 2003 by CRC Press LLC
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in developing the maps. The technology existed for high-resolution maps with grids of sizes as small as 5 m (16.7 ft) square, but this would result in a relatively small spatial coverage with large computational grids and painful computations. It was decided to produce maps at 125 m (417 ft) resolution, based on Titov and Synolakis [1997], who had argued that dense grids may improve numerical accuracy but do not improve the realism if the available bathymetric/topographic sets are not of similar resolution. In the State of California, the best available sets varied in resolution between 50 m (167 ft) and 150 m (500 ft). Also, given the uncertainties in locating and understanding source mechanisms, results with higher resolution would be misleading. The next question was whether to provide emergency planners with inundation results at different levels of risk. For example, one suggestion was to include low- and high-risk lines on the inundation maps. Another suggestion was to provide separate lines for near-field and far-field events. On discussing these issues with emergency preparedness professionals across the state, it was felt that a single line representing a worst-case scenario was preferable, for it simplified the preparedness response of city officials and it better informed the general public. Further, without a probabilistic hazard assessment it was difficult to rank the relative risk from different scenarios. Lines identifying risk zones for near-field and far-field events could also prove cumbersome and confusing for the public. It was therefore decided to consider, for every locale in the region under consideration, the worst-case near-shore event that was plausible based on the available historic earthquake and tsunami information. The inundation mapping effort first identified offshore faults and offshore landslide and slump hazards. Difficulties encountered included the lack of detailed high-resolution marine surveys over all target coastlines. With the exception of marine surveys undertaken by the U.S. Geological Survey off Santa Monica Bay and of the Monterey Bay Aquarium Marine Institute (MBARI) off Santa Barbara and Monterey Bay, high-resolution surveys are not available for other parts of the state, if indeed they do exist at all. Hence, and given that on-shore earthquakes can trigger submarine landslides, in regions where marine geology data did not exist, steep submarine soft sediment slopes were considered as possible sources. Offshore faults and slide-prone areas were then used to develop initial tsunami waves as discussed in Borrero et al. [2001], and then the inundation model MOST was used to obtain inundation heights and penetration distances along the target coastline. The inundation predictions for any given event are highly bathymetry and topography dependent and vary substantially along the coast. Since the location of the source is seldom accurately known, the source was moved around within the range of uncertainty. Along California’s flat coastlines, this relocation of the tsunami sources resulted in relocation of the maximum along the coast. When asked, emergency planners preferred to have a single value for each region identifying the maximum elevation that tsunami waves from the different local offshore sources would attain. This practice would simplify the communication of the risk to the public and it would provide information that was easy to remember and implement in regional emergency preparedness. For example, a region could plan for tsunami evacuation areas above a certain minimum elevation across its jurisdiction. Hence, in the development of the maps, sources were relocated along the coast and the highest inundation value among different runs identified. Interestingly, in the areas studied there were no areas that consistently experienced higher run-up than adjacent locales. Synolakis et al. [2002c] found that most low-lying coastal areas could experience high run-up, if the source was relocated in an appropriate direction, within the uncertainties of defining the source. Thus, the inundation maps for California do not represent the inundation from any particular event or characteristic earthquake, but the locus of maximum penetration distances from relocating worst-case scenario events. Once draft versions of the maps became available, OES presented them in regional meetings with emergency preparedness officers and other interested parties such as the State Lands, Seismic Safety and Coastal Commissions. Further input was solicited, and an emergency response manual [OES, 2002] with guidelines for mitigation was produced. OES also produced a video for school use and distributed numerous copies of other commercial video programs describing tsunami hazards. The development of the state’s inundation maps was featured in four Discovery channel television documentaries and in numerous national and local news stories. One representative map for South San Francisco is shown in Figure 9.39. © 2003 by CRC Press LLC
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FIGURE 9.39 Example of a California inundation map for South San Francisco.
Since many engineers are occasionally asked to make recommendations on using inundation maps, it is appropriate to end with some of the guidelines from OES’s [2000] Local Planning Guidance on Tsunami Response: • The development of a tsunami plan requires a multidisciplinary approach and should involve local specialists (emergency responders, planners, engineers, utilities and community based organizations). The city or county administrative office should appoint a tsunami plan working group and designate a chairperson, usually the emergency services manager. • One of the most critical elements of a tsunami plan is the evacuation and traffic control plan. A distant-source tsunami may allow several hours to evacuate. A near-source tsunami may require immediate self-evacuation through areas damaged by the earthquake. Each jurisdiction should analyze how much time an evacuation would require and build that into the decision-making procedure. • Inundation projections and resulting planning maps are to be used for emergency planning purposes only. They are not based on a specific earthquake and tsunami. Areas actually inundated © 2003 by CRC Press LLC
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by a specific tsunami can vary from those predicted. The inundation maps are not a prediction of the performance in an earthquake or tsunami of any structure within or outside the projected inundation area. • Elements to consider in developing an evacuation plan are 1. Locate optimum evacuation routes. The primary objective is to move up and inland away from the coast. Finally, for further information on tsunamis, the author recommends the following URLs: http://www.pmel.noaa.gov/ http://www.pmel.noaa.gov/tsunami/home.html http://www.usc.edu/dept/tsunamis http://www.geophys.washington.edu/tsunami/ http://www.wsspc.org/tsunami/tsunami.html http://geopubs.wr.usgs.gov/open-file/of99–360/ http://www.civil.tohoku.ac.jp/english/tunami/node1.html http://walrus.wr.usgs.gov/staff/egeist/egeist.html http://www.earth.northwestern.edu/research/okal/ http://yalciner.klare.metu.edu.tr/ http://www.tsunami.org/ http://www.mbari.org/data/mapping/SBBasin/basin.htm http://omzg.sscc.ru/tsulab http://tsun.sscc.ru/htdbpac
Acknowledgments The author acknowledges the work of his former Ph.D. students, Drs. Utku Kanoglu, Vasily Titov, Cristophe Ruscher, Jose Borrero, and Srinivas Tadepalli, and his current students, Irina Hoffman, Diego Arcas, Matt Swensson, and Burak Uslu. They are all magnificent. The intellectual contributions of Professors Raichlen, Okal, Liu, Yeh, and Yalciner and of NOAA-PMEL Director Dr. Eddie Bernard and Frank Gonzalez are gratefully acknowledged here. I am equally grateful to Rich Eisner and Dick McCarthy and to my colleagues at the LA County Emergency Preparedness Commission for all their ideas, enthusiasm, and encouragement. Without the generous support of the Earthquake Hazard Mitigation Program of the National Science Foundation and of its project manager, Dr. Cliff Astill, we would still be estimating tsunami hazards with slide rules. Charles Scawthorn and Joanne Blake provided invaluable editing assistance. Finally, the author acknowledges Chris Gaudiot, whose support in the benwillian saga made it all possible.
References Abe, K. and Ishil, H. 1980. “Propagation of Tsunami on Linear Slope between Two Flat Regions. II. Reflection and Transmission,” J. Phys. Earth, 28, 543–552. Abramowitz, M. and Stegun, I.A. 1964. Handbook of Mathematical Functions, National Bureau of Standards Applied Mathematics Series 55, U.S. Department of Commerce, Washington, D.C. Berkhoff, J.C.W. 1972. “Computation of Combined Refraction-Diffraction,” Proc. 13th Coastal Engineering Conference, Vancouver, vol. 1, pp. 471–490, American Society of Civil Engineers, New York. Berrard, A. and Burch, J.M. 1987. Introduction to Matrix Methods in Optics, University Microfilms International, John Wiley & Sons, New York. Bohannon, R.G. and Gardner, J.V. 2002. “Submarine Landslides of San Pedro Sea Valley, Southwest Los Angeles Basin,” in Prediction of Underwater Landslide Hazards, in preparation. Borrero, J., Ortiz, M., Titov, V., and Synolakis, C. 1997. “Field Survey of Mexican Tsunami Produces New Data, Unusual Photos,” Eos Trans. Am. Geophys. Union, 78, 85, 87–88. © 2003 by CRC Press LLC
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Borrero, J.C., Dolan, J.F., and Synolakis, C.E. 2001. “Tsunamis within the Eastern Santa Barbara Channel,” Geophys. Res. Lett., 28(4), 643–646. Briggs, M.J., Synolakis, C.E., Harkins, G.S., and Hughes, S.A. 1993. “Large Scale Three-Dimensional Laboratory Measurements of Tsunami Inundation,” Pure Appl. Geophys. Briggs, M.J., Synolakis, C.E., Harkins, G.S., and Green, D. 1994. “Laboratory Experiments of Tsunami Runup on a Circular Island,” Pure Appl. Geophys., 144, 569–593. Briggs, M.J., Synolakis, C.E., Harkins, G.S. et al. 1995. “Laboratory Experiments of Tsunami Runup on a Circular Island,” Pure Appl. Geophys., 144 (3–4), 569–593. Carrier, G.F. 1966. “Gravity Waves of Water of Variable Depth,” J. Fluid Mech., 24, 641–659. Carrier, G.F. and Greenspan, H.P. 1958. “Water Waves of Finite Amplitude on a Sloping Beach,” J. Fluid Mech., 17, 97–110. Chrystal, G. 1905. “On the Hydrodynamical Theory of Seiches,” Trans. R. Soc. Edinburgh, 41 (Part III), 599–649. Cross, R.H. 1967. “Tsunami Surge Forces,” J. Waterways Harbor Division, 93 (4), 201–231. Dean, R.G. and Harleman, D.R.F. 1966. “Interaction of Structures and Waves,” in Coastline and Estuarine Hydrodynamics, Ippen, A.T., Ed., McGraw Hill, New York, 341–402. Demirbilek, Z., 1994. “Comparison between REFDIFS and CERC Shoal Laboratory Study,” unpublished report, Waterways Experimental Station, Vicksburg, MS, p. 53. Demirbilek, Z. and Pachang, V. 1998. “CGWAVE: A Coastal Surface Water Wave Model of the Mild Slope Equation.” Demirbilek, Z., Xu, B., and Pachang, V. 1996. “Wave-Current Interaction at Inlets,” in Proc. 25th International Coastal Engineering Conference, 1219–1232. Eaton, J.P., Richter, D.H., and Ault, W.U. 1961. “The Tsunami of May 23, 1960 on the Island of Hawaii,” Bull. Seismol. Soc. Am., 51 (2), 135–157. Edwards, B.D., Lee, H.J., and Field, M.E. 1995. “Seismically Induced Mudflow in the Santa Barbara Basin, California,” in Submarine Landslides: Selected Studies in the U.S. Exclusive Economic Zone, Schwab, W.C., Lee, H.J., and Twichell, D.C., Eds., U.S. Geological Survey Bulletin, pp. 167–175. Eissler, H.K. and Kanamori, H. 1987. “A Single-Force Model for the 1975 Kalapana, Hawaii, Earthquake,” J. Geophys. Res. Solid Earth, 92 (6), 4827–4836. Fryer, G.J., Watts, P., and Pratson, L.F. 2001. “Source of the Tsunami of 1 April 1946: A Landslide in the Upper Aleutian Forearc,” Unpublished manuscript. Fujima, K. and Shuto, N. 1990. “Formulation of Friction Laws for Long Waves on a Smooth Dry Bed,” Coastal Eng., 33 (1), 25–47. Gardarsson, S.M. 1997. “Shallow-Water Sloshing,” Ph.D. thesis, University of Washington, Seattle. Gerard, A. and Burch, J.M. 1987. Introduction to Matrix Methods in Optics, University Microfilms International, John Wiley & Sons, New York. Gjevik, B. and Pedersen, G. 1981. Run-Up of Long Waves on an Inclined Plane, Preprint Series, Institute of Mathematics, University of Oslo, Norway. Goring, D.G. 1978. Tsunamis: the Propagation of Long Waves onto a Shelf, Report No. Kh-R-38, W.M. Keck Laboratory of Hydraulics and Water Resources, Division of Engineering and Applied Science, California Institute of Technology, Pasadena. Green, G. 1837. Cambridge Philosophical Transactions, Vol. 6, p. 457. Green, H.G., Maher, N., and Paull, C.K. 2000. “Landslide Hazards off of Santa Barbara California (Abstr.),” American Geophysical Union Fall Meeting.` Gusiakov, V.K. 2001. “Basic Pacific Tsunami Catalogs and Database, 47 BC–2000 AD,” in Proc. International Tsunami Symposium, August 7–10, Seattle, WA, pp. 263–272. Gustafsson, B. and Kreiss, H.-O. (1979). “Boundary Conditions for Time Dependent Problems with an Artificial Boundary,” J. Comp. Phys., 30, 333–351. Gutenberg, B. 1939. “Tsunamis and Earthquakes,” Bull. Seismol. Soc. Am., 29(4), 517–526. Hall, J.V. and Watts, J.W. 1953. “Laboratory Investigation of the Vertical Rise of Solitary Waves on Impermeable Slopes,” Tech. Memo 33, Beach Erosion Board, U.S. Army Corps of Engineers. © 2003 by CRC Press LLC
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Hasegawa, H.S. and Kanamori, H. 1987. “Source Mechanism of the Magnitude 7.2 Grand Banks Earthquake of November 1929: Double Couple or Submarine Landslide?” Bull. Seismol. Soc. Am., 77(6), 1984–2004. Heinrich, P. 1992. “Nonlinear Water Waves Generated by Submarine and Aerial Landslides,” J. Waterway Port Coastal Ocean Eng., 118 (3), 249–266. Houston, J.R. 1980. “Type 19 Flood Insurance Study,” Waterways Experiment Station Rep. H-80-18, U.S. Army Corps of Engineers. Houston, J.R. and Garcia, A.W. 1974. “Type 16 Flood Insurance Study,” Waterways Experiment Station Rep. H-74-3, U.S. Army Corps of Engineers. Imamura, F., Synolakis, C.E., Gica, E., Titov, V., Listanco, E., and Lee, H.J. 1995. “Field Survey of the 1994 Mindoro Island, Philippines Tsunami,” Pure Appl. Geophys., 144 (3–4), 875–890. Imamura, F., Subandono, D., Watson, G., Moore, A., Takahashi, T., Matsutomi, H., and Hidayatt, R. 1996. “Irian Jaya Earthquake and Tsunami Cause Serious Damage,” Eos Trans. Am. Geophys. Union Ippen, A.T. (Ed.). 1996. Coastline and Estuarine Hydrodynamics, McGraw-Hill, New York. Jiang, L. and LeBlond, P.H. 1992. “The Coupling of a Submarine Slide and the Surface Waves which it Generates,” J. Geophys. Res. Oceans, 97 (C8), 12731–12744. Kanamori, H. 1985. “Non-Double-Couple Seismic Source (Abstr.),” Proceedings of the 23rd General Assembly, International Association of Seismological Physics Earth International, Tokyo, p. 425. Kanamori, H. 1972. “Mechanisms of Tsunami Earthquakes,” Phys. Earth Planet Int., 6, 346–359. Kanamori, H. and Anderson, D.L. 1975. “Theoretical Basis of Some Empirical Relations in Seismology,” Bull. Seismol. Soc. Am., 65 (5), 1073–1095. Kanoglu, U. 1996. “The Runup of Long Waves around Piecewise Linear Bathymetries,” Ph.D. thesis, University of Southern California, Los Angeles. Kanoglu, U. and Synolakis, C.E. 1988. “Long Wave Runup on Piecewise Linear Topographies,” J. Fluid Mechanics, 374, 1–28. Keller, J.B. and Keller, H.B. 1964. “Water Wave Runup on a Beach,” ONR Rep. Contract NONR-3828(00), Department of the Navy, Washington, D.C. Kobayashi, N. and Greenwald, J.H. 1987. “Wave Reflection and Runup on Rough Slopes,” J. Waterways Ports Coastal Eng., 113, 282–298. Korgen, B.J. 1995. “Seiches,” Am. Sci., 83, 330–341. Lamb, H. 1932. Hydrodynamics, 6th ed., Dover, New York. Lee., J.J. 1969. “Wave Induced Oscillations in Harbors of Arbitrary Shape,” Ph.D. thesis, California Institute of Technology, Pasadena. Lee, J.J., Lai, C.P., and Li, Y. 1998. “Application of Computer Modeling for Harbor Resonance Studies of Long Beach Los Angeles Harbor Basins,” Proc. 26th ICCE, Copenhagen, Denmark, American Society of Civil Engineers, New York. LeMehaute, B. and Wilson, B.W. 1962. “Harbor Paradox,” J. Waterways Harbors Division, (May), 173–195. Liu, P.L.-F. and Synolakis, C.E. 2003. Tsunami Hydrodynamics, World Scientific, London, in preparation. Liu, P.L.-F., Synolakis, C.E., and Yeh, H.H. 1991. “Report on the International Workshop on Long Wave Runup,” J. Fluid Mech., 229, 675–688. Liu, P. L.-F., Cho, Y.-S, Briggs, M.J., Kanoglu, U., and Synolakis, C.E. 1995. “Runup of Solitary Waves on a Circular Island,” J. Fluid Mech., 320, 259–285. Locat, J., Locat, P., and Lee, H.J. 2001. “Numerical Analysis of the Mobility of the Palos Verdes Debris Avalanche, California, and its Implications for the Generation of Tsunamis,” Unpublished manuscript. Mansinha, L. and Smylie, D.E. 1971. “The Displacement Fields of Inclined Faults,” Bull. Seismol. Soc. Am., 61, 1433–1440. McCarthy, R.J., Bernard, E.N., and Legg, M.R. 1993. “The Cape Mendocino Earthquake: A Local Tsunami Wakeup Call?” in Proc. Eighth Symposium on Coastal and Ocean Management, New Orleans, pp. 2812–2828.
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McCulloch, D.S. 1985. “Evaluating Tsunami Potential,” in Evaluating Earthquake Hazards in the Los Angeles Region: An Earth Science Perspective, U.S. Geological Survey Professional Paper 1360, pp. 375–414. Mei, C.C. 1989. The Applied Dynamics of Ocean Surface Waves, World Scientific, London. Merian, J.R. 1828. Über die Bewegung tropfbarer Flüssigkeiten in Gefassen, Basle, see Von der Muhll, Math. Ann. 27, 575. Meyer, R.E. 1988. “On the Shore Singularity of Water Wave Theory,” Physical Fluids, 29, 3142–3183. Miles, J. and Munk, W. 1961. “Harbor Paradox,” J. Waterways Harbors, WW3, 111–130. Newman, A.V. and Okal, E.A. 1998. “Teleseismic Estimates of Radiated Seismic Energy: The E/M0 Discriminant for Tsunami Earthquakes,” J. Geophys. Res., 103, 26885–26898. Okada, Y. 1985. “Surface Deformation Due to Shear and Tensile Faults in a Half-Space,” Bull. Seismol. Soc. Am., 75 (4), 1135–1154. Okal, E.A. 1992. “Use of the Mantle Magnitude Mm for Reassesment of the Seismic Moment of Historical Earthquakes. I. Shallow Events,” Pure Appl. Geophys., 139, 17–57. Okal, E.A., Fryer, G.J., Borrero, J.C., and Ruscher, C. 2002a. ”The Landslide and Local Tsunami of 13 September 1999 on Fatu Hiva (Marquesas Islands; French Polynesia),” Bull. Soc. Geol. France, in press. Okal, E.A., Synolakis, C.E., Fryer, G.J., Heinrich, P., Borrero, J.C., Ruscher, C., Arcas, D.R., Guille, G., and Rousseau, D. 2002b. “A Field Survey of the 1946 Aleutian Tsunami in the Far Field,” Bull. Seismol. Soc. Am., in press. Pelayo, A.M. and Wiens, D.A. 1990. “The November 20, 1960 Peru Tsunami Earthuake: Source Mechanism of a Slow Event,” Geophys. Res. Lett., 17(6), 661–664. Pelinovsky, E., Yuliadi, D., Prasetya, G., and Hidayat, R. 1997. “The 1996 Sulawesi Tsunami,” Natural Hazards, 16 (1), 29–38. Prager, E.J. 1999. Furious Earth, McGraw-Hill, New York. Raichlen, F. 1966. “Harbor Resonance,” in Coastline and Estuarine Hydrodynamics, Ippen, A.T., Ed., McGraw-Hill, New York, 281–340. Ramsden, J.D. and Raichlen, F. 1990. “Forces on Vertical Wall Caused by Incident Bores,” J. Waterway Port Costal Ocean Eng., 116 (5), 592–613. Ruscher, C. 1998. “The Sloshing of Trapezoidal Reservoirs,” Ph.D. thesis, University of Southern California, Los Angeles. Satake, K. and Somerville, P. 1992. “Location and Size of the 1927 Lompoc, California Earthquake from Tsunami Data,” Bull. Seismol. Soc. Am., 82, 1710–1725. Shaw, J. and Suppe, J. 1994. “Active Faulting and Growth Folding in the Eastern Santa Barbara Channel, California,” Geol. Soc. Am. Bull., 106, 607–626. Shaw, J. and Suppe, J. 1996. “Earthquake Hazards of Active Blind-Thrust Faults under the Central Los Angeles Basin, California,” J. Geophys. Res., 101 (B4), 8623–8642. Shaw, R.P. 1974. “Long Wave Trapping by Axisymmetric Topographies,” JTRE Internal Report No. 119, Joint Tsunami Research Effort, University of Hawaii, Honolulu. Shuto, N. 1967 “Run-Up of Standing Waves in a Front of a Sloping Dike,” Coastal Eng. Jpn., 10, 23–38. Soloviev, S.L. and Go, Ch.N. 1974. A Catalogue of Tsunamis on the Western Shore of the Pacific Ocean (in Russian), Nauka Publishing, Moscow (English trans. 1984, Canada Institute for Scientific and Technical Information, National Research Council, Ottawa). Soloviev, S.L. and Go, Ch.N. 1975. A Catalogue of Tsunamis on the Eastern Shore of the Pacific Ocean (in Russian), Nauka Publishing, Moscow (English trans. 1984, Canada Institute for Scientific and Technical Information, National Research Council, Ottawa). Stoker, J.J. 1947. “Surface Waves in Water of Variable Depth,” Q. Appl. Math., 5, 1–54. Striem, H.L. and Miloh, T. 1975. “Tsunamis Induced by Submarine Slumpings off the Coast of Israel,” Israel Atomic Energy Commission. Synolakis, C.E. 1986. “The Runup of Long Waves,” Ph.D. thesis, California Institute of Technology, Pasadena. Synolakis, C.E. 1987. “The Runup of Solitary Waves,” J. Fluid Mech., 185, 523–545. © 2003 by CRC Press LLC
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Synolakis, C.E. 1988. “On the Roots of f(z) = J0(z)-iJ1(z),” Q. Appl. Math., 46, 105–107. Synolakis, C.E. 1990. “Generation of Long Waves in the Laboratory,” J. Waterways Port Coastal Ocean Eng., 116, 252–266. Synolakis, C.E. and Skelbreia, J.E. 1993. “Evolution of Maximum Amplitude of Solitary Waves on Plane Beaches,” J. Waterway Port Coastal Eng., 119 (3), 323–342. Synolakis, C.E. and Uslu, B.B. 2003. “Estimates of the Initial Height of Landslide Waves,” Manuscript in preparation. Synolakis, C.E., Imamura, F., Tsuki, Y., Matsutomi, H., Tinti, S., Cook, B., Chandra, Y.P., and Usman, M. 1995. “Damage Conditions of East Java Tsunami 1994 Analyzed,” Eos Trans. Am. Geophys. Union, 76(26), 257, 261–262. Synolakis, C.E., Liu, P., Carrier, G., and Yeh, J. 1997a. “Tsunamigenic Sea-Floor Deformations,” Science, 278 (5338), 598–600. Synolakis, C.E., McCarthy, R., and Bernard, E.N. 1997b. “Evaluating the Tsunami Risk in California,” in Proceedings of the Conference of the American Society of Civil Engineers, California and the World Ocean ’97, San Diego, CA, American Society of Civil Engineers, New York, p. 1225–1236. Synolakis, C.E., Bardet, J.P., Borrero, J.C., Davies, H., Okal, E.A., Silver, E.A., Sweet, S., and Tappin, D.R. 2002a. “Slump Origin of the 1998 Papua New Guinea Tsunami,” Proc. R. Soc. London Ser. A, 458, 763–789. Synolakis, C.E. et al. 2002b. Science Tadepalli, S. and Synolakis, C.E. 1994. “Roots of Jn(z) ± iJn+1(z) and the Evaluation of Integrals with Cylindrical Function Kernels,” Q. Appl. Math., 52, 103–112. Tadepalli, S. and Synolakis, C.E. 1996. “Model for the Leading Waves of Tsunamis,” Phys. Rev. Lett., 77 (10), 2141–2144. Titov, V.V. and Synolakis, C.E. 1993. “A Numerical Study of the Wave Runup of the September 1, 1992, Nicaraguan Tsunami,” in Proc. IUGG International Tsunami Symposium, Wakayama, Japan, pp. 627–634. Titov, V.V. and Synolakis, C.E. 1994. “The Runup of N-Waves on Sloping Beaches,” Proc. R. Soc. London Ser. A, 445, 99–112. Titov, V.V. and Synolakis, C.E. 1995. “Modeling of Breaking and Non-Breaking Long-Wave Evolution and Runup Using VTCS-2,” J. Waterway Port Ocean Coastal Eng., 121 (6), 308–316. Titov, V.V. and Synolakis, C.E. 1997. “Extreme Inundation Flows during the Hokkaido-Nansei-Oki Tsunami,” Geophys. Res. Lett., 24 (11), 1315–1318. Titov, V.V. and Synolakis, C.E. 1998. “Numerical Modeling of Tidal Wave Runup,” J. Waterway Port Ocean Coastal Eng., 124 (4), 157–171. Watts, P. 1997. “Water Waves Generated by Underwater Landslides,” Ph.D. thesis, California Institute of Technology, Pasadena. Watts, P. 1998. “Wavemaker Curves for Tsunamis Generated by Underwater Landslides,” J. Waterway Port Ocean Coastal Eng., 124 (3), 127–137. Watts, P. 2000. “Tsunami Features of Solid Block Underwater Landslides,” J. Waterway Port Ocean Coastal Eng., 126 (3), 144–152. Watts, P. and Borrero, J.C. 2001. “Probability Distributions of Landslide Tsunamis,” in Proc. International Tsunami Symposium, August 7–10, Seattle, WA, pp. 697–710. Wiegel, R.L. 1955. “Laboratory Studies of Gravity Waves Generated by the Movement of a Submerged Body, ”Trans. Am. Geophys. Union, 36(5), 759–774. Wilson, B.W. 1972. “Seiches,” in Advances in Hydroscience, vol. 8, Chow, V.T., Ed., Academic Press, New York, 1–89. Xu, B.Y. and Pachang, V. 1993. “Outgoing Boundary-Conditions for Finite-Difference Elliptic WaterWave Models,” Proc. R. Soc. London Ser. A, 441 (1913), 575–588. Yanenko, N.N. 1971. The Method of Fractional Steps (trans. M. Holt), Springer-Verlag, New York. Yeh, H., Liu, P.F., and Synolakis, C.E. 1992. Long Wave Runup Models, World Scientific, London. Zelt, J.A. 1991. “The Runup of Breaking and Nonbreaking Solitary Waves,” Coastal Eng., 125, 205–246. © 2003 by CRC Press LLC
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10 Soil–Structure Interaction
10.1 Soil–Structure Interaction: Statement of the Problem Elements of SSI Analysis · A Significant SSI Experiment
10.2 Specification of the Free-Field Ground Motion Control Motion and Earthquake Characteristics · Control Point · Spatial Variation of Motion and Kinematic Interaction · Validation of Ground Motion Variation with Depth of Soil · Validation of Kinematic Interaction · Variation of Ground Motion in a Horizontal Plane
10.3 Modeling of the Soil Field Exploration
10.4 Soil–Structure Interaction Analysis SSI Parameters and Analysis · Modeling of the Foundation · Modeling of the Structure
James J. Johnson James J. Johnson and Associates Alamo, CA
10.5 Soil–Structure Interaction Response Defining Terms References
10.1 Soil–Structure Interaction: Statement of the Problem The response of a structure during an earthquake depends on the characteristics of the ground motion, the surrounding soil, and the structure itself. For structures founded on rock or very stiff soils, the foundation motion is essentially that which would exist in the soil at the level of the foundation in the absence of the structure and any excavation; this motion is denoted the free-field ground motion. For soft soils, the foundation motion differs from that in the free field due to the coupling of the soil and structure during the earthquake. This interaction results from the scattering of waves from the foundation and the radiation of energy from the structure due to structural vibrations. Because of these effects, the state of deformation (particle displacements, velocities, and accelerations) in the supporting soil is different from that in the free field. As a result, the dynamic response of a structure supported on soft soil may differ substantially in amplitude and frequency content from the response of an identical structure supported on a very stiff soil or rock. The coupled soil–structure system exhibits a peak structural response at a lower frequency than would an identical rigidly supported structure. Also, the amplitude of structural response is affected by the additional energy dissipation introduced into the system through radiation damping and material damping in the soil.
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Kinematic Interaction Foundation Input motion
Free-field Motion
M F
Soil profile
Foundation Impedance
SSI
Structural Model
FIGURE 10.1 Schematic representation of the elements of soil–structure interaction.
Much of this chapter focuses on structures for which soil–structure interaction (SSI) is an important phenomenon in the design process of the structure and for systems and components housed therein. The type of structure and its foundation determines the importance of SSI. SSI effects can usually be ignored for conventional structures without significant embedment. Even for conventional structures with embedded foundations, ignoring SSI is usually conservative. However, even for conventional structures, it is prudent to consider and evaluate the potential effects of SSI on structure, system, and component design to assure oneself that excessive conservatism is not being introduced. SSI is most important for massive, stiff structures with mat foundations or with foundation systems significantly stiffened by the structure’s load-resisting system. Typical nuclear power plant structures, founded on soil, are particularly affected by SSI. Hence, the references and examples herein are drawn from the nuclear power industry.
10.1.1 Elements of SSI Analysis The analysis of SSI depends on the specification of the free-field ground motion and the idealization of the soil and structure. Modeling the soil involves determining its configuration and material properties. Modeling the structure includes the structure itself and its foundation. The calculated responses must be interpreted in light of differences between the idealized system and the real physical situation, and the uncertainties known to exist in the phenomenon. Figure 10.1 shows the elements of seismic analysis necessary to calculate seismic response, including SSI effects. Table 10.1 lists the various aspects, including interpretation and recognition of uncertainties in the process. The state of knowledge of SSI was well documented in 1980 in a compendium [Johnson, 1981] of contributions from key researchers (Luco, Roesset, Seed, and Lysmer) and drew upon other researchers and practitioners as well (Veletsos, Chopra). This reference provided a framework for SSI over the 1980s and 1990s, which were characterized by the accumulation of substantial data supporting and clarifying the roles of the various elements of the SSI phenomenon. Also, significant progress was made in the development and implementation of SSI analysis techniques. In the international nuclear power industry, © 2003 by CRC Press LLC
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TABLE 10.1 Elements of a Seismic Response Analysis Including Soil–Structure Interaction Specification of the Free Field Ground Motion Control point Control motion (peak ground acceleration and response spectra) Spatial variation of motion (wave propagation mechanism) Magnitude, duration Models of soils and structures Soil Properties Nominal properties (low and high strain) Variability SSI Parameters Kinematic interaction Foundation impedances Structure models Important features (torsion, floor flexibility, frequency reduction with strain, etc.) Variability (frequency and mode shapes, damping) Nonlinear behavior SSI Analysis Interpretation of Responses
the 1980s and 1990s saw a revision of important regulatory practices to conform to the current state of knowledge. Documentation of the state of knowledge of SSI was updated in 1991 and 1993 [Johnson and Chang, 1991; Johnson and Asfura, 1993]. The specific purpose of this update was to identify realistic approaches to the treatment of SSI and its uncertainties. This new understanding of the SSI phenomenon permitted the implementation and use of less conservative, more realistic procedures for the design of structures, systems, and components, and for the evaluation of structures, systems, and components when subjected to beyond-design basis earthquake events. The reader is directed to two other recent references that highlight the current state of the art and practice of SSI analysis. Tseng and Penzien [2000] discuss the SSI problem and its treatment in the context of multi-supported structures, such as bridges. Wolf and Song [2002] summarize numerous elements of the SSI phenomenon and their treatment analytically.
10.1.2 A Significant SSI Experiment Before proceeding further, it is useful to discuss an important SSI experiment. Very few opportunities exist to record free-field motion and structure response for an earthquake. In the mid-1980s, the Electric Power Research Institute (EPRI), in cooperation with Taiwan Power Company (TPC), constructed two scale-model reinforced concrete nuclear reactor containment buildings (one quarter and one twelfth scale). The scale models were located within an array of strong motion instruments (SMART-l, Strong Motion Array Taiwan, Number 1) in Lotung, Taiwan, sponsored by the U.S. National Science Foundation and maintained by the Institute of Earth Sciences of Academia Sciences of Taiwan. The experiment was extensively instrumented in the free field and in the structures. The objectives of the experiment were to measure the responses at instrumented locations due to vibration tests, and due to actual earthquakes, sponsor a numerical experiment designed to validate analysis procedures and to measure free-field and structure response for further validation of the SSI phenomenon and SSI analysis techniques. This Lotung site was chosen based on its known high seismicity. Using this data base, a cooperative program to validate SSI analysis methodologies was sponsored by EPRI, TPC, and the U.S. Nuclear Regulatory Commission (NRC). Numerous publications document the results of the SSI analysis studies. A two-volume EPRI report [EPRI, 1989] contains the proceedings of a workshop held in Palo Alto, California on December 11–13, 1987 to discuss the experiment, data © 2003 by CRC Press LLC
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collected, and analyses performed to investigate SSI analysis methodologies and their application. Johnson et al. [1989] performed one set of analyses from which results are presented here to demonstrate various aspects of the SSI phenomenon. A summary of lessons learned was published [Tseng and Hadjian, 1991]. Finally, a summary of sensitivity studies performed was documented in 1997 as the field experiment was completed. When appropriate throughout this chapter, data from the Lotung experiment are presented and discussed.
10.2 Specification of the Free-Field Ground Motion The term free-field ground motion denotes the motion that would occur in soil or rock in the absence of the structure or any excavation. Describing the free-field ground motion at a site for SSI analysis purposes entails specifying the point at which the motion is applied (the control point), the amplitude and frequency characteristics of the motion (referred to as the control motion and typically defined in terms of ground response spectra, power spectral density functions, and/or time histories), the spatial variation of the motion, and, in some cases, duration, magnitude, and other earthquake characteristics. In terms of SSI, the variation of motion over the depth and width of the foundation is relevant. For surface foundations, the variation of motion on the surface of the soil is important; for embedded foundations, the variation of motion over both the embedment depth and the foundation width should be known.
10.2.1 Control Motion and Earthquake Characteristics The control motion is defined by specifying the amplitude and frequency content of the earthquake to be considered. Two purposes exist for SSI analysis of a structure: design or evaluation of a facility for a specified earthquake level, or the evaluation of a structure for a specific event. In the former case, statistical combinations of recorded or predicted earthquake motions are typically the bases. In the latter case, recorded earthquake acceleration time histories typically comprise the free-field ground motions. The frequency content of the motion is one of the most important aspects of the free-field motion as it affects structure response. For linear structural behavior and equivalent linear SSI, the frequency content of the free-field motion compared to important frequencies of the soil–structure system determines response. For structures expected to behave inelastically during the earthquake (and, in particular, structures for which SSI is not important), structure response is determined by the frequency content of the free-field motion, i.e., in the frequency range from the elastic frequency to a lower frequency corresponding to a certain amount of inelastic deformation. 10.2.1.1 Aggregated Ground Motions A wide variety of ground response spectra has been specified for design of major facilities, such as nuclear power plants, major bridges, critical facilities (e.g., LNG storage and processing plants), and major infrastructure projects. For nuclear power plants, depending on the vintage of the plant and the site soil conditions, the majority of the design ground response spectra has been relatively broad-banded spectra representing a combination of earthquakes of different magnitudes and distances from the site. Construction of such design spectra is usually based on a statistical analysis of recorded motions and frequently targeted to a 50% or 84% nonexceedance probability (NEP). Three points are important relative to these broad-banded spectra. First, earthquakes of different magnitudes and distances control different frequency ranges of the spectra. Small magnitude earthquakes contribute more to the high frequency range than to the low frequency range and so forth. Second, it is highly unlikely that a single earthquake will have frequency content matching the design ground response spectra. Hence, a degree of conservatism is added when broad-banded response spectra define the control motion. Third, a single earthquake can have frequency content that exceeds the design ground response spectra in selected frequency ranges. The likelihood of the exceedance depends on the NEP of the design spectra. Figure 10.2 compares several ground response spectra used in the design or evaluation process. U.S. NRC Regulatory Guide 1.60 [U.S. Atomic Energy Commission, 1973] response spectra defined design criteria © 2003 by CRC Press LLC
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1 Reg Guide 1.60 0.9 84th CR-0098 Soil 0.8
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10
100
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FIGURE 10.2 Examples of aggregated ground motion response spectra.
for U.S. nuclear power plants designed after about 1973. These spectra were targeted to an 84% NEP of the data considered, but exceed this target in selected frequency ranges. Figure 10.2 shows an additional set of broad-banded spectra for rock and alluvial sites and for 50% and 84% NEP. U.S. NRC NUREG0098 is the source. These spectra have been used extensively for defining seismic margin earthquakes, for which beyond design basis assessments have been performed for nuclear power plants in the United States and other countries. This broad-banded spectral shape is also used to define design criteria for new design. In addition to the site-independent ground response spectra discussed above, two additional forms of ground response spectra are being generated and used for site-specific design or evaluations. First, sitespecific spectra are generated by accumulating recorded data that meet the design earthquake characteristics and local site conditions, analyzing the data statistically, calculating ground response spectra of various statistical attributes, and selecting response spectra for design or reevaluation. Figure 10.3 shows an example for a specific site; the 84% NEP was selected. Second, seismic hazard studies are performed to generate families of seismic hazard curves which yield estimates of the probability of exceedance of earthquakes with specified peak ground acceleration (PGA) values or greater. Confidence limits for these seismic hazard estimates are derived from the family of curves. Companion to the seismic hazard curves are uniform hazard spectra (UHS), which are ground response spectra generated for a specified return period or probability of exceedance, with various confidence limits. Figure 10.4 shows example UHS for a specific site, 10–4 probability of occurrence per annum (sometimes termed a “10,000-year return period”), and 15, 50, and 85% confidence limits. Such spectra are generated by the same probabilistic seismic hazard methodology as is used in generating the seismic hazard curves for PGAs. In almost all cases, design ground response spectra are accompanied by ground motion acceleration time histories — artificial acceleration time histories generated with response spectra that match or exceed the design ground response spectra. Artificial acceleration time histories are generated by numerical methods and not recorded motions. Due to the enveloping process, additional conservatism is © 2003 by CRC Press LLC
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0.
1
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FIGURE 10.3 Site-specific response spectrum.
introduced. Ground motion time histories are used to generate in-structure response — loads, response spectra, displacements, etc. 10.2.1.2 Individual Recorded Events The previous sections discussed aggregated motions as derived from recorded data or empirical models based on recorded data. These aggregated motions do not represent a single event. They have been developed for various design and evaluation purposes. It is informative to present recorded motions from actual earthquakes and visualize differences between a single event and the aggregated motions. Two earthquakes of note from a SSI standpoint were the May 20, 1986 and November 14, 1986 events which affected the Lotung scale model structures. Figure 10.5 contains response spectra generated from the acceleration time histories recorded on the soil-free surface for the May 20, 1986 event. Each earthquake produced PGAs greater than about 0.2 g in the horizontal direction with principally low frequency motion, i.e., less than about 5 Hz. 10.2.1.3 Magnitude Effects Ground motion frequency content is strongly dependent on specific factors of the earthquake and site. Two particularly important characteristics of the earthquake are its magnitude and epicentral distance from the site. Small magnitude events are characterized by narrow-banded response spectra and high frequency in comparison to moderate magnitude events. Figure 10.6 [Chang et al., 1985] illustrates the effect of magnitude on response spectral shape. In the figure, the response spectral shape obtained from a series of small magnitude (ML < 4) earthquakes is compared with the response spectral shape from a moderate magnitude (ML = 6.5) event. As shown, the small magnitude earthquakes are characterized by a narrow-banded response spectral shape and greater high frequency content than the moderate magnitude event. © 2003 by CRC Press LLC
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10−4 spectra
103
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102
85 101 50
15 100
10−1 10−2
10−1
100
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FIGURE 10.4 Uniform hazard spectra.
10.2.1.4 Soil vs. Rock Sites One of the most important parameters governing amplitude and frequency content of free-field ground motions is the local site conditions, i.e., soil vs. rock and shallow, soft soil overlying a stiff soil or rock. Two sets of data dramatically demonstrate the difference in motions recorded on rock vs. soil for the same earthquake and sites in close proximity. The Ashigara Valley in Japan is located about 80 km southwest of Tokyo. A digital strong-motion accelerograph array network [Kudo et al., 1988] was installed in this seismically very active area. The geological profile of the Ashigara Valley is shown in Figure 10.7. The valley is an alluvial basin with rock outcrops at the mountain side and soft sedimentary soil layers at the basin. Accelerometers were installed in the rock outcrop (KR1), at the surface of the soft layers (KS1 and KS2) and inside the soil (KD2). Figure 10.8 shows response spectra of motions recorded at the rock outcrop (KR1) and at the surface of soft layers (K2S) for an earthquake occurring on August 5, 1990. The figure clearly shows differences in motions due to different site conditions. High frequencies of about 10 Hz and greater are dominant at the rock site and frequencies below about 5 Hz are dominant at the soil surface. Figure 10.8 clearly shows the large amplification of the low frequency waves due to the soil response and the deamplification of the high frequency waves due to the filtering effect of the soft soil. The Loma Prieta earthquake, October 17, 1989, with epicenter near San Francisco, provided the opportunity to collect and evaluate recorded motions on rock and soft soil sites, in some cases immediately © 2003 by CRC Press LLC
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.3
.1
.1 .0 10−1
N-S Component
.10 .8 .6 .4 .2 .0 10−1
100 101 Frequency (Hz)
102
FIGURE 10.5 Response spectra of free-field ground surface motions of the May 20, 1986 earthquake, recorded at Lotung, Taiwan.
adjacent to each other. Figure 10.9 compares response spectra for recorded motions on rock (Yerba Buena Island) and on soil (downtown Oakland). Significant differences in amplification are obvious, with the rock motions being less. Similar observations were made when comparing response spectral amplification factors for soil (Treasure Island) vs. rock (Yerba Buena Island). For horizontal motions, significant amplification of soil over rock is apparent. For vertical motions, the relationship between the rock and soil values was not as clear. As observed in other locations, it is surmised that the presence of a high water table and its effect on vertical ground motion are uncertain. Note that Treasure Island and Yerba Buena Island are the north and south ends of a single land mass (Yerba Buena Island is a natural island with highest elevation several hundred feet above the San Francisco Bay, while the contiguous Treasure Island is of similar areal extent, only a few feet above the bay, and was created by hydraulic land fill in the 1930s). The evidence supporting the differences between rock and soft soil motions continues to mount, emphasizing the effect of local site conditions on the amplitude and frequency content of the motion.
10.2.2 Control Point The term control point designates the location at which the control motion is defined. The control point should always be defined on the free surface of soil or rock at the site of interest. Specifying the control point at locations other than a free surface ignores the physics of the problem and the source of data used in defining the control motion. Past nuclear regulatory practice specified the control point to be at foundation level in the free field, which is technically untenable. It not only ignores the physics of the problem and the source of recorded data, but also results in motions on the free surface whose response spectra display peaks and valleys associated with frequencies of the embedment layer that are unrealistic. The frequencies of these peaks correspond to the frequencies of the soil layer between the foundation and the free surface. These free surface motions are dependent on the foundation depth rather than © 2003 by CRC Press LLC
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Spectral Acceleration Fast Ground Acceleration
7
6
EXPLANATION 1979 Imperial Valley, California Earthquake (ML 6.6) 1975 Oroville, California Earthquake after shocks, and 1980 Mammoth Lakes, California Earthquake (Records from Earthquake with ML 4.0 + 0.2)
5
Damping Rate = 0.02
4
3
2
1
0 0.01
0.03
0.1
0.3 Period, sec
1
3
10
FIGURE 10.6 Illustration of effect of earthquake magnitude on response spectral shape obtained from statistical analysis.
free-field site characteristics. In addition, the peak acceleration of the resulting free surface motion is typically calculated to be significantly greater than the control motion. Hence, by all seismological definitions, a design or evaluation earthquake is increased. A 0.25-g earthquake may become a 0.35-g earthquake, or greater, depending on the embedment depth, soil properties, and control motion characteristics. Finally, specification of the control point at foundation level rather than the soil free surface effectively penalizes partially embedded structures compared to surface-founded structures, which contradicts common sense and observations. Simplistic SSI analyses frequently ignore wave scattering effects (kinematic interaction) for embedded foundations. In so doing, the foundation input motion is assumed to be identical to the control motion. Implicit in this assumption is the definition of the control point as any point on the foundation and no spatial variation of ground motion. This assumption is almost always conservative and frequently extremely conservative. Recognition of this conservatism is important in interpreting the results of the SSI analysis.
10.2.3 Spatial Variation of Motion and Kinematic Interaction Spatial variations of ground motion refer to differences in amplitude and/or phase of ground motions with horizontal distance or depth in the free field. Spatial variations of ground motion are associated with different types of seismic waves and various wave propagation phenomena, including reflection at the free surface, reflection and refraction at interfaces and boundaries between geological strata having © 2003 by CRC Press LLC
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Earthquake Engineering Handbook
KR1
100
50
KS1 Vs 150m/s Vs 700m/s
0
KS2
Vs 70m/s
Vs 400m/s
−50 Vs 700m/s
SCALE 0
500(m) Vs 800m/s
KD2
−100
FIGURE 10.7 Ashigara Valley, Japan.
different properties, and diffraction and scattering induced by nonuniform subsurface geological strata and topographic effects along the propagation path of the seismic waves. A vertically incident body wave propagating in such a medium will include ground motions having identical amplitudes and phase at different points on a horizontal plane (neglecting source-to-site attenuation effects over short horizontal distances). A plane wave propagating horizontally at some apparent phase velocity will induce ground motion having identical amplitudes but with a shift in phase in the horizontal direction associated with the apparent horizontal propagation velocity of the wave. In either of these ideal cases, the ground motions are considered to be coherent, in that amplitudes (acceleration time histories and their response spectra) do not vary with location in a horizontal plane. Incoherence of ground motion, on the other hand, may result from wave scattering due to inhomogeneities of soil/rock media and topographic effects along the propagation path of the seismic waves. Both of these phenomena are discussed below. In terms of the SSI phenomenon, variations of the ground motion over the depth and width of the foundation (or foundations for multifoundation systems) are the important aspect. For surface foundations, the variation of motion on the surface of the soil is important; for embedded foundations, the variation of motion on both the embedded depth and foundation width is important. Spatial variations of ground motions are discussed in terms of variations with depth and horizontal distances.
10.2.4 Validation of Ground Motion Variation with Depth of Soil 10.2.4.1 Variation of Ground Motion with Depth of Soil For either vertically or nonvertically incident waves, ground motions vary with depth. These variations can generally be expressed in terms of peak amplitudes, frequency content, and phase. Variations of ground motion with depth due to vertically and nonvertically incident body waves and surface waves have been extensively studied analytically by many investigators [Chang et al., 1985]. These studies, based
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.10 KS2S, Comp. 090, Alluvium Site .9
KR1S, Comp. 090, Rock Site 5% Damping
.8 .7
Sa (g)
.6 .5 4 .3 .2 .1 .0 .01 .02
.05
1
(a)
2 5 1 Period (sec)
2
5
10
.10 KS2S, Comp. 000, Alluvium Site KR1S, Comp. 000, Rock Site
.9
5% Damping
.8 .7
Sa (g)
.6 .5 .4 .3 .2 .1 .0 .01
(b)
.02
.05
.1
.2 5 Period (sec)
1
2
FIGURE 10.8 Response spectra at rock and alluvium sites, Ashigara Valley, Japan.
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.8 Oakland 2_STY BLDG (No.56224). Comp. 200. Soil Site. .7
Yerba Buena Island (No.58163). Comp. 000. Rock Site. 5% Damping
.6
Sa (g)
.5
.4
.3
.2
.1
.0
.01 .02
.05
.1
(a)
.2 .5 Period (sec)
1
2
5
10
.8 Oakland 2_STY BLDG (No.56224). Comp. 290. Soil Site. .7
Yerba Buena Island (No.58163). Comp. 090. Rock Site.
.6
5% Damping
Sa (g)
.5
.4
.3
.2
.1
.0 .01
(b)
.02
.05
.1
.2 .5 Period (sec)
1
2
FIGURE 10.9 Response spectra at rock and soil sites, Loma Prieta earthquake.
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TABLE 10.2 Free-Field Downhole Arrays Location
Instrument Depth (m)
Natimasu, Tokyo Waseda, Tokyo Menlo Park, CA Richmond Field Station, CA Ukishima Park, Tokyo Futtsu Cape, Chiba Kannonzaki, Yokosuka City Tokyo International Airport Ohgishima Station, Kawasaki City Earthquake Research Institute Miyako, Tokyo Tomakomai, Hokkaido Tateyama, Tokyo Higashi-Matsuyama City, Saitama Shuzenji-cho, Shizuoka Choshi City, Chiba Beatty, Nevada Fukushima Nuclear Power Plant Lotung, Taiwan, ROC
–1, –5, –8, –22, –55 –1, –17, –67, –123 GL, –12, –40, –186 GL, –14.5, –40 GL, –27, –67, –127 GL, –70, –110 GL, –80, –120 GL, –50; GL, –65 GL, –15, –38, –150 GL, –82 –0.5, –18, –26.5 GL, –30, –50 –26; –38, –100 –1, –58, –121 –36, – 100, –49, –74 GL, –18 GL, –41 GL, –50; –0.5, –3, –8.5, –23.5 GL, –6, –11, –17, –47
Turkey Flat, CA Ashigara Valley, Japan Games Valley, CA
GL, –10, –20 GL, –30, –95 GL, –6, – 15, –22, –220
Reference Chang et al. (1985) Chang et al. (1985) Chang et al. (1985) Chang et al. (1985) Chang et al. (1985) Chang et al. (1985) Chang et al. (1985) Chang et al. (1985) Gazetas, G. and Bianchini, G. (1979) Chang et al. (1985) Chang et al. (1985) Chang et al. (1985) Chang et al. (1985) Chang et al. (1985) Chang et al. (1985) Chang et al. (1985) Chang et al. (1985) Yanev et al. (1979); Tanaka et al. (1973) Chang et al. (1990); Chang et al. (1991); Hadjian et al. (1991) Cramer (1991); Proceedings (1992) Proceedings (1992); Midorikawa (1992) Seale and Archuleta (1991)
on the physics of plane wave propagation through layered media, all indicate that, due primarily to the free surface effect, ground motions generally decrease with depth. The nature of the variation is a function of frequency content and wave type of the incident waves, soil layering, and dynamic soil properties of each soil layer, including shear and compressional wave velocities, damping ratio, and mass density. 10.2.4.2 Free-Field Motion A review and summary of observational data on the variations of earthquake ground motion with depth was conducted by Seed and Lysmer [Johnson, 1981] and Chang et al. [1985] reflecting the state of knowledge as of 1980 and 1985, respectively. Recordings from two downhole arrays in Japan were analyzed [Chang et al., 1985] and a review of published data from a number of downhole arrays in Japan and the United States was conducted. Based on the review of these data on the variations of ground motion with depth, it was concluded that there is a good body of data to show that, in general, both peak acceleration and response spectra decrease significantly with depth in the range of typical embedment depths of structures, i.e., less than approximately 25 m; and it appears that deconvolution procedures assuming vertically propagating shear waves provide reasonable estimates of the variations of ground motion with depth. Table 10. 2 summarizes the sources of data evaluated by Seed and Lysmer [Johnson, 1981] and Chang et al. [1985]. Since 1985, substantial additional data have been recorded and evaluated. These sources are included in Table 10.2 and one of the most relevant is discussed next. 10.2.4.3 Lotung, Taiwan As part of the Lotung experiment, downhole free-field data were recorded at depths of 6, 11, 17, and 47 m. Figure 10.10 [EPRI, 1989] shows the configuration of the arrays. Equivalent linear deconvolution analyses and nonlinear convolution analyses were performed. Deconvolution analysis has as the starting point the free-field surface motion with the objective being to calculate the motion at various depths in the soil. For the Lotung experiment, the depths at which the earthquake responses were calculated corresponded to the
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FA1-5 DHB
30.48m Arm 1 6.10m
1.5m
5.10m 3.05m
FA1-1 FA2-1
FA3-1 FA3-5
Arm 3
Arm 2
Triaxial accelerometers
Limits of Backfill FA2-5
(a) Surface Instrument Arrays
3.2m 1/4-scale model 4.57m 10.52m
45.7m
DHA 6m
DHB 6m DHB6 DHB11
11m 17m
DHB17
5m 6m
30m
47m
DHB47
(b) Downhole Instrument Arrays
FIGURE 10.10 Location of (a) surface and (b) downhole accelerographs at the Lotung, Taiwan site.
locations of the downhole accelerometers for comparison purposes. Convolution analysis is the inverse process, i.e., starting with the recorded motion at depth in the soil, calculate the earthquake motion at the free surface or at other depths. These extensive studies investigating analytical modeling of the phenomenon clearly support the observed and analytically determined variation of motion with depth in the soil and, in fact, a reduction of motion with depth as expected. In addition, the assumption of vertically propagating shear waves, and an equivalent linear representation of soil material behavior, well models the wave propagation phenomenon, especially at depths in the soil important to SSI [EPRI, 1989]. Figure 10.11 compares recorded and analytically predicted responses for one of the models.
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Spectral Acceleration (g)
Spectral Acceleration (g)
Spectral Acceleration (g)
Spectral Acceleration (g)
Soil–Structure Interaction
E−W
−5
N−S
−4 −3 −2
DHB6
DHB6
DHB11
DHB11
DHB17
DHB17
−1 0 −5 −4 −3 −2 −1 0 −5 −4 −3 −2 −1 0 −5 −4
Recorded (CDS4.7DHB) Computed (S7CDe12080)
−3 −2
DHB47
DHB47
−1 0 −1 −2 −5
1 2 5 10 20 50 100 −1 −2 −5 1 2 5 10 20 50 100 Frequency (Hz) Frequency (Hz)
FIGURE 10.11 Comparison of recorded and computed response spectra (5% damping), deconvolved with iterated strain-compatible properties, Event LSST07.
10.2.5 Validation of Kinematic Interaction 10.2.5.1 Foundation Response The SSI phenomenon can be thought of as two elements: kinematic and inertial interaction. Kinematic interaction is the integrating effect that occurs as portions of the structure and foundation that interface with the soil or rock are subjected to differing free-field ground motion. Variations in translational freefield ground motion result in net translations and accompanying rotations due to this integration or averaging process. Kinematic interaction is typically treated separately from a conceptual standpoint and frequently from a calculational standpoint. The result of accounting for kinematic interaction is to generate an effective input motion, which is denoted foundation input motion. The mathematical transformation from the free-field surface motion to the foundation input motion is through the scattering matrix. Inertial interaction denotes the phenomenon of dynamic behavior of the coupled soil–structure system. The base excitation is defined by the foundation input motion accounting for kinematic interaction. The behavior of the foundation on the soil is modeled by foundation impedances (generalized soil springs) that describe the force-displacement and radiation damping characteristics of the soil. The structure is modeled by lumped mass and distributed stiffness models representing its dynamic response characteristics. These elements are combined to calculate the dynamic response of the structure, including the effects of SSI. © 2003 by CRC Press LLC
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T−5/GL−1m Y
1.5
T−5/GL−1m Y 10.0
Fourier Spectral Ratio
5.0 1.0
Ground 1.0 0.5
Estimated Input Motion Bottom slab
0.5
0.1 0.05
0.0 0.0
2.0
4.0 Frequency (Hz)
6.0
8.0
0.01 0.05 0.1
0.5
1.0
5.0 T (sec)
FIGURE 10.12 Observed transfer function between foundation level motion (–26.2 m) of a large-scale belowground LNG tank and free-field (–l m) horizontal motion. (——), observed average value over 18 earthquakes; (– – – –), theoretical.
Validation of the component pieces of the process proceeds by considering kinematic interaction. A comparison of motions recorded in the free field and on the base of partially embedded structures provides excellent data validating the effects of kinematic interaction and the spatial variation of ground motion. All recorded data on structures include the effects of SSI to some extent. For purposes of validating the spatial variation of motion with depth in the soil, observations of kinematic interaction are sought. The ideal situation is one where free-field surface motions and foundation motions are recorded for a structure whose embedded portion is stiff, approaching rigid behavior, and the dynamic characteristics of the structure are such that inertial interaction is a minimal effect. 10.2.5.2 Free-Field Surface Motions vs. Foundation Response Typically, differences in peak values, time histories, and response spectra were observed and transfer functions relating foundation response to free-field surface motion were generated. These frequencydependent transfer functions are, in essence, one element of the scattering matrix when inertial interaction effects are minimal, i.e., the component relating foundation input motion to horizontal free-field surface motion. In no case was enough information available to generate the rocking component of the scattering matrix from recorded motions. To do so requires recorded rotational acceleration time histories or the ability to generate them from other measurements. 10.2.5.3 LNG Tanks, Japan Eighteen deeply embedded LNG tanks of varying dimensions were instrumented and motions recorded on their foundations and in the free field for a large number of earthquakes. Many of the earthquakes were microtremors, but detailed response for at least one larger event was obtained. Transfer functions between free-field surface motions and foundation response were generated and compared with a calculated scattering element. Results compared well. A significant reduction in foundation response from the free surface values was observed. The mass and stiffness of the tanks were such that kinematic interaction dominated the SSI effects. Figure 10.12 presents the data [Ishii et al., 1984]. 10.2.5.4 Humboldt Bay Nuclear Power Plant The Humboldt Bay Nuclear Power Plant in northern California has experienced numerous earthquakes over the years. Four events of note are the Ferndale earthquake of June 7, 1975 and the Lost Coast earthquake sequence of April 25, 1992. Accelerometers in place in the free field and on the base of a deeply embedded caisson structure (80 ft) recorded acceleration time histories. Figure 10.13 compares
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EXPLANATION
1.2
Free-field finished grade
1.0 0.8
Sa (g’s)
Base of Reactor Caisson (84 ft Embedment Depth)
Transverse Direction Damping Ratio = 0.05
0.6 0.4 0.2
0 0
Medium to stiff clay Medium dense sand Dense sand Very stiff clay
50 75
0.025
CAISSON
Depth - ft
25
1.2
1.0
2.5
1.0
2.5
Longitudinal Direction Damping Ratio = 0.05
1.0
Dense sand
0.1 Period (seconds)
0.8 Sa (g’s)
100 125
0.6 0.4 0.2 0 0.025
0.1 Period (seconds)
FIGURE 10.13 Comparison of response spectra of accelerograms recorded at finished grade in the free field and at the base of the reactor caisson at the Humboldt Bay plant during the June 6, 1975, Femdale, California earthquake.
TABLE 10.3 Peak Accelerations (Surface/Caisson) Earthquake
E-W
N-S
Vertical
6/1/75 4/25/92 (11:06 PDT) 4/26/92 (00:14 PDT) 4/26/92 (04: 18 PDT)
0.35/0.16g 0.22/0.14g 0.25/0.12g 0.13/0.07g
0.26/0.12g 0.22/0.11g 0.23/0.12g 0.098/0.057g
0.06/0.10g 0.05/0.08g 0.05/0.12g 0.031/0.037g
free-field surface response spectra with those recorded on the caisson’s base for the 1975 event. Table 10.3 shows a comparison of peak accelerations. For horizontal motions, significant reductions are apparent, i.e., reductions up to 55%. For vertical motions, peak accelerations remained the same or slightly increased. Additional data for vertical motions will undoubtedly illuminate this phenomenon. The major interest for the design and evaluation of structures is horizontal motions, which clearly exhibit reduction with depth. The dominant SSI phenomenon here, as for the LNG tanks, is likely to be kinematic interaction due to the deep embedment of the caisson. Numerous other data exist and are highlighted in other sources, e.g., Johnson and Asfura [1993]. 10.2.5.5 Buildings With and Without Basements A series of buildings in close proximity to each other, with and without basements, subjected to the San Fernando earthquake of 1971 were investigated. Comparing recorded basement motions for buildings © 2003 by CRC Press LLC
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7,150
11 10
6
2,000
2,390
4,000 0
2,900
5,000
5
4,150
2,000
4
GL
3
6,800
2
3,650
1
6,000
Pickups of seismograph
FIGURE 10.14 Cross section through chemical engineering plant model, Chiba Field Station.
with and without embedment documented the effects of kinematic interaction. The results show a definite reduction in motion of embedded foundations compared to surface foundations or free-field surface values. Numerous comparisons are presented by Chang et al. [1985]. 10.2.5.6 Model Structures Two model structures in Japan and the Lotung scale model structures in Taiwan have been instrumented and have recorded ground motions from a number of earthquakes. One model structure is located at the Fukushima Nuclear Power Plant site in northern Japan. Tanaka et al. [1973] report on data recorded in the free field and structure. A reduction in peak acceleration of about 20% is observed from free-field surface motion to foundation. The second model structure is located at Chiba Field Station, Institute of Industrial Science, University of Tokyo. The purpose of the model was to instrument it for earthquakes, record earthquake motions, and investigate variability in ground motion and response. Figure 10.14 [Shibata, 1978; Shibata, 1991] shows a cross section through the scale model structure including components (piping, hanged tank, and vessel) and instrument locations. As of 1978, Shibata shows graphically that the mean response factor for peak acceleration on the foundation compared to the free field is about 0.68, with a coefficient of variation of 0.125 in the horizontal direction, and 0.83, with a coefficient of variation of 0.136 in the vertical direction. A clear reduction in response of the foundation is observed. The third model structure is the Lotung, Taiwan case. Comparing the May 20, 1986 measured free-field surface response with foundation response demonstrates the reduction in free-field motion with depth.
10.2.6 Variation of Ground Motion in a Horizontal Plane Variations observed in the motions of two points located on a horizontal plane are mainly due to the difference in arrival times of the seismic waves at the two points and to the amplitude and frequency © 2003 by CRC Press LLC
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modification that those seismic waves undergo due to the geotechnical characteristics of the media between the two points. The former is sometimes referred to as a first-order effect and is characterized by an apparent horizontal wave propagation velocity (speed and, in some cases, direction). The latter is often denoted a second-order effect and is characterized by a set of horizontal and vertical ground motion “coherency functions.” Understanding of the variation of ground motion over a horizontal extent was significantly advanced with the installation of several dense accelerograph arrays, e.g., SMART 1 and LSST arrays in Taiwan, El Centro and Parkfield in California, and the Chusal differential array in the former U.S.S.R., and the analysis of the recorded data collected from them. Thus, the spatial variation of ground motions over a horizontal plane is characterized by an apparent horizontal wave propagation velocity, which in the absence of detailed site data is generally assumed to be on the order of 2 to 3 km/ sec. Complex-valued, frequency-dependent coherency functions have been derived from the recorded data of the differential arrays discussed above. These functions strongly depend on the distance between recording or site locations and on the frequency of the seismic waves. This spatial variation of ground motions is a critical element in the seismic analysis of structures on large foundations and in the analysis of long structures on multiple foundations, such as bridges [Tseng and Penzien, 2000]. For long structures on multiple foundations, accounting for both aspects of horizontal spatial variation of ground motion is essential. For these cases, apparent horizontal wave propagation velocities and coherency functions are used directly in the SSI analysis. For structures supported on large, stiff foundations, recorded data support a “base averaging” effect on the free-field ground motions. That is, certain frequency ranges may be filtered out of the foundation input motion due to the base averaging effect. In the absence of performing detailed SSI analyses incorporating the coherency functions, a simpler approach may be taken, i.e., a filtering of motions. For a 50-m plan dimension foundation, reductions in spectral accelerations of 20% in the > 20-Hz frequency range, of 10% to 15% in the 10- to 20-Hz range, and of 5% in the 5- to 10-Hz range are supported by the data.
10.3 Modeling of the Soil For soil sites, describing the soil configuration (layering or stratigraphy) and the dynamic material properties of soil is necessary to perform SSI analysis and predict soil–structure response. Determining soil properties to be used in the SSI analysis is the second most uncertain element of the process — the first being specifying the ground motion. Modeling the soil can be visualized in two stages: determining the low strain in situ soil profile and associated material properties; and defining the dynamic material behavior of the soil as a function of the induced strains from the earthquake and soil–structure response. In general, dynamic stress–strain behavior of soils is nonlinear, anistropic, elastoplastic, and loading path dependent. It is also dependent on previous loading states and the degree of disturbance to be expected during construction. Practically speaking, all of these effects are not quantifiable in the current state of the art and, hence, contribute to uncertainty in describing soil stress–strain behavior. In a majority of cases, soil is modeled as a linear or equivalent linear viscoelastic medium in SSI analyses for earthquake motion. In some instances, in particular where foundations or footings are founded underwater, it is important to characterize nonlinear behavior of the supporting medium, albeit with substantial uncertainty taken into account. In addition, there have been numerous studies where nonlinear behavior of soil has been analyzed for research objectives. The assumption in this chapter is that the majority of SSI analysis cases of interest to the reader are those where the nonlinear behavior of soil may be treated appropriately as equivalent linear viscoelastic material. In other cases, the reader is referred to sources such as Tseng and Penzien [2000]. A linear viscoelastic material model is defined by three parameters — two elastic constants (frequently shear modulus and Poisson’s ratio, although shear modulus and bulk or constrained modulus may be more appropriate) and material damping. The equivalent linear method approximates the nonlinear stress–strain relation with a secant modulus and material damping values selected to be compatible with the average shear strain induced during the motion using an iterative procedure. Requirements for this model are low strain shear modulus and Poisson’s ratio (or bulk or constrained modulus), material © 2003 by CRC Press LLC
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damping values, and their variations with strain. The following discussion assumes an equivalent linear viscoelastic material model for soil. Three aspects of developing soil models are field exploration, laboratory tests, and correlation of laboratory and field data. Much of the discussion refers to Woods [1978], which is the most comprehensive documentation of the state of the art at the time of publication. In the ensuing years, a number of authors have published updates to selected aspects of the subject, in particular, measurement of parameters for nonlinear models of soil material behavior, liquefaction, and lateral spreading. Two such publications are CH2M Hill [1991] and Ishihara [1996].
10.3.1 Field Exploration Field exploration, typically, relies heavily on boring programs, which provide information on the spatial distribution of soil (horizontally and with depth) and produce samples for laboratory analysis. In addition, some dynamic properties are measured in situ, for example, shear wave velocity which leads to a value of shear modulus at low strains. Woods [1978] provides a summary of field exploration, in general, and of boring, sampling, and in-situ testing, in particular. Low strain shear and compressional wave velocities are typically measured in the field. Various field techniques for measuring in situ shear and compressional wave velocities exist, including the seismic refraction survey, seismic cross-hole survey, seismic downhole or uphole survey, and surface wave techniques. The advantages and disadvantages of these techniques are discussed by Woods [1978]. For sites having a relatively uniform soil profile, all of these techniques are appropriate. However, for sites having layers with large velocity contrasts, the most appropriate technique is the cross-hole technique. The cross-hole data are expected to be the most reliable because of better control over and knowledge of the wave path. The downhole technique does not permit as precise resolution because travel times in any layer are averaged over the layer. Most seismic field survey techniques are capable of producing ground motions in the small shearing strain amplitude range (less than 10–3 %). Hence, field exploration methods yield the soil profile and estimates of important low strain material properties (shear modulus, Poisson’s ratio, water table location). 10.3.1.1 Laboratory Tests Laboratory tests are used principally to measure dynamic soil properties and their variation with strain: soil shear modulus and material damping. Currently available laboratory testing techniques have been discussed and summarized by Woods [1978]. These techniques include resonant column tests, cyclic triaxial tests, cyclic simple shear tests, and cyclic torsional shear tests. Each test is applicable to different strain ranges. The resonant and torsional shear column tests are capable of measuring dynamic soil properties over a wide range of shear strain (from 10–4 to 10–2 % or higher). The cyclic triaxial test allows measurement of Young’s modulus and damping at large strain (larger than 10–2 %). Typical variations of shear modulus with shear strain for clays, compiled from laboratory test data, are depicted in Figure 10.15. Generally, the modulus reduction curves for gravelly soils and sands are similar. Figure 10.16 shows material damping as a function of shear strain, also for clays. Shear modulus decreases and material damping increases with increasing shear strain levels. 10.3.1.2 Correlation of Laboratory and Field Data Once shear modulus degradation curves and material damping vs. strain curves have been obtained, it is necessary to correlate laboratory-determined low strain shear modulus values with those in situ. Laboratory-measured values of shear moduli at low levels of strain are typically smaller than those measured in the field. Several factors have been found to contribute to lower moduli measured in the laboratory. These factors include effects of sampling disturbance, stress history, and time (aging or period under sustained load). Thus, when the laboratory data are used to estimate in situ shear moduli in the field, considerations should be given to these effects. When laboratory data do not extrapolate back to the field data at small strains, one of the approaches used in practice is to scale the laboratory data up to the field data at small strains. This can be done by proportionally increasing all values of laboratory moduli to match the field data at low strain values or by other scaling procedures.
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1.0
0.8 Typical Sand Curve
G/Gmax
0.6
0.4
0.2
0.0 10−4
10−3
10−2 10−1 Shear Strain, percent
1
10
FIGURE 10.15 Normalized modulus reduction relationship for clays with plasticity index between 40 and 80.
Damping Ratio, percent
40 Seed and Idris (1970)
30
20
10
0 10−4
10−3
10−2 10−1 Shear Strain, percent
1
10
FIGURE 10.16 Strain-dependent damping ratios for clays.
10.3.1.3 Equipment Linear Soil Properties Given the low-strain soil profile determined from the combination of field and laboratory tests, and the variation of material parameters with strain level, a site response analysis is performed to estimate equivalent linear soil properties for the SSI analysis. The computer program SHAKE [Schnabel et al., 1972] has become an international standard for such analyses. 10.3.1.4 Uncertainty in Modeling Soil/Rock at the Site There is uncertainty in each aspect of defining and modeling the site soil conditions for SSI analysis purposes. The soil configuration (layer or stratigraphy) is established from the boring program. Even after such a program, some uncertainty exists in the definition of the soil profile. Soils are seldom homogeneous, and they seldom lie in clearly defined horizontal layers — the common assumptions in
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SSI analysis. In general, complicated soil systems introduce strong frequency dependence in the site behavior. Modeling the dynamic stress–strain behavior of the soil is uncertain in two respects. First, modeling soil as a viscoelastic material with parameters selected as a function of average strains is an approximation to its complex behavior. Second, there is uncertainty in defining low strain shear moduli and in defining the variations in shear modulus and observed damping with strain levels, Variability can be observed in reporting test values for a given site and for reported generic test results. The range of coefficients of variation on “stress–strain behavior” estimated by the American Society of Civil Engineers (ASCE) Committee on Reliability of Offshore Structures [ASCE, 1979] is 0.5 to 1.0. Similarly, the ASCE Standard, Seismic Analysis of Safety-Related Nuclear Structures and Commentary [1998] recommends implementation of a variation in low-strain shear moduli of 0.5 to 1.0 depending on specific site data acquired and its quality. In the former case, one is dealing with offshore structures with foundations founded underwater, which certainly adds to the uncertainty in the dynamic behavior of soil foundation. In the latter case, variation in shear moduli is intended to account for sources of uncertainty in the SSI analysis process in addition to the uncertainty in soil material behavior. Considering only uncertainty in soil shear modulus itself and the equivalent linear estimates to be used in the SSI analysis, a coefficient of variation of 0.35 to 0.5 on soil shear modulus is estimated. Uncertainty in low strain values is less than uncertainty in values at higher strains. The Lotung SSI experiment provides a unique opportunity to quantify the uncertainty in estimates of equivalent linear soil properties. The bases for determining the equivalent linear soil properties included field and laboratory tests and the results of forced vibration tests on the structure. The latter responses permitted system identification techniques to be employed to refine estimates of the low strain profile. Soil property data were extracted from Chang et al. [1985] and are plotted in Figures 10.17 and 10.18. Ten independent sets of data were available and their variability is apparent from the figures. To quantify this variability, the data were evaluated statistically and a weighted coefficient of variation (COV) calculated for soil shear modulus and damping; the weighting factors were soil thickness to a depth of about 100 ft. The resulting COVs for shear modulus and damping were 0.48 and 0.39, respectively. This emphasizes that uncertainty in soil behavior should be taken into account in any SSI analysis.
10.4 Soil–Structure Interaction Analysis 10.4.1 SSI Parameters and Analysis Several approaches for categorizing SSI analysis methods have been used [Johnson, 1981; Tseng and Penzien, 2000]. Two approaches are direct methods, which analyze the soil–structure system in a single step, and the substructure approach, which treats the problem in a series of steps, e.g., determination of the foundation input motion and the foundation impedances, modeling of the structure, and the analysis of the coupled system. For truly nonlinear analysis, the direct method must be employed, since the equations of motion are solved time step by time step, accounting for geometric and material nonlinearities, as appropriate. In the context of the present discussion, it is informative to continue to view the SSI phenomenon in the steps of the substructure approach. Figure 10.1 shows schematically the substructure approach. The key elements not previously discussed follow below. 10.4.1.1 Foundation Input Motion Section 10.2.3 introduced the concept of foundation input motion which differs from the free-field ground motion in all cases, except for surface foundations subjected to vertically incident waves, provided the spatial variation of the free-field ground motion is taken into account. This is due, first, to the variation of free-field motion with depth in the soil, and second, due to the scattering of waves from the
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LEGEND EIE 0
OHSAKI TAJIMI CRIEPI BASLER HOFFMAN EQE
−50
BECHTEL IMPELL DEPTH (ft)
SARGENT & LUNDY UCSD −100
−150
−200 0
500
1000 1500 2000 SHEAR MODULUS (ksl)
2500
3000
FIGURE 10.17 Variability of equivalent linear shear modulus due to different SSI analyses, earthquake, May 20, 1986, Lotung, Taiwan.
soil-foundation interface, because points on the foundation are constrained to move according to its geometry and stiffness. 10.4.1.2 Foundation Impedances Foundation impedances describe the force-displacement characteristics of the soil. They depend on the soil configuration and material behavior, the frequency of the excitation, and the geometry of the foundation. In general, for a linear elastic or viscoelastic material and a uniform or horizontally layered soil deposit, each element of the impedance matrix is complex-valued and frequency-dependent. For a rigid foundation, the impedance matrix is 6 × 6, which relates a resultant set of forces and moments to the six rigid-body degrees of freedom. 10.4.1.3 SSI Analysis The final step in the substructure approach is the actual analysis. The result of the previous steps — foundation input motion, foundation impedances, and structure models — are combined to solve the equations of motion for the coupled soil–structure system. The entire process is sometimes referred to as a complete interaction analysis, which is separated into two parts: kinematic interaction described by the scattering matrix and inertial interaction comprised of the effects of vibration of the soil and structure. In terms of SSI parameters, the scattering functions model kinematic interaction and the foundation impedances model inertial interaction. It is these two parameters which are highlighted in the ensuing sections.
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0
−50 LEGEND
DEPTH (ft)
EIE OHSAKI −100
CRIEPI BASLER HOFFMAN EQE BECHTEL IMPELL
−150
SARGENT & LUNDY UCSD
−200 0
5
10 DAMPING (percent)
15
20
FIGURE 10.18 Variability of equivalent linear damping due to different SSI analyses, earthquake, May 20, 1986, Lotung, Taiwan.
One other point is that the SSI analysis, typically, calculates overall dynamic response of the soil–structure system. The overall structural response is then applied to a detailed structure model as appropriate load cases for structure element and foundation design. In-structure response spectra are delivered to equipment and commodity designers for their seismic qualification. Hence, the SSI analysis is often an intermediate step, albeit an essential one.
10.4.2 Modeling of the Foundation Three aspects of modeling structure foundations are important: stiffness, embedment, and geometry. 10.4.2.1 Stiffness The stiffness of a structural foundation is of importance because in almost all SSI analyses, by either direct or substructure methods, foundation stiffness is approximated. Most substructure analysis approaches assume the effective foundation stiffness to be rigid. For direct methods, various representations of foundation stiffness have been used depending on the geometry and other aspects of the structure–foundation system. Most foundations of the type common to major building structures cannot be considered rigid by themselves. However, structural load-resisting systems, such as shear wall systems, significantly stiffen their foundations. Hence, in many instances, the effective stiffness of the foundation is very high and it may be assumed rigid. One study which has investigated the effects of foundation flexibility on structure response for a complicated nuclear power plant structure of large plan dimension was performed [Johnson and Asfura, 1993]. In this study, the stiffening effect of the structure on the foundation was treated exactly. Even though the structure had nominal plan dimensions of 350 ft by 450 ft, the effect of foundation flexibility on structure response was minimal. The largest effect was on rotational accelerations of the foundation segment as one would expect. Translational accelerations and response spectra, © 2003 by CRC Press LLC
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quantities of more interest, on the foundation and at points in the structure were minimally affected (5%). This conclusion emphasizes the importance of considering the stiffening effect of walls and floors on the foundation when evaluating its effective stiffness. A counter example is encountered when considering a relatively thin slab supporting massive structurally independent components, such as dry nuclear spent fuel storage casks [Bjorkman et al., 2001]. In the referenced study, sensitivity studies were performed on the dynamic response of dry fuel storage casks and the reinforced concrete pad supporting them. Numerous combinations of number of casks, thickness of pad, and stiffness of soil were considered. In order of significance, the most important parameters affecting cask dynamic response were thickness of the pad, arrangement and number of casks on the pad, and stiffness of the soil. Hence, practically speaking, for design and evaluation of major structures with stiff load-resisting systems, the assumption of rigid foundation behavior is justified. For predicting the response of a structure to a single recorded event, more refined modeling of the foundation may be required. For structure–foundation conditions of differing characteristics, appropriate sensitivity studies need to be performed to justify all assumptions made, including those related to foundation stiffness modeling. 10.4.2.2 Embedment Foundations are typically fully embedded and structures are partially embedded. Foundation embedment has a significant effect on SSI. Both the foundation input motion and the foundation impedances differ for an embedded foundation compared to a surface foundation. Foundation input motion for embedded foundations was discussed extensively in Section 10.2. Foundation impedances comprise a second aspect of foundation modeling. As discussed above, a common and appropriate assumption for many cases is rigid foundation behavior. For a rigid foundation, the impedance matrix describing force-displacement characteristics is, at most, a 6 × 6 complex-valued, frequency-dependent matrix. The literature, as summarized by Johnson [1981], contains numerous exact and approximate analytical representations of foundation impedances. Also, many analytical/experimental correlations exist with relatively good results reported. Figure 10.19 shows one such example. Figure 10.20 demonstrates the effect of embedment on foundation response for embedded and nonembedded configurations of an assumed rigid foundation. Forced vibration tests were performed. The results clearly demonstrate the effect on inertial interaction of embedment. 10.4.2.3 Geometry The geometry of major structure foundations can be extremely complicated. Fortunately, many aspects of modeling the foundation geometry are believed to have second-order effects on structure response, in particular, modeling the precise shape of the foundation in detail. However, other overall aspects, such as nonsymmetry, that lead to coupling of horizontal translation and torsion and vertical translation and rocking, can be very important and need to be considered. Modeling the foundation is important with respect to structure response. This is one area where knowledge and experience of the practitioner are invaluable. Complicated foundations must be modeled properly to calculate best estimates of response, i.e., including the important aspects as necessary. Foundation modeling plays a key role in assessing whether two-dimensional models are adequate or three-dimensional models are required.
10.4.3 Modeling of the Structure 10.4.3.1 Linear Dynamic Behavior Structures for which SSI analysis is to be performed require mathematical models to represent their dynamic characteristics. The required detail of the model is dependent on the complexity of the structure or component being modeled and the end result of the analysis. Structure models are typically of two types: lumped-mass stick models and finite element models. Lumped-mass stick models are characterized by lumped masses defining dynamic degrees of freedom.
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×108t/m Method A C
×1011tm/rad
1.5
B D
Method A C
B D
− K R(REAL)
− K H(REAL)
2.0
0
0 −2.0 0
4
6
0
Hz
×108t/m
2
4
6
Hz
×1011tm/rad
1.5
− K R(IMAG.)
2.0
− K H(IMAG.)
2
0
0 −2.0 0
2 4 (a) swaying spring
6
0
Hz
2 4 (b) rotational spring
6
Hz
FIGURE 10.19 Analytical/experimental foundation impedances.
30
Amplitude (µm/ton)
Non-embedment: 20 Half-embedment: 10 Full-embedment:
0 0
10
20
30 (Hz)
FIGURE 10.20 Comparison of horizontal displacement resonance curves at foundation bottom, forced vibration test.
For buildings, masses are usually lumped at floor slab elevations and simplified assumptions as to diaphragm or floor behavior are made; in particular, floors are frequently assumed to behave rigidly inplane and, often, for out-of-plane behavior, also. Diaphragm flexibility can be modeled when necessary. Connections between lumped masses are usually stiffness elements whose stiffness values represent columns and/or groups of walls running between the floor slabs. In some instances, an offset is modeled between the center of mass and center of rigidity at each floor elevation to account for coupling between horizontal translations and torsion. Also, lumped-mass stick models are frequently used to model other © 2003 by CRC Press LLC
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regular structures, an example being cylindrical structures (tanks, containment shells, caissons, etc.). Finite element models are used to represent complex structures. They permit a more accurate representation of complicated situations without requiring significant simplifying assumptions. Either model type may be adequate depending on the structural configuration, the detail included in the model, and the simplifying assumptions. Lumped-mass stick models are mathematically simpler than finite element models and usually have a smaller number of degrees of freedom. Lumped-mass stick models take advantage of the judgment of the analyst as to the expected behavior of the structure. Modeling methods and techniques will not be discussed in detail here. The ASCE Standard, Seismic Analysis of Safety-Related Nuclear Structures and Commentary [1998] presents many aspects of modeling and a bibliography from which additional information may be obtained. Modal equivalent models can be used for computational efficiency and to maintain equivalency between the dynamic characteristics of a detailed model in the SSI analysis. A modal equivalent model is comprised of a family of single-degree-of-freedom (SDOF) models, each having the dynamic characteristics of an individual mode of the detailed model (finite element or otherwise). Each SDOF has a mass equal to the modal mass of the detailed model mode, the mass is located at the point above the base to produce the equal moment on the base, and the stiffness elements are selected to reproduce the frequency of the detailed model mode. Each of these SDOFs is exactly equivalent to including the detailed model mode. One p oint of note for shear wal l structures is that o ver the last half of the 1980s, testing o f shear walls as indi vidual elements and as a p ortion of a structure asse mblage has b een performed. One result o f these t ests is the ap parent reduction in stiffness fr om the linear ly calculat ed values d ue to small cracks and othe r phenomena. The ASCE D ynamic Analysis Committee’s Working Group o n Stiffness o f Concrete [1992] e valuated the r elevant data and r ecommended approaches to account for increases and d ecreases in st iffness p reviousl y not treated explicitl y. Increases r esult fr om items such as incr ease d concrete strength d ue to ag ing and a chieving minim um specified strengths in a conservative manner. 10.4.3.2 Nonlinear Structure Models The nonlinear behavior of structures is important in two regards: (1) evaluating the capacity of structural members and the structure itself and (2) estimating the environment (in-structure response spectra and structural displacements) to which equipment and commodities are subjected. Nonlinear structural behavior is characterized by a shift in natural frequencies to lower values, increased energy dissipation, and increased relative displacement between points in the structure. Four factors determine the significance of nonlinear structural behavior to dynamic response. 10.4.3.3 Frequency Content of the Control Motion vs. the Frequencies of the Structure Consider a rock-founded structure. Depending on the elastic structure frequencies and characteristics of the control motion, the shift in structure frequency due to nonlinear structural response may result in a relatively large reduction in structure response with a substantial reduction in input to equipment when compared to elastic analysis results. If the structure elastic frequency is located on the peak or close to the peak of the control motion’s response spectra, the frequency shift will result in a decrease in response. If the elastic frequency is higher than the peak of the control motion’s response spectra, the shift in frequency tends to result in increased response. The same type of reduction occurs for structures excited by earthquakes characterized by narrow-band response spectra where the structure elastic frequency tends to coincide closely with the peak of the ground response spectra. 10.4.3.4 Soil–Structure Interaction Effects The effect of nonlinear structure behavior on in-structure response (forces, accelerations, and response spectra) appears to be significantly less when SSI effects are important at the site. This is principally due to the potential dominating effect of SSI on the response of the soil–structure system. The soil can have a controlling effect on the frequencies of the soil–structure system. Also, if SSI is treated properly, the input motion to the system is filtered such that higher frequency motion is removed, i.e., frequency © 2003 by CRC Press LLC
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content which may not be suppressed by nonlinear structural behavior if the structure were founded on rock. SSI can have a significant effect on the energy dissipation characteristics of the system due to radiation damping and material damping in the soil. Accounting for the effect of the inelastic structural behavior on structure response must be done carefully for soil-founded structures to avoid doublecounting of the energy dissipation effects. 10.4.3.5 Degree of Structural Nonlinearity The degree of structural nonlinearity to be expected and permitted determines the adequacy assessment for the structure and can have a significant impact on in-structure responses. Past reviews of testing conducted on shear walls have indicated that element ductilities of up to about four or five can be accommodated before significant strength degradation begins to occur. However, the allowable achieved ductility for many evaluations will be substantially less. The effect of nonlinear structure behavior on instructure response spectra has been considered to only a limited extent. In general, increased levels of nonlinearity lead to increasingly reduced in-structure response spectra for a normalized input motion. However, in some instances, higher frequency, i.e., higher than the fundamental frequency, peaks can be amplified. This is an area in which research is currently being performed, which will provide guidance in the future. 10.4.3.6 Magnitude Effects Earthquake magnitude as it affects the control motion has been discussed earlier. Recall, however, smaller magnitude, close-in earthquakes may be narrow-banded, which are significantly affected by nonlinear behavior as described above.
10.5 Soil–Structure Interaction Response Numerous guidelines exist defining the required steps to perform SSI analysis for design or evaluation purposes. All methods of analysis are treated. Selected guideline documents are: ASCE Standard, Seismic Analysis of Safety-Related Nuclear Structures and Commentary [1998] EPRI Guidelines for Soil–Structure Interaction Analysis [Tseng and Hadjian, 1991] Earthquakes and Associated Topics in Relation to Nuclear Power Plant Siting [IAEA, 1991] Seismic Design and Qualification for Nuclear Power Plants [IAEA, 1992] The validation of SSI analysis through field data has been difficult due to the lack of well-documented and instrumented structures subjected to earthquakes. Very few cases exist where the data necessary to effectively analyze a soil–structure system have been developed or measured. In addition, for those with data, typically, not all aspects of the SSI phenomenon are important. One case in point is the Lotung one quarter scale model. All appropriate data have been developed and measured but the high stiffness of the structure and the very soft soil conditions eliminate structure vibration as a significant phenomenon. Comparisons of measured and calculated response produced an excellent match. Hence, elements of the SSI analysis process were validated. In addition to the Lotung experiment, there is a recognition in the technical community that additional data appropriate for SSI analysis methods benchmarking and development are necessary. One example was an additional experiment, denoted the Hualien large-scale seismic test for SSI research, constructed in Taiwan in the early 1990s. This experiment intended to eliminate some of the deficiencies of the Lotung experiment by siting a model structure on a stiffer site than Lotung, thereby bringing dynamic structure response into importance. Unfortunately, this experiment has not received the funding necessary to progress. Instrumenting large bridge structures in seismically active areas would be an additional source of data to be pursued. Many aspects of SSI are well understood and any valid method of analysis is able to reproduce them. Sections 10.2, 10.3, and 10.4 detailed the various aspects of the problem and the current capability to model them. Clearly, uncertainties exist in the process: randomness associated with the earthquake ground motion itself, and the dynamic behavior induced in soil and structures. Even assuming perfect © 2003 by CRC Press LLC
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modeling, randomness in the response of structures and components is unavoidable. Perhaps the best evidence of such randomness is the Chiba Field Station. Shibata [1991] reports the results of 20 years of recorded motion on the model structure; 271 events when taken in total. Analyzing the measured responses of the hung tank yields a coefficient of variation of response of about 0.45 conditional on the horizontal peak ground accelerations of the earthquake. Of course, arguments can be made that many of the events were low amplitude, that grouping events by epicentral area reduced variability, etc. However, the indisputable fact is that significant variability in response of structures and components due to earthquakes is to be expected. No deterministically exact solution of the SSI problem can be obtained by existing techniques. However, given the free-field ground motion and data concerning the dynamic behavior of soil and structure, reasonable response predictions can be made. These responses can confidently be used in design and evaluation procedures. It is on this premise that analysis guidelines cited above are based. In addition, uncertainties in each of the elements do not necessarily combine in such a fashion as to always increase the uncertainty in the end item of interest (structure response). Finally, when evaluating the SSI model and the resulting analytical results, one should evaluate intermediate and end results including: • Fixed-base vs. soil-structure system frequencies • Amount of soil stiffness softening due to earthquake excitation compared to low strain values • Effect of soil property variations on dynamic model parameters, such as system frequency, important response parameters, and structural damping values used For partially embedded structures, response at grade level floors should, as a general rule, be less than the free-field ground surface motion.
Defining Terms Control motion — Amplitude and frequency characteristics of the input motion. Control point — Point at which input motion is applied, in an SSI analysis. Free field — The ground surface in the absence of any structures. Free-field ground motion — Motion that would essentially exist in the soil at the level of the foundation in the absence of the structure and any excavation.
Uniform hazard spectra (UHS) — Ground response spectra generated so as to have the same probability of exceedance for all structural frequencies of interest.
References ASCE. (1998). “ASCE Standard, Seismic Analysis of Safety-Related Nuclear Structures and Commentary,” ASCE 4–98, American Society of Civil Engineers, Reston, VA. ASCE Committee on Reliability of Offshore Structures, Subcommittee on Foundation Materials. (1979). Probability Theory and Reliability Analysis Applied to Geotechnical Engineering of Offshore Structure Foundations, American Society of Civil Engineers, Reston, VA. ASCE. (1992). Dynamic Analysis Committee Working Group Report on Stiffness of Concrete, American Society of Civil Engineers, Reston, VA. Bjorkman, G.S., Moore, D.P., Nolin, J.J., and Thompson, V.J. (2001). “Influence of ISFSI Design Parameters on the Seismic Response of Dry Storage Casks,” W01/3, Proc. Structural Mechanics in Reactor Technology, August 12–17, Washington, D.C., SMIRT Secretariat, North Carolina State University, Raleigh. CH2M Hill. (1991). Proc. NSF/EPRI Workshop on Dynamic Soil Properties and Site Characterization, EPRI NP-7337, vol. 1, Electric Power Research Institute, Palo Alto, CA.
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Chang, C.-Y., Power, M.S., Idriss, I.M., Somerville, P.G., Silva, W., and Chen, P.C. (1985). “Engineering Characterization of Ground Motion, Task II: Observational Data on Spatial Variations of Earthquake Ground Motion,” NUREG/CR-3805, vol. 3, prepared for the U.S. Nuclear Regulatory Commission, Washington, D.C. Chang, C.-Y. et al. (1990). “Equivalent Linear Versus Nonlinear Ground Response Analyses at Lotung Seismic Experiment Site,” Proc. Fourth U.S. National Conference on Earthquake Engineering, Palm Springs, CA. Chang, C.-Y. et al. (1991). “Development of Shear Modulus Reduction Curves Based on Lotung Downhole Ground Motion Data,” Proc. Second International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, St. Louis, MO. Cramer, C.H. (1991). “Turkey Flat, USA Site Effects Test Area, Report 6 Weak-Motion Test: Observations and Modeling,” Technical Report No. 91–1, California Department of Conservation, Division of Mines and Geology, Earthquake Shaking Assessment Project, Sacramento, CA. EPRI. (1989). Proc. EPRI/NRC/TPC Workshop on Seismic Soil Structure Interaction Analysis Techniques Using Data from Lotung, Taiwan, EPRI NP-6154, vols. 1 and 2, Electric Power Research Institute, Palo Alto, CA. Gazetas, G. and Bianchini, G. (1979). “Field Evaluation of Body and Surface-Wave Soil-Amplification Theories,” Proc. Second U.S. National Conference on Earthquake Engineering, Electric Power Research Institute, Stanford University, Palo Alto, CA. Hadjian, A.H. et al. (1991). “A Synthesis of Predictions and Correlation Studies of the Lotung Soil Structure Interaction Experiment,” Report No. NP-7307-M, Electric Power Research Institute, Palo Alto, CA. IAEA. (1991). “Earthquakes and Associated Topics in Relation to Nuclear Power Plant Siting: A Safety Guide,” Safety Series No. 50-SG-S1 (Rev. 1), International Atomic Energy Agency, Vienna, Austria. IAEA. (1992). “Seismic Design and Qualification for Nuclear Power Plants: A Safety Guide,” Safety Series No. 50-SG-D15, International Atomic Energy Agency, Vienna, Austria. Ishihara, K. (1996). Soil Behavior in Earthquake Geotechnics, Oxford Engineering Science Series, no. 46, Oxford University Press, London. Ishii, K., Itoh, T., and Suhara, J. (1984). “Kinematic Interaction of Soil-Structure System Based on Observed Data,” Proc. 8th World Conference on Earthquake Engineering, San Francisco, vol. 3, Earthquake Engineering Research Center, Berkeley, CA, pp. 1017–1024. Johnson, J.J. (1981). Soil Structure Interaction: The Status of Current Analysis Methods and Research,” Lawrence Livermore National Laboratory (LLNL), UCRL-53011, NUREGICR-1780, prepared for the U.S. Nuclear Regulatory Commission, Washington, D.C. Johnson, J.J. and Asfura, A.P. (1993). “Soil Structure Interaction (SSI): Observations, Data, and Correlative Analysis,” in Developments in Dynamic Soil-Structure Interaction, P. Gulkan and R.W. Clough, eds., Kluwer Academic Publishers, Dordrecht, pp. 219–258. Johnson, J.J. and Chang, C.-Y. (1991). “State of the Art Review of Seismic Input and Soil-Structure Interaction,” Appendix E in A Methodology for Assessment of Nuclear Power Plant Seismic Margin (Rev. l), EPRI NP-6041-SL, Electric Power Research Institute, Palo Alto, CA. Johnson, J.J., Maslenikov, O.R., Mraz, M.J., and Udaka, T. (1989). “Analysis of Large-Scale Containment Model in Lotung; Taiwan: Forced Vibration and Earthquake Response Analysis and Comparison,” Proc. EPRI/NRC/TPC Workshop on Seismic Soil Structure Interaction Analysis Techniques Using Data From Lotung, Taiwan, EPRI NP-6154, vols. 1 and 2, Electric Power Research Institute, Palo Alto, CA, pp. 13-1–13-44. Kudo, K., Shima, E., and Sakane, M. (1988). “Digital Strong Motion Accelerograph Array in Ashigara Valley — Seismological and Engineering Prospects of Strong Motion Observations,” Proc. 9th World Conference on Earthquake Engineering, vol. 8, Earthquake Engineering Research Center, Berkeley, CA, pp. 119–124.
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Midorikawa, S. (1992). “A Statistical Analysis of Submitted Predictions for the Ashigara Valley Blind Prediction Test” (Subcommittee for the Prediction Criteria of the Ashigara Valley Blind Prediction Test), Proc. International Symposium on the Effects of Surface Geology on Seismic Motion, Odawara, Japan. Newmark, N.M. and Hall, W.J. (1978). Development of Criteria for Seismic Review of Selected Nuclear Power Plants, NUREG/CR-0098, prepared for the U.S. Nuclear Regulatory Commission, Washington, D.C. Proceedings of the International Symposium on the Effects of Surface Geology on Seismic Motions. (1992). Odawara, Japan. Schnabel, P.B., Lysmer, J., and Seed, H.B. (1972). SHAKE: A Computer Program for Earthquake Response Analysis of Horizontally Layered Sites, Report No. EERC 72–12, Earthquake Engineering Research Center, University of California, Berkeley. Seale, S.H. and Archuleta, R.J. (1991). “Analysis of Site Effects at the Games Valley Downhole Array Near the San Jacinto Fault,” Proc. Second International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, Paper No. 8.13, St. Louis, MO. Seed, H.B. and Idriss, I.M. (1970). Soil Moduli and Damping Factors for Dynamic Response Analysis, Report No. EERC 70–10, Earthquake Engineering Research Center, University of California, Berkeley. Shibata, H. (1978). “On the Reliability Analysis for Structural Design Including Pipings and Equipment,” presented at the Seminar on Probabilistic Seismic Analysis of Nuclear Power Plants, January 16–19, Berlin. Shibata, H. (1991). “Uncertainty in Earthquake Engineering in Relation to Critical Facilities,” Bulletin of Earthquake Resistant Structure Research Center, Institute of Industrial Science, University of Tokyo, No. 24, 93–104. Tanaka, T. et al. (1973). “Observations and Analysis of Underground Earthquake Motions,” Proc. 5th World Conference on Earthquake Engineering, Rome, vol. 1, pp. 658–667. Tseng, W.S. and Hadjian, A.H. (1991). “Guidelines for Soil Structure Interaction Analysis,” EPRI NP7395, Electric Power Research Institute, Palo Alto, CA. Tseng, W.S. and Penzien, J. (2000). “Soil-Foundation-Structure Interaction,” in Bridge Engineering Handbook, W.F. Chen and L. Duan, eds., CRC Press, Boca Raton, FL, pp. 42-1–42-52. U.S. Atomic Energy Commission. (1973). “Regulatory Guide 1.60, Design Response Spectra for Seismic Design of Nuclear Power Plants,” Rev. 1, U.S. Atomic Energy Commission, Washington, D.C. Wolf, J.P. and Song, C. (2002). “Some Cornerstones of Dynamic Soil-Structure Interaction,” Eng. Struct., 24, 13–28. Woods, R.D. (1978). “Measurement of Dynamic Soil Properties,” Proc. ASCE Specialty Conference on Earthquake Engineering and Soil Dynamics, vol. 1, Pasadena, CA, pp. 91–178. Yanev, P.I., Moore, T.A., and Blume, J.A. (1979). “Fukushima Nuclear Power Station, Effect and Implications of the June 12, 1978, Miyagi-ken-Oki, Japan, Earthquake,” prepared by URS/John A. Blume & Associates, Engineers, San Francisco.
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III Structural Aspects
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11 Building Code Provisions for Seismic Resistance 11.1 Introduction 11.2 Historical Development Early Prescriptive Codes · Early Lateral Force Requirements · 1927 Uniform Building Code · Code Development in the 1930s and 1940s · 1958 Uniform Building Code · Code Development 1958 to 1970 · 1971 San Fernando Earthquake · National Seismic Provisions
11.3 2000 NEHRP Recommended Provisions Overview · Performance Intent and Objectives · Seismic Hazard Maps and Ground Motion Parameters · Seismic Design Categories · Permissible Structural Systems · Design Coefficients · Analysis Procedures · Load Combinations and Strength Requirements · Drift Limitations · Structural Detailing
Ronald O. Hamburger Simpson Gumpertz & Heger, Inc. San Francisco, CA
11.4 Performance-Based Design Codes Defining Terms References Further Reading
11.1 Introduction The purpose of building codes is to promote and protect the public welfare. The public welfare may be broadly construed to include considerations of the health and safety of individual citizens, as well as the economic well-being of the community as a whole. Building codes accomplish this purpose by setting minimum standards for the materials of construction that may be used for structures of different types and occupancies, the minimum permissible strength of these structures, and the amount of deformation that may be tolerated under design loading. Governments have the power to enforce these standards through the code adoption process, i.e., converting the code into a legal standard. If building code criteria were not specified in a uniform manner, design and construction practice would vary widely, and many structures would be unable to afford their occupants adequate protection against collapse. Design loading levels are typically set by building codes at levels that have a moderate to low probability of occurrence during the life of the structure. For example, buildings may be designed for earthquake shaking likely to be experienced one time every 500 years, wind loads anticipated, on the average, one time every 100 years, or for snow loads that would be anticipated to occur, on average, one time every
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20 years. The significant difference in recurrence intervals adopted by codes for these various hazards is a function of the hazard itself, and the adequacy of a given return period to capture a maximum, or near maximum, credible event. Building code provisions typically require design for such loading to accomplish two main objectives. The first is to provide a low probability of failure under any likely occurrence of the loading type. This is typically accomplished through prescription of minimum required levels of structural strength. The second is to provide sufficient stiffness such that deflections do not affect the serviceability of the structure, or result in cracking or other damage that would require repair following routine loading. For most structural elements and most loading conditions, these dual design criteria result in structures that are capable of resisting the design loading with either elastic or near-elastic behavior. Consequently, engineered buildings rarely experience structural damage as a result of the effects of dead, live, wind, or snow loads, and rarely completely fail under such loading. Building code provisions for earthquake-resistant design are unique in that, unlike the provisions for other load conditions, they do not intend that structures be capable of resisting design loading within the elastic, or near-elastic range of response — that is, some level of damage is permitted. Building codes intend only that buildings resist large earthquake loading without life-threatening damage and, in particular, without structural collapse or creation of large, heavy falling debris hazards. This unique earthquake design philosophy evolved over time based primarily on two motivating factors. First, even in zones of relatively frequent seismic activity, such as regions around the Pacific Rim, intense earthquakes are rare events, affecting a given region at intervals ranging from a few hundreds to thousands of years. Most buildings will never experience a design earthquake and, therefore, design to resist such events without damage would be economically impractical for most structures. The second reason for this design approach relates to the development history for building code seismic provisions, which is briefly discussed in the next section. Building code provisions governing design for earthquake resistance may be traced back as far as building regulation enacted in Lisbon, Portugal, following the great earthquake of 1755 [Tobriner, 1984]. Early building code provisions for seismic resistance focused on prohibiting certain types of construction observed to behave poorly in past earthquakes, and to require the use of certain construction details and techniques observed to provide better performance. These features remain an important part of modern codes. However, modern codes supplement these prescriptive requirements with specifications of minimum permissible structural strength and stiffness. Although most developed countries develop and enforce their own building codes, the seismic provisions currently used throughout the world generally follow one of four basic models: • NEHRP Recommended Provisions, developed by the Building Seismic Safety Council in the United States [BSSC, 1997] • Building Standards Law of Japan • New Zealand Building Standards Law • Eurocode 8 Although each individual code has many unique requirements and provisions, in general all are based on and incorporate similar concepts. This chapter principally discusses the NEHRP Recommended Provisions which, together with related publications by the Structural Engineers Association of California [SEAOC, 1999], forms the basis for most building codes in use in the Americas today as well as in other parts of the world.
11.2
Historical Development
Building code provisions for earthquake resistance may generally be traced to one of three bases. The first of these, herein termed the experience basis, consists of observation of the behavior of real structures in earthquakes, and the development of prescriptive rules intended to prevent construction of buildings with characteristics that are repeatedly observed to result in undesirable behavior. © 2003 by CRC Press LLC
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The second basis is herein termed the theoretical basis. It consists of the body of analytical and laboratory research that has been developed over the years, largely by the academic community, and which provides an understanding of the way structures of different types respond to earthquakes and why. The final basis is one of designer judgment. The building design community and, in particular, structural engineers — primarily through the SEAOC, the American Society of Civil Engineers (ASCE), the Building Seismic Safety Council (BSSC), and other similar groups — have historically taken a leadership role in the development of these building code provisions. These structural engineers have consistently tempered and moderated the information obtained from the experience and theoretical bases, with their independent design judgment, assuring political acceptability of the building code within the design community, if not completely rational or justifiable provisions.
11.2.1 Early Prescriptive Codes The earliest building code provisions were strictly experience based. It was observed that certain types of construction consistently performed poorly, so rules were developed to regulate the features of these construction types to improve their performance. In the United States this process is thought to have been initiated with the observation of the poor performance of unreinforced brick masonry bearing wall buildings in the San Francisco Bay Area, following the Hayward earthquake of 1868. It was observed in this and other early California earthquakes that brick masonry walls frequently pulled away from the floor and roof systems, then toppled to the ground. It was similarly observed that the brick walls were not strongly bonded together, and that the walls would literally fall apart, into the component brick pieces (Figure 11.1). Based on these observations, some building codes in California began to include prescriptive provisions regulating the construction detailing of unreinforced masonry buildings. To avoid the frequently observed out-of-plane failure of masonry walls, in which they would pull away from the floors and roofs and topple to the ground, codes FIGURE 11.1 Typical failure of masonry walls started to require the provision of out-of-plane anchors in unreinforced masonry bearing wall buildings, between the walls and floor and roof diaphragms. 1989 Loma Prieta earthquake. (Courtesy U.S. Anchors were not designed for specific forces, but rather Geological Survey) were specified to be of a standard size and spacing. The most common such anchors consisted of steel rods that extended to the exterior face of the masonry wall, typically terminating with a round plate washer or rosette for bearing against the masonry, and tying to the floor framing by means of a 90ο bend that “dogged” into the side of the wood members. Evidence of these anchors can be commonly observed on older unreinforced masonry structures in the form of rows of rosette plates along the exterior faces of walls just below the floor and roof levels, typically at 6- to 8-ft spacing. To address the commonly observed in-plane failures of unreinforced masonry walls, some codes in the San Francisco Bay Area required the placement of “bond irons” in the masonry. These bond irons consisted of 1/4-in. thick flat bars, laid horizontally in the mortar courses of masonry walls at approximately 24-in. vertical spacing. Riveted together at lap joints, these bond irons were a primitive form of reinforcing. Neither code-required wall anchors nor bond irons were designed for a specified loading. In fact, engineers of the day had little understanding of the strength of earthquake ground shaking, the © 2003 by CRC Press LLC
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mechanisms by which this shaking induced forces in building components or the magnitude of these forces. They did observe, however, that unreinforced masonry buildings constructed without wall anchors and bond irons tended to collapse when earthquakes occurred and that this resulted in life loss. Thus, the primary goal of these first earthquake provisions in building codes was simply to avoid building collapse and the resulting life endangerment. Over the years, as the building codes evolved, this goal remained as the primary objective of building code earthquake provisions.
11.2.2 Early Lateral Force Requirements In the early 20th century, building codes around the world began to introduce requirements that structures intended to resist earthquakes be provided with sufficient strength to resist a specified lateral force. These requirements, though substantially refined, are retained in most building codes today as a basic design method and are frequently termed the equivalent lateral force (ELF) technique. Perhaps the first of these requirements appeared in the building code published by the City of San Francisco, following the great 1906 earthquake. This code required that all buildings be designed for a lateral pressure of 30 pounds per square foot on the projected area of the building façade, as a protection against both wind and earthquake. Following a devastating magnitude 7.5 earthquake in Messina, Italy, that caused 80,000 casualties in 1908, a special committee of practicing engineers and engineering professors was commissioned to recommend improved construction requirements. The resulting report included a recommendation that the first story of structures be designed for a horizontal force equal to 1.5% of the weight above and the second and third stories be designed for one eighth of the building weight above. This appears to have been the first formal recommendation to provide earthquake resistance by providing lateral strength equal to a fraction of the structure’s supported weight [Housner, 1984]. The ELF concept was introduced in Japan in 1914, but not required. Following the great 1923 Tokyo earthquake, the Japanese Urban Building Law Enforcement Regulations were revised to require lateral design for a strength equal to 10% of the structure’s supported weight.
11.2.3 1927 Uniform Building Code The first modern code containing seismic provisions is generally acknowledged to be the first edition of the Uniform Building Code published by the Pacific Coast Building Officials in 1927 [PCBO, 1927], following the 1925 Santa Barbara earthquake. The Pacific Coast Building Officials later became the International Conference of Building Officials, and continued to publish the Uniform Building Code (UBC) for another 70 years, the last edition being published in 1997 [ICBO, 1997]. The seismic provisions of the UBC were based primarily on the SEAOC recommendations and remained in a leadership role over the full 70 years. The 1927 edition of the UBC incorporated the lessons engineers had learned in observing a series of earthquakes that had affected California during the period 1868 to 1925. These included the 1868 Hayward, 1906 San Francisco, and 1925 Santa Barbara earthquakes, as well as other smaller events. The earthquake requirements of the 1927 code were included in a nonmandatory appendix, where they remained for nearly 30 years. In addition to the vulnerability of unreinforced masonry structures already discussed, the 1927 code built upon engineers’ observations that the primary damaging effect to structures appeared to be a lateral shaking motion and that this lateral shaking tended to be much more severe in areas with deep, soft soil deposits, termed infirm soils. The code required design of such structures for the simultaneous application of a lateral force at each roof and floor level equal to 10% of the structure’s weight tributary to that floor. Structures sited on firm soils were designed for one third of this force, recognizing in an approximate manner, the reduced intensity of ground shaking on sites with firm soil profiles. Since there were no records of actual ground motion available in 1927 (the first accelerometer had yet to be installed), and structural dynamics was a newly developing science, the selection of a 10% design lateral strength level must surely have been judgmental, and may have been influenced in part by the © 2003 by CRC Press LLC
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similar requirement that had been recently adopted in Japan. However, it did set an important precedent. As engineers began to design structures to these new code requirements, they also began to rely on a lateral strength equal to 10% of the supported weight as being adequate to provide earthquake resistance. Even as dramatic improvements in understanding of ground motion and structural response occurred, over the years, engineers tended to apply judgment and scale code provisions so that they produced design forces approximating this same level. With the publication of the 1927 code, the process of observing the behavior of buildings designed to the code began, and of modifying the code to produce better performing structures and incorporate the findings of engineering research. It is important to stress that the observation of earthquake damage to engineered structures has been as significant a factor in this development as analytical and laboratory work performed by the academic community.
11.2.4 Code Development in the 1930s and 1940s In the years between 1927 and 1940 seismic provisions in codes changed relatively little, as relatively few earthquakes occurred, and engineering knowledge was limited. However, following the 1933 Long Beach earthquake, which caused extensive damage to unreinforced masonry buildings, and in particular, several public schools (Figure 11.2), the State of California adopted a number of regulations that would later have significant impact on the UBC. First, California prohibited further construction of unreinforced masonry buildings. The UBC would later pick up this same prohibition in zones of high seismicity. Also, California adopted two acts, the Riley Act and Field Act, which regulated building construction for earthquake resistance. The Riley Act required that all buildings in California be provided with a lateral strength equal to 3% of the weight of the structure, making seismic design mandatory. This provision was also adopted by the UBC and remains in the NEHRP Provisions today, albeit in somewhat modified form. The Field Act established the Office of the State Architect and charged this department with responsibility for the regulation of public school construction. The Office of the State Architect established rigorous standards for structural design, plan review, and inspection of construction that would affect structural engineering practice throughout California and eventually find its way into the building code requirements applicable to all forms of construction.
FIGURE 11.2 Collapse of John Muir School, 1933 Long Beach, CA earthquake. (Courtesy NOAA, www.ngdc.gov, photo: W.L. Huber.)
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In the 1937 edition of the UBC the concept of differentiating seismic risk by means of a zonation map was introduced. This first map divided the continental United States into three seismic zones and the required lateral strength for a structure was regulated based on these seismic zones. In the 1940s, engineers began to understand the science of structural dynamics. Based on rudimentary understanding of this science and on observations that tall structures seemed to perform better in earthquakes than low-rise construction, a base shear equation was introduced into the 1946 edition of the UBC. For structures located in the highest seismic zone, this base shear equation adjusted the design lateral forces for a structure, based on the number of stories present: V=
0.6 W N + 4.5
(11.1)
where N is the number of stories and W is the building weight. Short structures were designed for the most severe lateral forces, equivalent to 10% of the structure’s weight, while the design forces for taller structures could be reduced in proportion to the number of stories, representing in an approximate manner the concept of spectral amplification.
11.2.5 1958 Uniform Building Code At about this same time, Biot, Housner, and other researchers at the California Institute of Technology began to formalize the concepts of dynamic spectral response. In 1952 these researchers, acting under the auspices of the American Society of Civil Engineers, together with practicing structural engineering members of the Structural Engineers Association of California, formed a joint volunteer committee to develop recommendations for incorporation of these concepts into the building codes. The report of this joint committee, known as the Separate 66 Report [Anderson et al., 1952], presented the first formalized recommendations for relating design lateral forces to structural period, based on spectral response concepts. These recommendations were incorporated by SEAOC into the first edition of the Recommended Lateral Force Requirements and Commentary [SEAOC, 1999], commonly known as the Blue Book, and were adopted into the 1958 edition of the UBC. In that building code, the total lateral force, now commonly known as the base shear, was given by the formula: V = ZKCW
(11.2)
In this equation, Z was a zone coefficient that related the design force to regional seismicity, as portrayed in a national seismic zonation map (Figure 11.3). Four seismic zones were presented ranging from 0 to 3. Zone 3 represented the most severe seismic environment and was assigned a zone coefficient Z having a value of 1.0. In zone 0 there was no requirement for seismic design. In zones 1 and 2, the design coefficient Z was assigned fractional values, for example, 1/2 or 1/4, that effectively adjusted the required seismic design forces in lower zones, relative to those required in zone 3. K was a structural system coefficient that adjusted the magnitude of seismic design forces based on the typical performance observed of structures of different construction types in past earthquakes. Four basic classes of structural systems were recognized: • The first of these were buildings of light timber frame construction, such as is commonly used in residential and light commercial construction in the United States. For this class of construction, the K coefficient was assigned a value of 1.0. • The second structural system was the building frame system. In this system, dead and live loads were carried to the foundations by columns while lateral forces were resisted either by diagonal bracing or shear walls that did not participate in the vertical load resisting system. This system was also assigned a K value of 1.0. • The third structural system was known as a “box system.” In this system, bearing walls or diagonal braced frames carried both vertical loads and lateral forces. This category of structures included © 2003 by CRC Press LLC
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Statute Miles 100 50 0
100
200
300
400
Kilometers 10050 0
200
400
600
800
Zone 0 - no damage Zone 1 - minor damage Zone 2 - moderate damage Zone 3 - major damage
FIGURE 11.3
Seismic zonation map, 1958 Uniform Building Code.
a number of building types, such as unreinforced masonry structures, that had repeatedly been observed to perform poorly in earthquakes. Recognizing this poor performance and also the fact that earthquake-induced damage to lateral-force-resisting elements in buildings of this type could also result in loss of vertical load carrying capacity, a K coefficient of 1.33 was assigned to this building type, requiring design forces that were 33% larger than those for either of the other two systems. • The fourth system was moment-resisting frames in which beams and columns were rigidly connected to provide lateral stability. Based on the observation that these structures were often highly redundant, and also that steel frames, the most common form of such structures, had performed well in the 1906 San Francisco earthquake and again in the 1925 Santa Barbara and 1933 Long Beach earthquakes, this system was assigned a preferential K value of 0.67, permitting them to be designed with two thirds of the lateral strength required for light frame and building frame systems. The C coefficient accounted for spectral amplification of ground motion by buildings having certain fundamental response periods. The C coefficient was given by the equation: C=
0.05 T
(11.3)
where T was the fundamental mode natural period of vibration of the structure, calculated using an empirical formula contained in the code, based on strong motion recordings from buildings. Alternatively, more exact techniques for establishing the structural period, such as the Rayleigh method, were also permitted. W was the total dead weight of the structure. Additional provisions of the code limited the value of C such that for structures qualifying for a K value of 1.0, the design base shear force would not have to exceed a value of 0.1, preserving the judgment contained in earlier building codes that most structures could survive a strong earthquake if provided with a lateral strength equal to 10% of their supported weight. In addition, a lower bound value of 0.03 was provided to conform to the Riley Act requirements adopted following the 1933 Long Beach earthquake.
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Once the base shear was determined, using Equation 11.3, lateral forces were distributed to each level of the structure, in proportion to the mass supported at that level, using the so-called uniform distribution method. The lateral forces at each level were distributed to the various vertical elements of the lateral-force-resisting system, considering both the stiffness of the individual vertical elements and the horizontal diaphragms, and the vertical elements were required to be designed, using allowable stress design procedures, for the combined shearing and overturning effects of these forces, taken together with gravity loads. Allowable stresses for load conditions containing earthquake forces were permitted to be increased by one third relative to those specified for gravity load resistance.
11.2.6 Code Development 1958 to 1970 During the 10 years following publication of the 1958 edition of the UBC, the seismic provisions remained quite stable and changes tended to be subtle, though in some cases important. Perhaps the most significant development introduced during this period was philosophical and related to a formalized statement of the intent of the code provisions, as published by SEAOC in its Blue Book. Specifically, the Blue Book recognized during this period that the actual forces imposed on structures by strong earthquakes were significantly larger than those that had historically been used for design purposes. It was postulated that, perhaps, the actual forces would be three to four times those used for design. However, it was rationalized, based largely on the observation of actual structure behavior, that structures designed for a fraction of the real imposed loading could survive earthquake shaking with damage but not collapse, as long as they were provided with continuous and tough lateral-force-resisting systems. Recognizing that actual earthquake forces resulting from design earthquake shaking were potentially significantly larger than the design strength of the structure, SEAOC also recognized that it was inevitable that structures designed in this manner would be damaged. SEAOC proposed that structures designed in accordance with the Blue Book recommendations would provide the following multitiered performance capabilities: • Resist minor earthquake shaking without damage • Resist moderate earthquake shaking without structural damage but possibly with some damage to nonstructural features • Resist major levels of earthquake shaking with both structural and nonstructural damage, but without endangerment of the lives of occupants This final goal came to be known as the life-safety criterion and it became commonly discussed among engineers, if not the public, that the intent of the code was to protect life safety, and not prevent damage or preserve capital investments in real property. Over time, the life-safety criterion was expanded to include the concept that the damaged building would retain adequate stability to avoid collapse while victims were extracted, and later still, that damage to buildings in major levels of shaking would be sufficiently limited, that occupants would be able to exit the buildings unassisted. In addition to the life-safety criterion, commentary in the Blue Book noted that buildings designed in accordance with its provisions should be capable of resisting the most intense levels of ground shaking ever likely to affect the building without collapse. This four-level performance criterion developed by SEAOC in the 1960s remains the intent of building code provisions to this day, though significant refinement and quantification of these performance goals has since occurred. Together with the recognition and admission that buildings were designed to be damaged, came the parallel recognition of the importance of toughness and redundancy to earthquake resistance, so that structures could sustain damage of their structural elements without collapse. These concepts were then used to rationalize and justify the K values that earlier had been assigned to the various structural systems. In particular, the high K value for box systems was justified on the basis of a lack of redundancy, and the fact that earthquake-induced damage of lateral-force-resisting elements could trigger vertical collapse. Similarly, building frame systems and repetitive light frame systems were viewed as highly redundant, justifying their presumed superior performance. Moment-resisting frames, in addition to © 2003 by CRC Press LLC
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having significant redundancy, relating to the large number of beams and columns participating in lateral resistance, were rationalized to have significant toughness, again justifying the reduced design forces for building conforming to that system. In parallel with these philosophical developments, researchers began to investigate the postyield behavior of typical framing elements. With this research, it began to be discovered that the way in which structural elements and their connections are detailed could have substantial impact on the toughness and ductility of the structural system. In particular, it was noted that reinforced concrete frames exhibited brittle behavior unless they are (1) detailed to provide for reversed loading, which favors flexural yielding as opposed to shear nonlinearity, and (2) provided with sufficient transverse reinforcement to provide confinement of the concrete cores of framing elements. The first provisions for ductile detailing of reinforced concrete frames were introduced into the 1967 edition of the UBC. In subsequent years these ductile detailing provisions would be refined and expanded, then developed to cover other structural systems as well, including systems of structural steel, masonry, and timber construction. As the concepts were slowly introduced, engineers began to believe that they had developed a rational and reliable set of building code provisions, able to reliably attain desired earthquake performance.
11.2.7 1971 San Fernando Earthquake The magnitude 6.6 earthquake that occurred February 9, 1971, near Sylmar, California was one of the more significant earthquakes of modern times, with regard to building code development. This large magnitude event, which occurred at the rim of the rapidly developing San Fernando Valley to the north of metropolitan Los Angeles, demonstrated that then-current building code provisions were not capable of meeting the performance goals suggested in SEAOC’s Blue Book. This earthquake caused partial and total collapse of a number of modern, code-conforming buildings, including a number of low-rise industrial and commercial buildings, single-family residences, and a recently completed county healthcare complex (Figure 11.4). It also induced the collapse of a number of older buildings, including several hospitals. It was evident that major revisions to the codes were necessary and that SEAOC could not accomplish this with the voluntary efforts of its members alone. As a result, SEAOC formed the Applied Technology Council (ATC) as a not-for-profit applied research agency, specifically to seek funding to perform the required structural engineering research and advance the practice of structural engineering. In 1978, ATC published its ATC-3.06 (1978) report, a seminal work in the development of seismic provisions. The ATC-3.06 report represented a major milestone in the development of building code provisions and remains as the foundation for current building code seismic provisions in the United States today. Among the milestone improvements introduced in the ATC-3.06 report was the formal introduction of dynamic analysis as the basis for building design for earthquake forces. The report introduced response spectrum analysis methods as the preferred procedure for design and rationalized and reformatted the equivalent lateral force procedure to clarify its use as a simplification of the more exact technique. By doing this, the report was able to directly relate design force levels to anticipated ground shaking accelerations and to the anticipated inelastic response capability of different structural systems. It also introduced the concepts of structural regularity and prohibited the construction of structures with certain types of irregularity. Although the ATC-3.06 report was a landmark in the development of building codes, it was not actually adopted as the basis for building codes until 12 years after its publication, when the seismic provisions of the 1988 UBC were rewritten by SEAOC and reformatted to adopt this approach. In the period of nearly 20 years between the occurrence of the 1971 San Fernando earthquake and the adoption of the 1988 UBC, many important incremental improvements were introduced into the SEAOC provisions that continued to serve as the basis of the UBC until 1988. These improvements were largely the result of observations of damage caused by the 1971 earthquake, but also earthquakes that occurred in Imperial Valley, California in 1979, and Mexico City in 1985. Noteworthy enhancements that occurred during this period included: © 2003 by CRC Press LLC
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FIGURE 11. 4 Partial collapse and extensive damage to the newly completed Olive View Hospital in the 1971 San Fernando earthquake.
• Introduction of a site factor to account for the effect of site soils on the frequency content and amplitude of ground shaking • Introduction of an occupancy importance factor to provide for more conservative design of important facilities • A one third increase in the minimum design force levels for all structures, as a general reaction to the poorer than anticipated performance of buildings • Requirements for positive direct interconnection of building components, particularly heavy wall panels connected to timber diaphragms, and requirements to develop the resulting anchorage forces into the lateral-force-resisting system • Introduction of interstory drift limits • Requirements to design anchorage for nonstructural components and to provide for the effects of interstory drift In addition to these important features introduced into the building code during this period, extensive prescriptive requirements for structural detailing of nearly all structural systems were introduced. These detailing requirements were based in part on observation of earthquake performance of buildings and in part on laboratory research, and are intended to provide for structural elements capable of extensive inelastic response, without degradation or failure.
11.2.8 National Seismic Provisions Although the provisions of the UBC were intended to be nationally applicable, the UBC was commonly adopted only in the western United States. Further, its provisions were dominated by the recommendations of SEAOC and were largely based on western United States and, in particular, California design practice. In the mid-1980s, using funding provided by the Federal Emergency Management Agency © 2003 by CRC Press LLC
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(FEMA), the Building Seismic Safety Council (BSSC) was formed as an independent council under the auspices of the National Institute of Building Sciences. BSSC was charged with converting the ATC-3.06 recommendations into a set of nationally applicable seismic provisions that could be adopted by building codes nationwide. BSSC’s work is performed by a Provisions Update Committee and a series of technical subcommittees. Membership on the committees is voluntary and by appointment. Committee participation is carefully selected to represent the best available knowledge in earthquake and structural engineering, while maintaining a balance in the geographic distribution of committee membership as well as uniform participation by design engineers, engineering researchers, code officials, and construction and materials industry interests. The work of the committees is subject to a national consensus balloting process, which enables rapid acceptance of the resulting provisions by the building regulation, design, and construction communities. The BSSC provisions were first published in 1985 as the NEHRP Recommended Provisions for Seismic Regulation for Buildings (NEHRP Provisions) and have since been updated and published on a 3-year cycle, matching that of the building codes. In 1993, the 1991 edition of the NEHRP Provisions was adopted as the basis of the seismic provisions in ASCE-7 [1991], which was then adopted by reference into two of the three model building codes used in the United States at that time. In 2000, the three model building codes that had served as the basis for building regulation for many years in the United States were replaced by a single code, the International Building Code (IBC) [ICC, 2000], published by a consortium of the organizations that developed the three prior codes. At the same time, the National Fire Protection Association (NFPA) began work on a competing building code, NFPA5000, scheduled to be published in 2002. The seismic design provisions in the IBC are transcribed from the 1997 edition of the NEHRP Provisions with some modification. The NFPA-5000 code will adopt seismic provisions by reference to the nearly identical 2002 edition of ASCE-7, which will be based on the 2000 edition of the NEHRP Provisions. The balance of this chapter focuses on the design requirements contained in the 2000 NEHRP Provisions.
11.3 2000 NEHRP Recommended Provisions 11.3.1 Overview The 2000 NEHRP Recommended Provisions for Seismic Regulation for Buildings and Other Structures (NEHRP Provisions) represents the current state of the art in prescriptive, as opposed to performancebased, provisions for seismic-resistant design. Its provisions form the basis for earthquake design specifications contained in the 2002 edition of ASCE-7, Minimum Design Loads for Buildings and other Structures, either through reference or direct incorporation, the seismic regulations in the 2003 edition of the IBC and also the 2002 edition of the NFPA 5000 Building Code [NFPA, n.d.]. As such, it will form the basis for most earthquake-resistant design in the United States, as well as other nations that base their codes on U.S. practices, throughout much of the first decade of the 21st century. The NEHRP Provisions assume significant amounts of nonlinear behavior will occur under design level events. The extent of nonlinear behavior that may occur is dependent on the structural systems employed in resisting earthquake forces, the configuration of these systems, and the extent to which the structural systems are detailed for ductile behavior under large cyclic inelastic deformation. The NEHRP Provisions may therefore be thought to consist of two component parts: • One part relates to specification of the required design strength and stiffness of the structural system • The second part relates to issues of structural detailing For this second part, the NEHRP Provisions adopt, with modification, design standards and specifications developed by industry groups such as the American Concrete Institute or the American Institute of Steel Construction. This second part of the NEHRP Provisions is not discussed in this chapter, but is covered in detail in each of the following chapters, which treat the individual structural materials. Instead,
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this chapter focuses primarily on the manner in which the NEHRP Provisions regulate the required strength and stiffness of structures.
11.3.2 Performance Intent and Objectives The NEHRP Provisions are intended to provide a tiered series of performance capabilities for structures, depending on their intended occupancy and use. Under the NEHRP Provisions, each structure must be assigned to a seismic use group (SUG). Three SUGs are defined and are labeled I, II, and III: • SUG-I encompasses most ordinary occupancy buildings, including typical commercial, residential, and industrial structures. For these facilities the basic intent of the NEHRP Provisions, just as with earlier codes, is to provide a low probability of earthquake-induced life safety endangerment. • SUG-II includes facilities that house large numbers of persons, persons who are mobility impaired, or large quantities of materials that, if released, could pose substantial hazards to the surrounding community. Examples of such facilities include large assembly facilities, housing several thousand persons, day care centers, and manufacturing facilities containing large quantities of toxic or explosive materials. The performance intent for these facilities is to provide a lower probability of life endangerment, relative to SUG-I structures, and a low probability of damage that would result in release of stored materials. • SUG-III includes those facilities such as hospitals and emergency operations and communications centers deemed essential to disaster response and recovery operations. The basic performance intent of the NEHRP Provisions with regard to these structures is to provide a low probability of earthquake-induced loss of functionality and operability. In reality, the probability of damage resulting in life endangerment, release of hazardous materials, or loss of function should be calculated using structural reliability methods as the total probability of such damage over a period of time [Ravindra, 1994]. Mathematically, this is equal to the integral, over all possible levels of ground motion intensity, of the conditional probability of excessive damage given that a ground motion intensity is experienced and the probability that such ground motion intensity will be experienced in the desired period of time. Although such an approach would be mathematically and conceptually correct, it is currently regarded as too complex for practical application in the design office. Instead, the NEHRP Provisions design for desired limiting levels of nonlinear behavior for a single design earthquake intensity level, termed maximum considered earthquake (MCE) ground shaking. In most regions of the United States, the MCE is defined as that intensity of ground shaking having a 2% probability of exceedance in 50 years. In certain regions, proximate to major active faults, this probabilistic definition of MCE motion is limited by a conservative deterministic estimate of the ground motion intensity anticipated to result from an earthquake of characteristic magnitude on these faults. The MCE is thought to represent the most severe level of shaking ever likely to be experienced by a structure, though it is recognized that there is some limited possibility of more severe motion occurring. Structures categorized as SUG-I are designed with the expectation that MCE shaking would result in severe damage to both structural and nonstructural elements, with damage perhaps being so severe that following the earthquake, the structure would be on the verge of collapse. This damage state has come to be termed collapse prevention, because the structure is thought to be at a state of incipient but not actual collapse. Theoretically, SUG-I structures behaving in this manner would be total or near total financial losses, in the event that MCE shaking was experienced. To the extent that shaking experienced by the structure exceeds the MCE level, the structure could actually experience partial or total collapse. SUG-III structures are designed with the intent that when subjected to MCE shaking they would experience both structural and nonstructural damage; however, the structures would retain significant residual structural resistance or margin against collapse. It is anticipated that when experiencing MCE shaking, such structures may be damaged to an extent that they would no longer be suitable for occupancy, until repair work had been instituted, but that repair would be technically and economically feasible. This superior performance relative to SUG-I structures is accomplished through specification that © 2003 by CRC Press LLC
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SUG-III structures be designed with 50% greater strength and more stiffness than their SUG-I counterparts. SUG-II structures are designed for performance intermediate to that for SUG-I and SUG-III, with strengths and stiffness that are 25% greater than those required for SUG-I structures.
11.3.3 Seismic Hazard Maps and Ground Motion Parameters The NEHRP Provisions incorporate a series of national seismic hazard maps for the United States and territories, developed by the United States Geologic Survey (USGS) specifically for this purpose (available at http://geohazards.cr.usfs.gov/eq/index.html). Two sets of maps are presented. One set presents contours of MCE, 5% damped, elastic spectral response acceleration at a period of 0.2 sec, termed SS. The second set presents contours of MCE, 5% damped, elastic spectral response acceleration at a period of 1.0 sec, termed S1. In both cases, the spectral response acceleration values are representative of sites with subsurface conditions bordering between firm soil or soft rock. Contours are presented in increments of 0.02 g in areas of low seismicity and 0.05 g in areas of high seismicity. By locating a site on the maps, and interpolating between the values presented for contours adjacent to the site, it is possible to rapidly estimate the MCE level shaking parameters for the site, given that it has a soft rock or firm soil profile. Figure 11.5 shows, for a portion of the western United States, contours of the 0.2-sec spectral acceleration with a 90% probability of not being exceeded in 50 years. As indicated in the figure, in zones of high seismicity these contours are quite closely spaced, making use of the maps difficult. Therefore, the USGS has furnished software, available both over the Internet (at the URL indicated above) and on a CD-ROM, that permits determination of the MCE spectral response acceleration parameters based on longitude and latitude. Since many sites are located neither on soft rock nor firm soil sites, it is necessary to correct the mapped values of spectral response acceleration to account for site amplification and deamplification effects. To facilitate this process, a site is categorized into one of six site class groups, labeled A through F. Table 11.1 summarizes the various site class categories. Once a site has been categorized within a site class, a series of coefficients are provided that are used to adjust the mapped values of spectral response acceleration for site response effects. These coefficients were developed based on observed site response characteristics in ground motion recordings from past earthquakes. Two coefficients are provided: • The Fa coefficient is used to account for site response effects on short period ground-shaking intensity • The Fv coefficient is used to account for site response effects of longer period motions Tables 11.2 and 11.3 indicate the values of these coefficients as a function of site class, and mapped MCE ground-shaking acceleration values. Site-adjusted values of the MCE spectral response acceleration parameters at 0.2 and 1 sec, respectively, are found from the following equations:
SMS = FaSS
(11.4)
SM1 = Fv S1
(11.5)
The two site-adjusted spectral response acceleration parameters, SMS and SM1, permit a 5% damped, maximum considered earthquake ground-shaking response spectrum to be constructed for the building site. This spectrum is constructed as indicated in Figure 11.6 and consists of a constant response acceleration range, between periods of T0 and TS, a constant response velocity range for periods in excess of TS and a short period range that ramps between an estimated zero period acceleration given by SMS /2.5 and SMS. Site-specific spectra can also be used. Regardless of whether site-specific spectra or spectra based on mapped values are used, the actual design values are taken as two thirds of the MCE values. The resulting design parameters are labeled, respectively, SDS and SD1 and the design spectrum is identical to the MCE spectrum, except that the ordinates are taken as two thirds of the MCE values. The reason for © 2003 by CRC Press LLC
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0.2 sec Spectral Accel. (%g) with 10% Probability of Exceedance in 50 Years site: NEHRP B-C boundary -124°
-122°
-120°
-118°
-116°
42°
-114°
42°
40°
%g 400 200 160 120 80 60 50 40 30 20 18 16 14 12 10 8 6 4 2 0
40°
38°
38°
36°
36°
34°
34°
32°
32° -124°
-122°
-120°
-118°
-116°
-114°
FIGURE 11.5 MCE seismic hazard map (0.2-sec spectral response acceleration) for the western United States. (Courtesy U.S. Geological Survey) Shown as Color Figure 11.5. TABLE 11.1 Site Categories Site Class A B C D E F
Description Hard rock Rock Very firm soil or soft rock Stiff soil Soil Special soils
Shear Wave Velocity –vs
Penetration – Resistance N
>5,000 ft/sec 2,500 ft/sec < –vs ≤ 5,000 ft/sec 1,200 ft/sec < –vs ≤ 2,500 ft/sec >50 >2,000 psf 600 ft/sec < –vs ≤ 1,200 ft/sec 15 to 50 1,000–2,000 psf v–s < 600 ft/sec <15 <1000 psf Soils requiring site-specific evaluations: 1. Soils vulnerable to potential failure or collapse under seismic loading such as liquefiable soils, quick and highly sensitive clays, collapsible weakly cemented soils 2. Peats and/or highly organic clays (H > 10 ft of peat and/or highly organic clay where H = thickness of soil) 3. Very high plasticity clays (H > 25 ft [8 m] with PI > 75) 4. Very thick soft/medium stiff clays (H > 120 ft [36 m])
– Note: –vs , N, –su represent the average value of the parameter over the top 30 m (100 ft) of soil. © 2003 by CRC Press LLC
Unconfined Shear Strength –su
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TABLE 11.2 Coefficient Fa as a Function of Site Class and Mapped Spectral Response Acceleration Mapped Maximum Considered Earthquake Spectral Response Acceleration at Short Periods Site Class A B C D E F
SS = 0.25
SS = 0.50
SS = 0.75
SS = 1.00
SS > 1.25
0.8 1.0 1.2 1.6 2.5 a
0.8 1.0 1.2 1.4 1.7 a
0.8 1.0 1.1 1.2 1.2 a
0.8 1.0 1.0 1.1 0.9 a
0.8 1.0 1.0 1.0 a a
Note: a — indicates site-specific evaluation required.
TABLE 11.3 Coefficient Fv as a Function of Site Class and Mapped Spectral Response Acceleration Mapped Maximum Considered Earthquake Spectral Response Acceleration at 1-sec Periods Site Class A B C D E F
S1 = 0.1
S1 = 0.2
S1 = 0.3
S1 = 0.4
S1 > 0.5
0.8 1.0 1.7 2.4 3.5 a
0.8 1.0 1.6 2.0 3.2 a
0.8 1.0 1.5 1.8 2.8 a
0.8 1.0 1.4 1.6 2.4 a
0.8 1.0 1.3 1.5 a a
Spectral Response Acceleration, Sa
Note: a — indicates site-specific evaluation required.
S MS Sa = SM 1
S MS
T
2 .5
T0=0.2TS
TS Period, T
FIGURE 11.6
Maximum considered earthquake response spectrum.
using design values that are two thirds of the maximum considered values is that the design procedures, described in later sections, are believed to provide a minimum margin against collapse of 150%. Therefore, if design is conducted for two thirds of the MCE ground shaking, it is anticipated that buildings experiencing MCE ground shaking would be at incipient collapse, the desired performance objective for SUG-I structures.
11.3.4 Seismic Design Categories The seismicity of the United States, and indeed the world, varies widely. It encompasses zones of very high seismicity in which highly destructive levels of ground shaking are anticipated to occur every 50 to © 2003 by CRC Press LLC
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TABLE 11.4 Categorization of Structures into Seismic Design Category, Based on Design Short Period Spectral Response Acceleration, SDS, and Seismic Use Group Seismic Use Group
Value of SDS SDS < 0.167 g 0.167 g ≤ SDS < 0.33 g 0.33 g ≤ SDS < 0.50 g 0.50 g ≤ SDS
I
II
III
A B C Da
A B C Da
A C D Da
a
SUG-I and -II structures located on sites with mapped MCE spectral response acceleration at 1-sec period, S1, equal to or greater than 0.75 g shall be assigned to SDC-E and SUG-III structures located on such sites shall be assigned to SDC-F.
TABLE 11.5 Categorization of Structures into Seismic Design Category, Based on Design 1-sec Period Spectral Response Acceleration, SD1 , and Seismic Use Group Seismic Use Group
Value of SD1 SD1 < 0.067 g 0.067 g ≤ SD1 < 0.133 g 0.133 g ≤ SD1 < 0.20 g 0.20 g ≤ SD1 a
I
II
III
A B C Da
A B C Da
A C D Da
See footnote to Table 11.4.
100 years and zones of much lower seismicity in which only moderate levels of ground shaking are ever anticipated. The NEHRP Provisions recognize that it is neither technically necessary nor economically appropriate to require the same levels of seismic protection for all buildings across these various regions of seismicity. Instead, the NEHRP Provisions assign each structure to a seismic design category (SDC) based on the level of seismicity at the building site, as represented by mapped shaking parameters, and the SUG. Six SDCs, labeled A through F, are defined. SDC A represents the least severe seismic design condition and includes structures of ordinary occupancy located on sites anticipated to experience only very limited levels of ground shaking. SDC F represents the most severe design condition and includes structures assigned to SUG-III and located within a few kilometers of major, active faults, anticipated to produce very intense ground shaking. A designer determines to which SDC a structure should be assigned by reference to a pair of tables, reproduced as Tables 11.4 and 11.5. A structure is assigned to the most severe category indicated by either table. Nearly all aspects of the seismic design process are affected by the SDC to which a structure is assigned. This includes designation of the permissible structural systems, specification of required detailing, limitation on permissible heights and configuration, the types of analyses that may be used to determine the required lateral strength and stiffness, and the requirements for bracing and anchorage of nonstructural components.
11.3.5 Permissible Structural Systems The NEHRP Provisions define more than 70 individual seismic-force-resisting system types. These systems may be broadly categorized into five basic groups that include bearing wall systems, building frame systems, moment-resisting frame systems, dual systems, and special systems:
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• Bearing wall systems include those structures in which the vertical elements of the lateral-forceresisting system comprise either shear walls or braced frames in which the shear-resisting elements (walls or braces) are required to provide support for gravity (dead and live) loads in addition to providing lateral resistance. This is similar to the “box system” contained in earlier codes. • Building frame systems include those structures in which the vertical elements of the lateral-forceresisting system comprise shear walls or braces, but in which the shear-resisting elements are not also required to provide support for gravity loads. • Moment-resisting frame systems are those structures in which the lateral-force resistance is provided by the flexural rigidity and strength of beams and columns, which are interconnected in such a manner that stress is induced in the frame by lateral displacements. • Dual systems rely on a combination of moment-resisting frames and either braced frames or shear walls. In dual systems, the braced frames or shear walls provide the primary lateral resistance and the moment-resisting frame is provided as a back-up or redundant system, to provide supplemental lateral resistance in the event that earthquake response damages the primary lateral-forceresisting elements to an extent that they lose effectiveness. • Special systems include unique structures, such as those that rely on the rigidity of cantilevered columns for their lateral resistance. Within these broad categories, structural systems are further classified in accordance with the quality of detailing provided and the resulting ability of the structure to withstand earthquake-induced inelastic, cyclic demands. Structures that are provided with detailing believed capable of withstanding large cyclic inelastic demands are typically termed “special” systems. Structures that are provided with relatively little detailing, and are therefore incapable of withstanding significant inelastic demands, are termed “ordinary.” Structures with limited levels of detailing and inelastic response capabilities are termed “intermediate.” Thus, within a type of structure, for example moment-resisting steel frames, or reinforced concrete bearing walls, it is possible to have special moment-resisting frames or bearing walls, intermediate moment-resisting frames or shear walls, and ordinary moment-resisting frames or shear walls. The various combinations of such systems and construction materials result in a wide selection of structural systems to choose from. The use of ordinary and intermediate systems, regarded as having limited capacity to withstand cyclic inelastic demands, is generally limited to SDC A, B, and C and to certain low-rise structures in SDC D.
11.3.6 Design Coefficients Under the NEHRP Provisions, required seismic design forces, and therefore required lateral strength, is typically determined by elastic methods of analysis, based on the elastic dynamic response of structures to design ground shaking. However, since most structures are anticipated to exhibit inelastic behavior when responding to the design ground motions, it is recognized that linear response analysis does not provide an accurate portrayal of the actual earthquake demands. Therefore, when linear analysis methods are employed, a series of design coefficients are used to adjust the computed elastic response values to suitable design values that consider probable inelastic response modification. Specifically, these coefficients are the response modification factor, R, the overstrength factor, Ω0, and the deflection amplification coefficient, Cd. Tabulated values of these factors are assigned to a structure, based on the selected structural system, and the level of detailing employed in that structural system. The response modification coefficient, R, is used to reduce the required lateral strength of a structure, from that which would be required to resist the design ground motion in a linear manner, to that required to limit inelastic behavior to acceptable levels, considering the characteristics of the selected structural system. Structural systems deemed capable of withstanding extensive inelastic behavior are assigned relatively high R values, as large as 8, permitting minimum design strengths that are only one eighth of that required for elastic response to the design motion. Systems deemed to be incapable of providing
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reliable inelastic behavior are assigned low R values, approaching unity, requiring sufficient strength to resist design motion in a nearly elastic manner. The deflection amplification coefficient, Cd , is used to estimate the total elastic and inelastic lateral deformation of the structure, when subjected to design earthquake ground motion. Specifically, lateral deflections calculated for elastic response of the structure to the design ground motion, reduced by the response modification coefficient R, are amplified by the factor Cd to obtain this estimate. The Cd coefficient accounts for the effects of viscous and hysteretic damping on structural response, as well as the effects of inelastic period lengthening. Structural systems that are deemed capable of developing significant amounts of viscous and hysteretic damping are assigned Cd values somewhat less than the value of the R coefficient. This results in an estimate of total lateral deformation that is somewhat lower than would be anticipated for pure elastic response. For structural systems with relatively poor capability to develop viscous and/or hysteretic damping, the Cd value may exceed R, resulting in estimates of lateral drift that exceed that calculated for elastic response. The overstrength coefficient, Ω0, is used to provide an estimate of the maximum force likely to be delivered to an element in the structure, considering that due to effects of system and material overstrength, this may be larger than the force calculated by elastic analysis of the structure’s response to design ground motion, reduced by the response modification coefficient R. This overstrength factor is used to compute the strength required to resist behavioral modes that have limited capacity for inelastic response, such as column buckling, or connection failure in braced frames. Figure 11.7 illustrates the basic concepts behind these design coefficients. The figure contains an elastic design response spectrum, an elastic response line, and an inelastic response curve for an arbitrary structure, all plotted in lateral inertial force (base shear) vs. lateral roof displacement coordinates. Response spectra are more familiarly plotted in coordinates of spectral response acceleration (Sa) vs. structural period (T). It is possible to convert a spectrum plotted in that form to the spectrum shown in the figure, through a two-step process. The first step consists of converting the response spectrum for Sa vs. T coordinates to Sa vs. spectral response displacement (Sd) coordinates. This is performed using the following relationship between Sa, Sd, and T: Sd =
T2 S 4π 2 a
(11.6)
Then the response spectrum is converted to the form shown in Figure 11.7 by recognizing that for a structure responding in a given mode of excitation, the base shear is equal to the product of the mass participation factor for that mode, the structure’s mass and the spectral response acceleration, Sa , at that period. Similarly, the lateral roof displacement for a structure responding in that mode is equal to the spectral response displacement times the modal participation factor. For a single degree of freedom structure, the mass participation factor and modal participation factor are both unity, and the lateral base shear, V, is equal to the product of the spectral response acceleration at the mode of response and the mass of the structure, while the lateral roof displacement is equal to the spectral response displacement. The dashed diagonal line in Figure 11.7 represents the elastic response of the arbitrary structure. It is a straight line because a structure responding in an elastic manner will have constant stiffness, and therefore, a constant proportional relationship between the applied lateral force and resulting displacement. The intersection of this diagonal line with the design response spectrum indicates the maximum total lateral base shear, VE , and roof displacement, DE , the structure would develop if it responded to the design ground motion in an elastic manner. The third plot in the figure represents the inelastic response characteristics of this arbitrary structure, sometimes called a pushover curve. The pushover curve has an initial elastic region having the same stiffness as the elastic response line. The point Vy , Dy on the pushover curve represents the end of this region of elastic behavior. Beyond Vy , Dy , the curve is represented by a series of segments, with sequentially reduced stiffness, representing the effects of inelastic softening of the
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Elastic response
R
Design response spectrum
VM
Inelastic response
Ω0
Base Shear V
VE
VY
DY
Cd
DI DE
Lateral Roof Displacement ∆ FIGURE 11.7
Schematic illustration of design coefficients.
structure. The lateral base shear force, VM, at the peak of the pushover curve, represents the maximum lateral force that the structure is capable of developing at full yield. The response modification coefficient, R, is used in the provisions to set the minimum acceptable strength at which the structure will develop its first significant yielding, Vy . This is given by the simple relationship:
VY =
VE R
(11.7)
The coefficient Ω0, is used to approximate the full yield strength of the structure through the relationship:
VM = Ω 0VY
(11.8)
The maximum total drift of the structure, DI, is obtained from the relationship:
DI = Cd DY
(11.9)
11.3.7 Analysis Procedures The NEHRP Provisions permit the use of five different analytical procedures to determine the required lateral strength of a structure and to confirm that the structure has adequate stiffness to control lateral drift. The procedures permitted for a specific structure are dependent on the structure’s SDC and its regularity. 11.3.7.1 Index Force Procedure The index force procedure is permitted only for structures in SDC A. In this procedure, the structure must be designed to have sufficient strength to resist a static lateral force, equal to 1% of the weight of the structure, applied simultaneously to each level. The forces must be applied independently, in two orthogonal directions. Structures in SDC A are not anticipated ever to experience ground shaking of © 2003 by CRC Press LLC
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sufficient intensity to cause structural damage, provided that the structures are adequately tied together and have a complete lateral-force-resisting system. The nominal 1% lateral force function used in this procedure is intended as a means of ensuring that the structure has a complete lateral-force-resisting system, of nominal, though somewhat arbitrary, strength. In addition to providing protection for the low levels of ground motion, anticipated for SDC A structures, this procedure is also considered to be a structural integrity provision, intended to provide nominal resistance against blast and other possible loading events. 11.3.7.2 Equivalent Lateral Force Analysis Equivalent lateral force (ELF) analysis may be used for any structure in SDC B and C, for any structure of light frame construction, and for all regular structures, with a calculated structural period T, not greater than 3.5Ts, where Ts is as previously defined in Figure 11.6. ELF analysis consists of a simple approximation to modal response spectrum analysis. It only considers the first mode of a structure’s lateral response, and presumes that the mode shape for this first mode of response is represented by that of a simple shear beam. For structures having sufficiently low periods of first mode response (T < 3.5Ts) and regular vertical and horizontal distribution of stiffness and mass, this procedure approximates modal response spectrum analysis well. However, for longer period structures, higher mode response becomes significant and neglecting these higher modes results in significant errors in the estimation of structural response. Also, as the distribution of mass and stiffness in a structure becomes irregular, for example, the presence of torsional conditions or soft story conditions, the assumptions inherent in the procedure with regard to mode shape also become quite approximate, leading to errors. In SDCs D, E, and F, this method is permitted only for those structures where these inaccuracies are unlikely to be significant. The procedure is permitted for more general use in other SDCs both because it is felt that the severity of design ground motion is low enough that inaccuracies in analysis of lateral response are unlikely to result in unacceptable structural performance and also because it is felt that designers in these regions of low seismicity may not be able to implement the more sophisticated and accurate methods properly. As with the index force analysis procedure, the ELF consists of the simultaneous application of a series of static lateral forces to each level of the structure, in each of two independent orthogonal directions. In each direction, the total lateral force, known as the base shear, is given by the formula: V=
SDS W RI
(11.10)
This formula gives the maximum lateral inertial force that acts on an elastic, single-degree-of-freedom structure with a period that falls within the constant response acceleration (periods shorter than Ts) portion of the design spectrum, reduced by the term R/I. In this formula, SDS is the design spectral response acceleration at short periods, W is the dead weight of the structure and a portion of the supported live load, R is the response modification coefficient, and I is an occupancy importance factor, assigned based on the structure’s SUG. For SUG-I structures, I is assigned a value of unity. For SUG-II and -III structures, I is assigned values of 1.25 and 1.5, respectively. The effect of I is to reduce the permissible response modification factor, R, for structures in higher SUGs, requiring that the structures have greater strength, thereby limiting the permissible inelasticity and damage in these structures. The base shear force given by Equation 11.10 need never exceed the following: V=
SD1 W ( R I )T
(11.11)
Equation 11.11 represents the maximum lateral inertial force that acts on an elastic, single-degree-offreedom structure with period T that falls within the constant response velocity portion of the design spectrum (periods longer than Ts), reduced by the response modification coefficient, R, and the occupancy © 2003 by CRC Press LLC
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importance factor, I. In this equation, all terms are as previously defined except that SD1 is the design spectral response acceleration at 1 sec. For short period structures, Equation 11.10 will control. For structures with periods in excess of Ts, Equation 11.11 will control. The shape of the design response spectrum shown in Figure 11.6 is not representative of the dynamic characteristics of ground motion found close to the fault rupture zone. Such motions are often dominated by a large velocity pulse and very large spectral displacement demands. Therefore, for structures in SDC E and F, the seismic design categories for structures located close to major active faults, the base shear may not be taken less than the value given by Equation 11.12. Equation 11.12 approximates the effects of the additional long period displacements that have been recorded in some near-field ground motion records: 0.5S1 RI
V=
(11.12)
The total lateral base shear force given by Equations 11.10, 11.11, and 11.12 must be distributed vertically for application to the various mass or diaphragm levels of the structure. For a structure with n levels, the force at diaphragm level x is given by the equation: Fx = C vxV
(11.13)
w x hx
(11.14)
where C vx =
n
∑w h
i i
i =1
and hx and hi, respectively, are the heights of levels x and i above the base of the structure. These formulas are based on the assumption that the structure is responding in its first mode, in pure sinusoidal motion, and that the mode shape is linear. That is, it is assumed that at any instant of time, the displacement at level x of the structure is equal to: δx =
hx δ hn n
(11.15)
where δx and δn are the lateral displacements at level x and the roof of the structure, respectively, and hn is the total height of the structure. For a structure responding in pure sinusoidal motion, the displacement δx, velocity vx, and acceleration ax, of level x at any instant of time t is given by the equations: 2π δ x = δ x max sin t T v x = δ x max
2π 2π cos t T T
ax = − δ x max
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4 π 2π sin t T T2
(11.16)
(11.17)
(11.18)
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Since acceleration at level x is directly proportional to the displacement at level x, the acceleration at level x in a structure responding in pure sinusoidal motion is given by the equation: ax =
hn a hx n
(11.19)
where an is the acceleration at the roof level. Since the inertial force at level x is equal to the product of mass at level x and the acceleration at level x, Equation 11.14 can be seen to be an accurate distribution of lateral inertial forces in a structure responding in a linear mode shape. The lateral forces given by Equation 11.13 are applied to a structural model of the building and the resulting member forces and building interstory drifts are determined. The analysis must consider the relative rigidity of both the horizontal and vertical elements of the lateral-force-resisting system, and when torsional effects are significant, must consider three-dimensional distributions of stiffness, centers of mass and rigidity. The structure must then satisfy two basic criteria. First, the elements of the lateralforce-resisting system must have sufficient strength to resist the calculated member forces, in combination with other loads, and second, the structure must have sufficient strength to maintain computed interstory drifts within acceptable levels. The specific load combinations that must be used to evaluate member strength and the permissible interstory drifts are described in succeeding sections. In recognition of the fact that higher mode participation can result in significantly larger forces at individual diaphragm levels than is predicted by Equation 11.14, forces on diaphragms are computed using an alternative equation, as follows:
∑ = ∑
n
Fpx
i=x n i=x
Fi
w px
(11.20)
wi
where Fpx is the design force applied to diaphragm level x, Fi is the force computed from Equation 11.14 at level i, wpx is the effective seismic weight at level x, and wi is the effective weight at level i. 11.3.7.3 Response Spectrum Analysis Response spectrum analysis is permitted for the design of any structure. The procedure contained in the NEHRP Provisions uses standard methods of elastic modal dynamic analysis, which are not described here, but are well documented in the literature [e.g., Chopra, 1981]. The analysis must include sufficient modes of vibration to capture participation of at least 90% of the structure’s mass in each of two orthogonal directions. The response spectrum used to characterize the loading on the structure may be either the generalized design spectrum for the site, shown in Figure 11.6, or a site-specific spectrum developed considering the regional seismic sources and site characteristics. Regardless of the spectrum used, the ground motion is scaled by the factor (I/R), just as in the equivalent lateral force technique. The NEHRP Provisions require that the member forces determined by response spectrum analysis be scaled so that the total applied lateral force in any direction not be less than 80% of the base shear calculated using the ELF method for regular structures nor 100% for irregular structures. This scaling requirement was introduced to ensure that assumptions used in building the analytical model not result in excessively flexible representation of the structure, and consequently, an underestimate of the required strength. 11.3.7.4 Response History Analysis Response history analysis is also permitted to be used for the design of any structure but, due to the added complexity, is seldom employed in practice except for special structures incorporating special base isolation or energy dissipation technologies. Either linear or nonlinear response history analysis is permitted to be used. When response history analysis is performed, input ground motion must consist of a suite of at least three pairs of orthogonal horizontal ground motion components, obtained from records
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of similar magnitude, source, distance, and site characteristics as the event controlling the hazard for the building’s site. Each pair of orthogonal records must be scaled such that with a period range approximating the fundamental period of response of the structure, the square root of the sum of the squares of the orthogonal component ordinates envelopes 140% of the design response spectrum. Simple amplitude, rather than frequency domain scaling, is recommended. Actual records are preferred, though simulations may be used if a sufficient number of actual records representative of the design earthquake motion is not available. If a suite of less than seven records is used as input ground motion, the maximum of the response parameters (element forces and deformations) obtained from any of the records is used for design. If seven or more records are used, the mean values of the response parameters obtained from the suite of records may be used as design values. This requirement was introduced with the understanding that the individual characteristics of a ground motion record can produce significantly different results for some response quantities. It was hoped that this provision would encourage engineers to use larger suites of records, and obtain an understanding of the variability associated with possible structural response. When linear response history analyses are performed, the ground motion records, scaled as previously described, are further scaled by the quantity (I/R). The resulting member forces are combined with other loads, just as they would be if the ELF or response spectrum methods of analysis were performed. When nonlinear response history analyses are performed, they must be used without further scaling. Rather than evaluating the strength of members using the standard load combinations considered with other analysis techniques, the engineer is required to demonstrate acceptable performance capability of the structure, given the predicted strength and deformation demands. The intention is that laboratory and other relevant data be used to demonstrate adequate behavior. This is a rudimentary introduction of performance-based design concepts, which will likely have significantly greater influence in future building codes.
11.3.8 Load Combinations and Strength Requirements Structures must be proportioned with adequate strength to resist the forces predicted by the lateral seismic analysis, together with forces produced by response to vertical components of ground shaking as well as dead and live loads. Unless nonlinear response history analysis is performed using ground motion records that include a vertical component of motion, the effects of vertical earthquake shaking are accounted for by the equation: E = QE ± 0.2SDS D
(11.21)
where QE are the element forces predicted by the lateral seismic analysis, SDS is the design spectral response acceleration at a 0.2-sec response period, and D are the forces produced in the element by the structure’s dead weight. The term 0.2SDSD represents the effect of vertical ground shaking response. For structures in zones of high seismicity, the term SDS has a value approximating 1.0 g and therefore, the vertical earthquake effects are taken as approximately a 20% increase or decrease in the dead load stress demands on each element. In fact, there are very few cases on record where structural collapse has been ascribed to the vertical response of a structure. This is probably because design criteria for vertical load resistance incorporate substantial factors of safety and also because most structures carry only a small fraction of their rated design live loads when they are subjected to earthquake effects. Therefore, most structures inherently have substantial reserve capacity to resist additional loading induced by vertical ground motion components. In recognition of this, most earlier codes neglected vertical earthquake effects. However, during the formulation of ATC-3.06, it was felt to be important to acknowledge that ground shaking includes three orthogonal components. The resulting expression, which was somewhat arbitrary, ties vertical seismic forces to the short period design spectral response acceleration, as most structures are stiff vertically and have very short periods of structural response for vertical modes. © 2003 by CRC Press LLC
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The earthquake forces on structural elements derived from Equation 11.21 are combined with dead and live loads in accordance with the standard strength level load combinations of ASCE-7. The pertinent load combinations are: Q = 1.4 D ± E
(11.22)
Q = 1.4 D + 0.75 ( L + E )
(11.23)
where D, L, and E are, respectively, the dead, live, and earthquake forces. Elements must then be designed to have adequate strength to resist these combined forces. The reduction factor of 0.75 on the combination of earthquake and live loads accounts for the low likelihood that a structure will be supporting full live load at the same time that it experiences full design earthquake shaking. An alternative set of load combinations is also available for use with design specifications that utilize allowable stress design formulations. These are essentially the same as Equations 11.22 and 11.23 except that the earthquake loads are further reduced by a factor of 1.4. The NEHRP Provisions recognize that it is undesirable to allow some elements to experience inelastic behavior as they may be subject to brittle failure and in doing so, compromise the ability of the structure to develop its intended inelastic response. The connections of braces to braced frames are an example of such elements. The provisions also recognize that inelastic behavior in some elements, such as columns supporting discontinuous shear walls, could trigger progressive collapse of the structure. For these elements, the earthquake force E that must be used in the load combination Equations 11.22 and 11.23 is given by the formula: E = Ω0QE ± 0.2SDS D
(11.24)
where the term 0.2SDSD continues to represent the effects of vertical ground shaking response and the term Ω0QE represents an estimate of the maximum force likely to be developed in the element as a result of lateral earthquake response, considering the inelastic response characteristics of the entire structural system. In Equation 11.24, the term Ω0QE need never be taken larger than the predicted force on the element derived from a nonlinear analysis or plastic mechanism analysis.
11.3.9 Drift Limitations It is important to control lateral drift in structures because excessive drift can result in extensive damage to cladding and other nonstructural building components. In addition, excessive lateral drift can result in the development of P-∆ instability and collapse. Lateral drift is evaluated on a story by story basis. Story drift, δ, is computed as the difference in lateral deflection at the top of a story and that at the bottom of the story, as predicted by the lateral analysis. If the lateral analysis was other than a nonlinear response history analysis, design story drift, ∆, is obtained from the computed story drift, δ, by the equation: ∆ = Cd δ
(11.25)
where Cd is the design coefficient previously discussed. The design interstory drift computed from Equation 11.25 must be less than a permissible amount, dependent on the SUG and structural system as shown in Table 11.6. The provisions require evaluation of potential P-∆ instability through consideration of the quantity θ given by the equation: θ=
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Px ∆ Vx hxCd
(11.26)
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TABLE 11.6 Permissible Drift Limits Seismic Use Group
Structure Structures, other than masonry shear wall or masonry wall frame structures, four stories or less in height with interior walls, partitions, ceilings, and exterior wall systems that have been designed to accommodate the story drifts Masonry cantilever shear wall structures Other masonry shear wall structures Masonry wall frame structures All other structures
I
II
III
0.025 hsx
0.020 hsx
0.015 hsx
0.010 hsx 0.007 hsx 0.013 hsx 0.020 hsx
0.010 hsx 0.007 hsx 0.013 hsx 0.015 hsx
0.010 hsx 0.007 hsx 0.010 hsx 0.010 hsx
In this equation, Px is the dead weight of the structure above story x, ∆ is the design story drift, computed from Equation 11.25, Vx is the design story shear obtained from the lateral force analysis, hx is the story height, and Cd is the coefficient previously discussed. If the quantity θ computed by this equation is found to be less than 0.1, P-∆ effects may be neglected. If the quantity θ is greater than 0.1, P-∆ effects must be directly considered in performing the lateral force analysis. If the quantity θ exceeds 0.3, the structure should be considered potentially unstable, and must be redesigned. This approach to P-∆ evaluation has remained essentially unchanged since its initial introduction in ATC-3.06. It was introduced in that document as a placeholder, pending the development of a more accurate method for evaluating drift-induced instability. Obvious deficiencies in this current approach include the fact that it evaluates drift effects at the somewhat artificial design-base shear levels. A more realistic evaluation would consider the actual expected lateral deformations of the structure, as well as the yield level shear capacity of the structure at each story. As contained in the current provisions, evaluation of P-∆ effects seldom controls a structure’s design.
11.3.10 Structural Detailing Structural detailing is a critical feature of seismic-resistant design but is not generally specified by the NEHRP Provisions. Rather, the provisions adopt detailing requirements contained in standard design specifications developed by the various materials industry associations, including the American Institute of Steel Construction, the American Concrete Institute, the American Forest Products Association, and the Masonry Society. Other chapters in this handbook present the requirements of these various design standards.
11.4 Performance-Based Design Codes Starting about 1990, the international design community began to be interested in the development of performance-based design concepts. Whereas current building code provisions are prescriptive in nature and require that buildings be designed with minimum specified strength and stiffness, performancebased procedures permit the designer to directly demonstrate that a design is capable of meeting certain standard performance objectives, independent of meeting prescriptive strength and stiffness criteria. Acceptable performance may be demonstrated through a variety of means, including prototype testing or analytical simulation. For many years, building codes have permitted such performance-based designs through language that allowed the application of alternative procedures, justified by rational engineering analysis to be capable of providing equivalent performance. However, these earlier codes provided little quantification of the performance objectives to be attained, making application of alternative approaches largely impractical.
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In the early 1990s, a series of performance-based design procedures intended for application to seismic rehabilitation of structures were published under efforts sponsored by FEMA [BSSC, 1997a] and the California Seismic Safety Commission [1996]. These documents began the process of formalizing the concept of performance objectives, as quantifiable levels of damage, for specified levels of hazard. These concepts were adopted and extended by SEAOC, in a preliminary manner, for application to the design of new construction [SEAOC, 1996]. Also, in a project supported by FEMA [SAC, 2000] to address unanticipated damage experienced by steel moment frame structures in the 1994 Northridge and 1995 Kobe earthquakes, a formal structural reliability basis was applied to these concepts. The International Code Council has published a performance-based code [ICC, 2001] that permits the application of performance-based concepts for design for a variety of structural, fire, and health hazards. The new NFPA-5000 code also includes specific provisions intended to permit performancebased design approaches. While these new codes do a better job of quantifying the performance objectives with which a design must comply, they do little to regulate how such compliance is demonstrated. Therefore, application of these concepts is likely to be limited. It is anticipated, however, that substantial development of performance-based design approaches will continue to occur and that future codes will include more guidance on their application.
Defining Terms Base shear — The total lateral force for which a structure is designed using equivalent lateral force techniques.
Damping — Energy dissipation that occurs in a dynamically deforming structure, either as a result of frictional forces, viscous behavior, or structural yielding. Increased damping tends to reduce the amount that a structure responds to ground shaking. Damage — Permanent cracking, yielding, or buckling of a structural element or structural assemblage. Degradation — A behavioral mode in which structural stiffness or strength is reduced as a result of inelastic behavior. Elastic — A mode of structural behavior in which a structure displaced by a force will return to its original state upon release of the force. Ground shaking — A random, rapid cyclic motion of the ground produced by an earthquake. Hysteresis — A form of energy dissipation that is related to inelastic deformation of a structure. Inelastic — A mode of structural behavior in which a structure, displaced by a force, exhibits permanent unrecoverable deformation. Mass participation — That portion of total mass of a multidegree of freedom structure that is effective in a given mode of response. Maximum considered earthquake (MCE) — The earthquake intensity forming the basis for design, in the NEHRP Provisions. Mode shape — A deformed shape, in which a structure can oscillate freely, when displaced. Natural mode — A characteristic dynamic property of a structure, in which it will oscillate freely. Participation factor — A mathematical relationship between the maximum displacement of a multidegree of freedom structure and a single degree of freedom structure. Period — The amount of time it takes a structure that has been displaced in a particular natural mode and then released to undergo one complete cycle of motion. Response spectrum — A graphical representation, usually as a function of period, of the maximum acceleration, displacement or velocity response of a structure, subjected to a given level of ground shaking excitation. Spectral acceleration — The maximum response acceleration that a structure of given period will experience when subjected to a specific ground motion. Spectral displacement — The maximum response displacement that a structure of given period will experience when subjected to a specific ground motion.
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Spectral velocity — The maximum response velocity that a structure of given period will experience when subjected to a specific ground motion.
Viscous — A form of energy dissipation that is proportional to velocity. Yielding — A behavioral mode in which a structural displacement increases under application of constant load.
References American Society of Civil Engineers. 1991. Minimum Design Loads for Buildings and Other Structures, Standard No. ASCE-7, American Society of Civil Engineers, Reston, VA. Anderson, J., Blume, J.A., Degenkolb, H.K. et al. 1952. “Lateral Forces of Earthquake and Wind,” Trans. Am. Soc. Civ. Eng., 117. Applied Technology Council. 1978. Tentative Recommended Provisions for Seismic Regulation of Buildings, Report no. ATC-3.06, Applied Technology Council, Redwood City, CA. Applied Technology Council. 1996. Evaluation and Upgrade of Reinforced Concrete Buildings, Report no. ATC-40, California Seismic Safety Commission, Sacramento, CA. BSSC. 1997a. NEHRP Guidelines for Seismic Rehabilitation of Buildings, Building Seismic Safety Council Report no. FEMA 273, Federal Emergency Management Agency, Washington, D.C. BSSC. 1997b. NEHRP Recommended Provisions for Seismic Regulations for Buildings and Other Structures, Building Seismic Safety Council Report no. FEMA 302/303, Federal Emergency Management Agency, Washington, D.C. Chopra, A.K. 1981. Dynamics of Structures, A Primer, Earthquake Engineering Research Institute, Oakland, CA. Housner, G. 1984. “Historical View of Earthquake Engineering,” in Proc. Post-Conf. Volume, Eighth, World Conf. on Earthquake Engineering, Earthquake Engineering Research Institute, Oakland, CA. ICBO. 1997. Uniform Building Code, Volume 2: Structural Engineering Provisions, 1997 ed., International Conference of Building Officials, Whittier, CA. ICC. 2000. International Building Code 2000, International Code Council, published by International Conference of Building Officials, Whittier, CA, and others. ICC. 2001. International Performance Code 2001, International Code Council, published by International Conference of Building Officials, Whittier, CA, and others. NFPA. n.d. NFPA 5000 Building Code, National Fire Protection Association, Cambridge, MA (publication pending). Otani, S. 1995. “A Brief History of Japanese Seismic Design Requirements,” Concrete Int., 17(12), 46–53. PCBO. 1927. Uniform Building Code. Pacific Coast Building Officials. Ravindra, M.K. 1994. “Seismic Risk Assessment,” in Probabilistic Structural Mechanics Handbook: Theory and Applications, Sundararajan, C., Ed., Chapman & Hall, New York. SAC Joint Venture. 2000. Recommended Seismic Design Criteria for Steel Moment-Frame Structures, Report no. FEMA-350, Federal Emergency Management Agency, Washington, D.C. SEAOC. 1996. Vision 2000, A Framework for Performance-based Seismic Design, Structural Engineers Association of California, Sacramento, CA. SEAOC, Seismology Committee. 1999. Recommended Lateral Force Requirements and Commentary, Structural Engineers Association of California, Sacramento, CA. Tobriner, S. 1984. “The History of Building Codes to the 1920s,” Proc. SEAOC, Sacramento, CA.
Further Reading There is an extensive body of literature on building codes, although it is surprisingly deficient in the history of the development of the seismic aspects. Neglecting the historic development, the following three references will give the reader an excellent overview of the current state of seismic design requirements:
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Structural Engineers Association of California, Seismology Committee. 1999. Recommended Lateral Force Requirements and Commentary. Structural Engineers Association of California, Sacramento, CA. Building Seismic Safety Council. 1997. NEHRP Recommended Provisions for Seismic Regulations for Buildings and Other Structures, Report no. FEMA 302/303. Federal Emergency Management Agency, Washington, DC. Structural Engineers Association of California. 1996. Vision 2000, A Framework for Performance-based Seismic Design, Structural Engineers Association of California, Sacramento, CA. This chapter has focused on U.S. practice and codes. Some useful sources re seismic code provisions in other countries include: Earthquake Resistant Design Codes in Japan, January, 2000, Japan Society of Civil Engineers, Tokyo, 2000. International Handbook of Earthquake Engineering: Codes, Programs, and Examples (IHEE), edited by Mario Paz, Kluwer Academic Publishers, Dordrecht, 1995. Regulations for Seismic Design: A World List, 1996 (RSD). Rev. ed. (update of Earthquake Resistant Regulations: A World List, 1992). Prepared by the International Association for Earthquake Engineering (IAEE), Tokyo, 1996; and its Supplement 2000: Additions to Regulations for Seismic Design: A World List, 1996. Available from Gakujutsu Bunken Fukyu-Kai (Association for Science Documents Information) c/o Tokyo Institute of Technology, 2-12-1 Oh-Okayama, Meguro-Ku, Tokyo, Japan 152-8550 (telephone: +81-3-3726-3117; fax:+81–3-3726-3118; e-mail:
[email protected]). The last is a comprehensive compendium of seismic regulations for more than 40 countries, which includes Eurocode 8 (the European Union’s seismic provisions).
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12 Seismic Design of Steel Structures 12.1 Introduction 12.2 Historic Development and Performance of Steel Structures 12.3 Steel Making and Steel Material Physical Properties of Structural Steel · Mechanical Properties of Structural Steel
12.4 Structural Systems Braced Frames · Design Approach
12.5 Unbraced Frames
Ronald O. Hamburger Simpson Gumpertz & Heger, Inc. San Francisco, CA
Niaz A. Nazir DeSimone Consulting Engineers San Francisco, CA
Special Moment-Resisting Frames · Intermediate MomentResisting Frames · Ordinary Moment Frames · Special Truss Moment-Resisting Frames
Defining Terms References Further Reading Appendix A
12.1 Introduction In many ways structural steel is an ideal material for the design of earthquake-resistant structures. It is strong, light weight, ductile, and tough, capable of dissipating extensive energy through yielding when stressed into the inelastic range. Given the seismic design philosophy of present building codes, which is to rely on the inherent ability of structures to undergo inelastic deformation without failure, these are exactly the properties desired for seismic resistance. In fact, other construction materials rely on these basic properties of steel to assist them in attaining adequate seismic resistance. Modern concrete and masonry structures, for example, attain their ability to behave in a ductile manner through the presence and behavior of steel reinforcing. Timber structures derive their ability to withstand strong ground motion through the ductile behavior of steel connection hardware, including bolts, nails, and various steel straps and assemblies used to interconnect wood framing. Steel is a mixture of iron and carbon, with trace amounts of other elements, including principally manganese, phosphorus, sulfur, and silicon. Steel is differentiated from the earlier cast and wrought irons by the reduced amounts of carbon relative to these other alloys and the reduced amounts of other trace elements. These differences make steel both stronger and more ductile than cast and wrought irons, both of which tend to be quite brittle. Although iron alloys have been in use for centuries, steel is a relatively modern material. For practical purposes the advent of steel as a construction material can be traced to
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the mid-19th century, when Sir Henry Bessemer developed the iron-to-steel conversion process that allowed production of steel in large quantities. Initial uses of steel were in the railroad industry, where it was used extensively to produce rails, and for armaments, including rifle and gun barrels. Andrew Carnegie imported the Bessemer process to the United States and constructed his first steel mill in 1870, initially for rail and machinery production. By the 1890s, however, steel was being applied to building construction and, with the advent of the elevator and high-rise construction, rapidly became the building material of choice for the new generation of tall buildings. The same properties that make it a desirable material for high-rise construction (light weight, strength, ease of fabrication and erection) also make it a popular construction material for structures involving long, clear spans. Today it is used in a variety of construction applications ranging from bridges to industrial plants to buildings. Throughout the relatively brief history of their use, structural steel buildings have been among the best performing structural systems and, prior to January 1994, when previously unanticipated connection failures were discovered in some buildings following the Northridge earthquake (M 6.7), many engineers mistakenly regarded such structures as nearly earthquake-proof. A year later, the Kobe earthquake (M 6.9) caused collapse of 50 steel buildings, confirming the potential vulnerability of these structures. This experience notwithstanding, structural steel buildings, if properly designed, can provide outstanding earthquake performance. To assure good behavior of steel structures, it is necessary to: • Configure the structural steel system so that inelastic behavior is well distributed throughout the structure, rather than concentrated in a few stories or elements • Provide columns with sufficient strength to resist earthquake-induced overturning loads without buckling • Provide adequate lateral bracing for flexural members to prevent lateral-torsional buckling • Proportion connections with sufficient strength that inelastic behavior occurs in the members themselves • Select compact sections for those members intended to experience inelastic behavior, to avoid local buckling and the rapid loss of strength that accompanies such behavior In addition, as with all structural materials, it is very important to assure that the structures are actually constructed as designed, that quality is maintained in fabrication and field welding operations, and that the structure is maintained over its life. This chapter discusses the historic performance of steel structures in earthquakes, the basic manufacturing processes and properties of structural steel, the basic structural systems used in steel structure design, and the current code requirements for the design of steel structures.
12.2 Historic Development and Performance of Steel Structures Prior to the late 1800s, the most common building materials were either timber or masonry. Timber structures were limited in height by the strength of the material and seldom exceeded three or four stories. Masonry buildings could be constructed taller than this; however, it was necessary to make the loadbearing walls quite thick, 30 in. or more, in buildings of six stories or taller. Until the advent of the elevator, these were not limiting factors on construction, as it was impractical to inhabit structures taller than four or five stories. With the elevator, however, it became practical to construct buildings that were ten or more stories in height. The elevator, together with structural steel being on the order of ten times stronger than masonry, enabled such construction to occur. The Home Insurance building, a 9-story structure erected in Chicago in 1885 and later expanded to 11 stories in 1891, is generally credited with being the first skyscraper [Chicago Public Library, 1997]. Throughout the 1890s and early 1900s, major cities in industrialized nations around the world began to build tall steel structures. The use of structural steel as a building construction material also found rapid application in long-span industrial structures, where the high strength and light weight of the material found practical application in the construction
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FIGURE 12.1
Large steel spans (left) detail St. Pancras Station, London; (right) Hamburg Hauptbahnof.
FIGURE 12.2
Typical built-up member in early steel construction.
12-3
of trusses to span over large manufacturing operations. Throughout the early 20th century, these two applications, high-rise and industrial construction, were the primary applications of steel construction in the building industry. Later in the 20th century, as labor became more expensive in industrialized countries, steel began to find application in low- and mid-rise construction as well, replacing the more labor-intensive concrete and masonry construction practices. As compared with other construction materials, steel construction requires a significant industrial infrastructure and a skilled labor force. Therefore, even today, it is commonly used as a building material only in industrialized nations (Figure 12.1). Steel building construction is typically of two basic types: braced frames or unbraced frames (also commonly called moment-resisting frames), or a combination of these types. Prior to the 1920s, members of steel frames commonly were constructed as complex built-up members with gusset plates and built-up connections, as illustrated in Figure 12.2. The members and connections were riveted, and the entire steel frame was normally encased in masonry or concrete for fire protection, and also to provide walls and partitions for the structure. Few, if any, of these steel structures were designed for seismic loading, since only wind load was considered prior to about 1930 (see Chapter 11). These buildings invariably included many stiff and strong unreinforced masonry walls and partitions. Structural engineers relied upon these walls and partitions to help resist lateral loads, but they performed no calculations of the stiffness and resistance provided by these walls [Roeder, 2000]. © 2003 by CRC Press LLC
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FIGURE 12.3
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Typical semirigid beam column connections with rolled structural shape.
Changes in steel frame construction began to evolve around 1920. Labor costs for the built-up elements were increasing at this time, and standard hot rolled shapes for beams and columns became the normal practice. The AISC Specification and Manual [AISC, 1928] was first developed in this period. These rolled shapes commonly were connected with riveted angles and T-sections as illustrated in Figure 12.3, and members and the connections were still encased in concrete for fire protection. These framing practices became standard and were designed with relatively simple calculations for the next 20 to 30 years. Unreinforced masonry curtain walls and partitions were still used, and the combined effect of the added strength and stiffness provided by these walls and the composite action due to the encasement supplied a major portion of the structural stiffness and resistance to lateral loads. These early structures tended to be highly redundant in that every beam–column connection was a semirigid moment-resistant connection, with a large but uncalculated stiffness, and significant uncalculated resistance was also provided by nonstructural elements such as architectural masonry walls and the concrete encasement for fire protection. This construction was commonly used until the mid-1950s or early 1960s. After about 1960, high strength bolts began to replace the rivets in the T-stub and double-flange-angle connection, but the connection details and geometry remained essentially the same as those used for riveted construction. Concrete encasement was also discontinued in favor of lighter fire protection materials. However, buildings of the 1950s and 1960s still had a substantial uncalculated strength and stiffness due to cladding and partitions, and they were very redundant, since the moment-resisting connections were used at every beam-to-column joint. This construction continued into the early 1970s, at which time field welding began to replace field bolting, particularly for application to moment-resisting connections and, at about the same point in time, single plate shear connections began to replace double angles and tees for non-moment-resisting connections. The period 1970 to 1994 is characterized by a gradual trend of building frames with reduced redundancy, in which fewer but larger framing elements were used to provide lateral resistance for structures. Moment-resisting connections were typically fabricated using a standard welded flange, bolted web connection (Figure 12.4). Failure of a number of these connections in the 1994 Northridge earthquake resulted in revised practice, discussed in later sections. Given the relatively short history of steel building construction and the fact that this construction material was widely used only in industrialized nations, the earthquake performance history for steel structures is rather limited. It begins with the 1906 San Francisco earthquake (M 7.9) and fire. At the time of the FIGURE 12.4 Typical welded flange, bolted web moment-resisting connecSan Francisco earthquake, construction in the city predomition commonly in use 1970 to 1994. nantly consisted of low-rise timber frame and masonry bearing © 2003 by CRC Press LLC
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FIGURE 12.5 View of downtown San Francisco following the 1906 earthquake and fire, and showing the survival of a number of taller steel frame buildings.
FIGURE 12.6 Tall building (left) on fire, 1906 earthquake; (right) in 1999, with newer cladding. (Photos: (left) anonymous; (right) C. Scawthorn)
wall buildings and taller steel frame buildings with unreinforced masonry infill walls. Engineers surveying the damage following the earthquake and fire remarked that damage to the taller steel frame buildings was much lighter than for other structures [USGS, 1907] (Figure 12.5), and, in fact, a number of these buildings are still in service today (Figures 12.6 and 12.7). The superior performance of steel buildings observed in this earthquake initiated the perception, commonly held by some engineers until the mid-1990s, that steel frame buildings were practically invulnerable to earthquake-induced structural damage. Reis and Bonowitz [2000] postulate that this perception was more a result of a lack of exposure of steel frame buildings to strong motion, rather than a significant body of data of good performance. However, it is probable that this perception evolved, at least in part, from the fact that the early steel frame structures, with extensive infill masonry, did perform remarkably better than contemporary structures of pure masonry or reinforced concrete construction. Hadley (n.d.), for example, reports that at the time of the great Kanto, Japan earthquake of 1923, steel © 2003 by CRC Press LLC
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FIGURE 12.7 Market Street at Third Street in San Francisco, April 1906. The tall steel frame building to the right is still in service today. (Source: anonymous)
building construction had been in use only for about 5 years in Japan. Four large steel buildings had been completed and two were almost complete. These buildings, with extensive masonry infill walls and partitions, suffered little to no damage of the frames, though extensive damage to the masonry infill is reported. Hundreds of collapses of masonry structures were reported. Similarly, reports of the 1925 Santa Barbara earthquake [CISC, n.d.] indicate that although 17 concrete and masonry buildings were destroyed or eventually demolished, 2 steel frame buildings with masonry infill, located closer to the epicenter, were barely damaged. The first earthquake to affect a large number of modern steel buildings was probably the 1971 San Fernando (M 6.6), California earthquake. Steinbrugge et al. [1971] reported on a study of 30 completed steel buildings in the greater Los Angeles area, noting some damage to stairs, concrete walls, and nonstructural elements, but no structural damage to the completed steel frames. However, two noteworthy steel buildings, the two 52-story ARCO Towers then under construction in downtown Los Angeles, did experience damage to their structural frames. These buildings probably saw ground motion with a peak horizontal acceleration on the order of 0.15 g. Damage consisted of cracking of welded beam to column connections and of welded connections in transfer trusses. These cracks were ascribed to poor weld quality, and as the buildings were then under construction, were repaired as part of the ongoing construction work. Osteraas and Krawinkler [1989] note that the 1985 Mexico City earthquake (M 8.1) was probably the first event in which a significant number of steel buildings, including modern ones, were subjected to a severe test. They report data on 79 steel structures, including 41 moment-resisting frames, 17 braced frame structures and 21 structures with concrete shear walls. Of these, 12 buildings were reported as having moderate to severe damage, including 2 buildings in the Piño Suarez complex that were total collapses (Figure 12.8). Piño Suarez was a five-building complex constructed over a subway station. A 21-story, braced frame structure collapsed onto an adjacent 14-story structure, also causing its collapse. Osteraas and Krawinkler ascribe this collapse to overstrength in the steel braces of the structure, which delivered greater overturning forces to the building’s built-up columns then they could withstand, inducing local, and then complete, buckling failure of the columns and building collapse. Study of this failure led to introduction of requirements in the building codes that columns in steel structures be designed considering the potential overstrength of the supported structure. © 2003 by CRC Press LLC
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FIGURE 12.8 Pino Suarez collapse, 1985 Mexico City earthquake. (Courtesy National Oceanographic and Atmospheric Agency) Shown as Color Figure 12.8.
Numerous other reports of damage to braced frame structures in various earthquakes may be found in the literature. Typical damage includes buckling of compression braces, fracture of braces at weak net sections and in the vicinity of local buckling of thin-walled brace sections, and failure of bolted end connections of braces. Figure 12.9, for example, shows a buckled brace in the three-story California Federal Savings Bank data center in Rosemead, California following the 1987 Whittier Narrows (M 5.9) earthquake. Such damage has typically been readily repairable. Extensive damage to welded moment-resisting connections was reported in buildings following the 1994 Northridge California (M 6.7) earthquake [Youssef et al., 1995]. The damage typically consisted of fractures, initiating at the root of complete penetration welded joints between beam bottom flanges and columns. Once initiated, these fractures would extend in a variety of paths and, in some cases, extended nearly completely across columns (Figure 12.10). Although only one structure, a two-story building owned by the California State Automobile Association, was damaged so severely that it was deemed irreparable, the widespread occurrence of this unanticipated damage caused great concern in the design community. Responding to this concern, the Federal Emergency Management Agency (FEMA) sponsored a 6year, $12 million research program known as the SAC Steel Program, to determine the cause of the damage and recommend design and construction procedures to mitigate the problems identified. The FEMA/SAC program concluded that the damage was a result of large stress and strain concentrations induced by the typical connection configuration, the frequent presence of large defects and flaws in the welded joints, and the common use of low toughness weld metals. An extensive series of design [SAC, 2000a], construction, and quality assurance [SAC, 2000b] recommendations were published by the FEMA/SAC project and are slowly being incorporated into standard design specifications. The project also developed procedures for seismic performance evaluation of steel structures [SAC, 2000c], postearthquake damage assessment criteria [SAC, 2000d], and an extensive collection of background technical report documents. On January 17, 1995, exactly 1 year after the Northridge earthquake, the Hyogo Ken Nambu earthquake (M 6.9) struck the city of Kobe, Japan and surrounding areas. This earthquake also caused extensive brittle fracture damage to steel structures. Nakashima [2000] reports 988 damaged steel buildings, including 432 moment-resisting frames, 168 buildings with braced frames, and 388 with unidentified framing systems. Figure 12.12 presents a breakdown of the severity of damage, by building height. More than 50 © 2003 by CRC Press LLC
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FIGURE 12.9
FIGURE 12.10
Earthquake Engineering Handbook
Buckled brace in California Federal Savings building, Rosemead, California.
Fracture through a column flange and web at a moment-resisting connection.
steel buildings collapsed in the Kobe earthquake, but none in excess of seven stories in height. Most of the collapsed buildings were older structures, employing tubular steel columns. Many of these buildings were very slender and experienced brittle fractures at column splices, resulting in overturning failures. As a result of the number of collapsed and severely damaged buildings, a study similar to that conducted in the United States following the Northridge earthquake was conducted by Japanese investigators. This study concluded that the failures were largely due to older construction practices and did not result in recommendations for major changes to design or construction practice.
12.3 Steel Making and Steel Material The behavior of steel structures in earthquakes is dependent on key mechanical properties of the steel material, including its strength, ductility, and toughness. These properties, in turn, are dependent on © 2003 by CRC Press LLC
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FIGURE 12.11 Brittle fractures in massive braced frames of Ashiyahama Complex. (Photo: C. Scawthorn)
FIGURE 12.12 Distribution of steel building damage in the Kobe earthquake by severity and building height. (From Nakashima, M., 2000. Appendix C, State of the Art Report on Past Performance of Steel Buildings in Earthquakes, FEMA-355E, Federal Emergency Management Agency, Washington, D.C.)
the processes used to produce the material. Structural steel is a mixture of iron and carbon with varying amounts of other elements — primarily manganese, phosphorus, sulfur, and silicon. These and other elements are either unavoidably present or intentionally added in various combinations to achieve specific characteristics and properties of the finished steel product. Table 12.1, excerpted from Frank et al. [2000], lists the primary elements found in structural steel and their effects on steel properties. Various steel-making furnaces have been developed over the years. The modern age of bulk production of steel was initiated with the Bessemer Converter. This was later replaced by the open hearth furnace and, more recently, the basic oxygen and electric arc furnaces. Steel making begins with a source of raw iron, either in the form of iron ore, reduced in a blast furnace, or scrap metal. The blast furnace reduces iron ore and other iron-bearing materials, coke, and limestone into pig iron. Coke is a carbon-rich material obtained by baking coal in an oxygen-free environment. The limestone acts as a cleaning agent by reacting with impurities in the ore. The iron ore and other iron-bearing materials, coke, and limestone proceed slowly down through the body of the furnace as they are exposed to a blast of hot air that burns the coke, releasing heat and gas, and reduces the iron ore to metallic iron. This metallic iron contains several chemical elements, including carbon, manganese, sulfur, phosphorus, and silicon in amounts higher than permitted for steel. Thus, it is drawn off periodically, to be refined further in a steel-making furnace. © 2003 by CRC Press LLC
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TABLE 12.1 Principle Elemental Components of Structural Steel Carbon
Manganese Phosphorus
Sulfur
Silicon Aluminum Vanadium and Columbium Titanium Nickel Chromium Copper Nitrogen Boron
Principal hardening element in steel, increases strength and hardness, decreases ductility, toughness, and weldability Moderate tendency to segregate Increases strength and toughness Controls negative effects of sulfur Increases strength and hardness, decreases ductility and toughness Considered as an impurity, but sometimes added for atmospheric corrosion resistance Strong tendency to segregate Considered undesirable except for machineability. Decreases ductility, toughness, and weldability Adversely affects surface quality Strong tendency to segregate Used to deoxidize or “kill” molten steel Increases strength Used to deoxidize or “kill” molten steel Refines grain size, thus increasing strength and toughness Small additions increase strength Refines grain size, thus increasing strength and toughness Small amounts refine the grain size, thus increasing toughness Increases strength and toughness Increases strength Increases atmospheric corrosion resistance Primary contributor to atmospheric corrosion resistance Increases strength Increases strength and hardness May decrease ductility and toughness Small amounts increase hardenability, used only in aluminum-killed steels Most cost effective at low carbon levels
The most common steel-making furnaces today are the basic oxygen furnace and electric arc furnace (EAF). In either furnace, the metallic iron from a blast furnace or scrap iron is charged into the furnace together with limestone and melted by gas jets, electric arcs, and oxygen lances. Fluxes are added to reduce sulfur and phosphorus contents to desired levels. As the melt progresses and a liquid pool can be contacted, the lanced oxygen “burns” dissolved oxidizable elements, such as carbon, manganese, silicon, and aluminum contained in the liquid; the energy from this reaction elevates the temperature of the liquid metal pool. In the final stages of melting, the oxygen is used to decarburize the melt. Sacrificial carbon is also commonly blown into the covering slag layer to react with excess oxygen. This reaction liberates additional energy. Working of the steel continues until the desired tap temperature and carbon level have been obtained. When this has occurred, the heat will be tapped into a refractory-lined ladle. Typical EAF heats range from 80 to 360 tons. Once the liquid steel has been processed to achieve the desired chemistry and temperature, it must be put into a solid form suitable for use by the rolling mill. The process of producing this solid product is known as casting. In traditional (historic) steel making, the liquid steel was poured from the ladle into a series of cast iron molds, cooled, and solidified into an ingot. Most modern steel production uses the continuous casting method. All structural shapes of domestic origin and the majority of foreign-produced shapes are continuously cast. In this process molten steel is continuously poured into a mold. The molds are made of copper, formed in the cross-sectional shape and size of the desired casting, and water-cooled. During steady-state casting, the steel streams into the open top of the mold and fills the mold cross section. Liquid steel that comes in direct contact with the water-cooled mold surface quenches to form a solid shell and joins to the existing shell already formed along the perimeter of the mold. As the shell forms, it is continually withdrawn from the bottom of the mold. During the short residence time within the mold, the thermal transfer is sufficient such that the shell grows to a thickness that is capable of maintaining its cross-sectional shape while containing a core of liquid steel. Outside of the mold, water and/or air sprays are employed to continue shell thickening. Mechanical restraint may also be used to help maintain the cast shape. Continuously cast shapes include billets, blooms, slabs, beam blanks, and near net shapes. © 2003 by CRC Press LLC
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Lamellar fracture
Plate subjected to thru-thickness tension strain
Welded joint
FIGURE 12.13 Schematic of lamellar tear-type fracture in heavy weldment.
Most structural shape and plate is produced from castings by the hot rolling process. The process consists of passing the hot cast material between a set of rolls revolving in opposite directions, and spaced such that the distance between the rolls is less than the thickness of the material entering the rolls. The rolls grip the piece, reducing its cross-sectional area and increasing its length. This process forms the steel into the desired cross-sectional shape, while improving the mechanical properties by modifying the original cast structure. Hot rolling causes grain refinement and elongation of those grains, deformable inclusions, and inhomogeneities in the rolling direction. The preferential alignment of structure along the rolling direction results in a shape with anisotropic properties. This is particularly true for ductility and fracture toughness. Hot rolling also tends to elongate segregated elements, such as sulfur, into flat discontinuities. When rolled steel is subjected to through-thickness tensile stresses, these discontinuities can produce planes of weakness that can later result in a form of failure known as lamellar tearing. Lamellar tearing is characterized by a step-like fracture surface, generally running parallel to the rolling direction (Figure 12.13). Lamellar tearing has occasionally occurred in thick materials under highly constrained conditions, such as in certain welded joint details. The tearing usually occurs during fabrication as a result of thru-thickness shrinkage strains and tensile stresses that occur as welded joints cool. Nondestructive testing procedures, including ultrasonic testing (UT) and radiographic testing (RT), can be used to detect zones of lamellar tearing. Modern steel produced by the EAF and continuous casting processes has reduced levels of sulfur relative to historic steels, and such steel is thought to be less susceptible to lamellar tearing.
12.3.1 Physical Properties of Structural Steel On the microstructural level, all metals are composed of grains. Grains are a three-dimensional matrix of atoms arranged in a regular and repeating crystal structure. The characteristics and properties of steels are a function of the microstructure and grain distribution. Microstructure, in turn, is determined by the chemistry, deformation, and thermal history of the steel. The microstructure of most common structural steels consists of a primary matrix of ferrite grains with a small dispersion of pearlite. The characteristics of the ferritic grain structure of steel dictate the properties and behavior at normal service temperatures. A fine grain size promotes increased strength, toughness, and weldability. The past thermal history of steel has significant influence upon properties of steel products. The principal thermal history effects are due to phase transformations and grain growth events. Steel is an unusual material in that, as its temperature decreases from the liquid state to ambient, it not only
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undergoes a liquid to solid-state change (freezing), but also two separate and distinct solid-state phase transformations. Very simplistically, solid steel grains are composed of a three-dimensional crystal matrix of regularly arranged iron atoms. The atomic diameter of carbon is roughly half the size of iron. Thus, carbon atoms easily fit into the interstices (spaces) between the iron atoms. The packing arrangement, and hence the interstitial hole size and distribution, is different in the different solid-state phases. Structural steel grades, upon solidification, form a solid phase known as delta-iron (δ-iron). This phase exists only at highly elevated temperatures. Upon further cooling, the atomic arrangement of iron atoms in δ-iron transforms to a different packing configuration known as austenite or gamma-iron (γ-iron). Atomic packing density of iron in the austenitic state is such that up to 2% of carbon can be dissolved into the iron matrix. Further cooling of austenite will induce the iron matrix to transform to a higher packing density known as ferrite or alpha-iron (α-iron). The volume of interstices in the new matrix is reduced, resulting in a maximum carbon solubility of 0.02%. The transformation from austenite to ferrite occurs over a temperature range that is dependent on chemical composition. Under equilibrium conditions, as the temperature is decreased through the transformation range, the excess carbon that is rejected by the formation of ferrite diffuses through the solid steel, concentrates, and forms iron carbide. Iron carbide forms in islands of alternating ferrite and iron carbide, known as pearlite. The total percentage of pearlite developed within steel depends on the carbon content. The pearlite lath spacing is a function of temperature and time of formation. The size of the pearlite islands and the spacing between laths strongly influence the hardness, ductility, and strength of the steel. Examples of structural steels having ferrite-pearlite microstructure are ASTM A36, A572, and A992, all of which are deemed to have suitable toughness, ductility, and weldability for use in seismic force-resisting systems. The solid-state diffusion (transport) of carbon atoms through the solid steel matrix is dependent on both time and temperature. If the temperature of the steel is lowered rapidly (quenched) through the transformation range such that sufficient time for carbon diffusion is not provided, metastable lowtemperature transformation products bainite or martensite will form. These phases are characterized as being harder, stronger, and less ductile than ferrite pearlite steels and not desirable components of seismic force-resisting systems. Martensite and bainite can form in structural steels if rapidly heated by welding, flame or arc cutting unless proper preheating is performed to control the cooling rate and avoid quenching. If after quenching, the temperature of the steel is again raised, sufficient thermal energy will be restored to the system for solid-state carbon diffusion to reinitiate. Ductility and toughness of the steel will be improved, but at the expense of the strength and hardness that bainite and martensite offer. By carefully controlling the temperature and time of reheating, the amount of decomposition can be controlled and thus a balance between increased strength and hardness can be obtained, with acceptable toughness and ductility. This process is known as tempering. ASTM A913 is an example of a structural steel material that is processed through a quenching and tempering process and has excellent properties of toughness and ductility. It is also suitable for use in seismic force-resisting systems.
12.3.2 Mechanical Properties of Structural Steel The primary properties of structural steel that are important to seismic performance are • • • •
Yield strength Tensile strength Ductility Fracture toughness
Each of these depends on the metallurgy and thermomechanical processing history, as discussed in previous sections, as well as the load application rate, temperature, and conditions of restraint at the time of load application.
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YIELD POINT
TENSILE STRENGTH
Fy STRESS f (Ksi)
ε = 0.005
εy 0
0.004
0.008
εsτ 0.012
0.016
0.020
0.024
STRAIN ε (in./in.)
FIGURE 12.14
Typical stress-strain curve for structural steel.
12.3.2.1 Tensile Properties Most mechanical properties important for design are determined from a standard tension test. In this test, a machined specimen, with standard cross section, is loaded in a universal testing machine while loadelongation data are recorded. These data are reduced into the form of a stress-strain curve (Figure 12.14). The initial straight line segment of the stress-strain curve represents the specimen’s elastic behavior where stress is proportional to strain and related by the Young’s Modulus, which has a value of 29,000 ksi for steel. As strain increases, stress and strain become nonlinear and the specimen experiences permanent plastic deformation. Many mild carbon steels exhibit a peak stress immediately after the stress-strain curve deviates from linearity, known as the yield point. Immediately after achieving the yield point, the stress dips with increasing strain, then remains at a constant value, known as the yield strength, for considerable amounts of additional strain. Thereafter, the steel strain hardens with increasing stress, until a peak, or ultimate, tensile strength is reached. With increasing strain beyond the tensile strength, the material exhibits necking and, ultimately, fracture. Standard ASTM material specifications include controls on the yield strength or yield point of the material as well as the tensile strength and elongation of the material at fracture. Although yield point is of no engineering significance, ASTM specifications permit mills to report either yield point or yield strength. Therefore, it is possible that some material conforming to the ASTM material specifications will have slightly lower yield stress than the nominal value contained in the specification. More typically, due to variations in the production process, yield and tensile properties will substantially exceed the minimum specified values, sometimes by as much as 40% or more. In general, tensile properties of steel vary with temperature. Tensile data for various steels show that their yield strength and ultimate strength increase by approximately 60 ksi when the temperature decreases from 70° to –320°F [Barsom, 1991]. Similarly, when steel is elevated to about 900°F it loses about half of its room temperature strength and modulus of elasticity. However, for the range of temperatures of interest for most structures (–60°F < T < 120°F), stress-strain properties of steel may be considered to be essentially constant. Tensile properties also vary with rate of loading. Tensile data for various steels subjected to monotonic dynamic loading show that the yield strength increases by about 4 to 5 ksi for each order of magnitude increase in rate of loading. The difference in yield strength under static loading as opposed to full impact loading (time to fracture <0.001 sec) is about 25 ksi. Tensile tests performed by mills to demonstrate compliance with ASTM material specifications are performed in accordance with ASTM standard A370. This standard permits tensile tests to be performed at rates between 10 and 100 ksi/min. Typical response
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σ3
σ2
σ1
FIGURE 12.15
Three principal stress components and planes of maximum shear stress.
of structures to seismic loading has rise times to peak loading on the order of one to a few seconds, which is approximately one order of magnitude larger than the test rate. Thus, the effective yield strength of structural steel when responding to earthquake motion may be 4 to 5 ksi larger than that reported by the mills. With the possible exception of some braces in braced frames, structural elements are seldom loaded in a uniaxial state of stress. The stress field for a typical material element can be described by three principal stresses that are aligned normal to each other on three orthogonal planes (Figure 12.15). Shearing stresses inclined with regard to these planes can be calculated from the principal stress components. Assuming that σ1 is the largest of the principal stress components and σ3 the smallest, the maximum shear stress component, τmax , is given by the equation: τ max =
(σ1 − σ3 ) 2
(12.1)
For a uniaxial tension test specimen, the applied tension produces tensile stress σ1, while σ2 and σ3 are both null. Therefore, in such a specimen, the maximum shear stress, τmax has a value equal to half the applied tensile stress σ1. Since plastic deformation and yielding occur when τmax reaches a critical value, in elements that are subjected to multiaxial loading, which is the more typical situation, the critical value of τmax may be achieved at maximum principal tensile stress values that are either lower or higher than attained in the uniaxial tensile test. For example, if one principal stress plane is in compression while a second is in tension, σ3 in Equation 12.1 will have a negative value, and a critical value of τmax will be attained at a lower value of applied tension σ1 than in the uniaxial case, lowering the effective yield strength. More commonly, if the material is constrained, as often occurs in connections, the material can develop a state of triaxial tensile stress. Under such conditions, τmax will approach 0 regardless of the applied tensile stress and yielding may never occur. Instead, the material will behave in an elastic manner until ultimate tensile stress is reached, at which point it will fracture. This is one reason why structures designed for seismic resistance should be proportioned such that yielding occurs in members, such as beams, columns, braces, etc., rather than at the connections of these members. 12.3.2.2 Ductility Material ductility is an important index of the ability of a material to withstand inelastic deformation without fracture and is a key property important to seismic performance of structures. Material ductility, µM , is usually represented by the equation: µM =
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εu εy
(12.2)
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Mo θ
Undeformed shape
Deformed shape FIGURE 12.16
Deformation of beam under applied external moment.
where εu and εy , respectively, are the material strains at fracture and onset of yield. At room temperature, typical structural steels will have static ductility on the order of 20. Under cyclic applied loads, the availability material ductility decreases as the material is subject to fatigue. Generally, the more cycles of strain the material must undergo, the lower available material ductility. Typical structural steels may be regarded as having available ductility for seismic purposes on the order of about 10. Ductility can also be expressed in terms of the inelastic deformation capacity of individual members. In the case of an axially loaded tension member, the member ductility, µ, would be given by the equation: µ=
δu δy
(12.3)
where δ u is the total brace elongation at failure and δ y is the total brace elongation at yield. Since axially loaded members have uniform stress and strain distribution across their cross sections and along their length, the ultimate elongation of such a brace would be given by the term: δu = εu L
(12.4)
where εu is ultimate material strain, previously discussed, and L is the member length. Similarly, the member yield deformation is given by: δy = εyL
(12.5)
where εy is the material yield strain. By substitution of the relationships of Equations 12.4 and 12.5 into Equation 12.3, it is seen that for axially loaded tensile members, member ductility and material ductility are the same. The same cannot be said for member ductility of flexural members. Consider the beam shown in Figure 12.16. This beam has uniform cross section, is pinned at both ends, is subjected to an applied moment at one end, Mo, and as a result of this, experiences an angular deformation at that end, θ . We will consider the behavior of this beam as the moment and rotation applied at the end are progressively increased in magnitude until failure occurs. Under initial, low-level loading, the beam will behave elastically. The moment M and curvature φ at any station, a, along the beam will be given by the equations: M (a ) = M o −
Mo a L
(12.6)
and φ (a) =
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M (a ) EI
(12.7)
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σy
ε
σy
ε Strain
FIGURE 12.17
σy
σy
σy
Partially Plastic Elastic Stress Stress Distribution Distribution
σy+dy
σy
Fully Plastic Stress Distribution
σy+dy Strain Hardening Stress Distribution
Strain and stress distribution in symmetric cross section at various levels of plasticity.
where the curvature, φ, is given by the equation: φ=
εT + εC d
(12.8)
and εT and εC are, respectively, the extreme tensile and compressive strains on the cross section at station a and d is the cross section depth. The rotation at the end of the beam is obtained by integrating the curvature along the beam and is given by the equation: θ=
ML 3EI
(12.9)
Once the strain at the outermost beam fibers reach the yield strain, however, these relationships no longer apply. Figure 12.17 shows the strain distribution across the beam cross section, which in this case is assumed to be symmetric, and the corresponding stress distribution in the beam as the curvature progresses from elastic to partially plastic to fully plastic behaviors. As the applied rotation at the end of the member increases beyond the elastic range, plasticity spreads from the outer beam fibers toward the center of the section until ful plasticity is achieved. Then, as further rotation is applied, the strains at outer fibers begin to enter the strain hardening range and the stresses slowly increase beyond the yield level until ultimate strain levels are achieved and the section fractures. For most beam sections, strain hardening will actually begin to occur at outer beam fibers before full plasticity is achieved across the cross section. A plot of applied moment at the beam end against applied curvature would typically take the form of Figure 12.18. As can be seen, as the cross section is deformed into increased levels of plasticity, the moment–curvature relationship is quite nonlinear. Eventually, as the section becomes fully plastic, the behavior again becomes approximately linear with a small postyield modulus, typically on the order of 2 to 3%. The rounded form of this curve, as the section plastifies, makes definition of a specific yield point difficult. Some engineers define the point of yield as that point at which the extreme beam fiber first yields. However, more typically, an inferred yield point is taken as the intersection of the extended elastic behavior and strain hardening behavior lines, with the yield curvature and yield rotation taken at this point. As indicated by Equations 12.6 and 12.7, when the beam is elastic, the distribution of curvature along the length of the beam is linear. As beam behavior becomes inelastic, the distribution of curvature along the beam also becomes nonlinear. Due to the effects of strain hardening, plasticity tends to distribute out along a finite length of the beam, lp , termed the plastic hinge zone (Figure 12.19), where a nearly © 2003 by CRC Press LLC
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Moment Mo
Seismic Design of Steel Structures
Inferred yield point
actual behavior
Curvature φ FIGURE 12.18 Inelastic moment-curvature behavior of beam.
Mp
Plastic hinge zone
φ
lp L FIGURE 12.19 Idealized moment-curvature distribution for inelastic beam.
constant moment Mp occurs. Mp is commonly termed the plastic moment, and has a lower bound value, neglecting strain hardening effects, of ZFy , where Z is the plastic section modulus. For structural members, the plastic hinge length, lp , is typically about three quarters of the beam depth, d, though this varies depending on the length of the beam and the moment gradient. Neglecting the small moment gradient within the plastic hinge zone, the end rotation of the beam and the curvature of the beam within the plastic hinge zone can be related by the expression: θ=
Mp 3L
(L − l )
2
p
+ φp
lp l L− p 2 L
(12.10)
As can be seen, for flexural members, the relationship between plastic curvature, φp , and end rotation, θ, is not directly proportional and an available material ductility of 10 does not imply an available beam ductility of the same amount. This becomes even more complex when the global ductility of an entire structural system is considered. Global system ductility can be defined by the expression: µ=
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∆u ∆y
(12.11)
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Total Lateral Base Shear Force - kips
7000
6000 Vy
5000
.
4000
3000 Du=39.5” 2000
Dmax = 31.8”
Dy = 8.5”
1000 Dy
0 0
5
10
15
20
25
30
35
40
Displacement (in.)
FIGURE 12.20
Pushover curve for an arbitrary structure.
where ∆u and ∆ y are, respectively, the lateral deflection of the structure at failure and onset of yielding. As with individual beams, determination of the point of yielding in a structure is somewhat difficult, as is selection of a point of ultimate strength. Figure 12.20 presents a pushover curve for an arbitrary steel structure, consisting of a plot of the applied lateral force on the structure against the resulting lateral displacement of the structure. A number of behaviors are discernible on this plot, including the • Yielding of individual beams, initiating at a displacement of about 5 in. • Failure of individual connections, initiating at a lateral deflection of about 30 in. • Eventually, at a lateral displacement of about 40 in., total loss of stability and collapse Typically the yield point for such a structure is taken, not at the point that the first beam yields, but rather at an approximate point taken as the intersection of the lines representing elastic and stable postelastic behaviors, in this case at a lateral deflection of about 8.5 in. Using this somewhat arbitrary definition of yield, for this structure, individual failures begin to occur at a deflection of 31.8 in., or a global ductility of about 3.75. Global failure occurs at a deflection of 39.5 in., or a global ductility of about 4.6. Typical seismic design codes anticipate structures will have global ductility capacities on the order of 3 to 4. As discussed above, it is important to recognize that global ductility is not synonymous with either material or member ductility. Most structures are proportioned to exhibit yielding behavior in relatively limited zones, for example, over the length of a brace, or in the end plastic hinge region of a flexural member. If structural yielding is not well distributed throughout the structure, approaching a state of uniform strain, in order to achieve global ductilities on the order of 3 to 4, it may be necessary to achieve material ductilities that are several times larger, approaching or even exceeding the capacity of the material. This is why it is important to configure steel structures to spread inelastic behavior throughout the structure. 12.3.2.3 Toughness Structural steels can fracture in either a ductile or a brittle manner. Brittle fracture is undesirable as it occurs at stresses and strains that are significantly less than the nominal ultimate values, and therefore has the effect of sharply reducing the availability of ductility. The fracture mode is governed by the metallurgical properties of the material, temperature at fracture, the rate at which loads are applied and the magnitude of the restraints that prevent plastic deformation. The effects of these parameters on the mode of fracture are reflected in the fracture-toughness behavior of the material. In general, fracture toughness increases with increasing temperature, decreasing load rate, and decreasing restraint. © 2003 by CRC Press LLC
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The Charpy V-notch impact test has been the most widely used for characterizing fracture-toughness behavior of steels. This test consists of striking a standard notched bar specimen with a standard hammer, imparting energy to the specimen. These specimens may be tested at different temperatures, and the impact fracture toughness at each test temperature may be determined from the energy absorbed during fracture, the percent shear (fibrous) fracture on the fracture surface, or the change in the width of the specimen (lateral expansion). At low temperatures, structural steels exhibit a low value of absorbed energy (about 5 ft-lb), and zero fibrous fracture and lateral expansion. The values of these fracture-toughness parameters increase as the test temperature increases until the specimens exhibit 100% fibrous fracture and reach a constant value of absorbed energy and of lateral expansion. This transition from brittle to ductile fracture behavior occurs at different temperatures for different steels, for individual heats of steel within a given specification, and even for different locations within a rolled structural section. Fracture toughness is an important parameter for elements that have notches, abrupt geometric discontinuities, or other defects and flaws. If the fracture toughness of a material is known, fracture mechanics concepts can be used to determine, based on the geometry of the discontinuity or notch and the fracture toughness of the material, the critical applied stress at which brittle fracture will initiate. A complete discussion of fracture mechanics concepts is beyond the scope of this chapter, but is presented elsewhere [e.g., Barsom and Rolfe, 1999]. In general, members with defects at their outside face are more susceptible to fracture than members without such defects or with defects within the interior of the member. Members under conditions of high restraint are more susceptible to fracture than members not under such restraint. Members subjected to rapidly applied loads are also more susceptible to fracture. When fracture toughness is an important parameter, the design engineer must establish and specify the necessary level of fracture toughness for the material to be used in the particular structure or in a critical component within the structure. Fracture toughness has been found to be important to the performance of exposed structures in cold regions. It has also been found to be an important parameter for welded joints in seismic service, as such joints typically have high restraint and may have large defects and flaws which can initiate brittle fracture. Recent design specifications identify minimum Charpy toughness values for deposited weld metal in the seismic-force-resisting systems of steel frames. 12.3.2.4 Effect of Cold Working Prior load history can also have significant impact on a structure’s strength and ductility. Figure 12.21 shows loading and unloading behavior for a carbon steel tensile specimen. Loading path ABCDE is a schematic illustration of the stress-strain behavior for a specimen loaded monotonically to failure. Loading and unloading the specimen in the inelastic region will alter the stress-strain behavior under future cycles of loading. For example, if the specimen is loaded on path ABCC', the residual stress-strain curve for the element will be given by C'CDE. The resulting specimen will have substantially reduced ductility available. This effect will be even more pronounced if the specimen is loaded along path ABDD''. Upon reloading, the residual stress-strain capacity would be given by the path D'DE, a behavior that exhibits both elevated yield strength and substantially reduced ductility. A specimen that is strained into the strain-hardening region, then unloaded and allowed to age in the unloaded condition for several days at room temperature, or for shorter times at moderately higher temperatures, may follow the reloading curve shown in Figure 12.22. This phenomenon is known as strain aging, and has the effect of further increasing yield strength, increasing tensile strength, and decreasing ductility. Fabrication and production of steel shape and plate frequently involve deforming the material into the strain-hardening range. One common source of such straining is the roller straightening process used by mills to ensure that the straightness of structural shapes meets industry standard tolerances. This can result in local reduced ductility and elevated strength in structural shapes before any fabrication is performed. Bending operations, to form curved or bent elements, produce further strain hardening and cold working of the steel. For these reasons, detailing of steel structure should avoid relying on inelastic behavior in bent or curved structural elements.
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INELASTIC RANGE
ELASTIC RANGE
STRAIN-HARDENING RANGE INCREASE IN YIELD POINT FROM STRAIN HARDENING
D E
C
STRESS
B
A C'
STRAIN
D' DUCTILITY AFTER STRAIN HARDENING
DUCTILITY AFTER DEFORMATION WITHIN PLASTIC RANGE
RESIDUAL STRAIN
DUCTILITY OF VIRGIN MATERIAL
FIGURE 12.21 Strain-hardening behavior of steel under repeat inelastic load applications.
STRESS
INCREASE IN YIELD POINT FROM STRAIN AGING
INCREASE IN TENSILE STRENGTH FROM STRAIN AGING
INCREASE IN YIELD POINT FROM STRAIN HARDENING
STRAIN
DUCTILITY AFTER STRAIN HARDENING AND STRAIN AGING
DUCTILITY OF VIRGIN MATERIAL
FIGURE 12.22 Strain-aging behavior of structural steel.
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12.4 Structural Systems The lateral-force-resisting systems for structural steel buildings and structures can generally be categorized into one of three broad classes: 1. Braced frames 2. Unbraced or moment-resisting frames 3. Dual systems, composed of a combination of the two systems, designed to act in unison Design and detailing requirements for these various structural systems are governed by the building code and building standards law requirements specific to each country. In the United States, limitations on the applicability of the various structural systems to different structures, minimum loading criteria and limitations on building stiffness are specified by the model building code. A companion chapter in this publication provides discussion of these issues (see Chapter 11). Criteria for proportioning and detailing of steel members and their connections for purposes of seismic resistance are governed by the AISC Seismic Provisions [AISC, 1997] and supplements [AISC, 2000]. The sections below describe the various structural systems commonly employed for seismic resistance of steel structures, the performance issues associated with these structural systems, and brief discussion of the U.S. building code requirements for design of these systems. In U.S. building codes, structural systems are typically categorized based on type, for example, braced frame, moment-frame, etc., and also based on the extent to which the structure is configured and detailed for superior seismic performance. Structures with favorable configuration and superior detailing are classed as “special,” while structures with limited control on configuration and detailing are classed as “ordinary.” Structures with intermediate levels of control on configuration and detailing are classed as “intermediate.” Structures classed as special may be proportioned for reduced lateral design forces, and therefore increased ductility demand, as compared, respectively, to intermediate and ordinary structures. Special structures may be used in any location, regardless of seismicity, or for any occupancy structure, while the use of intermediate and ordinary structures is restricted in application based on structure size, occupancy, and, for some structures, may be used only in regions of low seismicity. In addition to these three categories, U.S. building codes also define a class of steel structure that is designed for seismic forces, but not provided with any seismic detailing or configuration controls. Such structures are permitted to be used only in zones of low seismicity and must be designed for relatively large design force levels. Readers are referred to the companion chapter on building codes for more information on these topics (see Chapter 11).
12.4.1 Braced Frames In braced frames, lateral stability of the structure is provided primarily through the presence of diagonal braces within the vertical plane of beam–column framing. Braced frames may generally be categorized as concentric braced frames (CBFs), eccentrically braced frames (EBFs), or incomplete braced frames. In a CBF, the frame is configured such that at the connection of the braces to the frame, the work-points for the braces and other elements are coincident, or nearly so. Such CBFs behave as vertical cantilevered trusses and resist lateral forces through the development of axial forces in the various members (Figure 12.23). Other braced frame configurations rely on a combination of vertical truss action plus bending in the beams and/or columns to provide lateral resistance. Figure 12.24 presents schematic elevations of a number of common braced frame configurations, though many variations of these configurations may be found. In general, the single diagonal, X-braced, chevron-braced, V-braced, and zipper-braced frames may be categorized as CBFs.
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V
sα4
α2
2
V
sα co V/
1
H
h3
α1
VH/D
D
Vertical truss action in braced frame.
X-Braced
Single Diagonal
K-Braced
FIGURE 12.24
sα
h2
co V/
h1
V
V(h4+h3)/D
α3
VH/D FIGURE 12.23
3
V(h 4+h3+h2)/D
sα co
V(H)/D
V(h4+h3+h2)/D
V
V
V/
V(h 4+h3)/D
V(h4 )/D
α4
V(h 4)/D
co V/
h4
V
Chevron Braced
Eccentric Braced
V-Braced
Incomplete Braced
Zipper Braced
Knee-Braced
Common braced frame configurations.
12.4.1.1 X-Braced Frames X-braced frames are among the most economical and popular configurations of braced frame structure, particularly in industrial applications, where the architectural impacts of large diagonals across a bay are often not a concern. Many X-braced frames are designed assuming that the braces are capable of resisting tensile loads only. When this approach is taken, the designer typically assumes that the compressive braces buckle under negligible load and can therefore be neglected in the analysis, resulting in a statically determinate structure, and a simplification of the design. Also, this assumption permits very slender elements to be used for the braces, including rods, single angles, flat bars, and cables, making for an economical structure. © 2003 by CRC Press LLC
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FIGURE 12.25
12-23
Fractured rod brace in support structure for an elevated water tank.
Although tension-only braced frames are popular with designers, they have not performed particularly well in past earthquakes and modern building codes discourage their use, except for smaller structures or in zones of low seismicity. There are several problems associated with tension-only braces. Many such braces are installed with some slack. When they are stressed into tension by the structure’s response to ground shaking, they experience an impact-type loading as slack is taken up. This impact loading can cause a brittle fracture of the brace. Similar effects can occur as tension braces that have been buckled by induced compression are pulled into tension, as the structure cycles from one direction of response to the opposite. This effect can be made more severe by the fact that buckling of the braces in compression often results in localized plastic hinging near end connections and at the mid-span of the brace. This can cause very high local strains and can lead to low-cycle fatigue-type fractures under a few cycles of motion. Figure 12.25 is a picture of fractured rod bracing on a water tank, one of many examples that are available in the literature. As a result of these problems, some building codes require that tensiononly frames be designed to resist design shaking in an elastic manner. While this does result in a stronger frame than would otherwise be required, it does not directly address the problems associated with this structural system and is probably an ineffective solution. If X-braced frames are designed for both tension and compressive behaviors, the braces must often be made quite heavy in order to meet minimum slenderness requirements contained in the codes. A common design question relates to the effective length that should be used when proportioning the braces for compression. Research conducted by Goel [1986] and others suggests that in X-braced frames the tension brace effectively braces the compression brace both for in-plane and out-of-plane loading so that the length of X braces may be taken as half the full diagonal length. In addition, if end connections provide significant rotational restraint, as is commonly the case for in-plane buckling behavior, effective length factors less than one may typically be applied. Hollow structural sections are commonly used as brace elements in X-braced frames because they are an economical section for obtaining large radius of gyration and meeting minimum slenderness requirements for compressive design. However, when these sections buckle they are subject to local buckling and a type of behavior known as oil-canning. This has frequently lead to brittle brace fracture. Goel [1992] recommended minimum width–thickness ratios for the flanges of tubular sections to avoid this behavior, or the filling of tubular members with a solid material, such as concrete, to brace the flanges
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e
Column
2t
ac Br
Plastic hinge line
Beam
FIGURE 12.26
Illustration of gusset plate detail for special CBF.
against local buckling. Codes specify minimum width–thickness ratios for elements of braces of various cross sections for the same reasons. X-braced frames may qualify either as special CBFs, ordinary CBFs, or nondetailed frames. To qualify as special CBFs, brace elements must be selected with adequate width–thickness ratios to minimize the potential for local buckling, braces must conform to minimum slenderness criteria, connections must be designed with adequate strength to ensure that inelastic behavior of the frame will be governed by brace buckling and/or yielding, rather than connection failure, and end connections of braces must be proportioned to accommodate buckling of the brace, without damage to the gusset plate. Figure 12.26 illustrates such a detail. In this detail, a plastic hinge line, perpendicular to the axis of the brace, is drawn across the gusset plate. The gusset plate must be free to rotate, in bending about this line, without restraint from the attachment of the plate to the beams or columns. The brace is held back a distance equal to twice the plate thickness from this free rotation line. Connections detailed in this manner will be able to accommodate brace buckling through benign plastic hinging of the plate along this rotation line. Ordinary X-braced frames may meet somewhat relaxed criteria for brace slenderness and width–thickness ratios relative to special X-braced frames, but the braces themselves must be designed somewhat stronger than for special frames. Brace connections must still be designed strong enough to force inelastic behavior to occur in the brace as opposed to the connection; however, there are no specific detailing or configuration requirements for the gusset plate. Nondetailed X-braced frames may be designed without regard to special limitations on slenderness or width–thickness ratios, except as contained in the standard design specification. Special CBFs were introduced as a structural system in the mid-1990s, due to specific concern about the poor performance of ordinary braced frames, as observed both in laboratories and in real buildings following earthquakes. Preferential design criteria, in the form of reduced design forces, were provided for special frames as inducement for engineers to specify them, but no penalties were applied to ordinary frames. It is likely that future codes will severely restrict the use of ordinary braced frame systems or further penalize the design requirements as a means of discouraging their use. 12.4.1.2 Single Diagonal Frames Single diagonal frames are similar to X-braced frames except that rather than pairs of opposing braces in each braced bay, only a single diagonal brace is provided. Since steel members are subject to significant © 2003 by CRC Press LLC
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Undeformed shape
Floor beam deflects downward
Buckled compression brace
FIGURE 12.27
Deformed shape of chevron-braced frame.
postbuckling strength degradation, this system tends to have poor inelastic cyclic response behavior. When this system is used, this can be mitigated somewhat by providing pairs of opposing frames with the braces in each of the frames oriented in opposing directions. This assures that regardless of the direction of ground motion, there will be some braces acting in tension at each level. Single diagonal frames can be designed as either special, ordinary, or nondetailed systems. The design requirements for this system are similar to that for X-braced systems. In addition, for special and ordinary systems, there is a requirement that not more than 70% of the lateral force in any direction be resisted by tension braces. This ensures a reasonable distribution of tension and compression braces in each potential direction of response. 12.4.1.3 Chevron, V-Braced, and Zipper Frames Chevron and V-braced frames are very popular for commercial building construction because they are an economical alternative and also because the V or inverted-V pattern of the bracing provides opportunity for relatively large and unobstructed window and door openings. When these frames are loaded laterally, the lateral loading will tend to induce tensile forces in one brace in each bay and compression forces in opposing braces. If the beams in braced bays are designed such that they rely on vertical support from the braces to resist dead and live loads, this structural system should be classified as a bearing walls system for the purposes of establishing the design seismic forces. Otherwise, the system may be classified as a building frame system under the provisions of the building code. Regardless of whether the beams are designed to support tributary gravity loads independent of the braces, this frame configuration has a significant performance issue related to post-elastic behavior. The nonlinear behavior of most chevron and V-braced frames is controlled by buckling of the braces that are loaded in compression. Once the compression side braces buckle, they tend to degrade in strength very quickly, while the tension brace will have reserve strength. As a result of this, as the compression braces degrade in compressive strength and the tensile braces remain effective in resisting additional load, each pair of braces will place an unbalanced vertical component of load on the beams. This load can be very large and has often resulted in undesirable vertical plastic deformation of the beams and supported floor systems (Figure 12.27). Starting in the mid-1980s, this undesirable performance characteristic came to be recognized and the design specifications were revised to require that chevron and V braces be designed stronger than their X-braced counterparts. This was done in part as a penalty, to dissuade engineers from using this system and also as a means of minimizing the amount of damage that occurred. However, the penalty was not sufficiently large to accomplish either objective. Chevron and V-braced frames may be designed as special, ordinary, or nondetailed systems. When designed as special CBFs, the beam at the apex of the chevron or V must be designed with sufficient strength to resist, in addition to gravity loads, the unbalanced vertical component of forces from the braces, assuming that the postbuckling strength of the compression brace is equal to 30% of the buckling load and that the tension brace develops its full yield strength. This results in a considerable design penalty. © 2003 by CRC Press LLC
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Undeformed shape
Buckled compression brace
Deformed column FIGURE 12.28
Deformed shape of K-braced frame.
The zipper-braced frame is an alternative approach to dealing with the problem of postbuckling behavior of multistory chevron and V-braced frames. In this frame system, a vertical post, or “zipper column,” is installed between the beams supporting the apex of the V or inverted-V braces, but not extending to the ground (Figure 12.24). When the compression braces start to buckle, this zipper column redistributes the unbalanced load to other stories of the structure, providing for improved inelastic response and reduced floor beam deformation. 12.4.1.4 K-Braced Frames K-braced frames are similar in configuration to chevron or V-braced frames except that the V formed by the braces is oriented horizontally and has its apex at a column rather than at a beam. This is an extremely undesirable configuration for braced frames intended for seismic resistance as, once one of the braces buckles in compression, the unbalanced force from the tensile brace will result in large lateral deformation on the column, which can initiate column buckling and structural collapse (Figure 12.28). For this reason K-braced frames are not permitted to be designed either as special CBFs or ordinary CBFs. They are permitted in nondetailed systems in zones of low seismic risk only. 12.4.1.5 Eccentric Braced Frames Eccentric braced frames (EBFs) are a relatively recent innovation, developed in the early 1980s, primarily on the basis of research conducted at the University of California at Berkeley [Popov et al., 1989]. A variety of EBF configurations are possible (Figure 12.29). In this framing system, the diagonal braces are intentionally configured such that their work points are nonconcentric either with beam column joints in the case of single-diagonal systems, or with other braces in multidiagonal systems. The resulting eccentricity induces flexural and shear stress in the beams. These systems are intentionally designed so that nonlinear behavior is developed through plasticity in the beams. This protects the braces from buckling and results in a substantial amount of energy dissipation, a desirable property for earthquake resistance. Either shear plasticity or flexural plasticity may occur, depending on the link length. The segment of the beam in which the plasticity occurs is called the link and the beam itself is called the link beam. Beams with long links will be controlled by flexural plasticity and the development of plastic hinges at either end of the link. Beams with short links will develop plasticity through shear yielding distributed along the length of the link. Short shear-dominated links are preferred to longer flexural-dominated links [Malley and Popov, 1984]. This is because the distributed plasticity along the length of the shear link provides for increased energy dissipation with reduced concentrated deformation and damage, as compared with flexural links.
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Link
FIGURE 12.29
Typical EBF configurations.
EBFs tend to be more flexible than CBFs, resulting in somewhat increased damage to nonstructural elements at low levels of ground motion. However, their behavior under intense ground shaking is far superior to that of CBFs. Consequently, they are permitted to be designed for substantially reduced lateral forces, relative to CBFs. Critical consideration in the design of EBFs include providing adequate bracing of the link beam, so that it can develop plasticity without experiencing flexural-torsional buckling, and provision of sufficient stiffener plates within the web of the link beam to avoid lateral buckling of the web. Design specifications include prescriptive requirements for these aspects of the design. In addition, the columns of the EBF frame must be designed with sufficient strength to resist the axial forces resulting from development of a full mechanism in the frame. 12.4.1.6 Incomplete Braced Frames Incomplete braced frames have diagonal bracing in some stories of the frame, but not in others. This is a common form of construction for industrial applications where vehicle or maintenance access is facilitated at the lower story. Essentially, this system behaves more like a moment-resisting frame than a braced frame. Deformation in these structures occurs primarily as a result of bending of the columns in the unbraced stories and nonlinear behavior typically occurs through development of plastic hinges in the columns and the formation of a story mechanism (Figure 12.30). This is an undesirable behavior mode as it can result in the development of very large interstory drifts within the unbraced story, and potentially, development of P-delta (P-∆) instability and collapse. This system is permitted only as a nondetailed seismic system, in zones of low seismic risk. 12.4.1.7 Knee-Braced Frames Knee-braced frames are another hybrid system with behavior characteristics more like that of a momentresisting frame than a braced frame. Essentially, in a knee-braced frame, rigidity of the beam–column joint is achieved by placing a short brace between the end region of the beam and the column. If properly designed, these structures can have good performance characteristics similar to those of a momentresisting frame. Important design considerations include ensuring that the brace and frame connections are able to develop the strength of the connected members, ensuring that nonlinear behavior of the frame is controlled through a preferential mode, such as flexural hinging of the beams, and ensuring that the intersection points of the knee braces with the beams and columns are adequately braced to prevent © 2003 by CRC Press LLC
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Plastic hinge
FIGURE 12.30
Deformed shape of incomplete braced frame.
initiation of torsional buckling. The codes do not include any provisions directly governing the design or detailing of these systems; however, they can be designed as a nondetailed system. If the above design considerations are not accounted for in the design, performance of such frames can be poor. 12.4.1.8 Unbonded Braced Frames Unbonded braced frames, also known as buckling-restrained braced frames, are a new technology developed in Japan (see www.unbondedbrace.com). These frames are configured similar to X-braced frames or single-braced frames; however, the braces are specially detailed to allow both tensile and compressive yielding to occur without onset of buckling or fracture. The brace consists of a flat bar structural member, inside a larger tubular member. The tubular member is provided only as a buckling restraint for the flat bar, which carries the actual bracing force. A filler material or devices are placed between the flat bar and the tube walls so that the bar cannot buckle. The resulting structural system has a number of seismic performance advantages. It is a relatively stiff system, so that the building will experience relatively little deformation and damage under low levels of ground motion. Under more intense levels of ground motion, the braces yield, both in compression and tension, producing extensive hysteretic energy dissipation and effectively reducing the level of structural response. Important considerations in the design of these systems include assuring that the connections are adequate to develop the yield strength of the brace and assuring that yielding is uniformly distributed along the length of the brace so that large inelastic strains and ductility demands, potentially leading to fracture, are not developed. Ensuring that the flat bar brace does not bind against the side walls of the tube is important to achieving this uniform stress and strain distribution.
12.4.2 Design Approach Braced-frame members are designed to resist the forces specified by the building code based on the type of structural system selected and the location of the building site relative to various faults and seismic source zones, as determined from seismic risk or zonation maps. Under the requirements of the AISC Seismic Provisions the brace members of an ordinary braced frame, except chevron configurations, are designed for the force corresponding to the application of the specified base shear force per the applicable building code. In the case of chevron or V braces, the design force is increased by 150%. However, this requirement of 150% increase in the design force is not applicable if the chevron is designed as a special concentric brace frame (SCBF). All bracing connections are required to be capable of resisting the maximum expected force that could be delivered to them by the bracing configuration. The design intent is that the strength of all of the brace frame components (beams, columns, connections) be larger than the expected maximum capacity of the brace member. By ensuring this, the failure of a braced-frame system is intended to be controlled by yielding and buckling of the braces only, not the other elements of the frame. As soon as braces yield in tension or buckle in compression, they start to plastify under increasing lateral loads. As © 2003 by CRC Press LLC
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full plastification occurs, the stiffness and load-carrying capacity of the brace are limited and, therefore, the load that may be attracted to the brace frame as a whole is limited. As a result only the brace member will be damaged and will require repairs after an earthquake, whereas all other components of the braced frame will be undamaged and require no repair. Note that as previously discussed, the design requirements for ordinary V- and chevron-braced frames are not adequate to accomplish this objective, as the beams at the apex of the V or chevron are vulnerable to damage. The AISC Seismic Provisions require that brace connections be designed for the lesser of the following forces: • The strength of the brace in axial tension, given by As Fy , where As is the area of the brace and Fy is the yield strength of the steel. • An overstrength factor (Ω0) times the design force in the brace including gravity loads. The value of Ω0 is specified by the building code, depending on the structural system, but typically has a value ranging between 2 and 3. • The maximum force that can be transferred to the brace by the system, considering other limiting factors, such as the capacity of diaphragms to transfer shear forces to the braced frames. Columns in braced frames must also be designed with adequate strength to resist the axial loads resulting from the above three load conditions. U.S. building codes permit structural steel elements to be designed to either of two specifications: • An allowable stress design (ASD) format specification [AISC, 1989] • A load and resistance factor (LRFD) specification [AISC, 2001] Although both are permitted, the LRFD specification is far more suitable to design for seismic loading, since it directly considers the yield state of various members and their connections.
12.5 Unbraced Frames Unbraced, or moment-resisting, frames rely on the flexural rigidity of their beams, columns, and beam–column connections for lateral-force resistance and stability. Figure 12.31 illustrates the typical lateral deformation pattern experienced by moment-resisting frames in the elastic regime of behavior. As the frame deforms laterally, there is a tendency for the angle between the beams and columns to change. The rigidity of the beam–column connection resists this change through development of bending moments and shears in the beams and columns. Connections in moment-resisting frames are designated either fully restrained or partially restrained, depending on the stiffness and strength of the connection, relative to that of the beams and columns. A fully restrained connection must be capable of holding the angle between the beam and column essentially constant, until the weaker of the beam and or column yields in flexure. All other connections are classified as partially restrained because they permit some change in the angle of intersection between the beam and column at load levels less than that which initiates yielding of the frame elements. Partially restrained connections may either be partial strength connections or partial rigidity connections. Partial strength connections may be fully rigid but exhibit yielding of the connection elements and increased flexibility at load levels lower than those that would cause yielding of the beams or columns. Partial rigidity connections are flexible and permit some angular rotation to occur at the beam column connection, even at low levels of loading. Both fully restrained and partially restrained frames may be classified as special moment-resisting frames, intermediate moment-resisting frames, ordinary moment-resisting frames, or nondetailed moment-resisting frames. Properly configured and detailed moment-resisting frames are capable of dissipating extensive amounts of energy and, therefore, can provide superior seismic performance. However, even frames with appropriate configuration and detailing tend to be quite flexible, which can lead to extensive damage to nonstructural building components. © 2003 by CRC Press LLC
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Undeformed shape
V
Deformed shape M
V/2 FIGURE 12.31
M
M
V/2
M
Lateral deflection of moment-resisting frame.
The configuration of a moment-resisting frame is a critical factor in its performance capability. Because moment-resisting frames tend to be relatively flexible, they can develop large interstory drifts when subjected to strong ground shaking. If interstory drifts become too large, the frame can develop P-delta instability and collapse. The amount of drift induced in a building by an earthquake is a function of the intensity of the ground shaking, the spectral content of the ground shaking, the dynamic properties of the structure, primarily, its natural period of vibration and natural mode shapes, and its nonlinear deformation characteristics. If a structure responds to ground shaking within its elastic range of behavior, the structure’s fundamental mode shape is particularly important. Figure 12.32 shows the natural mode shape for two twostory structures. In the structure on the left, the stiffness of the structure is uniformly distributed vertically, relative to the mass of the structure. Therefore the structure experiences approximately the same amount of lateral deflection, termed interstory drift, in each story. The structure on the right is much stiffer in the upper story than it is in the lower story. As a result, most of the lateral deflection in this structure is accommodated through interstory drift in the first story. Such structures are commonly termed softstory structures. If the two structures in the figure have the same natural period of vibration, the total lateral displacement demand (i.e., at the top of the structure) induced on the two structures by a given ground motion will be the same. However, in the structure with uniform stiffness, each story of the structure will experience approximately the same amount of interstory drift, approximately equal to one half the total drift demand on the structure. On the other hand, the weak story structure will accommodate almost all the drift in a single story. This can lead to an accumulation of damage in this story, premature degradation and failure of the framing in that story, and also the development of P-delta instability and collapse. For this reason, it is particularly important to design moment-resisting frame structures without soft-story configurations. Even structures that have uniform distributions of elastic stiffness can develop inelastic soft-story conditions if an inappropriate pattern of plastic hinges form in the structure as it undergoes nonlinear lateral deformation. When a moment-resisting frame structure becomes completely plastic it is said to form a mechanism, that is, a behavioral mode in which the structure exhibits neutral stability and can deform laterally without application of load. Frame structures can form a variety of different types of lateral mechanisms. The most common types are illustrated in Figure 12.33. The frame on the left side of the figure develops inelastic behavior through the formation of plastic hinge zones at the ends of the beams, adjacent to the columns. Once a plastic hinge forms at both ends of each beam and also at the base of each column, the frame can undergo free lateral translation through a rigid body rotation of the columns. This is termed a beam-hinge mechanism and is a preferred mode © 2003 by CRC Press LLC
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Uniform Stiffness Distribution
FIGURE 12.32
Soft Story Stiffness Distribution
Mode shape for structures with uniform stiffness and soft-story stiffness distributions.
∆ Beam Hinge Mechanism
FIGURE 12.33
∆
∆ Panel Zone Hinge Mechanism
Column Hinge Mechanism
Various lateral frame mechanisms.
of behavior because it distributes inelastic deflection uniformly throughout all stories. The frame in the middle of the figure develops inelastic behavior through the formation of shear yielding in the panel zone of the connections between the beams and columns. These so-called panel zone hinges allow the beams to rotate freely, relative to the column, and also permit free lateral displacement of the frame to occur through rigid body rotation of the columns. This behavioral mode is not as desirable as the beam hinging mode because yielding of the column panel zone, though quite ductile and capable of dissipating extensive energy, can result in local kinking of the column flanges and can initiate failure in certain types of beam–column connections. The frame on the far right in Figure 12.33 develops a mechanism through the formation of plastic hinges at the tops and bottoms of the columns in a single story. This permits free lateral displacement of the structure through rigid body rotation of the columns in that particular story, without participation of the other columns. This condition is known as a single-story mechanism. Like the weak story configuration, it is undesirable because it concentrates deformation and damage in a relatively small region of the structure and can result in large interstory drifts in a single story and possible P-delta instability. Five basic moment-resisting frame systems are available in the building codes. These are termed: • • • • •
Special moment-resisting frames Intermediate moment-resisting frames Ordinary moment-resisting frames Special-truss moment frames Nondetailed moment frames
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As with nondetailed braced frames, the nondetailed moment frame may be used only in regions of very low seismic risk and must be designed for relatively large design forces. There are no specific requirements with regard to the detailing and configuration of the frame, other than the standard limitations on slenderness and section compactness contained in the design specifications for resisting loads other than seismic. Frames that employ partially restrained connections are subject to the same requirements as frames employing fully restrained connections, except the reduction in stiffness and strength of the frame introduced by these connections must be accounted for in the structural analysis used to evaluate the design forces and lateral deflections. Often, this requires the use of a nonlinear analysis methodology. The remaining sections discuss the design considerations for special momentresisting frames, intermediate moment-resisting frames, ordinary moment-resisting frames, and specialtruss moment-resisting frames.
12.5.1 Special Moment-Resisting Frames Special moment-resisting frames (SMFs) are configured and detailed to provide a high level of system ductility. Members of special moment-resisting frames must be either hot-rolled structural shapes or welded built-up shapes and must conform to material specifications capable of providing adequate ductility. In the United States, A-36, A572, Grade 50, and ASTM A913 Grade 50 or Grade 65 are approved for use in special moment-resisting frames. Structural shapes in moment-resisting frames must conform to strict limitations on width–thickness ratios, called compact section criteria, so that plastic hinging can form without premature fracture of the section. In addition to these requirements, the frame must be configured such that there are no soft or weak stories, as described above. Under the AISC Seismic Provisions, weak stories are avoided through the requirement that at each beam–column connection, the following relationship be satisfied:
∑M ∑M
* pc * pb
> 1.0
(12.12)
In this equation, the top term is the sum of the plastic moment capacities of the columns framing into the joint, reduced for the effect of axial load on the columns, while the bottom term is the sum of the plastic moment capacities of beams framing into the joint. The plastic moment capacity of the beams framing into the joint are calculated considering potential overstrength of the beam, that is, the potential that the actual yield strength of the steel will be somewhat larger than the nominal strength for the material specification and also strain-hardening effects. This is accomplished through the following formula: M pb = 1.1 Ry Fy Z
(12.13)
where Ry is a material specification-related coefficient that represents the ratio between the median strength of steel produced to a particular specification and the nominal strength, Fy is the nominal yield strength, and Z is the plastic section modulus for the beam section. For most structural steels Ry is assigned a value of 1.3. Frames that satisfy this requirement are known as “strong-column” frames because the columns are stronger in flexure than the beams and the frame will develop either a beam-hinge or column panel-zone type hinge mechanism. Early moment-resisting frames were highly redundant with nearly every beam–column connection provided with moment resistance so that the entire structural frame would participate in lateral force resistance. As bolted connections were replaced by welded connections in the 1970s, the labor cost associated with making moment-resisting connections became significant; to economize, engineers began to configure frames with fewer participating beams and columns, so as to minimize the number of welded connections required. As the number of beams and columns in the frames was reduced and the frames © 2003 by CRC Press LLC
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became less redundant, it became necessary to use relatively large members for the frames providing lateral resistance. This trend continued until 1994 and the Northridge earthquake, after which a number of moment-resisting frames were found to have experienced brittle fractures of welded moment-resisting connections. The lack of redundancy in modern steel frame construction both surprised and shocked a number of engineers and code writers [Holmes and Somers, 1996]. In addition, under the FEMA/SAC program research that was initiated in response to these failures, it was determined that momentconnections in deep members are more likely to experience brittle fracture than those in shallower members. Consequently, in 1997, the building codes were amended to require that minimum levels of redundancy be provided in SMFs. This is accomplished through the calculation of a redundancy coefficient, ρx , per the following equation: ρx = 2 −
20 rmax x Ax
(12.14)
where Ax is the floor area, in square feet at level x of the structure, and rmaxx the maximum of the sum of the shears in any two adjacent columns in the plane of a moment frame divided by the story shear. Special moment-resisting frames are not permitted to have configurations that result in values of ρx exceeding 1.25. During the period 1970 to 1994, most moment-resisting frames were constructed using a standard connection in which beam shears were transferred to the column through a shear plate that was welded to the column and high-strength bolted to the beam web, while flexural stresses were transmitted through a complete joint penetration butt weld of the beam flanges to the column. This fully restrained connection was considered to be capable of providing acceptable performance based on limited cyclic testing conducted at the University of California at Berkeley [Popov and Stephen, 1972]. Only a few such tests were performed, and many of these tests were on small structural sections. However, in 1985, the building codes adopted provisions requiring that this connection be used unless suitable test data were provided to substantiate the performance capability of alternative details. During research on the behavior of eccentric braced frames, Ksai and Popov [1986] and Engelhardt and Popov [1989] noted the vulnerability of this connection when subjected to cyclic inelastic deformation. However, these warnings were largely overlooked by the profession until the occurrence of the 1994 Northridge earthquake. The FEMA/SAC program conducted extensive research into the causes of the brittle fractures of these connections. Roeder [2000] determined that the behavior of these connections was both brittle and erratic. Based on extensive review of cyclic tests performed on these connections, Roeder suggested a mean plastic rotation capacity, θp, in radians, for this connection as given by the equation: θ p = 0.051 − 0013 db
(12.15)
where db is the beam depth, in inches, and a standard deviation given by the equation: σ p = 0.0044 + 0.0002 db
(12.16)
For 36-in.-deep beam sections, these equations provide a mean plastic rotation capacity of 0.004 radians and a coefficient of variation of 280%. For shallower sections, the behavior is somewhat better. For example, 24-in.-deep sections have a mean plastic rotation capacity of 0.02 radians and a coefficient of variation of 50%. The FEMA/SAC project concluded that this poor behavior was due to a variety of factors previously discussed above. Based on the FEM/SAC recommendations the building code adopted requirements that connection details used in SMFs be qualified through approved programs of cyclic inelastic testing, to be capable of withstanding at least 0.03 radians of cyclic plastic rotation without developing brittle fracture or experiencing significant strength degradation. The FEMA/SAC project developed a series of details © 2003 by CRC Press LLC
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Reduced Beam Section (RBS)
Bolted End Plate (BEP)
FIGURE 12.34
Welded Flange, Welded Web (WUF-W)
Free Flange (FF)
Bolted Flange Plate (BFP)
Bolted T-Sub (BTS)
Prequalified special moment-resisting frame connections.
L/2 Plastic hinge
P
s Note: If 2Mpr /L’ is less than the gravity shear in the free body (in this case P/2 + wL’/2), then the plastic hinge location will shift and L’ must be adjusted accordingly.
L’ L
P Mpr=1.1RyZbFy
Mpr Vp
w L’
VA “A” Mpr
taking the sum of moments about “A” = 0 Vp ={Mpr + Mpr + P L’/2 + wL’2/2}/L’
FIGURE 12.35
Determination of beam shear at formation of plastic mechanism.
that were recommended as prequalified for this service, based on testing and analysis of these connections performed as part of the project. These connection details are illustrated in Figure 12.34. Included in the FEMA-350 guidelines are specific design criteria for each of these connection types. The design criteria include specific detailing requirements, weld metal and base metal physical property requirements, quality assurance requirements, and limitations on the size of member for which the connection is qualified. The design procedure for each of these connections is strength based and considers the formation of a beam-hinge type mechanism in the frame. Specifically, the connection is designed so that a plastic hinge will form in the beam at a predetermined distance, s, from the face of the column. Based on this, the shear in the beam at the formation of a beam-hinge mechanism is determined, as indicated in Figure 12.35. Then a series of free bodies are taken of the connection and a portion of the column, and using these free bodies, as shown in Figure 12.36, the critical strength demands on various elements of the connection are determined. Each of these various elements, including the column panel zone, as well as the various welds, plates, and bolts, must be provided with adequate strength to ensure that plastic hinging in the beam can occur. Appendix 12A illustrates application of the design procedure for a typical reduced beam section-type connection. © 2003 by CRC Press LLC
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Plastic hinge
Plastic hinge
Mpr
Mf
Vp
dc
x
Vp x+dc/2
Mf=Mpr +Vpx
Mf=Mpr +Vp(x+dc/2)
Critical Section at Column Face
FIGURE 12.36
Mpr
Mc
Critical Section at Column Centerline
Typical free body diagrams used to determine required design strength of connection elements.
Mct Vct Vb
Tfct
Cfct
Tfb Vpz
Vcb
Cfb
Tfcb
Mb
Cfcb
Mcb
FIGURE 12.37
Forces on column panel zones.
Since the range of applicability of the prequalified connections is limited to configurations and section sizes tested and evaluated under the FEMA/SAC program, the prequalified connections are not applicable to all possible frame designs. For those cases where no prequalified connection is applicable, the AISC Seismic Provisions require a program of qualification testing and evaluation to substantiate the performance capability of the design. Appendix S of the AISC Seismic Provisions specifies the requirements of the qualification program. Column panel zones at beam–column connections are a key consideration in SMF design. The transfer of flexural stresses between beams and columns at a moment-resisting connection is accomplished through shearing of the panel zone. Figure 12.37 illustrates this behavior. The figure shows a momentresisting beam–column connection. The panel zone is that portion of the column web between the top and bottom beam flanges. The stress resultants applied by the beam to the panel zone are a moment Mb and shear Vb . The top and bottom portions of the column, respectively, apply moments and shears Mct , Vct, Mcb , Vcb to the panel zone. Each of these moments can be idealized as being applied as a couple of © 2003 by CRC Press LLC
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forces, applied at the centroid of the beam and or column flanges. These are shown in the figure as forces Tfb , Cfb for the beam, and with similar notation for the column. By cutting a section through the panel zone, just below the beam top flange, it is seen that the panel zone has a net shear demand Vpz, given by the equation: Vpz = Tfb − Vct
(12.17)
If the panel zone shear exceeds the shear strength of the material, the panel zone will yield, creating the effect of a pinned connection between the beam and column and limiting the forces on these elements. In the 1970s, design specifications required that panel zones in SMFs be capable of developing the strength of the beam. Panel zone strength was calculated as the quantity 0.55Fydctw , where Fy is the nominal yield strength of the column steel, dc is the column depth, and tw is the column web thickness. Often this required that the panel zones be reinforced, typically with the placement of a flat plate, commonly termed a doubler plate, adjacent to the web, welded to the column and any stiffener plates present. In the 1980s, concurrent with research performed on eccentric braced frames, it was postulated that panel zone shear yielding was a desirable behavior, capable of extensive energy dissipation and that this, in fact, might be preferable to frame behaviors that rely on the formation of plastic hinges in the beams. The 1985 Uniform Building Code [ICBO, 1985] was modified to permit the use of weaker panel zones by permitting panel zones that could develop only a fraction, 85% of the beam plastic flexural strength. In addition, a revised formulation was used for calculation of panel zone shear strength that accounted for the fact that complete yielding of the panel zone also required flexural yielding of the column flanges. This new formulation was: 3b t 2 Vy = 0.6 Fydc t w 1 + cf cf dbdc t w
(12.18)
where bcf and tcf are the width and thickness of the column flange, db is the depth of the beam, and other terms are as previously defined. These combined actions resulted in panel zones that were substantially weaker than those previously used. In the FEMA/SAC research, it was determined that excessively weak panel zones were detrimental to connection ductility. In particular, the flexural yielding of the column flanges, relied on in Equation 12.18, resulted in severe distortion of the column flanges at the beam–flange connection, and this could initiate weld fracture at this location. The research also found that maximum frame ductility could be achieved when the yielding at beam–column connections was shared between the beam and the column panel zone. Therefore the design procedures for the new prequalified connections attempt to balance the strength of the panel zone with the flexural strength of the beam. In addition to the prequalified connections developed by the FEMA/SAC program, several proprietary connection technologies are available in the marketplace. The developers of these proprietary technologies have developed qualification data for these connections, using procedures generally following those contained in Appendix S of the AISC Seismic Provisions, and now license the use of these technologies for individual projects. One such technology, known as the slotted web connection, is similar to the standard bolted web, welded flange connection commonly used prior to the Northridge earthquake, except that long slots are cut into the beam web adjacent to the top and bottom beam flanges. These slots significantly reduce the stress concentrations inherent in the standard pre-Northridge connection. A second technology, known as the side plate connection, uses a series of heavy shear plates to transfer flexural stresses from the beam to the column. A pair of shear plates is placed on each side of the column and beam, and additional plates are used to transfer flexural stresses from the beam flanges to these shear plates, then back to the column flanges. Information on these and other proprietary technologies may be obtained directly from the licensors.
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12.5.2 Intermediate Moment-Resisting Frames Intermediate moment-resisting frames (IMFs) are similar to SMFs except that the detailing and configuration requirements are somewhat relaxed and, in particular, a broader collection of beam–column connection details may be used. In particular, strong column–weak beam and panel zone strength requirements specified for SMFs are not required for IMFs. Also, connections in IMFs need only be qualified to be capable of resisting 0.01 radians of plastic rotation demand, as specified in Appendix S of the AISC Seismic Provisions. A wide range of partially restrained and fully restrained connection details are available to meet these requirements. The building codes require that IMFs be designed stronger than SMFs, reducing the amount of ductility demand on IMF frames as compared to SMFs. In addition, the building codes generally limit the use of IMF structures to buildings in zones of moderate seismicity and to certain classes of low-rise construction in zones of higher seismicity. These frames are commonly used in light residential construction due to their relative economy.
12.5.3 Ordinary Moment Frames Ordinary moment frames (OMFs) are similar to IMFs except that a single prescriptive beam–column connection detail, similar to that commonly in use for SMFs prior to the Northridge earthquake, is specified by the AISC Seismic Provisions for this system. Just as with the original SMF connection, commonly used in the 1970s and 1980s, the prescriptive connection employs a shear plate, welded to the column and bolted to the beam web for shear transfer and complete joint penetration groove welds to join the beam flanges to the column. Several improvements have been specified for this connection, however. First, weld filler metal used in joining beam flanges to columns must provide minimum specified toughness. Second, weld runoff tabs and backing bars must be removed from the completed weld; the weld must be backgouged and rewelded to remove any surface defects or discontinuities. Finally, weld access holes, cut in the webs of beams to permit welding continuously across the beam flange, must conform to a specified shape criterion to minimize the potential for stress and strain concentrations around this discontinuity. OMFs must be designed with larger strength levels than IMFs and are subject to additional limitation with regard to the size of structure and zones of seismicity in which they can be utilized.
12.5.4 Special Truss Moment-Resisting Frames Long-span and industrial structures commonly employ fabricated trusses, rather than rolled shapes, as the horizontal members of frames. For many years, buildings and other structures were commonly designed as SMF structures, but using trusses as the horizontal framing elements. Unfortunately, the flexural strength of a truss used as a girder in a frame will almost always exceed the flexural strength of frame columns, and therefore moment-resisting frames employing trusses as the girder elements almost always have weak-story configurations and will form single-story mechanisms, an undesirable condition. The special truss moment-resisting frame (STMF) was developed based on research performed at the University of Michigan [Goel and Itani, 1994] specifically to address this problem. In the STMF, the truss is specifically designed to have inelastic behavior controlled by shear yielding of the truss, in specially designed panel zones, near the truss mid-span. Figure 12.38 illustrates this behavior. In order to accommodate this inelastic behavior, prescriptive requirements are specified for the design of the special shear zone of the truss as well as other members in the system, to ensure that yielding will indeed occur in the special zone. Yielding must be limited to the middle one third of the truss span and X-pattern diagonals must be used in this zone. Truss chords must be compact and laterally braced. Though relatively few of these structures have been constructed, it is anticipated that they will perform in a manner comparable with other SMF structures.
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Undeformed shape
Deformed shape
Shear Yield Zone
Plastic hinge
FIGURE 12.38
Inelastic deformation of special truss moment frame.
Defining Terms Brace — An axially loaded diagonal member of a frame. Braced-frame — A structure that relies on braces for lateral resistance. Butt weld — A type of welded joint in which two pieces of metal that abut are joined by filling the groove between the two pieces with molten metal. See also groove weld.
Complete joint penetration — A method of welding in which weld metal is deposited for the full depth or thickness of the structural elements being joined.
Concentric braced frame — A braced frame structure in which the line of action of beams, columns, and braces at a connection are coincident.
Connection — The assemblage of welds, bolts, and other joining techniques used to fasten one member to another.
Ductility — A property of a material, structural element, or structure, by which it can withstand inelastic straining without failure. Elastic — A type of structural behavior in which deformation is proportional to applied force and in which upon unloading, a structure will return to its original undisturbed condition. Fracture — The formation of an unstable rupture plane or crack within a piece of material. Fracture mechanics — The engineering mathematics used to predict the propensity of materials and structures to fracture. Fracture toughness — A mechanical property of a material that relates to its ability to absorb and dissipate energy without developing fracture. Groove weld — A type of welded joint in which a groove between two pieces of metal is filled with molten weld metal, also sometimes called a butt weld. Hysteresis — The property of a steel structure or element by which it dissipates strain energy through plastic straining. Mechanism — A behavioral state for a structure under which it can experience free motion. Mode shape — A characteristic deformed shape, in which a structure can move in free vibration. Modulus of elasticity — A material-dependent proportionality constant that expresses the relationship between stress and strain during elastic loading of a structure; for steel it has the value 29,000,000 lb/in.2. Moment-resisting frame — A structure that relies on the flexural rigidity and strength of beams and columns for lateral resistance. © 2003 by CRC Press LLC
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P-delta (P-∆) — The effect of vertical forces on a laterally displaced structure, typically a condition of secondary stress.
Period — The amount of time, in seconds, it takes a structure in free vibration to experience one complete cycle of motion. Plastic — A type of structural behavior in which increasing deformation can occur under constant load, which upon unloading is not recoverable. Plastic hinge — A zone in a flexural member where inelastic flexural rotation occurs. Principal stress — The direct stress on a material, perpendicular to a plane across which there is no shear stress. Rolled shape — A structural member with a cross section formed by a rolling process. Strain — A dimensionless measure of deformation within a material or member, reflective of the percent elongation or contraction of the material or member under applied loading. Strain hardening — A type of structural behavior that occurs at loading exceeding the plastic range, in which increased loading is required to produce increased deformation. Stress — A measure of the distribution of force across a structural section, in units of pounds per square unit length, such as pounds per square inch (lb/in.2). Tensile strength — The peak stress in a standard axially loaded steel tensile specimen, prior to onset of fracture; also called ultimate stress. Truss — A structure comprised of multiple elements including diagonal members that resists load primarily through axial behavior of its members. Ultimate stress — See tensile strength. Weld — A means of joining two pieces of metal together by heating them sufficiently to allow melting of both pieces, and resolidification, perhaps with supplemental molten metal, into a single piece. Yield strength — The stress in a standard axially loaded steel tensile specimen at which plastic deformation can occur at uniform stress, typically the stress at an elongation of 0.005 in./in.
References AISC. 1928. Steel Construction, 1st ed., American Institute of Steel Construction, New York. AISC. 1989. Specification for Structural Steel Buildings, Allowable Stress Design and Plastic Design, American Institute of Steel Construction, Chicago. AISC. 1997. Seismic Provisions for Structural Steel Buildings, American Institute of Steel Construction, Chicago. AISC. 2000. Seismic Provisions, Supplement No. 2, American Institute of Steel Construction, Chicago. AISC. 2001. Load and Resistance Factor Design Specification for Structural Steel Buildings, American Institute of Steel Construction, Chicago. Barsom, J.M. 1991. “Properties of Bridge Steels,” in Highways Structure Design Handbook, Vol. 1, Steel Bridge Alliance, Chicago, chap. 3. Barsom, J.M. and Rolfe, S.T. 1999. Fracture and Fatigue Control in Structures: Applications of Fracture Mechanics, 3rd ed., American Society for Testing and Materials, Conshohocken, PA. CISC. n.d. Why Take a Chance? California Institute of Steel Construction, Southern California Division. Chicago Public Library. 1997. City of Chicago, a Chronological History of Chicago 1673–Present, Chicago Public Library, Chicago. Engelhardt, M.D. and Popov, E.P. 1989. “On Design of Eccentrically Braced Frames,” Earthquake Spectra, 5, 495–511. Frank, K.H., Barsom, J.M., and Hamburger, R.O. 2000. State of the Art Report on Base Metals and Fracture, FEMA-355E, Federal Emergency Management Agency, Washington, D.C. Goel, S.C. 1992. Cyclic Post Buckling Behavior of Steel Bracing Members: Stability and Ductility of Steel Structures Under Cyclic Loading, CRC Press, Boca Raton, FL. Goel, S. and El-Tayem, A.A. 1986. “Effective Length Factor for the Design of X-Bracing Systems,” AISC Eng. J., 23, 41–45. © 2003 by CRC Press LLC
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Goel, S.C. and Itani, A. 1994. “Seismic Resistant Special Truss Moment Frames,” J. Struct. Eng., 120. Goel, S.C. and Lee, S. 1992. “A Fracture Criterion for Concrete-Filled Tubular Bracing Members under Cyclic Loading,” Proceedings of the 1992 ASCE Structures Congress, American Society of Civil Engineers, Reston, VA. Hadley, J.M. n.d. How Buildings Withstood the Japanese Earthquake and Fire, Portland Cement Association, Portland, OR. Holmes, W.T. and Somers, P. 1996. “Steel Buildings,” in Northridge Earthquake of January 17, 1994, Reconnaissance Report, Vol. 2, chap. 2, Earthquake Spectra, Suppl. C to Vol. 11. ICBO. 1997. Uniform Building Code, International Conference of Building Officials, Whittier, CA. Ksai, K.C. and Popov, E.P. 1986. “General Behavior of WF Steel Shear Link Beams,” J. Struct. Eng., 112, 362–382. Malley, J.O. and Popov, E.P. 1984. “Shear Links in Eccentrically Braced Frames,” J. Struct. Eng., 110, 2275–2295. Nakashima, M. 2000. “Overview of Damage Observed to Steel Building Structures in the 1995 Kobe Earthquake,” Appendix C, in State of the Art Report on Past Performance of Steel Buildings in Earthquakes, FEMA-355E, Federal Emergency Management Agency, Washington, D.C. Osteraas, J. and Krawinkler, H. 1989. “The Mexico Earthquake of September 19, 1985, Behavior of Steel Buildings,” Earthquake Spectra, 5, 51–88. Popov, E.P. and Stephen, R.M. 1972. “Cyclic Loading of Full-Size Steel Connections,” AISI Bulletin, 21, American Iron and Steel Institute, Washington, D.C. Popov, E.P., Engelhardt, M.D, and Ricles, J.M., 1989. “Eccentrically Braced Frames: U.S. Practice,” Eng. J., 26, 66–80, American Institute of Steel Construction, Chicago. Reis, E. and Bonowitz, D. 2000. State of the Art Report on Past Performance of Steel Buildings in Earthquakes, FEMA-355E, Federal Emergency Management Agency, Washington, D.C. Roeder, C. 2000. State of the Art Report on Steel Connections, FEMA-355D, Federal Emergency Management Agency, Washington, D.C. SAC. 1996. Background Reports on Metallurgy, Fracture Mechanics, Welding Moment Connections and Frame Systems Behavior, FEMA 288, Federal Emergency Management Agency, Washington, D.C. SAC. 2000a. Recommended Seismic Design Criteria for Welded Steel Moment-Frame Structures, SAC Joint Venture, FEMA-350, Federal Emergency Management Agency, Washington, D.C. SAC. 2000b. Recommended Specifications and Quality Assurance Guidelines for Welded Steel Moment-Frame Construction for Seismic Applications, SAC Joint Venture, FEMA-353, Federal Emergency Management Agency, Washington, D.C. SAC. 2000c. Recommended Seismic Evaluation and Upgrade Criteria for Welded Steel Moment-Frame Buildings, SAC Joint Venture, FEMA-351, Federal Emergency Management Agency, Washington, D.C. SAC. 2000d. Recommended Postearthquake Inspection, Evaluation and Repair Criteria for Welded Steel Moment-Frame Buildings, SAC Joint Venture, FEMA-352, Federal Emergency Management Agency, Washington, D.C. Steinburgge, K.V., Schader, E.E., Bridgestone, H.C., and Weers, C.A. 1971. San Fernando Earthquake, February 9, 1971, Pacific Fire Rating Bureau, San Francisco, CA. USGS (U.S. Geological Survey). 1907. “The San Francisco Earthquake and Fire of April 18, 1906 and their Effects on Structures and Structural Materials,” reports by G.K. Gilbert, R.L. Humphrey, J. S. Sewell, and F. Soule, Bull. 324, Government Printing Office, Washington, D.C. Youssef, N., Bonowitz, D., and Gross, J.L. 1995. A Survey of Steel Moment Frame Buildings Affected by the 1994 Northridge Earthquake, NISTIR 5625, National Institute of Standards and Technology, Washington, D.C.
Further Reading Selected state-of-the-art reports [Reis and Bonowitz, 2000; Roeder, 2000; Frank et al., 2000] and the SAC series of reports [SAC 1996, 2000a, 2000b] are recommended for additional detail on seismic aspects of steel design and performance. AISC [1997] and Barsom and Rolfe [1999] are also recommended. © 2003 by CRC Press LLC
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Appendix A: Design Procedure for a Typical Reduced Beam Section-Type Connection Design a reduced beam section (RBS) connection at the second-floor level for the multistory (end bay) special moment-resisting frame shown in Figure A-1. The design is based upon FEMA 350 guidelines. Third Floor
Moment Connection under Consideration
W14x311
Second Floor
W21x73
W14x311
13 ft.
13 ft.
22 ft. 8 in.
FIGURE A-1 Special moment-resisting frame.
Frame dimensions Story h (above) = Story h (below) = Bay width L =
156 in. 156 in. 272 in.
htop = 67.38 in. hbot = 67.38 in. Column exterior
Section properties Beam W 21 × 73 db = 21.24 in. bf = 8.295 in. tf = 0.74 in. tw = 0.455 in. Zxb = 172 in.3 Sb = 151 in.3 Fyb = 50 ksi
© 2003 by CRC Press LLC
Column W 14 × 311 dc = 17.12 in. bcf = 16.23 in. tcf = 2.26 in. tcw = 1.41 in. Zxc = 603 in.3 Sc = 506 in.3 Fyc = 50 ksi
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Beam loads and assumed axial stresses in columns w = 0.17 k/in.
STEP 1
fa = 15 ksi
Trial values for RBS dimensions a, b, and c a = (0.5 to 0.75) bf = 4.1 in. to 6.2 in. b = (0.65 to 0.85) db = 13.8 in. to 18.1 in. c = 0.2 bf < 0.25 bf = 1.7 in. to 2.1 in.
STEP 2
a-avrg = 5.2 in. b-avrg = 15.9 in. c-avrg = 1.9 in.
Try a Try b Try c R
Plastic and section modulus at the minimum section of the RBS ZRBS = Zxb – 2.c.tf.(db – tf ) = 111 in.3 SRBS = Sb – 2.c.tf.(db – tf )2/db = 92 in.3
a
b
Column
c
Continuity plate
Panel zone
REDUCED SECTION BEAM (RSB) c
Beam
Continuity plate
STEP 3
STEP 4
tw
Beam reduced section
Expected yield stress of the beam and column Ryb = 1.1 Ryc = 1.1
Fyb = Ryb.Fyb = 55 ksi Fyc = Ryc.Fyc = 55 ksi
Probable plastic moment and at the center of the RBS Mpr = 1.15*ZRBS*Fye =7021 in.-kip
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c
tf
db
= 5 in. = 16 in. = 2 in. = 17.00 in.
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STEP 5
Shear force at the centers of the RBS at each end of the beam L′ = L – dc – 2(a + b/2) = 229 in. Vp = 2Mpr /L' + wL'/2 = 81 kips V’p = 2Mpr /L' – wL'/2 = 42 kips dc
a
b
b
a
dc
Uniform load (w)
Plastic hinge location
Plastic hinge location
L' = L-dc-2(a+b/2)
L Uniform load (w)
Mpr
Mpr
L' = L-dc-2(a+b/2) Vp = 2Mpr/L' + wL'/2
STEP 6
V'p = 2Mpr/L' - wL'/2
Maximum moment and shear force expected at the face of the column Mf = Mpr + Vp(a + b/2) + w(a + b/2)2/2 = 8088 in.-kip Vf = Vp + w.(a + b/2) = 83 kip
w
Mf
Mpr
Vp
Vf a+b/2
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Check beam flexural capacity at the face of the column Mpe = Zxb.Fye = 9460 in.-kip Mf/Mpe = 0.85
STEP 8
Beam capacity OK dimensions a, b, c
Check beam shear capacity Vn = Aw.Fy = (db.tf ).Fyb = 786 kips Vf/Vn = 0.11
STEP 8
Beam capacity OK dimensiones a, b, c
Strong column-weak beam check h = (htop + hbot +db) = Vc = [Mpr + Vp*(dc/2 + a + b/2)]/h = Vc = [2Mpr + (Vp+V’p)*(dc/2 + a + b/2)]/h = Mctop = Vc * htop = Mcbot = Vc * hbot = Mctop + Mcbot = S [Zc*(Fyc – fa)]/(Mctop + Mcbot)] =
156 in. 56 kips
average story height exterior column interior column
3787 in.-kip 3787 in.-kip 7574 in.-kip 5.57
OK
Vc
ht Mct Mpr
Mpr db Mcb V'p
Vp hb
Vc a+b/2
STEP 9
dc
a+b/2
Continuity plate requirement minimum required thickness of column flange when no continuity plates are required 0.4*sqrt(1.8*bf.tf.FybRyb/(FycRyc)) = 1.3 in. bf/6 1.4 in. continuity plates not required Recommended thickness of continuity plate (one-sided exterior connection) = thickness of beam flange Use continuity plates 3/4 thick
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STEP 10 Panel zone strength requirement Cpr = Cy = 1/(Cpr*Zbrs/Sbrs) = h = t req = Cy.Mf.(h – db)/h/(0.9*0.6Fye.dc.(db – tf )) = t wc = t doubler plates = (treq – tcw)/2 No doubler plate required
© 2003 by CRC Press LLC
1.15 0.72 156 in. 0.49 in. 1.41 in. –0.462 in.
peak connection strength coefficient average column height required thickness web thickness
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13 Reinforced Concrete Structures 13.1 Introduction 13.2 Basic Concepts Earthquake Demands · Structural Capacity · Ductile vs. Brittle Structures · Ductility · Energy Dissipation · Residual Deformation
13.3 Seismic Behavior Materials · Structures
13.4 Analytical Models Flexural Members · Structural Walls
13.5 Seismic Design Columns · Structural Walls · Design Approach · Detailing Requirements
13.6 Seismic Retrofit Columns · Buildings
Y. L. Mo University of Houston Houston, Texas
Defining Terms References Further Reading
13.1 Introduction Many aspects of the design of reinforced concrete structures to resist earthquakes apply to structures of any material or combination of materials. This chapter discusses certain aspects that may not be covered elsewhere in this book and emphasizes others that apply directly to reinforced concrete buildings and bridges. Since recent earthquakes [Seible et al., 1997; MCEER, 2000] have demonstrated repeatedly that the key elements for buildings and bridges are structural walls and columns, respectively, both structural walls and bridge columns will be the focus of this chapter.
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Great strides have been made in recent decades in the fields of earthquake engineering and structural dynamics. These advances have been made possible by increased general interest in, and support of, intensive studies of earthquake problems. This interest in turn has resulted from continuing earthquakes and resulting disasters in many parts of the world, coupled with a growing fund of knowledge and data, significant new concepts, and improved facilities with which to work, such as information technology. Some of the concepts and techniques are so new as not to be generally understood, or to be generally applied in design. Recently some have been included in building code provisions for earthquake resistance. Although there is much more to be learned in the future, if what is now known were to be generally applied in the design and construction of reinforced concrete structures, the risk associated with the future earthquake shaking for such structures would be reduced to a very low level.
13.2 Basic Concepts There are certain basic concepts that must be recognized in order, first, to understand the nature of the earthquake problem for reinforced concrete structures and, second, to properly cope with the problem in design. These have to do with the earthquake demands, the structural capacity, and the fact that reinforced concrete may be designed to be ductile and have great energy dissipation capacity prior to failure [Blume, 1970].
13.2.1 Earthquake Demands The demands of the earthquake on the structure are uncertain as to time, frequency of occurrence, and intensity. Assuming for the moment that lateral forces represent the earthquake loading, it is not the case that the design forces prescribed by seismic codes are the maximum forces to which a structure in an active seismic area may be subjected. The actual forces — so long as the structure remains elastic — may be as much as several times the code specified forces during severe earthquake demand. Whether a particular structure would ever be subjected to such great forces depends not only on its structural and dynamic characteristics, but also upon compound probabilities involving: • • • • • • •
Earthquake location relative to the structure Earthquake energy Depth of the earthquake focus Media of the source, the propagation path, and of the point of reception of the earthquake waves Duration of shaking Frequency composition of the disturbing waves Other factors
No other phase of structural loading includes such a wide variation of possible demands. Although equivalent forces long have been used for floor live loading, for wind, for train or truck loading on bridges, etc., these demands do not exceed the accepted equivalent design forces by such an amount as is possible in the earthquake problem. This leads to fundamental questions and issues such as: • What should the design basis be? • What is the probability of what loading? • What probability should be the basis for design? One simple approach is to consider the average frequency of occurrence for a specific area based upon the data available. At best, this rate-of-return method is unsatisfactory given sparse real data. Assume that a certain type and intensity of earthquake demand has occurred an average of once in 100 years, based upon a short 200-year history. This provides no real answer as to when the next demand will be — it could occur tomorrow, or several hundred years from now. There are, of course, more sophisticated © 2003 by CRC Press LLC
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approaches to the problem of risk (beyond the scope of this chapter — see Chapters 8 and 11), but they all suffer from lack of adequate data. It may be convenient to take refuge in a small probability, for example, that associated with 2 or 3 standard deviations, as being of no concern or as an “accepted risk.” It is not logical, however, to consider a once-in-50-year possibility as being of no concern during the design of a 40-year life structure — the “once” may occur in the first, or in any, year of the structure’s life. The most sensible approach is to design on some reasonable basis, to recognize the uncertain nature of the demands, and to provide all the reserve capacity that can be mobilized in a severe future emergency but at little or no extra cost in initial construction cost. Of course, unusual risks should have additional design considerations and refinements.
13.2.2 Structural Capacity If demand exceeds capacity, failure results. Although the demand — with few exceptions — is a random variable beyond the control of the designer, the mean capacity is to a large extent in his or her hands. A basic concept is that energy dissipation or structural capacity is a more meaningful measure of earthquake capacity for most structures than strength alone. It is to be noted, however, that in the elastic or linear range of structural response, energy capacity is proportional to the applied force. The problem is that the code lateral forces may be exceeded during actual earthquakes and the unit deformations associated with the yield point — or its equivalent — may be greatly exceeded. The performance of the structure in such cases depends upon its properties beyond the initial yield point. If there is no ductility and if there is no alternate stress path, the structure collapses under continued earthquake demands of similar or greater amount. On the other hand, ductility and reserve inelastic energy capacity and/or alternate and stronger stress paths may be available and may save the structure. Although seismic codes specify lateral forces rather than energy capacity, some attempts have been made to allow for the value of ductility and to include the parameter of deformation as well as strength. More extensive procedures are available to more rationally provide for energy capacity. It can be demonstrated that earthquake response depends upon the natural periods and damping of structures, as well as the frequency content and time history of the earthquake motion. In the short period portion of a spectral response diagram, acceleration is the most meaningful criterion. In the long period portion, displacement is most meaningful. In the remaining portion — and generally the most significant band for most building natural periods — velocity is the most significant index. Of course, acceleration or displacement can be converted to velocity at any frequency with the generally justified assumption of harmonic response motion. Since kinetic energy (demand) is related to the square of velocity, it follows that energy capacity is a most meaningful parameter for buildings.
13.2.3 Ductile vs. Brittle Structures The most important point in this chapter is that reinforced concrete structures may be essentially brittle or they may have great inelastic energy capacity, depending upon the amount and the disposition of the reinforcing steel relative to the concrete sections. New design procedures are required to ensure ductility and energy dissipation, the importance of which can be inferred from the uncertainty of the earthquake demand previously discussed. Because of the significance of ductility, and some confusion as to terms and procedures, ductile concrete is so designed as to ensure that in flexural members shear failure and compression failure in the concrete cannot occur prior to stretching of the tensile bars, and in compression members shear failure cannot occur and any concrete that fails in compression will be confined. Any other concrete may or may not be subject to failure as described for ductile concrete, depending upon several conditions not checked or controlled in the design process. The capacity of a structure, based upon the ability to dissipate earthquake energy rather than on strength alone, is vastly increased with ductile concrete as compared to a brittle material. Figure 13.1 indicates the relative energy capacities of two hypothetical elements or structures, each with the same yield point strength. The area under the curves to δµb and to δµd , respectively, represents energy capacity, © 2003 by CRC Press LLC
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Earthquake Engineering Handbook
Force
Ductile behavior
δµd
Brittle failure, δµb Deformation FIGURE 13.1 Brittle vs. ductile behavior.
which is obviously much greater — along with the probability of survival in a strong earthquake — for the ductile element.
13.2.4 Ductility It is convenient to define ultimate ductility µu as the ratio of the maximum deformation prior to failure to the deformation at initial yield. Although this term is generally used in connection with elastoplastic behavior, it can be applied to any inelastic behavior pattern if failure deformation is defined as that deformation beyond which the slope of the force-deformation plot remains negative. Ductility µ may be considered as demand ductility or the ratio of the required deformation under any demand i to that at the yield point. Thus: µu =
δu δy
(13.1)
µi =
δi δy
(13.2)
where δy is the yield point deformation; δu is the deformation beyond which point the slope of the forcedeformation curve is always negative; δi is the deformation under condition or trial i; and µi, µu are ductility factors as defined above. It is important to note that the maximum deformation δu may be established by direct stress, secondary stress, buckling, local failure, or by whatever condition or combination of conditions — for the particular element or structure under consideration — leads to the minimum value of δu. Where there is indeterminacy or there are multiple stress paths in a structure or element such as a building story, there may be local failure at one or several points, but the overall force-deformation characteristic may not be at the initial yield. Of course, the element or overall δu is established at whatever point an overall failure mechanism first develops as defined above. Ductility also may be measured in rotational units, such as the ratio of ultimate member curvature to curvature at yield. More recently, using the concepts of performance-based design [Fajfar and Krawinkler, 1998; Krawinkler, 1998], the Federal Emergency Management Agency [FEMA 2000a, 2000b] has set the acceptance criteria by relating the ductility (or drift) to the residual strength ratio.
13.2.5 Energy Dissipation Ductility alone is not adequate for energy reconciliation. There could be a large value of µ associated with a small force, and the area under the curve would be inadequate. At the other extreme, a very great force could develop sufficient energy in the elastic range or at a value of µ between 0 and 1. In most
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buildings, however, µu should greatly exceed 1 under normal code design conditions in order that the structure is able to mobilize adequate energy capacity in the event of a severe earthquake. The reserve energy technique discussed subsequently provides for both energy and force development under seismic code conditions and normal design terminology. Earlier, a great many laboratory tests of materials, members, and of assemblies of members were not extended into the inelastic range of deformation. Thus, there is a wealth of data on ultimate loads and yield point unit stresses but a relatively small amount on µu and inelastic energy capacity. It is only in recent years that the inelastic range has been of interest to engineers as a means of reconciling earthquake performance with structural characteristics. A compilation of references on inelastic test data on various materials has been developed. An intensive study of the inelastic behavior of reinforced concrete members and of means of providing ductility and energy dissipation capacity has been reported. Considerable testing has been done in the inelastic behavior of reinforced concrete members, joints, and assemblies. It has been clearly shown that reinforced concrete can be designed to have ductile characteristics, and the seismic design codes, such as the International Building Code [2000] require ductility for tall, and certain other, buildings.
13.2.6 Residual Deformation After the 1995 Kobe earthquake, it was found that many bridges and buildings did not collapse, but could not be used anymore because their residual deformations were too large [Watanabe et al., 1995; Watanabe and Nishiyama, 2001; Iemura and Takahashi, 2001]. As mentioned above, the key of ductility-based seismic design is to provide energy dissipation capacity (inelastic rotational capacity) to potential plastic hinges in beams, columns, and walls. The hinge ductility results in larger material damage and may impose considerable residual deformation or displacement on structures after earthquakes. If continuous use of the structure is expected without costly repairing work, the residual deformation or displacement is required to be a small acceptable value. Two practical methods have been successfully implemented in Japan to reduce residual deformation of structural members while providing them with adequate energy dissipation during earthquakes. One is the combined use of high strength and ordinary strength rebars in a reinforced concrete column [Watanabe et al., 1995; Iemura and Takahashi, 2001]. The other is graded composite strand, which consists of high strength wires (with yield strength around 2000 Mpa, or 290 ksi) and ordinary strength wires (yield strength around 400 Mpa or 60 ksi) for prestressed concrete members [Watanabe and Nishiyama, 2001]. In these systems ordinary strength steel provides energy dissipation due to its inelastic response and high strength steel acts as an elastic spring to reduce residual deformation or displacement. It is clear that the seismic design requirements in future codes will set an acceptable value for the residual deformation, in addition to the ductility and dissipated energy.
13.3 Seismic Behavior 13.3.1 Materials The evaluation of the nonlinear hysteretic response of reinforced concrete structures under cyclic excitations and, in particular, severe earthquake excitations, necessitates the development of accurate and computationally efficient models of components and constituent materials. While component models might suffice for the determination of global parameters of structural response, constitutive material models become necessary in the local response evaluation and damage assessment of existing and new structures. The development of an accurate and computationally efficient model for concrete and steel is, therefore, an important task in the nonlinear response evaluation of these structures by finite element methods [Balan et al., 1998].
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fs (stress) E 1s original (εy , f y ) Softened branch to simulate stress reversal
εs (strain) FIGURE 13.2 Softened branch.
fs (stress) Tensile Test Maximum strength
fsu fsr
Low-Cycle Fatigue
εy
3εy ~5εy
0.7εsu
εsu
εsr
εs (strain)
FIGURE 13.3 Low-cycle fatigue.
13.3.1.1 Steel When a rebar is subjected to cyclic loading, it was found by Mander [1983] that the reversal branch of the steel stress-strain relationship in each hysteretic loop is a parabolic curve. This phenomenon is called the softened branch relation, as shown in Figure 13.2. To describe the softened branch relation of a rebar, the model suggested by Mander [1983] can be employed. In addition, when a rebar is subjected to cyclic loading, the maximum strength is less than the maximum strength of monotonic tensile tests. This phenomenon is called low-cycle fatigue. According to the studies performed by Mander et al. [1994] and Monti et al. [1992], the strain corresponding to the maximum stress in the condition of low-cycle fatigue is about three to five times the yield strain, and the ultimate strain and stress are about 70% of that obtained in tensile tests. Figure 13.3 indicates the curve of low-cycle fatigue that is basically dependent on buckling length of a rebar. Therefore, the center-to-center spacing between lateral reinforcements should not exceed six longitudinal bar diameters in concrete members [Mander et al., 1994]. This concept can also be employed in the stress-strain relationship of longitudinal rebars in the analytical model. 13.3.1.1.1 Cyclic Constitutive Relationships The average cyclic stress-strain relationship of steel bars in concrete is shown by the solid curves in Figure 13.4 [Mansour, 2001]. This figure also includes the monotonic stress-strain relationship of bare steel bar, as shown by the dotted lines. It can be observed from Figure 13.4 that the cyclic stress-strain © 2003 by CRC Press LLC
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Reinforced Concrete Structures
(fs )
Steel Stress
Bare steel bar Steel bar in concrete
fy Stage 2T
fn
(ε i , f i )
Stage 4
εn ε y
εu
Steel Strain (ε s )
εp Stage
3
(ε i +1, f i+1)
Stage 2C
FIGURE 13.4 Average cyclic stress-strain curves of steel bars in concrete.
relationship for a steel bar embedded in concrete is expressed by two groups of curves: the first group is the monotonic loading curve [Belarbi and Hsu, 1994], which includes stage 1 before the yielding of steel bar, stage 2T after the yielding of steel bar in tension, and stage 2C after the yielding of steel bar in compression. The second group is the unloading and reloading curves, which include stage 3 for unloading and stage 4 for reloading. 13.3.1.2 Concrete 13.3.1.2.1 Flexural Members In practice, concrete may be confined by transverse reinforcement, commonly in the form of closely spaced steel spirals or hoops. In this case, at low levels of stress in the concrete, the transverse reinforcement is hardly stressed; hence, the concrete is unconfined. The concrete becomes confined when at stresses approaching the uniaxial strength, the transverse strains become very high because of progressive internal cracking and the concrete expands outward against the transverse reinforcement, which then applies a confining reaction to the concrete. Thus, the transverse reinforcement provides passive confinement. Tests by many investigators have shown that confinement by transverse reinforcement can considerably improve the stress-strain characteristics of concrete at high strains, as shown in Figure 13.5. The increase in strength and ductility with content of confining steel is very significant. Tests have demonstrated that circular spirals confine concrete much more effectively than rectangular or square hoops. The effect of the different transverse steel on the ductility is quite appreciable, but the effect on strength is much smaller [Park and Paulay, 1975]. 13.3.1.2.2 Cyclic Constitutive Relationships The monotonic loading stress-strain curve is assumed to form an envelope to the cyclic loading stressstrain response. That is, the monotonic curve is assumed to be the skeleton curve. This was found to be the case in two studies by Sinha et al. [1964] and Karsan and Jirsa [1969] for tests on unconfined (plain) concrete specimens. The test results for confined concrete by Mander et al. [1983] show that this assumption is also reasonable for reinforced concrete specimens. © 2003 by CRC Press LLC
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Compressive Stress, fc
Confined concrete
f cc'
First hoop fracture
f co'
Unconfined concrete Assumed for cover concrete
Ec
Esec
ε co
εt ft '
2ε co ε sp
ε cc
ε cu
Compressive Strain, ε c
FIGURE 13.5 Stress-strain model proposed for monotonic loading of confined and unconfined concrete.
(ε un, f un )
fc
Eu
εa
Ec ε pl
εc
FIGURE 13.6 Stress-strain curves for unloading branch and determination of plastic strain εpl from common strain εa.
Unloading of the concrete may occur from either the compressive or tensile portion of the skeleton stress-strain curve as described below [Mander et al., 1988a; 1988b]. Figure 13.6 shows a stress-strain curve including an unloading branch. To establish a reversal stressstrain curve from the compressive loading curve, a plastic strain εpl based on the coordinate at the reversal point (εun, fun) on unloading needs to be determined. The procedure adopted here is similar to the approach used by Takiguchi et al. [1976] but modified so that it is suitable for both unconfined and confined concrete. The plastic strain εpl lies on the unloading secant slope, as shown in Figure 13.6, which in turn is dependent on the given strain εa at the intersection of the initial tangent and the plastic unloading secant slopes. Figure 13.7 shows the stress-strain curves including unloading and reloading branches. The coordinates of the point of reloading (εro, fro) may be from either the unloading curve or from the cracked state in © 2003 by CRC Press LLC
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Reinforced Concrete Structures
(ε un , f un ) (ε , f ) re re
fc
(ε un , f new )
(ε ro , ε pl
f ro
) εc
FIGURE 13.7 Stress-strain curves for reloading branch.
which εro = (εpl − εt) and fro = 0, as shown in Figure 13.7. A linear stress-strain relation is assumed between εro and εun to a revised stress magnitude to account for cyclic degradation. 13.3.1.2.3 Shear Elements The cyclic stress-strain curves of concrete in a shear element are shown in Figure 13.8 [Mansour, 2001]. Two groups of curves are identified: the monotonic loading curves that made up the envelopes and the unloading and reloading curves that are required specifically for reversed cyclic loading. 1. Monotonic loading envelopes (C1, C2, T1, and T2) • Monotonic compressive stress-strain envelope. As pointed out by Mansour et al. [2001], the envelope curve for the compressive cyclic stress-strain curves of concrete can be expressed by the monotonic compressive stress-strain curve of concrete proposed by Belarbi and Hsu [1995]. • Monotonic tensile stress-strain envelope. The envelope curve for the tensile cyclic stress-strain curves of concrete can be expressed by the monotonic tensile stress-stain curve of concrete proposed by Belarbi and Hsu [1995]. 2. Unloading and reloading curves • Refer to Figure 13.8 and let us start the cyclic load in tension. As long as the tensile stress is less than the cracking stress at point TA (fcr) the response is elastic. The loading and unloading behavior follow the straight line T1. If the load is reversed from tension to compression before cracking, the compressive response follows the dotted line with a slope equal to the initial modulus of concrete Ec. Once the cracking stress of concrete at point TA is exceeded, the tensile response follows a concave curve T2. As the load is reversed from the tensile direction to the compressive direction at point TB, there is initially a region that represents the closure of the cracks (stage T3) up to point TC. As the crack continues to close, the second region, stage T4, will be stiffer. This stage T4 represents the increase in concrete stiffness before the complete closing of the crack. Stage T4 ends at point TD where the stress is taken to be a function of the maximum tensile stress attained at point TB. As the load progresses in the compression region, the first compressive virgin loading, after cracking, follows the envelope compression curves, stage C1 and stage C2. As the load is reversed at point CB from the compressive direction to the tensile direction, the response follows two straight lines, stage C3 and stage C4, with slopes of 80% and 20%, respectively, of the initial modulus of elasticity of concrete, Ec . A straight line is also assumed in stage C5, when the strain continues to increase in the positive direction from point CD to point TB. If in stage C5 the direction of loading is reversed at point CE, the compressive reloading response will follow stage C6 up to point CF. The slope of stage C6 was chosen to decrease as the horizontal distance between point CC and point CE increases. © 2003 by CRC Press LLC
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Tensile stress TA T2 TB
Compressive strain
CD'
C5'
CE
T3 Ec
T3'
Tensile strain
TC'
T4'
TD'
CC' CF
CC C7
CF C3'
TC T4 TD
C6
C4
TB'
CD C5
C4'
T1
C6'
CA: (εo ,ζfc' )
CF'
' CB: (εcC2 , fcC 2)
C7' C1
C3
' ' ' ' CC: (εcC2 − εcC 2 ,0.2 fcC2 );εcC2 = fcC2 / Ec ' CD: (εcC2 − 2εcC 2 ,0) ' CE: (εcC5 , fcC 5)
C7'
' ' CF : ((2(εcC2 − εcC 2 ) + εcC5 ) / 3,0.2 fc );εcC5 ≤ 0 ' CG: (0.98εcC2 ,0.85 fcC 2)
TA: (εcr , fcr )
CG' C2
Not to Scale
TB: (εcT2 , fcT' 2 )
CG
TC : (εcT2 / 3,−0.2 fcr )
CB'
TD: (0, −1.5fcr + 0.8 fcT2 ) '
CB CA
Compressive stress
FIGURE 13.8 Mansour and Hsu model for smeared cyclic stress-strain curves of concrete.
13.3.2 Structures 13.3.2.1 Columns Several prototypes of rectangular hollow bridge piers were tested under a constant axial force of approximately 0.08 fc'Ag and a cyclically reversed horizontal load at the National Center for Research on Earthquake Engineering [Yeh et al., 2001, 2002]. Two specimens are reported here. The column and foundation of each of the specimens were designed according to the American Concrete Institute (ACI) seismic provisions [ACI Committee 318, 1995]. Figure 13.9 indicates the dimensions of the cross section of the two specimens. Note that this configuration of lateral reinforcement currently is being used in bridge design in Taiwan. The cross section of each of the prototypes is 1.5 m × 1.5 m. The wall thickness of the specimens is 300 mm. The moment arms (distance between the horizontal loading point and the top of the reinforced concrete foundation) are 6.5 m and 3.5 m. The spacing of the confining reinforcement in specimen PS1 satisfies both the design requirements of the ACI code [1995], and the requirements suggested by Priestley et al. [1996], in which the spacing needs to be less than six times the diameter of longitudinal rebars. For specimen PS1, the shear reinforcement provided is more than that required by the ACI code to avoid shear failure. For specimen PI2, the provided shear reinforcement is only approximately 20% of that required by the ACI code. The material properties of the two specimens are fc' = 34 Mpa (5 ksi) for PS1 and 32 MPa (4.6 ksi) for PI2, as well as fy = 460 MPa (67 ksi) for PS1 and 418MPa (60 ksi) for PI2.
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1500 1385 a b
64-#7
150
150
900 900
1500
a
170
170
b a
#4@80
30 0
115
(a) Specimen PS1
115
66 168 132 168 132 168 132 168 132 168
1410
1500 a b
a
12 5
64-#7
10 0
100
#3@200
66 168 132 168 132 168 132 168 132 168
(b) Specimen PI2
10 0 i
j
210
900
1500
12 5
b a
900
30 0
205
j
i
12 5
FIGURE 13.9 Dimensions of cross sections of specimens PS1 and PI2 (unit: mm).
According to the ACI requirements [1995], specimen PS1 has sufficient shear reinforcement, while specimen PI2 has insufficient shear reinforcement. Specimen PS1 developed displacement ductility of 10.8. The ultimate performance for specimen PS1 was dominated by the load-carrying capacity due to the rupture of tensile longitudinal rebars at the bottom of the piers, as shown in Figure 13.10a. The rupture of tensile longitudinal rebars followed after the steel buckling at the compression cycles. This rupture mode is a typical low-cycle fatigue, which can be improved with the small spacing of the transverse reinforcement. Specimen PI2 was provided with extremely insufficient shear reinforcement when compared to the ACI code [1995]. Therefore, the shear failure occurred at a displacement ductility of 3.7. Although some longitudinal rebars buckled in the loading stage close to the failure, no rupture of tensile longitudinal rebars happened, as shown in Figure 13.10b. 13.3.2.2 Shear Elements Fifteen reinforced concrete membrane elements were subjected to reversed cyclic shear using the Universal Panel Tester at the University of Houston [Mansour, 2001]. The test results of only two panels, CA3 and CE3, are reported here. The dimensions and the steel grid orientation of panels CA3 and CE3 are shown in Figure 13.11. The thickness of a typical membrane element was 178 mm (7 in.). Both specimens were reinforced with equal percentage of reinforcement in the longitudinal direction (l) and transverse direction (t), respectively. The steel percentage for panel CA3 was 1.7%, while the steel percentage of panel CE3 was 1.2%. The material properties of the two panels are fc' = 46 MPa (6.6 ksi) for CA3 and 50 MPa (7.3 ksi) for CE3, εo = 0.0024, fy = 425 Mpa (62 ksi). The test results of panels CA3 and CE3 are shown in Figure 13.12a and Figure 13.12b, respectively. The x axis and the y axis in these figures represent the shear strain and shear stress, respectively. It can be seen that the robust hysteretic loops of panel CE3 cycle without any trace of pinching. The load-deformation response of R/C membrane elements (panels) subjected to reversed cyclic shear showed that the orientation of the steel bars with respect to the principal coordinate of the applied stresses has a strong effect on the pinching effect in the post-yield hysteretic loops. When the steel bars were oriented in the directions of the applied principal stresses, there was no pinching effect. When the steel bars were oriented at an angle of 45° to the applied principal stresses, there was a severe pinching effect. It was obvious that the pinching effect is caused by the orientation of the steel bars, rather than the bond slips between the steel bars and the concrete as surmised by many researchers. © 2003 by CRC Press LLC
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-7
-6
-5
-4
-3
-2
Drift Ratio(%) -1 0 1
2
3
4
5
6
7
4000 3000 µ=1
µ=3
µ=5
µ=7
µ=10
2000
Force(kN)
1000 0 -1000
concrete cracking yielding of long. bar concrete crushing concrete spalling rupture of long. bar
-2000 -3000 -4000 -500
-400
-300
-200
-100
0
100
200
300
400
500
Displacement(mm)
(a) Specimen PS1 -14 -12
-10
-8
-6
-4
4000
Drift Ratio(%) 0 -2 2
4
6
8
10
12
14
µ=2 µ=1 µ=4
3000
Force(kN)
2000 1000 0 -1000 concrete cracking
-2000
yielding of long. bar concrete crushing
-3000
shear failure
-4000 -500
-400
-300
-200
-100 0 100 Displacement(mm)
200
300
400
500
(b) Specimen PI2
FIGURE 13.10 Hysteretic loops of specimens: (a) PS1 and (b) PI2.
13.4 Analytical Models 13.4.1 Flexural Members 13.4.1.1 Constitutive Laws of Materials 13.4.1.1.1 Concrete A number of constitutive laws of confined concrete have been proposed over the past three decades. In this chapter, nine constitutive models for normal strength concrete and four constitutive models for highstrength concrete are discussed. Excepting the unconfined model, all models can reasonably predict the behavior of flexural members. 1. Unconfined Kent and Park model [Kent and Park, 1971] did not consider confinement of concrete. 2. Confined Kent and Park model [Kent and Park, 1971] supposed the confined concrete reached its maximum strength and maintained its residual strength 0.2 fc' at large strain.
© 2003 by CRC Press LLC
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Reinforced Concrete Structures
V
l V
H
165 267
267
267
l
t
1398 mm
267
σH
165 267 267
a) Panel CA3 α 2 = 45°
σV 267 165
t
α 2 = 45°
H
267 165
1398 mm V
σV
b) Panel CE3 α 2 = 90°
165 267 267 267 267 165
t
σH H
165
267
267
267
267
t
V
l H
α 2 = 90°
l
165
FIGURE 13.11 Steel layout and dimensions of test specimens CA3 and CE3.
3. Modified Kent and Park model [Park et al., 1982] was modified to let the confined concrete increase its initial stiffness. 4. Muguruma et al. [1978a, 1978b] model was similar to the Confined Kent and Park model with different stress-strain curve shape except for an ultimate confined concrete strain. 5. Sheikh and Uzumeri [1980, 1982] model was similar to the Modified Kent and Park model except for a flat ultimate strength within a strain range. The parameters of the Sheikh and Uzumeri model were affected by the effectively confined core area, which was based on tests of square specimens. 6. Mander et al. [1988a, 1988b] model used confining pressure to affect the shape of the stress-strain curve. The confining pressure was affected by the effectively confined core area, which was based on tests of rectangular specimens. 7. Fujii et al. [1988] model was similar to the Muguruma et al. model, but had different control parameters. 8. Saatcioglu and Razvi [1992] model seemed to modify the Modified Kent and Park model with effective confining pressures of both directions of the rectangular cross section. 9. Hoshikuma et al. [1997] model did not use the concept of the effectively confined core area and had residual strength 0.5 fc' at large strain. 10. Sheikh el al. [1994] model was established by testing 120 standard cylindrical specimens made of high strength concrete, and did not incorporate confinement effect. 11. Diniz et al. [1997] proposed a model for high strength concrete using reliability assessment. 12. Cusson and Paultre [1995] refined the concept of confinement index [Park et al., 1982; Muguruma et al., 1978b; Saatcioglu et al., 1992] and proposed the so-called effective confinement index, and established their stress-strain model accordingly. 13. Modified Razvi and Saatcioglu [1999] model basically modified the descending branch of Saatcioglu and Razvi [1992] model.
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Earthquake Engineering Handbook
8.0
CA 3 6.0
Shear Stress (MPa)
α2 = 45°; ρ l = ρt = 1.7%
4.0 2.0 0.0
-0.025 -0.020 -0.015 -0.010 -0.005 0.000
0.005
0.010
0.015
0.020
0.025
0.030
-2.0 -4.0 -6.0 -8.0
Shear Strain 8.0 6.0
Shear Stress (MPa)
CE 3
4.0
α 2 = 90°; ρl = ρ t = 1.2%
2.0
-0.025
-0.020
-0.015
-0.010
-0.005
0.0 0.000
0.005
0.010
0.015
0.020
0.025
-2.0 -4.0 -6.0 -8.0
Shear Strain
FIGURE 13.12 Experimental shear stress-strain curves of panels CA3 and CE3.
13.4.1.1.2 Reinforcing Steel A typical monotonic (tensile) stress-strain curve of reinforcing steel consists of three segments, namely, elastic linear branch, yielding plateau, and strain hardening branch. When reversed (tension-compression) axial loading is applied, however, the well-known Bauschinger effect emerges and the stress-strain curve becomes nonlinear at a stress lower than the initial yield strength [Park and Paulay, 1975]. The softened branch relation proposed by Mander [1983] to describe the Bauschinger effect on the reversed stress-strain behavior can be used. In addition, the buckling effect of rebars (also called low-cycle fatigue) is a phenomenon that has been identified experimentally and theoretically [Monti and Nuti, 1992; Mander et al., 1994; and Rodriguez et al., 1999]. As the slenderness ratio of rebars becomes larger, which is usually the case for reduced-scale model tests, this effect gets more prominent and cannot be ignored. Therefore, the effect of low-cycle fatigue can be taken into account in the analytical model by using a reduction factor according to the tests of Mander et al. [1994]. 13.4.1.2 Moment-Curvature Analysis Based on the equilibrium of internal forces of the cross section, and the assumption of the linear distribution of normal strain (plane section remains plane after bending), the section characteristics are determined by conventional moment-curvature analysis for RC members, iteratively. Through this © 2003 by CRC Press LLC
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Reinforced Concrete Structures
L A
A
ϕcr
FIGURE 13.13 Illustration of curvature diagram (cracking state).
L1
L2
A
A
A3 ϕcr ϕy
L3
FIGURE 13.14 Illustration of curvature diagram (yielding state).
analysis, such sectional parameters as the cracking state (Mcr , ϕcr ), yielding state (My , ϕy), and ultimate state (Mu , ϕu) are obtained in the ascending branch, and a trilinear idealization [Mo, 1994] can be made for the moment-curvature for the section. 13.4.1.3 Load-Displacement Relationship The entire load-displacement relationship can be divided into two parts, namely, ascending and descending branches, and can be determined by the moment-area method as shown below. 13.4.1.3.1 Ascending Branch 1. Cracking state (Figure 13.13): θcr =
M cr L 2EI
(13.3)
M L2 1 δ cr = θcr × L − × L × θcr = cr 3 3EI
(13.4)
where Mcr = crack moment EI = flexural rigidity of section θcr = rotation angle at cracking δcr = lateral displacement at cracking 2. Yielding state (Figure 13.14): θy =
(
)
1 1 × L × ϕ cr + ϕ cr + ϕ y × L2 2 1 2
(
(13.5)
)
2 1 1 × L × × L × ϕ cr + L3 × × ϕ cr + ϕ y × L2 3 1 2 1 2 1 1 2 = × ϕ cr × L1 + × ϕ cr + ϕ y × L2 × L3 3 2
δy =
(
© 2003 by CRC Press LLC
)
(13.6)
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Earthquake Engineering Handbook
L4
L2
L1
A
A1
A3 ϕcr
A5
ϕy
L3
ϕu
L5
FIGURE 13.15 Illustration of curvature diagram (ultimate state).
where θy = rotation angle at yielding δy = lateral displacement at yielding L3 = distance from centroid of area A3 to end A 3. Ultimate state (Figure 13.15):
(
)
(
)
(
)
1 1 1 × L1 × ϕ cr + × ϕ cr + ϕ y × L2 + × ϕ y + ϕ u × L4 2 2 2 1 1 2 = × ϕ cr × L1 + × ϕ cr + ϕ y × L2 × L3 3 2
θu =
(
)
(
(13.7)
)
1 1 1 2 × L × × L × ϕ cr + L3 × × ϕ cr + ϕ y × L2 + L5 × × ϕ y + ϕ u × L4 3 1 2 1 2 2 1 1 1 2 = × ϕ cr × L1 + × ϕ cr + ϕ y × L2 × L3 + × ϕ y + ϕ u × L4 × L5 3 2 2
δu =
(
where θu δu L3 L5
)
(
)
(13.8)
= rotation at ultimate state = lateral displacement at ultimate state = distance from centroid of area A3 to end A = distance from centroid of area A5 to end A
13.4.1.3.2. Descending Branch As illustrated in Figure 13.16, the curvature in the descending branch can be expressed as: ϕ = ϕm − ϕe + ϕr
(13.9)
where φ φm φe φr
= curvature in the descending branch = curvature corresponding to the maximum moment Mm = elastic restoration curvature = reloading curvature
Figure 13.17a indicates the elastic restoration curvature diagram of a column. The yielding curvature ϕy and the yielding moment My correspond to the first yielding of longitudinal bars. The elastic flexural rigidity (EI)e is the secant modulus at My . ϕcr and Mcr are the curvature and moment at the crack state, respectively. At the maximum moment state, the column length L can be divided to three regions L1, L2, and plastic hinge length Lp .
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Reinforced Concrete Structures
Moment
Mm M My Mcr
(EI)e
(EI)r
ϕcr ϕy
ϕeϕy
ϕ
ϕm
Curvature
ϕr
FIGURE 13.16 Moment-curvature curve for descending branch. Lp
L2
L1 Top point ϕcr
Mm/L(EI)e
ϕy
ϕe
(a) Elastic restoration curvature
Lp
L2
L1 Top point ϕcr*M/Mm
M/L(EI)e
ϕy*M/Mm ϕr
M/L(EI)e M/L(EI)r
(b) Reloading curvature
FIGURE 13.17 Curvature diagram for descending branch.
It is assumed that the reloading curvature diagram of a column is indicated in Figure 13.17b. Note that the reloading curvature distribution in the plastic hinge region is assumed to be a third-order polynomial, which can be determined by using the four boundary conditions (i.e., at the yielding point, the curvature is ϕy M/Mm and the slope of the curvature is M/L(EI)e; at the end point, the curvature is ϕr and the slope of the curvature is M/L(EI)r . (EI)r is the flexural reloading rigidity as shown in Figure 13.16. With the analytical model, the moment-curvature diagram of the bottom section of a column can be obtained. From this moment-curvature diagram, the distribution of curvature in a column can be obtained with the various loads at the top of a column. The corresponding displacement at the top of a column was calculated according to the curvature diagram of the entire column. Then the load-displacement relationship of this column can be established. © 2003 by CRC Press LLC
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Earthquake Engineering Handbook
4000
Force(kN)
3000
2000
Tests
1000
ACI UCSD UCB 0 0
1
2
3
4
5
Ductility FIGURE 13.18 Shear force-ductility relationship of specimen PI2.
13.4.1.4 Shear Capacity Five approaches to estimate the shear capacity are found: • • • • •
ACI 318 [1995] Code Provisions UCB model [Aschheim et al., 1992] UCSD equations [Priestley et al., 1993a, 1993b, 1994] Caltrans model [Caltrans, 1995] USC model [Xiao et al., 1998]
Note that the USC model is a modification of the UCSD equations, in which the k coefficient is modified to suit for high strength concrete. Hence, the USC model can be used for high strength concrete specimens only. The predicted results by the ACI 318 [1995], UCB model [Aschbeim et al., 1992], and UCSD model [Priestley et al., 1993a, 1993b, 1994] are compared with the experimental data of specimen PI2, as shown in Figure 13.18. Except for the ACI 318 [1995] approach, it is recognized that the shear capacity varies with the displacement ductility factor, so that the shear capacity can be calculated point by point along the loadingdisplacement curve.
13.4.2 Structural Walls Structural walls in a frame building should be so proportioned that they possess the stiffness needed to reduce the relative interstory distortions caused by seismic-induced motions. Such walls are termed structural (or shear) walls. Their additional function is to reduce the possibility of damage to the nonstructural elements that most buildings contain. Buildings stiffened by structural walls are considerably more effective than rigid frame buildings with regard to damage control, overall safety, and integrity of the structure. This performance is due to the fact that structural walls are considerably stiffer than regular frame elements and thus can respond to or absorb greater lateral forces induced by the earthquake motions, while controlling interstory drift. The past three decades have seen a rapid development of knowledge regarding shear in reinforced concrete. Various rational models have been proposed that are based on the smeared-crack concept and
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Reinforced Concrete Structures
σ(+) t
τ(+) tl
t
σ(+)
σd(+) τ(+) lt
l
l
τ(+) lt
(+) τdr t
σ(+)
σt(+)
(a) Stationary t − l axes and stresses using basic sign convention (α = 0)
σ(+) r t
α
sinα
l σ(+) r
τ(+) rd
r
d
r
d
l
τ(+) tl
(+) τrd
(+) τdr
(b) Rotating r − d axes (rotate counterclockwise by any angle α )
cosα 1
σd(+)
−sinα
α 1
l −cosα
(c) Transformation geometry
FIGURE 13.19 Transformation of stresses.
can satisfy Navier’s three principles of mechanics of materials (i.e., stress equilibrium, strain compatibility, and constitutive laws of materials). These rational or mechanics-based models on the “smeared-crack level” (in contrast to the “discrete-crack level” or “local level”) include the compression field theory [Vecchio and Collins, 1981], the rotating-angle softened truss model [Belarbi and Hsu, 1994, 1995; Pang and Hsu, 1995], the fixed-angle softened truss model [Pang and Hsu, 1996; Hsu and Zhang, 1997; and Zhang and Hsu, 1998], the softened membrane model [Hsu and Zhu, 1999; Zhu, 2000], and the cyclic softened membrane model [Mansour et al., 2001a, 2001b; Mansour, 2001]. Vecchio and Collins [1981] proposed the earliest rational theory, compression field theory (CFT), to predict the nonlinear behavior of cracked reinforced concrete membrane elements. However, the CFT was unable to take into account the tension stiffening of the concrete in the prediction of deformations because the tensile stress of concrete was assumed to be zero. The rotating-angle softened-truss model (RA-STM), a rational theory developed at the University of Houston (UH) from 1994 to 1995, had two improvements over the CFT: (1) the tensile stress of concrete was taken into account so that the deformations could be correctly predicted, and (2) the average stressstrain curve of steel bars embedded in concrete was derived at the smeared crack level so that it could be correctly used in the equilibrium and compatibility equations, which are based on continuous materials. By 1996 the UH group reported the fixed-angle softened-truss model (FA-STM) that is capable of predicting the concrete contribution (Vc) by assuming the cracks to be oriented at the fixed angle. Recently, Zhu et al. [2001] derived a rational shear modulus and produced a solution algorithm of FASTM that is as simple as that of RA-STM. Another significant advancement is the improvements on the softened truss models (rotating-angle and fixed-angle). As they were, these models could predict the ascending response curves of shear panels, but not the post-peak descending curves. By incorporating two new Hsu/Zhu ratios into the FA-STM, a new softened membrane model (SMM) was established [Hsu and Zhu, 1999; Zhu, 2000], which can satisfactorily predict entire response curves, including both the ascending and the descending branches. More recently, 15 reinforced concrete panels under reversed cyclic stresses were tested by Mansour et al. [2001a]. Test results showed that the orientation of the steel grid in a panel has an important effect on the shear stiffness, the shape of the hysteretic loops, the shear ductility, and the energy dissipation capacity of the panel. The cyclic softened membrane model proposed by Mansour et al. [2001a] is able to predict rationally the pinching effect in the hysteretic loops, the shear ductility, and the energy dissipation capacity of the panels. In this chapter, only the RA-STM will be introduced, as described below.
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13.4.2.1 Principle of Transformation The stresses in a membrane element are best analyzed by the principle of stress transformation [Hsu, 1993]. Figure 13.19a shows a concrete element in the stationary l − t coordinate system, defined by the directions of the longitudinal and transverse steel. To find the three stress components in various directions, a rotating d − r coordinate system is introduced in Figure 13.19b. The d − r axes have been rotated counterclockwise by an angle of α with respect to the stationary l − t axes. The three stress components in this rotating coordinate system are σd , σr , and τdr (or τrd). The relationship between the rotating stress components, σd , σr , and τdr and the stationary stress components, σl, σt, and τlt is the stress transformation. This relationship is a function of the angle α. The relationship between the rotating d − r axes and the stationary l − t axes is shown by the transformation geometry in Figure 13.19c. A positive unit length on the l axis will have projections of cos α and −sin α on the d and r axes, respectively. A positive unit length on the t axis should give projections of sin α and cos α. Hence, the rotation matrix [R] is: cos α
sin α cos α
[R] = − sin α
(13.10)
The relationship between the stresses in the l − t coordinate [σlt] and the stresses in the d – r coordinate [σdr] is:
[σ ] = [ R ] [σ ] [ R ] T
lt
dr
(13.11)
where σ l
[σ ] = τ lt
tl
σd
[σ ] = τ dr
rd
τ lt σt
(13.12)
τ dr σr
(13.13)
If the d − r axes are defined as the principal axes, τdr must vanish. Introducing the reinforced concrete sign convention and performing the matrix multiplications, as well as noticing that τlt = τtl and τdr = τrd give the following equations when only the concrete struts are considered: σ lc = σ d cos 2 α + σ r sin 2 α
(13.14)
σtc = σ d sin 2 α + σ r cos 2 α
(13.15)
τ ltc = (−σ d + σ r ) sin α cos α
(13.16)
13.4.2.2 Equilibrium Equations When a concrete element reinforced orthogonally with longitudinal and transverse steel bars, as shown in Figure 13.20a, is studied, the three stress components σl , σt, and τlt are the applied stresses on the reinforced concrete element viewed as a whole. The stresses on the concrete strut itself are denoted as σlc , σtc , and τltc , as shown in Figure 13.20b. The longitudinal and transverse steel provide the smeared stresses of ρl fl and ρt ft , as shown in Figure 13.20c. It is significant to recognize the difference between the two sets of stresses: σl , σt , and τlt for the reinforced concrete element and σlc , σtc , and τlt for concrete struts. Both sets of stresses (σl , σt , τlt and σlc , © 2003 by CRC Press LLC
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Reinforced Concrete Structures
τ(−) lt
σ(+) t
σ(+) l
τ(−) ltc
σ(+) tc
ρt ft
σ(+) l
σ(+) lc
τ(+) lt
τ(+) ltc
(a) REINFORCED CONCRETE
(b) CONCRETE STRUTS
ρl fl
(c) STEEL REINFORCEMENT
FIGURE 13.20 Stress condition in reinforced concrete.
σtc , τltc) satisfy the transformation equations. In summing the concrete stresses and the steel stresses in the l and t directions, a fundamental assumption is made, according to Hsu [1993]. It is assumed that the steel reinforcement can take only axial stresses. Any possible dowel action is neglected. Hence, the superposition principle for concrete and steel becomes valid and gives the general equilibrium equations for reinforced concrete: σ l = σ d cos 2 α + σ r sin 2 α + ρl fl
(13.17)
σt = σ d sin 2 α + σ r cos 2 α + ρt ft
(13.18)
τ lt = (−σ d + σ r ) sin α cos α
(13.19)
13.4.2.3 Compatibility Equations The same principle of transformation for stresses can be applied to strains. Therefore, the following compatibility equations can be derived: ε l = ε d cos 2 α + ε r sin 2 α
(13.20)
εt = ε d sin 2 α + ε r cos 2 α
(13.21)
γ lt = (ε d + ε r ) sin α cos α 2
(13.22)
13.4.2.4 Constitutive Laws Softened compression stress-strain relationship of concrete: The truss model has been applied to treat shear and torsion of reinforced concrete since the turn of the 20th century. However, the prediction based on the truss model consistently overestimated the shear and torsional strengths of tested specimens. This nagging mystery has plagued researchers for over half a century. The source of this difficulty was first understood by Peter [1964], who realized that a reinforced concrete panel element subjected to tension is actually subjected to biaxial compression-tension stresses. Viewing the action as a two-dimensional problem, he discovered that the compressive strength in one direction was reduced by cracking due to tension in the perpendicular direction. Applying the softening effect of concrete struts to nine test panels, he concluded that a reduction of 15% for the effective compressive strength should be taken into account in biaxial compression-tension stresses. Apparently, the mistake in applying the truss model theory before 1964 was the use of the compressive stress-strain relationship of concrete obtained from the uniaxial test of standard cylinders without considering the two-dimensional softening effect.
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Earthquake Engineering Handbook
Hognestad Parabola
FIGURE 13.21 Compression softening models with the Hognestad curve.
Peter’s tests could not delineate the variables that govern the softening parameter because of the technical difficulties in the biaxial testing of large panels. The quantification of the softening phenomenon, therefore, had to wait for almost two decades until a unique “shear rig” test facility was built in 1981 by Vecchio and Collins [1981]. Based on their tests of 17 panels of 89 cm square and 7 cm thick, they proposed a softening parameter that was a function of the ratio of the tensile principal strains to the compression principal strain, εr/εd. The discovery and the quantification of this softening phenomenon have provided the major breakthrough in understanding the shear problem in reinforced concrete. During the past 20 years, a number of diverse analytical models have been proposed according to the test results [Peter, 1964; Robinson and Demorieux, 1968; Vecchio and Collins, 1981; Schlaich et al., 1982, 1983; Vecchio and Collins, 1986; Eibl and Neuroth, 1988; Miyahara et al., 1988; Kolleger and Mehlhorn, 1990; Mikane et al., 1991; Ueda et al., 1991; Hsu, 1993; Belarbi and Hsu, 1995; Vecchio and Collins, 1993; Vecchio et al., 1994]. The effect of these softening models on low-rise framed shear walls was studied by Mo and Rothert [1997]. In this section the softening model proposed by Belarbi and Hsu [1994, 1995] is briefly introduced below. The original softening model derived from test data proposed the use of a softening parameter ζ, with ζ being a function of the ratio of principal tensile strain to principal compressive strain (εr/εd). The proposed model by Belarbi and Hsu [1995] involved modifying the Hognestad parabola (Figure 13.21), which was used as the base curve describing the uniaxial compressive response of concrete. ε ε 2 σ d = ζ f 2 d − d ζε 0 ζε 0 ε ζε − 1 2 0 σ d = ζ fc' 1 − d 2 ζ −1 ' c
ζ=
ε d ζε 0 ≤ 1 ε d ζε 0 > 1
0.9 1 + 600 ε r
(13.23a)
(13.23b)
Tensile stress-strain relationship of concrete: From the tests of panels subjected to shear, it was clear that the tensile stress of concrete, σr , is not zero as assumed in the simple truss model. Based on the tests of 35 full-size panels [Hsu, 1993], a set of formulas was recommended as follows:
© 2003 by CRC Press LLC
If ε r ≤ ε cr ,
σr = Ε c ⋅ ε y
If ε r > ε cr ,
ε σ r = fcr ⋅ cr εr
(13.24) 0.4
(13.25)
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Reinforced Concrete Structures
where Ε c = 47, 000 fc' , and both fc' and
fc' are in pounds per square inch
ε cr = strain at cracking of concrete = 0.00008 fcr = 3.75 fc' Stress-strain relationship of steel: The stress-strain curve of a steel bar in concrete relates the average stress to the average strain of a large length of bar crossing several cracks, whereas the stress-strain curve of a bare bar relates the stress to the strain at a local point [Okamura and Maekawa, 1991]. In other words, a steel bar in concrete is stiffened by tensile stress of concrete. If the tensile strength of concrete is neglected, as assumed in most truss models, the following equations are used:
If εt ≤ εty ,
fl = Ε s ε l
(13.26)
If ε l > ε ly ,
fl = fly
(13.27)
where Es = modulus of elasticity of steel bars fly = yield stress of longitudinal steel bars εly = yield strain of longitudinal steel bars It was recommended by Belarbi and Hsu [1995] that both the tensile strength of concrete, presented in the previous section, and the average stress-strain curve of steel stiffened by concrete be taken into account. In this model, the following equations are used for describing the stress-strain relationship of steel:
If ε l Ε s ≤ fly' ,
fl = Ε s ⋅ ε l
If ε l Ε s ≤ fly' ,
2 − α 45o fl = 1 − (0.91 − 2B) fly + (0.02 + 0.25B)Ε s ε l 1000 ⋅ ρl
(13.28)
[
]
(13.29)
where
(
[ (
B = (1 ρl ) fcr fly
)
(13.30)
)
]
(13.31)
1.5
fly' = 1 − 2 − α 45o 1000ρl (0.93 − 2B) fly 13.4.2.5 Solution Procedures
Figure 13.22 shows a framed shear wall. This kind of shear wall will be analyzed in this section. As discussed by Hsu and Mo [1985], in the design of low-rise structural walls the boundary elements are reinforced to resist the applied bending moment, while the webs are designed to resist the applied shear force. The size and shape of the boundary elements do not have a significant influence on the shear behavior, as long as they are sufficient to carry the required bending moment. The effect of the boundary elements on structural walls has been studied by Mo and Kuo [1998]. Due to the restriction of the boundary elements, the strain of transverse steel in low-rise framed shear walls can be neglected, as verified by the PCA tests, i.e., εt = 0. Therefore, adding Equations 13.20 and 13.21 gives: εr = εl − εd
© 2003 by CRC Press LLC
(13.32)
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VER.DIR.
Earthquake Engineering Handbook
HOR.DIR.
σdb cos α
τb cot α τb
V
A
I
A
cot α
hw
I
α τ(I)
sα
co
I (b) WALL ELEMENT
(a) GENERAL VIEW
tf b A
C
B
D
d (c) SECTION I-I
FIGURE 13.22 A framed shear wall.
Inserting εt sin2 α = εr – εr cos2 α into Equation 13.20 gives: cos 2 α =
εr − εl εr − εd
(13.33)
Substituting Equations 13.32 and 13.33 into Equation 13.17 results in:
fl =
1 ρl
(−εd ) − σ (εl − εd ) σ l − σ d ⋅ (εl − 2εd ) r (εl − 2εd )
(13.34)
Neglecting the tensile strength of concrete, i.e., σr = 0, gives: fl =
1 ρl
(−εd ) σ l − σ d ⋅ (εl − 2εd )
(13.35)
For low-rise framed shear walls, the average shear stress τ on the horizontal cross section is defined as: τ=
© 2003 by CRC Press LLC
V bd
(13.36)
0068_C13_fm Page 25 Monday, August 19, 2002 1:51 PM
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Reinforced Concrete Structures
where d is the effective depth, which is defined as the distance between the centroids of the longitudinal bars in the two flanges, b is the width of the web, and V is the horizontal shear force. The deflection at the top of the shear wall, δ, is determined by: δ = γh
(13.37)
where h is the height of the shear wall. Based on the softened truss model theory presented above, the algorithm is shown in Figure 13.23 [Mo and Jost, 1993; Mo and Shiau 1993] and is explained below. Select a given εd . Assume a value of εl . Calculate εr from Equation 13.32. Calculate ζ using Equation 13.23b. Calculate σd from Equation 13.23a. Calculate σr from Equation 13.24 or 13.25. Calculate fl from Equation 13.34 or 13.35. Check fl using Equations 13.26 to 13.27 or Equations 13.28 to 13.31. If the calculated value for fl determined in step 8 is not sufficiently close to the value shown in step 7, repeat steps 2 through 7. 9b. If the calculated value for fl determined in step 8 is sufficiently close to the value shown in step 7, proceed to calculate τ (or V) and γ (or δ) from Equation 13.19 or 13.36 and Equation 13.21 or Equation 13.37, respectively. This will provide one set of solutions. 1. 2. 3. 4. 5. 6. 7. 8. 9a.
Select other values of εd and repeat steps 1 through 9 for each εd . This will provide a number of sets of quantities. From these sets of quantities the shear stress vs. distortion curve (or shear force vs. deflection curve), the longitudinal steel strain vs. deflection curve, and the longitudinal steel strain vs. concrete strain curve can be plotted. In general the maximum εd value can be chosen as 0.003 with an increment of 0.00005.
13.5 Seismic Design 13.5.1 Columns 13.5.1.1 Flexural Plastic Hinge Mechanism To confine a flexural plastic hinge region in a circular column for standard design ductilities, a volumetric reinforcement ratio of:
ρs =
ks fc' f yh
P 0.5 + 1.25 ' + 0.13 (ρl − 0.01) fc Ag
(13.38)
is required, based on Priestley et al. [1996], in the plastic hinge zone. Equation 13.38 depends on the longitudinal column reinforcement ratio As/Ag and on a factor ks which is calibrated with experimental results based on an energy balance approach, which compares the vertical strain energy stored in the confined concrete at crushing with the strain energy provided by the horizontal hoop reinforcement up to bar rupture. For mild steel reinforcement hoops ks = 0.16 is applied [Priestley et al., 1996]. Note that P is the axial force and fyh is the yield strength of the horizontal reinforcement. 13.5.1.2 Shear Mechanism Many different models exist to describe the complex transfer of so-called shear forces in a reinforced concrete member. A simple model that seems to fit the experimental data best was put forward by Priestley © 2003 by CRC Press LLC
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Select
εd
Estimate
ε
Calculate
εr
Calculate
ζ
Calculate
σd
Calculate
σr
Calculate
fl
l
NO
Check if the error for
fl
is
acceptable YES Calculate τ , γ , v, δ
NO
Check if
εd > 0.003 YES END
FIGURE 13.23 Algorithm for framed shear wall analysis.
et al. [1993a, 1993b] and assumes a combination of three different mechanisms to contribute to the nominal shear capacity Vn in the form: Vn = Vc + Vs + Vp
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where Vc is the concrete contribution provided primarily in the form of aggregate interlock, which decreases with increasing crack width and flexural ductility, Vs is the horizontal reinforcing steel contribution as part of an assumed truss mechanism, and Vp is the horizontal component from the applied axial load compression strut between the column ends. Due to the aggregate interlock degradation with increasing crack width or flexural ductility, the Vc component needs to be tied to the column displacement ductility level µ∆ in regions where inelastic flexural plastic hinging occurs. Thus, the concrete contribution to the shear resistance needs to be assessed both inside the plastic hinge region Lc as Vci and outside the plastic hinge region over Lv as Vco. Thus, Vci = k fc' Ae Vco = 3 fc' Ae
(13.40)
where the effective concrete shear area Ae = 0.8Ag or 80% of the gross column area, and k represents a strength reduction factor based on the column displacement ductility µ∆ in the form of: k=3 k = 5 − µ∆ k = 1.5 − µ ∆ 8 k = 0.5
for for for for
µ∆ < 2 2 ≤ µ ∆ < 4 4 ≤ µ ∆ < 8 µ ∆ ≥ 8
(13.41)
Note that Equation 13.41 is for shear design and is thus slightly more conservative than concrete shear reductions proposed for assessment of expected capacities in existing columns. The horizontal reinforcing steel contribution Vs can be determined as: Vs = Vs =
π Ah fhy D' cot θ (circular) 2 s nAh fhy D' s
cot θ (rectangular)
(13.42a)
(13.42b)
where Ah n fhy s θ
= = = = =
the area of one leg of the horizontal reinforcement the number of legs of horizontal column ties in the loading direction the yield strength of the horizontal reinforcement the spacing of the horizontal reinforcement or the spiral pitch the angle of the principal compression strut to the column axis or the shear crack inclination D' = the core column dimension in the loading direction from center to center of the peripheral horizontal reinforcement
Conservatively, θ = 45° or cot θ = 1 can be assumed for design or, more accurately for assessment, principal compression strut inclinations of 30° can be assumed for bridge columns and 45° for pier walls. The axial load shear contribution is simply defined as the horizontal component of the inclined compression strut as: Vp = P tanα
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Mass F (t) (a) Low-rise shear wall with a mass at the top
y SPRING
(b) Model for a nonlinear single-degree-of-freedom system
DAMPER
ki ∆ yi
F (t)
Mass
mi ∆ ÿi
∆I
ci ∆ ÿi
(c) Free body diagram showing the incremental inertial force and the incremental external force
FIGURE 13.24 A model for dynamic analysis.
where P represents the axial load at the column top and α the compression strut inclination or angle with the vertical column axis. Thus, tan α can be defined as:
D−c for single bending 2L D−c for double bending L where c represents the distance between the neutral axis and the extreme compression fiber, D the column dimension in the loading direction, and L the clear column height.
13.5.2 Structural Walls 13.5.2.1 Dynamic Analysis In dynamic analysis, a low-rise structural wall can be modeled as a nonlinear single degree of freedom system (Figure 13.24) [Mo, 1988]. The dynamic incremental equilibrium is shown in Figure 13.24c. The equation of the equilibrium is:
m∆˙˙y i + c i ∆y˙ i + ki ∆y i = ∆Fi
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FIGURE 13.25 Linear variation of acceleration during time interval ∆t.
where m is the total mass at roof level plus one third the mass of the wall. The coefficients ci and ki are calculated for values of velocity and displacement corresponding to time t and assumed to remain constant during the increment of time ∆t. ∆ÿi , ∆ y˙ i, and ∆yi are the incremental acceleration, incremental velocity, and incremental displacement, respectively. To perform the step-by-step integration of Equation 13.44, the linear acceleration method is employed. In this method, it is assumed that the acceleration may be expressed by a linear function of time during the time interval ∆t. Let ti and ti +1 = ti + ∆t be, respectively, the designation for the time at the beginning and at the end of the time interval ∆t. When the acceleration is assumed to be a linear function of time for the interval of time ti to ti +1 = ti + ∆t as shown in Figure 13.25, the acceleration may be expressed as: ˙˙y (t ) = ˙˙y i +
∆˙˙y i (t − t i ) ∆t
(13.45)
Integrating Equation 13.45 twice with respect to time between the limits ti and t = ti + ∆t and using the incremental displacement ∆y as the basic variable gives: ∆˙˙y i =
6 6 ∆y − y − 3 ˙˙y i ∆t 2 i ∆t i
(13.46)
∆y˙ i =
3 ∆t ˙˙y ∆y i − 3 y˙ i − ∆t 2 i
(13.47)
and
The substitution of Equations 13.46 and 13.47 into Equation 13.44 leads to the following form of the equation of motion: 6 ∆t 6 3 ˙˙y + k ∆y = ∆Fi m 2 ∆y i − y˙ − 3 ˙˙y i + c i ∆y i − 3 y˙ i − ∆t ∆t 2 i i i ∆t i
(13.48)
Transferring in Equation 13.48 all the terms containing the unknown incremental displacement ∆yi to the left-hand side gives: ki ∆y i = ∆Fi
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(13.49)
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where ki = ki +
6m 3c i + ∆t 2 ∆t
(13.50)
and ∆t 6 ˙˙y ∆Fi = ∆Fi + m y˙ i + 3 ˙˙y i + c i 3 y˙ i + ∆t 2 i
(13.51)
It should be noted that Equation 13.49 is equivalent to the static incremental-equilibrium equation and may be solved from the incremental displacement by simply dividing the equivalent incremental load ∆Fi by the equivalent spring constant ki. The displacement yi+1 and the velocity y˙ i+1 at time ti+1 = ti + ∆t are: y i +1 = y i + ∆y i
(13.52)
y˙ i +1 = y˙ i + ∆y˙ i
(13.53)
and
The acceleration ˙˙y i+1 at the end of the time step is obtained directly from the differential equation of motion to avoid the errors that generally might tend to accumulate from step to step. It follows that: ˙˙y i +1 =
[
1 F (t i +1 ) − c i +1 y˙ i +1 − ki +1 y i +1 m
]
(13.54)
where the coefficients ci+1 and ki+1 are now evaluated at time ti+1. It should be noted that according to a Nuclear Regulatory Commission regulatory guide, the damping coefficient ci+1 is 7 and 4% of critical damping ccr for reinforced concrete structures subjected to safe shutdown earthquake (or blast loading) and operating-basis earthquake, respectively: c i +1 = ξ(c cr )i +1 = 2ξ(ki +1m)
1/ 2
(13.55)
After the displacement, velocity, and acceleration have been determined at time ti+1 = ti + ∆t, the procedure just outlined is repeated to calculate these quantities at the following time step ti +2 = ti+1 + ∆t. In general, sufficiently accurate results can be obtained if the time interval is taken to be no longer than one tenth of the natural period of the structure. The natural period T can be expressed as: T = 2π
m k
(13.56)
13.5.3 Design Approach 13.5.3.1 Design Considerations To ensure ductile failure, the two design limitations for over-reinforcement and minimum reinforcement can be derived in terms of the inclination angle α of the diagonal concrete struts. Over-reinforcement: Mo [1987] shows the inclination angle of the diagonal compression struts in the “lower balanced reinforcement,” αlb , to be:
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ε 8ε 2 1 α lb = cos−1 ly 1 + 20 − 1 ε ly 2 2ε o
(13.57)
αlb is a function of only one variable, the yield strain of longitudinal steel εly . In under-reinforced design, the angle α should be chosen greater than αlb. Minimum reinforcement: Mo [1987] also shows the inclination angle for minimum reinforcement αm to be: 1/3 f α m = cos−1 0.0025 ly' fc
(13.58)
αm is a function of two variables, the yield strain in longitudinal steel εly and the concrete strength fc' . Equations 13.57 and 13.58 give the lower and upper limits, respectively, for the range of α, which ensures ductile failure. After the range of the inclination angle α is found, a preliminary angle α can be selected within this range. The wall size bd can then be determined by substituting τ = V/bd and σ d = fc' cos α into τ = σ d sin α cos α [Hsu and Mo, 1985; Mo, 1988]: bd =
V fc' sin α cos 2 α
(13.59)
The effective length d in Equation 13.59 is usually given in design, and the web width b needs to be chosen by the designer. After the wall size bd is determined, the actual inclination angle α can be refined by solving α in Equation 13.59. The longitudinal steel can be determined from Al fl = τbd cot α [Hsu and Mo, 1985; Mo, 1988], noting that τbd becomes Vn at maximum shear: Al fly = Vn cot α
(13.60)
The transverse (horizontal) steel can be determined by the specified minimum value [Hsu, 1993]: ρt = 0.0045
(13.61)
13.5.3.2 Design Procedures For a given dynamic loading history (or seismogram) and given material properties ( f c' , f ly , ξ) , the procedures to design the size of the wall, the vertical steel, and the horizontal steel are as follows: 1. Assume a shear force (Vn). 2. Determine the range of αs by Equations 13.57 and 13.58. 3. Select an α value and b find and d from Equation 13.59. After b and d are selected, the actual angle of inclination can be refined. 4. Determine the longitudinal steel by Equation 13.60 and the horizontal steel by Equation 13.61. 5. Determine the load-deflection relationship using the algorithm mentioned in Figure 13.22. 6. Calculate the stiffness at the ultimate state. 7. Determine the natural period at the ultimate state by Equation 13.56. 8. Select the time interval ∆t ≤ 0.1 times the natural period at the ultimate state. 9. Calculate the initial stiffness using the load-deflection relationship. 10. Calculate the damping coefficient by Equation 13.55. 11. Calculate the effective stiffness by Equation 13.50.
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12. 13. 14. 15. 16. 17. 18. 19. 20.
Calculate the incremental effective force by Equation 13.51. Solve for the incremental displacement by Equation 13.49. Calculate the incremental velocity by Equation 13.47. Calculate displacement and velocity at the end of the time interval by Equations 13.52 and 13.53. Calculate shear force using the load-deflection relationship. Calculate acceleration at the end of the time interval by Equation 13.54. Steps 9 through 17 will provide one set of solutions. Repeat steps 9 through 17 for each time interval. This will provide a number of sets of solutions. Determine the calculated maximum shear force in the entire loading history. a. If the value of the calculated maximum shear force is not greater than the shear force assumed, the design is finished. b. If the value of the calculated maximum shear force is greater than the shear force assumed, reassume a new value for shear force Vn and repeat steps 2 through 19 until step 19a is satisfied.
The algorithm presented in this section has been extended to box tubes subjected to dynamic shear and torsion [Mo and Yang, 1996] and to hybrid reinforced concrete frame–steel wall systems [Mo and Perng, 2000, in press]. 13.5.3.3 Design Example A shear wall 10 ft (3.05 m) high by 15 ft (4.57 m) wide (Figure 13.26a) is designed to withstand the missile impact having the force-time relationship shown in Figure 13.26b and acting at the top of the wall. For simplicity, the force-time relationship of the missile impact is used instead of the earthquake seismogram. It is assumed that the mass at the top of the wall and one third the mass of the wall m are 0.5 k⋅sec2/in. (0.088 kN⋅sec2/mm). The material properties are given as follows: fly = 60 ksi (414 MPa), fc' = 4000 psi (27.6 MPa), Es = 29 × 106 psi (2.0 × 105 MPa), εo = 0.002, and ξ = 0.07. The wall thickness b and the reinforcement in the wall ρl and ρt are to be determined. Design of the boundary columns, which should be designed to resist the bending moment, will not be described. Solution: 1. Assume Vn = 1600 kips (7117 kN). 2. Determine the range of α: 1 0.00207 α > cos−1 2 2(0.002)
2 8(0.002) 1+ 1 − 2 0 00207 . ( )
(13.57)
α = 60.4° 1 0.0025)(60, 000) 3 ( α ≤ cos 4000 −1
α = 70.4°
(13.58)
∴ 60.4° < α ≤ 70.4° 3. Select α = 60.4° and d = 180 in. (4572 mm): b≥
1, 600, 000
(180)(4000) sin 60.4 cos2 60.4
b ≥ 10.48 in. (266 mm)
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y
k · sec2/in.
m = 0.5
1.2 x 103K
F(t) F (t) 10′
ξ = 0.07 t (sec) 0.02
15′
0.1
(b) LOADING
(a) SHEAR WALL 1 k.sec/in. = 0.175 kN· sec/mm 1 ft = 0.3048 m SHEAR FORCE v (kips)
1 k = 4.448 kN 1 in. = 25.4 mm
1500
1000
500
0.1
0.2 0.3 DISPLACEMENT y (in.)
0.4
(c) SHEAR FORCE − DISPLACEMENT RELATIONSHIP
FIGURE 13.26 Shear wall subjected to missile impact.
Let us select b = 12 in. (305 mm). Calculate α = 62.9° from Equation 13.59: α = 62.9° < 70.4° OK 4. Determine ρl and ρt: ρl =
1, 600, 000 cot 62.9 = 0.0063 (12)(180)(60, 000) ρt = 0.0045
(13.60)
(13.61)
5. Determine the load-deflection relationship. Using the algorithm mentioned in Figure 13.22 the load-deflection relationship is determined as shown in Figure 13.26c. 6. Calculate the stiffness at the ultimate state: ku =
1609.9 = 3879.3 k / in. (679 kN / mm 0.415
7. Determine the natural period at the ultimate state: Τu = 2π
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0.5 = 0.071 sec 3879.3
(13.56)
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8. Select ∆t : ∆t = (0.1)(0.071) = 0.0071 sec Let us select ∆t = 0.005 sec ∆t = 0.005 sec < 0.0071 sec
OK
9. Calculate the initial stiffness k: k=
572.2 = 7354.8 k / in. (1288 kN / mm) 0.0778
10. Calculate the damping coefficient C:
[
]
C = (0.07)(2) (0.5)(7354.8)
1
2
= 8.49 k ⋅ sec/ in. (1.49 kN ⋅ sec/ mm )
(13.55)
11. Calculate the effective stiffness k : k = 7354.8 +
6 (0.5)
(0.005)
2
+
3 (8.49) = 132, 448.8 k / in. (23194 kN / mm ) 0.005
12. Calculate the incremental effective force: ∆F = 300 kips (1334 kN) 6(0) 0.005 (0) ∆F = 300 + (0.5) + 3 (0) + (8.49) 3 (0) + = 300 kips (1334 kN) 2 0.005 13. Determine the incremental displacement ∆y: ∆y =
300 = 0.002265 in.(0.058 mm) 132, 448.8
(13.49)
14. Determine the incremental velocity ∆y˙ : ∆y˙ =
3 (0.002265) − 3 (0) − 0.005 (0) = 1.359 in. / sec(34.52 mm / sec) 0.005 2
(13.47)
15. Calculate displacement and velocity at the end of the time interval: y i+1 = 0 + 0.002265 = 0.002265 in. (0.058 mm)
(13.52)
y˙ i+1 = 0 + 1.359 = 1.359 in./sec (34.52 mm/sec)
(13.53)
16. Determine shear force V. From Figure 13.26c, V = 16.7 kips (74.3 kN) when y = 0.002265 in. (0.058 mm).
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TABLE 13.1 Nonlinear Response: Linear Acceleration Step-by-Step Method for Design Example sec
kip
in.
in./sec
kip
in./sec
k/in.
k/in.
kip
kip
in.
in./sec
0 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 0.045 0.050 0.055 0.060 0.065 0.070 0.075 0.080 0.085 0.090 0.095 0.100 0.105 0.110 0.115 0.120 0.125 0.130
0 300 600 900 1200 1125 1050 975 900 825 750 675 600 525 450 375 300 225 150 75 0 0 0 0 0 0 0
0 0.0023 0.0172 0.0524 0.1091 0.1807 0.2509 0.3045 0.3311 0.3255 0.2997 0.2698 0.2391 0.2108 0.1874 0.1701 0.1588 0.1519 0.1472 0.1421 0.1342 0.1225 0.1091 0.0963 0.839 0.0715 0.0591
0 1.36 4.86 9.23 13.19 13.64 12.83 8.17 2.28 –4.55 –5.68 –6.17 –6.00 –5.22 –4.10 –2.82 –1.77 –1.07 –0.90 –1.24 –1.97 –2.62 –2.64 –2.49 –2.49 –2.49 –2.49
0 17 126 385 700 1015 1300 1455 1530 989 870 732 590 459 351 271 219 187 165 142 105 51 0 0 0 0 0
0 544 865 947 776 4 –669 –1063 –1347 –280 –164 –31 101 202 253 246 186 90 –19 –116 –183 –67 36 0 0 0 0
7355 7355 7355 7355 5549 4399 4060 2892 2820 4621 4621 4621 4621 4621 4621 4621 4621 4621 4621 4621 4621 4621 4621 0 0 0 0
132,449 132,449 132,449 132,449 129,971 128,341 127,846 126,084 125,976 128,659 128,659 128,659 128,659 128,659 128,659 128,659 128,659 128,659 128,659 128,659 128,659 128,659 120,000 120,000 120,000 120,000 120,000
300 300 300 300 –75 –75 –75 –75 –75 –75 –75 –75 –75 –75 –75 –75 –75 –75 –75 –75 0 0 0 0 0 0 0
300 1977 4658 7514 9309 9004 6852 3349 –709 –3322 –3846 –3948 –3645 –3009 –2232 –1449 –888 –603 –661 –1019 –1502 –1723 –1532 –1491 –1491 –1491 –1491
0.0023 0.0149 0.0352 0.0567 0.0716 0.0702 0.0536 0.0266 –0.0056 –0.0258 –0.0299 –0.0307 –0.0283 –0.0234 –0.0173 –0.0113 –0.0069 –0.0047 –0.0051 –0.0079 –0.0117 –0.0134 –0.0128 –0.0124 –0.0124 –0.0124 –0.0124
1.36 3.50 4.37 3.96 1.45 –1.81 –4.66 –5.89 –6.83 –1.13 –0.49 0.17 0.78 1.13 1.28 1.05 0.69 0.17 –0.34 –0.74 –0.64 –0.03 0.16 0 0 0 0
Note: kN/mm. 1kip = 4.448 kN; 1 in. = 25.4 mm; 1 in./sec= 25.4 mm/sec; 1 in./sec2 = 25.4 mm/sec;2 1 kip/in. = 0.175
17. Calculate acceleration at the end of the time interval: ˙˙y i+1 =
[
]
1 300 − (8.49)(1.359) − 16.7 = 543.5 in./sec2 (13,805 mm/sec2) 0.5
Steps 9 through 17 provide one set of solutions. 18. Repeating steps 9 through 17 for each time interval gives a number of sets of solutions, as illustrated in Table 13.1. 19. Determine the calculated maximum shear force. From Table 13.1, Vmax = 1530 kips (6805 kN) < assumed Vn = 1600 kips (7117 kN). OK The dynamic inelastic response calculated in Table 13.1 is plotted in Figure 13.27. Also plotted for comparison is the linear elastic response obtained by a similar step-by-step analysis. The effect of the inelastic response on the displacement shows up clearly in this comparison.
13.5.4 Detailing Requirements According to the detailing requirements of the ACI code [1995], a brief description is introduced by Nawy [1996], as summarized below.
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36 32
1 in. = 25.4 mm
28 DISPLACEMENT y (10−2 in)
INELASTIC RESPONSE 24 20 ELASTIC RESPONSE
16 12 8 4 0
10
20
30
40
50
-4
60 70 80 90 TIME t (10−3 sec)
100 110 120 130
-8
FIGURE 13.27 Comparison of inelastic with elastic response.
13.5.4.1 Longitudinal Reinforcement 1. In seismic design, when the factored axial load Pu is negligible or significantly less than Ag fc' 10 , the member is considered a flexural member (beam). If Pu > Ag fc' 10 , the member is considered a beam-column, because it is subjected to both axial and flexural loads, as columns are. 2. The shortest cross-sectional dimension ≥ 12 in. (300 mm). 3. The limitation on the longitudinal reinforcement ratio in the beam-column element is: 0.01 ≤ ρ g =
As ≤ 0.06 . Ag
For practical considerations, an upper limitation of 6% is too excessive, because it results in impractical congestion of longitudinal reinforcement. A practical maximum total percentage ρg of 3.5 to 4.0% should be a reasonable limit. 4. A minimum percentage of longitudinal reinforcement in flexural members (beams) is: a. For positive reinforcement,
ρ≥
3 fc' fy
≥
200 fy
(13.62)
≥
200 fy
(13.63)
b. For negative reinforcement,
ρ≥
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6 fc' fy
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But under no condition should ρ exceed 0.025. The stresses fc' and fy in these expressions are in psi units. All reinforcement has to be continued through the joint. 5. In building design, main reinforcement should be chosen on the basis of the strong column–weak beam concept of the ACI code:
∑M
col
≥
6 5
∑M
bm
(13.64)
13.5.4.2 Transverse Confining Reinforcement Transverse reinforcement in the form of closely spaced hoops (ties) or spirals has to be adequately provided. The aim is to produce adequate rotational capacity within the plastic hinges that may develop as a result of the seismic forces. 1. For column spirals, the minimum volumetric ratio of the spiral hoops needed for the concrete core confinement is: ρs ≥
0.12 fc' f yh
(13.65)
or A f' ρs ≥ 0.45 g − 1 c Ach f yh
(13.66)
whichever is greater, where ρs = ratio of volume of spiral reinforcement to the core volume measured out to out Ag = gross area of the column section Ach = core area of section measured to the outside of the transverse reinforcement fyh = specified yield strength of transverse reinforcement, psi 2. For column rectangular hoops, the total cross-sectional area within spacing s is: Ash ≥ 0.09shc
fc' f yh
(13.67)
or A f' Ash ≥ 0.3shc g − 1 c Ach f yh
(13.68)
whichever is greater, where Ash = total cross-sectional area of transverse reinforcement (including cross ties) within spacing s and perpendicular to dimension hc hc = cross-sectional dimension of column core measured c-c of confining reinforcement (in.) Ach = cross-sectional area of structural member, measured out to out of transverse reinforcement s = spacing of transverse reinforcement measured along the longitudinal axis of the member (in.) The maximum allowable spacing is one quarter of the smallest cross-sectional dimension of the member or 4 in., whichever is smaller (UBC code [1997] requires 4 in.).
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3. The confining transverse reinforcement in columns should be placed on both sides of a potential hinge over a distance o . The largest of the following three conditions governs: a. Depth of member at joint face b. One sixth of the clear span c. 18 in. 4. For beam confinement, the confining transverse reinforcement at beam ends should be placed over a length equal to twice the member depth h from the face of the joint on either side or of any other location where plastic hinges can develop. The maximum hoop spacing should be the smallest of the following four conditions: a. One fourth effective depth d b. 8 × diameter of longitudinal bars c. 24 × diameter of the hoop d. 12 in. (300 mm) 13.5.4.3 Beam–Column Connections Test of joints and deep beams have shown that shear strength is not as sensitive to joint (shear) reinforcement as for that along the span. On this basis, the ACI code [1995] has assumed the joint strength as a function of only the compressive strength of the concrete and requires a minimum amount of transverse reinforcement in the joint. The minimal shear strength of the joint should not be taken greater than the forces Vn specified below for normal-weight concrete. 1. Confined on all faces by beams framing into the joint: Vn ≤ 20 fc' A j
(13.69)
2. Confined on three faces or on two opposite faces: Vn ≤ 15 fc' A j
(13.70)
Vn ≤ 12 fc' A j
(13.71)
3. All other cases:
A framing beam is considered to provide confinement to the joint only if at least three quarters of the joint is covered by the beam. The value of allowable Vn should be reduced by 25% if lightweight concrete is used. Also, test data indicate that the value in Equation 13.71 is unconservative when applied to corner joints. Aj = effective cross-sectional area within a joint, in a plane parallel to the plane of reinforcement generating shear at the joint. 13.5.4.4 Development of Reinforcement at the Joint For bars of sizes numbers 3 through 11 terminating at an exterior joint with standard 90° hooks in normal concrete, the development length ldh beyond the column face should not be less than the following:
© 2003 by CRC Press LLC
ldh ≥ f y db 65 fc'
(13.72)
ldh ≥ 8 db
(13.73)
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Reinforced Concrete Structures
ldh ≥ 6 in.
(13.74)
where db is the bar diameter. The development length provided beyond the column face must be no less than ld = 2.5ldh when the depth of concrete cast in one lift beneath the bar ≤ 12 in. or ld = 3.5 × ldh when the depth of concrete cast in one lift beneath the bar exceeds 12 in. All straight bars terminated at a joint are required to pass through the confined core of the column boundary member. Any portion of the straight embedment length not within the confined core should be increased by a factor of 1.6. 13.5.3.2 Shear Walls Forces and reinforcement in shear walls and diaphragms: High-rise shear walls with height-to-depth ratio in excess of 2.0 essentially act as vertical cantilever beams. As a result, their strength is determined by flexure rather than shear. If they are subjected to factored in-plane seismic shear forces Vuh > Acv fc' , they have to be reinforced with a minimum percentage ρv ≥ 0.0045. At least two curtains of reinforcement are needed in the wall if the in-plane factored shear forces exceed a value of Vuh > Acv fc' : ρv = Asv Acv
(13.75)
Acv = net area of concrete cross section = thickness × length of section in direction of shear considered Asv = projection on Acv of area of distributed shear reinforcement crossing the plane of Acv If the extreme fiber compressive stresses exceed 0.2 fc', the shear walls have to be provided with boundary elements along their vertical boundaries and around the edges of openings. The nominal shear strength Vn of structural walls and diaphragms of high-rise buildings with aspect ratio greater than 2 should not exceed the shear force calculated from:
(
Vn = Acv 2 fc' + ρn f y
)
(13.76)
where ρn is the ratio of distributed shear reinforcement on a plane perpendicular to the plane of Acv . For low-rise walls with aspect ratio hw l w less than 2, the ACI code [1995] requires that the coefficient 2 in Equation 13.76 be increased linearly up to a value of 3 when the hw l w ratio reaches 1.5 in order to account for the higher shear capacity of low-rise walls. In other words:
(
VN = Acv α c fc' + ρn f y
)
(13.77)
where αc = 2 when hw l w ≥ 2 and α c = 3 when hw l w = 1.5; Vu = φVn φ = 0.6 for designing the joint, if nominal shear is less than the shear corresponding to the development of the nominal flexural strength of the member The nominal flexural strength is determined considering the most critical factored axial loads including earthquake effects. The maximum allowable nominal unit shear strength in structural walls is 8Acv fc' where Acv is the total cross-sectional area (in.2) previously defined and fc' is in psi. However, the nominal shear strength of any one of the individual wall piers can be permitted to have a maximum value of 10Acp fc' , where Acp is the cross-sectional area of the individual pier.
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13.6 Seismic Retrofit 13.6.1 Columns Steel jackets [Aboutaha et al., 1999] and fiber-reinforced plastic composites [Gergely et al., 1998; Saadatmanesh et al., 1996] have been used successfully for the retrofit of bridge columns. At the University of California at San Diego (UCSD), a series of systematic tests [Seible, 1994a, 1994b, 1995a, 1995b, 1995c, 1995d] have been performed on seismic retrofit of columns. A brief summary is introduced by Seible et al. [1997], as shown below. 13.6.1.1 Flexural Plastic Hinge Retrofit For carbon fiber jackets Equation 13.38 can be interpreted as: ρj =
4t j D
=
k j fc' P 0.5 + 1.25 ' + 0.13 (ρl − 0.01) f ju fc Ag
(13.78)
Based on the energy balance considerations [Seible, 1997], the characteristic hoop reinforcement strain energy for elastoplastic stress-strain characteristics of mild steel in the form of [ fhy εhu] can be expressed for carbon jackets with essentially linear elastic stress-strain characteristic in the form of [ 12 fju εju], which for typical mild steel ( fy = 66 ksi, εsu = 15%) and unidirectional carbon tows ( fju = 200 ksi, εju = 1%) would result in an efficiency reduction to approximately 10% for the carbon jacket due to the low strain limits. However, tests on carbon fiber jacketed columns at UCSD [Seible et al., 1994a, 1994b, 1995a, 1995b, 1995c, 1995d] have shown that significantly higher compression strains (by a factor of three to four) can be achieved in the confined concrete than predicted by the energy balance approach, which can be attributed to the reduced concrete dilation due to the lower ultimate strain limits in the carbon jacket. Thus, for carbon jacket retrofit designs the confinement efficiency can conservatively be increased by at least a factor of two, resulting in an equivalent confinement factor of: ks = 5ks = 0.8 2 × 0.1
(13.79)
D fc' P 0.5 + 1.25 ' + 0.13 (ρl − 0.01) 5 f ju fc Ag
(13.80)
kj = or a carbon jacket thickness: tj =
The ultimate compression strain in the confined concrete can be expressed based on Mander et al. [1988b] as: ε cu = 0.004 +
2 × 1.4 ρ j f ju ε ju fcc'
(13.81)
where fcc' = the compression strength of the confined concrete conservatively taken as 1.5 fc' and the factor 2 again represents the conservative estimate of increased compression strains based on the observed experimental data from carbon fiber jacket confined plastic hinges. With this ultimate concrete strain and a depth cu for the flexural compression zone calculated as part of normal flexural strength calculations or from a moment curvature analysis, the resulting ultimate curvature: φu =
© 2003 by CRC Press LLC
ε cu cu
(13.82)
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can be determined. Together with the φy from an equivalent bilinear moment curvature approximation (obtained from the moment curvature section analysis) the curvature ductility: µφ =
φu φy
(13.83)
can be determined, which in turn can be expressed in the form of a member ductility factor:
) L 1 − 0.5 L
(
µ∆ = 1 + 3 µφ − 1
Lp
Lp
(13.84)
where Lp is the equivalent plastic hinge length defined as: L p = 0.08 L + 0.022 fsydb
(13.85)
where fsy is the yield strength [ksi] and db is the bar diameter of the longitudinal column reinforcement. Note Equation 13.85 is the same as the one used to assess unretrofitted columns since 90° carbon fiber wraps do not contribute to longitudinal column capacities or provide restrictions to the plastic hinge development. Alternatively, for a given εcu , which can directly be derived based on design ductility requirements from back calculation of Equations 13.84 to 13.81, the required jacket thickness can be expressed as: tj =
ρjD 4
= 0.09
D (ε cu − 0.004) fcc' f ju ε ju
(13.86)
which generally results in a more economical jacket thickness than required by the standard confinement Equations 13.38 and 13.80. To prevent column bar buckling in the plastic hinge region [Priestley et al., 1996], a volumetric transverse reinforcement ratio of: ρs =
0.45 ⋅ n ⋅ fs2 E ds Et
(13.87)
is required, where E ds =
(
4E s E i Es + Ei
)
2
(13.88)
and Et = the modulus of elasticity of the transverse reinforcement n = the number of longitudinal reinforcing bars fs = steel stress at a strain of 4% in the longitudinal reinforcement or 74 ksi (510 MPa) for grade 60 steel Es = the secant modulus from fs to fu Ei = the initial elastic modulus of the longitudinal reinforcement
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For longitudinal grade 60 steel Eds can thus be determined as 657 ksi (4530 MPa), resulting in: ρs = 3.75
n Et
(13.89)
with Et in [ksi] units. For a carbon fiber jacket Equation 13.89 can be expressed as: ρs =
4t j D
= 3.75
n E j [ksi]
(13.90)
The antibuckling requirement of Equation 13.90 only needs to be checked for slender columns where Li, the distance between maximum moment location and point of inflection, is greater than 4D, i.e., M/(VD) > 4. Note that all of the above considerations apply to circular columns. 13.6.1.2 Design of Flexural Confinement Retrofits For confinement of flexural plastic hinge regions where the ultimate jacket stress controls the design, a long-term durability strength reduction factor of 0.9 should be employed for the carbon jacket design. For other composite materials appropriate strength reduction factors based on their expected durability characteristics should be assigned. Circular columns: For circular columns with column diameter D, longitudinal reinforcement ratio ρ, expected concrete strength fc' , axial load P, gross section area Ag, and ultimate jacket modulus fju, the carbon jacket thickness t can be determined as:
tj =
Dfc' 4.5 f ju
P 0.5 + 1.25 ' + 0.13 (ρl − 0.01) fc Ag
(13.91)
The resulting member ductility should be checked based on Equations 13.81 to 13.84. Alternatively, for a given member ductility µ∆ and required ultimate concrete strain εcu : t j = 0.09
D (ε cu − 0.004) fcc' 0.9 f ju ε ju
= 0.1
D (ε cu − 0.004) fcc' f ju ε ju
(13.92)
can be provided. To prevent column bar buckling for columns with shear span L D = M (V ⋅ D) > 4 a minimum jacket thickness of: tj =
nD [in. ] E j [ ksi ]
(13.93)
should be provided. Rectangular columns: For side aspect ratios ≤ 1.5, rectangular columns can be retrofitted for flexural confinement with rectangular jackets under the following design considerations: 1. The corners need to be rounded to a radius of ≥ 2 in. (1 in. was used in the laboratory tests) 2. The jacket thickness t should be twice that determined from a column with equivalent circular jacket diameter De
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In all other cases where the side aspect ratio > 1.5, oval or circular carbon jackets should be designed by adding oval or circular concrete segments to the bridge column sides prior to wrapping and curing. Extent of flexural hinge confinement retrofit: The jacket thickness tj must be extended beyond the expected plastic hinge region. For bridge columns with typical axial load ratios P / ( fc' Ag ) ≤ 0.3, the confinement length Lc1 should be greater than L/8 and greater than 0.5D, measured from the location of maximum moment. In addition, a reduced jacket thickness of 0.5tj should be extended for a distance Lc2 defined by the same criteria as Lc1 but starting at Lc1. Furthermore, where jackets and/or concrete bolsters add significantly to the column dimension in the loading direction, a gap g between the retrofit measure and the adjacent bridge bent member (cap or footing) needs to be provided to avoid any strength and stiffness increase from the retrofit. For most bridge columns and retrofits a gap of 2 in. (51 mm) is sufficient to meet this objective. Other gap widths can be explicitly calculated based on the maximum expected hinge rotation and column bar buckling considerations. Shear retrofit: Carbon jackets of thickness tj contribute an additional or fourth term to the shear resistance mechanism outlined in Equation 13.39 in the form: π f t D cot θ (circular) 2 jd j V j = 2 f jd t j D cot θ (rectangular) Vj =
(13.94)
where tj is the carbon jacket thickness, fjd the design stress level in the jacket, and D the column dimension in the loading direction. Again, conservatively, a 45° force transfer mechanism, or cot θ = 1 can be assumed for the jacket design. While Equation 13.94 clearly indicates that the jacket contribution depends on the jacket stress, a stress level less than the ultimate capacity fju is assumed to limit the horizontal column dilation. Tests at UCSD [Priestley et al., 1993a, 1993b; Priestley and Seible, 1991] have shown that, when the column dilation exceeds 0.4 to 0.6% in the loading direction, the concrete contribution to the shear capacity degrades rapidly, thus a strain limit rather than a strength limit needs to be employed for the jacket design. A strain limit of εjd = 0.4% is a conservative design value, which is well below the ultimate strain limit of −1% for carbon jacket but higher than the yield strain of the horizontal column reinforcement, which will ensure that the column reinforcement shear contribution in Equation 13.42 will be fully activated. Thus, in Equation 13.94: f jd = 0.004 E j
(13.95)
should be used for the composite jacket shear design. The carbon jacket shear retrofit design can be summarized as follows. The shear design demand originates, based on the capacity design principles, from the plastic column shear or the shear at full over strength Vo . With a shear strength reduction factor φ = 0.85, the column shear design requires that: Vn = Vc + Vs + Vp + V j ≥
Vo φ
(13.96)
Unless more reliable actual plastic shear information is available Vo can be conservatively estimated as 1.5 times Vyi or 1.5 times the ideal shear capacity of the column at ductility µ∆ = 1, or: Vj ≥
© 2003 by CRC Press LLC
(
Vo − Vc + Vs + Vp φ
)
(13.97)
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For circular columns the jacket thickness tj can be determined as:
(
)
(
)
Vo − Vc + Vs + Vp 159 Vo φ = − Vc + Vs + Vp tj = π E jD φ ⋅ 0.004E j ⋅ D 2
(
)
(13.98)
and for rectangular columns: Vo − Vc + Vs + Vp 125 Vo φ = − Vc + Vs + Vp tj = 2 × 0.004 E j ⋅ D E jD φ
(
)
(13.99)
Since the concrete shear contribution Vc is different inside the plastic hinge confinement region (Lc) and outside (Lv), two jacket thicknesses for shear have to be derived and provided over the regions Liv and Lov , respectively. To avoid shear problems within and in direct proximity to the flexural plastic hinge, the shear retrofit length Liv should be extended to Liv = 1.5D or one and a half times the column dimension in the loading direction measured from the point of maximum moment.
13.6.2 Buildings 13.6.2.1 Problem Statement The soft first story concept [Fintel and Khan, 1969] is an attempt to reduce accelerations in a building by allowing the first-story columns to yield during an earthquake and produce energy-dissipation action. However, excessive drifts in the first story coupled with P-∆ effects on the yielded columns make buildings collapse [Fintel, 1991]. Hence, seismic retrofit of these kinds of buildings is needed. The problem can be corrected by either introducing additional energy dissipation capacity in order to reduce first-story energy or by providing a mechanism to reduce P-∆ effects or both. Such modifications of the soft first story concept are now a reality [Boardman et al., 1983]. More recently, nonductile columns fitted with Teflon sliders were suggested to reduce P-∆ effects on building design [Chen and Constantinou, 1990]. However, it is not practical because nonductile columns to resist strong earthquake forces and remain elastic are not economical. In general, it is accepted that inelastic behavior and thus damage to the building will occur. Inelastic action has the effect of lengthening the fundamental period of the building and of generating damping or energy-absorbing action and in this way reducing the accelerations at the upper levels of the building. The goal should be to reduce the accelerations in buildings to be less than the ground accelerations, and to do this the building must be flexible. Flexibility in a structural frame will cause problems in the fabric of the building. Windows may fall out in the wind; partition walls will crack; floors will vibrate under foot. In a low- or medium-rise building the necessary flexibility can only be achieved at the foundation level by the use of base isolation [Kelly, 1986]. A new approach was proposed by Mo and Cheng [1993]. In this system, Teflon sliders are placed on the top of the first story reinforced concrete framed shear walls. These shear walls are framed by columns and beams, and are designed to carry a portion of the weight of the superstructure and the lateral load determined by the frictional characteristics of the Teflon sliders. The remaining first-story columns are designed for ductile behavior in order to accommodate large drifts. According to this proposed system, an analytical model is described. To determine the effects of variables on the dynamic response of the proposed system, parametric studies are performed, and the results are discussed in detail. 13.6.2.2 Proposed System In the proposed system a major part of the weight of the building is carried by the Teflon sliders placed on top of the most heavily loaded shear wall of the first story. The least loaded columns on the first floor © 2003 by CRC Press LLC
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Reinforced Concrete Structures
(a)
(b) m7
m7
K7
4.8 m K7 4.2 m 3.75 m 3.75 m 3.75 m 3.75 m
m1
m1 A
4.2 m
K1 6.2 m
2.7 m 3.9 m
mS kS
K1DC
Shear wall Teflon Slider
(c)
(d) A
m7 K7
I st floor Teflon sheet Stainless steel plate
Shear wall m1
mS Pf(t)
K1DC
kS
FIGURE 13.28 (a) Reinforced concrete seven-story frame; (b) model of the proposed system; (c) detail of the firststory shear wall with Teflon sliders on top; (d) dynamic model of the proposed system.
(termed ductile columns) are designed to accommodate large drifts. Figure 13.28a shows a reinforced concrete seven-story frame. This structure is a hospital located in Tianjing City, China. When the proposed system is applied to this structure, it becomes the form shown in Figure 13.28b. A portion of the weight of the structure is carried by the first-story shear wall, which is fitted with Teflon sliders on top. The first-story shear wall is designed for a lateral load determined by the frictional characteristics of the Teflon sliders [Constantinou et al., 1990]. The proposed system is also able to reduce P-∆ effects, when a framed shear wall is used. The lateral force is shared by the ductile columns and the framed shear wall, which behave in distinctly different ways. Drift in the framed shear wall is very small and P-∆ effects are, therefore, insignificant. 13.6.2.3 Computer Model To illustrate the analytical model of the proposed system, the hospital mentioned previously is employed again. It should be noted that Figure 13.28a is a conventional frame structure; Figure 13.28b is a proposed system; Figure 13.28c is a detailing for the first-story shear wall with Teflon sliders on top; Figure 13.28d © 2003 by CRC Press LLC
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is the dynamic model for the proposed system. In Figure 13.28c, uplift control is not considered because for reinforced concrete construction of up to seven stories, uplift on the bearing will not occur and will be unimportant [Kelly, 1986]. The stiffness of the shear wall, ks, varies depending on stress level. The first-story ductile columns have total initial stiffness K1DC and yield displacement Y1DC given by: K1DC = K1 (1 − n)
(13.100)
Y1DC = Y1R
(13.101)
in which n is the portion of weight carried by the sliders normalized by the total weight, K1 and Y1 are the initial stiffness and yield displacement, respectively, of the first story of the conventionally designed structure, and R is a reduction factor applied to the yield displacement of the first-story columns of the conventional design. The shear wall together with its beam is treated as an inelastic single degree of freedom system with mass, ms: 1 ms = nm1 3
(13.102)
where m1 is the mass at the first floor. The factor 1/3 in Equation 13.102 reflects the fact that the mass of the beam at the top of the shear wall is less than that of the first floor [Chen and Constantinou, 1990]. When R = 1.0 and n = 0.0, we have the conventional design. For n = 0.0, and R less than unity we have a conventional soft first story [Chopra et al., 1973]. Other combinations of n and R result in systems with the characteristics of the proposed system. The equations of motion of the system are: MX˙˙ + CX˙ + KX + Pf = − MX˙˙ g
(13.103)
ms x˙˙s + c s x˙ s + ks x s − p f = −ms X˙˙ g
(13.104)
in which M, C, and K are the mass, damping, and stiffness matrices, respectively. X˙˙ g is the ground acceleration and X is the floor displacement vector with respect to the ground. KX represents the vector of the restoring forces, which are described by Takeda’s degrading stiffness model [Takeda et al., 1970]. ms, cs, and ks are mass, damping, and stiffness, respectively, for the shear wall. xs represents the displacement of the top of the shear wall with respect to ground. ksxs is the restoring force in the shear wall, which is described by Mo’s model [Mo, 1988; Jost and Mo, 1991]. Pf is the vector of frictional force which has one non-zero entry at the first-floor level equal to pf . pf is the frictional force mobilized at the sliding interfaces, and is described by the following equation [Constantinou et al., 1990; Mokha et al., 1990]: p f = µ( x˙ r ) nWZ
(13.105)
in which nW is the portion of the weight carried by the sliding bearings. Z is a parameter taking values in the range (−1, 1) and µ is the coefficient of sliding friction, which is a function of the relative velocity between the first floor and the top of the shear wall, x˙ r = x˙ 1 − x˙ s . For Teflon sliding against polished stainless steel of mirror finish the sliding coefficient of friction is given by:
(
µ = f max − Df × exp − a x˙ r
)
(13.106)
Experimentally determined parameters fmax, Df, and a are friction parameters and are given elsewhere [Mokha et al., 1990]. It should be noted that these parameters depend on the condition of interface and © 2003 by CRC Press LLC
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TABLE 13.2 Parameters in Model of Friction of Teflon Bearings Bearing Pressure (MPa) 6.9 13.8 6.9
Type of Teflon
fmax
Df
a (s/m)
Unfilled Unfilled Glass filled at 15%
0.1193 0.0870 0.1461
0.0927 0.0695 0.1060
23.62 23.62 23.62
Source: Mokha, A. et al., 1990, J. Struct. Eng., 116(2), 438–454.
bearing pressure. fmax is the maximum value of the friction coefficient which is mobilized at large velocities. (fmax − Df) represents the value of the coefficient of friction at essentially zero velocity of sliding. For the cases studied, bearing pressure is 6.9 MPa for which fmax = 0.1193, Df = 0.0927, and a = 23.62 s/m (see Table 13.2). 13.6.2.4 Discussion The structural system described relies on the frictional properties of sliding bearings on top of the shear wall and on the energy absorption capability of a number of accurately designed ductile columns to protect the structure from large lateral forces. In this system the sliding bearings play an important role and, consequently, factors affecting their frictional properties are of paramount importance. The frictional properties of Teflon sliding bearings are influenced by a number of parameters. One of the most influential parameters is the velocity of sliding. This effect has been properly accounted for. However, the value of friction used has been based on experiments that were conducted on fresh and clean specimens with the load sustained for a short interval of time. The effects of surface contamination and dwell of load on the frictional properties are important considerations in design. Surface contamination is known to cause substantial increase in the coefficient of friction. Bearings in service should be provided with skirts or bellows to prevent airborne contamination. The effect of dwell of load is an important consideration in the system described because, unlike bridge applications, the bearings may sustain load for a number of years before any sliding movement occurs. This effect has been studied. A specimen had been under load for almost 2 years before testing. The effect of the 2-year dwell of load on the recorded frictional properties was found to be insignificant. Interestingly in these tests, the polished stainless steel plate in the testing arrangement, which had been stored in a highly humid environment, showed no deterioration and in particular no change in the degree of surface roughness. 13.6.2.5 Algorithm The procedures for the system being described are explained as follows (Figure 13.29). Right after initialization is performed, sliding friction force needs to be determined. As a result, the SDOF shear wall and the MDOF frame can be analyzed for seismic response. The remaining procedures are similar to those for pure frame systems. When the responses are found at the time ti+1, the same procedures as mentioned above are repeated for time until the end of the time history. The algorithm is demonstrated in Figure 13.29. 13.6.2.6 Parametric Studies 13.6.2.6.1 Shear Building Modeling The primary concern of these studies is whether the ductility demand and damage in the upper stories of a building with the proposed system are significantly reduced in comparison with the ductility demand and damage in the conventional design. For this purpose the 1940 El Centro motion, scaled to 0.4 g, is used. The structure analyzed is as shown in Figure 13.28. This structure is a reinforced concrete sevenstory hospital building, located in Tianjing City, China, and was designed according to the Chinese seismic design code for a 0.2 g peak ground acceleration. Following the 1976 Tangshan earthquake, in which the structure suffered a moderate degree of damage, a comprehensive study of it was performed. The actual mass, stiffness, and strength distribution of the structure were determined in the study. Table 13.3 presents the story initial stiffness, yield strength and displacement, and the floor weight in a © 2003 by CRC Press LLC
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Initialize values Find sliding friction force Perform response analysis for SDOF shearwall Perform response analysis for MDOF frame Calculate incremental load
Calculate effective incremental load
Find incremental displacement for extended time interval
Calculate incremental acceleration for extended time interval
Calculate incremental acceleration for normal time interval
Calculate incremental velocity and displacement for normal time interval Calculate displacement and velocity at time ti+1 Calculate acceleration at time ti+1 Output displacement and force, etc.
FIGURE 13.29 Algorithm for dynamic analysis of the proposed system.
TABLE 13.3 Properties of Seven-Story Structure Story
Initial Stiffness Ki (kN/mm)
Yield Strength Yi (mm)
Yield Strength Fyi (kN)
Weight (kN)
1 2 3 4 5 6 7
64.5 63.4 72.2 72.1 68.7 52.3 16.8
17.70 17.28 13.09 10.01 8.56 8.21 15.93
1141 1095 951 722 588 430 268
1011 953 953 934 982 1059 751
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(b) 7
7
6
6
5
5 n = 0.0 R = 1.0 R = 0.5 R = 0.3 R = 0.1
4 3 2 R
1.0
0.5
0.3
Story
Story
(a)
3 2
0.1
R
1
1.0
0.5
0.3
0.1
1 Drift 0.0119 0.0214 0.0281 0.0238
Drift 0.0042 0.0127 0.0186 0.0269 0
0 0.0
1.0
2.0 3.0 4.0 Ductility Demand
0.0
5.0
(c)
1.0
2.0 3.0 4.0 Ductility Demand
5.0
(d) 7
7
6
6
5
5 n = 0.5 R = 1.0 R = 0.5 R = 0.3 R = 0.1
4 3 2 R
1.0
0.5
0.3
Story
Story
n = 0.3 R = 1.0 R = 0.5 R = 0.3 R = 0.1
4
n = 0.8 R = 1.0 R = 0.5 R = 0.3 R = 0.1
4 3 2
0.1
R
1
1.0
0.5
0.3
0.1
1 Drift 0.0371 0.0340 0.0380 0.0414
Drift 0.0202 0.0300 0.0243 0.0295 0
0 0.0
1.0
2.0 3.0 4.0 Ductility Demand
5.0
0.0
1.0
2.0 3.0 4.0 Ductility Demand
5.0
FIGURE 13.30 Displacement response of seven-story structure for scaled El Centro motion.
shear-type representation of the structure. The total weight of the frame is 6643 kN and the fundamental period is 1.15 s. The shear wall used in these studies have the following properties: concrete compressive strength, fc' = 28 Mpa; longitudinal steel yield strength, fly = 420 Mpa; longitudinal steel ratio = 0.0025. The height, width, and thickness are 3.05 m, 4.41 m, and 12.7 cm, respectively, and the bearing pressure of Teflon sliders with unfilled sheet type remains 6.9 MPa for all the cases. Specific values considered are R = 1.0, 0.5, 0.3, and 0.1 and n = 0.0, 0.3, 0.5, and 0.8. For example, the case n = 0.5, R = 0.5 corresponds to a design in which 50% of the superstructure’s weight is carried by sliders and the yield displacement of the first-story ductile columns is half the yield displacement of the original conventional design. The results for ductility demand, damage assessment, fundamental mode shape, restoring forcedisplacement loops, and displacement-time history are discussed below. Figures 13.30 and 13.31 present the displacement ductility demands of the described seven-story building when subjected to the scaled El Centro motion and when the yield strength of the first story is reduced by factor R ( = 1.0, 0.5, 0.3, 0.1) and parameter n takes values of 0.0, 0.3, 0.5, and 0.8, respectively. The case n = 0.0 corresponds to the conventional soft first story. The drifts in the first stories are normalized by story height. Clearly, the ductility demand in the superstructure reduces with increasing values of n and decreasing values of R. Figure 13.32 shows the damage assessment of the described seven-story building when the double index criteria are used. The damage criterion proposed by Chen and Gong [1986], also plotted in Figure 13.32, distinguishes minor, moderate, and severe damage. Minor damage is defined with the occurrence of minor cracks with partial crashing of concrete in columns. Moderate damage corresponds to the occurrence of extensive large cracks, whereas severe damage corresponds to extensive crushing of concrete or collapse. Minor and moderate damage are considered repairable. It can be seen that the damage indices reduce quite a lot when R = 1.0 and n = 0.0 are changed to R = 1.0 and n = 0.5, and the © 2003 by CRC Press LLC
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(b) 7
7
6
6
5
5 R = 1.0 n = 0.0 n = 0.3 n = 0.5 n = 0.8
4 3 2 n
0.0
0.3
0.5
Story
Story
(a)
R = 0.5 n = 0.0 n = 0.3 n = 0.5 n = 0.8
4 3 2
0.8
n
1
0.3
0.5
0.8
Drift 0.0127 0.0214 0.0300 0.0340
0
0 0.0
1.0
2.0 3.0 4.0 Ductility Demand
5.0
(c)
0.0
1.0
2.0 3.0 4.0 Ductility Demand
5.0
(d) 7
7
6
6
5
5 R = 0.3 n = 0.0 n = 0.3 n = 0.5 n = 0.8
4 3 2 n
0.0
0.3
0.5
Story
Story
0.0
1 Drift 0.0042 0.0119 0.0202 0.0371
R = 0.1 n = 0.0 n = 0.3 n = 0.5 n = 0.8
4 3 2
0.8
n
1
0.0
0.3
0.5
0.8
1 Drift 0.0186 0.0281 0.0243 0.0380
Drift 0.0269 0.0238 0.0295 0.0414
0
0 0.0
1.0
2.0 3.0 4.0 Ductility Demand
5.0
0.0
1.0
2.0 3.0 4.0 Ductility Demand
5.0
FIGURE 13.31 Displacement ductility response of seven-story structure for scaled (0.4 g) 1040 El Centro motion. Drift is normalized by story height (n varies).
7.0 6.0 5.0 Energy Index
Severe damage 4.0 R = 1.0 ; n = 0.0 R = 1.0 ; n = 0.5 R = 0.5 ; n = 0.5
3.0
2.0
Moderate Minor
1.0
No damage 0.0 0.0
1.0
2.0
3.0 4.0 5.0 Ductility Index
FIGURE 13.32 Damage assessment of the seven-story structure.
© 2003 by CRC Press LLC
6.0
7.0
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TABLE 13.4 Natural Period of First Four Modes of Each Case (in sec) Case
Mode 1
Mode 2
Mode 3
Mode 4
C n n n
1.147 1.209 1.310 1.679
0.452 0.466 0.480 0.524
0.302 0.312 0.321 0.338
0.213 0.220 0.225 0.233
3.0
R = 1.0 ; n = 0.0 R = 1.0 ; n = 0.8
Displacement (cm)
2.0 1.0 0.0 −1.0 −2.0 −3.0 0.0
2.0
4.0 6.0 Time (sec.)
8.0
10.0
FIGURE 13.33 Displacement-time history for the top story.
damage indices further reduce significantly when both R and n are changed to 0.5 (i.e., severe damage becomes no damage). The effect of parameter n on the natural period of the seven-story building is also studied. Table 13.4 gives the results for the first four modes. It can be seen from Table 13.4 that the natural period is increased with increasing values of n. Finally, Figure 13.33 gives the deflection-time history for the top story with R = 1.0 and n = 0.0 or 0.8. Clearly, the deflection reduces significantly when parameter n is changed from 0.0 to 0.8. 13.6.2.6.2 Two-Dimensional Modeling The primary concern of these studies is whether the energy dissipation and story drift in the upper stories of a building with the proposed system are significantly reduced in comparison with those in the conventional design. For this purpose the 1940 El Centro motion, scaled to 0.4 g, is used. The structure analyzed is shown in Figure 13.34. The properties of this structure are also shown in this figure. The shear wall used in these studies has the following properties: concrete compressive strength, fc' = 31.1 MPa; longitudinal steel yield strength, fly = 350 MPa; longitudinal steel ratio = 0.0025. The height, width, and thickness are 27.9 cm, 30.5 cm, and 5.0 cm, respectively, and the bearing pressure of Teflon sliders with unfilled sheet type keeps 6.9 MPa [Chen and Constantinou, 1990] for all the cases. Specific values considered are R = 1.0, 0.5, 0.3, and 0.1 and n = 0.0, 0.3, 0.5, and 0.8. For example, the case n = 0.5, R = 0.5 corresponds to a design in which 50% of the superstructure’s weight is carried by sliders and the yield displacement of the first-story ductile columns is half of the yield displacement of the original conventional design. The results for moment-curvature hysteretic loops, steel yield locations, normalized drifts, and displacement history are discussed. Figures 13.35 and 13.36 show the moment-curvature hysteretic loops of the exterior column in the first story. Figure 13.35 indicates the results for the cases when R = 0.5 and n varies, while Figure 13.36 shows those for n = 0.5 and R varies. It can be seen from Figure 13.35 that the energy dissipated by the moment-curvature hysteretic loops increases with increasing value of n. It can also be seen from Figure 13.36 that for the case when R = 1.0 and n = 0.5, the moment-curvature relationship is linear © 2003 by CRC Press LLC
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3 @ 305 mm
1
1
2
2
279 mm
2
2
2
2
3
4
4
3
= 0.227 N-sec2 / mm
2
2
2
mass per floor
3
3
3
3
As2 = 12.75 mm2
2
2
2
As1 = 8.5 mm2
3
3
3
3
fcy = 31.1 MPa
2
2
2
fsy = 350 MPa
3
3
3
3
ρc = 0.268
2
2
2
ρs = 0.0039
3
3
3
3
Ec = 20,733 MPa
2
2
2
Es = 200,000 MPa
3
3
3
3
3
3
3
3
3
3
3 1
8 @ 229 mm
1
1
1
3
3
3
3
3
39 mm
39 mm 6.36
39 mm
As1
As2 6.36
6.36
As2 6.36
As1
section 1
4
4
4
4
50.9 mm
279 mm
cross-section type
39 mm 38.1 mm
1
1
1
section 2 section 3
section 4
FIGURE 13.34 A ten-story frame.
(i.e., no energy dissipated), and the case with R = 0.5 and n = 0.5 has greater energy dissipations than the remaining cases. Figures 13.37 and 13.38 show the steel yield locations in the frame. Figure 13.37 indicates the results for the cases when n = 0.5 and R varies, while Figure 13.38 shows those for R = 0.3 and n varies. It can be seen from Figure 13.37 that the number of steel yield locations decreases with decreasing the value of R. It can also be seen from Figure 13.38 that the number of steel yielding locations decreases with increasing the value of n. In conclusion, a new system for the seismic retrofitted reinforced concrete buildings has been presented, in which first-story shear walls are fitted with Teflon sliders while the remaining first-story columns are designed with reduced yield strength. With this system energy dissipation is increased and the number of steel yield locations, normalized story drifts, and displacements in the superstructure are significantly reduced. © 2003 by CRC Press LLC
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21000
21000
case ; R = 0.5 ; n = 0.0
7000 0 −7000 −14000
7000 0 −7000 −14000
−21000 −0.05
18000
−0.02 0.00 0.02 Curvature (1/cm)
−21000 −0.05
0.05
15000
case ; R = 0.5 ; n = 0.5
−0.03 0.00 0.03 Curvature (1/cm)
0.06
case ; R = 0.6 ; n = 0.6
10000 Moment (N-cm)
12000 Moment (N-cm)
case ; R = 0.5 ; n = 0.3
14000 Moment (N-cm)
Moment (N-cm)
14000
6000 0 −6000 −12000
5000 0 −5000 −10000
−18000 −0.07
−0.03 0.00 0.03 Curvature (1/cm)
−15000 −0.12
0.07
−0.06 0.00 0.06 Curvature (1/cm)
0.12
FIGURE 13.35 Restoring moment curvature loops of the first story.
18000
18000
case ; R = 1.0 ; n = 0.5
6000 0 −6000
6000 0 −6000
−12000
−12000
−18000 −0.0012 −0.0006 −0.0000 0.0006 0.0012 Curvature (1/cm)
−18000 −0.07
15000
10600
case ; R = 0.5 ; n = 0.5
5000 0 −5000 −10000 −15000 −0.10
−0.00 0.03 Curvature (1/cm)
0.07
case ; R = 0.1 ; n = 0.5
3600 0 −3600 −7000
−0.06
−0.00 0.06 Curvature (1/cm)
0.10
−10600 −0.07
FIGURE 13.36 Restoring moment curvature loops of the first story.
© 2003 by CRC Press LLC
−0.03
7000 Moment (N-cm)
10000 Moment (N-cm)
case ; R = 0.5 ; n = 0.5
12000 Moment (N-cm)
Moment (N-cm)
12000
−0.03
−0.00 0.03 Curvature (1/cm)
0.07
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R = 1.0 ; n = 0.5
R = 0.5 ; n = 0.5
R = 0.3 ; n = 0.5
R = 0.1 ; n = 0.5
indicates “already yielded” FIGURE 13.37 Yielded locations in the plane frame with n = 0.5.
R = 0.3; n = 0.0
R = 0.3; n = 0.3
R = 0.3; n = 0.5
R = 0.3; n = 0.8
indicates “already yielded” FIGURE 13.38 Yielded locations in the plane frame with R = 0.3.
Defining Terms Bauschinger effect — In the reversed loading of steel, after loading past the yield point in one direction, the yield stress in the opposite direction is reduced. Column — A vertical member of approximately equal dimensions in both horizontal planes, and carrying vertical load. Columns may or may not be part of the lateral-force-resisting system. Confined concrete — Concrete is confined by transverse reinforcement, commonly in the form of closely spaced steel spirals or hoops to increase the ductility of concrete. Damage assessment — An assessment to evaluate the damage of a structure due to large loads. Damping coefficient — The ratio of the viscous damping to the critical damping.
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Ductility — The ratio between the maximum displacement for elastoplastic behavior and the displacement corresponding to yield point.
Energy dissipation — The area bounded by the hysteretic loops of the load-displacement relationships of a structure. Inelastic response — A structure is subjected to a large excitation, resulting in yielding of longitudinal rebars. Load-displacement relationship — The relationship between the load on a structure and the correspond displacement. Low-cycle fatigue — When a rebar is subjected to cyclic loading, the maximum strength is less than the maximum strength of monotonic tensile tests. Natural period — The time interval for a vibration system in free vibration to do one oscillation. P − ∆ effect — The secondary effect on shears, axial forces, and moments of frame members induced by the vertical loads on the laterally displaced building frame. Performance-based design — The integrated effort of design, construction, and maintenance needed to produce engineered facilities of predictable performance for multiple performance objectives. Pinching effect — When a structure is subjected to reversed cyclic loading, the deformation with a small load becomes very large at the beginning of the reloading state. Plastic hinge length — A region in which longitudinal rebars in a member yield. Residual deformation — The remaining deformation after unloading of a structure. Seismic retrofit — A retrofit may be completed if the results of the detailed seismic assessment indicate the seismic demand is greater than the capacity. Shear capacity — The capacity of a member to resist shear force. It is reduced with increasing ductility. Shear retrofit — If the shear demand is greater than the shear capacity, a shear retrofit is needed. Soft first story — An attempt to reduce accelerations in a building by allowing the first-story columns to yield during an earthquake and produce energy dissipation action. Softened branch relation — When a rebar is subjected to cyclic loading, the reversal branch of the stress-strain relationship in each hysteretic loop is a parabolic curve. Softened compression stress-strain relationship of concrete — Viewing the shear action on a membrane element as a two-dimensional problem, the compressive strength of concrete in one direction is reduced by cracking due to tension in the perpendicular direction. Softening parameter — When a membrane element is subjected to shear, the compressive strength of concrete is reduced to approximately 40% to 60%. Stress strain-strain curve of a steel bar in concrete — A steel bar in concrete is stiffened by tensile stress of concrete. It relates the average stress to the average strain of a large length of bar crossing several cracks. Structural wall — An in-plane wall to reduce the relative interstory distortions of a building caused by seismic-induced motions.
References Aboutaha, R.S., Engelhardt, M.D., Jirsa, J.O., and Kreger, M.E. (1999). “Rehabilitation of Shear Critical Concrete Columns by Use of Rectangular Steel Jackets,” ACI Struct. J., 96, 68–78. ACI Committee 318 (1995). Building Code Requirements for Reinforced Concrete (ACI 318–95), American Concrete Institute, Detroit, MI, p. 369. Aschhiem, M., Moehle, J.P., and Werner, S.D. (1992). Deformability of Concrete Columns, Project report under Contract No. 59Q122, California Department of Transportation, Division of Structure, Sacramento, CA, June. Balan, T., Filippou, F., and Popov, E. (1998). “Hysteretic Model of Ordinary and High-Strength Reinforcing Steel,” J. Struct. Eng. (ASCE), 124, 288–297. Belarbi, A. and Hsu, T.T.C. (1994). “Constitutive Laws of Concrete in Tension and Reinforcing Bars Stiffened by Concrete,” Struct. J. Am. Concrete Inst., 91, 465–474. © 2003 by CRC Press LLC
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Belarbi, A. and Hsu, T.T.C. (1995). “Constitutive Laws of Softened Concrete in Biaxial Tension-Compression,” Struct. J. Am. Concrete Inst, 92, 562–573. Blume, J.A. (1970). “Design of Earthquake-Resistant Poured-in-Place Concrete Structures,” in Earthquake Engineering, R.L. Wiegel, Ed., Prentice-Hall, Englewood Cliffs, NJ, chap. 18. Boardman, P.R., Wood, B.J., and Carr, A.J. (1983). “Union House: A Cross Braced Structure with Energy Dissipators,” Bull. NZ Nat. Soc. Earthquake Eng., 16, 83–97. Caltrans. (1995). Memo to Designers Change Letter 02, California Department of Transportation, Sacramento, CA, March. Chen, Y.Q. and Constantinou, M.C. (1990). “Use of Teflon Sliders in a Modification of the Concept of Soft First Story,” Eng. Struct., 12, 243–253. Chen, Y.Q. and Gong, S. (1986). “Double Control Damage Index of Structural Ductility and Dissipated Energy during Earthquakes,” Chinese J. Building Struct., 7, 35–48 (in Chinese). Chopra, A.K., Clough, D.P., and Clough, R.W. (1973). “Earthquake Resistance of Buildings with a Soft First Story,” Earthquake Eng. Struct. Dyn., 1, 347–355. Constantinou, M.C., Mokha, A., and Reinhorn, A.M. (1990). “Teflon Bearings in Base Isolation. II. Modeling,” J. Struct. Eng. ASCE, 116, 455–475. Cusson, D. and Paultre, P. (1995). “Stress-Strain Model for Confined High-Strength Concrete,” J. Struct. Eng. ASCE, 121, 468–478. Diniz, M.C. and Frangopol, M. (1997). “Strength and Ductility Simulation of High-Strength Concrete Columns,” J. Struct. Eng. ASCE, 123, 1365–1373. Eibl, J. and Neuroth, U. (1988). Untersuchungen zur Druckfestigkeit von bewehrtem Beton bei gleichzeitig wirkendem Querzug, Institut für Massivbau and Baustofftechnologie, Universität Karlsruhe, Germany. Fajfar, P. and Krawinkler, H. (1998). “Seismic Design Methodologies for the Next Generation of Codes,” Proc. Sixth SECED Conference on Seismic Design Practice into the Next Century, Oxford, U.K., March 26–27, pp. 459–466. FEMA (Federal Emergency Management Agency) (2000a). “Prestandard and Commentary for the Seismic Rehabilitation of Buildings,” FEMA 356, Federal Emergency Management Agency, Washington, D.C., November. FEMA (Federal Emergency Management Agency) (2000b). “Global Topics Report on the Prestandard and Commentary for the Seismic Rehabilitation of Buildings,” FEMA 357, Federal Emergency Management Agency, Washington, D.C., November. Fintel, M. (1991). “Shearwalls: An Answer for Seismic Resistance?” Concrete International, July, 48–53. Fintel, M. and Khan, F.R. (1969). “Shock-Absorbing Soft Story Concept for Multistory Earthquake Structures,” ACIJ, 66, 381–390. Fujii, M., Kobayashi, K., Miyagawa,T., Inoue, S., and Matsumoto, T. (1988). “A Study on the Application of a Stress-Strain Relation of Confined Concrete,” Proc. JCA Cement Concrete, Japan Cement Assn., Tokyo, Japan, vol. 42, 311–313. Gergely, I., Pantelides, C.P., Nuismer, R.J., and Reaveley, L.D. (1998). “Bridge Pier Retrofit Using FiberReinforced Plastic Composites,” J. Composites Construct., 2, 165–174. Hoshikuma, J., Kawashima, K., Nagaya, K., and Taylor, A.W. (1997). “Stress-Strain for Reinforced Concrete in Bridge Piers,” J. Struct. Eng. ASCE, 123, 624–633. Hsu, T.T.C. (1993). Unified Theory of Reinforced Concrete, CRC Press, Boca Raton, FL. Hsu, T.T.C. and Mo, Y.L. (1985). “Softening of Concrete in Low-Rise Shear Walls,” J. Am. Concrete Inst., 82, 883–889. Hsu, T.T.C. and Zhang, L.X. (1997). “Nonlinear Analysis of Membrane Elements by Fixed-Angle SoftenedTruss Model,” J. Am. Concrete Inst., 94, 483–492. Hsu, T.T.C. and Zhu, R.H. (1999). “Post-Yield Behavior of Reinforced Concrete Membrane Elements: The Hsu/Zhu Ratios,” Proceedings Volume, U.S.–Japan Joint Seminar on Post-Peak Behavior of Reinforced Concrete Structures Subjected to Seismic Loads, Recent Advances and Challenges on Analysis and Design, Tokyo/Lake Yamanaka, Japan, Oct. 25–29, 1999, vol. 1, pp. 43–60. © 2003 by CRC Press LLC
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IBC (2000). International Building Code, International Code Council, Inc., International Conference of Building Officials, Whittier, CA. Iemura, H. and Takahashi, Y. (2001). “Development of High Seismic Performance RC Piers with Unbonded Bars,” Workshop on High Performance Materials in Bridges and Buildings, Hona, HI, July 29–August 3. Jost, S.D. and Mo, Y.L. (1991). “An Algorithm for Seismic Analysis of Low-Rise Structural Walls,” Nuclear Eng. Des., 131, 263–270. Karsan, I.D. and Jirsa, J.O. (1969). “Behavior of Concrete under Compressive Loadings,” J. Struct. Eng. ASCE, 95, 2543–2563. Kelly, J.M. (1986). “Aseismic Base Isolation: Review and Bibliography,” Soil Dyn. Earthquake Eng., 5, 202–216. Kent, D.C. and Park, R. (1971). “Flexural Members with Confined Concrete,” J. Struct. Div. ASCE, 97, 1969–1990. Kollegger, J. and Mehlhorn, G. (1990). “Experimentell Untersuchungen zur Bestimmung der Druckfestigkeit des gerissenen Stahlbetons bei einer Querzugbean-spruchung,” Report 413, Deutscher Ausschuβ für Stahlbetons, Berlin, Germany. Krawinkler, H. (1998). “Issues and Challenges in Performance Based Seismic Design,” Structural Engineers World Congress, San Francisco, CA, July 19–23. Mander, J.B. (1983). “Seismic Design of Bridge Piers,” Ph.D. thesis, Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand, chap. 8. Mander, J.B., Priestley, M.J.N., and Park, R. (1988a). “Theoretical Stress-Strain Model for Confined Concrete,” J. Struct. Div. ASCE, 114, 1804–1826. Mander, J.B., Priestley, M.J.N., and Park, R. (1988b). “Observed Stress-Strain Behavior of Confined Concrete,” J. Struct. Div. ASCE, 97, 1969–1990. Mander, J.B., Panthaki, F.D., and Kasalanati, A. (1994). “Low-Cycle Fatigue Behavior of Reinforcing Steel,” C J. Mat. Civ. Eng. ASCE, 6, 453–468. Mansour, M.Y. (2001). “Behavior of Reinforced Concrete Membrane Elements under Cyclic Shear: Experiments to Theory,” Ph.D. thesis, Department of Civil and Environmental Engineering, University of Houston, Houston, TX. Mansour, M.Y., Hsu, T.T.C., and Lee, J.Y. (2001a). “Cyclic Stress-Strain Curve of Concrete and Steel Bars in Membrane Elements,” J. Struct. Eng. ASCE, 127, 1402–1411. Mansour, M.Y., Hsu, T.T.C., and Lee, J.Y. (2001b). “Pinching Effect in Hysteretic Loops of R/C Shear Elements,” ACI Special Publication, American Concrete Institute, Toronto, Canada. MCEER (Multidisciplinary Center for Earthquake Engineering Research) (2000). “The Chi-Chi, Taiwan Earthquake of September 21, 1999: Reconnaissance Report,” Technical Report MCEER-00–0003, State University of New York at Buffalo. Mikame, A., Uchida, K., and Noguchi, H. (1991). “A Study of Compressive Deterioration of Cracked Concrete,” Proc. Int. Workshop on Finite Element Analysis of Reinforced Concrete, Columbia University, New York. Miyahara, T., Kawakami, T., and Maekawa, K. (1988). “Nonlinear Behavior of Cracked Reinforced Concrete Plate Element under Uniaxial Compression,” Concrete Library International, Japan Soc. Civ. Eng., 11, 131–144. Mo, Y.L. (1987). “Discussion of ‘Shear Design and Analysis of Low-Rise Structural Walls,’ by S.T. Mau and T.T.C. Hsu,” ACI Struct. J., 84, 91–92. Mo, Y.L. (1988). “Analysis and Design of Low-Rise Structural Walls under Dynamically Applied Shear Forces,” ACI Struct. J., 85, 180–189. Mo, Y.L. (1994). Dynamic Behavior of Concrete Structures, Elsevier, Amsterdam, 37–38. Mo, Y.L. and Chang, Y.F. (1993). “Effect of First Story Shearwalls with Teflon Sliders on EarthquakeResistant Buildings,” Mag. Concrete Res., 45, 293–299. Mo, Y.L. and Jost, S.D. (1993). “Tool for Dynamic Analysis of Reinforced Concrete Framed Shearwalls,” Comp. Struct., 46, 659–667. © 2003 by CRC Press LLC
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Mo, Y.L. and Kuo, J.Y. (1998). “Experimental Studies on Low-Rise Structural Walls,” Mat. Struct., RILEM, 31, 465–472. Mo, Y.L. and Perng, S.F. (2000). “Hybrid RC Frame-Steel Wall Systems,” SP-196, ACI Special Publication on Composite and Hybrid Systems, American Concrete Institute, Detroit, MI, pp. 189–213. Mo, Y.L. and Perng, S.F. (in press). “Analytical Model for Hybrid RC Frame-Steel Wall Systems,” ACI Fall Convention, Dallas, TX, American Concrete Institute. Mo, Y.L. and Rothert, H. (1997). “Effect of Softening Models on Behavior of Reinforced Concrete Framed Shearwalls,” ACI Struct. J., 94, 730–744. Mo, Y.L. and Shiau, W.C. (1993). “Ductility of Low-Rise Structural Walls,” Mag. Concrete Res., 45, 131–138. Mo, Y.L. and Yang, R.Y. (1996). “Dynamic Response of Box Tubes to Combined Shear and Torsion,” J. Struct. Eng. ASCE, 122, 47–54. Mokha, A., Constantinou, M.C., and Reinhorn, A.M. (1990). “Teflon Bearing in Base Isolation. I. Testing,” J. Struct. Eng. ASCE, 116, 438–454. Monti, G. and Nuti, C. (1992). “Nonlinear Cyclic Behavior of Reinforcing Bars Including Buckling,” J. Struct. Eng. ASCE, 118, 3268–3284. Muguruma, H., Watanabe, S., Tanaka, S., Sakurai, K., and Nakaruma, E. (1978a). “A Study on the Improvement of Bending Ultimate Strain of Concrete,” Proc. J. Struct. Eng., 24, 109–116. Muguruma, H., Watanabe, S., and Tanaka, S. (1978b). “A Stress-Strain Model of Confined Concrete,” Proc. JCA Cement and Concrete, Japan Cement Assn., Tokyo, Japan, vol. 34, pp. 429–432. Nawy, E.G. (1996). Reinforced Concrete — A Fundamental Approach, 3rd ed., Prentice-Hall, Upper Saddle River, NJ. Pang, X.B. and Hsu, T.T.C. (1995). “Behavior of Reinforced Concrete Membrane Elements in Shear,” Struct. J. Am. Concrete Inst., 92, 665–679. Pang, X.B. and Hsu, T.T.C. (1996). “Fixed-Angle Softened-Truss Model for Reinforced Concrete,” Struct. J. Am. Concrete Inst., 93, 197–207. Park, R. and Paulay, T. (1975). Reinforced Concrete Structures, John Wiley & Sons, New York. Park, R., Priestley, M.J.N., and Gill, W.D. (1982). “Ductility of Square-Confined Concrete Columns,” J. Struct. Div. ASCE, 108, 929–950. Peter, J. (1964). “Zur Bewehrung von Scheiben and Schalen für Hauptspannungen schiefwinklig zur Bewehrungsrichtung,” Dissertation, Lehrstuhl für Massivbau, Technische Hochschule Stuttgart, Germany. Priestley, M.J.N. and Seible, F., Eds. (1991). “Seismic Assessment and Retrofit of Bridges,” Structural Systems Research Project, Report No. SSRP-93/06, University of California, San Diego, CA, July, p. 426. Priestley, M.J.N., Seible, F., Verma, R., and Xiao, Y. (1993a). “Seismic Shear Strength of Reinforced Concrete Columns,” Structural Systems Research Project, Report No. SSRP-93/06, University of California, San Diego, CA, July, p. 120. Priestley, M.J.N., Verma, R., and Xiao, Y. (1993b). “Shear Strength of Reinforcement Concrete Bridge Columns,” Second Annual Seismic Research Workshop, Caltrans, Division of Structures, March 16–18. Priestley, M.J.N., Verma, R., and Xiao Y. (1994). “Seismic Shear Strength of Reinforcement Concrete Columns,” J. Struct. Eng. ASCE, 120, 2310–2329. Priestley, M.J.N., Seible, F., and Calvi, G.M. (1996). Seismic Design and Retrofit of Bridges, John Wiley & Sons, New York, pp. 147, 686. Razvi, S.R. and Saatcioglu, M. (1999). “Confinement Model for High-Strength Concrete,” J. Struct. Eng. ASCE, 125, 281–289. Robinson, J.R. and Demorieux, J.M. (1968). “Essais de Traction-Compression sur Modeles d’Âme de Poutre en Beton Arme,” Institute de Recherches Appliquées du Beton Arme (IRABA). Part I, June. Robinson, J.R. and Demorieux, J.M. (1972). “Essais de Traction-Compression sur Modeles d’Âme de Poutre en Beton Arme,” Institut de Recherches Appliquées du Beton Arme (IRABA). Part II, May. Rodriguez, M.E., Botero, J.C., and Villa, J. (1999). “Cyclic Stress-Strain Behavior of Reinforcing Steel Including Effect of Buckling,” J. Struct. Eng. ASCE, 125, 605–612. © 2003 by CRC Press LLC
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Saadatmanesh, H., Ehsani, M.R., and Jin, L. (1996). “Seismic Strengthening of Circular Bridge Pier Models with Fiber Composites,” ACI Struct. J., 93, 639–647. Saatcioglu, M. and Razvi, S.R. (1992). “Strength and Ductility of Confined Concrete,” J. Struct. Div. ASCE, 118, 1590–1607. Schlaich, J. and Schafer, K. (1983). “Zur Druck-Querzug-Festigkeit des Stahlbetons,” Beton-and Stahlbetonbau, March, pp. 73–78. Schlaich, J., Schafer, K., and Schelling, G. (1982). Druck und Querzug in bewehrten Betonelementen. Bericht, Institut für Massivbau, Universität Stuttgart, Germany, November. Seible, F. (1997). “Seismic Bridge Damage and Advanced Composite Retrofit of Bridge Columns,” Technical Seminar on Advanced Technologies for Bridge Infrastructure Renewal, National Taiwan University, Taipei, Taiwan, May 21–23. Seible, F., Hegemier, G.A., Priestley, M.J.N., Innamorato, D., Weeks, J., and Policelli, F. (1994a). “Carbon Fiber Jacket Retrofit Test of Circular Shear Bridge Column, CRC-2,” Advanced Composite Technology Transfer Consortium, Report No. ACTT-94/02, University of California, San Diego, September, p. 49. Seible, F., Hegemier, G.A., Priestley, M.J.N., and Innamorato, D. (1994b). “Seismic Retrofitting of Squat Circular Bridge Piers with Carbon Fiber Jackets,” Advanced Composites Technology Transfer Consortium, Report No. ACTT-94/04, University of California, San Diego, November, p. 55. Seible, F., Hegemier, G.A., Priestley, M.J.N., Innamorato, D., and Ho, F. (1995a). “Carbon Fiber Jacket Retrofit Test of Rectangular Flexural Column with Lap Spliced Reinforcement,” Advanced Composites Technology Transfer Consortium, Report No. ACTT-95/02, University of California, San Diego, June, p. 78. Seible, F., Hegemier, G.A., Priestley, M.J.N., Innamorato, D., and Ho, F. (1995b). “Rectangular Carbon Jacket Retrofit of Flexural Column with 5% Continuous Reinforcement,” Advanced Composites Technology Transfer Consortium, Report No. ACTT-95/03, University of California, San Diego, April, p. 52. Seible, F., Hegemier, G.A., Priestley, M.J.N., Innamorato, D., and Ho, F. (1995c). “Carbon Fiber Jacket Retrofit Test of Circular Flexural Columns with Lap Spliced Reinforcement,” Advanced Composites Technology Transfer Consortium, Report No. ACTT-95/04, University of California, San Diego, June, p. 78. Seible, F., Hegemier, G.A., Priestley, M.J.N., Innamorato, D., and Ho, F. (1995d). “Rectangular Carbon Jacket Retrofit Test of a Shear Column with 2.5% Reinforcement,” Advanced Composites Technology Transfer Consortium, Report No. ACTT-95/05, University of California, San Diego, July, p. 50. Seible, F., Priestley, M.J.N., Hegemier, G.A., and Innamorato, D. (1997). “Seismic Retrofit of RC Columns with Continuous Carbon Fiber Jackets,” J. Composites Construct. ASCE, 1, 52–62. Sheikh, S.A. and Uzumeri, S.M. (1980). “Strength and Ductility of Tied Concrete Columns,” J. Struct. Div. ASCE, 106, 1079–1102. Sheikh, S.A. and Uzumeri, S.M. (1982). “Analytical Model for Concrete Confinement in Tied Columns,” J. Struct. Div. ASCE, 108, 2703–2722. Sheikh, S.A., Shah, D.V., and Khoury S.S. (1994). “Confinement of High-Strength Concrete Columns,” ACI Struct. J., 123, 100–111. Sinha, B.P., Gerstle, K.H., and Tulin, L.G. (1964). “Stress-Strain Relation for Concrete under Cyclic Loading,” Am. Concrete Inst. J., 61, 195–211. Takeda, T., Sozen, M.A., and Nielsen, N.N. (1970). “Reinforced Concrete Response to Simulated Earthquakes,” Proc. ASCE, 96, 2557–2573. Takiguchi, K. et al. (1976). “Analysis of Reinforced Concrete Sections Subjected to Biaxial Bending Moments,” Trans. AIJ, 250, 1–8. UBC (1997). 1997 Uniform Building Code, International Conference of Building Officials, Whittier, CA. Ueda, M., Noguchi, H., Shirai, N., and Morita, S. (1991). “Introduction to Activity of New RC,” Proc. Int. Workshop on Finite Element Analysis of Reinforced Concrete, Columbia University, New York.
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Vecchio, F.J. and Collins, M.P. (1981). “Stress-Strain Characteristic of Reinforced Concrete in Pure Shear,” IABSE Colloquium, Advanced Mechanics of Reinforced Concrete, Delft, Final Report, International Association of Bridge and Structural Engineering, Zurich, Switzerland, pp. 221–225. Vecchio, F.J. and Collins, M.P. (1986). “The Modified Compression Field Theory for Reinforced Concrete Elements Subjected to Shear,” ACI Journal, 83, 219–231. Vecchio, F. and Collins, M.P. (1993). “Compression Response of Cracked Reinforced Concrete,” J. Struct. Eng. ASCE, 119, 3590–3610. Vecchio, F.J., Collins, M.P., and Aspiotis, J. (1994). “High-Strength Concrete Elements Subjected to Shear,” ACI Struct. J., 91, 423–433. Watanabe, F. and Nishiyana, M. (2001). “Controlled Yield Sequence of Reinforced in Concrete Memebers,” Workshop on High Performance Materials in Bridges and Buildings, Kona, HI, July 29–Aug.3. Watanabe, F., Lee, J.Y., and Nishiyama, M. (1995). “Structural Performance of Reinforced Concrete Columns with Different Grade Longitudinal Bars,” ACI Struct. J., 92, 412–418. Xiao, Y. and Martirossyan, A. (1998). “Seismic Performance of High-Strength Concrete Columns,” J. Struct. Eng. ASCE, 124, 241–251. Yeh, Y.K., Mo, Y.L., and Yang, C.Y. (2001). “Seismic Performance of Hollow Circular Bridge Piers,” ACI Struct. J., 98, 862–871. Yeh, Y.K., Mo, Y.L., and Yang, C.Y. (2002). “Seismic Performance of Rectangular Hollow Bridge Columns,” J. Struct. Eng. ASCE, 128, 60–68. Zhang, L.X. and Hsu, T.T.C. (1998). “Behavior and Analysis of 100 MPa Concrete Membrane Elements,” J. Struct. Eng. ASCE, 124, 24–34. Zhu, R.H. (2000). “Softened Membrane Model for Reinforced Concrete Elements Considering Poisson Effect.” Ph.D. thesis, Department of Civil and Environmental Engineering, University of Houston, Houston, TX. Zhu, R.H., Hsu, T.T.C., and Lee, J.Y. (2001). “A Rational Shear Modulus for Smeared Crack Analysis of Reinforced Concrete,” Struct. J. Am. Conc. Inst., 98, 343–350.
Further Reading Specific topics related to reinforced concrete structures subjected to earthquake loads can be found in the following references. Dowrick, D.J. (1987). Earthquake Resistant Design, 2nd edition, John Wiley & Sons, New York. FEMA (Federal Emergency Management Agency) (2000a). “Prestandard and Commentary for the Seismic Rehabilitation of Buildings,” FEMA 356, Federal Emergency Management Agency, Washington, D.C., November. FEMA (Federal Emergency Management Agency) (2000b). “Global Topics Report on the Prestandard and Commentary for the Seismic Rehabilitation of Buildings,” FEMA 357, Federal Emergency Management Agency, Washington, D.C., November. Hsu, T.T.C. (1993). Unified Theory of Reinforced Concrete, CRC Press, Boca Raton, FL. JSCE (Japan Society of Civil Engineers). (2000). Earthquake Resistant Design Codes in Japan, Earthquake Engineering Committee, Japan Society of Civil Engineers, Tokyo, Japan. Mo, Y.L. (1994). Dynamic Behavior of Concrete Structures, Elsevier, Amsterdam. Okamura, H. and Maekawa, K. (1991). Nonlinear Analysis and Constitutive Models of Reinforced Concrete, University of Tokyo, Tokyo, Japan. Naeim, F. and Kelly, J. M. (1999). Design of Seismic Isolated Structures, John Wiley & Sons, New York. Paulay, T. and Priestley, M.J.N. (1992). Seismic Design of Reinforced Concrete and Masonry Buildings, John Wiley & Sons, New York. Priestley, M.J.N., Seible, F., and Calvi, G.M. (1996). Seismic Design and Retrofit of Bridges, John Wiley & Sons, New York. Wakabayashi, M. (1986). Design of Earthquake-Resistant Buildings, McGraw-Hill, New York. Williams, A. (1998). Seismic Design of Buildings and Bridges, 2nd edition, Engineering Press, Austin, TX. © 2003 by CRC Press LLC
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14 Precast and Tilt-Up Buildings 14.1 Introduction 14.2 Precast and Tilt-Up Buildings Precast Buildings · Tilt-Up Buildings
14.3 Performance of Precast and Tilt-Up Buildings in Earthquakes Precast Buildings · Tilt-Up Buildings
14.4 Code Provisions for Precast and Tilt-Up Buildings Precast Buildings · Tilt-Up Buildings
14.5 Seismic Evaluation and Rehabilitation of Tilt-Up Buildings
Charles Scawthorn Consulting Engineer Berkeley, CA
David L. McCormick ABS Consulting San Francisco, CA
Out-of-Plane Wall Anchors · Girder Anchorage Failures at Pilasters · Retrofit Details and Recommendations · Development of Wall Anchor Loads into Diaphragms · Retrofit Details and Recommendations · Collectors · Retrofit Details and Recommendations
Defining Terms References Further Reading
14.1 Introduction This chapter discusses seismic aspects of precast concrete and tilt-up buildings. Precast concrete refers to concrete components not cast in place but rather, cast off site (usually at precast yards) or in a location different from their final location. Precasting offers economies based on speed of construction and the use of the components as architectural elements. Precast1 components are typically beam, column, floor, roof, or wall units. This chapter addresses buildings assembled in part or entirely of such units, where the units perform a structural function.2 Precast components are typically used where a large number of identical units are required. Due to this mass production in a controlled environment, precast components usually have lower unit cost and more uniform and higher quality, more like a manufactured unit (which they are), than a field-fabricated reinforced concrete beam, for example. The size of precast building components is usually limited only by transport limits — that is, typically, by the largest components that can be transported by truck, or by crane or space limitations. Precast components often utilize prestressing, which is a structural concrete technique involving stresses introduced into the structural member prior to its service, typically similar in magnitude but opposite in
1
Precast is synonymous with precast concrete. Precast concrete components can also perform a nonstructural function, such as exterior building cladding, or precast concrete floor planks — however, this aspect is not addressed in this chapter. 2
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pattern to the stresses expected during the member’s service. Prestressing is usually achieved via highly tensioning steel cables or bars within the member, in such a manner that the tension forces in the steel cable or bar are transferred as compressive forces to the concrete member. Prestressed members can be either pretensioned in the casting yard (cables are pretensioned prior to casting concrete), or post-tensioned at the site, prior to the introduction of loads. Cables may be bonded or unbonded to the concrete. Precast concrete construction was first developed in the 1930s, but was not widely used until the 1960s. It is widely used in certain types of buildings in the United States, such as parking garages and low-rise commercial buildings, and is even more widely employed in certain other countries. In the western United States its use until recently has been limited primarily to gravity framing in parking structures, tilt-up buildings, and architectural cladding. Until recently, precast concrete frames have not been widely used to resist lateral loads in high seismic zones. Several efforts have been made over the last decade to change this situation. For example, the National Science Foundation (NSF), the Precast Concrete Institute (PCI), and the Prestressed/Precast Concrete Manufacturers Association (PCMAC) sponsored the PRESSS (Precast Structural Seismic Systems) program to develop innovative precast framing systems suitable for use in all seismic regions, and to produce comprehensive design guidelines. Recently in phase III of the PRESSS program a complete building was constructed and tested in the laboratory. The structure included precast components connected by unbonded prestressing. Although such structures have relatively little damping, they can undergo large deformations without yielding because the changes in strain are small. Consequently, such a structure will recenter itself after the ground motion stops [Stanton and Nakaki, 2001]. The reader is referred to papers generated as part of the PRESSS project for further information. The National Institute of Standards and Technology (NIST) has also sponsored related research. Several projects have been completed using the results of these studies, including a 39-story building in San Francisco. One of the most common types of precast buildings in the western United States are tilt-up buildings, in which large concrete panels are often cast on the ground at the job site, and then tilted up, to form the building’s walls (tilt-up construction is discussed further below). The next section describes what differentiates precast and tilt-up buildings from other building types. This is followed by a review of the performance of these types of buildings in recent earthquakes in the United States and elsewhere, a brief review of code provisions for precast and tilt-up building design, and then a somewhat lengthier discussion of major seismic deficiencies in existing tilt-up buildings, and their remediation. The chapter concludes with listings of Defining Terms, References, and Further Reading.
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14.2.1 Precast Buildings A building with various precast elements is shown in Figure 14.1, and is essentially a post-and-beam system in concrete, where columns, beams, or slabs are prefabricated and assembled on site. Various types of members are used: • Vertical load-carrying elements may be typical column shapes, Ts, cross shapes, or arches and are often more than one story in height. Note that columns are often formed with corbels (i.e., beam seats). • Beams are often Ts, double Ts, or rectangular sections. • Wall panels may be several stories in height, and may be load bearing, or nonload bearing (i.e., curtain walls). Precast frames are divided into two broad categories: 1. Emulated moment frames of precast concrete are “those precast beam–column systems that are interconnected using reinforcing and wet concrete in such a way as to create a system that will act to resist lateral loads in a manner similar to cast-in-place concrete systems” [FEMA 274, 1997]. © 2003 by CRC Press LLC
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FIGURE 14.1 Precast concrete building — typical details. (From FEMA 154, 1988, Rapid Visual Screening of Buildings for Potential Seismic Hazards: A Handbook, Earthquake Hazards Reduction Series 41, Federal Emergency Management Agency, Washington, D.C.)
2. Other than emulated cast-in-place moment frames: Frames of this classification “are assembled using dry joints; that is, connections are made by bolting, welding, post-tensioning, or other similar means. Frames of this nature may act alone to resist lateral loads, or they may act in conjunction with shear walls, braced frames, or other elements to form a dual system” [FEMA 274, 1997]. The appendix to Chapter 9 of the 1997 NEHRP Recommended Provisions [FEMA 302, 1998] contains a trial version of code provisions for new construction of this nature, but it was felt to be premature in 1997 to base actual provisions on the material in the appendix. The concern with these types of structures is that because the members are stiffer than the connections, the majority of the deformations must be absorbed in deformation of the connections. The lateral-force-resisting system for a precast building can be a box or shear wall system (where walls act as shear panels to transmit lateral forces between stories), or a moment frame. Figure 14.2 shows, for example, a building under construction, where the shear wall and columns are cast in place, © 2003 by CRC Press LLC
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(A)
(B) FIGURE 14.2 (A) Precast concrete building under construction — note large shear wall. (B) Note precast beam supported by corbel on column. (Photos: C. Scawthorn)
and the beams and floor planks are precast. This sometimes leads to splitting of responsibility between two engineers, one for the precast framing, and one for the lateral-load system.
14.2.2 Tilt-Up Buildings One of the most common low-rise commercial building types in the western United States is the tilt-up building, which utilizes precast wall elements in a box-type lateral-force-resisting system (Figure 14.3). In traditional tilt-up buildings, concrete wall panels are cast on the ground then tilted upward onto their final positions (Figure 14.4). Tilt-up buildings are an inexpensive form of light industrial and commercial construction. Walls are concrete panels, and the roof is typically plywood or oriented strand board (OSB) diaphragms supported by wood purlins and glue-laminated (glulam) wood beams or a light steel deck and truss joist system, supported in the interior on steel pipe columns. Discussions in this chapter will be limited primarily to tilt-ups with wood diaphragms, as they are more common in higher seismic zones. © 2003 by CRC Press LLC
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4 2 3 1
7
5 6
Details: 5. anchor bolted wooden ledger for roof/floor support
Wall systems: 6. cast-in-place columns– square, "T" shape, and "H" shape 7. welded steel plate type panel connection
FIGURE 14.3 Tilt-up building — typical details. (From FEMA 154, 1988, Rapid Visual Screening of Buildings for Potential Seismic Hazards: A Handbook, Earthquake Hazards Reduction Series 41, Federal Emergency Management Agency, Washington, D.C.)
In many cases, panelized roof systems are used to minimize the cost of constructing a wood diaphragm. The primary components of existing buildings typically include 5 1/8 - or 6 3/4 -in. wide glulam beams (usually spaced on 20- to 24-ft modules), 4× sawn lumber purlins (framing to the glulam beams on an 8-ft module), 2 × 4 or 2 × 6 subpurlins (framing to the purlins on a 2-ft module), and plywood sheathing. The 8-ft by 4-ft plywood panels are framed with a subpurlin along each of the long sides and a third subpurlin along the centerline, to span between purlins. Panel sections are fabricated on the ground with purlins and subpurlins overlain with sheets of plywood. The grids are then lifted into position and connected to glulam beams and purlins already in place. Recent code requirements have resulted in 3× subpurlins being used as struts for attachment of wall anchors. In most tilt-up buildings, a ledger member attached to the walls with embedded anchors (Figure 14.5) supports the perimeter of the roof. Diaphragm shear transfers through the nails into the ledgers, and then through the ledger bolts into the wall panels. Ledgers on most modern and nearly all older buildings are solid 3× or 4× sawn lumber members. Some newer buildings have steel ledger angle (L) or channel (C) sections with or without a wood nailer attached at the top. Glulam beams are typically directly supported by the walls or pilasters at the building perimeter and by interior steel columns. (Occasionally steel columns adjacent to the walls support the beams.) Wall supports for glulam beams may either consist of bearing seats on top of pilasters or fabricated steel “bucket” hardware anchored to the walls with reinforcing steel or stud anchors. Glulam beams are usually designed to cantilever over the interior supports to provide economy in member selection. Suspended spans of glulam beams are supported from hinge-type connection hardware by the cantilevered beams (Figure 14.6). Purlins and subpurlins are normally supported at their ends by metal hangers. The metal deck roofs of tilt-up structures are commonly composed of fluted sheets with gage thickness between 22 and 14. Flute depths vary from 1 1/2 to 3 in. in most cases. Decking units are attached to © 2003 by CRC Press LLC
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(A)
(B) FIGURE 14.4 Details of two-story tilt-up building under construction, showing wall panels propped up. (Photos: C. Scawthorn)
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Plywood
Purlin or subpurlin Hanger Ledger Wall panel
FIGURE 14.5 Typical tilt-up wood ledger detail. (From Structural Engineers Association of Northern California, 2001, Guidelines for Seismic Evaluation and Rehabilitation of Tilt-Up Buildings and Other Rigid Wall/Flexible Diaphragm Structures, D. McCormick, Ed., International Conference of Building Officials, Whittier, CA. With permission.)
(N) Side Strap (Both Sides)
Hinge Connector
Plywood
Suspended GLB Cantilevered GLB
Use (N) Steel Shim Plate Each Side of Beam to Clear Hinge Connector
FIGURE 14.6 Typical tilt-up hinge connector detail for cantilevered glulam beam. (From Structural Engineers Association of Northern California, 2001, Guidelines for Seismic Evaluation and Rehabilitation of Tilt-Up Buildings and Other Rigid Wall/Flexible Diaphragm Structures, D. McCormick, Ed., International Conference of Building Officials, Whittier, CA. With permission.)
adjacent units and to structural steel supports by welds (typically puddle welds) or mechanical fasteners. Metal decks with nonstructural concrete fill (e.g., vermiculite) are sometimes used on the roof. Metal decks with structural concrete topping are commonly used on floors for two-story tilt-ups. Reinforcing for the concrete ranges from light wire mesh to a grid of reinforcing bars. Concrete has structural properties that significantly add to diaphragm stiffness and strength. Thus, two-story tiltups often have flexible roof diaphragms and rigid floor diaphragms.
14.3 Performance of Precast and Tilt-Up Buildings in Earthquakes 14.3.1 Precast Buildings The earthquake performance of precast buildings varies greatly and is sometimes poor. This type of building performs well if a lateral-force-resisting system is present, and the details used to connect the structural elements have sufficient strength and ductility (toughness). As noted in FEMA 274 [1997]: © 2003 by CRC Press LLC
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FIGURE 14.7 Collapse of precast concrete building, Leninakan (1988 Armenia earthquake). (Photo: EQE International)
FIGURE 14.8 Collapse of precast concrete building, 1999 Marmara (Turkey) earthquake. (Photo: C. Scawthorn)
Many types of precast concrete frames have been constructed since their inception in the 1950s. Some have inherent limited lateral-load-resisting capacity because of the nature of their construction details and because they were consciously designed for wind or earthquake loads. Except for emulated systems and braced systems…these frames have capacities to resist lateral loads that are limited by elastic level deformations. In many double tee and single tee systems, as well as others, there is a lack of a complete load path. Brittle welded connections are very common. Many columns and beams lack sufficient confinement steel to provide ductility, and some column systems have inadequate shear capacity as well as base anchorage. Other columns have moment capacity at the base plate that is far beyond their ability to accept the deformations imposed by the global system. Each system may contain details or configuration characteristics that make it unique. In older precast buildings, and in certain foreign countries, lateral-force-resisting systems may not be present or adequate, resulting in collapse (Figures 14.7 and 14.8). Because structures of this type often employ cast-in-place concrete or reinforced masonry (brick or block) shear walls for lateral load © 2003 by CRC Press LLC
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(A)
(B) FIGURE 14.9 Collapsed precast parking garage, 1994 Northridge earthquake, illustrating lack of member connectivity/diaphragm adequacy. (Photos: EQE International) Shown as Color Figure 14.9.
resistance, they experience the same types of damage as other shear wall building types. Some of the problems specific to precast buildings include: • • • •
Improper design, or no real lateral-force-resisting system Inadequate diaphragms Poorly designed connections between prefabricated elements Loss of vertical support, which can occur due to inadequate bearing area and/or insufficient connection between floor elements and columns • Preexisting damage due to restraint of drying or thermal shrinkage • Corrosion of metal connectors between prefabricated elements An example of a building with inadequate diaphragm/connections is illustrated in Figure 14.9, which shows a collapsed new, large, three-story, precast, prestressed concrete garage at the Northridge Fashion Center, following the 1994 Northridge earthquake. Figure 14.10 shows a modern, four-level, precast © 2003 by CRC Press LLC
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concrete garage at California State University, Northridge, partially collapsed in the 1994 Northridge earthquake. The structure was only 18 months old and presumably was in nominal conformance with the building code requirements. The design included a perimeter “ductile” concrete frame, with the exterior columns designed to carry all earthquake loads and the interior columns designed to carry only vertical (nonearthquake) loads.
14.3.2 Tilt-Up Buildings Although numerous tilt-up buildings were constructed in the western United States following World War II, these buildings were not subjected to a significant earthquake until the 1964 Alaska earthquake, in which the first known collapse of a tilt-up warehouse occurred (at Elmendorf Air Force Base). The cause of the failure was reported to be pull out of pilaster anchor bolts [SEAONC, 2001]. However, it was not until the 1971 San Fernando (California) earthquake, in which many tilt-ups in the epicentral region performed very poorly, that severe deficiencies in this type of construction were recognized. Typical failures included separation between tilt-up panels and roofs, with and without collapse, roof diaphragm damage, and other damage caused by various connection failures — particularly the connections between the heavy tilt-up panels and the light, timber-frame and plywood-sheathed roofs (Figure 14.11). A fundamental flaw in the typical wall-diaphragm connection was observed (Figure 14.12) involving the wood ledger being placed in cross-grain bending, due to the out-of-plane forces on the wall resulting from the seismic acceleration of the wall’s mass. Wood is especially weak in cross-grain bending, and codes of that era and design practice did not consider this aspect of the lateral force path. In reaction to the numerous failures observed in the 1971 San Fernando earthquake, relevant seismic requirements of the Uniform Building Code (UBC) were extensively modified in 1973 (direct wall anchor connections, pilaster ties, continuous ties), 1976 (subdiaphragms), and again in 1979 (wall anchor forces). It was expected that tilt-up buildings conforming to these more stringent requirements would generally perform better than would older, unstrengthened structures. The detail shown in Figure 14.12 was modified to have a positive connection between the beam, purlin or subpurlin, and the wall (Figure 14.13). Additional modifications to the code were made in 1991 (introduction of amplified forces in the middle of the diaphragm), based on research from the 1984 Morgan Hill, the 1987 Whittier-Narrows, and the 1989 Loma Prieta events. In the 1994 Northridge earthquake, however, a large proportion of concrete tiltup buildings located in the region of strong shaking had serious structural damage, including partial collapses. The City of Los Angeles estimated that more than 400 of the 1200 tilt-up buildings in the San Fernando Valley had significant structural damage, including partial roof collapse and collapse of exterior walls [Brooks, 1994]. It was estimated that about 40% of the pre-1973/1976 and 25% of the post-1973/ 1976 tilt-up and reinforced masonry buildings had roof connection failures. Figure 14.14, for example, is an aerial view of an industrial park taken shortly after the Northridge earthquake, in which several buildings can be seen to be missing wall panels or roof bays. Another example of tilt-up damage is Figure 14.15, which shows a large commercial building that lost its rear tilt-up wall when the wall-to-roof connections failed. These connections appeared to conform to typical code standards dating from 1973 to 1990. The particular detail involved steel brackets anchored into the wall and bolted through the wood roof beams. The collapse was caused by the bolts pulling through the ends of the wood beams. This particular structure, however, may have undergone particularly strong ground motions because it was located on soft alluvium, next to a river channel.
14.4 Code Provisions for Precast and Tilt-Up Buildings 14.4.1 Precast Buildings Section 1921.2.1.6 of the 1997 UBC requires that precast lateral-force-resisting systems shall either be designed to “emulate the behavior of monolithic reinforced concrete construction…or…rely on the unique properties of a structural system composed of interconnected precast elements.” That is, unless © 2003 by CRC Press LLC
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(A)
(B)
(C) FIGURE 14.10 International)
Collapsed precast Cal State Northridge parking garage, 1994 Northridge earthquake. (Photo: EQE
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FIGURE 14.11 Collapse of tilt-up building, 1971 San Fernando earthquake. (Photo: EQE International)
FIGURE 14.12 Ledger detail showing cross-grain bending, typical of pre-1971 tilt-up buildings.
it can be shown otherwise (i.e., via testing and analysis), the lateral-force-resisting system of precast frame buildings must emulate the behavior of reinforced concrete construction. However, precast buildings can be constructed where the gravity load-carrying system is of precast construction, and the lateral-forceresisting system is, for example, a monolithic reinforced concrete shear wall, etc. (see Figure 14.2).
14.4.2 Tilt-Up Buildings Design of tilt-up buildings is governed by the applicable building code. The discussion herein is in the context of the 1997 UBC, which embodied a major change from previous codes, involving a move from service level to strength level design (see SEAONC, 2001 for a discussion of previous codes governing design of tilt-ups in the western United States), as well as modifications based on lessons learned in the 1994 Northridge earthquake. The 2000 International Building Code (IBC) has similar design provisions [International Code Council, 2000]. Other relevant documents include the 1997 Uniform Code for Building Conservation (UCBC), Appendix Chapter 5, and its successor, Chapter 2 of the Guidelines for Seismic Retrofit of Existing Buildings (GSREB) [ICBO, 2001]. The base shear equation and other equations used to determine design forces in the 1997 UBC are: V = Cv IW/RT © 2003 by CRC Press LLC
(14.1a)
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"Hold-Down" Type Connector Plywood Sheathing
Ledger Embedded Anchor
Glulam Beam
Wall Panel
FIGURE 14.13 Revised detail for wall-diaphragm connection. (Photo: EQE International)
FIGURE 14.14 Aerial view showing damaged tilt-ups, 1994 Northridge earthquake. (Photo: EQE International)
but need not exceed: V = 2.5CaIW/R
(14.1b)
where W is the building weight, I is the importance factor (normally 1.0), and the other factors are discussed below. Equation 14.1b serves as an upper cap for the value of the base shear in Equation 14.1a, and corresponds to the plateau on the design spectrum for short period structures. Tilt-up buildings typically are designed for the capped value as they are considered stiff structures. The values for Ca and Cv are determined from Tables 16-Q and 16-R of the 1997 UBC, respectively, and are functions of both the soil type and seismic zone. In seismic zone 4, Ca and Cv are also dependent on the near-source factors Na and Nv , respectively. The near-source factors are related to both proximity to a major fault and maximum capable magnitudes and slip rates of the faults, as set forth in Tables 16-S, © 2003 by CRC Press LLC
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16-T, and 16-U. For major faults (moment magnitude greater than 7 and slip rate of 5 mm/year or more) Na varies from 1.5 (located less than 2 km to the fault) to 1.0 (greater than 10 km). The value of Na used to determine Ca need not exceed 1.1 for regular, redundant (see below) structures located at a site with a soil profile of SA through SD . Simple tilt-up buildings can qualify for this exemption. The soil classifications have been expanded from a four-tier (S1 through S4) to a six-tier (SA through SF) scheme (Section 1636 of the 1997 UBC). If the soil properties are not known in sufficient detail to determine the soil profile type, type SD shall be used (Section 1629.3). For zone 4, Ca varies from 0.32Na (for SA) to 0.44Na (for SD), and Cv varies from 0.32Nv to 0.96Nv . R in Equation 14.1 is a numerical coefficient representative of the inherent overstrength and global ductility capacity of lateral-force-resisting systems. For shear wall systems that are also bearing walls R has a value of 4.5. Thus, for a typical tilt-up building of standard importance in seismic zone 4 (more than 10 km from a major fault) for which no soil information is known, the base shear equation yields V = 2.5CaIW/R = (2.5)(0.44)(1)W/4.5 = 0.24W. Consideration of vertical earthquake loads does not have a significant effect on the design of tilt-up buildings and will not be considered here. A redundancy/reliability factor ρ is incorporated into design load combinations, which is intended to increase the design forces for less redundant structures. The redundancy/reliability factor ρ is defined by:
[
ρ = 2 − 20 rmax AB
]
(14.2)
where rmax is the maximum element-story shear ratio and AB is the ground floor area of the structure in square feet. ρ shall not be taken less than 1.0 (highly redundant) and need not be greater than 1.5. Thus, the effect ranges from either leaving the base shear from Equation 14.1 unchanged to increasing it by up to 50%. This increase in load applies only to the vertical resisting elements and foundations, and typically not to collectors, the diaphragm, and other components (including the design of wall anchors). For a given direction of loading, the general definition of ri is the ratio of the design story shear in the most heavily loaded single element divided by the total design story shear for level i. (rmax is the highest value for ri in the bottom two thirds of the structure.) However, for buildings with shear walls a more specific definition is provided. For tilt-up buildings, ri shall be taken as the maximum value of the product of the wall shear and 10/lw (lw is the length of solid wall in feet) divided by the total story shear. This in effect penalizes buildings with shorter length walls, thereby increasing base shear for buildings that depart significantly from the original box-system concept. It may also penalize buildings with reentrant corners or interior walls regardless of the total length of wall available. This is because the short wall at the reentrant corner may resist up to 50% of the base shear based on tributary area. The redundancy/reliability factor has been widely debated since its introduction, and numerous modifications have been proposed. The overstrength factor Ωo is incorporated into special design load combinations (e.g., to axial forces in columns supporting discontinuous walls, and for collectors and collector connections.) It is intended to account for structural overstrength and has a value of 2.8 for shear wall systems. It is analogous with the use of 3Rw/8 in previous editions of the UBC. The application of this amplification to collectors and collector connections (Section 1633.2.6) is a new provision in the 1997 UBC. The value of the wall anchor force can be determined by the lesser of Equations 32–1 and 32–2 of the 1997 UBC:
Fp = 4.0 Ca I pWp , h a pCa 1 + 3 x hr F p= Wp Rp
© 2003 by CRC Press LLC
(14.3a)
(14.3b)
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where ap Ca Ip Wp hx
is the in-structure component amplification factor. is the seismic coefficient, as set forth in Table 16-Q of the UBC. is the importance factor specified in Table 16-K of the UBC. is the weight of an element or component. is the element or component attachment elevation with respect to grade. hx shall not be taken less than 0.0. hr is the structure roof elevation with respect to grade. Rp is the component modification factor that shall be taken from Table 16-O. Note that the equation for determining wall anchor forces in the 2000 IBC is not dependent on diaphragm height with respect to roof diaphragm height. Equation 14.3b can be simplified for wall anchorage for the roof by setting hx = hr (element or component attachment level equals the height of the roof). The value of hx should not mistakenly be taken as the center of gravity of the walls. Then Equation 14.3b becomes Fp = 4apCa IpWp /Rp . ap is the instructure component amplification factor that varies from 1.0 to 2.5. Section 1632.2 states that the component response modification factor Rp shall be reduced to 1.5 if shallow anchors (embedment length to diameter less than 8) are used, and 1.0 if nonductile materials are used. However, Section 1623.2.8.1 states that Rp = 3 shall be used for wall anchorage, regardless of anchor type. Using the ap and Rp values provided for bearing walls and flexible diaphragms in Section 1633.2.8.1 (1.5 and 3, respectively), Equation 14.3b becomes 4CaIpW/3, which obviously is less than in Equation 14.3a. For a typical structure of standard importance in seismic zone 4 with Ca = 0.44 (soil type SD and distant from a major fault), Equation 14.3b yields an anchor force of 0.88W. This force must be multiplied by 0.85, 1.0, and 1.4 for the design of wood elements, concrete embedments, and steel elements in the wall anchorage system, respectively. These factors were introduced in an attempt to provide similar factors of safety for all materials. (The 1.4 factor is used for all materials in the 2000 IBC.) Multiplying by these factors results in strength design anchor forces of 0.75W, 0.88W, and 1.23W for wood, concrete, and steel, respectively. Unlike earlier codes (1991 and 1994 UBC), the design wall anchorage force is not amplified only in the center of the diaphragm. A constant amplified value was assigned over the full length of the diaphragm because a flexible diaphragm is a shear yielding beam, not a flexural beam. Finally, a change in the 1997 UBC is the restriction that subdiaphragm length-to-depth ratios should be limited to 2.5:1 instead of 4:1 as permitted in previous codes. This effectively limits subdiaphragm shear stresses. Appendix Chapter 5 of the 1997 UCBC and Chapter 2 of the 2001 GSREB include design forces that are reduced with respect to the UBC. In the case of the GSREB, the loads are 75% of those in the 1997 UBC, and the primary focus is on the wall anchorage system. It is not required that diaphragms or wall stresses be evaluated. It appears that both the 2001 GSREB and FEMA 356 will be incorporated or referenced in the 2003 International Existing Building Code (IEBC).
14.5 Seismic Evaluation and Rehabilitation of Tilt-Up Buildings The evaluation and rehabilitation of tilt-up buildings consist of identifying and remediating deficiencies in the lateral-force-resisting system. The following discussion on evaluation and rehabilitation of deficiencies is based on a recent Structural Engineers Association of Northern California (SEAONC) publication [SEAONC, 2001], to which the reader is referred for additional detail as well as a methodology for prioritization of identified deficiencies. The guidelines identify eight features or components of tilt-up structures that can be evaluated for deficiencies. Although it is not possible to state absolute priorities for all buildings, the component priorities are generally judged to be:
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• High: wall anchors, continuity ties and subdiaphragms, and collectors • Moderate: diaphragms and shear walls loaded in plane • Low: chords, ledgers, and out-of-plane loading on walls These priorities are based on knowledge of performance in past earthquakes. Only issues associated with the High category of deficiencies will be discussed herein, and the reader is referred to the SEAONC guidelines for more detail, as well as discussion of the Moderate and Low categories of priorities. Although relative priorities remain basically the same regardless of the expected severity of ground shaking, the priorities are basically applicable to seismic zone 4 of the UBC. When trying to compare the significance of deficiencies in different seismic regions, judgment should be used to increase these priorities for structures located near major active faults, and decrease the priorities for structures in lower seismic zones.
14.5.1 Out-of-Plane Wall Anchors The absence of wall anchors (or a wall anchorage system) is the most critical deficiency that a tiltup structure can possess. As first dramatically illustrated in the San Fernando earthquake, inadequate anchorage can lead to a sudden roof and wall collapse once the walls and roof framing separate (Figure 14.11). During the 1994 Northridge earthquake even structures designed and built to the requirements of the latest building codes experienced serious damage, including partial collapses (Figure 14.15) in areas of strong ground shaking. Although there is some speculation regarding the relative roles of inadequate design provisions, quality of construction, and designer errors, improvements in the as-built capacity of wall anchorage systems are clearly necessary. Analysis of the damage observed after the Northridge earthquake suggested that: 1. Peak ground accelerations (PGAs) are amplified by flexible diaphragms in accordance with the amplified portion of response spectrum. 2. The effects of relative stiffness and eccentric loads (especially on subpurlins) must be considered. 3. The implicit code philosophy of assuming ductility in wall anchors that are inherently brittle is inappropriate. 4. The effects of overstrength of the diaphragm are not considered in design. The typical wall anchor detail for buildings constructed prior to the 1971 San Fernando earthquake consisted of the plywood diaphragm nailed to the wood ledger that is in turn bolted to the wall (Figure 14.5). Manufactured metal hangers for purlins and subpurlins provide bearing support but no direct tension connection to the walls. As clearly demonstrated in the San Fernando earthquake, this detail is extremely weak and subject to failure at even moderate levels of shaking (e.g., PGAs of approximately 0.20 g). Glulam beams and girders were typically supported on pilasters and anchored to the top of the pilasters with anchor bolts and beam seat hardware. Thus, in the direction parallel to the glulam beams, some wall anchorage capacity was provided locally, but cross-grain bending in the ledgers also occurred near the midspan of the panels. Ledgers failed and pilaster–glulam connections were too weak and failed. Parallel to purlins where no wall anchorage was provided, the wall anchor capacity for unretrofitted pre-1971 buildings relies totally on the combination of cross-grain bending of the ledgers, transfer of shear through the nails, and tension in the plywood (Figure 14.12). Typical wall anchorage detailing utilized by designers following adoption of the 1973 UBC is depicted in Figure 14.16. All of the details provide an alternative load path to the one described above (i.e., crossgrain bending); however, anchor flexibility, installation problems, and eccentric loads caused these details to remain prone to damage. During the Northridge earthquake, failures of all types of anchors of all ages were observed [Hamburger et al., 1995]. A study of 88 buildings [SEAOSC, 1994] in the epicentral area revealed virtually no difference in performance of buildings of different ages constructed after 1971. However, buildings that had been retrofitted did perform better than buildings that had not been retrofitted. This suggests that the types of anchors used in retrofit (i.e., stiffer anchors such as © 2003 by CRC Press LLC
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(A)
(B) FIGURE 14.15 Aerial view (A) and close-up (B) showing failed wall in tilt-up building, 1994 Northridge earthquake. (Photos: EQE International) Part (B) shown as Color Figure 14.15.
hold-downs) have a larger overstrength than the steel strap-type anchors (tension ties) that are cast in walls and bent over to attach to framing. The Northridge earthquake demonstrated that, due to lack of appreciation of the different factors of safety for the wood, reinforced concrete, and steel components of the wall anchorage system, the performance of the system once the seismic loads exceeded those associated with working stresses was not adequately predicted. Manufactured steel hardware had safety factors (defined as the ratio of allowable load, including 1.33 factor, to ultimate strength) ranging from 1.8 for steel straps to 2.5 or more for holddown devices. Not surprisingly, tension ties were observed to fail more frequently than hold-down devices. Consequently, new material load factors (intended to provide consistent overstrengths in the 3+ range) were introduced into the 1996 UBC and UCBC Supplements. Wall anchorage systems designed using post-Northridge design provisions are expected to be capable of resisting loads associated with diaphragm accelerations of over 1.2 g if detailed properly. © 2003 by CRC Press LLC
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A. Hold-Down Type Anchor
D. Twisted Strap Anchor With Metal Ledger
B. Twisted Strap Anchor
E. V- Strap
C. Top Strap Anchor
F. Splayed-Strap Anchor
FIGURE 14.16 Examples of wall anchorage details. (Photo: EQE International)
Failures associated with tension ties observed during the Northridge earthquake include: • • • • •
Brittle fracture at the first bolt or rivet hole Nail pull-out Buckling Brittle failure where the strap is bent over ledger (at face of wall) Embedment pull-out
Failures of the steel portions of manufactured metal strap anchors (as opposed to the fasteners) are more likely for the longer straps because many manufacturers use straps with a single cross-sectional area for tension ties of different capacity and length. Thus, a shorter strap will be governed by the nail capacity, while a longer strap with more fasteners is governed by the capacity of the steel strap. Nail failure has been observed to be significantly more ductile and desirable than failure of the straps. Consequently shorter straps used at more locations (due to the lower capacities) are preferred in design and retrofit. Net-section failures at connector holes were noted for twisted straps and tension ties with rivets. Presumably, these failures occurred because the ultimate capacity at the net section was less than the © 2003 by CRC Press LLC
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yield capacity at the gross section. Some of the manufactured hardware is made with ASTM A446 (grade A) steel with an ultimate tensile stress of 45 ksi and a yield stress of 33 ksi. The ratio of the ultimate stress to yield stress is only 1.4, significantly less than the 1.6 for A36 steel determined by using Fu = 58 ksi and Fy = 36 ksi. However, recent tests for A36 steel indicated Fu/Fy values can be much lower because no attempt was made to control the ratio. It is recommended that hardware with bolt holes be conservatively sized or, alternatively, hardware with nail holes only (minimal reduction in gross section) be used instead. The capacity of twisted straps installed at significant angles from the horizontal is limited in three ways: 1. The horizontal component of the force in the inclined portion of a strap must match the horizontal wall anchorage load. Thus, the design load for the strap increases with installation angle. Although some manufacturers currently specify maximum installation angles, no limit was specified in older catalogs. Inclinations of 45° or more have been observed in the field. 2. The fasteners must develop perpendicular-to-the-grain stresses to resist the vertical component of the load. The perpendicular-to-the-grain capacity of the strut is lower than the parallel-to-grain capacity, which is the basis of the capacity included in the catalog. For installations with large angles with respect to the horizontal, the strength of the bolted connection should be calculated using Hankinson’s formula for the angle of load to grain. Calculations should include reductions due to inadequate edge distance for perpendicular-to-the-grain-loading. 3. The vertical component is limited by the dead load on the member plus the uplift capacity of the joist hanger (which is typically low). For a typical purlin, dead load reactions can range from 800 to 1,600 lb. For subpurlins, they are significantly less. If the vertical component of the anchor force exceeds the dead load, flexural stresses are developed in the strap at the first bolt hole. The combined axial tension and flexure act on the net section of the strap. Thus, twisted straps with high loads can fail for members with light gravity loads (i.e., subpurlins). Failure modes for tension ties applied over the top of roofing framing members included: • • • •
Tension failures at the net section Pull-out due to improper anchor embedment Fastener failure Buckling at the wall interface
The buckling of the tension ties can probably be attributed to the flexibility in the wall anchorage system in combination with the presence of a gap between the anchored framing member and the ledger. Poor alignment of tension ties can result in the installation of fewer nails than required by the manufacturer, as well as large installation angles, and subsequently less capacity. It is believed that installation procedures involving bending straps upwards during construction to allow for panel erection and framing installation, and then bending them back down after the roof framing was installed, contributed to tension tie failure. Although manufacturers indicate that they believe bending the straps back into place once is acceptable, the extra number of bends that some straps encounter during the construction process weakens the ties. During the Northridge earthquake failures of subpurlins (typically 2 in. wide by 4 or 6 in. deep) with single-sided (anchors located on only one vertical face of the framing member) hold-down devices were noted. Splitting is the typical ultimate failure mode in bolted connections, but many failures seemed to have been caused prematurely by eccentric loading. The eccentric loading induces bending about the minor axis of the framing member, which combines with the axial loads due to seismic, and the bending stresses due to gravity loads in the framing members. Until very recently, such stresses were not considered in any hardware manufacturer catalogs and are often overlooked by designers.
14.5.2 Girder Anchorage Failures at Pilasters Prior to the San Fernando earthquake, there were no standards for providing ties around vertical bolts that anchor beams into the tops of pilasters. In some cases, no ties were supplied. More commonly, small © 2003 by CRC Press LLC
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ties with wide spacing and inadequate edge distance were provided. Such ties have inadequate tensile capacity to resist the out-of-plane forces that develop. As a result, the tops of the pilasters cracked and spalled due to wall anchor forces. Loss of anchorage capacity and sometimes partial or complete roof collapse occurred. In the Northridge earthquake, some damage to the tops of pilasters meeting the 1994 UBC requirements were observed, although the pilaster performance was generally satisfactory compared with that of pre1971 buildings. No cases of loss of girder bearing due to pilaster shear failures in the newer buildings were observed. However, shearing of studs or bolts, or failure of the welds between the studs and the plates attached to the girders, did occur. Poor quality control was noted in instances of damage. The pilaster tends to act as a vertical stiffener in the wall panel, and wall anchorage forces concentrate at the top of the pilaster due to two-way slab action. The beam seat connection hardware typically was not designed for these larger anchorage forces. In addition, these pilaster connectors are typically substantially stiffer than connectors used for adjacent subpurlins to resist wall loading (e.g., straps or twisted straps), and consequently they resist a larger portion of the load. As a result of the larger wall anchorage loads, even the pilasters designed and constructed using more recent code provisions crack and spall, allowing the beam seat to pull free of the walls.
14.5.3 Retrofit Details and Recommendations Ideally, wall anchors provided as part of a retrofit should: • • • • • •
Have adequate capacity to meet minimum 1997 UBC requirements Have adequate stiffness (calculated deflection less than 1/8 in. under working stress loads) Apply wall anchor loads concentrically to struts (no one-sided anchors) Install properly with ease (no oversized holes or large installation angles) Resist anchor loads in compression as well as tension Perform in a ductile manner (no brittle failure)
Prior to evaluating and designing a retrofit for an existing building, it is important to perform a detailed survey to document field conditions. Existing design documents cannot always be relied upon to accurately reflect existing conditions. During the survey, the type, extent, and quality of existing anchors should be established. Items to check for include missing nails and/or bolts, improper fastener type or sizes, misaligned or bent anchors (including rods or straps), inadequate embedment, oversized bolt holes, and inadequate fastener edge distance. Wall anchorage forces for single-story buildings should be determined by assuming that the wall panels are each simply supported at the base and the roof level regardless of the actual conditions (i.e., some fixity at the base). An exception includes wall panels that are laterally supported at two different elevations near the base, such as may occur at a loading dock. For two-story buildings, the panels are typically continuous for the full height of the building, and thus continuity can be assumed at the second level. For the case when pilasters exist at both edges of a wall panel (and extend up to the girder or purlin), the wall should be checked as two-way slab in order to get the amplified anchorage force for the girder supported at the pilaster. Any textbook or standard for the design of slabs supported on four edges may be used to determine reactions at each edge of the panel. An alternative evaluation procedure for determining the anchor forces is to use the yield line approach. A colleague of the authors performed a finite element analysis of wall panels with pilasters at each end. Wall panels were 24 ft wide with pilasters at each edge. Wall panel thickness and height, and pilaster width and depth were varied to study the effect on the pilaster wall anchor force. For the different geometries studied, the ratio of the calculated pilaster force to the wall anchor force based on tributary area varied from 1.07 to 1.27. The ratios increased with increase in wall panel height and pilaster stiffness. Use of the above ratios would be unconservative as no attempt was made to study the effect of relative
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stiffness of pilaster wall anchor hardware and subpurlin wall anchor hardware. It is judged that a reasonable increase in wall anchor force at the pilaster would be 50%. A minimal lateral load (Fp) equal to the weight of wall panel ( Wp) multiplied by Cp = Ca Ip ap /Rp (1 + 3 hx /hr) in the 1997 UBC should be applied. For the design of the wall anchors, the larger ap value used in parapet design is not included to determine design loads. This minimum lateral load Fp applies to the full length of the diaphragm. In the 1997 UBC, the amplification due to near-fault effects is included through the increase of Ca by a factor of Na . Wall anchorage capacity could be increased over piers adjacent to openings, to which spandrels transfer their out-of-plane forces, and may be decreased directly over the openings to account for the reduced wall weight associated with the opening. However, except in extreme cases (e.g., where piers are thickened substantially with respect to pilasters), it is recommended that uniform wall anchor size and spacing (except at pilasters) be maintained for ease of construction and to allow for possible future building modifications (i.e., introduction of or infilling of openings in wall panels). In the Northridge earthquake there were a large number of wall anchorage failures on the short sides of the diaphragms. These failures can be at least partly understood by considering the effect of overstrength of the diaphragm in elongated buildings (here elongated is taken to mean buildings with a length to width of approximately two or more). Overstrength in elongated buildings is a function of the plywood thickness, plywood layout, and nailing. Typically nailing zones are such that the greatest strength is provided at the edges of the diaphragm, (1) because diaphragm shears are highest at this location and (2) to take advantage of that strength for developing subdiaphragms. As a result, the diaphragm shear strength can far exceed the UBC-required design strength, especially along the long direction, resulting in large wall anchor forces on the short end walls (because the diaphragm response remains elastic and does not limit the roof accelerations). It can be demonstrated that the detrimental effect of diaphragm overstrength on wall anchorage is primarily a problem for PGAs greater than 0.4 g. Reliance on the ductility of the wall anchor system to compensate for overstrength is not recommended as ledger nails may be damaged during the elongation of the wall anchorage associated with inelastic behavior. For elongated buildings located in areas where ground shaking in a major earthquake is expected to be more severe than 0.4 g (within 10 km of major faults), it is recommended that Cp = Fp /Wp be increased, as indicated below for the case where loading occurs in the long direction (strong direction for the diaphragm): C ps = K ∗ C p K =
[(diaphragm strength seismic weight)
s
(diaphragm strength seismic weight)t ] ≥ 1.0
(14.4a) (14.4b)
where the subscript s stands for the strong or long direction, and the subscript t stands for transverse direction. The above formulation assumes a typical design where the diaphragm capacity provided in the transverse direction is approximately equal to code design base shear. If the diaphragm has excess strength in both directions, then the above formula cannot be used directly. For the case when edge nailing is constant around the entire length of the perimeter of the building, and when the walls are relatively solid and uniform in thickness and height, Cps can be found by simply scaling Cp by the ratio of the length of the building and the width of the building. However, if the nailing varies in the two directions, or is not constant over the length of the wall, the total capacity of the diaphragm along each length of wall [Σ(length)(shear capacity)] should be determined. In the above formula, seismic weight is the weight per foot due to the diaphragm and the portions of the perpendicular walls tributary to the diaphragm. If a large number of openings for truck doors are provided along the short side of the building, or if the longer walls are thicker, the appropriate Cps value can be similar to that for the long direction Cp . For irregular plan shapes, the above formula would not apply without modification and approximations. © 2003 by CRC Press LLC
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The retrofit for deficiencies in wall anchors for perimeter (exterior) walls is one of the most costeffective ways to reduce the seismic vulnerability of this type of structure. If retrofit is required, the use of through-bolts, undercut anchors, or adhesive anchors is recommended. Expansion anchors are not recommended. If wall thicknesses are such that more embedment than required is available, it is recommended that the engineer be conservative and provide additional embedment to offset any potential installation problems. The engineer is cautioned to avoid using anchor loads for manufacturers’ catalogs without consideration of the capacity of the strut itself for the applied loads. Details that produce eccentricities or loads at angles to the struts should be avoided, unless calculations indicate that combined stresses are acceptable. A difficult wall anchor retrofit condition is to provide anchorage for an existing 2× subpurlin (especially when no reroofing is planned). Such subpurlins typically have inadequate capacity to resist loads applied eccentrically, and provision of two anchors provides excess capacity (inefficient). The use of 2× struts in new design is no longer permitted. A possible solution is to transfer tension loads into the diaphragm via a tension rod to a purlin or a block that spans between two subpurlins. Thus, the two subpurlins share the load, and additional diaphragm nailing may not be necessary. However, this connection cannot transfer compressive loads unless the rod is very short. For cases when longer rods are used, shimming the ends of the adjacent subpurlins is recommended so that compression loads can be transferred to them directly. Shims should be nailed or glued into place to prevent them from falling out prior to or during the earthquake. If no parapet exists, attaching the subpurlin to the top of the walls, while providing sufficient edge distance for the bolt embedded in the walls, is difficult. A possible solution is to provide horizontal steel braces inclined at angles from the deeper glulam beams to the wall at the one third points. Another solution would be to provide plywood on the underside of two adjacent subpurlins with a new strut nailed to the underside of the plywood. The wall anchor can then be attached to this new strut at a lower elevation, eliminating the concern about the edge distance for the anchor bolt. Girders supported at wall panels without pilasters are typically supported by steel bucket hardware. The steel buckets are typically fastened to the wall with a number of steel studs, and usually have one or two bolts into the end of the girder. In many cases the capacity of the bucket performing as a wall anchor is governed by the capacity of the bolts into the girder. Providing additional side plates using existing bolts (i.e., removing and replacing nuts) and new bolts through the girder can increase the capacity. Welding of the side plates to the existing bucket and bolting through the girder is also possible. There are two primary concerns for anchorage of girders at pilasters. One is that the existing wall anchorage details are inadequate due to a lack of stiffness or a lack of closely spaced ties or shear reinforcement. The second is that the pilasters have a stiffening effect on the wall panel and may attract a substantially larger portion of the wall anchorage force than the wall anchors for the adjacent subpurlins. Strengthening of girder anchorage details within adequate confinement typically consists of providing new anchorage to the wall panels that “bypass” the existing anchors. If such a technique is to be used, it should be realized that typical girder-to-pilaster connections (vertically aligned bolts embedded into the pilaster) are relatively stiff. Unless the new retrofitted connection is very stiff (or the bolts for the existing connection are removed), the existing pilaster connection could resist a large portion of the load until the top of the pilaster cracks. For this reason, the new retrofitted connection should have sufficient capacity to resist the entire wall anchor load. Ideally the new connection would connect directly to the pilaster instead of the weaker wall panel above the pilaster, but this is often not possible without an elaborate connection due to concerns about edge distance and congestion from the ties. It is generally appropriate to place the wall anchors as close to the top of the pilaster as possible (the effect of the eccentric load on the glulam beam must also be checked). Since the early 1960s, there has been a UBC requirement that the wall anchorage capacity (working stress) exceed 200 lb/ft. This minimum force requirement was increased as a result of damage in the Northridge earthquake. The 1997 UBC and UCBC require a minimum wall anchorage capacity exceeding 300 and 250 lb/ft, respectively. (The 1997 UBC requires a minimum wall anchorage strength of 420 lb/ft or 300 lb/ft working stress capacity.) It is recognized that this limit is somewhat arbitrary. The minimum © 2003 by CRC Press LLC
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capacity was originally provided to ensure sufficient capacity for wind loads. The limit was increased to 300 lb/ft because it was estimated that the ledger nails might actually have stiffness comparable to that provided by wall anchors with only 200 lb/ft out-of-plane capacity. (Excess flexibility is more likely to occur with weaker anchors.) Relative stiffness of wall anchors and nails is most likely to be a problem along the shorter side of a large building where reduced nail spacing will be required to resist high diaphragm shears and twisted straps are used as wall anchors for purlins. If less than 300 lb/ft capacity exists in seismic zone 4, retrofit should be undertaken if the anchors do not appear to have at least twice the stiffness of the ledger nails within the tributary width of each anchor. However, lack of data on nail stiffness limits the ability to perform quantitative checks of relative stiffness of wall anchors. In practice, wall anchors with less than 300 lb/ft capacity probably are deficient in some other respect (e.g., capacity provided is less than Fp , or loading is eccentric), so this deficiency is unlikely to be the only reason that wall anchors are retrofitted.
14.5.4 Development of Wall Anchor Loads into Diaphragms After the 1971 San Fernando earthquake, continuous cross ties were required to transfer seismic loads associated with walls into the diaphragm. In order to satisfy this requirement without an excessive number of connections, the concept of subdiaphragms was introduced in the 1976 UBC. The designer is permitted to define a series of subdiaphragms, each of which has boundary members on the sides, chords at the top and bottom, and which must conform to the aspect ratio limitations of the code for diaphragms (Figure 14.17). Using this concept, the wall anchors need only be provided with struts across the individual subdiaphragms — from chord (wall) to chord (purlin or beam). However, the subdiaphragms must be designed to have adequate shear capacity to transfer all of the wall anchorage forces transmitted to them to the overall diaphragm and into the boundary members. If necessary, subdiaphragm depths can be increased through the use of continuity or strut ties. The boundary members for the subdiaphragms then must become cross ties for the larger diaphragm and must be continuous from chord to chord. It is possible to build a nested series of subdiaphragms, such that only a relatively few cross ties need be provided across the entire width of the building. However, the recent reduction in allowable subdiaphragm length-to-depth ratio (1997 UBC), and the requirement that cross ties be spaced at a maximum of 24 ft (1996 UCBC Supplement) makes nesting of subdiaphragms in future designs less likely than in the past. The use of subdiaphragms is merely a mechanism by which buildings can be tied between diaphragm chords without requiring the splicing of an excessive number of cross ties. Subdiaphragms do not actually perform as independent elements in an earthquake. It is not expected that the wall anchorage forces are actually transferred into the diaphragm in the manner predicted by the UBC-dictated subdiaphragm analyses. But subdiaphragms do serve as useful tools for constructing a system of interconnected elements leading from the point where the wall-to-diaphragm anchorage occurs inward to a point where a cross tie, such as a girder, can be extended from diaphragm chord to diaphragm chord. Wall forces can be effectively transferred into the subdiaphragm when the framing members are perpendicular to the wall. However, where framing members are only parallel to the wall, blocking is required to obtain adequate development length to transfer the wall anchorage force into the subdiaphragm. Damage associated with inadequate wall anchor load transfer into the diaphragm in past earthquakes primarily has occurred when structures lacked wall anchorage systems. In Northridge, two roofs are known to have collapsed due to lack of continuity ties. No instances of failure of continuity ties or cross ties leading directly to collapse are known. Two types of damage observed included failure of the plywoodto-purlin nailed connection at the first purlin (or beam) parallel to the perimeter walls (cross-grain tension), and failure of interior span glulam hinge bearing supports with no axial capacity. The failure at the first purlin involved either tearing of nails through the edge of the plywood, splitting of the purlin, or pull-out of the nails (analogous to failures at the ledger due to cross-grain bending discussed above), and led to partial collapse of the roof. The glulam hinge connectors were pulled apart by tensile forces induced by the wall anchor loads, allowing interior suspended girder spans to fall. © 2003 by CRC Press LLC
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Plywood Sheathing
Purlins @ 8' o.c. Exterior Wall Panels
Subpurlins @ 2' o.c.
Glulam Beams @ 24' o.c.
(A)
Diaphragm Cross Ties
Primary Subdiaphragm
Primary Subdiaphragm
Subdiaphragm Continuity Ties
(B) FIGURE 14.17 Tilt-up diaphragms: (A) typical panelized roof construction, (B) subdiaphragm concept, (C) wallanchor-load development system. (From Structural Engineers Association of Northern California, 2001, Guidelines for Seismic Evaluation and Rehabilitation of Tilt-up Buildings and other Rigid Wall/Flexible Diaphragm Structures, D. McCormick, Ed., International Conference of Building Officials, Whittier, CA. With permission.)
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Strut Anchor Subdiaphragm Chords
Diaphragm Cross-tie
End Shear Wall
Subdiaphragm Length (L1)
Width (D)
End Shear Wall
Subdiaphragm
Main Diaphragm Width (B)
Main Diaphragm Span (L)
Masonry Wall
Direction of Earthquake
(C) FIGURE 14.17 (CONTINUED)
14.5.5 Retrofit Details and Recommendations The term continuous ties is used here to describe the combination of cross ties (framing members) and continuity ties (connectors). Many existing tilt-up buildings constructed prior to the adoption of the 1973 UBC were not provided with continuous ties across the roof diaphragm. Cross-tie forces should be determined by summing the tributary wall anchor forces — the design cross-tie force is the sum of the reactions for the adjacent subdiaphragms. Note that the wall anchor at the end of the cross tie need not be designed for the cross-tie force, but can be designed for a wall anchor load considering the two-way action of the wall panel if pilasters are present. If a conservative load is used for the girder-to-pilaster wall anchor connection, it is overly conservative to sum the girder-topilaster wall anchor load and the tributary strut loads to get the continuity tie design force. In a wood diaphragm, cross-tie forces are typically transferred into the diaphragm through nailing. It is not acceptable to assume edge nailing at the glulam beams without visual verification as it is possible that the plywood panels are staggered over the glulam beams, and that field nailing is not present in at least some of the plywood panels. It could be argued that continuity tie capacity need not be constant over the depth of the diaphragm. As one moves farther away from the walls, the forces are distributed into the diaphragm, and continuity tie capacity could be reduced. If such an approach (reduction in cross-tie capacity) is to be used in a voluntary upgrade, it must be verified that the continuity tie-capacity reduction is less than the reduction in cross-tie force achieved through force transfer by diaphragm nailing. In addition, it is recommended that a minimum continuity tie capacity of 50% of that required at the perimeter walls be maintained throughout the diaphragm. Use of the full capacity of the nails to transfer force from the cross tie to the diaphragm may not be appropriate as the nails are required to perform other functions, such as transfer of diaphragm shear. Continuous ties can be subjected to both tension and compression forces as the wall panels move away from or towards the diaphragm. Historically, engineers have not been as concerned about the compression forces as the walls were expected to bear against the roof diaphragm and its framing members. However, because of construction tolerances, there are often gaps at the ends of framing members that prevent direct bearing. If direct bearing on framing members does not occur, diaphragm nails at ledgers and interior framing members will be required to transfer the load in cross-grain bending. Consequently, it © 2003 by CRC Press LLC
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is recommended that continuity ties with compressive capacity comparable to the tensile capacity be used. In existing buildings that have continuity ties capable of tensile loading only, shimming of gaps, especially close to the building perimeter, is recommended. In the event that a continuity tie with substantial flexibility exists it is recommended that strengthening be undertaken, especially at the connections nearest the walls. Similarly, strengthening is recommended if the continuous tie is eccentric (one side of framing member only), unless it can be demonstrated that the eccentricity does not cause excessive stresses in the wood members when combined with the stresses due to gravity loads. No one third increase in allowable stresses for seismic loads should be used for checking eccentric connections. It is very rare that the additional axial loads associated with cross-tie forces represent a significant increase in stress for a glulam beam. A reasonable cross-tie force of 10 to 15 kips causes an axial stress of approximately 100 to 150 psi in a typical glulam, a stress that can easily be accommodated by the increase in capacity due to load duration. However, if purlins are used as cross ties, 10 kips can represent a significant axial stress and the purlin should be checked for the combined effects of gravity (dead and snow) loads (bending) and seismic loads. In the case where reroofing is scheduled (or the roofing is relatively old), engineers often choose to provide flat straps over the top of existing members as continuity ties. Prior to choosing such a scheme, it is recommended that the engineer consider potential nonstructural issues. It is possible that a thick strap on top of a glulam beam will create a bump in the roofing, especially if lag screws are used and protection board is placed over the straps. Straps over the top of hinge hardware for glulam beams invariably create large bumps. Such bumps can create localized ponding problems. If existing continuity ties are deficient, a new, stiffer connector that has sufficient capacity to resist the entire design load should be provided unless the new and existing continuity ties have comparable stiffness. If the existing ties are eccentric, an appropriate retrofit is to provide an identical piece of hardware on the opposite side of the member. As hardware dimensions have changed over the years, this may not be possible for some older hardware, and new connectors will have to be staggered with respect to existing connectors. Note that installation of continuity ties in an existing building typically will involve some compromises due to interference problems. For example, if there are roof screens or mechanical equipment on the roof, some of the strap locations could be difficult to access. Similarly, ducts under the roof may make it difficult to install a connector on one side of a purlin or glulam beam. Relocating hardware to adjacent purlins, or providing occasional eccentric connections is not viewed as critical in the overall performance of the diaphragm. However, such modifications should only be made with the engineer’s direction or approval. If the spacing of the cross ties is too large, the diagonal tensile forces that develop in the diaphragm will be transferred, at least in part, through the nails at panel edges. Consequently a limit of 24 ft (or the existing girder spacing) has been placed on cross-tie spacing in the 1997 UCBC. (This requirement is not included in the UBC.) Due to its arbitrary nature, the 24-ft limit need not be taken too literally. It could be argued that maximum spacing should be a function of the depth of the diaphragm, just as stirrups spacing in a concrete beam are a function of depth. Clearly well-designed, stiff continuity ties at 26 ft or even 28 ft (whatever the existing beam spacing is) may be acceptable if it is not cost-effective to provide new continuous ties across the building. As the area closest to the perimeter walls is believed most critical, some extra measures may be taken to provide extra capacity in this area. When wall anchor loads are large, existing subdiaphragm depths may be inadequate, and continuity ties typically must be provided at the first purlins or beams to engage enough nailing to transfer the loads. According to the 1997 UBC, these ties must be sized for the wall anchor loads with a material load factor of 1.4 for steel. Alternatively, additional nails or staples can be added through the plywood and into the strut to increase the shear capacity of the subdiaphragm, as long as they do not produce splitting of the strut. Predrilling prior to nailing can help reduce the possibility of splitting.
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Currently struts are required by the UBC to be 3× or larger. Retrofit can be performed by either the addition of new struts, or nailing additional 2× members to the sides of the existing struts. Provision of new or replacement struts will require diaphragm nailing. Plywood nailing, and consequently reroofing, may or may not be required when a new 2× member is nailed to an existing 2× subpurlin. There is often an incentive to try to retrofit a building without requiring reroofing. In the event that thick sheathing or plywood has been used for the diaphragm, framing clips and either short nails or screws can be used to attach blocking to the roof in lieu of removing the roofing. However, it should be noted that screws are typically brittle compared with nails, especially if the threads are included in the shear plane. Thus, the use of screws in this application should be discouraged unless based on test data. When evaluating subdiaphragm shears it is common practice not to add subdiaphragm shears to global shears. In determining subdiaphragm shear, it is most appropriate to use wall anchor loads for struts developed by ignoring the concentration of wall anchor forces at the girder/pilaster connection. The subdiaphragm shear is simply the total wall anchor load per foot multiplied by half the subdiaphragm length, divided by the depth of the subdiaphragm. That is:
(
)
Subdiaphragm Shear = Wpanel ( L sub ) 2 ( Dsub )
(14.5)
where Wpanel is the wall anchor force at the diaphragm level per foot of wall Lsub is the length of the subdiaphragm Dsub is the depth of the subdiaphragm The 1996 UCBC Supplement limits the subdiaphragm shear to 250 lb/ft. This limit recognizes that much of the excess capacity of the diaphragm may be used up for the global shear, and that limited excess capacity exists. The limit of 250 lb/ft can be waived if steps are taken to improve the original diaphragm capacity such as adding blocking or improving nailing. The 250-lb/ft limit is intended for diaphragms with “typical” capacity. For heavily nailed diaphragms, the value can be increased, and for lightly nailed diaphragms, the value should be decreased. The limit of 250 lb/ft was not included in the 1997 UBC. When subdiaphragms were introduced into the UBC, the allowable length-to-depth ratios were the same as those for regular diaphragms supporting rigid walls, namely 3:1 for diagonal- or straight-sheathed lumber and 4:1 for plywood. After the 1994 Northridge earthquake, the allowable length-to-depth ratio was decreased to 2.5:1. It is difficult to attribute any of the damage directly to excessive length-to-span ratio of subdiaphragms. Reducing this ratio is recognition that deformation incompatibility is a potential problem. Restrictions on subdiaphragm length-to-depth ratio in the 1997 UBC effectively accomplish the same thing as reducing the subdiaphragm shear capacity to 250 lb/ft in the UCBC. It is believed that since the behavior of the subdiaphragm is complex, a maximum span-to-depth of 2.5:1 is prudent. Also, the material load factor for wood in the 1997 UBC is 0.85. This factor may be applied to the design of subdiaphragms. Retrofit of subdiaphragms with inadequate shear capacity can be achieved by providing additional nailing (requires roofing removal), or by adding continuity ties to increase the depth of the subdiaphragms (and thereby decrease the shear). It is also possible to provide additional plywood sheathing on the underside of roof framing, effectively creating two subdiaphragms. The material load factor for wood of 0.85 may be applied to the design of subdiaphragms. Each subdiaphragm must have two chords to resist the flexure associated with the wall anchor loads. Although either chord may theoretically be in compression or tension, the load case of primary concern is when the wall is trying to separate from the diaphragm. In such a case, the tilt-up wall panel acts as the tension chord, and the purlin or glulam at the interior edge of the subdiaphragm acts as the compression chord. Typically the chord forces are very low with respect to the reinforced concrete or masonry wall capacity, so that the tension chord can usually be assumed adequate.
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Chord forces (axial) need to be combined with the gravity loads (bending). However, a 1.33 increase in allowable load is permitted. Thus, as long as the chord force is less than approximately 33% of the allowable axial stress, a dead load check is not required. Subdiaphragm chord forces typically do not result in a need to upgrade framing member capacities, except in the case of very large subdiaphragms with purlins or bar joists or girders acting as chord members.
14.5.6 Collectors Collectors (also called drag struts) are major transfer elements that deliver the lateral loads from a horizontal diaphragm to a vertical element (e.g., shear wall, braced frame, moment frame) of the lateral-load-resisting system. Failure of a collector or its connection to the vertical element can lead to catastrophic failure of the structure, such as a roof collapse and subsequent exterior wall collapse. The collector and its connection to the vertical element should be considered equally as important as the associated resisting vertical element (if it transfers a significant portion of the load to the wall), and its connections should be detailed accordingly. The current design philosophy (1997 UBC) is that collectors and their connections to the vertical elements should be strong enough to force inelastic action into the diaphragm or the vertical elements. This philosophy was not included in the 1994 UBC. Thus, the collector connections and possibly the collectors in most existing structures will be deficient by current standards. In a typical tilt-up structure with a timber roof, shears in the roof (or floor) diaphragm are transferred from the roof through nails into the collector member (typically a beam or purlin). A collector for an interior wall should have increased plywood nailing to reflect that it is collecting loads from the diaphragm on both sides of the collector, unless a continuous plywood joint coincides with the top of the collector. The diaphragm loads are usually assumed to be transferred into the collector at a uniform rate over the length of the collector, so the collector load also increases uniformly along the length of the collector as one approaches the vertical element to which the load is being transferred. The length of the collector must be sufficient to transfer the total load into the diaphragm through nailing, welding, or other means. If the collector member is not continuous, connections must be used to splice the individual collector members together at their ends. These splice connections can have different capacities to reflect the varying collector force along the length of the collector. In many cases the collector also serves as a continuity tie for lateral loading in one direction. The engineer should consider that collector connections may be required to transfer continuity tie forces in addition to collector forces, even though it is not common practice to explicitly combine the two loads. Because collector forces vary over the length of the collector, and continuity tie design forces do not, it is possible the collector forces will govern connection design closer to the wall, and the continuity tie forces will govern further from the wall. Often, collectors also serve as chords when lateral forces are generated in a direction perpendicular to the collector load. When this occurs, the larger of the two forces will govern the design at the particular section analyzed. For buildings with plan irregularities (Table 16-M, 1997 UBC), concurrent loading of a member as a collector and chord should be considered. In general, collector connections at reentrant corners in tilt-up buildings represent a challenge for the designer, as dissimilar building materials must be connected in two orthogonal directions at one location. This is especially true for tilt-up wall panels with no cast-in-place pilasters, as the collector connection in one direction must either pass through or bypass the wall panel aligned in an orthogonal direction. In existing buildings, eccentric connections are common at such locations. Retrofit priority is a function of the importance of the vertical lateral-load-resisting element (e.g., shear wall) to which the collector delivers load. A collector transferring load to a primary wall is more important than a collector transferring load to a secondary wall. A wall is defined as a primary shear wall if its failure will lead to significant overstresses in other portions of the building, including other walls, and/or the roof or floor diaphragms. A primary shear wall is a wall that was intended to be part of the lateral load system of the building. It is different from a short return wall at a reentrant corner, which may have simply been ignored in the seismic design of the structure. In existing buildings, studying the roof nailing © 2003 by CRC Press LLC
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pattern typically will provide insights into whether a return wall was considered in the design. Such return walls, whose failure do not substantially affect the other shear walls in the structure, are referred to as secondary walls. Also, collectors that are beams are considered more important than purlins as they support larger tributary gravity loads. In past earthquakes there have been many observed cases of damage to inadequately designed collectors, collector connections (at the vertical element), and splice connections (connections between adjacent collector elements). The most commonly damaged element is the connection to the vertical element. Such damage can include cracking and spalling of a pilaster or wall, failure of bolts in a glulam beam, or loss of bearing and partial collapse. Damage has also been observed at skewed corners where no struts or inadequate connections have been provided to take the load that develops perpendicular to the walls.
14.5.7 Retrofit Details and Recommendations For new buildings, collectors and their connections should be designed with strength adequate to resist the maximum seismic force the diaphragm can deliver. For working stress design, this can be estimated as the lesser of the allowable plywood diaphragm shear, the rocking load, or the calculated design load multiplied by Ωo. An allowable increase in stresses of 1.33 is permitted. In the 1997 UBC, the design loads are multiplied by Ωo = 2.8, with an increase in allowable loads of 1.7 rather than 1.33. For existing buildings, it can be difficult to provide the capacity required in the 1997 UBC, especially if the collectors are undersized. Therefore, it is recommended that for the retrofit of existing buildings, a collector and its connections should be strengthened to at least resist the forces included in the 1994 UBC or 75% of the forces in the 1997 UBC. If it is cost-effective, the collector and connections should be retrofitted for those forces recommended for the design of new buildings (1997 UBC). Increased loads due to proximity of faults (near-fault effects in the 1997 UBC) should be considered. The redundancy factor ρ need not be considered in the design of collectors, except in cases where loads from discontinuous vertical elements are transferred through the floor diaphragm. Collectors in existing tilt-up buildings typically include beams and purlins although occasionally special members are provided solely to act as collectors. As collectors typically carry dead and live loads in addition to seismic loads, they must be checked for the proper load combinations. Only dead and snow loads need be combined with seismic loads for the design of roof members, but dead, live, and seismic loads must be used for the design of floor members. Consequently, roof framing members often have more “excess” load capacity to act as collectors than floor framing members. For single-story tilt-up structures, lateral loads are distributed to shear walls according to tributary areas. Thus, a wall that is short in length near the middle of the diaphragm, or a short wall created by a reentrant corner may in fact be required to resist a substantial portion of the lateral load for the building based on tributary area. If the collector connection is unable to transfer the load to the wall, the connection may fail, and loss of bearing may ensue. Similarly, if the wall is so short in length that it is unstable when the design load is applied, it may rock and, again, loss of bearing may occur. The two-story structure tilt-up structure commonly has a flexible roof and a rigid floor. Roof loads are distributed to collectors and walls based on tributary areas, and loads are distributed to the walls at the lower level based on their relative rigidities. As a result, large diaphragm shears and collector loads can develop at the second floor level. Although the redundancy factor ρ is not typically applied to diaphragms, it should be applied to transfer diaphragms (diaphragms that transfer loads carried by one shear wall at one level, to another shear wall at another level), and thus logically to the collectors. However, it seems appropriate to check the collector using Ωo and ρ separately, and then to choose the load case that is most critical. The need for collectors and collector connections within long walls with many openings is sometimes overlooked. A long wall with large openings and narrow piers over much of its length, and a solid wall at only one end, should have adequate collector and splice connections. Collector forces can be substantial, and can easily exceed the capacity of the chord steel or splices (especially if proper welding procedures were not followed, and weld embrittlement occurs). The collector not only has to transfer any shear forces © 2003 by CRC Press LLC
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from the diaphragm, but also to collect the seismic forces generated by the mass of the narrow piers, and deliver the forces to the solid panels designated as shear walls. Primary shear walls with no collectors, or inadequate collectors, are relatively rare compared with walls with inadequate collector connections. This is especially true for collectors such as glulam beams that have substantial axial capacities. However, the UBC design base shear increased 33% for tilt-up structures in the 1976 UBC. The use of a 33% increase in allowable stresses for load combinations including earthquake for buildings with reentrant corners was eliminated in the 1985 UBC. Thus, collectors for older structures may have been designed for substantially lower collector forces than newer buildings (1.33 × 1.33 = 1.77 times less force). (In the 1997 UBC collector forces must be multiplied by Ωo = 2.8 with an allowable increase in stresses of 1.7.) Thus, using these criteria, collectors in older buildings are even more likely to be noncompliant. A quick check of the beams supporting a roof can be made by ignoring the stresses caused by dead load and checking to see if the axial demand due to collector loads exceeds 33% of the allowable axial stress. If the collector is at a reentrant corner this quick check may not be appropriate, as the 33% increase in allowable stress is not permitted. Instead, the increase in axial stress due to earthquake loads can be checked against the flexural stress resulting from the roof live load, which is ignored when load combinations including earthquake are considered. For flexible diaphragms, live load represents a large portion of the gravity load (assuming no snow loads), and sufficient excess capacity typically exists. If the glulam is relatively deep and narrow, and collector loads are large, bracing of the bottom against buckling may be required. This can be achieved at the ends by bolting 2× members or 1-in. thick plywood to the face of the wall or perpendicular beam and snug up against the bottom of each side of the lower flange of the collector. If a purlin (rather than a beam) acts as a collector for a primary shear wall, it is more likely that collector loads will overstress it, and detailed checks are usually appropriate. In cases where inadequate collector capacity exists, strengthening can be achieved by bolting steel channels or tubes to the side of the existing member along the length of the collector that is inadequate. Use of steel sections with no compression capacity (e.g., straps) is not recommended. In some cases steel members that increase collector capacity have been lag bolted to the top of existing beams or purlins through the roof. However, concerns about ponding and drainage may prevent such a retrofit. If no collector exists, provision of a collector can be achieved with blocking members spliced together (i.e., with structural steel shapes or with tension ties on the underside if the blocking is cut snug) to avoid cutting and resupporting existing framing. It is a common practice in such cases to discontinue the blocking after a distance long enough to develop the collector force into the diaphragm. In almost all cases, such fixes will include nailing into the diaphragm (and consequently, reroofing). The length of the collector should consider the global stress in the diaphragm.
Defining Terms Boundary element — An element at edges of openings or at perimeters of shear walls or diaphragms. See Chord.
Chord — A boundary element of a diaphragm or shear wall that is assumed to take axial forces analogous to the flanges of an I-beam. Typically for tilt-up type buildings, diaphragm chords consist of extra continuous horizontal reinforcing bars located within the wall near the roof or floor diaphragm level. Continuity is usually achieved by welded connections at the wall panel joints. Continuous steel ledger angles may also be provided. Collector — A horizontal (or nearly horizontal) member or element parallel to the applied load that collects and transfers lateral forces from a portion of the structure to a vertical element (e.g., shear wall, braced frame, moment frame) of the lateral-load-resisting system. Such members may take axial tension or compression. Continuity ties — The connectors used to transmit forces from the end of one cross tie to the other.
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Continuous ties — The combination of cross ties (framing members) and continuity ties (connections). Corbel — A projection from a column or wall face, integral with the column or wall, which serves as a support for a beam or truss. Cross ties — Continuous ties or struts between diaphragm chords to distribute the wall anchorage forces from masonry or concrete walls into the diaphragm. Added chords may be used to form subdiaphragms to transmit the anchorage forces to the main cross ties. Diaphragm — A diaphragm is a horizontal or nearly horizontal system acting to transmit lateral forces to the vertical-resisting elements. The term “diaphragm” includes horizontal bracing systems. Emulated — Precast beam–column systems that are interconnected using reinforcing and wet concrete in such a way as to create a system that will act to resist lateral loads in a manner similar to cast-in-place concrete systems. Flexible diaphragms — Roofs or floors including, but not necessarily limited to, those sheathed with plywood, wood decking, or metal decks without structural concrete topping slabs. Metal decks with lightweight fill may or may not be flexible. Diaphragms are considered flexible when the maximum lateral deformation of the diaphragm is more than two times the average story drift of the associated story. This may be determined by comparing the computed midpoint in-plane deflection of the diaphragm itself under lateral load with the drift to adjoining vertical elements under tributary lateral load. Lateral-force-resisting system — The system of continuous load paths, which convey horizontal (i.e., lateral) forces such as due to earthquake or wind, from all points in a structure to the foundation and ground. Pier — A pier is differentiated from a column in a frame system by possessing a width-to-thickness ratio in excess of 2.5. Pilaster — Thickened portion of wall panel that usually supports a beam or purlin. Typically located at edge of panel. May be poured monolithically with wall panel or cast in place to tie panels together. Precast concrete — Concrete components not cast in place but rather cast off site (usually at precast yards) or cast at the site and tilted into position. Precast concrete and precast are synonymous. Prestressing — Structural technique involving introduction of stresses into a structural member prior to its service. The imposed stresses are typically similar in magnitude but opposite in pattern to the stresses expected during the member’s service. Prestressing is usually achieved via tensioning steel cables or bars within the member, in such a manner that the tension forces in the steel cable or bar are transferred as compressive forces to the member. Primary shear wall — A shear wall is defined as a primary shear wall if its failure will lead to significant overstresses in other portions of the building, including other walls and/or the roof diaphragm. A primary shear wall is a wall that is intended to be part of the lateral load system of the building. Purlin — A horizontal framing member in a roof, at right angles to the principal beams or trusses, and supported by them. Purlins commonly support subpurlins if there are any, or the roof sheeting. Shear wall — A shear wall is a wall designed to resist lateral forces parallel to the plane of the wall. Stitch column — Stitch columns are cast-in-place segments between adjacent wall panels that are flush with interior and exterior surfaces of wall panels. They are essentially cast-in-place pilasters with the same thickness as the wall panels. Strut tie — The connectors used to transmit forces from the end of one strut to the other in order to make the strut continuous from one subdiaphragm chord to the other. Strut — A horizontal (or nearly horizontal) member parallel to the applied loads to which a wall anchor is connected. It may be a subpurlin, a purlin, or a beam. The strut forces are transferred from the wall into the diaphragm or subdiaphragm. Such members may take axial tension or compression. Subdiaphragm — A portion of a larger diaphragm designed to anchor and transfer local forces to continuity ties and the main diaphragm. The subdiaphragm must meet the depth-to-span © 2003 by CRC Press LLC
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limitations specified by the code for roof and floor diaphragms. Subdiaphragms are a concept intended as a design tool. It is acknowledged that due to deflection compatibility requirements and other considerations, actual behavior of the diaphragms differ from those assumed using the subdiaphragm concept. Tension tie — Wall anchor that has no compressive capacity, and typically consists of a thin (light gage) metal strap. Tilt-up wall — A form of precast concrete panel construction for low-rise commercial buildings popular in the western United States, where the panel is cast in a horizontal position, either at the construction site or off site, and after curing, tilted upright to be incorporated into the structure as a vertical panel. The walls are structurally connected to the horizontal diaphragms and are intended to act as shear walls in resisting lateral loads. The walls may or may not be bearing walls. Wall anchor — A tie that transfers out-of-plane forces associated with a wall into a horizontal diaphragm. Wall anchors are intended to prevent the wall from separating from the roof or floor diaphragm that can lead to collapse of the wall and loss of vertical support for the roof or floor. Tension ties are wall anchors that can resist tension forces only. Wall anchorage system — Includes all structural elements that support the wall in the lateral direction, including wall anchors, struts, cross ties, continuity ties, and subdiaphragms.
References Brooks, H. 1994. Tilt-up and Earthquakes, A Post-Northridge Assessment (http://www.tilt-up.com/ default2.asp). FEMA 154. 1988. Rapid Visual Screening of Buildings for Potential Seismic Hazards: A Handbook, Earthquake Hazards Reduction Series 41, prepared by the Applied Technology Council for the Federal Emergency Management Agency, Washington, D.C. FEMA 273. 1997. NEHRP Guidelines for the Seismic Rehabilitation of Buildings, prepared by the Building Seismic Safety Council for the Federal Emergency Management Agency, Washington, D.C. FEMA 274. 1997. NEHRP Guidelines for the Seismic Rehabilitation of Buildings: Commentary, prepared by the Building Seismic Safety Council for the Federal Emergency Management Agency, Washington, D.C. FEMA 302. 1998. NEHRP Recommended Provisions for Seismic Regulations for New Buildings and Other Structures, Part 1, Provisions, prepared by the Building Seismic Safety Council for the Federal Emergency Management Agency, Washington, D.C. FEMA 303. 1998. NEHRP Recommended Provisions for Seismic Regulations for New Buildings and Other Structures, Part 2, Commentary, prepared by the Building Seismic Safety Council for the Federal Emergency Management Agency, Washington, D.C. Hamburger, R.O., S.K. Harris, S.C. Martin, and D.L. McCormick of EQE International, Inc., and P.G. Somerville of Woodward-Clyde Federal Services. 1995. “Response of Tilt-up Buildings to Seismic Demands: Observations and Case Studies from the 1994 Northridge Earthquake,” based on work supported by National Science Foundation under Grant No. CMS-9416232. International Code Council. 2000. International Building Code, International Code Council, Falls Church, VA. International Conference of Building Officials. 2001. “Guidelines for Seismic Retrofit of Existing Buildings,” International Conference of Building Officials, Whittier, CA. Nghiem, D. 1994. Northridge Earthquake SEAOSC/COLA Special Investigation Committee, Tilt-up Subcommittee. Final Report. September 25, Structural Engineers Association of Southern California and City of Los Angeles, CA. Priestley, M.J.N. 1996. “The PRESSS Program — Current Status and Plans for Phase III,” PCI Journal, 41, 22–40.
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SEAONC (Structural Engineers Association of Northern California). 2001. Guidelines for Seismic Evaluation and Rehabilitation of Tilt-Up Buildings and Other Rigid Wall/Flexible Diaphragm Structures, D. McCormick, Ed., International Conference of Building Officials, Whittier, CA. SEAOSC (Structural Engineers Association of Southern California). 1994. Findings and Recommendations of the City of Los Angeles/SEAOSC Task Force on the Northridge Earthquake. November 12, Los Angeles, CA. Simpson Strong-Tie Co. 2001. Wood Construction Connectors, Catalog C-2001, Dublin, CA. Stanton, J.F. and S.D. Nakaki. 2001. “Precast Concrete Frames Designed for Seismic Conditions,” SEAOC 2001 70th Annual Convention Proceedings, Structural Engineers Association of Southern California, Los Angeles, CA. UBC. 1997. Uniform Building Code, International Conference of Building Officials, Whittier, CA.
Further Reading Relevant publications on the performance, evaluation, and rehabilitation of tilt-up buildings are the SEAONC Guidelines 2001 and the 2001 Guidelines for Seismic Retrofit of Existing Buildings (GSREB) [ICBO, 2001], and the 1999 Recommended Lateral Force Requirements and Commentary by the Structural Engineers Association of California (Bluebook), all available through ICBO. Manufacturers’ catalogs and technical manuals [e.g., Simpson, 2001] are also very informative. Information concerning the use of prestressed components to resist lateral loads in high seismic zones can be found in Precast Concrete Frames Designed for Seismic Conditions [Stanton and Nakaki, 2001] and The PRESSS Program — Current Status and Plans for Phase III [Priestley, 1996].
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15 Wood Structures 15.1 Introduction Types of Wood-Based Products · Types of Structures · Design Standards
15.2 Wood As a Material 15.3 Seismic Performance of Wood Buildings General · 1971 San Fernando Earthquake, California · 1989 Loma Prieta Earthquake, California · 1994 Northridge Earthquake, California
15.4 Design Considerations Building Code Loads and Load Combinations
15.5 Resistance Determination Bending Members · Axial Force Members · Combined Loading
15.6 Diaphragms Stiffness vs. Strength · Flexible vs. Rigid Diaphragms · Connections to Walls · Detailing around Openings · Typical Failure Locations
15.7 Shear Walls Rationally Designed Walls · Prescriptive Construction
15.8 Connections
J. Daniel Dolan Brooks Forest Products Research Center Virginia Polytechnic Institute and State University Blacksburg, VA
Design Methodology · Small-Diameter Dowel Connections · Large-Diameter Dowel Connections · Heavy Timber Connectors
Defining Terms References Further Reading
15.1 Introduction Stone and wood were the first materials used by man to build shelter, and in the United States wood continues to be the primary construction material for residential and commercial buildings today. In California, for example, wood accounts for 99% of residential buildings [Schierle, 2000]. Design and construction methods for wood currently used by the residential construction industry in North America have developed through a process of evolution and tradition. Historically, these construction methods have been sufficient to provide acceptable performance under seismic loading mainly due to the relatively light weight of wood and the historical high redundancy in single-family housing. However, in recent years architectural trends and society’s demands for larger rooms, larger windows, and a more open, airy feel to the structure have resulted in a reduction in the structural redundancy of the typical house, as well as a reduction in symmetry of stiffness and strength that was inherent in traditional structures. If one were to review the type of structure that was built in the 1930s, 1940s, and even into the 1950s, one would realize that the average house had a pedestrian door, small double-hung windows, and
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relatively small rooms with lots of walls. If one compares this typical construction to buildings that are being built in the early 2000s, newer buildings have large windows, if not four walls of primarily glass, large great rooms, and often a single room that pierces the first-story ceiling, becoming two stories high and causing a torsional irregularity in the second-floor structure. If one then includes multifamily construction, which includes apartments, condominiums, and townhouses, the structures become fairly stiff and strong in one direction while the orthogonal direction (the side with the windows and the doors to the hallways or patio) become very weak and flexible, due to the lack of structural wall space. In general, modern structures typically have more torsional irregularities, vertical irregularities such as soft stories, and uneven stiffness and strength in orthogonal directions when compared to traditional buildings. As a result, it was observed in the 1994 Northridge earthquake that “most demolished singlefamily dwellings and multi-family dwellings (as a percentage of existing buildings) were built 1977–1993” [Schierle, 2000]. An additional need for improved understanding of the material and structure used in modern timber buildings is the continued movement toward performance-based design methods and an increased concern over damage. If one considers that the house is the single largest investment that the average person makes in his or her lifetime, it should be no surprise that concern over accumulated damage due to moderate seismic events has begun to be discussed in the context of model building codes. To support the seismic design of timber structures, the wood industry has sponsored the development of the Standard for Load and Resistance Factor Design (LRFD) for Engineered Wood Construction [American Forest and Paper Association, 1996; American Society of Civil Engineers, 1995]. However, most designers continue to use the National Design Specification (NDS®) for Wood Construction and its supplements [American Forest and Paper Association, 1997] for designing wood structures in North America. The NDS is an allowable stress design methodology, while the LRFD is a strength-based design methodology, that is intended to provide a better design for seismic concerns. The NDS has been repackaged into the ASD [Allowable Stress Design] Manual for Engineered Wood Construction [American Forest and Paper Association, 1999]. This section reviews the types of wood products available for use in timber construction, the types of structures that are typically designed and built in North America, the design standards that are available for directing the design process, the industry resources that are available, the performance of wood buildings in recent earthquakes, and some of the restrictions that are placed on wood structures due to issues other than seismic concerns. While the rest of the chapter will focus primarily on strength-based design (i.e., LRFD), the NDS will be referred to from time to time where differences are significant. Since the average design firm continues to use ASD for wood structures, it is important that these differences be highlighted.
15.1.1 Types of Wood-Based Products There are a wide variety and an increasing number of wood-based products available for use in building construction. While the largest volume of wood-based products includes dimensional lumber, plywood, and oriented strand board (OSB), new composites include structural composite lumber (SCL), I-joists, laminated veneer lumber (LVL), and plastic wood (Figure 15.1). In addition, when large sizes are required, glued-laminated lumber (glulam) and SCL, such as Paralam, can be used. The current trend is to move toward increased use of wood-based composites in building construction. This is due to the increased difficulty in obtaining large sizes of timber because of restrictions on logging and changes in the economic structure of manufacturing. Therefore, designers should become familiar with the SCL, LVL, and glulam when long spans or heavy loads are anticipated. Many of the new composites can be custom manufactured to the size and strength required for a particular application. Designers must obtain the proprietary technical information required to design structures with most of the new composites from the suppliers of the products.
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C A
B
FIGURE 15.1 Prefabricated I-joists with laminated veneer lumber flanges and structural panel webs. One experimental product has (A) a hardboard web; the other two commercial products have (B) oriented strandboard and (C) plywood webs. (From U.S. Department of Agriculture. 1999. Wood Handbook: Wood as an Engineering Material, Agriculture Handbook 72, Forest Products Laboratory, USDA, Madison, WI.)
15.1.2 Types of Structures Timber structures can be classified in two general categories: 1. Heavy timber construction includes buildings such as sports arenas, gymnasiums, concert halls, museums, office buildings, and parking garages. These heavier structures are usually designed to resist higher levels of loading and are therefore designed with the intent of using large section timbers that typically require the use of glulam timber, LVL, structural composite lumber, or similar products. These types of structures require a fairly high level of engineering to ensure the safe performance of the structure due to the lower redundancy of the structure. 2. Light-frame construction is by far the largest volume of timber construction in North America. These types of buildings include one- and two-family dwellings (Figure 15.2), apartments, townhouses, hotels, and other light-commercial buildings. These types of structures are highly redundant and indeterminate, and there are currently no computer analysis tools that provide a detailed analysis of these structures. Light-frame construction consists of 2-in. nominal dimension lumber that ranges in size from 2 × 4 to 2 × 12. While the design specifications have geometric parameters that include 2 × 14, the availability of such large sizes is questionable. The lattice of framing comprised of 2× dimensional lumber is then typically sheathed with panel products that include plywood, OSB, fiberboard, gypsum, stucco, or other insulation-type products (Figure 15.2). This system of light-framing sheathed with load-distributing
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Wall systems: 4. stud wall (platform or balloon frame) 5. horizontal siding
Roof/floor span systems: 1. wood joist and rafter 2. diagonal sheathing 3. straight sheathing
2 3 5
1 4 9
6 7 8 Foundation/connections: 6. unbraced cripple wall 7. concrete foundation 8. brick foundation
Bracing and details: 9. unreinforced brick chimney 10. diagonal blocking 11. let-in brace (only in vintage)
FIGURE 15.2 Schematic of wood light-frame construction. (From Federal Emergency Management Agency. 1988. Rapid Visual Screening of Buildings for Potential Seismic Hazards: A Handbook, FEMA 154, FEMA, Washington, D.C.)
elements then acts to transmit the load horizontally through the roof and floors and vertically through the walls, constituting the lateral-force-resisting system (Figure 15.3). This results in a highly redundant and indeterminate structure that has a good history of performance in seismic loading. With modern architectural trends, the reduction in redundancy results in an increased need to involve structural engineering to ensure good performance. Light-frame construction can be broken into two principal categories: fully designed and prescriptive. Currently the design requirements for using mechanics-based design methods are in the International Building Code (IBC) [International Code Council, 2000a] or the National Fire Prevention Association NFPA 5000 Building Code [National Fire Prevention Association, 2002]. Requirements for prescriptive construction are contained in the International Residential Code (IRC) [International Code Council, © 2003 by CRC Press LLC
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Seismic inertial forces
Load path (flows down through structure)
Resistance path (flows up through structure)
FIGURE 15.3 Lateral-force-resisting system. The load is transmitted horizontally through the roof and floors and vertically through the walls.
2000b], which is a replacement for the Council of American Building Officials’ (CABO) One- and TwoFamily Dwelling Code [Council of American Building Officials, 1995]. The IRC allows for a mix between a fully designed and rationalized system and the prescriptive systems. In other words, a building that is primarily designed and constructed according to the prescriptive rules of the IRC can have elements that are rationally designed to eliminate such things as irregularities in the structure due to form. The IRC and IBC have consistent seismic provisions as far as the load determination is concerned.
15.1.3 Design Standards Design standards can be broken into two categories. One is the performance requirements, which are typically covered by the building codes; the other is the required design methodology to provide that performance, which is included in the design standards. In North America, buildings are typically governed by the IBC or NFPA 5000 for engineered systems. The IRC provides the performance requirements and the methodology to provide the required resistance for one- and two-family residential structures. All of the model building codes available in the United States, plus the ASCE-7: Minimum Design Load for Buildings and Other Structures [American Society of Civil Engineers, 1990] base their seismic design requirements on the NEHRP Recommended Provisions for Seismic Regulations for New Buildings and Other Structures [Building Seismic Safety Council, 2000a]. All model building codes in effect in the United States recognize either the LRFD standard [American Forest and Paper Association, 1996; American Society of Civil Engineers, 1996] for strength-based design, or the NDS [American Forest and Paper Association, 1999; American Society of Civil Engineers, 1995] for allowable stress design for engineered wood construction. In order to parallel the format of the LRFD design manual, the NDS has been incorporated into the ASD Manual for Wood Construction [American Forest and Paper Association, 1999]. In this format, all of the wood-based structural products available to be used in the design and construction of timber structures are available to the designer. Most of the provisions of the LRFD standard are similar to those used in the NDS or ASD manual. The difference is that the ASD design methodology bases its requirements in terms of working stresses or allowable stresses, while the LRFD manual bases its design values on the nominal strength values. The two design methodologies also use different load combinations. Since the NEHRP provisions require the use of strengthbased design methodology, this chapter will focus on LRFD. © 2003 by CRC Press LLC
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In addition to the ASD and LRFD manuals, the designer may utilize industry documents that are available for most of the trade associations associated with the timber industry. Some of these references include the Timber Construction Manual [American Institute of Timber Construction, 1994], the Plywood Design Specification [APA, 1997], and the Engineered Wood Construction Guide [APA, 2001]. The Timber Construction Manual [American Institute of Timber Construction, 1994] provides the designer with guidance in the use of glulam construction and the associated issues such as heavy timber connectors, notching and drilling of beams, and the design of arches and other curved members. The Plywood Design Specification and its supplements provide guidance on the use of plywood and other structural panel products, especially for nontypical applications such as plywood box beams, folded plate roofs, and spanning the product in the weak direction across supports. The Engineered Wood Construction Guide is a general document that provides information on how structural panel products are graded and marked, the design of floor and roof systems, as well as providing design values for allowable stress design of shear walls and diaphragms. Additional documents and guidance can be obtained from various industry associations such as the American Forest and Paper Association, APA, Engineered Wood Association, Canadian Wood Council, Wood Truss Council of America, Truss Plate Institute, Western Wood Products Association, Southern Forest Products Association, and others. While the design and construction of relatively tall structures are technically achievable, a typical building code restricts the use of light-frame construction as well as heavy timber construction to lowrise buildings. Both light-frame and heavy-timber construction are classified as combustible materials. However, heavy-timber construction can be classified as fire resistant and can be built, according to most building codes, as high as five stories. Light-frame construction is typically limited to four stories. There is, however, a move to allow a higher number of stories for light-frame, provided fire suppression systems, such as sprinklers, are included in the building.
15.2 Wood As a Material Wood in general can be considered a relatively brittle material from a structural standpoint. Wood is a natural material that is viscoelastic and anisotropic, but is generally considered and analyzed as an orthotropic material. Wood has a cellular form that enhances the hygroscopic or affinity to water response. In general, from a structural engineering point of view, wood can be considered similar to over-reinforced concrete, and one might consider designing a wood building as building with overreinforced concrete members that are connected with ductile connections. One needs to differentiate between wood and timber. In this chapter, wood is considered to be small clear specimens that one might idealize as perfect material. On the other hand, timber comes in the sizes that are typically used in construction and has growth characteristics such as knots, slope of grain, splits and checks, and other characteristics due to the conditions under which the tree grew or the lumber was manufactured. These growth characteristics contribute to significant differences in the performance between wood and timber. They also provide inherent weakness in the material that the structural engineer or designer needs to be aware of. Since wood is a natural material and is hygroscopic and viscoelastic, certain environmental end-use conditions affect the long-term performance of the material. Some of these variables include moisture content, dimensional stability, bending strength, stiffness, and load duration. Each of these variables will be dealt with individually. Moisture content is one of the most important variables that a designer needs to consider when designing timber structures. Any inspection of wood buildings should include testing of the moisture content with standard moisture meters that are available on the commercial market. Moisture content is determined as the weight of water in a given piece of timber divided by the weight of the woody material within that member in an oven-dried state. Moisture content affects virtually all mechanical properties of timber. One can consider wood as being similar to a sponge; as the water is absorbed from the dry state, it enters the walls of the individual cells of the material. At some point these walls become saturated and any additional water is then stored in the lumen of the cell. The point at which the walls © 2003 by CRC Press LLC
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become saturated is known as the fiber saturation point. The fiber saturation point varies for different species, and even within a single species, but ranges somewhere between 23 and 35%. The average fiber saturation point is usually assumed to be 30% for most general applications. Dimensional stability of timber is affected directly by the moisture content. One can assume a linear variation of shrinkage or swelling with changes of moisture content between the oven-dry state and the fiber saturation point. Once the fiber saturation point is reached any additional increase in moisture content only adds water to the air space of the member and does not affect the dimensional portions of the member. One can estimate the dimensional stability or dimensional changes of an individual wood member using shrinkage coefficients that are available in resources such as the Wood Handbook [U.S. Department of Agriculture, 1999]. However, one can usually assume that shrinkage in the perpendicularto-grain directions (either radial or tangential) may be significant, while shrinkage parallel-to-grain can be considered as negligible. This is why connections that are restrained by steel plates through significant depths (even as little as 12-in. members) cause the wood to split, because as the wood dries out it will shrink while the steel and the connectors holding the wood to the steel prevent it from moving. Moisture content changes have effects in addition to simply changing the perpendicular-to-grain dimension. Restrained wood, subjected to the cycling of moisture content, can cause distortion of the members. General issues of warping can include checking or splitting of the lumber due to restraint of the connections, or wood members with grain oriented perpendicular to each other can cause the member to bow, warp, or cup. Cup is often seen in lumber deckboards that are laid with the growth rings on the cross section oriented such that the center of the tree is facing up. All distortional responses can have adverse effects from a structural standpoint, and many cause serviceability concerns. Due to the effects of dimensional change on the straightness and mechanical properties of timber, it is strongly recommended that designers specify, and require without substitution, the use of dry material for timber structures. Bending strength of timber is affected by moisture content as well. Bending strength may increase as much as 4% for each 1% decrease in moisture content below the fiber saturation point. While the cross section of the member will also decrease due to shrinkage, the strengthening effect of drying out is significantly larger than the effects of the reduction in cross section. Stiffness also increases with a decrease in moisture content, and again, the effect of stiffening of the material is greater than the effect of the reduction in cross section due to shrinkage. This is why it is recommended that timber structures be constructed with dry material that will remain dry during its service life. The less moisture content change within the material at the time it is constructed and used, the less shrinkage occurs, and the maximum bending and stiffness values can be used by the designer. The final two variables to be considered in this section have to do with viscoelastic properties. Because wood, and therefore timber, is viscoelastic, it tends to creep over time and also has a duration of load effect on strength. Creep is the continued increase in deflection that occurs in the viscoelastic material that sustains a constant load. In wood that is dry when installed and remains dry during service, the creep effect may cause a 50% increase in elastic deflection over a period of one year. However, if the material is unseasoned at time of installation and allowed to dry out in service, the deflections can increase by 100% over the elastic response. Finally, if the moisture content is cycled between various moisture contents during its lifetime, the deflections can be increased to as much as 200% over the initial elastic response. A clear difference between wood and timber is that wood is affected by moisture content at all times, while timber is only affected by moisture content in the stronger grade levels. This is why Select Structural grade lumber is affected more than number 3 grade lumber, and the design manuals have a check for minimum strength before the moisture effect or wet service factor is applied. Duration load is a variable that is directly accounted for in both the LRFD and ASD manuals. Load duration factor CD is based on experimental results from the 1950s at the U.S. Forest Products Laboratory. This curve is often referred to as the Madison curve. It forms the basis of the provisions in the LRFD and ASD manuals. There is one significant difference in how load duration is dealt with in the two design methodologies. In LRFD, the reference time is set at a duration of between 5 and 10 min. This duration is associated with a CD of 1.0, with longer durations having factors less than 1. The ASD manual uses a © 2003 by CRC Press LLC
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reference duration of 10 years, with an associated value of CD of 1.0. All values of CD for load durations shorter than 10 years are given values greater than 1.0 for ASD. The designer is responsible to change the reference time, depending on which design methodology is used. Finally, ductility and energy dissipation, which are important concepts for seismic design, are beneficial for most wood structures. Provided the structure’s connections are detailed properly, timber structures have relatively high values of ductility and energy dissipation. Provided the connections yield, such as would occur for nail and small-diameter bolted connections, ductilities in the range of four to eight are not uncommon. Energy dissipation, on the other hand, from a material standpoint is very low for wood. Typically the material damping that occurs in timber structures is less than 1%. However, the hysteretic energy dissipation of structural assemblies such as shear walls is very high. Equivalent viscous damping values for timber assemblies can range from a low of 15% to a high of more than 45% critical damping.
15.3 Seismic Performance of Wood Buildings 15.3.1 General As noted above, wood frame structures tend to be mostly low rise (one to three stories, occasionally four stories). The following discussion of the seismic performance of wood buildings is drawn from several sources. In the next few paragraphs, we provide an overview of wood construction and performance drawn from FEMA 154 [1988], followed by a limited discussion of performance in specific earthquakes drawn from various sources. Vertical framing may be of several types: stud wall, braced post and beam, or timber pole. Stud wall structures (“stick-built”) are by far the most common type of wood structure in the United States, and are typically constructed of 2-in. by 4-in. nominal wood members vertically set about 16 in. apart. These walls are braced by plywood or by diagonals made of wood or steel. Most detached single and low-rise multiple family residences in the United States are of stud wall wood frame construction. Post-and-beam construction is not very common and is found mostly in older buildings. These buildings usually are not residential, but instead are larger buildings such as warehouses, churches, and theaters. This type of construction consists of larger rectangular (6 in. by 6 in. and larger) or sometimes round wood columns framed together with large wood beams or trusses. Stud wall buildings have performed well in past earthquakes due to inherent qualities of the structural system and because they are lightweight and low rise. Cracks in the plaster and stucco (if any) may appear, but these seldom degrade the strength of the building and are therefore classified as nonstructural damage. In fact, this type of damage dissipates a lot of the earthquake-induced energy. The most common type of structural damage in older buildings results from a lack of connection between the superstructure and the foundation. Houses can slide off their foundations if they are not properly bolted to the foundation, resulting in major damage to the building as well as to plumbing and electrical connections. Overturning of the entire structure is usually not a problem because of the low-rise geometry. In many municipalities, modern codes require wood structures to be bolted to their foundations. However, the year that this practice was adopted will differ from community to community and should be checked. Another problem in older buildings is the stability of cripple walls. Cripple walls are short stud walls between the foundation and the first floor level (Figure 15.4). Often these have no bracing and thus may collapse when subjected to lateral earthquake loading (Figure 15.5). If the cripple walls collapse, the house will sustain considerable damage and may also collapse. This type of construction is generally found in older homes. Plywood sheathing nailed to the cripple studs may have been used to strengthen the cripple walls. Garages often have a very large door opening in one wall with little or no bracing. This wall has almost no resistance to lateral forces, which is a problem if a heavy load such as a second story sits on top of the garage. Homes built over garages have sustained significant amounts of damage in past earthquakes, with many collapses. Therefore the house-over-garage configuration, which is found commonly in lowrise apartment complexes and some newer suburban detached dwellings, should be examined more carefully and perhaps strengthened. © 2003 by CRC Press LLC
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First Floor
Exterior wall
Cripple wall
Anchor/tie down bolts
Sill plate
Foundation
FIGURE 15.4
Cripple wall. (From Benuska, L., Ed. 1990. Earthquake Spectra, 6 (Suppl.). With permission.)
FIGURE 15.5 Houses damaged due to cripple wall failure, 1983 Coalinga earthquake. (Courtesy EQE International)
15.3.2 1971 San Fernando Earthquake, California The San Fernando earthquake occurred on February 9, 1971 and measured 6.6 on the Richter scale. The following commentary is excerpted from Yancey et al. [1998]: There were approximately 300,000 wood-frame dwellings in the San Fernando Valley of which about 5% were located in the region of heaviest shaking [Steinbrugge et al., 1971]. A survey of 12,000 singlefamily wood-frame houses was conducted by the Pacific Fire Rating Bureau [Steinbrugge et al., 1971]. © 2003 by CRC Press LLC
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FIGURE 15.6 Collapsed apartment buildings Marina district of San Francisco, 1989 Loma Prieta earthquake. (Courtesy EQE International)
Most of the dwellings were constructed within the two decades prior to the earthquake. Typical types of foundations were either slab on-grade or continuous concrete foundation around the perimeter with concrete piers in the interior, with the former being more common. The majority of the houses were single-story. The survey showed that within the region of most intense shaking, 25% of the woodframe dwellings sustained losses greater than 5% of the dwelling’s value, with the remainder sustaining smaller losses. The number of houses with damage above the 5% threshold is equivalent to 1% of all the wood-frame dwellings in the San Fernando Valley.
15.3.3 1989 Loma Prieta Earthquake, California The Loma Prieta earthquake occurred on October 17, 1989 in the San Francisco Bay region and measured 7.1 on the Richter scale [Lew, 1990]. The following general observation and commentary are excerpted from Yancey et al. [1998]: © 2003 by CRC Press LLC
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Property damage was estimated at over $6 billion and over 12,000 people were displaced from their homes. A survey of the damage to wood-framed structures was conducted by a group of three engineers from the American Plywood Association (APA) [Tissell, 1990]. Their main findings were: 1. Damage was caused by failure of cripple walls. The failures of cripple walls were the result of inadequate nailing of plywood sheathing. When adequate nailing was provided, no failure was observed. 2. Lack of connection between the major framing members and the foundation was the cause of failure of two severely damaged houses. 3. Damage caused by soft stories was observed in the Marina District. The phenomenon of soft stories, first observed in this earthquake, results from garage door or large openings on the ground floor of apartment buildings and houses that reduce the lateral resistance of that story. The reduced lateral resistance causes severe racking to occur or increases lateral instability. 4. Chimney damage was common. Chimneys were typically unreinforced and not sufficiently tied to the structure. 5. Upward ground movements caused doors to be jammed and damage to basement floors. 6. Post-supported buildings were damaged because of inadequate connections of the floor to the post foundation and unequal stiffnesses of the posts due to unequal heights. Houses where the poles were diagonally braced were not damaged. A particularly noteworthy concentration of damage was in the Marina section of San Francisco, where seven 1920s-era three- to five-story apartment buildings collapsed, and many were severely damaged. The excessive damage was due in large part to the man-made fill in the Marina, which liquefied and greatly increased ground motion accelerations and displacements during the shaking. However, the primary cause of the collapse was the soft-story nature of the buildings, due to required off-street parking. The buildings lacked adequate lateral-force-resisting systems and literally were a “house of cards.”
15.3.4 1994 Northridge Earthquake, California An earthquake with a magnitude of 6.8 struck the Northridge community in the San Fernando Valley on January 17, 1994. The effects of this earthquake were felt over the entire Los Angeles region. Approximately 65,000 residential buildings were damaged with 50,000 of those being single-family houses [U.S. Department of Housing and Urban Development, 1995]. The estimated damage based on insurance payouts was over $10 billion [Holmes and Somers, 1996] for single- and multifamily residences. City and county building inspectors estimated that 82% of all structures rendered uninhabitable by the earthquake were residential. Of these, 77% were apartments and condominiums, and the remaining 23% were single-family dwellings. A week after the earthquake, approximately 14,600 dwelling units were deemed uninhabitable (red or yellow tagged). Severe structural damage to residences was found as far away as the Santa Clarita Valley to the north, south-central Los Angeles to the south, Azusa to the east, and eastern Ventura County to the west. 15.3.4.1 Multifamily Dwellings Particularly vulnerable were low-rise, multistory, wood-frame apartment structures with a soft (very flexible) first story and an absence of plywood shear walls. The soft first-story condition was most apparent in buildings with parking garages at the first-floor level (Figure 15.7). Such buildings, with large, often continuous openings for parking, did not have enough wall area and strength to withstand the earthquake forces. The lack of first-floor stiffness and strength led to collapse of the first floor of many structures throughout the valley. The main reason for failure was the lack of adequate bracing, such as plywood shear walls. Most older wood-frame structures had poor if any seismic designs and resisted lateral forces using stucco, plaster and gypsum board wall paneling, and diagonal let-in bracing. © 2003 by CRC Press LLC
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FIGURE 15.7 Typical soft story “tuck-under” parking, with apartments above. (Courtesy EQE International) Shown as Color Figure 15.7.
15.3.4.2 Single-Family Dwellings Widespread damage to unbolted houses and to older houses with cripple-stud foundations occurred. Newer houses on slab-on-grade foundations were severely damaged because they were inadequately anchored. Two-story houses without any plywood sheathing typically had extensive cracking of interior sheetrock, particularly on the second floor. Nine hillside houses built on stilts in Sherman Oaks collapsed. All but one of the homes were constructed in the 1960s — predating the major building code revisions made after the 1971 San Fernando earthquake.
15.4 Design Considerations Design considerations can be broken into essentially three categories: 1. Material choice 2. Performance requirements 3. Resistance determination These are governed by the location of the project, the adopted building code regulations, and the design process of choice. Once the choice of designing a wood structure is made, the designer must also consider what types and what grades of wood products are readily available in the region of the project. Both LRFD and ASD include a wide variety of products, product sizes, and grades of products. Local building supply companies rarely stock all of the available products. The economics of building with wood is often the reason for choosing the material for a project, and the choice of products within the broad spectrum of available products that are locally available and stocked greatly improves the economics of a project. If products are specified that must be specially ordered or shipped long distances relative to what is already available in the market, the cost of the project will increase. Performance requirements for a given building are usually determined by the building code that is enforced for the jurisdiction. However, there are also the local amendments and local conditions that must be considered when determining the performance requirements of a given project. Resistance determination and sizing of lumber for a given project are governed by the choice of design methodology used. If LRFD is used, one set of load combinations from the building code or ASCE 7 is required. If ASD is used, another set of load combinations should be used.
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15.4.1 Building Code Loads and Load Combinations Building codes that are in effect in the United States reference the ASCE load standard [American Society of Civil Engineers, 1990] to provide guidance to the engineer for which load combination is to be used. The 2000 IBC and the NFPA 5000 Building Code both reference the ASCE 7–98 load standard. The following load combinations are to be considered when designing wood structures when using the LRFD design methodology: 1. 2. 3. 4. 5. 6. 7.
1.4 (D + F) 1.2 (D + F + T) + 1.6 (L + H) + 0.5 (Lr or S or R) 1. 2D + 1.6 (Lr or S or R) + (0.5L or 0.8W) 1. 2D + 1.6W + 0.5L + 0.5 (Lr or S or R) 1. 2D + 1.0E + 0.5L + 0.2S 0.9D + 1.6W + 1.6H 0.9D + 1.0E + 1.6H
D E F H L Lr R S T W
= dead load = earthquake load = load due to fluids with well-defined pressures and maximum heights = load due to lateral earth pressure, groundwater pressure, or pressure of bulk materials = live load = roof live load = rain load = snow load = self-straining force = wind load
(15.1)
where
If the designer is using ASD, the ASCE 7–98 standard provides different load combinations to use. The following load combinations should be used when designing timber structures following ASD: 1. 2. 3. 4. 5.
D D + L + F + H + T + (Lr or S or R) D + (W or 0.7E) + L + (Lr or S or R) 0.6D + W + H 0.6D + 0.7E + H
(15.2)
Since components within a timber structure will be stressed to their capacity during a design seismic event, it is strongly recommended that designers use the LRFD format when considering seismic performance. This is the reason why the NEHRP provisions require that LRFD be used.
15.5 Resistance Determination The Load and Resistance Factor Design (LRFD) Manual for Engineered Wood Construction [American Forest and Paper Association, 1996] divides nominal design values for visually and mechanically graded lumber connections and has supplements to provide guidance for all other wood-based products. This document provides both the reference design mechanical property and the applicable adjustment factors to account for end-use and environmental conditions. The reference properties that are included in the document are Fb , bending strength, Ft , tension parallel-to-grain strength, Fs , shear strength, Fc , the compression parallel-to-grain strength, Fc⊥, the compression strength perpendicular-to-grain, and E, the modulus of elasticity. Two values for modulus of elasticity are typically provided in the supplements: the mean and fifth percentile values. It should be stressed that the resistance values provided in the LRFD manual should not be mixed or combined with values obtained from the ASD manuals. The two design © 2003 by CRC Press LLC
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methodologies use different reference conditions on which to base their design, and mixing the values may result in nonconservative designs. Similar resistance values for the mechanical properties of woodbased materials for allowable stress design are provided in the ASD Manual for Engineered Wood Construction [American Forest and Paper Association, 1999]. The significant difference between ASD and LRFD is that ASD bases the design values for a normal duration of load of 10 years, while LRFD resistance values are based on a 5- to 20-min load duration. Since wood is a viscoelastic material, the duration of load has a significant effect on the strength and deflections of timber structures. Two exceptions for adjustment of mechanical properties for load duration are modulus elasticity and compression perpendicular-to-grain. Both values are based on mean mechanical properties, and are not adjusted for load duration since compression perpendicular-to-grain is not associated with fracture-type failure and deflection is considered a serviceability rather than safety criterion. Since wood is a natural material that is affected by environmental conditions, and has characteristics inherent to the material that cause size or volume effects, several adjustments are made to the design values to account for these variables. Reference strength is adjusted with factors that include the time effect factor (load duration factor), wet service factor, temperature factor, instability factor, size factor, volume factor, flat use factor, incising factor, repetitive member factor, curvature factor, form factor, calm stability factor, shear stress factor, buckling stiffness factor, and bearing area factor. While many of these variables affect virtually all members of design, most factors only affect special situations. Therefore, the more commonly used factors will be covered here, and the reader is directed to either the LRFD or ASD manuals for a full description of the less used factors. In addition to these, the LRFD specification includes adjustment factors for preservative treatments and fire retardant treatments. The values that should be used for these last two variables should be obtained from the supplier of the products, since each product used is proprietary in nature and each affects the performance of the timber differently. Values of the adjustments are all equal to 1.0 unless the application does not meet the reference conditions. Both LRFD and NDS use the following reference conditions as the basis: 1. Materials are installed having a maximum equilibrium moisture content (EMC) not exceeding 19% for solid wood and 16% for glued products. 2. Materials are new (not recycled or reused material). 3. Members are assumed to be single members (not in a structural system, such as a wall or floor). 4. Materials are untreated (except for poles or piles). 5. The continuous ambient temperature is not higher than 100°F with occasional temperatures as high as 150°F (if sustained temperatures are between 100 and 150°F, adjustments are made. Timber should not be used at sustained temperatures higher than 150°F). The effect of load duration will be discussed later in this section. The reference design values are adjusted for conditions other than the reference conditions using adjustment factors. The adjustment factors are applied in a cumulative fashion by multiplying the published reference design value by the appropriate values of the adjustments. The equation for making the adjustments is: R'= R ∗ C1 ∗ C 2 ∗ C3 ∗ K Cn
(15.3)
where, R' is the adjusted design value for all conditions, R is the tabulated reference design resistance, and C1, C2 , C3 … Cn are the applicable adjustment factors. Most factors for adjusting for end use are common between the LRFD and ASD methodologies, and many are a function of the species of lumber, strength grade, or width of lumber. Most adjustment factors are provided either by the LRFD or ASD manuals. However, some adjustments are associated with proprietary products (chemical treatments) and must be obtained from the product supplier. Since wood is a viscoelastic material and therefore affected by time, the load duration variable is of particular interest to designers. The LRFD and ASD design methodologies handle the time effects or load
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TABLE 15.1 LRFD Load Combinations and Time Effect Factors LRFD Load Combination
Time Effect Factor
1.4D 1.2D + 1.6L + 0.5(Lr or S or R)
1.2D + 1.6(Lr or S or R) + (0.5L or 0.8W) 1.2D + 1.3W + 0.5L + 0.5(Lr or S or R) 1.2D+ 1.0E + 0.5L + 0.2S 0.9D – (1.3W or 1.0E)
0.6 0.7 for L representing storage 0.8 for L representing occupancy 1.25 for L representing impact 0.8 1.0 1.0 1.0
TABLE 15.2 ASD Design Loads and Associated Load Duration Factors Design Load Type
Load Duration Factor Value
Dead load Occupancy live load Snow load Construction load Wind or seismic load Impact load
0.9 1.0 1.15 1.25 1.6 2.0
duration differently. Regardless of which design methodology is used, the shortest duration load in the load combination will determine the value of the time effect factor. This is because the failure of timber is governed by a creep-rupture mechanism. This implies that timber can sustain higher magnitude loads for short periods of time. In the LRFD design methodology, the time effect factor λ is based on the load combinations considered and the design methodology specifically defines a time effect factor for each combination. These combinations, along with associated time effect factors, are shown in Table 15.1. The reference load duration for LRFD is 5 to 10 min, and this duration is given a value of 1.0. All others follow the Madison curve for load duration, and therefore longer duration loads have time effect factors that are less than 1.0. The ASD design methodology assumes a load duration of 10 years accumulative, at the design level. Therefore, the load duration factor used in the ASD has a value of 1.0 for normal duration loads, which is 10 years. The shortest duration load included in a given load combination determines which load duration factor is applicable. All load combinations with individual loads that have a cumulative duration of less than 10 years have load duration factor values greater than 1.0. The loads associated with various load duration factors for ASD are provided in Table 15.2. Therefore, the adjusted values for either design methodology are determined essentially following the same process, only using the appropriate values. First, the reference design values are obtained from the appropriate table and then adjusted for the end-use conditions, size effects, etc. by multiplying the reference value by a string of adjustment factors. The final adjustment is for the time effect, and the corresponding time effect factor is determined depending on which load combination is being considered.
15.5.1 Bending Members The most common application for sawn lumber, LVL, glulam timber structural composite lumber, and I-joists is to resist bending forces. In fact, since it is the most common application for dimensional timber members, the visual and machine stress-rated grading rules for lumber are developed around the concept that the members will be placed in bending about their strong axis. In this application, the bending members must account for size effects, duration load, and end-use conditions for the structure. Many times, load distribution elements such as sheathing on floors and walls can provide load sharing between © 2003 by CRC Press LLC
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bending members, which can be accounted for in design by use of the repetitive member factor (ASD) or load-sharing factor (LRFD.) Beams must be designed to resist moment, bending shear, bearing, and deflection criteria. The moment, shear, and bearing criteria are all designed using similar formats. The design format for LRFD is: Lu ≤ λ θ R'
(15.4)
where Lu is the resultant of the actions caused by the factored load combination, λ is the time effect factor associated with load combination being considered, θ is the resistance factor (flexure = 0.85, stability = 0.85, shear = 0.75), and R' is the adjusted resistance. The moment, shear, or bearing force being considered is determined using engineering mechanics and structural analysis. The assumption of linear elastic behavior is typically made for this analysis and is appropriate considering that timber behaves as a brittle material. Nonlinear analysis is acceptable; however, experimental data will probably be required to support such an analysis. The resistance value involves consideration of the lateral support conditions, load sharing conditions, and whether the member is or is not part of a larger assembly. The adjusted resistance is obtained by multiplying the published reference strength values for bending, shear, or compression perpendicularto-grain by the appropriate adjustment factor. The adjustment factor includes the end use and adjustments based on product. The end-use adjustment factors include the wet service factor (CM), temperature (Ct), preservative treatment factor (Cpt), and fire retardant treatment (Crt). Adjustments for member configuration include composite action (CE), load sharing factor (Cr), size factor, (CF), beam stability factor (CL), bearing area (Cb), and form factor (Cf ). Additional adjustments for structural lumber and glulam timber include shear stress (CH), stress interaction (CI), buckling stiffness (CT), volume effect (CV), curvature (Cc), and flat use (Cfu). The form of the equation for determining the adjusted resistance is: R'= (G ) × F × C1 ⋅ C 2 ⋅ C3 …Cn
(15.5)
where R' is the adjusted resistance (e.g., adjusted strong-axis moment, adjusted shear), G is a geometry variable consistent with the resistance calculated (e.g., SX), F is the reference design strength (e.g., Fb for bending strength, Fv for shear strength, Fc for perpendicular-to-grain compression strength), and Ci is the appropriate adjustment factor(s). The reader is referred to the LRFD or ASD manuals for a full description of the adjustment factors and the values associated with the various conditions. Adjustment factors account for conditions that do not meet the reference conditions. For example, when lumber is being used for bending about its weak axis, the flat use factor will be used, or if the beam is not fully supported against lateral movement along the compression edge, the beam stability factor CL will be required. One of the most commonly used variables for adjusting a bending strength is the load sharing factor Cr , which is a variable that provides an increase in design bending resistance that accounts for the load sharing that occurs when beams are used in parallel. The condition under which the load sharing factor is applicable and causes an effective increase in the bending resistance occurs when the spacing between beams is no more than 610 mm (24 in.) on center and the beams are connected together using a loaddistributing element, such as structural wood panel sheathing or lumber decking. This factor essentially accounts for the system effects that an effective connection between parallel beams provides for floor, roof, and wall systems. Because of the strong correlation between the variability of a given product and the magnitude of the system effect, the load sharing factor has different values depending on the products used for the beams. Table 15.3 provides the load sharing factors associated with the more common products used as beams in timber construction. The load sharing factor Cr applies only to the moment resistance and is not applicable to any of the other design resistances. When shear strength is being checked, the shear stress adjustment factor CH may be used to increase the shear resistance. However, this is not recommended for general design because at the design stage, the designer is unable to guarantee that any given piece of dimensional lumber used as a beam will not © 2003 by CRC Press LLC
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TABLE 15.3 Load Sharing Factor, Cr , Values Bending Member Product Type
Cr
Dimensional lumber Glulam timber, I-beams, and structural composite lumber Prefabricated I-joists with visually graded lumber Prefabricated I-joists with machine stress-graded lumber products Prefabricated I-joists with structural composite lumber flanges
1.15 1.05 1.15 1.07 1.04
have checks or splits on the wide face of the lumber. In addition, the designer is not able to guarantee that the member will not split during the lifetime of the structure. It is recommended that the shear stress factor only be used when analyzing existing structures, when inspection has been used to determine the length of splits that are present.
15.5.2 Axial Force Members Axial force members are considered to be either tension or compression members and are handled with single equations in both cases. Compression members, that is, columns, have been historically classified as short, intermediate, and long columns depending on whether material crushing or Euler elastic buckling was the controlling mechanism of failure. With the commonplace use of computers, the ability to program complex equations has eliminated the need for the three classifications of columns. 15.5.2.1 Compression Members Compression members are usually called columns, although the term may include drag struts and truss members. There are essentially three basic types of columns. The most common one is the solid or traditional column, which consists of a single member, usually dimensional lumber, post and timbers, poles and piles, or glulam timber. The second type of column is the spaced column, which is made of two or more parallel single-member columns that are separated by spacers, located at specific locations along the column and rigidly tied together at the ends of the column. The third type of column is the built-up column, which consists of two or more members that are mechanically fastened together such as multiple nailed studs within a wall supporting a girder. The slenderness ratio defines the primary mechanism of failure. Shorter columns obviously will be controlled by the material strength of the wood parallel-to-grain, while longer columns will be controlled by Euler buckling. The slenderness ratio is defined as the ratio of the effective length of the column, le, to the radius of gyration, which is: r=
I A
(15.6)
where I is the moment of inertia about the weak axis and A is the cross-sectional area. The effective length, le, is determined by multiplying the unbraced length by the buckling length coefficient: le = K e ∗ l
(15.7)
where Ke is the buckling length coefficient, l is the unbraced length of the column. Ke is dependent on the end support conditions of the column and whether side-sway of the top or bottom of the column is restrained or not. Theoretical values for ideal columns and empirical values for the buckling length coefficient, Ke , that are recommended by NDS and LRFD manuals are provided in Table 15.4. The LRFD and NDS specifications require that the maximum permitted slenderness ratio be 175. The LRFD design equation that must be satisfied for solid columns has a similar form to the other equations, and is: Pu ≤ λφc Pc ' © 2003 by CRC Press LLC
(15.8)
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TABLE 15.4 Buckling Length Coefficient for Compression in Wood Column Design End Support Conditions Fixed-fixed Pin-fixed Fixed-fixed Pin-pin Pinned-fixed Fixed-pinned
Side-Sway Restraint
Theoretical Coefficients
Empirical Recommended Coefficients
Restrained Restrained Free Restrained Free Free
0.5 0.7 1.0 1.0 2.0 2.0
0.65 0.8 1.2 1.1 2.1 2.4
where Pu is the compressive force due to the factored load combination being considered, λ is the applicable time effect factor for the load combination being considered, θc is the resistance factor for compression parallel to grain (0.9), and P'c is the adjusted compressive resistance parallel-to-grain. The adjusted compressive resistance P'c is determined as the gross area times the adjusted compressive strength parallel-to-grain, F'c . The adjusted compressive strength is determined in the same manner as all mechanical properties for wood, which is to multiply the reference compressive strength parallel-tograin by all the applicable adjustment factors such as duration load, temperature, etc. The one additional factor for columns is that the column stability factor Cp must be calculated. Cp accounts for the partial lateral support provided to a column, and is determined by:
Cp =
1 + αc 2c
2
1 + αc αc − 2c c
(15.9)
where αc =
Pe =
φs Pe λφc P0 '
π 2E 05 ' I
( K el )
2
=
(15.10)
π 2E 05 ' A l Ke r
2
(15.11)
and c is a coefficient based on the variability of the material being used for the column (c = 0.8 for dimensional lumber, 0.85 for round poles and piles, and 9.0 for glulam members and structural composite lumber). φs is the resistance factor for stability which has a value of 0.85, E'05 is the adjusted modulus of elasticity at the fifth percentile level, A is the cross-sectional area, Ke is the effective length factor, and r is the radius of gyration. If a prismatic column is notched at a critical location, then the factored compressive resistance is determined using the net section rather than the gross cross section. In addition, Cp should be computed using the properties of the net area if the notches or holes are located in the middle half of the length between inflection points of the column and the net moment inertia is less than 80% of the gross moment of inertia, or if the longitudinal dimension of the knot or hole is greater than the larger cross-sectional dimension of the column. If the notch is located in noncritical locations, then the adjusted compressive resistance can be computed using the gross cross sectional area and Cp , or the net cross-sectional area times the factored compressive strength of the material. Spaced columns are another common form of compression members that consist of two or more dimensional members connected together at a specific spacing using blocking to form a set of parallel © 2003 by CRC Press LLC
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columns that are restrained in a common manner. Figure 15.8 illustrates the concept of a spaced column. The general form of a spaced column has the ability to buckle in more than one manner. First, the overall column could buckle. Second, the individual members making up the column could buckle between the spacing blocks. Therefore, the design specifications restrict the geometry of spaced columns to prevent unexpected element buckling. The following maximum length-to-width ratios are imposed by the LRFD manual: 1. In a spaced column direction L1 /d1 shall not exceed 80. 2. In a spaced column direction l3 /d1 shall not exceed 40. 3. In solid column direction l2 /d2 shall not exceed 50. Spaced columns that do not conform to these restrictions must be designed considering that each element within the column is acting as an independent column, unless a rational analysis can be used to account for restraint conditions used. Built-up columns are the final type of column. Built-up columns consist of two or more dimensional members that are mechanically fastened together to act as a single unit. Built-up columns can have the form of multiple studs nailed together to form a column to support a girder bearing on top of the wall or they may have the shape of a hollow column made of members that are nailed together to form the outer circumference of the shape. The capacity of this type of column can conservatively be estimated by considering each of the elements that make up the column as independent columns and adding their collective compressive strengths together. In all cases, the fasteners that connect the members together must be designed and spaced appropriately to transfer the shear and tension forces that occur within and between the members of the built-up column.
l3 l2
l1
d2 d1
FIGURE 15.8 Illustration of variables associated with the design of spaced columns.
15.5.2.2 Tension Members Compared to compression members, tension members are relatively easy to design and the adjustment factors for the factored resistance are all tabulated values and do not require independent calculations. The basic design equation for designing tension members in the LRFD manual has the form: Tu ≤ λφtT '
(15.12)
where Tu is the tension force due to the load combination being considered, λ is the time effect factor corresponding to the load combination being considered, φt is the resistance factor for tension (φt = 0.8), and T' is the adjusted tension resistance parallel-to-grain, which is calculated based on the net section and the adjusted tension strength. The adjusted tension strength parallel-to-grain, Ft', is determined by multiplying the reference tension strength parallel-to-grain by the appropriate adjustment factors, which include temperature, size effects, and load duration, among others. None of the adjustment factors require independent calculations. If the tension forces are imparted into the member such that the eccentricity between the connection centroid and the centroid of the member is greater than 5% of the member dimension, then the member must be designed considering combined loading of tension and bending.
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15.5.3 Combined Loading Combined loading for member design in wood structures consists of three different categories: 1. Biaxial bending 2. Bending plus tension 3. Bending plus compression Biaxial bending is a subset of either bending plus tension or bending plus compression. Essentially, biaxial bending uses the same equations only setting the axial force being considered in those equations equal to 0. The simplified equation takes the form of: M uy M ux + ≤ 1.0 λφb M s' λφb M y'
(15.13)
where Mu is the factored load moment for the load combination being considered, λ is the time effect factor for the load combination being considered, φb is the resistance factor for bending (φb = 0.85), M's is the computed bending resistance moment about the X-axis with the beam stability factor, CL = 1.0, and any volume factor, Cv (used when designing glulam members), is included. M'y is the adjusted moment resistance about the weak axis considering the lateral bracing conditions. Combined bending and axial tension is the second easiest combination to calculate for combined loading. However, there are two conditions that must be considered. First is the condition along the tension face, for which lateral stability is not a concern; and second, the condition along the compression face for which lateral stability is of concern. Therefore, the following two equations must be satisfied for designing members with combined bending and axial tension: Tension face: M uy Tu M ux + + ≤ 1.0 λφtT ' λφb M s' λφb M y'
(15.14)
Compression face: d M ux − Tu 6 + λφb M x'
M uy M ux λφb M y' 1 − φ bMe
2
≤ 1.0
(15.15)
where Tu is the tension force due to the factored load combination being considered, Me is the elastic lateral buckling moment of the member, and d is the member depth. If Equation 15.15 is used for nonrectangular cross sections, the variable d/6 should be replaced by the ratio of the strong axis section modulus to the gross cross-sectional area, Sx/A. When the member is being designed for combined bending and compression, the following equation must be satisfied for the design conditions being considered: 2
M my Pu M mx λφ P' + λφ M ' + λφ M ' ≤ 1.0 c b x b y
(15.16)
where Pu is the axial compressive force due to the factored load combination being considered; P' is the adjusted resistance for axial compression parallel-to-grain acting alone for the axis of buckling providing the lower buckling strength; Mmx and Mmy are the factored moment resistances, including any magnification for second-order effects for strong and weak axis bending, respectively; Mx' and My' are the adjusted © 2003 by CRC Press LLC
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moment resistances for the strong and weak axes, respectively, from multiplying the section properties by the nominal bending resistance and appropriate adjustment factors. The moments Mmx and Mmy may be determined using second-order analysis for a simplified magnification method that is outlined in the design manual. The extent of the simplified method is sufficient that the reader is referred to the design specification rather than including it here.
15.6 Diaphragms When resisting lateral loads such as seismic forces, most light-frame wood buildings can be conceptualized as a box system. Forces are transmitted horizontally through diaphragms (i.e., roofs and floors) to reactions that are provided by the shear walls at the ends of the diaphragms. These forces are then in turn transmitted to the lower stories and finally to the foundations. Some designers consider shear walls as vertical diaphragms, since the reaction to loading is similar to half of a diaphragm. However, this chapter will consider shear walls as separate elements. A diaphragm is a structural unit that acts as a deep beam or girder that may or may not be able to transfer torsional loads, depending on the relative stiffness of the diaphragm and supporting shear walls. The analogy to a girder is somewhat more appropriate because girders and diaphragms can be made as assemblies. The sheathing acts as a web which is assumed to resist all of the shear loads applied to the diaphragm, and the framing members at the boundaries of the diaphragm are considered to act as flanges to resist tension and compression forces due to moment. The sheathing is stiffened by intermediate framing members to provide support for gravity loading and to transfer the shear load from one sheathing element to the adjacent sheathing element. Chords act as flanges, and often consist of the top plates of the walls, ledgers that attach the diaphragm to concrete or masonry walls, bond beams which are part of the masonry walls, or any other continuous element at the parameter of the diaphragm. The third type of element of a diaphragm is the struts. Struts provide the load transfer mechanism from the diaphragm to the shear walls at the ends of the diaphragm and act parallel to the loading of the diaphragm. Chords act to resist internal forces acting perpendicular to the general loading of the diaphragm direction. The chord can serve several functions at the same time, providing resistance to loads and forces from different sources, and functioning as the tension or compression flange of the diaphragm. It is important that the connection to the sheathing be designed to accomplish the shear transfer since most diaphragm chords consist of many pieces. It is important that splices be designed to transmit the tension or compression occurring at the location of the splice. It is also important to recognize that the direction of application of the seismic forces reverses. Therefore, it should be recognized that chords need to be designed for equal magnitude torsion and compression forces. When the seismic forces are acting at 90° to the original direction analyzed, the chords act as the struts for the diaphragm to transfer the reaction loads to the shear walls below. If the shear walls are not continuous along the length of the diaphragm, then the strut may act as the drag strut between the segments of the shear wall as well. Diaphragms often have openings to facilitate stairwells, great rooms that are more than one story high, or access to roof systems and ventilation. The transfer of forces around openings can be treated similarly to openings in the webs of steel girders. Members at the edges of the openings have forces due to flexure and the high web shear induced in them, and the resulting forces must be transferred into the body of the diaphragm beyond the opening. In the past, wood sheathed diaphragms have been considered to be flexible by many registered design professionals and most code enforcement agencies. Recent editions of the model building codes recognize that diaphragms have a relative stiffness to the walls that are supporting them, and this relative rigidity determines how the forces will be distributed to the vertical resistance elements.
15.6.1 Stiffness vs. Strength Often in large diaphragms, as an economic measure, the designer will change the nailing and/or blocking requirements for the diaphragm to remove the high nail schedule and/or blocking requirements in the © 2003 by CRC Press LLC
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central section of the diaphragm where the shear loading is lowest. It is therefore imperative that the designer distinguish between the stiffness of the diaphragm and the strength of the diaphragm. However, at locations where blocking requirements change and/or the nail schedule is increased, the stiffness of the diaphragm also goes through a significant change. These locations result in potential stress concentrations and when a nail schedule or blocking schedule is changed, the designer should consider assuring the change occurs at locations where the loads are not simply equal to the resistance, but rather that the loads are sufficiently below the changing resistance at that location. Timber-framed diaphragms and structures with light-frame shear walls are capable of being relatively rigid compared to the vertical resistance system. Added stiffness due to concrete toppings, blocking, and adhesives also makes the relative stiffness greater. Therefore, determination of the stiffness of the diaphragm relative to the vertical resistance system must be considered in the design to determine whether a flexible or rigid analysis is required. Currently, the equation used to estimate the deflection of diaphragms was developed by APA and can be found in several references [APA, 1997; Applied Technology Council, 1981; National Fire Prevention Association, 2000]. The mid-span deflection of a simple-span, blocked, structural panel sheathed diaphragm, uniformly nailed throughout, can be calculated by use of: ∆=
∑ (∆c X ) 5 vl 3 vl + + 0.188 len + 8 wEA 4 Gt 2w
(15.17)
where ∆ is the calculated deflection, v is the maximum shear due to factored design loads in the direction under consideration, l is the diaphragm length, w is the diaphragm width, E is the elastic modulus of chords, A is the area of chord cross section, Gt is the panel rigidity through the thickness, en is the nail deformation, and Σ(∆c X) is the sum of individual chord-splice slip values on both sides of the diaphragm, each multiplied by its distance to the nearest support. If the diaphragm is not uniformly nailed, the constant 0.188 in the third term must be modified accordingly. Guidance for using this equation can be found in ATC 7 [Applied Technology Council, 1981]. This formula was developed based on engineering principles and modified testing. Therefore, it provides an estimate of diaphragm deflection due to loads applied in the factored resistance shear range. The effects of cyclic loading and energy dissipation may alter the values for nail deformation in the third term, as well as the chord splice effects in the fourth term, if mechanically spliced wood cords are used. The formula is not applicable to partially blocked or unblocked diaphragms. Recent research, part of the wood frame project of the Consortium of Universities for Research in Earthquake Engineering (CUREE), was conducted as part of the shake table tests by Fischer et al. [2001] and Dolan et al. [2002]. These new studies provide deflection equations that are broken into two components: one for bending deflection and one for shear deflection. The tests used nailed chord splices. If other types of splices are utilized in a design, additional terms to account for the deformation of the splice effects on the diaphragm need to be added. In addition, the CUREE equations are useful for working stress level loads and have not been validated for deflections approaching those associated with the capacity of the diaphragm. However, the equations are derived based on cyclic tests and the average cyclic stiffness within the reasonable deflection range. The provisions are based on assemblies having energy dissipation capacities that were recognized in setting the R factors included in the model building codes. For diaphragms utilizing timber framing, the energy dissipation is almost entirely due to nail bending. Fasteners other than nails and staples have not been extensively tested under cyclic load applications. When screws or adhesives have been tested in assemblies subjected to cyclic loading, they have had brittle failures in adhesives and provide minimal energy dissipation. For this reason, adhesives have been prohibited in light-frame shear wall assemblies in high seismic regions. However, the deformation range typically experienced by diaphragms during seismic events has not justified the restriction of using adhesives in the horizontal diaphragms. In fact, the addition of adhesives in most timber diaphragms provides significantly more benefits in the form of higher strength and rigidity to distribute loads to the horizontal members more efficiently. While in the Dolan et al. [2002] diaphragm study, the adhesives by themselves did not have as large an effect on © 2003 by CRC Press LLC
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stiffness as blocking; the use of adhesives provided a more uniform deflection pattern and was viewed as enhancing the behavior of the diaphragm over a nailed-only diaphragm.
15.6.2 Flexible vs. Rigid Diaphragms The purpose of determining whether a diaphragm is flexible or rigid is to determine whether a diaphragm should have the loads proportioned according to the tributary area or the relative stiffness of the supports. For flexible diaphragms, the loads should be distributed according to the tributary area, whereas for rigid diaphragms, the load should be distributed according to the stiffness. The distribution of seismic forces to the vertical elements of the lateral force resistance system is dependent first on the relative stiffness of the vertical elements vs. the horizontal elements, and second on the relative stiffness of the vertical elements when they have varying deflection characteristics. The first issue defines when a diaphragm can be considered flexible or rigid. In other words, it sets limits on whether the diaphragms can act to transmit torsional resistance or cantilever. When the relative deflections of the diaphragm and shear walls are determined at the factored load resistance level, and the mid-span deflection of the diaphragm is determined to be more than two times the average deflection of the vertical resistant elements, the diaphragms may be considered as being flexible. Conversely, a diaphragm should be considered rigid when the diaphragm deflection is equal to or less than two times the shear wall drift. Obviously, the performance of most diaphragms falls in a broad spectrum between perfectly rigid and flexible. However, at the current time, there are no design tools available to provide for analyzing diaphragms in the intermediate realm. Therefore, model building codes simply differentiate between the two extreme conditions. The flexible diaphragm seismic forces should be distributed to the vertical resisting elements according to the tributary area and simple beam analysis. Although rotation of the diaphragm may occur because lines of vertical elements have different stiffness, the diaphragm is not considered sufficiently stiff to redistribute the seismic forces through rotation. The diaphragm may be visualized as a single-span beam supported on rigid supports in this instance. For diaphragms defined as rigid, rotational or torsional behavior is expected and the action results in a redistribution of shear to the vertical force-resisting elements. Requirements for horizontal shear distribution involve a significantly more detailed analysis of the system than the assumption of flexibility. Torsional response of a structure due to an irregular stiffness at any level within the structure can be the potential cause of failure in the building. As a result, dimensional and diaphragm aspect ratio limitations are imposed for different categories of construction. Also, additional requirements are imposed on the diaphragm when the structure is deemed to have a general torsional irregularity such as when reentering corners or diaphragm discontinuities are present. In an effort to form a frame of reference in which to judge when stiffness of the diaphragm may be critical to the performance of the building, one can consider two different categories of diaphragms. The first category includes rigid diaphragms that must rely on torsional response in order to distribute the loads to the building. A common example would be an open front structure with shear walls on three sides, such as a strip mall. This structurally critical category has the following limitations: 1. The diaphragm may not be used to resist the forces contributed by masonry or concrete in structures over one story in height. 2. The length of the diaphragm normal to the opening may not exceed 25 ft, and the aspect ratios are limited to being less than 1:1 for one-story structures or 1:1.5 for structures over one story in height. Where calculations show that the diaphragm deflections can be tolerated, the length shall be permitted to increase so as to allow aspect ratios not greater than 1.5:1 when the diaphragm is sheathed with structural use panels. The aspect ratio for diaphragms shall not exceed 1:1 when sheathed with diagonal sheathing. The second category of rigid diaphragms that may be considered is those that are supported by two or more shear walls in each of the two perpendicular directions, but have a center of mass that is not coincident with the center of rigidity, thereby causing a rotation in the diaphragm. This category of © 2003 by CRC Press LLC
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diaphragm may be divided into two different categories where category 2a would consist of diaphragms with a minimal eccentricity that may be considered on the order of incidental eccentricities, in which case the following restrictions would apply: 1. The diaphragm may not be used to resist forces contributed by masonry or concrete in structures over one story. 2. The aspect ratio of the diaphragm shall not exceed 1:1 for one-story structures or 1:1.5 for structures greater than one story in height. On the other hand, flexible diaphragms or nonrigid diaphragms have minimal capacity for distributing torsional forces to the shear walls. Therefore, limitations of aspect ratios are used to limit diaphragm deformation such that reasonable behavior will occur. The resulting deformation demand on the structure is also limited such that higher aspect ratios are allowed provided calculations demonstrate that the higher diaphragm deflections can be tolerated by the supporting structure. In this case, it becomes important to determine whether the diaphragm rigidity adversely affects the horizontal distribution and the ability of the other structural elements to withstand the resulting deformations. Several proposals to prohibit wood diaphragms from acting in rotation have been advanced following the 1994 Northridge earthquake. However, the committees that have reviewed the reports to date have concluded that the collapses that occurred in that event were due in part to a lack of deformation compatibility between the various vertical resisting elements, rather than solely due to the inability of the diaphragm to act in rotation. Often diaphragms are used to cantilever past the diaphragm’s supporting structure. Limitations concerning diaphragms cantilevered horizontally past the outermost shear walls or other vertical support element are related to, but slightly different from, those imposed due to diaphragm rotation. Such diaphragms can be flexible or rigid, and the rigid diaphragms may be categorized in one of the three categories previously discussed. However, both the limitations based on the diaphragm rotation, if they are applicable, and a diaphragm limitation of not exceeding the lesser of 25 ft or two thirds of the diaphragm width must be considered in the design. This is due to the additional demand placed on a structure due to the irregularity resulting from the cantilever configuration of the diaphragm. Further guidance considering the design and detailing of diaphragms can be obtained from Breyer et al. [1998] and Faherty and Williamson [1999], which both provide significant detail on dealing with torsional irregularities of wood diaphragms.
15.6.3 Connections to Walls When postevent reports are reviewed for many historical earthquakes, one finds that the principal location of failures in diaphragms occurs at the connection between the diaphragm and supporting walls. Two of the most prevalent failures are due to cross-grain bending of ledger boards that are used to attach diaphragms to concrete and masonry walls, or to the use of the diaphragm sheathing to make the connection between the wall and diaphragm. When one uses the ledger board to attach a wood diaphragm to a masonry or concrete wall, the diaphragm will tend to pull away from the wall, which causes crossgrain bending to occur in the ledger board. Cross-grain bending is not allowed in the design specifications for wood construction and is one of the weakest directions in which wood can be loaded. The same mechanism causes splitting of sill plates on shear walls due to the uplift forces of the sheathing. When diaphragms are attached to walls, regardless of the construction of the wall, the connections must be made directly between the framing or reinforcement elements of the wall and the framing of the diaphragm. Straps should extend into the diaphragm a significant distance to provide adequate length in which to develop the forces experienced. Sheathing rarely provides sufficient capacity to transfer diaphragm forces and the sheathing nailing will inevitably fail. These straps also should extend down along the timber frame wall and attached to the studs of the wall, or for masonry and concrete walls, be attached to reinforcement in the wall near the location.
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15.6.4 Detailing around Openings Openings in diaphragms may be designed similar to the way openings in steel girders are designed. After the bending and shear forces are determined, then connections to transfer those loads can be designed. Construction of such connections often requires the use of blocking between the framing members and straps that extend past the opening, often for multiple joist spacings. It is imperative that connections to transfer such loads be made to the framing members and not simply to the sheathing. This is also an area where a designer should consider requiring special inspection, to assure that the nailing used to make the connection is actually located in the framing, and not simply through the sheathing into air.
15.6.5 Typical Failure Locations As stated earlier, the typical locations for failure of diaphragms are the connections between the diaphragm and the vertical force-resisting elements. However, additional areas need to be considered. These include openings in the diaphragm, where shear transfer is being designed and locations where nail schedules and/or blocking requirements change. Often openings are placed in diaphragms without the design considering the force transfer required due to the absence of sheathing. This location also results in a difference or an anomaly in the stiffness distribution along the length of the diaphragm. These two actions combine to cause the sheathing nailing, and possibly the framing nailing, to separate, thus causing local failures.
15.7 Shear Walls Shear walls are typically used as the vertical elements in the lateral-force-resisting system. The forces are distributed to the shear walls of the building by the diaphragms and the shear walls transmit the loads down to the next lower story or foundation. A shear wall can be defined as a vertical structural element that acts as a cantilever beam where the sheathing resists the shear forces and the end studs, posts, or chords act as the flanges of the beam in resisting the induced moment forces associated with the shear applied to the top of the wall. The sheathing is stiffened by the intermediate studs and is therefore braced against buckling. An exploded view of a typical light-frame shear wall is shown in Figure 15.9. Light-frame shear walls can be broken into two categories: designed and prescriptive. Designed walls are sized and configured using a rational analysis of the loads and design resistance associated with the sheathing thickness, and fastener size and schedule. Prescriptive walls are often called shear panels rather than shear walls to differentiate them from the walls designed using rational analysis. Prescriptive walls are constructed according to a set of rules provided in the building code. In all cases, the current building code requires that all shear walls using wood structural panels as the sheathing material must be fully blocked. Adhesives are not allowed for attaching sheathing to the framing in shear walls. Whereas adhesives are encouraged for attaching sheathing to roof and floor diaphragms as a method to improve their ability to distribute the loads to the shear walls, the use of adhesives in shear walls changes the ductile system usually associated with light-frame construction to a stiff, brittle system that would have to be designed with a significantly lower R factor. Adhesives are allowed to be used in regions with low seismic hazard since it improves the performance of the building when wind loading is considered. An R factor of 1.5 is recommended for seismic checks even in the low seismic hazard regions [Building Seismic Safety Council, 2000a].
15.7.1 Rationally Designed Walls Rationally designed light-frame shear walls can be further divided into two categories. The first is the traditional or segmented shear wall design, which involves the use of tables or mechanics to design. The second method of design is the perforated shear wall method, which is an empirically based method that accounts for the openings in a wall line. The principal difference between the two methods is the © 2003 by CRC Press LLC
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Tie-down (if applied) fastened with 32 16d sinkers 8d brite common @ 6in. oc 12in .oc field
16d brite common.
16d brite common @ 12 in.
13 gage 1.5in. 7in. o.c. (perimeter) 10in. o.c. (field) 16d brite common @ 24 in.
FIGURE 15.9 Typical shear wall assembly (shown lying on its side, rather than vertical). (From Heine, C.P. 1997. “Effect of Overturning Restraint on the Performance of Fully Sheathed and Perforated Timber Framed Shear Walls,” M.S. thesis, Virginia Polytechnic and State University, Blacksburg, VA. With permission.)
assumptions associated with the free-body diagrams used in each method. Each of these design methods will be discussed independently. 15.7.1.1 Segmented Wall Design The segmented shear wall design method is the traditional method for designing light-frame shear walls. This method assumes a rigid free-body diagram and a uniform distribution of shear along the top of the wall line. Both this method and the perforated shear wall method assume that the top of all wall segments in a wall line will displace the same amount. In other words, the assumption is that the tops of the wall segments are tied together with either the platform above, the top plate of the wall, or collectors between wall segments, providing sufficient connectivity to ensure the wall segments will displace together as a unit. The segmented wall design method assumes that collectors will be detailed to transmit the shear forces distributed to the wall over the openings by the diaphragm to the adjoining wall segments. Each segment is assumed to resist the portion of the load according to its relative length in the wall line. In other words, the shear force per length of wall that is applied to the wall segment is determined by: v= V ∑ Li
(15.18)
where v is the unit shear (force/length), V is the total shear load applied to the wall line, and ΣLi is the summation of all of the fully sheathed wall segments in the wall line. It is assumed that this unit shear is distributed uniformly to all of the fully sheathed wall segments. Upon this assumption being made, the individual wall segments are then designed assuming a rigid-body free-body diagram, similar to that shown in Figure 15.10. The simple assumption of using rigid-body mechanics makes the determination of induced overturning forces in the chords an easy task of summing moments about one of the bottom corners of the wall
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Applied load top framing plate
shear along sheathing edges
nail shears part to sheathing edge
sheathing compression framing stud
axial tension in framing
nail shears parallel to sheathing edge VH B bottom framing plate V
VH B
VH B
VH B
Anchorage forces axial compression in framing
bottom framing plate
bearing stresses VH B
Anchorage force
FIGURE 15.10 Rigid free-body diagram assumed for segmented shear wall design. (From Stewart, W.G. 1987. “The Seismic Design of Plywood Sheathed Shearwalls,” Ph.D. dissertation, University of Canterbury, New Zealand. With permission.)
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segment. The required mechanical anchor to resist this overturning load can then be sized according to the uplift force determined. However, the assumption of a rigid body also opens an opportunity for error in the calculations. If one assumes that there is an imposed dead load due to the structure above (say, the floor of the story above), one might assume that the vertical forces due to this dead load may act to resist the imposed overturning action of the lateral load on the individual wall segment. In this case, the size of the mechanical anchor would be determined for the difference in the uplift force due to the overturning moment and the resisting force due to the dead load of the structure above. If the assumption of rigid-body action were valid, this would be an acceptable mechanism of resistance. However, if one investigates the construction of light-frame shear walls, the vertical load is applied to the wall across the top plate as a distributed load. However, the top plate of the wall is usually a double 2 × 4 nominal framing member, which has questionable ability to transmit vertical loads along the length of the wall through bending action. In addition, this top plate is supported by repetitive framing members called studs that would transmit the vertical load to the base of the wall rather than allow the top plate to distribute the load to the end stud or chord for the wall. Currently, there are therefore two schools of thought on how the mechanical anchors to resist overturning forces should be determined. One is to use the full dead load acting on the top of the wall to reduce the uplift forces at the chord. The other is to assume that little or none of the dead load acts to resist the uplift forces. The latter is obviously the more conservative assumption, but it also considers the top plate of the wall as a beam on an elastic foundation, for how vertical loads are transmitted along the length of the wall. The final step in the design of the segmented shear wall is to determine the thickness of the sheathing and associated nail schedule to be used to attach the sheathing to the framing. This information is usually obtained using design tables available in the building code or design specification. However, it is permitted to use the properties of the individual nail connection and engineering mechanics to determine the resistance of a given sheathing thickness and nailing configuration. 15.7.1.2 Perforated Shear Wall Design The perforated shear wall method was introduced into the 2000 edition of the NEHRP Provisions [Building Seismic Safety Council, 2000] and the 2000 IBC [International Code Council, 2000a] for use in seismic design. It had been adopted earlier for wind design by the Building Officials and Code Administrators (BOCA) and Southern Building Code Congress International (SBCCI) building codes. The method is an empirical design method that accounts for the added resistance provided by the wall segments above and below window and door openings in the wall, if they are sheathed with equivalent sheathing to that used in the fully sheathed segments of the wall. The method was originally developed by Sugiyama and Matsumoto [1994] using reduced-scale light-frame wall specimens, and the method was validated for full-scale wall construction under cyclic loads by Dolan and Johnson [1997a, 1997b] and Dolan and Heine [1997a, 1997b]. The perforated shear wall method of design assumes that the segments of wall above and below openings are not specifically designed for force transfer around the opening. Rather, the only assumptions are that the top of the wall line will displace uniformly (i.e., tied together with the top plate of the wall line) and the end full-height sheathed wall segments have mechanical overturning restraint at the extreme ends of the wall line. Other assumptions are that the bottom plate of the wall is attached to the floor platform or foundation sufficiently to resist the distributed shear force applied to the wall and a distributed uplift force equal to the distributed shear force is resisted along the wall length. This anchorage can be accomplished with nails, screws, lag screws, or other type of fastener capable of resisting the shear and uplift forces. The basic difference in the assumed free-body diagram for the perforated shear wall method is that the shear force is not assumed to be uniform along the length of the wall line, and the individual wall segments are not assumed to act as rigid bodies. The end wall segment that has to resist an uplift force in the end post is assumed to reach the full design capacity as if it were a segmented wall since the uplift force will be resisted by a mechanical, overturning anchor. The rest of the wall segments are assumed to perform similar to a prescriptively constructed wall, with the overturning forces being resisted by the © 2003 by CRC Press LLC
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H
v
FIGURE 15.11 Free-body diagram for interior wall segment for perforated shear wall or prescriptive wall segment. (From Salenikovich, A.J. 2000. “The Racking Performance of Light-Frame Shear Walls,” Ph.D. dissertation, Virginia Polytechnic Institute and State University, Blacksburg, VA. With permission.)
O
uw
v M L
Perforated shear wall
H
L1
L2
L3
L Overturning Restraint (each end)
FIGURE 15.12
Perforated shear wall configuration (Example 1).
sheathing nails at the bottom of the wall. A free-body diagram for an interior wall segment of a perforated shear wall is illustrated in Figure 15.11. Due to the difference in overturning restraint between the different segments of the shear wall, the shear force cannot possibly be resisted as a uniformly distributed load, and the end wall segment must resist significantly more of the load than the interior wall segments. As an illustration, two examples from the commentary for the 2000 NEHRP Provisions [Building Seismic Safety Council, 2000b] for applying the perforated shear wall method are included in this section. Many jurisdictions that have allowed the perforated shear wall method as an alternative method of design for shear walls have used the provisions in the 2000 IBC [International Code Council, 2000a] as the empowering language, and the two examples included in this section as examples of what is required to comply with the provisions. In addition, the American Iron and Steel Institute has introduced the perforated shear wall method for cold-formed steel framing as a change proposal for the 2003 edition of the IBC. Example 1: Perforated Shear Wall Problem description: The perforated shear wall illustrated in Figure 15.12 is sheathed with 15/32-in. wood structural panel with 10d common nails with 4-in. perimeter spacing. All full-height sheathed © 2003 by CRC Press LLC
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sections are 4 ft wide. The window opening is 4 ft high by 8 ft wide. The door opening is 6.67 ft high by 4 ft wide. Sheathing is provided above and below the window and above the door. The wall length and height are 24 ft and 8 ft, respectively. Hold-downs provide overturning restraint at the ends of the perforated shear wall and anchor bolts are used to restrain the wall against shear and uplift between perforated shear wall ends. Determine the shear resistance adjustment factor for this wall. Solution: The wall defined in the problem description meets the application criteria outlined for the perforated shear wall design method. Hold-downs provide overturning restraint at perforated shear wall ends and anchor bolts provide shear and uplift resistance between perforated shear wall ends. Perforated shear wall height, factored shear resistances for the wood structural panel shear wall, and aspect ratio of full-height sheathing at perforated shear wall ends meet requirements of the perforated shear wall method. The process of determining the shear resistance adjustment factor involves determining percent fullheight sheathing and maximum opening height ratio. Once these are known, a shear resistance adjustment factor can be determined from Table 12.4.3–2a of the 2000 NHERP Provisions [Building Seismic Safety Council, 2000b]. From the problem description and Figure 15.12: Percent full-height sheathing = sum of perforated shear wall segment widths, ΣL 4 ft + 4 ft + 4 ft * 100 = 50% 24 ft Maximum opening height ratio = maximum opening height
Length of perforated shear wall = =
Wall height, h =
6.67 ft 5 = 8 ft 6
For a maximum opening height ratio of 5/6 (or maximum opening height of 6.67 ft when wall height h = 8 ft) and percent full-height sheathing equal to 50%, a shear resistance adjustment factor of C0 = 0.57 is obtained from Table 12.4.4–1 of the 2000 NEHRP Provisions [Building Seismic Safety Council, 2000a]. Note that if wood structural panel sheathing were not provided above and below the window or above the door, the maximum opening height would equal the wall height h. Example 2: Perforated Shear Wall Problem Description: Figure 15.13 illustrates one face of a two-story building with the first- and secondfloor walls designed as perforated shear walls. Window heights are 4 ft and door height is 6.67 ft. A trial design is performed in this example based on applied loads, V. For simplification, dead load contribution to overturning and uplift restraint is ignored and the effective width for shear in each perforated shear wall segment is assumed to be the sheathed width. Framing is Douglas fir. After basic perforated shear wall resistance and force requirements are calculated, detailing options to provide for adequate shear, v, and uplift, t, transfer between perforated shear wall ends are covered. Configuration A considers the condition where a continuous rim joist is present at the second floor. Configuration B considers the case where a continuous rim joist is not provided, as when floor framing runs perpendicular to the perforated shear wall with blocking between floor framing joists. Solution, second-floor wall: Determine wood structural panel sheathing thickness and fastener schedule needed to resist applied load, V = 2.250 kips, from the roof diaphragm, such that the shear resistance of the perforated shear wall is greater than the applied force. Also determine anchorage and load path requirements for uplift force at ends, in plane shear, uplift between wall ends, and compression. Maximum opening height ratio = Percent full-height sheathing =
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4 ft 1 = 8 ft 2
4 ft + 4 ft × 100 = 50% 16 ft
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Second Floor Perforated Shear Wall 16.0 ft P.S.W. Segment 4.0 ft
P.S.W. Segment 4.0 ft
Second Floor Perforated Shear Wall h = 8.0 ft
V = 2250 #
Tie Down
Tie Down
2813#
2813# 1
1
V = 2250 + 350
First Floor Perforated Shear Wall h = 8.0 ft
= 2600 # 1
1
Tie Down
Tie Down
5836#
3023#
2
2
2 P.S.W. Segment 4.0 ft
Tie Down for Load Path from 2nd Floor 2813#
2 P.S.W. Segment 4.0 ft
First Floor Perforated Shear Wall 12.0 ft FIGURE 15.13
Perforated shear wall (Example 2), two-story building.
Shear resistance adjustment factor, Co = 0.80 Try 15/32 rated sheathing with 8d common nails (0.131 by 2.5 in.) at 6 in. perimeter spacing. Unadjusted shear resistance, Table 12.4.3–2a = 0.36 klf [Building Seismic Safety Council, 2000b] Adjusted shear resistance = (unadjusted shear resistance) (C0) = (0.36 klf) (0.80) = 0.288 klf Perforated shear wall resistance = (adjusted shear resistance) (Σ Li) = (0.288 klf) (4 ft + 4 ft) = 2.304 kips; 2.304 kips > 2.250 kips OK Required resistance due to story shear forces, V: Overturning at shear wall ends, T: T =
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2.25 kips (8 ft) Vh = = 2.813 kips Co ΣLi 0.80 (4 ft + 4 ft)
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2.25 kips V = = 0.352 klf Co ΣLi 0.80 (4 ft + 4 ft)
Uplift, t, between wall ends: t = v = 0.352 klf Compression chord force, C, at each end of each perforated shear wall segment: C = T = 2.813 kips Solution, first-floor wall: Determine wood structural panel sheathing thickness and fastener schedule needed to resist applied load, V = 2.600 kips, at the second-floor diaphragm such that the shear resistance of the perforated shear wall is greater than the applied force. Also determine anchorage and load path requirements for uplift force at ends, in plane shear, uplift between wall ends, and compression. Percent full-height sheathing =
4 ft + 4 ft × 100 = 67% 12 ft
Shear resistance adjustment factor, C0 = 0.67 Unadjusted shear resistance – Table 12.4.3–2a = 0.49 klf [BSSC, 2000b] Adjusted shear resistance = (unadjusted shear resistance) (Co) = (0.49 klf) (0.67) = 0.328 klf Perforated shear wall resistance = (adjusted shear resistance) (ΣLi) = (0.328 klf) (4 ft + 4 ft) = 2.626 kips 2.626 kips > 2.600 kips OK Required resistance due to story shear forces, V: Overturning at shear wall ends, T: T =
Vh 2.600 kips (8 ft) = = 3.880 kips Co ΣLi 0.67 (4 ft + 4 ft)
When maintaining load path from story above, T = T from second floor + T from first floor = 2.813 kips + 3.880 kips = 6.693 kips In-plane shear, v: ν =
2.600 kips V = = 0.485 klf Co ΣLi 0.67 (4 ft + 4 ft)
Uplift, t, between wall ends: t = v = 0.485 klf Uplift, t, can be cumulative with 0.352 klf from story above to maintain load path. Whether this occurs depends on detailing for transfer of uplift forces between end walls. Compression chord force, C, at each end of each perforated shear wall segment: C = T = 3.880 kips When maintaining load path from story above, C = 3.880 kips + 2.813 kips = 6.693 kips. Hold-downs and posts and the ends of perforated shear wall are sized using calculated force, T. The compressive force, C, is used to size compression chords as columns and ensure adequate bearing. Configuration A: Continuous Rim Joist See Figure 15.14. Second floor: Determine fastener schedule for shear and uplift attachment between perforated shear wall ends. Recall that v = t = 0.352 klf. Wall bottom plate (1.5-in. thickness) to rim joist: Use 20d box nail (0.148 by 4 in.). Lateral resistance φλZ' = 0.254 kips per nail and withdrawal resistance φλW' = 0.155 kips per nail. Nails for shear transfer = (shear force, v)/φλZ' = 0.352 klf/0.254 kips per nail = 1.39 nails per ft Nails for uplift transfer = (uplift force, t)/φλW' = 0.352 klf/0.155 kips per nail = 2.27 nails per ft Net spacing for shear and uplift = 3.3 in. on center Rim joist to wall top plate: Use 8d box nails (0.113 by 2.5 in.) toe-nailed to provide shear transfer. Lateral resistance φλZ' = 0.129 kips per nail.
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Configuration A
20d box at 8.6" o.c. for shear and 20d box at 5.3" o.c. for uplift
2nd Floor
(3.3" net spacing, stagger nails)
8d box toe-nail at 4.4" o.c. for shear or alternatively
Continuous rim joist
Wood Structural Panel sheathing etal plate connector (e.g. 35 F at 42" o.c.)
1
Steel plate washer 2x preservatively treated sill plate Concrete foundation
1/2" Dia. anchor bolt at 42" o.c. for shear and uplift (378 plf) (Check axial strength and size plate
washer)
2
Configuration B
20d box at 8.6" o.c. for shear 2nd Floor
Strap at 2'-0" o.c. for uplift (352 plf) Blocking between joists
8d box toe-nail at 4.4" o.c. for shear or alternatively OR
Metal plate connector (e.g. A35 F at 42" o.c.) or metal angle
Wood Structural Panel sheathing 1
Strap at 2'-0" o.c. for uplift (730 plf) or alternatively
Check axial strength
Steel plate washer 2x preservatively treated sill plate Strap lapped
1/2" Dia. anchor bolt at 42" o.c. for shear
under sill plate
2
Concrete foundation
FIGURE 15.14 Details for perforated shear wall (Example 2).
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Nails for shear transfer = (shear force, v)/φλZ’ = 0.352 klf/0.129 kips per nail = 2.73 nails per ft Net spacing for shear = 4.4 in. on center See detail in Figure 15.14 for alternate means for shear transfer (e.g., metal angle or plate connector). Transfer of uplift, t, from second floor in this example is accomplished through attachment of secondfloor wall to the continuous rim joist, which has been designed to provide sufficient strength to resist the induced moments and shears. Continuity of load path is provided by hold-downs at the ends of the perforated shear wall. First floor: Determine anchorage for shear and uplift attachment between perforated shear wall ends. Recall that v = t = 0.485 klf. Wall bottom plate (1.5-in. thickness) to concrete. Use .05-in. anchor bolt with lateral resistance φλZ' = 1.34 kips. Bolts for shear transfer = (shear force, v)/φλZ' = 0.485 klf/1.34 kips per bolt = 0.36 bolts per ft Net spacing for shear = 33 in. on center Bolts for uplift transfer: Check axial capacity of bolts for t = v = 0.485 klf and size plate wasters accordingly. No interaction between axial and lateral load on anchor bolt is assumed (e.g., presence of axial tension does not affect lateral strength). Configuration B: Blocking between Joists See Figure 15.14. Second floor: Determine fasteners schedule for shear and uplift attachment between perforated shear wall ends. Recall that v = t = 0.352 klf. Wall bottom plate (1.5-in. thickness) to rim joist: Use 20d box nail (0.148 by 4 in.). Lateral resistance φλZ' = 0.254 kips per nail. Nails for shear transfer = (shear force, v) φλZ' = 0.352 klf/0.254 kips per nail = 1.39 nails per ft Net spacing for shear = 8.63 in. on center Rim joist to wall top plate: Use 8d box nails (0.113 by 2.5 in.) toe-nailed to provide shear transfer. Lateral resistance φλZ' = 0.129 kips per nail. Nails for shear transfer = (shear force, v) φλZ' = 0.352 klf/0.129 kips per nail = 2.73 nails per ft Net spacing for shear = 4.4 in. on center See detail in Figure 15.14 for alternative means for shear transfer (e.g., metal angle or plate connector). Stud to stud: Provide a metal strap for transfer of uplift, t, from second-story wall studs to first-story wall studs. Size strap for 0.352 klf uplift and place at 2 ft on center to coincide with stud spacing. This load path will be maintained by transfer of forces through first-floor wall framing to the foundation. First floor: Determine anchorage for shear and uplift attachment between perforated shear wall ends. Recall that v = t = 0.485 klf. Wall bottom plate (1.5-in. thickness) to concrete. Use 0.5-in. anchor bolt with lateral resistance φλZ' = 1.34 kips. Bolts for shear transfer = (shear force, v)/φλZ' = 0.485 klf/1.34 kips per bolt = 0.36 bolts per ft Net spacing for shear = 33 in. on center Uplift transfer: A metal strap embedded in concrete at 2 ft on center and attached to first-story studs maintaining load path with second story is used. In this case all uplift forces, t, between perforated shear wall ends are resisted by the metal strap. Size metal strap and provide sufficient embedment for uplift force, t = 0.485 klf + 0.352 klf = 0.837 klf.
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An alternative detail for uplift transfer uses a metal strap lapped under the bottom plate. Size metal strap, anchor bolt, and plate washers for uplift force, t = 0.485 klf + 0.352 klf = 0.837 klf to maintain load path from the second story. No interaction between axial and lateral load on anchor bolt is assumed (e.g., presence of axial tension does not affect lateral strength).
15.7.2 Prescriptive Construction The rules for prescriptive wall construction are provided in the appropriate building code (IRC [International Code Council, 2000b] or CABO [Council of American Building Officials, 1995]). This construction method is often referred to as “conventional construction” and the individual wall segments are often called shear panels as a method of differentiating them from rationally designed walls. These rules set the required size of nail and spacing, along with the minimum percentage of wall area that must be sheathed, determined based on the location of the building and at which level of the building the wall panel is located. These provisions are not based on any rational analysis, but rather are based on the tradition of constructing wall systems under these rules. Using the analysis models and wall test results currently available to the engineering community, it is not possible to calculate sufficient resistance to resist the design loads expected for the seismic design categories designated in the building code. However, the code drafting and technical update committees have decided that the overall historic performance of buildings constructed following these rules has been sufficient to justify their use. The basis of performance for these walls is that the overturning forces, associated with the lateral loading, are resisted by the sheathing nails at the bottom of the wall. Nailing for these walls is set at 6 in. around the perimeter of each sheet of sheathing and 12 in. along the intermediate supporting framing members. The free-body diagram for this type of wall is shown in Figure 15.11. The inherent weakness of this type of construction is the low overturning resistance supplied by the sheathing nails. Usually the assumed capacity of this type of construction ranges from 140 to 300 plf, which is substantially below the capacities associated with the minimum nail schedule for segmented wall construction. This low resistance to lateral loading is why the masonry veneers are limited to one story in height when applied to prescriptive construction wall systems.
15.8 Connections As stated earlier, timber structures rely on their connections to provide ductility and energy dissipation. Therefore, it is imperative that connections be given significant consideration when determining how to detail a structure for good seismic performance. In general, the concept for good performance of timber structures is to design connections where the steel yielding in the connection is the governing behavior, rather than the wood crushing. While both steel yielding and wood crushing occur in all connections that are loaded beyond their elastic range, the connection can be designed to favor the steel yielding as the dominate mechanism. There are many types of connections used in wood. They range from nails, screws, and bolts (referred to as dowel connections) to metal plate connectors, shear plates, split rings, and other proprietary connectors. This chapter focuses on nails and bolts, since these are the most widely used connectors in timber structures. Connectors such as metal plate connectors and expanded tubes are proprietary connectors and the designer must contact the suppliers of these products to obtain the necessary information to safely design with them. Dowel connections can be divided into two principal groups: small and large dowel connections. The designation refers to the relative length of the fastener in the wood member to the diameter, similar to the slenderness ratio for columns. This differentiation of dowel connections can be made because small dowel connections tend to be governed by the yield strength of the dowel, and are usually considered to share the load equally. This is because as the individual fasteners yield, the load is redistributed to the other fasteners in the connection and all of the fasteners will yield and bend before the wood fails. On © 2003 by CRC Press LLC
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the other hand, large dowel connections tend to be increasingly governed by the crushing strength of the wood. Imperfections in the connection due to construction tolerances and variability of the wood material cause the load to be carried unequally between the individual fasteners in the connection (group action effects). The differentiation diameter for dimensional lumber connections is approximately 1/4 in.
15.8.1 Design Methodology In recent years, the design standards for timber construction in the United States changed the lateral design methodology for dowel connections from an empirical, restrictive basis to one based on mechanics. The new basis of lateral design is based on the yield strength of the fastener and the bearing strength of the materials being joined. This results in the ability to configure the connection assembly to provide a connection that is governed by the dowel yielding and bending, the dowel remaining straight and the wood crushing, or a combination of the two. This change also provides flexibility to the designer in choosing connection configurations that were more applicable to special situations, where the previous design methods were restricted to a few typical configurations unless special testing was performed. The new design method is called the yield theory and is best illustrated in Figure 15.15. As can be seen in the figure, there are basically four classes of yielding that are considered by the theory. Mode I is governed by crushing of the wood material by the dowel, and the bolt is held firmly by one member and does not even rotate as the connection displaces. Mode II is also governed by the crushing of the wood, but the dowel rotates as the connection displaces. Mode III is governed by a combination of the dowel yielding and the wood crushing. A single plastic hinge is formed in the dowel as the connection displaces. Finally, mode IV is governed by the dowel yielding, and two plastic hinges are formed in the dowel as the connection displaces. The designer is referred to either the LRDF or ASD design standards for the complete set of applicable design equations for the particular type of dowel fastener being used. Each type of fastener (i.e., nails, spikes, wood screws, lag screws, bolts, and dowels) has a slightly different set of design equations that predict the yield mode and associated design value, since each type of fastener has different geometries for both the fastener itself and the connection as a whole.
15.8.2 Small-Diameter Dowel Connections Small dowels, such as nails and screws, are by far the most prevalent fasteners used in wood construction. The framing in light-frame construction is typically nailed together and the sheathing applied to most timber structures is nailed to the framing. The driven fastener has several advantages over other options, in that it is easily installed (typically completed with pneumatic nailing tools and does not require predrilling), provides reasonable resistance to lateral and withdrawal loads, reduces splitting of the timber (unless the spacing is very close), and distributes the resistance over a larger area of the structure. In addition, these types of fasteners easily yield and provide significant levels of damping to the structure. 15.8.2.1 Lateral Resistance of Small-Diameter Fasteners While these connections can be configured to yield in all of the modes, nails and screws are governed by a reduced set of equations due to the fact that certain subsets of the yield modes are not possible since the fastener does not pass through the entire connection for nails and screws. In dimensional lumber and larger sizes, small-diameter fasteners typically yield in Modes II and IV. These two yield modes provide the highest ductility and energy dissipation since the metal of the dowel yields in plastic yielding and the friction associated with the connection displacement is significant. Since small dowel connections typically yield in the highly ductile yield modes, the displacement of the connection is such that by the time the assembly load reaches near capacity, all of the fasteners will have yielded and the load is assumed to be shared equally by all of the fasteners. In other words, there
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Single Shear Connections
Double Shear Connections
Mode Im
Mode Is
Mode II
(not applicable)
Mode IIIm
(not applicable)
Mode IIIs
Mode IV
FIGURE 15.15 Yield modes considered for dowel connections in wood construction. (From American Forest and Paper Association. 1999. ASD Allowable Stress Design Manual for Engineered Wood Construction and Supplements, Washington, D.C. With permission.)
is no group action factor and the capacity of a multiple-fastener connection is equal to the sum of all of the connectors. In equation form, the resistance of a multiple nail or screw connection is: R' = λφ z
∑ Z' = λφ nZ' z
(15.19)
where R' is the total factored resistance, λ is the applicable time effect factor, φz is the resistance factor for connections (0.65), Z' is the factored resistance for a single fastener, and n is the number of fasteners in the connection. Small dowels are also not typically affected by grain direction. Nail and screw connections are typically governed almost completely by the yielding of the fastener. This implies that even the perpendicular-tograin embedment strength of the wood is sufficiently high that the yielding still is governed by the bending of the dowel.
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15.8.2.2 Withdrawal Resistance of Small-Diameter Fasteners Withdrawal of smooth shank nails can be problematic to the performance of timber structures. In some cases, such as when the nail is driven into the end-grain of a member (i.e., typically how the framing of light-frame timber walls are connected), the design resistance of the fastener is zero. On the other hand, driven into the side-grain of the member, the smooth shank nail may provide sufficient resistance to withdrawal. Smooth shank fasteners are also significantly affected by changes in moisture content of the wood during the life of the connection. If the connection is above 19% at any time during its life, and then dries out to below 19%, or vice versa, then 75% of the design withdrawal resistance is lost. If the connection is fabricated at one moisture condition and remains in this condition throughout its life, there is no reduction. Under these same changing moisture content conditions, the lateral design values for the connection is reduced by 30%. This implies that if a designer specifies, or allows, green lumber to be used to construct shear walls and roof systems, the design values used for the shear walls and roof systems should be reduced by a significant amount. Hardened threaded nails overcome this weakness in performance by the way the deformed nail shank interlocks with the wood fibers. The result is that the design values of the threaded nails are not affected by changes in moisture content. This implies that if a designer allows green lumber to be used in a project, and does not wish to impose the design value reductions associated with moisture content changes, they should specify hardened threaded nails. Helically threaded nails provide the best performance of all of the deformed shank nails available. This is because the deformation pattern allows the nail to withdraw a significant amount without a drop in resistance. This is due to the nail being able to withdraw without tearing the wood fibers around the nail itself. Other types of deformed nails such as ring-shank nails provide higher withdrawal resistance than smooth shank nails, but the resistance drops quickly as the nail withdraws due to the localized damage to the wood fibers.
15.8.3 Large-Diameter Dowel Connections Large-diameter dowel connections can be designed to yield in any of the four modes shown in Figure 15.15. The relative diameter to the thickness of the timber member will determine the mode of yield that occurs. For a given thickness of timber member, the larger the diameter of the dowel, the lower the yield mode will be, and the less ductile the connection will be. This is the reason why the design standards have been reducing the maximum size of the bolt that is included in the design standard. While there is no restriction against designing with larger diameter bolts, the LRFD and ASD manuals have 1-in.-diameter bolts as the largest diameter included in any of the tables. If one uses the yield equations for bolts, lag screws, or dowels in the design standard, larger sizes can be used. When determining the size of dowel to use in a given connection, a balancing act of choosing between a few large-diameter fasteners with high capacity or a larger number of fasteners with lower capacity must be used by the designer. In both cases, the higher number of fasteners used in a given row of fasteners results in a group action effect. This means that the capacity of the connection is less than the sum of capacities of the individual fasteners. Large-diameter bolts do not share the load equally due to placement tolerances and variation in the material properties of the timber. The design specification provides an equation that determines the reduction factor associated with multiple-fastener connections, and should be used for all connections that utilize more than one fastener per row. If one reviews Figure 15.15 again, it becomes clear that connections that yield in Modes I and II will fail in a brittle manner, since wood as a material fails in a brittle manner. By the same deduction process, connections that yield in Modes III and IV will behave in a more ductile manner and provide higher damping ability. Thus, connections that yield in Modes III and IV should be the preferred connection configurations for seismic design. This is not always possible, due to the fact that this implies that a larger number of smaller diameter fasteners will be used, and space limitations may not allow the large number
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1.60
Group Action Factor
1.40
1.20
Heine (2001) 7D Bolt Spacing 1.00
0.80
Test Single Row
0.60
Heine (2001) 4D Bolt Spacing
Test Two Row 0.40 1
2
3
4
5
6
7
8
9
10
# Bolts per Row FIGURE 15.16 Experimental and theoretical (Heine) group action factor for 1/2-in. bolts and variable spacing requirements. (From Anderson, G.T. 2002. “Experimental Investigation of Group Action Factor for Bolted Wood Connections,” M.S. thesis, Virginia Polytechnic Institute and State University, Blacksburg, VA. With permission.)
of fasteners to be used. If connections yielding in Modes I or II must be used in the design, and these connections are the controlling connections in the structure, then the designer should assume that the structure will remain essentially elastic so that the potential for a brittle failure is minimized. Recent research by Anderson [2002] and Heine [2001] indicates that the current design specifications provide nonconservative results for multiple-bolt, single-shear connections. There are possibly two problems currently in the design specification. The first is that the minimum spacing requirement of four times the bolt diameter for full design strength may be insufficient to prevent the failure from occurring between the bolts. The second problem is that the current group action factors are derived based on an assumption of elastic response. Together these two issues result in connections that perform as much as 40% below the predicted strength. There is some evidence that the capacity of large connections (100 kip plus design loads) may not be able to achieve the anticipated design values. Figure 15.16 illustrates the experimental and theoretical results for connections made with 1/2-in.-diameter bolts. Notice that the 4D spacing has a significant weakening effect on the connection. If one were to consider the LRFD group action factor for this same configuration, the smallest it would be is 0.88. Due to this problem, the 2001 edition of the ASD manual has a new appendix that provides guidance in designing multiplebolt connections. The new appendix recommends additional checks on the capacity of the wood members to prevent block shear and other potential modes of failure in multiple-bolt connections. This discussion of the yield modes and group action factor provides some guidance to the designer. First, the designer should try to use, when possible, connections that yield in Modes III and IV to provide the highest possible ductility and energy dissipation for the structure. Second, where possible, the spacing between bolts should be increased to at least seven times the diameter of the bolt (the minimum spacing for full design load that is required by the European design standard). This will minimize the group action effects in multiple-bolt connections. Third, the designer should follow the additional checks outlined in the new appendix for the 2001 ASD manual for preventing unintentional failure modes from occurring in multiple-bolt connections.
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15.8.4 Heavy Timber Connectors Shear plates and split rings are timber connectors that have very high capacities, but also tend to fail in more brittle modes. Historically, these connections have been used in heavy timber and glulam timber structures. Several applications have been in large timber bow-string truss and glulam timber connections. Design of these connections is covered by the LRDF [American Forest and Paper Association, 1999] and ASD [American Forest and Paper Association, 1999] manuals, and the reader is referred to either of these documents for a clear description of how to design these connections. Additional guidance on design of these types of connections as well as general heavy timber structure design may be found in the Timber Construction Manual [American Institute of Timber Construction, 1994]. These connections should be considered in a similar class of connection to large-dowel connections. The connections are susceptible to group action and geometry effects in similar ways that large dowel connections experience the same phenomena. While these connectors are good for situations where large numbers of smaller dowel connections might be required, there are potential problems associated with their use. The first problem is that most contractors are not familiar with the installation of these specialized connectors. There are special tools for drilling and cutting the required surfaces to ensure proper bearing of the connectors in the connection, and the contractor would be advised to manufacture a couple of trial connections before beginning the real connections to learn how to use the cutting tools properly. Second, the connection cannot easily be inspected to ensure proper installation after the members are joined. The main components in these two types of connections need to bear uniformly around their perimeter. If the holes are overdrilled, not drilled circular, or both sides of the connection do not exactly line up for all of the connectors, the connection will not perform properly and will fail at load levels below the intended design level. Also, once the connection is assembled, there is no way to see whether the shear plate or split ring is even present, let alone installed properly. Therefore, these types of connections need to be constructed by a conscientious contractor who can be trusted to perform the installation properly, or continuous inspection of the installation by a responsible party is recommended.
Defining Terms Anisotropic — Having different properties in different directions (i.e., not isotropic, which is to have the same properties in all directions).
Bow — The distortion of lumber in which there is a deviation, in a direction perpendicular to the flat face, from a straight line from end to end of the piece.
Box system — A type of lateral-force-resisting system (LFRS) in which forces are transmitted via horizontal diaphragms (i.e., roof and floors) to gravity load-bearing walls which act in shear, and thus form the main vertical elements of the LFRS. Checking — A lengthwise separation of the wood that usually extends across the rings of annual growth and commonly results from stresses set up in wood during seasoning. Creep — The continued increase in deflection that occurs in the viscoelastic material that sustains a constant load. Cripple walls — Short stud walls between the foundation and the first-floor level. Cup — A distortion of a board in which there is a deviation flat-wise from a straight line across the width of the board. Diaphragm — A nearly horizontal structural unit that acts as a deep beam or girder when flexible relative to supports, and as a plate when its stiffness is higher than the associated stiffness of the walls. Dowel — A wood connector, such as a nail, screw, or bolt. Glulam — Glued-laminated lumber is an engineered product made by gluing together 50-mm (2-in.) or thinner pieces of lumber. Hygroscopic — Readily absorbing moisture, as from the atmosphere.
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I-joists — Wood joists that are structural members composed of an OSB or plywood web and two LVL, oriented strand lumber, or solid lumber flanges, the newest and fastest growing engineered wood product, partially due to the declining availability of high-quality, large-dimension lumber for which it substitutes. Laminated veneer lumber (LVL) — A structural composite lumber product made by adhesively bonding thin sheets of wood veneer oriented with the grain parallel in the long direction. Primary uses include headers, beams, rafters, and flanges for wood I-joists. Lateral-force-resisting system (LFRS) — Any continuous load path potentially capable of resisting lateral (e.g., seismic) forces. Lumber — Timber sawed into boards, planks, or other structural members of standard or specified dimensions. Oriented strand board (OSB) — A structural panel made by adhesively bonding chips of small-diameter softwoods and previously underutilized hardwoods. Orthotropic — Having different properties at right angles. Plywood — A structural panel made from wood sheets (typically 1/8 in. thick) peeled from tree trunks and adhesively laminated so as to orthogonally orient the wood grain in alternate plies. Spaced column — Compression member made of two or more parallel single-member columns that are separated by spacers, located at specific locations along the column, and are rigidly tied together at the ends of the column. Structural composite lumber (SCL) — A structural member, made by adhesively bonding thin strips of wood, oriented with the grain parallel to the long axis of the member. Primarily used for headers, heavily loaded beams, girders, and heavy timber construction. Timber — Trees considered as a source of wood. Also timbers used in the original round form, such as poles, piling, posts, and mine timbers. Viscoelastic — A material that exhibits both viscous (time-dependent) and elastic responses to deformation. Warp — Any variation from a true or plane surface. Warp includes bow, crook, cup, and twist, or any combination thereof.
References American Forest and Paper Association. 1996. Load and Resistance Factor Design (LRFD) Manual For Engineered Wood Construction, American Forest and Paper Association, Washington, D.C. American Forest and Paper Association. 1997. National Design Specification for Wood Construction, American Forest and Paper Association, Washington, D.C. American Forest and Paper Association. 1999. ASD Allowable Stress Design Manual for Engineered Wood Construction and Supplements, American Forest and Paper Association, Washington, D.C. American Forest and Paper Association/American Society of Civil Engineers. 1995. Standard for Load and Resistance Factor Design (LRFD) for Engineered Wood Construction, 16–95, American Forest and Paper Association/American Society of Civil Engineers, Washington, D.C. American Institute of Timber Construction. 1994. Timber Construction Manual, 4th ed., John Wiley & Sons, New York. American Society of Civil Engineers. 1990. Minimum Design Loads for Buildings and Other Structures, ASCE 7–98, American Society of Civil Engineers, New York. American Society of Civil Engineers. 1996. Load and Resistance Factor Design (LRFD) for Engineered Wood Construction, AF&PA/ASCE 16–95, American Society of Civil Engineers, New York. Anderson, G.T. 2002. “Experimental Investigation of Group Action Factor for Bolted Wood Connections,” M.S. thesis, Virginia Polytechnic Institute and State University, Blacksburg, VA. APA, The Engineered Wood Association. 1997. The Plywood Design Specification and Supplements, APA, Tacoma, WA.
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APA, The Engineered Wood Association. 2001. Engineered Wood Construction Guide, APA, Tacoma, WA. Applied Technology Council. 1981. Guidelines for the Design of Horizontal Wood Diaphragms, ATC-7, Applied Technology Council, Redwood, CA. Benuska, L., Ed. 1990. “Loma Prieta Earthquake Reconnaissance Report,” Earthquake Spectra, 6 (Suppl.). Breyer, D., Fridley, K.J., and Cobeen, K.E. 1998. Design of Wood Structures, 4th ed., McGraw-Hill, New York. Building Seismic Safety Council. 2000a. NEHRP Recommended Provisions for Seismic Regulations for New Buildings and Other Structures. Part I: Provisions FEMA 368, Building Seismic Safety Council, Washington, D.C. Building Seismic Safety Council. 2000b. NEHRP Recommended Provisions for Seismic Regulations for New Buildings and Other Structures. Part 2: Commentary FEMA 369, Building Seismic Safety Council, Washington, D.C. Council of American Building Officials. 1995. CABO One- and Two-Family Dwelling Code, Council of American Building Officials, Falls Church, VA. Dolan, J.D. and Heine, C.P. 1997a. Monotonic Tests of Wood-Frame Shear Walls with Various Openings and Base Restraint Configurations, Timber Engineering Center Report no. TE-1997–001, Virginia Polytechnic Institute and State University, Blacksburg, VA. Dolan, J.D. and Heine, C.P. 1997b. Sequential Phased Displacement Cyclic Tests of Wood-Frame Shear Walls with Various Openings and Base Restraint Configurations,Timber Engineering Center Report no. TE-1997–002, Virginia Polytechnic Institute and State University, Blacksburg, VA. Dolan, J.D. and Johnson, A.C. 1997a. Monotonic Performance of Perforated Shear Walls, Timber Engineering Center Report no. TE-1996–001, Virginia Polytechnic Institute and State University, Blacksburg, VA. Dolan, J.D. and Johnson, A.C. 1997b. Sequential Phased Displacement (Cyclic) Performance of Perforated Shear Walls, Timber Engineering Center Report no. TE-1996–002, Virginia Polytechnic Institute and State University, Blacksburg, VA. Dolan, J.D., Bott, W., and Easterling, W.S. 2002. Design Guidelines for Timber Diaphragms, CUREE Publication W-XX, Consortium of Universities for Research in Earthquake Engineering, Richmond, CA. (in press). Faherty, K. and Williamson, T. 1999. Wood Engineering and Construction Handbook, 3rd ed., McGraw-Hill, New York. Federal Emergency Management Agency. 1988. Rapid Visual Screening of Buildings for Potential Seismic Hazards: A Handbook, FEMA 154, Federal Emergency Management Agency, Washington, D.C. Fischer, D., Filliatrault, A., Folz, B., Uang, C.-M., and Seible, F. 2001. Shake Table Tests of a Two-Story Woodframe House, CUREE Publications W-06, Consortium of Universities for Research in Earthquake Engineering, Richmond, CA. Heine, C.P. 1997. “Effect of Overturning Restraint on the Performance of Fully Sheathed and Perforated Timber Framed Shear Walls,” M.S. thesis, Virginia Polytechnic Institute and State University, Blacksburg, VA. Heine, C.P. 2001. “Simulated Response of Degrading Hysteretic Joints with Slack Behavior,” Ph.D. dissertation, Virginia Polytechnic and State University, Blacksburg, VA. Holmes, W.T. and Somers, P., Eds. 1996. “Northridge Earthquake Reconnaissance Report, Vol. 2,” Earthquake Spectra, 11 (Suppl. C), 125–176. International Code Council (ICC). 2000a. International Building Code (IBC), Falls Church, VA. International Code Council (ICC). 2000b. International Residential Code (IRC), Falls Church, VA. Lew, H.S., Ed. 1990. Performance of Structures during the Loma Prieta Earthquake of October 17, 1989, NIST Special Publication 778, National Institute of Standards and Technology, Gaithersburg, MD. National Fire Prevention Association. 2002. NFPA 5000 Building Code, National Fire Prevention Association, Boston, MA.
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Schierle, G.G. 2000. Northridge Earthquake Field Investigations: Statistical Analysis of Woodframe Damage, CUREE Publication W-02, Consortium of Universities for Research in Earthquake Engineering, Richmond, CA. Salenikovich, A.J. 2000. “The Racking Performance of Light-Frame Shear Walls,” Ph.D. dissertation, Virginia Polytechnic Institute and State University, Blacksburg, VA. Steinbrugge, K.V., Schader, E.E., Bigglestone, H.C., and Weers, C.A. 1971. San Fernando Earthquake February 9, 1971, Pacific Fire Rating Bureau, San Francisco, CA. Stewart, W.G. 1987. “The Seismic Design of Plywood Sheathed Shearwalls,” Ph.D. dissertation, University of Canterbury, New Zealand. Sugiyama, H. and Matsumoto, T. 1994. “Empirical Equations for the Estimation of Racking Strength of a Plywood Sheathed Shear Wall with Openings,” Mokuzai Gakkaishi, 39, 924–929. Tissell, J. 1990. “Performance of Wood-Framed Structures in the Loma Prieta Earthquake,” in Wind and Seismic Effects: Proceedings of the Twenty-Second Joint Meeting of the U.S.–Japan Cooperative Program in Natural Resources Panel on Wind and Seismic Effects, NIST SP 796, National Institute of Standards and Technology, Gaithersburg, MD, September, pp. 324–330. U.S. Department of Agriculture. 1999. Wood Handbook: Wood as an Engineering Material, Agriculture Handbook 72, Forest Products Laboratory, U.S. Department of Agriculture, Madison, WI (available online at http://www.fpl.fs.fed.us/documnts/FPLGTR/fplgtr113/fplgtr113.htm). U.S. Department of Housing and Urban Development. 1995. Preparing for the “Big One”: Saving Lives through Earthquake Mitigation in Los Angeles, California, HUD-I511- PD&R, January 17, U.S. Department of Housing and Urban Development, Washington, D.C. Yancey, C.W. et al. 1998. A Summary of the Structural Performance of Single Family Wood Framed Housing, NISTIR 6224, Building and Fire Research Laboratory, National Institute of Standards and Technology, Gaithersburg, MD.
Further Reading The Wood Handbook [U.S. Department of Agriculture, 1999] is a good introduction to properties of wood and wood products. The several wood design handbooks [American Forest and Paper Association, 1996, 1999; American Institute of Timber Construction, 1994; APA, 1997, 2001] are all required references for wood structure designers, and contain much useful background information. Breyer et al. [1998] is a good overall text for wood structure design. The Building Seismic Safety Council [2000a, 2000b] provides the current consensus guidelines specific to seismic design of wood buildings. The CUREE project (www.curee.org) is a major research effort to better understand wood building performance, and develop improved design data and practices. The CUREE Web site provides publications and other information.
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16 Seismic Behavior, Design, and Retrofitting of Masonry 16.1 Introduction 16.2 Masonry in the United States Fundamentals · Modern Masonry Construction in the United States · Historical Structural Masonry in the United States
16.3 Performance of Masonry in U.S. Earthquakes Before the 1933 Long Beach Earthquake · The 1933 Long Beach Earthquake · The 1971 San Fernando Earthquake · The 1989 Loma Prieta Earthquake · The 1994 Northridge Earthquake · The 2001 Nisqually Earthquake · Concluding Remarks on Performance of Masonry in U.S. Earthquakes · Relevant Information from Earthquakes Outside the United States
16.4 Fundamental Basis for Seismic Design of Masonry in the United States Design Approaches for Modern U.S. Masonry
16.5 Masonry Design Codes Used in the United States Introduction to Masonry Design Codes · The Future of Design Codes for Masonry in the United States
16.6 Analysis Approaches for Modern U.S. Masonry Overall Analytical Approach
16.7 Seismic Retrofitting of Historical Masonry in the United States
Richard E. Klingner University of Texas Austin, TX
Observed Seismic Performance · Laboratory Performance · Basic Principles of Masonry Retrofitting · History of Unreinforced Masonry Retrofitting in the Los Angeles Area
References
16.1 Introduction Masonry is traditionally defined as hand-placed units of natural or manufactured material, laid with mortar. In this chapter, the earthquake behavior and design of masonry structures is discussed, extending the traditional definition somewhat to include thin stone cladding. Masonry makes up approximately 70% of the existing building inventory in the United States [Masonry Society, 1989]. U.S. masonry comprises Indian cliff dwellings, constructed of sandstone at Mesa Verde (Colorado); the adobe missions constructed by Spanish settlers in Florida, California, and the southwestern United States; bearing-wall buildings such as the 16-story Monadnock Building, completed in 1891 in Chicago; modern reinforced bearing-wall buildings; and many veneer applications. Clearly, the earthquake behavior and design of each type of masonry is distinct. In this chapter, fundamental applications
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and nomenclature of U.S. masonry are discussed; major construction categories are reviewed; historical seismic performance of masonry is presented; and principal design and retrofitting approaches are noted. The purpose of the chapter is to give designers, constructors, and building officials a basic foundation for further study of the seismic behavior, design, and retrofitting of masonry.
16.2 Masonry in the United States 16.2.1 Fundamentals Masonry can be classified according to architectural or structural function. Each aspect is discussed later in this chapter. Regardless of how it is classified, U.S. masonry uses basically the same materials: units, mortar, grout, and accessory materials. In this section, those materials are discussed, with reference to the national consensus specifications of the American Society for Testing and Materials (ASTM). Additional information is available at the Web sites of associations such as the National Concrete Masonry Association (NCMA), the Brick Industry Association (BIA), and The Masonry Society (TMS). 16.2.1.1 Masonry Units Of the more than 20 different classifications of commercially available masonry units in the United States, only the most widely used are discussed here. Clay or shale masonry units: The most common structural clay or shale masonry units are building brick and facing brick. The former are specified using ASTM C62 Building Brick (Solid Masonry Units Made from Clay or Shale). The latter, specifically intended for use when appearance is important, are specified using ASTM C216 Facing Brick (Solid Masonry Units Made from Clay or Shale). Units are usually cored rather than completely solid. The net cross-sectional area of the unit must be at least 75% of the gross area, that is, the cores occupy less than 25% of the area of the unit. Many different sizes and shapes of clay or shale masonry units are available, varying widely from region to region of the United States. One common size is the “modular” unit, which measures 7 5/8 in. (194 mm) long by 2 1/4 in. (57 mm) high by 3 5/8 in. (92 mm) deep. Using mortar joints 3/8 in. (9 mm) thick, this unit produces modules 8 in. (203 mm) wide by 2 2/3 in. (68 mm) high, that is, three courses of such units produce modules 8 in. (203 mm) wide by 8 in. high. Clay or shale masonry units are sampled and tested in terms of ASTM C67 (Methods of Sampling and Testing Brick and Structural Clay Tile). Specified properties include compressive strength and durability. Facing brick can have more restrictive dimensional tolerances and appearance requirements. Concrete masonry units: The most common concrete masonry units are hollow load-bearing concrete masonry units, specified in ASTM C90 (Loadbearing Concrete Masonry Units). The units are typically made from low- or zero-slump concrete. In the eastern United States, these units are used for unreinforced inner wythes of cavity walls. In the western United States these units are used for reinforced, fully grouted shear and bearing walls. The net area of the units is usually about 55 to 60% of their gross cross-sectional area. These units are commonly 15 5/8 in. (397 mm) long by 7 5/8 in. (194 mm) high by 7 5/8 in. (194 mm) thick. Using mortar joints 3/8 in. (9 mm) thick, this unit produces modules 8 in. (203 mm) wide by 8 in. high. These modules are compatible with those of the modular clay brick discussed above. Concrete masonry units are sampled and tested in terms of ASTM C140 (Methods of Sampling and Testing Concrete Masonry Units). Specified properties include shrinkage and compressive strength. 16.2.1.2 Mortar Mortar holds units together, and also compensates for their dimensional tolerances. In the United States, mortar for unit masonry is specified using ASTM C270 (Specification for Mortar for Unit Masonry), which addresses three cementitious systems: portland cement-lime, masonry cement, and mortar cement. These cementitious systems are combined with sand and water to produce mortar. Portland cement-lime mortar consists of portland cement and other hydraulic cements, hydrated masons’ lime, sand, and water. Masonry cement mortar consists of masonry cement, sand, and water. The contents of masonry cement and mortar cement, specified under ASTM C91 and ASTM C1329, © 2003 by CRC Press LLC
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respectively, vary from manufacturer to manufacturer and are not disclosed. They typically include portland cement and other hydraulic cements, finely ground limestone, and air-entraining and waterretention admixtures. Mortar cement has a minimum specified tensile bond strength and a lower maximum air content than masonry cement. Model codes prohibit the use of masonry cement in seismic design categories C and higher. Portland cement-lime and mortar cement mortars are not restricted in this respect. Within each cementitious system, masonry mortar is also classified according to type. Types are designated as M, S, N, O, and K (derived from every other letter of the phrase “MaSoN wOrK”). These designations refer to the proportion of portland cement in the mixture. Type M has the most; S less; and so on. Higher proportions of portland cement result in faster strength gain, higher compressive strength, and higher tensile bond strength; they also result in lower long-term deformability. Mortar types S and N are typically specified. Within each cementitious system, mortar can be specified by proportion or by property, with the former being the default. For example, type S portland cement-lime mortar, specified by proportion, consists of 1 vol. portland cement, 1/2 vol. of hydrated masons’ lime, about 4 1/2 vol. of masons’ sand, and sufficient water for good workability. Type S masonry cement mortar and mortar cement mortar are made with 1 vol. of masonry cement or mortar cement, respectively, 3 vol. of masons’ sand, and sufficient water for good workability. 16.2.1.3 Grout Masonry grout is essentially fluid concrete, used to fill spaces in masonry, and to surround reinforcement and connectors. It is specified using ASTM C476 (Grout for Masonry). Grout for masonry is composed of portland cement and other hydraulic cements, sand, and (in the case of coarse grout) pea gravel. It is permitted to contain a small amount of hydrated masons’ lime, but usually does not. It is permitted to be specified by proportion or by property, with the former being the default. A coarse grout specified by proportion would typically contain 1 vol. portland cement or other hydraulic cements, about 3 vol. of masons’ sand, and about 2 vol. of pea gravel. Masonry grout is placed with a slump of at least 8 in. (203 mm), so that it will flow freely into the cells of the masonry. Because of its high water-to-cement (w/c) ratio at time of grouting, masonry grout undergoes considerable plastic shrinkage as the excess water is absorbed by the surrounding units. To prevent the formation of voids due to this process, the grout is consolidated during placement, and reconsolidated after initial plastic shrinkage. Grouting admixtures, which contain plasticizers and waterretention agents, are also useful in the grouting process. If grout is specified by property (compressive strength), the compressive strength must be verified using permeable molds, duplicating the loss of water and decreased w/c ratio that the grout would experience in actual use. 16.2.1.4 Accessory Materials Accessory materials for masonry consist of reinforcement, connectors, sealants, flashing, coatings, and vapor barriers. In this section, each is briefly reviewed. Reinforcement consists of deformed reinforcing bars or joint reinforcement. Deformed reinforcing bars are placed vertically in the cells of hollow units, horizontally in courses of bond-beam units, or vertically and horizontally between wythes of solid units. Model codes require that it be surrounded by grout. Joint reinforcement is placed in the bed (horizontal) joints of masonry, and is surrounded by mortar. Connectors are used to connect the wythes of a masonry wall (ties); to connect a masonry wall to a frame (anchors); or to connect something else to a masonry wall (fasteners). Sealants are used to prevent the passage of water at places where gaps are intentionally left in masonry walls. Three basic kinds of gaps (joints) are used: • Expansion joints are used in brick masonry to accommodate expansion • Control joints are used in concrete masonry to conceal cracking due to shrinkage • Construction joints are placed between different sections of a structure © 2003 by CRC Press LLC
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Single - Wythe Barrier Wall
Composite Wall (filled collar joint)
FIGURE 16.1 Examples of barrier walls.
expansion joint with sealant Drainage Wall (brick veneer over CMU backup)
Drainage Wall (brick veneer over steel studs)
ties ties
flashing, weepholes
FIGURE 16.2 Examples of drainage walls.
Flashing is a flexible waterproof barrier, intended to permit water that has penetrated the outer wythe to re-exit the wall. It is placed at the bottom of each story level (on shelf angles or foundations); over window and door lintels; and under window and door sills. Flashing should be lapped, and ends of flashing should be defined by end dams (flashing turned up at ends). Directly above the level of the flashing, weepholes should be provided at 24-in. spacing. Flashing is made of metal, polyvinyl chloride (PVC), or rubberized plastic (EPDM). Metallic flashing lasts much longer than plastic flashing. Nonmetallic flashing is subject to tearing. Modern EPDM self-adhering flashing is probably the best compromise between durability and ease of installation. 16.2.1.5 Masonry Nomenclature by Architectural Function The architectural functions of masonry include acting as a building envelope to resist liquid water. Masonry walls are classified in terms of this function into barrier walls and drainage walls. Barrier walls act by a combination of thickness, coatings, and integral water-repellent admixtures. Drainage walls act by the above, plus drainage details. Examples of each are shown in Figures 16.1 and 16.2. In drainage walls, an outer wythe (thickness of masonry) is separated from an inner wythe of masonry or from a backup system by a cavity with drainage details. 16.2.1.6 Masonry Nomenclature by Structural Function From the viewpoint of structural function, U.S. masonry can be broadly classified as nonload-bearing or load-bearing. The former resists gravity loads from self-weight alone, and possibly out-of-plane wind loads or seismic forces from its own mass only. The latter may resist gravity and lateral loads from overlying floors or roof. Both classifications of masonry use the same materials. Nonload-bearing masonry includes panel walls (an outer wythe of masonry connected to an inner wythe of masonry or a backup system), curtain walls (masonry spanning horizontally between columns), and interior partitions. © 2003 by CRC Press LLC
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Load-bearing masonry walls resist out-of-plane loads by spanning as horizontal or vertical strips, resist eccentric gravity loads by acting as a shallow beam-column bending perpendicular to the plane of the wall, and resist in-plane shear forces by acting as a deep beam-column loaded in the plane of the wall. 16.2.1.7 Masonry Nomenclature by Design Intent From the viewpoint of design intent, U.S. masonry can be broadly classified as unreinforced or reinforced. Unreinforced masonry is designed assuming that flexural tension is resisted by masonry alone, and neglecting stresses in reinforcement. Reinforced masonry is designed assuming that flexural tension is resisted by reinforcement alone, and neglecting the flexural tensile resistance of masonry. Both types of masonry are designed assuming that masonry has some diagonal tensile resistance, because both types permit some shear to be resisted without shear reinforcement. To decipher design intent may be impossible by examination of the masonry alone, with no knowledge of its design process. Masonry elements, no matter how they are designed, are required (except in the lowest design category) to have minimum prescriptive reinforcement whose location and percentage depend on the seismic design category of the structure in which they are located. Differences in historical tradition have led to potentially confusing differences in nomenclature. For example, in parts of the United States where the Uniform Building Code (UBC) has been dominant (roughly speaking, to the west of Denver), “partially reinforced” masonry referred to reinforced masonry whose reinforcement did not comply with UBC requirements for prescriptive reinforcement in zones of highest seismic risk. East of Denver, however, “partially reinforced masonry” referred to masonry whose only reinforcement was bed-joint reinforcement.
16.2.2 Modern Masonry Construction in the United States A decade ago it might have been possible to distinguish between modern masonry in the eastern vs. the western United States, the latter characterized by more emphasis on seismic design. As model codes increasingly adopt the philosophy that almost all regions of the United States have some level of seismic risk, such regional distinctions are disappearing. 16.2.2.1 Modern Masonry Veneer Modern masonry veneer resists vertical loads due to self-weight only, and transfers out-of-plane loads from wind or earthquake to supporting elements such as wooden stud walls, light-gage steel framing, or a backup wythe of masonry. Veneer is most commonly clay masonry units, but concrete masonry units, glass block, and glazed tile are also used. Stone cladding can be laid like manufactured masonry units, using masonry mortar. Thin stone can also be attached without mortar to a backup frame, using stainless steel connectors. 16.2.2.2 Modern Masonry Partition Walls Modern masonry partition walls are interior elements designed to resist vertical loads due to self-weight only, and out-of-plane loads due to inertial forces from their own mass only. They are of clay or concrete masonry units, glass block, or glazed tile. 16.2.2.3 Modern Masonry Panel Walls Modern masonry panel walls are combinations of a veneer wythe and a backup system. They resist vertical loads due to self-weight only. The veneer wythe transfers out-of-plane loads from wind or earthquake to the backup system. The backup system is not intended to resist in-plane shear loads or vertical loads from overlying roofs or floors. If the space between the masonry veneer and the backup system is separated by a cavity at least 2 in. (50 mm) wide, and is provided with drainage details, the result is a drainage wall. 16.2.2.4 Modern Masonry Curtain Walls Curtain walls are multistory masonry walls that resist gravity loads from self-weight only, and out-ofplane loads from wind or earthquake. Their most common application is for walls of industrial buildings, warehouses, gymnasiums, or theaters. They are most commonly single-wythe walls. Because they occupy © 2003 by CRC Press LLC
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Vertical steel - Hold in position top and bottom and at intervals of 200 bar diameters.
Metal lath under bond beam to confine grout. Steel in bond beams is set in place as wall is laid up. Cells containing steel are filled solidly with grout. Vertical cores should provide a continuous cavity, free of mortar droppings.
Floor slab
Unless wall is fully grouted, place mortar on cross webs adjacent to grouted cells to confine grout to the grout space. Footing
FIGURE 16.3 Typical details of reinforced masonry wall using hollow concrete masonry units. (Courtesy the National Concrete Masonry Association)
multiple stories, curtain walls are generally designed to span horizontally between columns or pilasters. If a single wythe of masonry is used, horizontal reinforcement is often required for resistance to out-ofplane loads. This reinforcement is usually provided in the form of welded wire reinforcement, placed in the horizontal joints of the masonry. 16.2.2.5 Modern Masonry Bearing and Shear Walls Bearing walls resist gravity loads from self-weight and overlying floor and roof elements; out-of-plane loads from wind or earthquake; and in-plane shears. If bearing walls are composed of hollow units (Figure 16.3), vertical reinforcement consists of deformed bars placed in vertical cells; and horizontal reinforcement consists either of deformed bars placed in grouted courses (bond beams), or bed-joint reinforcement. Bearing walls, whether designed as unreinforced or reinforced, must have reinforcement satisfying seismic requirements. If bearing walls are composed of solid units (Figure 16.4), vertical and horizontal reinforcement generally consist of deformed bars placed in a grouted space between two wythes of masonry. Although model codes sometimes distinguish between bearing walls and shear walls, in practical terms every bearing wall is also a shear wall, because it is impossible in practical terms for a wall to resist gravity loads from overlying floor or roof elements, yet be isolated from in-plane shears transmitted from those same elements. Reinforced masonry shear walls differ from reinforced concrete shear walls primarily in that their inelastic deformation capacity is lower. They are usually not provided with confined boundary elements, because these are difficult or impossible to place. Their vertical reinforcement is generally distributed uniformly over the plan length of the wall. Sections of masonry shear wall that separate window or door openings are commonly referred to as “piers.” Using this type of construction, 30-story masonry bearing wall buildings have been built in regions of seismic risk in the United States [Suprenant, 1989]. Masonry infills are structural panels placed in a bounding frame of steel or reinforced concrete. They are rare in modern masonry, and are not addressed directly by design codes. Historical masonry infills are addressed in a later section of this chapter. 16.2.2.6 Modern Masonry Beams and Columns Other modern masonry elements are beams and columns. Masonry beams are most commonly used as lintels over window or door openings, but can also be used as isolated elements. They are reinforced © 2003 by CRC Press LLC
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FIGURE 16.4 Typical details of reinforced masonry wall using solid clay masonry units. (From FEMA 154, Federal Emergency Management Agency.)
horizontally for flexure. Although shear reinforcement is theoretically possible, it is difficult to install and is rarely used. Instead, masonry beams are designed deep enough that shear can be resisted by masonry alone. Isolated masonry columns are rare. The most common form of masonry beam-column is a masonry bearing wall subjected to a combination of axial load from gravity, and out-of-plane moment from eccentric axial load or out-of-plane wind or seismic loads. 16.2.2.7 Role of Horizontal Diaphragms in Structural Behavior of Modern Masonry Horizontal floor and roof diaphragms play a critical role in the structural behavior of modern masonry. In addition to resisting gravity loads, they transfer horizontal forces from wind or earthquake to the lateral force resisting elements of a masonry building, which are usually shear walls. Modern horizontal diaphragms are usually composed of cast-in-place concrete, or of concrete topping overlying hollowcore, prestressed concrete planks or corrugated metal deck supported on open-web joists.
16.2.3 Historical Structural Masonry in the United States 16.2.3.1 Historical Unreinforced Masonry Bearing Walls Unreinforced masonry bearing walls were constructed before 1933 in the western United States, and as late as the 1950s elsewhere in the United States. They commonly consisted of two wythes of masonry, bonded by masonry headers (Figure 16.5), and sometimes also had an interior wythe of rubble masonry. 16.2.3.2 Historical Masonry Infills Masonry infills are structural panels placed in a bounding frame of steel or reinforced concrete. Before the advent of drywall construction, masonry infills of clay tile were often used to fill interior or exterior © 2003 by CRC Press LLC
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FIGURE 16.5 Typical details of two-wythe historical masonry. (From FEMA 154, Federal Emergency Management Agency.)
bays of steel or reinforced concrete frames. Although sometimes considered nonstructural, they have high elastic stiffness, and are usually built tight against the bounding frame. As a result, they can significantly alter the seismic response of the frame in which they are placed. 16.2.3.3 Role of Horizontal Diaphragms in Structural Behavior of Historical Masonry Horizontal diaphragms play a crucial role in the seismic resistance of historical as well as modern masonry construction. In contrast to their role in modern construction, however, the behavior of horizontal diaphragms in historical masonry is usually deficient. Historical diaphragms are usually composed of lumber, supported on wooden joists inserted in pockets in the inner wythe of unreinforced masonry walls. Such diaphragms are not strong enough, and not sufficiently well connected, to transfer horizontal seismic forces to the building’s shear walls. Out-of-plane deformations of the bearing walls can cause the joists to slip out of their pockets, often resulting in collapse of the entire building. For this reason, horizontal diaphragms are among the elements addressed in the seismic rehabilitation of historical masonry.
16.3 Performance of Masonry in U.S. Earthquakes For historical reasons that will be explained in this section, a summary of the historical performance of masonry in the United States can be conveniently divided into two periods: before the 1933 Long Beach earthquake, and after that earthquake. In this section, that history is summarized, with emphasis on design implications.
16.3.1 Before the 1933 Long Beach Earthquake The United States has several regions that have historically been recognized as having relatively high seismic risk. These include Alaska, Hawaii, California, parts of Montana and Idaho, the New Madrid area in southeast Missouri, and the Charleston, South Carolina area. This judgment is based on historical records of strong earthquakes there, throughout the past several centuries. Those early earthquakes did not cause significant damage to masonry buildings because few or no such buildings existed in seismic regions of the United States until about the middle of the 1700s. California mission records contain references to such earthquakes. The series of earthquakes that occurred between December 1811 and March 1812 in the New Madrid area of southeast Missouri rang church bells in Boston and caused local changes in the bed of the Mississippi River, but caused little structural damage because few structures existed. The Charleston earthquake of August 31, 1886, with an estimated Richter magnitude of 7.6, was felt from Cuba to New York, killed 110 people, and damaged 90% of the masonry buildings in Charleston. An example of this damage is shown in Figure 16.6. © 2003 by CRC Press LLC
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FIGURE 16.6 Damage to masonry in the Charleston, South Carolina earthquake of August 31, 1886.
FIGURE 16.7 Damage from the San Francisco earthquake and subsequent fire.
The most destructive historical U.S. earthquake was undoubtedly the San Francisco earthquake of April 18, 1906, which had an estimated Richter magnitude of about 8.0, and ruptured more than 400 km of the San Andreas Fault. The earthquake caused extensive damage to masonry buildings throughout the area, and San Francisco was almost completely destroyed by the combination of the earthquake and subsequent fire (Figure 16.7). Total damage was estimated at $500 million. The 1925 Santa Barbara earthquake, while having a magnitude of only 6.3, was notable because it prompted several cities in California to adopt earthquake regulations in the 1927 Uniform Building Code, published by the Pacific Coast Building Officials Conference, which later became the International Conference of Building Officials. That document had an optional appendix on seismic design, by which buildings were designed for an equivalent static force applied horizontally at each floor level. The force at each level was obtained by multiplying the dead plus live load at that level by a foundation-dependent factor equal to 0.075 for good soil. © 2003 by CRC Press LLC
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FIGURE 16.8 Collapse of part of Jefferson Junior High School in the 1933 Long Beach earthquake. (Courtesy Portland Cement Association)
16.3.2
The 1933 Long Beach Earthquake
The earthquake that shook Long Beach, California on March 10, 1933, though having a Richter magnitude of only 6.3, caused 115 deaths and $40 million in property damage. While reinforced concrete buildings generally behaved well, unreinforced masonry (URM) buildings, including many school buildings, collapsed (Figure 16.8) [Binder, 1952]. The ensuing public outcry led to the passage, less than 1 month later, of the Field Act, which mandated earthquake-resistant design and construction for public schools in California, and prohibited the use of URM for such schools. Public opinion extended this prohibition to many other buildings as well. When masonry construction was revived in California during the middle 1940s, it was required to comply with the new provisions of the 1943 Uniform Building Code, which were based on the reinforced concrete design practice of the time. The provisions required that minimum seismic lateral forces be considered in the design of masonry buildings, that tensile stresses in masonry be resisted by reinforcement, and that all masonry have minimum percentages of horizontal and vertical reinforcement. Those provisions led to the development of grouted, reinforced masonry constructed primarily of hollow concrete masonry units, which became the de facto standard for reinforced masonry on the west coast of the United States up to the present.
16.3.3 The 1971 San Fernando Earthquake On February 9, 1971, the San Fernando Valley (in the northwest portion of greater Los Angeles) was shaken by an earthquake that, although having a magnitude of only 6.7, produced extensive damage to modern buildings such as the new Olive View Hospital [Lew et al., 1971]. It also produced extensive damage to URM. For example, the San Fernando Veterans Administration Hospital and complex, built in 1926, collapsed, causing 47 of the 58 deaths attributed to the earthquake (Figure 16.9). Failures in this earthquake of URM structures built before 1933 prompted the development of URM retrofitting ordinances, discussed later in this chapter.
16.3.4 The 1989 Loma Prieta Earthquake At 5:04 p.m. on October 17, 1989, the San Francisco Bay area was shaken by a Richter magnitude 7.1 earthquake whose epicenter was located about 10 mi northeast of Santa Cruz along a segment of the San Andreas Fault [EQE, 1989]. © 2003 by CRC Press LLC
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FIGURE 16.9 San Fernando Veterans Administration Hospital. (Courtesy U.S. Geological Survey)
FIGURE 16.10 Collapsed unreinforced masonry buildings in Santa Cruz after the Loma Prieta earthquake. (Courtesy International Masonry Institute) Shown as Color Figure 16.10.
Although damage to modern reinforced masonry buildings was generally low, many unretrofitted URM buildings experienced heavy damage. A large area of URM buildings in the Pacific Garden Mall in Santa Cruz collapsed (Figure 16.10). The Marina District of San Francisco, a large region of unconsolidated fill, was the scene of many collapses of nonengineered houses and apartments with wooden frames and masonry veneer (Figure 16.11).
16.3.5 The 1994 Northridge Earthquake The Northridge earthquake, whose epicenter was located in the northwest part of the greater Los Angeles area, occurred at 4:31 a.m. on January 17, 1994. The earthquake had a moment magnitude of 6.7, and strong shaking lasted 15 to 20 seconds in the epicentral region. The following description is taken from The Masonry Society’s report on the earthquake [Masonry Society, 1994]. © 2003 by CRC Press LLC
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FIGURE 16.11 Collapsed wooden apartments with stucco veneer in the Marina District of San Francisco after the Loma Prieta earthquake. (Courtesy International Masonry Institute) Shown as Color Figure 16.11.
FIGURE 16.12 Seventeen-story high-rise masonry hotel, with no visible damage from the Northridge earthquake. (Courtesy The Masonry Society)
The greater Los Angeles area contains tens of thousands of masonry structures, many of which were strongly shaken. In newer communities such as Northridge and Van Nuys (both in the epicentral region), the most common use of masonry by far was in one-story, reinforced masonry buildings, usually of fully grouted and reinforced hollow concrete block. Some multistory, reinforced masonry bearing-wall structures were also found there, as well as steel or concrete frames with masonry veneer. In residential areas throughout Los Angeles, masonry site walls and brick chimneys were common. In older communities such as Hollywood, Santa Monica, and Pasadena (all 15 mi or more from the epicenter), URM structures, usually two- or three-story storefront buildings, are common. In accordance with the City of Los Angeles’ Division 88 ordinance, most such structures have been retrofitted with parapet braces and floor-wall ties. © 2003 by CRC Press LLC
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FIGURE 16.13 Masonry veneer stripped off wall by the Northridge earthquake. (Courtesy The Masonry Society) Shown as Color Figure 16.13.
Throughout Los Angeles were many reinforced masonry schools, post offices, fire stations, and police stations. Most of these buildings showed little apparent structural damage, and continued operating after the earthquake. In the greater Los Angeles area, and particularly in the epicentral region, very little distress was shown by modern one-story reinforced masonry, or by multistory, reinforced bearing-wall buildings (Figure 16.12). In some cases, however, masonry veneer was attached using connection details that were inadequate to resist the required inertial forces (Figure 16.13). Performance of masonry chimneys and site walls was quite variable; many failures were observed (Figure 16.14). Although no freeway noise barriers collapsed, some showed significant damage. URM buildings retrofitted in response to Division 88 requirements generally had parapet and wall damage, but did not collapse. Unretrofitted URM buildings, in contrast, generally had more extensive damage, and some collapses. In general, masonry structures built since the 1950s that were engineered, grouted, reinforced, and inspected in accordance with then-current building codes experienced little damage in the January 17, 1994 earthquake. URM structures that had been retrofitted in accordance with Division 88 requirements experienced less damage than similar URM structures that had not been retrofitted.
16.3.6 The 2001 Nisqually Earthquake At 10:55 a.m. on February 28, 2001, an earthquake with a magnitude of 6.8 struck near Seattle, Washington. Although the earthquake was of low intensity, local newspapers estimated the damage at nearly $2 billion. Observed damage to modern masonry structures was generally light. Older URM structures, however, experienced parapet damage, cracking, and evidence of pounding (Figure 16.15). New as well as older homes with masonry veneer generally appeared to have performed well, although a number of chimneys sustained damage or completely collapsed [Masonry Society, 2001].
16.3.7 Concluding Remarks on Performance of Masonry in U.S. Earthquakes As noted in the introduction to this section, since the 1940s, masonry structures in the western part of the United States have generally been designed and constructed with minimum prescriptive requirements © 2003 by CRC Press LLC
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FIGURE 16.14 Collapsed chimney, Northridge earthquake. (Courtesy The Masonry Society) Shown as Color Figure 16.14.
for reinforcement that are similar to those required in higher seismic design categories today. Such buildings have experienced little damage in U.S. earthquakes. Unreinforced masonry structures, in contrast, have experienced severe damage or collapse. URM structures with basic seismic retrofitting have experienced much less damage.
16.3.7 Relevant Information from Earthquakes Outside the United States In recent decades, considerable information has been obtained on the performance of masonry in earthquakes outside the United States. Examples are the Santiago, Chile and Mexico City earthquakes of 1985, the Quindío, Colombia earthquake of 1999, and the Izmit, Turkey earthquake of 1999. Such information is relevant to U.S. practice if the construction is similar to that found in the United States, and if the lessons learned are new. In most cases, both questions are answered in the negative. Earthquakes that occur outside the United States show, over and over again, that unreinforced masonry buildings and infilled frame structures in which the contribution of masonry infills is neglected in design, behave poorly in earthquakes. A large proportion of such buildings collapse or are heavily damaged. Because this information is not relevant to modern U.S. practice, and is not new, it is discussed only briefly here. 16.3.7.1 The 1985 Santiago, Chile Earthquake On March 3, 1985, an earthquake of magnitude 7.8 occurred off the coast of central Chile. It caused significant damage to Santiago and surrounding areas. Nonengineered masonry structures suffered heavy © 2003 by CRC Press LLC
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FIGURE 16.15 Partial collapse of a URM bearing wall near Pioneer Square in Seattle. (Courtesy The Masonry Society)
FIGURE 16.16 U.S.-type masonry building after Santiago, Chile earthquake of 1985. (Photo: R.E. Klingner)
damage. Many Chilean masonry buildings were designed and constructed in accordance with U.S. practice at that time. As exemplified by Figure 16.16, those U.S.-type masonry buildings suffered only slight damage, in the form of minor flexural and shear cracking [Klingner, 1990]. 16.3.7.2 The 1985 Mexico City Earthquake The Mexico City earthquake of September 19, 1985, with a magnitude of 8.1, occurred off the west coast of Mexico, causing some damage in the epicentral region, and extensive damage in Mexico City, 400 km inland. At least 8000 were killed, and 30,000 made homeless. Resonant response of the deep, soft clay deposits underlying the central part of the city caused near-sinusoidal, long-period ground motions more than 60 sec in duration, with maximum accelerations near 20% g [International Masonry Institute, 1985]. Older, low-rise masonry construction sometimes performed well, because such structures were stiff enough so that they were not excited significantly by the long-period ground motion. In many cases, © 2003 by CRC Press LLC
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FIGURE 16.17 Damage to unreinforced masonry infill in Quindío, Colombia Earthquake. (From Earthquake Engineering Research Institute, 1999. The Quindío, Colombia Earthquake of January 25, 1999, Special Earthquake Report, Earthquake Engineering Research Institute, Oakland, CA. With permission.)
however, URM structures with no formal design collapsed or suffered heavy damage [International Masonry Institute, 1985]. 16.3.7.3 The 1999 Quindío, Colombia Earthquake On January 25, 1999, an earthquake of magnitude 6.2 occurred near the cities of Armenia and Pereira in Colombia. It caused the collapse of many nonengineered masonry structures, and extensive damage to unreinforced masonry infills (Figure 16.17) [Earthquake Engineering Research Institute, 1999]. 16.3.7.4 The 1999 Izmit, Turkey Earthquake On August 17, 1999 a magnitude MW 7.4 earthquake struck the province of Kocaeli in western Turkey, near the city of Izmit. The unofficial death toll was more than 30,000, most of which were caused by the collapse of multistory commercial or residential buildings. The most common form of urban construction, reinforced concrete frames with unreinforced clay masonry infills, suffered heavy damage, exemplified by Figure 16.18 [EQE, 1999].
16.4 Fundamental Basis for Seismic Design of Masonry in the United States Seismic design of masonry in the United States is based on the premise that reinforced masonry structures can perform well in earthquakes, provided that they meet the following conditions: 1. They must have engineered lateral-force-resisting systems, generally consisting of reinforced masonry shear walls distributed throughout their plan area, and acting in both principal plan directions. 2. Their load-displacement characteristics under cyclic reversed loading must be consistent with the assumptions used to develop their design loadings. a. If they are intended to respond primarily elastically, they must be provided with sufficient strength to resist elastic forces. Such masonry buildings are typically low-rise, shear-wall structures. b. If they are intended to respond inelastically, their lateral force resisting elements must be proportioned and detailed to be capable of the reversed cyclic deformations consistent with
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FIGURE 16.18 Damage to reinforced concrete frame with unreinforced masonry infill in Kocaeli earthquake. (Courtesy EQE International)
that inelastic response. They must be proportioned, and must have sufficient shear reinforcement so that their behavior is dominated by flexure (“capacity design”). The most desirable structural system for such response is composed of multiple masonry shear walls, designed to act in flexure, and loosely coupled by floor slabs. As noted in the previous section dealing with observed seismic response, U.S. masonry has shown good performance under such conditions. Good load-displacement behavior has also been observed in laboratory conditions. This research is described extensively in U.S. technical literature over the last two decades. A representative sample is given in NAMC [1985, 1987, 1990, 1993, 1996, 1999]. Of particular relevance is the U.S. Coordinated Program for Masonry Building Research, also known as the Technical Coordinating Committee for Masonry Research (TCCMAR) Program [Noland, 1990]. With the support of the National Science Foundation and the masonry industry, the TCCMAR was formed in February 1984 for the purpose of defining and performing both analytical and experimental research and development necessary to improve masonry structural technology, and specifically to lay the technical basis for modern, strength-based design provisions for masonry. Under the coordination of TCCMAR, research was carried out in the following areas: • • • • • • • • •
Material properties and tests Reinforced masonry walls: in-plane shear and combined in-plane shear and vertical compression Reinforced masonry walls: out-of-plane forces combined with vertical compression Floor diaphragms Bond and splicing of reinforcement in masonry Limit state design concepts for reinforced masonry Modeling of masonry components and building systems Large-scale testing of masonry building systems Determination of earthquake-induced forces on masonry buildings
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Work began on the initially scheduled research tasks in September 1985, and the program lasted for more than 10 years. Numerous published results include the work of Hamid et al. [1989] and Blondet et al. [1991], who studied masonry walls loaded out-of-plane; and He and Priestley [1992], Leiva and Klingner [1994], and Seible et al. [1994], who studied masonry walls loaded in-plane. In all cases, flexural ductility was achieved without the use of lateral confinement. Using pseudodynamic testing procedures, Seible et al. [1994] subjected a full-scale, five-story masonry structure to simulated earthquake input. The successful inelastic performance of this structure under global drift ratios exceeding 1% provided additional verification for field observations and previous TCCMAR laboratory testing. With proper proportioning and detailing, reinforced masonry assemblies can exhibit significant ductility. Limited shaking-table testing has been conducted on reinforced masonry structures built using typical modern U.S. practice: • Gulkan et al. [1990a, 1990b]: a series of single-story, one-third scale masonry houses were constructed and tested on a shaking table. The principal objective of the testing was to verify prescriptive reinforcing details for masonry in zones of moderate seismic risk. • Abrams and Paulson [1991]: two three-story, quarter-scale reinforced masonry buildings were tested to evaluate the validity of small-scale testing. • Cohen [2001]: two low-rise, half-scale, reinforced masonry buildings with flexible roof diaphragms were subjected to shaking-table testing. Results were compared with the results of static testing and analytical predictions. Results of these tests have generally supported field observations of satisfactory behavior of modern reinforced masonry structures in earthquakes.
16.4.1 Design Approaches for Modern U.S. Masonry Three design approaches are used for modern U.S. masonry: allowable-stress design, strength design, and empirical design. In this section, each approach is summarized. 16.4.1.1 Allowable-Stress Design Allowable-stress design is the traditional approach of building codes for calculated masonry design. Stresses from unfactored loads are compared with allowable stresses, which are failure stresses reduced by a factor of safety that is usually between 2.5 and 4. 16.4.1.2 Strength Design Within the past decade, strength-design provisions for masonry have been developed within the 1997 UBC; the 1997 and 2000 NEHRP documents; and the 2000 IBC. The Masonry Standards Joint Committee (MSJC) has recently approved strength-design provisions, and those provisions will probably be referenced by future model codes. Strength-design provisions for masonry are generally similar to those for concrete. Factored design actions are compared with nominal capacities reduced by understrength factors. Strength-design provisions for masonry differ from those for reinforced concrete in three principal areas: unreinforced masonry, confining reinforcement, and maximum flexural reinforcement. Some masonry can be designed as unreinforced (flexural tension resisted by masonry alone). For this purpose, nominal flexural tensile capacity is computed as the product of the masonry’s tensile bond strength (modulus of rupture), multiplied by the section modulus of the section under consideration. This nominal strength is then reduced by an understrength factor. Because it is impractical to confine the compressive zones of masonry elements, the inelastic strain capacity of such elements is less than that of confined reinforced concrete elements. The available displacement ductility ratio of masonry shear walls is therefore lower than that of reinforced concrete shear walls with confined boundary elements, and corresponding R factors (response modification factors) are lower. © 2003 by CRC Press LLC
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Maximum flexural reinforcement for masonry elements is prescribed in terms of the amount of steel required to equilibrate the compressive stress block of the element under a critical strain gradient, which depends on whether the element is loaded in- or out-of-plane, and whether it has been designed based on an ability to withstand reversed cyclic inelastic deformations. In practical terms, if inelastic response is possible, an element cannot be designed to work above its balanced axial load. The intent of these provisions is to ensure, for inelastic elements, that the flexural reinforcement can yield and begin to strain harden before the compression toe crushes. This approach is more conservative than that now used for reinforced concrete, which permits columns and shear walls to work above their balanced axial load, but with a decreased understrength factor. 16.4.1.3 Empirical Design At the end of the 19th century, masonry bearing-wall buildings were designed using empirical rules of thumb, such as using walls 12 in. (305 mm) thick at the top of a building, and increasing the wall thickness by 4 in. (102 mm) for every story. The Monadnock Building, built FIGURE 16.19 Monadnock Building, Chiin Chicago in 1891 (Figure 16.19), is 16 stories high, of cago (1891). unreinforced masonry, and has bearing walls 6 ft (1.83 m) thick at the base. It is still in use today. Today’s empirical design is the descendant of those rules, adapted for the characteristics of modern structures. They involve primarily limitations on length-to-thickness ratios of elements, with some rudimentary axial stress checks and limits on the arrangement of lateral-force-resisting elements and the plan aspect ratio of floor diaphragms.
16.5 Masonry Design Codes Used in the United States 16.5.1 Introduction to Masonry Design Codes The United States has no national design code, primarily because the United States Constitution has been interpreted as delegating building code authority to the states, which in turn delegate it to municipalities and other local governmental agencies. Design codes used in the United States are developed by a complex process involving technical experts, industry representatives, code users, and building officials. As it applies to the development of design provisions for masonry, this process is shown in Figure 16.20 and is described as follows: 1. Consensus design provisions and specifications for materials or methods of testing are first drafted in mandatory language by technical specialty organizations, operating under consensus rules approved by the American National Standards Institute (ANSI). Those consensus rules can vary from organization to organization, but must include requirements for: Balance of interests (producer, user, and general interest). Written balloting of proposed provisions, with prescribed requirements for a successful ballot. Resolution of negative votes. Negative votes must be discussed and found nonpersuasive before a ballot item can pass. A single negative vote, if found persuasive, can prevent an item from passing. © 2003 by CRC Press LLC
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MASONRY DESIGN PROVISIONS IN THE US ANSI rules (balance of interests, letter balloting, resolution of Negatives, public comment) NEHRP ACI
TMS
ASCE
CMA BIA CA
Technical Specialty Organizations
ASTM
MSJC
Model Code Organizations
ICBO (Uniform Building Code)
SBCC (Southern Building Code)
BOCA (Basic Building Code)
ICC (International Building Code)
(adopted by local governmental authority)
Building Code (Law) (contract between society and Architect / Engineer)
Material Specifications (part of contract between owner and contractor)
FIGURE 16.20 Schematic of code-development process for masonry in the United States.
Public comment. After being approved within the technical specialty organization, the mandatorylanguage provisions must be published for public comment. If significant public comments are received (usually more than 50 comments on a single item), the organization must respond to the comments. 2. These consensus design provisions and specifications are adopted, sometimes in modified form, by model code organizations, and take the form of model codes. 3. These model codes are adopted, sometimes in modified form, by local governmental agencies (such as cities or counties). Upon adoption, but not before, they acquire legal standing as building codes. 16.5.1.1 Technical Specialty Organizations Technical specialty organizations are open to designers, contractors, product suppliers, code developers, and end users. Their income (except for FEMA, a U.S. government agency) is derived from member dues and the sale of publications. Technical specialty organizations active in the general area of masonry include the following: 1. American Society for Testing and Materials (ASTM): Through its many technical committees, ASTM develops consensus specifications for materials and methods of test. Although some model code organizations use their own such specifications, most refer to ASTM specifications. Many ASTM specifications are also listed by the ISO (International Standards Organization). 2. American Concrete Institute (ACI): Through its many technical committees, this group publishes a variety of design recommendations dealing with different aspects of concrete design. ACI Committee 318 develops design provisions for concrete structures. ACI is also involved with masonry, as one of the three sponsors of the Masonry Standards Joint Committee (MSJC). This committee was formed in 1982 to combine the masonry design provisions then being developed by ACI, ASCE, TMS, and industry organizations. It currently develops and updates the MSJC design provisions and related specification [Masonry Standards Joint Committee, 2002a, 2002b]. © 2003 by CRC Press LLC
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3. American Society of Civil Engineers (ASCE): ASCE is a joint sponsor of many ACI technical committees dealing with concrete or masonry. ASCE is the second of the three sponsoring societies of the MSJC (see above). ASCE publishes ASCE 7–98 [1998], which prescribes design loadings and load factors for all structures, independent of material type. 4. The Masonry Society (TMS): Through its technical committees, this group influences different aspects of masonry design. TMS is the third of the three sponsoring societies of the MSJC (see above). TMS publishes a Masonry Designers’ Guide to accompany the MSJC design provisions. 16.5.1.2 Industry Organizations 1. Portland Cement Association (PCA): This marketing and technical support organization is composed of cement producers. Its technical staff participates in technical committee work. 2. National Concrete Masonry Association (NCMA): This marketing and technical support organization is composed of producers of concrete masonry units. Its technical staff participates in technical committee work and also produces technical bulletins that can influence consensus design provisions. 3. Brick Industry Association (BIA): This marketing, distributing, and technical support organization is composed of clay brick and tile producers. Its technical staff participates in technical committee work and also produces technical bulletins that can influence consensus design provisions. 4. National Lime Association (NLA): This marketing and technical support organization is composed of hydrated lime producers. Its technical staff participates in technical committee work. 5. Expanded Clay, Shale and Slate Institute (ECSSI): This marketing and technical support organization is composed of producers. Its technical staff participates in technical committee meetings. 6. International Masonry Institute (IMI): This is a labor-management collaborative supported by dues from union masons. Its technical staff participates in technical committee meetings. 7. Mason Contractors’ Association of America (MCAA): This organization is composed of nonunion mason contractors. Its technical staff participates in technical committee meetings. 16.5.1.3 Governmental Organizations The Federal Emergency Management Agency (FEMA) has jurisdiction over the National Earthquake Hazard Reduction Program (NEHRP), and develops and periodically updates the NEHRP provisions [NEHRP, 1997], a set of recommendations for earthquake-resistant design. That document includes provisions for masonry design. The document is published by the Building Seismic Safety Council (BSSC), which operates under a contract with FEMA. BSSC is not an ANSI consensus organization. Its recommended design provisions are intended for consideration and possible adoption by consensus organizations. The 1997 NEHRP Recommended Provisions [1997] is the latest of a series of such documents, now issued at 3-year intervals, and pioneered by ATC 3–06, which was issued by the Applied Technology Council in 1978 under contract to the National Bureau of Standards. The 1997 NEHRP Recommended Provisions addresses the broad issue of seismic regulations for buildings. They contain chapters dealing with the determination of seismic loadings on structures and the design of masonry structures for those loadings. 16.5.1.4 Model-Code Organizations Model-code organizations are composed primarily of building officials, although designers, contractors, product suppliers, code developers, and end users can also be members. Their income is derived from dues and the sale of publications. The United States has three model-code organizations: 1. International Conference of Building Officials (ICBO): In the past, this group developed and published the Uniform Building Code (UBC). The latest is the 1997 UBC. 2. Southern Building Code Congress (SBCC): In the past, this group developed and published the Standard Building Code (SBC). The latest is the 1999 SBC. 3. Building Officials/Code Administrators (BOCA): In the past, this group developed and published the Basic Building Code (BBC). The latest is the 1999 BBC. © 2003 by CRC Press LLC
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In the past, certain model codes were used more in certain areas of the country. The UBC has been used throughout the western United States and in the state of Indiana. The SBC has been used in the southern part of the United States. The BBC has been used in the eastern and northeastern United States. Since 1996, intensive efforts have been under way in the United States to harmonize the three model building codes. The primary harmonized model building code is called the IBC. It has been developed by the International Code Council (ICC), composed primarily of building code officials of the three model code organizations. The first edition of the IBC [International Code Council, 2000] was published in May 2000. In most cases, it references consensus design provisions and specifications. It is intended to take effect when adopted by local jurisdictions. It is intended to replace the three current model building codes. Although not all details have been worked out, it is generally understood that the IBC will continue to be administered by the three model code agencies. Another harmonized model code is being developed by the National Fire Protection Association, composed primarily of fire protection officials. 16.5.1.5 Masonry Design Provisions of Modern Model Codes Over the next 3 to 5 years, as the IBC is adopted by local jurisdictions, its provisions will become minimum legal design requirements for masonry structures throughout the United States. The IBC 2000 permits two design approaches for masonry, strength design and working-stress design. Its strength design provisions come from the 1997 UBC and the 1997 NEHRP Recommended Provisions; and its allowablestress design provisions reference the 1999 MSJC Code, which has no strength design provisions. Strength design provisions very similar to those of the IBC 2000 have just been approved for the MSJC Code 2002. The next IBC (2003) will probably reference the strength design provisions and the allowablestress provisions of the MSJC 2002. 16.5.1.5.1 Strength Design Provisions of the 2000 International Building Code Strength design provisions of the 2000 IBC are representative of those in other model codes. Because the 2000 IBC has already been published, and will supersede the individual model codes of the three model code agencies that have developed it, it is discussed briefly here. Strength design provisions for URM address failure in flexural tension, in combined flexural and axial compression, and in shear. Nominal capacity in flexural tension is computed as the product of the masonry’s flexural tensile strength and its section modulus. Nominal capacity in combined flexural and axial compression is computed using a triangular stress block, with an assumed failure stress of 0.85 fm' (the specified compressive prism strength of the masonry). Nominal capacity in shear is computed as the least of several values, corresponding to different possible failure modes (diagonal tension, crushing of compression diagonal, sliding on bed joints). Each nominal capacity is multiplied by an understrength factor. Strength design provisions for reinforced masonry address failure under combinations of flexure and axial loads, and in shear. Nominal capacity under combinations of flexure and axial loads is computed using a moment–axial force interaction diagram, determined assuming elastoplastic behavior of tensile reinforcement and using an equivalent rectangular stress block for the masonry. The diagram also has an upper limit on pure compressive capacity. Shear capacity is computed as the summation of capacity from masonry plus capacity from shear reinforcement, similarly to reinforced concrete. Nominal capacity of masonry in shear is computed as the least of several values, corresponding to different possible failure modes (diagonal tension, crushing of compression diagonal, sliding on bed joints). Each nominal capacity is multiplied by an understrength factor. Strength-design provisions of the 2000 IBC impose strict upper limits on reinforcement, which are equivalent to requiring that the element remain below the balanced axial load. Nominal flexural and axial strength are computed neglecting the tensile strength of masonry, using a linear strain variation over the depth of the cross section, a maximum usable strain of 0.0035 for clay masonry and 0.0025 for concrete masonry, and an equivalent rectangular compressive stress block in masonry with a stress of 0.85 fm'.
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16.5.1.5.2 Allowable-Stress Design Provisions of the 2000 International Building Code The allowable-stress provisions of the 2000 IBC directly reference the 1999 MSJC Code and Specification [Masonry Standards Joint Committee, 1999a, 1999b]. The allowable-stress provisions of the 1999 MSJC Code are based on linear elastic theory. Allowable-stress design provisions for URM address failure in flexural tension, in combined flexural and axial compression, and in shear. Flexural tensile stresses are computed elastically, using an uncracked section, and are compared with allowable flexural tensile stresses, which are observed strengths divided by a factor of safety of about 2.5. Allowable flexural tensile stresses for in-plane bending are zero. This in effect prohibits unreinforced masonry beams, and requires that unreinforced masonry walls act in-plane as gravity walls. Flexural and axial compressive stresses are also computed elastically, and are compared with allowable values using a so-called “unity equation.” Axial stresses divided by allowable axial stresses, plus flexural compressive stresses divided by allowable flexural compressive stresses, must not exceed unity. Allowable axial stresses are one quarter the specified compressive strength of the masonry, reduced for slenderness effects. Allowable flexural compressive stresses are one third the specified compressive strength of the masonry. Shear stresses are computed elastically, assuming a parabolic distribution of shear stress based on beam theory. Allowable stresses in shear are computed corresponding to different possible failure modes (diagonal tension, crushing of compression diagonal, sliding on bed joints). The factor of safety for each failure mode is at least 3. Allowable-stress design provisions for reinforced masonry address failure in combined flexural and axial compression, and in shear. Stresses in masonry and reinforcement are computed using a cracked transformed section. Allowable tensile stresses in deformed reinforcement are the specified yield strength divided by a safety factor of 2.5. Allowable flexural compressive stresses are one third the specified compressive strength of the masonry. Allowable capacities of sections under combinations of flexure and axial force can be expressed using an allowable-stress moment–axial force interaction diagram, which also has a maximum allowable axial capacity as governed by compressive axial stress. Shear stresses are computed elastically, assuming a uniform distribution of shear stress. Allowable shear stresses in masonry are computed corresponding to different possible failure modes (diagonal tension, crushing of compression diagonal, sliding on bed joints). If those allowable stresses are exceeded, all shear must be resisted by shear reinforcement, and shear stresses in masonry must not exceed a second, higher set of allowable values. The factor of safety for shear is at least 3. 16.5.1.6 Seismic Design Provisions for Masonry in the 2000 International Building Code In contrast to wind loads, which are applied forces, earthquake loading derives fundamentally from imposed ground displacements. Although inertial forces are applied to a building as a result, these inertial forces depend on the mass, stiffness, and strength of the building, as well as the characteristics of the ground motion itself. This is true as well for masonry buildings. In this section, the seismic design provisions of the 2000 IBC are summarized as they apply to masonry elements. Modern model codes in the United States address the design of masonry for earthquake loads by first prescribing seismic design loads in terms of the building’s geographic location, its function, and its underlying soil characteristics. Those three characteristics together determine the building’s seismic design category. Seismic Design Category A corresponds to a low level of ground shaking, typical use, and typical underlying soil. Increasing levels of ground shaking, an essential facility, and unknown or undesirable soil types correspond to higher seismic design categories, with Seismic Design Category F being the highest. In addition to being designed for the seismic forces corresponding to their seismic design category, masonry buildings must comply with four types of prescriptive requirements, whose severity increases as the building’s seismic design category increases from A to F: 1. 2. 3. 4.
Seismic-related restrictions on materials Seismic-related restrictions on design methods Seismic-related requirements for connectors Seismic-related requirements for locations and minimum percentages of reinforcement
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The prescriptive requirements are incremental, for example, a building in Seismic Design Category C must also comply with prescriptive requirements for buildings in Seismic Design Categories A and B. 16.5.1.6.1 Determination of Seismic Design Forces For structural systems of masonry, as for other materials, seismic design forces are determined based on the structure’s location, underlying soil type, degree of structural redundancy, and the system’s expected inelastic deformation capacity. The last characteristic is described indirectly in terms of shear wall types: • • • • •
Ordinary plain Ordinary reinforced Detailed plain Intermediate reinforced Special reinforced
As listed, those types are considered to have increasing inelastic deformation capacity, and a correspondingly increasing response modification coefficient, R, is applied to the structural systems comprising them. Higher values of R correspond, in turn, to lower seismic design forces. 16.5.1.6.2 Seismic-Related Restrictions on Materials In Seismic Design Categories A through C, no additional seismic-related restrictions apply beyond those related to design in general. In Seismic Design Categories D and E, Type N mortar and masonry cement are prohibited, due to their relatively low tensile bond strength. 16.5.1.6.3 Seismic-Related Restrictions on Design Methods In Seismic Design Category A, masonry structural systems can be designed by strength design, allowablestress design, or empirical design. They are permitted to be designed including the flexural tensile strength of masonry. In Seismic Design Category B, elements that are part of the lateral-force-resisting system can be designed by strength design or allowable-stress design only, but not by empirical design. Elements not part of the lateral-force-resisting system, however, can still be designed by empirical design. No additional seismic-related restrictions on design methods apply in Seismic Design Category C. In Seismic Design Category D, elements that are part of the lateral-force-resisting system must be designed as reinforced, by either strength design or allowable-stress design. No additional seismic-related restrictions on design methods apply in Seismic Design Categories E and F. 16.5.1.6.4 Seismic-Related Requirements for Connectors In Seismic Design Category A, masonry walls are required to be anchored to the roof and floors that support them laterally. This provision is not intended to require a mechanical connection; the anchorage can be accomplished by friction or a mortar joint. No additional seismic-related restrictions on connection forces apply in Seismic Design Category B. In Seismic Design Category C, connectors for masonry partition walls must be designed to accommodate story drift. Horizontal elements and masonry shear walls must be connected by connectors capable of resisting the forces between those elements, and minimum connector capacity and maximum spacing are also specified. No additional seismic-related requirements for connectors apply in Seismic Design Categories D and higher. 16.5.1.6.5 Seismic-Related Requirements for Locations and Minimum Percentages of Reinforcement In Seismic Design Categories A and B, there are no seismic-related requirements for locations and minimum percentages of reinforcement. In Seismic Design Category C, masonry partition walls must have reinforcement meeting requirements for minimum percentage and maximum spacing. The reinforcement is not required to be placed parallel © 2003 by CRC Press LLC
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to the direction in which the element spans. Masonry walls must have reinforcement with an area of at least 0.2 in.2 (129 mm2) at corners, close to each side of openings, movement joints, and ends of walls, and spaced no farther than 10 ft (3 m) apart. In Seismic Design Category D, masonry walls that are part of the lateral-force-resisting system must have uniformly distributed reinforcement in the horizontal and vertical directions, with a minimum percentage in each direction of 0.0007 and a minimum summation (both directions) of 0.002. Maximum spacing in either direction is 48 in. (1.22 m). Closer maximum spacing requirements apply for stack bond masonry. Masonry shear walls have additional requirements for minimum vertical reinforcement and hooking of horizontal shear reinforcement. In Seismic Design Categories E and F, stack-bonded masonry partition walls have minimum horizontal reinforcement requirements. Stack-bonded masonry walls that are part of the lateral-force-resisting system have additional requirements for spacing and percentage of horizontal reinforcement. Masonry shear walls must be specially reinforced.
16.5.2 The Future of Design Codes for Masonry in the United States The next decade is likely to witness increased harmonization of U.S. model codes, and increasing direct reference to the MSJC Code and Specification. In the MSJC design provisions, the Specification is likely to be augmented by a code chapter dealing with construction requirements.
16.6 Analysis Approaches for Modern U.S. Masonry In this section, structural analysis techniques for masonry are discussed. Emphasis is placed on analytical considerations that are often different for masonry than for other common structural systems. General considerations related to the analysis of reinforced concrete and masonry structures are given in other references [American Concrete Institute, 1991], and are not repeated here. Similarly, the analysis of masonry structures for gravity loads involves techniques that are routine. In the remainder of this section, analysis of masonry for lateral loads is emphasized. Analysis of masonry structures for lateral loads, alone or in combination with gravity loads, must address the following issues: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
Analytical approaches (hand vs. computer) Elastic vs. inelastic behavior Selection of earthquake input Two-dimensional vs. three-dimensional behavior Load modeling Material modeling Structural element modeling Flexural cracking Soil-foundation flexibility Floor diaphragm flexibility
In this section, each of these issues is briefly discussed. Additional details are presented in Klingner et al. [1990] and Jalil et al. [1993]. Additional information on analysis of masonry buildings, including diaphragm flexibility, is presented in Tena-Colunga and Abrams [1996].
16.6.1 Overall Analytical Approach Hand-type as well as computer-type analysis approaches are available. Hand-type approaches usually emphasize the plan distribution of shear forces in wall elements. These can be quite simple (shears in each plan direction can be assigned to wall elements in proportion to their plan lengths, and torsional effects are neglected). They can also be more complex (pier stiffnesses are computed including the effects © 2003 by CRC Press LLC
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of shearing and flexural deformations, and torsional effects are included). For buildings with regular plan configurations, even the simplest hand methods are adequate for predicting the distribution of shear among wall elements (errors of 10% or less). Hand methods, however, are not sufficiently accurate for computing wall moments; critical design moments can be overestimated by factors as high as 3. Given the adequacy of the simplest hand methods for estimating wall design shears, and the frequent inadequacy of hand methods for estimating wall moments, there seems to be little justification for using any but the simplest of hand methods. If more precision is required, computer-type analysis approaches should be used. Many microcomputer-based structural analysis programs are available. Some of these are intended for building-type structures only, while others are more general. Different analytical assumptions related to computer-type analyses of masonry structures are discussed below. 16.6.1.1 Elastic vs. Inelastic Behavior When flexural yielding or shear degradation of significant portions of a masonry structure are anticipated, inelastic analyses should be considered. However, in many cases, masonry structures can be expected to respond in the cracked elastic regime, even under extreme lateral loads. Masonry buildings with regular plan configurations, and with plan wall areas (in each principal plan direction) of at least several percent of their plan area, will probably crack in flexure but not yield, and will probably not experience serious shear cracking. Therefore, the behavior of such buildings can be predicted using elastic analyses, provided that the effects of flexural cracking are accounted for by appropriately reducing the element stiffnesses. Because those stiffnesses do not change further during the analysis, the structure is still linear elastic. 16.6.1.2 Selection of Earthquake Input Because structural response is generally expected to be linear elastic (with appropriate consideration for the effects of flexural cracking), response spectra are sufficient. 16.6.1.3 Two-Dimensional vs. Three-Dimensional Analysis In a two-dimensional analysis, a building is modeled as an assemblage of parallel planar frames, free to displace laterally in their own planes only, subject to the requirement of lateral displacements compatibility between all frames at each floor level. Buildings so modeled cannot exhibit torsional response in plan. In the “pseudo three-dimensional” approach, a building is modeled as an assemblage of planar frames, each of which is free to displace parallel and perpendicular to its own planes. The frames exhibit lateral displacement compatibility at each floor level. However, compatibility of vertical displacements is not required of common columns in intersecting frames. In a true three-dimensional approach, the building is modeled as a single three-dimensional frame, and appropriate displacement compatibilities are maintained among all frame elements. Because microcomputer-based programs employing a true three-dimensional approach are widely available, there seems little justification for using a less sophisticated level of analysis. 16.6.1.4 Modeling of Loads Gravity loads should be based on self-weight, plus an estimate of the probable live load. A uniform distribution of mass should normally be assumed over each floor, except for the masses from the exterior walls, which should normally be included discretely. 16.6.1.5 Modeling of Material Properties Material properties should be estimated based on test results. A value of Poisson’s ratio of 0.35 can be used for masonry. This value is greater than that corresponding to compressive tests of masonry prisms. However, it gives a realistic value of the shear modulus, which is very important for the correct estimation of lateral drifts in low-rise masonry wall buildings.
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16.6.1.6 Modeling of Structural Elements Masonry wall buildings are normally modeled using beams and panels (shell elements), with occasional columns. In-plane modeling of floor diaphragms is discussed below. Modeling of walls, and of the outof-plane behavior of floor diaphragms, is discussed here. 16.6.1.6.1 Modeling of Walls The most crucial point in wall modeling is that the walls be included. Masonry buildings are occasionally modeled as frame-type structures composed only of the frame elements, completely neglecting the influence of the masonry. This “frame-only” approach, though often believed to be conservative, is in fact unconservative and erroneous: • It greatly increases the building’s calculated period of vibration, thereby decreasing (usually) its calculated seismic inertia forces. • It gives an incorrect estimate of the internal distribution of shears among wall elements, and of the building’s plan center of rigidity. • It gives significant errors in calculating the lateral resistance of the building. Buildings with essentially unperforated shear walls can usually be modeled adequately considering the walls as solid panels. This approach, however, is inadequate for the design and analysis of low-rise masonry buildings having structural walls with large openings. For such buildings, two alternatives are available: • The walls can be modeled with solid panels having equivalent axial, shear, and flexural stiffnesses. Those equivalent stiffnesses should be determined by separate finite element modeling of the original panel. • The building should be modeled using finite elements with appropriately placed openings. 16.6.1.6.2 Modeling of Beams The effective widths of cast-in-place reinforced concrete slabs acting as coupling elements between walls have been modeled successfully as four times the slab thickness on each side when the slab acted as part of a solid panel, and as three times the thickness of the coupled walls for a coupling slab without a supporting beam. As a rule of thumb, the flexural inertia of T and L beams can be approximated, respectively, as 2.0 and 1.5 times the inertia of the rectangular web. Torsional stiffness can be evaluated as in Section 13.7.5 of ACI 318–02. Effective shear areas of beams should be computed using the web area only. 16.6.1.7 Flexural Cracking of Walls Whenever analyses of masonry buildings indicate flexural cracking, the analytical model should be modified to take this into account. 16.6.1.7.1 Flexural Cracking Criterion The cracking moment for a wall should be determined by multiplying the modulus of rupture of the wall under in-plane flexure by the section modulus of the wall. If experimentally determined values of the modulus of rupture are not available, the modulus of rupture can conservatively be taken as the allowable tensile bond stress, normal to the bed joint, for the corresponding combination of masonry materials. 16.6.1.7.2 Consequences of Flexural Cracking of Walls Flexural cracking reduces the wall’s stiffness from that of the uncracked transformed section to that of the cracked transformed section. For reinforced concrete beams, stiffness reduction factors of 2 to 3 are typical. For walls, however, flexural cracking reduces the stiffness by factors of 5 or more, depending on the cross-sectional shape of the wall and the longitudinal reinforcement ratio. In some cases, this stiffness reduction changed the distribution of shears and moments in the complete structure. In one building [Klingner et al., 1990], consideration of reduced flexural stiffness due to flexural © 2003 by CRC Press LLC
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cracking decreased the computed maximum moments by 20%. These computed maxima correlated well with observed damage. 16.6.1.8 Soil-Foundation Flexibility When soil and foundation flexibility are included in the analytical model of a low-rise masonry building, two things happen: • Regardless of how the building’s foundation is modeled, the building’s periods of vibration increase, and lateral force levels can change significantly. • If the building’s foundation is considered flexible, the resulting increase in support flexibility at the bases of wall elements causes their base moments to decrease substantially. For low-rise, stiff buildings, these effects can be significant. For example, a four-story masonry wall building showed an increase in fundamental period from about 0.13 sec to about 0.35 sec when soilfoundation flexibilities were included in the model, assuming large soil strains. Moments in the critical wall were reduced by about 30% [Klingner et al., 1990]. For more flexible buildings, however, having masonry veneer over a structural frame, these effects were found not to be significant. It is recommended that soil-foundation flexibility be included if a building’s calculated fundamental period (assuming a rigid base) is 0.15 sec or less, and if the underlying soil is soft. Foundation flexibility can be addressed by modeling the foundations as part of the lowest story of panels in each building, and by using equivalent soil springs, placed under the building. Depending on the characteristics of a building’s foundation, it may be appropriate to idealize the underlying soil flexibility by a single spring under a stiff mat-type foundation, or by a number of separate springs, each underlying an individual strip footing. Two procedures can be used to calculate the equivalent spring stiffness: • Foundations are idealized as circular foundations with equivalent plan areas and inertias. • Explicit stiffnesses are obtained for strip footings and foundations of arbitrary plan shape. The second procedure is more sound theoretically. Details of the calculation of soil-foundation stiffness are given in Klingner et al. [1990]. 16.6.1.9 In-Plane Floor Diaphragm Flexibility Structures in general are often modeled using special-purpose analysis programs that assume that floor diaphragms are rigid in their own planes. This assumption is reasonable for many framed structures, because the in-plane stiffness of their floor diaphragms is much greater than the lateral stiffness of their framing systems. For many masonry wall structures, it is also reasonable [Jalil et al., 1993]. However, many masonry wall structures have floor slabs with features that could increase the effects of in-plane floor flexibility: • Small openings in critical sections of the floor slab • Rectangular floor plans with large aspect ratios in plan • Variations of in-plane rigidity within the slab In general, for low-rise masonry buildings considered in the cited study [Klingner et al., 1990], only slight differences were observed between results obtained using otherwise identical analytical models with and without floor diaphragm flexibility. Results did not change by much, because of the following characteristics shared by all the buildings of this study: • • • •
Their masses were distributed uniformly in plan. Their floor slabs were cast in place, and were stiff in their own planes. Their floor slabs consisted mainly of solid areas with small openings. The solid areas of their floor slabs were connected so that the lateral rigidities of the overall buildings were distributed symmetrically in plan.
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In-plane flexibility of roof diaphragms is very important in the seismic response of warehouse-type buildings. Walls oriented perpendicular to the direction of ground motion are affected most significantly not by the shaking of the ground itself, but rather by the response of the roof diaphragm to which they are connected. 16.6.1.10 Explicit Inelastic Design and Analysis of Masonry Structures Subjected to Extreme Lateral Loads In the above discussion of issues related to modeling of masonry structures for lateral loads, it was assumed that response would be essentially elastic (with appropriate consideration of flexural cracking). If inelastic response of a masonry structure is anticipated, a general design and analysis approach has been proposed, involving the following steps [Leiva and Klingner, 1994]: 1. Select a stable collapse mechanism for the wall, with reasonable inelastic deformation demand in hinging regions. Using that collapse mechanism, predict the lateral load capacity of the wall in terms of its flexural capacity in hinging regions. 2. Using general plane-section theory to describe the flexural behavior of reinforced masonry elements, provide sufficient flexural capacity and flexural ductility in hinging regions. 3. Using a capacity design philosophy, provide wall elements with sufficient shear capacity to resist the shears consistent with the development of the intended collapse mechanism. Calculate the shear capacity of masonry elements, and the shear transfer capacity between adjacent elements, using current strength-design provisions. 4. Using reinforcing details from current strength-design provisions, detail the wall reinforcement to develop the necessary strength and inelastic deformation capacity. This approach was used for the design of multistory masonry specimens tested under the TCCMAR program [Leiva and Klingner, 1994; Seible et al., 1994]. It has been found to lead to masonry walls with predictable strength and stable load-deflection behavior under many cycles of reversed cyclic load, and it is recommended for design of reinforced masonry walls in seismic zones. 16.6.1.11 Inelastic Finite Element Analysis of Masonry Structures A number of finite element models have been developed in recent years to evaluate the inelastic behavior of masonry. Even though such analysis may require considerable computing resources and can be difficult to perform, it is sometimes desirable for a number of reasons. The inelastic behavior of a masonry structure can be very complicated. In the absence of experimental data, finite element analysis is the most viable method to quantify the ductility and post-peak behavior of masonry structures. In addition, the load-deformation relation of a masonry component obtained from a finite element analysis can be used to calibrate structural component models, which in turn can be used for the push-over analysis or dynamic analysis of large structural systems. Furthermore, in the absence of precise material information, finite element analysis can be used to study the inelastic behavior of masonry structures in a qualitative manner to identify possible failure mechanisms and to provide guidance for the repair and retrofit of existing structures. Inelastic finite element analysis of masonry structures is described in detail in Shing and Klingner [1997]. It is not required for design, and is not discussed further here.
16.7 Seismic Retrofitting of Historical Masonry in the United States The preceding sections of this chapter have dealt primarily with the seismic performance of masonry built under the reinforced masonry provisions that were introduced in the western United States as part of the reaction to the 1933 Long Beach earthquake. Such masonry generally behaves well. Unreinforced masonry, in contrast, often collapses or experiences heavy damage. This is true whether the masonry was built in the western United States prior to 1933 or in other places either before or after 1933. As a result © 2003 by CRC Press LLC
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of this observed poor behavior, recent decades have witnessed significant interest in the seismic retrofitting of historical masonry in the United States. In this section, those retrofitting efforts are briefly reviewed.
16.7.1 Observed Seismic Performance As noted earlier in this chapter, URM buildings have performed poorly in many U.S. earthquakes. The 1933 Long Beach, California earthquake severely damaged many URM buildings, particularly schools. One consequence of this damage was the passage of California’s Field Act, which prohibited the use of masonry (as it was then used) in all public buildings in the state. When masonry construction was revived in California during the mid-1940s, it was required to comply with newly developed UBC provisions. Those provisions, based on the reinforced concrete design practice of the time, required that minimum seismic lateral forces be considered in the design of masonry buildings, that tensile stresses in masonry be resisted by reinforcement, and that all masonry have at least a minimum percentage of horizontal and vertical reinforcement.
16.7.2 Laboratory Performance Although laboratory testing of historical U.S. masonry is difficult, some testing has been carried out on masonry specimens cut from existing structures. Much more extensive testing has been carried out on reduced-scale replicas of unreinforced masonry construction. Some is typical of the United States; some is typical of that found in other countries. That testing includes the following: • Benedetti et al., 1998: 24 simple, two-story, half-scale, unreinforced masonry buildings were tested to varying degrees of damage, repaired and strengthened, and tested again. • Tomazevic and Weiss, 1992: two three-story, reduced-scale, plain and reinforced masonry buildings were tested. The efficacy of reinforcement was confirmed. • Costley and Abrams, 1996: two reduced-scale brick masonry buildings were tested on a shaking table. Observed and predicted behavior were compared, and also used to make recommendations for the use of FEMA retrofitting guidelines. • Gulkan et al., 1990a, 1990b: single-story unreinforced masonry houses, 16 ft square in plan, made of full-sized masonry units, were tested on a shaking table, and performed satisfactorily under levels of shaking representative of then-current code requirements for the Phoenix area.
16.7.3 Basic Principles of Masonry Retrofitting Over the past 15 years, efforts have focused on the seismic response and retrofitting of existing URM buildings. The goals of seismic retrofitting are: • To correct deficiencies in overall structural concept • To correct deficiencies in behavior of structural elements • To correct deficiencies in behavior of nonstructural elements The most basic elements of seismic retrofitting involve bracing parapets to roofs and connecting floor diaphragms to walls using through anchors (mechanical, grouted, or adhesive).
16.7.4 History of Unreinforced Masonry Retrofitting in the Los Angeles Area 16.7.4.1 Division 88 In 1949 the City of Los Angeles passed the Parapet Correction Ordinance, which required that URM or concrete parapets above exits, and parapets above public access, be retrofitted to minimize hazards. As a result, such parapets were either laterally braced or removed. Consequently, many URM buildings withstood the 1971 San Fernando earthquake better than previous earthquakes [Lew et al., 1971].
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FIGURE 16.21 Schematic of Division 88 retrofitting techniques for URM.
Following the February 1971 San Fernando earthquake, the City of Los Angeles, the federal government and the Structural Engineers Association of Southern California joined forces in a 10-year investigation. As a result of this investigation, Los Angeles adopted an ordinance known as Division 68 on February 13, 1981. Division 68 required seismic retrofitting of all URM bearing-wall buildings that were built, under construction, or for which a permit had been issued prior to October 6, 1933. The ordinance did not include one- or two-family dwellings or detached apartment houses comprising fewer than five dwelling units and used solely for residential purposes. The 1985 edition of the Los Angeles Building Code revised Division 68 into Division 88, and included provisions for the testing and strengthening of mortar joints to meet minimum values for shear strength. Furthermore, Division 88 required that URM be positively anchored to floor and roof diaphragms with anchors spaced not more than 6 ft apart. There were also parapet height limitations, based on wall thickness. Continuous inspection was also required on the retrofitting work. These retrofitting measures are shown schematically in Figure 16.21. Alternatives to these specific provisions were also possible. Division 88 was renamed Chapter 88 in the 1988 City of Los Angeles Code. In addition to masonry bearing walls, veneer walls constructed before October 6, 1933 were included. This edition also added Section 8811 (“Design Check: Compatibility of Roof Diaphragm Stiffness to Unreinforced Masonry Wall Out-of-Plane Stability”). At the time of the Northridge earthquake, it is believed that essentially all URM buildings in the City of Los Angeles had their parapets either removed or laterally braced. Unconfirmed reports are that in the City of Los Angeles, about 80% of URM buildings had been retrofitted to comply with Division 88; however, the percentage was reported to be considerably lower in other cities in the Los Angeles area. 16.7.4.2 Other Retrofitting Guidelines The NEHRP in conjunction with FEMA has produced a series of documents dealing with the seismic evaluation and retrofitting of structures, including masonry structures: • FEMA 172 [1992], Handbook of Techniques for the Seismic Rehabilitation of Existing Buildings, provides a general list of retrofitting techniques. • FEMA 178 [1992], NEHRP Handbook for the Seismic Evaluation of Existing Buildings, presents an overall method for engineers to identify buildings or building components that present unacceptable risks in case of an earthquake. • FEMA 273 [1997] and 274 [1997], NEHRP Guidelines and Commentary for the seismic rehabilitation of buildings, provide code-type procedures for the assessment, evaluation, analysis, and rehabilitation of existing building structures. • FEMA 306 [1998], Evaluation of Earthquake-Damaged Concrete and Masonry Wall Buildings, Basic Procedures Manual (270 pp.), provides guidance on evaluation of damage and on performance analysis and includes newly formulated Component Damage Classification Guides, and Test and Investigation Guides. The procedures characterize the observed damage caused by an earthquake in terms of the loss in building performance capability. © 2003 by CRC Press LLC
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• FEMA 307 [1998], Evaluation of Earthquake-Damaged Concrete and Masonry Wall Buildings, Technical Resources (271 pp.), contains supplemental information, including results from a theoretical analysis of the effects of prior damage on single-degree-of-freedom mathematical models, additional background information on the Component Damage Classification Guides, and an example of the application of the basic procedures. • FEMA 308 [1998], Repair of Earthquake-Damaged Concrete and Masonry Wall Buildings (81 pp.), discusses the technical and policy issues pertaining to the repair of earthquake-damaged buildings and includes guidance on the specification of individual repair techniques and newly formulated repair guides.
References Abrams, D. and Paulson, T., 1991. “Modeling Earthquake Response of Concrete Masonry Building Structures,” ACI Struct. J., 88, 475–485. American Concrete Institute, 1991. Earthquake-Resistant Concrete Structures: Inelastic Response and Design, Special Publication SP-127, S.K. Ghosh, Ed., American Concrete Institute, Farmington Hills, MI, April, pp. 479–503. American Concrete Institute, 2002. Committee 318, Building Code Requirements for Reinforced Concrete (ACI 318–02), American Concrete Institute, Farmington Hills, MI. American Institute of Steel Construction, 1992. Manual of Steel Construction, Load and Resistance Factor Design, 2nd ed., American Institute of Steel Construction, Chicago. American Society of Civil Engineers, 1998. Minimum Design Loads for Buildings and Other Structures (ASCE 7–98), American Society of Civil Engineers, Reston, VA. Applied Technology Council, 1978. Tentative Provisions for the Development of Seismic Regulations for Buildings (ATC 3–06), Applied Technology Council, National Bureau of Standards, Washington, D.C. Basic Building Code, 1999. Building Officials/Code Administrators International, Country Club, IL. Benedetti, D., Carydis, P., and Pezzoli, P., 1998. “Shaking-Table Tests on 24 Simple Masonry Buildings,” Earthquake Eng. Struct. Dyn., 27, 67–90. Binder, R.W., 1952. “Engineering Aspects of the 1933 Long Beach Earthquake,” Proceedings of the Symposium on Earthquake Blast Effects on Structures, Berkeley, CA, pp. 186–211. Blondet, M. and Mayes, R.L., 1991. The Transverse Response of Clay Masonry Walls Subjected to Strong Motion Earthquakes, Vol. 1, General Information, TCCMAR Report No.3.2(b)-2, U.S.–Japan Coordinated Program for Masonry Building Research, Cohen, G.L., 2001. “Seismic Response of Low-Rise Masonry Buildings with Flexible Roof Diaphragms,” M.S. thesis, University of Texas at Austin, May. Costley, A.C. and Abrams, D.P., 1996. “Response of Building Systems with Rocking Piers and Flexible Diaphragms,” Proceedings of the Structures Congress, American Society of Civil Engineers, Chicago, April 15–18, pp. 135–140. Earthquake Engineering Research Institute, 1999. The Quindío, Colombia Earthquake of January 25, 1999, EERI Special Earthquake Report, Earthquake Engineering Research Institute, Oakland, CA. EQE, 1989. The October 17, 1989 Loma Prieta Earthquake, EQE International, Oakland, CA. EQE, 1999. Izmit, Turkey Earthquake of August 17, 1999 (M7.4), EQE Briefing, EQE International, Oakland, CA, October. FEMA 172, 1992. Handbook of Techniques for the Seismic Rehabilitation of Existing Buildings, Building Seismic Safety Council, Washington, D.C. FEMA 178, 1992. NEHRP Handbook for the Seismic Evaluation of Existing Buildings, Building Seismic Safety Council, Washington, D.C. FEMA 273, 1997. NEHRP Guidelines for the Seismic Rehabilitation of Buildings, Building Seismic Safety Council, Washington, D.C., October. © 2003 by CRC Press LLC
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FEMA 274, 1997. NEHRP Commentary on the Guidelines for the Seismic Rehabilitation of Buildings, Building Seismic Safety Council, Washington, D.C., October. FEMA 306, 1998. Evaluation of Earthquake-Damaged Concrete and Masonry Wall Buildings: Basic Procedures Manual, Federal Emergency Management Agency, Washington, D.C. FEMA 307, 1998. Evaluation of Earthquake-Damaged Concrete and Masonry Wall Buildings: Technical Resources, Federal Emergency Management Agency, Washington, D.C. FEMA 308, 1998. Repair of Earthquake-Damaged Concrete and Masonry Wall Buildings, Federal Emergency Management Agency, Washington, D.C. Gulkan, P., Clough, R.W., Mayes, R.L., and Manos, G., 1990a. “Seismic Testing of Single-Story Masonry Houses, I,” J. Struct. Eng., 116, 235–256. Gulkan, P., Clough, R.W., Mayes, R.L., and Manos, G., 1990b. “Seismic Testing of Single-Story Masonry Houses, II,” J. Struct. Eng., 116, 257–274. Hamid, A., Abboud, B., Farah, M., Hatem, K., and Harris, H., 1989. Response of Reinforced Block Masonry Walls to Out-of-Plane State Loads, TCCMAR Report No. 3.2(a)-1, U.S.-Japan Coordinated Program for Masonry Building Research, available from The Masonry Society, Boulder, CO. He, L. and Priestley, M.J.N., 1992. Seismic Behavior of Flanged Masonry Shear Walls, TCCMAR Report No. 4.1–2, U.S.–Japan Coordinated Program for Masonry Building Research. International Code Council, 2000. International Building Code, International Code Council, Falls Church, VA. International Masonry Institute, 1985. Mexico Earthquake: September, 1985, International Masonry Institute, Washington, D.C. Jalil, I., Kelm, W., and Klingner, R.E., 1993. “Performance of Masonry and Masonry Veneer Buildings in the 1989 Loma Prieta Earthquake,” Proceedings, Sixth North American Masonry Conference, Drexel University, Philadelphia, June 6–9. Klingner, R.E., Villablanca, R., Blondet, M., and Mayes, R.L., 1990. “Masonry Structures in the Chilean Earthquake of March 3, 1985: Behavior and Correlation with Analysis,” Masonry Soc. J., 9, 20–25. Leiva, G. and Klingner, R.E., 1994. “Behavior and Design of Multi-Story Masonry Walls under In-Plane Seismic Loading,” Masonry Soc. J., 13, 15–24. Lew, H.S., Leyendecker, E.V., and Dikkers, R.D., 1971. Engineering Aspects of the 1971 San Fernando Earthquake, Building Science Series 40, United States Department of Commerce, National Bureau of Standards, Washington, D.C. Masonry Society, 1989. Proceedings of an International Seminar on Evaluating, Strengthening and Retrofitting Masonry Buildings, Construction Research Center, University of Texas at Arlington, October, The Masonry Society, Boulder, CO. Masonry Society, 1994. Performance of Masonry Structures in the Northridge, California Earthquake of January 17, 1994, Technical Report 301–94, Klingner, R.E., Ed., The Masonry Society, Boulder, CO, June. Masonry Society, 2001. Performance of Masonry Structures in the Nisqually, Washington Earthquake of February 28, 2001, Technical Report 301–01, Hamilton, H.R. III, Ed., The Masonry Society, Boulder, CO, December. Masonry Standards Joint Committee, 1999a. Building Code Requirements for Masonry Structures (ACI 530–99/ASCE 5–99/TMS 402–99), American Concrete Institute, Farmington Hills, MI; American Society of Civil Engineers, Reston, VA; The Masonry Society, Boulder, CO. Masonry Standards Joint Committee, 1999b. Specifications for Masonry Structures (ACI 530.1–99/ASCE 6–99/TMS 602–99), American Concrete Institute, Farmington Hills, MI; American Society of Civil Engineers, Reston, VA; The Masonry Society, Boulder, CO. NAMC, 1985. Proceedings of the Third North American Masonry Conference, University of Texas, Arlington, June 3–5, The Masonry Society, Boulder, CO. NAMC, 1987. Proceedings of the Fourth North American Masonry Conference, University of California, Los Angeles, August 16–19, The Masonry Society, Boulder, CO. © 2003 by CRC Press LLC
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NAMC, 1990. Proceedings of the Fifth North American Masonry Conference, University of Illinois, UrbanaChampaign, June 3–6, The Masonry Society, Boulder, CO. NAMC, 1993. Proceedings of the Sixth North American Masonry Conference, Drexel University, Philadelphia, June 7–9, The Masonry Society, Boulder, CO. NAMC, 1996. Proceedings of the Seventh North American Masonry Conference, University of Notre Dame, Notre Dame, IN, June 2–5, The Masonry Society, Boulder, CO. NAMC, 1999. Proceedings of the Eighth North American Masonry Conference, University of Texas at Austin, June 6–9, The Masonry Society, Boulder, CO. NEHRP (National Earthquake Hazards Reduction Program), 1997. Recommended Provisions for the Development of Seismic Regulations for New Buildings (FEMA 222), Building Seismic Safety Council, Federal Emergency Management Agency, Washington, D.C. Noland, J.L., 1990. “1990 Status Report: U.S. Coordinated Program for Masonry Building Research,” Proceedings of the Fifth North American Masonry Conference, University of Illinois at UrbanaChampaign, June 3–6, The Masonry Society, Boulder, CO. SBC, 1999. Standard Building Code, Southern Building Code Congress International, Birmingham, AL. Seible, F., Hegemier, A., Igarashi, A., and Kingsley, G., 1994a. “Simulated Seismic-Load Tests on FullScale Five-Story Masonry Building,” J. Struct. Eng., 120, 903–924. Seible, F., Priestley, N., Kingsley, G., and Kurkchubashe, A., 1994b. “Seismic Response of Full-Scale FiveStory Reinforced-Masonry Building,” J. Struct. Eng., 120, 925–947. Shing, P.U.B. and Klingner, R.E., 1997. “Analysis of Masonry Structures,” in Monograph on Nonlinear Analysis of Building Structures, ASCE Committee on Methods of Analysis, American Society of Civil Engineers, Reston, VA, chap. 6. Suprenant, B.A., 1989. “A Floor a Week per Tower,” Masonry Construction, 2(11), 478–482. Tena-Colunga, A. and Abrams, D.P., 1996. “Seismic Behavior of Structures with Flexible Diaphragms, J. Struct. Eng., 122, 439–445. Tomazevic, M. and Weiss, P., 1994. “Seismic Behavior of Plain- and Reinforced-Masonry Buildings,” J. Struct. Eng., 120, 323–338. UBC, 1997. Uniform Building Code, International Conference of Building Officials, Whittier, CA.
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17 Base Isolation 17.1 17.2 17.3 17.4 17.5
Yeong-Bin Yang and Kuo-Chun Chang Department of Civil Engineering, National Taiwan University, Taipei Taiwan, R.O.C.
Jong-Dar Yau Department of Architecture and Building Technology Tamkang University, Taipei Taiwan, R.O.C.
Introduction Philosophy behind Seismic Isolation Systems Basic Requirements of Seismic Isolation Systems Design Criteria for Isolation Devices Design of High Damping Rubber Bearings Design Flow Chart for HDR Bearings · Shear Strain and Stability Conditions for HDR Bearings
17.6 Design of Lead Rubber Bearings Design Procedure for Lead Rubber Bearings · Shear Strain and Stability Checks
17.7 Design of Friction Pendulum Systems 17.8 Design Examples High Damping Rubber Bearings · Lead Rubber Bearings · Frictional Pendulum Systems
17.9 Concluding Remarks References
17.1 Introduction Conventionally, seismic design of building structures is based on the concept of increasing the resistance capacity of the structures against earthquakes by employing, for example, the use of shear walls, braced frames, or moment-resistant frames. However, these traditional methods often result in high floor accelerations for stiff buildings, or large interstory drifts for flexible buildings. Because of this, the building contents and nonstructural components may suffer significant damage during a major earthquake, even if the structure itself remains basically intact. This is not tolerable for buildings whose contents are more costly and valuable than the buildings themselves. High-precision production factories are one example of buildings that contain extremely costly and sensitive equipment. Additionally, hospitals, police and fire stations, and telecommunication centers are examples of facilities that contain valuable equipment and should remain operational immediately after an earthquake. In order to minimize interstory drifts, in addition to reducing floor accelerations, the concept of base isolation is increasingly being adopted. Base isolation (BI) has also been referred to as passive control, as the control of structural motions is not exercised through a logically driven external agency, but rather through a specially designed interface at the structural base or within the structure, which can reduce or filter out the forces transmitted from the ground. In contrast, the techniques of active or structural control, which are still under research and development for the seismic resistance of structures, require the installation of some logically controlled external agencies, such as actuators, to counteract the structural motions. One drawback with active control techniques is the relatively high cost of maintenance for the control system and actuators, which should remain functional at all times in order to respond to a major earthquake. There also exists a third category of techniques, called hybrid control, that make use of the best of both passive control and active control devices. In this chapter, there is no discussion of either active or hybrid control. © 2003 by CRC Press LLC
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FIGURE 17.1 Elastomeric bearing.
FIGURE 17.2 Laminated rubber bearing with lead core.
The effect of base isolation can be achieved through installation of certain devices between the building and the supporting foundation, so as to separate or isolate the motion of the building from that of the ground, making them basically uncoupled. The applicability of the concept of base isolation need not be restricted to the structure in its entirety. It can be applied as well to the isolation of sensitive equipment mounted inside a building from undesired floor vibrations through, for example, installation of an isolation system between the equipment base and the supporting floor. There are generally two basic approaches to base isolation, which have certain features in common. One approach is to install some bearings of relatively low horizontal stiffness, but high vertical stiffness, between the structure and its foundation. With such devices, the natural period of the structure will be significantly lengthened and shifted away from the dominant high frequency range of the earthquakes. The elastomeric bearing shown in Figure 17.1 is typical of this category, which is composed of alternating layers of steel and hard rubber and, therefore, is also known as a laminated rubber bearing. This type of bearing is stiff enough to sustain vertical loads, yet is sufficiently flexible under lateral forces. The ability to deform horizontally enables the bearing to reduce significantly the shear forces induced by the earthquake. While the major function of elastomeric bearings is to reduce the transmission of shear forces to the superstructure through lengthening of the vibration period of the entire system, they should provide sufficient rigidity under the service load levels for wind and minor earthquakes. In reality, the reduction in seismic forces transmitted to the superstructure through installation of laminated rubber bearings is achieved at the expense of large relative displacements across the bearings. If substantial damping can be introduced into the bearings or the isolation system, then this large displacement problem can be alleviated. It is for this reason that the laminated rubber bearing with inclusion of a central lead plug has been devised, as shown in Figure 17.2. Other forms of supplemental dampers, such as hydraulic dampers, steel coils, and viscous dampers, also serve to increase the damping of the isolated structure. © 2003 by CRC Press LLC
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FIGURE 17.3 Friction pendulum system.
The other approach for increasing flexibility in a structure is to provide a sliding or friction surface between the foundation and the base of the structure. The shear force transmitted to the superstructure across the isolation interface is limited by the static friction force, which equals the product of the coefficient of friction and the weight of the superstructure. The coefficient of friction is usually kept as low as is practical. However, it must be sufficiently high to provide a friction force that can sustain strong winds and minor earthquakes without sliding. One particular problem with a sliding structure is the residual displacements that occur after major earthquakes. To remedy this problem, the sliding surface is often made concave so as to provide a recentering force. This is the idea behind the most popular frictional device, the so-called friction pendulum system (FPS), which utilizes a spherical concave surface, as shown in Figure 17.3. To guarantee that a sliding structure can return to its original position, other mechanisms, such as high-tension springs and elastomeric bearings, can be used as an auxiliary system to generate the restoring forces. Sliding isolation systems have been successfully used for nuclear power plants, emergency fire water tanks, large chemical storage tanks, and other important structures. Numerous researchers have studied the dynamic behaviors of base-isolated structures under earthquakes using different devices for seismic isolation. Skinner et al. [1993] provided a comprehensive study on the application of isolation devices to practical structures. As for the application of rubber bearings to seismic design, Kelly [1993] gave a detailed procedure for the analysis of rubber isolation systems mounted on building structures. However, for base-isolated buildings located at near-fault sites, the design engineer is faced with very large design displacements for the isolators. To reduce these displacements, some researchers and design engineers suggested the addition of supplemental dampers alongside the isolators [Hall, 1999; Hall and Ryan, 2000]. It was argued by Kelly [1999] that increasing the damping in an isolation system may result in significant increase in the floor accelerations and interstory drifts of the isolated buildings. He went on to suggest some alternative strategies for overcoming this problem, such as the adoption of a gradual increasing curvature for the disk of the friction pendulum system, and the use of increased stiffness and increased damping for elastomeric isolators. A review of the isolation devices that have been studied and used from 1900 to 1984 was conducted by Kelly [1986]. In general, most isolation systems are nonlinear in terms of the force–displacement relationships. For a wide range of problems encountered, however, a linear analysis of the base-isolated structure using simple models allows us to gain insight into the dynamics of these systems, while identifying the key parameters involved [Chopra, 1995]. With such an approach, the superstructure of the base-isolated structure is often assumed to be elastic and even treated as a single-degree-of-freedom (SDOF) system, the elastomeric bearing as a combination of elastic spring and viscous damper, and the sliding surfaces as flat surfaces obeying the law of static friction. It should be realized that in the final stage of design, the nonlinear properties of the base isolators or their effects should be taken into account. © 2003 by CRC Press LLC
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Considering the geometric and material nonlinearities of elastomeric bearings with high damping rubber, Salomon et al. [1999] proposed a finite element model for analyzing base-isolated buildings with elastomeric isolators. Concerning the effect of torsional coupling on the seismic response of a base-isolated structure, an analytical study was carried out by Jangid and Kelly [2000]. Their results indicated that the effect of torsional coupling can significantly influence the response of the isolated structure but, when the torsional frequency is larger than the lateral frequency, the effect is reduced. Using the Rayleigh-Ritz procedure, Ryan and Chopra [2002] presented three approximate methods for analyzing the eccentricity effect of an asymmetric-plan base-isolated building subjected to ground motions. They concluded that the rigid structure method, which is often used for studying the dynamics of base-isolated systems, is not suitable for systems with zero isolation eccentricity, due to neglect of the structural flexibility and eccentricity. As for sliding structures, the most fundamental theories have been laid out in the works by Westermo and Udwadia [1983] and Mostaghel et al. [1983]. The effect of higher modes of vibration on multidegree-of-freedom (MDOF) structures was investigated by Yang et al. (1990), in which the concept of a fictitious spring was adopted to overcome the discontinuities encountered in analysis of the sliding and nonsliding phases of the system. Also, using the concept of fictitious springs, the dynamics of equipment mounted in a sliding structure was studied by Lu and Yang [1997]. For friction pendulum systems with spherical sliding surfaces, Tsai [1997] suggested that the local bending moment effects be considered for isolated structures to ensure their safety during earthquakes. The book written by Naeim and Kelly [1999] dealt particularly with the procedural aspects of design for seismic isolated structures. In the chapter by Mayes and Naiem [2001], the most recent International Building Code [ICC, 2000] design provisions for seismic isolation were discussed in detail, along with the procedures of design for various isolators. The objective of this chapter is to provide a rather practical coverage of the design procedures for base isolators used in building structures.
17.2 Philosophy behind Seismic Isolation Systems When a structure is subjected to a strong earthquake, the system energy of the structure can be conceptually expressed as: KE + DE + SE = IE
(17.1)
where KE denotes the kinetic energy, DE the dissipated energy, which equals the sum of VE and HE, with VE denoting the viscous energy and HE the hysterestic energy; SE is the strain energy and IE the seismic input energy. In Equation 17.1, KE and SE are the portion of the energy of the structure that is recoverable, whereas VE and HE are the portion that is dissipative. For a fixed-base building structure, when IE is not so large, the energy input to the structure will be dissipated in the form of VE. When a strong earthquake occurs, if all the input energy cannot be dissipated by the viscous damping of the structure, then the residual energy will be dissipated in the form of HE. If the structure has been designed to have sufficient ductility, then it may undergo plastic deformations in certain joints, members or specially added components, but the phenomenon of collapse must be avoided. This is the ductility concept of design for the traditional fixed-base structures. The dynamic characteristics of a base-isolated building can be modeled as a single-story building with a linear isolator, as shown in Figure 17.4. Let us assume that the mass and rigidity of the base-isolated building are much greater than those of the isolators. By treating the isolated part of the building as a rigid mass, the base-isolated building can be simulated as an SDOF system, for which the equation of motion is: Mu˙˙ + Cu˙ + Ku = − Mu˙˙g
© 2003 by CRC Press LLC
(17.2)
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FIGURE 17.4 Isolated structure: (a) initial position, (b) deformed position.
where u˙˙g denotes the ground acceleration, u the displacement of the structure, M the mass of the structure, C the damping, and K the stiffness of the isolator. By Duhamel’s integral, the response u(t) of the base-isolated system can be given by: u (t ) =
1 ωd
t
∫ −u˙˙ (τ)e 0
− ξω(t − τ )
g
sin ω d (t − τ) dτ
(17.3)
where the natural frequency ω, damped natural frequency ωd , and damping ratio ξ are defined as follows: ω=
K C , ωd = ω 1 − ξ2 , ξ = M 2Mω
(17.4)
Correspondingly, the natural period of vibration, T, and the natural period of damped vibration, Td , are: T=
2π M = 2π , ω K
Td =
2π T = ωd 1 − ξ2
(17.5)
For a given ground motion u˙˙g , the deformation and acceleration responses, u and ü, of an SDOF structure depend only on the natural period of vibration T and damping ratio ξ of the structure. Thus, for a specific earthquake, by first selecting a damping ratio ξ, one can compute the peak deformation u for a structure with a period of vibration T, i.e., with given values of M, C, K, using Equation 17.3. Repeating such a procedure for a wide range of period T, while keeping the damping ratio ξ constant, provides one curve similar to those shown in Figure 17.5. By varying the damping ratio ξ, one can construct the deformation response spectra for all SDOF structures under a given earthquake, as shown schematically in Figure 17.5. The pseudo-acceleration response A(t) of a system can be computed from the deformation response u(t) of the system by: 2
2π A (t ) = ω 2u (t ) = u (t ) T
(17.6)
In seismic engineering, the pseudo-acceleration response A(t) is an important quantity, since it can be multiplied by the mass M to yield the equivalent static force or base shear of the structure considered. The pseudo-acceleration response spectra, as shown schematically in Figure 17.6, represent plots of the peak value of A(t) with respect to the natural period of vibration T of the structure, which can be obtained
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FIGURE 17.5 Schematic of deformation response spectra.
FIGURE 17.6 Schematic of pseudo-acceleration spectra.
as a by-product of the deformation response spectra shown in Figure 17.5 through use of the relation in Equation 17.6. Two important features can be observed from the response spectra given in Figures 17.5 and 17.6. The first is the so-called period shift effect. As indicated by Figure 17.6, substantial reduction in the pseudoacceleration or the base shear of a structure is possible, if the period of vibration of the structure is significantly lengthened, for example, through installation of base isolators. The level of reduction depends primarily on the nature of the ground motion and the period of the fixed-base structure. In general, the additional flexibility needed to lengthen the period of the structure will give rise to large relative displacements across the isolators, as indicated by Figure 17.5. The second is the so-called energy dissipating effect. If additional damping is introduced into the structure, then the deformation of the structure can be significantly reduced (see Figure 17.5). Also, it can be seen that a smaller base shear force will be induced on a structure should it have larger damping (see Figure 17.6), and that a structure responds less sensitively to variations in ground motion characteristics, as indicated by the smoother response curves for structures with higher damping levels in both figures. As revealed by the aforementioned two seismic response spectra, the philosophy behind the installation of base isolators is to lengthen the period of vibration of the protected structure, so as to reduce the base shear ind uced by the ear thquak e, while providing addit ional damping f or reducing the r elat ive displacements ac ross the isolators themselves. This is why most seismic design codes suggest the use of base isolation systems that have the dual function of period elongation and energy dissipation. Moreover, it © 2003 by CRC Press LLC
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is required that the isolators be stiff enough under service load levels, e.g., under the wind loads or minor earthquakes, so as not to create frequent vibration annoyances to the occupants. Two additional factors should be considered before base isolation is regarded as a feasible means for aseismic design [Mayes and Naeim, 2001]. First, most benefits of base isolation can be achieved only for stiff structures, i.e., with a fixed-base fundamental period of 1.0 sec or less. For these structures, the fundamental period can be elongated to the range of 1.5 to 2.5 sec through the installation of base isolators, resulting in the largest margin that can be achieved for period shifting. Clearly, base isolation is a technique most applicable to low-rise and medium-rise buildings, and less effective for high-rise buildings, as the natural period of vibration of a building generally increases with increasing height. It is not uncommon that the natural periods of high-rise buildings are so long that their design is governed in general by wind loads, rather than by earthquake loads. If there still exist concerns for improving the performance of high-rise buildings, then energy dissipation devices, including tuned-mass dampers, that do not depend on lengthening of the structural periods, should be considered. The second factor to be considered is soil condition. When we mention earthquakes, we mean the ground motion u˙˙g used as the input to the base of the isolated system in Equation 17.2, based on which the response spectra in Figures 17.5 and 17.6 have been constructed. The form of the ground motion u˙˙g , as it arrives at the base of a structure, will be filtered by the properties of the underlying soils through which the earthquake waves travel. For hard soils, the ground motion u˙˙g is composed mainly of high frequency components, while for soft soils, it is dominated by low frequency components. All these properties will be carried over to the response spectra constructed for the particular earthquake. At this point, it should be mentioned that the seismic response spectra shown schematically in Figures 17.5 and 17.6 are typical of earthquakes that have a predominance of high frequency (or low-period) ground motions, in the range of 0.1 to 1 sec. It is for this kind of earthquake, and the stiff soil conditions it implies, that the concept of base isolation is most applicable. There exist cases where the ground motion u˙˙g is dominated by low frequency ground vibrations. One extreme example was the 1985 Mexico City earthquake, which contained a significant portion of longperiod vibrations, in the range of 1.5 to 2.5 sec, as the city is located in a soft lake-bed. For this kind of soil condition, larger response will be expected for structures with a fundamental period in the range of 1.5 to 2.5 sec, which is exactly the desired range that is supposed to be achieved through installation of base isolators for structures. Thus, lengthening of the period of a stiff structure will not result in reduction, but rather amplification, of the base shear. Obviously, for structures located on soft soil strata, the application of base isolators is not helpful, but harmful. For the purpose of reducing the structural response, one can only have recourse to energy-dissipating devices, such as viscous dampers and hydraulic dampers.
17.3 Basic Requirements of Seismic Isolation Systems A practical seismic isolation system should meet the following three requirements: 1. Sufficient horizontal flexibility to increase the structural period and spectral demands, except for very soft soil sites 2. Sufficient energy dissipation capacity to limit the displacements across the isolators to a practical level 3. Adequate rigidity to make the isolated building no different from a fixed-base building under general service loading Most commonly used seismic isolating systems can satisfy all the above requirements. Certainly, if the seismic isolating system can be equipped with fail-safe devices for avoiding the total collapse of the isolated structure in cases where excessive displacements occur, then the system will most likely be satisfactory. In the past two decades, the technology of seismic isolation has evolved along the lines of similar principles, resulting in the invention of one isolation device after the other [Johnson and Kienholz, 1982; Dynamic Isolation System, 1990; Bridgestone, 1990; Earthquake Protection Systems, 1993]. Most of the © 2003 by CRC Press LLC
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seismic isolation devices available in the market satisfy the basic requirements identified above, while having their own characteristics. Commercially available seismic isolation systems can be classified according to their dynamic characteristics and how they are formed from individual devices. The combination of elastomeric bearings and dampers represents a broad category of seismic isolators that have been used. The elastomers used by this kind of seismic isolators are usually made of natural rubber. Depending on how the elastomeric bearings and dampers are combined, this kind of seismic isolators can be further divided into two categories, as single-combination and separate-combination. In the single-combination, a single unit of isolator can provide the dual function of horizontal flexibility and energy dissipation. One typical example is the lead-rubber bearing (LRB), which combines the natural rubber bearing with a central lead core (Figure 17.2). In the separate-combination, the elastomeric bearings are supplemented by a number of dampers in separate units. The dampers used in this regard include: • The yielding type dampers or hysteretic dampers that are made of steel plates, steel bars, steel rings, and the like • The viscous dampers that are made of viscous materials, silicon fluid, etc. [Iwan and Gates, 1979; Iwan, 1980] The high damping rubber bearing (HDR) is similar in shape to the elastomeric bearing shown in Figure 17.1, except that it is made of specially compounded rubber that exhibits effective damping between 0.1 and 0.2 of critical. Because the ingredients used by each design firm in producing the HDR are generally different, drastic differences in the dynamic properties of the HDRs produced by various firms can be observed. One common feature of these dampers is that they all share the desired feature of high damping capacity. The most popular friction or sliding systems that apply low frictional interfaces to reduce the transmission of shear force to the isolated structure include the Electricite de France (EDF) system, resilientfriction base isolator (R-FBI), friction pendulum systems (FPSs) (see Figure 17.3), and Teflon and polished stainless steel formed sliding systems. As for the EDF system, the sliding surface is linked to neoprene bearings and the isolated structure has the potential of sliding downward due to inhomogeneous settlement of the isolation system. For the R-FBIs containing a rubber core in the center, blocking may occur and concentrate in certain Teflon layers. If a steel bar is inserted in the center of the R-FBI to drive all Teflon layers with the same level of sliding, then the problem of being unable to return the structure to its original position usually exists after a strong earthquake. Compared with the elastomeric and LRB bearings, most friction systems have the advantage that they are not affected either by the natural frequency of the isolated structure or the frequency content of the earthquake. The coefficient of friction is the key parameter that determines whether or not sliding will occur with the system. However, most friction systems have the drawback that they are incapable of returning the structure to its original position. It is likely that permanent offset may exist between the sliding parts of the system after a major earthquake. The problem of permanent offset or residual displacements can be overcome through use of the FPS shown in Figure 17.3, for which the sliding surface takes a spherical shape. For a spherical sliding surface, the radius of curvature R is constant, so that the bearing exhibits a linear restoring force, that is, under the constant gravity load W the stiffness is equal to W/R [Zayas et al., 1987]. The advantages of the FPS include the following: relatively small construction cost, small net-height required for installation, high vertical rigidity, well-proved durability against temperature and corrosion, and coincidence of mass center with shear center, which implies small torsional effects. For these reasons, the FPS is becoming one of the most popular friction systems used in seismic isolation. Each of the seismic isolation systems mentioned above has specific dynamic properties and functions. Even for isolators of the same category, it is likely that variations in material properties may exist among the products offered by different manufacturers. Moreover, since most of the isolation systems reported in the literature are patented products (the same is also true with most newly invented products), not all of them are readily available for procurement and application. In preparing this chapter on base © 2003 by CRC Press LLC
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isolation, we can only use those materials that are readily available to us. No intention is made to refer to any specific products. If any data have been included, they are considered mainly for the purpose of illustration. Although the general principles of design remain valid, it is the responsibility of the designers to verify that the cases presented in the following sections can really fit their situations.
17.4 Design Criteria for Isolation Devices A complete design for base isolation should ensure that the isolators can support the maximum gravity service loads of the structure throughout its life, and the isolators can provide the dual function of period shift and energy dissipation to the isolated structure during earthquakes. In accordance with these design aims, the following design steps should be undertaken [Mayes and Naeim, 2001]: 1. Determine the minimum plan size required and locations of isolators under the maximum gravity loads 2. Compute the dimensions of the isolators that will result in the desired period shift for reducing the earthquake forces 3. Determine the damping ratio of the isolator such that the displacement of the structure can be controlled within the design limit under wind loads 4. Check the performance of the isolators under gravity, wind, thermal, earthquake, and other possible load conditions To implement the design procedure for the seismic isolators, three different isolation systems, that is, the high damping rubber bearing, lead-core rubber bearing, and FPS, are considered in this chapter. The primary purpose herein is to illustrate the concepts involved in the preliminary sizing of isolators for a given project.
17.5 Design of High Damping Rubber Bearings The rubber layers constituting the high damping rubber bearing (HDR) are usually made of materials that are highly nonlinear in terms of shear strains. Effective damping in the range of 0.10~0.20 of critical can easily be exhibited by the HDR, which is achieved through addition of special chemical compounds that can change the material properties of the rubber. As was stated previously, the stiffness and damping of the HDR are required to be large enough to resist wind and minor earthquakes. In practice, the stiffness and damping properties of the HDR remain quite stable under one or more design earthquakes. Thus, similar to what has been undertaken in most previous studies, the HDR is assumed to be linear elastic and isotropic in this chapter, for the purpose of preliminary design.
17.5.1 Design Flow Chart for HDR Bearings The design flow chart for the high damping rubber bearings is shown in Figure 17.7. In the following, each of the parameters is defined at the place where it first appears, unless it is given a different meaning. The design procedure for the HDR is explained as follows: 1. Specify the soil condition for the isolated structure. 2. Select the design shear strain γmax and effective damping ratio ξeff for the bearing, and the target design period TD for the isolated structure. The former can be obtained from the material supplier. 3. Use code formulas, or static or dynamic analysis, to determine the effective horizontal stiffness Keff and maximum horizontal (design) displacement D of the bearing. 4. Select the material properties, including Young’s modulus E and shear modulus G, from the manufacturer’s test report. 5. Calculate the total height of rubber, tr, in the bearing according to the design displacement D and design shear strain γmax : tr = © 2003 by CRC Press LLC
D γ max
(17.7)
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17-10
FIGURE 17.7 Design flow chart for HDR.
© 2003 by CRC Press LLC
Earthquake Engineering Handbook
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17-11
Base Isolation
6. Calculate the effective area A and thickness t of individual rubber layers. a. Select the shape factor S under no rocking condition: Ec ⋅ A E ⋅ 1 + 2 kS 2 Kv t E = r = c = ≥ 400 for S > 10 Kh G ⋅ A G G tr
(
)
(17.8)
where Kv Kh G E Ec A tr k S Af
= vertical stiffness of the bearing = horizontal stiffness of the bearing = shear modulus, in the range of 0.4 to 1.0 MPa = Young’s modulus, in the range of 1.5 to 5.0 MPa = compression modulus of the rubber-steel composite, Ec = E(1 + 2kS2) = full cross-sectional area (loaded area) of the bearing = total height of rubber layers = modified factor, in the range of 1 to 0.5 = shape factor = A/Af [Kelly, 1993] = load-free area around the bearing (Figure 17.8)
In Equation 17.8, the stiffness ratio Kv /Kh is required to be greater than 400 for S > 10, since the P-δ effect has been ignored in computing the horizontal stiffness Kh. The material constants G, E, and k can be related to the rubber hardness, say, similar to those shown in Table 17.1 [Bridgestone, 1990]. If no published data are available, G and E should be determined by test. b. Determine the effective cross-sectional area A0 of the bearing based on the allowable stress σc for the vertical load case PDL+LL: σc =
PDL + LL ≤ 80 kgf cm 2 = 7.84 MN m 2 A0
(17.9)
FIGURE 17.8 Load-free area Af .
TABLE 17.1 Relation of Rubber Hardness and Material Constants Rubber Hardness IRHD ±2
Young’s Modulus E (N/cm 2)
Shear Modulus G (N/cm 2)
Modified Factor k
30 35 40 45 50 55 60 65 70 75
92 118 150 180 220 325 445 585 735 940
30 37 45 54 64 81 106 137 173 222
0.93 0.89 0.85 0.8 0.73 0.64 0.57 0.54 0.53 0.52
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FIGURE 17.9 Reduced cross-sectional area of circular bearing.
c. Determine the effective cross-sectional area A1 of the bearing from the shear strain due to the vertical load PDL+LL: γc
DL + LL
= 6S
PDL + LL ε b ≤ E c A1 3
(17.10)
where εb is the elongation of rubber at break. The limit of εb /3 is selected according to the American Association of State Highway and Transportation Officials [1983] Guide Specifications. d. Obtain the minimum cross-sectional area Asf for shear failure of the bearing: Asf =
K eff ⋅ t r G
(17.11)
Use Asf to determine the dimensions of the bearing. Then compute the effective cross-sectional area A2 as the reduced area Are given below (see Figure 17.9 for circular bearings): Are = L ⋅ ( B − ∆ S ) for a rectangular bearing Are =
d2 (β − sin β) for a circular bearing 4 ∆ β = 2 cos−1 S d
© 2003 by CRC Press LLC
(17.12)
(17.13)
(17.14)
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Base Isolation
where L, B = plan dimensions of the bearing perpendicular and parallel to the displacement, respectively = horizontal displacement of the bearing ∆s e. The design cross-sectional area A of the bearing is the maximum of the three values computed: A0, A1, and A2. f. Select proper dimensions for the rubber layer based on the design cross-sectional area A. 7. Single layer thickness, t, and number of rubber layers, N: a. Use the shape factor S and dimensions of the rubber layer to determine the thickness of individual rubber layer, t: S=
L⋅B 2 ( L + B) ⋅ t
for a rectangular bearing
(17.15)
S=
πd 2 4 d = πdt 4t
for a circular bearing
(17.16)
where L, B = plan dimensions of a rectangular bearing (L ≤ B) d = diameter of a circular bearing t = thickness of individual rubber layers b. Use tr = N × t to determine the required number of rubber layers, N 8. Steel plate thickness, ts: ts ≥
2 (t i + t i +1 ) ⋅ PDL + LL Are ⋅ FS
≥ 2 mm
(17.17)
where ti, ti+1 Fs Fy Are
= = = =
rubber layer thickness in top and bottom of the steel plate 0.6 Fy yield strength of the steel plates (= 274.4 MN/m2) reduced cross-sectional area of the bearing under horizontal displacement
9. All the parameters determined for the bearing should be checked against the shear strain and stability conditions given below. If these requirements cannot be satisfied, then repeat steps 2 to 8 for an improved design.
17.5.2
Shear Strain and Stability Conditions for HDR Bearings
1. The rubber layers selected should satisfy the shear strain requirement under the vertical load PDL+LL: γ c , DL + LL = 6S ⋅ ε c = 6S ⋅
PDL + LL ε b ≤ Ec ⋅ A 3
(17.18)
where the compression strain εc is: εc =
∆ c PDL+ LL = tr Ec ⋅ A
∆ c = compression displacement of the bearing ε b = elongation of rubber at break © 2003 by CRC Press LLC
(17.19)
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2. Stability condition: To prevent the bearing from becoming unstable, the average compressive stress σc of the bearing should be less than a preset tolerance: σc =
P G ⋅S ⋅L < σ cr = A 2.5 ⋅ t r
(17.20)
where L is the least plan dimension of the rectangular bearing or the diameter d of the circular bearing. It should be noted that the following formulas were used by Naeim and Kelly [1999]: πG ⋅ S ⋅ d 2 2 ⋅t P r σ c = < σ cr = πG ⋅ S ⋅ L A 6 ⋅ t r
for a circular bearing (17.21) for a rectangular bearing
3. Shear strain condition for the earthquake load: γ sc + γ eq + γ sr ≤ 0.75 ε b
(17.22)
with γ sc = 6 S ⋅
PDL + LL + EQ E c ⋅ Are
(17.23)
D tr
(17.24)
γ sr =
B2 ⋅ θ 2 ⋅ t ⋅ tr
(17.25)
θ=
12 De b2 + d 2
(17.26)
γ eq =
where
γsc PDL+LL+EQ γeq γsr θ e b, d
= shear strain under compression, same as in Equation 17.18, except that PDL+LL is replaced by PDL+LL+EQ = combination of dead load, live load, and earthquake load = shear strain under earthquake = shear strain under rotation = rotation angle of the bearing induced by earthquake = actual eccentricity + 5% of accidental eccentricity = dimensions of the structure with rectangular plan
4. To avoid rollout of the bearing, the displacement of the bearing under the earthquake load should fulfill the following condition: D ≤ δ roll-out =
© 2003 by CRC Press LLC
PDL + LL + EQ ⋅ L PDL + LL + EQ + K eff ⋅ h
(17.27)
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Base Isolation
FIGURE 17.10 Bearing in rollout position.
where Keff = effective stiffness of the bearing h = total height of the bearing (rubber plus steel) L = least plan dimension of a rectangular bearing or diameter d of a circular bearing Equation 17.27 can be derived from the following two equations established for the bearing in the deformed position, as shown in Figure 17.10: F ⋅ h = PDL + LL + EQ ⋅ ( L − δ roll-out )
(17.28)
F = K eff ⋅δ roll-out
(17.29)
where F is the shear force acting on the bearing and δroll-out the corresponding roll-out displacement.
17.6 Design of Lead Rubber Bearings Lead rubber bearings (LRBs) are usually made of alternating layers of steel plates and natural rubber with a central hole into which the lead core is press-fitted. When subjected to lateral shear forces, the lead core deforms almost in pure shear, yields at low level of shear stresses, approximately 8 to 10 MPa at normal (20°C) temperature, and produces rather stable hysteretic deformation behavior over a number of cycles. One feature of the lead core is that it can recrystallize at normal temperature and will not encounter the problem of fatigue failure under cyclic loadings. Sufficient rigidity is always ensured by the LRBs for the structure under service loads. In this section, the design procedure for LRBs is outlined.
17.6.1 Design Procedure for Lead Rubber Bearings The design procedure for LRBs is similar to that for HDRs, except that there is an additional need to design the lead core. 1. Specify the soil condition for the isolated structure. 2. Select the design shear strain γmax and effective damping ratio ξeff for the bearing, and the target design period TD for the isolated structure. The former can be obtained from the material supplier. 3. Use code formulas, or static or dynamic analysis to determine the effective horizontal stiffness Keff and maximum horizontal (design) displacement D of the bearing. © 2003 by CRC Press LLC
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4. Select the material properties, including Young’s modulus E and shear modulus G, from the manufacturer’s test report. 5. Calculate the total height of rubber layers, tr, in the bearing according to the design displacement D and design shear strain γmax: tr =
D γ max
(17.30)
6. Lead core design: Determine the cross-sectional area Ap and diameter dp of the lead core based on the short-term yield force Qd and yield strength fpy: Ap =
Qd f py
(17.31)
fpy = yield strength of the lead plug in shear = 1500 psi = 10 MPa [Mayes and Naeim, 2000] Qd = yield force of the lead plug ≅ WD /(4D) WD = energy dissipated per cycle = 2πKeff D 2ξeff D = design displacement of the bearing 7. Determine the area A and thickness t of individual rubber layers. a. Select the shape factor S under no rocking condition: Ec ⋅ A E ⋅ 1 + 2 kS 2 Kv t E = r = c = ≥ 400 Kh G ⋅ A G G tr
(
)
(17.32)
b. Compute the effective cross-sectional area A0 of the bearing based on the allowable axial stress σc under the vertical load case PDL+LL: σc =
PDL + LL ≤ 80 kgf / cm 2 = 7.84 MN / m 2 A0
(17.33)
c. Determine the effective cross-sectional area A1 of the bearing from the shear strain due to the vertical load PDL+LL: γc
DL + LL
= 6S
PDL + LL ε b ≤ E c A1 3
(17.34)
d. Determine the elastic modulus Kr of the bearing: A K d = K r 1 + 12 p A0
(17.35)
where Kd = post-yield stiffness of the LRB in horizontal direction [Naeim and Kelly, 1999]: K d = K eff −
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Qd D
(17.36)
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Base Isolation
e. Obtain the minimum cross-sectional area Asf for shear failure of the bearing: Asf =
Kr ⋅ tr G
(17.37)
Use Asf to determine the dimensions of the bearing. Then compute the effective cross-sectional area A2 as the reduced area Are given below: Are = L ⋅ ( B − ∆ S ) for a rectangular bearing Are =
d2 (β − sin β) for a circular bearing 4
(17.38)
(17.39)
f. The design cross-sectional area A of the bearing is the maximum among the three values computed: A0, A1, and A2. g. Select proper dimensions for the rubber layer based on the design area A. 8. Thickness of individual rubber layer, t, and the number of rubber layers, N: a. Determine the thickness of individual rubber layer, t, from the shape factor S and dimensions of the rubber layer: S=
L⋅B 2 ( L + B) ⋅ t S=
d 4t
for a rectangular bearing
for a circular bearing
(17.40)
(17.41)
b. Use tr = N × t to determine the required number of rubber layers, N. 9. Steel plate thickness, ts: ts ≥
2 (t i + t i +1 ) ⋅ PDL + LL Are ⋅ FS
≥ 2 mm
(17.42)
where each parameter has been defined previously. 10. The shear strain and stability conditions are given in the section to follow. If the dimensions determined for the bearing cannot satisfy the shear strain and stability requirements, then repeat steps 2 to 9 for an improved design.
17.6.2 Shear Strain and Stability Checks 1. In the design of rubber layers, the following shear strain condition for the normal load case should be satisfied: γ c , DL + LL = 6 S ⋅ ε c = 6 S ⋅
PDL + LL ε b ≤ Ec ⋅ A 3
(17.43)
where all the parameters have been defined following Equation 17.18. 2. Stability condition: To prevent the bearing from becoming unstable, the average compression stress σc of the bearing should fulfill the following condition: σc =
© 2003 by CRC Press LLC
P G ⋅S ⋅L < σ cr = A 2.5 ⋅ t r
(17.44)
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Earthquake Engineering Handbook
where it should be noted that L is the least dimension of a rectangular bearing or the diameter d of a circular bearing. 3. Lead core size: The lead core provides the initial stiffness and energy dissipation capability to the bearing, whose dimensions should meet the following condition: 1.25 ≤
Hp
≤ 5.0
dp
(17.45)
where Hp = effective height of the lead core dp = diameter of the lead core 4. Load combination including the earthquake: γ sc + γ eq + γ sr ≤ 0.75 ε b
(17.46)
where all the parameters have been defined following Equation 17.22. 5. To protect the bearing from the occurrence of rollout, the displacement D of the bearing under the earthquake load should fulfill the following condition: D ≤ δ roll-out =
PDL + LL + EQ ⋅ L PDL + LL + EQ + K d ⋅ h
(17.47)
where Kd indicates the post-yield stiffness of the bearing in the horizontal direction.
17.7 Design of Friction Pendulum Systems The frictional pendulum bearing allows the supported structure to return to its original position through use of a spherical concave sliding surface, rather than a flat sliding surface, thereby conquering the problem of recentering. Since the frictional pendulum bearing allows the isolated structure to vibrate in a way similar to the pendulum, it implies a natural period of vibration, TD . In design of the frictional pendulum bearing, one key concern is to make the natural period TD long enough, such that the forces transmitted from the ground to the superstructure can be greatly reduced. The period TD of the friction pendulum system (FPS) isolated structure can be designed through a proper choice of the radius of curvature, RFPS , for the spherical sliding surface, that is, TD = 2π
RFPS g
(17.48)
where g is the acceleration of gravity. As can be seen from Equation 17.48, the period of the FPS is independent of the mass of the supported structure. Such a property represents an advantage of the FPS in controlling the response of the isolated structure. Because of the use of a concave sliding surface, the FPS provides a recentering mechanism for the isolated structure to return to its original position after earthquake shaking. Let the vertical load carried by each FPS at the column base be W. The effective stiffness of the FPS is: K eff =
© 2003 by CRC Press LLC
W µW + RFPS D
(17.49)
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Base Isolation
where µ is the frictional coefficient of the sliding surface and D the design displacement. As indicated by Equation 17.49, the effective stiffness Keff of the FPS depends on the supported load W, which makes it difficult for designers to select suitable isolation systems for columns with different sustained loads. The effective damping ratio ξeff provided by the isolation system is a function of the design displacement, which can be expressed as: ξeff =
2 µ π µ + D RFPS
(17.50)
The vertical displacement δv of the structure caused by the curved surface of the isolator can be estimated as: δv ≅
D2 2RFPS
(17.51)
To ensure that the isolated structure will return to its original position, the horizontal displacement D of the structure under the earthquake load should meet the requirement that the restoring force F (= WD/RFPS) is not less than the friction force µW, that is: D ≥µ RFPS
(17.52)
This is exactly the condition to be checked for recentering of the isolated structure.
17.8 Design Examples A three-story reinforced concrete shear-wall office building is located on a rock site, i.e., site class B, and far away from active faults. If the building is constructed with a fixed base, the reduction factor is R = 6. According to Section 1623.2.5.2 of the IBC [ICC, 2000], if the building is base isolated, the reduction factor RI should be modified as: 3 1.0 ≤ RI = R ≤ 2.0 8 For all the isolation cases to be presented, the reduction factor is taken as RI = 2. The plan of the building is given in Figure 17.11. The story heights are 5 m for the first story and 4 m for the second and third stories. The sizes of the columns, beams, walls, and slabs are given as follows: Interior column C1: Exterior column C2: Beams B, G: Equivalent wall W1 thickness: Slab thickness S:
0.30 × 0.30 m 0.25 × 0.25 m 0.25 × 0.40 m 0.08 m 0.15 m
The story loads on the building are: dead load = 10 kN/m2 and live load = 2.5 kN/m2. The building has a regular plan with three columns spaced at 6 m along the x direction, and also three columns at 4 m apart along the y direction, as shown in Figure 17.11. The total weight WT of the building is 5,209 kN. Due to the limitation of site boundaries, the allowable horizontal displacement of the building at the base is 30 cm. By a static analysis using the ETABS program [CSI, 1997], the loads computed for all the columns at their base, where the bearings are to be installed, are shown in Figure 17.12. The natural periods of vibration for the fixed-base building along the x and y directions are 0.24 and 0.16 sec, respectively. © 2003 by CRC Press LLC
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Earthquake Engineering Handbook
FIGURE 17.11 Plan of three-story building.
FIGURE 17.12 Column loads of the building.
For the purpose of illustration, only the design of one bearing is considered. This is the one that will be installed at the base of the interior (central) column, of which the maximum sustained load is PDL+LL = 1,347 kN = 1.347 MN.
17.8.1 High Damping Rubber Bearings For this example, the design target period TD of the isolated structure should be greater than three times the fixed-base period. Let us assume that: (1) the target period TD = 2.5 sec, (2) the laminated rubber bearing has a maximum shear strain γmax = 150%, and (3) the effective damping ratio is ξeff = 20%. From Table 1623.2.2.1 of the IBC 2000, for an isolation system with ξeff = 20%, the damping coefficient BD is 1.5. From Table 1615.1.2(2) of the same code, for the site of the isolated building with long periods, the seismic coefficient is SD = 0.4.
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Base Isolation
17.8.1.1 Analysis The effective horizontal stiffness Keff of the isolator is:
K eff
W 2π = g TD
2
2
= W = PDL + LL
1347 2π = 868 kN / m = 0.868 MN / m 9.8 2.5
Based on Equation 16-79 of IBC 2000, the design displacement DD is: 9.8 0.4 × 2.5 g S T DD = 2 D D = 2 × = 0.17 m ≤ 0.3 m → OK 4 π BD 4π 1.5 17.8.1.2 Design 1. Determine the isolator size. 1.1 The total rubber height tr = DD / γmax = 0.17/1.5 = 0.11 m Use tr = 0.12 m. 1.2 Select the rubber properties from Table 17.1. Use the following for the rubber: hardness = IRHD-60, elongation at break εb = 500%. The material properties are obtained as follows: E = 445 N/cm2 = 4.45 MN/m2 G = 106 N/cm2 = 1.06 MN/m2 k = 0.57 1.3 Calculate the area A and thickness t of individual rubber layers. a. Select the shape factor S:
(
E ⋅ 1 + 2kS 2
) ≥ 400 → 445 ⋅ (1 + 2 × 0.57S ) ≥ 400 2
106
G → S > 9.09 → Use S = 20
(
)
(
)
E c = E ⋅ 1 + 2kS 2 = 445 ⋅ 1 + 2 × 0.57 × 20 2 = 203365 N / cm 2 = 2033.65 MN / m
2
b. Determine the effective area A0 for the bearing based on the allowable axial stress σc for the vertical load case PDL+LL: σc =
PDL + LL 1.347 kN ≤ 7.84 MN / m 2 → ≤ 7.84 MN / m 2 A0 A0
→ A0 > 0.172 m 2 c. Determine the effective area A1 for the bearing from the shear strain condition under the vertical load case PDL+LL: 6S =
PDL + LL ε b 1.347 500% ≤ → 6 × 20 × ≤ E c ⋅ A1 3 2033.65 × A1 3
→ A1 > 0.048 m 2
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d. Obtain the minimum area Asf for shear failure of the bearing: G=
K eff ⋅ t r Asf
→ Asf =
K eff ⋅ t r G
=
0.868 × 0.12 = 0.098 m 2 1.06
For a circular bearing, the diameter corresponding to the area Asf is d = 0.35 m. It follows that the effective area can be computed from Equations 17.13 and 17.14 as A2 = 0.039 m2. e. The design cross-sectional area for the bearing is: A = max(A0, A1, A2) = max(0.172, 0.048, 0.039) = 0.172 m2 f. Determine the size of rubber layers: Use the following equations for a circular bearing: Are ≤
d2 (β − sin β) 4
D β = 2 cos−1 D d → Diameter d = 0.7 m, area A = 0.385 m2, reduced area Are = 0.267 m2 g. Single layer thickness, t, and number of layers, N: For a circular bearing: S=
d 70 → 20 = → t = 0.88 cm; use t = 1 cm 4t 4t
1.4 Determine the steel plate thickness, ts: ts ≥ ts ≥
2(t i + t i +1 ) ⋅ PDL + LL Are ⋅ FS
≥ 2 mm
2 ⋅ (0.01 + 0.01) × 1.347 = 0.0012 m = 1.2 mm 0.267 × (0.6 × 274.4)
Use t s = 2 mm where, for A36 steel: Fs = 0.6Fy = 0.6 × 274.4 MN/m2 Are = 0.267 m2, β = 2 × cos–1(0.17/0.7) 1.5 Total height h of the bearing: Assume both the top and bottom cover plates are 2.5 cm thick. The total height of the bearing is: h = t r + 11 × ts + 2 × 2.5 cm = 12 cm + 11 × 2 mm + 5 cm = 19.2 cm 2. Shear strain and stability conditions 2.1 Vertical load PDL+LL\: γ c , DL + LL = 6S ⋅ ≤
© 2003 by CRC Press LLC
PDL + LL 1.347 = 6 × 20 × = 0.206 Ec ⋅ A 2033.65 × 0.385
ε b 500% = = 1.667 → OK 3 3
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Base Isolation
2.2 Stability check: σc =
P 1347 = = 3500 kN / m 2 A 0.385
≤ σc =
G ⋅ S ⋅ L (1.06 × 103 ) × 20 × 0.7 = = 49467 kN / m 2 → OK 2.5 ⋅ t r 2.5 × 0.12
3. Design result: dimensions of the HDR: Diameter of the bearing, d = 70 cm Total height of the bearing, h = 19.2 cm Number of rubber layers, N = 12 Thickness of individual layers, t = 1 cm Number of steel plates, Ns = 11 Thickness of individual plates, ts = 2 mm Thickness of top and bottom cover plates = 2.5 cm 4. Earthquake response analysis: 4.1 Structural periods obtained from dynamic analysis by ETABS [CSI, 1997]: TDpx = 1.71 sec TDpy = 1.67 sec 4.2 Minimum base shear Vb at the isolation interface: Vb,1 = K H × DD =
(∑ K ) × D eff
= (868 × 9) × 0.17 = 1328 kN
D
2
Vb, 2 =
WT g
(
2 2π 5209 2π × D = × 0.17 = 1278 kN T D 9.81 1.67 Dp
)
Vb = max Vb,1 , Vb, 2 = 1328 kN Design earthquake force of the superstructure above the isolation interface: Vs = Vb /RI = 1328/2 = 664 kN = 0.128 W T where the reduction factor RI is equal to 2 for all the isolation cases, as was mentioned previously. It must be noted that the design shear force Vs should be greater than the base shear of the fixed-base structure situated at the same site with a target period of 2.5 sec. 4.3 Vertical distribution of design earthquake forces: The lateral force Fx acting at level x of the isolated structure can be computed from the base shear force Vs by: Fx =
w x hx N
∑w h
× Vs
i i
i =1
where wx and wi are the weights at levels x and i, respectively, hx and hi are the respective heights of the structure above the isolation interface. By the preceding formula, the lateral forces computed for levels RF, 3F, and 2F are 320, 221, and 123 kN, respectively. The lateral force at level 1F is 1328 kN. By considering 5% of accidental eccentricity of the building dimensions, and by applying simultaneously 100% of the vertical and horizontal loads for the x direction and 30% of the horizontal loads for the y direction, the maximum compression force computed by the ETABS [CSI, 1997] program for the central isolator under the earthquake load PDL+LL+EQ is 1387 kN. Moreover, the drift ratios computed for levels RF, 3F, and 2F are 0.263%, 0.265%, and 0.261%, indicating that the isolated structure behaves like a rigid body under the earthquake motions. © 2003 by CRC Press LLC
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5. Checks on stability and rollout under the earthquake load: 5.1 Shear strain condition including the earthquake effect: PDL+LL+EQ = 1387 kN = 1.387 MN γ sc = 6S ⋅
PDL + LL + EQ Are ⋅ E c
= 6 × 20 ×
1.387 = 0.307 0.267 × 2033.65
γ eq = D / t r = 0.17 / 0.12 = 1.417 θ=
12DD × e 12 × 0.17 × (0.05 × 12) = = 0.006 b2 + d 2 122 + 82
γ sr =
B 2 ⋅ θ 70 2 × 0.006 = = 1.225 2 × 1 × 12 2 ⋅ t ⋅ tr
(Here B is interpreted as the diameter d for circular bearings): γ sc + γ eq + γ sr = 0.307 + 1.417 + 1.225 = 2.95 < 0.75 ε b = 0.75 × 500% = 3.75 → OK 5.2 Rollout condition: δ roll −out =
PDL + LL + EQ ⋅ L 1 1 1387 × 0.7 × = × 2 PDL + LL + EQ + K eff ⋅ h 2 1387 + 868 × 0.192
= 0.31 m = 31 cm > DD = 17 cm → OK (Here L is interpreted as the diameter d for circular bearings)
17.8.2 Lead Rubber Bearings Assume the following for the isolated structure with LRBs: (1) the design target period TD = 2.5 sec; (2) the laminated rubber bearing has a maximum shear strain of γmax = 50%; and (3) the effective damping ratio is ξeff = 10%. From Table 1623.2.2.1 of IBC 2000, the damping coefficient BD corresponding to the effective damping of ξeff = 10% for the LRB isolation system is 1.2. For the site condition of the isolated building with long period, the seismic coefficient is taken as SD = 0.4. 17.8.2.1 Analysis The effective horizontal stiffness of the isolator is: K eff =
W g
2π T D
2
2
= W = PDL + LL
1347 2π = 868 kN / m = 0.868 MN / m 9.8 2.5
The design displacement DD is: 9.8 0.4 × 2.5 g S T DD = 2 D D = 2 × = 0.21 m ≤ 0.3 m → OK 4 π BD 4π 1.2 The short term yield force Qd is: Qd =
© 2003 by CRC Press LLC
WD π π = K ξ D = × 868 × 10% × 0.21 = 28.6 kN 4 DD 2 eff eff D 2
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Base Isolation
The post-yield horizontal stiffness Kd is: Qd 28.6 = 868 − = 773 kN DD 0.21
K d = K eff − 17.8.2.2 Design
1. Design lead core: Assume the yield strength of the lead core to be fpy = 8.82 MN/m2. The required lead area is: Ap =
Qd 28.6 = = 0.325 × 10 −2 m 2 = 32.5 cm 2 f py 8.82 × 103
Use diameter dp = 7 cm. 2. Design the area and dimensions of rubber layers: 2.1 Total height of rubber layers: t r = DD /γmax = 0.21/0.5 = 0.42 m 2.2 Select the rubber properties from Table 17.1. Assume the rubber hardness to be IRHD-60 and the elongation of rubber at break is εb = 500%. The material properties obtained from Table 17.1 are: E = 445 N/cm2 = 4.45 MN/m2 G = 106 N/cm2 = 1.06 MN/m2 k = 0.57 2.3 Select the shape factor, S:
(
E ⋅ 1 + 2kS 2
) ≥ 400 → 445 ⋅ (1 + 2 × 0.57S ) ≥ 400 2
G → S > 9.09 → Use S = 20
(
)
(
106
)
E c = E ⋅ 1 + 2kS 2 = 445 ⋅ 1 + 2 × 0.57 × 20 2 = 203365 N / cm 2 = 2033.65 MN / m
2
2.4 Determine the effective area A0 of the bearing based on the allowable normal stress σc under the vertical load case PDL+LL: σc =
PDL + LL 1347 kN ≤ 7.84 MN / m 2 → ≤ 7.84 MN / m 2 A0 A0
→ A0 > 0.172 m 2 2.5 Determine the effective area A1 from the shear strain condition for the vertical load case PDL+LL: 6S
PDL + LL ε b 1.347 500% ≤ → 6 × 20 × ≤ E c ⋅ A1 3 2033.65 × A1 3
→ A1 > 0.048 m 2 2.6 Elastic stiffness Kr of the bearing: A 127 K d = K r 1 + 12 p → 773 = K r 1 + 12 × 1720 A0 → K r = 630 kN / m © 2003 by CRC Press LLC
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2.7 Determine the effective area A of individual rubber layers based on shear failure condition: Kr ⋅ tr K ⋅t 630 × 0.42 → Asf = r r = = 0.250 m 2 Asf G 1.06 × 103
G=
For a circular bearing, the diameter corresponding to the area Asf is d = 0.56 m. It follows that the effective area can be computed from Equation 17.39 as A2 = 0.132 m2: A = max(A0, A1, A2) = max(0.172, 0.048, 0.132) = 0.172 m2 2.8 Determine the size and dimensions of rubber layers. For circular bearings: Are ≤
d2 (β − sin β) 4
D β = 2 cos−1 D d → Diameter d = 0.7 m, area A = 0.385 m2, reduced area Are = 0.267 m2 2.9 Single layer thickness, t, and number of layers, N. For circular bearing: d 70 → 20 = → t = 0.88 cm; use t = 1 cm 4t 4t t r = N × t → 42 = N × 1 → N = 42 S=
Use N = 42. 2.10 Steel plate thickness ts: ts ≥ ts ≥
2(t i + t i +1 ) ⋅ PDL + LL Are ⋅ FS
2 ⋅ (0.01 + 0.01) × 1.347 = 0.0012 m = 1.2 mm 0.267 × (0.6 × 274.4)
Use t s = 2 mm. where, for A36 steel, Fs = 0.6Fy = 0.6 × 274.4 MN/m2 = 164.6 MN/m2: Are = 0.267 m2, β = 2 × cos–1(0.17/0.7) 2.11 Total height h of the bearing. Assume the thickness of the top and bottom cover plates both to be 2.5 cm. The total height is: h = t r + 41 × ts + 2 × 2.5 cm = 42 cm + 41 × 2 mm + 5 cm = 55.2 cm 3. Shear strain and stability conditions: 3.1 Vertical load PDL+LL: γ sc , DL + LL = 6S ⋅ ≤
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PDL + LL 1.347 = 6 × 20 × = 0.206 Ec ⋅ A 2033.65 × 0.385
ε b 500% = = 1.667 → OK 3 3
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3.2 Stability check: σc =
P 1347 = = 3498 kN / m 2 A 0.385
≤ σc =
G ⋅ S ⋅ L (1.06 × 103 ) × 20 × 0.7 = = 14,133 kN / m 2 → OK 2.5 ⋅ t r 2.5 × 0.42
3.3 Check on diameter of the lead core: 1.25 ≤
Hp dp
=
42 = 3.23 ≤ 5.0 → OK 13
4. Design result: dimensions of LRB: Diameter of the bearing, d = 70 cm Total height of the bearing, h = 55.2 cm Number of rubber layers, N = 42 Thickness of individual layers, t = 1 cm Diameter of the lead core, dp = 13 cm Number of steel plates, Ns = 41 Thickness of steel plates, ts = 2 mm Thickness of top and bottom cover plates = 2.5 cm 5. Earthquake response analysis: 5.1 Structural periods obtained from dynamic analysis by ETABS [CSI, 1997]: TDpx = 1.71 sec TDpy = 1.67 sec 5.2 Minimum base shear Vb at the isolation interface: Vb,1 = K H × DD =
(∑ K ) × D eff
D
= (868 × 9) × 0.21= 1,641 kN
2
2 W 2π 5209 2π Vb, 2 = T × D = × 0.21= 1,578 kN D g TDp 9.81 1.67
Vb = max (Vb,1 , Vb, 2 ) = 1, 641 kN Design earthquake force of the superstructure above the isolation interface Vs = Vb /RI = 1641/2 = 820 kN = 0.157 W T where RI = 2 has been used. 5.3 Vertical distribution of design earthquake forces. The lateral force Fx acting at level x of the isolated structure can be computed using the equation given below: Fx =
w x hx N
∑
× Vs
w ihi
i =1
where all the parameters are defined as those given previously. The lateral forces computed for levels RF, 3F, and 2F are 395, 273, and 152 kN, respectively. The lateral force for level 1F is 1641 kN. By considering 5% of accidental eccentricity of the building dimensions, and by applying simultaneously 100% of the vertical and horizontal loads for the x direction and © 2003 by CRC Press LLC
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30% of the horizontal loads for the y direction, the maximum compression force computed by the ETABS [CSI, 1997] program for the central isolator under the earthquake load PDL+LL+EQ is 1554 kN. The drift ratios computed for levels RF, 3F, and 2F are 0.325%, 0.327%, and 0.322%, indicating that the superstructure behaves essentially like a rigid body. 6. Checks on stability and rollout conditions under the earthquake load: 6.1 Shear strain condition for the earthquake load: PDL+LL+EQ = 1554 kN = 1.554 MN γ sc = 6S ⋅
PDL + LL + EQ Are ⋅ E c
= 6 × 20 ×
1.554 = 0.343 0.267 × 2033.65
γ eq = D / t r = 21 / 42 = 0.5 θ=
12DD × e 12 × 0.17 × (0.05 × 12) = = 0.006 b2 + d 2 122 + 82
γ sr =
B 2 ⋅ θ 70 2 × 0.006 = 0.35 = 2 × 1 × 42 2 ⋅ t ⋅ tr
γ sc + γ eq + γ sr = 0.34 + 0.5 + 0.35 = 1.19 < 0.75 ε b = 0.75 × 500% = 3.75 → OK 6.2 Rollout condition: δ roll-out =
1 PDL + LL + EQ ⋅ L − Qd ⋅ h 1 1554 × 0.7 − 28.6 × 0.552 × = × 2 2 1554 + 773 × 0.552 PDL + LL + EQ + K d ⋅ h
= 0.27 m = 27 cm > DD = 21 cm → OK
17.8.3
Frictional Pendulum Systems
Use the same target period of TD = 2.5 sec for the FPS isolated structure. Let the friction coefficient of the spherical sliding surface of the FPS be 0.06 and the design horizontal displacement D be 20 cm. 1. Determine the size of the FPS. The radius of curvature of the spherical sliding surface of the isolator is: 2
2
T 2.5 RFPS = g D = 9.8 = 1.55 m; use RFPS = 1.5 m 2π 2π 2. The total effective stiffness of the isolation system is given by:
∑K
eff
=
WT µWT 5209 0.06 × 5209 + = + = 5, 035 kN m RFPS D 1.5 0.2
Thus, the average effective stiffness Keff for a single FPS isolator is 5,035/9 = 560 kN/m. 3. The effective damping ξeff provided by the isolator depends on the design displacement D, which can be computed as: ξeff =
© 2003 by CRC Press LLC
2 2 0.06 µ = = 0.20 = 20% π µ + D / R π 0.06 + 0.2 / 1.5
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From Table 1623.2.2.1 of IBC 2000, the damping coefficient BD corresponding to ξeff = 20% for the FPS isolation system is found to be 1.5. For the site condition of the isolated building with long period, the seismic coefficient is taken as SD = 0.4. 4. Check the design displacement DD : 9.8 0.4 × 2.5 g S T DD = 2 D D = 2 × = 0.17 m ≤ D = 0.2 m → OK 4 π BD 4π 1.5 5. Estimate of the vertical displacement δv : δv ≅
D2 0.22 = = 0.013 m = 1.3 cm 2RFPS 2 × 1.5
Use depth δ = 1.7 cm for the disk. Use diameter d = 45 cm for the disk of the FPS (> 2D).
Check:
(d / 2)2 = (0.45 / 2)2 = 0.017 m ≥ 0.013 m → OK
2 × RFPS
2 × 1.5
6. Check on the recentering condition for the earthquake load case: D 0.2 = = 0.13 ≥ µ = 0.06 RFPS 1.5 → OK 7. Dimensions for the FPS: Radius of curvature of the spherical surface, RFPS = 1.5 m Depth of the disk, δ = 1.7 cm Diameter of the disk, d = 45 cm 8. Earthquake response analysis: 8.1 Structural periods obtained from dynamic analysis by ETABS [CSI, 1997]: TDpx = 2.042 sec TDpy = 2.036 sec 8.2 Minimum base shear Vb of the isolated building at the isolation interface: Vb,1 = K H × D =
(∑ K ) × D = 5035 × 0.2 = 1,007 kN eff
2
Vb, 2 =
WT g
2 2π 5209 2π × D = × 0.2 = 1,012 kN T 9.81 2.036 Dp
Vb = max (Vb,1 , Vb, 2 ) = 1, 012 kN Design earthquake force of the superstructure above the isolation interface: Vs = Vb /RI = 1012/2 = 506 kN = 0.097 W T where RI = 2 has been used.
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8.3 Vertical distribution of design earthquake forces. The lateral force Fx acting at level x of the isolated structure can be computed according to the following equation: Fx =
w x hx N
∑w h
× Vs
i i
i =1
where all parameters have been defined before. Using the preceding formula, the lateral forces computed for levels RF, 3F, and 2F are 244, 168, and 94 kN, respectively. The lateral force at level 1F is 1012 kN. By considering 5% of accidental eccentricity of the building and by applying simultaneously 100% of the vertical and horizontal loads for the x direction and 30% of the horizontal loads for the y direction, the minimum and maximum compression forces computed by the ETABS [CSI, 1997] program for the isolators under the earthquake load PDL+LL+EQ are 74 kN and 1410 kN, respectively. This result indicates that all the FPSs are subjected to the action of compressive forces, ensuring that the effect of friction can be developed. The drift ratios computed for levels RF, 3F, and 2F are 0.024%, 0.024%, and 0.019%, respectively, indicating that the superstructure can be essentially regarded as a rigid body.
17.9 Concluding Remarks While the application of various isolation devices for building construction has increased rapidly in recent years, the concept of seismic isolation is not a new one. Nowadays, many new materials and devices continue to be proposed for use in base isolation. The procedures presented in this chapter serve merely to illustrate the key concepts involved in initial sizing of the base isolation systems. It is the duty of the designer to make sure that the principles introduced herein are not violated by the specific isolators selected for their projects. For devices that tend to elongate the period of the protected structure, it is important to make sure that the structure is not located on a site with soft soils. For structures that are situated on soft soils or are of relatively long periods, only devices with energy dissipation mechanisms should be used. Compared with new construction, extra care must be taken in applying isolators to the rehabilitation of existing buildings, as there may exist additional restraints (historical, architectural, or other reasons) concerning the selection and installation of isolators.
References American Association of State Highway and Transportation Officials (AASHTO), 1983. Guide Specifications for Seismic Design of Highway Bridges, Washington, D.C. Bridgestone Corporation, 1990. Multi-Rubber Bearings, International Industrial Products Department, Tokyo. Chopra, A.K., 1995. Dynamics of Structures, Prentice-Hall, Englewood Cliffs, NJ. Computers and Structures, Inc. (CSI), 1997. ETABS Version 6.2: Three-Dimensional Building Systems, Berkeley, CA. Dynamic Isolation System, Inc., 1990. Force Control Bearings for Bridges, Berkeley, CA. Earthquake Protection Systems, Inc., 1993. Friction Pendulum Seismic Isolation Bearings, Berkeley, CA. Hall, J.F., 1999. “Discussion on ‘The Role of Damping in Seismic Isolation’,” Earthquake Eng. Struct. Dyn., 28, 1717–1720. Hall, J.F. and K.L. Ryan, 2000. “Isolated Buildings and the 1997 UBC Near-Source Factors,” Earthquake Spectra, 16, 393–411. International Code Council (ICC), 2000. International Building Code, International Code Council, Falls Church, VA.
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Iwan, W.D., 1980. “Estimating Inelastic Response Spectra from Elastic Spectra,” Earthquake Eng. Struct. Dyn., 8, 375–388. Iwan, W.D. and N.C. Gates, 1979. “The Effective Period and Damping of a Class of Hysteretic Structures,” Earthquake Eng. Struct. Dyn., 7, 199–221. Jangid, R.S. and J.M. Kelly, 2000. “Torsional Displacements in Base-Isolated Buildings,” Earthquake Spectra, 16, 443–454. Johnson, C.D. and D.A. Kienholz, 1982. “Finite Element Prediction of Damping in Structures with Constrained Viscoelastic Layers,” AIAA J., 20, 1284–1290. Kelly, J. M., 1986. “Aseismic Base Isolation: Review and Bibliography,” Soil Dyn. Earthquake Eng., 11, 135–146. Kelly, J. M., 1993. Earthquake-Resistant Design with Rubber, Springer-Verlag, New York. Kelly, J. M., 1999. “The Role of Damping in Seismic Isolation,” Earthquake Eng. Struct. Dyn., 28, 3–20. Lu, L.Y. and Y.B. Yang, 1997. “Dynamic Response of Equipment in Structures with Sliding Supports,” Earthquake Eng. Struct. Dyn., 26, 61–77. Mayes, R.L. and F. Naiem, 2001. “Design of Structures with Seismic Isolation,” in The Seismic Design Handbook, 2nd ed., Naiem, F., Ed., Kluwer Academic Publishers, Boston. Mostaghel, N., M. Hejazi, and J. Tanbakuchi, 1983. “Response of Sliding Structures to Harmonic Support Motions,” Earthquake Eng. Struct. Dyn., 11, 355–366. Naiem, F. and J.M. Kelly, 1999. Design of Seismic Isolated Structures, John Wiley & Sons, New York. Ryan, K.L. and A.K. Chopra, 2002. “Approximate Analysis Methods for Asymmetric Plan Base-Isolated Buildings,” Earthquake Eng. Struct. Dyn., 31, 33–54. Salomon, O., S. Oller, and A. Barbat, 1999. “Finite Element Analysis on Base Isolated Buildings Subjected to Earthquake Loads,” Int. J. Numer. Meth. Eng., 46, 1741–1761. Skinner, R.I., W.H. Robinson, and G.H. McVerry, 1993. An Introduction to Seismic Isolation, John Wiley & Sons, New York. Tsai, C.S., 1997. “Finite Element Formulations for Friction Pendulum Seismic Isolation Bearings,” Int. J. Numer. Meth. Eng., 40, 29–39. Westermo, B. and F. Udwadia, 1983. “Periodic Response of a Sliding Structure to Harmonic Excitation,” Earthquake Eng. Struct. Dyn., 11, 135–146. Yang, Y.B., T.Y. Lee, and I.C. Tsai, 1990. “Response of Multi-Degree-of-Freedom Structures with Sliding Supports,” Earthquake Eng. Struct. Dyn., 19, 739–752. Zayas, V.A., S.S. Low, and S.A. Mahin, 1987. The FPS Earthquake Resisting System: Experimental Report, Report No. UCB/EERC-87/01, Earthquake Engineering Research Center, University of California, Berkeley.
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18 Bridges 18.1 Introduction 18.2 Earthquake Damages to Bridges 18.3 Seismic Design Philosophies Design Evolution · No-Collapse-Based Design · PerformanceBased Design
18.4 Seismic Conceptual Design 18.5 Seismic Performance Criteria ATC/MCEER Guidelines · Caltrans
18.6 Seismic Design Approaches ATC/MCEER Guidelines, 2001 · Caltrans Seismic Design
18.7 Seismic Analysis and Modeling
Lian Duan California Department of Transportation Sacramento, CA
Wai-Fah Chen University of Hawaii at Manoa Honolulu, HI
Equivalent Static Analysis · Elastic Response Spectrum Analysis · Nonlinear Dynamic Analysis · Global and Stand-Alone Analysis · Inelastic Static Analysis: Push Over Analysis · Moment-Curvature Analysis · Random Vibration Approach
18.8 Seismic Detailing Requirements ATC/MCEER Guidelines · Caltrans SDC
Defining Terms. References
18.1 Introduction Bridges are very important elements in the modern transportation system. Recent earthquakes, particularly the 1989 Loma Prieta and the 1994 Northridge earthquakes in California, the 1995 Hyogo-Ken Nanbu earthquake in Japan, the 1999 Jiji earthquake in Taiwan, and the 1999 Kocaeli earthquake in Turkey, have caused collapse of, or severe damage to, a considerable number of major bridges [Moehle and Eberhard, 2000; Yashinsky, 2000]. Since the 1989 Loma Prieta earthquake in California [Housner, 1990], extensive research [Caltrans, 1991, 1993, 1994, 1996, 1998, 2001; FHWA, 1995, 1997; Kawashina and Unjoh, 1997; Park, 1994; Astaneh-Asl and Roberts, 1993, 1997; Housner, 1994; Priestley et al., 1996; FHWA-NSF, 2000 ] has been conducted on seismic design and retrofit of bridges in Japan and the United States, especially in California. This chapter first addresses seismic bridge design philosophies and conceptual design in general, and then discusses seismic design practice in the United States to illustrate the process.
18.2 Earthquake Damages to Bridges Past earthquakes have shown that the damage induced in bridges can take many forms, depending on the ground motion, site conditions, structural configuration, and specific details of the bridge [Moehle and Eberhard, 2000]. Damage within the superstructure is rarely the primary cause of collapse. Most of the severe damage to bridges has taken one of the following forms [Moehle and Eberhard, 2000]:
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FIGURE 18.1 Collapse of the eastern portion of the San Francisco–Oakland Bay Bridge in the 1989 Loma Prieta earthquake. (Courtesy California Department of Transportation, Sacramento, CA) Shown as Color Figure 18.1.
• Unseating of the superstructure at in-span hinges or simple supports due to inadequate seat lengths or restraint. A skewed, curved, or complex configuration further increases the vulnerability. Figure 18.1 shows the collapsed upper and lower decks of the eastern portion of the San Francisco–Oakland Bay Bridge (SFOBB) in the 1989 Loma Prieta earthquake, which can be attributed to fixed-shoe anchor bolt failures allowing shoes to move east. Figure 18.2 shows the collapsed I-5 Gavin Canyon Undercrossing in the 1994 Northridge earthquake, which can be attributed to geometric complexities arising from 66° skew angle abutments, in-span expansion joints, and an inadequate 300-mm seat width. For simply supported bridges, these failures are most likely when ground failure induces relative motion between the spans and their supports. • Column brittle failure due to deficiencies in shear design and inadequate ductility. In reinforced concrete columns, the inadequate shear design and ductility usually stems from inadequate lateral and confinement reinforcement. Figure 18.3 shows the 600-m collapsed portion of the Hanshin Expressway in the 1995 Hyogo-Ken Nanbu earthquake in Japan. These failures were attributed to deficiencies in shear design and poor ductility. In steel columns, the inadequate ductility usually stems from progressive local buckling, fracture, and global buckling leading to collapse. • Unique failures in complex structures. Figure 18.4 shows the collapsed Cypress Street Viaduct in the 1989 Loma Prieta earthquake, where the unique vulnerability was the inadequately reinforced pedestal above the first level. In outrigger column bents, the vulnerability may be in the cross-beam or the beam–column joint.
18.3 Seismic Design Philosophies 18.3.1 Design Evolution Seismic bridge design has been improving and advancing, based on research findings and lessons learned from past earthquakes. In the United States, prior to the 1971 San Fernando earthquake, the seismic design of highway bridges was partially based on lateral force requirements for buildings. © 2003 by CRC Press LLC
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FIGURE 18.2 Collapse of the I-5 Gavin Canyon Undercrossing, California, in the 1994 Northridge earthquake. Shown as Color Figure 18.2.
FIGURE 18.3 Collapse of the Hanshin Expressway in the 1995 Hyogo-Ken Nanbu earthquake in Japan. (Courtesy Mark Yashinsky) Shown as Color Figure 18.3.
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FIGURE 18.4 Collapse of Cypress Viaduct, California in the 1989 Loma Prieta earthquake.
Lateral loads were considered as levels of 2 to 6% of dead loads. In 1973, the California Department of Transportation (Caltrans) developed new seismic design criteria related to site, seismic response of the soils at the site, and dynamic characteristics of bridges. The American Association of State Highway and Transportation Officials (AASHTO) modified the Caltrans 1973 provisions slightly, and adopted interim specifications. In 1981 the Applied Technology Council (ATC) developed guidelines, ATC-6, for seismic design of bridges [ATC, 1981]. AASHTO adopted ATC-6 as the guide specifications in 1983 and later, in 1991, incorporated it into the Standard Specifications for Highway Bridges [1996]. Prior to the 1989 Loma Prieta earthquake, bridges in California were typically designed using a singlelevel, force-based design approach based on a “no-collapse” design philosophy. Seismic loads were determined based on a set of soil conditions and a suite of four site-based standard acceleration response spectra (ARS). Structures were analyzed using the three-dimensional elastic dynamic multimodal response spectrum method. Structural components were designed by using a reduction Z factor to reduce seismic forces for ductility and risk. Minimum transverse reinforcement confinements were required [Caltrans, 1990]. In Japan, seismic design for highway bridges started in 1924, 1 year after the 1923 Great Kanto earthquake. In 1971 the modern Specifications for Seismic Design of Highway Bridges, which introduced design methods for soil liquefaction and unseating prevention devices, was published. In 1980 it was revised and integrated as “Part V: Seismic Design” in Design Specifications of Highway Bridges including the primitive check method for ductility of reinforced concrete piers. In 1990 it was further modified to recommend a detailed ductility check method for reinforced concrete piers, soil liquefaction, dynamic response analysis, and design detailing. After the destructive 1995 Hyogo-ken Nanbu earthquake, the bridge seismic design specifications were completely revised and new comprehensive Design Specifications of Highway Bridges [Japan Road Association, 1996] were published in 1996. The design procedure was moved from the traditional seismic coefficient method to the ductility design method. A detailed discussion can be found in “Seismic Design Practice in Japan” by Unjoh [2000]. Since 1989, the design criteria specified in Caltrans BDS [1990] and several design manuals [Caltrans, 1995a, 1995b, 1999, 2000] have been updated continuously to reflect recent research findings and development in the field of seismic bridge design. Caltrans has been shifting toward a displacementbased design approach emphasizing capacity design. The performance-based project-specific design criteria [Caltrans, 1997, 1999; IAI, 1995] have been developed for important bridges in California since 1989. FHWA updated its Seismic Design and Retrofit Manual for Highway Bridges in 1995 [FHWA, 1987, © 2003 by CRC Press LLC
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1995]. ATC published the improved seismic design criteria recommendations for California bridges in 1996 [ATC, 1996], and for U.S. bridges and highway structures [Rojahn et al., 1997] in 1997. Caltrans published the performance- and displacement-based Seismic Design Criteria (SDC) Version 1.2 [Caltrans, 2001a], which focuses mainly on concrete bridges, and the Guide Specifications for Seismic Design of Steel Bridges [Caltrans, 2001b] in 2001. Most recently, the NCHRP 12–49 team developed a new set of LRFD Guidelines for the seismic design of highway bridges [ATC/MCEER, 2001], compatible with the AASHTO-LFRD Bridge Design Specifications [AASHTO, 1998–2000]. Significant advances in earthquake engineering have been made during this last decade of the twentieth century.
18.3.2 No-Collapse-Based Design The basic design philosophy is to prevent bridges from collapse during severe earthquakes [Caltrans, 1995a, 1995b, 1999, 2000, 2001a, 2001b; ATC/MCEER, 2001] that have only a small probability of occurring during the useful life of the bridge. To prevent collapse, two alternative approaches are commonly used in design. The first is a conventional force-based approach where the adjustment factor Z for ductility and risk assessment [Caltrans, 1990], or the response modification factor R [AASHTO, 1996; ATC/MCEER, 2001], is applied to elastic member forces obtained from a response spectra analysis or an equivalent static analysis. The second approach is a more recent displacement-based approach [Caltrans, 1999, 2001a] where displacements are a major consideration in design. For more detailed information, reference can be made to comprehensive discussions in Seismic Design and Retrofit of Bridges [Priestley et al., 1996] and the Bridge Engineering Handbook [Chen and Duan, 2000] [see also Priestley, 1993; Kowlasky et al., 1994].
18.3.3 Performance-Based Design Following the 1989 Loma Prieta earthquake, bridge engineers [Housner, 1990] have faced three essential challenges: • Ensure that earthquake risks posed by new construction are acceptable. • Identify and correct unacceptable seismic safety conditions in existing structures. • Develop and implement the rapid, effective, and economic response mechanism for recovering structural integrity after damaging earthquakes. The performance-based project-specific criteria [Caltrans, 1997, 1999; IAI, 1995] and the design memoranda [Caltrans, 1999] have been developed and implemented for the design and retrofitting of important bridges by California bridge engineers. These performance-based criteria included guidelines for development of site-specific ground motion estimates, capacity design to preclude brittle failure modes, rational procedures for concrete joint shear design and the definition of limit states for various performance objectives [Housner, 1994]. The performance-based criteria usually require two-level design. The first level of design is to ensure the performance (service) of a bridge in earthquake events that have relatively small magnitude but may occur several times during the life of the bridge. The second level of design is to achieve the performance (no collapse) of a bridge under the severe earthquakes that have only a small probability of occurring during the useful life of the bridge. The performance-based criteria should include guidelines for development of site-specific ground motion estimates, capacity design to preclude brittle failure modes, rational procedures for joint shear design in concrete, and the definition of limit states for various performance objectives. Figure 18.5 shows a flowchart for development of performance-based seismic design criteria.
18.4 Seismic Conceptual Design Bridge design is a complex engineering process involving consideration of numerous important factors, such as bridge systems, materials, dimensions, foundations, aesthetics, and local landscape and surrounding environment [Priestley et al., 1996; Troitsky, 2000]. Selecting an appropriate earthquake-resisting © 2003 by CRC Press LLC
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Criteria Development START
Establish Post-Earthquake Performance Requirements
Determine Bridge Specific Loads and Combinations
Determine Materials and Their Properties
Determine Analysis Methods for Demand Evaluation
Determine Detailed Procedure for Capacity Evaluation
Establish Detailed Performance Acceptance Criteria
Criteria Development END FIGURE 18.5 Development of performance-based seismic design criteria.
system to resolve the potential conflicts between the configuration and seismic performance should be completed as early as possible in the design effort. For a desirable seismic-resistance design, the following guidelines may be useful: • Bridge type, component and member dimensions, and aesthetics should be investigated to reduce the seismic demands to the greatest extent possible. Aesthetics should not be the primary reason for producing undesirable frame and component geometry. • Bridges should be as straight as possible. Curved bridges complicate and potentially magnify seismic responses. • Superstructures should be continuous with as few joints as possible. Necessary restrainers and sufficient seat width should be provided between adjacent frames at all expansion joints, and at the seat-type abutments to eliminate the possibility of unseating during a seismic event. Simply supported spans should not rely on abutments for any seismic resistance. • Skew angles should be as small as possible, i.e., abutments and piers should be oriented as close to perpendicular to the bridge longitudinal axis as possible even at the expense of increasing the bridge length. Skewed abutments and piers are highly vulnerable to damage due to undesired rotation response and increased seismic displacement demands. • Adjacent frames or piers should be proportioned to minimize the differences in the fundamental periods and skew angles, and to avoid drastic changes in stiffness and strength in both © 2003 by CRC Press LLC
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the longitudinal and transverse directions. Dramatic changes in stiffness result in damage to the stiffer frames or piers. It is strongly recommended [Caltrans, 2001] that the effective stiffness between any two bents within a frame, or between any two columns within a bent, not vary by a factor of more than two. Similarly, it is highly recommended that the ratio of the shorter fundamental period to the longer fundamental period for adjacent frames in the longitudinal and transverse directions be larger than 0.7. Each frame should provide a welldefined load path with predetermined plastic hinge locations and utilize redundancy whenever possible. Balanced mass and stiffness distribution (Figure 18.6) in a frame results in a structure response that is more predictable and is more likely to respond in its fundamental mode of vibration. Simple analysis tools can then be used to predict the response of the structure with relative accuracy, whereas irregularities in geometry increase the likelihood of complex nonlinear response that is difficult to accurately predict by elastic modeling or plane frame inelastic static analysis. The following techniques may be used to achieve balanced geometry to create a uniform and more predictable structure response [Keever, 2000]: • Use oversized pile shafts • Adjust effective column lengths (e.g., lower footings, isolation casings) • Modify end fixities • Reduce/redistribute superstructure mass • Vary the column cross section and/or longitudinal reinforcement ratios • Add or relocate columns/piers • Modify the hinge/expansion joint layout • In the event that other constraints prevent the designer from achieving balance between frames of a bridge, the following recommendations may be considered [Caltrans, 2001a]: • Isolate adjacent frames longitudinally by providing a large expansion gap to reduce the likelihood of pounding. • Provide adequate seat width to prevent unseating at hinges. Seat extenders may be used; however, they should be isolated transversely to avoid transmitting large lateral shear forces between frames. • Limit the transverse shear capacity between frames to prevent large lateral forces from being transferred to the stiffer frame. • Avoid placing hinge seats between unbalanced frames by placing expansion joints between frames with short cantilever spans that butt up to one another. • Seismic protective devices, i.e., energy dissipation and isolation devices, may be provided at appropriate locations, thereby reducing the seismic force effects. The energy dissipation devices increase the effective damping of the structure by adding dampers to the structure, thereby reducing forces, deflections, and impact loads. Isolation devices lengthen the fundamental mode of vibration by providing isolation at bearing locations so that the structure is subject to lower earthquake forces. • For concrete bridges, structural components should be proportioned to direct inelastic damage into the columns, pier walls, and abutments. The superstructure should have sufficient overstrength to remain essentially elastic if the columns/piers reach their most probable plastic moment capacity. The superstructure–substructure connection for nonintegral caps may be designed to fail prior to generating inelastic response in the superstructure. The girders, bent caps, and columns should be proportioned to minimize joint stresses. Concrete columns should be well proportioned, moderately reinforced and easily constructed. Moment-resisting connections should have sufficient joint shear capacity to transfer the maximum plastic moments and shears without joint distress.
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FRAME 1
FRAME 2
BENT 2
BENT 6 BENT 3 BENT 5
BENT 4
T1 m2
T2
m3
m4
m5
k2
m6 k6
k3
k4
k5
k2
k1
BENT 3
FIGURE 18.6 Frame stiffness. (From Caltrans. 2001a. Seismic Design Criteria, Version 1.2, California Department of Transportation, Sacramento, CA, December.)
• Initial sizing of columns should be based on slenderness ratios, bent-cap depth, compressive deadto-live load ratio, and service loads. Columns should demonstrate dependable postyield displacement capacity without an appreciable loss of strength. Thrust-moment curvature (P-M-Φ) relationships should be used to optimize a column’s performance under service and seismic loads. Abrupt changes in the cross section and the capacity of columns should be avoided. Columns must have sufficient rotation capacity to achieve the target displacement ductility requirements. • For steel bridges, structural components should be generally designed to ensure that inelastic deformation only occurs in the specially detailed ductile substructure elements. Inelastic behavior in the form of controlled damage may be permitted in some of the superstructure components, such as the cross frames, end diaphragms, shear keys, and bearings. The inertial forces generated by the deck must be transferred to the substructure through girders, trusses, cross frames, lateral bracings, end diaphragms, shear keys, and bearings. As an alternative, specially designed ductile end diaphragms may be used as structural mechanism fuses to prevent damage in other parts of structures. • Steel multicolumn bents or towers should be designed as ductile moment-resisting frames (MRF) or ductile braced frames, such as concentrically braced frames (CBF) or eccentrically © 2003 by CRC Press LLC
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Longitudinal
Longitudinal
Abutment resistance not required as part of ERS
Abutment not required as part of ERS
Plastic hinges in inspectable locations or elastic design of columns. Knock-off backwalls permissible
Isolation bearings accomodate full displacement
Transverse
Abutment not required in ERS, breakaway shear keys permissible Plastic hinges in inspectable locations or elastic design of columns.
Longitudinal and Transverse
Isolation bearings with significant energy dissipation capacity or energy dissipators are used at the abutment to limit overall displacements Plastic hinges in inspectable locations or elastic design of columns.
Transverse or Longitudinal
Abutment resistance required, but abutment able to resist 3% in 75-year earthquake elastically and passive soil pressure in longitudinal direction is less than 0.70 × presumptive value.
Longitudinal
Multiple simply supported spans with adequate seat widths. Plastic hinges in inspectable locations or elastic design of columns.
FIGURE 18.7 Permissible earthquake-resisting systems. (From ATC/MCEER Joint Venture. 2001. Recommended LRFD Guidelines for the Seismic Design of Highway Bridges, Parts I, II, and III. ATC-49a and ATC-49b, Applied Technology Council, Redwood City, CA and MCEER-02-SP01, Multidisciplinary Center for Earthquake Engineering Research, State University of New York at Buffalo. With permission.)
braced frames (EBF). For components expected to behave inelastically, elastic buckling (local compression and shear, global flexural, and lateral torsion) and fracture failure modes should be avoided. All connections and joints should preferably be designed to remain essentially elastic. For MRFs, the primary inelastic deformation should preferably be columns. For CBFs, diagonal members should be designed to yield when members are in tension and to buckle inelastically when they are in compression. For EBFs, a short-beam segment designated as a “link” should be well designed and detailed. • The ATC/MCEER-recommended LRFD guidelines [ATC/MCEER, 2001] classify earthquakeresisting systems (ERS) into permissible and not recommended categories (Figures 18.7 to 18.11) based on consideration of the most desirable seismic performance ensuring, wherever possible, postearthquake serviceability. Figure 18.12 shows design approaches for the permissible ERS.
18.5 Seismic Performance Criteria 18.5.1 ATC/MCEER Guidelines Table 18.1 gives the seismic performance criteria for highway bridges specified in the proposed ATC/ MCEER guidelines [ATC/MCEER, 2001]. As a minimum, bridges should be designed for the life-safety © 2003 by CRC Press LLC
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Above ground plastic hinges Plastic hinges below cap beams including pile bents
Seismic isolation bearings (or bearings designed to accommodate expected seismic displacements with no damage)
Tensile yielding and inelastic compression buckling of ductile concentrically braced frames
Piles with ‘pinned-head’ conditions Columns with moment reducing hinge details Capacity-protected pile caps, including caps with battered piles, which behave elastically
Plastic hinges at base of wall piers in weak direction
Spread footings that meet 1\2 uplift criteria
Wall piers designed to resist 3% in 75-year induced elastic forces in transverse direction
Passive abutment resistance required as part of ERS Passive strength = 0.70 × presumptive value
Seat abutments whose backwall is not designed to fuse, whose gap is not sufficient to accommodate the seismic movement, and which is designed for the expected impact force
FIGURE 18.8 Permissible earthquake-resisting elements. (From ATC/MCEER Joint Venture. 2001. Recommended LRFD Guidelines for the Seismic Design of Highway Bridges, Parts I, II, and III. ATC-49a and ATC-49b, Applied Technology Council, Redwood City, CA and MCEER-02-SP01, Multidisciplinary Center for Earthquake Engineering Research, State University of New York at Buffalo. With permission.)
level of performance. The higher level of performance may be required depending upon the bridge’s importance and owner’s requirements. The seismic performance criteria shown in Table 18.1 can be achieved with the following design objectives: • Columns as primary energy dissipation mechanism: The main objective is to force the inelastic deformations to occur primarily in the columns in order that the earthquake damage can be easily inspected and readily repaired after an earthquake. The amount of longitudinal steel in the reinforced columns should be minimized to reduce foundation and connection costs. • Abutments as an additional energy dissipation mechanism: The objective is to expect the inelastic deformations to occur in the columns as well as the abutments in order to either minimize column size and/or reduce ductility demand on the column. © 2003 by CRC Press LLC
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• Isolation bearings as main energy dissipation mechanism: The objective is to lengthen the period of a relatively stiff bridge and result in a lower design force. Energy dissipation will occur in the isolation bearings and columns are expected to perform elastically. • Structural components between deck and columns/abutments as energy dissipation mechanism: The objective is to design ductile components which do not result in reduced design force but will reduce the ductility demands on the columns in order to minimize the energy that is dissipated in the plastic hinge zone of columns. • Replaceable/renewable sacrificial plastic hinge elements as energy dissipation mechanism: The objective is to control damage and permit significant inelastic deformation to occur at specially designed, replaceable/renewable sacrificial plastic hinge elements in the plastic hinge zone of a column. The concept is similar to the conventional ductile design concept that permits significant inelastic deformation in the plastic hinge zone of a column. The difference with the conventional ductile design is that construction details in the plastic hinge zone of concrete columns provide a replaceable/renewable sacrificial plastic hinge elements. The concept has been extensively tested [Chang and Mander, 1997] but has not been used in practice.
18.5.2 Caltrans Table 18.2 outlines Caltrans’ seismic performance criteria [1999], including the bridge classification and service and damage levels established in 1994 [Housner, 1994]. A bridge is categorized as “Important” or “Ordinary”. For standard Ordinary bridges, the displacement-based, one-level safety-evaluation design (“no-collapsed” design) is only required in the Caltrans SDC [Caltrans, 2001a]. Nonstandard Ordinary bridges feature irregular geometry and framing (multilevel, variable width, bifurcating, or highly horizontally curved superstructures, different structure types, outriggers, unbalanced mass and/or stiffness, high skew) and unusual geologic conditions (soft soil, moderate to high liquefaction potential, and proximity to an earthquake fault). In this case, project specific criteria need to be developed to address their nonstandard features. For Important bridges such as the SFOBB and the Benicia-Martinez Bridge, performance-based project-specific, two-level seismic design criteria [Caltrans, 1997, 1999; IAI, 1995] are required. The seismic performance criteria shown in Table 18.2 can be achieved with the following design objectives: • All bridges should be designed to withstand deformation imposed by the design earthquake. • All structural components have sufficient strength and/or ductility to ensure collapse will not take place during a maximum credible earthquake (MCE), the largest earthquake that can occur, based on current geologic information. Ductile behavior can be provided by inelastic actions either through selected structural members and/or through protective systems — seismic isolations and energy dissipation devices. • Inelastic behavior should be limited to the pre-identified locations, i.e., ductile components explicitly designed for ductile performance, within the bridge that are easily inspected and repaired following an earthquake. Because inelastic response of concrete superstructures is difficult to inspect and repair and superstructure damage may cause the bridge to be in an unserviceable condition, inelastic behavior on most concrete bridges should preferably be located in columns, pier walls, backwalls, and wingwalls. • Structural components not explicitly designed for ductile performance, i.e., capacity-protected components, should be designed to remain essentially elastic. That is, response in concrete components should be limited to minor cracking or limited to force demands not exceeding the nominal strength capacity determined by current Caltrans SDC [2001a]; and response in steel components should be limited to force demands not exceeding the nominal strength capacity determined by current Caltrans guidelines [2001b]. To assure the desired yielding mechanism occurs the capacity design principle is exercised by providing overstrength for those capacityprotected components. © 2003 by CRC Press LLC
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Passive abutment resistance required as part of ERS Passive strength = presumptive value OANR: Use 70% of presumptive strength
Sliding of spread footing abutment allowed to limit force transferred OANR: Design for no sliding
Ductile diaphragms in superstructure
OANR: Yielding restricted to substructure
Foundations permitted to rock beyond 1/2 uplift limit or exceed ultimate bearing stress and a linear stress distribution OANR: Use 1/2 uplift and linear stress distribution
Seat abutments whose backwall is not designed to fuse, whose gap is not sufficient to accommodate the seismic movement, and which is not designed for the expected impact force OANR: Design to fuse or design for the appropriate design forces and displacements Wall piers on pile foundations that are not strong enough to force plastic hinging into the wall, and are not designed for the 3% in 75-year elastic forces
OANR: Force hinging into the wall with multiple pile lines and pile cap
More than the outer line of piles in group systems allowed to plunge or uplift under seismic loadings
OANR: Only outer line is permitted to reach tension capacity Plumb piles that are not capacity-protected (e.g. integral abutment piles or pile-supported seat abutments that are not fused transversely)
OANR: Use seat abutment or a detail that allows movement Batter pile systems in which the geotechnical capacities and/or in-ground hinging define the plastic mechanisms
In-ground hinging in shafts or piles (Deformation limits in Section 5)
OANR: Plastic hinging forced to occur above ground in column Columns with Architectural Flares − with or without an isolation gap
OANR: Force hinging to occur above ground with larger in-ground shaft isolation gap optional
OANR: Remove flare Note: OANR means a design alternative where owners’ approval is not required and a higher level of analysis (pushover in SDAP E) can be avoided.
FIGURE 18.9 Permissible earthquake-resisting elements that require owner’s approval. (From ATC/MCEER Joint Venture. 2001. Recommended LRFD Guidelines for the Seismic Design of Highway Bridges, Parts I, II, and III. ATC49a and ATC-49b, Applied Technology Council, Redwood City, CA and MCEER-02-SP01, Multidisciplinary Center for Earthquake Engineering Research, State University of New York at Buffalo. With permission.)
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Plastic hinges in superstructure
Bearing systems that do not provide for the expected displacements and/or forces (e.g. rocker bearings)
Cap beam plastic hinging (particularly hinging that leads to vertical girder movement) also includes eccentric braced frames with girders supported by cap beam
Battered-pile systems that are not designed to fuse geotechnically or structurally by elements with adequate ductility capacity
FIGURE 18.10 Earthquake-resisting elements that are not recommended for new bridges. (From ATC/MCEER Joint Venture. 2001. Recommended LRFD Guidelines for the Seismic Design of Highway Bridges, Parts I, II, and III. ATC49a and ATC-49b, Applied Technology Council, Redwood City, CA and MCEER-02-SP01, Multidisciplinary Center for Earthquake Engineering Research, State University of New York at Buffalo. With permission.) Knock-off curb
Shear key fuse
Knock-off backwall Knock-off top at roadway level
Seat and superstructure gap adequate to accommodate displacement Knock-off tab
FIGURE 18.11 Methods of minimizing damage to abutment foundation. (From ATC/MCEER Joint Venture. 2001. Recommended LRFD Guidelines for the Seismic Design of Highway Bridges, Parts I, II, and III. ATC-49a and ATC-49b, Applied Technology Council, Redwood City, CA and MCEER-02-SP01, Multidisciplinary Center for Earthquake Engineering Research, State University of New York at Buffalo. With permission.) © 2003 by CRC Press LLC
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Are abutments assumed to resist lateral forces? Yes
No
SDAP D and E
FIGURE 18.12 Design approaches for permissible earthquake-resisting systems. (From ATC/MCEER Joint Venture. 2001. Recomme nded LRFD Guidelines for the Seismic Design of Highway Bridges, Parts I, II, and III. ATC-49a and ATC-49b, Applied Technology Council, Redwood City, CA and MCEER-02-SP01, Multidisciplinary Center for Earthquake Engineering Research, State University of New York at Buffalo. With permission.)
Yes
SDAP B, C, D and E
Owners’ Approval Required. Is inelastic response required at substructure location that is not inspectable?
No
TABLE 18.1 Recommended LRFD Guidelines: Design Earthquakes and Seismic Performance Objectives Performance Level(1)
Probability of Exceedance for Design Earthquake Ground Motions(4) Rare earthquake (MCE) 3% PE in 75 years/1.5 mean deterministic Expected earthquake 50% PE in 75 years
Life Safety Service(2) Damage(3) Service Damage
Significant disruption Significant Immediate Minimal
Operational Immediate Minimal Immediate Minimal to none
Notes: (1) Performance levels are defined in terms of their anticipated performance objectives in the upper level earthquake: life safety in an MCE event — the bridge should not collapse but partial or complete replacement may be required. Since a dual-level design is required, the life-safety performance level will have immediate service and minimal damage for the expected design earthquake; operational for both rare and expected earthquakes, the bridge should be immediate service and minimal damage. (2) Service levels: immediate — full access to normal traffic should be available to traffic following an inspection of the bridge; significant disruption — limited access (reduced lanes, light emergency traffic) may be possible after shoring; however, the bridge may need to be replaced. (3) Damage levels: none — evidence of movement may be present but no notable damage; minimal — some visible signs of damage and minor inelastic response may occur, but postearthquake damage is limited to narrow flexural cracking in concrete and the onset of yielding in steel, permanent deformation are not apparent, and any repairs could be made under nonemergency conditions with the exception of superstructure joints; significant — although there is no collapse, permanent offsets may occur and damage consisting of cracking, reinforcement yield, and major spalling of concrete and extensive yielding and local buckling of steel columns, global and local buckling of steel braces, and cracking in the bridge deck slabs at shear studs on the seismic load path is possible. These conditions may require closure to repair the damage. Partial or complete replacement of columns may be required in some cases. For sites with lateral flow due to liquefaction, significant inelastic deformation is permitted in the piles, whereas for all other sites the foundations are capacity-protected and no damage is permitted in the pile. Partial or complete replacement of the columns and piles may be necessary if significant lateral flow occurs. If replacement of columns or other components is to be avoided, the design approaches producing minimal or moderate damage such as seismic isolation or the control and repairability design concept should be assessed. (4) The upper-level earthquake considered in the guidelines is designated the Maximum Considered Earthquake, or MCE. In general the ground motions or national MCE ground motion maps have a probability of exceedance (PE) of approximately 3% PE in 75 years; however, adjacent to highly active faults, ground motions on MCE maps are bounded deterministically as described in the Commentary for Article 3.2. When bounded deterministically, MCE ground motions have a probability of exceedance higher than 3% PE in 75 years not to exceed 1.5 times the mean deterministic values. The performance objective for the expected earthquake is either explicitly included as an elastic design for the 50% PE in 75-year force level or results implicitly from design for the 3% PE in 75-year force level. Source: ATC/MCEER Joint Venture, ATC Report Nos. ATC-49a and ATC-49b, Applied Technology Council, Redwood City, CA; and Report No. MCEER-02-SP01, Multidisciplinary Center for Earthquake Engineering Research, State University of New York at Buffalo, November 2001. With permission.
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TABLE 18.2 Caltrans Seismic Performance Criteria Level of Damage and Postearthquake Service Ground Motions at the Site Functional — Evaluation Ground Motion Safety — Evaluation Ground Motion
Ordinary Bridge
Important Bridge
Service: Immediate Damage: Repairable Service: Limited Damage: Significant
Service: Immediate Damage: Minimal Service: Immediate Damage: Repairable
Definitions: Important bridge: a bridge meets one or more of the following requirements, 1. required to provide postearthquake life safety, such as access to emergency facilities; 2. time for restoration of functionality after closure would create a major economic impact; 3. formally designed as critical by a local emergency plan. Ordinary bridge: any bridge not classified as an important bridge. Functional evaluation ground motion (FEGM): this ground motion may be assessed either deterministically or probabilistically. The determination of this event is to be reviewed by a Caltrans-approved consensus group. Safety evaluation ground motion (SEGM): this ground motion may be assessed either deterministically or probabilistically. The deterministic assessment corresponds to the MCE, the probabilistic ground motion for the safety evaluation typically has a long return period (approximately 1000—2000 years). MCE: the largest earthquake that is capable of occurring along an earthquake fault, based on current geologic information as defined in the 1996 Caltrans Seismic Hazard Map. Service levels: immediate: full access to normal traffic is available almost immediately following the earthquake; limited: limited access (e.g., reduced lanes, light emergency traffic) is possible within days of the earthquake, full service is restorable within months. Damage levels: minimal: essentially elastic performance; repairable: damage that can be repaired with a minimum risk of losing functionality; significant: a minimum risk of collapse, but damage that would require closure to repair. Source: Caltrans, Bridge Memo to Designers, California Dept. of Transportation, Sacramento, CA, 1999.
18.6 Seismic Design Approaches 18.6.1 ATC/MCEER Guidelines, 2001 18.6.1.1 Seismic Loads Seismic loads are represented by the design response spectrum curve for a damping ratio of 5% (Figure 18.13): SDS 0.6 T T + 0.4SDS 0 Sa = SDS S D1 T
for T ≤ T0 = 0.2TS for T0 < T ≤ TS =
SD1 SDS
(18.1)
for T > TS
Sps = FaSs
(18.2)
SD1 = Fv S1
(18.3)
where SDS = design earthquake response spectral acceleration at short periods SD1 = design earthquake response spectral acceleration at 1-sec period Ss = 0.2-sec period spectral acceleration on Class B rock from national ground motion maps [U.S. Geological Survey, 2001] S1 = 1-sec period spectral acceleration on Class B rock from national ground motion maps [U.S. Geological Survey, 2001] Fa = site coefficient (Table 18.3) for short-period portion of design response spectrum curve Fv = site coefficient (Table 18.4) for long-period portion of design response spectrum curve © 2003 by CRC Press LLC
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Response Spectral Acceleration S DS
Earthquake Engineering Handbook
SDS = Fa Ss
Sa = SD1/T SD1= FvS1
0.4SDS T0
0.2
1.0
TS
Period T (seconds) FIGURE 18.13 AASHTO-LRFD guidelines: design response spectrum curve. (From ATC/MCEER Joint Venture. 2001. Recommended LRFD Guidelines for the Seismic Design of Highway Bridges, Parts I, II, and III. ATC-49a and ATC-49b, Applied Technology Council, Redwood City, CA and MCEER-02-SP01, Multidisciplinary Center for Earthquake Engineering Research, State University of New York at Buffalo. With permission.)
TABLE 18.3 Recommended LRFD Guidelines: Site Coefficient Fa Mapped Spectral Response Acceleration at Short Periods
Site Class
Ss ≤ 0.25 g
Ss = 0.5 g
Ss = 0.75 g
Ss = 1.00 g
Ss = 1.25 g
A B C D E F
0.8 1.0 1.2 1.6 2.5 a
0.8 1.0 1.2 1.4 1.7 a
0.8 1.0 1.1 1.2 1.2 a
0.8 1.0 1.0 1.1 0.9 a
0.8 1.0 1.0 1.0 0.9 a
Note: Use straight line interpolation for intermediate values of Ss . a = Site-specific geotechnical investigation and dynamic site-response analysis should be performed. For purpose of defining Seismic Hazard Levels, Type E values may be used for Type F soils. Source: ATC/MCEER Joint Venture, ATC Report Nos. ATC-49a and ATC-49b, Applied Technology Council, Redwood City, CA; and Report No. MCEER-02-SP01, Multidisciplinary Center for Earthquake Engineering Research, State University of New York at Buffalo, November 2001. With permission.
For site Class F, which is not included in Table 18.5, soils vulnerable to potential failure or collapse under seismic loading, such as liquefiable soils, quick and highly sensitive clays, and collapsible weakly cemented soils, site-specific geotechnical investigation and dynamic site-response analyses should be performed [ATC/MCEER, 2001]. The effects of vertical ground motion may be ignored if the bridge site is located more than 50 km from an active fault. If the bridge is located within 10 km of an active fault, site-specific response spectra and acceleration time histories, including vertical ground motions, should be considered. Seismic-force effects from different vibration modes should be combined. For modal response closely spaced in frequency and ground motion in one direction, the complete quadratic combination (CQC) method should be used. For combining the contribution of orthogonal and uncorrelated © 2003 by CRC Press LLC
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TABLE 18.4 Recommended LRFD Guidelines: Site Coefficient Fv Mapped Spectral Response Acceleration at 1-sec Period
Site Class
S1 ≤ 0.1 g
S1 = 0.2 g
S1 = 0.3 g
S1 = 0.4 g
S1 ≥0.5 g
A B C D E F
0.8 1.0 1.7 2.4 3.5 a
0.8 1.0 1.6 2.0 3.2 a
0.8 1.0 1.5 1.8 2.8 a
0.8 1.0 1.4 1.6 2.4 a
0.8 1.0 1.3 1.5 2.4 a
Note: Use straight line interpolation for intermediate values of S1 . a = Site-specific geotechnical investigation and dynamic site-response analysis should be performed. For purpose of defining Seismic Hazard Levels, Type E values may be used for Type F soils. Source: ATC/MCEER Joint Venture, ATC Report Nos. ATC-49a and ATC-49b, Applied Technology Council, Redwood City, CA; and Report No. MCEER-02-SP01, Multidisciplinary Center for Earthquake Engineering Research, State University of New York at Buffalo, November 2001. With permission.
TABLE 18.5 Recommended LRFD Guidelines: Site Classification Site Class
–ν s (m/sec)
N or Nch (blows/0.3 m)
–s u (kPa)
E D C B A
< 180 180 to 360 360 to 760 760 to 1500 > 1500
< 15 15 to 50 > 50 — —
< 50 50 to 100 > 100 — —
Note: –νs = average shear wave velocity for top 30 m of a site; N = average standard penetration test blow count for top 30 m of a site; Nch = average standard penetration test blow count for cohesionless layers of top 30 m of a site; –su = average undrained shear strength of cohesive layers for top 30 m of a site. Source: ATC/MCEER Joint Venture, ATC Report Nos. ATC-49a and ATC-49b, Applied Technology Council, Redwood City, CA; and Report No. MCEER-02-SP01, Multidisciplinary Center for Earthquake Engineering Research, State University of New York at Buffalo, November 2001. With permission.
ground motion components to a single seismic forces, the square root sum of squares (SSRC) method or 100%–40% rule is used. For a bending moment, the combination rules are as follows: SSRC combination Mx =
(M ) + (M ) + (M ) T x
2
L x
2
V x
2
(18.4)
100%–40% combination M xLC1 = 1.0M Tx + 0.4 M xL + 0.4 M Vx
(18.5)
M xLC 2 = 0.4 M Tx + 1.0 M xL + 0.4 M Vx
(18.6)
M xLC 3 = 0.4 M Tx + 0.4 M xL + 1.0 M Vx
(18.7)
For circular columns, the vector moments and axial forces should be obtained for biaxial design:
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TABLE 18.6 Recommended LRFD Guidelines: SHL, SDAP, and SDR
Seismic Hazard Level (SHL) I II III IV
Seismic Design and Analysis Procedure (SDAP) and Seismic Design Requirements (SDR) Life Safety Operational
SD1 (FvS1)
SDS (FaSs)
SD1 ≤ 0.15 0.15 < SD1 ≤ 0.25 0.25 < SD1 ≤ 0.40 0.40 < SD1
SDS ≤ 0.15 0.15 < SDS ≤ 0.35 0.35 < SDS ≤ 0.60 0.60 < SDS
SDAP
SDR
SDAP
SDR
A1 A2 B/C/D/E C/D/E
1 2 3 4
A2 C/D/E C/D/E C/D/E
2 3 5 6
Source: ATC/MCEER Joint Venture, ATC Report Nos. ATC-49a and ATC-49b, Applied Technology Council, Redwood City, CA; and Report No. MCEER-02-SP01, Multidisciplinary Center for Earthquake Engineering Research, State University of New York at Buffalo, November 2001. With permission.
SSRC combination • For bridges with skew angle less than 10°, the maximum of
(
M x2 + 0.4 M y
)
2
and
M y2 + (0.4 M x )
2
with the maximum axial load ± P • For bridges with skew angle greater than 10°, M x2 + M y2 with the maximum axial load ± P 100%–40% combination • The maximum of
(M ) + (M ) LC1 x
2
LC1 y
2
and
(M ) + (M ) LC 2 x
2
LC 2 y
2
and
(M ) + (M ) LC 3 x
2
LC 3 y
2
with the maximum axial load ± P, where subscripts x and y represent two horizontal axes, x-x and y-y, respectively; superscripts L, T, V indicate the longitudinal, transverse, and vertical directions, respectively; and superscripts LC1, LC2, and LC3 are Load Cases 1, 2, and 3, respectively. 18.6.1.2 Seismic Design and Analysis Procedures (SDAP) Depending on the seismic hazard levels specified in Table 18.6, each bridge should be designed, analyzed, and detailed in accordance with Table 18.6. 18.6.1.2.1 Single Span Bridges Single span bridges need not be analyzed for seismic loads and design requirements are limited to the minimum seat widths and connection forces, which should not be less than the product of FaSS /2.5 and the tributary permanent load. 18.6.1.2.2 SDAP A1 and A2 For a low seismicity area, only minimum seat widths and connection design forces for bearings and minimum shear reinforcement in concrete columns and piles in the Seismic Design Requirement (SDR) 2 are deemed necessary for the life-safety performance objective. The primary purpose is to ensure that the connections between the superstructure and its supporting substructures remain intact during the design earthquake. SDAP A1 and A2 require that the horizontal design connection forces in the restrained directions should not be taken to be less than 0.1 and 0.25 times the vertical reactions due to tributary permanent loads and assumed existing live loads, respectively. 18.6.1.2.3 SDAP B: No-Analysis Approach The no-analysis approach allows that the bridge is designed for all nonseismic requirements without a seismic demand analysis and the capacity design principle is used for all components connected
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to columns. For geotechnical design of the foundations, the moment overstrength capacity of columns that framed into the foundation, Mpo = 1.0 Mn, where Mn is nominal moment capacity of a column. SDAP B applies only to regular bridges meeting the following restrictions: • The maximum span length is less than both 80 m and 1.5 times the average span length. • The maximum skew angle is less than 30°. • The ratio of the maximum interior bent stiffness to the average bent stiffness of the bridge is less than 2. • The subtended angle in horizontally curved bridges is less than 30°. • For frames in which the superstructure is continuous over the bents and some bents do not participate in the ERS, Fv S1(Nbent /Ners) < 0.4 cosαskew , where Nbent and Ners are total number of bents in the frame and number of bents participating in the ERS in the longitudinal direction, respectively, and αskew is the skew angle of the bridge. • Fv S1 < 0.4 cosαskew . • The bridge site has a potential for liquefaction and the piers are not seated on spread footing. • For concrete column and pile bents, column axial load, Pe < 0.15 fc'Ag (f 'c is specified minimum concrete compression strength and Ag is gross cross-sectional area of column); longitudinal reinforcement ratio, ρl > 0.008; column transverse dimension, D > 300 mm; and maximum column moment-shear ratio, M/VD < 6. • For concrete wall piers with low volumes of longitudinal steel, Pe < 0.1 fc'Ag ; ρl > 0.0025; wall thickness or smallest cross-sectional dimension, t > 300 mm; and M/Vt < 10. • For steel pile bents framing into concrete caps, Pe < 0.15 Py (Py is axial yield force of steel pile); pile dimension about the weak axis bending at the ground level, Dp > 250 mm; and L/b < 10 (L is the length from the point of maximum moment to the inflexion point of the pile when subjected to a pure transverse load and b is the flange width; for a cantilever column in a pile bent configuration, L is equal to the length above ground to the top of the bent plus 3 pile diameters). • For timber piles framing into concrete caps or steel moment-frame columns, Pe < 0.1Pc (and Pc is axial compression capacity of the pile or the column); Dp > 250 mm; and M/VDp < 10. 18.6.1.2.4 SDAP C: Capacity Spectrum Design Method The capacity spectrum design method combines a demand and capacity analysis and is conceptually the same as the Caltrans displacement-based design method. The primary difference is that the SDAP C begins with nonseismic design and then assesses the adequacy of the displacement. The key equations represent the relationship between the seismic coefficient, Cs, and displacement, ∆: 2
F S Cs ∆ = v 1 g 2πBL Cs =
Fa Ss BS
(18.8)
(18.9)
where BL BS g ∆
= = = =
response reduction factor for long period structures as specified in Table 18.7 response reduction factor for short period structures as specified in Table 18.7 acceleration due to gravity (9.8 m/sec2) lateral displacement of the pier; taken as 1.3 times the yield displacement of the pier when the long period equation governs
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TABLE 18.7 Recommended LRFD Guidelines: Capacity Spectrum Response, Reduction Factors for Bridge with Ductile Piers Earthquake 50% PE in 75-year 3% PE in 75-year/1.5 Mean Deterministic
Performance Level
Bs
BL
Life Safety Operational Life Safety Operational
1 1 2.3 1
1 1 1.6 1
Source: ATC/MCEER Joint Venture, ATC Report Nos. ATC-49a and ATC-49b, Applied Technology Council, Redwood City, CA; and Report No. MCEER-02-SP01, Multidisciplinary Center for Earthquake Engineering Research, State University of New York at Buffalo, November 2001. With permission.
The lesser of Equations 18.8 and 18.9 should be used to assess Cs for two-level earthquakes. The required lateral strength of the bridge is Vn = CsW where W is the weight of the bridge responding to earthquake ground motion. The procedure applies only to bridges that behave essentially as a single-degree-of-freedom system and very regular bridges satisfying the following requirements: • The number of spans per frame does not exceed six. • The number of spans per frame is at least three, unless seismic isolation bearings are utilized at the abutments. • The maximum span length is less than both 60 m and 1.5 times the average span length in a frame. • The maximum skew angle is less than 30° and skew of piers or bents differs by less than 5° in the same direction. • The subtended angle in the horizontally curved bridges is less than 20°. • The ratio of the maximum bent or pier stiffness to the average bent stiffness is less than 2, including the effects of foundation. • The ratio of the maximum lateral strength (or seismic coefficient) to the average bent strength is less than 1.5. • Abutment shall not be assumed to resist the significant forces in both the transverse and longitudinal directions. Pier wall substructures must have bearings to permit transverse movement. • For concrete column and pile bents, Pe ≤ 0.2 fc' Ag ; ρl > 0.008; and D > 300 mm. • Piers and bents must have pile foundation when the bridge site has a potential for liquefaction. 18.6.1.2.5 SDAP D: Elastic Response Spectrum Method The elastic response spectrum method uses either the uniform load or multimode method of analysis with cracked section properties taken into consideration. The analysis should be performed for the governing design earthquakes, either the 50% PE in 75 years or the 3% PE in 75 years/1.5 mean deterministic earthquakes. Elastic forces obtained from analyses should be modified using the response modification factor R. 18.6.1.2.6 SDAP E: Elastic Response Spectrum Method with Displacement Capacity Verification SDAP E is a two-step design procedure. The first step is the same as SDAP D. The second step is to perform a two-dimensional nonlinear static (push over) analysis to verify substructure displacement capacity. 18.6.1.3 Response Modification Factor R It is generally recognized that it is uneconomical and sometimes impractical or impossible to design a bridge to resist large earthquakes elastically. Columns are assumed to deform inelastically where seismic forces exceed their design levels, which is established by dividing the elastically computed force effects by the response modification factor R. The R factors specified in the following were based on an evaluation
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Moment
Me
M Mb = M e /R
∆b
∆y
∆max
∆e Draft
FIGURE 18.14 AASHO-LRFD guidelines: basis for conventional ductile design. (From ATC/MCEER Joint Venture. 2001. Recommended LRFD Guidelines for the Seismic Design of Highway Bridges, Parts I, II, and III. ATC-49a and ATC-49b, Applied Technology Council, Redwood City, CA and MCEER-02-SP01, Multidisciplinary Center for Earthquake Engineering Research, State University of New York at Buffalo. With permission.)
of existing test data, engineering judgment, and the equal displacement principle as shown in Figure 18.14. It is used principally for conventional ductile design. For substructures: R = 1 + ( RB − 1)
T ≤ RB T*
(18.10)
where RB = base response modification factor specified in Table 18.8 T = natural period of the structure T * = 1.25 Ts where Ts is as defined in Section 18.6.1.1 For connections (superstructure to abutment; expansion joints within a span of the superstructure, columns, piers, or pile bents to cap beam or superstructure; and column or piers to foundations), an R factor of 0.8 should be used for those cases where capacity design principles are not used to develop the design forces to design the connections. It is assumed that if R < 1.5, columns should remain essentially elastic for design earthquake; if 1.5 < R > 3.0, columns should be repairable; if R > 3.0, significant plastic hinging may occur and columns may not be repairable. 18.6.1.4 Capacity Design Principle The main objective of the capacity design principle is to ensure the desirable mechanisms can dissipate most energy and inelastic deformation (plastic hinging) that occurs at expected locations (in top and/or bottom of columns) where they can be readily inspected and/or repaired. To achieve this objective, the overstrength force effects developed from the plastic hinges in columns shall be dependably resisted
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TABLE 18.8 Recommended LRFD Guidelines: Base Response Modification Factor for Substructures RB Performance Objective Life Safety Substructure Element
SDAP D
Wall-type pier — large dimension Columns — single and multiple Pile bents and drilled shafts — vertical piles — above ground Pile bents and drilled shafts — vertical piles — 2 diameters below ground level — no owner approval required Pile bents and drilled shafts — vertical piles — in ground — owner approval required Pile bents with batter piles Seismically isolated structures Steel braced frame — ductile components Steel braced frame — normally ductile components All elements for expected earthquake
Operational
SDAP E
SDAP D
SDAP E
2 4 4
3 6 6
1 1.5 1.5
1.5 2.5 2.5
1
1.5
1
1
N/A
2.5
N/A
1.5
N/A 1.5 3 1.5
2.5 1.5 4.5 2
N/A 1 1 1
1.5 1.5 1.5 1
1.3
1.3
0.9
0.9
Notes: The substructure design forces resulting from the elastic analysis divided by the appropriate R factor for SDAP E cannot be reduced below 70% at the R-factored reduced forces or the 50% PE in 75-year design forces as part of the pushover analysis. There may be a design situation (e.g., architecturally oversized column) where a designer opts to design the column for an R = 1 (i.e., elastic design). In concrete columns the associate elastic design shear may be obtained from the elastic analysis forces using an R factor of 0.67 or by calculating the design shear by the capacity design procedures using a flexural overstrength factor of 1.0. In steel braced frame if an R = 1.0 is used the connection design forces should be obtained using an R = 0.67. If an R = 1.0 is used in any design the foundation should be designed for elastic forces plus the SDR detailing requirements are required for concrete piles (i.e., minimum shear requirements). Unless specifically stated, the R factor applies to both steel and concrete. N/A means that owner approval is required and thus SDAP E is required. Source: ATC/MCEER Joint Venture, ATC Report Nos. ATC-49a and ATC-49b, Applied Technology Council, Redwood City, CA; and Report No. MCEER-02-SP01, Multidisciplinary Center for Earthquake Engineering Research, State University of New York at Buffalo, November 2001. With permission.
by column shear and adjoining elements such as cap beams, spread footing, pile cap, and foundations. The moment overstrength capacity (Mpo) can be assessed using one of the following approaches:
M po
1.5 M n 1.2 M n 1.3 M n = 1.5 M n 1.0 M n
for concrete column for steel column, M n based on expected yield strength for concrete - filled steel tubes for steel piles in weak axis bending and, for steel members in shear (e.g., eccentrically braced frames) for geotechnical design force in SDR 3
(18.11)
For reinforced concrete columns [Mander and Chang, 1997]: 2 P − Pb M po = M bo 1 − e Pto − Pb
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(18.12)
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where Pe = axial compression load based on gravity load and seismic (framing) action Pb = axial compression capacity at the maximum nominal (balanced) moment on the section = 0.425 β1 fc'Ag β1 = compression stress block factor ≤ 0.85 Pto = axial tensile capacity of the column = −Ast fsu Ast = area of longitudinal reinforcement fsu = ultimate tensile strength of the longitudinal reinforcement 1 − κo M bo = K shape Ast fsu D′ + Pb D 2
(18.13)
D' = pitch circular diameter of the reinforcement in a circular section, or the out-to-out dimension of the reinforcement in a rectangular section; this generally may be assumed as = 0.8D
K shape
0.32 0.375 = 0.25 0.5
for circular sections for square sections with 25% of the longitudinal reinforcement placed in each face for walls with strong axis bending for walls with weak axis bending
(18.14)
κo = a factor related to the centroid of compression stress block and should be taken as 0.6 and 0.5 for circular and rectangular sections, respectively It should be pointed out that Equations 18.12 and 18.13 are rearranged as the above simpler format. • For reinforced concrete columns, a moment-curvature section analysis taking into account the expected strength, confined concrete properties, and strain hardening effects of longitudinal reinforcement • For steel columns, nominal flexural resistance (Mn) should be determined either in accordance with the AASHTO-LRFD [1998–2000] or: Pu M n = 1.18 M px 1 − ≤ M px Ag Fye Ag Fye Mpx Pu
= = = =
(18.15)
gross cross-sectional area of a steel column expected specified minimum yield strength of steel plastic moment under pure bending, calculated using Fye factored axial compression load
18.6.1.5 Plastic Hinge Zones The top plastic hinge zones (Lp) for typical concrete and steel columns, pile bents, and drilled shaft and bottom zones of columns above a footing or above an oversized in-ground drilled shaft shall be the maximum of the following:
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For reinforced concrete columns: Dmax L 6 tan θ D cot θ + 2 L p = maximum of M 1.5 0.08 + 4000 ε y db V My M V 1 − M po 450 mm
(18.16)
where D Dmax db L M V My εy θ
= = = = = = = = =
transverse column dimension in direction of bending maximum cross-sectional dimension of a column diameter of longitudinal reinforcement clear height of a column maximum column moment maximum column shear column yield moment yield strain of longitudinal reinforcement principal crack angle = 1.6 ρ A v v tan -1 A Λ ρ t g
Av
=
ρv ρt Λ
= = =
0.25
with θ ≥ 25° and θ ≥ tan–1 (D '/L) shear area of concrete, which may be taken as 0.8Ag for a circular section and bwd for a rectangular section ratio of transverse reinforcement volumetric ratio of longitudinal reinforcement fixity factor taken as 1 for fixed-pinned and 2 for fixed-fixed ends
For steel columns: L L p = maximum of 8 450 mm
(18.17)
For flared columns, the plastic hinge zone shall be extended from the top of the column to a distance equal to the maximum of the above criteria below the bottom of the flare.
18.6.2 Caltrans Seismic Design 18.6.2.1 Seismic Loads For Ordinary bridges, safety-evaluation ground motion is based on deterministic assessment corresponding to the MCE. A set of ARS curves developed by ATC-32 are adopted as standard horizontal ARS curves © 2003 by CRC Press LLC
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2.0 Soil Profile Type D Magnitude: 6.5 ± 0.25 0 .6g (0
Note: Peak ground acceleration values not in parentheses are for rock (Soil Profile Type B) and Peak ground acceleration values in parentheses are for Soil Profile Type D.
.6g
0 .5g
)
(0
1.2
.5 0.4g
)
g
(0
4g 0.3g (0 ) . 36 g)
.4
Spectral Acceleration (g)
1.6
0.8
0.2g (0.
g)
0.1g (0. 16
0.4
0.0
28
g)
0
1
2 Period (sec)
3
4
50
Spectral Displacement (in)
40
30
20 0.6g (0.6g) 0.5g (0.5g) 0.4g (0.44g) 0.3g (0.36g)
10
0.2g (0.28g) 0.1g (0.16g)
0
0
1
2 Period (sec)
3
4
FIGURE 18.15 Typical Caltrans acceleration response spectrum curves. (From Caltrans. 2001a. Seismic Design Criteria, Version 1.2, California Department of Transportation, Sacramento, CA, December.)
in conjunction with the peak rock acceleration from the Caltrans Seismic Hazard Map 1996 to determine the horizontal earthquake forces. Figure 18.15 shows typical ARS curves. Vertical acceleration shall be considered for bridges with nonstandard structural components, unusual site conditions, or close proximity to earthquake faults and can be approximated by an equivalent static vertical force applied to the superstructure. For structures within 15 km from an active fault, the spectral ordinates of the appropriate standard ARS curves should be increased by 20%. For long period structures (T ≥ 1.5 sec) on deep soil sites (depth of alluvium ≥ 75 m) the spectral ordinates of the appropriate standard ARS curves should be increased by 20%; the increase applies to the portion of the curves with periods greater than 1.5 sec. 18.6.2.2 Design Approaches The displacement-based design approach is used to ensure that the structural system and its individual components have enough displacement capacities to withstand the deformation imposed by © 2003 by CRC Press LLC
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the design earthquake. Using displacements rather than forces as a measurement of earthquake damages allows a structure to fulfill the required functions. The displacements of the global system and the local ductile system shall satisfy the following requirement: ∆ D ≤ ∆C
(18.18)
where ∆D ∆C
= displacement demand determined by the global analysis, the stand-alone analysis, or the larger of the two if both types of analyses are necessary = displacement capacity when any plastic hinge capacity reaches its ultimate capacity
In a displacement-based analysis, proportioning of the structure is made first based on strength and stiffness requirements. The appropriate analysis is run and the resulting displacements are compared to the displacement capacity, which is dependent on the formation and rotational capacity of plastic hinges and can be evaluated by an inelastic static pushover analysis. This procedure has been used widely in seismic bridge design in California since 1994. Figure 18.16 shows the design flowchart for the Ordinary standard bridges. 18.6.2.3 Displacement Demands on Bridges and Ductile Components Seismic demands on bridge systems and ductile components are measured in terms of displacements rather than forces. Displacement demands should be estimated from either equivalent static analysis (ESA) or elastic dynamic analysis (EDA, i.e., elastic response spectrum analysis) for typical bridge periods of 0.7 to 3 sec. Attempts should be made to design bridges with dynamic characteristics (mass and stiffness) so that the fundamental period falls within the region between 0.7 and 3 sec, where the equal displacement principle applies. For short period bridges, linear elastic analysis underestimates displacement demands. The inability to accurately predict displacements by a linear analysis can be overcome by either designing the bridge to perform elastically, multiplying the elastic displacement by an amplification factor, or using seismic isolation and energy dissipation devices to limit seismic response. For long period (T > 3 sec) bridges, a linear elastic analysis generally overestimates displacements and a linear elastic displacement response spectrum analysis should be used. 18.6.2.4 Force Demands on Capacity-Protected Components Seismic demands on capacity-protected components, such as superstructures, bent caps, and foundations, are measured in term of forces rather than displacements. Force demands for capacity-protected components should be determined by the joint–force equilibrium considering plastic hinging capacity of the ductile component multiplied by 1.2 of an overstrength factor. The overstrength factor accounts for the possibility that the actual ultimate plastic moment strength of the ductile components exceed its estimated idealized plastic capacity based on the expected properties. This 1.2 of overstrength factor affects not only the demands on the capacity-protected members, but is also used to determine shear demands on the columns themselves. 18.6.2.5 Seismic Capacity 18.6.2.5.1 General Strength and displacement capacities of a ductile flexural element should be evaluated by momentcurvature analysis based on the expected material properties and anticipated damages. The impact of the second-order P-∆ effect on the strength and displacement capacities of all members subjected to combined bending and compression shall be considered. Components may require redesign if the P-∆ effect is significant.
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Proportion column size and reinforcement for DL and LL
Check balanced stiffness requirements: Any bents with a frame: K ie m j / K ej mi ≥ 0.5 Adjacent bents with a frame: K ie m j / K ej mi ≥ 0.75
Estimate seismic displacement demand ∆D by ESA or EDA
Estimate displacement capacity ∆C by IAS
Check global and local: ∆D ≤ ∆C and µD ≤ µlimt
Check
Pdl ∆r ≤ 0.2 M col p
Design for shear and details for ductile members
Design capacity-protected members: joints, superstructure and footings
Design Abutments FIGURE 18.16 Caltrans seismic design procedure for Ordinary Standard bridges.
18.6.2.5.2 Displacement Capacity Displacement capacity of a bridge system should be evaluated by an inelastic static analysis, i.e., a static push over analysis. The rotational capacity of all plastic hinges should be limited to a safe performance level. The plastic hinge regions should be designed and detailed to perform with minimal strength degradation under cyclic loading. Displacement capacity of a local member can be evaluated by its rotational capacity. The displacement capacity of a cantilever member (Figure 18.17) can be calculated as: ∆ c = ∆col Y + ∆p 2
L ∆col Y =
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3
× φY
(18.19) (18.20)
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∆c
C.L. Column
∆p
∆ Ycol
C.G.
L
Force
Idealized Yield Curvature Capacity Equivalent Curvature
Lp
∆p
Actual Curvature
θP
φu
φp
∆Y φY
∆c Displacement
FIGURE 18.17 Displacement of a cantilever member. (From Caltrans. 2001a. Seismic Design Criteria, Version 1.2, California Department of Transportation, Sacramento, CA, December.)
L ∆ p = θp × L − p 2
(18.21)
θ p = Lp × φ p
(18.22)
φ p = φu − φY
(18.23)
where L Lp ∆p ∆y col φY φp φu θp
= = = = =
distance from the point of maximum moment to the point of contra-flexure equivalent analytical plastic hinge length as defined in Section 18.8.2.6 idealized plastic displacement capacity due to rotation of the plastic hinge idealized yield displacement of the column at the formation of the plastic hinge idealized yield curvature defined by an elastic–perfectly plastic representation of the M-φ curve of the cross section (see Figure 18.18) = idealized plastic curvature capacity (assumed constant over Lp) = curvature capacity at the failure limit state, defined as the concrete strain reaching εcu or the confinement reinforcing steel reaching the reduced ultimate strain εsuR = plastic rotation capacity of a plastic hinge
However, it should be pointed out that Equation 18.19 may overestimate the displacement capacity for a reinforced concrete column [Duan and Cooper, 1995]. Column slenderness, high compression axial loads, and a low percentage of reinforcement all contribute to the overestimating of the displacement capacity. Special attention, therefore, should be paid to the estimation of displacement capacity. It was recommended [Duan and Cooper, 1995] that the P-∆ effect should be taken into account in calculating lateral load-carrying capacity and the displacement capacity, especially for medium-long and long columns. The lateral displacement capacity ∆ c can be chosen as the displacement that corresponds to the condition when the lateral load-carrying capacity degrades to a certain acceptable level, say a minimum of 80% of the peak resistance (Figure 18.19) peak load [Duan and Cooper, 1995; Park and Paulay, 1975; Akkari and Duan, 2000]. © 2003 by CRC Press LLC
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Moment col
Mp
Mne My
φy φ Y
φu Curvature
FIGURE 18.18 Idealized moment-curvature curve. (From Caltrans. 2001a. Seismic Design Criteria, Version 1.2, California Department of Transportation, Sacramento, CA, December.)
V Response Envelope
Vu
µ∆ =
> 0.8Vu
Vy ∆u ∆y
∆y
∆u
∆
FIGURE 18.19 Lateral load displacement curve. (From Caltrans. 2001b. Guide Specifications for Seismic Design of Steel Bridges, California Department of Transportation, Sacramento, CA, December.)
18.6.2.5.3 Shear Capacity Shear capacity of concrete members shall be calculated using nominal material properties as: φ Vn = φ (Vc + Vs )
(18.24)
φ = 0.85
(18.25)
(
Vc = νc 0.8 Ag
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)
(18.26)
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3.0 (0.25)
1.5
ρ s f yh = 50 psi (0.34 MPa)
∼
ρ s f yh = 350 psi (2.38 MPa)
Factor 2
Factor 1
Interpolate
0.3 (0.025) 1
2
3
4
5
1
0
6
Ductility Demand Ratio µd
1000 psi (6.8 Mpa)
Compressive Axial Stress
FIGURE 18.20 Shear factors. (From Caltrans. 2001a. Seismic Design Criteria, Version 1.2, California Department of Transportation, Sacramento, CA, December.)
Concrete shear capacity is influenced by flexural and axial loads and is calculated separately for regions within the plastic hinge zone, and regions outside this zone. In the plastic hinge zone, concrete shear capacity is modified based on the level of confinement and the displacement ductility demand (Figure 18.20). • Inside the plastic hinge zone: v c = Factor 1 × Factor 2 ×
fc' ≤ 0.33 fc'
(MPa)
(18.27)
(MPa)
(18.28)
• Outside the plastic hinge zone: v c = 0.25 × Factor 2 × Factor 1 = 0.025 ≤
fc' ≤ 0.33 fc'
ρs f yh 12.5
Factor 2 = 1 +
+ 0.305 − 0.083 µ d < 0.25 Pc ≤ 1.5 13.8 Ag
(18.29)
(18.30)
To ensure reliable capacity in the plastic hinge regions, all column lateral reinforcement is required to be butt welded or spliced hoops capable of resisting the ultimate capacity of the reinforcing steel. • For confined circular or interlocking core sections: Vs =
π nAb f yh D' 2 s
(18.31)
• For pier wall in weak direction: Vs =
Av f yhd s
(18.32)
where Ab = area of individual interlock spiral or hoop Av = total area of shear reinforcement perpendicular to flexural tension reinforcement D' = cross-sectional dimension of confined concrete core measured between the centerline of the peripheral hoop or spiral © 2003 by CRC Press LLC
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fvh d n s
= = = =
specified minimum yield strength of transverse reinforcement area of shear reinforcement perpendicular to flexural tension reinforcement number of individual interlock spiral or hoop core sections spacing of transverse reinforcement
18.7 Seismic Analysis and Modeling 18.7.1 Equivalent Static Analysis The equivalent static analysis (ESA) method specified in Caltrans SDC [2001a] can be used for simpler structures that have balanced spans, similar bent stiffness, and low skew and seismic response is primarily captured by the fundamental mode of vibration. In the ESA method, the fundamental period is determined using tributary mass and stiffness at each bent. The applied seismic force is the product of the period-dependent ARS coefficient and the tributary weight.
18.7.2 Elastic Response Spectrum Analysis Elastic response spectrum analysis (ERSA), including the uniform load method and the multimode dynamic analysis method, is a linear elastic spectral analysis with the appropriate response spectrum and an adequate number of modes considered to capture a minimum of 90% mass participation, and shall be used for complex structures. The uniform load method specified in ATC/MCEER guidelines [2001] is essentially an ESA method that uses a uniform lateral load distribution to approximate the effect of seismic loads. It may be used for both transverse and longitudinal directions if structures satisfy the requirements in Table 18.9. In both ESA and ERSA analyses, effective stiffness of the components should be used in order to obtain realistic evaluation of the structure’s period and displacement demands. The effective stiffness of ductile components should represent the component’s actual secant stiffness near yield. The effective stiffness should include the effects of concrete cracking, reinforcement, and axial load for concrete components; residual stresses, out-of-straightness, and axial load for steel components; and the restraints of the surrounding soil for pile. For ductile concrete column members, effective moments of inertia Ieff should be based on cracked section properties and can be determined from the initial slope of the M-φ curve between the origin and the point designating first yield of reinforcement. The torsional moment of inertia of concrete column Jeff may be taken as 0.2 times Jgross. For capacity-protected concrete members, Ieff shall be based on their level of cracking. For conventionally reinforced concrete box girder superstructures, Ieff can be estimated between 0.5 and 0.75 times Igross, the moment of inertia of a gross section. For prestressed concrete superstructures, Ieff is assumed the same as Igross because prestressing steel limits the cracking of concrete superstructures. TABLE 18.9 Recommended LRFD Guidelines: Requirement for Uniform Load Method Parameter Number of Spans Maximum subtended angle for a horizontally curved bridge Maximum span length ratio from span to span Maximum bent/pier stiffness ratio from span to span, excluding abutments
2
Value 4
3 ο
20
3 —
2 4
20
ο
30
ο
2 4
5 30
6 ο
1.5 4
30ο 1.5 2
Source: ATC/MCEER Joint Venture, ATC Report Nos. ATC-49a and ATC-49b, Applied Technology Council, Redwood City, CA; and Report No. MCEER-02-SP01, Multidisciplinary Center for Earthquake Engineering Research, State University of New York at Buffalo, November 2001.
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The following are major considerations in seismic analysis and design practice: • A beam-element model with three or more lumped masses for each member is usually used [Caltrans, 1995a, 1995b]. • A larger cap stiffness is often used to simulate a stiff deck. • Compression and tension models are used to simulate the behavior of expansion joints. In the tension model, superstructure joints, including abutments, are released longitudinally but the restrainers are modeled as truss elements. In the compression model, all restrainers are considered to be inactive and all joints are locked longitudinally. • Simplistic analysis models should be used for initial assessment of structural behavior. The results of more sophisticated models shall be checked for consistency with the results obtained from the simplistic models. The rotational and translational stiffness of abutments and foundations modeled in the seismic analysis must be compatible with their structural and geotechnical capacity. The energy dissipation capacity of the abutments should be considered for bridges whose response is dominated by the abutments [Caltrans, 2001c]. • For ERSA, the viscous damping ratio inherent in the specified ground spectra is usually 5%. • For time history analysis, in lieu of measurements, a damping ratio of 5% for both concrete and timber constructions and 2% for welded and bolted steel construction may be used. • For one- or two-span continuous bridges with abutment designed to activate significant passive pressure in the longitudinal direction, a damping ratio of up to 10% may be used in longitudinal analysis. • Soil-spring elements should be used to the soil–foundation–structure interaction. Adjustments are often made to meet force–displacement compatibility, particularly for abutments. The maximum capacity of the soil behind abutments with heights larger than 2.5 m may be taken as 370 kPa and will be linearly reduced for backwall height less than 2.5 m. • Pile footing with pile cap and spread footing with soil types A and B [ATC/MCEER, 2001] may be modeled as rigid. If footing flexibility contributes more than 20% to pier displacement, foundation springs should be considered. • For pile bent/drilled shaft, estimated depth to fixity or soil-spring based on p-y curves should be used. • Force–deformation behavior of a seismic isolator can be idealized as a bilinear relationship with two key variables: second slope stiffness and characteristic strength. For design, the force–deformation relationship can be represented by an effective stiffness based on the secant stiffness and a damping coefficient. For more detailed information, reference can be made to ATC/MCEER and AASHTO guide specifications [ATC/MCEER, 2001; AASHTO, 2000] and a comprehensive chapter by Zhang [2000].
18.7.3 Nonlinear Dynamic Analysis The nonlinear dynamic analysis procedure is normally used for the 3% PE in 75-year earthquakes. A minimum of three ground motions including two horizontal and one vertical components should be used and the maximum actions for those three motions should be used for design. If more than seven ground motions are used, the design action may be taken as the mean action of ground motions. The result of a nonlinear dynamic analysis should be compared with a multi-mode response spectrum analysis (MRSA) as a check for reasonableness of the nonlinear model.
18.7.4 Global and Stand-Alone Analysis The global analysis specified in Caltrans SDC [2001a] is an EDA that considers the entire bridge modeled from abutment to abutment. It is often used to determine displacement demands on multiframe structures. The stand-alone analysis is an EDA that considers only one individual frame. To avoid having © 2003 by CRC Press LLC
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individual frames dependent on the strength and stiffness of adjacent frames, the separate stand-alone model for each frame must meet all requirements of the SDC.
18.7.5 Inelastic Static Analysis: Push Over Analysis Inelastic static analysis (ISA), commonly referred to as the “push over analysis,” shall be used to determine the displacement capacity of a bridge. ISA should be performed using expected material properties for modeled members. ISA can be categorized into three types of analysis: 1. Elastic-plastic hinge 2. Refined plastic hinge 3. Distributed plasticity The simplest method, elastic-plastic hinge analysis, may be used to obtain an upper bound solution. The most accurate method, distributed plasticity analysis, can be used to obtain a better solution. Refined plastic hinge analysis is an alternative that can reasonably achieve both computational efficiency and accuracy. In an elastic-plastic hinge (lumped plasticity) analysis, material inelasticity is taken into account using concentrated “zero-length” plastic hinges that maintain plastic moment capacities and rotate freely. When the section reaches its plastic capacity, a plastic hinge is formed and element stiffness is adjusted [King et al., 1992; Levy et al., 1997]. For regions in a framed member away from the plastic hinge, elastic behavior is assumed. It does not, however, accurately represent the distributed plasticity and associated P-δ effects. This analysis predicts an upper bound solution. In the refined plastic hinge analysis [Chen and Toma, 1994], a two-surface yield model considers the reduction of plastic moment capacity at the plastic hinge due to the presence of axial force, and an effective tangent modulus accounts for the stiffness degradation due to distributed plasticity along a frame member. This analysis is similar to the elastic-plastic hinge analysis in efficiency and simplicity and also accounts for distributed plasticity. Distributed plasticity analysis models the spread of inelasticity through the cross sections and along the length of the members. This is also referred to as plastic zone analysis, spread-of-plasticity analysis, and elastoplastic analysis by various researchers. In this analysis, a member needs to be subdivided into several elements along its length to model the inelastic behavior more accurately. Two main approaches have been successfully used to model plastification of members in a second-order distributed plasticity analysis: • Cross-sectional behavior is described as an input for the analysis by means of moment-thrustcurvature (M-P-φ) and moment-thrust-axial strain (M-P-ε) relations, which may be obtained separately from a moment-curvature analysis or approximated by closed-form expressions [Chen and Atsuta, 1977]. • Cross sections are subdivided into elemental areas and the stresses and strains are traced explicitly using the proper stress–strain relations for all elements during the analysis.
18.7.6 Moment-Curvature Analysis The main purpose of moment-curvature analysis is to study the section behavior. The following assumptions are usually made: • • • •
Plane section before bending remains plane after bending. Shear and torsional deformation is negligible. Stress–strain relationships for concrete and steel are given [Caltrans, 2001a]. For reinforced concrete, a perfect bond between concrete and steel rebar exists.
The mathematical formulas used in the section analysis are (Figure 18.21): © 2003 by CRC Press LLC
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FIGURE 18.21 Section analysis modeling.
Compatibility equations: φx = ε y
(18.33)
φy = ε x
(18.34)
Equilibrium equations: P =
∫
n
σ dA =
A
Mx =
∫ A
© 2003 by CRC Press LLC
∑σ A i
(18.35)
i
i =1
n
σ y dA =
∑σ y A i i
i =1
i
(18.36)
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My =
∫
n
σ x dA =
A
∑σ x A i i
i
(18.37)
i =1
For a reinforced concrete member, the cross section is divided into a proper number of concrete and steel layers or filaments representing the concrete and reinforcing steel as shown in Figure 18.21. Each concrete and steel layer or filament is assigned its corresponding stress–strain relationships. Confined and unconfined stress–strain relationships are used for the core concrete and for the cover concrete, respectively. For a structural steel member, the section is divided into steel layers or filaments and a typical steel stress–strain relationship is used for tension and compact compression elements, and an equivalent stress–strain relationship with reduced yield stress and strain can be used for a noncompact compression element. The analysis process starts by selecting a strain for the extreme concrete (or steel) fiber. Using this selected strain and assuming a section neutral axis (NA) location, a linear strain profile is constructed and the corresponding section stresses and forces are computed. Section force equilibrium is then checked for the given axial load. By changing the location of the NA, the process is repeated until equilibrium is satisfied. Once the equilibrium is satisfied, and for the assumed strain and the given axial load, the corresponding section moment and curvature are computed by Equations 18.36 and 18.37. A moment-curvature (M-φ) diagram for a given axial load is constructed by incrementing the extreme fiber strain and finding the corresponding moment and the associated curvature. An interaction diagram (M-P) relating axial load and the ultimate moment is constructed by incrementing the axial load and finding the corresponding ultimate moment using the above procedure. For a reinforced concrete section, the yield moment is usually defined as the section moment at onset of yielding of the tension reinforcing steel. The ultimate moment is defined as the moment at peak moment capacity. The ultimate curvature is usually defined as the curvature when the extreme concrete fiber strain reaches ultimate strain or when the reinforcing rebar reaches its ultimate (rupture) strain (whichever take place first). Figure 18.22a shows typical M-P-φ curves for a reinforced concrete section. For a simple steel section, such as a rectangular, circular-solid, or thin-walled circular section, a closed-form of M-P-φ can be obtained using the elastic–perfectly plastic stress–strain relations [Chen and Atsuta, 1977]. For all other commonly used steel sections, numerical iteration techniques are used to obtain M-P-φ curves. Figure 18.22b shows typical M-P-φ curves for a wide-flange section.
18.7.7 Random Vibration Approach The random vibration approach is a well-recognized and advanced seismic response analysis method for linear multisupport structural systems and long-span structures [Kiureghian and Neuenhofer, 1992; Heredia-Zavoni et al., 1994]. This approach provides a statistical measure of the response that is not controlled by an arbitrary choice of the input motions, and also significantly reduces the response evaluation to that of a series of linear one-degree systems in a way that fully accounts for the multisupport input and the space–time correlation structure of the ground motion [HerediaZavoni et al., 1994]. Although the random vibration approach has been adopted by the Eurocode [European Committee for Standardization, 1995] and is widely used by Chinese engineers, it has not been accepted as a practical method of analysis for complex long-span structures by U.S. practicing engineers due to computation difficulties [Kiureghian and Neuenhofer, 1992]. During the 1990s, Lin and his team [Lin et al., 1994a, 1994b, 1997, 2001] developed a new series of algorithms, i.e., the pseudo excitation method (PEM) series, on structural stationary/nonstationary random response analysis. The PEM is an accurate and extremely efficient method to solve complicated © 2003 by CRC Press LLC
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(a)
(b) FIGURE 18.22 Typical moment-thrust-curvature curves: (a) reinforced concrete section; (b) steel section.
random vibration problems. The cross correlation terms between all participating modes and between all excitations are all included in the responses. Most recently, the PEM has been used to analyze several long-span bridges in China. Cheng [2000] analyzed the Hunan Yue-Yang cable-stayed bridge with a total length of 5700 m and a main span of 880 m, in which 2700 degrees of freedom, 15 multisupport ground motions, and 200 modes were used. Fan et al. [2001] used PEM to analyze the Second Yangtze River Bridge at Nancha, a cable-stay bridge with a total length of 1238 m and a main span of 628 m, in which 300 modes in the fast CQC (i.e., PEM) analysis and 12 multisupport ground motions were used. The computations showed that the “wave passage effect” may cause differences of some demands of up to 40%. © 2003 by CRC Press LLC
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18.8 Seismic Detailing Requirements 18.8.1 ATC/MCEER Guidelines 18.8.1.1 Minimum Seat Requirements In SDR 1 and 2, the minimum seat width is: 2 (1 +1.25Fv S1 ) B N min = 0.1 + 0.0017 L + 0.007 H + 0.05 H 1 + 2 L cos α
(18.38)
B 3 ≤ L 8
(18.39)
where L = distance between joints (m) H = height of the tallest pier between joints (m) B = width of the superstructure (m) In SDR 3, 4, 5, and 6, the minimum seat width is either Equation 18.38 or 1.5 times the displacement of the superstructure at the seat according to the following equation: ∆ = Rd ∆ e 1 T* 1 + 1 − R T R Rd = 1
(18.40) for T < T * for T ≥ T
(18.41)
*
where ∆e = displacement demand from the seismic analysis ∆ Requirements 18.8.1.2 P-∆ In SDR 3 to 6, the displacement of a pier or bent in the longitudinal and transverse directions determined by Equation 18.40 shall satisfy: V ∆ ≤ 0.25Cs H = 0.25 n W
H
(18.42)
where Vn = lateral strength of the pier W = dead load of the pier H = height of the pier from the point of fixity for foundation The basis of this requirement is that maximum displacement is such that the reduction in resisting force is limited to a 25% reduction from the lateral strength assuming no postyield stiffness. The inequality in Equation 18.42 is to keep the bridge pier from being significantly affected by P-∆ moments. 18.8.1.3 Minimum Displacement Capacity Requirements For SDAP E, the following equation should be satisfied:
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∆ c ≥ 1.5 ∆
(18.43)
where ∆c is lateral displacement capacity of the pier or bent. It is defined as the displacement at which the first component reaches its maximum deformation. The factor of 1.5 on displacement demand recognizes the approximation of the modeling and analysis. 18.8.1.4 Structural Steel Design Requirements 18.8.1.4.1 Limiting Width-to-Thickness Ratios In SDR 2 to 6, the width-to-thickness ratio of compression elements of the columns in ductile MRF and single column structures shall satisfy the limiting ratios specified in Table 18.10. Full penetration flange and web welds are required at beam–column connections. 18.8.1.4.2 Limiting Slenderness Ratio In SDR 2 to 6, Table 18.11 summarizes the limiting slenderness ratio (KL/r) for various steel members. Recent studies found that more stringent requirements for slenderness ratios may be unnecessary, provided that the connections are capable of carrying at least the member’s tension capacity. The ratios shown in Table 18.11 reflect those relaxed limits. 18.8.1.4.3 Limiting Axial Load Ratio High axial load in a column usually results in the early deterioration of strength and ductility. The ratio of factored axial compression due to seismic load and permanent loads to yield strength (Ag Fy) for columns in ductile MRFs and single column structures shall not exceed 0.4 for SDR 2 and SDR 3 to 6, respectively. 18.8.1.4.4 Plastic Rotation Capacities In SDR 3 to 6, the plastic rotational capacity shall be based on the appropriate performance level and may be determined from tests and/or a rational analysis. The maximum plastic rotational capacity θp should be conservatively limited to 0.035, 0.005, and 0.01 radians for life safety, operational performance, and ground hinges, respectively. 18.8.1.5 Concrete Design Requirements 18.8.1.5.1 Limiting Longitudinal Reinforcement Ratios The ratio of longitudinal reinforcement to the gross cross section should not be less than 0.008 and more than 0.04. 18.8.1.5.2 Shear Reinforcement The shear strength shall be determined by either an implicit approach or an explicit approach. In the end regions, the explicit approach assumes that the shear-resisting mechanism is provided by the struttie model (explicit approach) such that:
(
φVs ≥ Vu − Vp + Vc Vp = 0.05 f 'b d c w Vc = 0.17 fc 'bw d
© 2003 by CRC Press LLC
)
Λ D' P 2 e L
(18.44)
(18.45)
for plastic hinge zone (18.46) for outside plastic hinge zone
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TABLE 18.10 Recommended LRFD Guidelines: Limiting Width-to-Thickness Ratios Width-to-Thickness Ratio (b/t)
Description of Element Flanges of I-shaped sections and channels in compression
bf /2tf
Webs in combined flexural and axial compression
hc /tw
Limiting Width-to-Thickness Ratio λp
Limiting Ratio k 0.3
135 Fy For
For Pu φ b Py 1365 Fy
Pu
≤ 0.125
1.54 Pu 1 − φ P b y
3.05 1 −
Pu φ b Py 500 Fy
D/t
Unstiffened rectangular tubes
b/t
Longitudinally stiffened plates in compression
b/t
1.54 Pu φ b Py
For
For
Hollow circular sections (pipes)
≤ 0.125
φ b Py
Pu
≤ 0.125
Pu 2.33 – φ P b y
≤ 0.125
φ b Py ≥
665 Fy
1.12 2.33 –
φ b Py
8950
200
Fy
Fy
300
Pu
≥ 1.48
0.67
Fy 145
0.32
Fy
Note: 1. bf and tf are the width and thickness of an I-shaped section and hc is the depth of that section and tw is the thickness of its web. b ≤ λp . 2. Limits λp is for format t 3. Limits k is for format
b t
≤k
E Fy
.
Source: ATC/MCEER Joint Venture, ATC Report Nos. ATC-49a and ATC-49b, Applied Technology Council, Redwood City, CA; and Report No. MCEER-02-SP01, Multidisciplinary Center for Earthquake Engineering Research, State University of New York at Buffalo, November 2001. With permission.
π Abh 2 s f yh D"cot θ Vs = Av f D"cot θ s yh
for circular section (18.47) for rectangular section
where Pe = compressive axial force including seismic effects D' = pitch circle diameter of the longitudinal reinforcement in a circular column, or the distance between the outermost layers of bars in a rectangular column L = column length Λ = fixity factor as defined in Section 18.6.1.5 © 2003 by CRC Press LLC
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TABLE 18.11 Recommended LRFD Guidelines: Limiting Slenderness Ratio Limiting Slenderness Ratio
KL r
Description of Members Unsupported distance for potential plastic hinge zone of columns
Limiting Length L (m)
17250 ry Fy
Ductile compression Bracing members
2600 Fy
Nominally ductile Bracing members
3750 Fy Limit is waived if members designed as tension-only bracing
Source: ATC/MCEER Joint Venture, ATC Report Nos. ATC-49a and ATC-49b, Applied Technology Council, Redwood City, CA; and Report No. MCEER-02-SP01, Multidisciplinary Center for Earthquake Engineering Research, State University of New York at Buffalo, November 2001. With permission.
bw d Abh Ash D'' θ
= = = = = =
web width of section effective depth of section area of one circular hoop/spiral rebar total area of transverse reinforcement in one layer in the direction of the shear force centerline section diameter/width of the perimeter spiral/hoops principal crack angle defined in Section 18.6.1.5
18.8.1.5.3 Transverse Reinforcement in Plastic Hinge Zones Figures 18.23 to 18.25 illustrate the typical transverse reinforcement. For confinement in plastic hinge zones, the ratio of transverse reinforcement ρs shall not be less than: ρs min = 0.008 ρs =
2 P f A fc ' α shape e + ρt y g − 1 ' ' U sf fc Acc fc Ag
4 Abh D' s
for circular sections
Ash A' + sh sB' sD''
for rectangular sections
(18.48)
(18.49)
where Acc Ash A'sh B'' sD' fy
= area of the column core concrete, measured to the centerline of the perimeter hoop or spiral = total area of transverse reinforcement in one layer in the direction of the applied shear = total area of transverse reinforcement in one layer perpendicular to the direction of the applied shear = core dimension of tied column in the direction of the applied shear = center-to-center diameter of the perimeter hoop or spiral = minimum specified yield strength of rebars
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FIGURE 18.23 Column single spiral details. (From ATC/MCEER Joint Venture. 2001. Recommended LRFD Guidelines for the Seismic Design of Highway Bridges, Parts I, II, and III. ATC-49a and ATC-49b, Applied Technology Council, Redwood City, CA and MCEER-02-SP01, Multidisciplinary Center for Earthquake Engineering Research, State University of New York at Buffalo. With permission.)
h hc
CROSSTIES ENGAGE LONGIT. REINFORCEMENT
HOOPS AND CROSSTIES 14” MAX CONTRIBUTE TO ASH
14” MAX 6d 45˚ 6” MAX WHERE ALTERNATE BARS ARE TIED
d D
X
X
6” MAX WHERE ALTERNATE BARS ARE TIED
14” MAX
hc FOR ASH CROSSING Y-Y AXIS
hc FOR ASH CROSSING X-X AXIS Y
Y 14” MAX
FIGURE 18.24 Column tie details. (From ATC/MCEER Joint Venture. 2001. Recommended LRFD Guidelines for the Seismic Design of Highway Bridges, Parts I, II, and III. ATC-49a and ATC-49b, Applied Technology Council, Redwood City, CA; and MCEER-02-SP01, Multidisciplinary Center for Earthquake Engineering Research, State University of New York at Buffalo. With permission.)
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FIGURE 18.25 Column interlocking spiral details. (From ATC/MCEER Joint Venture. 2001. Recommended LRFD Guidelines for the Seismic Design of Highway Bridges, Parts I, II, and III. ATC-49a and ATC-49b, Applied Technology Council, Redwood City, CA; and MCEER-02-SP01, Multidisciplinary Center for Earthquake Engineering Research, State University of New York at Buffalo. With permission.)
s = vertical spacing of transverse reinforcement, not exceeding 100 mm Usf = strain energy capacity of transverse reinforcement = 110 MPa αshape = 12 and 15 for circular sections and rectangular section, respectively To restrain buckling of longitudinal reinforcement in plastic hinges, the transverse reinforcement shall satisfy the following requirements: For circular section: D s f ρs = 0.016 ρt y s db f yh
(18.50)
f Abh = 0.09 Ab y f yh
(18.51)
For rectangular section:
where D db fy fyh Ab Abh s
= = = = = = =
diameter of circular column diameter of longitudinal reinforcement bars being restrained by hoop or spiral minimum specified yield strength of longitudinal reinforcement bars minimum specified yield strength of transverse reinforcement bars area of longitudinal reinforcement bars being restrained by hoop or spiral area of hoops or spiral or ties restraining the longitudinal steel vertical spacing of transverse reinforcement restraining the longitudinal steel
The transverse reinforcement shall be provided in the plastic hinge zones as defined in Section 18.6.1.5. The transverse reinforcement shall meet the following spacing: 6 db s ≤ 0.25 (minimum member dimension) 150 mm
(18.52)
18.8.1.5.4 Joint Reinforcement • Moment-resisting integral connections shall be designed to resist the maximum plastic moment. • The principal tension stress pt and compression stress pc shall be calculated by:
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2
pt f + fv f + fv 2 = h m h + v hv 2 pc 2
Ajv
(18.53)
Ajv within D/2 Ast
>D/2 + Id
>D/2 + Id
Additional beam steel required both transversely and longitudinally = 0.08 Ast
D Note: Id = development length
FIGURE 18.26 Additional cap beam bottom reinforcement for joint force transfer. (From ATC/MCEER Joint Venture. 2001. Recommended LRFD Guidelines for the Seismic Design of Highway Bridges, Parts I, II, and III. ATC-49a and ATC-49b, Applied Technology Council, Redwood City, CA; and MCEER-02-SP01, Multidisciplinary Center for Earthquake Engineering Research, State University of New York at Buffalo. With permission.)
fh
= average axial stress in the horizontal direction within the plans of the connection under consideration (positive is compressive stress) (MPa) fh = average axial stress in the vertical direction within the plans of the connection under consideration (positive is compressive stress) (MPa) vhv = average shear stress within the plans of the connection (MPa) • The principal compression stress pc shall not exceed 0.25 fc ' • When the principal tension stress pt ≤ 0.29 fc' , for circular columns, or columns with intersecting spirals, the volumetric ratio of transverse reinforcement in the form of spirals or hoops to be continued into the cap or footing ρs shall not be less than 0.29 fc' / f yh, where fyh is the yield stress of the horizontal hoop/tie reinforcement in the joint. • When the principal tension stress stress pt > 0.29 fc ' the additional reinforcement shown in Figure 18.26 shall be provided as follows: •
On each side column, vertical stirrups: Ajv = 0.16Ast
•
Inside joint: the required vertical tie: Ajt = 0.08Ast
•
Longitudinal reinforcement: Ajl = 0.08Ast
•
Column hoop or spiral reinforcement into the cap: ρs ≥ 0.4Ast / l2ac
where Ast is the total area of longitudinal steel anchored in the joint and lac is the length of column reinforcement embedded into the joint. 18.8.1.5.5 Plastic Rotation Capacities In SDR 3 to 6, the plastic rotational capacity shall be based on the appropriate performance level and may be determined from tests and/or a rational analysis. The maximum plastic rotational capacity θp should be conservatively limited to 0.035 (0.05), 0.01, and 0.02 radians for life safety (for liquefiable pile foundation), operational performance, and in ground hinges, respectively. For the life-safety performance, the plastic hinge of the column should be calculated by: © 2003 by CRC Press LLC
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θ p = 0.11
Lp D'
(N )
2 ≤ N f = 3.5 (Tn )
−0.5
f
−1/3
≤ 10
(18.54)
(18.55)
where Nf = number of cycles of loading expected at maximum displacement amplitude, for liquefiable soil, take Nf = 2 Lp = effective plastic hinge length M 0.08 V + 4400 ε ydb Lp = L + 8800 ε d y b g εy Lg D' db
= = = =
for common columns
(18.56)
for columns with isolation gap
yield strain of longitudinal reinforcement gap length between the flare and adjacent element distance between outer layers of the longitudinal reinforcement diameter of the main longitudinal reinforcement bars
18.8.2 Caltrans SDC 18.8.2.1 Minimum Seat Width Requirements To prevent unseating of superstructures at hinges, piers, and abutments, the seat width should be available to accommodate the anticipated thermal movement, prestressing shortening, concrete creep and shrinkage, and the relative longitudinal earthquake displacement, and should not exceed the following minimum seat requirements [Caltrans, 2001a]: For seat width at hinges: ∆ ps + ∆ cr +sh + ∆temp + ∆ eq + 100 N min = larger of 600 mm
(18.57)
For seat width at abutments: ∆ ps + ∆ cr +sh + ∆temp + ∆ eq + 100 N min = larger of 760 mm
(18.58)
where ∆ps , ∆cr+sh, ∆temp and ∆eq are relative displacement due to prestressing, concrete creep and shrinkage, and earthquake, respectively (mm). ∆ Effects 18.8.2.2 P-∆ The P-∆ effects tend to increase the displacement and decrease lateral load-carrying capacity of a bridge column. These effects can typically be ignored if the moment (PDL∆) is less than or equal to 20% of the column plastic moment, i.e., PDL ∆ ≤0. 2 M col p . 18.8.2.3 Minimum Displacement Ductility Capacity To ensure the dependable ductile behavior of all columns regardless of seismic demand, a minimum local displacement ductility capacity of µc = ∆c /∆Y ≥ 3 is required, and target local ductility of µc ≥ 4 is
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recommended. The local displacement ductility capacity should be calculated for an equivalent member that approximates a fixed-base cantilever element. 18.8.2.4 Maximum (Target) Displacement Ductility Demand The engineers are encouraged to limit displacement ductility demands, defined as µD = ∆D /∆Y to the values shown in Table 18.12. TABLE 18.12 Caltrans Limiting Displacement Ductility Demand Values Item
Limiting µD = ∆D /∆Y
Single-column bents supported on fixed foundations Multi-column bents supported on fixed or pinned footings Pier walls (weak direction) supported on fixed or pinned footings Pier walls (strong direction) supported on fixed or pinned footings
4 5 5 1
Source: Caltrans, Seismic Design Criteria, Version 1.2, California Department of Transportation, Sacramento, CA, December 2001.
18.8.2.5 Minimum Lateral Strength Although providing ductile detailing is essential for achieving the expected performance requirements, each column should be designed to have a minimum lateral flexural capacity to resist a lateral force of 0.1 g. 18.8.2.6 Structural Steel Design Requirements Guide [Caltrans, 2001b] 18.8.2.6.1 Limiting Width-to-Thickness Ratios For capacity-protected components, the width-to-thickness ratios of compression elements shall not exceed the limiting value λr as specified in Table 18.13. For ductile components, width-to-thickness ratios shall not exceed the λp as specified in Table 18.13. Welds located in the expected inelastic region of ductile components are preferably complete penetration welds. Partial penetration groove welds are not recommended in these regions. If the fillet welds are the only practical solution for an inelastic region, quality control (QC) and quality assurance (QA) inspection procedures for the fracture critical members shall be followed. 18.8.2.6.2 Limiting Slenderness Ratio The slenderness parameter λc for compression members and λb for flexural members shall not exceed the limiting values, λcp and λbp , as specified in Table 18.14. 18.8.2.6.3 Limiting Axial Load Ratio High axial load in a column usually results in the early deterioration of strength and ductility. The ratio of factored axial compression due to seismic load and permanent loads to yield strength (Ag Fy) for columns in ductile moment-resisting frames and single column structures shall not exceed 0.3. 18.8.2.6.4 Shear Connectors Shear connectors shall be provided on the flanges of girders, end cross frames, or diaphragms to transfer seismic loads from the concrete deck to the abutments or pier supports. The cross frames or diaphragms at the end of each span are the main components to transfer the lateral seismic loads from the deck down to the bearing locations. Recent tests on a 0.4 scale experimental steel girder bridge (18.3 m long) conducted by the University of Nevada, Reno [Carden et al., 2001] indicated that too few shear connectors between the girders and deck at the bridge end did not allow the end cross frame not to reach its ultimate capacity.
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TABLE 18.13 Caltrans Limiting Width-to-Thickness Ratios No.
1
2
3
4
5
6
7
Description of Elements
Examples
Unstiffened Elements Flanges of I-shaped rolled beams Figure 18.27a and channels in flexure Figure 18.27c Outstanding legs of pairs of angles Figure 18.27d in continuous contact; flanges of Figure 18.27e channels in axial compression; angles and plates projecting from beams or compression members
Stiffened Elements Flanges of square and rectangular box and hollow structural section Figure 18.27b of uniform thickness subject to bending or compression; flange cover plates and diaphragm plates between lines of fasteners or welds. Unsupported width of cover Figure 18.27d plates perforated with a succession of access holes
Width-Thickness Ratios
λr
b/t
370
137 Fy
Fy – 69 b/t
b/t h/tw
Webs. in flexural compression
Figures 18.27a, d, f
h/tw
Figures 18.27a, c, d, f
h/tw
137
Fy
Fy
290
Fy (tubes)
400
Fy (others)
Fy
b/t
Figures 18.27a, c, d, f
250
625
b/t
All other uniformly compressed stiffened elements, i.e., supported along two edges
Webs. in combined flexural and axial compression
λp
830
400
Fy
Fy
665
290
Fy (w / lacing)
400
Fy (others)
Fy
2550
Fy
2550
1365
Fy
Fy
×
For Pu ≤ 0.125 φb Py 1365
0.74 P 1 − φ P b y
Fy
1.54 P 1 − φ P b y
For Pu > 0.125 φb Py 500 Fy ≥
P 2.33 – φ P b y 665 Fy
8
Longitudinally stiffened plates in Figure 18.27e compression
b/t
9
Round HSS in axial compression or flexure
D/t
297 k Fy
197 k Fy
17930 Fy
8950 Fy
Note: 1. Width-to-thickness ratios shown in bold are from AISC-LRFD [1999] and AISC, Seismic Provisions, 1997. Fy is MPa 2. k = buckling coefficient specified by Article 6.11.2.1.3a of AASHTO-LRFD, 1998; for n = 1, k = (8 Is /bt 3)1/3 ≤ 4.0; for n = 2, 3, 4, and 5, k = (14.3 Is /bt 3n4)1/3 ≤ 4.0; n = number of equally spaced longitudinal compression flange stiffeners; Is = moment of inertia of a longitudinal stiffener about an axis parallel to the bottom flange and taken at the base of the stiffener Source: Caltrans. 2001b. Guide Specifications for Seismic Design of Steel Bridges, California Department of Transportation, Sacramento, CA, December. © 2003 by CRC Press LLC
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b
b 3 Flexure or Axial Compression 1 Flexure 2 Axial Compression
h or b
c 5 Axial Compression 6 Flexure 7 Flexure and Axial Compression
(a) Rolled I Section
(b) Hollow Structural Tube
b
b 1 Flexure 2 Axial Compression
1 Flexure 2 Axial Compression
h c
5 Axial Compression 6 Flexure 7 Flexure and Axial Compression
5 Axial Compression 6 Flexure 7 Flexure and Axial Compression
(c) Built up Channels
(d) Built Up I Section
b
8 Flexure or Axial Compression 2 Flexure and Axial Compression
h or b
b
5 Flexure 6 Axial Compression
5 Axial Compression 6 Flexure 7 Flexure and Axial Compression
b
b
(e) Longitudinally Stiffened Built Up Box Section
(f) Built up Box
FIGURE 18.27 Selected steel cross sections. (From Caltrans. 2001b. Guide Specifications for Seismic Design of Steel Bridges, California Department of Transportation, Sacramento, CA, December.)
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TABLE 18.14 Caltrans Limiting Slenderness Parameters Member Classification Compression Member Flexural Member Compression Member Flexural Member
Ductile Capacity-Protected KL
Fy
Limiting Slenderness Parameters λcp λbp λcp λbp
0.75 17240/Fy 1.5 1970/ Fy L
Note: λc = rπ E (slenderness parameter for compression members); λb = r (slenderness parameter for flexural members); λcp = limiting slenderness parameter for compression members; λbp = limiting slenderness parameter for flexural members; K = effective length factor of a member; L = unsupported length of a member (mm); r = radius of gyration (mm); ry = radius of gyration about the minor axis (mm); Fy = specified minimum yield strength of steel (MPa); E = modulus of elasticity of steel (200,000 MPa) Source: Caltrans, 2001b. Guide Specifications for Seismic Design of Steel Bridges, California Department of Transportation, Sacramento, CA, December. y
18.8.2.7 Concrete Design Requirements 18.8.2.7.1 Limiting Longitudinal Reinforcement Ratios The ratio of longitudinal reinforcement to the gross cross section shall not be less than 0.001 and 0.005 for columns and pier walls, respectively, and more than 0.04. 18.8.2.7.2 Transverse Reinforcement in Plastic Hinge Zones For confinement in plastic hinge zones (larger of 1.5 times cross-sectional dimension in the direction of bending and the regions of column where the moment exceeds 75% of overstrength plastic moment, M col p ), transverse reinforcement shall not be less than [Caltrans, 2000]: 4A For spiral and hoops ρs = bh : D' s
ρs min
1.25P f 'A 0.45 c g − 1 0.5 + ' e f y Ac fc Ag = fc ' 1.25Pe 0.12 0.5 + ' fy fc Ag
for D ≤ 0.9 m (18.59) for D > 0.9 m
For ties:
Ash, min
1.25P f 'A 0.3 s hc c g − 1 0.5 + ' e f A fc Ag y c = larger of 1.25Pe fc ' 0.12 s hc 0.5 + ' fy fc Ag
(18.60)
where Ash = total cross-sectional area of tie reinforcement including supplementary cross tie within a section having limits of s and hc hc = core dimension of tied column in the direction under consideration (out-to-out of ties) s = vertical spacing of transverse reinforcement D' = center-to-center diameter of perimeter hoop or spiral
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The spacing of the transverse reinforcement in the plastic hinge zones shall meet: 6 db s ≤ 0.2 Dmin 220 mm
(18.61)
Dmin = the least cross section dimension for columns and one half of the least cross section dimension of piers 18.8.2.7.3 Joint Proportion and Reinforcement [Calrans, 2001a; Zelinsky, 1994] • Moment-resisting integral connections shall be designed to resist the overstrength capacity M col p and associated shear. • The principal tension stress pt and compression stress pc shall not exceed 1.0 fc' and 0.25 fc ' , respectively. The bent cap width shall not be less than the cross section dimension of the column in the direction of bending plus 600 mm. • When the principal tension stress pt ≤ 0.29 fc ' , for circular columns, or columns with intersecting spirals, the volumetric ratio of transverse reinforcement in the form of spirals or hoops to be continued into the cap or footing ρs shall not be less than 0.29 fc ' / f yh. • When the principal tension stress pt > 0.29 fc ' the additional reinforcement as shown in Figures 18.28 and 18.29 shall be provided and well distributed within D/2 from the face of the column. All joint shear reinforcement should be as follows: • On each side column, vertical stirrups: Asjv = 0.2 Ast • Horizontal stirrups or tiles: Asjh = 0.1Ast • Longitudinal side reinforcement: Assf ≥ 0.1 Acap, where Acap is area of bent cap top or bottom flexural steel • Column hoop or spiral reinforcement into the cap: ρs ≥ 0.4 Ast / lac2 • Horizontal reinforcement shall be stitched across the cap in two or more intermediate layers. The reinforcement shall be shaped as hairpins, spaced vertically at not more than 460 mm. The hairpins shall be 10% of column reinforcement. Spacing shall be denser outside the column than that used within the column. • For bent caps skewed greater than 20°, the vertical J-bars hooked around the longitudinal deck and bent cap steel shall be 8% of column steel (see Figure 18.30). The J-bars shall be alternatively 600 mm and 750 mm long and placed within a width of the column dimension on either side of the column centerline. • All vertical column bars shall be extended as high as practically possible without interfering with the main cap bars. 18.8.2.7.4 Effective Plastic Hinge Length The effective plastic hinge length is used to evaluated the plastic rotation of columns. 0.08 L + 0.022 f ye db ≥ 0.044 f ye db L p = G + 0.044 f yedb * D + 0.06 H ′
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for columns and Type II shafts for horizontally isolated flared columns for non-cased Type I shafts
(18.62)
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Bent Cap Details, Section at Column for Bridges with 0 to 20-Degree Skew. (Detail Applies to Sections Within 2 x Diameter of Column, Centered About CL of Column). (Detail Applies to T-Beam and Box Girder Bridges Where Deck Reinforcement is Placed Parallel to Cap). Construction Joint
jv As Joint Shear Reinforcement @ 300 through column area
@ __ Beyond column area 75 min jh As Horiz. Cross Ties or sf As
L=0.75(skew cap width)
300 mm Typ
Transverse Column Reinforcement
Dc
FIGURE 18.28 Example of cap joint shear reinforcement — skews 0o to 20o. (From Caltrans. 2001a. Seismic Design Criteria, Version 1.2, California Department of Transportation, Sacramento, CA, December.)
where fye = expected yield stress of the longitudinal reinforcement L = member length from the maximum moment to the point of contra-flexure H' = length of pile shaft/column from the ground surface to the point of contra-flexure above ground D* = less cross section dimension of shafts
Defining Terms Capacity-protected component — A component expected to experience minimum damage and to behave essentially elastically during the design earthquakes.
Concentrically braced frame (CBF) — A diagonally braced frame in which all members of the bracing system are subjected primarily to axial forces.
Connections — A combination of joints used to transmit forces between two or more members. Design earthquake — Earthquake loads represented by acceleration response spectrum (ARS) curves specified in design specifications or codes.
Displacement ductility — Ratio of ultimate to yield displacement. © 2003 by CRC Press LLC
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Bent Cap Elevation. Horizontal Cross Tie and J-bar Placing Pattern. CL Column = Line of Symmetry Limits of J-bars Limits of Horiz. Cross ties Vertical Stirrups J-bars. Alternate Vertical Lengths 600 and 700 mm jh As Horiz. Cross Ties or
L=0.75(skew cap width) for skew<20 L=0.75(cap width) for skew>20 Dc/2
Dc
Dc/2
FIGURE 18.29 Location of horizontal joint shear reinforcement. (From Caltrans. 2001a. Seismic Design Criteria, Version 1.2, California Department of Transportation, Sacramento, CA, December.)
Ductile component — A component expected to experience repairable damage during the FEE and significant damage but without failure during the SEE. Ductility — Ratio of ultimate to yield deformation. Eccentrically braced frame (EBF) — A diagonally braced frame that has at least one end of each bracing member connected to a link. Expected nominal strength — Nominal strength of a component based on its expected yield strength. Functional evaluation earthquake (FEE) — A lower level design earthquake that has relatively small magnitude but may occur several times during the life of the bridge. It may be assessed either deterministically or probabilistically. The determination of this event is to be reviewed by a Caltrans-approved consensus group. Joint — An area where member ends, surfaces, or edges are attached. Link — In EBF, the segment of a beam that is located between the ends of two diagonal braces or between the end of a diagonal brace and a column. Under lateral loading, the link deforms plastically in shear thereby absorbing energy. The length of the link is defined as the clear distance between the ends of two diagonal braces or between the diagonal brace and the column face. Liquefaction — Seismically induced loss of shear strength in loose, cohesionless soil that results from a build-up of pour pressure as the soil tries to consolidate when exposed to seismic vibrations. Maximum credible earthquake (MCE) — The largest earthquake that is capable of occurring along an earthquake fault, based on current geologic information as defined by the 1996 Caltrans Seismic Hazard Map.
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Bent Cap Details, Section at Column for Bridges with Skew Larger than 20 Degrees. (Detail Applies to Sections Within 2 x Diameter of Column, Centered About CL of Column). (Detail Applies to T-Beam and Box Girder Bridges Where Deck Reinforcement is Placed Normal or Radial to CL Bridge). Construction Joint J-bars. Alternate Vertical Lengths 600 and 700 mm
jv As Joint Shear Reinforcement
75 min
@ 300 through column area
@ __ Beyond column area
sf As
jh As Horiz. Cross Ties or
L=0.75(cap width) 300 mm Typ
Transverse Column Reinforcement
Dc
FIGURE 18.30 Example of cap joint shear reinforcement — skews more than 20o. (From Caltrans. 2001a. Seismic Design Criteria, Version 1.2, California Department of Transportation, Sacramento, CA, December.)
Moment-resisting frame (MRF) — A frame system in which seismic forces are resisted by shear and flexure in members, and connections in the frame.
Nominal strength — The capacity of a component to resist the effects of loads, as determined by computations using specified material strength, dimensions and formulas derived from acceptable principles of structural mechanics or by field tests or laboratory tests of scaled models, allowing for modeling effects and differences between laboratory and field conditions. Overstrength capacity — The maximum possible strength capacity of a ductile component considering actual strength variation between the component and adjacent components. It is estimated by an overstrength factor of 1.2 times expected nominal strength. Plastic hinge — A concentrated “zero length” hinge that maintains its plastic moment capacity and rotates freely. Plastic hinge zone — A region of structural components that are subject to potential plastification and thus must be detailed accordingly. Seismic performance criteria — The levels of performance in terms of postearthquake service and damage that are expected to result from specified earthquake loadings.
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Safety evaluation earthquake (SEE) — An upper level design earthquake that has only a small probability of occurring during the life of the bridge. It may be assessed either deterministically or probabilistically. The deterministic assessment corresponds to the MCE. The probabilistically assessed earthquake typically has a long return period (approximately 1000 to 2000 years). Ultimate displacement — The lateral displacement of a component or a frame corresponding to the expected damage level, not to exceed the displacement when the lateral resistance degrades to a minimum of 80% of the peak resistance. Upper bound solution — A solution calculated on the basis of an assumed mechanism that is always at best equal to or greater than the true ultimate load. Yield displacement — The lateral displacement of a component or a frame at the onset of forming the first plastic hinge.
References AASHTO (American Association of State Highway and Transportation Officials). 2000. Guide Specifications for Seismic Isolation Design, American Association of State Highway and Transportation Officials, Washington, D.C. AASHTO (American Association of State Highway and Transportation Officials). 1998–2000. LRFD Bridge Design Specifications, 2nd ed. (1998), and 1999–2000 interim versions, American Association of State Highway and Transportation Officials, Washington, D.C. AASHTO (American Association of State Highway and Transportation Officials). 1996. Standard Specifications for Highway Bridges, 16th ed., American Association of State Highway and Transportation Officials, Washington, D.C. AISC (American Institute of Steel Construction). 1997. Seismic Provisions for Structural Steel Buildings (1997), Supplement No. 1 (1999) and Supplement No. 2 (2000). American Institute of Steel Construction, Chicago, IL. AISC (American Institute of Steel Construction). 1999. Load and Resistance Factor Design Specification for Structural Steel Buildings, 3rd ed., American Institute of Steel Construction, Chicago, IL. Akkari, M. and Duan, L. 2000. “Nonlinear Analysis of Bridge Structures,” in Bridge Engineering Handbook, Chen, W.F. and Duan, L., Eds., CRC Press, Boca Raton, FL, chap. 36. Astaneh-Asl, A. and Roberts, J., Eds. 1993. Seismic Design, Evaluation and Retrofit of Steel Bridges: Proceedings of the First U.S. Seminar, San Francisco, CA, October 18, Department of Civil Engineering, University of California, Berkeley. Astaneh-Asl, A. and Roberts, J., Eds. 1997. Seismic Design, Evaluation and Retrofit of Steel Bridges: Proceedings of the Second U.S. Seminar, San Francisco, CA, November 20–21, Department of Civil Engineering, University of California, Berkeley.. ATC (Applied Technology Council). 1981. Seismic Design Guidelines for Highway Bridges, ATC-6, Applied Technology Council, Redwood City, CA. ATC (Applied Technology Council). 1996. Improved Seismic Design Criteria for California Bridges: Provisional Recommendations, ATC-32, Applied Technology Council, Redwood City, CA. ATC/MCEER Joint Venture. 2001. Recommended LRFD Guidelines for the Seismic Design of Highway Bridges, Part I: Specifications; Part II: Commentary and Appendixes, Preliminary Report, ATC Report nos. ATC-49a and ATC-49b, and MCEET Technical Report no. MCEER-02-SP01, Applied Technology Council, Redwood City, CA and Multidisciplinary Center for Earthquake Engineering Research, State University of New York at Buffalo, November. Caltrans. 1990. Bridge Design Specifications, California Department of Transportation, Sacramento, CA. Caltrans. 1991. First Annual Seismic Research Workshop, Division of Structures, California Department of Transportation, Sacramento, CA.
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Caltrans. 1993. Second Annual Seismic Research Workshop, Division of Structures, California Department of Transportation, Sacramento, CA. Caltrans. 1994. The Third Annual Seismic Research Workshop, Division of Structures, California Department of Transportation, Sacramento, CA. Caltrans. 1995a. Bridge Memo to Designers (20–4), California Department of Transportation, Sacramento, CA. Caltrans. 1995b. Bridge Design Aids, California Department of Transportation, Sacramento, CA. Caltrans. 1996. The Fourth Caltrans Seismic Research Workshop, Engineering Service Center, California Department of Transportation, Sacramento, CA. Caltrans. 1997. San Francisco–Oakland Bay Bridge West Spans Seismic Retrofit Design Criteria, prepared by Reno, M., and Duan, L. edited by Duan, L., California Department of Transportation, Sacramento, CA. Caltrans. 1998. The Fifth Caltrans Seismic Research Workshop, Engineering Service Center, California Department of Transportation, Sacramento, CA. Caltrans. 1999a. Bridge Memo to Designers (20–1): Seismic Design Methodology, California Department of Transportation, Sacramento, CA, January. Caltrans. 1999b. San Francisco–Oakland Bay Bridge East Span Seismic Safety Project Design Criteria, Version 7, prepared by TY Lin/Moffatt & Nichol Engineers, California Department of Transportation, Sacramento, CA, July 6. Caltrans. 2000. Bridge Design Specifications: LFD Version, California Department of Transportation, Sacramento, CA, April. Caltrans. 2001a. Seismic Design Criteria, Version 1.2, California Department of Transportation, Sacramento, CA, December. Caltrans. 2001b. Guide Specifications for Seismic Design of Steel Bridges, California Department of Transportation, Sacramento, CA, December. Caltrans. 2001c. Seismic Design of Abutments for Ordinary Standard Bridges, Division of Structure Design, California Department of Transportation, Sacramento, CA, March 20. Caltrans. 2001d. The Sixth Caltrans Seismic Research Workshop, Division of Engineering Services, California Department of Transportation, Sacramento, CA, June 12–13. Carden, L., Garcia-Alvarez, S., Itani, A, and Buckle, I. 2001. “Cyclic Response of Steel Plate Girder Bridges in the Transverse Direction,” in The Sixth Caltrans Seismic Research Workshop, Division of Engineering Services, California Department of Transportation, Sacramento, CA, June 12–13. Chen, W.F. and Atsuta, T. 1977. Theory of Beam-Columns, Vols. 1 and 2, McGraw-Hill, New York. Chen, W.F. and Duan, L., Eds. 2000. Bridge Engineering Handbook, CRC Press, Boca Raton, FL. Chen, W.F., and Toma, S. 1994. Advanced Analysis of Steel Frames, CRC Press, Boca Raton, FL. Cheng, C.T. and Mander, J.B. 1997. Seismic Design of Bridge Columns Based on Control and Repairability of Damage, NCEER-97–0013, State University of New York at Buffalo. Cheng, W. 2000. “Spectrum Simulation Models for Random Ground Motions and Analysis of Long-Span Bridges under Random Earthquake Excitations,” Ph.D. dissertation, Hunan University, Changsha, China. Duan, L. and Cooper, T.R. 1995. “Displacement Ductility Capacity of Reinforced Concrete Columns,” ACI Concrete Int., 17, 61–65. European Committee for Standardization. 1995. Eurocode 8: Structures in Seismic Regions — Design, Part 2: Bridges, European Committee for Standardization, Brussels, Belgium. Fan, L.C., Wang, J.J., and Chen, W. 2001. “Response Characteristics of Long-Span Cable-Stayed Bridges under Non-Uniform Seismic Action,” Chinese J. Comput. Mech., 18, 358–363. FHWA (Federal Highway Administration). 1987. Seismic Design and Retrofit Manual for Highway Bridges, Report no. FHWA-IP-87–6, Federal Highway Administration, Washington, D.C. FHWA (Federal Highway Administration). 1995. Seismic Retrofitting Manual for Highway Bridges, Publ. No. FHWA-RD-94–052, Federal Highway Administration, Washington, D.C.
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FHWA and Caltrans. 1995. Proceedings of First National Seismic Conference on Bridges and Highways, San Diego, CA, December 10–13, Federal Highway Administration, Washington, D.C. and California Department of Transportation, Sacramento, CA. FHWA and Caltrans. 1997. Proceedings of Second National Seismic Conference on Bridges and Highways, Sacramento, CA, July 8–11, Federal Highway Administration, Washington, D.C. and California Department of Transportation, Sacramento, CA. FHWA-NSF. 2000. Proceedings 16th U.S.–Japan Bridge Engineering Workshop, Lake Tahoe, Nevada, Oct. 2–4, Federal Highway Administration, Washington, D.C. Heredia-Zavoni, E. and Vanmarcke, E.H. 1994. “Seismic Random-Vibration Analysis of MultisupportStructural Systems,” J. Eng. Mech., 120, 1107–1128. Housner, G.W. 1990. Competing Against Time, Report to Governor George Deuknmejian from the Governor’s Broad of Inquiry on the 1989 Loma Prieta Earthquake, Sacramento, CA. Housner, G.W. 1994. The Continuing Challenge: The Northridge Earthquake of January 17, 1994, Report to Director, California Department of Transportation, Sacramento, CA. IAI (Imbsen and Association, Inc.). 1995. Benicia-Martinez Bridge Seismic Retrofit: Main Truss Spans Final Retrofit Strategy Report, Imbsen and Association, Sacramento, CA. Japan Road Association. 1996. Design Specifications of Highway Bridges, Part I: Common, Part II: Steel, Part III: Concrete Bridges, Part IV: Foundations, and Part V: Seismic Design (English Version, July 1998). Kawashima, K. and Unjoh, S. 1997. “The Damage of Highway Bridges in the 1995 Hyogo-Ken Naubu Earthquake and its Impact on Japanese Seismic Design,” J. Earthquake Eng., 1, 505. Keever, M.D., “Caltrans Seismic Design Criteria,” in Proceedings of 16th U.S.–Japan Bridge Engineering Workshop, Lake Tahoe, Nevada, Oct. 2–4, Federal Highway Administration, Washington, D.C. King, W.S., White, D.W., and Chen, W.F. 1992. “Second-Order Inelastic Analysis Methods for Steel-Frame Design,” J. Struct. Eng., 118, 408–428. Kiureghian, A.D. and Neuenhofer, A. 1992. “Response Spectrum Method for Multisupport Seismic Excitations,” Earthquake Eng. Struct. Dyn., 21, 713–740. Kowalsky, M.J., Priestley, M.J.N., and MacRae, G.A. 1994. Displacement-Based Design, Report no. SSRP94/16, University of California, San Diego. Levy, R., Joseph, F., and Spillers, W.R. 1997. “Member Stiffness with Offset Hinges,” J. Struct. Eng., 123, 527–529. Lin, J.H., Zhang, W.S., and Williams, F.W. 1994a. “Pseudo-Excitation Algorithm for Nonstationary Random Seismic Responses,” Eng. Struct., 16, 270–276. Lin, J.H., Zhang, W.S., and Li, J.J. 1994b. “Structural Responses to Arbitrarily Coherent Stationary Random Excitations,” Comp. Struct., 50, 629–633. Lin, J.H., Li, J.J., Zhang, W.S., and Williams, F.W. 1997. “Non-stationary Random Seismic Responses of Multi-Support Structures in Evolutionary Inhomogeneous Random Fields,” Earthquake Eng. Struct. Dyn., 26, 135–145. Lin, J.H., Zhang, Y.H., and Zhao, Y. 2001. “High Efficiency Algorithm Series of Random Vibration and Their Applications,” Proceedings 8th International Conference on Enhancement and Promotion of Computational Methods in Engineering and Science, Shanghai, China, pp. 120–131. Lin, J.H., Zhao, Y., and Zhang, Y.H., “Accurate and Highly Efficient Algorithms for Structural Stationary/ Non-Stationary Random Responses,” Computer Meth. Appl. Mech. Eng., 191, 103–111. Mander, J.B. and Cheng, C.T. 1997. Seismic Resistance of Bridge Piers Based on Damage Avoidance Design, NCEER-97–0014, State University of New York at Buffalo. Moehle, J.P. and Eberhard, M.O. “Earthquake Damage to Bridges,” in Bridge Engineering Handbook, Chen, W.F. and Duan, L., Eds., CRC Press, Boca Raton, FL, chap. 34. Park, R., Ed. 1994. Seismic Design and Retrofitting of Reinforced Concrete Bridges: Proceedings Second International Workshop, Queenstown, New Zealand, August 9–12, Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand. Park, R. and Paulay, T. 1975. Reinforced Concrete Structures, John Wiley & Sons, New York. © 2003 by CRC Press LLC
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Priestley, M.J.N., Seible, F., and Calvi, G.M. 1996. Seismic Design and Retrofit of Bridges, John Wiley & Sons, New York. Priestley, N. 1993. “Myths and Fallacies in Earthquake Engineering: Conflicts between Design and Reality,” in Proc. Tom Paulay Symposium: Recent Development in Lateral Force Transfer in Buildings, University of California, San Diego. Rojahn, C. et al. 1997. Seismic Design Criteria for Bridges and Other Highway Structures, Report no. NCEER-97–0002, National Center for Earthquake Engineering Research, State University of New York at Buffalo. (ATC-18, Applied Technology Council, Redwood City, CA.) Troitsky, M.S. 2000. “Conceptual Bridge Design,” in Bridge Engineering Handbook, Chen, W.F. and Duan, L., Eds., CRC Press, Boca Raton, FL, chap. 1. Unjoh, S. 2000. “Seismic Design Practice in Japan,” in Bridge Engineering Handbook, Chen, W.F. and Duan, L., Eds., CRC Press, Boca Raton, FL, chap. 44. U.S. Geological Survey. 2001. http://www.geohazards.cr.usgs.gov/eq/. Yashinsky, M. 2000. “Earthquake Damage to Structures,” in Structural Engineering Handbook CRCnetBase 2000, Chen, W.F. and Duan, L., Eds., CRC Press, Boca Raton, FL, chap. 29a. Zelinski, R. 1994. Seismic Design Memo Various Topics Preliminary Guidelines, California Department of Transportation, Sacramento, CA. Zhang, R. 2000. “Seismic Isolation and Supplemental Energy Dissipation,” in Bridge Engineering Handbook, Chen, W.F. and Duan, L., Eds., CRC Press, Boca Raton, FL, chap. 41.
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19 Structural Control 19.1 Introduction History of Structural Control · Structural Control for Specific Seismic Performance of Structures · Ductility Demand vs. Structural Control
19.2 Structural Control Concepts Passive, Active, Hybrid, and Semiactive Control · Type of Control · Principles of Seismic Structural Response Control
19.3 Structural Control Hardware and Software Passive Control · Active Control · Hybrid Control · Semiactive Control
19.4 Examples of the Application of Semiactive Control
Hirokazu Iemura and Mulyo Harris Pradono Department of Civil Engineering Systems Kyoto University Kyoto, Japan
Semiactive Control of Full-Scale Structures Using a Variable Joint Damper System · Application of Structural Control Technologies to Seismic Retrofit of a Cable-Stayed Bridge
19.5 Concluding Remarks Defining Terms References Further Reading
19.1 Introduction Structural control is basically the modification of the properties of a structure, such as a building or bridge, in order to achieve a structurally desirable response to a given external load. The modification of the structure’s properties includes changes in the damping and stiffness of the structure, so that it can respond more favorably to the external loading. Structural control is most typically employed in cases involving dynamic loads, so that the potential exists for modification of the structure’s properties to permit a reduction in the level of excitation transmitted to the structure. Although the concept of structural control is appealing and exciting, the basic concepts of structural control themselves are not new. They have been the staple of electrical and control engineering for decades, and have been applied successfully in a variety of disciplines, such as aerospace and mechanical engineering. However, structural control of civil engineering structures has a more recent origin, and its application to civil engineering structures is unique and presents a host of new challenges, especially for reducing earthquake structural responses, because of the uncertainties and the mighty power of earthquake forces.
19.1.1 History of Structural Control Since a special theme session entitled “Seismic response control of structural systems” was held at the Ninth World Conference on Earthquake Engineering (9WCEE) in 1988 in Japan, active vibration control of buildings and other civil structures has attracted a growing interest worldwide as an innovative
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technology in earthquake engineering. In line with this fact, and a growing demand for active vibration control research in Japan, the Japan Panel on Structural Response Control Research was established in the Liaison Committee of Earthquake Engineering Research of the Science Council of Japan, in September 1989. The objectives of this panel are (1) to summarize the state of the art of structural response control in different engineering fields in Japan, (2) to exchange current information on structural control response with foreign countries, and (3) to develop future programs for international collaboration. In recognition of the growing awareness by civil engineers worldwide of the potential of active (hybrid) protective systems for natural hazard mitigation, the U.S. Panel on Structural Control Research was established in 1990 under the auspices of the National Science Foundation. The panel’s objectives are: 1. 2. 3. 4. 5.
Facilitating the transmission of information concerning state-of-the-art developments in the field Identifying and prioritizing needed research and development Developing preliminary plans for analytical and experimental advancement in the field Developing plans for the performance of full-scale testing and demonstration Collaborating with international organizations
In March 1990, the first U.S.–Japan Panel Joint Committee was held in Tokyo, welcoming Professors G. Housner, S. Masri, and T.T. Soong. Plans were developed to convene individual national workshops and to hold a joint international workshop. In October 1990, the first U.S. National Workshop was held at the University of Southern California, where Professor Kobori and other researchers from Japan were invited to attend. In 1994, the First World Conference on Structural Control was held in Pasadena, California. It was followed by the Second World Conference on Structural Control in 1998 in Kyoto, Japan, where Professor Kobori was the president of the organizing committee. The Third World Conference on Structural Control was held in 2002 in Como, Italy, where Professor F. Casciati served as the president of the organizing committee. The conferences showed a growing interest among researchers, as well as innovations and applications of structural control technologies in civil structures. It is worth noting that a very early application of structural control response in earthquakes was that by John Milne when he was professor of engineering at the Imperial Engineering College in Tokyo in the 1880s. He put a small structure on ball bearings of rough, irregular shape, thus isolating the structure from the ground and also providing some damping [Housner, 1992]. However, structural control systems in reality existed several centuries earlier in Japan, due to an unknown engineer. They were applied to the construction of a Gojunoto (pagoda). The pagoda was five stories tall and was constructed of closely fitting, mortised wooden beams and columns (Figure 19.1). During an earthquake, the vibrations of such a vertical cantilever structure would produce bending moments that could not be resisted by tension at the mortised joints. To overcome this weakness, a long wooden pole was suspended freely from the upper part of the pagoda to act as a pendulum if the pagoda were excited into motion by an earthquake. The weight of the pole exerted a compressive prestress on the pagoda, thus increasing the bending resistance. The bottom of the pole extended into a cylindrical hole in the ground that was of larger diameter than the pole. Thus, when the pagoda was excited into vibrations by an earthquake, some of the vibrational energy would be transferred into oscillations of the pole, and the impact of the pole on the sides of the hole would dissipate energy.
19.1.2 Structural Control for Specific Seismic Performance of Structures Severe damage in the 1995 Kobe earthquake led to a public demand in Japan for satisfactory seismic performance of civil infrastructures. Civil infrastructures are constructed with taxes paid by the public, so that collapse or near collapse with irreparable damage cannot be accepted, even under a very rare earthquake loading. Civil infrastructure is also expected to serve as a public resource to help with the reconstruction of an earthquake-stricken society. For this purpose, civil infrastructure must be repaired in a relatively short time, even though its functions are temporarily lost under severe earthquake loading. This public demand for acceptable seismic performance of infrastructure shows that structural damage must be limited (Figure 19.2). These motivations have led to the development of innovations in structural control. © 2003 by CRC Press LLC
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Wooden Pagoda
Suspended pole
FIGURE 19.1 Sketch of wooden pagoda with suspended pole that is free to oscillate. (From Tanabashi, R. 1960. “Earthquake Resistance of Traditional Japanese Wooden Buildings,” in Proc. Second World Conference on Earthquake Engineering, Vol. 1, p. 151.) Earthquake Performance Level Operational Near collapse Fully Life safe Operational Frequent (T=43 years)
Earthquake Design Level
Occasional (T=72 years)
Unacceptable Performance (for New Construction)
Rare (T=475 years) Very rare (T=970 years)
FIGURE 19.2 Public demand for seismic performance of infrastructures.
19.1.3 Ductility Demand vs. Structural Control Methods for design against earthquake forces can be grouped into three categories [Kobori, 1992], which are schematically illustrated in Figure 19.3: 1. Conventional ductility demand (or inelastic) design methods 2. Base isolation design methods 3. Dynamic response control methods © 2003 by CRC Press LLC
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Moving Mass Control
Ductility Demand Design Ductility of Members
Viscous Type Damping
Aseismic Wall Joint Damper
Hysteretic Type Damping
Braces Active Varying Stiffness
Base Isolation Design
Base Isolation Bearings
Dynamic Control
FIGURE 19.3 Schematic illustration of ductility demand design, base isolation, and dynamic control.
19.1.3.1 Ductility Demand Design Methods The basic concept of conventional inelastic design is to provide a structure sufficient dynamic strength and ductility, enabling the structural system as a whole to absorb the seismic energy. To make a structure as resistant to earthquakes as it would be if its dynamic strength were increased 10 times (e.g., from 0.2 to 2.0 g), the structure must have sufficient ductility to maintain its resistance when substantially deformed. Although some damage will occur, such as the cracking of concrete and yielding of steel materials, the structure should not suffer major collapse. With the inelastic seismic design methods, lower elastic strength is required for structures with higher ductility. However, when structural response goes far into the plastic range (ductility factor µ = 10), the structure may not be operational or repairable after the earthquake. 19.1.3.2 Base Isolation Methods In recent years, especially after the 1995 Kobe earthquake, base isolation techniques were actively adopted in the construction of buildings, bridges, and other structures in Japan. The basic principle of base isolation is to reduce the input earthquake energy with soft bearings, and to suppress excessive displacement by damping. Code provisions for base-isolated buildings and bridges have been developed in Japan and employed for actual structures. Recent earthquake records obtained from base-isolated buildings during the 1994 Northridge and 1995 Kobe earthquakes show effective reduction of earthquake response in base-isolated structures. In the restoration of the Hanshin Expressway, Kobe Route, base isolation bearings were used at the foot of the columns of the frame-type highway viaduct to reduce seismic forces acting on the foundations. This is a unique method of implementation of isolation bearings, in which effects of variation of the axial and rotational forces cannot be neglected. The reliability of base-isolated bearings under these combined loads has been experimentally tested by Iemura and coworkers [1996a].
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19.1.3.3 Dynamic Response Control Methods For increased reliability of structures under severe earthquake motion, structural control techniques, which effectively reduce the seismic force to the structure, are required. Although there were no structures with seismic response control devices in the area affected by the 1995 Kobe earthquake, the importance of structural control techniques emerged with the realization that the function of important structures must be maintained. The rapid development of information technology has stimulated researchers to intensify development of a new concept with the new philosophy of aseismic design, i.e., design of intelligent or controlled structures.
19.2 Structural Control Concepts 19.2.1 Passive, Active, Hybrid, and Semiactive Control Systems for control of structural response can be divided into four groups: passive, active, hybrid, and semiactive. 19.2.1.1 Passive Control Maintenance of passive control systems is relatively easy because they do not require sensors, actuators, or controllers. In passive systems, whether they are dynamic absorbers of vibrations, systems for additional energy dissipation, or even seismic isolation systems, the controlling forces develop at the locations of installation of the mechanism itself. The energy necessary for generation of these forces is provided through the motion of the mechanism during the dynamic excitation. The relative motion of the mechanism defines the amplitude and the direction of the controlling force. 19.2.1.2 Active Control Due to recent developments of sensoring and digital control techniques, active and semiactive control methods of dynamic response of structures are emerging and some are being implemented in buildings and bridges. The advantage of active control methods is that they are effective for a wide frequency range, as well as for transient vibrations. However, active control methods require a large external energy supply, as well as a high level of maintenance. When a linear feedback control law with constant control gain is used, saturation of the control force cannot be avoided at the time of strong earthquake ground motions. Hence, a nonlinear control algorithm with variable gain has been proposed, and its effectiveness is now being tested on a full-scale building model at the Disaster Prevention Research Institute (DPRI) of Kyoto University. The full-scale model and nonlinear control algorithm are explained in detail by Iemura and coworkers [1996b]. 19.2.1.3 Hybrid Control Hybrid control methods, which combine both passive and active devices, have been proposed and implemented, utilizing the advantages and avoiding the disadvantges of the passive and active methods, so that higher levels of performance may be achieved. Additionally, the resulting hybrid control system can be more reliable than a fully active system, although it is often somewhat more complicated. One example of a hybrid system is a TMD (tuned mass damper) with actuators that are put between the TMD mass and its support to increase the effectiveness of the TMD. Figure 19.4 illustrates a schematic diagram of passive TMD, active AMD (active mass damper), and hybrid ATMD (active tuned mass damper). A more detailed explanation of hybrid ATMD is presented in Section 19.3. Another example of hybrid control that has been studied by many researchers is a combination of base isolation with some form of active control to limit excessive displacement [Kageyama et al., 1992; Fujii et al., 1992; Reinhorn and Riley, 1994; Feng et al., 1993].
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Auxiliary Mass
Auxiliary Mass
m2
m2
Spring
Damper
m1
Auxiliary Mass
m2 Control
Control
G
G
Actuator
m1
m1 Sensor
Passive
Active
Sensor
Hybrid
FIGURE 19.4 Schematic diagram of passive, active, and hybrid mass damper system.
Excitation
Structure
Response
Control Actuators
Sensors
Controller
Sensors
FIGURE 19.5 Schematic diagram of structural control.
19.2.1.4 Semiactive Control Semiactive control systems are basically derived from passive systems that are modified to make adjustment or correction of their mechanical characteristics possible. Unlike active systems, controlling forces are developed at places of installation of semiactive mechanisms, whereas external energy is used only for adjustment of the mechanical characteristics of the system [Rakicevic and Jurukovski, 2001]. Semiactive control systems combine the best features of both passive and active approaches, offering the reliability of passive devices and maintaining the versatility and adaptability of fully active systems. Semiactive control devices have properties that can be adjusted in real time but cannot input energy into the structure being controlled. Such devices typically have very low power requirements, which is particularly critical during seismic events when the main power source to the structure may fail. Various semiactive devices have been proposed that utilize forces generated by surface friction or viscous fluids to dissipate vibratory energy in a structural system.
19.2.2 Type of Control A fully active structural control system has the basic configuration shown schematically in Figure 19.5. The structural control system in the figure basically consists of sensors, controllers, and actuators. Sensors are used to measure either external excitations or structural responses, or both. Controllers process the measured information and compute necessary control forces based on a given control algorithm. Actuators are used to produce the required forces and are usually powered by external energy sources. Active control can be classified into three categories, depending on the characteristics of the controlling effects [Rakicevic and Jurukovski, 2001]: 1. Closed-loop (feedback) control 2. Open-loop (feedforward) control 3. Open-closed loop (feedback-feedforward) control
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When only the structural response variables are measured, the control configuration is referred to as feedback control or closed-loop control, because the structural response is continually monitored and this information is used to make continual corrections to the applied control forces. An open-loop or feedforward control results when the control forces are regulated only by the measured excitation. Hence, if some unexpected factor causes the output to deviate from the desired output, there is no way of correcting the deviation. Open-closed loop control is the term used in the case where the information on both the response quantities and excitation is utilized for control design.
19.2.3 Principles of Seismic Structural Response Control From the previous explanation of structural control, there are basically five principles concerning earthquake-induced structural response control that are important to consider: 1. Isolating the structure from the input energy of the earthquake ground motion: a. Floating structures b. Frictional structures 2. Isolating the natural frequencies of the structure from the predominant seismic power components: a. Base-isolated structures b. Long-period structures 3. Providing nonlinear structural characteristics and establishing a nonstationary state nonresonant system: a. Inelastic structures b. Varying stiffness and damping structures 4. Utilizing an energy absorption mechanism: a. Viscous damper b. Viscoelastic damper c. Inelastic behavior 5. Supplying control force to suppress the structural response: a. Active mass damper b. Active tendon c. Joint damper
19.3 Structural Control Hardware and Software Because structural control depends on specialized hardware and software, this section provides some background information on these aspects.
19.3.1 Passive Control For passive systems, there are TMDs, fluid viscous dampers, viscoelastic dampers, friction dampers, yielding metal dampers, joint dampers, and so on. Passive control does not need software to control the passive device characteristics. The characteristic is determined once by an appropriate design method before the devices are placed in operation. 19.3.1.1 TMD and TLD TMD is a vibration system with a mass, spring, and viscous damper usually installed on the top of a structure. When the structure starts to vibrate, the TMD is excited by the movement. Hence, the kinetic energy of the structure goes into the TMD system to be absorbed by the viscous damper. The basic mechanism of the tuned liquid damper (TLD) is the same as that of TMD. Because both TMD and TLD require some time to become effective in absorbing the energy, they may not work well for near-field
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earthquake ground motions with high nonstationarity, as opposed to the case of far-field earthquake motions with long time duration. 19.3.1.2 Yielding Metal Dampers Inelastic hysteretic behavior of steel or lead elements absorbs the energy, reducing the structural vibration. Hysteresis loops of steel elements may be represented by bilinear models. For medium and small earthquake motions, a large amount of energy absorption may not be expected because of the high stiffness of the elements; however, for large earthquake motions, high damping effects can be expected with large hysteresis loops. Lead dampers have lower post-yield stiffness than steel dampers, and a lead damper’s hysteresis loop may be represented perfectly by an elastoplastic model, which shows a stable energy-absorbing capacity. Yielding metal dampers are used in Japan as a part of base isolation bearings, energy-absorbing braces, and a joint damper system, which connects buildings with different stories. 19.3.1.3 Friction Dampers Friction dampers absorb the energy of vibration with hysteresis loops due to friction. Cylinder-type and the steel plate sandwich-type devices have been developed. Most recently, a friction-type base isolation bearing was also developed. 19.3.1.4 Viscoelastic and Fluid Viscous Dampers A typical viscoelastic damper consists of viscoelastic layers bonded to steel plates. Conventional fluid viscous dampers are also used to dissipate the energy with velocity proportional damping. Recently, smart dampers using ER and MR fluids are being investigated for practical implementation [Spencer et al., 1998].
19.3.2 Active Control Some recent developments in active and hybrid control techniques are reviewed in this section by introducing recent experimental projects and projects being implemented in Japan. Active control can be grouped into active mass damper and active tendon and bracing systems. 19.3.2.1 Active Mass Damper (AMD) The AMD system was designed to improve living comfort in the objective building during moderate and small earthquakes and strong winds. Control of structural response using an AMD-type system provides a control force to reduce the response of the structure to earthquakes and strong winds by operating an auxiliary mass installed by means of actuators. Various systems are proposed, some of which have already been implemented in actual buildings. The Kyobashi Seiwa Building, built in 1989, is the first building in the world to have an active control system [Kobori et al., 1990a, 1990b; Ikeda et al., 2001]. It was reported that the building had experienced several moderate earthquakes and strong winds. An AMD system was installed to suppress dynamic response. Remarkable reductions in response amplitude due to the AMD system were confirmed [Koshika et al., 1992]. The system consists of two AMDs installed on the eleventh floor of the building to suppress the x-directional (by the primary AMD, 4-ton mass) and the torsional vibration (by the secondary AMD, 1-ton mass). This is required due to the structure being very slender and the weight distribution of each floor being eccentric in the y-direction. The control strategy was introduced as an output feedback control law simplified from a state feedback control law in the linear quadratic regulator problem. The control law was described in detail as the design process by Kobori and coworkers [1991a, 1991b]. The AMD system was preliminarily designed to measure only the x-directional velocities relative to the base at the mass locations and on the masses themselves. The relative velocities were replaced by the corresponding relative accelerations because accelerometers can be more economically provided. This
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Road
Highway Tendon Rod Road
Actuator
FIGURE 19.6 Active mass damper system. (From Aizawa, S. et al. 1990. “Experimental Study of Dual Axis Active Mass Damper,” in Proc. U.S. National Workshop on Structural Control Research, October, University of Southern California, Los Angeles.)
FIGURE 19.7 Active tendon system for highway viaduct. (From Yahagi, K. and Yoshida, K. 1985. “An Active Control of Traffic Vibration on the Urban Viaducts” (in Japanese), Proc. JSCE, No. 356/1-3.)
is because a control system generally becomes stable when it measures at least velocity responses at the locations to which control forces are applied. The control law can be represented as: u1(t ) = g 1x˙˙1(t ) + g 2 x˙˙AMD 1(t )
(19.1)
u2 (t ) = g3 ( x˙˙2 (t ) − x˙˙1 (t )) + g4 x˙˙AMD2 (t )
(19.2)
where u1(t) and u2(t) are the control forces by AMD1 and AMD2, respectively; x˙˙1(t ) and x˙˙ AMD1(t ) are the relative accelerations to the base at the AMD1 location and on the mass itself, respectively; x˙˙2 (t ) and x˙˙ AMD2 (t ) are the relative accelerations at the AMD2 location and on the mass, respectively; and g1 to g4 are four feedback gains corresponding to the measured relative accelerations. By tuning the controller to the objective building, the dynamic properties of these feedback gains are identified as the frequency transfer functions [Kobori et al., 1990a; Ikeda et al., 2001]. Gains of g1 and g3 both incorporate nonlinearity in the control circuit to adapt their values to a vibration level to operate the AMD system effectively within its capacity. An AMD system that can operate in two horizontal directions was installed in a six-story experimental building [Aizawa et al., 1990]. Two actuators set in two horizontal directions operate a 6-ton mass (Figure 19.6). Extensive experiments have been carried out to confirm the efficiency of the control system. In addition, an active bracing system was installed at the first story of this building, and observations are being conducted. 19.3.2.2 Active Tendon and Bracing Systems The most direct way to control vibrations is through active tendons or active braces installed in the structure. The first active tendon system in Japan to control structural vibration was developed for the Metropolitan Expressway in Tokyo [Yahagi and Yoshida, 1985]. As shown in Figure 19.7, the active tendon was installed between the first and second stories of a steel frame viaduct to reduce traffic-induced vibration. The main objective of this active tendon control was to reduce the vibration of the adjacent houses for the comfort of residents. Takenaka Construction Company in Japan and the State University of New York at Buffalo conducted a joint research project on an active brace system for buildings. The system was tested on a full-scale structure [Reinhorn and Soong, 1990]. A biaxial bracing system was assembled in the middle frames in two orthogonal directions. The bracing system consists of two diagonal circular, tubular braces attached within the first floor in each bay of the frame. A hydraulic actuator of 312 kN capacity is incorporated in each brace at the connection to the center column of the structure. © 2003 by CRC Press LLC
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FIGURE 19.8 Pendulum-type tuned active mass damper. (From Matsumoto, T.T. et al. 1990. “Study on Powered Passive Mass Damper for High-Rise Buildings” (in Japanese), in Proc. AIJ Annual Meeting, October.)
19.3.3 Hybrid Control 19.3.3.1 Active Tuned Mass Dampers (ATMD) In order to increase the energy efficiency of the actively generated control force, the combined use of TMD and an active control force has recently become popular. In addition to vibration reduction with passive-type TMD, active control force helps to reduce transient and higher-mode vibration of structures. Because of the combined use of passive and active control forces, this ATMD is also called a hybrid control system or hybrid damper. A pendulum-type ATMD has been developed (Figure 19.8) [Matsumoto et al., 1990]. The system has a multistage suspended damper mass that can be housed in a single story of a high-rise building. The hanger of the mass is wound to increase the natural period of the pendulum and also to save space. When sensors detect sway vibration, the computer-controlled servomotors drive ball screws to position the damper mass. It has been installed on the top floor of a 70-story building (296 m high) and also on the top of the tower of the Akashi Kaikyo Bridge (300 m high). A hybrid mass damper using a TMD supported on multistage high-damping rubber bearings and actuators has been developed [Tamura et al., 1992]. The significant advantage of using high-damping rubber bearings is that they can take up the roles of spring, viscous damper, and supporting guide for movement. The actuator is composed of AC servomotors and screws. The system has been mounted on a tower-type, seven-story steel frame building, and verification tests are being carried out. Fujita et al. [1992] has developed a new ATMD supported on multistage rubber bearings with hydraulic actuators. It can be operated in both active and passive modes by controlling the bypass valve of an actuator. In active control mode, control gain is adjusted, depending on the structural response level, to obtain the maximum efficiency of the actuator. When the displacement of ATMD becomes larger than the stroke of the actuator due to very strong winds or earthquakes, the system can be operated in pure TMD mode. In the implementation of this system for an actual high-rise building, heat storage tanks are used as the mass of TMD. A two-axis hybrid mass damper has been developed to reduce the vibration of tall bridge towers and high-rise building structures (Figure 19.9) [Tanida et al., 1990]. A sliding mass shaped in an arc segment is combined with active control by an AC servomotor. The movement of the arc segment on roller bearings is similar to that of a pendulum taking the role of a TMD. After some experiments were made with the tower structural model, it has been applied to actual bridge towers and high-rise buildings.
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FIGURE 19.9 A two-axis hybrid-type mass damper. (From Tanida, K. et al. 1990. “Development of Hybrid-Type Mass Damper Combining Active-Type with Passive-Type” (in Japanese), in Proc. Dynamics and Design Conference, Kawasaki, July.)
19.3.3.2 Shaking Table Tests of a Flexible Structural Model with TMD, AMD, and ATMD at Kyoto University For practical implementation of TMD, AMD, and ATMD for structures, it is important to determine the efficiency of each control system for random excitations. The author made analytical and numerical studies on the efficiency of different control methods [Iemura et al., 1992]. To verify the results, a threedegree-of-freedom structural frame model with and without control devices was tested on the shaking table at Kyoto University (Figure 19.10). Natural periods for modes 1, 2, and 3 were 0.6578, 0.2580, and 0.1568 sec, respectively. The Velocity Meter relevant participation factors for each mode were 1.2204, 0.3493, and Velocity –0.1341, respectively. The moving mass and other mass of the TMD Meter Motor Moving Mass were 3.5 and 5.5 kg, respectively. Spring constant was 0.581 kgf/cm. Damping ratio was 25.06%. These properties were used for the experiment. The mass of the TMD consisted of the AC servomotor, moving Velocity Meter mass, driving guides, and velocity meter. At the time of the experiment of the TMD, the moving mass was fixed and the TMD was hung from the third floor. In order to work as a hybrid-type ATMD, the moving mass was driven by the motor. For the pure active control Velocity Meter experiment, the motor and the moving mass were set directly on the third floor. It was clearly found that the second mode response was not reduced by TMD but was effectively reduced by AMD and ATMD. TMD was effective only in the first mode frequency range, while Velocity Meter active control force covered a wide frequency range. Shaking Table It was also found that the control force of the ATMD was much lower than that of the AMD, especially in the first mode frequency range. The first mode response was reduced mainly by TMD and the FIGURE 19.10 3-DOF experimental model. second mode response was reduced by AMD, verifying the energy efficiency of ATMD. This is the reason that the concept of ATMD is now popularly used for practical applications.
19.3.4 Semiactive Control One of the significant disadvantages of active control of structures is the large amount of energy required to reduce the vibration of large structural systems. Active variable stiffness (AVS) and active variable damper (AVD) control systems were developed to overcome this disadvantage. In AVS and AVD, stiffness and damping capacity are changed by merely adjusting the valves in oil circuits; hence, almost no energy is required. © 2003 by CRC Press LLC
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Sensor
semi-active Hydraulic Damper (SHD)
Control computers and Uninterruptible power supply
FIGURE 19.11 Building outline with SHD. (From Kurata, N. et al., 1999. “Actual Seismic Response Controlled Building with Semi-Active Damper System, “Earthquake Eng. Struct. Dyn., 28, 1427–1447.)
In a nonresonant-type controlled structure, the system actively controls the vibration characteristics of a structure so that resonance with input motion can be avoided and the response can be suppressed. To achieve this objective, the AVS system was developed and applied to a three-story steel building [Kobori et al., 1990a, 1990b]. Braces were placed in the transverse direction of the building, and the variable stiffness device was installed between the top of the brace and the upper beam. The earthquake motion analysis type of feedforward control scheme was adopted. Depending on the predominant frequency of the excitation in the previous cycle of structural response, three types of structural stiffness (rigid, medium, soft) were selected to reduce the dynamically amplified response. A variable damper is being developed at the Public Works Research Institute [Kawashima et al., 1991]. The viscous damping force of this damper varies, depending on the response of highway bridges. The damping coefficient of the damper takes large values for a small amplitude as a damper stopper for traffic and wind loads. As amplitude becomes larger due to earthquake excitations, the damping coefficient is decreased for optimum energy dissipation, and inertial force is adjusted appropriately. For excessive amplitude, the damping coefficient is increased again to suppress the response. Kurata et al. [1999] presented the first application of a semiactive damper system to an actual building. The semiactive hydraulic damper (SHD) can produce a maximum damping force of 1000 kN with an electric power of 70 W. The semiactive damper system was applied to an office building comprising five stories and a basement located in Shizuoka City, Japan. The building height is 19.75 m, the total floor area is 1685.36 m2, and the total mass is 1,102,300 kg. It was designed in accordance with the Japanese seismic resistance design standards as a steel frame structure. The eight SHDs were installed in combination with steel braces on each story from the first to the fourth on both gable ends in the short side direction. Incidentally, elastoplastic steel dampers were installed in the long side direction. The configuration of the SHD system is shown in Figure 19.11. This system consists of velocity sensors on each floor, computers in the control room on the first floor, SHDs, and a UPS (uninterruptible power supply) unit. The SHD produces a damping force in accordance with the command from the computer. The damping force fvi of the ith SHD is expressed by the following equation:
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f vi = f max × sign(v i )ui × v i > 0, ui > f max
(19.3a)
f vi = c max × v i ui × v i > 0, ui / v i > c max , ui ≤ fmax
(19.3b)
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f vi = c i (t ) × v i = ui ui × v i > 0, ui / v i > c max , ui ≤ fmax
(19.3c)
f vi = 0 ui × v i ≤ 0
(19.3d)
where ui is the damping force command from the computer to the ith SHD, vi is the ith SHD velocity, and fmax and cmax are the upper limit values of the damping force and the maximum damping coefficient of the SHD, respectively. The damping force command to the SHD was designed to minimize the building’s response, and various control theories can be applied to the calculation. The relative velocity feedback law based on the linear quadratic regulator (LQR) was adopted [Kurata et al., 1999]. Other, more detailed examples of semiactive control applications carried out by the authors can be found in the next section.
19.4 Examples of the Application of Semiactive Control 19.4.1 Semiactive Control of Full-Scale Structures Using a Variable Joint Damper System 19.4.1.1 Background of Study In order to verify the effectiveness of the semiactive control technique to the joint damper system, seismic response control tests using full-scale multistory steel frame structures, excitation devices, and a variable damper were performed at the Kyoto University DPRI. The variable damper allows external control of damping force by the electric servo valve that regulates the oil flow through the cylinder/piston mechanism. The test results show that the variable damper was successfully controlled with high accuracy, and that the advantage of the joint damper system application of the semiactive control in reducing the dynamic response of structures over the conventional passive control was demonstated. Comparison of the semiactive control algorithms in terms of the feasibility and the advantage in the engineering application to a joint damper system (JDS) was also based on the test results. Extensive research has been conducted on the semiactive control approach to reduce the seismic response of structures, induced especially by strong earthquake ground motions. A joint damper system, which aims to achieve the dynamic response reduction of adjacent structures by the use of connection devices with energy-absorbing capability, has been considered a promising approach to establish effective semiactive structural systems for earthquakes. The purpose of this study was to experimentally verify the effectiveness of application of the semiactive control to the JDS. Seismic response control tests using full-scale, multistory frame structures, excitation devices, and a variable damper were performed at the Kyoto University DPRI. The variable damper allows external control of damping force by the electric servo valve that regulates the oil flow through the cylinder/piston mechanism. Two types of semiactive control algorithms were employed: the LQR control theory and the newly proposed pseudo-negative stiffness control for joint damper systems. Parameter-setting strategies for the algorithms were studied prior to the tests through numerical simulations based on the modeling of the full-scale steel frame structures and the control device used in the tests. 19.4.1.2 Test System Setup Full-Scale Structural Steel Frame As shown in Figure 19.12, the test structure of the joint damper system consisted of two full-scale structural steel frames: a five-story frame (1 × 2 span) and a three-story frame (1 × 1 span). The dimensions and natural frequencies of both frames are shown in Table 19.1. In this test system, mass-driver devices were used to reproduce the vibration conditions under both sinusoidal and real earthquake inputs. One-directional horizontal earthquake excitation was applied. Although three mass-driver systems can be seen in the figure, only two of them were used at the same
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Variable Damper
Velocity Sensors
Shaker
Data Acq. PC
Damper Shaker Control PC Control PC
FIGURE 19.12 Schematic diagram of the test system. TABLE 19.1 Test Frames and Mass Drivers
Height Weight First mode natural frequency Mass driver
Five-Story
Three-Story
17.22 m 163.1 ton/f 1.78 Hz Five-ton mass at fourth floor
10.65 m 62.1 ton/f 2.41 Hz Two-ton mass at third floor
time. Accuracy of simulated response using the mass-driver devices was verified by research conducted prior to this study. Velocities, relative displacements, and absolute accelerations of all floors were measured through instrumentation. All measured responses were sent to a digital signal processing (DSP)-based system for the feedback control. Variable Damper As the control device in the joint damper system, a variable damping device (variable damper) was used in the test system. The variable damper was installed at the third story of the five-story frame so as to connect the two frames. The mechanism of the variable damper is shown in Figure 19.13. It is a semiactive hydraulic damper consisting of a cylinder/piston mechanism filled with oil, double rods which connect the frames, a bypass pipe with a flow control valve, and an accumulator (not shown in the figure), which keeps the bypass line pressure constant. Opening ratio of the flow control valve can be changed by a servo controller using an external signal (Figure 19.14). Flow volume through the valve can be regulated to control the pressure loss. The delay time for the opening ratio control is sufficiently short to allow real-time control. 19.4.1.3 Control Algorithms In this study, three types of control algorithms were used: linear viscous damper control, LQR control, and pseudo-negative stiffness control. The linear viscous damper control algorithm was intended to be the reference response in the case of passive control, and the effectiveness of the semiactive control was demonstrated by comparing the other two cases with the linear viscous damper control case. Linear Viscous Damper Control In this algorithm, the damping force demanded by the variable damper Fd(t) is:
Fd (t ) = Cc vr (t ) © 2003 by CRC Press LLC
(19.4)
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Bi-Pass Channel Servo Valve
F vr Cylinder 1
Cylinder 2
FIGURE 19.13 Variable damper system.
Damping force F (kN)
30
h = 0.05
h = 0.1
20
h = 0.2 h = 0.5
10
h = 0.8
0 −10 −20 −30 −10
−5
0 5 Relative velocity vr (kine)
10
FIGURE 19.14 Piston velocity-force relationship (h: valve opening ratio).
where Cc is the connecting damping coefficient and vr is the relative velocity of the damper position. Real-time control of the valve opening ratio is required to generate the demanded control force Fd with the variable damper, even for this simplest control algorithm. Linear Quadratic Regulator (LQR) Control The LQR control theory was used as a semiactive control algorithm in this study, as it had been extensively used in past studies. In the LQR control algorithm, optimal control force Fd is regarded as the demand force, and variable damper is controlled to track the demand force as closely as possible within the constraint, depending on the piston velocity. Control gain parameters are determined on the basis of numerical simulation in consideration of the capacity of the variable damper. The control force was calculated in the following manner:
Fd (t ) = −Gx(t )
(19.5)
where G is the optimal gain matrix given by the LQR control theory and x(t) is the state vector for the structural frames. Pseudo-Negative Stiffness Control If the main purpose of a joint damper system is the response reduction of the upper floors in the adjacent structures, the most interesting feature of the system is obtained by connecting them at lower stories with a negative stiffness element. Although this characteristic has been reported theoretically and analytically in many studies, there have been many problems in applying an active control device at the
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present time, mainly due to the difficulty in realizing the negative stiffness by a passive control device. However, semiactive devices such as the variable damper can generate an apparent negative stiffness by controlling the damping. Therefore, taking into account a joint damper system and negative stiffness, a new simple control algorithm to realize pseudo-negative stiffness with a damping element was proposed in this study. To generate the negative stiffness, the demand force of the variable damper Fd was defined as follows:
Fd (t ) = Kc x r (t ) + Cc vr (t )
(19.6)
where Kc and Cc are the connecting stiffness (negative value) and the damping coefficient, respectively, and xr and vr are the relative displacement and velocity of the damper piston, respectively. It follows that this algorithm simulates the state when the frames are connected by a negative stiffness and positive damping element. The eigenvalue analysis was used to determine the values of Kc and Cc . This pseudo-negative stiffness algorithm has great advantages in practical application. Most of the previously proposed control algorithms require direct measurement of the structural system for feedback and calculation of the demand control force, which means that a considerable number of sensors are required to be installed in the object structure. Considering practical application, it is difficult to install many sensors because of cost. On the other hand, for the pseudo-negative stiffness algorithm, only relative displacement and velocity are used for feedback and a sensor is required only at the damper. Although simple to install, the required parameters were limited to the connecting stiffness and damping. 19.4.1.4 Test Results The response of the variable damper to sinusoidal input with 1.8 Hz (max 10 gal), which was approximately the first resonance frequency in the connected state, is shown in Figure 19.15. The five-story topfloor velocity response and pseudo-negative stiffness in the LQR control theory were smaller than that in the viscous damper, especially the peak value in pseudo-negative stiffness, which was improved at 25% compared to that in the viscous damper, although the velocities at the top story of the three-story frame were almost equal for all control algorithms. On the other hand, LQR control theory can reduce the peak response of both frames compared to the viscous damper. When the objective is to moderate the response of the total system, LQR control theory is the most effective algorithm of the three. Based on the test, semiactive controls based on LQR control theory and pseudo-negative stiffness can reduce the peak responses of the total system more effectively than the viscous damper-type passive control. Under earthquake excitation (El Centro, 1940 north–south and Kobe, 1995 north–south, scaled to 20 gal max), the influence of variable damper friction appears in the dynamic characteristics of the variable damper at every control algorithm, due to the relatively small responses. The relative velocity and displacement responses of variable dampers in both semiactive controls were larger than that in the viscous damper. Judging from the test result, it was confirmed that the variable damper is controlled effectively in the different control algorithms to real earthquake inputs. With respect to the velocity response of the top story of the three-story frame, responses were not so different irrespective of the control algorithm. On the other hand, for the five-story top-floor response, both semiactive controls can reduce the response more effectively than the passive control to real earthquake excitation. Semiactive controls were more effective than passive controls to reduce the response of the top story of the fivestory frame in the earthquake excitation cases. Figure 19.16 shows hysteretic loops resulting from viscous-type and pseudo-negative stiffness-type controls. It is obvious that a pseudo-negative hysteretic loop can be achieved experimentally by using a variable damper. The physical advantage of the pseudo-negative stiffness hysteretic loop is explained in the next section.
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Viscous LQR control theory Pseudo negative stiffness
8
Velocity (kine)
6 4 2 0 −2 −4 −6 −8
8
8.2
8.4
8.6 8.8 t (sec) At the top story of 3-story frame
9
8
8.2
8.4
9
15
Velocity (kine)
10 5 0 −5 −10 −15
8.6 8.8 t (sec) At the top story of 5-story frame
FIGURE 19.15 Variable damper response in the sinusoidal excitation test.
Force (kN)
(a)
Velocity (kine)
Displacement (cm)
(b) Force (kN)
Velocity (kine)
Displacement (cm)
FIGURE 19.16 (a) Viscous type control and (b) pseudo-negative stiffness-type control.
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FIGURE 19.17 Side view of the Tempozan Bridge.
19.4.2 Application of Structural Control Technologies to Seismic Retrofit of a Cable-Stayed Bridge 19.4.2.1 Background of Study Due to severe damage to bridges caused by the Hyogo-ken-Nanbu earthquake in 1995, very high ground motion (level II design) is now required in the new bridge design specifications set in 1996, in addition to the relatively frequent earthquake motion specifications (level I design) by which old structures were designed and constructed. Hence, seismic safety of cable-stayed bridges that were built prior to the present specification must be reviewed, and seismic retrofit must be performed, if necessary. In order to study the effectiveness of passive and semiactive controls to the seismic retrofit of a cablestayed bridge, a numerical analysis on a model of a cable-stayed bridge was carried out. An existing cablestayed bridge with fixed-hinge connections between deck and towers was modeled and its connections were replaced by isolation bearings and dampers. The isolation bearings were assumed to be of the elastic and hysteretic type. The dampers were linear and variable. The objective was to increase the damping ratio of the bridge by using passive and semiactive control technologies. Calculation of the structural damping ratio at the main mode was feasible as the passive and semiactive controls produced a certain hysteretic loop under harmonic motion and the main mode had effective modal mass that was larger than 90%. Soil–structure interaction effects on the structural damping ratio were studied. 19.4.2.2 Tempozan Bridge The Tempozan Bridge, built in 1988, is a three-span, continuous steel, cable-stayed bridge situated on reclaimed land [Hanshin Highway Public Corporation, 1992]. It crosses the mouth of the Aji River in Osaka, Japan. The total length of the bridge is 640 m with a center span of 350 m, while the length of side spans are 170 and 120 m (Figure 19.17). The main towers are A-shaped to improve the torsional rigidity. The cable in the superstructure is a two-plane, fan pattern, multicable system with nine stay cables in each plane. The bridge is supported on a 35-m-thick soft soil layer and the foundation consists of cast-in-place reinforced concrete piles of 2-m diameter. The main deck is fixed at both towers to resist horizontal seismic forces. The bridge is relatively flexible with a predominant period of 3.7 sec. As to the seismic design in transverse direction, the main deck is fixed at the towers and the end piers. Figure 19.18 shows the original design spectrum used for designing the bridge and the new design spectrum specified in the bridge design specifications set in 1996 for level I and level II earthquakes [Japan Roadway Association, 1996]. A level II earthquake considers both Type I (inter-plate type) and Type II (intra-plate type) events. As can be seen in the figure, the new design spectrum shows higher acceleration response in all period ranges except the original.
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Acceleration
10000
1000
100
New Design Spectrum Level II (Type I) New Design Spectrum Level II (Type II) New Design Spectrum Level I Original Design Spectrum
10 0.1
1
10
Natural Period
FIGURE 19.18 Design spectra for bridges.
(a) Original Structure System
Fixed Hinge
(b) Retrofitted Structure System
Isolation Bearings + Passive or Semi Active Dampers
FIGURE 19.19 Cable-stayed bridge models.
19.4.2.3 Basic Concept of Retrofit If the deck is connected with very flexible bearings to the towers, the induced seismic forces will be kept to minimum values but the deck may have a large displacement response. On the other hand, a very stiff connection between the deck and the towers will result in lower deck displacement response but will attract much higher seismic forces during an earthquake, which is the case of the original bridge structure, the Tempozan Bridge. Therefore, it is important to replace the existing fixed-hinge bearings with special bearings or devices at the deck-tower connection to reduce seismic forces, absorb large seismic energy, and reduce the response amplitudes. Additionally, energy-absorbing devices may also be put between the deck-ends and piers. However, because doing so will attract a relatively large lateral force to the piers, this is avoided for this bridge at present. 19.4.2.4 Structure Modeling The bridge model that represents the existing Tempozan Bridge is called the original bridge model; the bridge model with spring and damper (viscous, hysteretic, and semiactive) between the deck and the towers is called the retrofitted bridge model. The original and retrofitted bridge models are shown in Figure 19.19. The original structure system has fixed-hinge connections between the towers and the deck and roller connections between the deck-ends and piers, so that the deck longitudinal movement is constrained by the towers (Figure 19.19a). For the retrofitted bridge, isolation bearings and dampers connect the deck to the towers (Figure 19.19b). The cables are modeled by truss elements, the towers and deck are modeled by beam elements, and the isolation bearings are modeled by spring elements. The models were analyzed by a commercial finite element program [Prakash and Powell, 1993]. The moment–curvature relationship of the members was calculated based on sectional properties of members and material used. © 2003 by CRC Press LLC
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top-left
(a) mid-left
AP3
AP2
(b)
FIGURE 19.20 First mode shape of original (a) and retrofitted (b) structures.
a
a elastic half space
FIGURE 19.21 Cable-stayed bridge model studied for flexible and energy-radiating foundation.
19.4.2.5 Modal Shape Analysis The first modes of the structures are interesting because these modes have the largest contribution to the longitudinal movement of the bridge. The mode shapes of the original bridge and the retrofitted bridge are shown in Figure 19.20. The first mode shape of the original structure is shown in Figure 19.20a. The natural period (T) of this mode is 3.75 sec, which is close to the design value for the bridge (3.7 sec) [Hanshin Highway Public Corporation, 1992]. This first mode has effective modal mass as a fraction of total mass of 84%. For the retrofitted structure, the stiffness of bearings was an important issue as large stiffness produces large bearing force and makes any energy-absorbing device work ineffectively in these connections (Figure 19.20b). However, very flexible connections produce large displacement response. Therefore, based on a study on a simplified model of the bridge under seismic motions, a bearing stiffness that produced a retrofitted main period (T ′) 1.7 times the original main period (T) was chosen. This bearing stiffness makes the energy-absorbing devices work well in reducing seismic-induced force and displacement. The main natural period of the retrofitted bridge (T′) then becomes 6.31 sec and the effective modal mass as a fraction of total mass is 92%. It is clear from the figures that smaller curvatures were found at the towers and the decks of the retrofitted structure than were found in those of the original structure. This shows that the retrofitted structure is expected to produce smaller moments at towers and decks than the original structure during a seismic attack. 19.4.2.6 Time History Analysis The models were analyzed by a commercial finite element program [Prakash and Powell, 1993] which produces a piecewise dynamic time history using Newmark’s constant average acceleration (β = 1/4) integration of the equations of motion, governing the response of a nonlinear structure to a chosen base excitation. The input earthquake motions were Type I-III-3, I-III-2, and I-III-1 earthquakes, which are artificial acceleration data used in Japan for design for soft soil condition. The data are intended as Type I (inter-plate type). With a numerical comparison (Figure 19.18), Type I earthquake motion has a higher effect on the bridge than Type II motion, in longer period range. Table 19.2 shows the seismic response © 2003 by CRC Press LLC
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TABLE 19.2 Maximum Earthquake Responses and Damping Ratios in Longitudinal Direction Retrofitted Structure Items
Original Structure
Deck displacement Tower momenta Tower axial force a Cable force Bearing force b Deck moment Deck axial force Damping ratio Natural period
2.37 m 3100 MN.m 48000 kN 24000 kN 94000 kN 370 MN.m 56000 kN 2% 3.75 s
Elastic Bearings
Elastic Bearing ± Viscous Damper
Hysteretic Bearings
4.17 m 2000 MN.m 15000 kN 3440 kN 44000 kN 95 MN.m 21000 kN 2% 6.31 s
1.50 m 900 MN.m 15000 kN 4000 kN 17000 kN 75 MN.m 11000 kN 35% 6.73 s
1.58 m 900 MN.m 21000 kN 5000 kN 25000 kN 95 MN.m 15000 kN 13.1% 3.86 and 6.31 s c
a
Base of tower AP3. At connection between deck and tower AP3. c Initial and post-yielding stiffness. b
effects due to different kinds of bearings and dampers: fixed-hinge bearings for the original bridge model, elastic bearings, elastic bearings plus viscous dampers, and hysteretic bearings for the retrofitted bridge model. The input earthquake was Type I-III-3 earthquake data and was in the longitudinal direction. From the table, if only elastic bearings are used for seismic retrofit, the sectional forces can be reduced to about 40% of the original ones; however, the displacement response increases to 176% of the original one. By adding viscous dampers to the elastic bearings, the sectional forces can be reduced to about 25% of the original ones and the displacement response is reduced to 63% of the original one. So the viscous dampers plus bearings work to reduce the seismic response of the retrofitted bridge. The structural damping ratio is calculated as 35%. If hysteretic bearings are used for seismic retrofit, the sectional forces are reduced to about 29% of the original ones and the displacement response is reduced to 67% of the original one. Equivalent structural damping ratio is calculated as 13.1% by using pushover analysis to obtain a hysteretic loop at the main mode. The hysteretic bearings are modeled by bilinear model and the second stiffness of the hysteretic bearings is 0.03 times the initial stiffness and produces a first mode natural period of 6.31 sec. 19.4.2.7 Soil–Structure Interaction Effects One method to study the soil–structure interaction (SSI) effects is to take into account the effects of flexible foundations and radiation of energy from foundations. In this method, the cable-stayed bridge is idealized as in Figure 19.21 [Kawashima and Unjoh, 1991]. Subsoil supporting the foundation was assumed as an elastic half space, with no energy dissipation. The foundation was idealized as a rigid massless circular plate. Radius of the rigid circular plate was simply assumed so that it gives the same surface area as the foundation. Dynamic stiffness of the foundation was assumed in a frequency-independent form: πGs a 2 8Gs a Cx = 2− υ Vs
(19.7)
0.25π 2(1 − υ) (1 − 2υ)Gs a 4 8Gs a3 Cr = 3(1 − υ) Vs
(19.8)
Kx =
Kr =
in which Kx and Cx represent spring and damping coefficients for sway motion, Kr and Cr represent those for rocking motion, and Vs and a represent shear wave velocity of subsoils and radius of foundation, respectively. © 2003 by CRC Press LLC
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TABLE 19.3 Maximum Earthquake Responses and Damping Ratios (SSI Model Included) Retrofitted Structure Items
Original Structure
Elastic Bearing ± Viscous Damper
Deck displacement Tower momenta Tower axial force a Cable force Deck moment Deck axial force Foundation displacement Damping ratio Natural period
2.78 m 1500 MN.m 36200 kN 12300 kN 228 MN.m 31900 kN 0.171 m 3.1% 5.04 s
2.57 m 800 MN.m 12500 kN 3010 kN 58 MN.m 9100 kN 0.079 m 23% 7.66 s
a b
Hysteretic Bearings 2.77 m 882 MN.m 19800 kN 4470 kN 86 MN.m 12300 kN 0.093 9.3% 5.13 and 7.46 s b
Base of tower AP3. Initial and post-yielding stiffness.
F
F
+
Connecting Stiffness
u
+
+
F F u F
=
= u
(a) ideal
Variable Damper
u
+ u
F
=
Total
u (b) realistic
FIGURE 19.22 Ideal and realistic artificial hysteretic loops using pseudo-negative stiffness variable damper.
The results show that the above model increased the natural period and the damping ratio of the original structure. However, the damping ratio of the retrofitted structure was reduced and the effectiveness of bearings and dampers in reducing seismic responses was also reduced (Table 19.3). This is mainly because the SSI model introduced flexibility on the base of the tower. A flexible base will reduce the frequency of the structure and relative movement of the devices. Smaller frequency and smaller relative movement at the device will reduce the effectiveness of devices in absorbing earthquake energy. Moreover, a flexible base will increase the elastic strain energy, which will reduce the damping ratio. If the SSI model possesses elemental damping ratio, as is usually the case for supporting soil, the structural damping ratio will depend on that elemental damping ratio and on the stiffness of the SSI model elements. 19.4.2.8 Semiactive Control The semiactive control uses a pseudo-negative stiffness algorithm so that the sum of damper force and bearing force (plus other connecting stiffness force) is expected to produce a hysteresis loop that is close to that of rigid–perfectly plastic force-deformation characteristics (Figure 19.22a). Moreover, no residual displacement is expected at the bearings after an earthquake attack, because the hysteresis loop is velocity dependent. The figure shows ideal and realistic force-deformation characteristics of bearing and variable damper if a pseudo-negative stiffness algorithm is used.
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Variable damping
F
F
Linear damping
u
u
Connecting stiffness
(a)
(b)
FIGURE 19.23 Connecting stiffness plus damper force for (a) linear damper and (b) variable damper.
Rigid element
Retrofitted structure system
k tu
ki
kc m
(a)
Isolation Bearings + Passive or Semiactive Dampers
k1
c (b)
FIGURE 19.24 Simplified model to model the main mode of the cable-stayed bridge.
One algorithm that can approach the hysteretic loop in Figure 19.22b requires damper force as (Iemura et al., 2001b):
Fd ,t = K d ut + Cd u˙t
(19.9)
where Kd is the connecting stiffness (negative value) and Cd is the damping coefficient (positive value). The algorithm is practical because displacement and velocity sensors are placed in the dampers. This algorithm will produce a hysteretic loop under harmonic motion, as shown in Figure 19.22b. It is clear from the figure that a variable damper is superior to a linear damper because the maximum variable damper plus connecting stiffness force can be set equal to the maximum connecting stiffness force (Figure 19.23b). One can calculate that the damping ratio of the hysteresis loop in Figure 19.23b is 53.4%. For the same damping ratio, the hysteresis loop in Figure 19.23a will produce a total force 1.46 times larger than the connecting stiffness force. Connecting stiffness between the deck and the tower of the retrofitted structures comes from the contribution of cable stiffness, upper tower stiffness, and bearing stiffness. 19.4.2.9 Simplified Model of the Bridge In order to study the effectiveness of this pseudo-negative stiffness algorithm in reducing seismic response in a cable-stayed bridge, a simplified model was developed to model the bridge at the main mode in the longitudinal direction. The same model was used by Branco and coworkers [2000]. The simplified model consists of a set of massless bar elements and one vibrating concentrated mass (Figure 19.24b). This mass corresponds to the mass associated with the first longitudinal vibration mode of the bridge. The lower vertical element (depicted in bold) simulates the stiffness of the bridge for a horizontal displacement of the towers at the deck level. The contribution of the cables and the towers above the deck level to the overall longitudinal stiffness of the bridge is simulated by other vertical elements. The simplified model is appropriate for modeling the main mode of the bridge in the longitudinal direction because the effective modal mass as a fraction of total mass in this mode is 92%. From the simplified model, the structural damping ratio of the system can easily be calculated.
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FIGURE 19.25 Seismic response of semiactive control in the bridge simplified model (Type I-III-I earthquake input).
F k
F
F k1
+
=
series
u ζ = 53.4%
k 1 .k/(k 1 +k) u2
u1
ζ = 35.6% typical for k = 0.5 k 1
Rigid element
k tu
k1
ki c
ζ : damping ratio
kc m u = u2 ñ u1
FIGURE 19.26 Main-mode structural damping ratio.
19.4.2.10 Seismic Response The model was analyzed by a time-history analysis program developed by the authors using MATLAB® software [MATLAB, 1997], which produces a piecewise dynamic time history, using Newmark’s average acceleration (β = 1/4) integration of the equations of motion, governing the response of a nonlinear structure to a chosen base excitation. The input earthquake motions were Type I-III-3, I-III-2, and I-III-1 earthquakes, which are artificial acceleration data used for design in Japan for soft soil condition. Figure 19.25 shows typical results for the simplified model of the bridge that incorporates a variable damper under Type I-III-1 earthquake motion. Figure 19.25a shows a structural hysteresis loop that is © 2003 by CRC Press LLC
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FIGURE 19.27 Seismic responses of the cable-stayed bridge models with passive and semiactive control (Type I-III-I earthquake input).
apparently lower in structural damping ratio, 35.6%. The reduction of this damping ratio is due to tower flexibility k1 (in this case, k = 0.5k1, or T ′ = 1.7 T). (The reduction is explained below.) Figure 19.25b shows a hysteresis loop of variable damper plus connecting stiffness (stiffness is k). This loop corresponds to a 53.4% elemental damping ratio. Figure 19.25c shows an apparent negative stiffness hysteresis loop produced by the variable damper. Figure 19.26 illustrates the effects of a spring set in series to the damping ratios. In this case, the tower stiffness is k1 and the total stiffness of bearings, upper tower, and cables is k. The strain energy of the system in one cycle (shaded area) is a summation of spring k1 and spring k. However, energy absorbed by the variable damper in one cycle is constant; therefore, for the case of k = 0.5 k1, one can calculate from the figure that the damping ratio is reduced by one third. If the variable damper is put between the deck and stiff support on the ground (e.g., abutments, foundations, etc.), the structural damping ratio will not be reduced as much. © 2003 by CRC Press LLC
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A comparison was made between simplified models using passive and semiactive controls, and a complete model using passive control (Figure 19.27). The figure shows that the semiactive control using pseudo-negative stiffness algorithm results in a lower seismic response than that of the passive control.
19.5 Concluding Remarks The history of structural control, its concept, and its applications have been introduced, starting with global knowledge about structural control and ending with two detailed applications carried out by the authors. It is clear that the concept of structural control is appealing and exciting, and its application to civil engineering structures is unique and presents a host of new challenges. The authors show the applicability and advantages of using pseudo-negative stiffness in controlling structural response against seismic forces by using semiactive control. The negative stiffness loop can be produced experimentally by a variable orifice viscous damper using a simple algorithm. Diagrams were used to explain the advantages of this negative hysteretic loop. The negative hysteretic loop combined with positive connecting stiffness produces nearly rigid–perfectly plastic force-deformation characteristics.
Defining Terms Accelerometers — Devices used to measure acceleration of a component. Active control — Control of structural vibration using systems that produce forces in a prescribed manner.
Active mass damper (AMD) — Active control that uses mass actuator (to replace the spring and damper in a tuned mass damper, TMD), sensors, and controllers, so that combination of AMD and the structure minimizes the vibration response. Actuators — Devices that produce force in the presence of a command signal. Base isolation — Isolation of structures from ground shaking with special devices. Connecting stiffness — Stiffness that exists between two points that are connected with a control device, e.g., between the deck and the towers of a cable-stayed bridge, between two adjacent buildings, between two adjacent floors in one building, and so on. Digital signal processing (DSP) — Used to process and analyze any input signal digitally with fast speed. Ductility — Ability of a structure to undergo large inelastic deformation without significant degradation of its restoring force. Feedback control — Vibration responses of the structure are measured to continually correct the command of the control system. Feedforward control — Excitation is measured to continually correct the command of the control system. Hybrid control — Combination of passive and active control. Hysteresis loops — Loops created by a force-deformation relationship curve that absorbs energy. Joint damper — Damper put between two adjacent structures to reduce vibration response of both structures. Mass driver devices — Mass with motor device used to input excitation force into a building. Passive control — Control of structural vibration using hardware systems alone, without sensors or control signal. Pseudo-negative stiffness control — Control system that produces negative-stiffness hysteretic loops at the device. Semiactive control — Control of structural vibration with systems that have changeable behavior by the presence of command during excitation.
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Semiactive hydraulic damper (SHD) — Hydraulic damper that has a changeable orifice valve so that the damping coefficient of the damper can be adjusted in real time.
Shaking table — Table that can generate excitation to a structure that is attached to it. Soil–structure interaction (SSI) — Interaction between a structure’s foundation and supporting soil that introduces flexibility and damping characteristics.
Tuned liquid damper (TLD) — The basic principle of TLD is the same as that of a tuned mass damper (TMD); however, TLD uses water or other liquid as the moving mass, and the restoring force is generated by gravity. Tuned mass damper (TMD) — Passive control device that uses adjusted mass, spring, and damper, so that combination of TMD and the structure maximizes the absorbed energy. Viscoelastic damper — Passive device that has a combination of elastic spring and viscous damping characteristics.
References Abdel-Ghaffar, A.M. 1991. “Cable-Stayed Bridges under Seismic Action,” in Cable-Stayed Bridges: Recent Developments and Their Future, M. Ito, Ed., Elsevier Science Publishers, Amsterdam. Aizawa, S. et al. 1990. “Experimental Study of Dual Axis Active Mass Damper,” in Proc. U.S. National Workshop on Structural Control Research, October, University of Southern California, Los Angeles. Branco, F.A., Mendes, P.M., and Guerreiro, L.M.C. 2000. “Special Studies for Vasco da Gama Bridge,” ASCE J. Bridge Eng., 5(3), August. Casciati, F. et al., Eds. 2002. Proceedings of the Third World Conference on Structural Control, 3 vols., International Association of Structural Control, Como, Italy. Chopra, A.K. 1995. Dynamics of Structures: Theory and Applications to Earthquake Engineering, PrenticeHall, New York. Feng, Q., Shinozuka, M., and Fujii, S. 1993. “Friction-Controllable Sliding Isolated Systems,” ASCE J. Eng. Mech., 119(9), 1845–1864. Fujii, S. et al. 1992. “Hybrid Isolation System Using Friction-Controllable Sliding Bearings” (in Japanese), Trans. Japan National Symposium on Active Structural Control, March. Fujita, T. et al. 1992. “Study of Biaxially Controlled Mass Damper with Convertible Active and Passive Modes” (in Japanese), Trans. Japan National Symposium on Active Structural Control, March. Hanshin Highway Public Corporation. 1992. Tempozan Bridge: Structure and Construction Data (in Japanese), Osaka, Japan. Housner, G.W. 1992. “Global Overview of Response Control,” in Proc. Japan National Symposium/ Workshop on Structural Response Control, Japan Panel on Structural Response Control Research, Architectural Institute of Japan, Japan Society of Civil Engineers, Japan Society of Mechanical Engineers, July. Housner, G.W. and Masri, S.F., Eds. 1990. Proceedings of the U.S. National Workshop on Structural Control Research, U.S. Panel on Structural Control Research, University of Southern California, Los Angeles, October. Housner, G.W., Masri, S.F., and Chassiakos, A.G., Eds. 1994. Proceedings of the First World Conference on Structural Control, Vols. 1–3, International Association of Structural Control, Pasadena, CA. Iemura, H. et al. 1992. “Comparison of Passive, Active, and Hybrid Control Techniques on Earthquake Response of Flexural Structures: Numerical Simulations and Experiments,” in Proceedings of the U.S.–Italy–Japan Workshop/Symposium on Structural Control and Intelligent Systems, Sorrento, July. Iemura, H., Igarashi, A., Chen, Y., and Nakajima, H. 1996a. “The Restoring Characteristics of LRB under the Influence of Rotational Deformation and Variable Axial Loads,” in Proc. First Colloquium on Seismic Isolation and Response Control, November. Iemura, H., Igarashi, A., Inoue, Y., and Sakamoto, M. 1996b. “Nonlinear Active Control Experiment of a Real Size Frame Structure,” Proc. Second International Workshop on Structural Control, December, pp. 241–252. © 2003 by CRC Press LLC
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Iemura, H., Adachi, Y., Okashiro, S., and Mizutani, T. 2001a. “Application of Structural Control Technologies to Seismic Retrofit of a Cable-Stayed Bridge,” in Proc. IABSE Conference, Seoul, June. Iemura, H., Igarashi, A., and Nakata, N. 2001b. “Semiactive Control of Full-Scale Structures Using Variable Joint Damper System,” in Proc. Fourteenth KKNN Symposium on Civil Engineering, November 5–7, Kyoto, Japan. Ikeda, Y., Sasaki, K., Sakamoto, M., and Kobori, T. 2001. “Active Mass Driver System as the First Application of Active Structural Control,” Earthquake Eng. Struct. Dyn., 30, 1575–1595. Japan Roadway Association. 1996. The Seismic Design Specification. Kageyama, M. et al. 1992. “Study on Super Quake Free Control System of Buildings” (in Japanese), Trans. Japan National Symposium on Active Structural Control, March. Kawashima, K. and Unjoh, S. 1991. “Seismic Behavior of Cable-Stayed Bridges,” in Cable-Stayed Bridges: Recent Developments and Their Future, M. Ito, Ed., Elsevier Science Publishers, Amsterdam. Kawashima, K. et al. 1991. “Current Research Efforts in Japan for Passive and Active Control of Highway Bridges against Earthquakes,” in Proc. 23rd Joint Meeting, U.S.–Japan Panel on Wind and Seismic Effects, UJNR, Tsukuba, May. Kobori, T.T. 1992. “Current Aspects of Active Control of Structural Vibrations,” in Proc. Japan National Symposium/Workshop on Structural Response Control, Japan Panel on Structural Response Control Research, Architectural Institute of Japan, Japan Society of Civil Engineers, Japan Society of Mechanical Engineers, July. Kobori, T.T. et al. 1990a. “Experimental Study on Active Variable Stiffness System: Active Seismic Response Controlled Structure,” in Proc. Fourth World Congress of Council on Tall Buildings and Urban Habitat, Hong Kong, November. Kobori, T. et al. 1990b. “Study on Active Mass Driver (AMD) System: Active Seismic Response Controlled Structure,” in Proc. Fourth World Congress of Council on Tall Buildings and Urban Habitat, Hong Kong, November. Kobori, T.T., Koshika, N., Yamada, K., and Ikeda, Y. 1991a. “Seismic-Response-Controlled Structure with Active Mass Driver System. I. Design,” Earthquake Eng. Struct. Dyn., 20, 133–149. Kobori, T., Koshika, N., Yamada, K., and Ikeda, Y. 1991b. “Seismic-Response-Controlled Structure with Active Mass Driver System. II. Verification,” Earthquake Eng. Struct. Dyn., 20, 151–166. Kobori, T.T., Inoue, Y., Seto, K., Iemura, H., and Nishitani, A., Ed. 1998. Proc. Second World Conference on Structural Control, Vols. 1–3, International Association of Structural Control, Kyoto, Japan. Koshika, N. et al. 1992. “Control Effect of Active Mass Driver System during Earthquakes and Winds,” in Proc. First International Conference on Motion and Vibration Control, Yokohama, pp. 261–266. Kurata, N., Kobori, T.T., Takahashi, M., Niwa, N., and Midorikawa, H. 1999. “Actual Seismic Response Controlled Building with Semi-Active Damper System,” Earthquake Eng. Struct. Dyn., 28, 1427–1447. MATLAB. 1997. The Math Works, Inc., Natick, MA. Matsumoto, T.T. et al. 1990. “Study on Powered Passive Mass Damper for High-Rise Building” (in Japanese), in Proc. AIJ Annual Meeting, October. Meirovitch, L. 1990. Dynamics and Control of Structures, John Wiley & Sons, New York. Prakash, V. and Powell, G.H. 1993. Drain-2DX, Drain-3DX, and Drain-Building: Base Program Design Documentation, Report no. UCB/SEMM-93/16, University of California, Berkeley, December. Rakicevic, Z. and Jurukovski, D. 2001. Optimum Design of Passive Controlled Steel Frame Structures, Report IZIIS 2001–59, Project 123/NIST, Skopje, December. Reinhorn, A. and Riley, M. A. 1994. “Control of Bridge Vibrations with Hybrid Device,” in Proc. First World Conference on Structural Control, California, pp. 50–59. Reinhorn, A. and Soong, T.T. 1990. “Full-Scale Implementation of Active Bracing for Seismic Control of Structures,” in Proc. U.S. National Workshop on Structural Control Research, University of Southern California, Los Angeles, October.
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Seto, K. and Matsumoto, Y. 1996. “A Structural Vibration Control Method for Flexible Buildings in Response to Large Earthquakes and Strong Winds,” in Proc. Second International Workshop on Structural Control, Hong Kong, pp. 490–496. Soong, T. T. 1990. Active Structural Control: Theory and Practice. Longman, London. Soong, T.T. and Constantinou, M.C., Eds. 1994. Passive and Active Structural Vibration Control in Civil Engineering, CISM Courses and Lectures No. 345, International Centre for Mechanical Sciences, Springer-Verlag, New York. Tamura, K. et al. 1992. “Study on Application of Hybrid Mass Damper System to a Tall Building” (in Japanese), in Trans. Japan National Symposium on Active Structural Control, March. Tanabashi, R. 1960. “Earthquake Resistance of Traditional Japanese Wooden Buildings,” in Proc. Second World Conference on Earthquake Engineering, Vol. 1, p. 151. Tanida, K. et al. 1990. “Development of Hybrid-Type Mass Damper Combining Active-Type with PassiveType” (in Japanese), in Proc. Dynamics and Design Conference, Kawasaki, July. Yahagi, K. and Yoshida, K. 1985. “An Active Control of Traffic Vibration on the Urban Viaduct,” (in Japanese), Proc. JSCE, No. 356/I-3. Yamada, Y., Ikawa, N., Yokoyama, H., and Tachibana, E. 1994. “Active Control of Structures Using the Joint Member with Negative Stiffness,” in Proc. First World Conference on Structural Control, Vol. 2, California, pp. 41–49.
Further Readings Casciati, F. et al., Eds. 2002. Proceedings of the Third World Conference on Structural Control, Vol. 1, International Association of Structural Control, Como, Italy, p. 3. Chopra, A.K. 1995. Dynamics of Structures: Theory and Applications to Earthquake Engineering, PrenticeHall, New York. Housner, G.W., Masri, S.F., and Chassiakos, A.G., Eds. 1994. Proceedings of the First World Conference on Structural Control, Vols. 1–3, International Association of Structural Control, Pasadena, CA. Kobori, T., Inoue, Y., Seto, K., Iemura, H., and Nishitani, A., Eds. 1998. Proceedings of the Second World Conference on Structural Control, Vols. 1–3, International Association of Structural Control, Kyoto, Japan. Meirovitch, L. 1990. Dynamics and Control of Structures, John Wiley & Sons, New York. Soong, T.T. 1990. Active Structural Control: Theory and Practice, Longman, London. Soong, T.T. and Constantinou, M.C., Eds. 1994. Passive and Active Structural Vibration Control in Civil Engineering, CISM Courses and Lectures No. 345, International Centre for Mechanical Sciences, Springer-Verlag, New York.
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20 Equipment and Systems 20.1 Introduction 20.2 Importance of Equipment Seismic Functionality 20.3 Historical Performance Investigation of Industrial Facilities and Equipment · The August 17, 1999 Izmit, Turkey Earthquake
20.4 Design Practices Commercial Buildings · Schools and Hospitals · Essential Facilities · Industrial Facilities · Oil Refineries and Chemical Plants · Offshore Oil Platforms · Pipelines · LNG Facilities · Nuclear Power Plants
20.5 Code Provisions Model Codes · 1994 UBC · 1997 UBC · 2000 IBC · Other Industry Codes and Standards
20.6 Assessment of Existing Facilities . Component Assessment · Systems Reliability Assessment
Gayle S. Johnson Han-Padron Associates Oakland, CA
20.7 Nonstructural Damage Defining Terms References Further Reading
20.1 Introduction This chapter discusses the seismic design and assessment of equipment and systems within facilities. The intent is to help the reader understand design and evaluation issues related to equipment by reviewing historical performance, typical design practice, and code provisions. The reader is also presented with methods for assessing existing systems that focus on systems reliability, an important operational consideration. Equipment is the mechanical, electrical, or other components required for system functionality. A system is an interconnected group of equipment and/or subsystems performing a function. Examples of equipment include pumps, electric generators, motor control cabinets, and even things as simple as overhead electric lights. Examples of systems are computer systems, a water supply system, or a highrise fire detection, alarm, and suppression system. Systems performing a critical function (i.e., of high
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Sprinklers may be broken Broken glass admits high winds fanning flames
Typical upper floor. Numerous electrical ignition sources Cafeteria (typ) potential for broken gas lines
Fire marshall room with smoke and fire alarms. HVAC controls etc.
Fire pump control panel
Secondary water supply
Sprinkler riser Water main
Fire pump Day tank for fire pump
FIGURE 20.1 Example of critical equipment system: high-rise fire detection, alarm and suppression system. (From Scawthorn, C. 1989. In Fire Safety in Tall Buildings, J. Zicherman, Ed., Council on Tall Buildings and Urban Habitat, Bethlehem, PA. With permission.)
importance, such as required for life safety, or involving significant financial loss if disrupted) are termed critical systems (see Figure 20.1). Thus, the primary focus of this chapter is on equipment and the systems they comprise. Nonstructural refers to the portions of buildings and facilities that do not perform a structural function — that is, that do not resist vertical or lateral loads. Nonstructural items include glazing, roofing, cladding (none of which are addressed here), and equipment. Items such as furniture and inventory are not normally included under the term nonstructural (rather, they are “contents”). The next section discusses the importance of this topic in more detail, providing examples of equipment performance from recent earthquakes. Section 20.3 provides background information on the historical performance of equipment and systems in earthquakes. While the general performance of most equipment in earthquakes has been satisfactory, even without specific seismic design, numerous earthquakes have demonstrated certain shortcomings that have proved critical. Section 20.4 discusses design practices for various industries and how they are applied to equipment and system design. This is followed by Section 20.5, which provides additional specific background on building code provisions for equipment and system design, and then Section 20.6, which discusses assessment methodologies to address the seismic evaluation of existing facilities. Two methods are presented: • A “conventional” method, that focuses on assessment of individual components • A system reliability assessment method These can be used for making decisions on retrofit priorities for existing facilities. Nonstructural items other than equipment are briefly discussed in Section 20.7.
20.2 Importance of Equipment Seismic Functionality While improving the earthquake structural safety of buildings, bridges, and other structures has received considerable attention in recent years, less effort has been historically directed at improving the performance of critical equipment, equipment systems, and processes during and after earthquakes.
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Monetary losses in earthquakes due to nonstructural damage can be much larger than the losses due to structural damage. This is especially true in industrial facilities, where the potential cost of lost product, lost business, and environmental impact can far outweigh the cost of structural damage. In order to continue operations following an earthquake, industrial facilities rely on the functionality of critical systems (e.g., power and water) as much as on the stability of the structures themselves. Recent earthquakes have exposed shortcomings in typical facility design practices and design standards, especially with regard to damage that can shut down or limit services of a facility. For example, in the 1994 Northridge, California earthquake, many facilities were partially disabled or entirely shut down, primarily due to equipment failure in a wide variety of systems. In particular, the earthquake caused considerable damage and service disruption to critical health care facilities and hospitals, including the Olive View Medical Center, the Holy Cross Medical Center, and the Indian Hills Medical Center, all in Sylmar; the Granada Hills Community Hospital; and the Veterans Administration Medical Center in Sepulveda [Gates and McGavin, 1998]. Service disruptions at all of these facilities were attributed primarily to equipment failure, including fire protection piping, heating, ventilation and air conditioning (HVAC), power distribution, and control system problems. Failures were reported in diverse equipment systems such as emergency power generation, hospital communications, and the medical gas system. The performance of these essential facilities is of special interest because building code requirements for hospitals in California attempt to maintain functionality of the facility, as well as preserve the life safety of the occupants. The area of southern California surrounding the Northridge earthquake was fortunate to have an extensive health care network that could respond to the demands of a large natural disaster even with the loss of multiple facilities. The consequences of similar postearthquake facility performance in other earthquake-prone regions of the United States may be devastating, especially if a major event occurs in an area with less overall earthquake preparedness than southern California. The August 17, 1999 Izmit, Turkey earthquake (M7.4), discussed in more detail later, struck in the heart of Turkey’s most heavily industrialized region and demonstrated many of the potential consequences of earthquakes affecting industrial facilities. Major fires and structural damage in Turkey’s largest refinery shut down that facility entirely for several months, and left it partially shut down for more than a year. Damage to other petrochemical and industrial plants shut down numerous facilities for 2 months or more. Damage to the petrochemical plants had regional economic consequences and led to supply shortages for other industries, such as the nearby rubber and tire industry. Examples of facilities shut down in the 1999 Turkey earthquake for “nonstructural” reasons include: • A light bulb factory that shut down entirely due to damage to a special “tube” in a glass furnace that had to be replaced from northern Europe • A steel mill unable to export its product because of damage to a neighboring facility’s pier that was used by the steel mill • A paper mill disabled due to loss of its transformers The inability of these facilities to function following a strong earthquake points to deficiencies in the design approach typically used for industrial facilities. Because of the focus on providing structural integrity (primarily through anchorage design) for a given component, other vulnerabilities that can inhibit functionality are overlooked. Differential displacement of system components and interactions with structural items are just two examples of non-anchorage-related concerns that can inhibit functionality.
20.3 Historical Performance 20.3.1 Investigation of Industrial Facilities and Equipment Significant effort has been expended to document the performance of equipment and systems in earthquakes that have occurred over the last 30 years. One of the major driving forces for detailed research © 2003 by CRC Press LLC
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into equipment and system performance has been the desire of the nuclear industry in the United States for highly reliable equipment and system functionality. There are three fundamental methods for assuring or qualifying equipment functionality under given seismic forces: 1. Analysis [EPRI, 1994] 2. Testing [e.g., Wilcoski et al., 1997] 3. Empirical (i.e., observed performance of the equipment under similar earthquake forces) [Nuclear Regulatory Commission, 1987] Each method has advantages and disadvantages. The analysis method is the most precise, although the analysis is often based on idealized models of the equipment item, cannot consider all details, and often cannot consider the installed “as-is” conditions. Testing can only examine a limited set of ground motions, is expensive, and is limited to the capabilities of the test equipment, which usually limits the size of the specimen tested as well as the ground motions. The empirical method is limited to the observed equipment in the specific installed conditions under the specific ground motions. However, when similar equipment has undergone similar earthquake experience, the empirical method offers advantages of costsavings as well as that the actual equipment has been tested in real-world and installed conditions, which is often not possible for laboratory testing. In order to qualify equipment, the nuclear industry therefore developed seismic equipment qualification requirements based on actual earthquake experience data. For additional reasons specific to the nuclear industry, such as the cost involved in requalifying irradiated and contaminated equipment that has been in service and the safety hazards associated with dealing with this type of equipment (e.g., radiation exposure), the nuclear industry and the Electric Power Research Institute (EPRI) have funded earthquake investigations to study the performance of mechanical and electrical systems in strong motion earthquakes, including the documentation of types and causes of damage, as well as systems that have survived without damage [Nuclear Regulatory Commission, 1992]. Because most of the equipment in nuclear plants is also common to other industrial and commercial facilities, the types of facilities investigated for nuclear qualification data collection have been diverse and extensive, including power plants, petrochemical facilities, water treatment plants, manufacturing facilities, large industrial facilities, hospitals, and any other relevant facilities where access was granted to investigators [Yanev, 1992; EPRI, 1991, 1998; Swan and Kassawara, 1998]. The EPRI funded numerous visits by engineers to power and industrial facilities affected by earthquakes throughout the world. Data were collected in the days immediately following earthquakes by interviewing facility personnel, performing damage surveys, reviewing facility operating logs, and collecting other available data. Follow-up visits often were used to collect very detailed data on undamaged systems in a facility. In recent years, earthquake investigations funded by the Federal Emergency Management Agency (FEMA), the National Science Foundation (NSF), and other groups have placed additional emphasis on this topic. The Earthquake Engineering Research Institute (EERI) has taken a primary role in organizing these investigations and disseminating information to practicing engineers through publications and postearthquake workshops [ATC, 1992, 1998]. The following section presents some of the investigative findings of one earthquake that hit a very heavily industrialized area.
20.3.2 The August 17, 1999 Izmit, Turkey Earthquake This M7.4 earthquake is of particular interest because of its epicentral location in Turkey’s industrial heartland [Scawthorn, 2000]. There are several concentrated areas of industry surrounding the Sea of Marmara and Izmit Bay, extending to Adapazari. Substantial damage to industrial facilities was observed over a large geographic area. Many of these facilities experienced extended down time. Numerous companies from various industries in the Izmit and Adapazari areas were surveyed in the days immediately following the earthquake, and in follow up visits over the next year. The performance of these industrial facilities is relevant to other areas of the world because Turkey has many modern, © 2003 by CRC Press LLC
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engineered facilities, which, in many cases, are owned by multinational companies. The industrial facilities visited generally were constructed with much higher quality control than observed in the residential structures. This section summarizes observations relevant to the seismic performance of industrial facilities, both in terms of damage and operational impact. Facilities surveyed included the following industries: petrochemical, automobile, tires, pharmaceutical, cement, paper mills, steel pipes, power plants and other manufacturing. The petrochemical industry performance is of special interest because of the observed damage and the location of these plants relative to the epicenter. There is a heavy concentration of petrochemical plants near Korfez, on the northern side of Izmit Bay, within approximately 10 km of the epicenter. Among the plants located there are the state-owned Tupras¸ refinery and Petkim petrochemical plants, the Igsas fertilizer plant, and on the order of 40 liquefied petroleum gas (LPG) terminals and storage facilities. The Tupras¸ refinery is the largest refinery in Turkey and produces over 220,000 barrels per day. This is about one third of Turkey’s total production, almost all for domestic consumption. The Petkim petrochemical plant is an important supplier of raw materials to the region’s extensive tire industry. Damage to these plants had significant impact on industries throughout the region. Performance of these facilities is also important because this is the first time in many years that large refineries and chemical plants have been so close to the epicenter of a major earthquake, and may be the largest concentration of petrochemical facilities ever to experience such strong ground motion. Most of these plants experienced peak accelerations on the order of 0.32 g, based on an instrument located at the Petkim petrochemical plant. The response spectra for that instrument indicate a large high-period response, with a duration of strong shaking of about 45 sec. Damage observed in these facilities, described in more detail in the following sections, includes complete collapses of stacks and cooling towers, structural damage to buildings, tank collapses, major fires, oil spills, and gas leaks. The automobile and tire manufacturing industries are also especially prominent throughout this area. A wide variety of multinational industrial companies, such as Pirelli Tires, Goodyear, and Hyundai, are located within a few miles of each other in the Kosekoy region, just to the east of Izmit. The Sabanci company has joint venture facilities with several companies in the area. The partnership with Bridgestone of Japan that manufactures rubber goods and tires is called BriSA. In the same complex are several other companies that supply this industry, including DuSA (Du Pont and Sabanci), BekSA (Bekaert, a Belgium company, and Sabanci), KordSA (steel belts for tires), and EnerjiSA (power for all of these plants). The company also owns 50% of the Toyota car manufacturing plant in Adapazari. Ford is building a new plant, damaged by fault movement, in Golcuk. Honda, Isuzu, and Renault also have plants in the area around the Sea of Marmara. Table 20.1 summarizes the performance of major industrial facilities surveyed after the earthquake. Estimated downtime is generally based on opinions of the facility management immediately following the earthquake. 20.3.2.1 Tupras¸ Refinery Damage The most widely publicized and spectacular damage to any industrial facility occurred at the massive refinery near Korfez, owned by the state-owned oil company, Tupras¸ , which experienced fires, oil spills, and severe structural damage. The facility was shut down completely for about 3 months, and some of the most severely damaged portions of the plant were still not operational 13 months after the earthquake. The refinery received international media attention because of tank farm fires that burned out of control for several days. The first fire was initiated in a floating roof naptha tank. Naptha is a highly volatile material with a low flashpoint, and is easily ignited. The sloshing of naptha in the tank caused the floating roof to breach its seal, allowing naptha to spill. The naptha was likely ignited by sparks from the friction between the steel roof and tank wall. The refinery had 36,000 m3 of fire water stored on site, which was all used up on the first day. The facility receives its main water supply through a dedicated pipeline from Lake Sapança, some 45 km to the east. Due to multiple breaks in the pipeline, the refinery quickly lost all water and all firefighting © 2003 by CRC Press LLC
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TABLE 20.1 Summary of Industrial Facility Performance —1999 Izmit, Turkey Earthquake Facility Name
Facility Type
Year Built
No. Employ.
Est. Downtime
Tupras¸
Refinery
1960s
Petkim
Petrochemical
1967–1975
Igsas
Fertilizer
1977
2–6 months
British Petroleum British Petroleum Hyundai
Gas Terminal
< 1 week
Gas Tanker Filling Plant Car Manuf.
1980s (?) 1974 1997
1–2 months
Toyota
Car Manuf.
1994
2 weeks
Ford
Car Manuf.
1999 (under constr.)
Pirelli
Tire Manuf.
1960s
Goodyear
Tire Manuf.
1963
BriSA
Tire Manuf.
1976 1989
KordSA DuSA
Steel Cord (for Tires) Tire Cord Fabric
1987
EnerjiSA
Power
1997
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1976
3 months (total) > 1 year (partial)
2,500
2 months
< 1 week
Not operational
500
Several weeks (partial) 2–3 weeks 2–3 weeks (partial)
1,100
Few weeks 6 months–1 year
50
Few days/weeks
Damage Description Tank farm fires Water supply line breaks Tank collapses “Sinking” of floating roofs Pile damage at port Pipeway collapse Cooling tower collapse Stack collapse Oil spill Fire due to chemicals mixing in warehouse Twisting of legs on LPG sphere Cooling tower collapse Pipeway collapse Port failure Water supply line breaks Cranes off rails Pipeway damage Building damage Reactor support structure damage Minor vessel movement Buckling of tank roofs Damage to tank walkways Lost connection bolts on steel frame Air handler duct failure Unzipped cable tray runs Collapsed storage racks Transformer jumped Movement of cars on line and unanchored items Large building displacement Building damage Building collapse Fire protection lines broken Minor structural damage Severe structural damage (walls fallen) Transformer damage Control room damage Building damage Severe building damage Process equipment moved Pipes “blocked” Instrument cables cut Boiler moved Structural damage to HRSG Transformer bushings broke
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TABLE 20.1 (CONTINUED) Summary of Industrial Facility Performance —1999 Izmit, Turkey Earthquake Facility Name BekSA NUH
Facility Type Steel Cord (for tires) Cement Plant
Year Built 1987
No. Employ. 240
1968–1973
Mannesmann Boru SEKA
Steel Pipe Factory 1955
200
Paper Mill
1936–1960
Pakmaya
Food Processing
1976
300
Philips
Incand. Bulb Factory
1964
77
Habas
1995 (tanks)
Citi
Liquified Gas Plant Glass Vial Manuf.
Toprak Ilic Toprak Saglik
Pharmac. Paper Products
1990 1993
240 170
Camlica
Soft Drinks
Cap
Textiles
1999 (under constr.) 1997
650
Est. Downtime
Damage Description
Few weeks Building collapse (partial) Windows broke Few days (partial) Minor structural damage and movement Falling monitors in control room Settlement at port Few weeks Building damage Crane collapse 2 weeks–2 months Water supply line breaks (maybe longer Complete collapse of port due to port) structure Multiple partial roof collapses Silo collapse Transformer damage 2 months Shifting of reactor vessels Vessel piping and support damage Steel frame structural collapse Fallen walls Steel frame building damage 1–2 weeks Minor structural damage to buildings Cracked water tower base Minor movement of items Few weeks Collapsed liquid oxygen (partial) tanks Few weeks Minor structural damage Minor equipment movement 2 months Storage rack collapse Few months Unanchored cabinet stand air tanks fell Product fell Some structural damage to building Not operational Partial roof and wall failures Permanent?
Building collapse
capabilities. A total of 89 fire trucks were sent to the site in the next 3 days from neighboring municipalities and from Bulgaria and Germany. As the fire spread to additional tanks, aircraft attempted to douse the fires by dropping foam. After 2 days, the refinery used diesel pumps to draw water directly from Izmit Bay to fight the fire, along with the aerial foam attack. The fires were finally declared under control on Sunday, some 5 days after the earthquake. While the fire was burning out of control, an area within 2 to 3 mi of the refinery was evacuated, including some areas where search and rescue operations were taking place in collapsed buildings. Train service was disrupted in the area because of the fire. The fire and heat eventually consumed numerous tanks in the tank farm (see Figure 20.2). It was reported that at least 17 tanks were considered to be total losses.
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FIGURE 20.2
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Tank damaged from fire during 1999 Turkey earthquake.
In addition to the tanks directly damaged by fire and heat, several tanks were damaged by sloshing of fluid. A few had ruptured walls near their tops and clear evidence of loss of material down the tank wall. Several tanks were reported to have had floating roofs “sink.” The sloshing of fluid in the tanks apparently caused damage to seals and allowed fluid on top of the floating roofs. The extra weight then caused the roofs to sink into the tank. Each of these tanks had to be drained, and the roofs decontaminated and often repaired or replaced. The main process units are located just beyond a berm from the tank farm. Four cooling towers, one concrete and three wood, are located at the berm. One of the wooden cooling towers was burned completely by radiant heat from the fire. A second cooling tower, some 50 m away, was shaken down completely, while the adjacent tower remained standing. A concrete tower on the other side of the burned tower appeared to be undamaged. A warehouse fire was caused by chemicals falling and mixing. Because of the need for firefighters in the tank farm and crude unit, this fire was allowed to burn. 20.3.2.2 Crude Unit and Stack Collapse The other area of severe and spectacular damage in the refinery occurred in one of their three crude units, when a 115-m high reinforced concrete heater stack collapsed. The break appeared to occur at about the height of the large-diameter heater duct. The weakness at the duct opening appears to have been confirmed by further forensic research sponsored by the U.S. National Science Foundation. The top of the stack fell into the unit (Figure 20.3), destroying the heater, while the bottom portion fell into a pipeway running around the perimeter of the unit (Figure 20.4). The destroyed pipeway was heavily congested with piping from all over the refinery. It took more than a year to identify, isolate, and repair damaged piping in this area. One of the pipes broken by the stack collapse was a naptha line from the original burning naptha tank in the tank farm. A fire started when the collapse occurred, and although it was extinguished relatively quickly, it flared up several times because of the new fuel from the broken pipe. The supply could not be stopped because the two block valves at the tank were inaccessible because of the fire, and downstream from the crude unit.
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FIGURE 20.3
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A stack (115 m [350 ft] high) collapsed in a crude unit and damaged the adjacent heater.
20.3.2.3 Port Damage and Oil Spill The Tupras¸ refinery has its own private port facility. Water depth is approximately 15 m. The wharf structure reportedly had several sheared piles at the waterline. This was attributed to a combination of earthquake loads and existing heavy corrosion. There was evidence of ground failure at the approach to the wharf. A steel frame pipeway on the wharf structure extending out from the shore partially collapsed, with broken frame connections and severely bent members. Damage was reported to supply and return lines due to this support damage. An oil spill occurred at the port. When the earthquake occurred during transfer operations, the vessel pilot reportedly panicked and moved his vessel away from the dock, ripping the transfer hose before the manual valve could be shut down. The damaged piping on the wharf also contributed to the oil spill, as well as overflow of the drainage system for the tank farm, made worse by emulsion from the firefighting efforts.
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FIGURE 20.4
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The collapsed stack also destroyed a pipeway.
20.3.2.4 Performance of Non-Building Structures at Other Facilities In addition to the damage described above at the Tupras¸ refinery, there were numerous other instances of damage to non-building structures. Wooden cooling towers collapsed at the Petkim petrochemical plant as well as the Tupras¸ refinery. These failures are unusual in that the towers shook down completely. It is believed that the duration of ground shaking contributed to the severity of this damage. In past earthquakes, heavy damage to wooden cooling towers has generally been caused primarily by the poor condition of the wood prior to the earthquake. According to management, that was not the case for these cooling towers. Numerous ports in the area were damaged, either structurally or by ground settlement or spreading. The port at the SEKA paper mill was severely damaged by the total failure of the approach bridge (Figure 20.5). The wharf structure at Petkim had severe damage to ten battered piles. Every pile was also severely damaged on both dolphins. Petkim also had severe damage to pipeways at the wharf. Fractured cantilever supports dropped over 100 m of fire protection pipe onto the deck, although the pipe itself was undamaged (Figure 20.6). The port at the Golcuk naval base was heavily damaged by fault rupture throughout the wharf area. A crane was dislodged from its base at this location. Cranes also came off their rails at Petkim. Two identical cranes collapsed at the Mannesmann Boru pipe factory. Storage racks collapsed at the Toprak pharmaceutical plant and the Toyota factory, both in Adapazari (Figure 20.7). 20.3.2.5 Tank Damage The most severe tank damage occurred at the Tupras¸ refinery, as described above. Much of the damage was caused by fire, with some evidence of elephant’s foot buckling. Sloshing of fluid was also a major cause of damage. Roofs of fixed tanks were also damaged at the British Petroleum gas terminal immediately adjacent to Tupras¸ . The damage consisted of local buckling of the roof skin due to sloshing of fluid. No containment was lost. In addition, damage to interconnecting walkways at the roof levels of tanks occurred in a few locations. The Habas plant in Izmit provides liquefied gases to commercial plants and medical facilities. The major damage observed at Habas was the collapse of two large storage tanks. Three identical 48-ft high tanks were built in 1995 and consisted of stainless steel shells with an interior diameter of 42 ft. The tanks were each supported on a 42-in. deep reinforced concrete platform, with © 2003 by CRC Press LLC
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FIGURE 20.5
Bridgeway to pier for SEKA paper mill collapsed. This was also used by adjacent steel mill.
FIGURE 20.6
Fire protection line fell at the Petkim petrochemical facility.
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16 20-in. diameter reinforced concrete columns, 100 in. tall. Two of the three tanks were filled with liquid oxygen at the time of the earthquake. Their column supports were not strong enough to resist lateral loads induced by the earthquake under high axial load, leading to collapse of the entire support frame in a brittle manner. An identical third tank was immediately adjacent to the collapsed tanks. This tank was reportedly full of liquid nitrogen and had no apparent damage. 20.3.2.6 Equipment Damage Most of the equipment damage observed was to unanchored equipment (Figure 20.8). Transformers were damaged in several locations, including the SEKA paper mill, Toyota car factory, EnerjiSA power plant, © 2003 by CRC Press LLC
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FIGURE 20.7
Collapsed storage racks at the Toprak pharmaceutical plant.
FIGURE 20.8
Collapse of unanchored cabinets at the Toprak Saglik facility.
Adapazari substation, and Ambarli power plant. Because of the time required to replace or repair these large equipment items, damage to the transformer was expected to cause a shutdown of one plant at the SEKA mill for several weeks (Figure 20.9). Damage observed at the Hyundai plant in Izmit included severe separation of a large air handling unit, with the duct offset by more than 1 ft. In addition, a cable tray system became unzipped and fell to the floor. A poor overhead connection detail that is easily subject to prying action from tray movement is the likely reason for the failure. Damage to a regulator valve for the gas furnace at the Bastas fluorescent bulb factory caused damage to the glass furnace itself. Staff reported that due to the heat problems after failure of that valve, a special © 2003 by CRC Press LLC
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FIGURE 20.9
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Damage to a transformer at the SEKA paper mill was expected to shut down this unit for several weeks.
“tube” was deformed and became unusable. A replacement had to be ordered from Holland, and was expected to cause a shutdown of 6 to 8 weeks. 20.3.2.7 Other Fires Although no major structural damage was observed at liquid propane gas (LPG) plants in the epicentral area, two truck drivers were killed in a fire ignited by driving through a gas leak from one of the facilities. Security monitors at one facility captured the drivers leaving the facility across the street, beginning to run down the road on foot, changing their minds and returning to their trucks, and driving away. The remains of their burned-out trucks and a burned-out building in the facility could be found less than a mile down the road. 20.3.2.8 Business Interruption As shown in Table 20.1, one of the notable lessons from this earthquake is the extensive business interruption at many facilities. Of the more than 25 facilities surveyed within 10 days of the earthquake, only one was operating. At least 6 were expected to be out of operation anywhere from 2 to 6 months or more. The reasons for large down-time estimates range from severe structural damage to inability to use undamaged critical equipment because of its location in a damaged building. © 2003 by CRC Press LLC
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Many of the industrial facilities affected by this earthquake are important because they impact the local, regional, and in some cases, global economies, as major employers, major producers, and major suppliers. In the months following the earthquake, many facilities discovered that production was limited because of difficulties with “just-in-time” delivery, or due to a lack of geographical dispersion of suppliers. 20.3.2.9 Summary of Performance in the Turkey Earthquake The epicentral area contained a high percentage of Turkey’s industry. As might be expected, the industrial facilities in the region generally had higher levels of engineering and much better construction quality control than the residential and commercial construction. However, damage was much more severe and extensive than seen in earthquakes with similar peak ground acceleration levels, with numerous examples of extended business interruption. Based on the type of structures damaged and the nature of the damage, it is likely that the long period motion and duration of the earthquake were major contributors to the extent of damage. This earthquake highlighted many of the possible situations encountered and hazards faced during earthquakes of this magnitude, such as emergency response, human response, fires, oil spills, and toxic releases, in addition to fundamental issues of structural and nonstructural damage. As additional information is gathered and studied from these facilities, we expect that lessons learned will be directly applicable to industrial facilities in other seismic regions of the world, including the United States.
20.4 Design Practices Specific seismic design practices and requirements may vary widely, depending on the industry and particular application. The design practices are generally determined by a combination of the following: • Regulatory requirements for a given facility • Industry practice for the type of facility • The owner’s awareness of the seismic risk and consequences The following sections summarize typical design practices for various types of facilities. Unless otherwise stated, these generally apply to applications within the United States.
20.4.1 Commercial Buildings Most equipment and systems in commercial buildings are designed to the minimum standards of seismic provisions included in model codes, such as the Uniform Building Code (UBC) or International Building Code (IBC). Specific provisions of these codes are discussed in more detail in Section 20.5. The typical design approach includes the following features: • Design for a single level of earthquake hazard with a low probability of occurrence (e.g., 500-year return period). • Design on a component-by-component basis. Redundancy is typically not added to equipment systems (e.g., spare pumps) because of seismic concerns. • Design commonly addresses only anchorage of permanently fixed equipment and structural design of equipment support structures (e.g., support frames for elevated vessels). • Equipment not purchased with specifications for functionality during or after an earthquake. • Temporary and portable equipment are often not restrained. Informed owners and tenants may use nonengineered restraints for temporary and portable equipment and items that could fall (e.g., bolting bookshelves to walls). • Certain nonstructural elements may have some level of seismic design, such as lights, piping, and HVAC within suspended ceilings, which should be independently supported.
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• Equipment vulnerabilities not specifically covered by codes are unlikely to be considered in design. • Once built, equipment is never required to be upgraded to current code requirements. Typically considered as “grandfathered.”
20.4.2 Schools and Hospitals Schools and hospitals designed in California come under a special regulatory jurisdiction. The design approach for these facilities is similar to those for commercial buildings, with the following exceptions: • Additional requirements for equipment design (anchorage) are intended to increase reliability. • Stricter documentation requirements and regulatory review process ensure compliance with requirements. • Facilities are required to upgrade to certain specifications to maintain licensed use of facility.
20.4.3 Essential Facilities Facilities such as police and fire stations and other government buildings may be considered to be essential. The design approach for these facilities is similar to those for commercial buildings, with the following exceptions: • Certain systems, such as uninterruptible power supply (UPS) and emergency communications may have specific designs that include seismic loads. • Seismic design codes may include an “importance factor” that adds a level of conservatism to the overall design by increasing all seismic loads.
20.4.4 Industrial Facilities Most equipment and systems in industrial facilities are also designed to the minimum standards of seismic provisions included in model codes, such as UBC or IBC. The typical design approach includes the following features: • Design for a single level of earthquake hazard with a low probability of occurrence (e.g., 500-year return period). • Design on a component-by-component basis. Redundancy may be added to equipment systems (e.g., spare pumps) but typically for reasons other than seismic concerns. • Design commonly addresses only anchorage of permanently fixed equipment and structural design of equipment support structures (e.g., support frames for elevated vessels). • Equipment typically not purchased with specifications for functionality during or after an earthquake. • Temporary and portable equipment often not restrained. Informed owners and tenants may use nonengineered restraints for temporary and portable equipment and items that could fall (e.g., bolting bookshelves to walls). • Equipment vulnerabilities not specifically covered by codes unlikely to be considered in design. • Insurance-related reviews may result in some upgrades and addressing of some concerns, especially those related to fire protection. • Once built, equipment is never required to be upgraded to current code requirements. Typically considered as “grandfathered.”
20.4.5 Oil Refineries and Chemical Plants Most equipment and systems in petrochemical facilities are designed to the minimum standards of seismic provisions included in model codes, such as the UBC or IBC. Many of the specific designs may also be © 2003 by CRC Press LLC
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addressed by industry specific standards, especially those covered by the American Petroleum Institute (API). The typical design approach includes the following features and considerations: • Design for a single level of earthquake hazard with a low probability of occurrence (e.g., 500-year return period). • Design on a component-by-component basis. Redundancy may be added to equipment systems (e.g., spare pumps) but typically for reasons other than seismic concerns. • Design commonly addresses only anchorage of permanently fixed equipment and structural design of equipment support structures (e.g., support frames for elevated vessels). • Process piping typically designed for pressure loads using applicable American National Standards Institute (ANSI) codes, and may include seismic assessment. • Equipment not purchased with specifications for functionality during or after an earthquake. • Temporary and portable equipment often not restrained. Aware owners and tenants may use nonengineered restraints for temporary and portable equipment and items that could fall (e.g., bolting bookshelves to walls). • Equipment vulnerabilities not specifically covered by codes unlikely to be considered in design. • Equipment vulnerabilities can be introduced during the life of a refinery or chemical plant, such as when routine or emergency maintenance is performed or when equipment is overhauled during turnarounds. • Steel often subject to corrosion due to presence of chemicals. This may also happen to steel reinforcing within concrete structures. • Once built, usually never required to be upgraded to current code requirements. Typically considered as “grandfathered.” Some jurisdictions may require reassessments as part of environmental evaluations for toxic releases. In reality, earthquakes are often considered a “minor” hazard in petrochemical facilities, relative to day-to-day operational risks that must be addressed.
20.4.6 Offshore Oil Platforms The entire design process for offshore oil platforms is different than for other facilities. The specific design is typically addressed by industry-specific standards, such as those issued by Det norske Veritas (DnV) in Norway, the United Kingdom Health and Safety Executive (HSE), or the American Petroleum Institute (API) in the United States. Numerous platforms have been installed in seismic regions offshore California and Alaska, and the design and evaluation methods used by API are fairly mature. Platforms are now being built in other seismic regions of the world, such as the Caspian Sea, Sakhalin Island, Russia, Trinidad, and Indonesia. The following features and considerations are incorporated into typical design using API criteria: • Definition of seismic hazards using site-specific hazards assessments. • Design for two levels of earthquake hazard. Design for little or no damage in an earthquake with a reasonable probability of occurrence within the lifetime of the platform. This earthquake, called the strength level earthquake (SLE), is typically a 200-year return period for offshore California. • Design for overall structural stability in a rare, intense earthquake. This ductility level earthquake (DLE) considers only overall collapse modes of the platform or equipment systems, and is typically based on earthquake return periods of 1000 to several thousand years. • Offshore platform structures are typically designed for the SLE, and checked for the DLE. The SLE analysis is typically a response spectrum analysis, while the DLE is a nonlinear time history analysis, checking for overall platform stability.
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• Process equipment on the deck of the platform is typically designed for only the SLE event. Lower allowable stress values are used in lieu of performing explicit ductility checks. • Current seismic design criteria for offshore platforms, as proposed in draft ISO standards, select a DLE event to achieve a target probability of failure. The SLE is then selected based on the expected reserve capacity of the platform and the ductility demand in order to achieve a cost-effective design. • Design may be governed by other significant loads, such as transportation. • Design of process equipment on a component-by-component basis. Redundancy is typically not added to equipment systems (e.g., spare pumps) to address seismic concerns but may be included for other reasons. • Design of equipment commonly addresses only anchorage of permanently fixed equipment and structural design of equipment support structures (e.g., support frames for elevated vessels). • Process piping typically designed for pressure loads using applicable ANSI codes and may include seismic assessment. • Equipment not purchased with specifications for functionality during or after an earthquake.
20.4.7 Pipelines Buried pipelines are designed primarily to resist the effects of permanent ground deformation (PGD) caused by major earthquakes, rather than the effects of ground shaking. PGD effects include liquefaction, spreading, and fault crossings. The pipelines are designed using strain-based criteria, with inelastic behavior allowed. See Chapter 23 for additional information on this topic.
20.4.8 LNG Facilities LNG facilities are typically designed using the criteria of NFPA 59A. These criteria require a two-level earthquake approach for essential systems. No damage should occur and functionality should be maintained for the operating basis earthquake (OBE). The OBE uses a return period similar to onshore building codes like the IBC and UBC. The safe shutdown earthquake (SSE) is defined as an earthquake with a return period of up to 5000 years. The system is designed for no loss of containment, with the structural design controlled by using stress limits.
20.4.9 Nuclear Power Plants Nuclear power plants are the most highly regulated facilities for seismic design throughout the United States. The seismic acceptance and performance criteria are subject to change, and are under the jurisdiction of the Nuclear Regulatory Commission (NRC). In general, equipment is designed for functionality if it has safety implications for the shutdown of the facility. Functionality requirements are often satisfied by shake table testing of the specific equipment items prior to installation. Requalification may be done by other methods, such as the use of seismic experience data.
20.5 Code Provisions Facility seismic design provisions may be specified by any number of codes rules and regulations. This section discusses the seismic design provisions for equipment and nonstructural components in the most widely used building codes in the United States. Other specific regulations that may govern a particular design are also presented.
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20.5.1 Model Codes Model code agencies develop codes that are widely adopted throughout regions of the United States. The codes become law only when officially adopted by a local or state jurisdiction. States generally mandate that local jurisdictions adopt a specific edition of a building code by a given date. The local jurisdictions may add specific provisions and create a local building code. The following is a partial list of code agencies and provisions in the United States that include seismic provisions. • • • •
National Building Code, Building Officials and Code Administrators International (BOCA) Uniform Building Code, International Conference of Building Officials (ICBO) Standard Building Code, Southern Building Code Congress International (SBCCI) International Building Code, International Code Council (ICC)
These model codes were updated on a regular basis. The IBC was prepared by committees consisting of representatives from BOCA, ICBO, and SBCCI with the intent of standardizing a single model code for use in the entire United States. As such, the other three building codes will no longer be updated. The UBC has long been the most widely used model code for seismic regions in the western United States. Provisions for non-building structures were first introduced only in 1988. Prior to that, engineers relied on interpretation of codes developed for buildings. The following paragraphs illustrate the changes incorporated into the seismic provisions for equipment and systems of the UBC and IBC over three code cycles, including the 1994 and 1997 UBC and the 2000 IBC.
20.5.2 1994 UBC The 1994 UBC categorized “non-building structures” into those that have structural systems resembling those of buildings and structural systems that do not resemble those of buildings. Examples of buildinglike structures would include transverse moment frames for pipeways. Examples of non-building structures would include tanks, vessels, exchangers, stacks, and towers. Combination structures support nonstructural elements whose weight exceeds 25% of the weight of the structure. Examples include tall vessels, furnaces, or tanks supported above grade on braced or moment-resisting frames. Electrical and mechanical equipment supported within a structure fall into the category of “subsystems.” 20.5.2.1 Seismic Loads The total horizontal base shear (V ) for a regular flexible building-like structure in any of the two orthogonal horizontal directions would be determined from a formulation similar to Equation 20.1 below, which is Equation 28-1 in the 1994 UBC: V = ZICW Rw
(20.1)
where V Z I Rw W C
= base shear = seismic zone factor given in the 1994 UBC, Table 16.I = importance factor given in Table 4.3, UBC = response modification factor = total seismic weight = numerical coefficient determined from the following formula: C = 1.25 S T
( 2/3)
(20.2)
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The value of C need not exceed 2.75 and this value may be used for any structure without regard for soil type or structure period. The minimum value of the ratio C/Rw is 0.075 for building-like structures and 0.4 for non-building-like structures. In Equation 20.1, each parameter represents a certain aspect of the earthquake loading as described below. Z represents the level of seismic ground motion expected at the site and is therefore site dependent. The zonation in the United States provided generic Z values for use which range from 0.1 to 0.4. I is a measure of the relevant importance of the structure, ranging from 1.0 to 1.25 for structures and from 1.0 to 1.5 for subsystems. For more important structures, higher seismic forces are prescribed. The importance factor, I, provides a means of increasing the design force levels for facilities that may have an unusual hazard, have a potential for releasing hazardous materials, or are important for emergency response. The I value for individual facilities often would be decided by the owner and/or the building official for those cases where items do not fall under the code definitions. Note that an entire facility need not use the same value of I. C represents potential amplification of seismic forces allowing for relative frequency content of the ground motion and considering the natural period of structure under consideration. The product ZC represents the spectral acceleration corresponding to the period of the structure. For cases where a sitespecific spectrum exists, the spectral ordinate corresponding to the period of the structure could be used in lieu of the ZC value, subject to approval of building officials. Care should be taken to allow for higher mode effects if the fundamental natural period of the structure is larger than the period corresponding to the spectral peak. One way to allow for this is to increase the ZC factor by a factor of 1.5 to allow for higher mode effects. The engineer was required to use judgment as to the method most applicable for determining the fundamental period of vibration, T. When using the 1994 UBC, it was recommended that the period be determined from UBC Equation (28–5), Section 1628.2.2, corresponding to Method “B” only. This formula is based on Rayleigh’s method and uses the structural properties and deformational characteristics of the structure as determined by a static analysis. For building-like structures only, Method “A” of the UBC could also be used in determining structural period. Alternatively, the fundamental period of the structure could be estimated by a frequency (modal) analysis. Seismic weight, W, includes the weight of the structure, attached equipment, equipment and vessel contents (operating loads), and code-specified portions of live and snow load. Rw is a measure of energy absorbing capability or ductility inherent in a particular type of structural system or structure. It represents an equivalent reduction in seismic forces by allowing energy dissipation once the structure begins to respond in the inelastic range. Rw factors are provided in the code and range from 3 to 12 for building-like structures, and 3 to 5 for non-building structures. It is recommended that lower values be used for building-like structures when designing structures in industrial facilities. This is because buildings tend to have structural redundancy due to multiple bays and frame lines and also contain nonstructural elements that effectively give the building greater damping and strength during strong ground motion response. Note also that using higher Rw values in design tends to result in a flexible structure that will tend to increase calculated displacements.
20.5.3 1997 UBC The base shear equations changed considerably between the 1994 and 1997 editions of the UBC. The major changes affecting the design of non-building structures included the following. The overall formulas and methods for calculating base shear changed significantly. The new base shear should be the minimum of Equations 20.3 and 20.4 (1997 UBC Equations 30-4 and 30-5, respectively): V = CV I W RT
(20.3)
V = 2 .5 C a I W R
(20.4)
and
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where V Cv Ca I R W
= = = = = =
base shear seismic coefficient, found in Table 16-R of the 1997 UBC seismic coefficient, found in Table 16-Q of the 1997 UBC importance factor response modification factor given in Table 16-P of the 1997 UBC total seismic weight
Amplification factors were included in the ground motion parameters Ca and Cv to account for nearfault amplifications. This applies to sites within 15 km of recognized active faults. The maximum accelerations increased by 50%. The Rw factor in the 1994 UBC was replaced by an R factor, with values ranging from 2.2 to 3.6. These are the equivalent values of 3 to 5 in the 1994 UBC when adjusted by a factor of 1.4 to account for strength design vs. working stress. One other major change in the 1997 UBC was incorporating the effects of in-structure amplification for equipment within buildings. The load equation for these systems includes an amplification factor ranging from 1 to 4 to account for the elevation of the equipment relative to the ground and roof. The amplification for equipment at roof level could be as much as four times the ground acceleration. The 1997 UBC also included flexibility factors for equipment within structures. This factor is 1.0 for “rigid” equipment and 2.5 for “flexible” equipment. The values are found in Table 16-O of the 1997 UBC. In addition, Table 16-O includes several footnotes with specific seismic design guidance for different types of equipment and piping. These footnotes attempt to clarify several of the provisions with respect to specific equipment design. For example, Footnote 14 provides restrictions related to the use of vibration isolators. Footnote 18 requires batteries on racks to be restrained from falling off the racks. Finally, the use of earthquake loads in load combinations requires use of an overstrength factor Ω0 , and a reliability/redundancy factor, ρ .
20.5.4 2000 IBC The 2000 IBC is very different in style and format from the 1997 UBC. Earthquake loads are based on the 2500-year response spectral accelerations at 0.2 sec (Ss) and 1.0 sec (S1). Rather than using zonations as in the UBC, the entire country is mapped for these two periods, and values are to be scaled from these maps. These values are then multiplied by site coefficients (Fa and Fv) to account for the soil at the site, and then multiplied by two thirds for the design accelerations. Architectural, mechanical, and electrical component design is given in Section 1621 of the IBC. The requirements are very similar to those of the 1997 UBC for non-building structures, including the ap flexibility factor of either 1.0 or 2.5. One major change from the 1997 UBC is that the amplification for location within a building ranges from 1 to 3 rather than 1 to 4. Specific guidance is now provided for calculating relative displacements for components with connection points on two structures. Detailed design guidance is written as specific provisions in the 2000 IBC, rather than footnotes in a table. These provisions cover numerous items, such as support of piping systems and HVAC, restrictions for use of vibration isolators on mechanical equipment (Section 1621.3.12.2), and specific requirements for wraparound restraints for batteries on racks (Section 1621.3.13.1). Section 1622 covers non-building structures that are similar to buildings, such as pipe racks, storage racks, and piers and wharves. Those non-building structures not similar to buildings include tanks and vessels, telecommunication towers, stacks and chimneys, and amusement structures. Many of the specific provisions defer to a “substantiated analysis using standards approved by the building official,” in recognition that many of these types of design are routinely done using standards developed specifically for that industry on a consensus basis of practicing engineers in that specialized area.
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20.5.5 Other Industry Codes and Standards It is very difficult for practicing engineers to keep up to date on continuously varying codes and standards of different vintage and intent. The following are examples of several of the numerous guidelines for specific design and construction practices that may be used in the seismic design or assessment of specific installations. These documents are often created, by consensus agreement, by professional organizations. Caution should be used when “mixing and matching” multiple codes. Various terms, such as ground motion parameters, may have different meanings when applied in different codes. Also, demand equations may be meant for application with different definitions of capacity. 1. American Concrete Institute (ACI) a. ACI 313, Recommended Practice for the Design and Construction of Concrete Bins, Silos, and Bunkers for Storage of Granular Materials b. ACI 318, Building Code Requirements for Reinforced Concrete and Commentary c. ACI 349, Code Requirements for Nuclear Related Structures d. ACI 530, Building Code Requirements for Masonry Structures e. ACI 530.1, Specifications for Masonry Structures 2. American Institute of Steel Construction (AISC) a. Manual of Steel Construction — Allowable Stress Design b. Load and Resistance Factor Design Specification for Structural Steel Buildings 3. American Iron and Steel Institute (AISI) a. Criteria for Structural Application of Steel Cable for Buildings b. Specification for the Design of Cold-Formed Steel Structural Members 4. American National Standards Institute (ANSI) a. ANSI B31.3, Chemical Plant Refinery Petroleum Piping b. ANSI B31.4, Liquid Petroleum Transportation Piping Systems c. ANSI B31.8, Gas Transmission and Distribution Piping Systems 5. American Petroleum Institute (API) a. API 650, Welded Steel Tanks for Oil Storage b. API 653, Tank Inspection, Repair, Alteration, and Reconstruction 6. American Society of Civil Engineers (ASCE) a. ASCE 7, Minimum Design Loads for Buildings and Other Structures b. ASCE 8, Specification for the Design of Cold-Formed Stainless Steel Structural Members c. Guidelines for the Seismic Design of Oil and Gas Pipeline Systems, Committee on Gas and Liquid Fuel d. Guidelines for Seismic Evaluation and Design of Petrochemical Facilities, Petrochemical Energy Committee 7. American Society of Mechanical Engineers (ASME) a. Boiler and Pressure Vessel Code b. ASME A17.1, Safety Code of Elevators and Escalators 8. American Society for Testing and Materials (ASTM) a. ASTM D32.99, Standard Specification for Filament-Wound Glass-Fiber-Reinforced Thermoset Resin Chemical-Resistant Tanks b. ASTM C635, Standard Specification for the Manufacture, Performance and Testing of Metal Suspension Systems for Acoustical Tile and Lay-in Ceiling Panels c. ASTM C636, Standard Practice for the Installation of Metal Suspension Systems for Acoustical Tile and Lay-in Ceiling Panels 9. American Water Works Association (AWWA) a. AWWA D100, AWWA Standard for Welded Steel Tanks for Water Storage b. AWWA D110, AWWA Standard for Wire-Wound Circular Prestressed-Concrete Water Tanks
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10. Applied Technology Council (ATC) a. ATC-14, Evaluating the Seismic Resistance of Existing Buildings b. ATC-3-06, Tentative Provisions for the Development of Seismic Regulations for Buildings c. ATC-33.03, Guidelines for the Seismic Rehabilitation of Buildings 11. Federal Emergency Management Agency (FEMA) a. FEMA 154/ATC-21, Rapid Visual Screening of Buildings for Potential Seismic Hazards: A Handbook b. FEMA 155/ATC-21-1, Rapid Visual Screening of Buildings for Potential Seismic Hazards: Supporting Documentation c. FEMA 172, NEHRP Handbook for the Seismic Rehabilitation of Existing Buildings, Building Seismic Safety Council d. FEMA 178, NEHRP Handbook for the Seismic Evaluation of Existing Buildings, Building Seismic Safety Council e. FEMA 222, NEHRP Recommended Provisions for the Development of Seismic Regulations for New Buildings - Provisions, Building Seismic Safety Council f. FEMA 223, NEHRP Recommended Provisions for the Development of Seismic Regulations for New Buildings: Commentary, Building Seismic Safety Council g. FEMA 74, Reducing the Risks of Nonstructural Earthquake Damage h. FEMA 368, NEHRP Recommended Provisions for the Seismic Regulations for New Buildings and Other Structures, 2000 Edition — Part 1: Provisions, Building Seismic Safety Council i. FEMA 369, NEHRP Recommended Provisions for the Seismic Regulations for New Buildings and Other Structures, 2000 Edition — Part 2: Commentary, Building Seismic Safety Council 12. Institute of Electrical and Electronic Engineers (IEEE) a. IEEE Standard 344, Recommended Practice for Seismic Qualification of Class 1E Equipment for Nuclear Power Generating Stations 13. National Fire Protection Agency (NFPA) a. NFPA-13, Standard for the Installation of Sprinkler Systems b. NFPA-59A, Standard for the Production, Handling, and Storage of Liquefied Natural Gas (LNG) 14. Rack Manufacturer’s Institute (RMI) a. Specification for the Design, Testing, and Utilization of Industrial Steel Storage Racks 15. Risk Management and Prevention Program (RMPP) Committee a. Proposed Guidance for RMPP Seismic Assessments 16. Sheet Metal and Air Conditioners National Association (SMACNA) a. HVAC Duct Construction Standards, Metal and Flexible b. Rectangular Industrial Duct Construction Standards c. Guidelines for Seismic Restraint of Mechanical Systems and Plumbing Piping Systems 17. Steel Joist Institute a. Standard Specification Load Tables and Weight Tables for Steel Joists and Joist Girders 18. Structural Engineers Association of California a. Recommended Lateral Force Requirements and Commentary 19. United States Department of Defense a. Tri-Service Manual TM 5-809-10, Seismic Design for Buildings b. Tri-Service Manual TM 5-809-119.1, Seismic Design Guidelines for Essential Buildings c. Tri-Service Manual TM 5-809-119.2, Seismic Design Guidelines for Upgrading Essential Buildings 20. United States Department of Energy a. DOE-STD-1020, Natural Phenomena Hazards Design and Evaluation Criteria for Department of Energy Facilities 21. United States Nuclear Regulatory Commission a. Generic Letter 87-02, Verification of Seismic Adequacy of Mechanical and Electrical Equipment in Operating Reactors, Unresolved Safety Issue (USI) A-46
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b. Generic Implementation Procedure (GIP) for Seismic Verification of Nuclear Plant Equipment [Winston and Strawn, et al.] c. NRC Regulatory Guide 1.60, Design Response Spectra for Seismic Design of Nuclear Power Plants
20.6 Assessment of Existing Facilities Assessment of equipment and systems within existing facilities may use one of two methods: • The conventional method is a component-by-component check, focusing on anchorage of equipment. It also includes checks for specific vulnerabilities known to affect the performance of specific types of equipment. • The second method is a systems reliability assessment. This can be especially useful in determining priorities for spending limited retrofit money, and can help the facility owner to focus investments on the specific areas that will provide the greatest increase in overall reliability. Each of these methods is described in the paragraphs below.
20.6.1
Component Assessment
The primary method of identifying seismic risks on a component-by-component basis consists of “walkdown” investigations of facility equipment installations by experienced engineers. The walkdown is an on-site, mostly visual review, where as-installed components are methodically “walked down” and evaluated for potential seismic vulnerabilities. The walkdown method takes advantage of lessons learned from the past earthquake performance of process and industrial facilities, such as from the investigations described above. Many of the issues are not covered in design codes, or are unique to existing facilities. These equipment walkdown evaluations are based primarily on the judgment of engineers performing the reviews, guided by their understanding of performance of similar items of equipment in past earthquakes. The walkdown emphasizes the identification of details and configurations that will be expected to perform poorly due to lack of strength, or because of their particular design and construction aspects. It does not generally focus on quantifying “strength” issues (e.g., whether a weld should be 1/4 in. or 3/8 in.). As such, the review does not rely heavily on calculations (although some calculations are often made), but rather on the expertise and experience of the walkdown engineers in identifying the types of problems that have occurred in past earthquakes and the specific conditions that may lead to similar problems. The walkdown generally focuses on four main areas: anchorage, structural load path, differential displacements, and equipment/system specific concerns. Inadequate or no anchorage is the most common cause of failure of equipment in earthquakes. The engineer should review anchorage on all vessels and equipment for adequate resistance to earthquake loads. The engineer should also look for possible vulnerabilities that might have been introduced during fabrication. For example, large welds that are installed over multiple shim plates may be assumed to have much more strength than they can actually provide and have been observed to fracture during earthquakes. It is also difficult to achieve high quality welds in certain conditions, such as welding to checker plate (Figure 20.10). Load path refers to the transfer of load from the center of mass to the foundation. A common concern here would be the use of vibration isolators (Figure 20.11). These spring devices are notoriously bad performers in earthquakes, as they can dismount by vertical action, or fracture if made of nonductile materials. They often are not designed for uplift loads (Figure 20.12). Another example concern would be batteries on racks. These are typically critical equipment items, as they are commonly associated with emergency generator systems. These batteries should be restrained by wraparound bracing to prevent them from falling off the rack (Figure 20.13).
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FIGURE 20.10
Earthquake Engineering Handbook
Good quality weld to checker plate is difficult to achieve.
FIGURE 20.11 Vibration isolators for rotating equipment are often not designed for seismic loads, and may be made of brittle material (e.g., cast iron) and may not resist uplift.
Another example issue would be reinforced concrete vessel supports from the early 1970s, before concrete design codes changed. Figure 20.14 shows one system being used to support a horizontal vessel, elevated well above ground level. Differential displacement concerns exist anywhere supports, equipment, or piping span across structural separations, or other areas where two supports could move in different directions. The primary concern is that items may be inadvertently overrestrained. The most common location for this problem is unanchored tanks with buried piping going directly into the ground. Uplift of the tanks can rupture the piping. Figure 20.15 shows an example of piping spanning between a “hard point” and an unanchored tank that could uplift. Equipment/system-specific concerns relate to issues specific to a given system. For example, piping is generally reviewed for adequacy of support systems and for adequate flexibility. Welded steel pipe © 2003 by CRC Press LLC
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FIGURE 20.12
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Bumpers to restrain lateral and vertical motion may be an acceptable mitigation.
generally performs very well in earthquakes provided that it maintains its overall support system integrity and does not have differential displacement concerns. However, specific support or system configuration details have been proven in past earthquakes to be problems under certain conditions, such as use of C-clamps, use of PVC, cast iron, or other nonductile materials, use of mechanical couplings associated with possible excessive displacements or impacts, etc.
20.6.3 Systems Reliability Assessment The assessment summarized in the previous section represents a standard engineering approach, addressing every major equipment item in the facility without consideration for relative importance. That methodology does not necessarily address all of the issues that affect the operational reliability of the facility, and it may miss major concerns. It also does not prioritize where upgrades will provide the most benefit. In order to prioritize these concerns, a systems reliability assessment of the facility systems should be performed. A reliability model can be constructed that shows qualitatively how systems and individual © 2003 by CRC Press LLC
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FIGURE 20.13
Earthquake Engineering Handbook
Battery racks should have wraparound restraints to prevent batteries from falling off the racks.
equipment items interact with each other and allows quantitative analyses. The method uses a fault tree approach to describe the possible scenarios that could disrupt operations. These fault trees are graphical representations of combinations of events that could lead to a major disruption in operations. Analyses can be performed to calculate the contribution to overall risk from each possible failure scenario. The overall risk is a function of both the probability of failure of an individual item and the system configuration, in terms of dependencies and redundancies. It should be noted that the primary value in performing this assessment is in the qualitative assessments made during the investigation of failure modes, safeguards, backup systems, etc. Interviews with staff and investigation of plant operations uncover possible failure scenarios and “weak links” in the systems. Actual probabilities of occurrence of various failure scenarios are used primarily in relative terms in prioritizing specific systems and equipment vulnerabilities. 20.6.3.1 Screening Methodology A system reliability-based screening methodology for critical equipment facilities has been developed [Johnson et al., 1999]. The following paragraphs summarize the mechanics of the screening process, including the scoring system and a description of how results are intended to be interpreted. The screening methodology uses the following procedure: 1. Identify which systems are required to remain functional during and/or after an earthquake. These systems may be necessary for life-safety purposes (e.g., fire protection) or for the facility to remain operable (e.g., power, HVAC). 2. For each system selected, identify major electrical and mechanical components, as well as support functions (water, power, HVAC) and distribution systems (piping, ducts). These equipment items are usually considered to be major items, such as pumps, transformers, distribution panels, etc. However, smaller items or subcomponents, such as a relay for a fuel transfer pump, may be identified specifically because of their importance to the operation of the overall system and a particular concern about their vulnerability. 3. Graphically sketch the system processes, identifying critical components, system dependencies, and redundancies. This systems evaluation should consider operator actions which are required to continue operation or to mitigate potentially dangerous situations (e.g., turning off gas valves or resetting relays). The process is similar to creating a fault tree or event tree. An example is shown in Figure 20.16. © 2003 by CRC Press LLC
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FIGURE 20.14
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Elevated vertical vessels on older reinforced concrete supports with no redundancy.
4. Perform a screening inspection of each of the components in the systems, using evaluation checklists developed by the Multidisciplinary Center for Earthquake Engineering and Research (MCEER) for specific components. Examples of these checklists are given in Figure 20.17 to Figure 20.21. Assign scores for each component according to the particular vulnerabilities present in that component, the location in the building and site hazard, the historical performance of that equipment item, and other factors. 5. Combine scores of individual components for each system to determine an overall score for that system, as explained below. A higher score indicates higher reliability. 6. Evaluate scores for individual components to identify “weak links” in individual components that affect functionality of the component. Use the scoring method to identify all vulnerabilities that may require some mitigation or further evaluation. 7. Use the results of the steps above to make risk management decisions. This may also include costbenefit analyses to evaluate different options and additional evaluations to confirm screening evaluation findings. © 2003 by CRC Press LLC
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FIGURE 20.15
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Rigid piping from unanchored tank could be damaged by any tank movement.
KEY SYMBOL
NAME
MEANING
Component above gate AND GATE functions if all components below function Component above gate OR GATE functions if any component below functions
Life-Safety Systems
Fire Response
Fire Detection and Alarm
Gas Shut-off
Active Fire Suppression Systems
Elevator Stopping System
Stairway Emergency Lighting
Air Duct Fire and Smoke Dampers
FIGURE 20.16 Example life-safety system logic diagram for a high-rise building. (From Johnson, G.S. et al., Seismic Reliability Assessment of Critical Facilities: A Handbook, Supporting Documentation, and Model Code Provisions, Technical Report MCEER 99–0008, Multidisciplinary Center for Earthquake Engineering Research, State University of New York, Buffalo, 1999. With permission.)
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20.6.3.2 Assigning Scores to Components The scoring methodology for an individual component uses the following logic: 1. Each component is assigned a basic score that is a function of the performance history of that type of equipment, and the seismicity of the site. Those scores have been developed for broad categories of major equipment components. These basic scores are derived from fragility data of equipment performance in past earthquakes and test programs. 2. The basic scores are modified by performance modification factors (PMFs) that indicate the decrease in reliability due to specific configurations or details that may be present in an equipment installation. Each detail that may affect the seismic vulnerability is assigned a PMF consistent with its relative effect on functionality, as described later. 3. The evaluation and checklist are completed such that the basic score and all applicable PMFs are identified. 4. The equipment item is assigned a score equal to its basic score minus the largest (worst case) applicable PMF. If further evaluations or system modifications lead to the determination that a particular PMF is no longer relevant, the second most critical PMF is then used. 20.6.3.3 Combining Component Scores to Determine System Score The scoring methodology for an entire system uses the following logic, as illustrated in the simplified representative system diagrams of Figure 20.22 to Figure 20.24. 1. Where a group of multiple components are all needed for a particular function — that is, the components are connected in series, like a chain, where the weakest link fails the group, the lowest score of the individual components is the net score for that combination of components. Series connectivity is indicated by an “and” gate:
2. Where there is redundancy — that is, the components are connected in parallel, where all components must fail for the group to fail, the user is given the option of using the highest value, or calculating a “composite” score using a formula that considers the highest value and the total number of redundant components. Parallel connectivity is indicated by an “or” gate:
Further discussion on this formulation is provided in Johnson et al., 1999. 20.6.3.4 Consideration of Site Seismicity The basic scores in the MCEER methodology have been developed considering the level of seismic hazard for the region of the nation in which the facility is located. This is done by assigning different scores for different levels of seismic hazard, derived here using the levels of seismic acceleration specified in the NEHRP Recommended Provisions for Seismic Regulations for New Buildings. The basic scores were derived by convolving vulnerability data in the form of fragility functions with seismicity data in the form of a seismic hazard curve. The resulting score is a measure of relative probability of failure. The reader is cautioned that the results are not intended to provide a rigorous estimate of probability of failure of a system, but rather an approximate estimate of the reliability, without the effort associated with a rigorous estimate.
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Rapid Visual Screening Score Sheet
EL-01
Motor Control Centers ID Number
______________________________
Comments _______________________________ ________________________________________ ________________________________________ ________________________________________
Earthquake Load Level (circle one letter) Location in Building Bottom Middle Top Third Third Third
NEHRP
UBC
Z
1-3
1
A
A
A
O
4-5
2
A
B
C
N
6
3
B
C
D
E
7
4
C
D
E
Scores and Modifiers - Motor Control Centers (circle a Basic Score and all PMFs that apply - use the column indicated by the Earthquake Load Level above) Description
Basic Score
A
B
C
D
E
5.2
4.3
3.8
3.4
3.1
1. No anchorage
0.5
0.5
0.5
0.5
0.5
2. “Poor” anchorage
0.5
0.5
0.5
0.5
0.5
M 3. Suspect load path
0.5
0.5
0.5
0.5
0.5
F
0.6
0.6
0.6
0.6
0.6
P
4. Pounding or impact concerns 5. Interaction concerns 6. Other _____________________
Final Score = Basic Score - largest applicable PMF Note that this is a screening process and is inherently conservative. If there is any question about an item, note it and select the appropriate PMF. See the following page for PMF guidelines.
(a )
FIGURE 20.17 Scoring worksheet for MCCs (From Johnson, G.S. et al., Seismic Reliability Assessment of Critical Facilities: A Handbook, Supporting Documentation, and Model Code Provisions, Technical Report MCEER 99–0008, Multidisciplinary Center for Earthquake Engineering Research, State University of New York, Buffalo, 1999. With permission.) © 2003 by CRC Press LLC
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EL-01
Performance Modification Factors (PMFs) 1, 2
As shown in the photo below, the anchorage of the MCC base to the floor or pad is sometimes difficult to see since it is typically behind the outer face of the unit. If you have reason to believe that there is no anchorage, select PMF 1. If the anchorage appears small compared to the size of the unit or appears to be damaged, select PMF 2.
3
There should be a definite and continuous load path from the internal components of the MCC to the anchorage at the base. The photo below shows a definite weakness in the load path. Another example is cut-outs in the sheet metal enclosure which could weaken its structural integrity. If these conditions exist, select PMF 3.
4
If adjacent cabinets are not attached and are within about 1/2” of each other, there is a potential for pounding between the two. If so, select PMF 4
5
If large items, such as non-structural walls, could fall and impact the MCC, PMF 5 should be selected.
6
For other conditions that the reviewer believes could inhibit MCC function following an earthquake, (e.g., a history of problems with this piece of equipment) assign a PMF value relative to the existing PMFs in the table. Add a descriptive statement for the concern.
1, 2
5 4
3 3
(b )
FIGURE 20.17 (CONTINUED)
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EL-06
Batteries and Racks
Earthquake Load Level (circle one letter) ID Number omments
_________________________ Location in Building Bottom Middle Top Third Third Third
__________________________
___________________________________
NEHRP
UBC
___________________________________
Z
1-3
1
A
A
A
___________________________________
O
4-5
2
A
B
C
N
6
3
B
C
D
E
7
4
C
D
E
Scores and Modifiers - Batteries and Racks (circle a Basic Score and all PMFs that apply - use the column indicated by the Earthquake Load Level above) Description
A
B
C
D
E
5.3
4.4
3.9
3.5
3.2
2. “Poor” anchorage
0.3
0.3
0.3
0.3
0.3
3. No battery spacers
0.7
0.7
0.7
0.7
0.7
5. No battery restraints
0.5
0.5
0.5
0.5
0.5
6. Interaction concerns
0.5
0.5
0.5
0.5
0.5
Basic Score 1. No anchorage
P
M 4. No longitudinal cross-bracing F
7. Other _____________________
Final Score = Basic Score - highest applicable PMF Note that this is a screening process and is inherently conservative. If there is any question about an item, note it and select the appropriate PMF. See the following page for PMF guidelines.
(a )
FIGURE 20.18 Scoring worksheet for batteries. (From Johnson, G.S. et al., Seismic Reliability Assessment of Critical Facilities: A Handbook, Supporting Documentation, and Model Code Provisions, Technical Report MCEER 99–0008, Multidisciplinary Center for Earthquake Engineering Research, State University of New York, Buffalo, 1999. With permission.) © 2003 by CRC Press LLC
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Rapid Visual Screening Score Sheet
EL-06
Performance Modification Factors (PMFs) 1, 2
If there are no anchor bolts at the base of the frame, select PMF 1. If the anchors appear to be undersized, if there are not anchors for every frame of the rack, or if the anchorage appears to be damaged select PMF 2.
3
Look for stiff spacers, such as Styrofoam, between the batteries that fit snugly to prevent battery pounding. If there are none, select PMF 3.
4
The rack should provide restraints to assure that the batteries will not fall off. The photo above shows a rack with no restraints, while the photo to the left shows a rack with restraints. Select PMF 4 if adequate restraint is not provided.
5
Racks with long rows of batteries need to be braced longitudinally as shown in the photo to the left. Select PMF 5 if no cross-bracing is present.
6
If large items such as non-structural walls could fall and impact the battery racks, select PMF 6.
7
For other conditions that the reviewer believes could inhibit battery function following an earthquake (e.g., a history of problems with this piece of equipment), assign a PMF value relative to the existing PMFs in the table. Add a descriptive statement for the concern.
4
3
6
1, 2
4
5
1, 2
(b )
FIGURE 20.18 (CONTINUED)
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EL-08
Engine Generators ID Number
______________________________
Comments _______________________________ ________________________________________ ________________________________________ ________________________________________
Earthquake Load Level (circle one letter)
NEHRP
UBC
Location in Building Bottom Middle Top Third Third Third
Z
1-3
1
A
A
A
O
4-5
2
A
B
C
N
6
3
B
C
D
E
7
4
C
D
E
Scores and Modifiers - Engine Generators (circle a Basic Score and all PMFs that apply - use the column indicated by the Earthquake Load Level above) Description
A
B
C
D
E
5.1
4.2
3.7
3.3
3.0
M 4. Rigid attachment concerns
0.4
0.4
0.4
0.4
0.4
F
5. Driver/fan diff. displacement
0.4
0.4
0.4
0.4
0.4
6. Interaction concerns
0.2
0.2
0.2
0.2
0.2
Basic Score 1. No anchorage 2. “Poor” anchorage P
3. Vibration isolator concerns
7. Other _____________________
Final Score = Basic Score - highest applicable PMF
Note that this is a screening process and is inherently conservative. If there is any question about an item, note it and select the appropriate PMF. See the following page for PMF guidelines.
(a )
FIGURE 20.19 Scoring worksheet for generators. (From Johnson, G.S. et al., Seismic Reliability Assessment of Critical Facilities: A Handbook, Supporting Documentation, and Model Code Provisions, Technical Report MCEER 99–0008, Multidisciplinary Center for Earthquake Engineering Research, State University of New York, Buffalo, 1999. With permission.)
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Rapid Visual Screening Score Sheet
EL-08
Performance Modification Factors (PMFs) 1, 2
Select PMF 1 if there is no anchorage. If the anchorage appears small compared to the size of the generator, or is damaged, select PMF 2.
3
Where vibration isolators are used there should be lateral restraints. If no lateral restraints exist, or they appear to be inadequate, select PMF 3.
4
If attached conduits do not have adequate flexibility to accommodate potential generator motions, select PMF 4.
5
As shown below, the driver and motor should be mounted to the same skid, if they aren’t, select PMF 5.
6
If large items, such as non-structural walls, could fall and impact the generator, PMF 6 should be selected.
7
For other conditions that the reviewer believes could inhibit generator function following an earthquake (e.g., a history of problems with this piece of equipment), assign a PMF value relative to the existing PMFs in the table. Add a descriptive statement for the concern.
3
5
5
1, 2
1, 2
(b )
FIGURE 20.19 (CONTINUED)
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MN-01
Pumps ID Number
_____________________________
Comments ______________________________ _______________________________________ _______________________________________ _______________________________________
Earthquake Load Level (circle one letter) Location in Building Bottom Middle Top Third Third Third
NEHRP
UBC
Z
1-3
1
O
4-5
2
N
6
3
E
7
4
C
A
A
A
A
B
C
B
C
D
D
E
Scores and Modifiers - Pumps (circle a Basic Score and all PMFs that apply - use the column indicated by the Earthquake Load Level above) Description
Basic Score
A
B
C
D
E
5.1
4.2
3.6
3.2
3.0
1. No anchorage 2. “Poor” anchorage P
3. Vibration isolator concerns
M 4. Motor/pump displacement
0.6
0.6
0.6
0.6
0.6
F
5. Piping support concerns
0.4
0.4
0.4
0.4
0.4
6. Interaction concerns
0.4
0.4
0.4
0.4
0.4
7. Other _____________________
Final Score = Basic Score - highest applicable PMF
(a )
FIGURE 20.20 Scoring worksheet for pumps. (From Johnson, G.S. et al., Seismic Reliability Assessment of Critical Facilities: A Handbook, Supporting Documentation, and Model Code Provisions, Technical Report MCEER 99–0008, Multidisciplinary Center for Earthquake Engineering Research, State University of New York, Buffalo, 1999. With permission.)
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Rapid Visual Screening Score Sheet
MN-01
Note that this is a screening process and is inherently conservative. If there is any question about an item, note it and select the appropriate PMF. See the following page for PMF guidelines. Performance Modification Factors (PMFs) 1, 2
Select PMF 1 if there is no anchorage from the motor or pump to the skid, or from the skid to the pad. If the anchorage appears small compared to the size of the pump, or is damaged, select PMF 2.
3
Where vibration isolators are used there should be lateral restraints as shown below. If no lateral restraints exist, or they appear to be inadequate, select PMF 3.
4
The motor and pump should be mounted on a common skid or pad to reduce the risk of differential displacement. Select PMF 4 if they are not.
5
Attached piping should be well supported to prevent excessive load transfer to the pump. If long, unsupported runs of piping terminate at the pump, select PMF 5.
6
If large items, such as non-structural walls, could fall and impact the pump, PMF 5 should be selected.
7
For other conditions that the reviewer believes could inhibit pump function following an earthquake (e.g., a history of problems with this piece of equipment), assign a PMF value relative to the existing PMFs in the table. Add a descriptive statement for the concern.
5
4 4 3 1, 2
3
1, 2
(b )
FIGURE 20.20 (CONTINUED)
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TK-05
Unanchored Vertical Tanks (at ground level) ID Number __________________________ Comments___________________________ ___________________________________
Diameter
H/D ≤ 0.5
Tank Category (circle one) Aspect Ratio 0.5 < H/D ≤ 0.8 < H/D ≤ 1.1 < H/D ≤ 0.8 1.1 1.4 I I I
1.4 < H/D ≤ 1.8 I
H/D ≥ 1.8
D≤ 10’
I
10’ < D ≤ 15’
I
15’ < D ≤ 20’
I
20’ < D ≤ 25’
I
25’ < D ≤ 30’
I
III
30’ < D ≤ 35’
II
IV
V
V
VI
VI
D ≥ 35’
III
V
V
VI
VI
VI
I
I
I
II
III
IV
I
III
IV
IV
V
III
IV
IV
V
V
IV
V
VI
VI
Demand Matrix (circle one) Tank Category II III IV
Seismi c Zone
I
V
VI
1
A
A
B
C
D
F
2
A
B
C
D
E
F
3
B
B
C
D
E
F
4
B
C
D
E
E
F
Scores and Modifiers - Vertical Tanks (circle a Basic Score and all PMFs that apply - use the column indicated by the Demand Matrix above) Description
A
B
C
D
E
F
Basic Score
6.5
5.5
4.5
3.5
2.0
2.0
P
2.1
2.0
1.3
0.5
0.0
0.0
1. Riveted shell seams
M 2. Rigid pipe attachments
1.0
0.9
0.2
0.0
0.0
0.0
F
0.0
0.0
0.0
0.0
0.0
2.0
3. Shell thickness unknown 4. Other ________________
Final Score = Basic Score largest applicable PMF
Note that this is a screening process and is inherently conservative. If there is any question about an item, note it and select the appropriate PMF.
(a )
FIGURE 20.21 Scoring worksheet for tanks. (From Johnson, G.S. et al., Seismic Reliability Assessment of Critical Facilities: A Handbook, Supporting Documentation, and Model Code Provisions, Technical Report MCEER 99–0008, Multidisciplinary Center for Earthquake Engineering Research, State University of New York, Buffalo, 1999. With permission.)
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Rapid Visual Screening Score Sheet
TK-05
Unanchored Vertical Tanks (in the top third of the building) ID Number __________________________ Comments___________________________ ___________________________________
H/D ≤ 0.5
Diameter
Tank Category (circle one) Aspect Ratio 0.5 < H/D ≤ 0.8 < H/D ≤ 1.1 < H/D ≤ 0.8 1.1 1.4 I I I
1.4 < H/D ≤ 1.8 I
H/D ≥ 1.8
II
III
IV
D≤ 10’
I
10’ < D ≤ 15’
I
15’ < D ≤ 20’
I
I
III
IV
IV
V
20’ < D ≤ 25’
I
III
IV
IV
V
V VI
I
I
I
25’ < D ≤ 30’
I
III
IV
V
VI
30’ < D ≤ 35’
II
IV
V
V
VI
VI
D ≥ 35’
III
V
V
VI
VI
VI
Demand Matrix (circle one) Tank Category II III IV
Seismi c Zone
I
V
VI
1
A
A
B
C
D
F
2
A
B
C
D
E
F
3
B
4
B
B
C
D
E
F
C
D
E
E
F
Scores and Modifiers - Vertical Tanks (circle a Basic Score and all PMFs that apply - use the column indicated by the Demand Matrix above) Description
A
B
C
D
E
F
Basic Score
5.5
4.5
3.5
2.0
1.0
1.0
P
1. Riveted shell seams
2.0
1.3
0.5
0.0
0.0
0.0
M 2. Rigid pipe attachments
0.9
0.2
0.0
0.0
0.0
0.0
F
0.0
0.0
0.0
0.0
0.0
2.0
3. Shell thickness unknown 4. Other ________________
Final Score = Basic Score largest applicable PMF
Tank Category Explanation
Note that this is a screening process and is inherently conservative. If there is any question about an item, note it and select the appropriate PMF.
(b )
FIGURE 20.21 (CONTINUED)
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TK-05
Determine the diameter (D) of the tank and the height (H) of the liquid in the tank. If the tank is normally twothirds full, use two-thirds of the tank height for the liquid height. The aspect ratio is the liquid height (H) divided by the diameter (D). Use these values to select the Tank Category for the tank. The Tank Category will be a Roman Numeral from I to VI that will indicate which column from the Demand Matrix to select the Demand Level. If the tank category is V, choose the Demand Level from Column V on the Demand Matrix. Circle the Demand Level in that column corresponding to your Seismic Zone. Performance Modification Factors (PMFs) 1.
Tanks with riveted seams are susceptible to tearing of the seams under seismic loads. If the tank has riveted seams select PMF 1.
2.
Certain pipe connections to tanks are likely to fail in an earthquake. If the pipe exiting the tank does not have adequate flexibility because it runs directly underground, has a rigid support or restraint within a few feet of the tank, or does not appear to be able to sustain several inches of displacement, select PMF 2. The pipe in the picture below has had flexible piping installed because it was too rigid.
3.
If the tank shell thickness is unknown or known to be less than about 1/2” for tanks with Demand Level “F” the tank will require more detailed analysis. Select PMF 3 which will give the final score of 0.0.
4.
For other conditions that the reviewer believes could cause the tank to release its contents following an earthquake (e.g. a history of problems with this tank), assign a PMF value relative to the existing PMFs in the table. Add a descriptive statement for the concern.
1
2
Note that this is a screening process and is inherently conservative. If there is any question about an item, note it and select the appropriate PMF.
(c )
FIGURE 20.21 (CONTINUED)
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KEY SYMBOL
NAME
MEANING
Component above gate functions AND GATE if all components below function OR GATE
For details see Figure 5-2
Component above gate functions if any component below functions
Fire Suppression 5.30 Smin = 4.90
Water Supply 4.90
Water Pumps 5.55
Smax+0.5(N-1) = 4.90
Piping 5.30
Smax+0.5(N-1) = 5.55
For details see Figure 5-3 City Water 3.50
Storage Tank 4.40
Smin = 5.05
Smin = 5.03
Smax+0.5(N-1) = 5.66
Building Power 3.75
Emergency Generator 5.16
Electric Pump 5.05
Storage Drums 6.19
Day Tank 5.18
Start System 5.31
Valves 5.39
Diesel Pump 5.03
Piping 5.30
FIGURE 20.22 Example scoring system. Numbers shown are for illustrative purposes only. (From Johnson, G.S. et al., Seismic Reliability Assessment of Critical Facilities: A Handbook, Supporting Documentation, and Model Code Provisions, Technical Report MCEER 99–0008, Multidisciplinary Center for Earthquake Engineering Research, State University of New York, Buffalo, 1999. With permission.)
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Water Supply 4.90
Smax+0.5(N-1) = 4.90
City Water 3.50
Storage Tank 4.40
The water supply can be provided by either an on-site storage tank or a connection to the municipal water supply. The score for this redundant subsystem is dependent on the number of redundant components (N = 2) and the highest component score (Smax = 4.40). The formula to calculate the water supply score is shown above. FIGURE 20.23 Example scoring system: redundant system. (From Johnson, G.S. et al., Seismic Reliability Assessment of Critical Facilities: A Handbook, Supporting Documentation, and Model Code Provisions, Technical Report MCEER 99–0008, Multidisciplinary Center for Earthquake Engineering Research, State University of New York, Buffalo, 1999. With permission.)
Pump System 5.03
Smin = 5.03
Storage Drums 6.19
Day Tank 5.18
Start System 5.31
Valves 5.39
Diesel Pump 5.03
Piping 5.30
The pump system will not function unless all its components function. The score for this dependent system is controlled by the lowest component score. In this case the diesel pump (S = 5.03) is the controlling component. FIGURE 20.24 Example scoring system: dependent system. (From Johnson, G.S. et al., Seismic Reliability Assessment of Critical Facilities: A Handbook, Supporting Documentation, and Model Code Provisions, Technical Report MCEER 99–0008, Multidisciplinary Center for Earthquake Engineering Research, State University of New York, Buffalo, 1999. With permission.)
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20.6.3.5 Practical Usage of Screening Method The purpose of the scoring system must be understood in the context of the overall MCEER program. It is intended for use as a rapid screening evaluation procedure and is not intended to replace detailed engineering evaluations. It must be recognized that, as a screening process, it is possible that seismically weak aspects of a system may be ignored entirely and the importance of certain equipment items may be overestimated or underestimated. However, when applied to an entire system or facility, the scoring method can identify where detailed investigation of a specific component or system modifications may have the most significant benefits in terms of system reliability. After completing the scoring for all of the systems in a facility, the user can review individual scores and determine which systems, subsystems, and components are the primary causes of low overall scores. A review of the checklist for a component will help to quickly identify the causes of low scores for that component, whether from the generic performance history of the equipment type (as shown in the basic score) or from a specific vulnerability or concern identified during the checklist review (as shown in the PMF). A flowchart for the risk management implementation process is shown in Figure 20.25. The impact of various mitigation options may also be assessed by simply recalculating scores with the potential modification or component scoring change. It will become apparent where repairs or modifications will increase the score and which vulnerabilities need to be addressed to have the largest impact. It will also become apparent where systems modifications, such as adding redundant components, may be more beneficial to increasing reliability than strengthening an individual component. The following examples illustrate the thought process used to interpret the results of the checklist evaluation and scoring process: • When the score of one component in a system is much lower than other component scores (i.e., is failing) and seems to control the system score, that component may be evaluated in more detail using other methods. • If more detailed evaluations show that the individual component identified above should be assigned a higher score, the system scores can be recalculated and reevaluated. For example, a drawing may be located that identifies anchorage that cannot be seen and was previously assumed not to exist, or a calculation may show that the capacity of a connection is much higher than judged by the person performing the screening review. • Similarly, if a detailed evaluation of an individual component indicates that a significantly higher score can be achieved by performing an inexpensive modification, an owner may consider performing that modification. Scores should then be recalculated, recognizing the revised condition of the equipment. For example, removing an impact hazard such as a bookshelf adjacent to a control panel may be all that is necessary to significantly increase the scores of the component and the system. • If the score for a component is low because the particular equipment type has low basic scores (e.g., due to poor seismic performance history) or because of many vulnerabilities that are difficult to alleviate, further evaluation or modification to the component may not significantly impact the system reliability and may have little or no benefit at a substantial cost. In such circumstances, systems modifications, such as adding redundancy, may be considered. If resources are available, the steps in the screening method can be easily extended to a formal quantitative risk assessment, with detailed fault and event trees. These analyses can also account for safeguards such as human intervention and partial protection (e.g., fire extinguishers). By assigning costs to various mitigation schemes, a risk-weighted selection of potential retrofits can be performed. Methods such as this reliability-based assessment allow facility owners to spend limited safety and facility dollars on the most effective updates, providing the most “bang for the buck.”
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Rank Systems by Score
Apply Acceptance Criteria
Any High or Very High Risk Systems?
No
Yes
Identify Components Causing Low System Scores Assess Emergency Response Plan Identify and Verify Sources of Low Component Scores
Select and Perform Appropriate Mitigation Method
Perform Detailed Analyses
Upgrade Component
Modify System
Other Justification
FIGURE 20.25 Risk management process. (From Johnson, G.S. et al., Seismic Reliability Assessment of Critical Facilities: A Handbook, Supporting Documentation, and Model Code Provisions, Technical Report MCEER 99–0008, Multidisciplinary Center for Earthquake Engineering Research, State University of New York, Buffalo, 1999. With permission.)
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FIGURE 20.26 Nonstructural items in a typical building. (From FEMA 74, Reducing the Risks of Nonstructural Earthquake Damage: A Pictoral Guide, Federal Emergency Management Agency, Washington, D.C., 1994.)
20.7 Nonstructural Damage While critical equipment and systems have been the focus of this chapter, some mention should be made of more mundane nonstructural items, such as water heaters, bookcases, ceilings, and other items which, it should be noted, can be significantly damaged and impact facility functionality. Figure 20.26 shows schematically the nonstructural items in a typical building, while Figure 20.27 shows the kind of damage these items can sustain, in this case in the Northridge earthquake. The general approach for seismically assuring nonstructural items is anchoring and restraining in an appropriate manner — an excellent guide in this regard is FEMA 74 [1994]. Figure 20.28 shows a few of many examples taken from FEMA 74, including how a water heater should be anchored (overturning water heaters are a significant source of ignitions in earthquakes, due to the gas released from broken pipes), how sprinklers should be laterally and longitudinally braced, and how suspended (“T-bar”) ceilings should be braced. The reader is referred to FEMA 74 for more detail.
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FIGURE 20.27 Figure 20.27.
Earthquake Engineering Handbook
Nonstructural damage, Northridge earthquake. (Courtesy EQE International) Shown as Color
(a ) FIGURE 20.28 (a) Anchorage of a water heater; (b) sprinkler piping bracing; (c) T-bar ceiling bracing. (From FEMA 74, Reducing the Risks of Nonstructural Earthquake Damage: A Pictoral Guide, Federal Emergency Management Agency, Washington, D.C., 1994.) © 2003 by CRC Press LLC
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(b )
(c )
FIGURE 20.28 (CONTINUED)
Defining Terms Battered piles — Piles installed at an angle (the “batter”) that resist lateral load in axial compression or tension.
Differential displacement. Displacement of adjacent support points of different amounts or out of phase. Typically occurs when a system is supported on two different structural systems.
Equipment. Mechanical, electrical or other components required for system functionality. Examples include pumps, electric generators, motor control cabinets, fire detection, alarm and suppression systems, computer systems, and even things as simple as overhead electric lights. Fault trees. Graphical representations of combinations of events that could lead to a major disruption in operations. Flashpoint. Temperature at which a hydrocarbon gas ignites. Function. The purpose of an equipment item or system, such as providing light, water for fire protection, or permitting safe shut-down of a potentially harmful system. HVAC. Heating, ventilating and air conditioning. Interactions. In this context, unintended effects on an equipment item, by another equipment item, or the structure. An example is a pipe with little clearance from a beam — during the earthquake it vibrates and pounds against (i.e., interacts with) the beam, and is damaged. © 2003 by CRC Press LLC
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LPG. Liquefied petroleum gas. Nonstructural. Portions of buildings and facilities that do not perform a structural function — that is, resist vertical or lateral loads. Nonstructural items include glazing, roofing, cladding and equipment. Contents, such as furniture and inventory, are not normally included under the term nonstructural. Parallel connectivity. The manner in which components are connected such that all components are required to fail, for the system to fail. Parallel systems have redundancy. Qualifying. Assuring the seismic performance of equipment. Redundancy. Back-up equipment or additional system path(s) that allows continued function in case of partial shutdown. Series. The manner in which components are connected such that if one component fails, the system fails. See also parallel connectivity. System. An interconnected group of equipment and/or subsystems, performing a function, such as a water supply system. Systems performing a critical function (i.e., of high importance, such as required for life safety, or involving significant financial loss if disrupted) are termed critical systems. Unzipping. The progressive collapse of the entire system of supports for a distributive system, such as HVAC, piping, or cable trays due to failure of a single support. Walkdown . An on-site, mostly visual review, where as-installed components are methodically “walked down” and evaluated for potential seismic vulnerabilities.
References ATC. 1992. Proceedings of Seminar on Seismic Design, Retrofit, and Performance of Equipment and Nonstructural Elements in Buildings and Industrial Structures, San Francisco. ATC-29. Applied Technology Council, Redwood City, CA. ATC. 1998. Proceedings of Seminar on Seismic Design, Retrofit, and Performance of Nonstructural Components, San Francisco. ATC-29-1. Applied Technology Council, Redwood City, CA. EPRI. 1991. Summary of the Seismic Adequacy of Twenty Classes of Equipment Required for the Safe Shutdown of Nuclear Plants, report NP-7149, Electric Power Research Institute, Palo Alto, CA, prepared by EQE Engineering Consultants. EPRI. 1994. Methodology for Developing Seismic Fragilities, report EPRI TR-103959, Electric Power Research Institute, Palo Alto, CA, prepared by Jack R. Benjamin and Associates, Mountain View, CA and RPK Structural Mechanics Consulting, Yorba Linda, CA. EPRI. 1998. SQUG Electronic Earthquake Experience Database User’s Guide, WINSQUG Version 2.0, Revison 0, report TR-110781. Electric Power Research Institute, Palo Alto, CA. FEMA. 1994. Reducing the Risks of Nonstructural Earthquake Damage: A Pictoral Guide, FEMA 74. Federal Emergency Management Agency, Washington, D.C. Gates, W.E. and McGavin, G. 1998. “Lessons Learned from the 1994 Northridge Earthquake on the Vulnerability of Nonstructural Systems,” in Proceedings of Seminar on Seismic Design, Retrofit, and Performance of Equipment and Nonstructural Elements in Buildings and Industrial Structures, San Francisco. ATC-29–1. Applied Technology Council, Redwood City, CA. Johnson, G.S., Sheppard, R.E., Quilici, M.D., Eder, S.J., and Scawthorn, C.R. 1999. Seismic Reliability Assessment of Critical Facilities: A Handbook, Supporting Documentation, and Model Code Provisions, Technical Report MCEER 99–0008, Multidisciplinary Center for Earthquake Engineering Research, State University of New York, Buffalo. NFPA. 1987. Standard for the Production, Handling, and Storage of Liquefied Natural Gas (LNG), NFPA59A. National Fire Protection Association, Quincy, MA. Nuclear Regulatory Commission. 1987. Seismic Qualification of Equipment in Operating Nuclear Power Plants, NUREG-1030. U.S. Nuclear Regulatory Commission, Washington, D.C.
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Nuclear Regulatory Commission. 1992. Generic Letter 87–02, Supplement No. 1, transmitting Supplemental Safety Evaluation Report No. 2 (SSER #2) on SQUG Generic Implementation Procedure, Revision 2 (GIP-2), as corrected on February 14, U.S. Nuclear Regulatory Commission, Washington, D.C., May 22, SQUG (GIP-2), issued December 2, 1988. Scawthorn, C. 1989. “Fire Following Earthquake in High-Rise Buildings,” in Fire Safety in Tall Buildings, J. Zicherman, Ed., Council on Tall Buildings and Urban Habitat, Bethlehem, PA. Scawthorn, C., Ed. 2000. The Marmara, Turkey Earthquake of August 17, 1999: Reconnaissance Report, Technical Report MCEER-019.0001, Multidisciplinary Center for Earthquake Engineering and Research, State University of New York at Buffalo. Scawthorn, C., Swan, S.W., Hamburger, R.O., and Hom, S. 1992. “Building Life-Safety Systems and PostEarthquake Reliability: Overview of Codes and Current Practice,” in Proceedings of Seminar on Seismic Design, Retrofit, and Performance of Equipment and Nonstructural Elements in Buildings and Industrial Structures, San Francisco, ATC-29. Applied Technology Council, Redwood City, CA. Swan, S.W. and Kassawara, R. 1998. “The Use of Earthquake Experience Data for Estimates of the Seismic Fragility of Standard Industrial Equipment,” in Proceedings of Seminar on Seismic Design, Retrofit, and Performance of Nonstructural Components, San Francisco. ATC-29-1. Applied Technology Council, Redwood City, CA. Wilcoski, J., Gambill J. B., and Smith S.J. 1997. The CERL Equipment Fragility and Protection Procedure (CEFAPP) Experimental Definition of Equipment Vulnerability to Transient Support Motions, USACERL Technical Report 97/58. U.S. Army Corps of Engineers Construction Engineering Research Laboratories, Champaign, IL. Yanev, P. 1992. “The EQE Earthquake Data Base and the Performance of Equipment and NonStructural Components,” in Proceedings of Seminar on Seismic Design, Retrofit, and Performance of Equipment and Nonstructural Elements in Buildings and Industrial Structures, San Francisco, ATC-29. Applied Technology Council, Redwood City, CA.
Further Reading There are many excellent sources on seismic performance and bracing of equipment. FEMA 74 [1994] is an excellent practical guide on the bracing and anchorage of ordinary nonstructural items. MCEER [1999] is an excellent overview of the performance of critical equipment, and industrial equipment, items, as well as providing a reliability-based methodology for the assessment of critical equipment systems. ATC-29 [1992] and ATC-29-1 [1998] are excellent collections of technical papers on the subject by many of the leading experts in the field.
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21 Seismic Vulnerability 21.1 Introduction Earthquake Risk Decision-Making · Meaning and Use of the Seismic Vulnerability Function · Fragility vs. Vulnerability
21.2 Method 1: Statistical Approach Calculating Statistically Based Seismic Vulnerability Functions · Example Statistical Vulnerability Functions · Empirical Data to Describe Component Fragility · Conclusions Regarding the Statistical Approach to Seismic Vulnerability Functions
21.3 Method 2: Expert Opinion Necessity and Efficiency of Expert Opinion: Scope and Perceived Shortcomings · Methods for Eliciting Expert Opinion · Vulnerability Functions Created Using Expert Opinion
21.4 Analytical Methods: General Czarnecki’s Method · The Method of Kustu and Scholl · HAZUS 99 Method · Assembly-Based Vulnerability
21.5 Validation of Vulnerability Functions 21.6 Catalog of Vulnerability Functions Buildings · Contents
21.7 Uses of Vulnerability Functions Probable Maximum Loss · National Standard for Loss Estimation · Other Applications
Keith A. Porter California Institute of Technology Pasadena, CA
21.8 Closing Remarks Defining Terms References Further Reading
21.1 Introduction This chapter addresses the subject of seismic vulnerability functions. These functions express the relationship between damage or loss to a structure or facility and earthquake effects (i.e., intensity). The earthquake effect most commonly addressed by seismic vulnerability functions, and the only effect discussed in this chapter, is earthquake shaking. This introduction discusses why seismic vulnerability functions are needed and how they can be used. Succeeding sections discuss the three fundamental approaches for the development of seismic vulnerability functions: • Statistical • Expert opinion • Analytical
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A catalog of useful seismic vulnerability functions is then provided, followed by a more detailed discussion of the uses and applications of seismic vulnerability functions, closing remarks, defining terms, and references and further reading.
21.1.1 Earthquake Risk Decision-Making Earthquakes cause damage to buildings, bridges, and other facilities by imposing excessive deformations and resulting stresses in their constitutive elements. Repair of this damage can be costly, and the time to restore the damage can cause substantial additional losses due to business interruption, lost revenues, and other disruptions to the function of the facility. These damages and economic losses are often significant enough to imperil the survival of businesses and threaten the lives of occupants. As a result, the need arises to estimate, or model, future earthquake losses, for planning and risk management purposes. Early efforts to create structural vulnerability functions were driven in part by a desire to document and understand the consequences of major earthquakes. Business interests also played a role — owners of buildings and other properties had a need to quantify their potential losses — and property insurers wished to understand the risks they were incurring through the sale of earthquake and other insurance. Property insurers, in particular, faced two challenges when providing earthquake coverage: • Solvency: Insurers need to assure that a catastrophic event simultaneously affecting many insured properties will not bankrupt the company. • Profitability: Insurers need adequate premium income to cover future claims and expenses, while yielding a profit and remaining competitive. Insurers approach most risks via the compilation of actuarial tables, which are normally compiled for most risks (e.g., fire, auto, life) on the basis of statistics of past losses. That is, claims to fire, auto, and other traditional insurance coverage occur frequently enough that reliable, recent statistics provide an adequate basis for predicting future losses. Earthquakes, however, differ in that they are high consequence–low probability (HCLP) events. That is, decades may pass between events that cause significant loss, by which time construction has changed so significantly that past events provide little insight into future losses. A newly founded insurance company can build a substantial portfolio of risks before it faces its first major earthquake, which can then be potentially disastrous. The insurance industry is not the only user needing to estimate future earthquake losses. Other examples include: 1. A government agency with an emergency-response mission must assure that adequate resources are available when an earthquake strikes a densely populated area. 2. A commercial lender must control losses associated with borrowers defaulting on their mortgage after an earthquake wipes out their equity. The probability of default is related to the degree of damage, which is estimated using seismic vulnerability functions. 3. A manufacturer may wish to mitigate the chance that an earthquake near a critical factory could interrupt production. 4. Building-code authorities wish to know whether the cost of a new code provision is justified by reductions in future damage. In each case, a purely statistical approach based on past experience is inadequate for reliable estimation of potential future losses. The tool to overcome this deficiency is probabilistic risk analysis (PRA). A seismic PRA characterizes the probability of occurrence of future earthquakes (the seismic hazard), and the damage or loss conditioned on the effects of the earthquake at the site of each asset (the seismic vulnerability). The general case of a seismic PRA seeks to establish the relationship between loss and probability (or frequency) of exceeding that loss in a particular future time period. Limited cases may deal solely with the loss associated
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Seismic Vulnerability
Loss probability distribution at S1
tion)
Loss
d devia
r "Uppe
bound"
tandar n+1s
(mea
"Lower bound"
s
ate of los
Best estim
ard deviation)
(mean - 1 stand
Ground motion intensity, S
S1
FIGURE 21.1 Probabilistic seismic vulnerability function.
with a particular occurrence frequency, or the loss conditioned on a particular event. In any case, the risk analysis depends on the use of seismic vulnerability functions, i.e., relationships between the degree of loss and intensity.
21.1.2 Meaning and Use of the Seismic Vulnerability Function The general case of a seismic PRA expresses loss as an uncertain function of intensity. Such a probabilistic seismic vulnerability function is depicted schematically in Figure 21.1, where the vertical axis measures loss as a function of seismic intensity (abscissa). Loss may be measured in terms of the costs to repair damage, the number of fatalities or injuries, the duration of loss of use, etc. The figure shows three levels of loss: the mean and two fractiles of loss. The figure also schematically depicts the probability density of loss at a particular shaking intensity S1. Before proceeding, let us define some terms: • Intensity refers to the degree of seismic excitation or other earthquake effect experienced at a particular location. It can measure shaking intensity (peak ground acceleration, various spectral response measures, Arias intensity, etc.) or degree of ground failure (e.g., degree of differential settlement); the former is more common. • Loss refers to the measure of the severity of an undesirable outcome, e.g., repair cost, insurance claim amount, number of fatalities, etc. It can be discrete or continuous. • Finally, a seismic vulnerability function must have a defined scope, meaning that it applies to any structure within a particular category (see Box 21.1 for sample building category systems); to a particular, unique structure (e.g., the Golden Gate Bridge or the Empire State Building); or a category of structure components (e.g., partitions constructed of 1/2-in. gypsum wallboard on 2 × 4 wood studs on 16-in. centers). In a site-specific PRA, the risk analysis seeks to estimate the relationship between frequency v and severity y of earthquake losses. Let v(y) represent the frequency (i.e., events/year) of loss at a particular site, exceeding y. To calculate v(y) requires two new tools: the seismic hazard function and the seismic vulnerability function. Seismic hazard is discussed in Chapter 8 of this handbook, but its use with the seismic vulnerability function in a PRA is summarized here. Let X represent the uncertain intensity of shaking that affects a site in a particular future earthquake. Let G(x) represent the average annual frequency with which large enough earthquakes occur close enough to the site to cause shaking intensity of X ≥ x. This is the frequency form of the seismic hazard function. Let Y represent the uncertain loss associated with a particular building and a particular event, and let y represent a particular value of that loss. Then, risk can be expressed as:
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BOX 21.1
A
Earthquake Engineering Handbook
STRUCTURE TYPES
vulnerability function is not completely defined until its scope is specified — that is, to which structure or category of structures does it apply? Is its applicability limited by geography, or time? Common taxonomies define structure categories by various combinations of use, era of construction, construction material, lateral force-resisting system, height, applicable building code, and quality. Two examples are presented here. ATC-13: The Applied Technology Council [ATC-13, 1985] developed a comprehensive taxonomy of structures and associated seismic vulnerability functions, for 78 classes of California industrial, commercial, residential, utility, and transportation structures, including 40 categories of California buildings. This taxonomy has continued to be employed with little change [e.g., FEMA 273, 1997]. Most of the ATC-13 building categories are defined by combining three basic attributes: one construction material, one lateral force-resisting system, and one height range, each of which is listed below. Not all combinations are feasible (e.g., high-rise woodframe, reinforced masonry braced frame), and some specialized structure types diverge from the general taxonomic system, e.g., tilt-up concrete (as distinct from reinforced concrete shear-wall, low-rise) and light metal buildings (as opposed to low-rise steel moment-resisting or braced frames). The three basic attributes are: Material: wood, reinforced masonry, unreinforced masonry, steel, cast-in-place reinforced concrete, precast concrete, light metal Lateral force-resisting system: frame, moment-resisting frame (distributed or perimeter), braced frame, nonductile moment-resisting frame, shearwall (with or without frames) Height ranges: low-rise (1 to 3 stories), mid-rise (4 to 6), high-rise (7 or more) HAZUS: A more recent taxonomy of HAZUS 99 [1999] is derived from the ATC-13 work and categorizes 36 structural classes, called model building types, by structural system, height, seismic design level, and seismic performance level or quality, listed below. Not all combinations are employed, e.g., precast concrete tilt-up buildings are not distinguished by height range, and some real buildings might not fit into a category, e.g., 3-story wood light frame. However, these model building types probably account for more than 99% of all U.S. structures. HAZUS addresses nonstructural building components separately from structural, recognizing two categories: driftsensitive and acceleration-sensitive. Structural system: wood light frame, wood commercial and industrial, steel moment frame, steel braced frame, steel light frame, steel frame with cast-in-place concrete shear walls, steel frame with unreinforced masonry infill walls, concrete moment frame, concrete shear walls, concrete frame with unreinforced masonry infill walls, precast concrete tilt-up walls, precast concrete frames with concrete shear walls, reinforced masonry bearing walls with wood or metal deck diaphragms, reinforced masonry bearing walls with precast concrete diaphragms, unreinforced masonry bearing walls, or mobile home. Height: low-rise (1 to 3 stories), mid-rise (4 to 7), high-rise (8 or more) Seismic design level: high-, moderate-, or low-code (designed for NEHRP Provisions map areas 7, 5, and 3, respectively [Federal Emergency Management Agency, 1997]), or pre-code (not designed for seismic resistance) Seismic performance level: code/ordinary, pre-code/inferior, and special/superior
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v ( y) =
∞
∫ (1 − P [Y ≤ y X = x]) g (x)dx
(21.1)
0
where g (x ) =
dG dX x
and P[Y ≤ y|X = x] = the probability that uncertain loss Y will be less than or equal to some particular value y, given ground-shaking x. The latter term is a general expression of the probabilistic seismic vulnerability function. It is often desirable to depict the probabilistic seismic vulnerability function as the product of a deterministic mean loss function that is dependent on shaking intensity, and a random error variable with unit mean and a known (or assumed) probability distribution: Y (x ) = y (x ) ε (x )
(21.2)
where Y(x) represents uncertain loss as a function of shaking intensity x, y–(x) refers to mean loss given shaking intensity x, and ε(x) is a random variable with mean value of unity and distribution appropriate to the structure and shaking intensity. This form is useful in that it expresses the general trend of loss via the mean vulnerability function and the uncertainty via the error term. When the seismic vulnerability function can be cast this way,
[
]
( )
P Y ≤ y X = x = FY X y x
y x = Fε X y x ( )
(21.3)
where Fε|X(e|x) represents the conditional cumulative distribution of the error term evaluated at e, conditioned on shaking of intensity x.
21.1.3 Fragility vs. Vulnerability It is important to distinguish between two terms related to seismic damageability — vulnerability and fragility. As discussed above, a seismic vulnerability function defines loss as a function of excitation, such as shaking intensity. By contrast, a seismic fragility function defines the probability of some undesirable event (e.g., collapse) as a function of excitation. For example, a fragility function can provide the probability that a building will collapse, or the probability that a factory may release hazardous materials into the atmosphere, given some level of shaking. Analogous vulnerability functions would provide the damage factor for the building (repair cost divided by replacement cost) or the quantity of hazardous materials released, given the shaking intensity. Figure 21.2 illustrates this contrast for an example facility. It is often possible to employ a set of fragility functions as a substitute for vulnerability. Let this discussion be limited to the case of a set of fragility functions that have a common input excitation x, where each fragility function defines the probability that a structure will reach or exceed some loss value, and where each fragility function refers to a different specific value of Y. (Let the discussion also be limited to the case of a single structure type c.) That is, consider ND fragility functions: Fi(x) = P[Y ≥ y i | X = x]: i = 1,2, … ND
(21.4)
where P[Y ≥ yi [X = x] refers to the probability that Y ≥ yi , given seismic excitation x, for any value of i from 1 to ND . © 2003 by CRC Press LLC
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1.00
1.00
0.75
0.75
Damage factor
Failure probability
90th percentile
0.50
0.25
0.00 0.00
Median
0.50
10th percentile 0.25
0.50
1.00
1.50
2.00
0.00 0.00
Spectral acceleration, g
0.50
1.00
1.50
2.00
Spectral acceleration, g
FIGURE 21.2 Sample fragility function (left) vs. vulnerability functions (right).
Let the fragility functions be ordered such that yi+1 > yi for i = 1, 2, … ND – 1. First, one can observe that corresponding to the ND fragility functions are ND + 1 mutually exclusive and collectively exhaustive states (typically referred to as damage states) D ∈ {0, 1, … ND} in which a structure can exist, after experiencing an event of shaking intensity x, and that the probability mass function (PMF) for the damage state D is given by: 1 − F1 ( x ) P D = d X = x = Fd ( x ) − Fd +1 ( x ) F ( x ) ND
[
]
d=0 1 ≤ d < ND d = ND
(21.5)
The damage-state PMF can be used to estimate loss if one knows the distribution of loss within a damage state, denoted by FY|D,X(y|d,x), or at least the expected value of loss given a damage state, denoted here by E[Y|D = d, X = x]. It is common to simplify the analysis by assuming that loss conditioned on damage state is independent of intensity, i.e., FY|D,X (y|d,x) = FY|D (y|d) and E[Y|D = d, X = x] = E[Y|D = d]. Then, n
[ ] ∑ P [D = d X = x ]E [Y D = d]
y (x ) = E Y X =
(21.6)
d =1
provides the mean vulnerability function. The value of E[Y|D = d] is sometimes estimated from other loss statistics (a case that will not be discussed here) or assumed to be the median value of loss between the yi, that is,
[
] 12 ( y
E Y D=d ≈
d
+ y d +1 ) for d = 1, 2,…, N D − 1
(21.7)
The case of d = ND can either be defined away, e.g., the loss has an upper bound such as E[Y|D = ND] = 100%, or else some value of loss conditioned on the NDth damage state can be assumed.
21.2 Method 1: Statistical Approach The statistical method for the development of structural vulnerability functions is empirical — that is, it employs loss data from historical earthquakes. Box 21.2 lists important data sources. The data include the loss (denoted here by y) and the intensity of ground motion (denoted by x) experienced by individual structures or groups or categories of structures. The seismic vulnerability function is created by examining the loss data by structure category, and regressing loss against shaking intensity. © 2003 by CRC Press LLC
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BOX 21.2
DATA SOURCES
C
reation of seismic vulnerability functions requires extensive data on loss, value exposed, and shaking intensity. These data can be acquired from a variety of sources. The following list is not exhaustive, but does show the sources that are most commonly used and some of their important limitations. Insurers: Insurers typically keep summaries of insured properties and claims data. The data are proprietary and difficult to acquire, both for propriety as well as practical reasons. In the last decade, the data have moved from hard copy to electronic formats, which has modestly increased its availability. There are several potential sources of statistical bias inherent in insurance data, both for value exposed and loss amount. Insurers tend to select for target markets by income category, type of business, etc., and therefore their data may not reflect the general population of structures. Insurers do not show value exposed per se, but rather limit of liability, which can poorly reflect replacement cost. Extracting loss data is also challenging. Some insurance-claims databases exclude buildings with repair costs greater than zero, but less than the deductible, which can be substantial. Claim amount can differ significantly from actual earthquake-induced damage because of loss-adjustment practices and insurers’ public-image and other business considerations. Finally, insurers do not record shaking intensity; and while they do typically record an address, which can be used to find intensity from other sources, the address might be the billing address or the address of the main insured facility, rather than the site where the loss occurred. Questionnaires and telephone surveys: Building owners can be asked to report their loss via questionnaire. Scawthorn [1981] discusses a survey of households affected by the 1978 Miyagiken-Oki (Japan) earthquake. The survey, performed shortly after the earthquake, yielded 145,000 questionnaires, for an overall response rate of 77%. Telephone surveys of local hospitals can be performed to gather exhaustive statistics on deaths and injuries associated with the earthquake. Postearthquake surveys: It is possible for building experts to gather a very approximate judgmental estimate of damage to a large number of structures by rapid assessments that can take only a few minutes each. For example, after the 1994 Northridge earthquake, building department officials from the City of Los Angeles estimated the repair cost to 85,000 structures within weeks of the earthquake [EQE International and the California Governor’s Office of Emergency Services, 1995]. Note that rapid estimates can fail to observe significant damage because the inspector is constrained from entering the structure or even from viewing it from all sides. Detailed surveys: Detailed inspections of an unbiased sample of structures can yield a smaller number of more reliable loss data. ATC-38 [2000] developed a data collection form that engineers used after the 1994 Northridge earthquake to compile detailed data on 530 buildings located near 31 strong-motion sensors affected by the earthquake. The data include 97 fields describing building location, construction, configuration, occupancy, ground failure, postearthquake safety, damage, injuries, and restoration. The data do not include repair cost. One might attempt to create a cost estimate using the damage description. The peril is potential error if the estimates are not made by a professional cost estimator, or if the estimator is uncomfortable costing a project of which he or she has only
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summary information. Such an effort requires that the survey form be highly detailed, unambiguous, and not require extensive use of judgment by surveyor or estimator. Construction permits: Before repair efforts can begin, a permit is typically required that states the location, nature of repairs, and an estimated cost. These data, combined with tax-assessor data on building features and use, can provide the information necessary to depict both the damage and the exposed inventory of structures [Schierle, 2000]. However, loss estimates based on building permits can fail to distinguish between repair and upgrade work. Furthermore, since the permit fee is linked to the cost of construction permits, and since the permit is filed before the repair work is undertaken, the permit can substantially underestimate the true repair cost. Aerial or satellite imagery: Radar and visible-spectrum imagery can be used to detect collapses or even identify structures that have undergone modest permanent deformation, and identify each imaged structure’s precise location for use in estimating shaking intensity. Height and building footprint can be used to estimate approximate replacement cost. Such imagery probably cannot detect lesser damage. This is an important emerging technology. Tax-assessor data: These files do not provide information on damage, but they are commonly used to estimate the value of taxable structures exposed to damage. Values in tax-assessor files are limited, however, because they can include land value or depreciation, or be long out of date, particularly in California where taxpayer revolt in the early 1980s prevented tax assessors from regularly updating building values. Shake maps: Maps of estimated or instrumentally recorded shaking intensity are commonly created shortly after an earthquake occurs, and are available for many historic earthquakes. They tend, however, to reflect smoothed, local average intensity, rather than site-specific shaking, which can vary significantly over distances of a hundred meters or less. Strongmotion instruments are currently too sparsely distributed to provide city-block-sized resolution of shaking intensity. Experience [Scawthorn, 1995] indicates reasonable accuracy for this approach, given good input data.
21.2.1 Calculating Statistically Based Seismic Vulnerability Functions Suppose one has collected a database of n shaking and loss pairs for a category c of structures, perhaps through one of the means listed in Box 21.2. Let the database be denoted by {(x, y)}c, let (xi, yi) refer to – refer to the expected value of loss experithe intensity and loss experienced by structure i, and let y(x) enced by a structure exposed to shaking intensity x. It is desired to fit a curve of central tendency (mean or median) and uncertainty (measured in terms of conditional coefficient of variation). Before presenting the mathematical techniques used to create the seismic vulnerability functions from these data, it is worthwhile to discuss the data themselves, in particular, the meaning of loss. First, loss can be ambiguous and should be carefully defined. Ideally, it should reflect the cost to repair the earthquake-induced damage, but loss data often reflect improvements unrelated to the damage and costs to repair preexisting, non-earthquake-induced damage, and in some cases can omit appropriate repairs to actual earthquake-induced damage. Furthermore, depending on the source of the loss data, they can reflect losses after deducting an insurance deductible, and can be inflated by post-earthquake cost increases (demand surge) or the desire of insurers to expedite claims adjustment. Second, it is typically most useful to express loss as a fraction of facility replacement cost. The ratio is called the damage factor. It is common to refer to the replacement cost as the value of the facility, but this can be ambiguous or misleading, since value can reflect land value, facility location, deterioration, and obsolescence. In any case, the analyst should be aware of, document, and carefully control these factors.
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To return to the data analysis, linear or multiple linear regression can typically be used to fit a vulnerability function, even if the form of the vulnerability function is assumed to be nonlinear. The analyst can typically transform a desired form of the vulnerability function to an equivalent linear system and perform the regression analysis. In summary, linear and multiple linear regression can be used as follows. (For more information on regression analysis, see, e.g., Ang and Tang [1975].) Linear regression – = mx + b that minimize the sum seeks to find the values of the parameters m and b in the equation y(x) of the squared error ∆2: n
∆2 =
n
∑ ( y − y (x )) = ∑ ( y − mx − b) 2
i
i
i
i =1
2
(21.8)
i
i =1
The least-squares estimates for parameters m and b are given by: n
∑ (x − x )( y − y ) i
i
ˆ = m
i =1
(21.9)
n
∑ (x − x )
2
i
i =1
ˆ bˆ = y − mx
(21.10)
and the conditional variance (constant for all intensities s) is given by: sY2 x =
∆2 n−2
(21.11)
where x and y are the average values of xi and yi , respectively, and s2 refers to sample variance. Other two-parameter functional forms can be transformed to linear ones and solved using linear regression. A power relation y = bxm can be transformed to y' = mx' + b' by calculating yi' = ln(yi), xi' = ln(xi), solving for b' and m, and recognizing that b = exp(b'). This solution yields an estimate for the median value of y(x), as opposed to the mean. Semilogarithmic and power relationships can be similarly transformed to linear, thus: y = m ln ( x ) + b = mx' +b
where x i ' = ln ( x i )
(21.12)
y = m exp ( x ) + b = mx' +b
where x i ' = exp ( x i )
(21.13)
Polynomial or other functional relationships between y and x that involve three or more parameters can often be solved using multiple linear regression. Multiple linear regression seeks to find the value of the parameters mj and b in: y = m1 g1 + m2 g 2 +… mk g k + b
(21.14)
that minimize the sum of the squared error ∆2: n
∆2 =
∑( i =1
© 2003 by CRC Press LLC
n
) ∑( y − m g
y i − y ( g i , g 2 , …) = 2
i
i =1
1 1,i
− m2 g 2,i − L mk g k ,i − b
)
2
(21.15)
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Least-squares estimates for the coefficients m1, m2, … mk and b are found by solving the k simultaneous equations: ) m1
n
∑ ( g1i − g1 ) i =1
2
) + m2
n
n
n
i =1
i =1
i =1
∑ ( g1i − g1 )( g 2i − g 2 ) + L m) k ∑ ( g1i − g1 )( g ki − g k ) = ∑ ( g1i − g1 )( yi − y)
… ) m1
(21.16) n
n
n
∑ ( g ki − g k )( g1i − g1 ) + m) 2 ∑ ( g ki − g k )( g 2i − g 2 ) + L m) k ∑ ( g1i − g1 ) i =1
i =1
i =1
n
2
=
∑(g i =1
ki
− g k ) ( yi − y )
and bˆ = y
(21.17)
To use this approach to fit a polynomial vulnerability function of the form: y = b + m1x + m2 x 2 +…mk x k
(21.18)
g ki = x ik
(21.19)
let
n
gk =
∑x
k i
(21.20)
i =1
and solve as above. Alternatively, if multiple intensity measures are employed, the gi can be used to account for these. To determine the distribution of loss about the mean, one can calculate the error statistics: εi =
yi y (xi )
(21.21)
n (ε ≤ e ) N
(21.22)
and compile their cumulative distribution: Fε (e ) =
where n(ε ≤ e) refers to the number of structures where the error statistic ε is less than the value e, and N refers to the total number of structures in the database. The observed distribution of ε can be compared with idealized distributions using goodness-of-fit tests such as Kolmogorov–Smirnov (see, e.g., Ang and Tang, 1975). The standard deviation of ε can be calculated for the entire dataset (used with a model that assumes a constant conditional coefficient of variation of loss), or for segments of the dataset, e.g., for 0 < x ≤ x1, x1 < x ≤ x2 , etc., which allows one to model a varying conditional coefficient of variation of loss.
21.2.2 Example Statistical Vulnerability Functions Example statistical studies of seismic vulnerability include Martel [1964], Scawthorn [1981], Steinbrugge and Algermissen [1990], and Schierle [2000]. Figure 21.3 presents Scawthorn’s empirical damage factors for Japanese mid-rise construction, plotted vs. elastic spectral displacement. Figure 21.4 presents empirically based mean damage factors for housing of all types, tabulated by Steinbrugge and Algermissen © 2003 by CRC Press LLC
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0.00
0.80
DAMAGE 1.60 2.40
3.20
4.00
SENDAI MID-RISE BLDGS. SRC R/C
0.00
0.40
0.80
1.20
1.60
2.00
2.40
2.80
3.20
3.60
4.00
RESPONSE SPECTRAL DISPLACEMENT (CM)
FIGURE 21.3 Vulnerability of Japanese mid-rise reinforced-concrete and steel-reinforced concrete composite construction (3 to 12 stories, n = 189). Regression analysis produces y = 1.26x0.7, r = 0.48. Damage is expressed as repair cost as percent of replacement cost. Spectral displacement is evaluated at the pre-earthquake period of the building (average of horizontal directions). (From Scawthorn, C.R. et al., Earthquake Eng. Struct. Dyn., 9, 93–115, 1981. With permission.)
Mean damage factor
0.50 0.40 0.30 0.20 0.10 0.00 5
6
7
8
9
10
Modified Mercalli Intensity FIGURE 21.4 Seismic vulnerability data. (After Steinbrugge, K.V. and S.T. Algermissen, Earthquake Losses to SingleFamily Dwellings: California Experience, U.S. Geological Survey Bulletin 1939-A, U.S. Geological Survey, Washington, D.C., 1990.)
[1990], who do not offer a regression line for the data. Figure 21.5 shows vulnerability functions created by Schierle [2000], who shows mean damage in the 1994 Northridge earthquake.
21.2.3 Empirical Data to Describe Component Fragility The statistical approach is useful for creating category-based vulnerability functions for whole structures, but it can also be used to characterize the fragility of components of buildings and other structures. A structure component could be a piece of equipment, a segment of architectural partition, or a steel moment-frame connection. The fragility of this component describes the probability that the component exceeds a predefined limit state after some level of seismic excitation. Swan and Kassawara [1998] describe a methodology for creating fragility functions for categories of equipment using an empirical dataset, © 2003 by CRC Press LLC
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$20 $18 $16 $14 $12 $10 $8 $6 $4 $2 $0
PGA > 60 30 - 60 < 30 SFD 0-40
MFD 0-40
SFD 41-76 MFD 41-76 SFD 77-93 MFD 77-93 Yearbuilt
FIGURE 21.5 Seismic vulnerability functions for six categories of dwellings surveyed after the 1994 Northridge earthquake. In the figure, SFD and MFD refer to single-family dwellings and multifamily dwellings, respectively. The figure shows six vulnerability functions, with the intensity axis into the page. (From Schierle, G.G., Northridge Earthquake Field Investigations: Statistical Analysis of Woodframe Damage, CUREE Publication No. W-02, Consortium of Universities for Research in Earthquake Engineering, Richmond, CA. With permission.)
where the limit state considered is inoperability and the seismic excitation is measured in terms of peak ground acceleration, but the approach applies equally to other categories of components and other limit states. In this methodology, one knows the postearthquake damage state of a set of J components of a predefined category, along with the seismic excitation to which each component was exposed. The excitation at which each component actually entered a damage state need not be known. The dataset must be unbiased with respect to damage, that is, it must not be selected solely from damaged components, or only from heavily damaged facilities, etc. Let
{ } d = {d , d ,…d } : d ∈{0,1}, i ∈{1, 2,… J } x = x1 , x 2 ,… x J 1
2
J
i
where di represents the damage state of assembly i, a value of di = 1 indicating that the assembly has exceeded the limit state in question, a value of 0 indicating otherwise. The term xi refers to the seismic excitation to which assembly i was exposed. The excitation parameter is selected to be appropriate for the assembly in question, such as peak transient drift, peak diaphragm acceleration, peak load, and so on. Failure frequency is calculated by dividing the number of failed components by the total number of observed components in K discrete ranges of excitation. The mean excitation in each range is used with calculated failure frequency in the regression analysis. The result of the regression analysis is a cumulative distribution of capacity. Let r = {r1 , r2 ,…rk }
r m = {rm1 , rm 2 ,…rmK } : rmi = ( x *i −1 + x *i ) 2, i ∈{1, 2,… K } n = {n1 , n2 ,…nK }
N = {N1 , N 2 ,…N K } : ΣN i = J
f = { f1 , f 2 ,… f K } : fi = ni N i , i ∈{1, 2,… K }
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where ri = (x*i–1, x*i] indicates the range of responses x*i–1 < x ≤ x*i , and rmi indicates the mean response of range ri . Ranges can be selected at equal intervals, or dictated by equal Ni . Also, let: ni = Σd j : x j ∈ri , i ∈{1, 2,… K }, j ∈{1, 2,… J } The vector n indicates the number of assemblies in the dataset that failed by response range ri and N indicates the total number of assemblies in the dataset by response range ri. The vector f then indicates failure frequency of assemblies within each response range. A cumulative probability distribution is fit to the (rm , f) data. If the distribution, denoted by FX(x), has a set of parameters Ψ, the fitting is performed by minimizing the objective function g(Ψ): g (Ψ) =
K
∑ (F (r X
mi
i =1
) − fi )
2
(21.23)
Note that the (rmi , fi) data points are independent, so it is acceptable to fit a curve to the cumulative distribution. Swan and Kassawara [1998] use a lognormal distribution for FX(x), measure excitation x in terms of peak ground acceleration, and d in terms of operational failure. However, the methodology is readily generalized to allow x to measure other response parameters, d to indicate limit states other than operational failure, and using distributions other than the lognormal. Several distributions can be tried. In general, for the same number of distribution parameters in FX(x), a lower value of the objective function g(Ψ*) indicates a better fit, where Ψ* indicates the optimum value of distribution parameters for a particular distribution. An alternative technique that uses earthquake experience data but avoids binning is to consider each component observed as a discrete data point (x, d). In this case, for a distribution FX(x) with parameters φ, the fitting is performed by minimizing the objective function g(φ): K
( ) ∑ (F ( x ) − d )
g φ =
X
i
2
i
(21.24)
i =1
Note that once again the (x, d) data are independent, so it is acceptable to fit a curve to the cumulative distribution. Thus, a binary regression analysis of performance data on a component-by-component basis can be performed. In theory, this approach reduces modeling uncertainty by preserving x-data that are otherwise lost to binning. In practice, the two methods produce nearly identical results in cases where a large sample set allows for small bin sizes. The disadvantage of the binary regression is that it is difficult to assess the distribution from a scatter diagram of (x, d) data because the di are either 0 or 1, unlike the binning approach, which produces a scatter diagram of (x, f) data. Of course, the binary approach can be used to create the fragility function, which can then be checked visually using the binning approach. A third empirical method to create fragility functions requires laboratory data of the components in question, including knowledge of the structural response x d = {xd1, xd2 , … xdJ} at which each tested component i ∈ {1, 2, … J} exceeded the limit state in question. (Such data are typically unavailable from earthquake experience.) In this case, x d represents the statistics of the component capacity, which can be used directly, or a distribution can be fit to the data.
21.2.4 Conclusions Regarding the Statistical Approach to Seismic Vulnerability Functions In conclusion, the statistical approach offers conceptual simplicity and a basis in real loss experience, and therefore credibility. Despite this advantage, there are several important limitations associated with statistically based seismic vulnerability functions. These are due to the functions reflecting aggregate or © 2003 by CRC Press LLC
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average losses within categories of buildings that have experienced strong motion, and cannot reflect the effects of differences with a category. Some important limitations are: • Statistically based seismic vulnerability functions cannot reflect the effects of construction differences or maintenance issues for a region that is absent from the database of strongly shaken structures. • The statistical approach cannot be used to account for any structure-specific details not distinguished by its category, which is particularly important for high-value or unusual structures. Additional structure-specific data, such as the structural or architectural drawings, cannot inform a statistically based loss analysis, beyond more definitely identifying structure category. • The statistical approach cannot be used to estimate the benefit (in terms of reduced losses) of a retrofit or redesign method that has not already been tested in many structures in past earthquakes. Similar limitations exist for casualty-oriented seismic vulnerability functions: cultural variables cannot be reflected in the seismic vulnerability function unless the variable has been distinguished in the dataset from a past earthquake, nor can the approach account for structure-specific occupancy features, nor the benefits of a newly proposed casualty-reduction measure. To overcome these limitations requires the use of expert opinion or an analytically based method.
21.3 Method 2: Expert Opinion 21.3.1 Necessity and Efficiency of Expert Opinion: Scope and Perceived Shortcomings Expert judgment can be an effective alternative to a statistical approach. The advantage of this approach is that it does not require costly or unavailable data about exposed buildings, their detailed structural characteristics, or historical damage. The approach is very versatile, as long as experts can be found who are willing to judge the loss value of interest. It can be building-specific or category-based. Difficulties can arise when asking experts to judge new conditions of which they have no experience. They may refuse to offer their judgment, or the resulting disagreement can produce an unacceptably large uncertainty. Alternatively, unless the interview process is structured very carefully, a number of heuristic biases can result in unreasonably low measures of uncertainty, or vulnerability functions that are unduly low or high. Furthermore, the use of expert opinion can be seen to weaken an argument, because it lacks a scientific (testable) basis.
21.3.2 Methods for Eliciting Expert Opinion Spetzler and Stael von Holstein [1972] summarize the literature on extracting and quantifying an individual’s judgment about uncertain quantities, and they detail a procedure that is sketched here. This procedure addresses the heuristic biases that can cause an expert to underestimate uncertainty, or to consistently under- or overestimate an uncertain value (see Tversky and Khaneman [1974] for detail on these biases). A detailed treatment of formal means to elicit expert opinion is beyond the scope of this chapter, but the bare outlines can be summarized as follows (Spetzler and Stael von Holstein [1972]): • Motivating: Establish rapport with the subject and explore possible motivational biases. • Structuring: Define and clearly structure the uncertain quantity. The definition must be unambiguous enough to pass “the clairvoyant test, i.e., a clairvoyant should be able to specify the outcome without asking additional questions for verification.” The structure must be such that the subject does not have to perform any additional modeling before making each judgment. • Conditioning: Condition the subject to think fundamentally about his or her judgment to avoid cognitive biases. Ask the subject to specify the most important bases for his or her judgment in order to identify a tendency for central bias (low uncertainty). Ask the subject what he or she is © 2003 by CRC Press LLC
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taking into account, to identify possible availability bias. Ask the subject to compose scenarios that would produce extreme outcomes. Ensure that the subject is not judging statistics of the average of many, if the quantity to be judged is the individual unit. • Encoding: Quantify the subject’s judgment in probabilistic terms. Begin by asking for extreme values of the uncertain quantity. Ask for scenarios that might lead to outcomes outside of the extremes, and ask for probability of these outcomes; this counteracts central bias. Next select values of the quantity x at random, and ask the subject for his or her judgment of the probability FX(x) of the quantity being less than that value. Plot FX(x). • Verifying: Test the judgments to ensure that the subject really believes them. Show the subject the plot of FX(x) and determine whether its shape agrees with the subject’s judgment. Offer pairs of bets, chosen so that the two bets would be equally attractive if the curve of FX(x) is consistent with the subject’s judgment. Gordon and Helmer [1964] discuss the Delphi Process, by which one can elicit and refine the judgment of a group of experts in situations where exact knowledge is unavailable or excessively costly, but where experts possess partial information or information relevant to judgments of the question at hand. The Delphi Process is designed to gather and synthesize this judgment. In the context of evaluating an uncertain quantity (such as the loss associated with a model building type subjected to a particular shaking intensity), the Delphi Process works as follows: • Assemble a panel of experts possessing relevant knowledge. • Create a first-round Delphi questionnaire that elicits judgments of the value to be determined. • Test the questionnaire’s wording, i.e., check for vagueness or ambiguities (see “structuring” in the Spetzler and Stael von Holstein [1972] procedure). • Transmit the questionnaire to the panelists. • Analyze the first-round responses. In the case of a loss estimate, the analysis would entail examination of the statistics of the responses. The analysis determines whether significant disagreement exists and whether the questionnaire appears adequately to have defined the problem. • Report results to the panelists. Discuss the nature of disagreements. This can include asking the panelists to explain their reasoning. • Prepare a second-round questionnaire, testing it if necessary. • Transmit the second-round questionnaire to the panelists. • Repeat the process until consensus or stable disagreement is reached. • Report final conclusions. Dalkey et al. [1970] find that one can obtain more accurate estimates by having the experts self-rate their expertise of the value in question. The uncertain value is then taken in the final analysis as the equally weighted average judgment of the subset of experts with some minimum self-rating.
21.3.3 Vulnerability Functions Created Using Expert Opinion One early application of expert opinion to earthquake vulnerability is found in Freeman [1932], who offers his judgment regarding future insurance losses for a variety of structure types and soil conditions, for all buildings throughout a region affected by a very large earthquake. Rutherford & Chekene Consulting Engineers [1990] use expert opinion to develop seismic vulnerability functions for unreinforced masonry buildings (UMBs). ATC-13 [1985] represents one of the most thorough, best-documented efforts to compile seismic vulnerability functions for an exhaustive set of structure categories. Despite extensive effort to compile empirically based seismic vulnerability functions, the ATC project found that inadequate empirical data existed to create a reliable and exhaustive set of vulnerability functions, and turned instead to a “modified” Delphi Process, drawing on 71 earthquake engineering academics and practitioners. (The Delphi Process © 2003 by CRC Press LLC
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TABLE 21.1 ATC-13 Damage States Damage State
Damage Factor Range (%)
Central Damage Factor (%)
1-None 2-Slight 3-Light 4-Moderate 5-Heavy 6-Major 7-Destroyed
0 0–1 1–10 10–30 30–60 60–100 100
0 0.5 5.0 20.0 45.0 80.0 100.0
Source: ATC-13, Earthquake Damage Evaluation Data for California, Applied Technology Council Redwood City, CA, 1985.
TABLE 21.2 Sample Damage Probability Matrix Probability of Damage, Given MMI
Damage State
Damage Factor Range (%)
Central Damage Factor (%)
VI
VII
VIII
IX
X
XI
XII
1-None 2-Slight 3-Light 4-Moderate 5-Heavy 6-Major 7-Destroyed
0 0–1 1–10 10–30 30–60 60–100 100
0 0.5 5 20 45 80 100
13.1 72.0 14.9 *** *** *** ***
*** 9.7 90.1 0.1 *** *** ***
*** 0.2 87.2 12.6 *** *** ***
*** *** 30.3 69.4 0.3 *** ***
*** *** 1.1 81.1 17.8 *** ***
*** *** *** 29.4 69.9 0.7 ***
*** *** *** 2.6 88.1 9.3 ***
Note: *** = very small probability. Source: ATC-13, Earthquake Damage Evaluation Data for California, Applied Technology Council, Redwood City, CA, 1985.
was “modified” in that the experts were queried by mail, rather than convening the experts in a room. Convocation of the experts in a room is a desirable step in the Delphi Process, to permit a dialogue among the experts.) The ATC-13 experts provided best-estimate (the value most likely to be observed), lower-bound (5th percentile), and upper-bound (95th percentile) estimates of damage factors for 78 classes of California construction at Modified Mercalli Intensities VI, VII, … XII. Three rounds of polling were performed and weighted averages of each statistic were reported. The weights are the experts’ own self-rating of their expertise. (As opposed to Dalkey et al. [1970], who equally weight the judgment of all experts whose self-rating exceeds a threshold level, and ignore all others.) Several types of building and content loss were evaluated: building repair cost, content repair cost, and loss-of-use duration. For each facility type and intensity level, a beta distribution was fit to the expert-opinion damagefactor data. This was done by first assigning the mean value of the experts’ best-estimate damage factor to the mean value of the distribution. The mean values of the experts’ lower-bound and upper-bound damage-factor estimates were taken as the 90% bounds of the distribution. Finally, the distribution was taken as bounded by 0.0 and 1.0, and the parameters of the distribution found by numerical methods. The distribution was then used to determine the probability that the damage would lie in each of seven damage-factor ranges, shown in Table 21.1. ATC-13 [1985] provides these probabilities in a set of damage probability matrices (DPMs), which show the probability of a building being in each of the damage states, conditioned on its experiencing a particular level of shaking intensity. The general form of the DPM is shown in Table 21.2, whose DPM data are for low-rise, reinforced-concrete shear wall buildings without moment-resisting frames. The mean damage factor (MDF) associated with ground shaking for a facility subjected to intensity MMI = x is calculated as: MDFS [ x ] = © 2003 by CRC Press LLC
7
∑ P [DS x]CDF i
i =1
i
(21.25)
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TABLE 21.3 Injury and Death Rates Fraction Injured*
Building Damage State
Minor
Serious
Fraction Dead*
1 2 3 4 5 6 7
0 3*10–5 3*10–4 0.003 0.03 0.3 0.4
0 4*10–6 4*10–5 4*10–4 0.004 0.04 0.4
0 1*10–6 1*10–5 1*10–4 0.001 0.01 0.2
Note: * For light steel and woodframe construction, multiply by 0.1. Source: ATC-13, Earthquake Damage Evaluation Data for California, Applied Technology Council Redwood City, CA, 1985.
where P[DSi | x] is the probability of the facility being in damage state i given x (from the DPM), and CDFi is the central damage factor for damage state i. The mean damage factor for a building and contents is given by the weighted average of the MDF for the building and the MDF for the contents, where the weighting factors are their respective values. To account for the effects of ground failure (liquefaction, lateral spreading), ATC-13 recommended multiplying the damage factor by the probability of ground failure and a factor of 5 to 10: MDFPG = 5 MDFS ⋅ P [GF ] for surface facilities
(21.26)
MDFPG = 10 MDFS ⋅ P [GF ] for buried facilities
(21.27)
where P[GF] is the probability of ground failure. The study also addresses human casualties, based on prior research and expert judgment. The fraction of occupants killed or injured is given as a function of the structure damage state, as shown in Table 21.3. Other studies have addressed the problem of estimating building performance at a higher resolution than category-based statistical approaches typically handle. ATC-21 [1988] employed the ATC-13 data to estimate the collapse threshold probability for 12 model building types given the design-basis earthquake (an event with shaking intensity having 10% exceedance probability in 50 years). The procedure then allows one to modify the basic collapse probability to account for combinations of seismic hazard region, poor condition, vertical or plan irregularity, soft story, torsion, pounding, heavy cladding, short columns, soil conditions, and era of construction. ATC-21 has recently been updated [in press], using the same probabilistic framework but more recent maps of seismic hazard and the HAZUS-derived building seismic capacities. ATC-50 [in progress] similarly accounts for 37 features of the foundation, structural and nonstructural elements, site conditions, and regional location, in its attempt to estimate the economic loss to woodframe buildings in a large, rare earthquake.
21.4 Analytical Methods: General Analytical approaches to creating seismic vulnerability functions tend to have three general steps: structural analysis, damage analysis, and loss analysis. These steps are depicted schematically in Figure 21.6. The facility and its site are characterized, along with ground motions corresponding to various levels of intensity. A structural analysis is performed to estimate the structural response to a ground motion, in terms of internal forces and deformations. The structural response is then input to a set of component fragility functions to determine the damage state of each component in the facility. Finally, the cost of damage is summed over all components to determine the total loss. To create a seismic vulnerability function, the process is repeated for many levels of earthquake intensity. © 2003 by CRC Press LLC
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X,O,B
X: ground motion O: site properties B: facility properties
Structural Analysis
Damage Analysis
P[ Z|X,O,B]
P[ D|Z]
P[Y|D]
P[X]
P[D]
P[Y]
Z: structural response
D: damage
Loss Analysis
Vulnerability Function
Y(X)
Y: loss
FIGURE 21.6 Schematic creation of analytical vulnerability functions. TABLE 21.4 Options for Structural Analysis
Linear Nonlinear
Pseudostatic
Dynamic
1 3
2 4
There are many approaches to each step. The ground motion, for example, can be characterized in terms of response spectra or in terms of acceleration time histories. The structural analysis can take any of four general forms: linear, nonlinear, pseudostatic, or dynamic, as illustrated in Table 21.4. However, the overall approach tends to be driven by the method of structural analysis. Three analytical approaches are described here: linear pseudostatic, nonlinear pseudostatic, and nonlinear dynamic. The linear dynamic method would be a special case of nonlinear dynamic, but the other two are distinct. Note that each step involves uncertainty. Key uncertainties include: • • • • • •
Details of the ground motion for a given intensity level. Effect of site soils on ground motion. Structural properties such as mass, damping, and force-deformation behavior. Effects of modeling simplifications on estimated structural response. Nonstructural components: their quantity, location, costs, and damageability. Repair costs conditioned on damage.
An ideal analytical model would address each source; a good model would address the important ones.
21.4.1 Czarnecki’s Method Czarnecki [1973] presents one of the first analytical methods for estimating loss to frame building using structural analysis and a combined damage and loss analysis, for a particular earthquake. His procedure for the structural elements of frame buildings requires three idealizations: • Only damage to columns is important. • All girders are rigid. • Computations of strain are based on elastic formulas. The loss calculation proceeds as follows: • For each column, compute AT , the inelastic portion of the area under the stress–strain curve up to the point at which the stress reaches is ultimate value. (AT is the same for all columns with the same steel specification or concrete mix.)
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• Perform a structural analysis to determine the peak interstory drift for each story. Compute the maximum bending strain at the quarter point of every column. (Under the rigid-girder assumption, upper and lower quarter points have the same maximum moment, and hence have the same maximum bending strain.) • Based on the bending strain computed in step 2 and the stress–strain relationship of the column material, compute AX, the inelastic portion of the area under the stress–strain curve, for each column. • Compute AX/AT for each column at each story. Compute D, the estimated cost to repair the structural damage, as a faction of the total cost to construct the structural elements of the building: D=
1 n
n
k
∑ ∑A i =1
1 k
AXi, j
(21.28)
Ti , j
j =1
where n = the number of stories in the building, k is the number of columns on floor i, AXi,j refers to AX for column j on story i, and ATi,j refers to AT for column j on story i. The repair costs for other building elements are calculated using component-level vulnerability functions developed by Czarnecki, who provides three: one for drywall partitions, one for glazing, and one for all other elements. These vulnerability functions use peak interstory displacement as the input excitation. They output the repair cost as a fraction of their construction cost (also denoted here by D). The loss for the building as a whole, denoted here by DT , is calculated as the weighted average of the D values. The weighting factor, denoted here by Vc , is the fraction of the total construction cost accounted for by the component. That is, DT =
∑V D c
c
(21.29)
c
where c is an index to refer to the four aggregated components: structural, partitions, glazing, and all others. This loss amount can be plotted against the intensity of the input earthquake. By repeating Czarnecki’s method for many earthquakes of varying intensity, one can produce a seismic vulnerability function. The vulnerability function is largely deterministic, in that it does not address uncertainties of structural analysis (i.e., mass, damping, and member force-deformation relationships) or in the component vulnerability functions. Its use of elastic structural analysis limits its accuracy in stronger shaking.
21.4.2 The Method of Kustu and Scholl Researchers at John A. Blume Associates further developed the analytical method to employ test data on the vulnerability of components of high-rise buildings. Scholl and Kustu [1981], Kustu et al. [1982], and Kustu [1986] present a methodology to estimate damage from a given earthquake. Scholl and Kustu [1981] enumerate several desired features of an analytical method and describe a general methodology that satisfies these requirements (Figure 21.7): • Basis in sound theory and engineering principles, using commonly known engineering analysis and design methods and parameters • Easily adaptable to all engineering structures • Provision for using laboratory and earthquake data • Account for uncertainty in ground motion, structural capacity, and analytical methods and assumptions (probabilistic approach) • Easily automated; modular structure
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Structure
Component inventory
Earthquake
Analysis model
Site ground motion
Structure response analysis
Maximum floor responses
Damage calculated for each component
Component motiondamage library
Floor damage = sum of damage to all components
Total damage = sum of damage to all floors
FIGURE 21.7 Damage prediction using structure component information. (From Kustu, O. and Scholl, R.E., Proc. Conference XIII, Evaluation of Regional Seismic Hazards and Risk, Open-file Report 81–437, U.S. Geological Survey, Reston VA, 162–213, 1981. With permission.)
They illustrate one theoretical approach by calculating the repair cost of a hypothetical reinforced concrete moment-frame building subjected to an earthquake with known elastic spectral response. First, the displacement of the roof relative to the ground (δroof ) is calculated considering only the building’s fundamental mode of vibration: δroof = γSd
(21.30)
where Sd denotes the damped elastic spectral displacement response and γ denotes the modal participation factor for fundamental mode with roof displacement normalized to unity. One then assumes that the fundamental building period, T, is approximated by: T = 0.1N
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(21.31)
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TABLE 21.5 Reinforced-Concrete Frame Buildings Sd = N∆u /γ Number of Stories, N 1 2 3 4 5 10 20 30 40
T (sec)
γ
Observable Damage
0.1 0.2 0.3 0.4 0.5 1.0 2.0 3.0 4.0
1 1.2 1.29 1.33 1.36 1.43 1.46 1.48 1.5
0.25 0.42 0.58 0.75 0.92 1.75 3.42 5.07 6.67
Yield Capacity
Ultimate Capacity
1.0 1.67 2.33 3.01 3.68 6.99 13.70 20.27 26.67
5.0 8.3 11.6 15.0 18.4 35.0 68.5 101.4 133.3
Source: Scholl, R.E. and Kustu, O., in Proc. Conference XIII, Evaluation of Regional Seismic Hazards and Risk, USGS Open-file report 81-437, 1981.
Based on a straight-line fundamental mode shape for a building of N stories, the interstory drift at any story is given by: ∆u ≈ δroof /Ν = γ Sd /N
(21.32)
Sd = N∆u/γ
(21.33)
or
If one knows the interstory drift ∆u associated with various levels of global building damage, one can tabulate Sd vs. N (Table 21.5), and plot building capacity in the same space as the elastic spectral response (Figure 21.8). Kustu et al. [1982] provide empirical test data relating component damage with structural response for a variety of high-rise building components.
21.4.3 HAZUS 99 Method An analytical method for estimating seismic vulnerability that uses nonlinear pseudostatic structural analysis is described by Kircher et al. [1997]. The methodology was developed for the National Institute of Building Sciences (NIBS) and the Federal Emergency Management Agency (FEMA) for use in the HAZUS software [HAZUS 99, 1999]. While the methodology was implemented for a variety of building categories (see Box 21.1), it can also be used on a structure-specific basis. 21.4.3.1 Structural Model In the HAZUS approach, the structure is idealized as an equivalent nonlinear, single degree of freedom (SDOF) subjected to a slowly increasing lateral loading pattern. ATC-40 [1996] specifies five loading patterns of varying sophistication. The “basic” pattern applies loads in proportion to story masses and first mode shape of the elastic model of the structure. The equation: Fx = V
w x φx
∑w φ x
(21.34) x
x
gives the force to be applied at level x, where wx is the reactive mass at level x, φx is the lateral deflection at level x in the first elastic mode shape, V is the slowly increasing total lateral force, and the sum is over the height of the structure. The load V is increased in pseudostatic fashion. The relationship between the top-level deflection, denoted here by Z, and base shear V is calculated, accounting for material and geometric nonlinearities. © 2003 by CRC Press LLC
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FREQUENCY − HZ 100.0 1000.0
10.0 I
1.0 II
III
IV
V
0.1 VI
VII
VIII
IX
9
.0 00 10
9
cm
100.0 7
7
60.0 6
6
30.0
Yield Capacity 5
d
5
0. 01 g
8
Ultimate Capacity
S T, EN M E V CE TI A cm LA SPL .0 RE DI 100
10.0 Observable Damage
4
4 .0
AC PS 0. CE EU 001 LE DO g RA A TI BS O OL N , S UT E
10
4.0
O
cm
PSEUDO RELATIVE RESPONSE VELOCITY, SV - CM/SEC
8
0. 1g
300.0
1940 E1 Centro Earthquake, N-S Component, 5% Damping
3
3
1.0
0
1. cm
2 0.
00
01
g
2
I
0.1 0.01
II
0.1
III
0.2
IV
0.4 0.6
V
VI
1.0
VII
2.0
VIII
4.0
IX
7.0 10.0
PERIOD − SEC
FIGURE 21.8 Response-spectrum amplitudes for various damage thresholds for reinforced concrete frame structures. (From Kustu, O. and Scholl, R.E., Proc. Conference XIII, Evaluation of Regional Seismic Hazards and Risk, Openfile Report 81–437, U.S. Geological Survey, Reston VA, 162–213, 1981. With permission.)
At low excitation, the system has initial elastic or nearly elastic stiffness that decreases as the load slowly increases (pseudostatic loading is assumed). At some point, the stiffness degrades significantly and some permanent structural damage is incurred. As the load increases, stiffness continues to degrade, and the slope of the pushover curve continues to drop, until the load reaches a maximum value, at which point the structure has neutral stability. If the stiffness becomes negative, the structure is unstable. The V–Z relationship is called the pushover curve by ATC-40 [1996]. Kircher et al. [1997] transform the pushover curve to the spectral displacement-spectral acceleration (Sd, Sa) space via the equations shown in Figure 21.9. The transformed curve is referred to as the capacity curve. They define the curve completely using two control points: yield and ultimate. The yield point is intended to reflect the lateral strength of the building, accounting for design strength, design redundancy, code conservatism, and expected (vs. nominal) material strength. The ultimate point is intended to reflect the lateral strength of the building when a collapse mechanism forms. Below yield, the capacity curve is linear from (0,0) to (Dy , Ay). Beyond ultimate (D > Du), the capacity curve is flat. The shape of the curve between the yield and ultimate is not specified in Kircher et al. [1997] or HAZUS [1999], other than to
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(Du, Au) Ultimate Point: Au = λAy Du = λµDy
(Dy, Ay) Yield Point Ay = Csλ/α1 Dy = 9.8AyTe2
λ
Cs = Design Value Te = Building Period γ, λ = Overstrength µ = Ductility
λµ
Spectral Displacement (inches)
FIGURE 21.9 Building capacity curve. (From Kircher, C.A. et al., Earthquake Spectra, 13, 663–682, 1997. With permission.)
say that “the capacity curve transitions in slope from an essentially elastic state to a fully plastic state.” 1 One can apply a power spline to this segment, giving: Ay D Dy K /K D −D e y u A = Au − Au − Ay Du − Dy Au
(
)
D < Dy Dy ≤ D < Du
(21.35)
D ≥ Du
where
Ke =
Ky =
Ay Dy
Au − Ay Du − Dy
(21.36)
(21.37)
The equation in Figure 21.9 for Au gives the median value, but Au is assumed to be lognormally distributed, with logarithmic standard deviation, denoted by β(Au), assumed to be 0.25 for code-designed buildings, and 0.30 for pre-code buildings. Parameters used in the figure are defined as follows, and are tabulated for the 36 model building types and their various combinations of seismic design level and seismic performance level, in HAZUS 99 [1999]:
1
The HAZUS code assumes an elliptical transition (Bouabid, personal communication).
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Cs = design strength coefficient (fraction of the building’s weight), which “approximately corresponds to the lateral-force design requirements of current seismic codes (e.g., 1994 UBC or 1994 NEHRP Provisions)” Te = expected elastic fundamental-mode period of vibration α1 = fraction of building weight effective in the pushover mode α2 = fraction of building height at the elevation where pushover-mode displacement is equal to spectral displacement γ = overstrength factor relating true yield strength to design strength λ = overstrength factor relating ultimate strength to yield strength µ = ductility ratio relating ultimate displacement to λ times the yield displacement 21.4.3.2 Structural Response The response of a structure in a particular earthquake is parameterized via the inelastic spectral displacement response. This displacement is calculated in a three-step process. In the following, Sa denotes the damped elastic pseudo-absolute acceleration response, Sv denotes the damped elastic pseudo-relative velocity response, and Sd refers to the damped elastic true relative displacement response. First, an idealized 5% damped elastic response spectrum is created by combining a constant-acceleration region and a constant-velocity region. Let SS denote the short-period spectral pseudo-acceleration response on rock (site class B), defined as Sa(0.3 sec). Let S1 denote the 1-sec spectral pseudo-acceleration response, defined as Sa(1.0 sec). Let FA and FV denote the soil amplification factors in the acceleration-controlled and velocity-controlled regions. In the velocity-controlled region, Sa = S1FV/T. Substituting 1/T = ω/(2π) = (Sa/Sd)0.5/(2π) and solving for Sa yields: Sa =
S12Fv2 4π 2Sd
(21.38)
The velocity- and acceleration-controlled regions meet at SSFA = S12FV2/(4π2Sd), or Sd = S12FV2/(4π2SSFA). The spectrum at the displacement-controlled region and higher T is ignored, as is the low-period region below the acceleration-controlled region. Hence, the elastic response spectrum in (Sd, Sa) space is given by: SS FA Sa = 2 2 S F 4π 2Sd 1 V
(
)
( ) (4π S F )
Sd ≤ S12FV2 4π 2SS FA Sd > S F
2 2 1 V
(21.39)
2
S A
The next step is to calculate the inelastic response spectrum, which is the elastic spectrum reduced by a damping-reduction factor to account for stiffness reduction and hysteretic damping. In the accelerationcontrolled region, the reduction factor is denoted by RA; in the velocity-controlled region, RV denotes the damping-reduction factor, as shown in Figure 21.10. The inelastic response spectrum is thus given by: SS FA RA Sa = 2 2 S F 4π 2 RV2 Sd 1 V
(
)
( (
Sd ≤ S12FV2 RA 4π 2 RV2 SS FA Sd > S12FV2 RA 4π 2 RV2 SS FA
) )
(21.40)
The structural response is taken as the point at which the (D, A) capacity curve intercepts the inelastic response spectrum, as shown in Figure 21.10. 21.4.3.3 Damage State The building is treated as three components: all the structural elements represent component 1; component 2 comprises all the nonstructural, drift-sensitive elements; and component 3 is all the nonstructural, acceleration-sensitive elements. Let Vc represent the replacement cost of component c, expressed as a fraction of the total facility value. Let Xc represent the seismic excitation to which component c is
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SS × FA
Spectral Acceleration (g's)
5%-Damped Response Spectrum (SS × FA)/RA
Demand Spectrum
Building Capacity Curve
A
(S1/T) × FV ((S1/T) × FV)/RV
D
Area
Spectral Displacement (inches)
FIGURE 21.10 Estimation of structural response. (From Kircher, C.A. et al., Earthquake Spectra, 13, 663–682, 1997. With permission.)
exposed, i.e., either D or A of the structural response (structural elements are taken as primarily sensitive to D). Thus, the vector of seismic excitation can be denoted by X = [D, D, A]T. Every component c is associated with ND fragility functions, denoted by Fci(x), for i = 1, 2, … ND . Each fragility function gives the probability that the repair cost for the component will exceed some fraction yi of the component replacement cost, when the component is subjected to excitation x. As before, the fragility functions are ordered such that yi +1 > yi for i = 1, 2, … ND − 1, and a set of ND + 1 damage states d = 0, 1, … ND is defined to refer to the condition that the component repair cost has exceeded yd but not yd+1, where y0 = 0. Thus,
[
]
Fc ,i ( x ) = P Y ≥ y i X c = x : i = 1, 2,…N D
(21.41)
The probability mass function for the damage state of component c is given by: 1 − Fc ,1 ( x ) Pc D = d X c = x = Fc , d ( x ) − Fc , d +1(x) F ( x ) c , ND
[
]
d=0 1 ≤ d < ND d = ND
(21.42)
The probabilistic damage state is then convolved with the mean damage factors for each damage state and with the value of each component to determine the expected value of the repair cost. The mean vulnerability function is given by: ND
Nc
[ ] ∑ ∑ E [Y D = d] P [D = d X
EYX =
Vc
c =1
c
d =1
c
c
=X
]
(21.43)
where E[Y|X] denotes the mean damage factor (expected value of repair cost as a fraction of replacement cost), conditioned on the occurrence of an earthquake producing seismic excitation X; NC = number of components — here, NC = 3; Vc = value of component c, expressed as a fraction of the facility replacement cost; ND = number of component damage states considered (other than undamaged); Ec[Y|D = d] is the mean damage factor for component c in damage state d, i.e., the mean cost to repair the component in
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TABLE 21.6 HAZUS Damage States Damage State
Damage Factor
None Slight Moderate Extensive Complete
0% 0–5% 5–20% 20–50% 50–100%
damage state d as a fraction of the component replacement cost; and Pc[D = d|Xc = x] denotes the probability that component c is in damage state d, conditioned on the earthquake producing structural response X. HAZUS 99 [1999] considers the damage states shown in Table 21.6. Mean damage factors are not documented. Fragility functions are taken as lognormal cumulative distributions and are provided for each aggregated component. They are partly empirically based and partly based on expert opinion: laboratory test data are used to create detailed fragility functions, which are then aggregated based on typical, approximate relative value of the detailed components. These are then adjusted using expert opinion [Holmes, 2000]. Structural fragility functions are provided for each structure type. The values Vc are also provided.
21.4.4 Assembly-Based Vulnerability This author has developed a method conceptually similar to Scholl and Kustu’s, with the additions of a detailed taxonomy of components to enhance the structure-specific nature of the vulnerability function, further elaboration of the treatment of uncertainty, and an algorithm for creating seismic vulnerability functions. The methodology, called assembly-based vulnerability (ABV), is summarized in Porter et al. [2001a], and detailed in Porter and Kiremidjian [2001] and Porter et al. [2001b]. ABV characterizes a structure as a unique collection of standardized, highly detailed assemblies. As used here, an assembly refers to a collection of construction materials assembled to form a structural or nonstructural element or item of content, assembled and in place. An example of an assembly is an 8- × 8-ft segment of gypsum board wall partition, constructed of 5/8-in. fire-resistant wallboard, on 3 5/8-in. metal studs on 16-in. centers, with wallboard connected to the studs by screws. A standardized, detailed taxonomy of assemblies is employed. It is extended from the RS Means Corp. [1997] assembly numbering system, with the addition of a numeric sequence to denote installation conditions that are relevant to earthquake damage, such as equipment anchorage. Each damageable assembly is associated with one or more damage states, defined in terms of the repair effort required to restore the assembly to the undamaged state. Each repair effort has an associated uncertain cost for a contractor to perform, and an uncertain repair duration, i.e., the time it takes a construction crew to perform the repair. The mathematical framework for ABV follows. First, two uncertain sources of loss to the facility owner are recognized: repair cost and loss-of-use cost, denoted by CR and CU, respectively. In a given earthquake: C = CR + CU
(21.44)
The interested reader is referred to Porter and Kiremidjian [2001] for details on an ABV approach to estimating CU . The present text addresses only CR. Consider CR as a construction cost estimate. It is given by the contractor’s costs to repair individual damaged assemblies, plus an additional cost to the owner to cover the contractors’ overhead and profit. Let Cj,d denote the uncertain unit cost to a contractor to restore a single damaged assembly of type j from damage state d. The fragility functions and unit costs are characteristic of the standardized assembly type, and can therefore be created once and reused. The unit costs, likewise characteristic of the assembly type and damage state, vary by geographic location and over time, but factors to account for location
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and inflation are commonly available. Let Nj,d denote the uncertain number of assemblies of type j that are in damage state d after a particular earthquake. Let P denote the (uncertain) contractor’s overhead and profit, expressed as a fraction of the costs to the contractor to perform all repairs. Thus:
∑ ∑C
C R = (1 + P )
j
j,d
N j,d
(21.45)
d
Contractor overhead and profit are typically 0.15 to 0.20. Mean values of the unit costs Cj,d can be readily estimated using standard construction cost-estimation techniques, but only if the damage states are clearly enough defined that a construction cost estimator can identify the particular labor, materials, supplies, and equipment required to perform the repair. This is one reason why ABV requires assemblies to be characterized at the level of detail familiar to cost estimators. Note that cost estimators typically deal with best-estimate values, but can provide estimates of uncertainty if requested to do so. Publications of unit costs primarily provide mean values, but they also provide estimates of contingency costs to deal with unexpected conditions. RS Means Corp. [1997] recommends a cost contingency of 20% for the overall cost of a repair project. Absent an estimator’s judgment of uncertainty on Cj,d, this figure can be employed in ABV by equating it with the coefficient of variation on each Cj,d, and taking the various Cj,d to be perfectly correlated. Thus, uncertain unit cost can be modeled as the product of the mean value C j , d and a random variable εC, with unit mean and a coefficient of variation either provided by a cost estimator or taken as a δC = 0.15 to 0.25 and perfectly correlated among all repair tasks: C j , d = C j , d εC
(21.46)
ln (e ) Fε C (e ) = Φ δC
(21.47)
where Φ( ) refers to the cumulate standard normal distribution. To calculate Nj,d , one must know the damage state of every assembly in the structure. Each damage state of each damageable assembly type is associated with a fragility function, which gives the probability that the assembly will reach or exceed the damage state when subjected to some input in seismic excitation, such as peak transient drift ratio, peak ductility demand, etc. Let Fj,d(z) denote the fragility function, i.e., the probability that an assembly of type j will reach or exceed damage state d when subjected to excitation z. Let ND represent the number of possible damage states (other than undamaged) for a particular assembly type. For assemblies with ND > 1, the damage states are defined to be mutually exclusive and collectively exhaustive, and sorted so that the effort and cost required to restore an assembly in a “higher” damage state exceeds those of a lower damage state. As with the NIBS/FEMA methodology, the probability of a particular assembly, indexed by k, being in a particular damage state d when subjected to excitation z, is given by: 1 − Fj ,1 ( z ) P Dk = d Z k = z = Fj , d ( z ) − Fj , d +1 ( z ) F ( z ) j , ND
[
]
d=0 1 ≤ d < ND d = ND
(21.48)
The fragility functions can be developed from laboratory tests or field observations (as described above), or from theoretical considerations (i.e., using reliability methods). Thus, if one knows the seismic excitation to which each assembly is subjected, and can draw upon a library of assembly fragility functions, one can create a probability mass function of the damage state of each damageable assembly in the structure. That uncertain excitation to assembly k is a function of the © 2003 by CRC Press LLC
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ground-motion time history, denoted by G, and uncertain structural characteristics: mass, damping, and force-deformation behavior of the structure, denoted schematically by M, B, and K: Z k = f1 (G, M , B, K )
(21.49)
This equation compresses all of time-history structural analysis into a single expression. The author assumes that the reader is familiar enough with structural analysis that no elaboration is required, other than to note that the responses of interest — peak transient interstory drift ratios, floor accelerations, internal member forces, ductility demand ratios, etc. — are readily produced by such an analysis. Let FG(g), FM(m), FB(b), and FK(k) denote cumulative probability distributions on ground motion, mass, etc. Except for the trivial case of an SDOF structure, each is a multidimensional joint CDF. Several probabilistic models of ground motion G are available that are based on geophysical considerations, stochastic processes, and hybrids of the two [see, e.g., Polhemus and Cakmak, 1981; Conte et al., 1992; and Aagard et al., 2001]. To characterize the multidimensional, uncertain nature of M, B, and K would require, at a minimum, knowledge of their mean values and covariance matrices. Only some of this knowledge is currently available. Ellingwood et al. [1980] present relationships between nominal structural characteristics and their observed, uncertain values. They offer observed values of δM (approximately 0.1) and the coefficient of variation of strength, denoted by δV , for various structural elements and materials (e.g., δV ≈ 0.08 for the flexural strength of reinforced concrete flexural members). A few statistics of modal damping are available that suggest δB is on the order of 0.3 to 0.4 [McVerry, 1979; Camelo et al., 2001; Taoko, 1981]. As of this writing, however, the correlations between elements of M, B, and K are largely unknown. A simplification is therefore adopted: the masses throughout the structure are taken to be perfectly correlated, having known mean values denoted by M and a common coefficient of variation (COV) of δM. Similarly, modal viscous damping is taken as having known mean values B and common COV of δB . Forces and deformations in the force-deformation relationships are given by their mean values and have a common COV of δK. Tangent stiffnesses are thereby held to be deterministic, and the uncertain hysteresis loop of any structural element is simply multiplied in both force F and deformation D directions by a random variable with unit mean and standard deviation of δF = δD . Let any control point on the force-deformation relationship be denoted by the vector K = (D, F). Thus, for any mass in the structure, its uncertain value M can be modeled as the product of its mean value M and εM , a random variable with unit mean and standard deviation of δM. Damping B and forcedeformation control points K are similarly modeled: M = Mε M B = B εB
(21.50)
K = KεK A special case assumes that the error terms are lognormal: ln (e εˆ M ) FεM (e ) = Φ βeM ln (e εˆ B ) FεB (e ) = Φ βeB ln (e εˆ K ) FεK (e ) = Φ βeK
(21.51)
where Φ(⋅) refers to the cumulative standard normal distribution, εˆ refers to the median value of ε and is given by εˆ = exp(– 0.5 β ε2 ), and βε refers to its logarithmic standard deviation. © 2003 by CRC Press LLC
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Start
Define building(s) to be analyzed
Structural models, assembly inventory
Assembly taxonomy
Repeat many times
Simulate structural model
Calculate structural response
Select ground motions
Simulate assembly damage
Compile assembly fragilities
Simulate total repair cost
Unit repaircost distributions
Regress vulnerability
Finish
FIGURE 21.11 Overview of ABV methodology.
Let X denote the instrumental intensity (e.g., spectral acceleration or Arias intensity) of a ground motion G. While intensity is a deterministic function of ground motion, the ground motion contains much more information than intensity, so G is an uncertain function of X. That is, the detailed ground motion is uncertain, given the intensity. It can be modeled in one of two ways: by collecting a large set of ground-motion time histories and assuming that they represent an unbiased sample of possible ground motions, or by simulation techniques that include explicit models of the parameters of time-varying amplitude, frequency content, and phase angles. It is now possible to relate repair cost to ground-motion intensity. ABV is readily implemented using simulation. A Monte Carlo approach proceeds as follows, as depicted in Figure 21.11: • Define the structure to be analyzed: its location, site soils, assemblies, and structural characteristics. The location, site soils, structure replacement cost, and structural configuration are assumed to be known, as are the mean values of mass, damping, and force-deformation behavior. © 2003 by CRC Press LLC
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• Simulate a structural model. Under the simplifications discussed above, the structural model can be simulated by drawing three samples from a random variate uniformly distributed on 0,1 (denoted by U(0,1)): uM, uB , and uK and using the inverse method to simulate εΜ , εΒ , and εΚ . For example: ε M = Fε−1 M (u M )
(21.52)
• For a lognormal distribution:
(
ε M = exp βεM Φ −1 (uM ) − 0.5 β ε2M
)
(21.53)
• Select an intensity level of interest, X. Simulate a ground-motion time history with that intensity, or alternatively, select a recorded ground-motion time history and scale to have the desired intensity. • Perform a nonlinear time-history structural analysis, capturing the peak structural responses Z needed as input to the assembly fragility functions. • For each damageable assembly in the structure, calculate the probability mass function for its damage state. Simulate its damage state by drawing a sample uD ~ U(0,1), and inverting the damage-state probability mass function to determine the damage state. • For each assembly type and damage state, simulate the unit-cost error term by drawing a sample uC ~ U(0,1), calculating εC = Fε−1 C (uC). Calculate the unit repair cost Cj,d and count the number of damaged assemblies of each type and each damage state, Nj,d. • Simulate the overhead and profit factor by drawing a sample P ~ U(0.15, 0.20). • Calculate CR . • The damage factor Y can be calculated as CR /V, where V denotes the replacement cost of the structure. • Repeat the above steps many times for each intensity level X of interest, and regress Y against X (Figure 21.11).
21.5 Validation of Vulnerability Functions No matter on which basis they are developed, vulnerability functions are intended for estimating future losses, in many cases for critical decisions involving life safety or large property values. They therefore need to be validated by comparison with historical events (i.e., by hindcasting). Empirically based vulnerability functions must be validated by comparison with events other than those on which they are based. To hindcast the loss for a single site requires evaluating the appropriate vulnerability functions at the level of the site’s historical shaking intensity (or calculating losses using actual ground-motion time history). To do so for many sites requires repeating the single-site process for each site. However, hindcasting historical losses can be problematic because of the various sources of uncertainty discussed above, plus the following additional sources of uncertainty: • Actual site shaking intensity (a function of magnitude and seismic attenuation, both of which are uncertain) • For category-based vulnerability functions, the accuracy of the structure-type assignment, the effects of regional differences in construction, and the effects of structure-specific features not reflected in the type • Knowledge of the true historical loss to the site(s) • Owners’ past decisions not to repair earthquake-induced damage, or non-earthquake-induced costs that appear as losses, such as tenant improvements performed at the same time as the repairs • For multiple sites and vulnerability functions that explicitly account for uncertainty, the correlation between site losses © 2003 by CRC Press LLC
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The problem is that no hindcasted estimate will match history exactly, so how much difference is reasonable? A reasonable rule of thumb is that, for a single site, if the actual loss falls outside the 95% confidence bounds (mean ± 2 standard deviations for losses distributed according to the Gaussian distribution), either the mean vulnerability functions are inaccurate, or the uncertainty is unreasonably low, or both. The uncertainty should account for both that of the model and that of the “observed” historical loss. These are most likely uncorrelated: 2 2 σ = σ model + σ history
(21.54)
For a group of sites subjected to a single event, several tests can theoretically be performed. First, one could compare the sum of the estimated site losses with the total loss from the event, and check that the actual loss falls within the 95% confidence bounds. The problem is the calculation of the standard deviation of the estimated total loss, and in particular determining the correlation between sites. For the total loss of a group of N sites, the standard deviation of the sum is given by: N −1
N
σ=
∑
N
∑∑ρ σ σ
σ i2 + 2
i =1
ij
i
j
(21.55)
i =1 j =1+1
So far, no empirical data seem to be available to estimate the correlation coefficient ρij. Correlation could reasonably be a function of site soils, distance between sites, structure types, difference in azimuth from the fault, structure type, site soils, the time after the earthquake when repairs were performed, etc.
21.6 Catalog of Vulnerability Functions This section presents a modest sample of seismic vulnerability functions for various buildings, building types, and contents. It draws on some of the sources discussed in this chapter, with emphasis on structures that are either very numerous or highly vulnerable. Seismic vulnerability functions for other facility types, such as bridges, pipelines, and other lifelines, are omitted from this discussion, although two significant sources are the ATC-13 [1985] and HAZUS 99 [1999] reports.
21.6.1 Buildings 21.6.1.1 Unreinforced Masonry Buildings Rutherford & Chekene Consulting Engineers [1990] use expert opinion to create seismic vulnerability functions for 15 prototypical unreinforced masonry buildings under as-is conditions and for three strengthening schemes. The prototypical buildings, illustrated in Figure 21.12, are grouped into five categories, U-1 through U-5, and each category is assigned a single seismic vulnerability function. The strengthening schemes are: • Out-of-place wall strengthening • Strengthening to meet the Uniform Code for Building Conservation Appendix Chapter 1 [International Conference of Building Officials, 1990] • Strengthening to meet the San Francisco Building Code Section 104(f) Table 21.7 presents the resulting seismic vulnerability functions. 21.6.1.2 Woodframe Buildings Figure 21.13 presents seismic vulnerability functions developed by various authors for low-rise woodframe buildings. The vulnerability functions include empirical, theoretical, and judgmentally derived relationships compiled by ATC-13 [1985]. Tables 21.8 to 21.16 present damage probability matrices for various common or high-risk building types, developed using expert opinion by ATC-13 [1985]. © 2003 by CRC Press LLC
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TABLE 21.7 Seismic Vulnerability Functions for Unstrengthened and Strengthened Unreinforced Masonry Buildings 0.05 g VI
0.11 VII
0.22 VIII
0.45 IX
0.7 X
0.01 0.01 0.01 0.01 0.01
0.05 0.06 0.07 0.08 0.1
0.14 0.18 0.22 0.26 0.28
0.27 0.32 0.37 0.42 0.47
0.39 0.43 0.5 0.55 0.6
0.52 0.58 0.67 0.7 0.73
0.65 0.7 0.8 0.8 0.8
(Strengthening scheme 1, out-of-plane wall strengthening) A, B, E, K 1–1 0.005 C, F, G, L, M, N 1–2 0.005 D, H, I, J, O 1–3 0.005
0.03 0.04 0.05
0.11 0.15 0.21
0.25 0.29 0.35
0.38 0.4 0.46
0.51 0.53 0.59
0.65 0.67 0.75
Strengthening scheme 2 (UCBC Appendix Chapter 1) A, B, E, F, G, H, K 2–1 0.005 C, D, I, J, L, M, N, O 2–2 0.005
0.02 0.03
0.1 0.12
0.18 0.23
0.28 0.34
0.44 0.47
0.6 0.6
Strengthening scheme 3 (SFBC Section 104(f)) A, B, C, E, F, G, H, K, L 3–1 D, I, J, M, N, O 3–2
0.01 0.02
0.06 0.08
0.15 0.17
0.24 0.28
0.39 0.41
0.55 0.55
Prototypes (Unstrengthened) A, K B, G, L, M C, H, N D, E, I, J F, O
ID
PGA MMI
U-1 U-2 U-3 U-4 U-5
0.005 0.005
0.9 XI
— XII
Source: Rutherford & Chekene Consulting Engineers, Seismic Retrofitting Alternatives for San Francisco’s Unreinforced Masonry Buildings, San Francisco, CA, 1990.
21.6.1.3 CUREE-Caltech Woodframe Project Figure 21.14 shows theoretical mean vulnerability functions and Figure 21.15 shows the coefficient of variation for four variants of a single-story, 1950s woodframe house, 30 by 40 ft in plan [Porter et al., 2001b]. The vulnerability functions were developed using ABV. Table 21.16 describes the variants. The lognormal distribution fits the vulnerability functions for Sa ≤ 0.8g. The intensity measure is the 5% damped elastic spectral acceleration response at the building’s fundamental period of vibration, 0.13 sec. 21.6.1.4 Other Vulnerability Functions Figure 21.16 presents a set of mean vulnerability functions for a particular pre-Northridge, welded-steel, moment-frame office building [Porter and Kiremidjian]. The figure also shows the costs associated with lost rental income for two cases of repair: one in which all spaces are repaired simultaneously, and the other where office spaces are repaired sequentially. That study found a relatively constant residual coefficient of variation of the damage factor, δY|Sa ≈ 0.57 for Sa ≤ 1.5g. The intensity measure is the 5% damped spectral acceleration response at the building’s smallamplitude fundamental period of vibration, 0.25 sec. Other useful data sets on building damage in the 1971 San Fernando and 1983 Coalinga earthquakes are given by Steinbrugge et al. [1969], McClure [1973], and Steinbrugge and Algermissen [1990].
21.6.2 Contents Saeki et al. [2000] present empirical data on household property loss resulting from the 1995 Kobe earthquake. The data come from 965 questionnaire respondents living in the Hyogo and Osaka prefectures. The questionnaires asked about a variety of durable possessions, such as furniture, and nondurables, such as clothing. They use regression analysis to determine parameters of a vulnerability function for each class of property, idealizing the vulnerability functions in the form of a cumulative normal distribution: ln ( I ) − µ P = Φ σ © 2003 by CRC Press LLC
(21.56)
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A. Small Area, One Story
B. Large Area, One Story
C. Irregular, Residential
D. Irregular, Nonresidential
E. Small Area, Industrial
F. Large Area, Industrial
G. Two And Three Story, Small Area, Office And Commercial
H. Two And Three Story, Large Area, Office And Commercial
I. Over Three Story, Small Area, Office And Commercial
J. Over Three Story, Large Area, Office And Commercial
K. Two And Three Story, Small Area, Residential
L. Two And Three Story, Large Area, Residential
M. Over Three Story, Small Area, Residential
N. Over Three Story, Large Area, Residential
O. Assembly
FIGURE 21.12 Rutherford & Chekene Consulting Engineers prototypical unreinforced masonry buildings. (From Rutherford & Chekene Consulting Engineers, Seismic Retrofitting Alternatives for San Francisco’s Unreinforced Masonry Buildings, San Francisco, CA, 1990. With permission.)
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where P I µ σ
= = = =
damage ratio [(damaged items)/(total items)] Japan Meteorological Agency (JMA) intensity mean intensity at which items experience damage standard deviation of intensity at which items experience damage
The authors offer vulnerability functions for six classes of durables and four of nondurable possessions. Each vulnerability function relates fraction of items of the class damaged to shaking intensity, measured in JMA intensity. The parameters are shown in Table 21.17. Tables 21.18 and 21.19 contain judgmentally derived damage probability matrices for residential and commercial equipment, including furnishings, from ATC-13 [1985].
60 PERCENT DAMAGE FACTOR
40
20
0
12
10
8
6
MMI Benjamin, 1974; Blume et al., 1975
Blume & Cunningham, 1980 (Pre-Code)
Blume & Cunningham, 1980 (UBC Zone 3 Design)
Sauter and Shah, 1978b
Martel, 1964
Steinbrugge, 1969
Wiggins, 1981
Hafen & Kinzter, 1977
Scholl & Blume, 1977
Scawthorn & Gates, 1983
ATC-13
FIGURE 21.13 Various seismic vulnerability functions for low-rise woodframe buildings. (From ATC, Earthquake Damage Evaluation Data for California, Applied Technology Council, Redwood City, CA, 1985. With permission.)
TABLE 21.8 Woodframe Low-Rise Damage Probability Matrix Central Damage Factor (%) 0 0.5 5.0 20.0 45.0 80.0 100.0
Probability of Damage, Given MMI VI
VII
VIII
IX
X
XI
XII
3.7 68.5 27.8 *** *** *** ***
*** 26.8 73.2 *** *** *** ***
*** 1.6 94.9 3.5 *** *** ***
*** *** 62.4 37.6 *** *** ***
*** *** 11.5 76.0 12.5 *** ***
*** *** 1.8 75.1 23.1 *** ***
*** *** *** 24.8 73.5 1.7 ***
Note: *** = very small probability. Source: ATC-13, Earthquake Damage Evaluation Data for California, Applied Technology Council, Redwood City, CA, 1985.
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TABLE 21.9 Mobile Homes Damage Probability Matrix Central Damage Factor (%) 0 0.5 5.0 20.0 45.0 80.0 100.0
Probability of Damage, Given MMI VI
VII
VIII
IX
X
XI
XII
25.6 44.2 30.2 *** *** *** ***
0.1 12.0 87.4 0.5 *** *** ***
*** 2.0 83.0 15.0 *** *** ***
*** *** 21.1 75.5 3.4 *** ***
*** *** *** 58.9 41.1 *** ***
*** *** *** 14.9 83.3 1.8 ***
*** *** *** 0.2 61.8 38.0 ***
Note: *** = very small probability. Source: ATC-13, Earthquake Damage Evaluation Data for California, Applied Technology Council, Redwood City, CA, 1985.
TABLE 21.10 Unreinforced Masonry Bearing Wall (Low-Rise) Damage Probability Matrix Central Damage Factor (%) 0 0.5 5.0 20.0 45.0 80.0 100.0
Probability of Damage, Given MMI VI
VII
VIII
IX
X
XI
XII
*** 9.1 90.5 0.4 *** *** ***
*** 0.6 55.5 43.4 0.5 *** ***
*** *** 10.9 66.0 22.9 0.2 ***
*** *** 0.5 22.4 65.9 11.2 ***
*** *** *** 2.0 35.0 62.5 0.5
*** *** *** 0.1 10.1 83.1 6.7
*** *** *** 0.1 3.4 50.4 46.1
Note: *** = very small probability. Source: ATC-13, Earthquake Damage Evaluation Data for California, Applied Technology Council, Redwood City, CA, 1985.
TABLE 21.11 Unreinforced Masonry with Load-Bearing Frame (Medium-Rise) Damage Probability Matrix Central Damage Factor (%) 0 0.5 5.0 20.0 45.0 80.0 100.0
Probability of Damage, Given MMI VI
VII
VIII
IX
X
XI
XII
0.5 15.3 81.2 3.0 *** *** ***
*** 2.9 66.6 30.1 0.4 *** ***
*** *** 13.5 69.3 17.2 *** ***
*** *** 1.9 40.6 54.4 3.1 ***
*** *** 0.3 14.1 63.4 22.2 ***
*** *** *** 2.0 28.4 67.5 2.1
*** *** *** 0.2 8.5 78.8 12.5
Note: *** = very small probability. Source: ATC-13, Earthquake Damage Evaluation Data for California, Applied Technology Council, Redwood City, CA, 1985.
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TABLE 21.12 Reinforced Masonry Shear Wall without Moment-Resisting Frame (Low-Rise) Damage Probability Matrix Central Damage Factor (%) 0 0.5 5.0 20.0 45.0 80.0 100.0
Probability of Damage, Given MMI VI
VII
VIII
IX
X
XI
XII
2.7 65.8 31.5 *** *** *** ***
*** 10.0 89.7 0.3 *** *** ***
*** 1.0 88.0 11.0 *** *** ***
*** *** 34.5 63.4 2.1 *** ***
*** *** 3.5 76.2 20.3 *** ***
*** *** *** 17.5 74.5 8.0 ***
*** *** *** 3.7 68.3 28.0 ***
Note: *** = very small probability. Source: ATC-13, Earthquake Damage Evaluation Data for California, Applied Technology Council, Redwood City, CA, 1985.
TABLE 21.13 Tilt-Up Reinforced Concrete (Low-Rise) Damage Probability Matrix Central Damage Factor (%) 0 0.5 5.0 20.0 45.0 80.0 100.0
Probability of Damage, Given MMI VI
VII
VIII
IX
X
XI
XII
0.3 35.2 64.5 *** *** *** ***
*** 1.2 97.7 1.1 *** *** ***
*** *** 49.7 50.3 *** *** ***
*** *** 8.7 85.7 5.6 *** ***
*** *** 1.2 56.6 42.0 0.2 ***
*** *** *** 13.0 73.6 13.4 ***
*** *** *** 0.7 40.1 59.2 ***
Note: *** = very small probability. Source: ATC-13, Earthquake Damage Evaluation Data for California, Applied Technology Council, Redwood City, CA, 1985.
TABLE 21.14 Moment-Resisting, Distributed, Nonductile Reinforced Concrete Frame (Medium-Rise) Damage Probability Matrix Central Damage Factor (%) 0 0.5 5.0 20.0 45.0 80.0 100.0
Probability of Damage, Given MMI VI
VII
VIII
IX
X
XI
XII
0.3 30.9 68.8 *** *** *** ***
*** 0.3 96.9 2.8 *** *** ***
*** *** 33.6 65.7 0.7 *** ***
*** *** 1.9 65.1 33.0 *** ***
*** *** 0.2 30.8 67.7 1.3 ***
*** *** *** 3.6 70.0 26.4 ***
*** *** *** 0.5 27.9 71.2 0.4
Note: *** = very small probability. Source: ATC-13, Earthquake Damage Evaluation Data for California, Applied Technology Council, Redwood City, CA, 1985.
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TABLE 21.15 Moment-Resisting, Perimeter Steel Frame (High-Rise) Damage Probability Matrix Central Damage Factor (%) 0 0.5 5.0 20.0 45.0 80.0 100.0
Probability of Damage, Given MMI VI
VII
VIII
IX
X
XI
XII
26.8 50.4 22.8 *** *** *** ***
*** 12.9 87.1 *** *** *** ***
*** 0.8 86.8 12.4 *** *** ***
*** *** 24.8 73.7 1.5 *** ***
*** *** 5.4 86.8 7.8 *** ***
*** *** *** 25.8 73.0 1.2 ***
*** *** *** 8.0 84.9 7.1 ***
Note: *** = very small probability. Source: ATC-13, Earthquake Damage Evaluation Data for California, Applied Technology Council, Redwood City, CA, 1985.
TABLE 21.16 Description of CUREE-Caltech Woodframe Project Small-House Variants Variant
Features
Poor
Poor stucco cripple walls: low-strength, thin stucco; extensive degradation, poor furring and connection of mesh, poor anchorage Poor stucco finish on exterior walls, similar to cripple walls Poor nailing of interior walls: many missing, overdriven or common nails Extra mass: 3 layers of roofing material instead of 2 Average-quality stucco on cripple walls Exterior walls above floor level similar to cripple walls Good nailing of interior walls, few missing or over-driven nails Reinforced concrete stem wall instead of stucco cripple wall Stucco: high strength, good thickness, good furring and connection of mesh, no deterioration Good nailing of interior walls Water heater strapped to wall Light mass: 1 layer of roofing instead of 2 Retrofit typical-quality variant with new partial-length plywood shearwalls at cripple walls
Typical
Superior
Braced
Source: Porter, K.A. et al., Improving Loss Estimation for Woodframe Buildings, Draft Final Report, Vol. 2, Consortium of Universities for Research in Earthquake Engineering, Richmond, CA, 2001b.
Mean damage factor
1.000
0.100
0.010
0.001 0.0
Small house, poor Small house, typical Small house, braced Small house, superior
0.5
1.0 Spectral acceleration, g
1.5
2.0
FIGURE 21.14 Mean vulnerability, CUREE-Caltech Woodframe Project, small house. (From Porter, K. et al., Earthquake Spectra, 17, 291–312, 2001a. With permission.) © 2003 by CRC Press LLC
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COV on damage factor
5 4
y = -0.41x + 1.43 R2 = 0.07
3
Small house, poor Small house, typical Small house, superior Small house, braced Linear (Small house, typical)
2 1 0 0.0
0.5
1.0
1.5
2.0
Spectral acceleration, g FIGURE 21.15 Coefficient of variation of vulnerability, CUREE-Caltech Woodframe Project, small house. (From Porter, K. et al., Improving Loss Estimation for Woodframe Buildings, Draft Final Report, Vol. 2, Consortium of Universities for Research in Earthquake Engineering, Richmond, CA, 2001b. With permission.)
TABLE 21.17 Parameters of Household Property Vulnerability Functions Property Type
µ
σ
Large free-standing storage furniture subject to overturning, e.g., chests, shelves, cupboards Large free-standing household electrical appliances subject to overturning, e.g., refrigerators and washing machines Small countertop household electrical appliances subject to falling, e.g., microwave ovens Household entertainment equipment subject to falling or overturning, e.g., audiovisual equipment, personal computers, musical instruments Floor-standing furniture subject to crushing, e.g., dining tables, chairs Heaters and air conditioning equipment subject to crushing or overturning Indoor accessories, e.g., curtains, health and medical equipment, sporting goods, bags, shoes, carpets Tableware Small home entertainment items subject to falling, e.g., clocks, cameras, lights, records, CDs, toys Clothing and bedclothes subject to damage or contamination by broken glass or other foreign matter
6.27 6.69
0.88 0.73
6.42 6.95
0.80 1.16
6.78 7.26 7.15 5.05 6.64 7.00
0.76 0.92 1.13 0.36 1.21 0.98
TABLE 21.18 Residential Equipment Damage Probability Matrix Central Damage Factor (%) 0 0.5 5.0 20.0 45.0 80.0 100.0
Probability of Damage, Given MMI VI
VII
VIII
IX
X
XI
XII
2.2 92.3 5.5 *** *** *** ***
*** 18.1 81.9 *** *** *** ***
*** 0.2 98.1 1.7 *** *** ***
*** *** 29.4 70.6 *** *** ***
*** *** 0.6 75.6 23.8 *** ***
*** *** *** 8.9 90.6 0.5 ***
*** *** *** 0.4 78.1 21.5 ***
Note: *** = very small probability. Source: ATC-13, Earthquake Damage Evaluation Data for California, Applied Technology Council, Redwood City, CA, 1985.
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TABLE 21.19 Office Equipment (Furniture, Computers, etc.) Damage Probability Matrix Central Damage Factor (%) 0 0.5 5.0 20.0 45.0 80.0 100.0
Probability of Damage, Given MMI VI
VII
VIII
IX
X
XI
XII
*** 73.9 26.1 *** *** *** ***
*** 0.7 99.3 *** *** *** ***
*** *** 97.6 2.4 *** *** ***
*** *** *** 95.2 4.8 *** ***
*** *** *** 76.1 23.9 *** ***
*** *** *** 1.0 96.3 2.7 ***
*** *** *** *** 64.5 35.5 ***
Note: *** = very small probability. Source: ATC-13, Earthquake Damage Evaluation Data for California, Applied Technology Council, Redwood City, CA, 1985.
Normalized total cost Y = C / V
1.00
0.75
Slow repair 0.468 y = 0.422s
0.50
Fast repair 0.466 y = 0.328 s
0.25
C R /V y = 0.273 s
0.470
0.00 0.0
0.5
1.0
1.5
S a (T 1), g FIGURE 21.16 Mean vulnerability, 3-story, pre-Northridge welded-steel perimeter moment-frame office building. (From Porter, K. and A.S. Kiremidjian, Assembly-Based Vulnerability and Its Uses in Seismic Performance Evaluation and Risk-Management Decision-Making, John A. Blume Earthquake Engineering Center, Stanford, CA, 2001. With permission.)
21.7 Uses of Vulnerability Functions 21.7.1 Probable Maximum Loss As noted at the beginning of this chapter, the need of earthquake insurers to evaluate their risk has largely driven the development of seismic vulnerability functions. In current practice, when earthquake insurers consider the seismic risk associated with the policy for a particular property, they typically are interested in a probabilistic upper-bound of future loss, which has historically been referred to as the probable maximum loss (PML) [Maffei, 2000]. Furthermore, commercial lenders commonly use PML to help decide whether to underwrite a mortgage. Though all working definitions involve the level of loss associated with a large, rare event, there is no commonly accepted quantitative definition of earthquake PML [Zadeh, 2000; Rubin, 1991]. Consider the following three competing definitions. Probabilistically upper-bound earthquakes, worst probabilistically upper-bound loss: All of the local seismic faults that could affect a facility are considered. For each fault, the magnitude of the earthquake © 2003 by CRC Press LLC
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with 10% exceedance probability in 50 years is identified from seismicity considerations. An earthquake with that magnitude is posited to occur on a segment of the fault closest to the site of interest. Seismic attenuation relationships are used to estimate the mean shaking intensity at the site. The seismic vulnerability function is then used to calculate the 90th percentile of loss for the facility. The process is repeated for all the faults, and the largest calculated loss is taken as the PML. This PML is given by:
[
PML1 = max i VFY X
−1
( p x )] i
(21.57)
where V represents the replacement value of the facility, FY|X(y|x) is the cumulative probability distribution on the damage factor, Y, conditioned on shaking intensity X (i.e., the cumulative distribution form of the probabilistic seismic vulnerability function), FY|X–1(p|xi) denotes its inverse evaluated at probability p (here, p = 0.90) and shaking intensity xi, for fault i. The shaking intensity xi for a given fault, magnitude, distance, and site soil is calculated using an appropriate seismic attenuation relationship [e.g., Campbell, 1997; Boore et al., 1997]. Probabilistically upper-bound shaking, mean loss: In a second approach, the PML is the mean loss conditioned on the shaking intensity with 10% exceedance probability at the site in 50 years, considering all the local faults, their distances, seismic activity, etc. This PML is given by:
( (
))
PML2 = V ⋅ y G −1 f ( p, t )
(21.58)
where V is the replacement value, y(x) is the mean damage factor for shaking intensity x (i.e., the mean seismic vulnerability function), G(x) is the mean annual frequency of events exceeding intensity x, G–1(f) is its inverse evaluated at frequency f, and f(p,t) is the frequency corresponding to nonexceedance probability p in time t, here 90% and 50 years, respectively. If earthquakes are assumed to arrive according to a Poisson process, then f(0.90,50 yr) ≈ 0.0021. Probabilistically upper-bound loss: In this approach, PML is the loss associated with 10% exceedance probability in 50 years. If earthquake losses are taken as Poisson arrivals, then the return period for this event is T = 475 years, and the PML is given by: PML3 = Vv−1 (1 T )
(21.59)
where V is the replacement value, v(y) is the frequency (events/year) of losses exceeding y, and v-1(1/T) is its inverse, evaluated at a return period of T. It has been already shown that: v ( y) =
∞
∫ (1 − P [Y ≤ y X = x]) g (x)dx
(21.60)
0
where P[Y ≤ y |X = x] = the probability that uncertain loss Y will be less than or equal to some particular value y, given ground-shaking x: g (x ) =
dG DX
x
and G(x) = mean annual frequency of events producing shaking intensity X ≥ x. The three PML values, PML1, PML2, and PML3, can be significantly different, even when based on the same seismicity information, seismic attenuation relationship, and seismic vulnerability function. (The period of 50 years is commonly used to represent the design life of an ordinary building. The 10% exceedance probability represents a reasonable upper-bound event.)
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21.7.2 National Standard for Loss Estimation The absence of a commonly understood, standard loss measure, such as PML, led the American Society for Testing and Materials [1999] to develop a national standard for estimation of building damageability in earthquakes. The standard, ASTM E2026–99, provides definitions for two new terms: probable loss (PL) and scenario loss (SL). It discourages future use of the term PML. The standard characterizes acceptable practice for estimating seismic loss. It defines parameters and methodologies, but is not intended to provide information on seismic hazard, seismic attenuation, site amplification of ground motion, structural response, component damageability, repair methods, costs, etc. It defines PL as “the earthquake loss to the building(s), not including contents or equipment, that has a specified probability of being exceeded in a given time period from earthquake shaking. PL values are expressed as a percentage of building replacement construction cost (current).” This is the general case of PML3 above. The SL is defined as “the earthquake loss to the building(s), not including contents or equipment, resulting from a specified scenario event on specific faults affecting the building, or specified ground motions.” Since SL is an uncertain quantity, the standard requires that the probability associated with any particular SL be specified. Furthermore, it defines two additional parameters, scenario expected loss, SEL (defined as the expected-value loss in the specified ground motion of the scenario selected), and scenario upper loss, SUL (defined as the scenario loss that has a 10% probability of exceedance due to the specified ground motion of the scenario considered). Note that SL is equivalent to the probabilistic seismic vulnerability function evaluated for a given event or shaking intensity, and SEL and SUL are its mean and 90th percentile.
21.7.3 Other Applications Problems of insurance and lending have already been discussed. Two more notable problems of earthquake engineering require the development or use of seismic vulnerability functions: Performance-based earthquake engineering (PBEE): Performance-based earthquake engineering guidelines are currently in development. At least one PBEE methodology will likely involve uncertain future seismic economic performance (i.e., repair costs) as a performance measure, with the objective that a developer, owner, or other stakeholder would specify the probabilistic level of future earthquake loss for which a structure would be designed [Pacific Earthquake Engineering Research Center, 2001]. Such an approach to design requires that the engineer can evaluate the probabilistic loss to a building, bridge, or other facility, for a given design and site location. Risk-management decision-making: Building owners or tenants often recognize that they are exposed to seismic risk and wish to evaluate alternatives for risk management. Common choices include the do-nothing alternative; buying earthquake insurance; providing additional strength or stiffness to a structure; providing additional resistance to building service equipment, contents, or other nonstructural components; providing for backup facilities; or moving sensitive operations to a less seismically vulnerable location. Each alternative has associated up-front costs and uncertain future earthquake losses. The future losses must be assessed using the seismic hazard and seismic vulnerability functions appropriate to each alternative.
21.8 Closing Remarks In closing, there are a number of situations in which one must make decisions about seismic risk. These include insurance and loan underwriting, risk management for building owners and tenants, and the design of new structures to meet economic performance goals. Each case requires one to estimate future seismic performance of a building or other facility. A facility located in earthquake country is exposed to various levels of seismic excitation (the most important form of which is shaking), so the estimation of future performance requires a functional relationship between performance and shaking. Two forms of this functional relationship are the seismic vulnerability function and the fragility function. The © 2003 by CRC Press LLC
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vulnerability function gives the loss conditioned in shaking intensity, while the fragility function gives the probability of some undesirable event, such as the probability that loss will exceed some specified amount, conditioned on the shaking level. There are three types of approaches to creating seismic vulnerability functions: statistical, expert opinion, and analytical methods. The statistical approach involves regression analysis of a substantial database of loss and associated shaking for facilities similar to the one of interest. The statistical approach is highly defensible, but frequently suffers from the problem of inadequate data. When such data are not available, expert opinion can be used as a substitute, e.g., using the Delphi Method or other structured means of eliciting expert judgment. This approach is efficient and highly versatile, but is more difficult to defend because of inherent difficulties in verification. When neither expert opinion nor the statistical approach is satisfactory, a variety of analytical methods are available that employ the principles of structural analysis, reliability, and construction contracting, to create theoretical seismic vulnerability functions. These approaches are modular in that each part can be independently improved with better knowledge, but they tend to be building-specific and therefore problematic for estimating societal losses.
Defining Terms Arias intensity (Ia) — An instrumental measure of ground motion defined as: π Ia = 2g
∞
∫ [a (t )] dt 2
0
where g is the acceleration due to gravity and a(t) is the ground acceleration at time t in units of gravity. Assembly — A collection of construction materials assembled to form a structural or nonstructural element or item of content, assembled and in place. Capacity curve — A relationship between seismic base shear and peak relative displacement (typically of the roof relative to the ground), transformed to the space of spectral displacement response and spectral acceleration response. Central damage factor (CDF) — A central value in a range of damage factors. Coefficient of variation (COV) — The ratio of the standard deviation of an uncertain quantity to its expected (mean) value. Component — A piece of a building or other facility. Cumulative distribution function (CDF) — A relationship giving the probability that an uncertainty quantity will not exceed and particular value, as a function of that value. Damage — Degradation of a building or other structure due, in this context, to earthquake effects. The degradation may be to the structural system, or to nonstructural components, such as walls and windows, or to the furnishings, fixtures, and equipment. Damage factor (DF) — Repair cost as a fraction of replacement cost. Damage probability matrix (DPM) — A matrix whose rows are increasing damage states or damage ranges; whose columns are discrete intensity levels or ranges of intensity; and whose entries are the probability that a facility will be in the damage state or range, given the intensity level. Each column sums to 100%. Damage ratio — Fraction of buildings suffering nonzero damage. Damage state — A degree of damage describing the condition of a building or other facility. Can be defined either by qualitative description of the facility’s physical appearance or functionality, or quantitatively in terms of repair cost. Damping — A measure of energy dissipated by a structure through its motion. Design-basis earthquake — An event with shaking intensity having 10% exceedance probability in 50 years. © 2003 by CRC Press LLC
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Expected value — The mean or average value of an uncertain quantity. Fragility — The probability of some undesirable event as a function of excitation. Here, the probability of reaching or exceeding a damage state as a function of seismic excitation. Hindcast — Estimation of past outcomes. Intensity — A measure of earthquake effect at a particular location due to a particular earthquake. Interstory drift — The displacement of the floor above a story relative to the floor below it. Loss — The measure of the severity of an undesirable outcome, e.g., repair cost, insurance claim amount, number of fatalities, etc. Mean — Average or expected value of an uncertain quantity. Mean damage factor (MDF) — Average repair cost as a fraction of replacement cost. Median — The value of an uncertain quantity with 50% probability of being exceeded. Modified Mercalli Intensity (MMI) — A qualitative description of shaking intensity with 12 discrete levels from I to XII. Monte Carlo simulation — A numerical method for evaluating an uncertain quantity that is defined as a deterministic function of one or more other uncertain quantities through a process of simulating the inputs, calculating the output, and iterating to compile statistics of the output value. Nonlinear time-history structural analysis — A structural analysis in which the seismic excitation and the response of the structure are evaluated at many discrete points in time, and geometric or material nonlinearities are accounted for. Peak ground acceleration — The maximum acceleration of a zero-period elastic structure during an earthquake. Performance-based earthquake engineering (PBEE) — A seismic design or analysis approach in which the behavior of a facility is characterized on a macroscopic level in terms of functionality, safety, repair cost, or restoration time, as opposed to the behavior of individual structural members or connections. Probabilistic risk analysis (PRA) — An analysis that characterizes the relationship between uncertain future loss and its probability of occurrence. Probabilistic seismic vulnerability function — A probabilistic relationship between loss and degree of seismic excitation (intensity). Probable maximum loss (PML) — A scalar value representing a probabilistic upper-bound of future loss. Pushover curve — A relationship between seismic base shear and peak relative displacement (typically of the roof relative to the ground). Response spectrum — A relationship between the structural response of a damped elastic single-degreeof-freedom system as a function of the system’s natural period of vibration and damping. Seismic hazard — A relationship giving the annual probability or frequency of events causing a shaking intensity exceeding a given value, as a function of that value. Seismic vulnerability function — A relationship between damage, or loss, and seismic excitation (i.e., intensity). Spectral acceleration response Sa — The maximum absolute acceleration experienced by an elastic single-degree-of-freedom system of specified period and damping, for a specified earthquake acceleration time-history. Spectral displacement response Sd — The maximum displacement relative to the ground of an elastic single-degree-of-freedom system of specified period and damping, for a specified earthquake acceleration time-history. Structural analysis — The calculation of structural deformations, internal member forces, and structural displacements, given external loading conditions or support displacements. Structural response — The deformation, displacement, or internal member forces of a structure subjected to specified loads or support displacements. © 2003 by CRC Press LLC
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Structure type — Taxonomic group of a structure, typically defined in terms of use, era of construction, construction material, lateral force-resisting system, height, applicable building code, or quality.
Ultimate point — The structural response at which the base shear reaches its maximum value. Unit cost — Here, the cost to perform a specified construction task for a specified quantity of work to be performed.
Yield point — The structural response at which permanent damage begins.
References Aagard, B.T., J.F. Hall, and T.H. Heaton, 2001. “Characterization of Near-Source Ground Motions with Earthquake Simulations,” Earthquake Spectra 17, 177–208. ASTM (American Society for Testing and Materials), 1999. E 2026–99 Standard Guide for the Estimation of Building Damageability in Earthquakes, American Society for Testing and Materials, West Conshohocken, PA. Ang, A.H.-S. and W.H. Tang, 1975. Probability Concepts in Engineering Planning and Design, Volume I: Basic Principles, John Wiley & Sons, New York. ATC (Applied Technology Council), 1985. Earthquake Damage Evaluation Data for California, ATC-13, Applied Technology Council, Redwood City, CA. ATC (Applied Technology Council), 1988. Rapid Visual Screening of Buildings for Potential Seismic Hazards: A Handbook, ATC-21, Applied Technology Council, Redwood City, CA. ATC (Applied Technology Council), 1996. Seismic Evaluation and Retrofit of Concrete Buildings, Volume 1, ATC-40, Applied Technology Council, Redwood City, CA. ATC (Applied Technology Council), 2000. Database on the Performance of Structures Near Strong-Motion Recordings: 1994 Northridge, California, Earthquake, ATC-38, by C. Rojahn, C. Poland, C. Scawthorn, S. King, and R.A. Bruce, Applied Technology Council, Redwood City, CA. ATC (Applied Technology Council), Seismic Rehabilitation Guidelines for Woodframe Homes, ATC-50, Applied Technology Council, Redwood City, CA, (in prep.). Boore, D.M., W.B. Joyner, and T.E. Fumal, 1997. “Equations for Estimating Horizontal Response Spectra and Peak Accelerations from Western North American Earthquakes: A Summary of Recent Work,” Seismol. Res. Lett., 68, 128–153. Camelo, V.S., J.L. Beck, and J.F. Hall, 2001. Dynamic Characteristics of Woodframe Structures, Consortium of Universities for Research in Earthquake Engineering, Richmond, CA. Campbell, K.W., 1997. “Empirical Near-Source Attenuation Relationships for Horizontal and Vertical Components of Peak Ground Acceleration, Peak Ground Velocity, and Pseudo-Absolute Acceleration Response Spectra,” Seismol. Res. Lett., 68, 154–179. Conte, J.P., K.S. Pister, and S.A. Mahin, 1992. “Nonstationary ARMA Modeling of Seismic Motions,” Soil Dyn. Earthquake Eng., 11(7), 411–426. Czarnecki, R.M., 1973. Earthquake Damage to Tall Buildings, Structures, Publication 359, Massachusetts Institute of Technology, Cambridge. Dalkey, N., B. Brown, and S. Cochrane, 1970. “Use of Self-Ratings to Improve Group Estimates,” Technol. Forecasting Int. J., 1, 283–291. Ellingwood, B., T.V. Galambos, J.G. MacGregor, and C.A. Cornell, 1980. Development of a ProbabilityBased Load Criterion for American National Standard A58, National Bureau of Standards, Washington, D.C. EQE International and the California Governor’s Office of Emergency Services, 1995. The Northridge Earthquake of January 17, 1994: Report of Data Collection and Analysis, Part A: Damage and Inventory Data, EQE International, Irvine, CA. FEMA (Federal Emergency Management Agency), 1997a. NEHRP Recommended Provisions for Seismic Regulations for New Buildings. Part 1, Provisions. FEMA 222A, Federal Emergency Management Agency, Washington, D.C.
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FEMA (Federal Emergency Management Agency), 1997b. NEHRP Guidelines for the Seismic Rehabilitation of Buildings. FEMA 273, Federal Emergency Management Agency, Washington, D.C. Freeman, J.R., 1932. Earthquake Damage and Earthquake Resistance, McGraw-Hill, New York. Gordon, T.J. and O. Helmer, 1964. Report on a Long Range Forecasting Study, RAND Paper P-2982, RAND Corporation, Santa Monica, CA. HAZUS 99, 1999. Earthquake Loss Estimation Methodology, HAZUS99 Service Release 1 (SR1) Technical Manual, developed by the Federal Emergency Management Agency, Washington, D.C. through agreements with the National Institute of Building Sciences, Washington, D.C. Holmes, W., 2000. Personal communication. International Conference of Building Officials, 1991. Uniform Code for Building Conservation, Whittier, CA. Kircher, C.A., A.A. Nassar, O. Kustu, and W.T. Holmes, 1997. “Development of Building Damage Functions for Earthquake Loss Estimation,” Earthquake Spectra, 13, 663–682. Kustu, O., 1986. “Earthquake Damage Prediction for Buildings Using Component Test Data,” Proc. Third U.S. National Conference on Earthquake Engineering, Aug. 24–28, Charleston, SC, Earthquake Engineering Research Institute, El Cerrito, CA, 1493–1504. Kustu, O., D.D. Miller, and S.T. Brokken, 1982. Development of Damage Functions for Highrise Building Components, URS/John A Blume & Associates, San Francisco, CA. Maffei, J., 2000. “The Corporate Sector,” Financial Management of Earthquake Risk, EERI Endowment Fund White Paper, Earthquake Engineering Research Institute, Oakland, CA, pp. 43–48. Martel, R.R., 1964. “Earthquake Damage to Type III Buildings in Long Beach, 1933,” Earthquake Investigations in the Western United States 1931–1964, Publication 41–2, U.S. Department of Commerce, Coast and Geodetic Survey, Washington, D.C. McClure, F.E., 1973. Performance of Single-Family Dwellings in the San Fernando Earthquake of February 9, 1971, U.S. Department of Housing and Urban Development, Washington, D.C. McVerry, G.H., 1979. Frequency Domain Identification of Structural Models for Earthquake Records, Report No. EERL 79–02, California Institute of Technology, Pasadena, CA (http://caltecheerl.library. caltech.edu/documents/disk0/00/00/02/23/00000223-00/7902.pdf). Pacific Earthquake Engineering Research Center, 2001. Pacific Earthquake Engineering Research Center Annual Report, University of California, Berkeley (http://peer.berkeley.edu/research/annual/toc.html). Polhemus, N.W. and A.S. Cakmak, 1981. “Simulation of Earthquake Ground Motions Using Autoregressive Moving Average Models,” Earthquake Eng. Struct. Dyn., 9, 343–354. Porter, K.A. and A.S. Kiremidjian, 2001. Assembly-Based Vulnerability and Its Uses in Seismic Performance Evaluation and Risk-Management Decision-Making, John A. Blume Earthquake Engineering Center, Stanford, CA. Porter, K.A., A.S. Kiremidjian, and J.S. LeGrue, 2001a. “Assembly-Based Vulnerability of Buildings and Its Use in Performance Evaluation,” Earthquake Spectra, 17, 291–312. Porter, K.A., J.L. Beck, H.A. Seligson, C.R. Scawthorn, L.T. Tobin, R. Young, and T. Boyd, 2001b. Improving Loss Estimation for Woodframe Buildings, Draft Final Report, Vol. 2, Consortium of Universities for Research in Earthquake Engineering, Richmond, CA (http://www.curee.org/projects/ woodframe_project/element4/task_4_1.html). RS Means Corp., 1997. Means Assemblies Cost Data, RS Means, Kingston, MA. Rubin, H.W., 1991. Dictionary of Insurance Terms, Barron’s Educational Services, New York. Rutherford & Chekene Consulting Engineers, 1990. Seismic Retrofitting Alternatives for San Francisco’s Unreinforced Masonry Buildings, Rutherford & Chekene, San Francisco, CA. Saeki, T., H. Tsubokawa, and S. Midorikawa, 2000. “Seismic Damage Evaluation of Household Property by Using Geographic Information Systems (GIS),” Proceedings, 12th World Conference on Earthquake Engineering, January 30–February 5, Aukland, New Zealand, International Association for Earthquake Engineering (Paper 1968). Scawthorn, C., 1995. “Insurance Loss Estimation: Performance After the Northridge Earthquake,” Contingencies, The Magazine of the American Academy of Actuaries, Washington, D.C., Sept./Oct., 26–36. © 2003 by CRC Press LLC
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Scawthorn, C.R. et al., 1981. “Seismic Damage Estimation for Low- and Mid-Rise Buildings in Japan,” Earthquake Eng. Struct. Dyn., 9, 93–115. Schierle, G.G., 2000. Northridge Earthquake Field Investigations: Statistical Analysis of Woodframe Damage, CUREE Publication No. W-02, Consortium of Universities for Research in Earthquake Engineering, Richmond, CA. Scholl, R.E. and O. Kustu, 1981. “Procedures and Data Bases for Earthquake Damage Prediction and Risk Assessment,” Proc. Conference XIII, Evaluation of Regional Seismic Hazards and Risk, Open-file Report 81–437, U.S. Geological Survey, Reston, VA, 162–213. Spetzler, C.S. and C.A.S. Stael von Holstein, 1972. “Probability Encoding in Decision Analysis,” Proc. ORSA-TIMS-AIEE 1972 Joint National Meeting, Atlantic City, NJ, 8–10 November, reprinted in Howard, R.A. and J.E. Matheson, Eds., The Principles and Applications of Decision Analysis, Volume II: Professional Collection, Strategic Decisions Group, Menlo Park, CA, 1989, pp. 601–625. Steinbrugge, K.V. and S.T. Algermissen, 1990. Earthquake Losses to Single-Family Dwellings: California Experience, U.S. Geological Survey Bulletin 1939-A, U.S. Geological Survey, Washington, D.C. Steinbrugge, K.V., F.E. McClure, and A.J. Snow, 1969. Studies in Seismicity and Earthquake Damage Statistics, U.S. Coast and Geodetic Survey, Washington, D.C. Swan, S.W. and R. Kassawara, 1998. “The Use of Earthquake Experience Data for Estimates of the Seismic Fragility of Standard Industrial Equipment,” ATC-29–1: Seminar on Seismic Design, Retrofit, and Performance of Nonstructural Components, Applied Technology Council, Redwood City, CA, 313–322. Taoko, G.T., 1981. “Damping Measurements of Tall Structures,” Proc. Second Specialty Conference on Dynamic Response of Structures: Experimentation, Observation, Prediction, and Control, January 15–16, Atlanta, GA, American Society of Civil Engineers, New York, 308–322. Tversky, A. and D. Kahneman, 1974. “Judgment under Uncertainty: Heuristics and Biases,” Science, 185, 1124–1131. Zadeh, M.M., 2000. “Understanding Risk Management,” Financial Management of Earthquake Risk, EERI Endowment Fund White Paper, Earthquake Engineering Research Institute, Oakland, CA, pp. 1–14.
Further Reading The ATC-13 [1985] and ATC-38 [2000], and the HAZUS 99 Technical Manual [1999], are good compendiums on earthquake damage and seismic vulnerability functions. ATC-21 [1988; 2002] provides a good overview of model building types, their identification, and typical seismic performance.
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IV Infrastructure Aspects
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22 Lifeline Seismic Risk
Ronald T. Eguchi ImageCat, Inc. Long Beach, CA
22.1 Introduction 22.2 Brief History of Lifeline Earthquake Engineering in the United States 22.3 Nonlinearity of Earthquakes 22.4 Indirect Economic Losses 22.5 Cost-Effective Mitigation Strategies 22.6 Federal and Industry Lifeline Initiatives 22.7 Lifeline Seismic Risk Defining Terms References
22.1 Introduction Infrastructure, such as highways, water and wastewater systems, electric power and communication systems, and natural gas systems, literally make up the arteries and lifeblood of modern society. Deprived of this infrastructure, such as in a major urban earthquake, mankind is reduced to a primitive existence. For this reason, we use the term lifeline. The focus of this chapter is on earthquake hazards and the issues and opportunities associated with the reduction of risks to urban lifeline systems. Even though the focus is on earthquakes, the concepts and ideas are applicable to all natural hazards. The basic thesis of this chapter is that the cost of rebuilding lifeline systems after major natural disasters is becoming prohibitively expensive, even for large federal budgets. As our cities continue to develop and expand geographically, we increase the chance of “direct hits” — that is, major urban catastrophes. Therefore, the design of our systems must consider these risks and, perhaps more importantly, develop ways of effectively reducing these risks through land-use planning, modification of hazardous site conditions, and increased design and/or retrofit. Recent disasters have underscored the need to assess the vulnerability of our nation’s lifeline systems to natural hazard effects. Published estimates of lifeline damage as a result of the 1994 Northridge earthquake are in excess of $2 billion. While this amount may appear low relative to other types of losses (e.g., damage to buildings), it only reflects those costs associated with the repair of damaged lifeline systems. Other costs, which may more accurately reflect the impact of damaged or disrupted systems — such as business losses due to lifeline disruption or fire damage resulting from loss of water supplies — may be several factors higher than these repair costs. Also, it must be recognized that the Northridge earthquake was a moderate-sized event and that the Los Angeles area is capable of generating earthquakes of much larger magnitude. Therefore, the relatively good performance of lifelines in the Northridge earthquake should not promote complacency in acceptable design measures for lifeline systems. This chapter concentrates on five areas relevant to earthquake hazard reduction for lifeline systems. First, a brief history of lifeline earthquake engineering in the United States is presented in order to identify important milestones with regard to lifeline seismic design and construction. Second, the nonlinear
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relationship between earthquake impacts and earthquake size and proximity to urban area is discussed. As will be seen, the United States has been fortunate not to have experienced a catastrophic earthquake in a major urban area, at least since 1906. The question of how U.S. response systems would function if a Kobe-type earthquake were to occur here is of particular interest. Third, a discussion of indirect vs. direct economic losses associated with the failure and disruption of lifeline systems in earthquakes is presented. As stated earlier, the larger impacts associated with damaged lifeline facilities may depend on how long these critical lifeline systems are out of service. Fourth, we offer several case histories that demonstrate where mitigation has been effective in reducing earthquake losses. An important program in this respect is the Caltrans bridge retrofit program. The cost-effectiveness of this program is reviewed against the experience of two major earthquakes in California, the 1989 Loma Prieta earthquake in the San Francisco Bay area and the 1994 Northridge earthquake in Los Angeles. Finally, several opportunities for impacting lifeline earthquake engineering design practices are discussed. We also discuss where these opportunities might build on federal initiatives. One important initiative focuses on the adoption of seismic design standards for private and public lifeline systems in the United States, an effort being spearheaded by the American Lifelines Alliance, a joint partnership between the Federal Emergency Management Agency (FEMA) and the American Society of Civil Engineers (ASCE).
22.2 Brief History of Lifeline Earthquake Engineering in the United States The following chronology provides a brief look at some of the more important milestones related to lifeline earthquake engineering in the United States. As can be seen, the major impetus to examine seismic design procedures for lifeline facilities was the 1971 San Fernando earthquake. Even though there had been prior earthquakes in the United States that highlighted the importance of lifeline systems after major disasters (e.g., the 1906 San Francisco earthquake), the 1971 San Fernando event resulted in a widespread and profound recognition of the lifeline seismic risk problem, and led to important changes in design and construction. Year
Milestone
1971
San Fernando Earthquake (M6.4)
1974
TCLEE
1977
NEHRP
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Significance Significant damage to lifeline systems. Start of long-term research program to study the effects of earthquakes on all lifeline systems (primarily funded by the National Science Foundation). Many changes to lifeline seismic design and construction initiated by this event. The Technical Council on Lifeline Earthquake Engineering (TCLEE) of the American Society of Civil Engineers was formed to address general issues regarding the state-of-the-art and practice of lifeline earthquake engineering in the United States. Since its formation, TCLEE has sponsored reconnaissance of major earthquakes, held five major quadrennial conferences on lifeline earthquake engineering, endowed the C. Martin Duke Lifeline Earthquake Engineering award, and published numerous monographs, design guideline documents, and special reports on lifeline earthquake engineering. National Earthquake Hazards Reduction Program established by Congress in 1977 (Public Law 95–124) to “reduce the risks to life and property from future earthquakes in the United States through the establishment and maintenance of an effective earthquake hazards reduction program.” [amended 1990 Public Law 101–614]. NEHRP’s mission includes improved understanding, characterization and prediction of hazards and vulnerabilities; improved model building codes and land use practices; risk reduction through postearthquake investigations and education; development and improvement of design and construction techniques; improved mitigation capacity; and accelerated application of research results. The Act designates FEMA as the lead agency of the program, and assigns several planning, coordinating, and reporting responsibilities. NEHRP has been a major pillar in the building of a national lifelines seismic risk reduction program.
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Year
Milestone
1985
BSSC Lifeline Workshop
1986
NCEER*
1989
Loma Prieta Earthquake (M7.1)
1990
Port of Los Angeles (POLA) Seismic Workshop
1990
Public Law 101–614 (Reauthorization of the National Earthquake Hazards Reduction Program) Lifeline Standards Workshop
1991
1991
1994
Workshop Sponsored by the National Science Foundation and the National Communications System Northridge Earthquake (M6.7)
1995
Kobe, Japan Earthquake (M6.9)
1996
FEMA/NIST Plan for Developing and Adopting Seismic Design Guidelines and Standards for Lifelines ASCE Lifelines Policymakers Workshop Deregulation of the Electric Power Industry
1997 1997
1998
American Lifelines Alliance
Significance As a result of this major workshop held by the Building Seismic Safety Council, an action plan for abating seismic hazards to lifelines was developed. The workshop had recommendations in four areas: public policy, legal, and financial strategies; information transfer and dissemination; emergency planning; and scientific and engineering knowledge. In order to address socioeconomic issues related to the seismic performance of lifeline systems, the NSF awarded a multi-year contract to the State University of New York at Buffalo to form the National Center for Earthquake Engineering Research (NCEER). This center has brought together researchers from many different technical disciplines to focus on multi-dimensional issues (e.g., socioeconomic impacts caused by the disruption of lifeline service). This earthquake reaffirmed the programs initiated in 1971, and the need to assess and improve seismic design and construction procedures for all lifeline facilities. Particular attention was subsequently given to the performance of highway bridge structures, due in part to the damage to the San Francisco–Oakland Bay Bridge. The purpose of this workshop was to develop a set of guidelines to be used by the Port to address seismic design issues in the design and construction of new landfill areas within the Port. This workshop reflected the culmination of many months of preparation and meetings among scientists, engineers, and policy makers. Passage of this law required the director of the Federal Emergency Management Agency (FEMA), in consultation with the National Institute of Standards and Technology (NIST), to submit to Congress a plan for developing and adopting seismic design and construction standards for all lifelines. The purpose of this workshop was to (1) obtain comments and suggestions for revising draft plans prepared in response to Public Law 101–614, examining lifeline issues, and (2) obtain priorities for various standard development and research activities. This was one of the first workshops to focus on the effects of earthquakes on communication lifeline systems. This workshop was followed by a second meeting in 1992 where different approaches to communication lifeline modeling was discussed. Performance of lifelines had significantly improved compared to prior earthquakes in this region (e.g., 1971 San Fernando earthquake). However, concern continued over the performance of highway bridges structures. Other lifelines were generally deemed to have performed satisfactorily even though the City of Los Angeles experienced a complete loss of electric power for the first time in its history. Performance of lifelines in this earthquake was extremely poor. Considerable damage was observed in virtually every type of lifeline system with restoration taking as long as several months in certain cases. This event was a reminder of what could happen in the United States if mitigation efforts are not continued. This plan was the result of Public Law 101–614. This plan emphasized the importance of forming public and private partnerships to implement its recommendations. Workshop held in Washington, D.C. to solicit input on how to implement the recommendations of the FEMA/NIST plan. The first real test in examining the impact of deregulation on seismic mitigation activities. In the past, these programs were mandated or strongly encouraged by state Public Utilities Commissions. Without these requirements and with economics playing a more important role in capital expenditures, the future of pro-active seismic mitigation programs is placed in jeopardy. Formed as a partnership between FEMA and ASCE, this nonprofit entity was assigned the responsibility for implementing the FEMA/NIST plan. To date, there have been a number of documents published by the ALA that help form the basis of evaluation or design guidelines for different lifelines.
* In 1997 NCEER changed its name to the Multidisciplinary Center for Earthquake Engineering Research (MCEER). © 2003 by CRC Press LLC
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22.3 Nonlinearity of Earthquakes The United States has been relatively fortunate not to have experienced a major earthquake (M7 or greater) in a highly urbanized area in modern times. The closest approach to this situation was the January 17, 1994 Northridge event. This earthquake occurred directly beneath the San Fernando Valley, a suburban area of Los Angeles. However, because of the depth and size (M6.7) of the earthquake, damage was generally limited to the suburban, moderately built-up area. A larger event, particularly one that might occur along one of the blind thrust faults in the Los Angeles area (e.g., the Elysian Park ramp fault that is located directly under downtown Los Angeles) would definitely cause an order of magnitude more damage than was observed in the January 1994 event. California has been host to a whole series of moderate and larger earthquakes. Table 22.1 shows a reverse chronological list of earthquakes that have affected California in the last 30 years or so. As is evident from this list, there are three events that dominate the loss picture. These are the 1971 San Fernando, 1989 Loma Prieta, and 1994 Northridge earthquakes. The total economic loss (only direct costs or losses) for all earthquakes since the San Fernando event is about $53 billion (in 1994 dollars). The three earthquakes mentioned previously account for over 98% of this total. The total number of deaths and injuries for all earthquakes are 190 and 16,000, respectively (see Table 22.1). The response and recovery from these California earthquakes has been quite effective, particularly from the standpoint of lifelines. In most cases, service was restored to affected populations in a matter of days and weeks. For example, as shown in Table 22.2, the longest restoration associated with a damaged lifeline system (not including transportation systems) in the Northridge earthquake was 12 days (natural gas system). Further, it is clear from Table 22.2 that the outages that were observed in the Northridge earthquake affected a very small percentage of the serviced population. It is also interesting to note in Table 22.2 that those lifeline systems that are eligible for federal assistance (LADWP, MWD, L.A. City and Caltrans) account for about 95% of the total losses in the table. Therefore, restoration of these systems is not just a Los Angeles or California problem, but also a federal problem. In a large event in an urbanized area, the response and recovery efforts may increase by many times. Unfortunately (or maybe fortunately), we don’t know how response and recovery systems will respond when demand for resources greatly exceeds available capacity, because we have not experienced a catastrophic event in the United States in recent times. In order to understand the resiliency of these systems, we need to learn from foreign earthquakes. The earthquake that occurred in Kobe, Japan exactly 1 year after the Northridge earthquake probably represents the closest available example of a nonlinear earthquake. Nonlinear earthquakes are defined in this chapter as events where the demand for resources greatly exceeds available capacity. Because manpower and repair resources will be overextended, restoration times will be stretched and delayed. Resources will eventually have to come from areas very distant from the affected areas. In addition, damage to local and regional transportation systems may also add an additional dimension to response times. In order to demonstrate this point, Table 22.3 shows an illustrative regional earthquake damage index. This index is nothing more than a qualitative attempt to describe the risk a particular region or area may have, given certain geographical and earthquake parameters. For example, within this context, it is assumed that risk or subsequent postearthquake damage can be described by two parameters: earthquake magnitude and proximity to urbanized region. The underlying theory here is that significant damage or risk only occurs when unfavorable values of each parameter occur at the same time. That is, risk is high if the earthquake, whether large or moderate, occurs in a densely populated area. In order to provide some quantitative scale to these indices, a simple and somewhat arbitrary set of descriptions are provided for each range of damage indices. In effect, what is being suggested here are the results of a general or crude seismic risk analysis. To illustrate this concept of nonlinearity, damage data from five different earthquakes have been collected from the literature. Table 22.4 presents the author’s best opinion of damage index levels for the various earthquakes.
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TABLE 22.1 Significant California Earthquakes, 1971 to Present Location
Year
Magnitude
Deaths
Injuries
Damage ($ Million)
Northridge Big Bear Landers Cape Mendocino Joshua Tree Sierra Madre Upland Loma Prieta Imperial Co Whittier Chalfant Oceanside Palm Spring Morgan Hill Coalinga Eureka Owens Valley Livermore Imperial Valley Gilroy-Hol Santa Barbara Pt. Magu San Fernando TOTAL
1994 1992 1992 1992 1992 1991 1990 1989 1987 1987 1986 1986 1986 1984 1983 1980 1980 1980 1979 1979 1978 1973 1971
6.7 6.7 7.6 7.1 6.1 5.8 5.5 7.1 6.6 5.9 6.0 5.3 5.9 6.2 6.4 7.0 6.2 5.5 6.4 5.9 5.7 5.9 6.4
57 — 1 — — 1 — 63 — 8 — 1 — — — — — 1 — — — — 58 190
9,000+ — 402 356 10 30+ 38 3,757 94 200+ — 28 — 27 47 8 13 44 91 16 65 — 2,000 16,226
44,000a 48.5 48.5 51.5 04 36 11.2 6,500 3.2 430 0.5 0.9 6.6 13.2 42 2.7 3 17.5 50.6 0.8 13.8 3 1,766 53,049.54
a
.
Source: Data from Eguchi, R.T. et al. 1998. Earthquake Spectra, 14.
TABLE 22.2 Lifeline Performance During the January 17, 1994 Northridge Earthquake Lifeline LADWP (Power) SoCal Edison LADWP (Water) MWD LA City (Sewer) SoCal Gas PacBell GTE Caltrans Total
Population w/o Service
Restoration Time
Damage ($ Million)
100% 25% ~15% — — 3% 8 communities <1% —
90% in 1 day 99.9% in 1 day 8 days — — 12 days — — —
136 0.5 44 5 36 60 26 3.5 1,450 1,761
Source: Eguchi, R.T. 1995. Proceedings of International Symposium on Public Infrastructure Systems Research, C.-K. Choi and J. Penzien, Eds., September 25–27, Seoul, Korea, pp. 109–118. With permission.
Figure 22.1 shows a plot of repair costs per customer for electric power systems for the five events, including the Northridge and Kobe events. The repair costs are associated with damaged electric power systems and represent very coarse estimates at best. Therefore, the figure is more illustrative than scientific. Figure 22.1 shows that there is a tendency for these normalized repair costs to increase in a nonlinear fashion with the simplified damage index. All of the U.S. events are well below the Kobe earthquake, both in terms of normalized repair cost and index. Therefore, perhaps the Kobe event may suggest the trend if we were to experience a major earthquake (M7 event or higher) in a highly urbanized area of the United States. It is hoped that this simple illustration points out the need to examine lifeline damage and restoration issues for large urban earthquakes. © 2003 by CRC Press LLC
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TABLE 22.3 Regional Earthquake Damage Index Magnitude Range Proximity to Urbanized Region
<5
5 to 6
6 to 7
7 to 8
>8
0 2 2
1 4 5
3 6 7
5 8 9
7 9 10
Remote Close Direct hit
Note: 0 = No impact; 1–3 = Minor regional damage; no major disruption, economic or otherwise. 4–6 = Moderate regional damage; measurable economic loss; recovery near immediate. 7–8 = Major damage; substantial economic loss; recovery takes weeks. 9–10 = Catastrophic damage; economic infrastructure significantly damaged; full recovery takes months and perhaps years. Source: Eguchi, R.T. 1995. Proceedings of International Symposium on Public Infrastructure Systems Research, C.-K. Choi and J. Penzien, Eds., September 25–27, Seoul, Korea, pp. 109–118. With permission.
TABLE 22.4 Estimated Repair Costs for Electric Power Systems Earthquake
Magnitude
Proximity to Urbanized Region
Repair Cost ($) per Customer
Damage Index
1971 San Fernando (SF) 1986 Palm Springs (PS) 1989 Loma Prieta (LP) 1994 Northridge (NOR) 1995 Kobe (KOBE)
6.4 5.9 7.1 6.7 ~7
Direct Hit Remote Remote Direct Hit Direct Hit
$30 $1 $7 $100 $1500
7 1 5 7 9
Repair Costs ($) per Customer
Source: Eguchi, R.T. 1995. Proceedings of International Symposium on Public Infrastructure Systems Research, C.-K. Choi and J. Penzien, Eds., September 25–27, 1995, Seoul, Korea, pp. 109–118. With permission. 10000 KOBE 1000 NOR 100 SF
LP
10 PS 1 0
2
4
6
8
10
Regional Earthquake Damage Index
FIGURE 22.1 Repair costs per customer for several recent earthquakes: electric power systems. (From Eguchi, R.T. 1995. Proceedings of International Symposium on Public Infrastructure Systems Research, C.-K. Choi and J. Penzien, Eds., September 25–27, 1995, Seoul, Korea, pp. 109–118. With permission.)
22.4 Indirect Economic Losses The failure of lifeline systems in large earthquakes can be devastating, hampering both response and recovery. Recent events, such as the 1994 Northridge and 1995 Kobe earthquakes, have demonstrated that indirect impacts associated with the failure of lifeline systems may far outweigh the direct costs associated with system repair. As a result, the problem of quantifying possible indirect losses is currently receiving increased attention. The performance of electric power systems is generally measured by the repair costs resulting from actual disasters. In the measurements, the indirect losses associated with factors such as utility outages, outage time, or the effects on dependent businesses are largely ignored. This is primarily due to the lack of statistical data or actuarial experience to quantify these impacts. In 1998, the Multidisciplinary Center © 2003 by CRC Press LLC
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TABLE 22.5 Repair Costs and Associated Direct and Indirect Economic Losses Due to the Failure and Disruption of Electric Power Service in a Large New Madrid Earthquake Loss Type
Amount ($Mill)
% of Total Loss
Ratio to Repair Costs
Repair costs Postearthquake direct losses Postearthquake indirect losses Total losses
401 787 2,180 3,368
12 23 65 100.0
1 2 5 —
Source: Shinozuka, M. et al. (eds.). 1998. Engineering and Socioeconomic Impacts of Earthquakes, MCEER Monograph 2, Multidisciplinary Center for Earthquake Engineering Research, Buffalo, NY. With permission.
for Earthquake Engineering Research (MCEER) outlined an approach for simulating these impacts using electric power systems as an example. These methods are documented in a monograph prepared by MCEER [Shinozuka et al., 1998]. Table 22.5 contains results from that study. The table lists expected repair costs to electric power facilities and the direct and indirect losses that would be incurred if a large earthquake in the New Madrid Seismic Zone were to occur today. The total repair cost was derived from data produced by Chang et al. [1996]. The results of the Chang report indicate that repair costs to major substations in a large New Madrid earthquake could be as high as $400 million. Most of this damage would occur in major gate stations. The direct and indirect economic losses were taken from Shinozuka et al. [1998]. Direct losses were interpreted as those associated with gross output losses that consider no bottleneck effect. In other words, each economic sector in a region (e.g., construction, wholesale, retail, etc.) would be impacted only by a disruption of electric power service and not additionally by supply input bottlenecks from other sectors. Indirect losses are then calculated by subtracting these nonbottleneck losses from those gross output losses that do account for bottleneck effects. These indirect losses model the so-called multiplier or ripple effects. A comparison of the various losses in Table 22.5 shows that indirect losses are approximately 5 times larger than expected repair costs and about 2.5 times larger than direct losses. More importantly, the combined total of direct and indirect losses is about seven times larger than expected repair costs. This ratio is significant since, in most earthquakes, the only economic loss data generally reported by electric power utility companies are the total repair costs. Therefore, the full economic impact of electric power failure and disruption is, in general, grossly understated.
22.5 Cost-Effective Mitigation Strategies With the recent wave of natural disasters in the United States (Hurricanes Andrew and Floyd, the Northridge earthquake, and the 1993 Midwest floods), it is becoming imperative that repair programs and strategies include mitigation elements. That is, the United States, as a nation, should attempt to improve the resistance of its lifeline structures to natural hazard effects at every opportunity possible. It has been shown in many examples that damage to structures or systems can be reduced if prudent planning is implemented. One of the best examples of cost-effective mitigation measures is the Caltrans program started immediately after the 1971 San Fernando earthquake. A report entitled “The Continuing Challenge: The Northridge Earthquake of January 17, 1994,” prepared for the California Department of Transportation by a Seismic Advisory Board formed by the Governor of California, presents a summary of Caltrans’ seismic retrofit program. Two of the major conclusions of the report were: 1. “All structures in the region of strong shaking [in the Northridge area] that were retrofitted since 1989 performed adequately.” 2. “The Board’s conclusion is that if the seven collapsed bridges had been retrofitted, they would have survived the [Northridge] earthquake with little damage.” © 2003 by CRC Press LLC
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TABLE 22.6 The Caltrans Bridge Retrofit Program Status as of June 1, 1994 Category of Structure
Estimated Total Cost ($ Million)
Construction Complete
Construction Under Way
Remaining
Single Col. Retrofit Multiple Col. Retrofit Toll Bridge Retrofits Total
$120 $1,650 $650 $2,420
87% 2% 0%
13% 7% 20%
0% 91% 100%
Source: Seismic Advisory Board, 1994.
The cost-effectiveness of the retrofit program is further justified by the data contained in one of the tables of the report. This table, which is reproduced here as Table 22.6, states that the total estimated cost of retrofit, by category of structure, for all seismically vulnerable bridges is about $2.4 billion. This total should be compared to the estimated cost of repair to Caltrans bridge structures that were damaged as a result of the Northridge earthquake ($1.5 billion). If the conclusions of the Caltrans report are valid, repair costs during Northridge could have been eliminated, or at least greatly reduced, if that money had been spent to complete the retrofit program. This is just one very real example of mitigation activities being clearly cost-effective.
22.6 Federal and Industry Lifeline Initiatives The U.S. federal government has historically played a major role in facilitating research and seismic evaluation programs for lifelines. With the reauthorization of the National Earthquake Hazards Reduction Program (NEHRP), Congress mandated that the Federal Emergency Management Agency (FEMA), in consultation with National Institute of Standards and Technology (NIST), develop a plan for assembling and adopting national seismic design standards for all lifelines, public and private. This plan was developed and was released in the mid-1990s. Important in this plan was the recommendation that public and private partnerships be developed in order to effect implementation. In 1998, FEMA, in partnership with the American Society of Civil Engineers (ASCE), formed the American Lifelines Alliance (ALA). The goal of the ALA is to establish methodologies for assessing lifeline performance and to identify actions to reduce their risk from earthquakes. The ALA is currently soliciting, funding, and managing specific projects that will improve or extend industry practices in the design and construction of utility systems (electric power, gas and liquid fuels, telecommunications, water and wastewater) and transportation systems (highways, waterways, rail, ports and harbors). The end products will be incorporated into national consensus guidelines that will be administered by different organizations (e.g., ASTM). For more information on this initiative, the reader can visit www.americanlifelinesalliance.org.
22.7 Lifeline Seismic Risk Several major lessons can be drawn from this brief look at lifeline earthquake engineering: 1. Lifelines have been shown to be extremely vulnerable to earthquakes and failures of these systems can result in significant direct and indirect loss. 2. This recognition began over 30 years ago, and steady progress has been maintained to develop broad, practical mitigation programs. 3. The United States has been fortunate in that recent damaging earthquakes have been moderate in size and/or have not occurred in highly urban areas. The Kobe earthquake is a guide for how restoration may be affected by inadequate resources, illustrating the nonlinear effects of earthquakes. 4. Indirect losses resulting from the failure or disruption of lifelines are many times the losses associated with the repair of the damaged systems. © 2003 by CRC Press LLC
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5. Mitigation of future risks through cost-effective retrofit or design strategies has been shown to be effective, as demonstrated by the performance of Caltrans facilities during the 1994 Northridge earthquake. 6. One important initiative that is being administered by FEMA and ASCE has the potential for significantly improving the earthquake performance of lifelines in future events. This initiative — the American Lifelines Alliance — calls for the development and adoption of seismic design standards for all public and private lifelines.
Defining Terms Bottleneck effect — Phenomena in economic flows where a shortage of supply of an item, due perhaps to damage to a factory manufacturing the item, results in economic disruption greatly out of proportion to the ordinary value of the item (for want of a nail…the kingdom was lost). Lifelines — Utilities (water, wastewater, electric power, gas, telecommunications) and transportation (highways, railroads, air, and water transport) systems whose loss of function in an urban area results in major disruption and potential loss of life. NEHRP — Earthquake Hazards Reduction Program established by Congress in 1977 (Public Law 95–124) to “reduce the risks life and property from future earthquakes in the United States through the establishment and maintenance of an effective earthquake hazards reduction program” [amended 1990 Public Law 101–614]. There are four NEHRP agencies: FEMA (Federal Emergency Management Agency), NIST (National Institute of Standards and Technology), NSF (National Science Foundation), and the USGS (United States Geological Survey). Nonlinear — Earthquakes where the demand for resources greatly exceeds available capacity.
References Chang, S.E., Seligson, H.A., and Eguchi, R.T. 1996. “Estimation of the Economic Impact of Multiple Lifeline Disruption: Memphis Light, Gas and Water Case Study,” Technical Report MCEER-96–0011, Multidisciplinary Center for Earthquake Engineering Research, Buffalo, NY. Eguchi, R.T. 1995. “Mitigating Risks to Infrastructure Systems through Natural Hazard Reduction and Design,” Proceedings of International Symposium on Public Infrastructure Systems Research, C.-K. Choi and J. Penzien, Eds., September 25–27, Seoul, Korea. Eguchi, R.T., Goltz, J.D., Taylor, C.E. et al. 1998. “Direct Economic Losses in the Northridge Earthquake: A Three-Year Post-Event Perspective,” Earthquake Spectra, 14, 245–264. Seismic Advisory Board. 1994. The Continuing Challenge, The Northridge Earthquake of January 17, 1994, Report to the Director, California Department of Transportation, Chairman: George W. Housner. Shinozuka, M., Rose, A., and Eguchi, R. (Eds.). 1998. Engineering and Socioeconomic Impacts of Earthquakes, MCEER Monograph No. 2, Multidisciplinary Center for Earthquake Engineering Research, Buffalo, NY.
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23 Buried Pipelines 23.1 Introduction 23.2 Pipeline Performance in Past Earthquakes Wave Propagation Damage · PGD Damage · System Performance
23.3 PGD Hazard Quantification Fault · Landslide · Lateral Spreading
23.4 Wave Propagation Hazard Quantification Effective Propagation Velocity · Ground Strain and Curvature Due to Wave Propagation · Effects of Variable Subsurface Conditions
23.5 Pipe Failure Modes and Failure Criterion Continuous Pipeline · Segmented Pipeline
23.6 Pipeline Response to Faulting Continuous Pipelines · Segmented Pipelines
23.7 Pipeline Response to Longitudinal PGD Continuous Pipelines · Influence of Expansion Joints · Segmented Pipelines · Distributed Deformation
23.8 Pipeline Response to Transverse PGD Continuous Pipelines · Segmented Pipelines
23.9 Pipeline Response to Wave Propagation Continuous Pipelines · Segmented Pipeline in Tension · Segmented Pipeline in Compression
23.10 Countermeasures to Mitigate Seismic Damage Routing and Relocation · Isolation from Damaging Ground Movement · Reduction of Ground Movements · High Strength Materials · Flexible Materials and Joints
Michael J. O’Rourke Rensselaer Polytechnic Institute Troy, NY
Defining Terms References Further Reading
23.1 Introduction This chapter addresses the earthquake performance of buried pipelines. Buried pipelines are vital to modern society, carrying water, gas and liquid fuels and other materials to a city’s residents, and conveying wastewater away. Historically, buried pipelines have sustained major damage in past earthquakes (Figure 23.1), so this chapter begins with a review of buried pipeline performance in past earthquakes. We then examine how seismic hazards are quantified for buried pipelines, the failure mechanisms of buried pipelines, and the response of continuous and segmented pipelines to wave propagation and various types of permanent ground deformation. The final section addresses various mitigation measures.
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FIGURE 23.1
Earthquake Engineering Handbook
Barrel break in 800-mm water transmission line, Kobe earthquake. (Photo: C. Scawthorn)
For at least the past 75 years, engineers have been taking earthquake effects into account when designing buried pipelines. In the San Francisco Bay area, for example, both Bay Division Pipeline numbers 1 and 2, which are the main water pipelines providing water service to the city and county of San Francisco, cross the Hayward fault. The original design of these two pipelines (in the 1920s and 1930s) incorporated expansion joints spaced about 60 ft on each side of what was presumed to be the Hayward fault trace. This approach demonstrated an understanding more than 70 years ago of the behavior of buried pipeline subject to earthquake effects. That is, irrespective of whether the seismic load is permanent ground deformation or wave propagation, the loading is displacement controlled. Hence successful design of buried pipelines for seismic effects typically involves compliant materials and systems, which can accommodate the imposed ground deformation, as opposed to stiff or brittle components which “carry the load.” In this regard, continuous pipe (e.g., welded steel) typically is better able to accommodate a given amount of ground movement than segmented pipe. Similarly, lateral ground movements, which tend to place a pipe (either continuous or segmented) into flexure, are more easily accommodated than longitudinal movements, which induce axial strain.
23.2 Pipeline Performance in Past Earthquakes For buried pipelines, seismic hazards can be classified as being either wave propagation hazards or permanent ground deformation (PGD) hazards. There have been some events where pipe damage has been due only to wave propagation. An example is damage in Mexico City caused by the 1985 Michoacan earthquake. More typically, pipeline damage is due to a combination of hazards. For example, O’Rourke et al. [1985] noted that roughly half the pipe breaks in the 1906 San Francisco event occurred within liquefaction-induced lateral spreading zones while the other half occurred over a somewhat larger area where wave propagation was apparently the dominant hazard. That is, PGD damage typically occurs in isolated areas of ground failure, with high damage rates, while wave propagation damage occurs over much larger areas, but with lower damage rates. Wave propagation hazards are characterized by the transient strain and curvature in the ground due to traveling wave effects. PGD (such as landslide, liquefaction-induced lateral spread, and seismic settlement) hazards are characterized by the amount, geometry, and spatial extent of the PGD zone. The faultcrossing PGD hazard is characterized by the permanent horizontal and vertical offset at the fault and the pipe–fault intersection angle. © 2003 by CRC Press LLC
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I
1.0 E
0.50
F
Pipe Damage Ratio (repairs per kilometer)
K Best Straight Line (Pts. A thru K)
0.20
J
A
0.10 Barrenberg Line (Pts. A thru D)
G
0.05 B C
0.02 0.01
H D
0.005
0.002 0.0001
1
2
5
10
20
50
100
Peak Horizontal Particle Velocity (cm/sec)
FIGURE 23.2
Wave propagation damage to common water system pipe vs. peak horizontal particle velocity.
Often the first step in the seismic upgrade of a pipeline system is an evaluation of the likely amounts of damage in the existing system due to potential earthquakes. For buried pipelines, empirical correlations between observed seismic damage and some measure of ground motion are typically used.
23.2.1 Wave Propagation Damage It appears that Eguchi was the first to separate wave propagation damage and PGD damage. For wave propagation, Eguchi [1983] summarized pipe-break rate vs. Modified Mercalli Intensity (MMI) for several earthquakes in the United States, and developed fragility relations for six different pipeline materials subject to wave propagation only. Eguchi [1991] modified that relationship and obtained a bilinear curve where the damage rates increase fairly rapidly for MMI ≤ 8, and then more slowly for MMI > 8. Based on data from three U.S. earthquakes, Barenberg [1988] established an empirical relation between seismic wave propagation damage to cast iron (CI) pipe and peak horizontal ground or particle velocity. Note that one would expect pipe damage to correlate fairly well with peak ground velocity since, as will be shown later, ground strain and hence pipe strain, is a function of Vmax. Including additional data from three other earthquakes, O’Rourke and Ayala [1993] prepared a plot of wave propagation damage rate vs. peak ground velocity, which includes CI pipe, concrete pipe, prestressed concrete pipe, and asbestos cement pipe. Both relations are shown in Figure 23.2, where the O’Rourke and Ayala best-fit straight line (point A through K) gives higher damage rates than Barenberg’s. The somewhat higher estimated damage rates using the O’Rourke and Ayala relation were not due to the inclusion of pipe materials other than cast iron, but rather are thought to be due at least in part to the effects of corrosion and variable subsurface conditions. More recently, various researchers have developed empirical wave propagation damage relations for different pipe materials [Eidinger et al., 1995] or for different diameter ranges [Honegger, 1995]. O’Rourke and Jeon [1991] developed a pipe damage relation, similar in form to Figure 23.2, for the 1994 Northridge event. However, there is almost an order of magnitude difference between estimated damage rates using these two relations. It is believed that the difference is due to the types of wave propagation; primarily surface waves for Figure 23.2 and exclusively body waves for Northridge data. © 2003 by CRC Press LLC
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7
Pipeline Damage (breaks/1000 ft)
6
Pre-1960 CI
5
4
Pre-1940 RS & WS
3
AWSS
2 Pre-1989 D I 1 Post-1940 WS & Post 1989 D I 0 0
10
20
30
40
50
60
Permanent Ground Displacement (inches) FIGURE 23.3 Pipe breaks vs. permanent ground displacement.
23.2.2 PGD Damage There are a variety of patterns of PGD. One type of PGD is localized abrupt (or concentrated) relative displacement, such as at the surface expression of a fault, or at the margins of a landslide. The second type of PGD is spatially distributed permanent displacement, which can result, for example, from liquefaction-induced lateral spreads, or ground settlement due to soil consolidation. For localized abrupt PGD, pipeline damage mainly occurs around the ground rupture trace. On the other hand, breaks for spatially distributed PGD may occur everywhere within the PGD zone. Empirical damage relations for both types of PGD (spatially distributed and abrupt) have been developed. 23.2.2.1 Spatially Distributed PGD Porter et al. [1991] developed an empirical relation for bell-and-spigot CI water pipes with lead and oakum joints. Shown as “Pre-1960 CI” in Figure 23.3, the damage rate is a function of permanent ground displacement. A bilinear curve is fitted to the data from the 1906 San Francisco and 1989 Loma Prieta earthquakes. The initial portion of the curve PGD < 5 in. (13 cm) is based on damage information for the Marina District in San Francisco during the 1989 Loma Prieta event (vertical settlements) while the later portion (PGD > 5 in.) is based on the 1906 San Francisco event (lateral spreads). When considering the PGD relation in Figure 23.3, one should keep in mind the difference in pipe response to transverse and longitudinal PGD. In this sense, the vertical settlement data (from the 1989 Loma Prieta event) used by Porter et al. [1991] corresponds to transverse PGD. Hence, caution should be used in applying these results to situations where one expects horizontal ground movement parallel to the pipe axis (i.e., longitudinal PGD). Finally, it should be noted that recent research (Prof. T. O’Rourke, personal communication) suggests that Marina District pipe damage in the 1989 Loma Prieta event was due to large transient strains resulting from shaking (wave propagation) of the “soupy” liquefied subsoil layer. Although the final (permanent) settlement, used by Porter et al., may correlate positively with the large transient strains, which apparently actually caused the damage, caution should be exercised for situations with PGD < 5 in. (13 cm). This is particularly true for settlement of dry sand where large transient strains are not expected. For PGD damage to continuous welded steel pipes, no empirical relation determined directly from observed damage is available. However, Porter et al. developed a pseudo-empirical relation based on the damage rate of CI pipelines vs. PGD, and a comparison of the damage rates for steel pipes and CI pipes © 2003 by CRC Press LLC
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from Hamada [1989] and Eguchi [1983]. Porter et al. assume that the rate of damage to gas-welded steel pipes was half of that for CI pipes. Similarly, the vulnerability of arc-welded steel pipes was taken as 12.5% of CI pipes. Porter’s pseudo-empirical relations for steel pipes and various other materials are also shown in Figure 23.3. More recent studies have suggested other empirically based relations between damage and the amount of ground movement. For example, Heubach [1995] suggests that expected damage to CI pipe with rigid joints is roughly a factor of four larger than that for modern welded steel pipelines. Along similar lines, Eidinger et al. [1995] propose PGD damage relations that are functions of pipe material and joint type. 23.2.2.2 Localized Abrupt PGD Porter et al.’s relations were obtained for spatially distributed PGD, specifically ground settlement and lateral spread. As such, it probably should not be used to predict damage to pipelines subject to localized abrupt PGD such as at a fault offset. This is because one expects higher pipe strain, for a given amount of PGD movement, where the PGD is abrupt (or concentrated) as opposed to distributed. For fault rupture, Eguchi [1983] presents a relationship between the damage rate and the amount of fault offset. It is based on damage from the 1971 San Fernando earthquake and applies to pipelines within 300 ft (91 m) each side of the predominate line of rupture. The break rate per 1000 feet for CI pipes is about 1.5 for abrupt PGD equal to 10 in. (25 cm) and 4.0 for abrupt PGD equal to 100 in. (2.5 m). However, for the same CI pipes, the break rate due to spatially distributed PGD given in Figure 23.3 is 3.2 for the displacement equal to 10 in. and 7.4 for the displacement equal to 100 in. This result is counterintuitive, since one expects higher pipe strain for abrupt PGD. The author understands that Eguchi currently considers this relation to be a lower bound, with expected damage being possibly a factor of three times the lower bound value.
23.2.3 System Performance There has been a large amount of research work over the past dozen of years or so on pipeline system performance. Notable contributions have been made by Isoyama and Katayama [1982], Sato and Shinozuka [1991], and Markov et al. [1994]. A detailed discussion of overall system modeling and performance is beyond the scope of this chapter, which focuses primarily on component performance, behavior, and design. However, a summary of the results of system performance evaluations as a function of buried pipeline component performance (specifically breaks per unit length) will be discussed briefly. Isoyama and Katayama [1982] evaluated water system performance following an earthquake for two supply strategies: (1) supply priority to nodes with larger demands and (2) supply priority to nodes with lowest demands. These two strategies correspond to the best and worst system performance, which is shown in Figure 23.4. Recently, Markov et al. [1994] evaluated the performance of the San Francisco
FIGURE 23.4
Serviceability index vs. average break rate for post-earthquake system performance evaluation.
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auxiliary water supply system (AWSS), while G&E [1994] did a similar study for the water supply system in the East Bay Municipal Utility District (EBMUD). Their results are also shown in Figure 23.4. Based on these results, NIBS (National Institute of Building Sciences) [1996] proposed a damage algorithm, in which the system serviceability index is a lognormal function of the average break rate.
23.3 PGD Hazard Quantification The principal forms of PGD are: • • • •
Surface faulting Landsliding Seismic settlement Lateral spreading due to soil liquefaction
Whether the buried pipeline fails when subjected to PGD depends, in part, on the amount and spatial extent of the PGD, discussed below.
23.3.1 Fault An active fault is a discontinuity between two portions of the earth crust along which relative movements can occur. The movement is concentrated in relatively narrow fault zones. Principal types of fault movement include strike-slip, normal-slip, and reverse-slip. In a strike-slip fault the predominant motion is horizontal, which deforms a continuous pipe primarily in tension or compression depending on the pipe–fault intersection angle. In normal and reverse faults the predominant ground displacement is vertical. When the overhanging side of the fault moves downward, the fault is normal, which deforms a horizontal pipe primarily in tension. When the overhanging side of the fault moves upward, the fault is reverse, which deforms a horizontal pipe primarily in compression. Various empirical relations between fault displacement and moment magnitude have been proposed, and are discussed in more detail in Chapter 4 of this handbook.
23.3.2 Landslide Landslides are mass movements of the ground which may be triggered by seismic shaking. A large number of systems have been developed to classify landslides. One based on the different effects on pipelines was established by Meyersohn [1991]. Empirical methods have been used to determine upper bounds for the occurrence of landslides. Figure 23.5 shows a relation [Applied Technology Council, 1985] in which the maximum distance of observed landslides to the fault rupture zone is plotted as a function of earthquake magnitude — that is, it shows the outer envelope within which landslides may occur. Recent work by Jibson and Keefer [1993] resulted in analytical estimation of the expected amount of landslide movement.
23.3.3 Lateral Spreading Lateral spreads develop when a loose, saturated sandy soil deposit is liquefied due to seismic shaking. Liquefaction causes the soil to lose its shear strength, which in turn results in the flow or lateral movement of liquefied soil. Although the ground movement is primarily horizontal, Towhata et al. [1991] observed that vertical soil movement often accompanies liquefaction-induced lateral spreading. However, the vertical component is typically small and will be disregarded herein. In terms of pipeline response, two situations are possible (Figure 23.6A): 1. In the first case, such as at the Ogata Primary School site during the 1964 Niigata event, the top surface of the liquefied layer is essentially at the ground surface. For this first case, a pipeline is subject to horizontal force due to liquefied soil flow over and around the pipeline, as well as uplift or buoyancy forces. © 2003 by CRC Press LLC
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1000 500
Maximum Distance of Landslide From Fault- Rupture Zone (km)
200 100 50 20 10 5 2 Disrupted Slides & Falls
1
Coherent Slides
0.5
Lateral Spreads & Flows 0.2 0.1 4.0
4.5 5.0
5.5
6.0
6.5 7.0
7.5
8.0
8.5 9.0 9.5
Magnitude (M)
FIGURE 23.5
Occurrence of landslide vs. magnitude of earthquake.
2. In the second case, such as at the Mission Creek site during the 1906 San Francisco event, the top surface of the liquefied layer is located below the bottom of a typical pipeline. That is, the pipeline is contained in a nonliquefied surface soil layer (or cap layer) which rides over the liquefied layer. For this second case, the pipeline is subject to horizontal forces due to nonliquefied soil–structure interaction but not subject to buoyancy effects. The direction of movement for the lateral spread is controlled by geometry (Figure 23.6B). When the lateral spread occurs at or near a free face, the movement is generally towards the free face. When the lateral spread occurs away from a free face, the movement is down the slope of the ground surface or down the slope of the bottom of the liquefied layer. The “towards a free face” spreads typically are observed from 10 to 300 m (33 to 984 ft) away from the free face, with an average value of 100 m [Bartlett and Youd, 1992]. For “PGD away from a free face” spreads, the observed slope is from 0.1 to 6% with an average value of 0.55%. There are four geometric characteristics of a lateral spread which influence pipeline response in a horizontal plane. With reference to Figure 23.6b, these are the amount of PGD movement δ, the transverse width of the PGD zone W, the longitudinal length of the PGD zone L, and the pattern or distribution of ground movement across and along the zone. 23.3.3.1 Amount of PGD In general, the potential for PGD to induce pipe damage is related to the amount of ground movement, the length and width of the PGD zone, and the pattern of deformation. Predicting the amount of ground displacement due to soil liquefaction is a challenging problem. Nevertheless, a number of studies have addressed this issue. Work by Hamada et al. [1986] suggests that the amount of PGD induced by liquefaction is closely related to the geometric configuration of the estimated liquefied layer. They proposed the following regression formula for the magnitude of horizontal PGD, δ, in meters: δ = 0.75 h © 2003 by CRC Press LLC
3
θg
(23.1)
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CAP LAYER
Lateral Spread
Subsidence
LIQUEFIABLE LAYER Float (Buoyancy) Viscous Drag (Flow Failure) Loss of Bearing
(A)
Length L
A
A
Width W
B
δ B (a) PlanView
W L (b)Transverse Pattern
(c) Longitudinal Pattern
(B) FIGURE 23.6 (A) Lateral spreading with or without cap layer; (B) geometric characteristics of a lateral spread.
where h is the thickness of the liquefied layers in meters, and θg is the slope of the lower boundary of the liquefied layer or the ground surface (%), whichever is larger. Note that the Hamada et al. relation does not distinguish between the amount of expected PGD at a free face as opposed to that for gently sloping ground. In addition, the thickness of the liquefied layer is, in a sense, a pseudo-parameter that accounts for the amount of ground shaking (related to earthquake magnitude and distance) as well as the soil characteristics at the site. According to Bartlett and Youd [1992], it produces a reasonable estimate for earthquakes with magnitude around 7.5 and epicenter distance in the 20 to 30 km range. Youd and Perkins [1987] introduced the concept of a liquefaction severity index (LSI), which is defined as the amount of PGD in inches, associated with lateral spreading on gently sloping ground and poor © 2003 by CRC Press LLC
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soil conditions. LSI is arbitrarily truncated at 100. Youd and Perkins established a correlation between LSI, earthquake magnitude, and distance for the western United States as follows: log LSI = –3.49 – 1.86 log Rd + 0.98 Mw
(23.2)
where Rd is the distance from the epicenter to the site, in kilometers, and Mw is the earthquake magnitude (moment magnitude). Using that correlation as a starting point, and data available for the 1811 to 1812 New Madrid earthquakes, Turner and Youd [1987] propose the following relation for the New Madrid area: log LSI = 4.252 – 1.276 log Rd
(23.3)
Two separate equations are provided to account for differences in attenuation of strong ground motion east and west of the Rocky Mountains. Note that LSI given above is not a function of local soil parameters (i.e., applies to the “worst” possible soil condition) or ground slope (it applies to ground slopes between 0.5 and 5%). In addition, as with Hamada’s work, the LSI relation does not distinguish between the expected amount of PGD at a free face as opposed to that for gently sloping ground condition. Using data from six U.S. and two Japanese earthquakes, Bartlett and Youd [1992] recently developed two empirical relations for the expected amount of PGD due to liquefaction. The first is for lateral spreads down gentle ground slopes and the second is for lateral spreads at a free face. For gently sloping ground condition, the relation is: log (δ + 0.01) = –15.787 + 1.178 M – 0.927 log Rd – 0.013 Rd + 0.429 log S + 0.348 log T15 + 4.527 log (100 – F15) – 0.922 D50
(23.4)
For PGD at a free face: log (δ + 0.01) = –15.787 + 1.178 M – 0.927 log Rd – 0.013 Rd + 0.429 log Y + 0.348 log T15 + 4.527 log (100 – F15) – 0.922 D50
(23.5)
where δ M Rd S Y F15 D50 T15
= = = = = = = =
the permanent horizontal displacement of ground (m) the earthquake magnitude the epicentral distance (km) the ground slope (in percent, shown in Figure 23.7A) the free face ratio (in percent, shown in Figure 23.7B) the average fines contents in layer T15 (in percent) the mean grain size in layer T15 (mm) the thickness (m) of saturated cohesionless soils with a corrected Standard Penetration Test (SPT) value less than 15
Both equations include the effects of shaking at the site, soil properties, and site topography. For a given amount of ground shaking (i.e., fixed magnitude and epicentral distance), the parameters that most strongly influence the amount of PGD are the average fines contents, followed by the mean grain size B
Ground surface A
B A Slip Surface
(a) Ground Slope, S = 100A/B FIGURE 23.7
(b) Free Face Ratio,Y = 100A/B
Elevation view showing (a) ground slope and (b) free face ratio.
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and the ground slope/free face ratio. The accuracy of the Bartlett and Youd [1992] empirical relations is relatively good, in that predicted values are generally within a factor of two of the observed values. As such, they are arguably the best currently available relations for use in the western United States. 23.3.3.2 Spatial Extent The width and the length of the PGD zone have a strong influence on pipe response to PGD. Unfortunately the currently available information on the spatial extent of lateral spread zones is somewhat limited. Although one expects that the spatial extent of the lateral spread zone strongly correlates with the plan dimensions of the area that liquefied, analytical or empirical relations are not currently available. Information on observed values for the spatial extent of the lateral spread zones has been developed by Suzuki and Masuda [1991]. For the 1964 Niigata and 1983 Nihonkai-Chubu earthquakes (both in Japan), almost all of the observed widths are distributed in the range of about 80 to 600 m (262 to 1968 ft), with the lateral displacement typically less than 2 m. Because of such variations, it seems that the expected length and width of a lateral spread zone, particularly for site-specific studies, should be based upon the expected plan area of liquefaction as opposed to the estimated ground movement. The response of buried pipelines to PGD is influenced by the pattern of deformation, that is, the variation of permanent ground displacement across the width (Figure 23.6B, part [b]) or along the length (Figure 23.6B, part [c]) of the lateral spread zone. The study by Hamada et al. [1986] of liquefaction in the 1964 Niigata and 1983 Nihonkai-Chubu earthquakes provides a wealth of information on observed longitudinal PGD patterns. Figure 23.8 shows longitudinal PGD observed along 5 of 27 lines in Noshiro City resulting from the 1983 Nihonkai-Chubu earthquake. In Figure 23.8 the height of the vertical line is proportional to the observed horizontal PGD at the point. 0 50 100 (m) 5 4 3 2 1
Permanent Ground Displacement (m)
(a) Section Line N-2
0
50
100 (m) 5 4 3 2 1
(b) Section Line S-15
0
50
100 (m) 5 4 3 2 1
(c) Section Line S-16
0
50
100 (m) 5 4 3 2 1
(d) Section Line S-4
0
50
100 (m) 5 4 3 2 1
(e) Section Line S-13
FIGURE 23.8
Observed longitudinal PGD.
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Note that about 20% of the observed patterns (6 out of 27) have the same general shape as Figure 23.8(a). That is, they show relatively uniform PGD movement over the whole length of the lateral spread zone. Information on transverse patterns of PGD, as shown in Figure 23.6B, part (b), is more limited.
23.4 Wave Propagation Hazard Quantification The wave propagation hazard for a particular site is characterized by the peak ground motion parameters (acceleration and velocity) as well as the appropriate propagation velocity. There are two types of seismic waves: body waves and surface waves. Body waves propagate through the earth, while surface waves travel along the ground surface. Body waves are generated by seismic faulting while, for the simplest case, surface waves are generated by the reflection and refraction of body waves at the ground surface. Body waves include compressional waves (P waves) and shear waves (S waves). In compressional waves, the ground moves parallel to the direction of propagation, which generates alternating compressional and tensile strain. For S waves, the ground moves perpendicular to the direction of propagation. The situation for surface waves is somewhat more complex. Rayleigh and Love waves are the two main types of surface waves generated by earthquakes. For the Love waves (L waves), the particle motion is along a horizontal line perpendicular to the direction of propagation, while for R waves the particle motion traces a retrograde ellipse in a vertical plane with the horizontal component of motion being parallel to the direction of propagation. For both L and R waves, the amplitude of motions decreases with depth below the ground surface. Note that if R waves are present, they occur after the arrival of the direct body waves. That is, P waves arrive at a site first, followed by S waves. If surface waves are present, they typically arrive after the body waves.
23.4.1 Effective Propagation Velocity 23.4.1.1 Body Waves For body waves, we consider here only S waves, since S waves carry more energy and tend to generate larger ground motion than P waves. For the S wave, the horizontal propagation velocity, that is, the propagation velocity with respect to the ground surface, is the key parameter. For vertically incident S waves, the apparent propagation velocity is infinite. However, there is typically a small angle of incidence in the vertical plane leading to nonzero horizontal ground strain. O’Rourke et al. [1982] have studied the apparent horizontal propagation velocity, C, for body waves. They developed an analytical technique, utilizing all three components of motion at the ground surface, and a ground motion intensity tensor for evaluating the angle of incidence of S waves. The apparent propagation velocity for S waves is then given by: C=
Cs sin γ s
(23.6)
where γs is the incidence angle of S waves with respect to the vertical and Cs is the shear wave velocity of the surface soils. Using the ground motion intensity method for the 1971 San Fernando and the 1979 Imperial Valley events, as well as more direct techniques for other events, the apparent propagation velocity for S waves ranged from 2.1 to 5.3 km/sec with an average of about 3.4 km/sec. 23.4.1.2 Surface Waves For surface waves, we only consider R waves, since L waves generate bending strains in buried pipelines which, particularly for moderate pipe diameters, are significantly less than axial strain induced by R waves. R waves will generate axial strain in a pipe situated parallel to the direction of wave propagation. Since R waves always travel parallel to the ground surface, the phase velocity of the R waves, Cph, is the apparent propagation velocity. Note that the phase velocity is defined as the velocity at which a transient vertical disturbance at a given frequency, originating at the ground surface, propagates across the surface © 2003 by CRC Press LLC
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FIGURE 23.9
Earthquake Engineering Handbook
Normalized dispersion curve for single layer over a half space.
of the medium. The phase velocity is a function of the variation of the shear wave velocity with depth, and, unlike body waves, is also a function of frequency. For R waves, the wavelength λ, frequency f, and the phase velocity Cph are interrelated by: Cph = λ f
(23.7)
The variation with frequency is typically quantified by a dispersion curve. O’Rourke et al. [1984] developed a simple procedure for determining the dispersion curve for layered soil profiles in which the shear wave velocity increases with depth. Figure 23.9 presents a normalized dispersion curve for a uniform layer of thickness, Hs , with shear velocity, CL, and Poisson’s ratio, νl , over a half space with shear velocity, CH and Poisson’s ratio, νH . The curves are for two values of the shear velocity ratio. The dispersion relationship is not strongly affected by the densities of the layer and half space and those parameters are excluded from Figure 23.9. Considering first the simplest case of a uniform layer over a half space, O’Rourke et al. [1984] found that at low frequencies (Hs f/CL ≤ 0.25), the wavelength is large compared to the layer thickness, and the phase velocity is slightly less than the shear wave velocity of the stiffer half space. That is, the R wave is not greatly affected by the “thin” layer. Conversely, at high frequencies (Hs f/CL > 0.5), the wavelength is comparable to or smaller than the layer thickness, and the phase velocity is slightly less than the shear wave velocity of the layer. The dispersion curve for an arbitrary single layer over a half space can be approximated by: 0.875C H 0.875C H − C L H s f C ph = 0.875C H − − 0.25 , 0.25 CL CL
Hs f ≤ 0.25 CL H f 0.25 ≤ s ≤ 0.50 CL Hs f ≥ 0.50 CL
(23.8)
where f is the frequency in Hz. This technique can also be extended to multiple soil layers.
23.4.2 Ground Strain and Curvature Due to Wave Propagation For the analysis and design of buried pipelines, the induced ground strain and curvature typically characterize the effects of seismic wave propagation. Newmark [1967] developed a simplified procedure to estimate the ground strain, based on a simple traveling wave with a constant wave shape. That is, on © 2003 by CRC Press LLC
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an absolute time scale, the acceleration, velocity, and displacement time histories, for two points along the propagation path, are assumed to differ only by a time lag, which is a function of the separation distance between the two points and the speed of the seismic wave. For such a case, he shows that the maximum ground strain εg (tension and compression) in the direction of wave propagation is given by: εg =
Vm C
(23.9)
where Vm is the maximum horizontal ground velocity in the direction of wave propagation and C is the propagation velocity of the seismic wave. Similarly, the maximum ground curvature, kg , which is the second derivative of the transverse displacement with respect to distance, is given by: kg =
Am C2
(23.10)
where Am is the maximum ground acceleration perpendicular to the direction of wave propagation. These two relations, for ground strain and curvature along the direction of wave propagation, are relatively straightforward. The ground motion parameters Vm and Am — that is, the maximum particle velocity and acceleration (also referred to as the peak ground acceleration, PGA, and the peak ground velocity, PGV) — can be obtained from earthquake records or from attenuation relations. For Rwave propagation, the ground strain parallel to the ground surface is given by Equation 23.9, where C is the phase velocity. However, these relations for ground strain and curvature need to be modified if the direction of interest is not parallel to the direction of wave propagation. Consider the case of S waves. If the pipeline is oriented parallel to the direction of propagation, S waves will induce bending in the pipeline. The corresponding ground curvature is given by Equation 23.10 where C is the apparent propagation velocity with respect to the ground surface given in Equation 23.6. If there is an angle in the horizontal plane between the pipe axis and the direction of propagation, there is a component of ground motion parallel to the pipe axis. The resulting ground strain along the pipe axis is a function of this angle in the horizontal plane. Yeh [1974] has shown that the ground strain is a maximum for an angle of 45° in the horizontal plane: εg =
Vm 2C
(23.11)
where C is the apparent propagation velocity with respect to the ground surface.
23.4.3 Effects of Variable Subsurface Conditions The ground strains and curvatures described above are due to wave propagation effects. The apparent propagation velocity relations apply to relatively uniform soil layering in the horizontal direction. However, as noted by Kachadoorian [1976] and Wang and O’Rourke [1978], damage to buried pipelines is often concentrated in areas with variable subsurface condition (i.e., nonuniform soil properties in a horizontal direction). In a more recent example, Hall [1995] notes relatively large amounts of buried pipeline damage during the 1994 Northridge event in areas where an inclined ground surface or an inclined soil–rock interface exists. It is believed that ground strain for sites with variable subsurface condition is due, in large part, to local differences in site response or site amplification. Nishio et al. [1983] carried out a series of laboratory tests to study the amplification response of ground due to the inclined soil–rock interface. Figure 23.10 shows one of the basic models they considered. The bottom of the model was shaken as a unit, corresponding to vertically incident waves (i.e., no horizontal wave propagation effects). For the single inclined subsurface in Model No. 2 the ground strain was largest © 2003 by CRC Press LLC
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Displacem ent (mm)
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Calculated
Measured
2 1 0
Strain ( x10 -3 )
3.75 2.50 1.25 0 A-7 S-5
S-4
A-6
A-5
A-4
S-3
S-2
S-1 A-2
A-3 A-1
Model No. 2
FIGURE 23.10
Axial strains and model for a half valley.
near the inclined surface. For a valley situation (i.e., two inclined subsurfaces), the ground strain was roughly symmetric about the center of the valley, and ground strain was also largest over the inclined subsurface.
23.5 Pipe Failure Modes and Failure Criterion 23.5.1 Continuous Pipeline The principal failure modes for corrosion-free continuous pipeline with burial depth of about 3 ft or more are tensile rupture and local buckling. Buried pipelines with burial depths less than about 3 ft (i.e., shallow trench installation) may experience beam buckling behavior. Beam buckling has also occurred during postearthquake excavation undertaken to relieve compressive pipe strain. 23.5.1.1 Tensile Failure When strained in tension, corrosion-free steel pipe with arc-welded butt joints is very ductile and capable of mobilizing large strains, associated with significant tensile yielding, before rupture. On the other hand, older steel pipe with gas-welded joints often cannot accommodate large tensile strain before rupture. In addition, welded slip joints in steel pipe do not perform as well as butt-welded joints. The 1994 Northridge event provides a case history of these differences in behavior. According to O’Rourke and O’Rourke [1995], none of the four arc-welded steel pipes with butt joints along Balboa Boulevard suffered tensile rupture when subjected to longitudinal PGD. However, three gas-welded pipes with slip joints suffered tensile rupture when subjected to the same PGD. The strain associated with tensile rupture is generally well above about 4% [Newmark and Hall, 1975]. For analysis and design, an ultimate tensile value of something on the order of 4% is often used, beyond which the pipeline is considered to have failed in tension. 23.5.1.2 Local Buckling Buckling refers to a state of structural instability in which an element loaded in compression experiences a sudden change from a stable to an unstable condition. Local buckling (wrinkling) involves local instability of the pipe wall. After the initiation of local shell wrinkling, all further geometric distortion caused by ground deformation or wave propagation tends to concentrate at the wrinkle. The resulting large curvatures (i.e., strains) in the pipe wall often then lead to circumferential cracking of the pipe wall and leakage. This is a common failure mode for steel pipe. Wave propagation in the 1985 Michoacan (Mexico) event caused this type of damage for a water pipe in Mexico City. PGD caused this type of damage to a liquid fuel pipeline in the 1991 Costa Rica event, and to water and gas pipelines in the 1994 Northridge event. © 2003 by CRC Press LLC
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Based on prior laboratory tests on thin wall cylinders, Hall and Newmark [1977] suggest that compressional wrinkling in a pipe normally begins at a strain of one third to one quarter of the theoretical value. Hence, in terms of a failure criterion, the onset of wrinkling occurs at strains in the range: 0.15 t/R ≤ εcr ≤ 0.20 t/R
(23.12)
where t is the pipe wall thickness and R is the pipe radius. This assumed wrinkling strain is thought to be appropriate for thin wall pipe but somewhat conservative for thicker wall pipe. The additional amount of longitudinal compressive deformation across the wrinkled zone which results in tearing of the pipe wall due to large curvature at individual wrinkles is, at present, not well established. 23.5.1.3 Beam Buckling Beam buckling of a pipeline is similar to Euler buckling of a slender column, in which the pipe or column undergoes a transverse (upward) displacement. The relative movement is distributed over a large distance and hence the pipe compressive strains are not large. As a result beam buckling of a pipeline in a ground compression zone is considered more desirable than local buckling, since the potential for tearing of the pipe wall is less. Intuitively, beam buckling is more likely to occur in pipelines buried in shallow trenches and/or backfilled with loose materials. That is, the beam buckling load is an increasing function of the cover depth. Hence, if a pipe is buried at a sufficient depth, it will develop local buckling before beam buckling. Based on this concept, Meyersohn [1991] determined a critical cover depth by setting the lowest beam buckling stress equal to local buckling stress. Any pipe buried with less cover than the critical depth would experience beam buckling before local buckling. Conversely, if the pipe is buried at a depth more than the critical depth, it will experience local buckling. Figure 23.11 shows the critical cover depth for Grade B and X-60 steel pipes. The shaded areas in the figure correspond to different degrees of backfill compaction. Note that critical depth for X-60 steel is larger than that for Grade B steel. That is, the stronger the pipe, the smaller the possibility of shell wrinkling as opposed to beam buckling. However, as noted by Meyersohn [1991], the t/D ratio is typically less than or about equal to 0.02. Hence, from Figure 23.11, the likelihood of beam buckling of buried pipelines is small since the critical depth is less than typical burial depths. 23.5.1.4 Welded Slip Joints The failure criterion for steel pipelines with arc-welded butt joints is based on the strength of the pipe material itself. However, for steel pipelines with slip joints, riveted joints or oxyacetylene/gas-welded joints, the failure criterion is based on the strength of the joints since it is less than that of the pipe material. Many such steel pipelines have suffered joint failure during past earthquakes. For example, during the 1971 San Fernando earthquake, the Granada Trunk line (1260 mm in diameter) was damaged at its welded slip joints [O’Rourke and Tawfik, 1983]. A number of researchers, including Tawfik and O’Rourke [1985], Moncarz et al. [1987], and Brockenbrough [1990], have analyzed the strength of slip joints. Considering 108 in. (2.74 m) diameter pipe with an inner weld, Moncarz et al. calculated a joint efficiency of 0.4 (strength of joint compared to strength of pipe) by using an inelastic finite element model. This efficiency decreases if there is a gap between the bell-and-spigot walls or if the weld is an outer fillet.
23.5.2 Segmented Pipeline For segmented pipelines, particularly those with large diameters and relatively thick walls, observed seismic failure is most often due to distress at the pipe joints. For example, in the 1976 Tangshan earthquake, Sun and Shien [1983] observed that around 80% of pipe breaks were associated with joints. Axial pull-out, sometimes in combination with relative angular rotation at joints, is a common failure mechanism in areas of tensile ground strain, since the shear strength of joint caulking materials is much © 2003 by CRC Press LLC
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FIGURE 23.11
Earthquake Engineering Handbook
Critical depth of cover for Grade B (a) and X-60 steel (b) pipe.
less than the tensile strength of the pipe. In areas of compressive ground strain, crushing of bell-andspigot joints (i.e., “telescoping”) is a fairly common failure mechanism in, for example, concrete pipes. For small-diameter segmented pipes, circumferential flexural failure has been observed in areas of ground curvature. For example, as observed by O’Rourke et al. [1991], more than 80% of the breaks in CI pipes with small diameters (100 mm to 200 mm [4 to 8 in.]) in the Marina District after the 1989 Loma Prieta earthquake were round cracks in pipe segments close to joints. 23.5.2.1 Axial Pull-out El Hmadi and O’Rourke [1989] summarized the then-available information on joint pull-out failure. Specifically, based on laboratory tests by Prior [1935], they established a cumulative distribution for leakage as a function of the normalized joint axial displacement uuj / d p shown in Figure 23.12. Note that uuj is the joint opening and dp is the joint depth.
FIGURE 23.12
Cumulative distribution function for leakage of lead caulked joints.
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As shown in Figure 23.12, the mean value of the joint opening corresponding to leakage is 0.52 dp with a coefficient of variation of 10%. More recently, laboratory tests on concrete cylinder pipes with rubber-gasketed joints by Bouabid and O’Rourke [1994] suggest that, at moderate internal pressures, the relative joint displacement leading to significant leakage corresponds to roughly half the total joint depth. Hence, it would appear that a relative axial joint extension of roughly half the total joint depth may be an appropriate failure criterion for many types of segmented pipes. 23.5.2.2 Crushing of Bell-and-Spigot Joints As noted by Ayala and O’Rourke [1989], most of the concrete cylinder pipe failures in Mexico City occasioned by the 1985 Michoacan event were due to joint crushing. Krathy and Salvadori [1978] proposed that the crushing failure criterion for concrete pipes can be taken as the ultimate compression force of the concrete core at joints. 23.5.2.3 Circumferential Flexural Failure and Joint Rotation When a segmented pipeline is subject to bending induced by lateral permanent ground movement or seismic shaking, the ground curvature is accommodated by some combination of rotation at the joints and flexure in the pipe segments. The relative contribution of these two mechanisms depends on the joint rotation and pipe segment flexural stiffnesses. For a flexible pipeline system such as ductile iron (DI) pipe with Tyton™ joints or FLEX joints, stress in the pipe segments starts to increase greatly only after the joint rotation capacity, typically about 4° and 15°, for Tyton™ joints or FLEX joints, respectively, is exceeded. On the other hand, for a more rigid segmented pipeline system such as CI pipe with cement/lead joints, ground curvature is accommodated from the start by some combination of joint rotation and flexure in the segments, as will be discussed in more detail later. In terms of failure criterion, it seems reasonable to take a base joint rotation failure/leakage criterion for “standard” segmented pipeline joints as some multiple (say 1.1 to 1.5) of the allowable angular offset for pipe-laying purposes contained in manufacturer’s literature. These allowable offsets are decreasing functions of pipe diameter, typically being 3° to 4° for 12 in. (30.5 cm) and 1.5° to 2° for 30 in. (76.2 cm) diameters, respectively. For CI or asbestos cement (AC) pipes subject to ground curvature, round flexural cracks in segments are a major failure mode. On the other hand, for concrete pipes subject to ground curvature, cracks typically occur at the bell-and-spigot ends due in part to the joint ring eccentricity similar to the slip joint effects mentioned previously. For round flexural cracks, it seems reasonable to use, as a failure criterion, the pipe curvature corresponding to the smaller of the ultimate tensile or compressive strains for the material.
23.6 Pipeline Response to Faulting Surface faulting has been a major cause of pipe breaks during past earthquakes. For example, although only one half of 1% of the area shaken during the 1971 San Fernando earthquake was influenced by the surface faulting, the fault movements resulted in over 1400 breaks in water, natural gas, and sewer pipelines [McCaffrey and O’Rourke, 1983]. In general, there are two modes of behavior for pipe subject to faulting: • Case I: pipes are distressed due to bending (caused by the transverse component of fault offset) and axial tensile force (caused by the longitudinal component). A normal fault and strike-slip fault with the intersection angle between the fault trace and the pipe axis, β (shown in Figure 23.13) less than 90°, are examples of this case. In these cases, the pipe failure mechanism will be tensile rupture. • Case II: pipes are distressed due to bending and axial compressive force. A reverse fault and strikeslip fault with the intersection angle, β, between the fault trace and the pipe axis, more than 90°, are examples of this case. In these cases, the pipe failure mechanism will be buckling. Note, since burial depths are typically larger than those shown in Figure 23.11, pipe wall wrinkling as opposed to beam buckling occurs. © 2003 by CRC Press LLC
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-
FIGURE 23.13
Plan view of the Newmark–Hall model for pipeline crossing a right lateral strike-slip fault.
23.6.1 Continuous Pipelines Newmark and Hall [1975] apparently were the first to analyze the fault-crossing problem for continuous pipe. They considered the model shown in Figure 23.13, with a total fault movement δf, in which a pipeline intersects a right lateral strike-slip fault at an angle β less than 90°. They assume that the pipe is firmly attached to the soil (i.e., no relative displacement, or slip, between pipe and soil) at two anchor points located at La from the fault trace, and neglect the bending stiffness of the pipe as well as lateral interaction at the pipe–soil interface. Kennedy et al. [1977] extended the ideas of Newmark and Hall, and incorporated some improvements in the method for evaluating the maximum axial strain. They considered the effects of lateral interaction in their analysis. Also, the influence of large axial strains on the pipe’s bending stiffness is considered. That is, the pipe bending stiffness becomes very small (roughly 0.5% of the initial stiffness) when axial strain is well beyond the yield strain. As a result, the bending strain in the pipe is relatively small in this approach. The bending strain occurs in the curved region, where a constant curvature 1/Rc is assumed. The bending strain, εb, is expressed as: εb =
D 2Rc
(23.13)
where Rc is the radius of curvature in the curved region, which can be evaluated by using an analog to internal pressure in a cylinder: Rc =
σπDt pu
(23.14)
where σ is the axial stress at fault crossing, pu is the lateral soil–pipe interaction force per unit length as given, for example, in the ASCE Guideline [1984]. The total strain in the pipe is given by: ε = εa +
D 2Rc
(23.15)
where εa is the maximum axial strain due to the elongation of the pipe induced by the fault offset. © 2003 by CRC Press LLC
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FIGURE 23.14
Tolerable fault movement vs. unanchored length.
The total elongation of the pipe, ∆ L, can be estimated by:
∆L = δ f
(δ cos β +
f
sin β
)
2
3Lc
(23.16)
where the first term is the elongation due to the axial component of the fault movement, while the second term is the elongation due to arc-length effects induced by the lateral component of the fault movement, and Lc is the horizontal projection of the laterally deformed pipe, which can be approximated by: Lc = Rc δ f sin β
(23.17)
Based on a Ramberg–Osgood representation for the stress–strain relation: r σ n σ ε= 1+ E 1 + r σ y
(23.18)
where σy is the yield strain and n and r are material constants, the total elongation can be expressed in terms of an integral of the axial strain. That is,
∆L =
2 E
n σ 1 + 1+r 0
La
∫
r σ σ dx y
(23.19)
Figure 23.14 shows the tolerable fault movement for a 3.5 ft. (42 in., 1.07 m) diameter pipe as a function of unanchored length. The critical tensile strain is taken as 4.5% for depth of burial Hc = 0.9 m, and 3.5% for Hc = 3.0 m, due to the substantial increase in bending strains and hoop ovaling for the deeper burial depth. As shown, the tolerable fault offset for the pipe is an increasing function of unanchored length and pipe–fault intersection angle, but a decreasing function of burial depth. 23.6.1.1 Normal and Reverse Fault Relatively little analytical work has been done for a pipe crossing a normal or reverse fault. For a pipe subject to a normal fault, the pipe–soil system is no longer symmetric, and the transverse interaction force at the pipe–soil interface for downward movement of the pipeline is much larger than that for upward movement, based upon soil–spring relations in the ASCE Guideline [1984]. For a pipe subject to a reverse fault, the behavior is difficult to generalize, in part because there are two angles of intersection © 2003 by CRC Press LLC
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(the angle in plan between the fault and the pipeline, as well as the dip angle of the fault) as well as the aforementioned asymmetric nature of the soil resistance in the vertical plane. The ASCE Guideline [1984] suggests using the finite element method.
23.6.2 Segmented Pipelines Both experimental and analytical results are available for segmented pipelines subject to fault offset (i.e., local abrupt differential ground movement transverse to the pipe axis). For example, Takada [1984] performed a laboratory test to analyze the response of segmented pipelines subject to transverse PGD. Two cases were studied in their tests. In Case A, the pipeline is composed of three longer segments, while in Case B it is composed of five shorter segments. The stresses in the pipeline with smaller-length segments (Case B) are much less than those for large-length segments (Case A), particularly for large values of the offset. For the geometry studied by Takada, that is, a pipe at 90° with respect to the fault or offset plane, flexural stresses in the pipe dominate. If one assumes rotationally flexible joints (i.e., no moment transfer across the joint), the portion of the pipe segment on one side of the fault plane acts as a cantilever beam subject to a distributed loading along its length due to transverse pipe–soil interaction forces and a concentrated load at its end (i.e., at the joint) due to shear transfer across the joint. Smaller pipe stresses in Case B are due, at least in part, to the shorter cantilever length. Analytical results for segmented pipes are also available. O’Rourke and Trautmann [1981] developed a simplified analytical method for evaluating the response of segmented pipelines subject to fault offset. They assume that segments are rigid and joints accommodate the ground deformation. The tolerable fault offset for segmented pipelines as a function of the intersection angle is shown in Figure 23.15. Similar to the response of continuous pipelines subject to fault offset, the tolerable fault offset for pipelines with either restrained or unrestrained joints is an increasing function of β for the intersection angle less than some optimal value. For example, the optimal intersection angle for pipe with mechanical joints is about 70°. According to O’Rourke and Trautmann, the decrease in capacity for β greater than the optimal value is caused by the larger bending moments developed in the pipeline for large intersection angles. Note that pipes with extra long restrained coupling are particularly effective only when the intersection angle is small. At these small intersection angles, axial effects dominate and the expansion capability of the special joints is useful. However, at large intersection angles (β > 60°), where flexural effects govern, the capacity of mechanical and special joints is similar.
FIGURE 23.15
Tolerable fault offset vs. intersection angle.
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23.7 Pipeline Response to Longitudinal PGD 23.7.1 Continuous Pipelines Under longitudinal PGD, a corrosion-free continuous pipeline may fail at welded joints, may buckle locally (wrinkle) in a compressive zone, and/or may rupture in a tensile zone. When the burial depth is very shallow, the pipeline may buckle like a beam in a ground compressive zone as discussed previously. A model of continuous buried pipe response to longitudinal PGD has been developed. The pipeline is assumed to follow a Ramberg–Osgood type stress–strain relation as given in Equation 23.18. This model is often appropriate for pipe with arc-welded butt joints, since the local buckling or tensile rupture failure modes typically occur when the pipe is beyond the linear elastic range. O’Rourke et al. [1995] assumed a block pattern of longitudinal PGD for determination of the circumstances leading to local buckling failure in a pipe with a Ramberg–Osgood material model. The block pattern corresponds to a mass of soil having length L, moving down a slight incline. The soil displacement on either side of the PGD zone is zero, while the soil displacement within the zone is a constant value δ. This is an idealization of the PGD pattern for sections line N-2 in Figure 23.8. Two cases for a buried pipeline subject to a block pattern of longitudinal PGD were considered: • Case I: the amount of ground movement, δ, is large and the pipe strain is controlled by the length, L, of the PGD zone. • Case II: L is large and the pipe strain is controlled by δ. The distributions of pipe axial displacement, force, and strain are shown in Figure 23.16 for Case I. Note that tu is the friction force per unit length at the pipe–soil interface as given, for example, in the ASCE Guidelines [1984], and Le is the effective length over which tu acts.
FIGURE 23.16
Distribution of pipe axial displacement, force, and strain for Case 1.
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As shown in Figure 23.16, the force in the pipe over the segment AB is linearly proportional to the distance from point A. Using a Ramberg–Osgood model, the pipe strain can be expressed as follows: r β p x n βpx ε (x ) = 1 + E 1 + r σ y
(23.20)
while the total elongation is expressed in terms of an integral of axial strain:
δ (x ) =
β p x 2 2 n βpx 1 + E 2 + r 1 + r σ y
r
(23.21)
where n and r are Ramberg–Osgood parameters, E is the modulus of elasticity of steel, σy is the effective yield stress, and βp is the pipe burial parameter, having units of pounds per cubic inch. For sandy soil (zero soil cohesion), the pipe burial parameter βp is defined as:
βp =
µγH t
(23.22)
where µ is the frictional coefficient at the soil–pipe interface. Using the Ramberg–Osgood pipe material model, O’Rourke et al. [1995] developed critical values for δ and L which result in wrinkling of the pipe wall in compression (critical strain in compression taken as midpoint of range given in Equation 23.12). Table 23.1 shows these critical values for Grade B (n = 10, r = 100) and X-70 (n = 5.5, r = 16.6) steel and a variety of burial parameters and R/t ratios (radius of pipe/thickness). A pipe fails in local buckling when both the length and displacement of the PGD zone are larger than the critical values given, for example, in Table 23.1. TABLE 23.1 Critical Length and Displacement for Compressive Failure of Grade B and X-70 Steel, for Various Burial Parameters and R/t Ratios βp = 1.0 pci
βp = 2.5 pci
βp = 5 pci
βp = 15 pci
βp = 25 pci
R/t
L(m)
δ(m)
L(m)
δ(m)
L(m)
δ(m)
L(m)
δ(m)
L(m)
δ(m)
Gr-B
10 25 50 100 150
1762 1744 1728 1704 1660
1.32 1.12 1.05 1.00 0.94
704 698 691 682 664
0.53 0.45 0.42 0.40 0.38
352 349 346 341 332
0.26 0.23 0.21 0.20 0.19
117 116 115 114 111
0.090 0.080 0.070 0.066 0.063
70 70 69 68 66
0.050 0.045 0.042 0.040 0.037
X-70
10 25 50 100 150
4488 4182 3833 2577 1718
10.30 6.87 5.18 2.25 1.00
1795 1673 1533 1031 687
4.10 2.75 2.10 0.90 0.40
898 836 768 515 344
2.10 1.37 1.04 0.45 0.20
299 279 256 172 115
0.690 0.460 0.350 0.150 0.067
180 167 153 103 69
0.410 0.280 0.210 0.090 0.040
23.7.2 Influence of Expansion Joints O’Rourke and Liu [1994] studied the influence of flexible expansion joints in a continuous pipeline subject to longitudinal PGD. Depending upon the location of the expansion joints, they may have no effect, have a beneficial effect, or have a detrimental effect. For example, referring to Figure 23.16 (Case I, pipe strain controlled by length L), if the expansion joint is located at a distance larger than L away from the center of the PGD zone (i.e., to the left of point A or to the right of point E in Figure 23.16), an expansion joint would have no effect on the pipe stress and strain induced by the longitudinal PGD since the axial force in the pipe would be zero there even with no expansion joints. Figure 23.17 illustrates the © 2003 by CRC Press LLC
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FIGURE 23.17
23-23
Pipe and soil displacement with two expansion joints outside PGD zone.
beneficial effects of two expansion joints close to the head and toe areas of a longitudinal PGD zone. In this case an expansion joint is located at a distance L1 (L1 < L/2) from the head of the PGD zone (point B) at L2 (L2 < L/2) from the toe (point E). This placement is beneficial since the peak tension and compression forces are limited to tuL1 and tuL2, respectively. Potential detrimental effects occur for a single expansion close to the head of a PGD zone. For Case I, the tensile stress is reduced, but the compression stress is increased. That is, a single expansion joint made the situation worse since the total load tu L is no longer shared equally at both the compression and tension zones. The use of expansion joints presupposes that they are able to accommodate the imposed relative expansion and contraction. For example, if the distances L1 and L2 in Figure 23.17 are small (expansion joints very close to the head and toe of the PGD zone), the required expansion and contraction capability would be essentially the same as the ground displacement δ. For an expansion joint at distance L1 (L1 < L/2) away from the head or toe, the required expansion or contraction capacity is δ − tu L12 /(AE). Finally, for expansion joints to be effective one needs a reasonably accurate estimate of both the location and extent of the PGD zone.
23.7.3 Segmented Pipelines Similar to the response of continuous pipelines, the behavior of a given buried segmented pipeline to longitudinal PGD is a function of the amount of ground movement δ, the spatial extent of the PGD zone, and the pattern of ground movement within the zone. Note in this regard that Suzuki [1988] concluded that damage due to longitudinal PGD was more common than damage due to transverse PGD. This conclusion was based on observed damage to segmented gas pipelines during the 1964 Niigata earthquake, in which joints were pulled out in the tension region and buckled in the compression region. In terms of the pattern, if the ground movement within the PGD zone is relatively uniform (i.e., such as the idealized block pattern of longitudinal PGD shown in Figure 23.16), one expects that a few pipe joints near the head and toe of the zone would have to accommodate essentially all the abrupt differential ground movement. Since the movement is often at least a few feet, one would expect damage to a typical segmented pipe joint. On the other hand, if the ground movement varies within the PGD zone (i.e., as in Section Line S-4 of Figure 23.8), the rate of change along the segmented pipeline leads to an “equivalent” ground strain. One expects that all joints within the zone, to a greater or lesser extent, would then experience relative axial displacement.
23.7.4 Distributed Deformation As used here, distributed deformation refers to cases of longitudinal PGD where the amount of ground deformation varies in a nominally linear fashion across the PGD zone. The response of segmented pipelines subject to a distributed deformation pattern of longitudinal PGD is similar to that for segmented © 2003 by CRC Press LLC
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pipelines subject to wave propagation in that the spatially distributed PGD results in a region of ground strain. For example, towards the right-hand side of the longitudinal PGD pattern of Section Line S-4 in Figure 23.8, the ground deformation increases in a more or less uniform fashion to a peak value of about 4 m over a distance of roughly 250 m. This results in a ground strain, εg, of 1.6% (4/250). By assuming that pipe segments are rigid and all of the longitudinal PGD is accommodated by the extension or contraction of the joints, the average relative displacement at the joints is given by the ground strain times the pipe segment length, Lo: ∆uavg = ε g Lo
(23.23)
Although Equation 23.23 represents the average behavior, the joint displacements for uniform ground strain would vary somewhat from joint to joint due to variations in joint stiffness. That is, a relatively flexible joint is expected to experience larger joint displacements than adjacent stiffer joints. Using realistic variations of joint stiffness, El Hmadi and O’Rourke [1989] determined the mean joint displacement and coefficients of variation as a function of ground strain for various diameters of CI pipe with leadcaulked joints and DI pipe with rubber-gasketed joints. The mean values for both CI and DI pipes are about equal to the value given in Equation 23.23. Expected joint openings can be calculated in order to gauge the effects of a distributed deformation pattern of longitudinal PGD on segmented pipe. For example, the minimum ground strain due to the distributed longitudinal PGD in Noshiro City (Japan) after the 1983 Nihonkai Chubu event was 0.008. The corresponding joint opening is 5 cm (2 in.). which is larger than the joint capacity of typical segmented pipelines (i.e., segmented joints typically leak for relative displacement on the order of half the total joint depth). Hence, typical segmented pipelines are vulnerable and consideration should be given to replacement by continuous pipelines or segmented pipelines with special joints (having large contract/expansion capacity and/or antipull-out restraints) when crossing a potential longitudinal PGD zone.
23.8 Pipeline Response to Transverse PGD As mentioned previously, transverse PGD refers to permanent ground movement perpendicular to the pipe axis such as sketched in Figure 23.6B, part (b). Similar to longitudinal PGD, pipeline response to transverse PGD is in general a function of the amount of PGD δ, the width of the PGD zone, as well as the pattern of ground deformation. Figure 23.18 presents sketches of two types of transverse PGD. For spatially distributed transverse PGD, Figure 23.18(a), the pipe strain is a function of both the amount and width of the PGD zone. For abrupt transverse PGD, Figure 23.18(b), the movement at each margin of the PGD zone corresponds more or less to a fault offset where the fault/pipeline intersection angle is 90°.
FIGURE 23.18
Patterns of transverse PGD.
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For the spatially distributed transverse PGD considered herein, the lateral soil displacement, y(x) is taken as: y (x ) =
δ 2
2π x 1 − cos W
(23.24)
where x is the nonnormalized distance from the margin of the PGD zone and W is the width of the zone. The maximum soil deformation occurs somewhere near the center of the PGD zone and the soil deformation at the margins is zero.
23.8.1 Continuous Pipelines When subject to transverse PGD, a continuous pipeline will stretch and bend as it attempts to accommodate the transverse ground movement. In this section, selected parametric results for continuous pipe subject to distributed transverse PGD developed using the finite element method (FEM) are presented, followed by simplified analytical expressions for elastic pipe. 23.8.1.1 Parametric Results (FEM) Liu and O’Rourke [1997] developed a finite element model, utilizing large deformation theory, nonlinear pipe–soil interaction forces (soil springs), and Ramberg–Osgood stress–strain relations for the pipe material. The pipe is modeled as a beam supported by both axial and lateral soil springs. The anchor length of the pipe is long enough (up to 400 m [1312 ft]) such that both the flexural and axial pipe strain are essentially zero at the two anchor points. The pipe is assumed surrounded by loose to moderately dense sand with a burial depth of 1.2 m (4 ft) from ground surface to the top of the pipe. The resulting elastoplastic soil springs are based on the ASCE Guidelines [1984]. Figure 23.19 shows the maximum tensile and compressive strains in the pipe vs. the ground displacement for width W = 10, 30, and 50 m. This figure is for an X-52 grade steel pipe with diameter of 0.61 m (24 in.), wall thickness of 0.0095 m (3/8 in.), and the ground deformation pattern given in Equation 23.23. Except for W = 10 m, Figure 23.19 indicates that the peak tensile strain is substantially larger than the peak compressive strain, particularly for larger values of δ. Also, for the three widths considered, the pipe strains are largest for W = 30 m. The maximum pipe displacement more or less matches the ground deformation up to a certain critical displacement δcr. Thereafter, the pipe strain remains relatively constant while the pipe displacement increases more slowly with ground deformation. For ground deformation greater than δcr, the maximum tensile strain remains more or less constant. The pipe deformation fairly well matches the ground deformation over the whole width of the PGD zone for δ = δcr . However, for δ > δcr , the maximum pipe displacement is less than the maximum ground
Maximum Pipe Strain
0.015 0.01
W=10m W=30m W=50m
0.005 0 - 0.005 - 0.01 0
0.5
1
1.5
2
2.5
3
Ground Displacement (m)
FIGURE 23. 19
Maximum pipe strain vs. ground deformation: X-52 grade steel.
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Pipe Moment (N
•
m, x 10 6 )
Earthquake Engineering Handbook
1.5 W=50m W=30m W=10m
1 0.5 0 -0.5 -1 -1.5
-40
-30
-20
-10
0
10
20
30
40
Distance from Center of PGD Zone (m)
FIGURE 23.20
Distribution of bending moment for three widths (δ = δcr)
5
Axial Force (N) (x 10 6 )
W=50m 4
W=30m W=10m
3
2
1
0 -200
-150
-100
-50
0
50
100
150
200
Distance from Center of PGD Zone (m)
FIGURE 23.21
Distribution of axial force for three widths (δ = δcr)
displacement, and the “width” of the deformed pipe (i.e., length over which the pipe has noticeable transverse displacement) is larger than the width of the PGD zone. Figures 23.20 and 23.21 show the distribution of bending moments and axial forces in the pipe at δ = δcr for W = 10, 30, and 50 m. As one might expect, the bending moments in Figure 23.20 are symmetric with respect to the center of the PGD zone and similar to those for a laterally loaded beam with fixed supports near the margins of the PGD zone. That is, there are positive moments near the center of the PGD zone and negative moments near the margins. The moments vanish at roughly 10 m beyond the margins. The axial forces in the pipe shown in Figure 23.21 are, as expected, also symmetric about the center of the PGD zone. The axial forces are maximum near the center of the zone and decrease in a fairly linear fashion with increasing distance from the center of the zone. Unlike the moments, the axial forces become small only at substantial distances beyond the margins of the zone (note the different distance scales in Figures 23.20 and 23.21). The transverse loading on the pipe also results in axial movement of the pipe, that is, inward movement towards the center of the PGD zone. This inward movement is an increasing function of the ground movement δ. 23.8.1.2 Simplified Analytical Expressions for Elastic Pipe The analytical relations developed below are for an elastic pipe. Although the inelastic pipe case is more complex, the elastic relations provide at least a basis for interpreting finite element results and, in some instances, are directly applicable to transverse PGD case histories. © 2003 by CRC Press LLC
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For small widths of the PGD zone, bending controls the critical ground deformation and pipe behavior. The critical ground deformation is given by: δ cr −bending =
5 puW 4 384 EI
(23.25)
For very large widths of the PGD zone, the pipe behaves like a flexible cable (i.e., negligible flexural stiffness). For this case, axial force primarily controls the critical displacement. For a parabolic cable, the relation between the axial force T at the ends and the maximum lateral deformation (or sag) δ is: T=
puW 2 8δ
(23.26)
The ground displacement is larger than the pipe displacement in the middle region of the PGD zone (assumed here to be W/2) over which the maximum transverse resistance per unit length, pu , at the pipe–soil interface (i.e., the distributed load) is imposed. Taking the “sag” over this middle region to be δ/2, the interrelationship between the tensile force, T, and ground displacement, δ, is given by: pu (W 2) p W2 = u 8 (δ 2) 16 δ 2
T = πDt σ =
(23.27)
where σ is the axial stress in the pipe (assumed to be constant within the PGD zone). Inward movement of the pipe occurs at the margin of the PGD zone due to this axial force. Assuming a constant longitudinal friction force, tu , beyond the margins, the pipe inward movement at each margin is: ∆ inward =
πDt σ 2 2Et u
(23.28)
The total axial elongation of the pipe within the PGD zone is approximated by the average axial strain from arc-length effects times the width W. This elongation is due to stretching within the zone (σW/E) and inward movement at the margins from Equation 23.28. That is, πDt σ 2 π 2δ 2 σW = +2 4W E 2Et u
(23.29)
The critical ground deformation, δcr-axial for “cable-like” behavior and the corresponding axial pipe stress, σ, can be calculated by simultaneous solution of Equations 23.27 and 23.29. For any arbitrary width of the PGD zone, between small and very large, both flexural (beam) and axial (cable) effects provide resistance. Considering these elements to be acting in parallel: δ cr =
1 1 δ cr −bending
+
1
(23.30)
δ cr −axial
The maximum strains in an elastic pipe are due to the combined effects of axial tension (cable behavior) and flexure (beam behavior) and can be expressed as:
ε elastic
δπ tu π 2δD ± δ ≤ δ cr . AEW W2 = 2 π 2δ cr D tu πδ . δ > δσ ± 2 AEW W2
where A is the pipe cross-sectional area. © 2003 by CRC Press LLC
(23.31)
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23.8.2 Segmented Pipelines In considering the response of segmented pipelines subject to transverse PGD, one must differentiate between spatially distributed transverse PGD and localized abrupt transverse PGD as sketched in Figure 23.18. As with continuous pipe, localized abrupt PGD is a special case of faulting as discussed previously. For segmented pipelines subject to spatially distributed transverse PGD, the failure modes include round cracks in the pipe segments and crushing of bell-and-spigot joints due to bending, and pull-out at the joint due to axial elongation (i.e., arc-length effects). For an assumed sinusoidal variation of ground movement across the width of the PGD zone as given by Equation 23.24, O’Rourke and Nordberg [1991] studied the maximum joint opening in segmented pipelines due to both joint rotation and axial extension. Assuming that the pipe segments are rigid (i.e., EA = ∞, EI = ∞) and that the lateral displacement at the midpoint of the rigid pipe segment exactly matches the spatially distributed PGD at that point, they developed the relative axial displacement at a joint: ∆ xt =
Lo πδ 2πx sin 2 W W
2
(23.32)
where x is the distance from the margin of the PGD zone and Lo is the pipe segment length. Assuming that the slope of the rigid pipe segment exactly matches the ground slope at the segment midpoint, the joint opening due to the joint rotation, ∆xr , is as follows: π 2δ DLo 2 ∆ xt = 2W π δ 2 DL o W 2
2πx W 2πx W
cos cos
∆xt > ∆θ ⋅ D / 2 ∆xt < ∆θ ⋅ D / 2
(23.33)
where D is the pipe diameter. The total maximum opening at one side of a joint, ∆x, due to transverse PGD, is simply the sum of axial extension plus rotation effects. However, the axial and rotational components are largest at different points as discussed previously. Combining these effects, the resulting maximum joint opening is: π 2 Loδ 2 2D 2 ∆ x = 2 W2 δ π Loδ 1 + ( D δ)2 2W 2
[
0.268 ≤ D / δ < 3.73
]
(23.34) Others
Note that the maximum joint opening is an increasing function of both the δ/W ratio and the D/δ ratio.
23.9 Pipeline Response to Wave Propagation There have been some events, such as the 1964 Puget Sound, 1969 Santa Rosa, 1983 Coalinga, and 1985 Michoacan earthquakes, for which seismic wave propagation was the predominate hazard to buried pipelines. For example, in the 1985 Michoacan event, the damage ratio of about 0.45 repairs/km for the water supply system in the Lake Zone (soft soil zone) of Metropolitan Mexico City has been attributed to wave propagation effects. As discussed previously, when a seismic wave travels along the ground surface, any two points located along the propagation path will undergo out-of-phase motions. Those motions induce both axial and bending strains in a buried pipeline due to interaction at the pipe–soil interface. For segmented pipelines,
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damage usually occurs at the pipe joints. Although seismic wave propagation damage to continuous pipelines is far less common, the observed failure mechanism is typically local buckling.
23.9.1 Continuous Pipelines In general, the axial strain induced in a straight continuous pipeline depends on the ground strain, the wavelength of the traveling waves, and the interaction forces at the pipe–soil interface. For small to moderate ground motion, one may simply assume that pipe strain is equal to ground strain. However, for large ground motion, slippage typically occurs at the pipe–soil interface, resulting in pipe strain somewhat less than the ground strain. Simplified procedures for assessing pipe response due to wave propagation were first developed by Newmark [1967], and have since been used and/or extended by a number of authors, e.g., Yeh [1974]. Newmark’s approach is based on three assumptions. The first assumption, which is common to virtually all the deterministic approaches, deals with the earthquake excitation. The ground motion (that is, the acceleration, velocity, and displacement time histories) at two points along the propagation path are assumed to differ only by a time lag. That is, the excitation is modeled as a traveling wave. The second assumption is that pipeline inertia terms are small and may be neglected [Wang and O’Rourke, 1978]. Experimental evidence from Japan [Kubo, 1974] as well as analytical studies [Sakurai and Takahashi, 1969; Shinozuka and Koike, 1979] indicate that this is a reasonable engineering approximation. The third assumption is that there is no relative movement at the pipe–soil interface and hence, the pipe strain equals the ground strain. For a horizontal pipeline subject to S-wave propagation in a vertical plane having an angle of incidence γs with respect to the vertical, the ground strain parallel to the pipe axis is: εg =
Vm sin γ s cos γ s Cs
(23.35)
where Vm is the peak ground velocity and Cs is the shear wave velocity. In terms of Equation 23.9, Vm cosγs is the ground velocity parallel to the pipe axis and, as noted in Equation 23.6, Cs/sinγs is the apparent propagation velocity with respect to the ground surface and the pipeline axis. Similarly, for R waves, the ground strain parallel to the pipe axis is: εg =
Vm C ph
(23.36)
Since bending strain in a pipe due to wave propagation is typically a second-order effect, our attention is restricted to axial strain in the pipe. Equations 23.35 and 23.36 overestimate pipe strain, especially when the ground strain is large. For those cases, slippage occurs at the pipe–soil interface and the pipe strain is less than the ground strain. In relation to Newmark’s assumption regarding pipeline inertia, Sakurai and Takahashi [1969] developed a simple analytical model for a straight pipeline surrounded by an infinite elastic medium (soil). They used D’Alembert’s principle to handle the inertia force. Their analytical results, which do not consider slippage at the pipe–soil interface, indicate that the pipe strain is about equal to free-field strain and hence the inertia effects are negligible. This result regarding inertia terms is not surprising in light of the fact that the unit weight of a fluid-filled pipe is not greatly different from that of the surrounding soil. In relation to Newmark’s assumption regarding no relative displacement at the pipe–soil interface, Shinozuka and Koike [1979] as well as O’Rourke and El Hmadi [1988] consider the effects of slippage. These approaches provide estimates of the ground strain for initial slippage, and in the case of Shinozuka and Koike, an estimate of pipe strain for partial slippage (slippage over a portion of the pipeline length).
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FIGURE 23.22
Earthquake Engineering Handbook
Friction strain model for wave propagation effects on buried pipelines.
A simpler approach is to consider slippage over the whole pipeline length. For a wave with wavelength λ , the points of zero ground strain (points A and B), as shown in Figure 23.22, are separated by a horizontal distance of λ/2. Assuming a uniform frictional force per unit length tu, the maximum pipe strain at point C due to friction is given by: ε =
tuλ 4 AE
(23.37)
That is, the soil friction force is applied over a quarter wavelength separation distance. For R waves, an analysis procedure to estimate the maximum pipe strain would be as follows. It is assumed that the soil strain is due to R waves propagating parallel to the pipe axis. Due to the dispersive nature of R-wave propagation (i.e., phase velocity an increasing function of wavelength), the soil strain is a decreasing function of separation distance or wavelength. The pipe strain due to the friction at the pipe–soil interface is an increasing function of separation distance or wavelength. At a particular separation distance (that is, for a particular wavelength), the friction strain matches the soil strain. This unique strain then becomes the peak strain that can be induced in a continuous pipeline by R-wave propagation. Note that this procedure for R waves conservatively assumes that the peak ground velocity, Vmax , applies to all frequencies (wavelengths) of R-wave propagation and that all frequencies (wavelengths) are present in the record. This procedure was applied by O’Rourke and Ayala [1990] as a case study to pipe damage in Mexico City. During the 1985 Michoacan earthquake, a welded steel pipeline with D = 107 cm (42 in.), t = 0.8 cm (5/16 in.), and made of API 120 X-42 steel suffered local buckling damaged at several locations within the Lake Zone in Mexico City. A dispersion curve for the fundamental R wave, corresponding to the subsoil conditions of the Lake Zone, was developed. For a pipe surrounded by loose sand with γ = 110 lb/ ft3 (17.2 kN/m3) and a coefficient of friction µ = 0.5, the estimated compressive strain was about 0.0023, as shown in Figure 23.23. Note in this figure, the friction strain is proportional to the quarter wavelength (i.e., separation distance) for strains less than about 0.001 (λ/4 ≈ 100 m). For larger separation distances, although the axial force is still proportional to separation distance, the strain is not, since the steel is now in the nonlinear portion of the stress-strain diagram. The local buckling strain is estimated to be about 0.0026 based upon D/t = 134 and Equation 23.12. That is, the analytical procedure suggests that the pipeline was very close to buckling. Note that the pipeline did, in fact, suffer a local buckling failure at several locations separated by distances of 300 to 500 m (984 to 1640 ft). These distances correspond
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FIGURE 23.23
Soil and friction strain for Mexico City pipeline.
reasonably well with the calculated wavelength of 520 m (1706 ft). That is, high compression regions are a wavelength apart. For seismic design of continuous buried pipe, a simpler procedure is arguably appropriate. That is, the axial strain in the pipe is simply taken as the smaller of the ground strain or the friction strain. For the case of R waves, which typically generate larger ground strains when they are present in a ground motion record, an ASCE/ASME task force has recently recommended using Cph = 500 m/sec and λ = 1.0 km in Equations 23.36 and 23.37, respectively.
23.9.2 Segmented Pipeline in Tension Seismic wave propagation damage to segmented pipelines most frequently occurs at joints, tees and elbows. The corresponding failure modes include pull-out at joints, crushing of bell-and-spigot joints, and circumferential cracks due to bending. For a long straight run of segmented pipe, the ground strain is accommodated by a combination of pipe strain and relative axial displacement (expansion/contraction) at pipe joints. As noted by Iwamoto et al. [1984], since the overall axial stiffness for segments is typically much larger than that for the joints, the ground strain results primarily in relative displacement of the joints. As a first approximation, assuming that the pipe segment axial strain can be neglected (i.e., rigid segment) and that all joints experience the same movement, the maximum joint movement ∆u is: ∆u = εmax · Lo
(23.38)
where Lo is the pipe segment length and εmax is the maximum ground strain parallel to the pipe axis. Note that in the model for Equation 23.38, the relative displacement at each joint is the same. That is, it does not capture the variation in displacement from joint to joint. This variation from joint to joint is considered important, since even for relatively large wave propagation damage, only a few joints require repair. For example, for surface wave propagation, one expects roughly 0.9 repairs per kilometer for a relatively high peak particle velocity of 50 cm/sec. This suggests only one repair for every 182 joints if the pipe segment length is 6.1 m (20 ft). That is, since it is reasonable to assume some variation in response from joint to joint, the few joints with largest response control damage, as opposed to joints with “average” response. With this in mind, El Hmadi and O’Rourke [1990] considered a model in which the joint properties vary from joint to joint. Specifically, a CI pipe with lead-caulked joints subject to tensile ground strain was considered. The expected variation in the joint slippage force was based upon results by O’Rourke and Trautmann [1980]. © 2003 by CRC Press LLC
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FIGURE 23.24 joints.
Earthquake Engineering Handbook
Relative joint displacement vs. ground strain for 41 cm diameter cast iron pipe with lead-caulked
A simplified Monte Carlo simulation technique is used to establish the characteristics of force–displacement relationships at each joint and soil restraint along each pipe segment. Figure 23.24 shows the joint deformation as a function of ground strain for a segmented pipe with a diameter of 0.41 m (16 in.). The average joint displacement is approximately equal to the product of the ground strain times the pipe segment length. However, 1 in 100 joints (1% probability of exceedence) have joint displacement about three times the average value while for the 0.1% exceedence probability (1 in 1000), the joint opening is about five times the average. This information, coupled with the probability of leakage as a function of the normalized joint opening, as shown, for example, in Figure 23.12, allows one to establish an analytically derived estimation of joint pull-out damage (repair per kilometer) as a function of ground strain.
23.9.3 Segmented Pipeline in Compression Extensive damage to concrete pipelines has occurred when these elements are subject to compressive ground strain. For wave propagation resulting in compressive ground strain, the failure mode of interest is crushing (i.e., telescoping) at pipe joints. When subject to compressive ground strain εg, the response of a segmented pipe is complicated by the presence of joints. Significant axial force can be transferred across the joint only if the joint is fully closed (i.e., contraction of the joint is ∆uult). Based upon a series of laboratory tests on reinforced concrete cylinder pipelines (RCC) with rubber-gasketed joints by Bouabid [1995], the joint compressive displacement, ∆uult , at lock-up typically ranges from 0.125 to 0.375 in. (0.32 to 0.95 cm). If there are n fully closed joints in sequence and the ground strain is assumed uniform over the corresponding number of pipe segments, the pipe segment compressive strain is: εp = εg −
n ∆uult n +1 Lo
(23.39)
where Lo is the length of pipe segment. There appears to have been relatively little analytical research on the wave propagation behavior of bends and elbows in segment pipe systems. However, measurements by Iwamoto et al. [1985] suggest that joint openings at bends and elbows are, in fact, different from those in long straight runs of pipe. In some cases, the response of the elbow joint was smaller than that for a straight pipe joint. However,
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in other cases, presumably for other angles of incidence, the elbow joint response was up to three times larger than the straight joint response. Similar behavior was observed for joints adjacent to valve boxes. For joints adjacent to buildings, the amplification factor is as large as 10.
23.10 Countermeasures to Mitigate Seismic Damage A variety of methods are available to mitigate against seismic damage to pipelines. These include: • • • • •
Avoiding or rerouting pipes around areas particularly susceptible to damaging ground movements Various methods to isolate the pipeline from ground movements Various methods to reduce the amount of ground movement High strength or high ductility materials for the pipelines themselves The use of joints with enhanced expansion/contraction or rotation capability
23.10.1 Routing and Relocation This technique involves simply avoiding areas that are susceptible to large ground movements. It is comparatively easy to implement during the initial design (i.e., route selection) stage for a new pipeline, but can also be used for an existing line. This method would typically be more effective for the PGD hazard such as landslides or areas susceptible to liquefaction. It can also be used for the fault crossing hazard if the end points for the line are both on the same side of the active fault. That is, relocation tends to be more effective when hazard exists only in an isolated area that can be avoided. Routing and relocation tend to be less effective for wave propagation damage, since this hazard typically exists over much larger areas. Finally, routing and relocation will typically be easier to implement for transmission pipe, for which there may be a number of options in terms of route selection, and more difficult for distribution pipe.
23.10.2 Isolation from Damaging Ground Movement Routing and relocation involves alternate locations (i.e., realignment in the horizontal plane). When such alternate locations are unavailable, impractical, or cost prohibitive, isolation techniques can be used to mitigate against seismic damage to pipelines. In this case, the pipeline traverses the hazardous area but is isolated from the effects of large ground movements by realignment in the vertical direction. A classic example is the placement of the trans-Alaskan pipeline on above-ground, “goal post”-type supports at fault crossing locations. That is, for strike-slip faults there is enough “rattle-space” between the uprights such that the potential fault movement can be accommodated without overstressing the pipe. This method can be used for most types of PGD hazards; however, proper implementation often requires a low-friction sliding surface between the pipe and its horizontal supporting member. For certain PGD hazards, the same objectives can be obtained by directional drilling technology. In this case, the pipe is isolated from potential damage by being located below the hazardous area. Directional drilling can be used for the landslide hazard as well as the liquefaction hazard. It is particularly attractive at river crossings, which may be susceptible to liquefaction-induced PGD of the bank. However, this technique cannot be used effectively at faults, since it is not possible to place the pipe “below” the fault. A third mitigation approach, within this isolation class, involves orientation of the pipe so as to reduce the potential for damage. The potential for damage to a continuous pipe subject to PGD is reduced as the line is oriented perpendicular to the direction of ground movement (i.e., transverse PGD as opposed to longitudinal PGD). Similarly, a continuous pipe subject to fault crossing hazard should be oriented such that the fault movement places the line in tension as opposed to compression. Theoretically, the optimum situation corresponds to the pipe at right angles to the fault. However, due to the difficulty associated with establishing the actual orientation of the fault line in a horizontal plane, an angle, β, of about 60° is often recommended. © 2003 by CRC Press LLC
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For segmented pipe, the preferred orientations are the same. That is, transverse PGD is preferable to longitudinal PGD, particularly if the joints are flexible. Also, at fault crossings, an angle close to 90° is marginally better for typical joint types.
23.10.3 Reduction of Ground Movements These mitigation techniques involve various types of field treatments to the soil, to reduce the potential for lateral spreading. The methods include increasing the density and strength of sand, lowering the ground water level, and modifications to permit the dissipation of pore water pressure. For example, Miyajima et al. [1992] proposed a vertical gravel drain system along the pipeline right-of-way that reduces the maximum pore water pressures. Fujii et al. [1992] suggest sand and compaction as a technique to increase soil density and strength, and thereby reduce the potential for liquefaction. Iwatate et al. [1988] performed experiments on buried culverts which drain groundwater away from the pipeline. Finally, one could replace liquefaction soils in the vicinity of the pipe with nonliquefiable materials such as gravel, to reduce the potential for liquefaction. These field treatment methods tend to be practical only when the spatial extent of the liquefied soil deposits is limited and the liquefiable soil layer is relatively close to the ground surface. They are less practical and cost effective for the typical landslide hazard.
23.10.4 High Strength Materials For continuous pipe, improved seismic performance results from the use of stronger materials (i.e., higher nominal yield stress) and larger pipe wall thickness. For example, Table 23.1 shows that the higher strength X-70 pipe can accommodate more longitudinal PGD than a corresponding Grade B pipe. One also obtains improved performance for pipe subject to transverse PGD and fault crossing. Similarly, one obtains improved performance for thicker wall pipe subject to longitudinal PGD, transverse PGD, and fault crossing. Note that this improved performance is for steel pipe with electric arc-welded butt joints. The performance of steel pipe with slip joints, rivet joints, or oxyacetylene welds is expected to be poorer. Another mitigation option involves reducing the load as opposed to increasing the strength. As shown in Section 23.7.1, the axial strain induced in a continuous pipe by longitudinal PGD is an increasing function of the pipe burial parameter βp , as defined in Equation 23.22. Hence, axial strain can be reduced by using the smallest possible burial depth (H), using low density backfill (γ), and/or using coatings which reduce the coefficient of friction at the soil–pipe interface (µ). Lastly, for segmented pipe, providing continuity across joints significantly improves performance, within limits. Figure 23.25 shows the joint restraint system developed about 1907 for San Francisco’s auxiliary water supply system (AWSS) following the 1906 San Francisco earthquake and fire, where many water pipes had failed in axial pull-out. The pipe bells and spigots are cast with integral “lugs,” which are connected by the large corrosion-resistant steel rods and nuts. The four rod–nut assemblies are then wired together, to prevent displacement of the rods. This system has performed very well in San Francisco for almost 100 years, including during the 1989 Loma Prieta earthquake. Restrained joints, using a different system, also performed very well in areas of large PGD during the 1995 Kobe earthquake.
23.10.5 Flexible Materials and Joints It has long been argued that the use of more flexible materials tends to improve the seismic performance of buried pipeline. This is due to the fact that the “seismic loading” on buried pipe is, in essence, displacement controlled. As shown in Figure 23.3, one expects improved seismic performance for flexible pipe materials, such as arc-welded steel and DI pipe, when subject to various PGD hazards. For segmented pipe, Isenberg and Richardson [1989], Ballantyne [1992], and Wang [1994] have suggested the use of flexible joints for pipeline subject to the PGD hazard. However, as explained in Section 23.7.2, expansion
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FIGURE 23.25 Workman installing joint restraint system, San Francisco’s AWSS. Bells and spigots are cast with integral “lugs,” which are connected by the large corrosion-resistant steel rods and nuts. The four rod–nut assemblies are then wired together, to prevent displacement of the rods. (Photo: C. Scawthorn)
joints need to be used with caution. For example, if an expansion joint is placed at only one end of a lateral spread zone, the strain in a continuous pipe induced by longitudinal PGD would actually be larger than that for a pipe with no expansion joints. For localized abrupt PGD offsets, such as at a fault crossing, Ford [1983] suggests the use of rotationally flexible ball-type joints in combination with an expansion joint. This combined rotation and extension flexibility could also be useful at other locations when differential movements are expected. Examples of such locations include the margins of areas with variable subsurface conditions, and the inlet/outlets to stiff structures such as tanks and buildings.
Defining Terms AC — Asbestos cement (pipe). CI — Cast iron (pipe). Compliant — Displacing in conformance with adjacent materials; for pipelines, moving with the surrounding soils.
Continuous — Pipe that generally has the same cross-section and properties everywhere along its length. Continuous pipe is laid in relatively long lengths, and joined so as to be continuous, such as via welding. Damage rate — Number of pipe damage occurrences, such as pipe breaks, normalized by the pipe length, so as to yield a damage rate of, for example, 1.5 breaks per kilometer. DI — Ductile iron (pipe). Liquefaction severity index (LSI) — The amount of PGD, in inches, associated with lateral spreading on gently sloping ground and poor soil conditions [Youd and Perkins, 1987]. Permanent ground deformation (PGD) — Deformation hazard due to ground failure, such that the ground is permanently displaced relative to its pre-earthquake condition. RCC — Reinforced concrete cylinder (pipe). Segmented — Pipe that is made up of relatively short sections or segments, such as bell-and-spigot pipe. Wave propagation — Deformation hazard due to transient seismic waves.
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References American Society of Civil Engineers (ASCE). (1984). Guidelines for the Seismic Design of Oil and Gas Pipeline Systems, Committee on Gas and Liquid Fuel Lifeline, ASCE, Reston, VA. Applied Technology Council. (1985). Earthquake Damage Evaluation Data for California, ATC-13, Redwood City, CA. Ayala, G. and O’Rourke, M. (1989). Effects of the 1985 Michoacan Earthquake on Water Systems and Other Buried Lifelines in Mexico, Technical Report NCEER-89-0009, Multidisciplinary Center for Earthquake Engineering Research, Buffalo, NY. Ballantyne, D. (1992). “Thoughts on a Pipeline Design Standard Incorporating Countermeasure for Permanent Ground Deformation,” in Proceedings of the Fourth Japan–U.S. Workshop on Earthquake Resistant Design of Lifeline Facilities and Countermeasures for Soil Liquefaction, Honolulu, Hawaii, Technical Report NCEER-92-0019, Multidisciplinary Center for Earthquake Engineering Research, Buffalo, NY, 875–887. Barenberg, M.E. (1988). “Correlation of Pipeline Damage with Ground Motions,” J. Geotech. Eng., 114, 706–711. Bartlett, S.F. and Youd, T.L. (1992). Empirical Analysis of Horizontal Ground Displacement Generated by Liquefaction-Induced Lateral Spreads, Technical Report NCEER-92-0021, Multidisciplinary Center for Earthquake Engineering Research, Buffalo, NY. Bouabid, J. (1995). “Behavior of Rubber Gasketed Concrete Pipe Joints during Earthquakes,” Ph.D. thesis, Rensselaer Polytechnic Institute, Troy, NY, December. Bouabid, J. and O’Rourke, M.J. (1994). “Seismic Vulnerability of Concrete Pipelines,” in Proceedings of the Fifth U.S. National Conference on Earthquake Engineering, vol. 4, Chicago, IL, Earthquake Engineering Research Institute, Oakland, CA, 789–798. Brockenbrough, R.L. (1990). “Strength of Bell-and-Spigot Joints,” J. Sruct. Eng., 116, 1983–1991. Eguchi, R.T. (1983). “Seismic Vulnerability Models for Underground Pipes,” in Earthquake Behavior and Safety of Oil and Gas Storage Facilities, Buried Pipelines and Equipment, PVP-77, American Society of Mechanical Engineers, New York, 368–373. Eguchi, R. (1991). Early Post-Earthquake Damage Detection for Underground Lifelines, Final Report to the National Science Foundation, Dames and Moore P.C., Los Angeles, CA. Eidinger, J.M., Maison, B., Lee, D., and Lau, B. (1995). “East Bay Municipal Utility District Water Distribution Damage in 1989 Loma Prieta Earthquake,” in Proceedings of the Fourth U.S. Conference on Lifeline Earthquake Engineering, American Society of Civil Engineers, Technical Council on Lifeline Earthquake Engineering, Monograph No. 6, August, pp. 240–247. El Hmadi, K. and O’Rourke, M.J. (1989). Seismic Wave Effects on Straight Jointed Buried Pipeline, Technical Report NCEER-89-0022, Multidisciplinary Center for Earthquake Engineering Research, Buffalo, NY. El Hmadi, K. and O’Rourke, M.J. (1990). “Seismic Damage to Segmented Buried Pipelines,” Earthquake Eng. Struct. Dyn., 19, 529–539. Ford, D.B. (1983). “Joint Design for Pipelines Subjected to Large Ground Deformations,” in Earthquake Behavior and Safety of Oil and Gas Storage Facilities, Buried Pipelines and Equipment, PVP-77, American Society of Mechanical Engineers, New York, June, pp. 160–165. Fujii, Y., Ohtomo, K., Arai, H., and Hasegawa, H. (1992). “The State of the Art in Mitigation of Liquefaction for Lifeline Facilities in Japan,” in Proceedings of the Fourth Japan–U.S. Workshop on Earthquake Restraint Design of Lifeline Facilities and Countermeasures for Soil Liquefaction, Honolulu, Hawaii, Technical Report NCEER-92-0019, Multidisciplinary Center for Earthquake Engineering Research, Buffalo, NY, pp. 889–909. G&E. (1994). NIBS Earthquake Loss Estimation Methods: Technical Manual (Water Systems), May, G&E Engineering Systems, Oakland, CA. Hall, J.F. (1995). “Northridge Earthquake of January 17, 1994, Reconnaissance Report,” Earthquake Spectra, April. © 2003 by CRC Press LLC
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Hall, W. and Newmark, N. (1977). “Seismic Design Criteria for Pipelines and Facilities,” in Current State of Knowledge of Lifeline Earthquake Engineering, American Society of Civil Engineers, New York, pp. 18–34. Hamada, M. (1989). “Damage to Buried Lifelines Due to Liquefaction-Induced Ground Displacements,” Proceedings of the Third U.S.–Japan Workshop on Earthquake Disaster Prevention for Lifeline Systems. Hamada, M., Yasuda, S., Isoyama, R., and Emoto, K. (1986). Study on Liquefaction Induced Permanent Ground Displacements, Association for the Development of Earthquake Prediction, Japan. Heubach, W.F. (1995). “Seismic Damage Estimation for Buried Pipeline Systems,” in Proceedings of the Fourth U.S. Conference on Lifeline Earthquake Engineering, Technical Council on Lifeline Earthquake Engineering, Monograph No. 6, American Society of Civil Engineers, New York, 312–319. Honegger, D.G. (1995). “An Approach to Extend Seismic Vulnerability Relationships for Large Diameter Pipelines,” in Proceedings of the Fourth U.S. Conference on Lifeline Earthquake Engineering, Technical Council on Lifeline Earthquake Engineering, Monograph No. 6, American Society of Civil Engineers, New York, 320–327. Isenberg, J. and Richardson, E. (1989). “Countermeasures to Mitigate Damage to Pipelines,” in Proceedings of the Second U.S.–Japan Workshop on Liquefaction, Large Ground Deformation and Their Effects on Lifelines, Technical Report NCEER-89-0032, Multidisciplinary Center for Earthquake Engineering Research, Buffalo, NY, 468–482. Isoyama, R. and Katayama, T. (1982). Reliability Evaluation of Water Supply Systems during Earthquakes, Report of the Institute of Industrial Science, University at Tokyo, February, vol. 30, no. 1. Iwamoto, T., Wakai, N., and Yamaji, T. (1984). “Observation of Dynamic Behavior of Buried DuctileIron Pipelines during Earthquakes,” in Eighth World Conference on Earthquake Engineering, San Francisco, vol. 7, pp. 231–238. Iwamoto, T., Yamamura, Y., and Hojo, S. (1985). “Observations and Analyses at the Bend and Tee Portions of Buried Ductile Pipelines during Earthquakes,” Seismic Performance of Pipelines and Storage Tanks, PVP-98–4, American Society of Mechanical Engineers, pp. 69–79. Iwatate, T., Ohtomo, K., Tohma, J., and Nozawa, Y. (1988). “Liquefaction Disaster Mitigation for Underground Structures,” in Proceedings of the First Japan–U.S. Workshop on Liquefaction, Large Ground Deformation and Their Effects on Lifeline Facilities, Tokyo, Japan, November, pp. 143–151. Jibson, R.W. and Keefer, D.K. (1993). “Analysis of the Seismic Origin of Landslides: Examples from the New Madrid Seismic Zone,” Geol. Soc. Am. Bull., 105, 521–536. Kachadoorian, R. (1976). “Earthquake: Correlation between Pipeline Damage and Geologic Environment,” J. AWWA, March, 165–167. Kennedy, R.P., Chow, A.W., and Williamson, R.A. (1977). “Fault Movement Effects on Buried Oil Pipeline,” J. Transport. Eng. Div., 103 (TE5), pp. 617–633. Krathy, R.G. and Salvadori, M.G. (1978). Strength and Dynamic Characteristics of Gasket-Jointed Concrete Water Pipelines, Grant Report, No. 5, Weidlinger Associates, New York. Kubo, K. (1974). “Behavior of Underground Water Pipes during an Earthquake,” Proceedings of the Fifth World Conference on Earthquake Engineering, Rome, pp. 569–578. Liu, X. and O’Rourke, M. (1997). “Behavior of Continuous Pipeline Subject to Transverse PGD,” J. Earthquake Eng. Struct. Dyn., 26, 989–1003. Markov, I., Grigoriu, M., and O’Rourke, T. (1994). An Evaluation of Seismic Serviceability of Water Supply Networks with Application to San Francisco Auxiliary Water Supply System, Technical Report NCEER-94–0001, Multidisciplinary Center for Earthquake Engineering Research, Buffalo, NY. McCaffrey, M.A. and O’Rourke, T.D. (1983). “Buried Pipeline Response to Reverse Faulting during the 1971 San Fernando Earthquake,” Earthquake Behavior and Safety of Oil and Gas Storage Facilities, Buried Pipelines and Equipment, PVP-77, American Society of Mechanical Engineers, New York, June, pp. 151–159. Meyersohn, W.D. (1991). “Analytical and Design Considerations for the Seismic Response of Buried Pipelines,” Thesis, Graduate School of Cornell University, Ithaca, NY, January.
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Miyajima, M., Yoshida, M., and Kitaura, M. (1992). “Small Scale Tests on Countermeasures against Liquefaction for Pipelines Using Gravel Drain System,” in Proceedings of the Fourth Japan–U.S. Workshop on Earthquake Resistant Design of Lifeline Facilities and Countermeasures for Soil Liquefaction, Honolulu, Hawaii, Technical Report NCEER-92-0019, Multidisciplinary Center for Earthquake Engineering Research, Buffalo, NY, pp. 381–391. Moncarz, P.D., Shyne, J.C., and Derbalian, G.K. (1987). “Failures of 108-Inch Steel Pipe Water Main,” J. Perform. Const. Fac., ASCE, 1, pp. 168–187. Newmark, N.M. (1967). “Problems in Wave Propagation in Soil and Rocks,” in Proceedings of the International Symposium on Wave Propagation and Dynamic Properties of Earth Materials, University of New Mexico Press, Albuquerque, pp. 7–26. Newmark, N.M. and Hall, W.J. (1975). “Pipeline Design to Resist Large Fault Displacement,” in Proceedings of the 1975 U.S. National Conference on Earthquake Engineering, Ann Arbor, MI, pp. 416–425. National Institute of Building Sciences (NIBS). (1996). Development of a Standardized Earthquake Loss Estimation Methodology, Vol. 2, NIBS, Washington, D.C. Nishio, N., Ukaji, T., Tsukamoto, K., and Ishita, O. (1983). “Model Experiments on the Behavior of Buried Pipelines during Earthquakes,” in Earthquake Behavior and Safety of Oil and Gas Storage Facilities, Buried Pipelines and Equipment, PVP- 77, American Society of Mechanical Engineers, New York, June, pp. 263–272. O’Rourke, M.J. and Ayala, G. (1990). “Seismic Damage to Pipeline: Case Study,” J. Transport. Eng., 116, 123–134. O’Rourke, M.J. and Ayala, G. (1993). “Pipeline Damage Due to Wave Propagation,” J. Geotech. Eng., 119, 1490–1498. O’Rourke, M.J. and El Hmadi, K.E. (1988). “Analysis of Continuous Buried Pipelines for Seismic Wave Effects,” Earthquake Eng. Struct. Dyn., 16, 917–929. O’Rourke, T. and Jeon, S. (1991). “Factors Affecting the Earthquake Damage of Water Distribution Systems,” in Proceedings of the Fifth U.S. Conference on Lifeline Earthquake Engineering, August 1988, Technical Council on Lifeline Earthquake Engineering Monograph No. 6, American Society of Civil Engineers, New York, pp. 379–388. O’Rourke, M.J. and Liu, X.J. (1994). “Failure Criterion for Buried Pipe Subjected to Longitudinal PGD: Benchmark Case History,” in Proceedings of the Fifth U.S.–Japan Workshop on Earthquake Resistant Design for Lifeline Facilities and Countermeasures Against Soil Liquefaction, Snowbird, UT, Technical Report NCEER-94-0026, Multidisciplinary Center for Earthquake Engineering Research, Buffalo, NY, pp. 639–652. O’Rourke, M. and Nordberg, G. (1991). “Analysis Procedures for Buried Pipelines Subject to Longitudinal and Transverse Permanent Ground Deformation,” in Proceedings of the Third Japan–U.S. Workshop on Earthquake Resistant Design of Lifeline Facilities and Countermeasures for Soil Liquefaction, San Francisco, CA, Technical Report NCEER-91-0001, Multidisciplinary Center for Earthquake Engineering Research, Buffalo, NY, pp. 439–453. O’Rourke, T.D. and O’Rourke, M.J. (1995). “Pipeline Response to Permanent Ground Deformation: A Benchmark Case,” in Proceedings of the Fourth U.S. Conference on Lifeline Earthquake Engineering, Technical Council on Lifeline Earthquake Engineering, Monograph No. 6, American Society of Civil Engineers, New York, pp. 288–295. O’Rourke, T.D. and Tawfik, M.S. (1983). “Effects of Lateral Spreading on Buried Pipelines during the 1971 San Fernando Earthquake,” in Earthquake Behavior and Safety of Oil and Gas Storage Facilities, Buried Pipelines and Equipment, PVP-77, American Society of Mechanical Engineers, New York, pp. 124–132. O’Rourke, T.D. and Trautmann, C.H. (1980). Analytical Modeling of Buried Pipeline Response to Permanent Earthquake Displacements, Report No. 80-4, School of Civil Engineering and Environmental Engineering, Cornell University, Ithaca, NY, July.
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O’Rourke, T.D. and Trautmann, C.H. (1981). “Earthquake Ground Rupture Effects on Jointed Pipe,” in Proceedings of the Second Specialty Conference of the Technical Council on Lifeline Earthquake Engineering, American Society of Civil Engineers, New York, August, pp. 65–80. O’Rourke, M.J., Bloom, M.C., and Dobry. R. (1982). “Apparent Propagation Velocity of Body Waves,” Earthquake Eng. Struct. Dyn., 10, 283–294. O’Rourke, M.J., Castro, G., and Hossain, I. (1984). “Horizontal Soil Strain Due to Seismic Waves,” J. Geotech. Eng., 110, 1173–1187. O’Rourke, M.J., Liu, X.J., and Flores-Berrones, R. (1995). “Steel Pipe Wrinkling Due to Longitudinal Permanent Ground Deformation,” J. Transport. Eng., 121, 443–451. O’Rourke, T.D., Gowdy, T.E., Stewart, H.E., and Pease, J.W. (1991). “Lifeline Performance and Ground Deformation in the Marina during 1989 Loma Prieta Earthquake,” in Proceedings of the Third Japan–U.S. Workshop on Earthquake Resistant Design of Lifeline Facilities and Countermeasures for Soil Liquefaction, San Francisco, Technical Report NCEER-91-0001, Multidisciplinary Center for Earthquake Engineering Research, Buffalo, NY, pp. 129–146. O’Rourke, T.D., Grigoriu, M.D., and Khater, M.M. (1985). “A State of the Art Review: Seismic Response of Buried Pipelines,” in Decade of Progress in Pressure Vessel Technology, C. Sundararajan, Ed., American Society of Mechanical Engineers, New York. Porter, K.A., Scawthorn, C., Honegger, D.G., O’Rourke, T.D., and Blackburn, F. (1991). “Performance of Water Supply Pipelines in Liquefied Soil,” in Proceedings of the Fourth U.S.–Japan Workshop on Earthquake Disaster Prevention for Lifeline Systems, Los Angeles, CA, August 19–21, jointly sponsored by the National Science Foundation, Washington, D.C. and the Public Works Research Institute, Japan, pp. 3–17. Prior, J.C. (1935). “Investigation of Bell and Spigot Joints in Cast Iron Water Pipes,” The Engineering Experiment Station, 4, Bulletin 87, Ohio State University Studies Engineering Series, January. Sakurai, A. and Takahashi, T. (1969). “Dynamic Stress of Underground Pipelines during Earthquakes,” in Proceedings of the Fourth World Conference on Earthquake Engineering, Chilean Association on Seismology and Earthquake Engineering, Santiago, Chile, pp. 811–895. Sato, R. and Shinozuka, M. (1991). “GIS-Based Interactive and Graphic Computer System to Evaluate Seismic Risks on Water Delivery Networks,” in Proceedings of the Third U.S. Conference on Lifeline Earthquake Engineering, Technical Council on Lifeline Earthquake Engineering, Monograph No. 4, American Society of Civil Engineers, New York, pp. 651–660. Shinozuka, M. and Koike, T. (1979). “Estimation of Structural Strains in Underground Lifeline Pipes,” in Lifeline Earthquake Engineering: Buried Pipelines, Seismic Risk, and Instrumentation, PVP-34, American Society of Mechanical Engineers, New York, pp. 31–48. Sun, S. and Shien, L. (1983). “Analysis of Seismic Damage to Buried Pipelines in Tangshan Earthquake,” in Earthquake Behavior and Safety of Oil and Gas Storage Facilities, Buried Pipelines and Equipment, PVP-77, American Society of Mechanical Engineers, New York, June, pp. 365–367. Suzuki, H. (1988). “Damage to Buried Pipes Caused by Large Ground Displacement,” in Proceedings of the First Japan–U.S. Workshop on Liquefaction, Large Ground Deformation and Their Effects on Lifeline Facilities, Tokyo, Japan, November 16–19, jointly sponsored by the Association for Development of Earthquake Prediction (Japan) and the National Center for Earthquake Engineering Research, Buffalo, NY, pp. 127–132. Suzuki, N. and Masuda, N. (1991). “Idealization of Permanent Ground Movement and Strain Estimation of Buried Pipes,” in Proceedings of the Third Japan–U.S. Workshop on Earthquake Resistant Design of Lifeline Facilities and Countermeasures for Soil Liquefaction, San Francisco, NCEER Report Number 91-0001, Multidisciplinary Center for Earthquake Engineering Research, Buffalo, NY, pp. 455–469. Takada, S. (1984). “Model Analysis and Experimental Study on Mechanical Behavior of Buried Ductile Iron Pipelines Subjected to Large Ground Deformations,” in Proceedings of the Eighth World Conference on Earthquake Engineering, San Francisco, vol. 7, 255–262.
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Tawfik, M.S. and O’Rourke, T.D. (1985). “Load-Carrying Capacity of Welded Slip Joints,” J. Pressure Vessel Technol., 107, 37–43. Towhata, I., Tokida, K., Tamari, Y., Matsumoto, H., and Yamada, K. (1991). “Prediction of Permanent Lateral Displacement of Liquefied Ground by Means of Variational Principle,” in Proceedings of the Third Japan–U.S. Workshop on Earthquake Resistant Design of Lifeline Facilities and Countermeasures for Soil Liquefaction, Technical Report NCEER-91-0001, Multidisciplinary Center for Earthquake Engineering Research, Buffalo, NY, pp. 237–252. Turner, W.G. and Youd, T.L. (1987). National Map of Earthquake Hazard, final report to the U.S. Geological Survey for Grant No. 14-08-001-G1187, Department of Civil Engineering, Brigham Young University, Provo, UT. Wang, L.R.L. (1994). “Essence of Repair and Rehabilitation of Buried Lifeline Systems,” in Proceedings of the Second China–Japan–U.S. Trilateral Symposium on Lifeline Earthquake Engineering,” Xi’an, China, April, pp. 247–254. Wang, L.R.L. and O’Rourke, M. (1978). “Overview of Buried Pipelines under Seismic Loading,” J. Tech. Councils, 104 (TC1), 121–130. Yeh, G. (1974). “Seismic Analysis of Slender Buried Beams,” Bull. Seismol. Soc. Am., 64, 1551–1562. Youd, T.L. and Perkins, D.M. (1987). “Mapping of Liquefaction Severity Index,” J. Geotech. Eng., 113, 1374–1392.
Further Reading MCEER Monograph No. 3, Response of Buried Pipelines Subject to Earthquake Effects, by M. O’Rourke and X.J. Liu (Multidisciplinary Center for Earthquake Engineering Research, State University of New York at Buffalo), provides a more detailed discussion of many of the topics covered in this chapter.
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24 Water and Wastewater Systems 24.1 Introduction Water and Wastewater Systems Are Lifelines · Historic Performance of Water Systems · Performance in Three Major Events
24.2 Performance Objectives 24.3 Analysis Overview Deterministic · Probabilistic · Reliability-Based Approach · Use of Evaluation Results
24.4 Hazards Seismicity · Wave Propagation · Permanent Ground Deformation · Hazard Mapping · Quantification of Liquefaction-Related PGD · PGD Soil Block Geometry · Uncertainty of Areal Extent of Liquefaction
24.5 Pipe Vulnerability and Damage Algorithms Development History · Pipe Performance · Pipe Vulnerability Methodology
24.6 System Component Vulnerability Supplies · Treatment Plants and Pump Stations · Reservoirs and Tanks
24.7 System Assessment 24.8 Mitigation Alternatives Introduction · Monitoring and Control · Pipeline Design Practices · Develop Alternative Sources or Supplies · Improve System Hardware So It Does Not Fail · Upgrade and Design of New Tanks, Pump Stations, and Treatment Plants
Donald B. Ballantyne ABS Consulting Seattle, WA
24.9 Summary and Conclusions Defining Terms References Further Reading
24.1 Introduction Water systems are essential to modern civilization, yet are significantly damaged in most large earthquakes affecting large cities. Large urban water systems normally include a source, treatment, storage (reservoirs and tanks), and distribution. Wastewater systems normally include a collection system with pump stations, treatment facilities, and disposal. Water and wastewater systems will be addressed together in this chapter, as many of the components are similar from an earthquake performance perspective.
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This chapter discusses historical performance of water/wastewater systems in earthquakes, and why they should be mitigated. This discussion begins with water system performance objectives, which form the basis for component and system analysis techniques. Common components include pipes, tanks, treatment plants, and pump stations, which are linked in an analysis via hydraulic network modeling. Short- and long-term mitigation measures are suggested, including a system post-earthquake monitoring and control strategy, and seismic design guidelines for new pipelines. The mitigation section also considers upgrade and design of new tanks, pump stations, and treatment plants.
24.1.1 Water and Wastewater Systems Are Lifelines Water and wastewater systems are lifelines, which are distinguished in three ways [Ballantyne, 1995b]: • Lifelines are vitally important to society as a whole. Water, for example, is essential to life, and water systems are designed to furnish water for fire suppression. Power and gas systems are designed to keep us warm on the coldest day in January, and cool on the warmest day in August. We expect a dial tone within an instant when we pick up the phone, and to be able to drive from one point to another without much delay. In nondisaster situations, we expect almost 100% reliability from each of these systems. • Water systems and lifelines, in general, depend on the function and interaction of many system components. For a water system to be functional components, including the source, transmission, treatment, storage, and distribution, all must be in working condition. In addition, lifeline systems can be interdependent on one another. Electric power is required to pump water, water is required to cool computers for communication systems, and power is required to operate telemetry systems for water systems. • Water systems, and all lifelines, extend over large areas with a large variation in earthquake hazards. For a given earthquake, shaking intensity on different system components will vary as a function of epicentral distance and the local geologic conditions. Other earthquake hazards, such as liquefaction and landslide, may occur in areas of unstable soils. The community served by a lifeline system is the client of the lifeline system owner. Lifeline system owners have a responsibility to the community to maintain a reasonable level of service following an earthquake. Lifelines are particularly important to support emergency response efforts. In the longer term, lifeline disruption will impact the community economically. Litigation can be a concern if a lifeline system owner has ignored the earthquake vulnerability issue.
24.1.2 Historic Performance of Water Systems Following the 1989 Loma Prieta and 1994 Northridge earthquakes in California, and the 1995 Kobe, Japan earthquake, major water supply systems were lost for fire suppression and for domestic use. None of these recent events turned out to be as catastrophic as the conflagrations following the 1906 San Francisco and 1923 Kanto, Japan earthquakes. However, the classic post-earthquake scenario developed in the Loma Prieta, Northridge, and Kobe earthquakes, where pipelines in both the transmission and distribution systems failed, reservoirs drained, and there was no water available for fire suppression or domestic use. Historic performance of water systems in earthquakes, as well as two instances of non-earthquakerelated water system failure, were reviewed to identify earthquake deficiencies that repeatedly occur, resulting in dysfunction of water systems [Ballantyne and Crouse, 1997]. These events included: Key earthquakes: Kobe, Japan, 1995; Northridge, California, 1994; and Loma Prieta, California, 1989 Less destructive earthquakes that caused water system damage: Landers/Big Bear, California, 1992; Cape Mendocino (Petrolia), California, 1992; and Whittier, California, 1987 Historic devastating earthquakes: Kanto, Japan, 1923; and San Francisco, 1906
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Potable water system outage from other natural disasters: Des Moines, Iowa flood, 1993 (12 days water outage resulting from flooding of a water treatment plant); and the Oakland, California hills fire, 1991, exacerbated by inadequate water supply conditions These hazard events are summarized in Table 24.1, where ratings are shown (5 high, 1 low) for system failure consequences and system component failures for each event. There is a correlation between incidents where there was inadequate water for fire suppression and where fire became a significant issue. The only two events where fire was a small or nonissue were Whittier, which was a relatively small earthquake, and Landers, where there is a sparse population and low building density. There is also a strong correlation between the three most significant fires, San Francisco in 1906, Kanto, and Kobe, and the ineffective use or unavailability of an alternate water supply. System component failures can be grouped by significance of impact on system dysfunction as follows: Very high impact: Pipe damage due to permanent ground deformation (PGD) High impact: Pipe damage due to wave propagation and raw water transmission pipeline failure Moderate impact: Water treatment plant damage, loss of power, and tank inlet/outlet pipe damage Low impact: Tank shell/structure damage, surface supply failure, and well casing and equipment damage Pipeline damage due to PGD and wave propagation, in both transmission and distribution systems, had the greatest impact in most of these events. Chapter 23 in this handbook focuses on this issue. Table 24.1 also shows the consequences of failure of the water supplies in these events: Fire suppression/lacked water supply — Lack of water limited fire suppression, if there were fires, in all of the listed events. A rating of 5 indicates complete, widespread water system disruption. Fire — This column identifies whether there was a fire, and the significance of the fire. Major fires, or conflagrations, occurred in Kobe, Kanto, and San Francisco. In the Loma Prieta and Northridge earthquakes, there were significant fires, but they were generally limited to a single block each. In Des Moines, one industry burned. Used alternate supply — In the Kanto earthquake, there were access points to Tokyo Bay as well as numerous rivers and inlets. Available equipment did not allow pumping from these supplies. San Francisco’s fire pumpers did not have capability to draft from San Francisco Bay in 1906. Both have ratings of 5. A rating of 3 indicates use of alternate supplies with moderate success with the following examples. In Kobe, water was pumped from cisterns, which were quickly drained; they were able to set a pump system from Osaka Bay many hours after the event. In Whittier, tankers normally used for grass fires were relocated, but were not needed. In the Oakland Hills fire, a portable water supply system was set up late in the response. Des Moines is rated as a 2, where tankers had been brought in to use in case of a fire, and were used to haul water to an industrial fire. A rating of 1 indicates aggressive, successful use of alternate supplies with the following examples. In Loma Prieta, the portable water supply system was used to pump water from San Francisco Bay and pump it to the fire. In Northridge, water was pumped from swimming pools. Cooling telephone central offices and computers — In both the Northridge earthquake and the Des Moines flood, tank trucks hauled in water to keep telephone central office air conditioners operating, to cool computer switches. Also in Des Moines, the Principal Insurance Company brought in water by tank truck to keep air conditioners operable to keep computers functioning.
24.1.3 Performance in Three Major Events This section describes water system performance in three recent earthquakes in Japan and the United States, in order to give the reader a better idea how these systems perform. The Kobe (Great Hanshin) earthquake (M 6.9) caused widespread failure to electrical power, water, natural gas, and transportation systems, as well as impairing function of telecommunications and wastewater systems to a service area of 1.5 million people. Electrical power was restored within 3 days. The natural gas system, with over 4000 distribution pipeline failures, took 3 months for restoration. © 2003 by CRC Press LLC
System Component Failure
Note: ? indicates data unclear.
© 2003 by CRC Press LLC
Fire
Used Alt. Supply
Cooling Telephone COs and Computers
Surface Supply Failure
Raw Water Transmission
WTP Damage
Well Casing/Equipment Damage
Loss of Power
Shell/Structure
Inlet/Outlet Pipe
PGD (lateral spread, landslide, fault offset)
Wave Propagation
Building Services
Average
Pipe
1906 1923 1987 1989
5 5 3 4
5 5 1 4
5 5 3 1
na na na 1
2 4 1 1
5 5 1 3
na 3 1 1
na 1 1 na
1 1 4 1
1 1 3 1
1 1 4 na
5 5? 5? 5
3 3? 3? 3
5 5 1 3
1992 1993 1994 1995
5 5 5 5
1 3 4 5
na 1 5 3
na na 4 ?
1 1 1 1
na na 5 5
na na 3 3
1 na na na
3 1 4 3
3 1 3 1
4 1 5 2
5 5? 5 5
5 3? 5 5
1 1 1 5
1991 1993
4 5
5 3
2 2
na 4
na 1
na 1
1 5
na na
4 4
na 1
na 1
na 2
na 1
5 1
4.6
3.6
3.0
3.0
1.4
3.6
2.4
1.0
2.6
1.7
2.4
4.7
3.4
2.8
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Earthquakes San Francisco Kanto Whittier Loma Prieta (San Francisco, EBMUD only) Landers/Big Bear Cape Mendecino Northridge Kobe Other Disasters Oakland Hills Fire Des Moines Flood
Tank
Fire Suppression/Lacked Water Supply
Disaster Event
Supply/Treatment
Year
Failure Consequences
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TABLE 24.1 Summary — Performance of Water Systems in Earthquakes
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Water service was initially lost to over 1 million people. As a result of 1600 pipeline failures in the distribution system, three quarters of water reservoirs serving the urban area drained within 6 hours; the balance within 24 hours. Firefighting was greatly impaired. The sixth floor of the City Hall Annex, which housed the Kobe Water Department, collapsed, impacting restoration efforts. Water service was completely restored after 2 months [Ballantyne, 1995c]. The Northridge earthquake (M 6.7) caused power outages throughout the Los Angeles basin for the first time since the grid was installed. Water was not available for fire suppression in the San Fernando and Santa Clarita valleys. Water service was not available for up to 100,000 customers for 3 days following the event. An estimated 1200 pipeline failures occurred in the water system in the San Fernando Valley; 50 crews were used for repair. Water was trucked in to provide cooling for a telephone central office in the San Fernando Valley. A boil-water order was in place in the Santa Clarita Valley for 10 days following the event. Water was brought in by tank truck and provided by local bottlers for drinking until the water system was restored. In excess of 50 natural gas-related permanent structure fires were reported. One hundred seventy mobile homes burned, primarily as a result of natural gas [Ballantyne, 1995d]. Evaluation of the performance of the San Francisco auxiliary water supply system (AWSS) in the 1989 Loma Prieta earthquake is particularly instructive because it was designed specifically to be resistant to earthquakes. The system reservoir is normally filled from the potable water system, but has an independent distribution system. The pipeline system is structurally very robust [Scawthorn, 1992]. The primary water source is stored in a 40,000-m3 reservoir on Twin Peaks. Two 650-lps (10,000 gpm) saltwater pump stations supply additional water in emergencies. The fireboat Phoenix can supply several different manifolds along the city waterfront to pump an additional 650 lps (10,000 gpm) into the system. In addition, there are 151 300-m3 cisterns located primarily in the northeast quadrant of the city. During the earthquake, Modified Mercalli Intensities (MMI) as high as IX were encountered in the Marina District, resulting in 69 pipe breaks in the potable water system. AWSS piping in that area was not damaged. There was damage to AWSS piping in other parts of the city. A 300-mm-diameter main broke on Seventh Street between Mission and Howard Streets at the boundary of a liquefaction area. The AWSS pipe settled over a pile-supported sewer, and broke. In addition, one 200-mm hydrant branch and five 200-mm hydrant elbows broke, all but one of which were in liquefaction areas. There was major leakage from these breaks that drained the AWSS’s smaller Jones Street Tank in 15 minutes. There was only residual water available from the system when fire engines first arrived on the fire scene in the Marina District. Due to uncertainty as to the number and location of AWSS pipeline breaks, valves between the Upper and Lower pressure zones were not opened. The two saltwater pump stations were kept off-line until broken mains were isolated. As a result, the AWSS Lower Zone was out of service for several hours following the earthquake. The saltwater pump stations were brought on 3 hours after the earthquake at half capacity to slowly refill the system while exhausting entrapped air. The Jones Street Tank was refilled within 5 hours following the event [Ballantyne, 1997a].
24.2 Performance Objectives Performance objectives are needed to define the desired level of post-earthquake service. The 1997 Uniform Building Code seismic design objective is that the building should not collapse in a design basis earthquake (DBE), which has a 10% probability of exceedance in 50 years. There is no similar widely used standard in the water industry. The performance objectives presented in Table 24.2 can provide a starting point for water purveyors. It ties five categories of water system performance to the probability of the defined earthquake ground motion being exceeded. Operating basis earthquakes (OBE), which have 50% probability of exceedance in 50 years, and a DBE, are set as reference points for the proposed post-earthquake performance objectives (Table 24.2).
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TABLE 24.2 Water Performance Objectives: Acceptable Adverse Consequence Levels for Two Earthquake Levels Acceptable Adverse Consequences Performance Category Life Safety Fire Suppression
OBE (50% chance in 50 years)
DBE (10% chance in 50 years)
Minimal — Injury or loss of life are not acceptable consequences. Minimal — With the exception of small isolated areas that are not densely populated, water for fire suppression should be available for entire service area.
Minimal — Injury or loss of life is not an acceptable consequence. Moderate — Water for fire suppression should be available for a minimum of 70% of the service area including all industrial areas and densely populated business and residential areas. Moderate — Provide service for at least 50% of system. Boil water order, or delivery by tanker truck acceptable. Restore 100% service in 1 week. Moderate — Service should be available for at least 50% of system. Restoration to 100% service within 1 week. Moderate — 100% loss of nonessential facilities acceptable if not cost-effective to upgrade and other performance objectives are met.
Public Health
Low — Water should be available for all but a few isolated areas. Boil water order acceptable for up to 48 hours.
System Restoration
Low — Water should be available for all but a few isolated areas.
Property Damage
Low — Any damage should not affect facility functionality and should be repairable.
24.3 Analysis Overview There are several approaches that have been used to assess post-earthquake water system reliability. Often, more than one of these approaches are used for a system evaluation [Ballantyne, 1997b].
24.3.1 Deterministic Conduct deterministic assessments of each water system component and use the component assessment results to develop a system performance scenario. Typically, three steps are involved: 1. The seismic hazards are defined. 2. Based on the seismic hazards and component characteristics, component/pipe vulnerability/fragility is then determined. 3. The final step is to use the component vulnerabilities/fragilities to predict overall system performance. This can be accomplished by either observation, discussing the likely performance with operations personnel, or modeling the hydraulic network.
24.3.2 Probabilistic Express component vulnerability in probabilistic terms and use probabilistic techniques to evaluate system reliability. This is a refinement of the deterministic approach above (moving from deterministic to probabilistic). There is a significant amount of uncertainty associated with earthquake hazards and the response of facilities subjected to earthquake hazards. Although accurately modeling this uncertainty is difficult, probabilistic assessments can be used to assess the magnitude and likelihood of variations from the expected outcome.
24.3.3 Reliability-Based Approach Although system reliability assessment techniques such as fault tree analysis have been used extensively in many applications, such as the nuclear industry, they have not been used as extensively by water utilities. Fault trees can be used to calculate failure probabilities, identify paths that may lead to failure,
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and identify those events that are most likely to lead to failure [Scawthorn, 1998; Odeh et al., 1995]. The benefit of a fault tree analysis is inherent in a hydraulic model. Geographic information system (GIS) technology allows calculation and graphic presentation of system risk assessment results that easily can be used and interpreted by planners, emergency response personnel, and engineers. Pipeline construction materials and joint types can be electronically overlaid on the earthquake hazards. Damage algorithms that relate pipe damage to ground shaking intensity and permanent ground displacement can be used to determine pipe vulnerability using the GIS. Pipe criticality can be determined and considered in the risk assessment determination.
24.3.4 Use of Evaluation Results A suite of system performance scenarios can be very useful for emergency planning, mitigation, estimating economic losses, and planning new pipeline corridors. Estimated pipeline and component damage can be used to predict the functionality of the water system for a given earthquake scenario. If the system is not expected to be functional, the information can be used to estimate the time it will take to restore the system to full operation. Some of the ways in which information has been used in the United States are described below. One of the crucial elements of an earthquake mitigation program is emergency planning. Immediately following an earthquake, resources required for effective response are in limited supply, and time becomes a very important parameter. Pipeline damage information can be used as an effective emergency planning tool, in the following ways: • • • •
Optimizing system postevent functionality by preplanning an operational strategy Preplanning dispatch of personnel and resources required for emergency response Providing information for fire departments regarding availability of water for fire suppression Providing information to customers as to potential outages, so that they can develop alternative supplies
Damage scenarios are being used as a tool to optimize mitigation planning. As utility budgets continue to shrink, it is crucial to make the best use of available funds for both capital improvements and maintenance. Damage information can be used to quickly calculate economic losses once damage has been estimated. For new systems, development of damage scenarios provides an excellent tool to assess relative risk, both earthquake and non-earthquake, for different pipeline corridors. Some applications are: • To compare estimated system performance with planning objectives to determine the extent of mitigation required. • To identify and prioritize upgrades for deficient pipeline segments/areas/functions. Expected losses in selected earthquake scenarios can also be used to: • Estimate probable maximum losses to use as a tool in negotiating insurance coverage and premiums. • Influence decision-makers: loss estimates, including pipeline losses, are compelling information to influence decision-makers to fund future earthquake risk-reduction programs.
24.4 Hazards Earthquake hazards are the damaging effects associated with earthquakes. Pipe damage algorithms/ fragility relationships are often developed for earthquake wave propagation and permanent ground deformation (PGD) (see Chapter 23). Seismicity is the probability of an earthquake occurrence, and hazard is the probability of experiencing a given ground motion at a selected location (see Chapter 4).
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24.4.1 Seismicity Typically, earthquake scenarios are selected that represent standardized probabilities of exceedance, or other measures meaningful to the particular community. Often, OBEs are selected that have a 50% chance of exceedance in a 50-year life of a facility. The premise is that the facility will probably experience the defined intensity of shaking during its life and should be designed to remain functional. The design basis earthquake, DBE, is often taken as an intensity that has a 10% chance of exceedance in that same 50year life of the facility. The facility will probably not be subjected to the prescribed earthquake intensity during its life but may, and should, be designed to at least maintain life safety. Note that, assuming a Poisson model of occurrence, the OBE and DBE mean durations between events (return period) are 72 years and 475 years, respectively. It is much easier to model an earthquake scenario rather than a probabilistic earthquake ground motion. Usually, a scenario is selected that approximately represents the ground motions comparable to the OBE or DBE. In some cases a specific earthquake scenario is of greater interest, such as the repeat of a specific earthquake that had previously occurred, such as the 1906 San Francisco earthquake for the San Francisco Bay area. Once these earthquake scenarios are selected, ground motion intensities are calculated across the study area using attenuation relations (see Chapters 5 and 6) and GIS [Ballantyne and Heubach, 1996].
24.4.2 Wave Propagation Propagating earthquake waves move the soil as they pass. The soil moves back to its original position once the wave has moved on. Most pipe can readily accommodate some lateral movement. Compression waves cause differential longitudinal movement along the pipe axis. Most pipe systems currently in use, such as concrete cylinder pipe, can accommodate some differential movement from wave passage by either accommodating it in the joint, or in pipe strain and ductility. Some damage from wave passage may occur, but it will be widely distributed throughout the system. If the length of pipe subjected to wave passage is much larger than that subjected to PGD, the total numbers of pipe failures from the two hazards may be comparable. Brittle pipe with rigid joints is subject to significant damage from wave passage [Ballantyne, 1995b]. This topic is discussed in more detail in Chapter 23 of this volume.
24.4.3 Permanent Ground Deformation Permanent ground deformation (PGD) can be caused by liquefaction, lateral spread, settlement, lurching, landslides, and fault rupture. It can put tension (Figure 24.1), compression, bending, and shear loads on pipelines. PGD can occur as a result of liquefaction-caused lateral spread when the soil moves down a slope or toward a free face. Ground shaking that consolidates soil particles, forcing out water from between the particles, causes liquefaction. As the water tries to escape, it turns the soils into a quick condition. Liquefaction can also result in loss of bearing capacity or flotation of buried pipes. For buried pipeline systems, significant flotation usually is limited to components with large voids, such as manholes (Figure 24.2), valve chambers, or sewers that are not filled with liquid, making them more buoyant. Pipes filled with liquid are approximately the same density as the liquefied soil, so that they have neutral buoyancy and tend not to float if liquefaction occurs. Chapter 7 of this volume discusses liquefaction in more detail. Settlement occurs when soil consolidation takes place, but there is no water present. Lurching occurs when soil masses are thrown (i.e., accelerated sufficiently to overcome soil cohesion) by earthquake ground motion and do not return to their original location. Landslides move down slope, with displacements ranging from millimeters when creep occurs, to tens and hundreds of meters when flow slides occur. Fault rupture moves soil on one side of the fault relative to the ground on the other side of the fault.
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FIGURE 24.1 Ductile iron pipe with pulled joint following 1995 Kobe earthquake. (Courtesy Kobe Water Department)
FIGURE 24.2 Floating manhole following 1964 Niigata earthquake (photographer unknown).
24.4.4 Hazard Mapping Given modern GIS technology, it is useful and efficient to map geologic hazards in an electronic format, especially given that a significant body of existing hazard mapping information is emerging, as well as that utility system pipelines and components are increasingly being databased using GIS. Washington, Oregon, Utah, and California all have hazard mapping programs with maps available for many urban
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areas. The U.S. Geological Survey has also funded a significant hazard mapping effort. However, there is still a wide variation of the quality of information available [Ballantyne and Heubach, 1996]. Typically liquefaction and landslide susceptibility are the basic hazard maps required. In California, Japan, Turkey, Taiwan, and other very active tectonic regimes, surface faulting must be taken into account. In Washington, Oregon, and other still active but less pronounced regimes, surface faulting is less common; seismicity may be dominated by other sources (e.g., subduction events) and is therefore generally not considered. In more sophisticated studies, site amplification is taken into account to better establish liquefaction and landslide probabilities (calculated for the specific scenario shaking intensity). Site amplification may also influence damage from wave propagation effects, although these are considered to be small compared to permanent ground displacement effects. Key parameters required to achieve reasonable reliability of mapping results include the areal extent of liquefaction and landslide, and lateral spread displacement. In earlier studies, it became apparent that an estimate of the percentage of the area that would deform as a result of liquefaction differed widely, while estimates of liquefaction probability had somewhat greater reliability. Geologists started to provide an estimate of areal extent. Lateral spread displacements are an important relationship in establishing the segmented pipe failure rates. Youd and Perkins [1987] and Youd et al. [1999] provided the liquefaction severity index (LSI) and multiple linear regression (MLR) analysis techniques, respectively, to estimate displacements. GIS provides an excellent tool to calculate displacements using digital elevation maps to calculate slopes and identify free faces used in the MLR calculation.
24.4.5 Quantification of Liquefaction-Related PGD In 1987, Youd and Perkins published the LSI approach to estimate the maximum PGD at a given site for a particular earthquake scenario. LSI is the maximum displacement, in inches, anticipated to occur given an earthquake of specified magnitude and distance. Initially, this information was not applied as a pipeline damage estimation tool [Youd, 1987]. More recently, Youd has refined the LSI method with the MLR method for estimating maximum PGD from liquefaction-related lateral spreading [Youd et al., 1999]. Their approach is useful in pipe evaluation studies.
24.4.6 PGD Soil Block Geometry In 1992, O’Rourke identified the significance of lateral spread block geometry on the extent of continuous (welded steel) pipeline vulnerability [O’Rourke, 1992; see Chapter 23, this volume]. He concluded that the larger (along the pipe axis) the block in which the pipe was embedded, the greater the strain that would be induced. This is analogous to the development length of reinforcing steel in reinforced concrete. It still remains that segmented pipe PGD-related damage is controlled by net PGD. A major problem related to this approach is being able to estimate the block size and ground breakup pattern.
24.4.7 Uncertainty of Areal Extent of Liquefaction When applying damage algorithms to pipes in liquefiable soils, the length of pipe in soils that actually liquefy needs to be calculated, compared to the length in soils defined to be liquefiable. This is defined as the areal extent of liquefaction effects. The areal extent generally ranges from 5 to 25%, with estimates as high as 100% in soils with very high liquefaction susceptibility subjected to very strong ground motions. In three projects where PGD was considered to be the primary hazard for pipelines, the project team geotechnical engineers were asked to make estimates on the areal extent of liquefaction. There was a significant level of uncertainty associated with those estimates because of the lack of available methods. These three studies all considered the liquefaction susceptibility of alluvial deposits in similar geotechnical settings along rivers ultimately discharging into the Pacific Ocean. The estimates for areal extent of liquefaction varied by a multiple of seven. The areal extent of liquefaction estimate is directly related to the damage estimate, so the degree of uncertainty is very important.
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24.5 Pipe Vulnerability and Damage Algorithms 24.5.1 Development History This section summarizes the development of pipeline earthquake loss estimation as well as methods used to estimate PGD in support of pipeline loss estimation. Empirically based water pipeline damage algorithms reviewed in this chapter were initiated in Japan and refined in both the United States and Japan as described below [Ballantyne, 1994b]. 24.5.1.1 Initial Japanese Efforts A method for estimating pipeline earthquake losses was introduced by Professor Katayama of Tokyo University in the mid-1970s. He developed pipeline damage algorithms relating pipe failures and earthquake peak ground acceleration, PGA. His damage algorithm enveloped loss estimates with specific estimates dependent on the soil characteristics, such as liquefaction susceptibility [Katayama, 1975]. 24.5.1.2 Segregation of Wave Propagation and PGD Effects Eguchi segregated pipeline damage from wave passage, fault rupture, and liquefaction in the early 1980s. He gathered empirical damage data from over 20 earthquakes worldwide, but was able to develop the most significant relationships based on damage data from the 1971 San Fernando earthquake [Eguchi, 1982, 1983]. He assumed that MMI was an indicator of wave propagation effects on pipelines. For cast iron pipe, the relationship between MMI and the failure rate was established. He then related damage rates for other pipe materials to cast iron for one intensity, establishing a family of damage algorithms. For that same earthquake, he also developed pipeline damage rates for liquefaction conditions for a family of pipe materials, but did not relate them to PGD from liquefaction. Finally, he developed damage rates based on the proximity to and displacement of fault offset. 24.5.1.3 Differentiation of Pipeline Failure Consequences In the late 1980s, Ballantyne segregated pipeline damage into pipeline breaks and pipeline leaks [Ballantyne, 1990]. This information became valuable for use in deterministic post-earthquake water system hydraulic modeling. As part of the same study, the question of areal extent of liquefaction along a pipeline corridor or in a microzone had a very significant effect on loss estimation results. It became clear to this author in that study that PGD-related pipeline damage would often control the overall system performance, and that pipeline unit damage rates for liquefaction and PGD were an order of magnitude greater than for wave passage. 24.5.1.4 San Francisco Liquefaction Study Following the 1989 Loma Prieta earthquake, the City and County of San Francisco selected a project team to estimate utility losses that might occur in liquefiable soil areas around the periphery of the city for a magnitude 8.3 San Andreas earthquake [Harding Lawson Assoc., 1991]. The project team developed damage algorithms relating pipeline damage to PGD using empirical damage data from the 1971 San Fernando earthquake, the 1989 Loma Prieta earthquake (including the San Francisco Marina District and the City of Santa Cruz data), and the 1983 Nihonkai Chubu, Japan earthquake. It was found to be very difficult to reliably estimate the PGD due to liquefaction, or to find pipeline damage data related to a record of PGD. 24.5.1.5 Strain-Related Pipeline Vulnerability Assessment Studies of the Greater Vancouver Regional District (GVRD) water system in British Columbia [Kennedy/ Jenks Consultants, 1993] and the British Columbia gas transmission system [Honegger, 1994] have used pipe strain induced by PGD as an indicator of vulnerability. In the GVRD study of their welded steel pipe system, PGD was estimated using the LSI approach. Pipeline strain was calculated considering the length along the pipeline where PGD was expected and the pipe wall thickness-to-radius ratio, t/R. This
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approach estimates the relative pipeline vulnerability but does not estimate the expected total number of failures. The British Columbia gas study applied a similar approach. Segments of pipe were identified where there was a high liquefaction susceptibility and lateral spread potential. In these locations, an estimate was made of the expected PGD. This information was then input into a finite element analysis of the pipeline segment. The findings indicated that pipelines with 90° bends in areas where significant PGD was expected were the most vulnerable. Again, an estimate of the number of failures could not be made using this method.
24.5.2 Pipe Performance Pipe performance in earthquakes is a function of the pipe material and joint as well as the earthquake hazards to which it is subjected [Ballantyne, 1995b, 1995f]. 24.5.2.1 Pipe Material and Joint Types Materials commonly used for potable water transmission and distribution pipe include ductile iron, steel, concrete cylinder, and polyvinyl chloride (PVC). Polyethylene has only recently been approved as an AWWA standard, and is becoming a more accepted water supply pipe material. Asbestos cement has been used extensively in the past, but sees minimal use for new installations. In the early 1970s, ductile iron replaced cast iron for new installations. Pipe joints commonly used for potable water pipelines include bell-and-spigot joints with brittle sealants (rigid joints); bell-and-spigot with elastomeric gasketed joints, or welded joints. Asbestos cement pipe is joined with couplings that work like a double bell, back-to-back. Steel and polyethylene can employ butt joints that are welded (steel pipe) or fused together (polyethylene pipe). Older (pre-1920) steel pipe barrels and joints were usually riveted. Until the 1950s, cast iron pipe joints were commonly sealed with lead and oakum or mortar, making them rigid. When conducting an evaluation of an existing pipeline system, knowing the date of installation can sometimes allow identification of the pipe type and joint type. There are many variations on pipes and joints. Material selection is often controlled by the cost of materials and the familiarity of operations and maintenance staff, design engineers, and local contractors in their use. Each water purveyor also has a preferred pipe material for each application (transmission, distribution, or service piping, corrosive soils, etc.). Generally, large-diameter transmission mains, larger than about 600 mm (24 in.) in diameter, are constructed of welded steel or concrete cylinder pipe. Smaller transmission mains may be constructed of ductile iron pipe. Ductile iron and PVC are the modern materials of choice for most distribution piping, while cast iron and asbestos cement are common for older distribution systems. Some jurisdictions continue to prefer ductile iron for distribution systems as they believe it is more reliable and easier to tap for building services. Other jurisdictions prefer PVC because it is resistant to corrosion and is less expensive to construct. Polyethylene pipe is available, but not widely used because of historic material failure problems in service lines. Polyethylene pipe uses fused joints. The AWWA has standards for each of these pipe materials, but they do not address seismic design. Welded steel and concrete cylinder pipe both employ bell-and-spigot joints. Sometimes the joints are welded and sometimes not. Welding is usually used to transfer thrust loads. Joints on pipe up to 600 mm are welded only on the exterior. On larger-diameter pipe, they are sometimes back-welded on the interior. Ductile iron pipe is available with bell-and-spigot push-on joints, mechanical joints, or flanged joints. Mechanical designs, and designs using wedges embedded in the gaskets, are used to restrain joints. PVC pipe can also be restrained using similar designs. There are no restrained joints allowing longitudinal movement available in the United States, similar to the Japanese S joint (Figure 24.3). Large inventories of asbestos cement and cast iron remain in most water purveyors’ systems, but neither is currently available or used for new pipe installations.
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FIGURE 24.3 Japanese seismic joint allows longitudinal movement of approximately 1.5% of its length.
24.5.2.2 Joint Restraint Joint restraint is an important parameter to evaluate earthquake vulnerability. Bell-and-spigot pipe joints and coupled (asbestos cement) pipe do not provide joint restraint unless special hardware is added. Both bolted and boltless restrained joint designs have been developed to be an integral part of the joint design. Restrained joint systems available in the United States offer only minimal longitudinal deformation once the joint is installed. This means that any longitudinal movement from the PGD in the surrounding soil along the pipe must be dissipated in pipe strain. This may put very large longitudinal loads on pipe joints, causing them to fail. Welded steel and fused polyethylene joints are inherently restrained. The Japanese have developed the S seismic joint that allows some longitudinal movement, to a point, when the retainer ring stops pull out. With this design, when longitudinal deformation is initiated, it will be taken up in the first joint. If the first joint does not have the extension capacity, it is passed along to the second joint, and so on, similar to the way railroad train car connections take up slack when a train starts. Strain buildup is minimized, which then controls longitudinal loading across pipe joints. 24.5.2.3 Pipe Performance Parameters Four pipeline performance parameters have been identified in an attempt to rate the earthquake vulnerability of pipelines (Table 24.3) [Ballantyne, 1995b]. These parameters were selected based on pipe material and joint type, and their respective earthquake damage mechanisms. The pipeline performance parameters are: Ruggedness is a function of pipe material strength and ductility. It is a factor in pipe failure in compression, shear, bursting, and, to a lesser degree, tension and bending. Resistance to bending failure of the pipe barrel (or body) is a function of the pipe barrel’s strength in bending. Nonductile pipe such as cast iron and asbestos cement, 8 in. and smaller, is particularly vulnerable in this category. Cast iron pipe may be slightly stronger, but the nominal laying lengths are half again as long as for asbestos cement pipe, allowing for a longer moment arm to cause bending failure. Large diameter, nonductile pipe typically has adequate strength to resist failure in bending. Alternatively, if the pipe barrel will bend while stressing the pipe material beyond its yield point, if the pipe bends in a ductile manner without breaking, it is considered to be resistant to bending failure.
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Joint Flexibility
Restraint
Total
Low vulnerability Ductile iron Polyethylene Steel Steel Steel Low/moderate vulnerability Concrete cylinder Ductile iron PVC Steel Moderate vulnerability AC > 8" D Cast iron > 8" D PVC Concrete cylinder Moderate/high vulnerability AC <=8" D Cast iron <=8" D Steel High vulnerability Cast iron
Joint Type
Bending
Material Type/Diameter
Ruggedness
TABLE 24.3 Relative Vulnerability of Pipe Materials
C1xx series C906 C2xx series None C2xx series
B&S, RG, R Fused Arc welded Riveted B&S, RG, R
5 4 5 5 5
5 5 5 5 5
4 5 4 4 4
4 5 5 4 4
18 19 19 18 18
C300, C303 C1XX series C900, C905 C2xx
B&S, R B&S, RG, UR B&S, R B&S, RG, UR
3 5 3 5
4 5 3 5
4 4 4 4
3 1 3 1
14 15 13 15
C4xx series None C900, C905 C300, C303
Coupled B&S, RG B&S, UR B&S, UR
2 2 3 3
4 4 3 4
5 4 4 4
1 1 1 1
12 11 11 12
C4xx series None None
Coupled B&S, RG Gas welded
2 2 3
1 1 3
5 4 1
1 1 2
9 8 9
None
B&S, riged
2
2
1
1
6
AWWA Standard
Note: B&S = bell and spigot; RG = rubber gasket; R = restrained; UR = unrestrained.
Joint flexibility is a function of a pipe’s ability to extend, compress, or bend (or rotate) around the joint without breaking the joint’s watertight seal. Joint restraint is a function of the pipe–joint system to hold together in extension. A fifth parameter, or condition, should be considered for existing pipe. Pipe that has corroded, as identified by soil corrosivity, field inspection, or poor maintenance history, will likely perform worse than similar pipe in good condition. 24.5.2.4 Pipe Damage Mechanisms Pipe earthquake damage mechanisms are important to consider when rating earthquake vulnerability. Damage mechanisms can be segregated into two groups, pipe joint and pipe barrel, and are listed below. The pipe performance parameter that is most significant in controlling the respective mechanism is listed following each, separated by a dash. Pipe joints usually fail in the following ways: • Extension (pulled joints) — joint restraint • Compression (split joints) — ruggedness • Bending/rotation — joint flexibility and ruggedness In the 1995 Kobe earthquake, approximately two thirds of the pipe failures were from joint extension or compression (Figure 24.1). One reason that other types of failures were minimized in Kobe is that 89% of the pipe was either ductile iron or welded steel.
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FIGURE 24.4 Fire hydrant damaged due to water hammer in the 1994 Northridge earthquake.
Pipe barrels usually fail in the following ways: • • • •
Shear — ruggedness Bending — resistance to bending failure and ruggedness Hole (condition) Split/burst — ruggedness and condition
Holes are usually a result of corrosion. Split or burst pipes can be the result of corrosion, often combined with water hammer (Figure 24.4). Pipes can collapse; usually this is limited to failure of nonpressure pipelines that have a weaker cross section. Pipe failures are often associated with bends and fittings, hydrant connections, service connections, and valves where there is a discontinuity in the pipeline. Sewers behave in a similar manner, except that gravity sewers and the associated manholes also sometimes float when located below the water table, within the liquefaction zone (Figure 24.2). This occurs because gravity sewers are often buried deeper and therefore have a greatly likelihood of being below the water table, and they are often only partially filled, making them more buoyant. 24.5.2.5 Welded Steel Pipe Joints Welded steel pipe joint vulnerability is differentiated by a range of issues, including gas vs. arc welding, lap vs. butt joints, and bell design. In both the 1971 San Fernando and 1994 Northridge earthquakes,
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gas-welded steel pipe performed much worse than arc-welded steel pipe. Typically, the gas-welded steel pipe was installed before 1940. Two considerations have been raised that may lead to its poor performance: quality control, particularly of weld penetration, and embrittlement of pipe material properties adjacent to the weld. Welded lap joints allow some eccentric loading in the joint as compared to butt-welded joints that have no eccentric loads. To some degree, this can be controlled by providing equal welding on both the inside and outside of the joint. Interior welding is limited by pipe diameter (i.e., insides of smaller pipes cannot be accessed for welding). It has been suggested that, in the bell manufacturing process, properties of the metal are changed when the bell is formed. This concern may be limited to larger-diameter pipelines as a result of the limitation of the manufacturing equipment. The radius of the bend at the back of the bell may also influence pipe bell load transfer characteristics. Therefore, gas-welded pipe joints are rated much more vulnerable than arc-welded joints. Pipe with butt-welded joints should be rated less vulnerable than pipe with lap-welded joints. 24.5.2.6 Pipe Material and Joint Type Rating Based on observations of pipeline performance in recent earthquakes, pipe material and pipe joint types can be rated for ruggedness, resistance to bending failure, joint flexibility, and joint restraint. The ratings for each parameter can then be combined to provide a net vulnerability (Table 24.3). Consideration can be given to weighting one performance parameter higher than others. Further evaluation, comparing earthquake performance and the resulting vulnerability ratings, indicated that no weighting (i.e., all parameters given equal weighting) provides results more consistent with experience. The results are summarized below: • Ruggedness: Pipe manufactured from asbestos cement and cast iron have a moderate to high vulnerability. Concrete cylinder pipe, a composite of steel and concrete, PVC, and gas-welded steel are considered to be moderately rugged. • Resistance to bending failure: Asbestos cement and cast iron pipe, 8 in. and smaller, are particularly vulnerable to bending. The rigid joint cast iron pipe includes all pipe diameters, so it does not have as low a rating. • Joint flexibility: Gas welded and rigid bell-and-spigot pipe are particularly vulnerable to joint movement. • Joint restraint: All unrestrained joint pipe is vulnerable to extension (pull apart) failures. Restrained joint concrete cylinder pipe and PVC are downgraded because the pipe barrel and restrainer attachments are not as strong as for steel and ductile iron pipe. An additional level, very low vulnerability, is proposed. It would include butt-welded steel and ductile iron pipe with the Japanese “seismic” joint (Figure 24.3). Butt-welded steel joints are stronger than belland-spigot welded steel joints. Seismic joint ductile iron pipe is designed to minimize strain buildup by providing some longitudinal extension before it restrains further movement. 24.5.2.7 Pipeline Linings and Coatings Pipelines have been evaluated on the merits of their basic material. In some cases, mortar and/or cement linings and coatings are added to pipelines to resist corrosion. These materials are less ductile than steel or concrete. In the case of mortar lined and coated ductile iron or steel pipe, the coating may have a tendency to limit the ductile performance of the pipe. If the pipe loading forces the pipe to deform significantly, the mortar may spall, allowing corrosion to begin. 24.5.2.8 Pipeline Fittings and Appurtenances A pipeline system is only as strong as its weakest component. Therefore, fittings and appurtenances such as valves and hydrants should be constructed of ductile materials. Air release valves and wet barrel
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hydrants should be designed to accommodate water hammer (Figure 24.4). Service connections should be designed to accommodate differential movement. This was clearly demonstrated in the Loma Prieta earthquake, where five of the seven breaks in the San Francisco AWSS system were in 8-in. elbows on hydrant brances [Scawthorn, 1997].
24.5.3 Pipe Vulnerability Methodology 24.5.3.1 Pipeline Damage Algorithms Pipeline damage is estimated by applying damage algorithms relating earthquake geologic hazards to pipeline categories, each with different parameters. These pipeline categories are then mapped using GIS. Pipeline parameters that are usually taken into account include ductility, geometry, condition, joint flexibility, and joint restraint [Ballantyne and Heubach, 1996]. Basic algorithms to estimate wave propagation losses relate MMI or peak ground velocity (PGV) to pipeline damage. Most of the empirical damage data used to develop these algorithms are based on MMI. The American Lifeline Alliance, ALA [2001] has developed pipeline damage algorithms for PGV. The relationships developed by ALA are as follows: Repair rate = K1 (0.00187) PGV (for wave propagation)
(24.1)
where repair rate is per 1000 feet PGV is in inches per second K1 is generally: high vulnerability pipe moderate vulnerability pipe low vulnerability pipe
0.9–1.3 0.4–0.8 0.15–0.3
Repair rate = K2 (1.06) PGD0.319 (for permanent ground deformation)
(24.2)
where repair rate is per 1000 feet PGD is in inches K2 is generally: high vulnerability pipe moderate vulnerability pipe low vulnerability pipe
0.8–1.0 0.5–0.7 0.15
Early damage algorithms for permanent ground displacements related liquefaction or landslide susceptibility to pipeline damage. The use of GIS has allowed easier input of parameters required to estimate ground displacements. This relationship is most applicable to segmented pipe. Continuous pipe damage is more closely related to lateral spread block size [O’Rourke, 1992; also Chapter 23, this volume]. A topic of research of interest to the pipeline community is information on establishing PGD block size. The results of the pipeline analysis are in terms of pipeline failures per unit length and per segment (node to node). Results are presented graphically in standard categories that are based on the probability of damage in unit lengths of pipe. Graphical presentation makes vulnerable areas become very apparent. Other corrections can be made for the pattern of liquefaction deformation, pipe orientation to PGD, corrosion condition/maintenance history, number of connections per unit length, and wall thickness/ pipe radius ratio (for welded steel pipe). Additional research is required to develop and expand upon these correction factors.
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24.6 System Component Vulnerability 24.6.1 Supplies Water sources usually include watersheds, dams, reservoirs, and wells. Watersheds are vulnerable to landslides that impact water quality. Older, earthen dams are vulnerable to liquefaction; rockfill and concrete dams are less vulnerable to earthquakes. Wells may be damaged if liquefaction occurs and the material surrounding wells moves laterally, bending the well casing. In all cases, related equipment and piping are vulnerable. Both watersheds and wells can be polluted if a contamination source is disrupted by the earthquake and feeds into the supply [Ballantyne, 1995d]. For example, in the 1923 Kanto earthquake, landslides covered Tokyo’s river intakes. A similar fate occurred to the Managua water supply in the 1976 event. In San Francisco in the 1906 earthquake, there was damage to supply impoundment dams, but they did not fail. In the 1971 San Fernando earthquake, the City of San Fernando’s unsealed wells were contaminated by sewage from a broken sewer main. Oil well casings collapsed in the 1983 Coalinga earthquake. In the 1990 Luzon, Philippines earthquake, wells serving Dagupan were bent over at the top by as much as 15 degrees as a result of liquefaction.
24.6.2 Treatment Plants and Pump Stations The following treatment plant and pump station components are vulnerable: 1. 2. 3. 4. 5.
Foundations Process tanks Buildings Equipment and piping Electrical power
Foundations are subject to damage if supporting soils fail. The Jensen Water Treatment Plant in Los Angeles provides an example where soil failure occurred in the 1971 San Fernando event. Soil improvements since 1971 limited the effect of soil failures at the plant in the 1994 Northridge event [Ballantyne, 1995e]. Below-grade tanks and channels can float or offset due to liquefaction, such as at the Higashinada Wastewater Treatment Plant in the 1995 Kobe earthquake (Figure 24.5). Wastewater facilities are particularly vulnerable to liquefaction, as they are often located in low-lying areas where liquefaction is likely to occur. Process tank appurtenances can be damaged from sloshing liquid contents. The most dramatic of these failures occurred in the Loma Prieta earthquake, where both water reactor/clarifiers (Figure 24.6) and wastewater digester floating covers were impacted [Ballantyne, 1990b]. Buildings associated with water and wastewater facilities are often conservatively designed, box-like structures with few wall openings. These shear wall structures perform well. Of great significance is the requirement for buildings to remain functional following an earthquake if there is an expectation that the lifeline system they support is to remain operable. Water department buildings collapsed or were condemned in the 1985 Mexico City earthquake, the 1990 Philippine earthquake, and the 1995 Kobe, Japan earthquake. Building functionality has historically been given very limited attention in the Uniform Building Code or other building codes, although this is now being addressed (see Chapter 11, this volume). Equipment and piping are vulnerable to shaking if they are not adequately anchored, and flexibility is not provided between components that may move differentially. One of the issues confronting some water/wastewater agencies that have not previously designed for earthquakes is a large inventory of significant equipment and piping that is unrestrained or supported by threaded rods hanging from the ceiling. Another vulnerable equipment element is spring vibration isolators often used on emergency generators. They fail, and can render the supported equipment useless. Techniques for assessing and retrofitting these items are discussed in Chapter 20 of this volume. © 2003 by CRC Press LLC
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FIGURE 24.5 Higashinada Wastewater Treatment Plant influent channel offset by about 1 m. The treatment plant site settled up to 1 m and moved laterally up to 2 m as a result of liquefaction.
FIGURE 24.6 Rinconada Water Treatment Plant reactor clarifier center assembly was moved by sloshing water, pulling launders from the tank walls and separating inlet/outlet piping. (Courtesy Ryder, Kennedy/Jenks)
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Failure of gaseous chlorination systems can have severe life-safety consequences. In four major earthquakes since 1989, chlorine releases have hospitalized water system operators. These systems usually incorporate equipment and piping. The author has observed ton-size chlorine containers stacked like firewood with no longitudinal restraint while connected by pigtails to a chlorine gas header (this condition has since been mitigated). Treatment plants and pump stations are dependent on electric power and instrumentation systems. Regional power is vulnerable, as evidenced in the Loma Prieta, Northridge, and Kobe earthquakes. The outages that occurred in California and Japan, where utilities have aggressive earthquake mitigation programs, only emphasize this issue. Other regions have even more vulnerable power, and therefore also water, systems. Emergency generators designed with secondary systems (fuel, cooling, starting, etc.) designed to resist earthquakes are highly recommended, and they should be operated regularly under load.
24.6.3 Reservoirs and Tanks Flat-bottomed vertical steel water storage reservoirs (tanks) have been damaged in numerous earthquakes. The most common failure mechanism is damaged connection piping. This occurs when unanchored tanks rock, and inlet/outlet piping, rigidly attached to the tank and buried in the ground, breaks, as occurred to a tank owned by the Los Angeles Department of Water and Power in the 1994 Northridge earthquake. In more severe cases, the tanks themselves are damaged. The tank wall lifts off the ground when the tank rocks. The tank wall then impacts the ground when the tank rocks in the opposite direction, causing severe compression loading and resulting in wall buckling. This phenomenon is often referred to as “elephant’s foot buckling” (Figure 24.7). Steel tank damage mitigation methods include addition
FIGURE 24.7 Tank elephant’s foot buckling in Northridge earthquake, 1994. © 2003 by CRC Press LLC
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of connecting pipe flexibility and anchoring the tank to its foundation. On occasion, the tank structure must be strengthened to accommodate seismic loading [Ballantyne, 1997b]. Elevated tanks can collapse (Imperial Valley, 1979) if not designed to resist encountered earthquake loadings. Wire-wrapped concrete tanks from the 1960s may have corroded reinforcing wire, and have failed when attempting to resist earthquake loading [Schiff, 1990]. Roof–wall and wall–foundation connections are also of concern. The AWWA incorporated optional (required in UBC Zone 4) earthquake design standards in the steel tank design standards starting in 1979 [AWWA, 1996]. Tanks designed in accordance with that standard have performed well. Natural periods and amplitudes of sloshing liquids in circular and rectangular tanks may be determined using Housner’s method [Housner, 1963]: M1 k1
Natural period = T = 2π
(24.3)
For circular tanks of radius R and water depth h:
h tanh 1.8 R M1 = 0.6 M h 1.8 R k1 = 5.4
d=
M12 gh M R2
(24.4)
(24.5)
kR 0.63 Sd 1 M1g S kR 1 − 0.85 d 1 R M1g
2
(24.6)
For rectangular tanks of length L and water depth h:
L tanh 1.7 R M1 = M L 1.7 R k1 = 3
d=
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M12 gh M L2
(24.8)
kL 0.84 Sd 1 M1g S kL 1− d 1 L M1g
(24.7)
2
(24.9)
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where g = acceleration of gravity M = total mass of water in the tank Sd = response spectral displacement at period T, for an appropriate level of damping (for most liquids, 0.5% is assumed) d = maximum amplitude of sloshing Wire-wrapped concrete tanks are less vulnerable to earthquakes than steel tanks, but have failed. Tanks that were constructed prior to use of “earthquake cables” used in current designs are the most vulnerable. Corrosion of the wire wrapping is also a concern. The AWWA tank design standards incorporate seismic design methods [AWWA, 1995]. Other analytical methods for analysis of existing tanks have been developed based on historic earthquake performance data. Tank shells suffered elephant’s foot buckling, and in a few cases, split in the Northridge, Landers/ Big Bear, and Whittier earthquakes. These failures are not thought to have been the primary cause for system failure. Tank inlet/outlet and drainpipes failed with major or significant system effects in the Northridge, and the Landers/Big Bear and Whittier earthquakes, respectively. The literature indicates that pipe connection failures were much more common, resulting in much greater impact on system performance than were tank structural failures. There was only one tank pipe inlet/outlet failure in Kobe.
24.7 System Assessment Once the number of pipeline failures is known, a system hydraulic analysis can be performed using a standard computer network hydraulic analysis package. A rule of thumb is that for failures due to wave propagation, 15 to 20% of the failures are breaks and the rest leaks, and that for failures due to PGD 80 to 85% are breaks, where a break results in loss of pipeline hydraulic continuity [Ballantyne, 1990]. The network hydraulic models that are used have been refined to account for negative pressures [Ballantyne, 1997a]. If the objective is to prioritize pipeline deficiencies for a mitigation program, pipeline criticality is developed. Pipeline criticality is a function of the pipeline redundancy, capacity, and/or ease of repair. In one system, the single raw water pipeline from the source to the treatment plant, and from the treatment plant to the distribution system, was given the highest criticality rating. In another instance, two redundant pipelines carried water between two points. Both were highly vulnerable. One was inaccessible. The other accessible pipeline was given a high criticality rating because it is the one the purveyor would depend on, repairing it if necessary, following an earthquake. Pipeline mitigation is prioritized considering both vulnerability and criticality, and the expected time to repair. (Repair times for some installations, such as river crossings, may be lengthy compared to pipeline repairs on accessible land.) GIS is a powerful tool to assess pipeline vulnerability and system functionality. Layers and data for ground motion, each hazard, and pipe type are established, and pipe vulnerability is calculated in terms of failures per segment based on empirical data. Independently, pipe segment importance is established on another layer. Vulnerability and criticality can then be combined as displayed graphically using GIS. HAZUS, a software earthquake loss estimation-modeling tool developed by the National Institute of Building Sciences (NIBS) and the Federal Emergency Management Agency (FEMA), has the capability to perform the hydraulic network analysis, rate pipe criticality, and prioritize replacement. A schematic of the methodology included in HAZUS is shown in Figure 24.8. HAZUS is available from NIBS (www.nibs.org). Once scenarios have been developed with estimated losses and restoration time, the results can be compared with performance objectives established at the outset of the project. Mitigation alternatives can then be considered using an iterative process to see what effects each mitigation measure would have on the system performance. The results of these system evaluations can be used to identify and prioritize mitigation alternatives and as tools for emergency planners. © 2003 by CRC Press LLC
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Hydraulic Model Hydraulic analysis UNDAMAGED System
Define seismic event PGA, PGD
Components Fragility Simulate damage state Apply system demands Hydraulic analysis
Mitigation
DAMAGED System
Monte Carlo Simulation
System Serviceability
FIGURE 24.8 HAZUS methodology schematic. (Courtesy EQE International)
24.8 Mitigation Alternatives 24.8.1 Introduction There is a range of mitigation strategies that can be used to maintain or quickly restore water service following an earthquake. No earthquake mitigation project has much significance until the first emergency response exercise is conducted, or the first piece of equipment is anchored, tank upgraded, or pipeline replaced. It is important to assemble an earthquake mitigation package that is saleable to decision-makers, including both potential losses as well as savings achieved through mitigation. Integrating projects with a non-earthquake capital improvement and/or maintenance program can minimize earthquake mitigation costs [Ballantyne, 1995d]. A typical earthquake mitigation program identifies an initial phase of low-cost items that can be implemented in the short term, and upgrades that can be implemented in the medium and long term. Integration of earthquake mitigation elements with utility comprehensive plans and/or maintenance programs is an effective mechanism to implement a mitigation program by minimizing the apparent significant economic impact. Low-cost mitigation measures can include: • • • • •
Emergency planning/emergency operations Equipment/nonstructural anchorage Emergency power acquisition Standards development/implementation (new facilities) Alternative supplies (development of supplies and acquisition of pumps and hoses may be relatively inexpensive and done in the short term, whereas development of a dedicated alternate supply may be costly and done over the long term)
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Vulnerable system components that may be life-safety threats, such as dams, hazardous chemical systems, and vulnerable buildings, should also be upgraded in an initial earthquake mitigation program phase. Medium- and long-term mitigation elements that are more expensive can include: • Tank upgrades • Treatment plant and pump station building upgrade (non-life-safety related) • Pipeline replacement
24.8.2 Monitoring and Control 24.8.2.1 Introduction Monitoring and control can be an important element of emergency response that is specific to the water supply and similar systems and should be considered in emergency operations planning [Ballantyne 1995a; Ballantyne and Crouse, 1997]. Earthquakes cause damage to lifeline systems, particularly buried pipelines and transportation facilities. Upgrade of these lifeline system elements to remain functional following design level earthquakes can be prohibitively expensive, and may not be technically feasible. Wholesale replacement of water system pipeline materials vulnerable to earthquakes is prohibitively expensive as an earthquake mitigation measure. For example, the Seattle water system has approximately 2400 km of pipelines less than 31 cm in diameter and approximately 550 km of pipelines larger than 31 cm in diameter. Approximately 6% are in areas highly vulnerable to liquefaction. Most of the system is cast iron pipe. The estimated cost to replace the entire system with ductile iron or welded steel pipe would be over $1.5 billion (1990 dollars). Replacing just the pipelines in areas susceptible to liquefaction would cost an estimated $100 million. These costs exceed the Seattle Water Department’s financial capability to replace vulnerable pipelines. A monitoring and control system alternative will mitigate the effects of some pipeline damage at a cost less than replacing vulnerable pipelines. The strategy can be used to isolate damaged sections of the system, so as to allow operation of other undamaged sections. Distribution system piping is vulnerable to earthquakes and expensive to replace with piping resistant to seismic activity. Systems to monitor post-earthquake system performance and isolate damaged sections can optimize overall post-earthquake system function by tracking (1) seismic hazard parameters, (2) structural component/soil parameters, and (3) system operational parameters. 24.8.2.2 Kobe and Northridge Earthquake Water System Monitoring and Control Performance The Kobe Water Department had a monitoring and control system in place on 21 reservoirs at the time of the Kobe earthquake. The system worked on 18 reservoirs. Each of the reservoirs was one of a pair; the other reservoir remained online. The objective of the system was to isolate 3 liters of drinking water per person, so as to provide 7 days of drinking water following the earthquake. Even though the system functioned in the 1995 earthquake, there were many complaints about inadequate drinking water. Approximately 1 million houses were without water as a result of leakage from 4200 pipeline failures. Two thirds of the nonisolated reservoir sites serving urban Kobe, providing water for drinking and fire protection, drained within 6 hours. The Los Angeles Department of Water and Power (LADWP) did not have any earthquake valves in their water system during the Northridge earthquake. They suffered approximately 1200 pipeline failures and lost service to much of the San Fernando Valley. They could not provide water from the system for fire suppression in all areas. LADWP staff made decisions not to close valves to isolate pipelines in order to maintain service for fire suppression. It is unknown whether a monitoring and control system would have improved system performance. The Northridge earthquake initiated 58 building structure fires, 51 of which involved natural gas; 172 mobile homes were destroyed by fire, most fueled by natural gas. An estimated 100,000 services were without water as a result of failure of 24 of LADWP’s major trunk lines and 700 distribution lines. Fire crews were using tankers to transport water to fires [Scawthorn et al., 1997]. © 2003 by CRC Press LLC
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24.8.2.3 Post-Earthquake System Monitoring and Control Strategy The mitigation strategy described herein is to monitor (1) seismic hazard parameters, (2) structural component and soil parameters, and (3) post-earthquake system operation, and with that information, to control secondary damage that might occur and/or keep systems functional to provide continued service. Secondary damage that may occur includes trains running off the tracks where embankments or bridges have failed, or natural gas from broken pipelines igniting. Continued service can be maintained in water systems by isolating damaged parts of the system that would then allow for water for fire suppression to flow to undamaged areas. Evaluation of seismic hazard parameters such as peak ground acceleration (PGA) enables identification of areas of high PGA where structural damage and soil failures are more likely to occur. One or more of these parameters can be combined to provide a more reliable assessment of the situation. In water systems, PGA, flow, rate of change of flow rate, and/or pressure can be combined for various levels of controlled response. PGA threshold levels for earthquake valves on reservoirs in the Kobe, Japan water system are set at the following levels with the corresponding action: • 40 gal: manual alarm (where 980 gal = 1 × gravity) • 80 gal combined with rate of change of flow: shut down • 250 gal: shut down Measuring offsets of structural component differential movement is being used both for building of active control systems and tunnels. The technology is available for monitoring pipe–joint displacement, but is probably too expensive for any but the most crucial pipelines and those serving as surrogates of long pipeline segments. In situ liquefaction monitoring technology has been developed by Tokyo Gas. System operation parameters, particularly flow, are being used both independently as well as in combination with shaking intensity as a control parameter. Ground motion instrument distribution can have a significant effect on the level of accuracy of ground motions at any given site. Kobe Water has a single ground motion instrument centrally located within their system that is used for post-earthquake control of the system (Figure 24.9).
FIGURE 24.9 Seismometer used to successfully shut down 18 of 21 seismic valves in Kobe water system following 1995 earthquake.
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24.8.2.4 Applications in Different Water System Configurations There are three basic applications for monitoring and control (isolation valves) in water systems: 1. Reservoir isolation 2. Pipelines vulnerable at rivers and/or fault crossings 3. Areas susceptible to liquefaction In all three cases, it is the intent to isolate the stored water from the damaged pipeline system. A refinement of the first application is the use of isolation valves on one of two reservoirs at a single site, maximizing system reliability, but still isolating some water from damaged pipelines. This application was in place in Kobe, Japan and worked effectively following the earthquake. Use of isolation valves to isolate areas susceptible to liquefaction is a key element in San Francisco’s AWSS system, although the valves have only recently been equipped with seismic sensors that activate when a set level of shaking is exceeded, but can be overridden by the system operator from the central control office (previously, crews had to manually close the valves, which proved ineffective in the 1989 Loma Prieta earthquake) [Scawthorn, 1997]. 24.8.2.5 System Control and Keeping the System Operating Water systems can be monitored and controlled either locally or from a central location. In an ideal local system, the parameters selected for control would be monitored at the location of interest and, when the set point was reached, the isolation valve would be actuated (this is how the San Francisco AWSS system now operates). Alternatively, parameters such as ground motion could be monitored locally and telemetered back to a central location; or parameters such as ground motion could be monitored at the central location (such as the Kobe system). Control decisions could then be made in the central location where trained staff could evaluate other system conditions and make a more informed decision. The advantage of the local system is high reliability; no communication system is required. The disadvantage is that the control parameters that control the local decision cannot consider other disaster-related activities. The best system is a combination where the local decision can be overridden from a central location (e.g., the San Francisco AWSS). The system that, to some degree, is built into most water distribution systems already is a SCADA (supervisory control and data acquisition) monitoring system, with manual control. In the event system damage is identified by recognizing excess flows and/or accelerated reservoir drawdowns, operation crews can be dispatched to close valves. The disadvantage of this approach is that it may take too much time (although it may possibly be as little as 15 to 30 min) to reach the critical valve before the reservoir is drained. In the Whittier earthquake, operations crews were able to get to a tank and close the valve before it drained. In the Loma Prieta earthquake, response crews were not able to get to critical valves before the tank drained in the San Francisco AWSS, as noted above. One advantage of a staffed central control system is that the water system will only be shut down as a last resort, only when the reservoir would otherwise drain. It is difficult to have an automated system make such a decision. In the Northridge earthquake, the LADWP decided to keep key transmission lines in operation to provide water for fire suppression to a neighboring community, even though they knew reservoirs ultimately would be drained. Major fires were probably averted. There is a fine line between system control and emergency response based on analysis of hazard information. Systems are in place in both Japan and southern California where emergency response crews are dispatched based on areas where earthquake damage is expected to be the most severe. 24.8.2.6 Appropriateness for Different Types of Systems It is more appropriate to implement a control system on a system that can be shut down without significant consequences. On potable water systems, system shutdown may result in water contamination due to back siphoning. Similarly, shutdown may render building sprinkler systems inoperable. Water from hydrants for fire suppression would be stopped, and water for general use at critical facilities such
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as hospitals would be stopped. If the situation is critical, system shutdown may still be appropriate; if the system is shut down inadvertently, or needlessly, there could be significant negative consequences. Damaged portions of dedicated fire protection systems could be shut down with minimal impact on other users. Isolation systems may have more application on dedicated systems. Construction of a dedicated water system recently has been economically justified in Vancouver, British Columbia [Scawthorn, 2000]. The existing potable water system did not meet fireflow requirements and was in need of a significant pipeline improvement program. The city decided to spend the money on a dedicated system that could be designed to high post-earthquake performance standards, including a monitoring and control system. 24.8.2.7 System Hardware Primary devices for measuring ground motion are available from a number of manufacturers. Instruments with adjustable set points for increasing ground motion levels are available. These devices can be integrated into systems with flow and pressure measuring devices with outputs to controllers that can be programmed to actuate isolation valves under specified conditions. All systems must be designed with a battery backup system. Vancouver selected butterfly valves requiring only one quarter turn by the actuator to be used as the isolation valves in their system. San Francisco uses motorized gate valves that were already in place on their AWSS system, with battery backup sufficient for four full open–close cycles. In all cases, a selfcontained energy supply for valve actuation must be provided. Compressed air works with one-quarterturn actuators; batteries with motorized operators. The most economical system can be provided by piggy-backing a seismically activated controller on the pilot control system of an existing pressure-reducing valve. These are usually in place between pressure zones cascading down to lower elevations. The advantage of this system is that the isolation valve is already in place and an additional energy source for valve actuation is not required. 24.8.2.8 Implementation Cost vs. Earthquake Risk The cost of implementation and system maintenance must be compared against the reduction of earthquake risk. The expense of an installation must be compared against consequences of system failure if it is not installed. Earthquake isolation valves can be more readily justified on major key facilities than on smaller installations. Areas of very high earthquake risk, such as coastal California, Japan, New Zealand, and similar active tectonic regions, can likely justify monitoring and control systems before areas of lower seismicity. One water system engineer in the Pacific Northwest related the cost of an earthquake valve to the cost of replacing a significant length of small-diameter vulnerable pipe with larger-diameter, restrained-joint ductile iron. He said he would benefit more from the pipe replacement than the isolation valve. The pipe would start working for him the first day it was installed, while the valve may not be needed for 50 years or more. Monitoring and control installations must be maintained. Maintenance of a system for decades without ever seeing it operate is difficult to justify psychologically, as well as being expensive. In more seismically active areas it may be more economically feasible. The majority of the cost is in the valves and actuator rather than the control system. Use of valves that are already in place for another reason is preferable. Regional earthquake monitoring systems are in place in California, and soon will be in place in Washington. Use of these regional systems may be less expensive for users with numerous facilities. 24.8.2.9 Monitoring and Control System Reliability Monitoring and control systems must be reliable. They must function when they are needed, even if that is only once every few decades. More importantly, they must not actuate isolation valves inadvertently. For example, in a non-earthquake situation, the Seattle Water Department lost their entire telemetry system when a backhoe severed a single cable connecting their control center to the system.
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Providing system redundancy in both the reservoir and pipeline system as well as in the control system can increase system reliability. The system should also be designed to remain functional following the design earthquake.
24.8.3 Pipeline Design Practices While pipeline failure has historically had the greatest impact, it is difficult to justify wholesale replacement of seismically vulnerable pipe unless it is a critical part of the backbone system. Seismic design consideration should be given to all new pipe installations. This section discusses design of new pipelines, including water system seismic-resistant design standards and guidelines that are used in the western United States. There are no design standards or guidelines that specifically address seismic design of water pipelines. There are seismic design provisions incorporated in standards developed by the AWWA for water storage tanks (AWWA D-100, D-110, and D-115). The American Concrete Institute (ACI) has incorporated seismic provisions in their standard for environmental structures (ACI 350). The Uniform Building Code (UBC) is the code used by most jurisdictions in the western United States to control design of building structures. It has very limited application to specialized structures used in the water industry, including pipe design. 24.8.3.1 Recommended Pipeline Seismic Resistant Design Practices There are no seismic-resistant pipeline standards in the water industry in the United States. The design practices described below are often recommended by the author to water purveyor clients [Ballantyne, 1997a]. Three hazard conditions are considered: 1. Wave propagation–ground acceleration < 40% × gravity (UBC Seismic Zone 3 or smaller). This condition exists where there are nonliquefiable soils, not subject to landslides, and not in fault zones. Most populated areas of the United States are in UBC Zone 3 or less, excluding much of California. For this condition, commonly used pipe materials, such as nonrestrained joint ductile iron, PVC, or concrete cylinder pipe, are acceptable. Modern bell-and-spigot joints with elastomeric gaskets are adequate to accommodate pipe strain induced by wave passage. 2. Wave propagation–peak ground acceleration 40% × gravity or greater (UBC Seismic Zone 4). This condition exists where there are nonliquefiable soils, not subject to landslides, and not in fault zones. UBC Zone 4 includes large parts of California and takes in the San Francisco and Los Angeles areas. For this condition, welded steel, restrained-joint ductile iron, or polyethylene pipe is recommended. Prior to the Kobe earthquake, it was believed that nonrestrained pipe joints, as recommended for UBC Seismic Zone 3, would be adequate where PGD was not expected. In Kobe, there were over 600 pulled ductile iron pipe joints in areas with no liquefaction. Therefore, use of restrained joints is now recommended. Concrete cylinder pipe is not included in the recommended list for this application because it is less ductile than steel. The effectiveness of restraints across joints is limited by the strength of the thin-walled steel can. PVC is not recommended for this application. PVC is more brittle than ductile iron. The PVC pipe bell–spigot assembly is designed like a wedge, and will split the bell when subjected to compressive strains. However, one purveyor had good success with PVC in the Northridge earthquake and recommends its use for seismic resistance. There has only been limited exposure of PVC pipe to earthquakes, so there is a limited empirical database on which to judge its performance. Most of the PVC pipe exposed in the Kobe earthquake was small diameter, typically less than 75 to 100 mm. It may not be representative of larger PVC pipe performance. 3. Permanent ground deformation > 5 cm expected (all UBC zones). The PGD condition exists anywhere there are liquefiable soils, areas of landslides, and locations in fault zones. This category is not UBC seismic zone dependent, but the liquefaction susceptibility has to be sufficient such that liquefaction is expected in the design basis earthquake. The multiple linear regression analysis, MLR [Youd et al., 1999], can be used to estimate the maximum PGD in liquefiable soils. For this condition, welded steel, restrained joint ductile iron, or polyethylene pipe is recommended. Use © 2003 by CRC Press LLC
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of these pipe materials will enhance seismic performance, but may not provide absolute assurance that the pipe will not fail. So, in addition to use of these materials, the following recommendations are made: Geotechnical mitigation Reduce liquefaction susceptibility by installing gravel columns, grouting, etc. Limit lateral spread by installing earth-retaining structures. Pipe structural mitigation Minimize anchors/provide flexibility where anchors are required. Anchors tie the pipe to the surrounding soil, limiting its capability to slide through the soil to relieve pipe strain. Examples of anchors include connections to buildings and vaults, tees or crosses, and bends. Minimize soil–pipe friction by wrapping the pipe in polyethylene. The angle of friction between the pipe and polyethylene is greatly reduced, allowing the pipe to slide through the soil and relieving pipe strain. System mitigation Provide valves around liquefiable areas so the area can be isolated from the undamaged area of the system. For transmission lines, provide connections on either side of the liquefaction or landslide area to allow quick installation of temporary piping. 24.8.3.2 Level of Reliability The level of expected performance must be considered when applying these design recommendations, and the criticality of the specific pipeline must be taken into account. For example, for key transmission lines, more conservative designs would be employed compared to designs used for small-diameter distribution pipelines.
24.8.4 Develop Alternative Sources or Supplies Provision of operational flexibility may provide the best opportunity of being able to provide post-earthquake service. Alternative water supplies to provide water for fire suppression can include dedicated fire protection systems, portable water supply systems, cisterns distributed throughout the service area, planned use of swimming pools and/or other recreational water-containing facilities, and the planned and tested ability to draft water from local water bodies. Most fire departments routinely plan on employing the latter two techniques as alternative water supplies; the recently constructed Vancouver dedicated fire protection system (DFPS) is an example of such a system, and systems in San Francisco (AWSS) and Japan are examples of combined dedicated fire protection systems and cisterns [Ballantyne, 1997b].
24.8.5 Improve System Hardware So It Does Not Fail Examples include replacing pipe, upgrading reservoirs, and providing emergency power. Improvement programs can be prioritized considering the importance of each component in operation of the overall system and the desired performance objectives. Vulnerability considers the probability of the hazard occurrence (and associated intensity) and the likelihood the component will become inoperable. Criticality or importance considers availability of redundant components and/or percent of the system capacity the component provides.
24.8.6 Upgrade and Design of New Tanks, Pump Stations, and Treatment Plants 24.8.6.1 Tanks, Concrete Basins, and Below-Grade Structures Tanks are commonly analyzed and designed in accordance with standards that have been developed by the AWWA as follows: © 2003 by CRC Press LLC
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D100 — Welded Steel Tanks for Water Storage D110 — Wire- and Strand-Wound, Circular, Prestressed Concrete Water Tanks D115 — Circular Prestressed Concrete Water Tanks with Circumferential Tendons Seismic loading in these tank standards is based on the UBC, with an importance factor assigned recognizing that tanks are important elements of lifeline systems. The seismic loading in tanks is contributed by the weight of the tank walls and roof, a portion of the water that moves with the tank walls (impulsive), and a portion of the water that sloshes across the tank in long-period motions. The percent of the water assigned to impulsive and convective loading is based on work done by Housner [1963], discussed above. In tanks with a small height-to-diameter ratio (i.e., large diameter and squat), most of the water sloshes (convective loading), whereas in tanks with a large height-to-diameter ratio (i.e., tall and slender), most of the water contributes to the impulsive load. The analysis approach takes into account the period of the tank contents and the energy included in the response spectrum at that period. As a result, per unit weight, sloshing water contributes much less lateral loading on the tank wall than does water causing impulsive loading. The sloshing water “runs up” the tank walls. If the tank has a roof, the sloshing water can damage the roof structure if adequate freeboard is not provided. The amplitude of sloshing can be determined via Equations 24.6 and 24.9. This same hydraulic loading also occurs in tanks used for water treatment. Baffles, for example, are often damaged due to the impulsive loading of water. Earthquake loading results in an overturning moment on the tank. Steel tanks are flexible structures. As water sloshes and moves to one side of a tank, it may cause the other side of the tank to uplift, damaging connecting piping, and causing the tank wall to fail in compression (wrinkling, also termed elephant’s foot buckling) when the tank impacts the ground as the water moves in the other direction. Steel tanks can be seismically upgraded to resist the effects of uplift by: • Installing flexible piping connections or moving bottom pipe connections away from the wall/ bottom connection where uplift is most likely to occur. Flexibility should not be required if the tank is adequately anchored so it will not move. • Making the tank base rigid by installing structural concrete inside the tank, connecting it to the tank walls. This will add weight to resist overturning, and allow the tank structure to respond as a more rigid body, making use of the weight of the water to hold it in place. • Anchoring the tank wall to the foundation. This will prevent the tank wall from uplifting. In some cases, the foundation may have to be strengthened to accommodate the uplift forces. Piles may be required. • Strengthening the tank wall with stiffeners or by increasing the wall thickness to accommodate compressive loads. • Enhancing the tank roof attachment in order to transfer the load generated by the roof to the tank wall, passing down to the foundation. • Lowering the water level in the tank to increase the free board and minimize sloshing loading on the roof. Lowering the water level will also reduce the lateral loading on the tank walls. Of course, lowering the water level will reduce the storage capacity and lower the hydraulic grade line of the tank, so this alternative may not be acceptable. Wire- or tendon-wrapped concrete tanks are subjected to the same loading, but because of their inherent design, they respond differently. The internal pressure increases due to vertical loading and results in increased loading on the circumferential reinforcing. Under extreme earthquake loading, the reinforcing may fail catastrophically. This can be exacerbated if the reinforcing has been weakened by corrosion. Tank wall uplift is less of a concern than in steel tanks, but sliding off the bottom/foundation can result in failure of its hydraulic continuity. These tanks are often designed to allow the tank to expand and contract as water is added and withdrawn. To accommodate this movement, the bottoms are usually allowed to move radially. Newer tanks limit the amount of movement with earthquake cables. Older © 2003 by CRC Press LLC
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tanks either have no limit device, or may have a curb that may be inadequate to limit movement caused by earthquakes. Some designs fix the tank walls to the bottom. This results in a vertical bending moment on the tank wall that must be accommodated in the design. Wire or tendon concrete tanks are sometimes upgraded by adding additional circumferential reinforcing and by adding/enhancing the device used to prevent the tank from sliding off its foundation. Cast-in-place reinforced concrete tanks are sometimes used for water storage, and often used for process tanks at treatment plants. The concrete walls are usually conservatively designed to minimize cracking. Hydraulic loading (impulsive and convective forces) requires consideration, particularly on interior walls and baffles that may not otherwise be designed for significant lateral load resistance. The ACI Standard 350, Environmental Engineering Concrete Structures, addresses design of concrete tanks. There have been instances where cast-in-place tanks failed when exposed to extreme levels of ground motion. Failures usually occur at expansion joints. The consequences of such a failure could be flooding a pipe gallery or other facilities down grade, and should be considered in a vulnerability assessment. Proper design of expansion joints to accommodate adequate relative movement between the wall sections should minimize failures of this type. Tanks (and below-grade structures such as sewage pump stations) are also vulnerable to foundation geotechnical failures. These are most predominant in wastewater facilities where facilities are inherently located in low-lying areas where soils may be susceptible to liquefaction. The foundation systems must be adequately designed to resist liquefaction or the tank can float (if empty), or settle (if the foundation system fails). These failures are applicable to all types of tanks but are especially of concern with castin-place concrete tanks, as this is the type usually used for wastewater process tanks. It is expensive to retrofit a tank on an inadequate foundation, and may be difficult to justify. In the United States, elevated tanks are commonly supported with steel frames or a single steel pedestal. In some countries where steel is less available, concrete structures are used to support these tanks. In either case, these structures can be analyzed using the methods presented elsewhere in this volume. 24.8.6.2 Nonstructural Equipment Movement and resulting failure of equipment and plant piping can occur even at moderate ground motion levels. Equipment should be anchored. Usually rotating equipment is adequately anchored, and generally should not require any special seismic anchorage. Electrical and control cabinets are often identified as being unanchored, and have historically toppled in earthquakes. Raised computer floors must be designed to transfer lateral loading to the “solid” floor below. Equipment in labs is often not anchored. It may be inappropriate to anchor equipment that is regularly moved. Systems have been developed to keep equipment in cupboards and on shelves by latching doors and installing retaining devices across the front of shelving. Failure of equipment can have severe consequences. If chlorine cylinders or other compressed gas cylinders topple, particularly while they are connected, the connection and/or valve can break, allowing the gas to release rapidly. Cylinders should be restrained in place. Ton-sized containers containing chlorine should be strapped in place, including to the scales when actively delivering chlorine. Tanks containing chemicals used for treatment should be anchored in accordance with the tank manufacturer’s recommendations (there are special structural analyses required for special materials used for chemical tanks, such as polyethylene and fiberglass). As with larger tanks, pipe connections to chemical feed tanks should be flexible if there is any opportunity for the tank to move during an earthquake event. Chemical feed systems should all have secondary containment in the event a release occurs. Piping should be braced both longitudinally and laterally. Flexible joints should be installed at the interface between segments that may move differentially (e.g., across expansion joints), and at connections with equipment. Equipment piping connections are seldom designed to resist the movement and resulting loading of connecting pipe. The Sheet Metal and Air Conditioning Contractors National Association’s Seismic Restraint Manual: Guidelines for Mechanical Systems provides direction for pipe support and bracing. The National Fire Protection Association NFPA 13, Installation of Sprinkler © 2003 by CRC Press LLC
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Systems, provides guidance for seismic design of sprinkler piping that can be applied to other pipe systems. 24.8.6.3 Emergency Power Commercial electrical power is not reliable following earthquakes, so systems where continuous operation is required should have emergency power. Such systems may include, but are not limited to, facilities/ systems required for emergency response, communication systems, critical water pump stations, sewage pump stations where failure may result in backup into inhabited spaces, critical control systems such as for SCADA systems and treatment plants, and HVAC systems for critical facilities. Either fixed or portable generators may provide the backup function; however, portable generators require someone to move and set up the equipment before it will function. In post-earthquake traffic conditions, this may be more time consuming than expected. Generator sets must be fueled on a regular basis to maintain operation. Fuel delivery may be a problem in post-earthquake conditions if bridges are not functional. Power (or a hand pump) must be available to pump fuel from underground storage tanks. Engine-generators and supporting systems are vulnerable. Supporting systems must each be functional in order for the engine-generator to function. Provision of adequate anchorage and/or flexibility for each of these systems is critical. Support systems include batteries (anchorage) or compressed air for starting, cooling (such as dependence on potable water supply), fuel (anchorage of day tanks), exhaust, and lubrication. Engine-generators are often supported on vibration isolators. Vibration isolators must be specially designed to accommodate earthquake loading, and may collapse if improper ones are used. They should be replaced or snubbers (devices to limit large amplitude movement) installed if they are found to be deficient. 24.8.6.4 Pump Stations, Treatment Plants, and Component Redundancy Pump station and treatment plant upgrades and new facilities can incorporate many of the design considerations described above (tanks, equipment, piping, and emergency power), as well as various types of building structures discussed elsewhere in this book. Treatment plant and pump station earthquake reliability can be enhanced by adding redundancy. Treatment plants are complicated systems with many interacting components. Each component is vulnerable to earthquake damage. Their reliability can be improved by providing as much redundancy as possible. In a series system where the individual component reliabilities are assumed independent, the reliability of the overall system can be calculated by multiplying together the reliability of the individual components as shown in Figure 24.10: X = [1 – A] × [1 – B] × [1 – C] where X = the probability of the series system remaining functional A, B, and C = probability of failure of the individual component.
FIGURE 24.10 Three-unit treatment process in series.
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FIGURE 24.11 Three-unit treatment process in series, each with a parallel (redundant) unit.
If A, B, and C each have a 15% probability of failure, the system reliability is 61%: X = [1 – 0.15] × [1 – 0.15] × [1 – 0.15] = 0.85 × 0.85 × 0.85 = 0.61 However, the probabilities of failure of A, B, and C are reduced by providing parallel redundant components (again, reliabilities are assumed independent), as shown in Figure 24.11: X = [1 – (A1 × A2)] × [1 – (B1 × B2)] × [1 – (C1 × C2)]
(24.11)
If A1 and A2, B1 and B2, and C1 and C2 are comparable units each with the same 15% probability of failure, the overall system reliability is: X = [1 – (0.15 × 0.15)] × [1 – (0.15 × 0.15)] × [1 – (0.15 × 0.15)] X = [1 – 0.02] × [1 – 0.02] × [1 – 0.02] = 0.94 The components with the highest probability of failure are the ones that have the greatest impact on the overall system probability of failure, and are therefore the ones where redundancy is preferred. In many situations, the full capacity of the system may not be provided for each redundant unit. The probabilities of failure for parallel units may be correlated (i.e., they have similar attributes and therefore cannot be assumed to be independent). The higher the correlation, the greater the probability they may fail at the same time. For example, one groundwater and one surface water supply may be preferred over two surface water supplies because both surface water supplies could be impaired by the same earthquake hazard (e.g., landslides). Multiple supplies are preferred even if the “alternate” supply may only be usable for a limited time. For example, if an “alternate” groundwater supply could only deliver the average daily demand for 60 days, it still may serve the desired result of providing complete redundancy for the length of time it would take to repair the primary supply. If only one supply is available, redundant facilities should be provided between the supply and treatment plant. Every component of the system has an associated risk of failure. Within the plant, parallel flow trains, with the ability to move water back and forth between the trains between processes, are preferred. The ideal system would have redundant treated water pumping systems that were not dependent on a common header. Similarly, peripheral systems such as chemical feed, power supply, and control should have redundant components particularly when they are vulnerable. If possible, it would be preferable to have available alternate peripheral systems that achieve the same result in different ways. For example, it would be better to have the ability to operate the system with alternate treatment chemicals in the event the ability to acquire one of the chemicals was lost due to earthquake damage at a production facility. To the extent possible, no single component should be “required” to operate the plant.
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24.9 Summary and Conclusions Water supply systems are critical for potable use, fire suppression, business, and industry. Wastewater systems are critical for public health, business, and industry. Implementing the following nine items will contribute to improving the earthquake reliability of these systems: 1. Set performance objectives to assist in selecting the appropriate level of mitigation as the earthquake mitigation program is developed. 2. Quantify hazards, including ground motion and PGD, for selected earthquake scenarios representative of probabilistic earthquake return periods. PGD can include liquefaction/lateral spread, landslides, lurching, and surface fault ruptures. 3. Develop/acquire damage algorithms for pipe for each hazard, including ground motion and PGD. Brittle pipe, such as cast iron, has a higher unit failure rate than does ductile pipe, such as welded steel. 4. Evaluate the fragility of reservoirs and tanks to each of the earthquake hazards. Tanks are usually founded on competent soil (with the exception of wastewater process tanks), so ground motion is usually the more significant hazard. 5. Analyze the water system. Input hazard and component damage relationship information. Evaluate the system by observation (system operators) of the damage states of the components and considering their effect on the overall system. Alternatively, perform a hydraulic network analysis using specialized software such as HAZUS. 6. Compare the expected system operation with the performance objectives. 7. Select and prioritize the highest-risk components (i.e., components that have a combination of the greatest hazard exposure, greatest fragility to that exposure, with a failure that will have the greatest impact on the system). 8. Mitigate short term. Implement low-cost–high-impact measures, such as emergency planning, equipment anchorage, emergency power acquisition, development of alternative emergency supplies, and design standards implementation. 9. Mitigate medium and long term by performing structural upgrades of tanks, pump stations, treatment plants, and replacing pipelines.
Defining Terms Annual frequency — Mean probability of occurrence of a defined event. Backbone system — The network of key transmission and distribution components which serve a significant portion of the region — if all else is lost but the backbone system survives, much of the region will have partial water, even if it may have to be tankered short distances. GIS — Geographic information systems. Hazard (earthquake) — Depending on context, either (1) a general reference to damaging effects of earthquakes, such as shaking, landsliding, liquefaction, etc.; or, more specifically, (2) the probability of experiencing a specific measure of intensity at a specific location. Intensity — A metric of the effect, or the strength, of an earthquake hazard at a specific location, commonly measured on qualitative scales such as MMI (see Chapter 4). Lifelines — Systems required for the function of modern cities, such as water, wastewater, electric power, transportation, and other systems (see Chapter 22). PGD — Permanent ground deformation (see Chapter 23). Return period — Mean duration between events, equal to the reciprocal of the annual frequency.
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References American Lifeline Alliance, 2001. Seismic Fragility Formulations for Water Systems, American Society of Civil Engineers, Reston, VA. American Water Works Association, 1995. AWWA Standard for Wire- and Strand-Wound Circular Prestressed-Concrete Water Tanks, ANSI/AWWA D110–95, American Water Works Association, Denver, CO. American Water Works Association, 1996. AWWA Standard for Welded Steel Tanks for Water Storage, ANSI/AWWA D100–96, American Water Works Association, Denver, CO. Applied Technology Council, 1992. A Model Methodology for Assessment of Seismic Vulnerability and Impact of Disruption of Water Supply Systems, ATC-25–1, prepared for ATC by C. Scawthorn and M. Khater, EQE International, Applied Technology Council, Redwood City, CA. Ballantyne, D. 1990. “Earthquake Loss Estimation Modeling of the Seattle Water System,” Report No. 886005, supported by U.S. Geological Survey Project Number 14–08–0001-G1526, Kennedy/Jenks Consultants. Ballantyne, D.B., 1994a. Minimizing Earthquake Damage: A Guide for Water Utilities, American Water Works Association, Denver, CO. Ballantyne, D., 1994b. “Changing Needs for Hazard Information for Pipeline Loss Estimation,” Proceedings of the Fifth U.S.–Japan Workshop on Earthquake Resistant Design of Lifeline Facilities and Countermeasures against Soil Liquefaction, Technical Report NCEER 94–0026, T.D. O’Rourke and M. Hamada, Eds., National Center for Earthquake Engineering Research, Buffalo, NY, November. Ballantyne, D.B., 1995a. “Monitoring and Control of Lifeline Systems To Enhance Post-Earthquake Operation,” Proceedings of the Fourth U.S. Conference on Lifeline Earthquake Engineering, American Society of Civil Engineers, San Francisco, August. Ballantyne, D., 1995b. “Relative Earthquake Vulnerability of Water Pipe,” Proceedings of the 1995 American Water Works Association Annual Conference, Anaheim, CA, June, pp. 285–298, American Water Works Association, Denver, CO. Ballantyne, D., 1995c. “Water System Performance in the Great Hanshin (Kobe) Earthquake,” Proceedings of the 1995 American Water Works Association Annual Conference, Anaheim, CA, June, American Water Works Association, Denver, CO. Ballantyne, D., 1995d. “An Overview of Lifeline Earthquake Engineering of Water and Wastewater Systems, Focusing on the Pacific Northwest,” Proceedings, American Public Works Association National Conference, Seattle, April. Ballantyne, D., 1995e. “Section 8, Water and Wastewater,” The Hanshin-Awaji Earthquake of January 17, 1995 Performance of Lifelines, Technical Report NCEER –95–0015, M. Shinozuka, Ed., National Center for Earthquake Engineering Research, Buffalo, NY, November. Ballantyne, D., 1995f. “Pipeline Performance Parameters for Earthquake Vulnerability,” Proceedings of the Sixth U.S.–Japan Workshop on Earthquake Disaster Prevention for Lifeline Systems, Public Works Research Institute, Osaka, Japan, July. Ballantyne, D., 1997a. “Seismic Vulnerability Assessment and Design of Water Pipelines in the United States,” Fourth International Symposium on Water Pipe Systems Proceedings, City of Kobe and the Japan Water Research Center, November. Ballantyne, D., 1997b. “Reliability and Restoration of Water Supply Systems for Fire Suppression and Drinking Following Earthquakes,” Proceedings of the Seventh U.S.–Japan Workshop on Earthquake Disaster Prevention for Lifeline Systems, Sponsored by National Institute of Standards and Technology, Washington, D.C., National Science Foundation, Washington, D.C., and PWRI, November. Ballantyne, D., 1998. “Maintaining and Restoring Water Lifeline Systems after an Earthquake,” World Urban-Earthquake Conference in Fukui, June.
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Ballantyne, D.B. and C.B. Crouse, 1997. Reliability and Restoration of Water Supply Systems for Fire Suppression and Drinking Following Earthquakes, prepared for the National Institute of Standards and Technology, Washington, D.C. Ballantyne, D.B. and W.F. Heubach, 1990. 1989 Loma Prieta Earthquake Damage Evaluation of Water and Wastewater Treatment Facility Nonstructural Tank Elements, Kennedy/Jenks Chilton Report No. 896086.00, NSF Grant Award BCS-9002459, prepared for the National Science Foundation, Washington, D.C. Ballantyne, D. and W. Heubach, 1996. “Use of GIS to Evaluate Earthquake Hazard Effects and Mitigation on Pipeline Systems: Case Studies,” Proceedings from the Sixth U.S.–Japan Workshop on Earthquake Resistant Design of Lifeline Facilities and Countermeasures against Soil Liquefaction, Technical Report NCEER 96–0012, T.D. O’Rourke and M. Hamada, Eds., National Center for Earthquake Engineering Research, Buffalo, NY, September. Ballantyne, D., R. Chung, T. O’Rourke, and A. Schiff, 1996. Performance of Lifeline Systems, The January 17, 1995 Hyogoken-Nanbu (Kobe) Earthquake, Performance of Structures, Lifelines and Fire Protection Systems, NIST Special Publication 901, Photo 31, National Institute of Standards and Technology, Washington, D.C. Eguchi, R.T., 1982. Earthquake Performance of Water Supply Components during the 1971 San Fernando Earthquake, J.H. Wiggins Company, CA, prepared for the National Science Foundation, Washington, D.C. Eguchi, R.T., 1983. “Seismic Vulnerability Models for Underground Pipes,” Earthquake Behavior and Safety of Oil and Gas Storage Facilities, Buried Pipelines and Equipment, PVP-77, American Society of Mechanical Engineers, New York, pp. 368–373. Harding Lawson Assoc., Dames & Moore, Kennedy/Jenks/Chilton, and EQE Engineering, 1991. Final Report, Liquefaction Study Marina District and Sullivan Marsh Area, San Francisco, CA. Prepared for the City and County of San Francisco, Department of Public Works. Honegger, D., 1994. “Assessing Vulnerability of BC Gas Pipelines to Lateral Spread Hazards,” presented at the National Center for Earthquake Engineering Research Fifth U.S.–Japan Workshop on Earthquake Resistant Design of Lifeline Facilities and Counter-Measures against Soil Liquefaction, Snowbird, UT, September. Housner, G. 1963. “The Dynamic Behavior of Water Tanks,” Bull. Seismol. Soc. Am., 53, 381–387. Katayama, T., K. Kuho, and N. Sato, 1975. “Earthquake Damage to Water and Gas Distribution Systems,” Proceedings of the First U.S. National Conference on Earthquake Engineering, Earthquake Engineering Research Institute, Berkeley, CA. Kennedy/Jenks Consultants in association with EQE Engineering and Design, 1993. A Lifeline Study of the Regional Water Distribution System, prepared for the Greater Vancouver Regional District, Vancouver, BC. Odeh, D.J., M. Khater, C. Scawthorn, F. Blackburn, and K. Kubick, 1995. “Reliability Analysis of a Dual Use Fire Protection/Reclaimed Water System San Francisco CA,” Proceedings of the Fourth U.S. Conference on Lifeline Earthquake Engineering, M.J. O’Rourke, Ed., ASCE Technical Council on Lifeline Earthquake Engineering, Monograph No. 6, American Society of Civil Engineers, New York, pp. 264–271. O’Rourke, M.J. and X. Liu, 1999. Response of Buried Pipelines Subject to Earthquake Effects, MCEER Monograph No. 3, Multidisciplinary Center for Earthquake Engineering Research, State University of New York, Buffalo, NY. O’Rourke, M.J. and C. Nordberg, 1992. Longitudinal Permanent Ground Deformation Effects on Buried Continuous Pipelines, NCEER-92–0014, National Center for Earthquake Engineering Research, Buffalo, NY. Porter, K.A., C. Scawthorn, D.G. Honegger, T.D. O’Rourke, and F. Blackburn, 1991. “Performance of Water Supply Pipelines in Liquefied Soil,” Proceedings of the Fourth U.S.–Japan Workshop on Earthquake Disaster Prevention for Lifeline Systems, Los Angeles, NIST Special Publication 840, National Institute of Standards and Technology, Washington, D.C., pp. 3–17. © 2003 by CRC Press LLC
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Scawthorn, C., 1997. “1989 Loma Prieta, California Earthquake: Water Supply Effects,” in Reliability and Restoration of Water Supply Systems for Fire Suppression and Drinking Following Earthquakes, D. Ballantyne and C.B. Crouse, Eds., prepared for the National Institute of Standards and Technology, Washington, D.C. Scawthorn, C., 1998. “Reliability-Based Design of Water Supply Systems,” Proceedings, International Water Works Association Workshop on Anti-Seismic Measures on Water Supply, Japan Water Works Association, Tokyo. Scawthorn, C., 2000. “Assessment of Earthquake Reliability of Fire Safety Systems,” International Workshop on Performance Based Design for Fire Safety, University of British Columbia, Vancouver. Scawthorn, C., K.A. Porter, and F.T. Blackburn, 1992. “Performance of Emergency Response Services after the Earthquake,” in The Loma Prieta, California Earthquake of October 17, 1989: Marina District, U.S. Geological Survey Professional Paper 1551-F, T.D. O’Rourke, Ed., Strong Ground Motion and Ground Failure, T.L. Holzer, Coordinator, U.S. Government Printing Office, Washington, D.C. Scawthorn, C., A.D. Cowell, and F. Borden, 1997. Fire-Related Aspects of the Northridge Earthquake, NISTGCR-98–743, Building and Fire Research Laboratory, National Institute of Standards and Technology, Gaithersburg, MD. Schiff, A. and L. Lund, 1990. “Lifelines,” Loma Prieta Earthquake Reconnaissance Report, Earthquake Spectra, Supplement to Vol. 6, Earthquake Engineering Research Institute, Oakland, CA. Towhata, I., K. Tokida, Y. Tamari, H. Matsumoto, and K. Yamada, 1990. “Prediction of Permanent Lateral Displacement of Liquefied Ground by Means of Variational Principle,” Proceedings of the Third Japan–U.S. Workshop on Earthquake Resistant Design of Lifeline Facilities and Countermeasures for Soil Liquefaction, San Francisco, CA, Technical Report NCEER-91-001, T.D. O’Rourke and M. Hamada, Eds., National Center for Earthquake Engineering Research, Buffalo, NY. Youd, T.L. and D.M. Perkins, 1987. “Mapping of Liquefaction Severity Index,” J. Geotech. Eng., 113, 1374–1392. Youd, T.L., C. Hansen, and S. Bartlett, 1999. “Revised MLR Equations for Predicting Lateral Spread Displacements,” in Proceedings of the Seventh U.S.–Japan Workshop on Earthquake Resistant Design of Lifeline Facilities and Countermeasures against Soil Liquefaction, Seattle, WA, Technical Report MCEER-99–0019, T. O’Rourke, J.-P. Bardet, and M. Hamada, Eds., Multidisciplinary Center for Earthquake Engineering Research, Buffalo, NY.
Further Reading A number of publications by the Technical Council of Lifeline Earthquake Engineering (TCLEE) of the American Society of Civil Engineers are of great value for the performance of lifelines in general, and water and wastewater systems specifically. The publications Reliability and Restoration of Water Supply Systems for Fire Suppression and Drinking Following Earthquakes [Ballantyne and Crouse, 1997], A Model Methodology for Assessment of Seismic Vulnerability and Impact of Disruption of Water Supply Systems (Applied Technology Council, 1992), and Response of Buried Pipelines Subject to Earthquake Effects [O’Rourke and Liu, 1999] all provide significantly more detail on selected aspects of the topic.
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25 Electrical Power Systems 25.1 Introduction Purpose · Basis for Recommendations · Scope · Organization and Use of the Chapter · Overview of the Configuration of a Typical Power System
25.2 Historical Response of Electrical Power Systems to Earthquakes Overall Power System Seismic Performance · Power Transmission and Distribution Systems · Power Generation Facilities · Control, Protection, and Communications Facilities
25.3 Code Provision, Standards and Guidelines for Electrical Systems 25.4 Earthquake Preparedness 25.5 Earthquake Hazard and System Vulnerability Evaluation Simplified Evaluation of Earthquake Hazard and System Vulnerability · Detailed Earthquake Hazard and System Vulnerability Evaluation · Seismic Analysis of Electrical Systems
25.6 Earthquake Preparedness — Disaster-Response Planning Procedures for Inspection of Utility Structures · Activation of the Emergency Operations Center · Document Restoration Costs · Document Damage and Contributing Factors
25.7 Earthquake Preparedness — Earthquake Mitigation Approach to Earthquake Mitigation · System Review and High Priority of Selective Upgrading
25.8 Earthquake Preparedness — Mitigation Substations · Transmission and Distribution Lines and Support Structures · Power Generating Facilities · System Control · Communication Systems · Ancillary Facilities and Functions
Anschel J. Schiff Stanford University Stanford, CA
25.9 Closing Remarks Defining Terms References Further Information
25.1 Introduction Recent moderate and strong earthquakes (e.g., 1994 Northridge, 1995 Kobe, 1999 Turkey, 1999 Taiwan) have demonstrated that parts of power systems are very vulnerable to damage. While system performance
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has been good, as measured by customer disruption, there has been considerable damage, so that the damage pattern suggests that system performance will not be acceptable for larger earthquakes, for earthquakes that impact larger areas or in regions that do not use good earthquake practices. These earthquakes have all had magnitudes of about 7, so the performance after a major earthquake (magnitude between 7 and 8) or a great earthquake (magnitude above 8) is not known. Starting with the 1971 San Fernando earthquake, 11 California earthquakes have damaged power system facilities. Most of these small to moderate earthquakes have shaken relatively small areas so that damage has been concentrated and limited primarily to one or two facilities. The 1989 Loma Prieta, California earthquake affected a large area, severely damaging three substations and disrupting the network in the region. The 1994 Northridge, California earthquake also affected a large area, damaging 11 power facilities and disrupting the network. Foreign earthquakes have also provided important lessons. While much less frequent, damaging earthquakes can be expected in many parts of the US; indeed, 31 states have experienced earthquakes of a magnitude that could be expected to damage power system facilities. Direct costs for repair and replacement of damaged facilities have not been overwhelming in terms of utility assets, but are nonetheless significant. In California alone, there were direct losses of about $45 million in the 1971 San Fernando earthquake (magnitude Mw = 6.6), $9 million in the 1986 North Palm Springs earthquake (magnitude Mw = 6.1), $100 million in the 1989 Loma Prieta earthquake (magnitude Mw = 6.9) and $183 million in the 1994 Northridge earthquake (magnitude Mw = 6.7). Some smaller, less costly earthquakes have been very disruptive. In the 1988 Tejon Ranch earthquake, the California Aqueduct, which supplies water to the Los Angeles area, was shut down for 4 days, and there is typically only a 15-day supply of water stored downstream from the point that was damaged. In the 1984 Morgan Hill, California earthquake, one of the three Pacific interties, major power circuits connecting the northwest and the southwest, was down for 3 days. In most earthquakes, it has been possible to bypass damaged equipment and continue to transfer power through or to route power around the damaged substation. In some cases, an entire switchyard has been bypassed. Fortunately, when transformers have been damaged, there has been adequate capacity in alternate routes to maintain service. The relatively short time to restore service in the face of extensive damage can be attributed to the high level of redundancy designed into power systems, and the resourcefulness and dedication of utility-maintenance personnel. However, it is easy to envision damage, particularly to transformers, that could cause lengthy disruptions. Looking at a utility’s response to moderate earthquakes helps put the recovery effort into perspective. In the 1986 North Palm Springs earthquake, where power system damage was limited to one substation, about 250 people worked 18-hour days for 3 days to clear damaged equipment from the site. About 180 people continued to work for about an additional 6.5 days to restore equipment and service to a critical line. To reduce the disruption time, this reconstruction was carried out by several crews working in parallel at all locations where possible. This damage occurred to a facility that used the then-current and most stringent earthquake mitigation practices. After the Loma Prieta and Northridge earthquakes, it took months to repair and replace damaged equipment, even though service was restored quickly. This experience suggests that larger earthquakes, those that impact larger areas, or those that occur in regions where less stringent seismic design practices and more vulnerable equipment are used, will have more-extensive earthquake damage that could overwhelm system redundancies. As a result, unacceptably large direct losses, indirect losses borne by customers, and lengthy disruption of service to the community are possible. In light of the recent experience, large California utilities have reevaluated the vulnerability of their systems and are adopting measures to improve their response. While many of these measures would be difficult to justify in regions of lower risk, some things that are cost effective in any region that has a history of damaging earthquakes can be done, particularly for new construction. It would be unfortunate if cost-effective measures were not implemented, and utilities and the communities they serve were exposed to avoidable risks.
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25.1.1 Purpose The purpose of this chapter is to provide information to improve the earthquake response of electric power systems. This can be achieved by the following: • Review how earthquakes affect power system facilities and equipment. • Raise the awareness and understanding of the vulnerabilities of power system facilities and equipment by reviewing their earthquake performance. • Suggest an overall approach to an earthquake mitigation program. • Provide insight into facility performance so that facilities could be evaluated to determine their earthquake vulnerability. • Suggest installation practice changes that could reduce earthquake damage.
25.1.2 Basis for Recommendations The recommendations in this chapter are primarily based on experience gained from California earthquakes and a few foreign earthquakes. Many of the recommendations have been drawn from innovations initiated by California utilities, whose contributions are gratefully acknowledged. Much of the information on earthquake damage to power systems has been gathered by the Earthquake Investigation Committee of the Technical Council on Lifeline Earthquake Engineering, a division of the American Society of Civil Engineers. Members of the committee have investigated earthquakes that have damaged power system facilities in 13 United States and nine foreign countries, including the 1978 Sendai, Japan; 1985 Chile; 1988 Soviet Armenia; 1990 Philippines; 1995 Kobe, Japan and the 2001 Gujarat, India earthquakes. The content of this chapter is heavily drawn from Manual 96, Guide to Improved Earthquake Performance of Electric Power Systems, published by the American Society of Civil Engineers, parts of which are reproduced here with permission [Schiff, 1999]. Because the guide is a 341-page document, this chapter has not covered all topics contained in it, and the content that has been covered has been condensed. In addition, more than 200 illustrations showing damage and good practices and most illustrations showing good seismic practices are not shown here. Because practices and equipment used in different parts of the United States vary, the effectiveness of some practices and equipment is unknown. Also, there may be differences in earthquakes and their effects in other parts of the country. For example, records of small “eastern” earthquakes indicate that ground motions are richer in higher frequencies, which may result in differences in equipment performance. Also, it is known that larger areas in the Midwest and Southeast are more vulnerable to soil liquefaction than in California. Some types of facilities have no significant earthquake experience. For example, there is no record of a coal-fueled power generating plant’s being subjected to a significant earthquake. There are no traditional coal-fired plants in California nor in the areas investigated after the 1985, Chile; 1978 Sendai, Japan or the 1995 Kobe, Japan earthquakes. It is important to realize that the seismic design of power systems is a work in progress. Future earthquakes, as in the past, can be expected to suggest changes in practice. Again, it should be noted that we have no experience with earthquakes of magnitude of 7 and above centered in a modern urban setting.
25.1.3 Scope This chapter deals with major power system elements — power generating stations, transmission and distribution lines, substations, system communications and control and ancillary facilities and functions. Emphasis is given to the elements that have exhibited poor earthquake performance. Thus, a large portion
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of the chapter is devoted to high-voltage substations, as this is where most power system damage has been concentrated. Where existing practices, even though they may not be well defined, have performed well, e.g., in power generating plants, recommendations will be limited to those areas where damage has been observed.
25.1.4 Organization and Use of the Chapter The initial sections in this chapter give an overview of the configuration of a typical power system, review the overall performance of power systems and power facilities and describe approaches for improving the earthquake performance of power systems. Subsequent sections deal with detailed technical issues associated with substations, transmission-line and distribution-line networks, power generating stations, system control, communication system facilities, and specialized facilities and ancillary facilities and functions. The final sections are Closing Remarks, Definition of Terms, References, and Further Information. Damage to some equipment can be mitigated on new construction or, in some cases, on existing facilities, in a cost-effective manner. Those measures that are particularly cost effective, such as anchoring station batteries and power transformers, should be given high priority in a mitigation program because of their demonstrated beneficial cost–benefit ratio. It is emphasized here that the most important task in a mitigation program is to begin it, rather than expending a major effort to optimize its execution. This is particularly important in those areas that are not at extreme risk.
25.1.5 Overview of the Configuration of a Typical Power System From an overall physical perspective, power systems consist of a number of nodes (substations and power plants) that are typically interconnected by redundant networks of transmission and subtransmission lines forming a grid network, often called loop systems. Emanating from some nodes (distribution substations) is a radial configured system (tree networks) of feeder lines and service lines that carry power to users. It should be noted that the nomenclature used to define some parts of the system varies between utilities. It should also be noted that, in the descriptions that follow, typical facilities and situations will be discussed. Some utilities organize their systems in different ways to better address their particular needs. The objective of the following descriptions is not to create a power system specialist, but to provide the engineer with some familiarity with power systems. Before describing the elements that make up a power system, it is important to understand a few characteristics of power networks that distinguish them from other lifeline networks, such as transportation or water system networks. First, power systems generate and distribute a commodity — electric power. The system does not store power (in its electrical form) so that it is used as soon as it is generated. Second, there is little control over the flow of power within the network once it has been generated. Electric power generated at a power plant will travel along all of the lines that interconnect the generator and the user. The current flowing over any path is inversely proportional to the impedance of the path; the lower the impedance the higher the current. The capacity of a path is not necessarily related to its impedance, particularly if the system is configured in an unusual way. If the current along any path exceeds the capacity of any element within the path, protective monitoring devices will cause a circuit breaker to open. This will stop all current in the path and alternative paths must carry the current formerly carried on the now opened circuit. To balance power generation and consumption, and to control the flow of current through the system, several things can be done. Power output of the generating stations distributed throughout the system can be adjusted, the configuration of the transmission network can be changed (switches can be opened or closed to change the linkage between nodes) and, in extreme cases, load can be dropped. The inability to store electrical energy in the system, and the immediate reallocation of the flow of energy within the system to any changes in the system configuration, requires a sophisticated and sensitive control system to provide reliable service in the face of numerous problems that commonly befall power systems. © 2003 by CRC Press LLC
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Generating Station
500 kV Transmission Line
Transmission Substation
230 kV Transmission Line
Distribution Substation
12 kV Distribution Line
FIGURE 25.1 Simplified schematic diagram of part of a power system. The control system and users are not shown. The transmission lines form loops so that the loss of a line will not isolate a substation. Generating stations are usually connected to a substation by one or more circuits. Distribution feeders typically form tree networks, so that if a line is disrupted, all customers away from the distribution station will lose power.
Three of the generalizations given above are not strictly true. Some utilities do have pumped-storage facilities that can store energy. A limited number of DC transmission facilities within the United States have the ability to control the power flowing over their lines. Many transformers have load tap changers that can make small changes in their output voltage and have minor control over power flows. However, the overall significance of the above points is valid. For the purpose of earthquake evaluation and mitigation, power systems can be divided into six major parts: 1. 2. 3. 4. 5. 6.
Power generating facilities Transmission and distribution lines Transmission and distribution substations Control and data acquisition systems Communications Ancillary facilities and functions
A simplified schematic diagram of part of a power network is shown in Figure 25.1, but the control system and the users are not shown. Most generating stations get their energy from fossil or nuclear fuels, which are used to generate steam that passes through a turbine that is connected to a generator to produce electric power. Hydroelectric plants use falling water to turn the turbine and generator. Photoelectric, geothermal, and wind-powered turbines generate relatively little power for the power grid and will not be discussed. Diesel and gas turbine units also provide small amounts of power, typically for peak loads during the day. The output voltage of generators is typically between 14 kV and 30 kV. To couple this power to the power grid,
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step-up transformers convert the generator output voltage to between 115 kV and 500 kV. Transmission lines then carry the power to a transmission substation that connects it to the power grid. A power control center for a utility or group of utilities monitors system operations, controls generation and energy transfers to keep supply in balance with demand, and provides additional system protection. Substations perform many functions. First, substation switchyards interconnect the lines at the same voltage. Most substations contain power transformers that serve to connect parts of the system that operate at different voltages. Substations contain equipment to monitor voltage on lines and current flowing through the conductors (bus) that connect the lines. They contain circuit breakers that can open to isolate a transformer or clear a line that is in an abnormal state, such as carrying too much current. Utilities use sophisticated systems to provide system protection. Often the system is unique to the specific utility. These systems use voltage and current measurements, timing circuits, and communications systems to isolate system faults with a minimum of disruption to the system. The communication systems (for protective relaying) can use microwave systems between substations, carrier frequencies on the power line, or optical fiber systems carried on transmission-line towers. The substation also contains switches that allow the substation, and thus the network, to be reconfigured. Apparently simple changes in the substation can significantly change network configuration, such as opening a bus-sectionalizing switch. Transmission lines are typically carried on transmission-line towers, although buried cables are occasionally used. Most utilities use one of the standardized transmission voltages, although there are variations. The transmission and subtransmission voltages most frequently encountered are 765 kV, 500 kV, 345 kV, 230 kV, 161 kV, 138 kV, 115 kV, and 60 kV. In the United States, at 500 kV and above, only one circuit (three conductors) is typically carried on a transmission tower. At lower voltages a tower can carry several circuits. In addition to the AC lines referred to above, there are a few DC lines. For transmission over long distances, DC circuits can be more efficient. DC lines and the special facilities at their terminals also allow the power flow in the line to be controlled. Distribution substations will convert power from transmission or subtransmission levels to distribution voltages. Besides connecting distribution lines, the output from most distribution substations goes into feeders that carry power through a radial network to the users. The feeders may provide power to vault transformers at intermediate-size customers such as shopping centers, industrial facilities, and large buildings, where it may be converted into one of several voltages, usually 2.4 kV, 480 V, or 220 V. Pole- or platform-mounted transformers typically supply service connections to individual residences at 240/120 V. Distribution lines, which generally operate at voltages of 4 kV, 12 kV, 16 kV, or 32 kV, are frequently buried — in new communities they are typically buried. Both transmission and distribution substations are often unstaffed, so that the status and value of important variables are communicated to a staffed substation or the control center. The control elements of power systems are not shown in Figure 25.1. The control center for an electric utility performs many functions. As noted above, it monitors the network and controls the output of the generating stations, referred to as power dispatch. In addition to keeping the generation supply in balance with demand, other factors can be considered. For example, dispatch is typically optimized to reduce costs, i.e., the most efficient generating stations generate the most power, and the less efficient, usually the older stations, generate less power or serve a standby function called spinning reserve. This is referred to as economic dispatch. Under certain conditions, it may be appropriate to optimize the generation so that pollution is minimized, particularly in certain areas during unfavorable atmospheric conditions. The control center also must assure an adequate capacity in reserve, so that capacity in the rest of the system can be quickly increased to meet demand if a generating unit unexpectedly goes off-line. For most systems, this requires that some generating units are kept in spinning reserve, that is, they are fired up and ready to start generating power. This is necessary because it might take more than 12 hours to get a cold plant up and running so that it can generate power. Even spinning reserve cannot respond instantly, so that it may take several minutes to start ramping up its power output. The control center also has to monitor and control the exchange of power between utilities. Power is continually being bought and sold by utilities. Finally, the geographical distribution
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of generating sources has to be consistent with the capability of the transmission system’s capacity to carry the power and to maintain a reserve capacity so that, if a line or generating source is lost, the remaining system can continue to operate.
25.2 Historical Response of Electrical Power Systems to Earthquakes Most earthquake damage to electrical systems has been due to the failure of porcelain elements in highvoltage substation equipment. Performance is strongly influenced by specific equipment designs and installation practices. There has also been damage to substation buildings, conductor support structures, cast aluminum hardware used on both low- and high-voltage equipment, equipment support structures, equipment anchorage, and parts of power generating stations. The performance of some communication and control systems has also been impaired following earthquakes. In this chapter, power systems have been grouped into three types of facilities: transmission and distribution facilities, power generating stations, and control and communications facilities. Facilities that do not immediately impact system operations, such as design offices and maintenance facilities, are not discussed here. The overall performance of the entire system and of each of these types of facilities is discussed. A detailed discussion of the performance of individual equipment and facilities is given in subsequent sections.
25.2.1 Overall Power System Seismic Performance Before the seismic performance of power facilities within the United States can be properly understood and interpreted, four factors must be kept in mind: 1. No data from a major or great earthquake centered in a modern metropolitan area exist. The evaluation of system performance is based primarily on several moderate and two strong California earthquakes. 2. Seismic practices in utilities and knowledge about earthquakes in California have been evolving since the 1920s. Since 1933, a stronger impetus has been given to the seismic design of power facilities, starting with 0.1 g static analysis, which was later revised to 0.2 g. This has been a slow process, because changes in design take a long time to be reflected in most facilities in the field. However, the vast majority of facilities subjected to earthquakes since 1970 have had significantly higher seismic specifications (particularly anchorage of substation equipment) than most such facilities outside of California. In the early 1970s, 0.5 g dynamic analysis methods were used, followed shortly thereafter by dynamic testing of vulnerable equipment. While some utilities may have more severe design specifications, such as those for high wind loads, the requirements typically have little effect on improving the seismic performance of substation equipment. 3. The moderate magnitude of most recent earthquakes and the high attenuation of seismic energy in California, as compared with most of the eastern United States, mean that in California relatively small areas have been exposed to damaging ground motions. As a result, the damage to power systems in most earthquakes has been confined to one or two facilities. In the eastern United States, earthquakes of equivalent magnitude will impact much larger areas that may have a high potential for soil liquefaction. Thus, an eastern earthquake may affect several facilities and be more disruptive to the network, and soil liquefaction at a power facility can be more damaging. 4. Large coal-fueled plants, with their heavy coal-storage silos located high in the steam-generation (boiler) structure, have not been put to the test by damaging earthquakes, so their seismic performance is unknown. Within California, all large fossil-fuel power-generating stations burn gas or oil rather than coal. No earthquake data on the performance of coal-fueled generating stations in seismic regions in other countries are available.
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Given these caveats, it can be said that system performance, as measured by power disruption, has been very good. Thus, to date, network redundancy has been adequate to overcome the extensive damage to isolated high-voltage substations. In the case of the Loma Prieta and Northridge earthquakes, where several substations were damaged, the character of the damage and the use of emergency procedures allowed expeditious service restoration.
25.2.2 Power Transmission and Distribution Systems The transmission and distribution system can be grouped into three types of elements: transmission lines, distribution lines, and substations. 25.2.2.1 Transmission Lines Transmission lines have been very resistant to earthquake damage; their main vulnerabilities are foundation failure of transmission towers or the loss of a tower due to a landslide. Both occurrences are relatively rare in the United States. It would appear that the low natural frequencies of lines decouple their mass from the high energy content of earthquakes, and the design for extreme wind, ice, and longitudinal load combinations is adequate for earthquakes. The 1999 Chi-Chi, Taiwan earthquake demonstrated that, even with conservative transmission-tower foundation construction, 11 high-voltage transmission towers were lost and hundreds were damaged, causing long-term blackouts in Taipei, which is located far from the epicenter and generally experienced minor earthquake damage. 25.2.2.2 Distribution Lines Distribution lines are also seismically robust. Their main vulnerability in the United States is from burndown when earthquake-induced vibrations cause adjacent phases of a circuit to come in contact. If they are energized, they will arc and may burn through the line, causing it to fall. Burned-down lines can be a significant source of fires; they have generated large numbers of calls by the general public to the emergency response system. While repair can be labor intensive, only limited numbers of customers are impacted by any given downed line and spare parts are usually not needed to effect a repair. The shortingtogether of adjacent phases can also cause fuse cutouts to blow and disrupt service. In the aggregate, restoration of this type of damage can be lengthy. The main cause of pole failure has been soil failure. 25.2.2.3 Substations Damage to porcelain members of high-voltage substation equipment has been a recurring problem. The damage shown in Figure 25.2 can be attributed to equipment vulnerability and lack of slack in conductors connecting the equipment. The damage shown in Figure 25.3 can be attributed to inadequate anchorage that allowed the transformers to fall from their pedestals, damaging bushings, radiators, and possibly internal components. Equipment operating at voltages of 115 kV and below performs very well when good seismic installation practices of anchorage and conductor interconnection flexibility are followed. Some types of equipment operating at voltages of 161 kV and above are vulnerable. Generally, the higher the operating voltage, the more vulnerable the equipment. The highest-voltage equipment to be subjected to earthquakes is 500 kV. Several types of failures are frequently observed: • Inadequately anchored rail-supported transformers have fallen from their elevated platforms and have been severely damaged. • Leaking transformer bushings and radiator piping are common and broken bushings have been observed. • Lack of adequate slack in conductors connecting equipment can load and damage bushings and post insulators. • Flexible equipment supports have allowed large relative displacements; this tends to aggravate problems with the lack of sufficient slack. Some equipment designs appear to be inherently vulnerable, while other equipment that serves the same function and operates at the same voltage
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FIGURE 25.2 Damage to switchyard equipment.
can be quite rugged, e.g., some live-tank circuit breakers are very vulnerable, while dead-tank circuit breakers are robust. • Current transformers, capacitive coupled voltage transformers, and line traps have been damaged; their loss has been disruptive to system function protection. One of the main difficulties when substation equipment is damaged is that there are limited numbers of spare parts or spare replacement equipment available. Also, repair and replacement of damaged equipment is a time-consuming and labor-intensive task.
25.2.3 Power Generation Facilities In general, the overall seismic performance of power-generating stations has been good, although coalfueled plants and large oil- and gas-fueled plants (500 MW and above) have had limited exposure. Within California, many generating stations are relatively small and old. Structural design practices used by California utilities have been based on the Uniform Building Code and structural performance has been good. Some equipment and facilities not causing the plant to shut down have been damaged. Some elements, e.g., water- and liquid-fuel-storage tanks, have had mixed performance. Generating stations have been forced off line by switchyard and substation damage, and have experienced delays in getting back on line. The discussion here excludes nuclear generating plants because they are under federal regulation, are designed to much more stringent criteria, and have not experienced earthquake damage. Also, because of their special character or limited number, wind, geothermal, and hydropower facilities are not discussed in this chapter. © 2003 by CRC Press LLC
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The switchyards associated with power plants are grouped with transmission and distribution facilities. Peaking generating units, which are often designated to serve as black start units, have consistently failed to operate in this role because of inappropriately designed control systems.
25.2.4 Control, Protection, and Communications Facilities In general, control, protection, and communications equipment have performed well. The exceptions are high-voltage equipment used for protection (instrument transformers, circuit breakers, line traps), uninterruptible power supplies, and emergency power supplies. Inadequate restraint of station batteries at power plants and substations has been a common problem. Protective relays have tripped due to earthquake-induced vibrations. The loss of instrumentation transformers has also disrupted or limited system protection. Damage to substation equipment may result in poorer system protection. For example, damage to instrumentation transformers may limit protection to just over-current conditions and prevent the determination of the location of faults. Public switched network telephone systems and cellular telephone systems are typically congested after an earthquake, so they cannot be counted on during the emergency response period. Utility-owned communication systems can also become congested, but the earthquake performance of these facilities has been good. Radio repeaters used to dispatch repair crews can lose power and stop operating; this impedes the dispatch and control of repair crews.
25.3 Code Provision, Standards and Guidelines for Electrical Systems A broad range of facilities make up a power system; the construction and operation of many are governed by codes and standards. However, from a seismic design perspective, there are few mandatory codes or regulations. Power systems contain many buildings, including power plants, substation control houses, control center structures, and engineering and administrative offices. The construction of all is governed by the local building codes, which now require seismic provisions to be applied in regions with seismic risk. While federal facilities are not governed by local building codes, they must conform to national codes. The design of liquid-storage tanks is controlled by the American Water Works Association, AWWA D100 [ANSI/AWWA, 1997] or the American Petroleum Institute, API 650 [ANSI/API, 1995] for water or liquid-fuel tanks, respectively. Many utility facilities are seismically vulnerable because they predate the use of seismic requirements or were constructed using less stringent requirements. Several national standards or guidelines are directed at earthquake effects on power systems, but these are voluntary rather than mandatory. Of particular note is the Institute of Electrical and Electronics Engineers Standard, IEEE Standard 693–1997, IEEE Recommended Practices for Seismic Design of Substations[IEEE, 1998]. While this standard covers many issues in seismic design of substations, its main focus is on establishing criteria and methods for seismically qualifying substation equipment. Utilities throughout the country are using these procedures, which should result in improved earthquake performance of equipment that conforms to the recommended practices. The American Society of Civil Engineers (ASCE)’s Manual No. 96, Guide to Improved Earthquake Performance of Electric Power System [Schiff, 1999], forms the basis of this chapter. It contains a detailed review of the seismic performance of power system facilities and equipment and provides recommendations for retrofitting or new construction to address observed equipment failures. ASCE is also preparing a guide, Substation Structure Design Guide [Kempner], which will provide design criteria for equipment support structures in substations.
25.4 Earthquake Preparedness Earthquake preparedness can be divided into two groups of activities: disaster-response planning and earthquake mitigation. Disaster-response planning accepts that there will be significant earthquake © 2003 by CRC Press LLC
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FIGURE 25.3 Damage to transformers due to inadequate anchorage.
damage and disruption and attempts to deal with the results of these effects by planning for them prior to the event. In this chapter, earthquake-mitigation activities are those that deal with the system as it exists (retrofitting) and new construction with the objective of reducing damage or the effects of damage on power system response. Because it is not cost effective to make all equipment, facilities, and systems “earthquake proof,” damage can be expected even if current good practices were used in the design and construction of a system from its inception. For this reason, disaster-response planning is always an important part of earthquake preparedness. Such planning is directed at creating disaster-response plans or making additions to or changes in physical facilities that will aid in post-earthquake response. Examples include enhancing communication capabilities, creating an emergency operations center, or creating an alternate energy control center. Although disaster-response plans are important, their detailed development is outside the scope of this chapter. A few comments on disaster-response plans are given below. Earthquake-mitigation activities are directed at reducing earthquake damage by using good installation practices on new construction and when refurbishing facilities. A limited number of cost-effective retrofits are also recommended. A schematic diagram showing the elements in a disaster-preparedness program is shown in Figure 25.4.
25.5 Earthquake Hazard and System Vulnerability Evaluation An initial hazard evaluation is needed to assess the potential for the occurrence of damaging earthquakes in the utility’s service area. An initial assessment of the vulnerability of power facilities is also needed to establish the scope of earthquake vulnerabilities and the need for an earthquake-preparedness program and possibly more detailed hazard and facility evaluations. The goal of the initial evaluation should be to get approximate, realistic, but conservative estimates for direct losses. The procedures for performing an evaluation of earthquake hazards are described below. There may be some situations where the cost and effort associated with a detailed evaluation may not be necessary or justified. After the initial evaluation of hazards and vulnerabilities, certain mitigation tasks may be obvious because of their high benefit–cost ratio. For these tasks, retrofitting can proceed without formulating an entire mitigation plan. Examples include providing adequate anchorage and earthquake-secure emergency power at generating stations and substations, and anchoring power transformers. © 2003 by CRC Press LLC
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Preliminary Hazard and Vulnerability Evaluation Detailed Hazard and Vulnerability Evaluation Mitigation
Response Planning
Expedited Implementation of Very High Benefit/Cost Tasks
Develop Disaster Response Plans
Develop Seismically Enhanced Manuals of Practice
Establish Emergency Operations Center
Adopt Seismic Criteria for Site Selection and Preparation
Establish Alternate Energy Control Center
Consider Seismic Issues in Facility Layout Include Seismic Specifications in Equipment Purchase Orders
Corporate Recovery Plan
Incorporate Good Design Practices in Manual of Practice Perform Seismic Quality Assurance for Engineering Drawings and Construction
Exercise Disaster Response Plans Other Earthquake Preparedness Actions
Mitigation Plan Implementation Diligently Use Good Practices on Renovation and New Construction Retrofit Selected High Benefit/Cost Item s Use Opportunities to Seismically Upgrade Evaluate and Install Seismically Hardened Power Paths Plan Long-Range Seismic Upgrade of Buildings Important Issues Support of Top Management Crucial Practices and the Program Must Be Cost Effective Need for Qualified Seismic Design Professionals
Periodic Review and Revision of Earthquake Preparedness Program
FIGURE 25.4 Flow chart of the steps in formulating and implementing an earthquake preparedness program.
25.5.1 Simplified Evaluation of Earthquake Hazard and System Vulnerability A team made up of a few individuals can make a useful earthquake-hazard and -vulnerability assessment relatively quickly. An engineer with an understanding of the seismic hazards in the utility’s service will be needed. The necessary information can be obtained by reviewing risk maps associated with model building codes that describe seismic vibration risks [IBC, 2000] and the procedure contained in IEEE 693 [IEEE, 1998]. The seismic risk in the service area is estimated by evaluating the expected peak acceleration, which can be obtained by modifying values taken from the 2% exceedance in a 50-year risk map by a factor determined by the soil characteristics at the site of interest. The soil descriptions and factors can be obtained from the International Building Code [IBC, 2000], and the chief dispatcher should be able to identify the sites that are important to system operation. Finally, an engineer who is familiar with the equipment at the sites and its seismic vulnerability can identify the important sites that are vulnerable. Information on equipment vulnerability can be obtained from the ASCE Power Guide [Schiff, 1999]. With this rapid evaluation, a simple earthquake preparedness plan can begin to be formulated. © 2003 by CRC Press LLC
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For many utilities, this may be the most productive approach to actually improving the earthquake performance of the utility. However, the cost and effort needed to mount a detailed hazard and risk evaluation may encounter such substantial resistance that a preparedness program never gets started. As a minimum, newly purchased substation equipment should be seismic-qualified to meet the requirements in IEEE 693 [IEEE, 1998] and installed with good seismic anchoring, conductor design, and installation practices.
25.5.2 Detailed Earthquake Hazard and System Vulnerability Evaluation The objective of this effort is to gather data to make a case to management to initiate a formal earthquake preparedness program. For many utilities, the losses associated with a damaging earthquake that impacts their service areas will have very significant financial impacts that responsible management should not ignore. The tasks for a detailed hazard- and system-vulnerability analysis are listed below: • • • • • •
Determine whether the earthquake hazard warrants a preparedness program. Obtain a rough assessment of direct damage and associated costs. Estimate the extent and duration of power disruption. Estimate damage reduction to be achieved by a long-term mitigation program. Identify the benefits to be achieved in the area of risk management. Identify ancillary benefits derived from a preparedness program.
Each of these tasks is discussed in more detail in the ASCE Power Guide [Schiff, 1999].
25.5.3 Seismic Analysis of Electrical Systems Several computer programs have been developed, primarily at academic institutions, to evaluate the potential impact of an earthquake on a power system. While the results of these programs can be useful, their implementation and analyses generally have several shortcomings. These programs are not commercial packages, so that implementation of the methods described in the literature may require a substantial effort when applied to an actual system. For any program to provide a realistic assessment of system performance, input data must accurately characterize the system, and this requires substantial knowledge and effort, including details of the specific equipment and its fragilities. For example, some live-tank circuit breakers fail at ground acceleration of less than 0.1 g, while dead-tank circuit breakers operating at the same voltage have survived acceleration as large as 1.0 g. The available programs do not use the existing utility databases that characterize the networks that are used for load flow or transient analysis. Some programs do take into account the redundancy in the network configuration to assess system performance, but none adequately incorporates the significant redundancy that is designed into substations. With the present state-of-the-art analysis programs, the simple evaluation described below will probably be more useful for the effort expended. Subsequent sections of this chapter discuss elements associated with disaster-response planning and earthquake mitigation.
25.6 Earthquake Preparedness — Disaster-Response Planning All power utilities, as required by the North American Electric Reliability Council, must have emergency response plans. Indeed, power systems encounter situations — whether wind, ice, or lightning storms — that require an emergency response on a regular basis, or when load and generation suddenly become unbalanced. Fortunately, disasters seldom occur, but earthquakes present unique characteristics that are not observed in other severe events that often affect utilities. Most emergencies that affect power systems are related to transmission and distribution lines, while earthquakes primarily affect substations. Normal emergency-response procedures should be enhanced because earthquakes occur without warning, they © 2003 by CRC Press LLC
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impact the communities’ transportation and communication systems and their impact can overwhelm typical emergency-response procedures and the robustness provided by system reliability. Key issues are listed below.
25.6.1 Procedures for Inspection of Utility Structures The utility should have a plan in place to have utility structural engineers or engineering firms on retainer to perform an inspection of important utilities structures. An inspection shortly after the earthquake will protect utility personnel should a damaged building collapse in an aftershock. In the aftermath of an earthquake, local government will often deputize engineers as building inspectors to inspect and tag buildings. These inspections are often done quickly and tend to be conservative. Once tagged, it may be difficult to remove the tag and access can be denied to critical facilities such as the control center, emergency operations center, and engineering offices that contain plans for equipment and structures.
25.6.2 Activation of the Emergency Operations Center The emergency operations center (EOC) will play a vital role in collecting damage assessments, coordinating power restoration, providing a central source for information to the community and emergency government, and securing additional resources needed for the response, such as activating mutual aide agreements, getting emergency supplies, and arranging for emergency funding.
25.6.3 Document Restoration Costs Public utilities can be partially reimbursed for restoration costs by the Federal Emergency Management Agency (FEMA) and insured utilities’ costs must be documented for reimbursement.
25.6.4 Document Damage and Contributing Factors When restoration costs are well documented, reimbursement will follow rapidly. The first priority in the aftermath of a damaging and disruptive earthquake is to restore service, and it is difficult to divert resources to document the damage and the factors that contributed to it. This type of documentation is best carried out by engineers who are familiar with power equipment, as this is usually where the damage is concentrated. In addition to a listing of what is damaged, factors contributing to the damage — inadequate anchorage, slack in electrical connection between equipment, or other factors — are important, because this information will enable the utility’s seismic practices to be improved. An ASCE monograph, Guide to Post-Earthquake Investigation of Lifelines [Schiff, 1997] reviews past earthquake damage and vulnerabilities to look for. In past earthquakes, members of the Earthquake Investigation Committee of the Technical Council on Lifeline Earthquake Engineering have conducted these investigations as part of their professional activity. It is vital that the documentation of damage be started immediately after the earthquake because damage is quickly removed to restore service, and assessing causes once the damaged equipment is removed is very difficult. As a minimum, engineers should document each failure with pictures so that analysis can be carried out later.
25.7 Earthquake Preparedness — Earthquake Mitigation 25.7.1 Approach to Earthquake Mitigation The implementation of an earthquake-mitigation program will lead to a progressive improvement in the seismic ruggedness of power facilities in a cost-effective and manageable way and will improve the earthquake response by reducing damage and having a disaster-response plan in place. The approach suggested here is to initiate the use of good seismic design practices for new facilities and for older facilities undergoing normal renovation. Simple measures that have been shown to be effective in © 2003 by CRC Press LLC
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FIGURE 25.5 Retrofitted transformer anchorage.
improving seismic performance can be used. For certain facilities or equipment for which malfunction would be very disruptive, expedited seismic retrofit may be justified. Finally, there are some power system elements, such as the structural systems in substation control houses and the building that contains the energy control center, that are not routinely refurbished. The seismic risks of these facilities should be evaluated and their renovation included in a long-term seismic upgrading program. Several of the tasks that make up a mitigation program are generally carried out in parallel. Examples include updating the manual of practice, identifying system vulnerabilities, retrofitting items with high benefit–cost ratios, and incorporating good seismic practices in normal renovation and new construction. Because retrofitting facilities is, in general, not very cost effective, the number of retrofitting tasks will probably be relatively small. One example of a cost-effective retrofitting task is the anchoring of power transformers. Figure 25.5 shows a transformer that has had its anchorage retrofitted. Because transformer designs vary widely, a universal retrofit method can probably not be devised. The one shown here used the lifting pads provided by the manufacturer. This is a good approach because these pads are designed for large loads and welding to the transformer case is avoided. One could agonize over the optimum order in which different items should be retrofitted. An issue more important than prioritization is that a program be started. Prioritization of mitigation actions will be significantly influenced by existing design and installation practices and the perceptions of the individuals managing and implementing the program. Upgrading the manual of practice should be given high priority to ensure that good installation procedures will be used for new construction.
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Most of the effort to improve the system’s earthquake performance will be carried out in the course of normal system renovation. The key to this process is to establish and implement good earthquake practices for new facilities and for routine upgrading of older facilities. Items that typically justify early action or retrofitting because of their favorable cost–benefit ratio and their potential for disruption, are highlighted in italics. These items are also selected because they are frequently damaged, can reduce damage and disruption, and are amenable to retrofitting. The elements of a mitigation program to reduce damage are listed below: • • • • •
Upgrading manuals of practice to incorporate good seismic design practices Using IEEE 693 to qualify new substation equipment Assessing the vulnerability of power system facilities Implementing a mitigation plan Periodically reviewing and revising the mitigation program
After the initial evaluation of hazards and vulnerabilities, certain mitigation tasks may be obvious because of their high benefit–cost ratio. For these tasks, retrofitting can proceed without formulating an entire mitigation plan.
25.7.2 System Review and High Priority of Selective Upgrading Some California utilities have implemented selective upgrading of some of their facilities to improve system earthquake performance. An evaluation of the system may indicate that one or more critical substations is vulnerable to damage. Rather than replace the entire substation, the seismic hardening of a critical power path through important substations can provide significant protection at relatively little cost. This will reduce the risk of long-term disruptions, and may even avoid disruptions entirely. 25.7.2.1 Taking Advantage of Upgrading Opportunities that Present Themselves Make minor upgrades that can improve seismic performance in the course of normal maintenance as opportunities present themselves. For example, the performance of some friction-clip equipment anchors has been poor. Welding of the clip to the equipment can significantly improve its performance. Thus, when welding equipment is scheduled to be used at a specific substation, this opportunity should be used to weld the friction clips on the most vulnerable equipment. 25.7.2.2 Incorporate Good Seismic Practices in Normal Facility Renovation and New Construction It is vital that the renovation of existing facilities and new construction incorporate good seismic practices. This is the fundamental premise for the suggested approach. Thus, it is important that manuals of practice be updated to reflect good practice. 25.7.2.3 Upgrading Facilities Not Normally Renovated In the normal course of development, some facilities are not renovated. For example, the structural systems of control-house buildings and the structure that houses the energy control center and emergency operations center are usually not modified when the equipment they contain is periodically replaced. These and other structures that affect personnel safety should be upgraded if necessary. Other examples include service center buildings, corporate offices and structures that house the engineering departments and the trouble board operations. Risks associated with structural vulnerabilities must be identified and a long-term seismic upgrading program established. 25.7.2.4 Seismically Upgrading Manuals of Practice The manual of practice as defined in this document is the collection of a utility’s standards to be used for site evaluation, selection and preparation, substation layout, standard clauses incorporated into equipment purchase order specifications, detailed engineering drawings of equipment anchorage, and conductor stringing practices in substations. It is vital that good seismic design practices be explicitly © 2003 by CRC Press LLC
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defined and incorporated into the manual of practice. Good design details for the installation of equipment in manuals of practice set the stage for long-term improvements in the earthquake response of a utility. The institutionalization of good practice into the normal practice of a utility will assure the longterm success of the earthquake-mitigation program. 25.7.2.5 Installation Practices Many of the changes to improve the manuals of practice will be related to methods of installing equipment. Manuals of practice should explicitly specify details that are important to facilities’ earthquake performance. Installation practices include proper torquing of bolts, leveling equipment and installation of conductors with adequate slack. Anchorage drawings for equipment should be based on the seismic outline drawings required in IEEE Standard 693 [IEEE, 1998], which specify anchorage loads. Drawings should specify the details of how conductors are to be connected to the equipment, including provisions for connector flexibility. Good installation practices for flexible conductors require that sufficient slack be provided to accommodate the sum of the expected seismic deflections of the equipment at each end of the conductor plus a factor of safety. When providing slack to flexible conductors, clearances required by the National Electrical Safety Code [IEEE, 1997] and short-circuit loads between phases must be provided. A rigid conductor should be configured with a dogleg rather than a straight connection between the equipment. A rigid conductor is often provided with devices to accommodate thermal expansion, however, these are generally inadequate for earthquake-induced motion.
25.8 Earthquake Preparedness — Mitigation This section is divided into six subsections, with an emphasis on substations where, as noted above, most damage has historically occurred. This material is drawn from ASCE Manual 96, Guide to Improved Earthquake Performance of Electric Power Systems [Schiff, 1999]. This 341-page guide discusses many topics that cannot be covered here and gives more detail on the earthquake performance of specific items of equipment, suggests emergency operation procedures to circumvent damage, and details mitigation measures to improve seismic performance. The seismic assessment of power systems in different parts of the country, where design practices vary significantly, shows a surprisingly similar set of high-priority mitigation tasks.
25.8.1 Substations Most earthquake damage has been concentrated in substations, and has been associated with porcelain failures — although one of the more disruptive types of failures has been of transformer bushings where the porcelain generally does not fail. Many of the failures can be attributed to inadequate anchorage of equipment and inadequate slack or flexibility in conductor connecting equipment. Some types of equipment are inherently vulnerable so that even the use of good practices cannot prevent damage. The performance of equipment operating at 115 kV and below has been good. Equipment operating at 161 kV and above has had problems, and the higher the voltage, the more vulnerable the equipment. Some damaged switchyard equipment, such as lightning arresters, capacitive coupled voltage transformers, potential transformers, circuit breakers, line traps, and disconnect switches can temporarily be bypassed to restore service. In extreme cases, entire switchyards have been bypassed. Damage to power transformers and station batteries have been common and very disruptive to service. Subsequent subsections deal with general issues of anchorage, conductor design and installation, and power transformers. Station batteries are covered in Section 25.13.4. 25.8.1.1 Anchorage Issues Equipment anchorage should have adequate strength to resist pullout and shear loads, and should be stiff. The design of an anchor should consider the entire load path from the equipment to the foundation. © 2003 by CRC Press LLC
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The consideration of the load path is vital to a stiff anchorage, which will reduce equipment motion and the demands on the provision for conductor slack connecting the equipment. Anchorage design should consider shear, vertical accelerations, overturning moments, prying action, and torsion due to mass eccentricities of the equipment. High-strength bolts should be avoided because the energy absorption characteristics of ductile action in the bolts is desirable. Headed studs rather than “J” and “L” cast-in-place anchor bolts should be used. If anchor bolts, rather than welding to embedments, are used for heavy switchyard equipment, the oversized bolt holes often provided in the equipment will allow the equipment to slide in an earthquake. This can cause impacting when the equipment hits the bolt and this impact can cause high stresses in the porcelain members of the equipment. This problem can be eliminated by welding a thick plate washer to the equipment base plate. A normal washer should also always be used under a nut, even if welded plate washers are used, as it can be used to determine whether the bolt has stretched after an earthquake. Some substation equipment, such as bulk-oil circuit breakers, is typically mounted on a skid anchored with friction clips. Friction clips have three undesirable characteristics. They inherently incorporate prying action that at least doubles the anchor bolt stress to vertical loads, they can rotate and then provide no restraint to vertical loads, and, when subjected to horizontal forces transverse to the length of the frame, the equipment can slide and all of the load is carried by the bolts on just one side, doubling the shear load. If friction clips are used, as they are convenient, they should be welded to the frame they are anchoring. This eliminates the problems noted above. The use of friction clips to secure individual legs of an equipment rack should be avoided; if they are used it is vital that they be welded. The anchorage of control cabinets should be through the frame of the cabinet. Cabinets lacking frames should use plate washers to prevent bolt heads from tearing through the sheet metal. Expansion anchors used to anchor control-house equipment racks should be at least 1/2 in. in diameter and satisfy the building code. Bolts should be placed near the base of side walls to provide a stiff anchorage. 25.8.1.2 Design and Installation of Conductor on Switchyard Equipment Post-earthquake investigations have demonstrated that a lack of slack in conductor-connecting equipment has contributed to the failure of bushings and post-insulator bus supports. It is common practice for the configuration of flexible conductor to be left to the installation crews with little or no guidance. Indeed, some crews install the conductor with no slack because it is viewed as a neater installation. Adequate flexibility should be provided to conductor connections to accommodate earthquake-induced motion of conductor anchor points. The conductor flexibility, be it rigid bus or flexible bus, should be able to accommodate the sum of the deflections of each anchor point. The size of the deflection is related to the voltage and natural frequency of the vibration of the equipment. For 230 kV equipment with low natural frequency, a deflection of 8 to 39 in. can be expected, while high-frequency equipment with the same voltage may have only 1 to 3 in. deflection. For 500 kV equipment with low natural frequency, a deflection of 12 to 59 in. can be expected, while high-frequency equipment with the same voltage may have only 4 to 12 in. of deflection. Additional guidance is contained in EIII 693 [IEEE, 1998]. Maintaining phase-to-phase separation on vertical conductor drops provided with adequate slack can be achieved by staggering the position of the upper attachment points. Rigid conductor must also be provided with adequate flexibility. Installing the bus with a dogleg bend can provide the needed flexibility. Several utilities are replacing rigid conductor connections to transformer bushings with short sections of flexible conductor. It must be emphasized that the provisions for thermal expansion in rigid bus are generally inadequate for seismic motions. Cast aluminum hardware is often used in a substation to hold rigid bus to post-insulator supports. The earthquake performance of this hardware has been poor and its design should take brittle failure into account. 25.8.1.3 Power Transformers Power transformers are not only the most expensive item in a substation and the most difficult to replace, but are also the most important, because their function cannot be bypassed or eliminated. Unfortunately, © 2003 by CRC Press LLC
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The embedment should extend well beyond the weld to distribute the load into the concrete The thickness of the plate should be adequate to prevent the welds from tearing out and distributing the load to the headed studs The weld should have good penetration and have adequate length Equipment being anchored
•
Soil Foundation slab Foundation pad rebar Headed studs should extend below the rebar to anchor the embedded plate and have adequate spacing Anchors should have adequate clearance to the edge of the foundation pad FIGURE 25.6 Important features in transformer anchorage design.
transformers have exhibited several failure modes and some are very common. The most common failures associated with transformers are inadequate anchorage, leaking of 161 kV and above bushings, failure of surge arresters supported from transformers, and oil leaks in radiator and conservator piping. Inadequate anchorage has resulting in major transformer damage. Many older transformers mounted on rails and restrained by chocks have rolled off the end of the rails and tipped over, which often damages the bushings, radiators and internal components. Newer transformers supported on slabs, but still unanchored, have moved and damaged bushings. Transformers should be anchored. Important issues associated with transformer anchorage for new construction are illustrated in Figure 25.6. When ordering transformers, require the manufacturer to identify locations where the tank can be welded to embedments in the slab, which is the preferred method of anchoring. Existing transformers’ anchorage should be retrofitted to prevent movement. Because of the wide variation in transformer design and installation configurations, a universal retrofit design is not possible. It is suggested that the transformer lifting lugs or pads be used in the anchorage design, as they have been designed by the manufacturers to take large loads. Welding to the lifting lugs can be done without the concerns associated with welding to the transformer tank. While retrofit anchorage may not be optimal, it can be adequate. Also, it can be implemented without moving the transformer or taking it out of service. The leaking of transformer bushings has been a recurring problem after earthquakes. While there has been some cracked porcelain, most of the leaks are due to slipping of the porcelain at the porcelain–flange interface. A low-cost retrofit that has been evaluated with shake table testing is to add a steel retainer ring over the bushing porcelain–flange interface. The ring is installed with about a 1/2 -in. gap between the inside of the ring and the outside of the bushing. This is then filled with a two-component elastomeric polyurea bonding compound. Parting compound is used to prevent bonding to the porcelain and flange. This will allow the transformer to remain in service until the bushing can be evaluated when it is convenient. The ring also should have L-shaped clips that extend under the flange to prevent the ring from rising. In tests, the ring did not prevent leaking during the shaking, but leaking stopped after the shaking stopped. It also limited the slippage between the porcelain and the flange. © 2003 by CRC Press LLC
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Lightning Arrester
Bushing
Boom
Transformer Case Case A
Case B Case C Typical Conductor Configurations
Locate connection away from bushings
Case D
Use light-weight conductor
Case E Case F Preferred Conductor Configurations
FIGURE 25.7 Variations in surge arrester conductor configurations.
One of the most common items to fail in substations has been transformer-supported surge arresters. In coastal California, where lightning is very rare, damaged surge arresters are removed and the transformer put back into service. One of the risks associated with such failures is that, in falling, the surgearrester can damage the transformer bushing by striking or pulling on it and damaging the conductor bonding post. Figure 25.7 illustrates several different methods of configuring the conductor and preferred methods. Another common transformer failure is the leaking of pipe connections connecting and supporting transformer radiators. Large radiators that use a manifold type of construction often develop leaks at the upper pipe flange connecting the manifold to the transformer case. Some California utilities have retrofitted their radiators by adding diagonal braces between the radiator and the transformer case at the top and bottom of the radiator.
25.8.2 Transmission and Distribution Lines and Support Structures Damage to transmission-line towers and distribution-line support structures has primarily been associated with soil and foundation failures rather than with structural failure. When possible, transmission-line towers should be positioned back from steep slopes. The design of transmission-tower foundations located on ridges and at the edge of steep slopes should be conservative. The design of transmission-tower foundations near water, such as at river crossings, should consider liquefaction and lateral spreading.
25.8.3 Power Generating Facilities Power stations that have been subjected to earthquakes have generally performed well. Within the United States, the structures have usually conformed to the seismic provisions of the Uniform Building Code. There have been problems with poorly anchored control cabinets, liquid storage tanks, emergency power and interaction between the turbine pedestal and powerhouse floor. Problems with switchyards are similar to those found at substations. © 2003 by CRC Press LLC
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The lack of adequate backup power has caused major turbine damage and disruption. Due to switchyard damage, power stations often lose offsite and station power. Typically, the backup power is a battery. If it fails (see Section 25.8.4) or is undersized, it is unable to operate the main bearing oil lubrication pumps, which are required when the turbine slows down. After the turbine stops, battery power is needed for the turning gear to prevent deformation in the main shaft as the turbine cools. Due to substation damage, generating stations frequently must go offline and shut down. To blackstart a generating station, plans often call for a peaking unit to provide the needed power. Normally, peaking units must be synchronized with line frequency when they come online. Unfortunately, their control systems are not designed to operate when there is no synchronizing frequency, which is the situation when offsite power is lost. Units designated to provide power for black-start should have appropriately designed control systems. The gap between the turbine pedestal and the turbine building operating floor should be large enough to accommodate relative motion between the structures and avoid impacts that can damage the turbine bearings. Steam-generating station sites located adjacent to bodies of water may be vulnerable to soil liquefaction. Designs should take into account the potential for differential settlement and lateral spreading that can affect turbines, liquid storage tanks, cooling water intakes and discharges, and stacks.
25.8.4 System Control The control center provides vital functions for the operation of the power system. The control center should be located in a building that is expected to have good earthquake performance. Keep in mind that building codes are primarily based on life safety, while the control center will have to remain operational after the earthquake. Most problems have been with inadequately anchored equipment and support systems, such as HVAC systems, raised computer floors, and emergency backup power. Equipment should be adequately secured or anchored. The following equipment should be evaluated: computers, computer monitors, private branch exchange (PBX) telephone switches, emergency batteries, backup power engine-generators, equipment on raised computer floors, suspended ceilings and light fixtures, water pipes above the control room, control consoles, cabinets, and status boards. Batteries are used for the uninterruptible power supply for the control center and in most substations. Because of the large weight of battery cells, their racks must be structurally sound and well anchored. In addition, the cells must be restrained to the rack. Figure 25.8 shows a battery rack and identifies important design features (see also Chapter 20 of this volume). Installation of engine-generator systems, including engine-generator support/anchorage, control console, starting system, day tank, main fuel tank, piping system, oil cooler, cooling system, exhaust system, and transfer switch, should be evaluated and seismically upgraded. Of particular concern are vibration isolator systems used to support the engine-generator; these systems should have snubbers to limit lateral movement. A schedule for periodic testing of emergency power systems should be established and followed. Operating procedures for emergency power systems should be documented and posted near the systems. The installation of an external power hookup for a mobile generator should be considered. Raised floors used in computer rooms should have floor-support pedestals bolted to the subfloor or held with high-strength bonding materials. Raised computer floors with stringers anchored to pedestals perform best. Equipment on raised floors should be provided with lateral restraint. The mitigation program should include the eventual seismic renovation or replacement of vulnerable buildings housing the control center and other critical control functions.
25.8.5 Communication Systems Communication systems play a vital role in the normal operation of power systems for dispatching and system protection. In the aftermath of an earthquake, additional communications are needed for system inspection and repair. Communication equipment is often installed using methods that are common to © 2003 by CRC Press LLC
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Wall support for heavy cables or connection hardware Crush-resistant spacer Plywood Restraint near cell C.G., all four sides of rack Cut-away view of end restraint Crush-resistant spacers between cells Restraint snug against cells front and back Diagonal brace front and back Cut-away view of base anchor Cast-in-place, grouted or undercut anchors FIGURE 25.8 Schematic diagram illustrating important battery rack design features.
the communication industry. As a result, equipment racks often have flexible anchorage details. Cable trays are often used to brace equipment racks; however, they are often fabricated using friction-clip connections that are inadequate to carry structural loads. Communication-equipment racks should be provided with stiff base-anchorage details or braced at the top to cable trays or walls. Cable-tray connections should be made to structural elements of a building (columns or structural walls); bolted connections and J bolts should not be used. Cable drops between cable trays and equipment should be provided with adequate slack. Circuit boards in communication equipment should have positive restraints to keep the cards in their card cages. PBXs should be anchored to their supports using the manufacturer’s recommendations. Small units, such as modems and remote terminal units, should be positively anchored, even if this is simply accomplished with tape, which may be adequate for these lightweight units. The backup power often used with communication equipment should be properly anchored. Radio equipment to communicate with mobile units is very important during disaster recovery. Base-station and repeater-site equipment should be anchored and adequate emergency power should be provided.
25.8.6 Ancillary Facilities and Functions Structures that house the service centers, inventory control system, spare parts, and the emergency operations center should be evaluated for earthquake vulnerability and post-earthquake serviceability. Their renovation or replacement should be included in the mitigation program. Equipment that requires power and is needed for post-earthquake operation should be provided with emergency power, for example, the inventory control system computer. An update of the inventory of critical supplies not included in the inventory control system, such as spare high-voltage transformer bushings, should be made. Spare parts should be stored so that they can survive an earthquake. Parts cabinets should be anchored and braced. Large items stored on the floor or in storage racks should be secured to shelves to prevent their damage. Critical parts, such as high-voltage bushings, should be completely bolted to anchored support structures. The utility’s emergency-response plan should include an emergency operations center (EOC). The seismic vulnerability of the EOC building should be assessed. An external emergency power hookup for a mobile © 2003 by CRC Press LLC
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generator should be provided to the EOC and the energy control center. EOC communications using the public switched network should request essential service lines and the utility should take advantage of the Government Emergency Telecommunications Service (GETS) system.
25.9 Closing Remarks Small and moderate earthquakes have demonstrated the vulnerability of power system facilities to earthquakes. Those items in this chapter in italics have been demonstrated to be cost-effective activities in most situations. After a very simple assessment of the seismic vulnerability using building code risk maps, work on these critical items can be started. When construction and installation practices are changed to improve earthquake performance, it is important to provide special training to inspectors to make sure construction crews are not using old practices out of habit. Because of the limited space available here, it is recommended that ASCE Manual 96 [Schiff, 1999] be consulted for additional details on good seismic practices for electric power systems.
Defining Terms Black start — The ability of a generating station to start without offsite power. Lateral spreading — A condition where liquefied soil on a slight slope moves laterally. Liquefaction — A condition where saturated soils subjected to vibration lose their bearing capacity and transform to a liquid state. Magnitude — A logarithmic measure of the size of an earthquake, usually related to energy release.
References ANSI/API Standard 650–1993. 1995. Welded Steel Tanks for Oil Storage, American Petroleum Institute, Washington, D.C. ANSI/AWWA D100–1996, 1997. Standard for Welded Steel Tanks for Water Storage, American Water Works Association, Denver, CO. GETS. URL is NCS.gov/n2/gets/gets98.html. IBC. 2000. International Building Code, International Code Council, Falls Church, VA. IEEE Standard C-2. 1997. National Electrical Safety Code, Institute of Electrical and Electronic Engineers. IEEE Standard 693–1997. 1998. IEEE Recommended Practices for Seismic Design of Substations, Institute of Electrical and Electronic Engineers. Kempner, L., Substation Structure Design Guide, American Society of Civil Engineers, New York (in preparation). Schiff, A.J., Ed., 1997. Guide to Post-Earthquake Investigation of Lifelines, ASCE Technical Council on Lifeline Earthquake Engineering, Monograph 11, American Society of Civil Engineers, New York. Schiff, A.J. Ed., 1999. Guide to Improved Earthquake Performance of Electric Power Systems, ASCE Manual 96, American Society of Civil Engineers, New York. Schiff, A.J., Ed., 1995. Northridge Earthquake — Lifeline Performance and Post-Earthquake Response, ASCE Technical Council on Lifeline Earthquake Engineering, Monograph 8, American Society of Civil Engineers, New York.
Further Information A Guide to Reliable Emergency Power is being prepared by ASCE. The Technical Council on Lifeline Earthquake Engineering, ASCE, has published a series of monographs dealing with earthquakes and lifelines, including power systems. There are many earthquake reports and additional reports on the 2001 Gujarat, India and 2001 Nisqually, Washington earthquakes. © 2003 by CRC Press LLC
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26 Dams and Appurtenant Facilities 26.1 Introduction 26.2 Dams and Earthquakes Overview · Performance of Embankment Dams · Performance of Concrete Dams · Performance of Spillways and Outlet Works · Dams and Faulting · Reservoir-Triggered Seismicity
26.3 Seismic Vulnerability of Existing Dams The Need for Vulnerability Assessment · National Inventory of Dams · Seismic Vulnerability Ranking for Multiple Dams
26.4 Seismic Evaluation of Dams Seismic Parameters for Dams · Dam Analysis Parameters · Analysis of Embankment Dams · Analysis of Concrete Dams · Analysis of Intake/Outlet Towers · Limitations of Current Analysis Methodologies · Physical Testing, Modeling, and Centrifuge Studies · Post-Earthquake Inspection
26.5 Seismic Upgrade of Existing Dams General · Seismic Upgrade of Embankment Dams · Seismic Upgrade of Concrete Dams · Seismic Upgrade of Appurtenant Structures
26.6 Seismic Design of New Dams General · New Embankment Dams · New Concrete Dams · New Appurtenant Structures
Gilles J. Bureau Consulting Engineer Piedmont, CA
26.7 Seismic Instrumentation of Dams Acknowledgments. Defining Terms References
26.1 Introduction Dams and reservoirs located near urbanized areas represent a potential risk to the downstream population and property in the event of uncontrolled release of the reservoir water due to earthquake damage. This chapter reviews the seismic performance of existing dams, describes procedures for analysis and safety evaluation, and briefly summarizes design features that improve performance under earthquake loading. In addition to the dam structure, the main structural and mechanical components of reservoir outlet works must be investigated to assure safe release of reservoir water in case of emergency. It should be noted that earthquake-triggered landslides may also affect the reservoir shoreline at some distance away from the dam.
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26.2 Dams and Earthquakes 26.2.1 Overview The first failure of a dam due to earthquake reported in the literature is Augusta Dam, GA, during the 1886 Charleston, SC earthquake. Worldwide, fewer than 30 dams have failed completely during earthquakes [USCOLD, 2000]. These were primarily tailings or hydraulic fill dams, or relatively small embankments of questionable design. Few large embankment or concrete dams have been severely damaged. One gravity dam failed as a result of fault rupture across its foundation [USCOLD, 2000]. No arch dam has ever suffered seismic damage that threatened the safe impoundment of its reservoir. There are more than 75,000 dams of all sizes listed in the U.S. National Inventory of Dams [U.S. Army Corps of Engineers, 2000] and thousands of large dams have been built worldwide. Hence, the record may appear outstanding. However, except for several well-known cases, few dams have been tested by ground motion equivalent to their Design Basis Earthquake [USCOLD, 1999]. Conversely, a few dams have experienced significant damage under moderate shaking. Performance data and detailed references regarding the approximately 400 dams that have been subjected to significant earthquake shaking are provided by USCOLD [1984, 1992b, 2000].
26.2.2 Performance of Embankment Dams Embankment dams comprise rockfill, earthfill, hydraulic fill, or tailings dams. Their seismic performance has been closely related to the nature and state of compaction of the fill material. Well-compacted modern dams can withstand substantial earthquake shaking with no detrimental effects. In particular, earth dams built of compacted clayey materials on competent foundations and rockfill dams have demonstrated excellent stability under extreme earthquake loading. In contrast, old embankments built of poorly compacted sands and silts or founded on loose alluvium, hydraulic fill dams, and tailings dams represent nearly all the known cases of failures. The following paragraphs summarize the experience and lessons learned from the most notable case histories. 26.2.2.1 1906: San Francisco earthquake (M 8.3, estimated) This event affected about 30 medium-sized earthfill dams within 50 km of the fault rupture trace (15 of these were less than 5 km away). Most survived the shaking with only minor damage. This satisfactory performance demonstrated the ability of clayey dams to withstand extreme seismic loading, despite the questionable methods of compaction used for these historic facilities. 26.2.2.2 1925: Santa Barbara earthquake (M 6.3) This earthquake caused catastrophic slope sliding failure of the 25-ft-high Sheffield Dam in Santa Barbara, CA. This was the first recognition that shaking of embankments with low relative density materials may cause liquefaction failures. 26.2.2.3 1971: San Fernando earthquake (M 6.5) Engineers’ concerns regarding the vulnerability of dams constructed of poorly compacted, saturated fine sands and silts were confirmed in 1971. The Lower Van Norman Dam, a 140-ft-high hydraulic fill dam, experienced widespread liquefaction and major slope failures, as shown in Figure 26.1. Flooding of the downstream area with its 70,000 residents was barely avoided, due to an unusually low reservoir level. The 80-ft-high Upper Van Norman Dam was also severely damaged. This experience triggered numerous reassessments of other dams and led to the development of modern numerical methods of dynamic analysis of dams. Following that earthquake, questionable or unsafe embankments in California were upgraded or decommissioned, or owners were mandated to operate the reservoirs at restricted levels. 26.2.2.4 1985: Mexico earthquake (M 8.1) Two large dams, La Villita (197 ft high) and El Infiernillo (485 ft high) were affected. Although neither experienced significant damage, these dams were shaken from 1975 to 1985 by a string of closely spaced © 2003 by CRC Press LLC
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FIGURE 26.1 Damaged Lower San Fernando Dam, 1971 San Fernando earthquake, looking west. Shown as Color Figure 26.1.
seismic events, five of magnitudes greater than 7.1. Cumulative earthquake-induced settlements of La Villita Dam, an earth-rockfill embankment with a wide, central clayey core, approach 2 ft and have increased in the latest events, perhaps due to progressive weakening of some of the materials. The deformations of El Infiernillo Dam, an earth-core rockfill dam, have remained small and consistent from one event to the next. 26.2.2.5 1989: Loma Prieta earthquake (M 7.1) A wide region around the San Francisco Bay was affected. About 100 embankment dams of various sizes were within 100 km of the epicenter, including most of those previously shaken by the 1906 earthquake. The bilateral fault rupture propagation reduced the duration of the strong phase of shaking of the 1989 event to about 10 sec. Given the season, most of the reservoirs were only filled to between 10 and 50% of maximum capacity, and all but one dam performed well. Austrian Dam, a 200-ft-high earth dam about 12 km from the epicenter, suffered substantial transverse abutment cracking and settled nearly 3 ft. The reservoir was half full at the time of the earthquake. Overall damage to the dam was extensive, considering the short duration of shaking. Austrian and other dams affected by the Loma Prieta earthquake must be capable of withstanding earthquakes considerably more demanding in intensity and duration of shaking than experienced in 1989. 26.2.2.6 1990: Philippines earthquake (M 7.7) Five large earth and rockfill dams were located between 1.5 and 12.5 miles from the fault rupture trace. Ground motion was estimated at these sites at between 0.35 and 0.70 g. None of the dams failed but they all experienced settlement, deformations, and cracking. One of the dams, Diayo Dam, 197 ft high, experienced a major slump along the total length (660 ft) of its upstream slope. The scarp of that slump was about 1 ft high on the downslope side. 26.2.2.7 1994: Northridge earthquake (M 6.7) The hypocenter was centered about 32 km west-northwest of the San Fernando Valley. This earthquake was significant for two reasons: (1) it reemphasized the seismic hazard associated with blind thrust faults © 2003 by CRC Press LLC
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in California and (2) it was the second significant event to affect the San Fernando Valley in less than 25 years. More than 100 dams were located within 75 km of its epicenter, including most of those shaken in 1971. Eleven earth and rockfill dams experienced cracking and slope movements but none threatened life and property. The 125-ft-high Lower Van Norman Dam (repaired since its damage in the 1971 San Fernando event, discussed previously) again suffered noticeable damage. Since 1971, the dam had been operated for flood control with an empty reservoir. It experienced longitudinal cracks several hundred feet long, up to 3.5 in. wide and 5 ft deep, and sand boils and a sinkhole along the upstream face. At the crest, maximum settlement was 8 in. and maximum horizontal movement about 4 in. upstream. The 82-ft-high Upper Van Norman Dam (also operated since 1971 with an empty reservoir) experienced transverse cracks near its abutments and along the downstream slope. These cracks were up to 60 ft long and 3 in. wide. Maximum crest settlement was about 2.4 ft, with over 6 in. of horizontal upstream movement. Between the Van Norman dams, and replacing them as a water supply facility, was the new 130-ft-high Los Angeles Dam. Ground shaking was very strong at the site (0.42 g peak ground acceleration [PGA] at the dam left abutment and 0.85 g at an instrument 4400 ft away). However, the dam showed only minor deformations and superficial cracking of the concrete lining of the reservoir. The crest moved 2.2 in. horizontally and settled 3.5 in. at the maximum section. Los Angeles Dam, constructed in 1977 to demanding seismic requirements, withstood the Northridge earthquake. In contrast, the Van Norman dams, designed and built of hydraulic fill in 1915, suffered major damage both in 1971 and in 1994. 26.2.2.8 1999: Kocaeli earthquake, Turkey (MW 7.4) Gokce Dam, a 200-ft-high earth core rockfill dam and Kirazdere Dam, a 356-ft-high earthfill embankment with clay core, sand and gravel filters, and rockfill shells are located within the area of strong damage. The only observed effect at Gokce Dam was a longitudinal crack along the upstream side of the crest, about 0.33 in. wide. Kirazdere Dam is located within 2 to 3 km of the epicenter and in close proximity to the causative fault, the North Anatolian Fault. There was about 7 ft of right-lateral movement within about 1 mi of the dam. A few longitudinal cracks, each about 0.1 in. wide, occurred on the crest gravel road. Overall, both dams performed satisfactorily and demonstrated the high seismic resistance of rockfill dams. 26.2.2.9 2001: Bhuj (Gujarat), India earthquake (MW 7.7) This event resulted in widespread soil effects and liquefaction in low-lying estuaries and young alluvial deposits. Strong ground motion lasted more than 85 sec, and lower-level shaking several min. Numerous embankment dams were damaged in the epicentral area, including seven medium-sized (40 to 120 ft high) earth dams (Rudramata, Niruna, Sasoi, Fategadh, Suvi, Kaswati, and Tapar). Fourteen smaller dams were also damaged, some extensively. The reservoirs were very low at the time of the earthquake but liquefaction of the foundation caused moderate to severe failure of the upstream and, locally, the downstream slopes of the dams.
26.2.3 Performance of Concrete Dams Concrete dam designs include cylindrical arch, thin arch with double curvature, multiple arch, gravity, buttress, hollow gravity, and combinations of these types, or composite embankment and concrete structures. Overall, the earthquake performance of concrete dams has been satisfactory, and thus can be inferred to indicate that they are more earthquake-resistant than embankment dams. Most concrete dams have been built to design standards higher than some embankment dams, and are less susceptible to aging, deterioration, seepage, and poor maintenance. However, only about 100 concrete dams have been significantly shaken by earthquakes, with only about 15 of these experiencing PGA greater than 0.20 g. No significant damage has ever been suffered by an arch dam, although several have experienced substantial ground motion. However, the true test of a nearby major earthquake, shaking a large thin arch with the reservoir at full capacity, has yet to occur. Concrete dams are prone to major damage in cases of fault movement across their foundation. The only reported case of complete failure is Shih-Kang Dam, a concrete buttress gravity dam intersected by the surface rupture of the 1999 Chi-Chi, Taiwan earthquake (MW 7.6). Earthquake experience with concrete dams include those described below. © 2003 by CRC Press LLC
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26.2.3.1 1906: San Francisco earthquake (M 8.3, estimated) Lower Crystal Springs Dam, a 127-ft-high, curved-concrete gravity dam built of interlocking blocks, withstood that earthquake without a single crack. The primary fault rupture, with a local right-lateral slip of about 10 ft, passed less than 600 ft from the dam. 26.2.3.2 1957: Great Britain earthquake (Intensity VIII, British Scale) This rare event was centered about 6.4 km from Blackbrook Dam, a 100-ft-high gravity dam with upstream brick and downstream stone facings. This is the only dam in Great Britain damaged by an earthquake. The mortar of the stone facing was cracked. All of the large coping stones topping the parapet walls on both sides of the crest were lifted from their mortar bed and dropped back, crushing it in the process. 26.2.3.3 1962: Kwangdong, China earthquake (M 6.1) Hsinfengkiang Dam, a 344-ft-high buttress dam with abutment gravity sections, was completed in 1959. Earthquake swarms occurred after the first filling of the reservoir, and the dam was strengthened to increase its seismic capacity. The 1962 earthquake induced shaking stronger than considered for the modified design. Cracks formed near the crest, at a change in section of the nonoverflow blocks on each side of the spillway. The earthquakes were considered to be possible cases of reservoir-triggered seismicity. The dam was strengthened again, and placed back in service. 26.2.3.4 1967: Koyna, India earthquake (M 6.5) Koyna Dam, a 338-ft-high straight gravity dam built of rubble concrete in 1963, was shaken by a nearby earthquake of magnitude 6.5. This earthquake was also suspected to be due to reservoir-triggered seismicity. Koyna Dam developed substantial longitudinal cracking near the top, at the location of a sharp change of slope of the downstream face, used to increase height and reservoir capacity. Another design weakness was the use of varying concrete strengths based on static analysis and decreasing from bottom to top, which could not accommodate large dynamic stresses that occurred in the upper portion of the dam. Similar design features are avoided in modern structures. Koyna Dam was repaired and is still in service. 26.2.3.5 1971: San Fernando earthquake (M 6.5) During that earthquake, the 372-ft-high Pacoima Dam, a thick arch, was subjected to an estimated peak base acceleration (PBA) of about 0.70 g. An unprecedented horizontal acceleration of 1.25 g was recorded on rock at the left abutment, slightly above the dam crest. The dam was used for flood control and the reservoir level was at about mid-height. Neither cracks nor relative block movements were reported. The left abutment was strengthened with post-tensioned anchors to stabilize two large rock wedges that moved several inches during the earthquake. The large accelerations and rock wedge movements in the left abutment illustrate ground motion amplifications (ridge) effects caused by a peculiar topographic configuration. 26.2.3.6 1990: Manjil, Iran earthquake (M 7.6) Sefid Rud Dam, a 348-ft-high gravity buttress dam built in 1962, is less than 10 mi from the epicenter. PGA was estimated at 0.72 g. The seven gravity monoliths and 23 head buttress units of the dam structure were designed with pseudostatic horizontal coefficients up to 0.25 g. The dam suffered severe cracking at lift joints in the upper part of the buttresses, accompanied by a 20-mm shear displacement toward downstream. Leakage occurred through the cracks and lowered the reservoir. Sefid Rud Dam represents an example of a concrete dam subjected to shaking substantially more severe than its design loads. The dam suffered significant damage but had overall satisfactory performance. It was repaired using posttensioned anchors. 26.2.3.7 1994: Northridge earthquake (M 6.7) Pacoima Dam was strongly shaken by this earthquake 23 years after the San Fernando earthquake. Peak accelerations at the top of the left abutment were again amplified by the local narrow ridge topography © 2003 by CRC Press LLC
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FIGURE 26.2 Damage to Shih-Kang Dam due to fault offset, 1999 Chi-Chi, Taiwan earthquake.
and shattered condition of the rock, and reached 1.76 g horizontal and 1.60 g vertical. The dam performed satisfactorily with a half-full reservoir. For the first time, this earthquake provided evidence of the opening and closing of vertical contraction joints. The joint between the left abutment and the left end of the arch opened a maximum of 2 in., due to movement of the rock wedges on the upper abutment. Minor horizontal cracking of concrete at the left end of the dam, and several minor horizontal and vertical block offsets occurred at the joints. The rock mass at the left abutment that had been stabilized after the San Fernando earthquake did not fail but several of the anchors were overstressed. 26.2.3.8 1999: Chi-Chi, Taiwan earthquake (MW 7.6) Shih-Kang Dam, a large gravity, radial-gated, water supply dam, is 50 km from the epicenter. It failed due to differential thrust fault movement at its north abutment. Over two thirds of the dam body were uplifted about 29 ft vertically, and displaced 6.5 ft horizontally (Figure 26.2). Damage was confined to the two bays overlying the fault rupture. The sixteen other bays were essentially intact. The dam experienced horizontal accelerations up to 0.50 g, and its performance would have been excellent had it been located outside of the rupture trace. The reservoir slowly drained through the failed bays, without causing major flooding. Another concrete gravity dam with radial gates, the Chi-Chi Diversion Dam, is less than 10 km from the epicenter and experienced no damage.
26.2.4 Performance of Spillways and Outlet Works Earthquake reconnaissance reports have often focused more on the dams than on their appurtenant facilities. However, spillways and outlet works are also exposed to potential earthquake damage. Outlet works may lose functionality at a critical time, due to possible loss of power supply. Spillway damage is rarely critical, as the probability of experiencing a significant earthquake during or immediately before major flooding is extremely low. Tall intake or outlet towers and their equipment, however, are particularly vulnerable. The 56-ft-high, 33-ft-wide hoist tower at Koyna Dam suffered considerable damage during the 1967 earthquake, and the precast concrete blocks and the main reinforced concrete framework cracked in many places [Gupta and Rastogi, 1976]. At the Van Norman dams, two of three tall outlet towers were lost during the 1971 San Fernando earthquake, including one complete collapse (Figure 26.3). Emergency lowering of the reservoir required pumps to be brought to the site. During the 1995 Hyogo-Ken Nanbu, Japan earthquake (MJMA 7.2), the foundation of the intake tower controlling the lower pool level at Koyoen Reservoir moved substantially, tilting the tower. The intake remained functional but the access bridge of © 2003 by CRC Press LLC
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FIGURE 26.3 Failed outlet tower, Lower Van Norman Dam, 1971 San Fernando earthquake. Shown as Color Figure 26.3.
that structure was shoved through the access door, illustrating how intake/outlet towers and their access bridges may respond differently to the shaking, and pound against each other or fail at supports and connections.
26.2.5 Dams and Faulting Many dams are built across streams or rivers that follow existing fault traces. While such faults are not necessarily active, the potential for differential movement across the dam foundation must be taken seriously and investigated. Sherard and coworkers [1974] discussed at length the problem of active faults across dam foundations. Two of these authors recently updated their 1974 paper on the same subject [Allen and Cluff, 2000]. The 88-ft-high San Andreas Dam, composed of a main and saddle dam, was nearly intersected by the 1906 rupture of the San Andreas Fault, which passed between the two embankments but did not cause damage. The fault rupture actually offset the submerged embankment of the Old San Andreas Dam, which, at the time of the earthquake, was abandoned in the north arm of the reservoir. Another example was Hebgen Dam, MT, during the West Yellowstone earthquake of 1959 (M 7.1). The fault rupture trace passed about 600 ft from the dam right abutment, and displayed about 16 ft of vertical upward movement. Simultaneously, the bedrock underlying the entire dam, spillway, and © 2003 by CRC Press LLC
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outlet conduit subsided uniformly by about 10 ft. The faulting did not affect Hebgen Dam, which experienced only moderate slumping and cracking. However, contrary to the two near-misses cited here, the example of Shih-Kang Dam (Section 26.2.3.8) reminds us what fault movement can do to a dam. Building a dam across an active fault should be avoided, if possible. In 1975, the Oroville, CA earthquake (M 5.7) ruptured the Cleveland Hill Fault, part of the Sierra Nevada Foothills Fault System then considered inactive. Subsequently, the U.S. Bureau of Reclamation (USBR) prudently abandoned its plans to construct Auburn Dam, a proposed 685-ft-high, double curvature thin arch, as faults of the same system were encountered during foundation excavation. This decision was made although detailed dynamic analyses showed that the dam would be undamaged in an M 6.5 local event. Recognizing the existence of an active or capable fault across the proposed alignment of a dam requires drastic measures and, preferably, abandoning the site, as USBR did in the case of Auburn Dam. However, an alternative site may not be available and a conservatively designed dam may need to be considered. The decision to proceed with construction of a dam across an active fault represents one of the most severe design challenges but has been made in a few cases. First, the rupture mechanism and amplitude of relative displacements must be rigorously assessed. Then, special features must be included in the design to accommodate such displacements. An example is Coyote Dam in California, which was built in 1936 across the main trace of the Calaveras Fault. The fault was then recognized as a main active seismogenic feature, capable of about 3 ft of vertical movement and nearly 20 ft of lateral displacement. A decision was made to construct a dam at the site, with the use of special design features, such as an oversize, compacted clayey core with transition layers and extra freeboard (22 ft, for a dam height of 125 ft). Another case is Cedar Springs Dam, 215 ft high, completed in 1971 after exploratory trenches in the foundation area showed the presence of several faults with evidence of Holocene activity (less than 11,000 years old). The original design of the dam was modified after the discovery of the faults. The dam height was reduced nearly one third compared with the initial plans, and the dam section was completely redesigned to include thick rockfill exterior shells and wide transition zones of well-graded coarse sandgravel mixture protecting the enlarged clay core. All of the core materials were imported from a distant borrow area to obtain better quality materials than available onsite. In another example, several potentially active branches of the Dunstan Fault were discovered when excavating the foundation of the 335-ft-high Clyde Dam, New Zealand, a concrete gravity dam [Hatton et al., 1991]. The design of the dam was modified to include a slip joint directly above the fault, with a rubber-sealed, steel-sheathed wedge plug, 328 ft long. The joint was designed to accommodate 6.5 ft of strike-slip and 3.3 ft of dip-slip movements. A few other examples of dams built across active faults are described in Sherard and coworkers [1974] and Allen and Cluff [2000]. Another type of challenge is encountered when it is discovered that an existing dam was unknowingly built on an active fault. This was the case with the 240-ft-high Matahina Dam, New Zealand, constructed in 1960 on recently recognized active splays of the Waiohau Fault, a major tectonic feature of the Alpine fault system and one of the longest and most active regional strike-slip faults. Various alternatives were considered to improve the safety of the dam, and the selected design consisted of placing a new thick filter, transition zones, and rockfill shell on the downstream face of the existing dam [Mejia et al., 1997]. This design will allow the filter zone to heal any potential cracking induced by the fault rupture, thereby maintaining the integrity of the reservoir. Additional information on features that improve the seismic performance of dams is presented in Section 26.6. In addition to the risk of sudden fault rupture, fault creep may also cause distress within a dam. Fault creep is a gradual, continuous, relative displacement that occurs generally at a low rate of slip. Fault creep has been observed across Bajina Basta and Lipovica dams in Yugoslavia [Bozovic and Markovic, 1999] but is considered to be a sufficiently rare phenomenon that can usually be dismissed in seismic studies for dam projects [Allen and Cluff, 2000].
26.2.6 Reservoir-Triggered Seismicity The creation of artificial lakes formed by large dams received considerable attention in the 1960s and 1970s as a potential source of seismicity, caused by filling of the reservoirs. The earthquakes that affected © 2003 by CRC Press LLC
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Hsinfengkiang Dam, China (1962) and Koyna Dam, India (1967) were believed to be clear cases of reservoir-induced seismicity. More than 30 other examples are known where the impounding of large reservoirs may have initiated or enhanced seismic activity [Gupta and Rastogi, 1976; USCOLD, 1986, 1997]. The most recognized of these other dams include Aswan, Egypt; Hoover (Lake Mead), NV and AZ; Kariba, Zambia; Kremasta, Greece; Monteynard, France; Nurek, Russia; Oroville, CA; and Vajont, Italy. Reservoir-induced seismicity has been potentially associated with incremental effective stressing and warping of the Earth’s crust due to the reservoir loading. However, although all of the reservoirs were quite deep (typically 300 ft or more), stress and pore pressure increases induced by reservoir loading are considerably less than stress changes associated with earthquakes. Models relating pore pressure increases to the mechanics of rock fractures were also developed over the years to explain the relationship between earthquakes and dams but obtaining reliable information regarding the initial and modified state of stress at the depth of several kilometers where earthquakes occur has not been practical. While experts still agree that filling a reservoir modifies the stress regime within crustal layers and reduces the effective shear strength of the rock mass, it is now generally agreed that such changes cannot cause fractures in intact rock. However, it is now believed that preexisting faulted rock with a high in situ state of stress can be brought to slip by the reservoir impoundment. Furthermore, most reservoir-induced seismic events have occurred in areas affected by Quaternary faulting. Hence, earthquakes were most likely triggered rather than induced by the reservoir, and such terminology is now considered to be more appropriate [USCOLD, 1997]. While the possibility of reservoir-triggered earthquakes should be considered for any reservoir deeper than 250 to 300 ft, experience suggests that the maximum reservoir-triggered earthquake should not exceed the design earthquake that must otherwise be specified for any site located within an area of recognized potential seismic activity. Furthermore, the likelihood of a reservoir-triggered earthquake being associated with significant surface fault displacement is exceedingly remote [Allen and Cluff, 2000].
26.3 Seismic Vulnerability of Existing Dams 26.3.1 The Need for Vulnerability Assessment Dam owners and regulators must ensure that dams are safely operated and present no risk to the public in case of an earthquake. While most existing or new dams in recognized seismic regions have been evaluated and analyzed for seismic loads (see Section 26.4), dams located in areas of moderate or infrequent seismicity have been given less systematic attention. In such cases, owners of many dams or officials in charge of dam safety programs may consider comparative assessment of the seismic risk associated with their dams and establish priorities, as needed. A methodology to perform such tasks was developed as part of a general earthquake risk and loss estimation program for the State of South Carolina [URS Corporation et al., 2002] and can be applied to any state using the National Inventory of Dams (NID) and the concepts described in Section 26.3.3.
26.3.2 National Inventory of Dams In the United States, various sources of information can be consulted to obtain information on dams, including (1) the National Inventory of Dams (NID) and (2) federal, state, or local agencies that have jurisdiction over dams in a given area. The NID is maintained and periodically updated by the U.S. Army Corps of Engineers (COE), under legislation enacted by Congress in 1986 as the Water Resources Development Act (P.L. 99-662). The NID was implemented in 1989 and has been updated several times. The COE has prime responsibility for maintenance and update of the NID and has been working closely with other involved federal and state agencies. The NID is accessed from an Internet site (http:// www.tec.army.mil/nid/index.html) or from a CD-ROM. Its current version includes 57 fields, which for each dam describe name(s), type, purpose, year completed or modified, owner, location, dimensions, reservoir storage capacity, hydraulics, downstream hazard, etc. The NID also provides information on © 2003 by CRC Press LLC
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TABLE 26.1 Definition of Dam Size Risk Factors Contribution to Total Risk Factor (weighting points) Risk Factor
Extreme
High
Moderate
Low
Capacity (acre-feet) (CRF) Height (feet) (HRF)
>50,000 (6) >80 (6)
50,000–1,000 (4) 80–40 (4)
1,000–100 (2) 40–20 (2)
<100 (0) <20 (0)
TABLE 26.2 Definition of Dam Age Rating Factors Dam Age ARF
<1900 6
1900–1925 5
1925–1950 4
1950–1975 3
1975–2000 2
>2000 1
the availability of an emergency action plan (EAP), inspection requirements, and state or federal agencies having jurisdiction on the facility. The NID is an evolving database and information may change over time, especially if the operation or configuration of any dam is modified.
26.3.3 Seismic Vulnerability Ranking for Multiple Dams Various risk factors and weighting points can be used to approximately quantify the total risk factor (TRF) of any dam [Bureau and Ballentine, 2002]. The TRF depends on the dam type, age, size, the downstream risk potential, and the dam vulnerability, which depends on the seismic hazard of the site. The TRF is expressed as: TRF = [(CRF + HRF + ARF) + DHF] × PDF
(26.1)
The dam structure influence is represented by the sum (CRF + HRF + ARF) of capacity, height, and age risk factors. The downstream hazard factor (DHF) is based on population and property at risk. The vulnerability rating is a function of the site-dependent seismic hazard and observed performance of similar dams, as defined by a predicted damage factor (PDF). Additional information regarding these various risk factors is provided in the following sections. Structure Influence Three factors quantify the risk of a dam and its reservoir. The capacity risk factor (CRF) and the height risk factor (HRF) indicate that high dams or large reservoirs can cause significant flooding. The age rating factor (ARF) expresses that old dams are often more vulnerable than modern dams because of possible deterioration, lack of maintenance, use of obsolete modes of construction (concrete masonry or hydraulic fill), insufficient compaction, reservoir siltation, or insufficient foundation treatment. The dam risk factors are defined in Tables 26.1 and 26.2. Downstream Risk The overall downstream hazard factor (DHF) is defined as: DHF = ERF + DRI
(26.2)
The downstream evacuation requirements factor (ERF) depends on the human population at risk. The downstream damage risk index (DRI) is based on the value of private, commercial, industrial, or government property in the potential flood path. These factors should preferably be obtained from a combination of detailed dam breach, inundation mapping, and economic studies. The DHF should be updated whenever new information becomes available or when the dam is repaired, modified, or raised (Table 26.3). When it is not cost-effective to obtain the ERF and DRI from detailed studies, the downstream hazard potential rating of the NID can be used to obtain a substitute value of the DHF, as shown in Table 26.4.
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TABLE 26.3 Definition of Downstream Risk Factors Contribution to Total Risk Factor (weighting points) Risk Factor
Extreme
High
Moderate
Low
Evacuation requirements (ERF) (persons) Downstream damage risk index (DRI)
>1,000 (12) High (12)
1,000–100 (8) Moderate (8)
100–1 (4) Low (4)
None (1) None (1)
TABLE 26.4 Downstream Hazard Factor Based on NID NID’s Downstream Hazard Potential Rating
Loss of Human Lives
Low
None expected
Significant High
None expected Likely, one or more expected
Economic, Environmental, or Lifeline Losses
Downstream Hazard Factor (DHF)
Low, generally limited to owner’s property Yes Yes or probable but not strictly required
2 12 24
Seismic Vulnerability Rating Dam vulnerability curves developed by Bureau and Ballentine [2002] from observed seismic performance of dams during earthquakes [USCOLD, 1992b, 2000] can be used to compute a predicted damage index (PDI). The PDI depends on the dam type and on the site seismic hazard and tectonic environment. The expected ground motion at the dam site for the scenario earthquake considered is expressed by the earthquake severity index (ESI), a robust estimate of the severity of shaking for dam evaluation purposes [Bureau et al., 1985]. The ESI is expressed as: ESI = PGA × (M – 4.5)3
(26.3)
where the PGA is measured in g, and M is the Richter or moment magnitude (MW , if available) of the causative event. The PDI depends on the ESI at each dam site, for each postulated earthquake scenario, and is obtained from graphical relationships shown in Figure 26.4. As is well known, hydraulic fill and tailings dams are clearly the most severely affected, based on historic experience. Arch dams have performed best but the corresponding data are limited. Several comments are appropriate regarding Figure 26.4. First and foremost, the relationships plotted do not predict failure or nonfailure of any specific dam for a given ESI. This requires detailed site-specific geologic, geotechnical, and seismic response studies. The vulnerability curves are intended only to be applied to a large family of dams and help identify the potentially most critical facilities in regional studies. The PDI rates only the relative vulnerability of each dam type, and includes a significant uncertainty, especially when extrapolated to large ESI values, which can be quantified from the standard deviations associated with the mean estimates. It should be recognized that many other important factors may affect the present or future risk associated with existing dams: (1) availability or lack of construction and maintenance records, (2) availability or lack of instrumentation data and surveillance records, (3) level of effort expended in safety evaluations, (4) planned upgrade of the dam, (5) planned enlargement of the reservoir, and (6) planned downstream developments. From the computed PDI, a PDF is assigned to each dam, as defined by the following equation: PDF = 2.5 × PDI
(26.4)
Bureau and Ballentine [2002] empirically selected the coefficient 2.5 to provide consistency between vulnerability estimates obtained from site-specific ground motion estimates defined by the ESI or, when
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FIGURE 26.4 Predicted damage index (PDI).
TABLE 26.5 Definition of Dam Risk Class Total Risk Factor (TRF) 2 to 25 25 to 125 125 to 250 > 250
Dam Risk Class I (low) II (moderate) III (high) IV (extreme)
such estimates were not available, from a combination of a dam type factor and a seismic zone factor derived from the Uniform Building Code Zone Factor. The last step of the assessment is to rank the dams by decreasing TRF and assign to each a Risk Class ranging from I (low risk) to IV (extreme risk), as shown in Table 26.5. The vulnerability ranking of over 4500 dams, including all dams in South Carolina plus some in neighboring states, was compiled in that fashion [URS Corporation et al., 2002]. The risk class can be used to establish the need for more detailed seismic safety evaluations and to establish priorities for such evaluations. The procedure presented in this section can be used to quickly assess the potentially most vulnerable facilities in a large dam inventory. The risk classification based on the TRF provides guidance to dam safety officials to select appropriate evaluation procedures and to assign priorities for seismic safety evaluations of the most critical dams.
26.4 Seismic Evaluation of Dams Since the late 1960s, considerable progress has been made in the understanding of earthquake effects on concrete or embankment dams. Better appraisals of the seismic response of dams have followed the rapid development of computer-based analytical procedures and the installation of instruments for accurate © 2003 by CRC Press LLC
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recording of earthquake motion at various locations on a dam and in its immediate vicinity. Considerable progress has been made in the definition of the seismic input. In addition to the development of sitespecific seismic criteria, dam analysis requires definition of the geometry and configuration of the structure and its foundation, characterization of the construction and foundation materials and their static and dynamic properties, and inclusion of the effects of internal water pressures and the influence of the reservoir. In some cases, local site topographic features may need to be taken into consideration in dam response calculations. For new dams, achieving an optimal configuration requires an iterative process of adjusting the use of available construction materials and locating the dam within a site of a given topography. The construction engineer and the analyst may have conflicting objectives to resolve issues when selecting a dam type and estimating the project’s behavior when subjected to an earthquake. The problem of seismic response and behavior of dams and their foundations, when formulated in general terms, is extremely complex. One must always keep in mind that even the best analytical methods do not provide precise numerical answers. They only provide insight into the design problems under consideration. Depending on the type and size of the dam, its seismic exposure, and other factors such as regulatory requirements, numerical analysis may be conducted using simplified or complex procedures. Ideally, one would incorporate three-dimensional interactive response of the dam body, the reservoir water, and the dam foundation. For demanding seismic input or unusual conditions regarding dam or foundation material properties or geometry, e.g., the possible presence of joints, it may be best to perform a nonlinear response analysis of the dam–foundation–reservoir system, which is always a major undertaking. The following sections describe input parameters and analysis procedures for seismic analysis of embankment and concrete dams.
26.4.1 Seismic Parameters for Dams The selection of site-dependent seismic input is essential to the safety evaluation of dams. The effort required in such an endeavor increases with the complexity of the analyses to be performed. Detailed information on this topic is provided in current guidelines for selecting seismic parameters for dam projects [USCOLD, 1999]. The present discussion only briefly describes the general requirements of each type of analysis. It does not address how to select distance and magnitude parameters and frequency content of the input motion, which is discussed elsewhere in this volume. Various earthquake levels considered for the analysis of dams include the operating basis earthquake (OBE), the maximum credible earthquake (MCE), the maximum design earthquake (MDE) and, occasionally, the reservoir-triggered earthquake (RTE) [see USCOLD, 1999, for a complete definition of these terms]. Because the primary requirement of earthquake-resistant design is to protect public safety and property, seismic criteria and analysis parameters for dams, as for the evaluation of critical nuclear facilities, are often selected more conservatively than for conventional structures. 26.4.1.1 Seismic Input for Embankment Dams Simplified procedures for embankment dam analysis only require the peak ground acceleration (PGA) and velocity (PGV) as input parameters [e.g., Newmark, 1965], or the PGA and the magnitude of the causative event [Bureau et al., 1985]. Other simplified methods need a response spectrum and the specified magnitude [Makdisi and Seed, 1977]. In all other cases, such as the classic (Newmark’s) doubleintegration method of dam evaluation and in equivalent-linear (EQL) or nonlinear (NL) detailed analyses, one or several horizontal acceleration time histories must be specified, depending on whether two- or three-dimensional analysis is considered. It is customary to use the largest component of horizontal motion in the upstream–downstream direction. Various natural strong motion records are normally considered to select acceleration time histories as seismic input. Selection criteria consist of magnitude and duration of the causative earthquake, mode of fault rupture, distance, subsurface conditions at the recording station, and possible presence of nearfield effects. A digitization interval of 0.02 sec is sufficient for embankment dam analysis. © 2003 by CRC Press LLC
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In most cases, the influence of the vertical motion has been considered negligible. However, this conclusion was based on EQL response analyses of flat-sloped earth dams, which are essentially unaffected by that component of motion. This is not true in the case of steep dam faces, for example, as encountered in rockfill dams [Von Thun and Harris, 1981], or in the case of NL analysis. As NL response is stresspath-dependent and because failure criteria depend on both normal and shear stresses, calculated permanent dynamic deformations will differ whether vertical excitation is included or not. Such differences can be appreciable, up to about 20% of the maximum deformation response [Bureau, 1997]. Therefore, the vertical component of motion must preferably be included in NL dam response analyses. This component, especially, may dominate the seismic input in the case of near-field thrust faulting. For earthfill dams, the duration of shaking is a most significant parameter, as it governs the extent of damage and buildup of excess pore pressures in the foundation or in the saturated portions of the embankment. Hence, considerable care must be given to selecting time histories of appropriate duration of the strong phase of shaking. 26.4.1.2 Seismic Input for Concrete Dams Except for the use of a horizontal seismic coefficient in the case of the simplified analysis of gravity dams, concrete dam analysis generally requires the use of one or several sets of horizontal and vertical acceleration time histories. For sites of moderate seismic activity, horizontal and vertical response spectra may be sufficient, as long as the allowable stresses are not exceeded. If that is not the case, acceleration time histories are required to obtain stress time histories and assess how many cycles exceed the allowable strength. As concrete dams respond at higher frequencies than embankment dams, it is customary to use time histories digitized at 0.01-sec intervals. Concrete arch dam analysis requires the use of three statistically independent components of motion. As for embankment dams, the largest horizontal component of motion is typically applied in the upstream–downstream direction. 26.4.1.3 Seismic Criteria for Appurtenant Structures Spillway walls can be analyzed with horizontal load coefficients, such as used for retaining walls. However, intake/outlet towers, which typically range from a few feet to more than 400 ft high, often respond within a range of spectral amplifications that dictates dynamic analysis. As failure of most towers would rarely cause uncontrolled flooding, significant damage might be acceptable for the MCE, and OBE-level seismic criteria are sufficient if acceptable performance is demonstrated. Towers required for emergency drawdown of the reservoir must be analyzed to the most demanding MCE or DBE requirements. A building code methodology (such as the Uniform Building Code) can be used for towers located in areas of moderate seismic hazard. However, this approach represents minimum seismic requirements. The code is primarily intended for buildings, and the applicability of the Rw factor to towers is questionable, as it implies more ductile behavior than available in many of these often under-reinforced structures. Detailed dynamic analysis is necessary for towers susceptible to amplifying ground motion significantly. In that case, seismic input is best described by horizontal and vertical response spectra. 26.4.1.4 Natural vs. Artificial Acceleration Records It has been common practice to scale and modify natural earthquake records to match a specified peak acceleration and spectral content (see Figure 26.5). For earth or concrete dam analysis purposes, it is desirable to minimize the modifications of natural records, as the number of induced stress cycles is more important to assess performance than the peak stress values. Current procedures for matching a specified spectral shape consist of scaling a natural record to the specified PGA and selectively adjusting the Fourier amplitude spectrum in the frequency domain, keeping the phase angles unchanged. Downward rather than upward scaling is recommended. The process is iterative. Modified Fourier amplitudes and original phase angles are then recombined in the time domain. The new acceleration history resembles the original record but matches the targeted response spectral shape. Spectrum-compatible records should preferably be baseline corrected to achieve zero velocity and displacement at the end of the excitation. Without such correction, solutions based on absolute rather than relative displacements will superimpose a global translation of the analysis model to the earthquake-induced deformations. This © 2003 by CRC Press LLC
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FIGURE 26.5 Spectrum-compatible acceleration time history.
does not affect the computed stresses, which depend on strains but the translation of the base of the model must be subtracted from the calculated displacements. 26.4.1.5 Other Factors of Significance Fault mechanism and local source and path variability strongly influence ground motion [Somerville et al., 1995]. Frequently, horizontal shear wave velocity pulses near a rupturing fault have larger amplitudes © 2003 by CRC Press LLC
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normal to the fault than parallel to it. Similarly, ground motions are more severe on the up-thrown wall of a reverse fault than on the stationary wall. Hence, the direction of arrival of ground motion pulses may be significant for dams located close to an active or capable fault. Except when records from an instrumented dam are used to back-calculate its observed response, input for dam analysis uses acceleration histories recorded at other sites. Hence, there is no particular relationship between the dam alignment and the fault rupture mechanism and direction of propagation associated with such records. The base motion may be applied either as if it represents seismic waves traveling from upstream to downstream, or the reverse. Hence, it is prudent to first use a specified time history, then its opposite (all acceleration values multiplied by –1). In NL analyses, calculated permanent displacements will differ when a horizontal base motion is replaced by its opposite. Parametric analyses to define the safe reservoir level of an existing hydraulic fill dam have shown that maximum computed nonrecoverable deformations may more than double locally when switching the input acceleration history to its opposite [URS Corporation, 2002]. Similarly, several records intended to represent a same earthquake scenario may lead to different deformations. Therefore, using a single set of acceleration histories to represent a specified evaluation earthquake is considered insufficient. Successive use of three to four sets of acceleration histories, plus their opposites, is recommended. For near-fault sites, the possible presence of large shear wave velocity pulses (fling) in the ground motion, first recognized by Bolt in 1971 [see Bolt, 1996], is of potential significance [Somerville and Graves, 1996]. Directivity and focusing effects can increase such pulses by a significant factor [Bolt, 1996]. Dams built perpendicular to a strike-slip fault may experience less severe rupture directivity effects than if parallel to such fault. Similarly, dams along a fault-controlled mountain front may experience the largest components of motion transverse to their axis. Hence, an unfavorable direction of arrival of the largest near-field pulses may increase response and contribute to larger cumulative displacements or a sharp increase in pore pressures. Such effects must be considered in the specification of the seismic input for dams near active faults and, especially, large or loose embankments that may respond at periods of vibration close to the period of those pulses. The alignment of a new dam can be optimized with respect to critical paths of traveling seismic waves through a parametric analysis. For analysis purposes, seismic input is normally taken as uniform along the dam footprint or at some depth within the foundation, although phase characteristics and amplitudes vary both transversely and longitudinally along the dam bottom. Such variations were observed at Los Angeles Dam during the 1994 Northridge earthquake [Davis and Sakado, 1994]. Abutment motions (free-field) were more severe than below the dam, and transverse components included more prominent near-field pulses than the longitudinal components. At this time, insufficient strong motion records at the base of dams and the lack of a rigorous theoretical basis prevent analyzing embankment dams using nonuniform base excitation, a potential shortcoming for large embankments. However, base shaking with input derived from free-field records, as typically used, should provide a response more conservative than motions recorded in depth. 26.4.1.6 Deterministic vs. Probabilistic Analysis Depending on the location of a dam and which agencies have jurisdiction, deterministic or probabilistic criteria have been used to develop seismic loads for dam safety evaluation. The Division of Safety of Dams (DSOD) of the State of California requires jurisdictional dams to be evaluated for the MCE, which represents the largest conceivable earthquake along a recognized capable or active fault or within a recognized tectonic province. The largest magnitude and shortest distance to the fault are considered for the MCE, and no consideration is given to its probability of occurrence. This deterministic approach results in significant variations of the risk associated with various dams, depending on whether the controlling faults have a very high or very low rate of slip. Conversely, some agencies now use probabilistic risk assessment procedures for dam safety management [U.S. Bureau of Reclamation (USBR), 1997]. When the deterministic approach is required, it may be desirable to perform an adjunct probabilistic seismic hazard analysis of the site and compute the return period of the specified earthquake motion. Then proper judgment may be used to select analysis parameters and avoid compounding multiple excessively conservative assumptions. © 2003 by CRC Press LLC
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26.4.2 Dam Analysis Parameters 26.4.2.1 Analysis Parameters for Embankment Dams This section discusses soil and other properties required for the seismic analysis of embankment dams. Field exploration and laboratory testing programs are essential to define the physical and strength properties of these dams and their foundations. Static Parameters Most analysis procedures require static properties (unit weight, moisture content, and total and effective stress strength parameters). The effective static shear strength is essential to some NL dynamic analyses [Dawson et al., 2001; Roth et al., 1991]. Finite element analyses used to define the initial state of static stresses often rely on hyperbolic soil models [Duncan et al., 1984] and variations of the initial tangent static modulus Ei with the confining pressure, as originally suggested by Janbu [1963]: Ei = K Pa (σ/Pa)n
(26.5)
in which K is a constant, σ the minor principal stress, Pa the atmospheric pressure, and n an exponent defining the rate of variation of Ei with σ. Depending on the type of analysis contemplated, some or all of the following dynamic properties may be required: shear and bulk modulus, damping ratio, cyclic shear strength, rate of pore pressure buildup, and residual shear strength. Modulus and Damping Ratio Strain-dependent equivalent dynamic shear moduli and damping ratios as first introduced by Seed and Idriss [1970a] (see Figure 26.6), are essential to EQL analyses. The dynamic shear modulus decreases with the average induced shear strain, while damping increases. Strain-controlled cyclic triaxial tests and resonant column tests may be used to obtain these parameters. Generic modulus degradation (G/Gmax) and damping curves may be used when it is not practical to perform dynamic testing. Geophysical measurements are recommended to define the low-strain dynamic modulus Gmax. Recent generic modulus relationships for sandy or clayey soils depend on the mean effective confining pressure (sands) or the plasticity index (clays). For NL analysis based on elasto-plastic constitutive models, modulus degradation and damping curves are not required. This is because stiffness degradation and damping occur through stress-strain looping and plastic flow. The low-strain modulus and initial damping are the only parameters needed. Cyclic Shear Strength When materials susceptible to liquefying are present, stress-controlled cyclic triaxial and cyclic simpleshear tests were originally used to develop cyclic strength curves. These tests cannot duplicate field conditions and failure modes observed in dams and, for existing dams and foundations, field penetration tests are now preferred to assess the potential for liquefaction. In situ standard penetration tests (SPT) or cone penetration tests (CPT) are used in fine-grained materials, and Becker hammer tests (BHT) in coarse materials. In the absence of comparison holes, the SPT may be more reliable than the CPT [Babbitt and Verigin, 1996] but CPT testing provides more continuous information. The penetration resistance depends on the depth where the test is performed, hammer and sampler types, hole size, possible use of drilling mud and the percentages of fines (materials passing the standard U.S. Sieve #200) of the soil tested. SPT tests are normally corrected in terms of the modified penetration resistance N1(60)cs of an equivalent clean sand [Seed, 1987]. The number 60 indicates that blow counts for the standard test with a rope and drum system correspond to drilling hammer impact energy of 60% of the energy delivered by free fall of the hammer. Correction factors for the fines are found in the literature [Idriss, 1999; Martin et al., 1994; Tokimatsu and Yoshimi, 1983]. Corrected SPT tests can be used to obtain normalized cyclic strength curves [Dawson et al., 2001], based on empirical liquefaction charts [Idriss, 1999; Seed and Idriss, 1982], and magnitude-scaling factors and the number of equivalent uniform stress cycles corresponding to a given earthquake magnitude [Idriss, 1999]. Cyclic strength curves relate the applied uniform cyclic stress ratio (CSR) and the number © 2003 by CRC Press LLC
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FIGURE 26.6 Typical strain-dependent average shear modulus and damping factors.
of cycles to liquefaction. SPT-based cyclic strength curves are conservative, as SPT-based liquefaction curves represent a lower-bound threshold of the CSR causing liquefaction. It is essential to recognize that the empirical liquefaction charts and, therefore, the SPT-based cyclic strength curves apply to cyclic simple-shear condition and a normalized confinement of 2000 psf. Hence, normalized cyclic strength curves must be corrected for the initial static shear and confinement conditions prevailing within the dam section. As the overburden pressure increases, the CSR causing excess pore pressure of 100% decreases. The CSR also depends on the initial static shear stress ratio α (shear stress divided by normal stress) acting on the soil element. Determining the influence of the initial state of stress on the CSR is done through dynamic laboratory testing of isotropically and anisotropically consolidated specimens, or through the use of empirical functions relating static state of stress and cyclic loading resistance [Seed, 1983; subsequently modified by Seed and Harder, 1990 and others (see Idriss, 1999)]. These functions correct the CSR through two factors, Kα related to the initial state of static shear, and Kσ related to the effective vertical stress. The CSR causing an excess pore pressure of 100% at the level α and σ of initial stresses is provided as: (CSR)α = α = (CSR)α = 0 × Kα × Kσ
(26.6)
Rate of Pore Pressure Buildup Also needed for dynamic NL effective-stress analysis is the rate at which excess pore pressures build up during earthquake loading. Fully coupled analyses relate volume changes and excess pore pressure buildup through constitutive models calibrated with the results of laboratory tests. If volume changes are ignored, the rate of pore pressure buildup can be expressed numerically by relationships such as that proposed by Martin and Seed [1978]: Ug /σ0′ = 0.64 arc sin (Neq /Nref )0.5/β
(26.7)
where Ug is the generated pore water pressure; σ0′ is the effective overburden pressure; Neq is the current number of cycles; Nref (reference) is the number of equivalent uniform cycles causing an excess pore water © 2003 by CRC Press LLC
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pressure of 100%; and β is a material-dependent coefficient. A β coefficient between 0.7 and 0.8 is typical of sandy soils. Post-Liquefaction Residual Shear Strength Another parameter significant to the seismic analysis of dams is the post-liquefaction, undrained residual strength, Su,r. This strength can be measured in the laboratory [Castro et al., 1987, 1989; Vaid and Thomas, 1994]. The applicable testing procedures are difficult to implement and sensitive to subjective interpretation. In lieu of laboratory testing, the residual strength can be developed from back-analysis of historic liquefaction failures in materials of known corrected penetration resistance [Seed and Harder, 1990; R.B. Seed, 1999]. The use of a post-liquefaction residual strength is justified for numerical analysis purposes but remains controversial if very low field penetration resistance is encountered, as such condition rarely yields undisturbed samples and is difficult to reproduce in the laboratory. Anderson and coworkers [1996] have suggested in studies of Tellico Dam, TN, that laboratory residual shear strengths can be substantially higher than those derived from SPT data or developed from the back-calculation of case histories of flow slides. In the relationship between Su,r and N1(60)cs, the definition of N1(60)cs differs from that used to evaluate the potential for liquefaction, as the clean sand correction factors are lower (R.B. Seed, 1999). The N1(60)cs obtained with such correction factors can be used with the Seed and Harder relationships to estimate Su,r . The post-liquefaction strength is used as a lower-bound strength limit in NL response analysis or in post-earthquake static slope stability analyses. 26.4.2.2 Analysis Parameters for Concrete Dams and Appurtenant Structures Seismic analysis of concrete dams and appurtenant structures requires the definition of the foundation materials, typically bedrock, and of the dam concrete or masonry. Of concern is the presence of contraction (vertical) and construction (horizontal, or lift joints), which may represent a weakness and cause nonlinear response. Static Properties For most concrete or masonry dams, cores are recovered and tested in the laboratory for unconfined compression and tension (direct or splitting tests). Cores of sufficient diameter, 6 in. or larger, and appropriate length-to-diameter ratios must be recovered [Electric Power Research Institute (EPRI), 1992]. As needed, direct shear tests shall be performed on in-place or carefully sampled lift joints. In the absence of testing, the tensile strength of mass concrete is taken as 10% of the compressive strength. The default shear strength is 12% of the compressive strength. The static modulus of elasticity (E), if not measured in the laboratory, can be derived from empirical formulas based on the compressive strength [Raphael, 1984]. A small reduction in modulus is often used to account for creep and other long-term effects. Poisson’s ratio is also required, and can be either measured or assigned an average value. Dynamic Properties The strength and stiffness of concrete show an increase under rapid (earthquake) loading condition, compared with slow testing. Current practice uses dynamic strength increase factors (20% for compression, 30% for shear, and 40% for tension). Tensile strength increase factors up to 50% have sometimes been justified, based on rapid loading test data [American Concrete Institute (ACI), 1987] or on the concept of apparent tensile strength [Raphael, 1984]. The modulus of elasticity is also typically increased by 25% for dynamic load condition. Strength of Joints Of interest to dam safety is the condition of joints. Lift joints must withstand earthquake-induced cantilever tensile stresses, especially near the top of arch dams. Lift surfaces often have tensile and shear strengths lower than mass concrete. Under seismic loads, vertical and horizontal joints can open or break shear keys, if any are present. Careful preparation of lift joints increases their strength. Prior to pouring new concrete, modern dam construction requires surface preparation of the in-place concrete by removing loose particles and laitance (by brushing or air/water jetting), thoroughly moistening (prewetting) © 2003 by CRC Press LLC
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previously placed concrete surfaces, and carefully vibrating the new concrete upon placement. Wet sand blasting or high-pressure water jetting can be used if previously placed concrete has significantly set. Mortar coats or bonding agents (e.g., epoxies) are sometimes added between old and new concrete. Depending on placement conditions, the tensile strength of lift joints varies from less than a third to more than 90% of the strength of intact concrete. The results of research studies on the strength of lift joints can be used to select strength reduction factors for various methods of surface treatment and concrete placement. Applicable references include Tarbox et al. [1979], Wall et al. [1986], EPRI [1992], Pacelli et al. [1993], Léger et al. [1997], and Harza Engineering Company [1997]. Average strength reduction factors were obtained from these references as follows: • Lift joints with no prior surface treatment. These achieve between 25 and 80% of the tensile strength of intact concrete. The mean strength reduction factor is 0.60, based on a compilation of published values. • Joints formed by placing new concrete on a dry concrete surface. Average strength reduction factors range from 0.55 to 0.90, depending on surface preparation treatments, with a mean value of 0.75. • Joints formed by placing new concrete on a wet concrete surface. Average strength reduction factors range from 0.53 to 0.96, depending on surface preparation and moisture condition, with a mean value of 0.80. Reservoir and Silt Loading Reservoir water pressure and any silt pressure loads must be applied to the upstream face of the dam. Based on experience and in the absence of specific silt sampling and geophysical measurements, one can assume an average density of 85 pcf and a compressive wave velocity of 1000 fps for reservoir bottom sediments.
26.4.3 Analysis of Embankment Dams The seismic safety of embankment dams is governed by whether loss of strength might occur within the dam or its foundation, and whether nonrecoverable deformations remain within acceptable limits. Large deformations reduce freeboard and often cause longitudinal or transverse cracking. The past 25 years have resulted in significant progress in methods and tools to evaluate the seismic performance of embankment dams. The simplest of these methods relies on empirical correlations and simplified procedures derived from observed or calculated seismic response data, and requires few input parameters. Field penetration data can be interpreted to assess the potential for liquefaction. Detailed analysis techniques include EQL (decoupled) solutions, and NL finite element and finite difference coupled or decoupled formulations. Information on applicable computer programs for dam engineering has been compiled in a USCOLD publication [1992a] and Bureau [1997] presented a review of various applicable procedures and some examples of their application. 26.4.3.1 Simplified Analysis Procedures Simplified procedures are used for small dams analysis or to assess the need for detailed studies of large dams. Two common procedures are described here. Newmark’s Method Newmark [1965] computed earthquake-induced displacements in embankments by assuming that movements occur when inertia forces on a rigid block of soils above a fixed potential failure surface exceed its sliding resistance. For planar sliding surfaces, he related the maximum displacement to the peak acceleration (A) and velocity (V) of the input motion and the yield acceleration (N, or Ky). The yield acceleration is the horizontal load coefficient (in g) that results in a factor of safety of exactly 1.0 for the sliding block. Newmark assumed a number of effective pulses for his standardized earthquake not greater than 6 and suggested that, for large magnitudes, the number of effective pulses (and computed displacements) be taken proportional to the square root of the estimated duration of shaking. The method can
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be applied to any soil mass and planar, circular, or noncircular failure surfaces by double-integrating the increments of an applied acceleration time history above the yield acceleration, for a downslope direction of movement. The sliding soil mass is defined by the slip surface with the lowest Ky in conventional static slope stability analyses. Computer programs such as STABL [Siegel, 1975] or UTEXAS3 [Wright, 1992] can be used to obtain Ky . The input acceleration time history is the specified ground motion, in the case of small dams, or is obtained by dynamic analysis at a suitable central location along the assumed slip surface, in the case of large dams. The main limitations of the method is that it assumes a well-defined sliding block that must be predefined and does not account for any progressive loss of soil strength during earthquake shaking. However, Ky may be adjusted as a function of time to consider strength degradation. A derivative of Newmark’s method consists of estimating crest settlement by vectorially combining the displacements of the upstream and downstream slopes [Vrymoed, 1996]. Makdisi–Seed’s Procedure A dam responds as a flexible body, and accelerations vary as a function of depth within the embankment. To take this into account, Makdisi and Seed [1977] estimated the peak crest acceleration (ümax) from a specified response spectrum and a square-root-of-the-sum-of-the-squares (SRSS) combination of the spectral accelerations of the first three modes of dam vibration. By interpreting the results of EQL finite element analyses of several dams, they related the average peak acceleration ratio of the sliding mass (Kmax) and ümax to the depth of the assumed failure surface. Then, for several magnitudes, they expressed the normalized peak displacement of the soil mass, ümax /Kmax gT0 , as a function of Ky /Kmax (Figure 26.7). In their investigation, Makdisi and Seed used the examples of clayey dams of medium height (75 to 150 ft). Hence, their procedure applies best to similar dams. For dams higher than 200 ft, it may be prudent to increase calculated displacements proportionately to the dam height. Due to the assumptions of no loss of strength during shaking and EQL properties, the procedure is questionable for severe ground shaking (0.50 g or greater) and only applies to dams built of materials experiencing little or no loss of strength during shaking (such as densely compacted sands or cohesive clays).
FIGURE 26.7 Simplified estimation of normalized displacements by Makdisi–Seed’s procedure.
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FIGURE 26.8 Crest settlement estimates for rockfill dams and sand embankments based on Earthquake Severity Index (ESI).
26.4.3.2 Empirical Methods Empirical methods are based on the observed or computed performance of existing dams and correlate crest settlement with peak ground motion parameters. Bureau et al.’s Method [1985, 1987] Observed performance of concrete face and earth core rockfill dams was used to develop an empirical relationship between the earthquake severity index (ESI, see Section 26.3.3) and the relative crest settlement for this type of dam. The dam is assumed founded on bedrock or hard soils, although several of the dams used in developing the correlation were on alluvial foundations. The original correlation was developed for compacted rockfill, a material that does not develop significant loss of strength during shaking. In 1987, the authors tested the correlation with friction angles lower than encountered in rockfill, using the results of physical model tests on dry sand embankments [Roth et al., 1986]. The extended correlations can be used for dams built of densely compacted granular materials, using the applicable friction angle (see Figure 26.8). Swaisgood’s Method [1995, 1998] Swaisgood estimated seismic crest settlements by statistical treatment of data collected from the seismic performance review of about 60 existing dams. In 1995, he related the crest settlement (CS), expressed in percent of combined dam and alluvium thickness, to a seismic energy factor (SEF) and three constants based on type of dam construction (Ktyp), dam height (Kdh), and alluvial thickness (Kat). Similar to the ESI, the SEF depends on the magnitude and peak ground acceleration of the causative earthquake. In 1998, Swaisgood streamlined his approach and expressed the crest settlement as the product of the SEF and a resonance factor (RF) differentiating between rockfill, earthfill, or hydraulic fill dams. As is the case with other simplified procedures, Swaisgood’s method is questionable when applied to loose embankments. 26.4.3.3 Other Simplified Approaches Other simplified approaches for estimating dam deformations can be found in the literature [e.g., Jansen, 1987; Romo and Resendiz, 1981]. If liquefaction is of concern to the dam or its foundation, the simplified © 2003 by CRC Press LLC
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procedure of Seed and Idriss [1970b] can be implemented for dams with flat slopes. A better approach is to assess the liquefaction potential from corrected field penetration data [Seed et al., 1983; Seed, 1983]. 26.4.3.4 Equivalent-Linear Response Analyses Equivalent-linear (EQL) analyses typically use two-dimensional numerical models of the maximum dam section. Static analysis is first required to establish the initial state of stress, such as using the computer program FEADAM84 [Duncan et al., 1984]. Gradual embankment construction and progressive reservoir filling can be simulated. Then dynamic response is computed with a different computer program. EQL response is sometimes obtained for representative soil columns within the dam section using SHAKE91 [Idriss and Sun, 1992]. Most frequently, two-dimensional finite element programs are used, such as FLUSH [Lysmer et al., 1975], SuperFLUSH [Civil Systems, Inc., 1980], DYNDSP [Von Thun and Harris, 1981] or QUAD4M [Hudson, Idriss, and Beikae, 1994]. These calculate total stress and strain response using iterated shear moduli and damping coefficients compatible with the average strain induced within each element of the model. SuperFLUSH and QUAD4M include simulation of a compliant base, which improves the solution. QUAD4M allows indirect calculation of dam deformations based on the concept of sliding wedges and seismic coefficients. If three-dimensional effects are expected, two-dimensional models can be stiffened so that the fundamental period of the modeled section matches that of the threedimensional dam, or three-dimensional analysis is performed with TLUSH [Mejia and Seed, 1983). Following the response analysis, induced stresses can be compared with stresses causing liquefaction [Seed, 1983], or computed acceleration histories used in Newmark’s Method to obtain displacement estimates. Attempts to convert EQL strains into nonrecoverable deformations have been made using the concepts of stiffness softening or strain potential [Serff et al., 1976]. Such concepts required significant judgment in their application, and are now rarely implemented. The reliability of EQL analyses decreases when the specified ground motion becomes very demanding. After such analyses, it is desirable to perform conventional stability analyses of the upstream and downstream slopes of the dam, using computer programs such as STABL or UTEXAS3 and assigning postliquefaction residual strength properties (see Section 26.4.2.1) to the affected zones of the embankment. 26.4.3.5 Nonlinear Analysis Recently developed methods of dam earthquake analysis include nonlinear (NL) finite element or finite difference analysis. These methods apply when loss of strength, large deformations, or liquefaction are a concern for the embankment or its foundation. A significant advantage of NL analysis is that the same numerical model can be used for both static and dynamic conditions. Post-earthquake stability can also be evaluated by pursuing the analysis through a period of quiet time after the end of the excitation and verifying whether the dam maintains a stable configuration. NL analyses include elasto-plastic (EPNL) and direct nonlinear (DNL) solutions. Dynamic pore pressures are semicoupled or fully coupled with deformations and volume changes. EPNL (two-dimensional) computer programs include DYNAFLOW [Prevost, 1981; Elgamal et al., 1984], DYNARD [Moriwaki et al., 1988] and FLAC [Itasca Consulting Group, 1992]. A three-dimensional version of FLAC (FLAC3D) was released in 1995. DNL (two-dimensional) programs include TARA-3 and TARA-3L [Finn and Yogendrakumar, 1989] and GEFDYN [Coyne and Bellier/ECP/EDF-REAL, 1991). The Bureau of Reclamation (USBR) has also used ADINA/BM [Bathe, 1978] with hyperbolic and cap models and an endochronic pore pressure generator based on computed strains [Harris, 1986]. Constitutive Models The previously mentioned programs use various constitutive models. TARA-3 and TARA-3L use total or effective stresses, hysteretic cyclic shear behavior, and undrained strength parameters. Response depends on the mean effective normal stress and hyperbolic stress-strain curves, with the tangent shear and bulk moduli being continuously updated during the calculations. Excess pore pressures are coupled with the strain response through the Martin–Finn–Seed model [1975]. Permanent deformations accumulate due to gravity action and consolidation of the softened soils. If liquefaction is triggered, the specified residual strength replaces the undrained shear strength. © 2003 by CRC Press LLC
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GEFDYN relies on the Hujeux–Aubry constitutive model [Aubry et al., 1982]. This model attempts to reproduce fully coupled fluid-soil behavior based on elasto-plastic strain softening/hardening and the concept of critical state, where soils continue to deform at constant stress and void ratio. GEFDYN requires common soil parameters (effective friction angle and cohesion; stress-dependent moduli and Poisson’s ratio) and critical state, dilatancy, deviatoric, and isotropic parameters [Martin and Niznik, 1993]. FLAC and FLAC3D are explicit, finite difference programs. Constitutive equations are solved incrementally [Cundall, 1976], thus allowing large strains, material anisotropies, sliding interfaces, and other nonlinearities. For dam analysis, the Mohr–Coulomb constitutive model has been shown to be particularly applicable [Roth et al., 1986]. Other models are built in the program or can be coded through a macro programming language. At every calculation step, incremental strains are computed in each elementary zone and resulting stress increments derived from the applicable constitutive relationship. Zone stresses and gridpoint displacements are updated, and new incremental strains are computed. Massand stiffness-dependent Rayleigh damping is used at low strain. At higher strains, damping occurs primarily through hysteretic looping. A semicoupled empirical procedure [Roth et al., 1991; Dawson et al., 2001], based on the concept of cumulative damage, has been used in FLAC to generate excess pore pressures at each calculation step. As an illustration of such procedure, Figure 26.9 shows the twodimensional finite element model of a large embankment dam, the time history of the computed settlement at the crest center, and shear stress and excess pore pressures histories obtained for a typical model grid zone. In another NL approach using Cundall’s equations, Beikae [1996] extended Newmark’s method to calculate three-dimensional seismic displacements in an embankment. The procedure uses a Lagrangian formulation, coded in the computer program BLOCK3D. It simulates gravity, hydrostatic, and seismic forces on elementary soil blocks with fixed masses representing the geometry of the embankment. Soil blocks can move, expand, compress, and distort in space relative to each other. The equations of motions are solved explicitly at the gravity center of each elementary block. A significant limitation is that BLOCK3D applies to materials not susceptible to developing excess pore pressures. NL Computer Program Validation An important step in the use of NL analysis is to perform calibration tests and verifications. TARA-3 was validated with centrifuge testing [Finn, 1991] and using the example of Matahina Dam, New Zealand [Finn et al., 1992]. GEFDYN has been tested using the observed performance of El Infiernillo Dam (see the proceedings of the International Benchmarks Workshops on Numerical Analysis of Dams, Bergamo, Italy, 1992, Paris, 1994, and Denver, CO, 1999 [ICOLD, 1992, 1994, 1999]). Verifications of FLAC for dam analysis purposes include prediction of centrifuge liquefaction testing results [Inel et al., 1993] and comparison between observed and back-calculated performances of South Haiwee Dam [Dames and Moore, 1991], Los Leones Dam [Bureau et al., 1994), Los Angeles Dam [Bureau et al., 1996], and Upper San Fernando Dam [Dawson et al., 2001].
26.4.4 Analysis of Concrete Dams The seismic safety evaluation of concrete dams is primarily governed by whether unacceptable stresses might occur within the dam or sliding of one or several blocks could be triggered along joints, the foundation, or the abutments. Evaluation methods have evolved considerably over the past 30 years. Earlier dams were designed through simple force and moment equilibrium considerations, while modern safety evaluations involve sophisticated linear-elastic or NL dynamic numerical response analyses. The effects of foundation flexibility on strains and stresses within the dam body must be accounted for. Of possible concern to the stability of concrete dams are uplift forces at lift joints and at the interface between the dam and its foundation, and joint opening. The 1992 USCOLD publication (see Section 26.4.3) also describes computer programs applicable to concrete dams. In addition to concrete, water, and foundation properties, viscous damping ratios of 3 to 5% for the OBE and between 5 and 10% for the MCE are considered appropriate input parameters. © 2003 by CRC Press LLC
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FIGURE 26.9 Nonlinear two-dimensional finite difference model of an embankment dam and typical analysis results.
26.4.4.1 Simplified Analysis Procedures Some old arch dams have been designed using force equilibrium methods, which do not consider cantilever action. Simplified analysis procedures based on such methods are now used only for small gravity dams, and assume that the dam is a two-dimensional rigid body that can slide on a rigid foundation. The updated “Engineering Guidelines for the Evaluation of Hydropower Projects” [Federal Energy Regulatory Commission (FERC), 2000] includes a methodology for such analysis. The guidelines require iterative crackedbase analysis with zero tensile strength and full reservoir head in the cracked zone.
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26.4.4.2 Detailed Analysis of Gravity Dams Many computer programs are available to analyze gravity dams. The most frequently used programs include multipurpose, three-dimensional codes such as ANSYS [Swanson Analysis Systems, Inc., 1970], ADINA [Bathe, 1978], SAP90 and SAP2000 [Wilson and Habibullah, 1988], and specialized two- or three-dimensional programs, such as EAGD-84 [Fenves and Chopra, 1984] and EACD-3D [Fok et al., 1986]. Most of these programs have been continuously updated since their first release. All perform timehistory response analysis but the general purpose programs also include response spectrum analysis. Leclerc and coworkers [2002] recently introduced CADAM, an interactive program for gravity dams, based on response spectrum analysis. Analysis of gravity dams is generally done using two-dimensional finite element models of the maximum section of the dam. Depending on the dam geometry, one may need to consider other sections or three-dimensional analysis. Plane-strain or plane-stress two-dimensional formulations can be used, depending on the spacing of construction joints. Added masses (Westergaard’s theory) represent the reservoir water, if more rigorous solutions are not provided. The original added mass concept is based on simplifying assumptions of vertical upstream face, rigid dam section, and incompressible water but was modified by Kuo [1982] for other orientations of the upstream face. Some computer programs simulate hydrodynamic pressures using a finite-element formulation and compressible or incompressible fluid elements (e.g., EACD-3D). A massless foundation is generally assumed, except for the half-space of EAGD-84. In that program, seismic input is entered at the bottom of the dam (top of the half-space) but, in others, the base of the foundation model is excited. A two-dimensional analysis ignores the forces that resist the thrust on the abutments of a curved concrete gravity dam. Plane-strain or plane-stress analysis, depending on which is applicable, is likely to be conservative for stress evaluation purposes, and three-dimensional analysis would generally reduce the maximum calculated tensions and compressions. In two-dimensional analysis, neglecting effects and crack opening patterns related to the valley topography may lead to overestimating the factor of safety against sliding [Brand, 1993]. However, the two-dimensional approach is often sufficient to demonstrate the safety of straight or some curved concrete gravity dams, and is a cost-effective solution if safety is demonstrated. Chopra [1988] used EAGD-84 to identify several factors of significance to gravity dam response: the influence of water compressibility, dam flexibility, and vertical component of earthquake motion on hydrodynamic pressures; the influence of wave propagation through the foundation rock; and the effect of seismic waves absorption by the reservoir bottom sediments. In EAGD-84, the dam monolith is idealized as an assemblage of planar, four-node, nonconforming, linear-elastic elements and the foundation as an isotropic, infinite half-space. The reservoir water is represented as a compressible fluid of constant depth and infinite length toward upstream. Hydrodynamic pressures are simulated through the solution of the two-dimensional wave equation. The absorption of compressive fluid waves by the bottom sediments and foundation rock is accounted for through a wave absorption coefficient. Tailwater is not represented in the model. Constant modal damping is used for the dam, and hysteretic damping for the foundation. A low foundation damping (e.g., 0.5%) and a large wave reflection coefficient (e.g., 0.8) for the elastic half-space imply near-full reflection of water pressure waves by the reservoir bottom, a conservative approach. Stresses are calculated at element centers. Despite major progress in numerical analysis procedures, consideration of the influence of uplift on the sliding stability relies upon simple principles. Dynamic uplift pressure fluctuations are not considered, and static uplift pressures are combined with the earthquake response to obtain the effective normal stresses at the dam–foundation interface. In the cracked-base approach [Federal Energy Regulatory Commission, 2000], full reservoir head is applied to any zone experiencing normal tension along the base of the dam by iteratively adjusting the length of cracking and relaxing or deleting the corresponding dam elements [Brand, 1993]. This procedure is best implemented using computer programs with interface elements (e.g., ANSYS, SAP2000, FLAC). Improved formulations regarding the simulation of planar discontinuities and concrete cracking have led to the consideration of nonlinear concrete behavior [Tarbox et al., 1979] and Mohr–Coulomb dam–foundation interfaces [Chavez and Fenves, 1993; Bureau,
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1996a; Bu, 2001]. Most importantly, it should be recognized that various well-accepted programs may yield different results because of their different formulations. Using three successive two-dimensional analyses (SAP90, EAGD-84, or FLAC) for the same dam, peak tension was reduced by 30% and peak compression increased by 60% when a sliding interface with no bond strength was placed between the dam and its foundation; sliding stability results, however, were consistent [Bureau, 1996a]. Overall, a thorough understanding of available evaluation methods is required, especially in the case of marginally stable gravity dams. 26.4.4.3 Detailed Analysis of Arch Dams Three-dimensional response analysis is typically required for arch dams. Early analyses of arch dams were based on the trial load method but that method has now been replaced by finite element analysis. The geometry of such dams is complex and must be represented with sufficient refinement. Dynamic effects must be superimposed with static effects. The latter, in the case of arch dams, must incorporate temperature effects, which are less significant and often ignored for gravity dams. Stresses are typically resolved as horizontal arch and vertical cantilever stresses along the upstream and downstream faces of the arch (see Figure 26.10). A correction factor may be used to obtain principal stresses. Seismic response analyses of arch dams can be conducted using specialized computer programs such as EADAP [Ghanaat and Clough, 1989], ADAP-88 [Fenves et al., 1989], GDAP and ADAP-NS [Quest Structures, 1993], and SCADA [Hall, 1997]. General purpose three-dimensional codes, such as SAP90, SAP2000, or ANSYS (see Section 26.4.4.2) can also be considered but a deficiency of these codes is that reservoir interaction effects can be represented only through the use of added masses. As the upper portion of an arch is more flexible than the top of a gravity dam, reservoir water compressibility can lead to significant pressure wave effects that modify response appreciably. Specialized programs include fluid elements and compressible water formulation. As for gravity dams, a large portion of the foundation bedrock must be included in the analysis of arch dams. GDAP is a graphics-based finite-element analysis program for linear-elastic static and dynamic analyses of concrete arch dams. It represents dam–reservoir interaction effects with an added-mass matrix computed using a finite-element formulation for an incompressible fluid volume. To achieve an efficient substructure solution, the full added-mass matrix is converted into an equivalent diagonal matrix that preserves hydrodynamic forces due to rigid body accelerations of the dam in the stream, cross-canyon, or vertical directions. ADAP-NS (an enhanced version of ADAP-88) has capabilities to represent potential zones of weakness in the dam, such as lift joints, dam–foundation interface, and significant cracks. ADAP-NS uses three-dimensional solid elements similar to those employed in GDAP to model the arch and the foundation bedrock, and three-dimensional fluid elements to represent the reservoir water. It uses a substructure solution procedure to carry out static and dynamic analyses. Any portion of the dam body bounded by contraction joints, lift joints, or the dam–foundation interface is considered as a linear substructure, for which a constant stiffness is used throughout the solution process. Nonlinear effects are restricted to joint elements whose possible opening is influenced by preexisting normal stresses. Normal and tangential stiffnesses and the assumed tensile strength control joint behavior. A large normal stiffness simulates joint closing. The tensile resistance of joints is cancelled when normal tensile stresses reach the specified tensile strength. Joints with no initial tensile strength open freely, if subjected to tensile normal forces. An example three-dimensional finite element model of an arch dam with discrete representation of selected lift and contraction joints is shown in Figure 26.11. Another form of NL analysis, used in SCADA, relies on the concept of smeared cracks. Such a solution not only attempts to model the opening and closing of contraction joints but also the formation of cracks in the concrete as a result of excessive tensile stresses. The smeared crack approach simulates nonlinearities by placing conditions on the stresses of the elements (shells) that represent the arch. The smeared crack approach is computationally more efficient and exhibits better convergence than discrete joint models. It allows formation of cracks based on the most critical orientation of induced stresses. As in the case of gravity dams, the sliding stability of each contact block must be evaluated. Peak static-plus-seismic driving and resisting forces can be compared, or a step-by-step, time-dependent factor © 2003 by CRC Press LLC
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FIGURE 26.10 Arch dam stress analysis results, plotted as arch and cantilever stress contours.
of safety can be computed for each block as the ratio of transient resisting-to-driving forces. The results of a typical block sliding stability analysis are presented in Figure 26.12. For such transient analyses, it should be noted that instantaneous dynamic factors of safety less than 1.0 do not necessarily indicate unacceptable behavior, if the duration of such occurrences is very short and, therefore, insufficient to induce significant sliding of the dam. © 2003 by CRC Press LLC
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FIGURE 26.11 Three-dimensional finite element model of arch dam with representation of contraction and lift joints. (Numerical model developed by Quest Structures, Orinda, CA.)
26.4.4.4 Detailed Analysis of Buttress Dams The evaluation of such dams normally requires three-dimensional considerations and is, therefore, similar to the evaluation of arch dams (see Figure 26.13). In the case of long-crested buttress gravity or multiple arch dams, it may be sufficient to evaluate only two adjacent buttresses and the portion of the dam between. Buttresses have often been built slender and are very sensitive to cross-valley seismic loads. Hence, one must successively take the largest component of horizontal motion as parallel or perpendicular to the dam crest. Some buttresses near the abutments may be affected by the possible presence of joints, shear zones, or foliation parallel to the valley slopes, and earthquake effects on the stability of rock blocks bounded by such features must be investigated.
26.4.5 Analysis of Intake/Outlet Towers Intake/outlet towers can reach significant heights (more than 400 ft tall) and may significantly amplify ground motion. For towers of simple configuration, Chopra and Fok [1984] concluded that the first two modes of tower response provide sufficient accuracy to compute shear forces and moments. For large, complex, or very flexible towers, dynamic response analysis is the most appropriate evaluation methodology. In addition to hydrodynamic interaction effects, the response of flexible towers can be influenced by the presence of internal equipment and wall openings, and by soil–structure or structure-to-structure interaction (access bridges). Finite element models with flexible three-dimensional beam elements and distributed or lumped masses (stick model) represent most towers adequately [Bureau, 1993b; USCOLD, 1995]. As few modes of vibration contribute significantly to dynamic response, 20 joints (nodal points) or less are generally sufficient to represent the tower shaft. Added mass coefficients are typically used to approximate hydrodynamic effects for various tower sectional shapes [Goyal and Chopra, 1989]. More complex formulations using incompressible or compressible fluid elements are also available. Most intake/ outlet towers are either founded on an enlarged base on the reservoir bottom or cantilevered into bedrock or hard soil. In situ monitoring of ambient and low-level forced vibrations of intake/outlet towers embedded in rock have shown apparent points of fixity several tens of feet below ground surface [Bureau and Scawthorn, 1986; Bureau, 1985]. Therefore, a significant depth of the foundation rock may need to be included in the analytical model. Plane strain axisymmetric or three-dimensional thick plate or solid elements can also represent complex tower wall configurations and the surrounding foundation [Dungar and Jackson, 1975]. Approximate three-dimensional analyses of outlet towers embedded in embankment © 2003 by CRC Press LLC
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FIGURE 26.12 Nonlinear block sliding stability analysis for a thick arch dam.
dams have been done using two-dimensional, equivalent-linear, plane-strain finite element models with unbalanced free-field boundary conditions [Bureau and Udaka, 1982] (see Figure 26.14). Light access footbridges have little effect on tower response. Some towers, however, are connected to massive reinforced concrete bridges with possible intermediate piers which must be included with the tower shaft in a detailed model (see Figure 26.15). Once a representative model has been developed, response is first calculated using elastic response spectra and gross section properties. As for concrete dams, viscous damping ratios of 3 to 5% for the OBE, and between 5 and 10% for the MCE are considered appropriate. Induced shear and moment loads © 2003 by CRC Press LLC
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FIGURE 26.13 Finite element model of triple arch dam and its foundation.
are compared to the gross (uncracked) capacity of the concrete or masonry. The SRSS method is appropriate to combine multidirectional loading components. If the uncracked capacity is not exceeded, such analysis is sufficient. If cracking is shown to occur, induced forces and moments are resisted by the steel reinforcement. Approximate or detailed nonlinear response analysis may be required to compute the post-cracking response and verify that the ultimate structural capacity (bending or shear) will not be exceeded. Cracking, especially, reduces the stiffness of a tower and lengthens the period of its principal modes of vibration, which may increase or decrease earthquake loads, depending on the peak of the specified response spectrum. Cracking of reinforced concrete is a highly nonlinear phenomenon. If sufficient ductility is available, idealized elasto-plastic moment vs. rotation curves can be developed for the tower shaft. For most towers, however, it is prudent to limit cumulative ductility factors to 2.0 in both bending and compression [Chopra and Liaw, 1975]. A possible approach to simulate cracking of a tower is an iterative equivalentlinear procedure [Bureau, 1993b]. The analysis properties of overloaded sections are modified to simulate crack formation and propagation. Where the cracking moment Mcr is exceeded, a procedure similar to that recommended for beams in ACI-318, “Building Code Requirements for Reinforced Concrete,” is used to obtain the ultimate shear and moment capacity. An equivalent (reduced) moment of inertia Ie is also derived from the gross (Ig) and cracked (Icr) section properties. The cracked moment of inertia Icr is the sum of the moments of inertia of the compression concrete and vertical steel reinforcement bars, and reduced moments of inertia are substituted for gross moments of inertia in cracked sections. Vertical steel provides the principal resistance to bending moments. In the ACI-318 procedure for estimating the ultimate capacity of reinforced concrete sections, an ultimate strain of 0.003 in./in. in the extreme fiber of the compression face of the tower section considered and a rectangular compressive stress block are employed. Moment-axial load interaction curves must be considered in bending capacity © 2003 by CRC Press LLC
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FIGURE 26.14 Approximate three-dimensional embankment tower seismic interaction model.
calculations. A typical load-moment interaction diagram is shown in Figure 26.16. The ultimate shear capacity of the shaft section can also be computed, using the provisions of ACI-318, as the sum of the shear capacity of the concrete (Vc) and the capacity of the shear reinforcement steel (Vs). The most overstressed shaft element is assumed to crack first, and the tower response is reevaluated. If overstressing extends beyond the initial cracked zone, cracking propagates upward or downward (or both) along the shaft, and the process is iterated. Stability against further cracking may be achieved or not, and this approximate procedure indicates with a reasonable degree of confidence if the ultimate seismic capacity of the tower will be exceeded. For towers embedded in embankment dams, one must also verify that cracking would not cause leakage or piping, even if the tower has sufficient capacity.
26.4.6 Limitations of Current Analysis Methodologies The ability of engineers to sample and test embankment dam materials meaningfully lags behind the ease of using, developing, or obtaining access to complex theoretical constitutive soil models and powerful © 2003 by CRC Press LLC
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FIGURE 26.15 Three-dimensional beam model of outlet tower, access bridge, and piers.
FIGURE 26.16 Typical moment-axial load interaction and cracked moment of inertia relationships for outlet tower shaft section.
numerical tools. First and foremost, one must keep in mind that modern computerized analysis tools operate at a level of apparent accuracy that far exceeds the engineer’s ability to obtain reliable measurements of field material properties and assess the variability of such properties within the dam or its foundation. Hence, regardless of their sophistication, the quality of numerical analyses is always limited by the quality of the material properties to be used as a basis to develop numerical models. © 2003 by CRC Press LLC
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Similarly, and despite careful verification and acceptance by review authorities, analysis tools for concrete dams include both useful features and potential limitations in their ability to solve the complex problem of dam response. As Professor Ray Clough stated in 1993, “…in judging the seismic response of a structure, the displacements that occur are much more important than the stresses” [Clough and Ghanaat, 1993]. Case histories have led to difficulties in questions regarding very large, calculated elastic stresses and the absence of conspicuous earthquake-induced cracking (e.g., Lower Crystal Springs Dam in 1906; Pacoima Dam in 1971 and 1994). Nonlinear analysis suggests that cantilever and arch stress calculations may merit less importance than that given to date, but it raises the question of what are acceptable computed amplitudes for joint opening and dam movements. For both embankment or concrete dam analysis, excessive conservatism is less forgiving in a nonlinear environment, and sophisticated solutions require more realistic assumptions, and perhaps new considerations. Until increased knowledge is gained, we must recognize the limits of our ability to duplicate the numerous and complex phenomena that are part of the seismic behavior of dams. Common sense, engineering judgment, and field and construction experience remain the most important components of any numerical analysis.
26.4.7 Physical Testing, Modeling, and Centrifuge Studies Physical testing and modeling of dams can be used to confirm analysis assumptions, develop insight into performance, identify modes of vibration, response or failure, and validate numerical models. Detailed discussion of these aspects is beyond the scope of this chapter, and only a few comments are appropriate. Observations of the behavior of dams in the linear-elastic range, using full-size shaking such as induced by mechanical vibrators, yields results that generally agree with computed values at low levels of excitation. A successful way to test dams and their appurtenant facilities has been the use of underwater pressure wave generators [Ostrom and Kelly, 1977] or explosive charges, placed at some depth in the reservoir, which apply low-level forced vibrations to the structure tested. While these low-level forced vibrations are useful for calibration of analytical models, it is difficult to extrapolate from those results to compute the anticipated response to strong seismic motion. Physical model (reduced-size) testing of earthquake effects on dams has been conducted in various research projects. The literature is rich with descriptions and results of model testing for stresses and deflections in concrete dams, soil–structure interaction and deformation, slope stability, and excess pore pressure generation in embankment dams [Clough and Niwa, 1982; Hall, 1997]. Scaling is a major issue in model testing and, especially, dynamic model testing. With the availability of powerful computer tools, computational ability has progressively replaced the ability to test, and the use of physical modeling is now limited to large universities or government laboratories for special cases. However, ability to successfully test embankment dams of relatively simple geometry has been enhanced by the development of testing devices that allow improved feedback controls and dynamic excitation at the base of the model (which is loaded statically through the rotation of the centrifuge). Detailed information and a comprehensive list of publications on centrifuge testing are provided in the proceedings of specialty conferences on the subject; see Centrifuge 88, Centrifuge 91, and Centrifuge 94, published by A.A. Balkema.
26.4.8 Post-Earthquake Inspection Competent operations personnel and engineers must inspect dams that have been subjected to significant earthquake ground motion. Post-earthquake inspections must include initial and follow-up site visits. Immediate inspection is critical to decisions regarding continued safe operation. Dam inspections are essential whether damage has occurred or not, as relevant information collected provides insight regarding the structural performance of the affected facility and may be used to subsequently calibrate or verify numerical analysis models. A post-earthquake inspection plan should be prepared, and should include the crest and faces of the dam, abutments, gates and spillways, outlet works, and penstocks and powerplant, if any. Inspections should focus on identifying any foundation or slope movements, soil cracks, © 2003 by CRC Press LLC
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fissures and settlement, increased or reduced seepage, evidence of concrete overstressing or joint movement, and reservoir margin defects, and actual or imminent landslides. Collection of recorded data from strong motion accelerometers, settlement monitoring devices, inclinometers, tiltmeters, etc. must proceed immediately. Crest and slope surveys may need to be performed if the dam is not instrumented. To make inspections more meaningful, inspectors should follow the applicable guidelines for inspections of dams, such as available from USBR [1983], ICOLD [1988], and FERC [2000].
26.5 Seismic Upgrade of Existing Dams 26.5.1 General Dams can be modified to increase their seismic capacity and repaired, strengthened, or replaced if damaged by earthquakes. Such modifications to dams started in the 1930s but systematic improvement programs for state and federal dams really began after the 1971 San Fernando earthquake. In the United States, more than 140 dams have been modified to better resist ground motion. Other dams have been abandoned, replaced, or converted to flood control instead of water storage. New dams can be designed and constructed to resist the most severe earthquake loads, as demonstrated by the outstanding performance of several modern dams. Many procedures used to upgrade existing dams apply to new dams. The philosophy for new design or for improvement of existing facilities to efficiently resist seismic loads requires a thorough analysis of the observed behavior of different types of dams during past earthquakes and an understanding of why performance has been poor or satisfactory.
26.5.2 Seismic Upgrade of Embankment Dams Embankment dams and foundations can be modified to prevent earthquake-induced overtopping, internal erosion, liquefaction, or a combination of these failure modes. A compendium of seismic upgrade methods used for such dams is provided in the following paragraphs. Several of these methods are often simultaneously implemented. The name of a representative completed dam upgrade is provided for each main type of improvements. The reader should consult the literature for more details. • Dam improvements: Embankments can be strengthened by enlarging, flattening, or adding berms to upstream or downstream slopes (Bradbury Dam, CA); increasing freeboard by raising the crest (Calaveras Dam, CA); installing crack stopper zones (Austrian Dam, CA); driving piles in upstream slope (Sardis Dam, MS); implementing compaction grouting (Pinopolis West Dike, SC); and constructing filters and drained buttresses (Steinaker Dam, UT). • Foundation improvements: Foundation improvements include performing vibroflotation-vibrocompaction (Scofield, Dam, UT); compaction grouting; removing or replacing subsurface materials with compacted soils (Austrian Dam, CA) or soil-cement mixture (Jackson Dam, WY); performing deep dynamic compaction (Folsom Dam, CA); installing drains (Hinckley Dam, NY) or stone columns (Lopez Dam, CA); and constructing impervious cutoffs (Hebgen Dam, MT).
26.5.3 Seismic Upgrade of Concrete Dams With regard to concrete dams, improvements may involve either the structure or its foundation, and are intended to limit overstressing, prevent sliding, control joint opening, and stabilize buttresses. Some of the improvements of embankment dam foundations can be used for concrete dam foundations. • Dam improvements: Methods that have been implemented include thickening the cross section with concrete or shotcrete, or adding buttresses of roller-compacted concrete (RCC) or mass concrete (Gibraltar Dam, CA); thickening or restraining buttresses laterally (Weber Dam, CA); epoxy-grouting the concrete (Sefid-Rud Dam, Iran); installing post-tensioned anchors through
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the dam (Railroad Canyon Dam, CA); installing cross-braces or strut multiple arches and Ambursen dams (Sutherland, CA); and installing relief drains. • Foundation or abutment improvements: Drainage, grouting, rock bolting, and anchorage with rock bolts or post-tensioned anchors (Pacoima Dam, CA).
26.5.4 Seismic Upgrade of Appurtenant Structures Means to improve facilities appurtenant to dams are the following: • • • • • • • • • • • •
Increasing freeboard by spillway lowering or gate removal (Henshaw Dam, CA) Plugging outlet tunnels or conduits exposed to differential fault movements (Calaveras Dam, CA) Constructing bypass outlets (Lake Madigan Dam, CA) Anchoring intake/outlet tower with post-tensioned multistrand cables (Tolt Dam, WA) Adding steel brace and shotcrete to outside of tower wall (San Gabriel Dam, CA) Building a moment-resisting structural frame around the tower (Shin Tsuroko Dam, Japan) Enlarging the diameter of the tower base mat and adding mass above Filling the lower portion of the inside shaft with concrete (proposed) Strengthening access bridge piers, replacing concrete deck with lighter steel deck Tying the bridge deck to the tower Building bulkhead where outlet tunnel joins tower (Lake Herman Dam, CA) Upgrading spillway gates (Matahina Dam, New Zealand).
26.6 Seismic Design of New Dams 26.6.1 General Seismic considerations affect many decisions in the design of new dams, ranging from site selection to the type of instrumentation to be installed. The selected dam type and design features should be tailored to the site configuration, geology, and the local and regional seismic environments. Topographic effects, joint orientations, and valley shape can affect the seismic response, and should be accounted for.
26.6.2 New Embankment Dams The foundation conditions should be thoroughly investigated and unsuitable materials removed, replaced, or compacted, and drainage features installed. The embankment must be designed to the highest standards. Particular considerations should be given to rockfill dams with concrete (CFRD) or asphalt concrete faces. Details of the connections of the face and toe slabs, and anchorage of the toe slab to its foundation should be carefully considered. Waterstops should be carefully designed and redundant waterstops utilized as needed. Drainage materials below the face slab should be placed on well-compacted rockfill. Listed below are various design or construction measures for the seismic design of new embankment dams. • Increase freeboard to lengthen lateral seepage paths at normal operating reservoir level and accommodate earthquake-induced settlement or seiches. • Increase the crest width to produce longer seepage paths through transverse cracks that might develop during a seismic event. • Excavate foundation to very dense materials or bedrock; or densify or replace loose layers with well-compacted materials. • Provide gentle shape, free of sharp and reentrant edges, to the foundation/core contact. Keep transverse upstream foundation slopes across the core to less than 1:4 (v:h), and slopes along the © 2003 by CRC Press LLC
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dam alignment to less than 1:2 (v:h). This will reduce or prevent transverse cracking. At the abutments of large dams, in the upper 100 ft, build transverse foundation slopes across the core zone horizontal or to a gentle slope toward upstream. This preserves watertight contact after shaking and reduces settlement. Flare the core contact, along the upper portions of the abutments, to provide longer seepage paths in case of abutment fissures. Thoroughly compact all zones of the embankment. This reduces earthquake-induced loss of strength, deformations, or settlement. Upstream from the water barrier or below the water table, avoid using fill materials that tend to develop excess pore water pressures. Provide high capacity internal drainage zones to intercept seepage from any earthquake-induced transverse cracking and prevent saturation in embankment zones designed to remain dry. Place filter zones along fractured foundation bedrock to prevent piping of the embankment through enlargement of these fractures. Widen filter and drain zones to maintain material continuity in case of offset and to heal transverse cracks. Select gradations for the transition zones that will be self-healing and facilitate healing of any cracks within the core zone. Avoid “brittle” materials for use as water barriers. Use more plastic materials in areas where tensions are prone to develop during earthquakes.
26.6.3 New Concrete Dams Buried narrow gorges in wide valley foundations may affect the dynamic response of concrete buttresses or monoliths. Such a condition must be mitigated, for example by plugging the largest gorges with mass concrete, or by selecting a different type of dam, such as rockfill embankment. A concern under seismic condition is the performance of combination structures, such as earth or rock structures wrapped around the end of concrete gravity dams and spillway structures, and composite gravity arch dams. Potentially critical are dynamic interaction and differential displacements of adjacent structures with incompatible periods of vibration. Design details that improve performance of concrete dams are listed as follows: • Design a regular and smooth geometry for the dam structure (symmetry is desirable but not essential). Increase the crest width to reduce incidence of through-cracking. Limit the ratio of crest length to dam height and reduce mass near top of the dam to control crest deflections and minimize distortions. • Avoid slope changes along the downstream face of gravity dams to eliminate local stress concentrations. • Minimize discontinuities in dam body, such as those caused by heavy parapet walls and thrust blocks. • Maintain continuous compressive loading along the foundation by shaping the dam–foundation interface or adding a plinth to support and transfer dam loads. • Improve quality of foundation bedrock by excavating, replacing with concrete or grouting poor quality rock, shears, cavities, etc. • Brace, widen, or enlarge the bottom portion of buttress walls in buttress dams to improve resistance earthquake loads parallel to the dam axis. • Provide contraction joints with strong interlocking through use of oversized shear keys. Prepare, clean, and wet lift surfaces to increase bond strength. • Maintain low concrete placement temperatures to minimize locked-in tensile stresses and reduce the occurrence of shrinkage cracks. • Slope and batter concrete interface in composite earth-concrete dams to maintain compressive embankment loading against the concrete; use plastic soils and wider filter zones in the embankments in the interface area. © 2003 by CRC Press LLC
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26.6.4 New Appurtenant Structures Seismic consideration must also be given to the design of appurtenant facilities and, especially, intake/ outlet towers. To mobilize a higher ductility in such structures, a key requirement is to provide adequate reinforcement and caging (i.e., confinement) for the concrete. Vertical and horizontal steel should be provided in several curtains, and bar sizes and spacing selected to adequately confine the concrete upon shear load reversals and prevent excessive tensile stresses in bending and compression buckling of the vertical steel. For highly seismic sites, inclined reinforced concrete towers, supported on the foundation over their entire length, may be considered. This solution is a compromise between structural safety and water quality requirements. If a vertical tower is preferable, then holding it down with post-tensioned anchors may provide a solution. The tower should be sited far from the dam, if concerns are raised regarding potential damage to the dam caused by tower failure. Internal or external elements, such as operating platforms, decks, access ladders, polar cranes, electrical control panels, control valves, slide or radial gates, and their guides and supports must be adequately anchored, especially since amplifications of the ground motion to the top of the tower subject internal equipment to large lateral forces. Care must be taken to prevent access bridge decks from overloading the tower. Light steel trusses or wooden decks are recommended. If a heavy bridge cannot be avoided, it should be structurally disconnected from the tower, supported on heavy piers or shear walls, and equipped with a collapsible or compressible joint at the bridge-tower connection.
26.7 Seismic Instrumentation of Dams High-quality performance data and strong-motion records on and near dams are essential to better understand the behavior of dams during earthquakes and calibrate and improve methods of numerical analysis. Conventional dam instrumentation should be provided, plus accelerometers or, preferably, strong-motion instruments producing digital records [USCOLD, 1989]. A network of instruments should preferably be deployed at selected locations in the valley, including sufficiently far from the dam to obtain free-field condition, at the base of the dam and top of the abutments, and at or near the center of the dam crest and along the downstream face. Three instruments are the bare minimum to consider. If a planned reservoir is large enough to be considered as a potential source of reservoir-triggered seismicity, a network of sensitive seismographic instruments may be installed around and beyond the reservoir perimeter to record local microseismic activity and establish a baseline prior to reservoir filling.
Acknowledgments This chapter was inspired by 15 years of involvement of the author as vice chairman of the Committee on Earthquakes of the U.S. Society on Dams (USSD, formerly USCOLD). Permission to borrow materials and information from relevant committee publications was received from Mr. Larry Stephens, Executive Director, USSD, and is gratefully acknowledged.
Defining Terms Added masses — Added masses may be used to represent the effect of hydrodynamic pressures in the reservoir water and lengthening of the natural periods of vibration of a dam (compared with the empty reservoir) as a result of earthquake shaking. The concept was originally developed by Westergaard [1933] for a vertical dam face and was subsequently extended to any dam face orientation by Kuo [1982]. Added masses can also be used for intake/outlet towers surrounded by the reservoir water [Chopra and Fok, 1984]. Contraction joint — An artificial, generally vertical, joint constructed (cut) in concrete dams to reduce tensions and prevent cracking of the concrete, after placement, as a result of cooling during curing.
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Cracked-base analysis — For gravity dams, this method of analysis is used to evaluate the influence of tensile stresses along the dam–foundation interface. Where normal tensions are computed across the interface, uplift is assumed to occur, and the bond strength of the concrete and bedrock is set to zero. Full reservoir pressure is also applied to the uplifted zone. The analysis is repeated with these new assumptions, and the process iterated and the length of the cracked zone increased, as needed, until no further tensions develop. Design basis earthquake (DBE) — The maximum earthquake employed for the design or analysis of a dam, usually specified in terms of acceleration time histories or response spectrum at the site or both. It may be defined in terms of magnitude and epicentral distance from the dam site. Equivalent-linear analysis — In an equivalent-linear analysis, embankment materials properties (damping coefficient and shear modulus) are iteratively adjusted in a series of successive linearelastic analyses to become compatible with the average computed shear strains within the elements of the numerical model. The average strain is taken as a fixed percentage of the peak strain in each element. Iterations are stopped when convergence is achieved for the estimated properties, based on the computed average strains. Excess pore pressure — Corresponds to an increase of internal pore water pressure within a saturated soil medium as a result of a reduction in skeleton volume caused by earthquake shaking. Fling — Very large velocities and displacements observed in strong ground motion records recovered at near-fault sites, resulting from tectonic deformation. Foliation — Parallel alignment of planar fabric elements in rock. Freeboard — Represents the elevation differential between the crest of a dam and the lowest portion of the spillway crest. A large freeboard provides extra safety, as it reduces earthquake loads and the possibility of overtopping. Free-field — The regions of the ground surface that are not influenced by man-made structures. Also designates a medium containing no structure (free-field profile) and where boundary effects do not significantly influence the response of the medium to earthquake motion. Hydraulic fill dam — Designates a dam built by deposition of loose granular materials, typically silts and sands, conveyed as a slurry to the site by hydraulic pumps and pipes. Lift joint — The surface between two consecutive concrete pours during the construction of concrete gravity or arch dams. Operating basis earthquake (OBE) — In the case of dams, represents the level of ground motion at the dam site with a 50% probability of not being exceeded in 100 years [USCOLD, 1999]. Maximum credible earthquake (MCE) — (Also Maximum considered earthquake) The largest earthquake considered in an analysis, that appears possible along a recognized fault or within a geographically defined tectonic province. Little regard is given to its probability of occurrence. Usually the largest reasonably conceivable event. MCE sometimes also used to denote maximum credible earthquake, although this term is not favored now. Moment magnitude (MW) — The moment magnitude MW of an earthquake is proportional to the logarithm of the seismic moment M0. M0 is a measure of the energy released and is related to the physical characteristics of the causative fault rupture. Rayleigh damping — In finite element analysis, the Rayleigh damping matrix [D] is proportional to the mass matrix [M] and stiffness matrix [K] of a flexible system, and is typically expressed by the formulation [D] = a[M] + b[K], where a and b are two constants. Reservoir-triggered earthquake (RTE) — The maximum level of ground motion capable of being induced at a dam site by the filling, drawdown or simple presence of the reservoir. Consideration of the RTE is generally limited to dams higher than 300 ft. Reservoir-triggered seismicity — Seismic activity potentially caused by the filling of a large reservoir. Response spectrum — A plot of the maximum values of acceleration, velocity, and displacement response of an infinite series of single-degree-of-freedom systems subject to a time-dependent
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dynamic excitation. The maximum response values are expressed as a function of the undamped natural period of each system, for a specified viscous damping coefficient. Spillway — A channel, pipe, tunnel, or overflow or gated concrete structure intended to evacuate excess flood flows and prevent overtopping of the dam. Tailings dam — A dam primarily intended to store solid waste (tailings) from mining operations. The dam may either be a conventional structure, behind which tailings are impounded, or be built from the tailings themselves, using hydraulic fill construction methods. Thrust fault — A fault along which relative movement of the overhanging side of the fault occurs upward (reverse displacement), and primarily due to a compressive tectonic stress regime. Unbalanced free-field boundary condition — In a two-dimensional finite element model, this condition corresponds to non-symmetric absorbing lateral boundary conditions for the free-field condition, e.g., as implemented in the computer program SuperFLUSH. This assumption differs from those used in the computer programs LUSH and FLUSH, where the left and right boundary conditions are identical, due to the simplifying assumption of horizontal soil layers for the freefield condition. The unbalanced free-field condition was developed to analyze structures embedded in embankment dams, the geometry of which significantly differs from a horizontally layered system. Waterstop — Designates a flat sheet of metal or PVC placed across a joint in a concrete dam to prevent leakage through the joint.
References Allen, C.R. and Cluff, L.S. 2000. “Active Faults in Dam Foundations: An Update,” Proc. 12th World Conference on Earthquake Engineering, January 29–February 5, Auckland, New Zealand, Vol. II, paper no. 2490, Earthquake Engineering Research Institute, Oakland, CA. American Concrete Institute. 1987. “Mass concrete. ACI 207.1,” American Concrete Institute, Detroit, MI. American Concrete Institute. 2002. “Building Code Requirements for Reinforced Concrete,” ACI Standard 318-02, American Concrete Institute, Detroit, MI. Anderson, R.J., Martin, P.P., and Wagner, C.D. 1996. “A Comparison of the Predictions of Tellico Dam’s Seismic Response by Simplified and Advanced Methods of Analysis,” Proc. 16th Annual USCOLD Lecture Series, Los Angeles, July 22–26, pp. 31–47. Aubry, D., Hujeux, J.C., Lassoudière, F., and Meimon, Y., Eds. 1982. “A Double Memory Model with Multiple Mechanisms for Cyclic Soil Behavior,” in International Symposium on Numerical Methods in Geomechanics, Zurich, A.A. Balkema, Rotterdam, pp. 3–13. Babbitt, D.H. and Verigin, S.W. 1996. “General Approach to Seismic Stability of Embankment Dams,” in Earthquake Engineering for Dams, Western Regional Technical Seminar, Association of State Dam Safety Officials (ASDSO), April 11–12, Sacramento, pp. 197–211. Bathe, K.J. 1978. “ADINA/BM: A General Computer Program for Nonlinear Analysis of Mines Structures,” Final report to Office of Assistant-Director of Mining, U.S. Department of the Interior, Contract no. 30255008. Beikae, M. 1996. “A Seismic Displacement Analysis Technique for Embankment Dams,” Proc. 16th Annual USCOLD Lecture Series, Los Angeles, July 22–26, pp. 91–109. Bolt, B.A. 1996. “The Joint Synthesis of Seismic Acceleration, Velocity and Displacement,” in Earthquake Engineering for Dams, Western Regional Technical Seminar, Association of State Dam Safety Officials, April 11–12, Sacramento, pp. 68–86. Bozovic, A. and Markovic, M. 1999. Neotectonics and Dams: Guidelines, Committee on Seismic Aspects of Dam Design, International Committee on Large Dams (ICOLD), Paris, France. Brand, B. 1993. “FERC’s Evolving Policy on Three-Dimensional Stability Analysis of Concrete Gravity Dams,” in Proc. WaterPower ’93, pp. 821–830. Bu, S. 2001. “Seismic Evaluation of Concrete Gravity Dams Using FLAC,” Proc. Second International FLAC Symposium, Lyon-Ecully, France. © 2003 by CRC Press LLC
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Bureau, G. 1985. “Seismic Safety and Rehabilitation of Dam Inlet/Outlet Structures,” 15th International Congress on Large Dams, Lausanne, Switzerland, Q. 59, R. 17. Bureau, G. 1993a. “Seismic Safety Evaluation of Priest Dam, California,” Proc. International Workshop on Dam Safety Evaluation, Grindelwald, Switzerland, April 26–28, Vol. 2, pp. 149–160. Bureau, G. 1993b. “Seismic Safety of Intake/Outlet Towers,” Proc. International Workshop on Dam Safety Evaluation, Grindelwald, Switzerland, April 26–28, Vol. 2, pp. 1229–1240. Bureau, G. 1996a. “Assessment of Conventional and Advanced Procedures for Seismic Safety Evaluation of Concrete Gravity Dams,” USCOLD Annual Lecture, July 22–26, Los Angeles, CA. Bureau, G. 1996b. “Numerical Analysis and Seismic Safety Evaluation of Embankment Dams,” Invited lecture, Boston Society of Civil Engineers Section of American Society of Civil Engineers, “Dam Inspection, Analysis, and Rehabilitation Seminar,” November 2, Waltham, MA, 54 pp. Bureau, G. 1997. “Evaluation Methods and Acceptability of Seismic Deformations in Embankment Dams,” 29th International Congress on Large Dams (ICOLD), Florence, Italy, May, Q. 73, R. 11, pp. 175–200. Bureau, G. and Ballentine, G.D. 2002. “A Comprehensive Seismic Vulnerability and Loss Assessment of the State of South Carolina Using HAZUS. Part VI. Dam Inventory and Vulnerability Assessment Methodology,” 7th National Conference on Earthquake Engineering, July 21–25, Boston, Earthquake Engineering Research Institute, Oakland, CA. Bureau, G.J. and Scawthorn, C. 1986. “Seismic Reevaluation of Lower Crystal Springs Outlet System,” in Seismic Evaluation of Lifeline Systems: Case Studies, Proceedings of a session sponsored by the Technical Council on Lifeline Earthquake Engineering of the American Society of Civil Engineers, Boston, October 27. Wang, L.R.L and Whitman, R.V., Eds., American Society of Civil Engineers, New York. Bureau, G. and Ghanaat, Y. 2000. “Seismic Evaluation of a Historic Curved Gravity Dam,” Proc. Dam Safety 2000 Conference, Providence, RI, September 26–29, Association of State Dam Safety Officials (ASDSO). Bureau, G. and Udaka, T. 1982. “Seismic Interaction of Control Towers Embedded in Embankment Dams,” 8th European Conference on Earthquake Engineering, September, Athens, Greece, Vol. 6, pp. 83–90. Bureau, G., Edwards, A., and Blümel, A.S. 1994. “Seismic Design of Stage IV Raising, Los Leones Dam, Chile,” Proc. 11th Association of State Dam Safety Officials (ASDSO) Conference, Boston, September, Suppl., pp. 77–86. Bureau, G., Inel, S., Davis, C.A., and Roth, W.H. 1996. “Seismic Response of Los Angeles Dam, During the 1994 Northridge Earthquake,” Proc. USCOLD Annual Meeting, Los Angeles, July 22–26, pp. 281–295. Bureau, G., Volpe, R.L., Roth, W.R., and Udaka, T. 1985. “Seismic Analysis of Concrete Face Rockfill Dams,” in Concrete Face Rockfill Dams: Design, Construction and Performance, ASCE International Symposium on CFRDs, Detroit, Oct. 21, pp. 479–508, American Society of Civil Engineers, New York. Bureau, G., Volpe, R.L., Roth, W.R., and Udaka, T. 1987. “Seismic Analysis of Concrete Face Rockfill Dams,” Closure, ASCE J. Geotechnical Eng. Div., 113(October), 10, pp. 1255–1264. Castro, G. et al. 1987. “On the Behavior of Soils during Earthquakes: Liquefaction,” in Soil Dynamics and Liquefaction, Cakmak, A.S., Ed., Elsevier, Amsterdam, pp. 169–204. Castro, G. et al. 1989. “Re-Evaluation of the Lower San Fernando Dam. Report 1: An Investigation of the February 9, 1971 Slide,” Report no. GL-89–2, U.S. Army Corps of Engineers, Waterways Experiment Station, Vicksburg, MS. Chavez, J.W. and Fenves, G.L. 1993. “Earthquake Analysis and Response of Gravity Dams Including Base Sliding,” EERC Report no. UCB/EERC-93–07, December, Earthquake Engineering Research Center, University of California, Berkeley.
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Chopra, A.K. 1988. “Earthquake Response Analysis of Concrete Dams,” in Advanced Dam Engineering for Design, Construction and Rehabilitation, Jensen, R.B., Ed., Van Nostrand Reinhold, New York, pp. 416–465. Chopra, A.K. and Fok, K.L. 1984. “Evaluation of Simplified Earthquake Analysis Procedures for IntakeOutlet Towers,” 8th World Conference on Earthquake Engineering, July, San Francisco, Vol. 7, Earthquake Engineering Research Institute, Oakland, CA, pp. 467–474. Chopra, A.K. and Liaw, C.Y. 1975. “Earthquake-Resistant Design of Inlet-Outlet Towers,” ASCE J. Structural Division, 101 (ST7), 1349–1366. Civil Systems, Inc. 1980. “SuperFLUSH,” User’s manual, Vols. I to III, report to Kozo Keikaku Engineering, Inc., Tokyo, October. Clough, R.W. and Ghanaat, Y. 1993. “Concrete Dams: Evaluation for Seismic Loading,” Proc. International Workshop on Dam Safety Evaluation, April 26–28, Grindelwald, Switzerland, Vol. 4, pp. 137–167. Clough, R.W. and Niwa, A. 1982. “Earthquake Simulator Research on Arch Dam Models,” in Dynamic Modeling of Concrete Structures, SP 73–5, American Concrete Institute, Detroit, pages 83–105. Coyne and Bellier/ECP/EDF-REAL 1991. “GEFDYN, a Computer Program for Geomechanics Finite Element Analysis: Two/Three-Dimensional Quasi-Static/Dynamic Coupled Mechanical-Hydraulics Software for Nonlinear Geomaterials Analysis, Paris, February. Cundall, P.E. 1976. “Explicit Finite-Difference Methods in Geomechanics,” 2nd International Conference on Numerical Methods in Geomechanics, Blacksburg, VA, June. Dames and Moore. 1991. “Stability Evaluation: South Haiwee Dam, Inyo County,” Report to Los Angeles Department of Water and Power, July. Davis, C.A. and Sakado, M.M. 1994. “Response of the Van Norman Complex to the Northridge Earthquake,” Proc. 11th Association of State Dam Safety Officials Conference, Boston, September, pp. 241–255. Dawson, E.M., Roth, W.H., Nesarajah, S., Bureau, G., and Davis, C.A. 2001. “A Practice-Oriented PorePressure Generation Model,” Proc. 2nd International FLAC Symposium, October, Lyon-Ecully, France, Itasca Consulting Group, Minneapolis, MN. Duncan, J.M., Seed, R.B., Wong, K.S., and Ozawa, Y. 1984. “FEADAM84: A Computer Program for Finite Element Analysis of Dams,” Geotechnical Engineering Research Report no. SU/GT/84–03, Department of Civil Engineering, Stanford University, Stanford, CA, November. Dungar, R. and Jackson, E.A. 1975. “The Seismic Analysis of the Bellmouth Spillway and Valve Tower for an Earth Dam,” in Numerical Analysis of Dams, Naylor, Stagg and Zienkiewicz, Eds., pp. 604–624. Electric Power Research Institute (EPRI). 1992. “Uplift Pressures, Shear Strengths, and Tensile Strengths for Stability Analysis of Concrete Gravity Dams,” Report no. EPRI TR–100345, Electric Power Research Institute, Palo Alto, CA. Elgamal, A.M., Abdel-Ghaffar, A.M., and Prevost, J.H. 1984. “Nonlinear Earthquake-Response Analysis of Earth Dams,” Report no. 84-SM-14, December, Princeton University, Princeton, NJ. Federal Energy Regulatory Commission (FERC). 2000. “Engineering Guidelines for the Evaluation of Hydropower Projects,” Office of Hydropower Licensing, Washington, D.C., June 2000 Peer Review Copy. Fenves, G. and Chopra, A.K. 1984. “EAGD-84: A Computer Program for Earthquake Analysis of Concrete Gravity Dams,” Report no. UCB/EERC–84–11, August, Earthquake Engineering Research Center, University of California, Berkeley. Fenves, G.L., Mojtahedi, S., and Reimer, R.B. 1989. “ADAP-88: A Computer Program for Static and Dynamic Analysis of Arch Dams,” Report no. UCB/EERC–89/12, November, Earthquake Engineering Research Center, University of California, Berkeley. Finn, W.D.L. 1991. “Estimating How Embankment Dams Behave during Earthquakes,” Water Power and Dam Construction, London, April, pp. 17–22. Finn, W.D.L. and Yogendrakumar, M. 1989. “TARA 3-FL: Program for Analysis of Liquefaction-Induced Flow Liquefaction,” University of British Columbia, Vancouver, Canada.
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Finn, W.D.L., Gillon, M.D., Yogendrakumar, M., and Newton, C.J. 1992. “Simulating the Seismic Response of a Rockfill Dam,” Proc. NUMOG-4, A.A. Balkema, Rotterdam, pp. 379–391. Fok, K.L., Hall, J.F., and Chopra, A.K. 1986. “EACD-3D User’s Manual,” Department of Civil Engineering, University of California, Berkeley; “Hydrodynamic and Foundation Flexibility Effects in Earthquake Response of Arch Dams,” ASCE J. Struct. Eng., 112 (no. 8), 1810–1828. Forrest, M., Bureau, G., Lazarte, C., and Hutchings, S. 2000. “Seismic Rehabilitation of Weber Dam,” Proc. Association of State Dam Safety Officials (ASDSO) 2000 West Region Annual Conference and Technical Seminar, Portland, OR, May 15–19, pp. 289–300. Ghanaat, Y. and Clough, R.W. 1989. “EADAP: Enhanced Arch Dam Analysis Program,” Report no. UCB/ EERC–89–07, November, Earthquake Engineering Research Center, University of California, Berkeley. Goyal, A. and Chopra, A.K. 1989. “Earthquake Analysis and Response of Intake-Outlet Towers,” Report no. UCB/EERC–89/04, July, Earthquake Engineering Research Center, University of California, Berkeley. Gupta, H.K. and Rastogi, B.K. 1976. Dams and Earthquakes, Elsevier, Amsterdam. Hall, J.F. 1997. “Efficient Numerical Analysis of Arch Dams: User’s Manual for SCADA — Smeared Crack Arch Dam Analysis,” Report no. EERL-96-01, Earthquake Engineering Research Laboratory, California Institute of Technology, Pasadena, CA. Hall, R.L., Chowdhury, M.R., and Matheu, E.E. 2001. “Seismic Testing of a 1/20-Scale 2D Model of Koyna Dam,” in Wind and Seismic Effects, Proc. 32nd Joint Meeting U.S.–Japan Cooperative Program in Natural Resources Panel on Wind and Seismic Effects, April, NIST SP 963, National Institute of Standards and Technology, Gaithersburg, MD, pp. 131–140. Harris, D.W. 1986. “Dynamic Effective Stress Finite Element Analysis of Dams Subjected to Liquefaction,” Report REC–ERC–86–4, Embankment Dams Branch, Division of Dam and Waterway Design, Engineering and Research Center, U.S. Department of the Interior, Bureau of Reclamation, Denver, CO, December. Harza Engineering Company. 1997. “Criteria Evaluation Memorandum, Big Tujunga Dam Reanalysis Study,” Unpublished memorandum, prepared for Los Angeles County Department of Public Works, January. Hatton, J.W., Foster, P.F., and Thomson, R. 1991. “The Influence of Foundation Conditions on the Design of Clyde Dam,” Proc. 17th International Congress on Large Dams, Vienna, Austria, Q. 66, R. 10, vol. III, pp. 157–178. Hudson, M., Idriss, I.M., and Beikae, M. 1994. “QUAD4M: A Computer Program to Evaluate the Seismic Response of Soil Structures Using Finite Element Procedures and Incorporating a Compliant Base,” May, Department of Civil and Environmental Engineering, University of California, Davis. ICOLD (International Committee on Large Dams). 1988. “Inspection of Dams Following Earthquakes: Guidelines,” Bulletin 62. ICOLD (International Committee on Large Dams). 1992. “Third Benchmark Workshop on Numerical Analysis of Dams,” Bergamo, Italy, International Committee on Large Dams and Italian Committee on Large Dams. ICOLD (International Committee on Large Dams). 1994. “Fourth Benchmark Workshop on Numerical Analysis of Dams,” Paris, France, International Committee on Large Dams and French Committee on Large Dams. ICOLD (International Committee on Large Dams). 1999. “Fifth Benchmark Workshop on Numerical Analysis of Dams,” June 2–5, Denver, CO, International Committee on Large Dams, Bureau of Reclamation and U.S. Committee on Large Dams. Idriss, I.M. 1999. “An Update of the Seed-Idriss Procedure for Evaluating Liquefaction Potential,” Proc. TRB Workshop on New Approaches in Liquefaction Analysis, Washington, D.C., January 10. Idriss, I.M. and Sun, J.I. 1992. “User’s Manual for SHAKE91,” November, Department of Civil and Environmental Engineering, University of California, Davis.
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Inel, S., Roth, W.H., and De Rubertis, C. 1993. “Nonlinear Dynamic Effective-Stress Analysis of Two Case Histories,” Session on Geotechnical Aspects of Recent Earthquakes, Proc. 3rd International Conference on Case Histories in Geotechnical Engineering, St. Louis, MO, June 1–6. Itasca Consulting Group. 1992. FLAC: Fast Lagrangian Analysis of Continua. vol. I. User's Manual; vol. II. Verification Problems and Example Applications, Itasca Consulting Group, Minneapolis, MN. Janbu, N. 1963. “Soil Compressibility as Determined by Oedometer and Triaxial Tests,” Proc. European Conference on Soil Mechanics and Foundation Engineering, Wiesbaden, Germany, vol. 1, pp. 19–26. Jansen, R.B. 1987. “The Concrete Face Rockfill Dam. Performance of Cogoti Dam under Seismic Loading,” Discussion of a paper presented at ASCE Symposium on Concrete Face Rockfill Dams, ASCE J. Geotech. Eng. Div., 113 (no. 10), 1135–1136. Kuo, J.S.H. 1982. “Fluid-Structure Interactions: Added Mass Computations for Incompressible Fluid,” Report no. UBC/EERC–82/09, Report to National Science Foundation, August, University of California, Berkeley. Leclerc, M., Léger, P., and Tinawi, R. 2002. “CADAM, User’s Manual Version 1.4.3,” Ecole Polytechnique de Montreal, Canada. Léger, P. et al. 1997. “Failure Mechanisms of Gravity Dams Subjected to Hydrostatic Overload: Influence of Weak Lift Joints,” Proc. 19th International Congress on Large Dams, Florence, Italy, Q.75, R.2, vol. IV, pp. 11–37. Lysmer, J., Udaka, T., Tsai, C.-F., and Seed, H.B. 1975. “FLUSH: A Computer Program for Approximate 3-D Analysis of Soil-Structure Interaction Problems,” Report no. EERC 75–30, November, Earthquake Engineering Research Center, University of California, Berkeley. Makdisi, F. and Seed, H.B. 1977. “A Simplified Procedure for Estimating Earthquake-Induced Deformations in Dams and Embankments,” EERC Report no. UCB/EERC–77/19, Earthquake Engineering Research Center, University of California, Berkeley. Martin, G.R., Finn, W.D.L., and Seed, H.B. 1975. “Fundamentals of Liquefaction under Cyclic Loading,” ASCE J. Geotech. Eng. Div., 101 (no. GT5), 423–438. Martin, P.P. and Niznik, J.A. 1993. “Prediction of Static and Dynamic Deformation Response of Blue Ridge Dam, Georgia, U.S.A.,” Proc. International Workshop on Dam Safety Evaluation, April 26–28, Grindelwald, Switzerland, vol. 2, pp. 133–147. Martin, P.P. and Seed, H.B. 1978. “Apollo: A Computer Program for the Analysis of Pressure Generation and Dissipation in Horizontal Sand Layers During Cyclic or Earthquake Loading,” Report no. UCB/EERC 78–21, Earthquake Engineering Research Center, University of California, Berkeley. Martin, P.P., Niznik, J.A., Kleiner, D.E., and Wagner, C.D. 1994. “TVA’s Seismic Safety Assessment Program of Its Embankment Dams,” 18th International Congress on Large Dams, Durban, South Africa, Question 68. Mejia, L.H. and Seed, H.B. 1983. “Comparison of 2-D and 3-D Dynamic Analysis of Earth Dams,” ASCE J. Geotech. Eng., 109 (no. GT11), 1383–1398. Mejia, L.H., Gillon, M., Freeman, S., and Berryman, K. 1997. “Design Criteria for Fault Rupture at the Matahina Dam, New Zealand,” Int. J. Hydropower Dams, 4 (2), 120–123. Moriwaki, Y., Beikae, M., and Idriss, I.M. 1988. “Nonlinear Analysis of the Upper San Fernando Dam under the 1981 San Fernando Earthquake,” Proc. 9th World Conference on Earthquake Engineering, Tokyo and Kyoto, Japan, vol. III, Earthquake Engineering Research Institute, Oakland, CA, and Japanese Meteorological Agency, Tokyo, Japan, pp. 237–241. Newmark, N.M. 1965. “Effects of Earthquakes on Dams and Embankments, Rankine Lecture,” Géotechnique 15 (2), 139–160. Ostrom, D.K. and Kelly, T.A. 1977. “Method for Dynamic Testing of Dams,” ASCE J. Power Div., 103 (no. P01), 27–36. Pacelli, W.A., Andriolo, F.R., and Sarkaria, G.S. 1993. “Treatment and Performance of Construction Joints in Concrete Dams,” Int. Water Power Dam Construction, 45 (11), 26–31.
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Prevost, J.H. 1981. “DYNAFLOW: A Nonlinear Transient Finite Element Analysis Program,” Princeton University, Princeton, NJ. QUEST Structures. 1993. “GDAP: Graphics-Based Dam Analysis Program — User’s Manual,” March, prepared for U.S. Army Corps of Engineers, Vicksburg, MS. Raphael, J.M. 1984. “Tensile Strength of Concrete,” ACI J. Technical Paper No. 81–17, (March-April), 158–165. Romo, M.P. and Resendiz, D. 1981. “Computed and Observed Deformations of Two Embankment Dams under Earthquake Loading,” in Dams and Earthquakes, Proceedings, Paper 30, Institute of Civil Engineers, London, Thomas Telford, London, pp. 267–274. Roth, W.H., Bureau, G., and Brodt, G. 1991. “Pleasant Valley Dam: An Approach to Quantifying the Effect of Foundation Liquefaction,” Proc. 17th International Congress on Large Dams, Vienna, June, pp. 1199–1223. Roth, W.H., Scott, R.F., and Cundall, P.A. 1986. “Nonlinear Dynamic Analysis of a Centrifuge Model Embankment,” 3rd U.S. National Conference on Earthquake Engineering, August 24–28, Charleston, SC, vol. I, Earthquake Engineering Research Institute, Oakland, CA, pp. 506–516. Seed, H.B. 1983. “Earthquake-Resistant Design of Earth Dams,” Proc. ASCE Symposium on Seismic Design of Embankments and Caverns, ASCE National Convention, Philadelphia, May 16–20, pp. 41–64, American Society of Civil Engineers, New York. Seed, H.B. 1987. “Design Problems in Soil Liquefaction,” ASCE J. Geotech. Eng., 113 (8), 827–845. Seed, H.B. and Idriss, I.M. 1970a. “Soil Moduli and Damping Factors for Dynamic Response Analysis,” Report no. EERC/70–10, December, Earthquake Engineering Research Center, University of California, Berkeley. Seed, H.B. and Idriss, I.M. 1970b. “A Simplified Procedure for Evaluating Soil Liquefaction Potential,” Report no. EERC 70–9, Earthquake Engineering Research Center, University of California, Berkeley. Seed, H.B. and Idriss, I.M. 1982. “Ground Motions and Soil Liquefaction During Earthquakes,” Monograph Series, Earthquake Engineering Research Institute, Berkeley, CA. Seed, H.B., Idriss, I.M., and Arango, I. 1983. “Evaluation of Liquefaction Potential Using Field Performance Data,” ASCE J. Geotech. Eng., 109 (3), 458–482. Seed, R.B. 1999. “Engineering Evaluation of Post-Liquefaction Residual Strength,” in New Approaches in Liquefaction Analyses, Proc. TRB Workshop, January 10, Washington, D.C. Seed, R.B. and Harder, L.F. Jr. 1990. “SPT-Based Analysis of Cyclic Pore Pressure Generation and Undrained Residual Strength,” Proc. H. Bolton Seed Memorial Symposium, vol. 2, BiTech Publishers, Canada, May. Serff, N., Seed, H.B., Makdisi, F.I., and Chang, C.K. 1976. “Earthquake-Induced Deformations of Earth Dams,” EERC Report no. EERC/76–4, Earthquake Engineering Research Center, University of California, Berkeley. Sherard, J.L., Cluff, L.S., and Allen, C.R. 1974. “Potentially Active Faults in Dam Foundations,” Géotechnique, 24 (3), 367–428. Siegel, R.A. 1975. “Computer Analysis of General Slope Stability Problems; STABL User’s Manual,” Joint Highway Research Project, Report No. JHRP-75-8, Project No. C-36-36K, File No. 6-14-11, Purdue University, Lafayette, IN, June. Somerville, P.G. and Graves, R.W. 1996. “Strong Ground Motions of the Kobe, Japan Earthquake of January 17, 1995, and Development of a Model of Forward Rupture Directivity Effects Applicable in California,” Proc. Association of State Dam Safety Officials Western Regional Technical Seminar, April 11–12, Sacramento, pp. 89–108. Somerville, P.G., Smith, N.F., Graves, R.W., and Abrahamson, N.A. 1995. “Accounting for Near-Fault Rupture Directivity Effects in the Development of Design Ground Motions,” Proc. ASME/SSME Conference, Hawaii, July, American Society of Mechanical Engineers, New York. Swaisgood, J.R. 1995. “Estimating Deformation of Embankment Dams Caused by Earthquakes,” Association of State Dam Safety Officials Western Regional Conference, Red Lodge, MT, May 22–25.
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Swaisgood, J.R. 1998. “Seismically-Induced Deformations of Embankment Dams,” 6th U.S. National Conference on Earthquake Engineering, June, Seattle, WA, Earthquake Engineering Research Institute, Oakland, CA. Swanson Analysis Systems, Inc. 1970. “ANSYS,” Houston, PA. Tarbox, G.S., Dreher, K.J., and Carpenter, L.R. 1979. “Seismic Analysis of Concrete Dams,” Thirteenth International Congress on Large Dams, New Delhi, Q. 51, R. 11, pp. 963–994. Tokimatsu, K. and Yoshimi, Y. 1983. “Empirical Correlation of Soil Liquefaction Based on SPT N-Value and Fines Content,” Soils and Foundations, 23 (4), 56–74. Uniform Building Code. 1997. With State of California Amendments, International Conference of Building Officials, Whittier, CA. URS Corporation. 2002. “Magalia Dam and Reservoir, Feasibility Study to Modify Restricted Reservoir Level,” Report to Paradise Irrigation District, January, Paradise, CA. URS Corporation et al. 2002. “Comprehensive Seismic Risk and Vulnerability Study for the State of South Carolina,” Report to the South Carolina Emergency Preparedness Division and HAZUS-Compatible CD. U.S. Army Corps of Engineers. 1989. National Inventory of Dams (NID), April 2000 update, U.S. Army Corps of Engineers, Washington, D.C. U.S. Bureau of Reclamation. 1983. “Safety Evaluation of Existing Dams” (SEED Manual), U.S. Department of the Interior, Denver, CO. U.S. Bureau of Reclamation. 1997. “Guidelines for Achieving Public Protection in Dam Safety DecisionMaking,” April, Denver, CO. USCOLD (U.S. Committee on Large Dams). 1984. “Bibliography on Performance of Dams during Earthquakes,” compiled by Philip Gregory, University of California, Berkeley. USCOLD (U.S. Committee on Large Dams). 1986. “Bibliography on Reservoir-Induced Seismicity.” Committee on Earthquakes, December, Denver, CO. USCOLD (U.S. Committee on Large Dams). 1989. “Strong Motion Instruments at Dams: Guidelines for their Selection, Installation, Operation and Maintenance,” U.S. Committee on Large Dams, Denver, CO. USCOLD (U.S. Committee on Large Dams). 1992a. “Directory of Computer Programs in Use for Dam Engineering in the United States,” Committee on Methods of Numerical Analysis of Dams, March, Denver, CO. USCOLD (U.S. Committee on Large Dams). 1992b. “Observed Performance of Dams during Earthquakes,” Committee on Earthquakes, July, Denver, CO. USCOLD (U.S. Committee on Large Dams). 1995. “Guidelines for Earthquake Design and Evaluation of Structures Appurtenant to Dams,” Committee on Earthquakes, May, Denver, CO. USCOLD (U.S. Committee on Large Dams). 1997. “Reservoir Triggered Seismicity,” Committee on Earthquakes, April, Denver, CO. USCOLD (U.S. Committee on Large Dams). 1999. “Updated Guidelines for Selecting Seismic Parameters for Dam Projects,” Committee on Earthquakes, April, Denver, CO. USCOLD (U.S. Committee on Large Dams). 2000. “Observed Performance of Dams during Earthquakes,” vol. II, Committee on Earthquakes, October, Denver, CO. Vaid, Y.P. and Thomas, J. 1994. “Post-Earthquake Liquefaction Behavior of Sand,” Proc. 13th International Conference on Soil Mechanics and Foundation Engineering, New Delhi, India. Von Thun, L. and Harris, C.W. 1981. “Estimation of Displacements of Rockfill Dams Due to Seismic Shaking,” Proc. International Conference on Recent Advances in Geotechnical Engineering and Soil Dynamics, St. Louis, MO, April 26–May 3, vol. I, pp. 417–423. Vrymoed, J.L. 1996. “Seismic Safety Evaluation of Two Earth Dams,” in Earthquake Engineering for Dams, Proc. Western Regional Technical Seminar, Association of State Dam Safety Officials, April 11–12, Sacramento, Association of State Dam Safety Officials, Lexington, KY, pp. 215–234.
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Wall, J.S. et al. 1986. “Testing of Bond between Fresh and Hardened Concrete,” Proc. RILEM and LCPC International Symposium on Adhesion between Polymers and Concrete, Aix-en-Provence, France, September 16–19, Chapman & Hall, London, pp. 335–344. Westergaard, H.M. 1933. “Water Pressures on Dams during Earthquakes,” Trans. ASCE, 98(paper no. 1835), 418–472. Wilson, E.L. and Abibullah, A. 1988. “SAP90: A Series of Computer Programs for the Static and Dynamic Finite Element Analysis of Structures,” Computers and Structures, Inc., Berkeley, CA. Wright, S.G. 1992. “UTEXAS3 Version 1.2, a Computer Program for Slope Stability Calculations,” Shinoak Software, Austin, TX.
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27 Port Structures 27.1 Introduction 27.2 Seismic Response of Port Structures Gravity Quay Walls · Anchored Sheet Pile Walls · Pile-Supported Wharf · Gantry Cranes · Breakwaters
27.3 Current Seismic Provisions for Port Structures Technical Standards for Ports and Harbor Facilities in Japan · U.S. Navy Seismic Design Guidelines · Seismic Guidelines for Ports, American Society of Civil Engineers–Technical Council on Lifeline Earthquake Engineering (ASCE–TCLEE), Ports Committee · European Prestandard, Eurocode 8 Design Provisions for Earthquake Resistance of Structures
27.4 Seismic Performance-Based Design 27.5 Seismic Performance Evaluation and Analysis 27.6 Methods for Analysis of Retaining/Earth Structures Simplified Analysis · Simplified Dynamic Analysis · Dynamic Analysis
27.7 Analysis Methods for Open Pile/Frame Structures
Susumu Iai Port and Airport Research Institute Yokosuka, Japan
Simplified Analysis · Simplified Dynamic Analysis · Dynamic Analysis
References Further Reading
27.1 Introduction This chapter deals with the seismic performance and design of port structures. Typical port structures are shown in Figure 27.1. Port structures have sustained major to catastrophic damage in a number of earthquakes during the past few decades. This damage is not only costly in itself, but represents a major impact on the regional economy, for which the port is the “doorway.” Figures 27.2 to 27.8 illustrate port damage from earthquakes in Chile and Japan, for example.
27.2 Seismic Response of Port Structures Following is a summary of modes of earthquake damage and deformation/failure for typical port structures.
27.2.1 Gravity Quay Walls A gravity quay wall is made of a caisson or other rigid wall put on the seabed, and maintains its stability through friction at the bottom of the wall. Typical failure modes during earthquakes involve seaward displacement, settlement, and tilt. For a quay wall constructed on a firm foundation, an increase in earth
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FIGURE 27.1 Typical port structures. (From PIANC. 2001. Seismic Design Guidelines for Port Structures, A.A. Balkema, Rotterdam. With permission.)
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FIGURE 27.2 Collapse of crane due to quay failure, 1985 M 7.8 Chile earthquake. (Courtesy EQE International)
FIGURE 27.3 Destruction of Port of Aonae due to tsunami, Okushiri Island, 1993 M 7.8 Hokkaid Nansei (Japan) earthquake. (Photo: C. Scawthorn)
pressure from the backfill plus the effect of an inertia force on the body of the wall result in the seaward movement of the wall, as shown in Figure 27.9(a). If the width-to-height ratio of the wall is small, tilt may also be involved. Case histories for gravity quay walls subjected to earthquake shaking often belong in this category. When the subsoil below the gravity wall is loose and excess pore water pressure increases in the subsoil, however, the movement of the wall is associated with significant deformation in the foundation soil, resulting in a large seaward movement involving tilt and settlement, as shown in Figure 27.9(b). The latter mode of failure is also shown in Figure 27.10, and has received wide attention since the Kobe, Japan earthquake of 1995. © 2003 by CRC Press LLC
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FIGURE 27.4 Damage to container quay and gantry crane, Port of Kobe, 1995 MW 6.9 Hanshin earthquake. (Photo: C. Scawthorn)
27.2.2 Anchored Sheet Pile Walls An anchored sheet pile wall is composed of a wall, anchors, and tie-rods. Each structural component contributes to the stability of the whole structure. In the ultimate state of stability, it should be decided whether the wall or the anchor should be the first to yield. Excessive displacements of the anchor are undesirable. A small movement of the anchor, however, contributes to reducing the tension in the tierods and the bending moment in the wall. Well-balanced response of the wall and anchor is essential for achieving a reasonable performance of the anchored sheet pile wall during earthquakes. A variety of geotechnical conditions can result in a variety of failure modes of an anchored sheet pile wall. In particular, three failure modes may be identified, depending on the extent of loose, saturated sandy soils relative to the position and geometry of the wall. If the deformation of a loose deposit mainly affects the stability of anchors as shown in Figure 27.11(a), the anchors will move toward the sea, resulting in the seaward movement of the wall. This mode of deformation/failure has been the most frequently
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FIGURE 27.5 Detail of Figure 27.4. (Photo: C. Scawthorn)
FIGURE 27.6 Detail of Figure 27.4. (Photo: C. Scawthorn)
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FIGURE 27.7 Failure of crane boom due to excessive accelerations, Port of Kobe, 1995 MW 6.9 Hanshin earthquake. (Courtesy EQE International)
FIGURE 27.8 Failure of crane booms due to excessive accelerations, Port of Kobe, 1995 MW 6.9 Hanshin earthquake. (Courtesy EQE International)
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(a) On firm foundation
Loose sandy foundation
(b) On loose sandy foundation
FIGURE 27.9 Cross section of caisson quay wall at Port of Kobe. (From PIANC. 2001. Seismic Design Guidelines for Port Structures, A.A. Balkema, Rotterdam. With permission.)
observed at waterfronts. If the deformation of the loose deposit mainly affects the backfill of the wall as shown in Figure 27.11(b), the earth pressure increase will cause an excessively large bending moment in the wall, resulting in yielding of the wall. This mode of failure has also been observed during past earthquakes. If the deformation of the loose sandy deposit mainly affects the stability of the embedment portion of the wall, as shown in Figure 27.11(c), a gross instability of the wall at the embedment portion will exist. This mode of failure, however, can occur only when the anchor is strong and firmly embedded, and both the wall and tie-rods are very strong. In current design practice, the wall is assumed to be relatively firmly embedded, and thus is designed for a fraction of the bending moment induced at the free-earth support conditions. If the conditions shown in Figure 27.11(c) are met, yielding of the wall or failure of the anchor will most likely precede the instability of the embedment portion. This may be the reason why there has not been a case history that fits the failure mode shown in Figure 27.11(c).
27.2.3 Pile-Supported Wharf A pile-supported wharf is composed of a deck supported by a substructure consisting of piles and a dike, often simply called a wharf. Because the dike is sloped, the piles between the deck and the dike will have various unsupported lengths. Three causes of failure may be identified for a pile-supported wharf. For a wharf constructed on a firm foundation having a rigid and stable dike, the seismic inertia force on the deck will be the main cause of failure, as shown in Figure 27.12(a). The maximum bending moment © 2003 by CRC Press LLC
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1.5∼2.2
4.2∼5.2
e Lin ail ce Fa rane R C
ne
Cra
l
Rai
Ground surface after the earthquake
+4.0
3.0∼4.0
H.W.L.+1.7m L.W.L.±0.0m
Backfill Soil Concrete Caisson
Rubble Backfill
Compaction
−14.50 −18.50
Alluvial Clay Layer
Foundation Rubble Backfill Sand for Replacing Clay Layer −34.00~ −36.00
Sand Drain −33.00~ −35.00 Unit (m)
FIGURE 27.10 Deformation/failure modes of gravity quay walls. (From PIANC. 2001. Seismic Design Guidelines for Port Structures, A.A. Balkema, Rotterdam. With permission.)
occurs at the row of pile heads most landward because these piles have the shortest unsupported length. If there is an excessively large displacement at the top of the dike or the retaining structures, the deck will be pushed seaward, resulting in a similar mode of failure as shown in Figure 27.12(b). For a wharf constructed on a loose foundation, the displacement in the dike will directly push the piles seaward, as shown in Figure 27.12(c). The first cause of failure has been well taken into account in conventional seismic design of pile-supported wharves. Increasing attention has been directed toward the effect of displacement of dikes on pile-supported wharves since the Loma Prieta, CA earthquake of 1989, where this behavior was observed at the Port of Oakland. The Kobe, Japan earthquake of 1995 again demonstrated the importance of this mode.
27.2.4 Gantry Cranes A crane consists of an upper structure for handling cargo and a supporting structure for holding in place and transporting the upper structure, as shown in Figure 27.13. The crane is generally made of a steel frame. The supporting structure is either of the rigid frame type or hinged leg type, with supporting structure resting on rails through the wheels. A crane at rest is fixed to rails or to a quay wall with clamps or anchors, whose strength provides the upper limit for the crane resistance against external forces. However, clamps or anchors do not support a crane in operation, and the lateral resistance of the crane against external forces is from friction and from the wheel flanges. Typical failure modes during earthquakes are derailment of wheels, detachment or pullout of vehicle, rupture of clamps and anchors, buckling, and overturning. As shown in Figure 27.13(a), widening of a span between the legs due to the deformation of the quay wall results in derailment or buckling of the legs. Conversely, as shown in Figure 27.13(b), narrowing of a leg span can also occur due to the rocking response of the crane. This is due to alternating action of the horizontal component of resisting forces from the quay wall during rockingtype response involving uplifting of one of the legs. Derailment and detachment of the wheel can also occur due to rocking. As shown in Figure 27.13(c), when differential settlement occurs on a quay wall below the crane, tilting or overturning of the crane may occur. If the crane has one-hinge type legs, the derailment can result in tilting and overturning of the crane, as shown in Figure 27.13(d). Though a clamp or anchor will provide more resistance to motion under the action of external forces, the internal stresses induced in the crane framework will become larger in comparison to the case with no clamp, thus allowing for rocking responses. Crane rails are often directly supported either by a portion of a © 2003 by CRC Press LLC
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(a) Deformation/failure at anchor
(b) Failure at sheet pile wall/tie-rod
(c) Failure at embedment
FIGURE 27.11 Deformation/failure modes of sheet pile quay walls. (From PIANC. 2001. Seismic Design Guidelines for Port Structures, A.A. Balkema, Rotterdam. With permission.)
retaining wall or by the deck of a pile-supported wharf. When the width of the gravity wall is small, or the quay wall is a sheet pile or cellular type, a separate foundation that often consists of piles is provided to support the rails. In order to achieve desirable seismic performance of quay walls with cranes, special consideration is required for the rail foundation, such as providing a dedicated and cross-tied upper structure to support the rails. © 2003 by CRC Press LLC
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(a) Deformation due to inertia force at deck
(b) Deformation due to horizontal force from retaining wall
Loose Subsoil
Firm Layer Firm Foundation (c) Deformation due to lateral displacement of loose subsoil
FIGURE 27.12 Deformation/failure modes of pile-supported wharves. (From PIANC. 2001. Seismic Design Guidelines for Port Structures, A.A. Balkema, Rotterdam. With permission.)
27.2.5 Breakwaters A breakwater is usually made of a rubble mound, a massive structure such as a caisson, or a combination of both placed on a seabed. Stability against a horizontal external load is maintained by shear resistance of rubble, friction at the bottom of the caisson, and with associated resistance to overturning and bearing © 2003 by CRC Press LLC
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FIGURE 27.13 Deformation modes of gantry cranes: (a) widening of span between the legs, (b) narrowing span between the legs due to rocking motion, (c) tilting of crane due to differential settlement of foundation, (d) overturning of one-hinged leg crane due to rocking/sliding. (From PIANC. 2001. Seismic Design Guidelines for Port Structures, A.A. Balkema, Rotterdam. With permission.)
capacity failure. Typical failure modes expected during earthquakes are shown in Figure 27.14. Breakwaters are generally designed to limit wave penetration and wave overtopping during specific design storms, and at the same time are designed to resist the related wave actions. It is unlikely that a major earthquake will occur simultaneously with the design sea state because the two events are typically not related. Consequently, design storm wave action and an earthquake can be treated as two independent load situations. Only wave actions from a moderate sea state should be considered together with the design earthquakes. Decision on this sea state has to be made based on the site-specific, long-term statistics of the storm. Selection of the appropriate design criteria depends on the functions of the breakwater and the type of earthquake-induced failure modes. However, for all breakwaters the main criterion is the © 2003 by CRC Press LLC
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FIGURE 27.14 Deformation/failure modes for breakwaters: (a) caisson resting on sea bed, (b) ‘vertically composite’ caisson breakwater, (c) ‘horizontally composite’ caisson breakwater, (d) rubble mound breakwater. (From PIANC. 2001. Seismic Design Guidelines for Port Structures, A.A. Balkema, Rotterdam. With permission.)
allowable settlement of the crest level because it determines the amount of overtopping and wave transmission. For breakwaters carrying roads and installations, additional criteria for allowable differential settlement, tilting, and displacement of superstructures and caissons are needed. Shaking of the breakwater may cause breakage of concrete armor units. Criteria have been proposed with regard to maximum breakage in terms of number of broken units that may occur while the breakwater remains
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serviceable [e.g., Zwamborn and Phelp, 1995]. The same criteria may be adopted for the earthquakerelated damage.
27.3 Current Seismic Provisions for Port Structures The following existing codes and guidelines used at various ports are reviewed with regard to their seismic design provisions.
27.3.1 Technical Standards for Ports and Harbor Facilities in Japan A dual-level approach is employed for structures of Special Class of Importance. However, the single-level approach is adopted for structures of Classes A, B, and C Importance. For structures of Special Class of Importance, the performance level is specified as follows [Ministry of Transport, Japan, 1999]: • For Level 1 (L1): Minor or no damage, little or no loss of serviceability. • For Level 2 (L2): Minor or little damage, little or short-term loss of serviceability. • For retaining structures of Special Class of Importance: Criteria for structural damage and criteria regarding serviceability are specified. The seismic coefficient for use in retaining structures is defined as follows for Special Class structures:
kh =
a max g
(a max ≤ 0.2g ) (27.1)
1
1 a max 3 kh = 3 g
(a max ≥ 0.2g )
For Class B structures (designed with importance factor of 1.0), the code-specified seismic coefficients are about 60% of those given by Equation 27.1. For a pile-supported wharf with vertical piles, analysis is performed based on a simplified procedure and pushover method. The ductility limits for use in the simplified procedure (discussed later) for L1 earthquake motion are specified. Pushover analysis is performed for Special Class structures and the strain limits prescribed are: • Level 1 motion: equivalent elastic • Level 2 motion: εmax = 0.44tp/Dp, for the embedded portion Pile-supported wharves with vertical steel piles are designed using response spectra for L1 motion, computed based on two-dimensional soil–structure interaction analysis for typical pile-supported wharf cross sections. For L2 motion, time-history analysis should be performed and the results should meet the ductility limits for L2 earthquake motion. Comprehensive guidelines are shown on liquefaction potential assessment and implementation of remedial measures [PHRI, 1997].
27.3.2 U.S. Navy Seismic Design Guidelines The U.S. Navy code [Ferritto, 1997a, 1997b] describes a dual level design and a performance level that is serviceable under L1 and repairable under L2. The damage criteria are deformation limits for wharf dikes and ductility limits for piles. The procedure requires a linear or nonlinear dynamic analysis. California State design is similar to the U.S. Navy design in principle but the ductility requirements are much more detailed and specified by strain limits. This procedure is still under development and will be finalized in the form of regulatory guidance.
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27.3.3 Seismic Guidelines for Ports, American Society of Civil Engineers–Technical Council on Lifeline Earthquake Engineering (ASCE–TCLEE), Ports Committee This reference represents one of the first guideline documents developed specifically for the seismic analysis and design of port structures and facilities in North America [Werner, 1998]. In addition to comprehensive treatment of seismic hazards, seismic design, and analysis in North American engineering practice, and guidelines for specific port components, this document presents pertinent information on seismic risk reduction, and emergency response and recovery at ports. It should be noted that the ASCETCLEE guidelines were developed with the primary objective of providing a framework for the establishment of improved seismic risk evaluation and reduction procedures for ports in the United States. The recommendations outlined in the guideline document are not to be interpreted as codes, nor are they intended to supercede local code requirements that may be applicable. The ASCE-TCLEE seismic guidelines present a dual-level design, consistent with the current state of practice at major ports in the United States. The multilevel design approach has been adopted at numerous ports in the form of twoand occasionally three-level design procedures. An example of the two-level approach as applied in the western United States follows. Level 1. Under this first level of design, Operating Level Earthquake (OLE) ground motions are established, which have a 50% probability of exceedance in 50 years (corresponding to an average return period of about 72 years). Under this level of shaking, the structure is designed so that operations are not interrupted and any damage that occurs will be repairable in a short time (possibly less than 6 months). Level 2. Under this second level of design, more severe Contingency Level Earthquake (CLE) ground motions are established that have a 10% probability of exceedance in 50 years (consistent with most building codes and corresponding to an average return period of about 475 years). Under this level of shaking, the structure is designed to undergo damage that is controlled, economically repairable, and not a threat to life safety. It should be noted that the exposure times adopted for the L1 and L2 events in this example application may vary regionally due to variations in the rate of seismicity, the type of facility, and economic considerations. The damage criteria outlined in the guideline document are presented in the form of general performance-based recommendations. As such, the recommendations address the evaluation and mitigation of liquefaction hazards and ground failures, deformation limits for retaining structures, earth structures, and other waterfront components, and ductility limits for piles. In order to evaluate these earthquake-induced loads and associated deformations, pseudo-static methods of analysis must often be supplemented with linear and nonlinear dynamic analysis, the level of analytical sophistication being a function of the intensity of the ground motions, the anticipated soil behavior, and the complexity of the structure. General guidance on the level of analysis required for a variety of geotechnical and structural applications is provided (including dynamic soil–structure interaction analyses).
27.3.4 European Prestandard, Eurocode 8 Design Provisions for Earthquake Resistance of Structures The methodology of the Eurocode 8 describes in general a dual-level approach; however, in low seismicity zones (adesign ≤ 0.1 g) and for well-defined structures in seismic zones with small design ground acceleration (adesign ≤ 0.04 g), a single-level approach can be sufficient [CEN, 1994]. The mentioned performance levels are: “No collapse” requirement: Retain structural integrity and a residual bearing capacity. “Damage limitation” requirement: No damage and associated limitations of use, the costs of which would be disproportionately high compared with the cost of the structure itself. Damage criteria in terms of maximum displacements and ductility levels are not specified. For piles, it is stated that they shall be designed to remain elastic. When this is not feasible, guidance is given for © 2003 by CRC Press LLC
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the design of potential plastic hinging and the region it will cover. For the analytical procedure, the design ground acceleration, adesign, tends to coincide with the actual peak acceleration for moderate- to high-magnitude earthquakes in cases of medium to long source-to-site distances, which are characterized (on firm ground) by a broad and approximately uniform frequency spectrum, while adesign will be more or less reduced relative to the actual peak for near-field, low-magnitude events. The adesign corresponds to a reference period of 475 years, or as specified by the national authority. For retaining structures kh = adesign/rBCg and kv = 0.5kh, where rBC = 2 for free gravity walls with acceptable displacements (mm) ≤ 300 adesign/g; rBC = 1.5 as above with displacements (mm) ≤ 200 adesign/g; and rBC = 1 for the rest of the retaining structures. For retaining structures 10 m or higher, a refined estimate of adesign can be obtained by a free-field one-dimensional analysis of vertically propagating waves. For a linear analysis design of pile-supported structures, design spectra are defined as: 0 ≤ T ≤ TB :
T S A (T ) = α ⋅ S ⋅ 1 + TB
TB ≤ T ≤ TC : S A (T ) = α ⋅ S ⋅
β0 q
β T = α ⋅ S ⋅ 0 ⋅ C TC ≤ T ≤ TD : S A (T ) q T ≥ [0.20] ⋅ α TD ≤ T :
(27.2)
β T = α ⋅ S ⋅ 0 ⋅ C S A (T ) q T ≥ [0.20] ⋅ α
where α is design ground acceleration; β0 is spectral acceleration amplification factor for 5% damping; q is damping correction factor with reference value q = 1 for 5% viscous damping. Values of the parameters S, kd1, and kd2 are given, depending on the subsoil class specified by shear wave velocity.
27.4 Seismic Performance-Based Design Performance-based design is an emerging methodology born from the lessons learned from earthquakes in the 1990s. The goal is to overcome the limitations present in conventional seismic design. Conventional building code seismic design is based on providing capacity to resist a design seismic force but it does not provide information on the performance of a structure when the limit of the force-balance is exceeded. If we demand that limit equilibrium is not exceeded in conventional design for the relatively high intensity ground motions associated with a very rare seismic event, the construction or retrofitting cost will most likely be too high. If force-balance design is based on a more frequent seismic event, then it is difficult to estimate the seismic performance of the structure when subjected to ground motions that are greater than those used in design. In performance-based design, appropriate levels of design earthquake motions must be defined and corresponding acceptable levels of structural damage must be clearly identified. Two levels of earthquake motions are typically used as design reference motions, defined as follows: Level 1: The level of earthquake motions that are likely to occur during the life span of the structure. Level 2: The level of earthquake motions associated with infrequent rare events that typically involve very strong ground shaking. The acceptable level of damage is specified according to the specific needs of the users and owners of the facilities and may be defined on the basis of the acceptable level of structural and operational damage © 2003 by CRC Press LLC
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TABLE 27.1 Acceptable Level of Damage in Performance-Based Designa Acceptable Level of Damage
Structural
Operational
Degree I: Serviceable Degree II: Repairable Degree III: Near collapse Degree IV: Collapsed
Minor or no damage Controlled damageb Extensive damage in near collapse Complete loss of structure
Little or no loss of serviceability Short-term loss of serviceabilityc Long-term or complete loss of serviceability Complete loss of serviceability
a
Considerations: Protection of human life and property, functions as an emergency base for transportation, and protection from spilling hazardous materials, if applicable, should be considered in defining the damage criteria in addition to those shown in this table. b With limited inelastic response and residual deformation. c Structure out of service for short to moderate time for repairs. d Without significant effects on surroundings.
TABLE 27.2 Performance Grades S, A, B, and C Design Earthquake Performance Grade Grade S Grade A Grade B Grade C
Level 1 (L1)
Level 2 (L2)
Degree I: Serviceable Degree I: Serviceable Degree I: Serviceable Degree II: Repairable
Degree I: Serviceable Degree II: Repairable Degree III: Near collapse Degree IV: Collapse
given in Table 27.1. The structural damage category in this table is directly related to the amount of work needed to restore the full functional capacity of the structure and is often referred to as direct loss due to earthquakes. The operational damage category is related to the amount of work needed to restore full or partial serviceability. Economic losses associated with the loss of serviceability are often referred to as indirect losses. In addition to the fundamental functions of servicing sea transport, the functions of port structures may include protection of human life and property, functioning as an emergency base for transportation, and as protection from spilling hazardous materials. If applicable, the effects on these issues should be considered in defining the acceptable level of damage in addition to those shown in Table 27.1. Once the design earthquake levels and acceptable damage levels have been properly defined, the required performance of a structure may be specified by the appropriate performance grade S, A, B, or C, defined in Table 27.2. In performance-based design, a structure is designed to meet these performance grades. The principal steps taken in performance-based design are shown in the flowchart in Figure 27.15. • Choose a performance grade from S, A, B, or C: This step is typically done by referring to Table 27.1 and Table 27.2, and selecting the damage level consistent with the needs of the users and owners. Another procedure for choosing a performance grade is to base the grade on the importance of the structure. Degrees of importance are defined in most seismic codes and standards. This procedure is presented in Table 27.3. If applicable, a performance grade other than those of S, A, B, or C may be introduced to meet specific needs of the users and owners. • Define damage criteria: Specify the level of acceptable damage in engineering parameters such as displacements, limit stress states, or ductility factors. The details are addressed in the guidelines [PIANC, 2001]. • Evaluate seismic performance of a structure: Evaluation is typically done by comparing the response parameters from a seismic analysis of the structure with the damage criteria. If the results of the analysis do not meet the damage criteria, the proposed design or existing structure should be modified. Soil improvement, including remediation measures against liquefaction, may be necessary at this stage. Details of liquefaction remediation can be found in the publication of the Port and Harbour Research Institute, Japan [PHRI, 1997]. © 2003 by CRC Press LLC
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Acceptable damage: I Serviceable II Repairable III Near Collapse IV Collapse
Earthquake level: Level 1 (L1) Level 2 (L2)
Performance grade: S, A, B, C
Analysis type: 1. Simplified analysis 2. Simplified dynamic analysis 3. Dynamic analysis
Input: Earthquake motions Geotechnical conditions Initial design or existing structure Damage criteria Analysis
Output: Displacements Stresses (Liquefaction potential)
No Are damage criteria satisfied?
Modification of cross section/ soil improvement
Yes
End of performance evaluation
FIGURE 27.15 Flowchart for seismic performance evaluation. (From PIANC. 2001. Seismic Design Guidelines for Port Structures, A.A. Balkema, Rotterdam. With permission.)
27.5 Seismic Performance Evaluation and Analysis The objective of analysis in performance-based design is to evaluate the seismic response of the port structure with respect to allowable limits (e.g., displacement, stress, ductility, and strain). Higher capability in analysis is generally required for a higher performance-grade facility. The selected analysis methods should reflect the analytical capability required in the seismic performance evaluation. © 2003 by CRC Press LLC
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TABLE 27.3 Performance Grade Based on the Importance Category of Port Structures
Performance Grade
Definition Based on Seismic Effects on Structures
Grade S
1. Critical structures with potential for extensive loss of human life and property upon seismic damage 2. Key structures that are required to be serviceable for recovery from earthquake disaster 3. Critical structures that handle hazardous materials 4. Critical structures that, if disrupted, devastate economic and social activities in the earthquake damage area Primary structures having less serious effects for 1–4 than Grade S structures, or 5, structures that, if damaged, are difficult to restore Ordinary structures other than those of Grades S, A, and C Small, easily restorable structures
Grade A
Grade B Grade C
Suggested Importance Category of Port Structures in Japanese Code Special Class
Special Class or Class A
Class A or B Class B or C
TABLE 27.4 Types of Analysis Related to Performance Grades Performance Grade Type of Analysis
Grade C
Grade B
Grade A
Grade S
Simplified analysis: Appropriate for evaluating approximate threshold level and elastic limit and order-of-magnitude displacements. Simplified dynamic analysis: Of broader scope and more reliable. Possible to evaluate extent of displacement, stress, ductility, and strain based on assumed failure modes. Dynamic analysis: Most sophisticated. Possible to evaluate both failure modes and extent of displacement, stress, ductility, and strain. Note: Black area is standard/final design. Gray area is preliminary design or low level of excitations.
A variety of analysis methods is available for evaluating the local site effects, liquefaction potential, and the seismic response of port structures. These analysis methods are broadly categorized based on a level of sophistication and capability as follows: • Simplified analysis: Appropriate for evaluating approximate threshold limit for displacements and elastic response limit, and an order-of-magnitude estimate for permanent displacements due to seismic loading. • Simplified dynamic analysis: Possible to evaluate extent of displacement, stress, ductility, and strain based on assumed failure modes. • Dynamic analysis: Possible to evaluate both failure modes and the extent of the displacement, stress, ductility, and strain. Table 27.4 shows the type of analysis that may be most appropriate for each performance grade. The principle applied here is that the structures of higher performance grade should be evaluated using more sophisticated methods. As shown in Table 27.4, less sophisticated methods may be allowed for preliminary design, screening purpose, or response analysis for low levels of excitation. The methods for analysis of port structures may be broadly classified into those applicable to retaining/ earth structures, including quay walls, dikes/slopes, and breakwaters, or those applicable to open pile/ frame structures, including a pile/deck system of pile-supported wharves and cranes.
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27.6 Methods for Analysis of Retaining/Earth Structures 27.6.1 Simplified Analysis Simplified analysis of retaining/earth structures is based on the conventional force-balance approach, sometimes combined with statistical analyses of case history data. The methods in this category are often those adopted in conventional seismic design codes and standards. In simplified analysis, retaining/earth structures can be idealized as rigid blocks of soil and structural masses. The rigid block analysis is typically applied for gravity, sheet pile, and cellular quay walls, and dike/slope/retaining walls for pile-supported wharves and breakwaters. Effects of earthquake motions in simplified analysis are represented by a peak ground acceleration or an equivalent seismic coefficient for use in conventional pseudo-static design procedures. These parameters are obtained from the simplified analysis of local site effects discussed in the previous section. A capacity to resist the seismic force is evaluated based on structural and geotechnical conditions, often in terms of a threshold acceleration or a threshold seismic coefficient, beyond which the rigid blocks of soil and structural masses begin to move. When soil liquefaction is an issue, the geometric extent of liquefaction must also be considered in the analysis.
27.6.2 Simplified Dynamic Analysis Simplified dynamic analysis is similar to simplified analysis, idealizing a structure by a sliding rigid block. In simplified dynamic analysis, displacement of the sliding block is computed by integrating the acceleration time history that exceeds the threshold limit for sliding over the duration until the block ceases sliding. Effects of earthquake motions are generally represented by a set of time histories of earthquake motion at the base of a structure. The time histories of earthquake motion are obtained from the simplified dynamic analysis of local site effects discussed in the previous section. In the sliding block analysis, structural and geotechnical conditions are represented by a threshold acceleration for sliding. A set of empirical equations obtained from a statistical summary of sliding block analyses is available. In these equations, peak ground acceleration and velocity are used to represent the effect of earthquake motion. In more sophisticated analyses, structural and geotechnical conditions are idealized through a series of parametric studies based on nonlinear Finite Element Method (FEM)/Finite Difference Method (FDM) analyses of soil–structure systems. The results are compiled as simplified charts for use in evaluating approximate displacements.
27.6.3 Dynamic Analysis Dynamic analysis is based on soil–structure interaction, generally using FEM or FDM. In this category of analysis, effects of earthquake motions are represented by a set of time histories of earthquake motion at the base of the analysis domain chosen for the soil–structure system. A structure is idealized as either linear or nonlinear, depending on the level of earthquake motion relative to the elastic limit of the structure. Soil is idealized either by equivalent linear or by an effective stress model, depending on the expected strain level in the soil deposit during the design earthquake. Fairly comprehensive results are obtained from soil–structure interaction analysis, including failure modes of the soil–structure system and the extent of the displacement, stress, and strain states. Because this category of analysis is often sensitive to a number of factors, it is especially desirable to confirm the applicability by using a suitable case history or a suitable model test result.
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27.7 Analysis Methods for Open Pile/Frame Structures 27.7.1 Simplified Analysis Simplified analysis of open pile/frame structures is typically done by idealizing the pile/deck system of pile-supported wharves or the frame of cranes by a single-degree-of-freedom (SDOF) or multidegreeof-freedom (MDOF) system. In this analysis, earthquake motions are generally represented by the response spectrum. Structural and geotechnical conditions are represented by a resonant frequency and damping factor of the pile/deck system and the cranes. A ductility factor may also be introduced. The movement of the dike/slope is generally assumed to be negligible. Results of the SDOF/MDOF analysis are useful to evaluate approximate limit state response of a pile/deck system or a crane.
27.7.2 Simplified Dynamic Analysis In simplified dynamic analysis of open pile/frame structures, the SDOF or MDOF analysis of pile/deck structure or cranes is combined with pushover analysis for evaluating the ductility factor/strain limit. The movement of the dike/slope is often assumed to be negligible but sometimes is estimated by a sliding block-type analysis. Movement of a pile-supported deck could thereby be estimated by summing up the dike/slope movement and structural deformation. Soil–structure interaction effects are not taken into account, and thus there is a limitation in this analysis. Interaction between the pile-supported wharves and cranes can be taken into account by MDOF analysis. Displacement, ductility factor, strain, and location of yielding or buckling in the structure are generally obtained as a result of the analysis of this category. Failure modes with respect to sliding of retaining walls, dikes, and slopes are not evaluated but assumed and, thus, there is another limitation in this type of analysis.
27.7.3 Dynamic Analysis Dynamic analysis is based on soil–structure interaction, generally using FEM and FDM. Similar comments to those related to the dynamic analysis of earth/retaining structures apply also to the open pile structures and cranes.
References CEN (European Committee for Standardization). 1994. Eurocode 8: Design Provisions for Earthquake Resistance of Structures. Part l-l: General Rules — Seismic Actions and General Requirements for Structures (ENV-1998–1–1); Part 5: Foundations, Retaining Structures and Geotechnical Aspects (ENV 1998–5). Ferritto, J.M. 1997a. “Design Criteria for Earthquake Hazard Mitigation of Navy Piers and Wharves,” Technical report TR–2069-SHR, Naval Facilities Engineering Service Center, Port Hueneme. Ferritto, J.M. 1997b. “Seismic Design Criteria for Soil Liquefaction,” Technical report TR–2077-SHR, Naval Facilities Engineering Service Center, Port Hueneme. Ministry of Transport, Japan, Ed. 1999. Design Standard for Port and Harbour Facilities and Commentaries (in Japanese), Japan Port and Harbour Association (English edition [2001] by the Overseas Coastal Area Development Institute of Japan), Yokosuka. PHRI (Port and Harbour Research Institute). 1997. Handbook on Liquefaction Remediation of Reclaimed Land (translated by Waterways Experiment Station, U.S. Army Corps of Engineers), A.A. Balkema, Rotterdam. PIANC (Permanent International Association for Navigation Congresses). 2001. Seismic Design Guidelines for Port Structures, A.A. Balkema, Rotterdam.
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Werner, S.D., Ed. 1998. Seismic Guidelines for Ports, Monograph No. 12, Technical Council on Lifeline Earthquake Engineering, American Society of Civil Engineers, Reston, VA. Zwamborn, J.A. and Phelp, D. 1995. “When Must Breakwaters Be Rehabilitated/Repaired?” in PORTS ’95, American Society of Civil Engineers, Reston, VA, pp. 1183–1194.
Further Reading Much of this section is based on the author’s involvement in the development of the publication Seismic Design Guidelines for Port Structures [PIANC, 2001], which is highly recommended to the reader, and the use of material therefrom is gratefully acknowledged.
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V Special Topics
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28 Human Impacts of Earthquakes 28.1 Introduction 28.2 Casualties in Historic Earthquakes Levels of Injury Severity · Types and Causes of Injuries · Injury Scales · Risk Factors for Injury
28.3 A Standardized Earthquake Injury Classification Scheme Hazard-Level Variables · Building-Level Variables · Individual-Level Variables
28.4 Casualty Estimation Methodology 1970s: NOAA Scenarios · 1980s: ATC-13 and Expert Opinion · 1990s: Geographic Information System (GIS)-Based Regional Loss Estimation Tools · Recent Developments: Epidemiologic Casualty Models and Loss-Estimation Model Refinements
28.5 Casualty Mitigation and Prevention 28.6 Public Health Impacts Mental Health Impacts · Chronic Diseases · Acute Diseases
Hope A. Seligson ABS Consulting Irvine, California
Kimberley I. Shoaf Center for Public Health and Disasters University of California at Los Angeles
28.7 Shelter Requirements Shelter Estimation Methodology
28.8 Closing Remarks Defining Terms References Further Reading
28.1 Introduction The primary impact of concern with regard to earthquakes is life safety. Historically, most earthquake engineering research and development efforts have been focused on ground motion, modeling of structural vulnerability, and aseismic design. However, the repeated large loss of human life in earthquakes1 has sparked renewed interest in the areas of casualty, or mortality and morbidity estimation. The results from these models provide engineers and government officials with estimates useful in all phases of disaster management, including planning and preparedness, emergency response, recovery, and mitigation. The flow of casualty information in the event of an earthquake is shown in Figure 28.1. The upward flow of post-disaster casualty estimates is indicated by the dashed lines, while the downward flow of actual field-collected data is shown by solid lines. As shown, casualty estimates may be used by emergency 1 For example, 50,000 killed in the 1990 Iran earthquake, 25,000 killed in the 1988 Armenia event, 17,000 killed in the 1999 Marmara, Turkey event and 6,000 killed in the 1995 Kobe event, to mention only a few of the more recent large life-loss earthquakes. See Chapter 1 for a list of 20th-century earthquake life loss.
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FIRST LINE RESPONDERS AND DATA GENERATORS: CASUALTY DATA: EMS USAR Hospitals/Clinics/Private Physicians Coroners Red Cross DAMAGE DATA: Engineers Building Inspectors
Actual Post-Disaster Data
PUBLIC HEALTH-ORIENTED DATA COLLECTORS: County Public Health Departments Red Cross State Agencies (Public Health, EMS Health Planning) Federal Agencies (CDC)
GENERAL EMERGENCY RESPONSE AND RECOVERY-ORIENTED DATA COLLECTORS: State Emergency Services(OES) Federal Agencies (FEMA)
RISK ASSESSMENT AND CASUALTY RESEARCHERS
Real-Time Post Disaster Casualty Estimates
FIGURE 28.1 Flow of earthquake casualty information.
responders and healthcare providers to prioritize reconnaissance efforts, deploy resources, and seek mutual aid. Further, actual post-disaster data should be collected to document the event and the expenditure of resources, as well as for eventual analysis and improvement of existing casualty models. The goal of this chapter is to provide the reader with background information on the impacts of earthquakes on humans, as well as provide a summary of the state of the art in human-impact modeling. Human impacts addressed in this chapter include deaths and injuries, mental health effects, shelter requirements, and other public health impacts such as communicable diseases.
28.2 Casualties in Historic Earthquakes Every year, natural disasters claim the lives of thousands of individuals and injure many more. Earthquakes represent a sizable portion of the impact on humans. From 1970 through 1994, earthquakes resulted in an average of 21,593 deaths annually [IFRC, 1996]. The number and severity of injuries resulting from earthquakes, however, vary with the intensity of the shaking, local soil conditions, built environment, time of impact, population density, location, and demographic characteristics and behavior of the
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TABLE 28.1 Casualty Information from Selected Earthquakes in the Past 50 Years Year
Location
Magnitude
Deaths
Serious Injuries
Minor Injuries
1952 1971 1972 1976 1976 1980 1985 1985 1987 1988 1989 1990 1993 1993 1994
Bakersfield, CA San Fernando, CA Nicaragua Guatemala Tangshan, China Italy Chile Mexico Whittier Narrows, CA Armenia Loma Prieta, CA Philippines Hokkaido, Japan Guam Northridge, CA
6.0+ 6.4 5.6 7.5 ? 6.5–6.8 7.8 8.1 5.9 6.9 7.1 7.7 7.8 8.1 6.7
2 58 4,200 (3–6,000) 22,778 240,000 3,000 180 211 3 25,000 62 592 231 0 33
32 2,543 16,800 76,506 160,000 8,000 14 3,850 121 12,200 3,757 1,412 ? 100* 138
? ? ? ? ? ? 2,575* 30,000 1,228 18,800 ? ? ? ? 8–24,000*
Note: *Estimate.
potential victims [Ghua-Sapir, 1991; Alexander, 1985; Mahoney and Reutershan, 1987; Jones et al., 1990; Bourque et al., 1997; Shoaf et al., 1998; Peek-Asa et al., 1998; Mahue-Giangreco, 2000]. A table summarizing injuries and deaths in 14 earthquakes between 1952 and 1993 was presented in Bourque et al. [1997], an adaptation of which is shown in this chapter as Table 28.1. It demonstrates a number of important issues for casualty estimation. First, casualties are not only a factor of magnitude. We note the 4200 deaths in Nicaragua from a magnitude 5.6 earthquake in 1972, compared with three deaths in the Magnitude 5.9 Whittier Narrows earthquake in 1987. Similarly, in larger events, we find only 62 deaths from the 1989 Loma Prieta earthquake (Magnitude 7.1) and 180 deaths in the Magnitude 7.8 earthquake in Chile in 1985, and 25,000 deaths in the 1988 earthquake in Armenia (Magnitude 6.8). Second, the table demonstrates that the relationship between injuries and fatalities is not simply a ratio of 3 or 4:1 for serious injuries, nor 40:1 for minor injuries, as has been used in various lossestimation studies (see Section 28.4). In some instances, the number of injuries is actually less than the number of fatalities (i.e., Armenia and Tangshan, China). In other earthquakes, the number of serious injuries can be as much as 40 times the number of deaths (e.g., San Fernando and Mexico City). Third, the table shows that there is actually very little information on the injuries and fatalities that are reported. Serious injuries are not all defined in the same way, nor are they even necessarily defined. For most of the earthquakes, there is no information at all on less serious injuries (in spite of the fact that they may represent a very large burden on healthcare resources). As Bourque points out [1997], the majority of the data reported in the table are from official statistics, newspaper reports, records from hospitals or disaster relief organizations, or anecdotal reports. Significantly different numbers are reported in different sources for the same event. These numbers do not necessarily represent complete information about the types or severity of the injuries incurred.
28.2.1 Levels of Injury Severity Recent earthquakes around the world have provided more information about the types, causes, and severity of injuries, as well as the relationship between fatalities and varying treatment levels for nonfatal injuries. Table 28.2 reflects available information about treatment levels for injuries and fatalities from five recent earthquakes. This table shows that there is not only a great deal of variability in the numbers of individuals injured, but also that the distribution of those injuries varies across levels of treatment. The most complete data on casualties in an earthquake are from the 1994 Northridge earthquake in California. These data come from a number of sources: © 2003 by CRC Press LLC
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• • • • •
Coroner’s reports of fatalities Medical records of persons admitted to hospitals in Los Angeles County Medical records from a sample of persons treated in Los Angeles County emergency departments Emergency department logs from a sample of area hospitals Telephone interview data from a random sample of households in Los Angeles County
The data allow us to look at the number of injuries and deaths, the type and severity of those injuries, risk factors associated with being injured, the level of treatment required for those injuries, and the relationship between casualties and building damage. These multiple data sets allow us to develop an injury pyramid that shows the relative size of the different injury severity levels, shown in Figure 28.2. TABLE 28.2 Distribution of Injuries in Five Recent Earthquakes
Earthquake Whittier Narrows, CA (1987) Loma Prieta, CA (only Santa Cruz County) (1989) Northridge, CA (1994) Kobe, Japan (1995) Quindio, Colombia (1999) 1 2 3 4 5 6 7
Fatalities/ 100,000 Population
Hospitalized/ 100,000 Population
Treat and Release/100,000 Population
Injury Rate/100,000 Population
0.031 2.11
— —
— 1067
8002 7002
0.373 2744 4016
1.563 3155 —
802 — —
27332 21504 15726
Based on official reports, as cited in Wagner, 1997. Based on survey data; see Shoaf et al., 1998. Based on reviews of hospital and coroner’s records; see Peek-Asa et al., 1998. Based on coroner’s data and official reports; see Yamazaki et al., 1997. Based on reviews of hospital records; see Kuwagata et al., 1997. Based on reviews of coroner’s and hospital logs submitted to the departmental public health agency; see EERI, 2000. Based on reviews of hospital data including treat and release, admissions, and deaths in Santa Cruz County; see Wagner, 1998.
DOA 0.37/ 100,000
Die in Hospital
18% of deaths
Hospitalized/Trauma Cases
6.5% of admissions Hospitalized/Non-Trauma 1.5/100,000 population
Emergency Department Treat and Release
3.3% of injured 6.6% of injured
8.2% of households
FIGURE 28.2 Injury pyramid for the 1994 Northridge earthquake.
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Out of Hospital Treat and Release
Injured, No Treatment
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In the Northridge earthquake, approximately 8% of households reported that at least one person in the household was injured as a result of the earthquake [Shoaf et al., 1998]. While the vast majority of those injured reported minor cuts and bruises, approximately 10% reported seeking some sort of medical care for those injuries. Of those who sought care, one third received medical care from hospitals, with the remainder receiving treatment from other sources including private physicians, first aid stations, and emergency medical services, among others. Following the earthquake, 138 people were admitted to a hospital in Los Angeles County, which represents a hospitalization rate of approximately 1.5 persons/ 100,000 population [Peek-Asa et al., 1999]. Approximately 6.5% of those admitted to a hospital had injuries that were considered serious enough to warrant treatment at a trauma center (a hospital classified as having the capacity to treat significant traumas (see http://www.emsa.cahwnet.gov/legislation/ regs7.asp). Thirty-eight individuals died as a result of injuries sustained in the earthquake, for a mortality rate of approximately 0.38 deaths/100,000 population. Eighteen percent of those who died did so after being admitted to the hospital [Peek-Asa et al., 1999]. While the majority of people who die as a result of earthquake-related injuries do so immediately or prior to being extricated from collapsed buildings, some die after being admitted to the hospital. In the Northridge earthquake, of the 33 deaths, 6 survived for as many as 8 days prior to expiring [Peek-Asa et al., 1998]. Likewise, in the Kobe earthquake, 6.6% of trauma patients admitted to the hospital died as a result of their injuries. Length of survival was associated with injury type. Among those with crush syndrome and injuries to vital organs, most patients died in the first 8 days, whereas the majority of those with unknown injuries died in the hospital primarily on the day of the earthquake. For those with fractures and other types of injuries, the increase in nonsurvivors continued for 2 weeks. It is important to note that, in Kobe, the majority of nonsurvivors (except those with unknown injuries, who primarily died on the day of the earthquake) were admitted to intensive-care units [Kuwagata et al., 1997].
28.2.2 Types and Causes of Injuries Another way of classifying injuries is by mechanism and body location. In three California earthquakes (Whittier Narrows, Loma Prieta, and Northridge), minor injuries resulted primarily from being struck by objects (not building parts) and from falls [Shoaf et al., 1998]. In the Northridge earthquake, the majority of hospitalized injuries (55.8%) were also caused by falls. An additional 15% resulted from being hit by
FIGURE 28.3 Urban search and rescue operations following the 1999 Chi-Chi earthquake in Taiwan. (Photo: T. Atsumi, MCEER)
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objects. Only 8% of hospitalized injuries resulted from being hit or trapped by building parts. In contrast, 71% of fatal injuries resulted from being hit or trapped by building parts [Peek-Asa et al., 1998]. In the Kobe earthquake, 59% of hospitalized injuries resulted from being crushed or pinned. An additional 19% were hit by falling material (not defined as either building-related or not) and 8% resulted from falls [Kuwagata et al., 1997]. The anatomical location of the injury tends to vary with the earthquake, possibly as a result of the time of the event. In the Loma Prieta earthquake, which occurred in the afternoon, the majority of injuries were to the trunk or torso (54.8%). In contrast, in the Northridge earthquake, the majority of injuries (68.4% as reported in interview, 72% of hospitalized injuries) were to the extremities, primarily the lower extremities [Shoaf et al., 1998]. In telephone interviews, injured respondents reported that, in the dark, they ran into or fell over objects that had moved in the earthquake. Similar trends appear in preliminary results from ongoing analyses of a survey of victims in the 1999 Turkey earthquake. Respondents to that study in the city of Golcûk also reported that the majority of injuries were to the lower extremities, resulting from running into objects in the dark. Thus, moving about in the dark could result in more injuries to the extremities.
28.2.3 Injury Scales A number of injury scales have been developed for various regions. Two scales deriving from the motor vehicle industry are given here. The Abbreviated Injury Scale (AIS, 1990 Revision, see http:// www.trauma.org/scores/ais.html) is an anatomical scoring system monitored by a scaling committee of the Association for the Advancement of Automotive Medicine. Injuries are ranked on a scale of 1 to 6, with 1 being minor, 5 severe, and 6 an unsurvivable injury. This represents the “threat to life” associated with an injury and is not meant to represent a comprehensive measure of severity. The AIS is an ordinal injury scale, in that the difference between AIS1 and AIS2 is not the same as that between AIS4 and AIS5. Injury
AIS Score
1 2 3 4 5 6
Minor Moderate Serious Severe Critical Unsurvivable
An anatomic injury severity score (ISS) [Baker et al., 1974] is based on the AIS. The scaling system relies on a list of injuries, each of which is assigned a severity code from 1 (minor injuries) to 6 (injuries that are untreatable and usually fatal). The ISS is based on AIS severity codes for six body regions: 1. 2. 3. 4. 5. 6.
Head and neck Face Chest Abdominal and pelvic contents Limbs and pelvic girdle External
To compute the ISS, one first identifies the highest AIS code in each of the six body regions. The squares of the highest three of the six coded are then added to obtain the ISS. The ISS ranges from 1 to 75. The higher the score, the poorer the patient’s condition. If a victim has any injury with an AIS value of 6, the ISS is assigned a value of 75. An example of an ISS calculation would be:
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Body Region
Injury Description
AIS
Square Top 3
Head and Neck Face Chest
Subarachnoid hemorrhage No injury Lung laceration with hemomediastinum Liver contusion (minor) Kidney laceration (hilum avulsed) Fractured tibia No injury Injury severity score
3 0 4
9 — 16
2 5 2 0
— 25 — — 50
Abdomen Extremity External
28.2.4 Risk Factors for Injury The demographic characteristics of the population may also have an effect on both the numbers and types of injuries in an earthquake. The two demographic characteristics that have been routinely examined in relationship to injuries in earthquakes are age and gender. Much of the literature has supported the idea that women and the elderly are more likely to be injured in earthquakes. While this does not always hold true, these characteristics should be taken into consideration. In the Northridge earthquake, women were slightly more likely to be injured than men. Across all levels of injury, women represented about 55% of the injured [Shoaf et al., 1998; Peek-Asa et al., 1998; Mahue-Giangreco et al., 2001]. The impact of age is more pronounced, especially as it relates to severity of injury. In the general population survey in the Northridge earthquake, age was inversely related to being injured, with every 10 years of age reducing the likelihood of being injured by 30%. Among those reporting injuries in the survey, older people were also less likely to seek care for their injuries [Shoaf et al., 1998]. However, in a study of emergency departments after the Northridge earthquake, it was reported that the age distribution of those injured resembled the age distribution in the population. This age distribution is significantly different from the normal age distribution of emergency department visits, where there are generally more young individuals. While age did not seem to be related to seeking care in an emergency department, the severity of injuries treated in the emergency department did increase with age. Twentysix percent of the injuries in those over the age of 60 were scored as serious (with an ISS greater than 9) compared with only 3% of injuries in those under the age of 60 [Mahue-Giangreco, 2001]. A similar trend is found in those whose injuries resulted in hospitalization or death. Those aged 60–79 were 10 times more likely to be hospitalized or to die as a result of their injuries than those aged 10–19; those aged 80 and above were 35 times more likely to have injuries that resulted in hospitalization or death. This trend is more apparent in those who are hospitalized than for those who died, with 76% of the hospitalized patients being over the age of 65 and 31% of the fatalities [Peek-Asa et al., 1998]. Thus, the age of the population can have a significant impact on the need for hospital care. To minimize future injuries from disaster, a better understanding of the risk factors associated with injuries such as those described above is needed. The current literature on casualties resulting from earthquakes is considerably limited in its ability to increase the understanding of risk factors associated with injuries and deaths from earthquakes. One major limitation is that the data and reporting across earthquakes are not collected in a standardized fashion that utilizes a standard set of definitions and methods. For the past 25 years, researchers in the earthquake casualty estimation field have called for an interdisciplinary standardized data collection system to improve casualty modeling.
28.3 A Standardized Earthquake Injury Classification Scheme This section presents a standardization of data definitions and methodologies developed by a multidisciplinary team to set standards that will prove useful to the many disciplines studying earthquake-related
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TABLE 28.3 Components for Classification of Earthquake-Related Casualties Hazard-Level Variables Earthquake source characteristics Local site hazard characteristics
Building-Level Variables
Individual-Level Variables
Building description Building damage
Demographics Injury characteristics Location Activity
casualties [Seligson et al., 2002]. It attempts to define a common language that can be used to study events across time and geography to improve our ability to estimate casualties in earthquakes. Furthermore, it provides a mechanism for understanding the risk factors associated with injuries in order to reduce those losses. The classification scheme for earthquake casualty estimation includes measures of the components relevant to estimation of injuries and fatalities from earthquakes, including characteristics of the hazard, of the built environment, of the resulting injuries, and of the population, as well as behavioral characteristics of the population. While the classification scheme is not necessarily all-inclusive, it does attempt to cover the majority of factors that need to be considered from both an engineering and a medical standpoint, and is intended to be applicable within the United States and abroad. The major components of the classification scheme are listed in Table 28.3. A full listing of the classification scheme is available at http://www.ph.ucla.edu/cphdr/scheme.pdf. To make the classification scheme as user-friendly as possible, existing measures were utilized whenever feasible. For example, the Abbreviated Injury Score (AIS) discussed above is a standard for classifying injuries accepted by injury epidemiologists around the world. Many of the definitions come from the International Classification of Disease (ICD), 9th Revision, a standard used by medical professionals internationally. Building-related definitions employed herein are generally those standardized by the Applied Technology Council (ATC) and the Federal Emergency Management Agency (FEMA).
28.3.1 Hazard-Level Variables Earthquake Source Characteristics: The characteristics of the earthquake source and the local hazard data have been taken from seismological standards. They include the following variables: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
Earthquake name and event number or ID Earthquake magnitude(s) (including scale(s) definition) Date, time, and day of the week of earthquake Earthquake location (epicenter latitude, longitude, depth, and description) Rupture length Rupture area Presence of surface rupture? Deepest point of rupture/bottom of rupture plane Shallowest point of rupture/top of rupture plane Fault source description (name, type, strike direction, dip, and dip direction)
The earthquake source characteristics allow researchers to compare data across events and evaluate the relative impact of the source on the outcomes measured. Local Site Hazard Characteristics: Local site hazard characteristics reported in the classification scheme include measures of ground motion as well as features that could contribute to secondary hazards that may be present. Earthquake ground motion data come from mapped data typically available from the U.S. Geological Survey (USGS) or other similar organizations. In some cases, the information is available in near real-time on the Internet (www.TRINET.ORG for information on real-time ShakeMaps in Southern California). Measures of ground motion include:
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TABLE 28.4 Building Description Variables
• • • • • •
Variable
Definition or Example
Structural system Building height Building size Year built Building seismic design quality Debris generation potential Occupancy type
Load-resisting structural system (HAZUS®) Number of stories, height category (ATC-13) Square feet Four-digit year Seismic design criteria for structure (HAZUS®) ATC-21-2 Building use category (HAZUS®)
Earthquake intensity (Modified Mercalli Intensity, MMI) Peak ground acceleration (PGA, measured in units of g) Peak ground velocity (PGV, measured in cm/sec) Spectral acceleration at 0.3-second period (measured in units of g) Spectral acceleration at 1.0-second period (measured in units of g) Spectral acceleration at 3.0-second period (measured in units of g)
Other factors considered in this portion of the classification scheme include soil conditions (surficial geology), and liquefaction and landslide susceptibility.
28.3.2 Building-Level Variables Building Description: Variables describing the built environment have been taken from published standards, primarily those used in HAZUS® (NIBS/FEMA 1999). The components considered include the structural system; the building height, size, and age; seismic design quality; potential for debris generation; and occupancy type and load. Table 28.4 lists the variables included in this section and the sources for the definitions. Building Damage: In casualty-estimation methodologies, building damage is generally considered the most proximate and relevant predictor of injuries. However, a number of different methodologies that vary from country to country are utilized to describe building damage. To date, there have not been sufficient studies to identify which component of building damage is most relevant to risk for injury. Six different measures of building damage are included and, in most cases, utilize existing metrics. These metrics include: • • • • • •
Whether a post-earthquake safety inspection was performed The presence (and color) of the building safety tag The dollar amount of damage The damage percent (relative to replacement cost) The damage state (relative to percent damage) Building collapse (none, partial, complete)
While these are the measures generally collected through engineering inspections, additional information on damage, including damage to contents and personal property, may be useful in describing injury mechanisms. It has been suggested that, while building damage (and more specifically collapse) may be the most relevant factor for deaths, injuries may be more strongly related to other effects of ground motion (i.e., movement of furniture and other personal property).
28.3.3 Individual-Level Variables Demographic Characteristics: Epidemiological studies of earthquake-related injuries suggest that demographic characteristics of the population can be risk factors for injuries [Peek-Asa et al.,1998; Shoaf et al., © 2003 by CRC Press LLC
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TABLE 28.5 Injury-Related Variables Variable A. Cause of injury: Relation to EQ/EQ relatedness Structural relatedness Secondary hazards Injury mechanism B. Injury severity C. Treatment Level of treatment Immediacy D. Costs Direct medical care costs Indirect costs E. Diagnoses
Definition or Example Adaptation of CDC methodology for hurricanes [Combs, 1999] Related to structural elements, nonstructural building elements, contents, infrastructure, or not related Directly, indirectly, or not related to any secondary hazard (fire, landslide, tsunami, hazardous materials release) ICD-9 E-codes (should use E909 <earthquake> and more proximate mechanism code) [see CPHA, 2001] Abbreviated Injury Scale if complete diagnoses are available, else use four broad categories Based on the level of sophistication of medical treatment required by the injury Based on triage system, reflects the urgency of seeking care for the injury Documented costs Include costs of bed-days, loss of work ICD-9 or Abbreviated Injury Scale
1998; Glass et al., 1977]. It is therefore important to gather information in a consistent manner across earthquakes to elucidate the relationship between demographic characteristics and hazard and building characteristics. Relevant demographic characteristics include age, gender, race/ethnicity, level of education, occupation, income, disabilities, and preexisting conditions. Having these data from a variety of earthquakes will improve our understanding of their relative importance in calculating the risk of injury or death. The complete classification scheme provides recommended categories for race or ethnicity, education level, occupation, and income based on current U.S. practices. Injury Characteristics: Characteristics of the injury, including relation to the earthquake, the diagnosis, severity, and mechanism of injury, are also classified utilizing standard methodologies and existing scales. The injury-related variables and their definitions are presented in Table 28.5. The injury mechanism and diagnoses utilize the International Classification of Diseases coding schemes, which are standard practice in medicine internationally. Injury severity is measured utilizing the Abbreviated Injury Scale (AIS) discussed above, which was developed by injury epidemiologists to study injuries in automobile crashes. This scale is recommended until more data are available from earthquakes internationally to validate a severity scale that is specific to earthquakes (or other disasters). The further development of a specific severity scale (or adaptation of the AIS) is necessary because injuries that are uncommon in automobile crashes (i.e., crush syndrome) are not represented in the AIS. The methodology and terminology for the other characteristics of the injury are either new developments or adaptations of related work. For example, the terminology for level of treatment required for the injury is based on levels of treatment in emergency medicine, but is not a standard in the field. The urgency of treatment variable is an adaptation of the triage system utilized by emergency medical personnel. The triage system, however, is situation dependent and not necessarily tied to a specific injury in all circumstances. Location: The location of the individual (at the time of the injury) is relevant to the risk of injury. The coding scheme for this variable includes locations in buildings (with specific rooms coded), in vehicles, on infrastructure, or out of doors. These locations are not necessarily mutually exclusive (i.e., a person could be in a car on a bridge) and multiple entries are allowed. Furthermore, the geographic location of the individual as an address (full address including street number, name, city, state, and zip code), as reported in census data (i.e., census tract) and as a geocoded reference (i.e., latitude and longitude), is also included. Activity: While there have been suggestions that individual behavior can be a risk factor for earthquakerelated injury, there has been little documentation of individual behaviors and resultant injuries. The classification scheme includes data on the first actions undertaken by individuals. The characteristics that are relevant include the starting position of the individual (i.e., lying, sitting, standing, etc.) and © 2003 by CRC Press LLC
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whether, how, and how far they moved during or immediately following the ground motion. These data are often best gathered through interviews, and the recommended coding practices are based on surveys conducted following earthquakes in California [Shoaf and Peek-Asa, 2000].
28.4 Casualty Estimation Methodology In the past, the focus of most earthquake-loss-estimation methodology development has been on seismic hazard assessment, building vulnerability, and damage modeling. Development of engineering-based casualty models received less attention in the research community. However, recent developments, such as the widespread availability of computerized GIS-based loss estimation programs in the United States (such as FEMA’s HAZUS® software), and recent earthquakes, including the 1999 Marmara, Turkey earthquake, have generated renewed interest in the enhancement of casualty models. This section describes the evolution of engineering-based casualty models, focusing on several landmark studies, and describes the data required for their application.
28.4.1 1970s: NOAA Scenarios Early loss estimation efforts [NOAA, 1972, 1973] focused on scenario estimates of casualties, impacts on medical resources, and damage to critical facilities and public infrastructure (e.g., transportation, utilities, schools). These two studies, which estimated regional impacts for large earthquakes in the San Francisco and Los Angeles areas, were intended to provide “… a rational basis for planning earthquake disaster relief and recovery operations … .” The studies tabulated casualties per 100,000 population for ten historic earthquake events, from the 1886 Charleston, South Carolina earthquake to the 1971 San Fernando earthquake (see Table 28.6). These statistics were used “… with judgment and in the context of the time of day, comparative construction, and appropriate Modified Mercalli Intensities” [NOAA, 1972, p. 109]. The results were judgment-based, scenario-specific casualty estimates, rather than a readily applicable, comprehensive casualty estimation methodology. The number of predicted deaths was estimated by applying selected historical death rates to the assumed population in various types of structures. For nighttime events, these structures included wood frame, 2- to 9-unit structures (modern and older), and greater than 10-unit structures (modern and older). For example, nighttime deaths for the population in wood-framed structures from a M8.3 earthquake on the Hayward or San Andreas fault were estimated using the 1971 San Fernando death ratio, excluding deaths associated with the VA Hospital collapse, of 12/100,000 population. Further, a death rate of 26/100,000, derived from estimates from the 1933 Long Beach earthquake, were used to estimate nighttime deaths for the population in older 2- to 9-unit residential structures. The final result was an overall nighttime death ratio estimate of 50/100,000, which included an additional allowance of 250 deaths for “catastrophic landslide or collapse of high-rise apartment building.” Daytime deaths were estimated in a similar fashion, and included an additional 200 deaths on freeway structures due to accident or freeway collapse, as well as 800 sidewalk deaths from falling facades (one person for each brick or steel building four stories and larger). A notable methodological contribution from these studies was the assumption that serious injuries (defined as injuries requiring hospitalization) could be determined from death estimates using a ratio of 4:1, while minor injuries could be estimated from deaths using a ratio of 30:1 [NOAA, 1972, p. 118]. In summary, the early casualty estimation efforts by NOAA relied on judgment, aggregate population and construction data, and aggregate historical earthquake statistics, but were essentially independent of the earthquake’s regional ground motion distribution or the estimated damage to buildings.
28.4.2 1980s: ATC-13 and Expert Opinion In the early 1980s, FEMA sponsored a study, conducted by the Applied Technology Council (ATC), to develop consensus damage models in a statistically rigorous manner, in order to facilitate estimation of © 2003 by CRC Press LLC
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TABLE 28.6 Historic Death Rates for 10 Significant Earthquakes Earthquake
Time of Day
1886 Charleston, SC 1906 San Francisco, CA
Nighttime (9:51 p.m.) Nighttime (5:12 a.m.)
1925 Santa Barbara, CA 1933 Long Beach, CA 1940 Imperial Valley, CA 1949 Puget Sound, WA 1952 Kern County, CA 1952 Bakersfield, CA 1964 Alaska 1971 San Fernando, CA
Nighttime (6:42 a.m.) Daytime (5:54 p.m.) Nighttime (8:37 p.m.) Nighttime (11:56 p.m.) Nighttime (4:52 a.m.) Daytime (3:41 p.m.) Daytime (5:36 p.m.) Nighttime (6:01 a.m.)
Death Rate (deaths/100,000 population) 113 124 San Francisco 116 Santa Rosa 80 San Jose 45 26 18 1 500 Tehachapi 3 9 Anchorage 12 (excluding VA Hospital) 62 (including VA Hospital)a
a
A comparison of the San Fernando death rate of 62/100,000 to the estimate of 58 total deaths provided in Table 28.1 demonstrates the wide variety in reported casualty statistics for a single earthquake. Source: Data from NOAA. 1972. “A Study of Earthquake Losses in the San Francisco Bay Area: Data and Analysis,” prepared for the Office of Emergency Preparedness by the National Oceanic and Atmospheric Administration, Washington, D.C.
TABLE 28.7 ATC-13 Building-Related Structure Classes Structure Classes
Height Classes
Wood frame Light metal Unreinforced masonry (URM), bearing wall URM, w/ load-bearing frame Reinforced concrete (RC) shear wall (SW), w/ moment-resisting frame (MRF) RC SW, w/out MRF Reinforced masonry (RM) SW, w/out MRF RM SW, w/ MRF Braced steel frame Moment-resisting (MR) steel (perimeter) frame MR steel (distributed) frame MR ductile concrete (distributed) frame MR non-ductile concrete (distributed) frame Pre-cast concrete, other than tilt-up Long span Tilt-up Mobile homes
Low-rise Low-rise Low-, mid-rise Low-, mid-, high-rise Low-, mid-, high-rise Low-, mid-, high-rise Low-, mid-, high-rise Low-, mid-, high-rise Low-, mid-, high-rise Low-, mid-, high-rise Low-, mid-, high-rise Low-, mid-, high-rise Low-, mid-, high-rise Low-, mid-, high-rise Low-rise Low-rise Low-rise
Source: Data from ATC. 1985. Earthquake Damage Evaluation Data for California, Report ATC-13, Applied Technology Council, Redwood City, CA.
the economic impacts of a major California earthquake. The major thrust of this effort was the development of Modified Mercalli Intensity-based damage functions for a variety of structures, but also included development of standardized structure and occupancy classification schemes. The structure (Earthquake Engineering Facility) classification scheme included more than 70 types of structures, and the 35 occupancy (Social Function) classifications were developed from the four-digit Standard Industrial Classification (SIC) codes of the Department of Commerce. The building-related structural and occupancy classes are listed in Tables 28.7 and 28.8, respectively.
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TABLE 28.8 ATC-13 Building-Related Occupancy Classes Occupancy Classes Residential
Commercial
Industrial
Agriculture Mining Institutional Government Education
Permanent dwelling Temporary lodging Group institutional housing Retail trade Wholesale trade Personal and repair services Professional, technical, and business services Healthcare services Entertainment and recreation Parking Heavy fabrication and assembly Light fabrication and assembly Food and drugs processing Chemicals processing Metal and minerals processing High technology Construction Petroleum Agriculture Mining Religion and nonprofit General services Emergency response services Education
Source: Data from ATC. 1985. Earthquake Damage Evaluation Data for California, Report ATC-13, Applied Technology Council, Redwood City, CA.
TABLE 28.9 ATC-13 Injury and Death Rates* Damage State 1 2 3 4 5 6 7
None Slight Light Moderate Heavy Major Destroyed
Range
Minor Injuries
Serious Injuries
Dead
0 0–1 1–10 10–30 30–60 60–100 100
0 3/100,000 3/10,000 3/1,000 3/100 3/10 2/5
0 1/250,000 1/25,000 1/2,500 1/250 1/25 2/5
0 1/1,000,000 1/100,000 1/10,000 1/1,000 1/100 1/5
* For light steel and wood-frame construction, multiply all numerators by 0.1. Source: Data from ATC. 1985. Earthquake Damage Evaluation Data for California, Report ATC-13, Applied Technology Council, Redwood City, CA, Table 9.3.
To facilitate the compilation of expert opinion data on a consistent basis, the ATC-13 project provided the experts with standardized damage-state definitions (see Table 28.9). Data from three rounds of questionnaires, completed by the more than 60 experts, were fitted using the beta distribution to develop consensus-based damage probability matrices (DPMs), as suggested in earlier work by Whitman and other researchers at MIT [see, for example, Whitman et al., 1974]. The DPMs were tabulations of the probability that a given structure type would be in a given damage state for a given level of ground shaking. The resulting report, ATC-13, Earthquake Damage Evaluation Data for California [ATC, 1985], documented the statistical analysis of expert opinion and provided weighted damage-factor statistics (developed from the DPMs) for 78 classes of structures, including the 40 building types, and 38 lifeline and other types of facilities and equipment. The damage-factor statistics allow the user to estimate mean damage (from the weighted mean value of the best estimate of the damage factor, found in Appendix G), © 2003 by CRC Press LLC
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TABLE 28.10
ATC-13 Occupant Load Model — Occupants per 1,000 ft2 Occupancy Classes
Day Load (3 p.m.)
Night Load (3 a.m.)
Residential–permanent dwelling Residential–temporary lodging Residential–group institutional housing Commercial–retail trade Commercial–wholesale trade Commercial–personal and repair services Commercial–professional, technical, and business services Commercial–healthcare services Commercial–entertainment and recreation Commercial–parking Industrial–heavy fabrication and assembly Industrial–light fabrication and assembly Industrial–food and drugs processing Industrial–chemicals processing Industrial–metal and minerals processing Industrial–high technology Industrial–construction Industrial–petroleum Agriculture Mining Religion and nonprofit Government–general services Government–emergency response services Education
1.2 0.6 2.0 10.0 1.0 4.0 4.0 5.0 6.0 0.2 3.0 5.0 2.5 2.5 1.2 3.0 4.0 2.5 0.2 4.0 65.0 4.0 3.0 20.0
3.1 2.5 3.0 — — 0.1 — 2.0 — — 0.3 0.3 0.3 0.3 0.1 0.3 0.3 0.3 — — — — 0.4 —
Source: Data from ATC. 1985. Earthquake Damage Evaluation Data for California, Report ATC-13, Applied Technology Council, Redwood City, CA.
as well as the standard deviation, from two pieces of data: Modified Mercalli Intensity and the facility’s class. Damage (damage factor, DF) was expressed as the ratio of dollar loss to the replacement cost of the structure. It should be noted that the damage functions in ATC-13 were intended to represent classes of California structures, rather than individual buildings. That is, the damage functions represent average California buildings of “standard construction” within each class. To estimate casualties, ATC-13 provided injury and death rates related to the building’s level of damage, or damage state — an approach first proposed by Whitman [see Whitman et al., 1974]. The ATC-13 rates, given in Table 28.9, represent a combination of the historical statistics (updated from the earlier NOAA work), other engineering models [Whitman], and “judgmental evaluation” [ATC, 1985, p. 259]. Interestingly, the rates as tabulated reflect the assumed 4:1 ratio of serious injuries to deaths and 30:1 ratio of minor injuries to deaths used by the NOAA studies. These rates can be used to estimate casualties when a building’s level of damage (or damage state) and occupancy level are known. If the actual number of occupants is not known, ATC-13 provides an algorithm to estimate approximate daytime or nighttime occupancy load, by occupancy class (as listed in Table 28.8). This relationship is provided in Table 28.10.
28.4.3 1990s: Geographic Information System (GIS)-Based Regional Loss Estimation Tools In the 1990s, technological advances in personal computing technology, relational database management systems, and geographic information systems facilitated the development of automated loss-estimation tools, building on available methodologies such as those described above. HAZUS®, developed by FEMA and the National Institute of Building Sciences (NIBS), is a standardized, nationally applicable earthquake loss-estimation methodology, implemented through PC-based GIS © 2003 by CRC Press LLC
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TABLE 28.11 HAZUS® Damage States Damage State Slight Moderate Extensive Complete
Damage Factor 0–5% 5–20% 20–50% 50–100%
software. To estimate damage and economic losses to regional building inventories, HAZUS® utilizes building damage functions that include: (1) fragility curves that describe the probability of reaching or exceeding different states of damage given peak building response, and (2) building capacity (pushover) curves used (with dampingmodified demand spectra) to determine peak building response [NIBS/FEMA, 1999]. These analytical models represent an enhancement over earlier MMI-based mean damage models. The HAZUS® methodology estimates damage expressed in terms of the probability of a building’s being in any of four damage states: Slight, Moderate, Extensive, and Complete. A range of damage factors (repair cost divided by replacement cost) is associated with each damage state, as shown in Table 28.11 [Bouabid, 2001]. Further, four severity levels are used to categorize injuries [NIBS/FEMA, 2002], as follows: Severity 1 — “Injuries requiring basic medical aid that could be administered by paraprofessionals. These types of injuries would require bandages or observation. Some examples are: a sprain, a severe cut requiring stitches, a minor burn (first degree or second degree on a small part of the body), or a bump on the head without loss of consciousness. Injuries of lesser severity that could be self treated are not estimated by HAZUS.” Severity 2 — “Injuries requiring a greater degree of medical care and use of medical technology such as x-rays or surgery, but not expected to progress to a life threatening status. Some examples are third degree burns or second degree burns over large parts of the body, a bump on the head that causes loss of consciousness, fractured bone, dehydration or exposure.” Severity 3 — “Injuries that pose an immediate life threatening condition if not treated adequately and expeditiously. Some examples are: uncontrolled bleeding, punctured organ, other internal injuries, spinal cord injuries, or crush syndrome.” Severity 4 — “Instantaneously killed or mortally injured.” Casualty rates are tabulated for indoor and outdoor casualties at each injury severity level by building type and damage state. The tabulated rates are based on available U.S. and worldwide casualty data. However, it was recognized by the model developers that the available data are not of the best quality and often have insufficient information about the types of structures where injuries occurred and the mechanism of the injury [NIBS/FEMA, 1999]. Within the most recent version of HAZUS® (HAZUS® 99 SR-2, 2002), indoor casualty rates for severity 3 and 4 do not show much variation across building types, with the exception of selected rates for unreinforced masonry (URM) and a few other types of structures. Outdoor casualty rates vary across the building types for all injury severity levels for the extensive and complete damage states. In addition, the casualty estimation model considers the impact of building collapse in the “Complete” damage state on indoor casualties. The HAZUS® 99 SR-2 casualty rates are provided in Table 28.12. Other automated loss-estimation tools include EPEDAT, the Early Post-Earthquake Damage Assessment Tool, a GIS-based computer program designed to produce regional damage and casualty estimates for emergency response and planning purposes, originally developed for the California Office of Emergency Services (OES) specifically for southern California. EPEDAT utilizes detailed information on local building construction to estimate regional damage and impacts. Building inventory data on the location, age, use, height, and structural type of buildings have been developed from data provided by the county © 2003 by CRC Press LLC
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HAZUS® Earthquake Loss Estimation Methodology Casualty Rates (HAZUS® 99, SR-2) Casualty Severity Level
Damage State
Slight Moderate Extensive Complete (No Collapse) Complete (With Collapse)
Slight Moderate
Extensive
Complete
Severity 1 (%)
Severity 2 (%)
0.05 0.2–0.25 (URM* = 0.35) 1.0 (URM = 2.0) 5.0 (URM = 10.0) 40.0
Indoor Casualties 0 0.025–0.030 (URM = 0.40) 0.1 (URM = 0.2) 1.0 (URM = 2.0) 20.0
0 0.05 (MH = 0, SLF = 0, URM = 0.15) 0.1–0.4 (MH = 0, SLF = 0, URM = 0.6, HR URMI* = 0.6) 2.0–3.0 (MH = 0.01, SLF = 0.01, URM = 5.0, HR URMI = 3.3, HR PC* = 3.3)
Outdoor Casualties 0 0.005 (MH = 0, SLF = 0, URM = 0.015) 0.01–0.04 (MH = 0, SLF = 0, URM = 0.06, HR URMI = 0.06) 0.5–1.2 (MH = 0.001, SLF = 0.001, URM = 2.0, HR URMI = 1.4, HR PC = 1.4)
Severity 3 (%)
Severity 4 (%)
0 0
0 0
(URM = 0.001) 0.001 (URM = 0.002) 0.01 (URM = 0.02) 5.0 (LRWF* = 3.0, MH* = 3.0, SLF* = 3.0)
(URM = 0.001) 0.001 (URM = 0.002) 0.01 (URM = 0.02) 10.0 (LRWF = 5.0, MH = 5.0, SLF = 5.0)
0 0
0 0
(LRWF = 0.0001, URM = 0.0003) 0.0001– 0.0004 (MH = 0, SLF = 0, URM = 0.0006, HR URMI = 0.0006) 0.1–0.3 (MH = 0.001, SLF = 0.001, URM = 0.4, HR URMI = 0.4, HR PC = 0.4)
(LRWF = 0.0001, URM = 0.0003) 0.0001–0.0004 (MH = 0, SLF = 0, URM = 0.0006, HR URMI = 0.0006) 0.1–0.4 (LRWF = 0.05, MH = 0.01, SLF = 0.01, URM = 0.6, HR URMI = 0.6, HR PC = 0.6)
Notes: URM = unreinforced masonry; LRWF = low-rise wood frame; MH = mobile home; SLF = steel, light frame; HR URMI = high-rise steel or concrete frame structures with URM infill walls; HR PC = high-rise precast concrete structures.
assessors in Los Angeles, Orange, Riverside, San Bernardino, and Ventura counties. More than 3,000,000 structures are represented in the EPEDAT database for southern California. More than 40 different building damage models, which relate building damage to ground motion indices as a percent of replacement cost, are employed within EPEDAT. Building damage models vary with building height, age, and structural type. In addition to traditional MMI-based damage models, EPEDAT includes spectral acceleration-based damage models for selected building types, including wood frame dwellings, developed from extensive data collected following the 1994 Northridge earthquake. Casualty models within EPEDAT are based on published models [ATC, 1985; Whitman, 1974]. As discussed, these casualty models estimate mean death and injury rates for any building within a given damage state, and each damage state includes a considerable range of possible damages. To adequately reflect the range of possible injuries within a given damage state, a beta probability distribution utilizing the mean casualty rate for each damage state was applied to each building damage algorithm [EQE, 1994]. In essence, injury rates are distributed within a given damage state such that injuries are more likely to occur in buildings at the upper end of the damage state than at the lower end. These enhanced beta-modified versions of the Whitman and ATC-13 models are used within EPEDAT. While both of these models represent advances in the automated application of loss-estimation techniques, the focus of their model development was damage and economic losses, with less emphasis placed on the modeling of casualties. Accordingly, there is an excellent opportunity to capitalize on the high-quality data collected from recent earthquakes to improve the way engineering-based models estimate building-related earthquake casualties. © 2003 by CRC Press LLC
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TABLE 28.13 Injury Rates for Fatal and Hospital-Admitted Injuries by Modified Mercalli Intensity (MMI) for the 1994 Northridge Earthquake Modified Mercalli Intensity (MMI)
Injury Rate per 100,000 Population 0.03 0.16 2.08 5.11 43.65
Source: Data from Peek-Asa, C. et al. 2000. “GIS Mapping of Earthquake-Related Deaths and Hospital Admissions from the 1994, Northridge, California, Earthquake,” Ann. Epidemiol., 10, 5–13.
28.4.4 Recent Developments: Epidemiologic Casualty Models and Loss-Estimation Model Refinements Epidemiological studies of recent earthquakes have provided some additional models relating selected types of injuries to various earthquake parameters. Following the 1994 Northridge earthquake, Peek-Asa et al. [2000] analyzed fatal injuries and injuries resulting in hospital admissions (per 100,000 population) relative to MMI. This relationship is provided in Table 28.13; its application allows the user to estimate the sum of the top four tiers in the injury pyramid, as shown in Figure 28.4, for a moderate-sized California earthquake similar to the 1994 Northridge earthquake. Further, Shoaf et al. [1998a] developed a similar relationship for minor injuries (including injuries requiring medical care, i.e., injuries treated and released from hospital emergency rooms, as well as other minor injuries, such as cuts and scrapes, that would not necessarily require professional care), from the results of a population-based survey. This relationship is provided in Table 28.14; its application allows the user to estimate the sum of the bottom three tiers in the injury pyramid, as shown in Figure 28.4, again for a moderate-sized California earthquake. Together, these relationships allow the user to estimate the total injury caseload for a moderate-sized earthquake in California from MMI alone, although the user would be unable to distinguish between the various tiers of the injury pyramid. It should be kept in mind that the results would be applicable only for an earthquake similar in size and exposure to the 1994 Northridge earthquake. That is, these relationships would not be applicable to an earthquake in a region where, for example, low-strength masonry was the predominant building material. Information such as that resulting from the recent epidemiological studies of the Northridge earthquake can also be used to improve existing engineering-based casualty models. A comparison of a model prediction to actual Northridge data was used to suggest modifications for existing loss-estimation tools (in this case, EPEDAT) that make the results more useful to the medical community. This model revision translates simple estimates of “injuries” and “deaths” to estimates of fatalities (nonhospital, i.e., DOA), fatalities requiring hospital care (i.e., ICU), trauma cases, nontrauma hospital admissions, emergency room treat and release, and out-of-hospital treatment. These represent the most important casualty categories for medical response planning. Because casualties suffered during the 1994 Northridge earthquake have been well documented, these data represent the best opportunity to validate and refine the casualty models implemented within regional loss estimation tools, such as HAZUS®, or, in this case, EPEDAT. Regional injury statistics for Northridge from hospital records and regional surveys, classified according to the newly developed standardized classification scheme, are given in the injury pyramid in Figure 28.4 [UCLA, 1998]. The information contained in this version of the injury pyramid is identical to that presented in Figure 28.2, except that all estimates are now presented in consistent terms; all estimates are in terms of the number of people (tiers 1–4) or households (tiers 5–7) with injuries.
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DOA 27 6
Die in Hospital Hospitalized/Trauma Cases
9 Hospitalized/Non-Trauma 129
Emergency Department Treat and Release
8,200 HH 16,400 HH
221,400 HH
Out of Hospital Treat and Release
Injured, No Treatment
FIGURE 28.4 Injury pyramid for the 1994 Northridge earthquake (persons or households with injuries).
These numbers were compared with the EPEDAT nighttime simulation results using the best available representation of actual ground motions in the Northridge earthquake (TriNet ShakeMap ground motions, see www.TriNet.org). Further, the baseline casualty estimates have been adjusted to reflect lifesafety mitigation of unreinforced masonry structures (a particularly vulnerable class of unreinforced brick buildings) required by ordinance within the City of Los Angeles, which was heavily impacted by the Northridge earthquake. The comparison can be summarized as follows: • Estimated Deaths within Los Angeles County: EPEDAT predicts approximately 100 deaths, 40% of which occur in wood-frame structures. This estimate is of the same order of magnitude as the actual number of deaths (33), and additional accuracy would be difficult to achieve within the limits of the data and analysis. • Estimated Injuries within Los Angeles County: EPEDAT’s best estimate predicts approximately 400 serious injuries, about three times the actual total of people admitted following the Northridge earthquake (138), but well below the total number seeking care at hospitals (8200 households). In addition, EPEDAT predicts approximately 3000 minor injuries. The best estimate of serious and minor injuries combined (3400) is less than, but within, the same order of magnitude as the total number seeking care at hospitals (8200 households). However, it should be noted that the regional number may underestimate the number of injuries because it is given in terms of households (e.g., may include more than one person). Further, EPEDAT’s upper bound on all injuries (80,000) falls within the bounds of the total number of households seeking care for injuries (24,600), and the total number of households reporting injuries (246,000). In summary, it appears that EPEDAT estimated casualties for the Northridge earthquake, while not matching casualty patterns precisely, provide a reasonable order-of-magnitude estimate of deaths and injuries. Using this comparison between EPEDAT and the injury pyramid for the Northridge earthquake, a recommended model for estimating the various levels of injuries from EPEDAT estimates has been constructed and is provided in Table 28.15. The resulting model provides injury estimates in a format consistent with injury data collected in the field that are meaningful and useful to medical professionals planning for and responding to disasters. In addition, data collected in future events can now be used to further refine and enhance the models. © 2003 by CRC Press LLC
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TABLE 28.14 Minor Injury Rates by Modified Mercalli Intensity (MMI) for the 1994 Northridge Earthquake Modified Mercalli Intensity (MMI)
Injury Rate per 100,000 Population
2,200 1,800 11,000 24,600 22,200
Source: Data from Shoaf, K.I. et al. 1998a. “Injuries as a Result of California Earthquakes in the Past Decade,” Disasters, 22(3): 218–235.
TABLE 28.15 Recommended Refinements to EPEDAT’s Casualty Models for Injury Planning and Response Pyramid Level Non-hospital fatalities In-hospital fatalities Trauma cases Hospital admits (non-trauma) Emergency department (ED) treat and release Out of hospital treat and release
Recommended Model
Description of Injury Category
82% of EPEDAT “best estimate” of deaths 18% of EPEDAT “best estimate” of deaths 6.5% of EPEDAT “best estimate” of serious injuries 93.5% of EPEDAT “best estimate” of serious injuries 16.5% EPEDAT upper bound total injuries 33% EPEDAT upper bound total injuries
DOA Majority require intensive care ISS* >15 (some require intensive care) ISS ≤15 Extremities (esp. in night), falls, blunt trauma, lacerations Similar to ED, may spill over into ED
* ISS = Injury Severity Scale [AAAM, 1990].
28.5 Casualty Mitigation and Prevention Casualty mitigation and prevention efforts can be aimed at three different components: • Structural mitigation • Non-structural mitigation • Behavioral changes Each of these three components is important because all address the causes of injuries at different levels of the pyramid. Structural mitigation of buildings most prone to collapse can significantly reduce the fatalities associated with earthquakes. It has been demonstrated in the Northridge earthquake and the Loma Prieta earthquake that, at least in the United States, fatal injuries in earthquakes are primarily caused by building collapse. In the Northridge earthquake, 16 of the 33 fatal injuries were sustained in the collapse of a single wood-frame apartment building. It appears that differences in fatality rates between U.S. earthquakes and those in other countries are primarily related to the rate of building collapse. Structural mitigation, however, is not necessarily the most appropriate activity to reduce the levels of nonfatal injuries. Both in the recent U.S. (Northridge) and Japanese (Kobe) earthquakes, being hit by objects and falls contributed significantly to the nonfatal injuries, including those requiring hospitalization. To reduce the rates of nonfatal injuries, both non-structural mitigation activities and behavioral changes within the population are necessary. The bolting of tall furniture and securing of loose items would reduce the number of flying objects that might strike occupants of the buildings. Furthermore, they would reduce the numbers of objects that are in the path to be tripped over or stepped on, especially in nighttime earthquakes. © 2003 by CRC Press LLC
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As mentioned earlier, survey participants following the Northridge earthquake indicated that many of the injuries were sustained when they tried to move about in the dark, either during or following the earthquake. While more research is needed, these data suggest that a recommendation to stay in bed during a nighttime earthquake might reduce injuries. Further research into the causes of nonfatal injuries would assist in the development of targeted non-structural mitigation schemes, as well as additional behavioral recommendations.
28.6 Public Health Impacts While injuries are by and large the most obvious human impacts of earthquakes, they are not the only ones. Other health impacts have been noted in a number of earthquakes, including mental health effects, increases in heart attacks, and complications of other chronic diseases, as well as increases in acute illnesses. While relatively modest, the body of literature in these areas is growing, but continues to be widely debated.
28.6.1 Mental Health Impacts It is generally accepted that earthquakes are stressful events that result in some degree of psychological distress among its victims. There is, however, considerable debate as to the nature and extent of the distress, as well as the causative agents of the distress. Research findings in this field have been inconsistent. To some degree, the controversies are based in disciplinary differences between clinically oriented psychology researchers and sociological researchers. Further, the findings from numerous studies on psychological distress have suffered from the same definitional and methodological problems that plague the literature on physical injuries [Tierney, 2000]. The mental health impacts of earthquakes can be viewed as a pyramid, similar to the physical injury pyramid (see Figure 28.5). The base of the pyramid is general emotional distress, with the next level up being those with general distress who seek professional treatment for that distress. The next level of the pyramid represents those who have a diagnosable mental illness as a result of the earthquake. The top of the pyramid represents the most serious level of psychological distress — suicide.
Suicide
Diagnosable Mental Illness
Seek Treatment for Distress
General Emotional Distress
FIGURE 28.5 Mental health pyramid.
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At the base of the pyramid, it is generally accepted that earthquakes have the capability of producing minor psychological distress in a substantial proportion of the population. Following the Northridge earthquake, respondents to a telephone interview were asked about any emotional injuries they might have suffered as a result of the earthquake. One third of respondents to that survey reported that they had been emotionally injured [Siegel, 2000]. When asked to describe those injuries, the majority of respondents reported general feelings of anxiety (86%) with fewer reporting psychosomatic symptoms (7%), panic (4%), or a startle response to sound or motion (2%) [Shoaf et al., 1998b]. These general feelings of anxiety or fear usually do not reach the levels of clinically diagnosable mental illness and rarely require treatment by mental health professionals. A small percentage of those reporting emotional distress said they sought professional help for those emotional injuries (7.9%). Those seeking assistance for their emotional injuries, however, do not necessarily have clinically diagnosable mental illness and those with clinically diagnosable mental illness do not necessarily seek treatment for their illness. The clinical diagnoses generally associated with disasters include post-traumatic stress disorder (PTSD), depression, and anxiety [Norris, 2001]. The above-mentioned survey included two separate measures of psychological distress, one (the Brief Symptom Inventory) that included measures for depression and anxiety and one that measured PTSD. Reports from both the Northridge and Loma Prieta earthquakes suggest that between 0.5% and 4.5% of respondents can be classified as cases of PTSD [Bourque et al., 2001]. Additionally, about 13% of respondents could be classified as depressed and 13% as suffering from anxiety. Unfortunately, the measures of PTSD, depression, and anxiety do not necessarily measure only distress as a result of the earthquake; rather, they are measures of symptomatology in a population that was exposed to the earthquake. In an analysis of these data, Siegel [Siegel et al., 2000] found no associations between earthquake exposure (i.e., damage to home, physical injury) and PTSD score. While there are associations between the measures for depression and anxiety and exposure to the earthquake, the relationship is not straightforward. There is a background level of psychological distress that is unknown in these samples. Furthermore, not all those who were classified as having PTSD, depression, or anxiety sought treatment for emotional injuries, nor did they all report being emotionally injured. About 30% of those who reported being emotionally injured and were classified with PTSD, and 13% of those who reported being emotionally injured and were classified with depression or anxiety, sought medical care for their emotional injuries. Therefore, the magnitude of this level of the pyramid, while definitely smaller than the preceding, cannot be calculated with the presently available data. The top level of the pyramid is the smallest and most difficult to quantify. The notion of suicides resulting from natural disasters is based primarily in anecdotal reports. Durkin [1995] reports that of the 72 deaths he calculated as related to the Northridge earthquake, one was the suicide of a businessman whose business failed because of the earthquake. Epidemiological studies of natural disasters, however, have failed to find an increase in suicide rates following earthquakes (or other events), partly because suicide is a rare event and increases in rates would be difficult to detect [Krug et al., 1998]. Studies of suicide rates following both the Northridge and the Kobe earthquakes actually found a decrease in suicides following the events [Bourque et al., 2001; Shioiri et al., 1999]. Only a small proportion of those with significant psychological distress commit suicide. It has been suggested that between 0.01% and 1% of persons suffering from major depression commit suicide [Oquendo et al., 2001]. Therefore, it is assumed that this tip of the pyramid is relatively small.
28.6.2 Chronic Diseases A great deal of discussion has been generated about heart attacks and other deaths from chronic diseases in earthquakes. For example, of the 59 persons reported by the Los Angeles County Coroner’s Office as having died in the Northridge earthquake, 24 of those deaths were due to medical conditions. While such deaths are reported as attributable to an earthquake, the evidence to link increases in heart attack and other medical conditions to the earthquake is equivocal. Following the Northridge earthquake, there was a twofold increase in heart attack deaths on the 17th of January compared with the first 16 days of © 2003 by CRC Press LLC
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January. However, during the following 2 weeks, the average number of heart attack deaths decreased below the average number for the first 16 days of the month. According to Kloner et al. [1997], there were 55 excess deaths due to ischemic and atherosclerotic heart disease on the day of the earthquake, but 144 fewer deaths due to these causes during the next 14 days. Deaths due to other types of heart disease or cerebrovascular disease associated with the earthquake showed no increases. Other studies have found similar increases in deaths due to heart disease following an earthquake; however, death rates remained elevated for longer periods of time. In the Athens earthquake of 1981, death rates remained elevated for 5 days [Trichopoulos, 1983]; in the Kobe earthquake, they were elevated for 3 months [Kario, 1997]; and in the Armenia earthquake, death rates remained elevated for 6 months [Armenian, 1998]. Reports of increases in other types of chronic disease also exist. In Japan following the Kobe earthquake, it was found that patients being treated for high blood pressure had elevated blood pressures for 6 weeks following the earthquake. The increase in blood pressure was greater for those who lived in areas of greater ground motion than for those in less affected areas [Saito, 1997]. It was found in this study that those patients whose hypertension was being treated with beta-blockers were less affected than those being treated with other types of medication. In a longitudinal study in Armenia, increases in reported new cases of high blood pressure, heart disease, diabetes, and arthritis were found in the first 6 months following that earthquake. They also found that the impact of the earthquake (measured as earthquakeinduced death or injury of family member, loss of dwelling, or loss of material possessions) was positively associated with reporting a new chronic illness [Armenian, 1998]. These studies suggest that earthquakes have the potential for negatively impacting the health of the affected population both in the short and longer term.
28.6.3 Acute Diseases After every earthquake, it seems that there are a great number of rumors about epidemics of infectious diseases. These rumors mostly suggest there will be outbreaks of cholera, typhoid, or other communicable diseases because of contamination of the water supply or because of the dead bodies in the rubble. For the most part, these rumors are unfounded and based on misperceptions about the transmission of such diseases. While it is true that the potential for outbreaks and even epidemics of infectious disease exists after any natural disaster, the actual occurrence of such outbreaks has been rare [Noji, 1997]. For the risk of an epidemic to exist, the disease of concern needs to exist in the population prior to the disaster. Diseases such as cholera or typhoid are not likely to occur in developed nations such as the United States or Japan, because they generally do not exist prior to an earthquake. In less-developed nations, it is possible for small outbreaks to occur when the healthcare system and infrastructure (especially water treatment and sanitation systems) fail in the earthquake. Following the earthquake in Turkey in October 1999, there was a great deal of speculation that outbreaks of cholera and typhoid would occur as a result of the large number of dead bodies. While there are sporadic cases of typhoid in Turkey, the disease is not common there. Emergency medical personnel following the earthquake treated one individual for typhoid, although the case was not confirmed as such, and the source of contagion was not identified. A single case of typhoid in an area where sporadic cases exist is not an outbreak. However, that case fueled a great deal of commotion in the media and the public health community. Dr. Claude deVille de Goyet of the Pan-American Health Organization wrote an op-ed piece for the New York Times, which, unfortunately, was not published. In that piece, Dr. de Goyet talked about the myth that disasters result in epidemics of infectious diseases, and emphasized instead the need for maintenance and quick restoration of sanitary services and potable water to the affected population, as well as surveillance of its health status. He also admonished postdisaster efforts aimed at both the quick disposal of bodies as a public health measure and large immunization campaigns geared to counter epidemics of specific infectious diseases that simply do not occur following these incidents [Shoaf, 2000]. Some increases in common diseases can be expected following earthquakes, when the public infrastructure is disrupted and populations are crowded into shelters. This is especially true if the earthquake © 2003 by CRC Press LLC
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occurs during a period of inclement weather or during a natural period of increased illness. For example, if an earthquake occurs during the influenza season, placing a large number of individuals into the same living space as occurs in temporary shelter situations, this will cause increased transmission of the flu. Furthermore, it has been suggested that dust generated from the rubble increases the likelihood or exacerbates pulmonary conditions. Following the earthquake in Arequipa, Peru in 2001, there were increases in respiratory diseases and complications of asthma [Shoaf, 2001]. One other acute illness problem occurs in earthquakes. Earthquakes can cause the release of soil containing spores, such as coccidioides immitis, causing clinical coccidioidomycosis. This occurred following the Northridge earthquake, causing a small outbreak in a community in southern Ventura County. This outbreak was very small and other such outbreaks have not been reported in other earthquakes.
28.7 Shelter Requirements Post-earthquake shelter requirements depend on a number of factors, including damage to residential structures, availability of lifeline services such as water and power, and other more intangible factors including residents’ previous earthquake experiences and their perceptions of risk. For example, a survey of 1000 households conducted by the City of Los Angeles at 15 shelters approximately 2 weeks after the Northridge earthquake indicated that, while 42% came from significantly damaged homes (red- or yellow-tagged), 34% had left homes that were green-tagged. Of the respondents whose homes were greentagged, 20% reported that they remained in the shelters out of fear [EERI, 1995]. The Northridge earthquake caused significant damage to residential structures. Approximately 34,500 dwelling units were vacated in the City of Los Angeles, including 2,000 single-family homes and 32,500 apartments and condominiums, reportedly displacing more than 50,000 occupants [OES, 1994]. In addition, 6,000 mobile homes fell off their foundations. In total, more than 112,000 structures were subject to post-earthquake safety inspections. Most of the displaced persons were found in the San Fernando, Simi, and Santa Clarita valleys, as well as Santa Monica and west Los Angeles. In response, 45 shelter sites were opened by the American Red Cross and the Salvation Army. Immediately after the earthquake, OES reported more than 14,000 people in formal shelters or camping in parks. This number grew to more than 20,000 people served by park shelters. (It should be noted that these figures do not include displaced persons finding other means of shelter, such as staying with friends or relatives.) To get a sense of the magnitude of the number of people actually displaced by the earthquake, FEMA received more than 350,000 applications for disaster-housing assistance, and by March 31, 1994 had provided more than $600 million in assistance [OES, 1994]. In a telephone survey following the Loma Prieta earthquake, Bourque et al. [1994] found that between 17% and 43% of respondents reported leaving their homes after the earthquake. Those who resided in Santa Cruz County were much more likely to report leaving their homes than those in other parts of the Bay Area. The reasons given for evacuation included damage to the home, recommendation from an official, nonfunctioning utilities, lack of transportation (roads blocked), because they were upset, or because they received invitations from others to stay with them. As many as 24% of respondents reported leaving their homes only because they were upset. Most people returned to their homes within 24 hours; however, in the Santa Cruz area, respondents were more likely to report being out of their homes for longer periods of time. This same study suggests that demographic characteristics may be predictive of sheltering need in areas where there is less damage, but in areas of heavy damage, the major predictor of sheltering need is damage to the residence.
28.7.1 Shelter Estimation Methodology Various loss estimation methodologies exist for assessing regional shelter requirements following earthquakes, including HAZUS® and EPEDAT. Both methodologies include engineering-based assessments of the potential number of displaced individuals based on damage to residential structures, while HAZUS® includes additional limited consideration of utility outage and selected socioeconomic factors. © 2003 by CRC Press LLC
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FIGURE 28.6 Temporary shelters following the 1999 Marmara, Turkey earthquake. (Photographs by W. Mitchell/ MCEER.)
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Within HAZUS®, loss of habitability (number of uninhabitable dwelling units and the associated number of displaced households) is determined from building damage, with additional habitability loss based on the probability that undamaged residences are without power or water. The HAZUS® module that estimates displaced households and shelter requirements is based on the following inputs: • Residential exposure (e.g., the number of single- and multifamily dwelling units and number of households, derived from census data) • Single-family residential damage state distribution (building damage module results indicating damage state probabilities for the various damage states) • Multifamily residential damage state distribution Within HAZUS® [HAZUS®99 SR-1; NIBS/FEMA, 1999], default values indicate that all residential structures (single-family homes and multifamily structures) in the complete damage state (see Table 28.11) are considered uninhabitable. Further, 90% of multifamily residential structures in the extensive damage state are also considered uninhabitable. In addition, structures might be rendered uninhabitable as a result of water or power outage. The portion of the displaced population seeking public shelter (short-term shelter needs) is assessed using selected socioeconomic weighting factors (household income, ethnicity, home ownership, and age) that consider, for example, increased use of public shelters among low-income families. While weighting factors are included for home ownership and age, their default values are zero. Recommended factor values were developed by J.R. Harrald and others at George Washington University, based on work performed for the Red Cross and 200 data points from Northridge. For further information, the reader is referred to the HAZUS® Technical Manual [NIBS/FEMA, 1999, 2002, Chapter 14].
28.8 Closing Remarks While many advances have been made in earthquake engineering, casualties and their modeling have not received similar attention. Nevertheless, a variety of models exist to facilitate casualty estimation from both building damage estimates and ground shaking patterns. These models and this subject area are the focus of a series of ongoing research projects, with the stated goal of standardizing the way earthquake-related injury data are categorized and collected, and integrating the data into existing loss models. The integrated approach to data collection and modeling will facilitate the use of data from recent and future events to refine engineering-based casualty models.
Defining Terms AIS — AIS is an anatomically based consensus-derived global severity scoring system that classifies each injury in every body region according to its relative importance on a six-point ordinal scale.
Atherosclerotic heart disease — the process of the development of plaque in the arteries through deposits of calcium and fats on the artery walls; can lead to ischemic heart disease.
Beta distribution — a statistical distribution commonly used for modeling various aspects of earthquake phenomena, including building damage.
Casualty — an individual who has experienced an injury as a result of an earthquake; includes both those who died as a result of the injury and those who survived the injury.
CDC — Centers for Disease Control (national agency in the United States engaged in research and response for epidemics and disaster medicine)
Cerebrovascular disease — disease resulting from pathologic changes in blood supply to the brain; one common form is a stroke. Coccidioidomycosis — a disease especially of humans and domestic animals caused by a fungus (Coccidioides immitis) and marked especially by fever and pulmonary symptoms (source: MerriamWebster online dictionary). © 2003 by CRC Press LLC
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Crush syndrome — a shock-like state that results after the release of a body part that has been compressed by a heavy object. The syndrome often includes kidney dysfunction and can quickly progress to a life-threatening situation. Damage factor — ratio of the dollar loss or repair cost of a damaged structure to the replacement cost of that structure. Damage probability matrices — tabulations of the probability that a given structure type would be in a given damage state for a given level of ground shaking. Damage state — ranges of damage typically used to describe the continuum of damage from none to total. Generally consists of a description of a structure’s damage in terms of a relative text descriptor and associated range of percent damage (e.g., light damage = 1–10% damage vs. moderate damage = 10–30% damage). EMS — emergency medical service. Epidemiology — a branch of the health sciences that deals with the incidence, distribution, and control of disease and injuries in a population. FEMA — Federal Emergency Management Agency (lead national agency in the United States responsible for disaster response). Hypertension — abnormally high blood pressure and especially arterial blood pressure (source: Merriam-Webster online dictionary) Injury mechanism — the cause of the injury, e.g., falling objects, falls, fires, etc. Injury severity — defined as the level of threat to an individual’s life caused by the pattern of injuries sustained. Ischemic heart disease — caused by decreased blood flow to the heart as a result of plaque in the arterial walls. Morbidity — the rate of injury in a given time, usually expressed as number of injuries per 100,000 population; also used to refer to all those persons who have been injured. Mortality — the rate of deaths in a given time, usually expressed as number of deaths per 100,000 population. OES — office of emergency services: a common name for the lead state or local agency responsible for disaster response (such as California OES). Post-traumatic stress disorder (PTSD) — a clinical diagnosis of psychological distress with specific symptoms in persons exposed to an extreme traumatic event. SAR — search and rescue. Trauma — a physical injury, sometimes referring only to severe injuries that are dealt with in the trauma system that has been set up in the U.S. medical system to deal with severe traumas. Triage — the sorting and allocation of treatment to patients and especially battle and disaster victims according to a system of priorities designed to maximize the number of survivors (source: Merriam-Webster online dictionary). USAR — urban search and rescue.
References AAAM. 1990. Abbreviated Injury Severity Scale, Association for the Advancement of Automotive Medicine, Des Plaines, IL. Alexander, D. 1985. “Death and Injury in Earthquake,” Disasters, 9(1): 57–60. Armenian, H.K., Melkonian, A.K., and Hovanesian, A.P. 1998. “Long Term Mortality and Morbidity Related to Degree of Damage Following the 1988 Earthquake in Armenia,” Am. J. Epidemiol., 148(11): 1077–1084. ATC. 1985. Earthquake Damage Evaluation Data for California, Report ATC-13, Applied Technology Council, Redwood City, CA.
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ATC. 1988. Earthquake Damaged Buildings: An Overview of Heavy Debris and Victim Extrication, Report ATC-21-2, Applied Technology Council, Redwood City, CA. Baker, S.P. et al. 1974. “The Injury Severity Score: A Method for Describing Patients with Multiple Injuries and Evaluating Emergency Care,” J. Trauma, 14: 187–196. Bouabid, J. 2000. personal communication. Bourque, L.B. and Russell, L.A., with the assistance of Krauss, G.L., Riopelle, D.D., Goltz, J.D., Greene, M., McAfee, S., and Nathe, S. 1994. Experiences during and Responses to the Loma Prieta Earthquake, Governor’s Office of Emergency Services, Sacramento, CA. Bourque, L.B., Peek-Asa, C., Mahue, M., Nguyen, L.H., Shoaf, K.I., Kraus, J.F., Weiss, B., Davenport, D., and Saruwatari, M. 1997. “Health Implications of Earthquakes: Physical and Emotional Injuries during and after the Northridge Earthquake,” in Int. Symp. Earthquakes and People’s Health: Vulnerability Reduction, Preparedness and Rehabilitation, World Health Organization Center for Health Development, Kobe, Japan. Bourque, L.B., Siegel, J.M., and Shoaf, K.I. 2001. “Psychological Distress and Use of Health Services Following Urban Earthquakes in California,” in Proc. 1st Workshop for Comparative Study on Urban Earthquake Disaster Management, January, Kobe, Japan. Combs, D.L., Quenemoen, L.E., Parrish, R.G., and Davis, J.H. 1999. “Assessing Disaster-Attributed Mortality: Development and Application of a Definition and Classification Matrix,” Int. J. Epidemiol., 28: 1124–1129. CPHA. 2001. International Classification of Diseases, 9th Revision, Clinical Modification (ICD-9-CM), 6th ed., Commission on Professional and Hospital Activities, Ann Arbor, MI. Durkin, M.E. 1995. “Fatalities, Nonfatal Injuries and Medical Aspects of the Northridge Earthquake,” in The Northridge, California, Earthquake of 17 January 1994, Woods, M.C. and Seiple, W.R., Eds., Special Publication 116, California Department of Conservation, Division of Mines and Geology, Sacramento, CA,. pp. 247–254. EERI (Earthquake Engineering Research Institute). 1995. “The Northridge Earthquake of January 17, 1994, Reconnaissance Report,” Earthquake Spectra, 11 (Suppl. C). EERI. 2000. “Health Impacts, the el Quindio, Colombia Earthquake, January 25, 1999, Reconnaissance Report,” Earthquake Engineering Research Institute, Oakland, CA. EQE International. 1994. “Status Report: Development of an Early Post-Earthquake Damage Assessment Tool for Southern California,” prepared for the United States Geological Survey by EQE International, Irvine, CA. Ghua-Sapir, D. 1991. “Rapid Assessment of Health Needs in Mass Emergencies: Review of Current Concepts and Methods,” World Health Stat. Q., 44(3): 171–181. Glass, R.I., Urrutia, J.J., Sibony, S., Smith, H., and Risso, L. 1977. “Earthquake Injuries Related to Housing in a Guatemalan Village,” Science, 197: 638–643. IFRC. 1996. World Disasters Report 1996, International Federation of Red Cross and Red Crescent Societies. Jones, N.P., Krimgold, F., Noji, E.K. et al. 1990. “Considerations in the Epidemiology of Earthquake Injuries,” Earthquake Spectra, 6: 507–528. Kario, K. and Ohashi, T. 1997. “Increased Coronary Health Diseases Mortality after the Hanshin-Awaji Earthquake Among the Older Community on Awaji Island,” J. Am. Geriatr. Soc., 45(5): 610–613. Kloner, R.A., Leor, J., Poole, W.K., and Perritt, R. 1997. “Population-Based Analysis of the Effect of the Northridge Earthquake on Cardiac Death in Los Angeles County, California,” J. Am. Coll. Cardiol., 30(5): 1174–1180. Krug, E.G., Kresnow, M., Peddicord, J.P. et al. 1998. “Suicide after Natural Disasters,” New Engl. J. Med., 338: 373–378 (retraction printed January 14, 1999). Kuwagata, Y., Oda, J., Tanaka, H., Iwai, A., Matsuoka, T., Takaoka, M., Kishi, M., Morimoto, F., Ishikawa, K., Mizushima, Y., Nakata, Y., Yamamura, H., Hiraide, A., Shimazu, T., and Yoshioka, T. 1997. “Analysis of 2,702 Traumatized Patients in the 1995 Hanshin-Awaji Earthquake,” J. Trauma Injury, Infection, Critical Care, 43(3): 427–432. © 2003 by CRC Press LLC
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Mahoney, L.E. and Reutershan, T.P. 1987. “Catastrophic Disasters and the Design of Disaster Medical Care Systems,” Ann. Emerg. Med., 16(9): 1085–1091. Mahue-Giangreco, M.L. 1999. “Risk Factors Associated with Moderate and Serious Injuries Attributable to the 1994 Northridge Earthquake, Los Angeles County,” UMI Dissertation Services. Mahue-Giangreco, M., Mack, W., Seligson, H.A., and Bourque, L.B. 2001. “Risk Factors Associated with Moderate and Serious Injuries Attributable to the 1994 Northridge Earthquake, Los Angeles, California,” Ann. Epidemiol., 2001(11): 347–357. MCEER. 2000. The 921 Chi-Chi Taiwan Earthquake of 1999 Collection, CD-ROM, Special Publication MCEER-00-SP03, Multidisciplinary Center for Earthquake Engineering Research, Buffalo, NY. NIBS/FEMA. 1999. HAZUS®99 Earthquake Loss Estimation Methodology, Service Release 1 (SR1) Technical Manual, developed by the Federal Emergency Management Agency through agreements with the National Institute of Building Sciences, Washington, D.C. NIBS/FEMA. 2002. HAZUS®99 Earthquake Loss Estimation Methodology, Service Release 2 (SR2) Technical Manual, developed by the Federal Emergency Management Agency through agreements with the National Institute of Building Sciences, Washington, D.C. NOAA. 1972. “A Study of Earthquake Losses in the San Francisco Bay Area; Data and Analysis,” prepared for the Office of Emergency Preparedness by the National Oceanic and Atmospheric Administration, Washington, D.C. NOAA. 1973. “A Study of Earthquake Losses in the Los Angeles, California Area,” prepared for the Federal Disaster Assistance Administration, Department of Housing and Urban Development by the National Oceanic and Atmospheric Administration, Washington, D.C. Noji, E., Ed. 1997. The Public Health Consequences of Disasters, Oxford University Press, New York. Norris, F., with Byrne, C.M. and Diaz, E. 2001. “50,000 Disaster Victims Speak: An Empirical Review of the Empirical Literature, 1981–2001,” Report for the National Center for PTSD and the Center for Mental Health Services (SAMHSA). OES. 1994. “Northridge Earthquake January 17, 1994 Interim Report,” California Governor’s Office of Emergency Services, Sacramento, CA. Oquendo, M.A., Ellis, S.P., Greenwald, S., Malone, K.M., Weissman, M.M., and Mann, J.J. 2001. “Ethnic and Sex Differences in Suicide Rates Relative to Major Depression in the United States,” Am. J. Psychiatry, 158: 1652–1658. Peek-Asa, C., Kraus, J.F., Bourque, L.B., Vimalachandra, D., Yu, J., and Abrams, J. 1998. “Fatal and Hospitalized Injuries Resulting from the 1994 Northridge Earthquake,” Int. J. Epidemiol., 27(3): 459–465. Peek-Asa, C., Ramirez, M.R., Shoaf, K.I., Seligson, H.A., and Kraus, J.F. 2000. “GIS Mapping of Earthquake-Related Deaths and Hospital Admissions from the 1994 Northridge, California, Earthquake,” Ann. Epidemiol., 10: 5–13. Saito, K., Kim, J.I., Meakawa, K., Ikeda, Y., and Yokoyama, M. 1997. “The Great Hanshin-Awaji Earthquake Aggravates Blood Pressure Control in Treated Hypertensive Patients,” Am. J. Hypertens., 10: 217–221. Seligson, H.A., Shoaf, K.I., Peek-Asa, C., and Mahue-Giangreco, M. 2002. “Engineering-Based Earthquake Casualty Modeling: Past, Present and Future,” in Proc. 7th National Conference on Earthquake Engineering, Boston, July, Earthquake Engineering Research Institute, Oakland, CA. Shioiri, T., Nishimura, A., Nushida, H., Tatsuno, Y., and Tang, S.W. 1999. “The Kobe Earthquake and Reduced Suicide Rate in Japanese Males,” Arch. Gen. Psychiatry, 56(3): 449. Shoaf, K.I. 2001. “Preliminary Observations on the Southern Peru Earthquake of June 23, 2001: Health Impacts of the Earthquake, EERI Special Earthquake Report,” EERI Newsletter, 36(11). Shoaf, K.I. and Peek-Asa, C. 2000. “Survey Research in Disaster Public Health,” Prehospital Disaster Med., 15(1): 57–63. Shoaf, K.I. and Rottman, S.R. 2000. “Public Health Impacts of Disasters,” Aust. J. Emerg. Manage., 15(3): 58–63.
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Shoaf, K.I., Sareen, H.R., Nguyen, L.H., and Bourque, L.B. 1998a. “Injuries as a Result of California Earthquakes in the Past Decade,” Disasters, 22(3): 218–235. Shoaf, K.I., Bourque, L.B., and Smith, L.V., with Giangreco, C., Nguyen, L.H., Sareen, H., Siegel, J.M., and Weiss, B. 1998b. “The Impact of the Northridge Earthquake on Los Angeles County: Health Effects,” Report prepared for the Los Angeles County Department of Health Services.. Siegel, J.M. 2000. “Emotional Injury and the Northridge, California Earthquake,” Natural Hazards Rev., November: 204–211. Siegel, J.M., Shoaf, K.I., and Bourque, L.B. 2000. “The C-Mississippi Scale for PTSD in Post-Earthquake Communities,” Int. J. Mass Emerg. Disasters, 18(2): 339–346. Tierney, K.J. 2000. “Controversy and Consensus in Disaster Mental Health Research,” Prehospital Disaster Med., 15(4): 55–61. Trichopoulos, D., Katsouyanni, K., Zavilsanos, S., Tzonou, A., and Dalla-Vorgia, P. 1983. “Psychological Stress and Fatal Heart Attack: The Athens (1981) Earthquake Natural Experiment,” Lancet, 1(8322): 441–444. UCLA. 1998. Center for Public Health and Disaster Relief Newsletter, 1(1), Department of Community Health Sciences, University of California at Los Angeles School of Public Health. Wagner, R.M. 1997. “A Case-Control Study of Risk Factors for Physical Injury during the Mainshock of the 1989 Loma Prieta Earthquake in the County of Santa Cruz, California,” UMI Dissertation Services. Wagner, R.M., Jones, N.P. et al. 1994. “Study Methods and Progress Report: A Case-Control Study of Physical Injuries Associated with the Earthquake in the County of Santa Cruz,” in The Loma Prieta, California, Earthquake of October 17, 1989: Loss Estimation and Procedures, S.K. Tubbesing, Ed., United States Geological Survey, Washington, D.C., pp. A39–A61. Webb, G.R. 2000. “Restoration Activities Following the Marmara Earthquake of August 17, 1999,” in The Marmara, Turkey Earthquake of August 17, 1999: Reconnaissance Report, C. Scawthorn, Ed., MCEER Technical Report, MCEER-00-0001, March, Multidisciplinary Center for Earthquake Engineering Research, Buffalo, NY. Whitman, R.V., Biggs, J.M., Brennan, J. III, Cornell, C.A., de Neufville, R., and Vanmarcke, E.M. 1974. “Seismic Design Decision Analysis: Methodology and Pilot Application,” Report MIT-CE-R74- 15, Structures Publication No. 385, sponsored by the National Science Foundation, Massachusetts Institute of Technology, Department of Civil Engineering, Cambridge, MA. Yamazaki, F., Nishimura, A. et al. 1996. “Estimation of Human Casualties due to Urban Earthquakes,” in Proc. 11th World Conference on Earthquake Engineering, Elsevier Science, Oxford, U.K.
Further Reading The reference list resulting from the interdisciplinary literature review of the medical, epidemiological, public health, and engineering literature can be found at http://www.ph.ucla.edu/cphdr/ projects.html. A full listing of the standardized classification scheme for all aspects of earthquake-related casualties, including such varied items as injury mechanism and building damage, is available at: http:// www.ph.ucla.edu/cphdr/scheme.pdf. ATC. 1985. Earthquake Damage Evaluation Data for California, Report ATC-13, Applied Technology Council, Redwood City, CA. NIBS/FEMA. 2002. HAZUS® 99 Earthquake Loss Estimation Methodology, Service Release 2 (SR2) Technical Manual, developed by the Federal Emergency Management Agency through agreements with the National Institute of Building Sciences, Washington, D.C. Noji, E., Ed. 1997. The Public Health Consequences of Disasters, Oxford University Press, New York, 496 pp.
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29 Fire Following Earthquakes 29.1 Introduction 29.2 Fires following Selected Earthquakes The 1906 San Francisco Earthquake and Fires · The 1923 Tokyo Earthquake and Fires · The 1989 Loma Prieta, California Earthquake and Fires · The 1994 Northridge, California Earthquake and Fires · The 1995 Hanshin (Kobe), Japan Earthquake and Fires · The 1999 Marmara, Turkey Earthquake and Fires · Summary
29.3 Analysis Ignition · Fire Report and Response · Fire Growth and Spread · Fire Response and Suppression · Final Burned Area · Example: Vancouver, B.C.
29.4 Mitigation Reduction of Damage · Automatic Suppression · Suppression by Citizens · Communications · Fire Department Assets · Water · Dedicated Fire Protection Systems
Charles Scawthorn Consulting Engineer Berkeley, CA
29.5 Conclusion Defining Terms References Further Reading
29.1 Introduction Earthquakes cause damage by a variety of damaging agents, including fault rupture, shaking, liquefaction, landslides, fires, release of hazardous materials, tsunami, etc. Shaking is present in all earthquakes, by definition, and is the predominant agent of damage in most earthquakes. Occasionally, however, building characteristics and density, meteorological conditions, and other factors can combine to create a situation in which fire following earthquake, or post-earthquake conflagration, is the predominant agent of damage. Large fires following an earthquake in an urban region are relatively rare phenomena, but have occasionally been of catastrophic proportions. In both Japan and the United States, fire has been the single most destructive seismic agent of damage in the twentieth century. The fires following the San Francisco 1906 and Tokyo 1923 earthquakes, which were both terribly destructive, rank as the two largest peacetime urban fires in man’s history. While not widely perceived today by the public or even many professionals in the earthquake or fire service fields, fire following earthquake is recognized by professionals specializing in this field as continuing to pose a very substantial threat in both countries.
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Although fire following the 1906 earthquake was the overwhelming cause of the damage to San Francisco and Santa Rosa, and has continued as a significant cause of damage since, it has received relatively little attention in the United States. This is perhaps due to several factors: • Earthquakes historically have been the professional concern of seismologists and structural engineers, who, as a class of professionals, are largely uninformed about fire. • Fire protection engineers and fire service personnel have similarly ignored earthquakes, seeing their goal as the mitigation of chronic fire losses by code implementation and other techniques, rather than as earthquake response. • Major conflagrations were a common occurrence in the United States prior to World War II, so that the 1906 experience was seen as more of a conflagration than an earthquake phenomenon. The subsequent decline in U.S. urban conflagrations, due to improved fire and building codes and to improved fire service response due primarily to the use of radios, has only increased this sense of “it can’t happen here.” Less apparent, but perhaps even more important, factors contributing to the lack of attention paid to post-earthquake fire have been: • The United States has not experienced a major urban earthquake since 1906. It is little appreciated that it takes a great earthquake, striking a large urban region, to create the condition of dozens or hundreds of ignitions overwhelming the fire service, thus creating a conflagration. San Francisco 1906 and Tokyo 1923 fulfilled this condition. Earthquakes since 1906 (in the United States: 1933 Long Beach, 1964 Alaska, 1971 San Fernando, 1987 Whittier, 1989 Loma Prieta, and 1994 Northridge; and in Japan: 1968 Tokachi-oki, 1978 Miyagiken-oki, 1984 Nihonkai-chubu, and 1995 Kobe) have generally not fulfilled this condition. Note, however, that there were many ignitions in 1971, 1989, 1994, and 1995, and that there were conflagrations of many acres in Kobe in 1995. • There is a general lack of awareness of the existence of an analytical framework within which to analyze the many factors involved in post-earthquake fire and to quantify these factors and the outcome — many small fires, or conflagration? That large fires following earthquakes remain a problem is demonstrated by ignitions following recent earthquakes such as the 1994 Northridge and 1995 Kobe earthquakes, as well as several recent large nonearthquake conflagrations, including the 1991 East Bay Hills and 1993 Southern California wild fires. While long a concern to fire departments and the insurance industry, consideration of the fire following earthquake problem has been subject to debate regarding the likelihood and severity of post-earthquake fires in any future events. Until recently, perhaps the only group at all concerned with post-earthquake fire has been the insurance industry, which, after 1906, became quite aware of the potential for catastrophic loss by way of this phenomenon. Steinbrugge [1982] presents probably the best summary of knowledge deriving from this field. Scawthorn et al. [1981], based on work by Hamada [1951], Horiuchi [n.d.], Kobayashi [1979], and others in Japan, developed a probabilistic post-earthquake fire ignition and spreading model that has subsequently been applied at two levels: 1. Jurdisdictional — a detailed modeling, with ignitions, fire loading, engine location, and other parameters modeled gridwise at about the 10-hectare level of resolution. Due to the sizable data collection and computational effort involved, this model has been applied to only one U.S. jurisdiction, the City of San Francisco [Scawthorn, 1984]. 2. Regional — a coarser model based on approximations derived from the jurisdictional model. Applied to the San Francisco and Los Angeles areas and other regions [Scawthorn, 1987; Scawthorn and Khater, 1992; Scawthorn and Waisman, 2001], this model for the first time permitted quantified estimates of the aggregate losses due to fire following earthquake. This work has largely served the needs of the insurance industry. The fact that fire following earthquake has been little researched or considered in North America is particularly surprising when one realizes that the conflagration in San Francisco after the 1906 earthquake © 2003 by CRC Press LLC
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was the single largest urban fire in history to that date. It remains today the single largest earthquake loss in U.S. history, in terms of life and economic loss. The loss over 3 days of more than 28,000 buildings within an area of 12 km2 was staggering: $250 million in 1906 dollars, and more than 3,000 killed.1 That fire has since only been exceeded in a peacetime urban fire by the conflagration following the 1923 Tokyo earthquake, in which more than 140,000 people were killed and 575,000 buildings destroyed (77% of those buildings were destroyed by fire) [Usami, 1996]. Fires following large earthquakes are a potentially serious problem because of the multiple simultaneous ignitions that fire departments are called to respond to, while, at the same time, their response is impeded by impaired communications, water supply, and transportation. Additionally, fire departments are called to respond to other emergencies caused by the earthquake, such as structural collapses, hazardous material releases, and emergency medical aid. Most recently, the January 17, 1994 Northridge (M 6.6) and January 17, 1995 Kobe (M 7.2) earthquakes have again emphasized the importance of the problem of fire following earthquake. To aid in an understanding of this problem, this chapter first discusses experiences regarding fires following selected earthquakes, next presents a methodology for analysis of the problem, and then discusses actions that can be taken to mitigate the problem.
29.2 Fires following Selected Earthquakes This section discusses selected U.S. and foreign earthquakes, with emphasis on the fires following these events. More general information on each event is provided in Chapter 1 of this book. Table 29.1 lists all U.S. twentieth-century events with post-earthquake ignitions.
29.2.1 The 1906 San Francisco Earthquake and Fires The April 18, 1906 earthquake was the most devastating earthquake in U.S. history. The region of destructive intensity extended over a distance of 600 km (see Chapter 1, this volume), with strong shaking over a wide area. Despite the strong shaking, the vast majority of the damage in the entire earthquake, and especially in San Francisco, was caused by fire. Scawthorn compiled data on the 52 known ignitions in the City of San Francisco (see Table 29.2). 29.2.1.1 Ignitions and Fire The conflagration following the 1906 earthquake was a complex fire, actually consisting of several separate major fires that grew together until there was one large, burnt area that comprised the northeast quadrant of the city and destroyed more than 28,000 buildings. The progress of these fires has generally been divided into four “periods” [NBFU, 1906; Bowlen, n.d.], although actual times for these periods differ between sources. Generally, the periods comprise the following times: 1. From the earthquake until mid or late in Day 1, when most of the south of Market section had been destroyed, but the higher value north of Market section still remained largely intact 2. The night of Day 1 and the early hours of Day 2, when the north of Market section was invaded by the fire progressing from the west 3. Continued progress of the fire to the north, and a bit to the south, during the remainder of Day 2 4. During Day 3, the last day, when the fire progressed almost entirely to the north, around Telegraph Hill, and burned down to the bay
1 Exact number of fatalities is unknown — until the 1980s, it was believed approximately 700 had been killed. Research by Gladys Hansen, San Francisco Librarian, indicated that far more people killed had not been accounted for. In painstaking research over many years, she slowly gathered evidence from letters of the time, gathered from all over the world, of many more deaths. Of particular interest was the fact that many minority fatalities, especially in San Francisco’s large Chinatown, were known in 1906, but not included in the official count. Her work is ongoing as of this writing, and the count is still increasing. See Hansen and Condon [1989].
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TABLE 29.1 Twentieth-Century Post-Earthquake Ignitions Year
M
City or Area Affected
Ignitions
MMI
1906 1906 1906 1906 1906 1906 1906 1933 1933 1933 1952 1957 1964 1969 1971 1971 1971 1971 1971 1979 1983 1984 1984 1986 1987 1989 1989 1989 1989 1989 1989 1989 1994 1994
8.3 8.3 8.3 8.3 8.3 8.3 8.3 6.3 6.3 6.3 7.7 5.3 8.3 5.7 6.7 6.7 6.7 6.7 6.7 6.4 6.5 6.2 6.2 5.9 6 7.1 7.1 7.1 7.1 7.1 7.1 7.1 6.8 6.8
Berkeley Oakland San Francisco San Jose Santa Clara San Mateo Co. Santa Rosa Los Angeles Long Beach Norwalk Bakersfield San Francisco Anchorage Santa Rosa Burbank Glendale Los Angeles Pasadena San Fernando El Centro Coalinga Morgan Hill San Jose N. Palm Springs Whittier Daly City Berkeley Marin Co. Mountain View San Francisco Santa Cruz Santa Cruz Co. Los Angeles Santa Monica
1 2 52 1 1 1 1 3 19 1 1 1 7 2 7 9 128 2 3 1 4 4 5 2 38 3 1 2 1 26 1 24 77 15
VIII-IX VII-IX VII-X VIII VIII-IX VIII X VI-VII IX VII-VIII VIII VII X VIII VII VI-VII VI-VII VII IX VII VIII VII VIII VI-VII VI VI VI VI VII VII VIII VII-VIII VI-IX VIII
Note: Various sources, compiled by author.
Figure 29.1 shows some of the ignitions in the Central Business District, around the foot of Market and Mission Streets and their spread during the first day, while Figure 29.2 shows the final extent of the burnt area. Figures 29.3 to 29.5 show scenes during and after the fire. 29.2.1.2 Fire Department Response The San Francisco Fire Department in 1905 protected approximately 400,000 persons occupying an urbanized area of about 21 mi2. The department consisted of 585 full-paid fire force personnel (resident within the city and on duty at all times), commanded by Chief Dennis T. Sullivan and deployed in 57 companies (38 engines, 1 hose, 10 ladders, 1 hose tower, and 7 chemical) [NBFU, 1905]. The distribution of these companies was well conceived, being centered about the congested high-value district (i.e., the Central Business District, or CBD, known in San Francisco as the Financial District), with 24 engines, 8 ladders, 1 water tower, and 7 chemical companies within 2 mi of the center of the CBD. All but 2 of the 38 steam engine companies dated from 1890 or later and were rated at an average of 680 gallons per minute (gpm), although the 8 engines tested in 1905 averaged only about 70% of their rated capacity, and the “ability of the men handling the engines was in general below a proper standard” [NBFU, 1905]. The rated pumping capacity of the 38 first-line and 15 relief and reserve engines totaled 35,100 gpm. In
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TABLE 29.2 San Francisco 1906 Earthquake — Ignitions in City of San Francisco No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52
Location 211 /ckat (100' W of Davis) 119-123 Clay St. 15 Fremont Drumm & Jackson Sts. (401 Drumm?) Dupont (Grant)@Pacific & Bdwy NW crnr William & O’Farrell 6th & Howard (130-134 6th St) Montgomery bet Bush & Pine 307-11 Davis nr Clay Blk bet Calif, Mkt & Davis Sansome North of Pine Calif & Battery, NW corner 219 Front nr Sacramento Mission & 22nd St GG Ave & Buchanan (NW crnr) Fulton & Octavia (NW crnr) Hayes & Laguna Ashbury & Walter Masonic & Waller Ashbury Hgts Homestead Dist (FIRES?) Homestead Dist (FIRES?) Pacific @ Leavenworth (NW crnr) 17th & Clement 3rd & Clement Oak nr Stanyon 2625 1/2 Harrison (22nd & 23rd Sts) “Butchertown” (Hunters Pt?) “Butchertown” (Hunters Pt?) Polk bet Bush & Pine (1312 Polk) Bay & Powell Bay & Kearny Steuart (E) @ Mission & Howard Fremont (E) @ Mission & Howard Howard E of 3rd St 282 Natoma (E of 4th St) Bet 5th & 6th Sts, Mkt to Harrison Bet 5th & 6th Sts, Mkt to Harrison 395? Hayes (S) 75' E of Gough Davis bet Pacific & Bdwy Front bet Vallejo & Bdwy Davis & Vallejo (crnr) East St bet Bdwy & Vallejo Golden Gate Ave nr Divisadero Bush & Kearny Market & Kearny Geary & Stockton (239-241 Geary) Howard & 12th (NW crnr) Sutter & Polk (1215 Sutter) Minna * 5th Jessie nr 3rd Market & Beale
Responding Company/Comments E12
T2 extinguished E2; exting w/sand (Capt. Brown) E6 retreated E fr 6th bet Folsom & Clementina No fire indicated; gas pressurized E12 extinguished Very rapid spread, frame bldg; E1 In basement, very rapid spread, frame bldg E1 respndd, no water Extinguished after 5 hrs; E13, 18, 24, 37, T7, E25 Extinguished after 5 hrs; E15, 23, 27, 30, 34 Extinguished after 5 hrs; E14, 21, 34, Chem4 Extinguished after 5 hrs; E14, 21, 34, Chem4, T6 E30, extinguished E30, extinguished E30 (Argonaut reports E30 exting 3 fires Asbury Hgts) E32; district is S of Mission dist, nr county line E32; district is S of Mission dist, nr county line E31; exting w/sand (NB; not same as E2) E36; exting by bucket brigade E26; exting small fire rear of store E22; exting? E25, T9; exting E11 E11 E3, T4 E28; stack collapse on kiln; exting in 2 hrs E20, no water; redirect to foot of Washington St fire E1, 9, 38 Little water Spilled coals; E4 (fire stn next dr), little water No. FIRES & locations unknown; T3 arrives at 0800 No. FIRES & locations unknown; T3 arrives at 0800 “Ham & Eggs fire”; E14, 24, 34; see NBFU Fig 14; no water Exting by Chem Co Exting by Chem Co Exting by Chem Co Exting by Chem Co E30 (poor water, fire confined to 1/4 blk; 12 hses lost) “Noticed in neighborhood” No water E2, exting, SAR E22, no water, attempted to draft fr sewer unsuccessfully T4, exting Soon merged with Jessie & 3rd fire Soon merged with Minna & 5th fire E1, but “a dozen powerful streams”
Source: Scawthorn, C. and O’Rourke, T.D. 1989. “Effects of Ground Failure on Water Supply and Fire Following Earthquake: The 1906 San Francisco Earthquake,” in Proc. 2nd U.S.–Japan Workshop on Large Ground Deformation, July, National Center for Earthquake Engineering Research, Buffalo, NY. © 2003 by CRC Press LLC
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FIGURE 29.1 San Francisco 1906 fire: ignitions and spread, Central Business District. (From Scawthorn, C. and O’Rourke, T.D. 1989. “Effects of Ground Failure on Water Supply and Fire Following Earthquake: The 1906 San Francisco Earthquake,” in Proc. 2nd U.S.–Japan Workshop on Large Ground Deformation, July, National Center for Earthquake Engineering Research, Buffalo, NY.)
summary, the department was rated by the National Board of Fire Underwriters [NBFU, 1905] as efficient, well organized, and, in general, adequate. The NBFU, however, concluded in 1905 that: In fact, San Francisco has violated all underwriting traditions and precedent by not burning up. That it has not done so is largely due to the vigilance of the fire department, which cannot be relied upon indefinitely to stave off the inevitable. © 2003 by CRC Press LLC
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FIGURE 29.2 San Francisco 1906 fire: final extents. (From USGS. 1907. The San Francisco Earthquake and Fire of April 18, 1906 and Their Effects on Structures and Structural Materials, Bull. No. 324, U.S. Geological Survey, Washington, D.C.)
FIGURE 29.3 San Francisco 1906 collapsed building, fire in background. (Courtesy the National Oceanic and Atmospheric Administration)
Within moments after the earthquake, Chief Dennis T. Sullivan was seriously injured as a result of the damage done to the fire station where he was sleeping, and later died. Ten fire stations sustained major damage [Tobriner, personal communication], although no engines were seriously disabled by the earthquake and all went into service [NBFU, 1906]. Street passage was, in general, not a problem, and a number of fires were quickly suppressed, although many more could not be responded to. That is: Fires in all parts of the city, some caused directly by earthquake, some indirectly, prevented an early mobilization of fire engines and apparatus in the valuable business district, where other original fires had started and were gaining headway. [NBFU, 1906] © 2003 by CRC Press LLC
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FIGURE 29.4 View down Sacramento Street during the San Francisco 1906 fire. (Photo: Arnold Genthe, Steinbrugge Collection, courtesy of the University of California Berkeley Earthquake Engineering Research Center.)
FIGURE 29.5 San Francisco destruction by fire: view looking west from Telegraph Hill, showing unburned houses on summit of Russian Hill. St. Francis Roman Catholic Church, with excellent brick walls, in foreground. (From USGS. 1907. The San Francisco Earthquake and Fire of April 18, 1906 and Their Effects on Structures and Structural Materials, Bull. No. 324, U.S. Geological Survey, Washington, D.C.)
The NBFU Conflagration Report [NBFU, 1906] concluded: The lack of regular means of communication and the absence of water in the burning district made anything like systematic action impossible: but it is quite likely that during the early hours of the fire the result would not have been otherwise, even had none of these abnormal conditions existed [sic]. That is, the NBFU concluded that, even under normal conditions, the multiple simultaneous fires would probably have overwhelmed a much larger department, such as New York’s, which had three times the apparatus. Nevertheless, Bowlen [n.d.] concluded that, by 1:00 p.m. (i.e., about 8 h after the earthquake), the fire department, except that it was without its leader, was in fairly good shape, that is the men and horses were in good trim for firefighting, the apparatus was in shape and could be worked where there was water. There is not one report of an engine or man going out of commission during the early hours of the fire, and the department was hard at work all the time, even though there was little to show for its effort. 29.2.1.3 Water System Performance Several factors contributed to the initial ignitions rapidly growing out of control. While the weather was relatively hot and dry, undoubtedly the primary factor leading to the conflagration was the failure of the water system [Scawthorn and O’Rourke, 1989]. In summary, in 1906, water to San Francisco was supplied from two series of reservoirs. South of San Francisco, water was impounded by earth and concrete dams © 2003 by CRC Press LLC
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N SAN FRANCISCO Lake Honda Reservoir
College Hill Reservoir
Lake Merced
Sa nA nd
City Line
s rea Fa ult
San Andreas Pipeline
Pilarcitos Pipeline
University Mound Reservoir
Crystal Springs Pipeline
San Andreas Reservoir Legend: Fault Pipeline Lateral spread damage Bridge damage Fault damage Scale: 0 2
4 km
Pilarcitos Reservoir Crystal Spring Reservoir
FIGURE 29.6 1906 San Francisco water supply (adapted from Schussler, 1906). (From Scawthorn, C. and O’Rourke, T.D. 1989. “Effects of Ground Failure on Water Supply and Fire Following Earthquake: The 1906 San Francisco Earthquake,” in Proc. 2nd U.S.–Japan Workshop on Large Ground Deformation, July, National Center for Earthquake Engineering Research, Buffalo, NY.)
to form the San Andreas, Crystal Springs, and Pilarcitos reservoirs. Transmission pipelines conveyed water from these reservoirs to a second series of smaller reservoirs within the city limits. Water then was distributed throughout the city by means of trunk and distribution pipelines. Figure 29.6 presents a plan view of the 1906 San Francisco water supply adapted from maps prepared by Schussler. At the time of the earthquake, the San Andreas, Crystal Springs, and Pilarcitos reservoirs held a combined volume of 88.7 billion liters. They supplied nearly all water for the city of San Francisco in 1906, whereas today, they represent approximately one half of the local storage capacity in the San Francisco Bay area. Transmission pipelines conveying water from the southern reservoirs were built mainly of wrought iron. Within the city limits there existed approximately 711 km of distribution piping at the time of the earthquake, of which roughly 18.5 and 66.5 km were wrought- and cast-iron trunk lines, respectively. These lines were larger than or equal to 400 mm in diameter. The bulk of the system had been constructed during the years 1870 to 1906. Superimposed on Figure 29.6 are the approximate locations of transmission pipeline damage caused by the earthquake. Flow from all transmission pipelines stopped shortly after the earthquake. Because telephone service was out, emergency control information had to be obtained by dispatching personnel © 2003 by CRC Press LLC
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FIGURE 29.7 Failure of Pilarcitos 30-inch pipeline. (From USGS. 1907. The San Francisco Earthquake and Fire of April 18, 1906 and Their Effects on Structures and Structural Materials, Bull. No. 324, U.S. Geological Survey, Washington, D.C.)
into the field, where maintenance crews reported on the damage. Right lateral strike-slip movement along the San Andreas Fault ruptured a 750-mm-diameter wrought-iron pipeline conveying water from the Pilarcitos to Lake Honda Reservoir (see Figure 29.7). More than 29 breaks were reported north of the San Andreas Reservoir, where the pipeline was constructed parallel to the San Andreas Fault. Fault movement near the San Andreas Reservoir was measured as 3.6 to 5.6 m. Pipeline ruptures were caused by tensile and compressive deformation of the line. More than 3 months were required to reconstruct the pipeline. Within 16 h after the earthquake, repairs were made to that part of the Pilarcitos conduit that was located within the city limits. Water then was pumped from Lake Merced through the Pilarcitos line into Lake Honda at a rate of approximately 25 million liters per day. Dynamic distortion of bridges was responsible for rupturing a 925-mm-diameter wrought-iron pipeline conveying water from the San Andreas Reservoir to College Hill Reservoir, and for rupturing, at three swamp crossings, an 11029-mmdiameter wrought-iron pipeline conveying water from Crystal Springs to the University Mound Reservoir. The wooden trestle bridges all were damaged by strong ground shaking, with no damage or misalignment observed in their timber pile foundations. Approximately 3 days were required to repair the 925-mmdiameter pipe, and over a month was required to restore the 1100-mm-diameter Crystal Springs Pipeline. Figure 29.8A is a map of the 1904 water supply within the San Francisco City limits. There were nine reservoirs and storage tanks, with a total capacity of 354 million liters. Approximately 92% of this total, or 325 million liters, was contained in the Lake Honda, College Hill, and University Mound Reservoirs. These and the pipelines linking them with various parts of the city were the backbone of fire protection. All trunk lines 400 mm or larger in diameter are plotted in Figure 29.8. Trunk lines are shown connected to the Lake Honda, College Hill, University Mound, Francisco Street, and Clay Street Reservoirs; all others were connected to piping 300 mm or less in diameter. Superimposed on the figure are the zones of lateral spreading caused by soil liquefaction, as delineated by Youd and Hoose [1978]. Breaks in the pipeline trunk system crossing these zones are plotted from records provided by Schussler [1906] and Manson [1908]. It can be seen that multiple ruptures of the pipeline trunk systems from the College Hill and University Mound Reservoirs occurred in the zones of large ground deformation, thereby cutting off supply of more than 56% of the total stored water to the Mission and downtown districts of San Francisco. Two pipelines, 400 and 500 mm in diameter, were broken by liquefaction-induced lateral spreading and settlement across Valencia Street north of the College Hill Reservoir. These broken pipes emptied the reservoir of 53 million liters, thereby depriving firefighters of water for the burning Mission District of San Francisco. Figure 29.8B shows a map of the San Francisco water supply and area burned during the fire. All trunk lines of the College Hill and University Mound Reservoirs downstream of the pipeline ruptures are removed from this figure to show the impact and lack of hydraulic conductivity caused by severing these conduits. With the College Hill and University Mound Reservoirs cut off, only the Clay Street tank and © 2003 by CRC Press LLC
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the Lombard and Francisco Street Reservoirs were within the zone of most intense fire, and therefore capable of providing water directly to fight the blaze. The combined capacity of these reservoirs was only 21 million liters, or 6% of the system capacity. The usefulness of such limited supply was further diminished by breaks in service connections caused by widespread subsidence and burning and collapsing buildings. Schussler [1906] identifies service line breaks as a major source of lost pressure and water. There were roughly 23,200 breaks in service lines, between 15 and 100 mm in diameter. Fallen rubble and collapsed structures often prevented firemen from closing valves on distribution mains to diminish water and pressure losses in areas of broken mains and services. As is evident in Figure 29.8B, the Lake Honda Reservoir was able to provide a continuous supply of water to the western portion of the city. The fire eventually was stopped along a line roughly parallel to Van Ness Avenue, where water still was available from the Lake Honda Reservoir. Moreover, the southern and southeastern extent of the fire was bounded by areas south and southeast of the trunk system ruptures. It is likely that these unburned areas had water from the University Mound Reservoir. Recognition of the critical role played by damage to the water system led to the construction of San Francisco’s Auxiliary Water Supply System, which is described later in this chapter.
29.2.2 The 1923 Tokyo Earthquake and Fires This section summarizes the fires that followed the 1923 Kanto earthquake, affecting Tokyo and nearby cities. The 1923 earthquake was followed by the largest urban conflagration in history, in which approximately 140,000 persons perished. The earthquake and conflagration are first briefly summarized, followed by a discussion of the effects on water supply components and a qualitative analysis of the contribution of the water supply damage to the occurrence of the conflagration. 29.2.2.1 Seismological and Overall Damage Aspects The M 7.9 Kanto earthquake [Usami, 1987] occurred at 11:58 a.m. local time September 1, 1923, with an epicenter located just offshore in Sagami Bay, at 139.5 E, 35.1 N. Damage was extensive, with major crustal movements (maximum 2 m uplift), significant numbers of engineered buildings sustaining structural damage [Freeman, 1932], destroying approximately 128,000 houses and damaging another 126,000 [Kanai, 1983], with extensive liquefaction [Hamada et al., 1992] (Figure 29.9) and landsliding [ASCE, 1929]. Shaking intensity has been estimated at JMA 6 (equivalent to MMI IX; Figure 29.10) [Kanai, 1983]. A major tsunami (4 to 6 m in height) affected the Miura and Boso peninsulas, destroying 868 houses [Kanai, 1983; Hamada et al., 1992]. Chapter 1 has additional details on this event. 29.2.2.2 Ignitions and Fire Because of a dense urban aggregation of wooden buildings, Tokyo had long been recognized as a major conflagration hazard. Following a recent dry period and nearby typhoon, meteorological conditions were particularly adverse at the time of the earthquake, with hot (approximately 26°C, 80°F) dry winds of approximately 12.5 m/sec (28 mph) at the time of the earthquake. Winds grew continuously all day, reaching a maximum of 21 m/sec (48 mph) at 11:00 p.m. that evening. The fire occurred just prior to lunchtime, when numerous small charcoal braziers were lighted for the noontime meal, resulting in approximately 277 outbreaks of fire, about 133 of which spread [Okamoto, 1984] (Figure 29.11). The result was a major conflagration with rapid firespread (Figure 29.12), which burned for several days, causing approximately 140,000 deaths and destroying approximately 447,000 houses [Kanai, 1983; Hamada et al., 1992]. 29.2.2.3 Damage to Water Supply Components Water supply systems for the cities of Tokyo, Yokohama, Kawasaki, and Yokosuka were all generally similar in configuration, drawing their supply from rivers emanating from the mountains surrounding the Kanto Plain, conveying the water by gravity to terminal stilling basins via concrete or cast-iron (CI) aqueducts, and thence via distribution systems composed mainly of CI pipe. The performance of each component
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Francisco St. Reservoir
Golden Gate
Legend:
Lombard Reservoir
Presidio Military Reservation
Clay St. Tank
Presidio Heights Reservoir
et
St
k ar
M
8 Breaks
Bay
Transmission Pipelines Trunk Pipelines (≥ 400 mm dia.) Zone of LiquefactionInduced Deformation Pipeline Break
n Fra
of Sa
Golden Gate Park
Lake Honda Reservoir
9 Breaks
Valencia St.
N
Clarendon Heights Reservoir
o
ncisc
13 Breaks Potrero Heights Reservoir
Conduit
it
College Hill Reservoir on sC Sa
nA
nd
rea
Pilorc
Pacific
Lake Merced
University Mound Reservoir
tal Crys gs n i r p S duit o C n
du
1000 m
0
itos
Ocean
Scale:
(A)
FIGURE 29.8 (A) Map of the 1904 San Francisco water system, with ground failures superimposed; (B) same map, showing final burned area. (From Scawthorn, C. and O’Rourke, T.D. 1989. “Effects of Ground Failure on Water Supply and Fire Following Earthquake: The 1906 San Francisco Earthquake,” in Proc. 2nd U.S.–Japan Workshop on Large Ground Deformation, July, National Center for Earthquake Engineering Research, Buffalo, NY.)
is detailed in an unpublished report by ASCE [1929]. Particularly relevant was the performance of the distribution system within the urbanized areas. Tokyo’s distribution system totaled 723 mi in length and included 255,000 linear feet of 16- to 60-in.diameter CI trunk line pipe, and secondary mains from 4 to 14 in., totaling about 700,000 lineal feet. No specific information is available regarding damage to the Tokyo distribution system, except that CI pipe throughout Tokyo suffered in places, especially in filled ground and along river banks. Yokohama’s distribution system totaled 170 mi of CI pipe, ranging in size from 4 to 36 in. All pipe trenches were excavated to recaulk joints — in general, smaller pipe was more damaged than larger, and fittings, tees, and elbows were the worst damaged. Wherever the pipe crossed bridges, pipes were broken. There were 83,600 services to houses — 80% of these houses were burned and their services were destroyed, while services to the 20% unburned were undamaged. Yokosuka’s distribution system comprised 117,000 linear feet (lf), about 50% of which was on reclaimed land. About 50% of the joints required recaulking — damage was greatest to smaller-diameter pipe and to fittings, etc., repeating Yokohama’s experience, as did the experience with burned houses also having services destroyed. In summary, distribution systems were constructed of CI and sustained substantial damage, mostly in smaller diameters, and at tees, elbows, and other fittings and mostly in softer ground.
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Francisco St. Reservoir
Golden Gate
Legend: Transmission Pipelines Trunk Pipelines (400 mm dia.) Zone of LiquefactionInduced Deformation Pipeline Break
Lombard Reservoir Presidio Military Reservation
Clay St. Tank
Burnt Sections of San Francisco
Presidio Heights Reservoir
of Bay San
Golden Gate Park
Fran
Lake Honda Reservoir
Clarendon Heights Reservoir
Potrero Heights Reservoir
cisco
N
Conduit
it
College Hill Reservoir du on sC rea nd nA Sa
Lake Merced
University Mound Reservoir
tal Crys gs n i r p S duit n o C
1000 m
itos
0
Pilorc
Pacific
Ocean
Scale:
(B)
FIGURE 29.8 (CONTINUED)
A major impact was the additional damage to the distribution system as the fire grew in size, due to damage to building services as the buildings burned. 29.2.2.4 Impacts of Water Supply Damage on Firefighting Analyses are not available as to whether Tokyo and Yokohama could have defended themselves against conflagration if meteorological conditions had been more favorable. In the actual event, conditions were extremely unfavorable — perhaps several hundred ignitions occurred almost immediately because of the lunch-hour timing of the earthquake, when thousands of small grills were being employed. The ignitions were fanned by high winds and grew rapidly in the densely built-up neighborhoods of almost exclusively wooden buildings, which had been made more flammable by a recent dry period. Tokyo and Yokohama, particularly the areas most heavily burned, are low-lying. Damage to the distribution systems in these areas was heaviest, so that hydrants were probably often dry. Another important factor was the impact of the fire on both demand and capacity. That is, as the fire grew, it impacted the water system in two mutually exacerbating ways: 1. Demand — In general, fire growth is exponential, for a plentiful fuel supply. While the perimeter that must be defended will grow as the square root of the area of the fire, in general, the net result is that the firefighting water demand increases exponentially over time. 2. Capacity — As the fire grows in area, relatively more of the distribution system is available for supply, so that it would be expected that water supply would increase. However, buildings within the fire are collapsing, breaking their services. In general, the net result is that the capacity of the distribution system is actually decreasing as the fire grows, due to the increased drain placed on the system by hundreds or thousands of broken services. © 2003 by CRC Press LLC
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EXPLANATION 7 6 Kasukabe
Soil Liquefaction 1−9 Investigated Sites
5
Urawa 4 TOKYO
Kofu
2
3 TOKYO BAY
8 Chiba
Kawasaki Yokohama Chigasaki 1
Numazu
SURUGA BAY
SAGAMI BAY Epicenter So 9 u (af rce TATEYAMA ter Ar An ea do ) 0
50 km
FIGURE 29.9 Map of Kanto and Chubu Districts showing areas principally affected by liquefaction during the 1923 Kanto earthquake. (From Hamada, M. et al. 1992. “Liquefaction-Induced Ground Deformations during the 1923 Kanto Earthquake,” in Case Studies of Liquefaction and Lifeline Performance during Past Earthquakes, Vol. 1, Japanese Case Studies, NCEER Technical Report 92–0001, M. Hamada and T.D. O’Rourke, Eds., National Center for Earthquake Engineering Research, Buffalo, NY.)
This situation is typical of urban conflagrations and undoubtedly existed in Tokyo, irrespective of the initial seismic damage to the distribution system. On the other hand, the portions of Tokyo and Yokohama most heavily burned are low-lying, with numerous canals and access to waterways. Therefore, secondary emergency water supply should have been available to the firefighters. However, it is likely the equipment of the time was limited in capacity and could not furnish the volume of water required to contain the large fires that quickly developed. Therefore, the primary factor leading to the conflagrations in Tokyo and Yokohama was not the seismic damage to the water supply system, but rather the rapid growth of numerous simultaneous ignitions under a situation of adverse meteorological and dense wooden-building conditions. These conditions would have overwhelmed the fire service and an undamaged distribution system, even had there been no earthquake. As in San Francisco in 1906, the city was waiting to burn. 29.2.2.5 Summary The 1923 Kanto earthquake resulted in strong shaking and widespread permanent ground deformations. In general, however, this did not severely damage the main water supplies to Tokyo and neighboring cities. The distribution systems, on the other hand, sustained numerous breaks, primarily in smaller pipes in low-lying ground. Notwithstanding the failure of the distribution system, however, the conflagrations that developed, which were the main agent of damage in this catastrophe, were primarily due to non-seismic factors. These included a conflagration-prone built-up environment and an extremely adverse ignition scenario and meteorological conditions. Under these circumstances, it is likely the fire service would have proved inadequate even had there been no earthquake. © 2003 by CRC Press LLC
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FIGURE 29.10 Distribution of earthquake intensity in Tokyo. (From Scawthorn, C. 1997a. “The 1923 Kanto, Japan, Earthquake,” in Reliability and Restoration of Water Supply Systems for Fire Suppression and Drinking Following Earthquakes, Report NIST GCR 97–730, D.B. Ballantyne and C.B. Crouse, Eds., National Institute of Standards and Technology, Gaithersburg, MD.)
29.2.3 The 1989 Loma Prieta, California Earthquake and Fires This section summarizes aspects of a significant fire following the 1989 Loma Prieta earthquake. The earthquake and damage are first briefly summarized, followed by a discussion of the effects on water supply components and an analysis of the interaction of water supply damage to the occurrence of fires.
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Sumida River
Ara River : Extinguished (144) : Spread (133)
Tokyo Bay i
FIGURE 29.11 Outbreaks of fires in the city of Tokyo (Kanto earthquake of 1923). (From Okamoto, S. 1984. Introduction to Earthquake Engineering, University of Tokyo Press, Tokyo. With permission.)
FIGURE 29.12 Firespread in Central Tokyo, showing direction and hourly progress of flame front, 1923 Kanto earthquake. (From Japanese government report.) © 2003 by CRC Press LLC
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29.2.3.1 Seismological and Overall Damage Aspects On October 17, 1989 at 5:04 p.m. local time, an M 7.1 earthquake occurred due to an approximately 40-km rupture along the San Andreas Fault. The epicenter of the 20-sec earthquake was located near Loma Prieta in the Santa Cruz mountains about 16 km northeast of Santa Cruz, 30 km south of San Jose, and about 100 km south of San Francisco. Major damage included the collapse of the elevated Cypress Street section of Interstate 880 in Oakland, the collapse of a section of the San Francisco–Oakland Bay Bridge, multiple building collapses in San Francisco’s Marina District, and the collapse of several structures in Santa Cruz and other areas in the epicentral region. Damage and business-interruption losses were estimated as high as $6 billion. Human losses were 62 people dead, 3700 reported injured, and more than 12,000 displaced. At least 18,000 homes were damaged, 960 were destroyed, and more than 2500 other buildings damaged and 145 destroyed. See Chapter 1 in this volume for more details. 29.2.3.2 Water Supply and Fire Protection San Francisco possesses three water supply systems: • The Municipal Water Supply System (MWSS), which is typical of water systems in any other city, is owned and operated by the San Francisco Water Department (SFWD), and serves both firefighting and municipal (potable water) uses. • The Auxiliary Water Supply System (AWSS) was first developed following the 1906 earthquake and fire and extended periodically thereafter (Figure 29.13). • The Portable Water Supply System (PWSS), developed in the 1980s, is primarily a truck-borne large-diameter hose system (Figure 29.14). The latter two systems are specifically dedicated to firefighting use and are owned and operated by the San Francisco Fire Department (SFFD). They were built following, and in direct response to, the 1906 earthquake and fire (see above). The greatest damage to the MWSS in the Loma Prieta incident consisted of approximately 150 main breaks and service line leaks. Of the 102 main breaks, over 90% were in the Marina, Islais Creek, and South of Market infirm areas. The significant loss of service occurred in the Marina area, where 67 main breaks and numerous service line leaks caused loss of pressure (Figure 29.15). The AWSS consists of several major components: • Static supplies. The main source of water under ordinary conditions is a 10 million-gallon reservoir centrally located on Twin Peaks, the highest point within San Francisco (approximately 750 ft elevation). • Pump stations. Because the Twin Peaks supply may not be adequate under emergency conditions, two pump stations exist to supply water from San Francisco Bay — each has 10,000 gpm at 300 psi capacity. Both pumps were originally steam powered but were converted to diesel power in the 1970s. • Pipe network. The AWSS supplies water to dedicated street hydrants by a special pipe network with a total length of approximately 120 mi. The pipe is bell-and-spigot, originally extra heavy CI (e.g., 1 in. wall thickness for 12 in. diameter), and extensions are now Schedule 56 ductile iron (e.g., 0.625 in. wall thickness for 12 in. diameter). Restraining rods connect pipe lengths across joints at all turns, tee joints, hills, and other points of likely stress. • Fireboat Phoenix.2 The pipe network has manifold connections located at several points along the city’s waterfront to permit the fireboat Phoenix to act as an additional “pump station,” drafting 2
Within days following the 1989 Loma Prieta earthquake, the San Francisco Fire Department purchased a fireboat that Vancouver, B.C. had just discarded. Renamed the Guardian, the fireboat is arguably the largest in North America, with 20,000 Igpm pumping capacity. The Phoenix and the Guardian are both active as of this writing, with each alternately in service for one to several months, and the other in reserve. Both are stationed near the foot of Folsom Street, close to the San Francisco-Oakland Bay Bridge. © 2003 by CRC Press LLC
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from San Francisco Bay and supplying the AWSS. The Phoenix’s pump capacity is 9600 gpm at 150 psi, about the same as Pump Station No. 2. • Cisterns. Finally, in addition to the above components, San Francisco has 151 underground cisterns, again largely in the northeast quadrant of the city. These cisterns are typically constructed of concrete with a 75,000-gallon capacity (about 1-hour supply for a typical fire department pumper).
(A)
Twin Peaks Reservoir (40,000 tons (10 mill. Gallons) Asbury Tank
240m
Jones St Tank
Upper Zone Pump Station
Lower Zone
(B)
FIGURE 29.13 San Francisco AWSS: (A) plan; (B) elevation (schematic).
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Portable Hydrant Cleeson Valve Gated Wye
S. F. Hay or Lake
Cleeson Valve
Gated Wye
Portable Hydrant
Portable Hydrant
Cleeson Valve Cistern
Cleeson Valve
Cistern
Portable Hydrant
FIGURE 29.14 San Francisco PWSS. (Source: C. Scawthorn)
Earthen Mole of San Francisco Gas Light Co. (1899)
1906 Waterfront
0
15
St. 150
200
300
Beach
100 150 200
200 200
150
150 200
300
Boy St. 1857
150
Shoreline
Chestnut St. Fillmore St.
EXPLANATION Service repair Main repair Repair at or near gate valve Pipeline, with diameter (in millimeters)
100
150
Scoll St.
150
150
150
100
Orvisodero St.
Baker St.
300
200
200 300 150
100
100
150 200
200 150
Blvd
Buchanon St.
Marina
150
N 0
200m
0
600 f1
FIGURE 29.15 MWSS Pipe Breaks, Marina District, 1989 Loma Prieta earthquake. (From O’Rourke, T.D. et al. 1992. “Lifeline Performance and Ground Deformation during the Earthquake,” in The Loma Prieta California Earthquake of October 17, 1989: Marina District, U.S. Geological Survey Professional Paper 1151–F, T.D. O’Rourke, Ed., Strong Ground Motion and Ground Failure, T.L. Holzer, Coordinator, U.S. Government Printing Office, Washington, D.C.)
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The AWSS is a system remarkably well designed to furnish large amounts of water for firefighting purposes under normal conditions and contains many special features to increase reliability in the event of an earthquake. The Loma Prieta earthquake resulted in only moderate shaking for most of San Francisco, typically of MMI VI, although selected areas sustained much greater shaking, perhaps as much as MMI IX in the Marina District, where 69 breaks in the domestic water supply and more than 50 service connections to water mains quickly dissipated all domestic water supply in the 40 blocks of the district. The AWSS main serving the Marina District remained intact. However, as a result of the shaking, in locations other than the Marina, the AWSS sustained significant damage. The most significant damage to the AWSS occurred on Seventh Street between Howard and Mission Streets, where a 12-in. main broke. This location is on the boundary of Infirm Area No. 3 and, moreover, the AWSS pipe at this location crosses over a sewer line. Soil settlements in this area are thought to have occurred prior to and also as a result of the earthquake, causing the AWSS pipe to settle onto the sewer line and break. Other breaks included (1) a break in an 8-in. hydrant branch on Sixth Street between Folsom and Howard Streets (where the hydrant branch crossed up and over a sewer line) and (2) five 8-in. elbow breaks, four within Infirm Area No. 3, including one on Bluxome Street where a portion of a building collapsed onto an AWSS hydrant. These breaks resulted in such major leakage that the Jones Street tank (controlling pressure for the Lower Zone) had completely drained in approximately 15 min. Leakage continued so that the first engines to arrive at the Marina fire found only residual water when they connected to AWSS hydrants. Due to uncertainty as to the number and location of AWSS breaks, valves connecting the Upper Zone to the Lower Zone were not opened, and Pump Stations 1 and 2, although available, were not placed in service immediately but only at 8:00 p.m., following identification and isolation of broken mains. As a result, all pressure in the AWSS Lower Zone was lost for several hours following the earthquake. The pump stations were operated at half capacity so as to fill the AWSS mains slowly, out of concern for entrapped air that was exhausted out of the Lower Zone through the Jones Street tank (air could be heard exhausting from the tank). This operation continued until 10:00 p.m., when full pressure was restored and the Jones Street tank had been filled with salt water. Other damage was confined to: • One 75,000-gallon cistern at Fifth and Harrison Streets, which developed a leak at the cold joint between the roof and sidewall due to earthquake damage and lost 20% of its water, leaving just 60,000 gallons for fire suppression purposes. • One high-pressure hydrant destroyed by falling structures and another damaged. 29.2.3.3 Water System Performance and Firefighting Twenty-six fires occurred in San Francisco as a result of the earthquake, 11 of them on October 17 [SFFD, 1990]. One of these fires, which occurred in the Marina District, threatened to become a major conflagration. Firefighting efforts were severely hampered by the lack of MWSS and AWSS service to hydrants caused by the severe liquefaction and resulting pipe breakage in the Marina and elsewhere. Firefighters were forced to resort to drafting from nearby lagoons, which, however, was inadequate, and the fire continued to grow. Deployment of San Francisco’s PWSS, in conjunction with the fireboat Phoenix, provided the only adequate source of firefighting water, and this was the only way the Marina fire was extinguished. A fire began in the four-story wood-frame building at 3701 Divisadero Street at the northwest corner of Beach Street. The building is a typical corner building in the Marina District. Built in the 1920s, it contained 21 apartments, with the ground floor being primarily a parking garage. The building’s lower two floors had collapsed in the earthquake, and the third and fourth floors were leaning southward several feet. The fire, initially quite small, was in the rear of the building. This, combined with the confusion following the earthquake, resulted in a delayed report, meaning that the first San Francisco Fire Department (SFFD) unit did not arrive until approximately 5:45 p.m. (all times estimated). The © 2003 by CRC Press LLC
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source of ignition has not been definitely determined as of this writing. Wind speed was virtually zero. Arrival of SFFD Trucks 10 and 16 was closely followed by Engine (E) 41. Based on the appearance of black smoke, the fire appeared to the officer in charge of E41 (Lt. P. Cornyn) to be a wood-structurefueled fire. E41 connected to the AWSS hydrant directly in front of the building (which actually was leaning over the hydrant) and charged the pump, but found no water pressure. Because of radiant heat, E41 then withdrew across the street. At about 6:25 p.m., the building at the northeast corner (2080 Beach) ignited. At about 6:30 p.m. 3701 Divisadero exploded (the fuel source was most likely leaking gas), flames shot 100 ft or more into the air, buildings across both Divisadero and Beach Streets were either burning or smoldering, and the fire had spread to the north and west neighboring buildings. At about this time, E41 and E10 were protecting the buildings across Divisadero and Beach Streets. E41 was being supplied by E16, which was relaying from a hydrant at Scott and Beach Streets, while E10 was being supplied by E21, which was drafting from a lagoon of the Palace of Fine Arts (located two blocks to the west) and relaying the water. By 6:50 p.m., the fire was burning northward; E3, E36, E22, E31, E14, E25, HT25, and an additional fire reserve engine also were on the scene. E22 attempted to draft from the Marina lagoon, but, due to low tide, was unsuccessful. Because the fire was located only two blocks from the Marina, the fireboat Phoenix was called for, arriving at about 6:30 p.m. At approximately the same time, PWSS hose tenders arrived at the scene and were able to connect to the Phoenix. In all, three PWSS hose tenders responded to the Marina fire (a fourth was in the shop being outfitted for service). Four major runs of hose (or portable water mains) were laid at the Marina fire, with some 6000 ft of 5-in. hose being deployed, using nine portable hydrants. The Phoenix pumped 6000 gpm at 180 psi for over 18 h. Fire spread was stopped at about 7:45 p.m. by master streams from the monitors on the hose tenders, as well as ladder pipes and hand lines. Figure 29.16 indicates the deployment of various SFFD apparatus, including the fireboat Phoenix, at about 6:24 p.m. 29.2.3.4 Summary The 1989 Loma Prieta earthquake provided a number of valuable observations and lessons, including: • The Marina fire was potentially very severe — it was a very large fire in a dense neighborhood of wood-frame construction — an unusually calm wind was a very fortuitous circumstance. • The fire was within 500 ft of San Francisco Bay and the Pacific Ocean — the largest body of water on Earth. However, these could not be drafted from by arriving fire engines, and the water was inaccessible. • The MWSS system had over 400 million gallons of storage within San Francisco, but the numerous breaks in the Marina prevented adequate pressure or volume at Marina hydrants; elsewhere in the city, MWSS performance was generally satisfactory. • The AWSS is designed for earthquake ground motions, and did not sustain damage in the Marina despite widespread liquefaction. Nevertheless, breaks several miles away caused a loss of pressure in the Lower Zone. • The “backup to the backup,” that is, the PWSS backing up the AWSS, which backs up the MWSS, provided firefighting water for extinguishment at the Marina fire. The PWSS’ flexibility and portability proved adequate to the task.
29.2.4
The 1994 Northridge, California Earthquake and Fires
The Northridge earthquake was the largest earthquake to have occurred within a U.S. city in more than 20 years. The 4:31 a.m. January 17, 1994 MW 6.7 earthquake was centered under the Northridge section of the San Fernando Valley area of the Los Angeles region. It resulted in shaking intensities greater than MMI VIII over approximately 700 mi2 of the northern Los Angeles area. The population most heavily affected was in the San Fernando Valley, which is primarily protected by the Los Angeles City Fire Department (LAFD). Table 29.3 lists fire departments significantly affected by the earthquake and their summary statistics (see Scawthorn et al., 1997, for additional detail). © 2003 by CRC Press LLC
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FIGURE 29.16 1989 Loma Prieta earthquake, Marina fire, SFFD deployment. (Source: C. Scawthorn)
As Sepponen [1997] reports: At the time of the earthquake there were 788 LAFD personnel on duty. During the quake firefighters were injured, and several fire stations suffered major damage. Most of the city was without electrical power. Structural damage was noted in 35 station buildings. Although most were repaired quickly, Station 90 was closed for one month for roof repair, Station 70 was out of service for six months, and Station 78 was condemned and demolished. (Ward, 1995) Once equipment and personnel were safely outside of buildings, reconnaissance patrols were sent out as designated in the Earthquake Emergency Operational Plan. The timing of the earthquake at 4:31 a.m., was advantageous for the LAFD because their 24-hour shift change occurs at 6:30 a.m. each day. So, soon after the earthquake occurred the new shift came to work and the other “old” shift continued to work due to the emergency, doubling the number of personnel available. This enabled reserve equipment to be easily put into service. © 2003 by CRC Press LLC
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TABLE 29.3 Fire Departments Affected by the January 17, 1994 Northridge Earthquake
Fire Department
Estimated Population (thousands)
Area (sq. miles)
Number of Stations
Fire Fighting Personnel
Number of Engines
Los Angeles City Los Angeles County Ventura County Santa Monica Burbank Pasadena Glendale South Pasadena Beverly Hills Culver City Fillmore
3,400 2,896 700 97 94 132 166 25 34 41 12
469 2,234 126 8 17 23 30 3 6 5 2
104 127 30 4 6 8 9 1 3 3 1
2,865 1,842 327 100 120 150 167 27 81 66 9
104 144 40+/– 5 6 8 9 2 7 5 1
Source: Scawthorn, C., Cowell, A.D., and Borden, F. 1997. “Fire-Related Aspects of the Northridge Earthquake,” Report prepared for Building and Fire Research Laboratory, NIST-GCR-98–743, National Institute of Standards and Technology, Gaithersburg, MD.
TABLE 29.4 Fire Following the January 17, 1994 Northridge Earthquake Community
Number of Earthquake-Related Fires
Los Angeles City Los Angeles County Ventura County Santa Monica Burbank Pasadena Glendale South Pasadena Beverly Hills Culver City Fillmore Total
77 ∼15 ∼10 4 0 1 0 0 1 0 2 ~110
Source: Scawthorn, C., Cowell, A.D., and Borden, F. 1997. “Fire-Related Aspects of the Northridge Earthquake,” Report prepared for Building and Fire Research Laboratory, NIST-GCR-98–743, National Institute of Standards and Technology, Gaithersburg, MD.
Approximately 110 fires were reported as earthquake-related on January 17, as shown in Table 29.4. The Northridge earthquake reportedly caused or was a contributing factor in 77 fires in the LAFD service area. These were among a total of 161 fires that occurred on the day of the earthquake. The time line in Figure 29.17 shows all calls for assistance with fires on the day of the earthquake. Among the earthquakerelated fires, structure fires predominate (86%). More than 70% (66) of the earthquake-related fires occurred in single- or multiple-family residences, as might be expected from the building stock that is typical in the San Fernando Valley. The major cause of ignition was electric arcing as the result of a short circuit, although gas flame from an appliance was also a recurring source of ignition. The breakdown of the day’s calls into dispatch categories is shown in Figure 29.18. The Northridge earthquake affected the water supply for portions of the San Fernando Valley [Heubach, 1997]. Breaks occurred in at least six trunk lines and a large number of leaks occurred at other locations. The Department of Water and Power estimated that approximately 3000 leaks were caused by the earthquake, including two lines of the Los Angeles Aqueduct. The damage to the system © 2003 by CRC Press LLC
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16 EQ Fires
14
Other Fires
Frequency
12 10 8 6 4 2 2330
2230
2130
2030
1930
1830
1730
1630
1530
1430
1330
1230
1130
1030
930
830
730
630
530
430
0
Hours
FIGURE 29.17 LAFD fires, 4:31 to 24:00 hours, January 17, 1994. (From Scawthorn, C. et al. 1997. “Fire-Related Aspects of the Northridge Earthquake,” Report prepared for Building and Fire Research Laboratory, NIST-GCR98–743, National Institute of Standards and Technology, Gaithersburg, MD.) Other 17%
EMS/Rescue 19%
Earthquake 1% Service Calls 7%
Good Intent Calls 10%
False Calls/Alarms 19%
Fires 12%
Hazardous Conditions 15%
FIGURE 29.18 LAFD incident response types, 1308 incidents, 4:31 to 24:00 hours, January 17, 1994. (From Scawthorn, C. et al. 1997. “Fire-Related Aspects of the Northridge Earthquake,” Report prepared for Building and Fire Research Laboratory, NIST-GCR-98–743, National Institute of Standards and Technology, Gaithersburg, MD.)
resulted in the water pressure dropping to zero in some areas. On January 22, 5 days after the earthquake, between 40,000 and 60,000 customers were still without public water service, and another 40,000 were experiencing intermittent service. Scawthorn et al. [1997] have documented a number of specific fires and fire department operations, as well as all ignitions, in this event. We provide a synopsis of one event here. 29.2.4.1 North Balboa Boulevard Fire 29.2.4.1.1 Site Description This fire scene is located in the Granada Hills area of the San Fernando Valley. It is a residential area with one- and two-story wood-frame single-family dwellings, many with swimming pools (see Figure 29.19A). A 56-in. water main under the street was broken, flooding the street and front yards of the homes (see Figure 29.19B). © 2003 by CRC Press LLC
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(A)
(B)
FIGURE 29.19 North Balboa Boulevard incident, 1994 Northridge earthquake: (A) aerial view; (B) surface view. (Author’s collection) Shown as Color Figure 29.19.
29.2.4.1.2 Location, Ignition, and Cause About 20 min after the earthquake struck, a broken 20-in. gas main under Balboa Boulevard was ignited by the driver of a nearby stalled pickup truck who was attempting to start his vehicle. Electric arcing in the ignition system ignited a large gas cloud, creating a fireball and setting fire to two dwellings on the east side of Balboa and three on the west side. Radiant heat from the gas fire was a major factor in the spread of the fire. Wind was 15 to 20 mph from the northeast. Five homes were destroyed, with minor damage to four others. 29.2.4.1.3 Fire Department Operations Firefighters from E8 and E18 were out on district survey, saw the fire, and responded. E74 responded to a radio request for assistance from E8. Firefighters from E8 arrived first and found Balboa Boulevard impassable because of the water flowing from the broken water main. Captain Rust took E8 around the streets parallel to Balboa (Paso Robles and McLennan Avenues) and cross streets Lorilland and Halsey to check the fire hydrants for water. They were dry. E8 firefighters entered the alley west of Balboa to protect the structures on that side of the fire. They located a swimming pool behind a home on Paso Robles and used it as a water source. Water from this swimming pool was also supplied to E18 at the south end of the alley. E18 firefighters entered the alley west of Balboa and set up to protect the homes at the south end. The heat from the fires was intense and forced firefighters to operate from protected areas. A Los Angeles County brush fire hand crew arrived on the scene as a mutual aid resource and was directed to cut and remove combustible shrubs, trees, fences, etc. around homes exposed to the fire. Firefighters from E74 arrived on the scene, checked the hydrants on the north side of the fire, found them dry, and entered the alley east of the fire. The alley was made impassable by debris from collapsed block walls. Resident volunteers removed the debris, and E74 firefighters proceeded south to use a swimming pool for a water source. They extinguished a fire in the attic of an exposed one-story dwelling and continued to direct water streams onto the exterior of this building. A group of local citizen volunteers formed a bucket brigade on the northeast side of the fire, again using a swimming pool for a water source. They protected the house exposed to the fire at that location. Engine companies 8, 18, and 74 pumped water between 1 1/2 and 2 hours during the firefighting operation. It took about 2 hours for the natural gas leak fire to be reduced in size such that it presented a minimal threat from radiated heat. The incident commander at the scene, Captain Rust, directed operations on the west side between his company and E18, and coordinated efforts with E74 on the east side. Heavy radio traffic use made radio communications very difficult. An aerial photograph of the scene after the structure fires were extinguished is shown in Figure 29.19A. Note that the ruptured gas main is still burning.
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11/2″ Siphon Ejector
E18
11/2″ Suppy
E8
Alley
11/2″
1″
Natural Gas Leak Fire Balboa Blvd Broken Water Main
11/2″ Siphon
1″
Ejector
E74
Volunteers with Buckets
16 Wi -20 nd M PH
Alley
FIGURE 29.20 LAFD Deployment 5:35 a.m., North Balboa Boulevard, 1994 Northridge earthquake. (From Scawthorn, C. et al. 1997. “Fire-Related Aspects of the Northridge Earthquake,” Report prepared for Building and Fire Research Laboratory, NIST-GCR-98–743, National Institute of Standards and Technology, Gaithersburg, MD.)
29.2.4.1.4 Water-Related Aspects Breaks in the water mains rendered all surrounding fire hydrants inoperative. Fortunately, several homes in the area had swimming pools that were used as water supply sources, providing approximately 70 min of water flow. E8 and E74 firefighters used their 1 1/2-in. siphon ejectors, which can supply water at 92 to 115 gpm, to draw water into their tanks. Hose layout as of 5:35 a.m. and water usage for the incident are shown in Figure 29.20 and Table 29.5, respectively.
29.2.5 The 1995 Hanshin (Kobe), Japan Earthquake and Fires The 5:46 a.m. January 17, 1995 MW 6.9 (JMA M7.2) Hanshin (official name: Hyogo-ken Nambu) earthquake was centered under the northern tip of Awaji Island near Kobe, in the Kansai region of Japan. The event resulted in shaking intensities greater than MMI VIII over approximately 400 km2 of the KobeAshiya-Nishinomiya area. Population of the affected area (MMI VIII or greater) is approximately 2 million. The Kobe Fire Department (KFD) is a modern, well-trained fire response agency, organized into Prevention, Suppression, and General Affairs sections and a Fire Academy. The city is served by 1298 uniformed personnel. Equipment includes two helicopters, two fireboats, and 196 vehicles. Approximately 100 fires broke out within minutes, primarily in densely built-up, low-rise areas of the central city, which comprise mixed residential-commercial occupancies, predominantly of wood construction. Within 1 to 2 hours, several large conflagrations had developed. A total of 108 fires were © 2003 by CRC Press LLC
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TABLE 29.5 Water Usage in the Balboa Boulevard Fire Engine 8
One 1 1/2-inch siphon ejector in pool supplying approx. 100 gpm One 1 1/2-inch supply line laid to Engine 18 for their water source
One 1 1/2-inch tip line with spray tip — 125 gpm TOTAL: 8,750 gallons Engine 18 One 1 1/2-inch supply line in to fill tank One 1-inch line with spray tip — 25 gpm TOTAL: 1,750 gallons Engine 74 One 1 1/2-inch siphon ejector in pool supplying approx. 100 gpm Two 1-inch lines/spray tips 50 gpm TOTAL: 3,500 gallons Total estimated water employed to control or extinguish fires: 14,000 gallons Source: Scawthorn, C., Cowell, A.D., and Borden, F. 1997. “Fire-Related Aspects of the Northridge Earthquake,” Report prepared for Building and Fire Research Laboratory, NIST-GCR98–743, National Institute of Standards and Technology, Gaithersburg, MD.
TABLE 29.6 Post-Earthquake Fire Ignitions Post-Earthquake Fires in Time Order for January 17–19 in Kobe City Kobe City by Ward Higashi-nada Nada Chuo Hyogo Nagata Suma Tarumi Kita Nishi Kobe City Total
1/17 ~6:00
~7:00
~8:00
~9:00
~24:00
1/17 Total
1/18 Total
1/19 Total
1/17–19 Total
10 13 8 11 13 4 0 0 1 60
1 0 4 0 1 4 0 0 0 10
2 1 2 2 0 0 0 0 0 7
1 1 1 2 0 4 0 0 0 9
3 2 2 2 3 1 6 1 0 23
17 17 17 17 17 13 6 1 1 109
2 2 2 4 1 2 0 0 0 14
4 0 0 3 4 1 0 0 0 15
23 19 19 24 22 16 6 1 1 138
Post-Earthquake Fires in Time Order for January 17–19 in Cities Other Than Kobe 1/17
Cities Other Than Kobe
~6:00
~7:00
~8:00
~9:00
~24:00
1/17 Total
1/18 Total
1/19 Total
1/17–19 Total
Ashiya Nishinomiya Takaradzuka Itami Kawanishi Amagasaki Awajicho Osaka Toyonaka Suita Other Cities Total
4 11 2 2 1 3 1 7 3 1 37
4 11 0 2 1 2 1 4 1 1 26
1 1 0 2 0 1 0 1 0 0 5
0 1 0 1 0 0 0 1 1 0 4
0 10 2 0 0 2 0 2 0 0 16
9 34 4 7 2 8 2 15 5 2 88
2 4 — — — — — — — — 6
2 3 — — — — — — — — 5
13 41 4 7 2 8 2 15 5 2 99
Note: " — " means no post-earthquake fire reported. (Data as of November 1995.) Source: Sekizawa, A. 1997. “Post-Earthquake Fires and Firefighting Activities in the Early Stage in the 1995 Great Hanshin Earthquake,” NIST Tech. Report NISTIR 6030, Building and Fire Research Laboratory, National Institute of Standards and Technology, Gaithersburg, MD.
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FIGURE 29.21 Aerial view of burned area, 1995 Kobe earthquake. (Author’s collection)
reported in Kobe on January 17 [Kobe Fire Department, 1995], the majority being in the wards of Higashi Nada, Nada, Hyogo, Nagata, and Suma. Fire response was hampered by extreme traffic congestion, collapsed houses and buildings, and rubble in the streets, rendering many areas inaccessible to vehicles. Table 29.6 lists time of ignitions for Kobe and other cities and Figure 29.21 is an aerial view of one of the burned areas. Firefighting water is taken primarily from the city water system, served by gravity from 30 reservoirs. Of these, 22 have dual tanks, with one tank having a seismic shutoff valve so that, in the event of an earthquake, one tank’s contents are conserved for firefighting. In this event, all 22 valves functioned properly, conserving 30,000 m3 of water, which, however, could not be delivered because of approximately 2000 breaks in the underground piping. Kobe has approximately 23,500 fire hydrants, typically flushmounted (i.e., under a steel plate in the sidewalk or street) with one 150-mm-diameter hose connection. The city has provided underground storage of water for disaster firefighting in 968 cisterns, generally of 40,000-liter capacity, sufficient to supply a pumper for about 10 min. All engines carry hard suction so that additional water can be drafted from Osaka Bay or the several streams running through Kobe. Kobe sustained approximately 2000 breaks in its underground distribution system. Water for firefighting purposes was available for 2 to 3 hours, including the use of underground cisterns. Subsequently, water was available only from tanker trucks. KFD attempted to supply water with a fireboat and relay system, but this was unsuccessful because of the relatively small hose used by KFD. The author flew over the area at about 5:00 p.m. on January 17 and was able to observe all of the larger fires (about eight in all) from an altitude of less than 300 m. No fire streams were observed, and all fires were burning freely — several with flames 6 m or more in height. No fire apparatus was observed in the vicinity of the large fires, although it could be seen at other locations (their activities were unclear from the air). Some residents formed bucket brigades (with sewer water) to try to control the flames. Selected aspects of the 1994 Northridge and 1995 Hanshin earthquakes are compared in Table 29.7. Several key observations include: • Earthquakes in urban areas continue to cause multiple simultaneous ignitions and degrade emergency response due to impaired communications, transportation, and water supply. • These events are replicable, as shown by comparison of the 1971 San Fernando and 1994 Northridge events [Scawthorn et al., 1995], and by comparison of the ignition rates and other factors in the Northridge and Hanshin events, providing some validation for simulation modeling and projections for larger events. • Under adverse conditions, large conflagrations are possible in modern cities, as shown by events in California (i.e., the 1991 East Bay Hills Fire and the 1993 Southern California wildfires) and by the Hanshin earthquake in Japan. © 2003 by CRC Press LLC
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TABLE 29.7 Hanshin and Northridge Earthquakes: Comparative Analysis Aspect Event
Region Ignitions
Response
Water Wind Gas Spread
Factor
Northridge
Magnitude (MW) Date (winter) Time Population (MMI VIII) Density (pop/sq km) Number (total) Structural fires Rate (MMI VII) Ign/pop FD communications Resources (ff/popul) Stations Traffic congestion Mutual aid Water system damage Cisterns
6.7 Jan 17 0431 1~1.5 million 1,000~1,500 110 86% 14,719 Manual dispatch 1,338 104 Minor Available — not needed Some Swimming pools Calm ? few% Minor
Automatic shutoffs
Hanshin 6.9 Jan 17 0546 2 million 4,000 108 97% 13,676 1,138 26 (Kobe) Major After 10 hr Total? 946, mostly 40 tons (10 min) Minor 70% — ineffective due to structl collapse Major: 5,000 bldgs
29.2.6 The 1999 Marmara, Turkey Earthquake and Fires The MW 7.4 Kocaeli (Izmit) earthquake occurred at 3:10 a.m. local time August 17, 1999 on the east–west-trending northern strand of the North Anatolian Fault Zone (NAFZ), about 100 km southeast of Istanbul [Scawthorn, 2000]. The 125-km-long fault and high damage area follows or is close to the south shore of Izmit Bay and has predominantly 2.2 m right lateral displacement, from Adapazari in the east to Yalova in the west. Significant vertical fault scarps of as much as 2 m occur at several locations. Peak ground accelerations of approximately 0.4 g were recorded near the fault and liquefaction and subsidence were observed on the shores of Izmit Bay and Lake Sapanca. Several million persons live in the Izmit region, which has experienced rapid growth and heavy industrialization in the last two decades. The predominant building type is mid-rise nonductile reinforced concrete frames with hollow clay tile infill, thousands of which collapsed in a pancake mode. Confirmed dead were approximately 17,000. Estimated population requiring short- to long-term shelter was 200,000. Lifelines generally performed well, with the exception of underground piping in the heavily affected areas, where major damage was reported. Electric power, highways, rail, and telephone were generally functional within several days following the earthquake and the Izmit Water Project (the regional water supply and transmission system) was only lightly damaged and fully functional. Fires occurred in a number of collapsed buildings but were generally confined to building of origin. Two fires broke out at the Tupras oil refinery, which burned for several days and which are of special interest. The most widely publicized and spectacular damage to any industrial facility, because of the tank farm fires that burned out of control for several days [Johnson et al., 2000], occurred at the massive U.S. $3.5 billion refinery near Korfez, owned by the state-owned oil company, Tupras. The first fire was initiated in a floating-roof naphtha tank. Naphtha, a highly volatile material with a low flashpoint, is easily ignited. The speculation is that the sloshing of naphtha in the tank caused the floating roof to breach its seal, allowing naphtha to spill. Sparks from the friction between the steel roof and tank wall likely ignited the naphtha. The refinery receives its entire water supply through a dedicated pipeline from Lake Sapanca, some 45 km to the east. Due to multiple breaks in the pipeline, the refinery quickly lost all water and all firefighting capabilities. As the fire spread to additional tanks, aircraft attempted to douse the fires by dropping foam. After a few days, along with the aerial foam attack, the refinery used diesel pumps to draw water directly from Izmit Bay to fight the fire. The fires were finally declared under control on Sunday, some 5 days after the earthquake. © 2003 by CRC Press LLC
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(A)
(B)
FIGURE 29.22 Tupras Refinery damage due to fire following earthquake: (A) burned and collapsed tank; (B) top of stack collapsed into unit, severely damaging heater unit. Top of stack is in foreground of photo. (Source: Gayle Johnson, EQE International.) Part (A) shown as Color Figure 29.22.
While the fire was burning out of control, an area within 2 to 3 mi of the refinery was evacuated, including some areas where search-and-rescue operations were taking place in collapsed buildings. Train service was disrupted in the area because of the fire. The fire and heat eventually consumed numerous tanks in the tank farm. It was reported that at least 17 tanks were considered to be total losses. They were generally crumpled by the intense heat, with one tank expanding as if ready to explode. The other area of severe and spectacular damage in the refinery occurred in one of their three crude units, when a 90-m-high reinforced concrete heater stack collapsed. The break appeared to occur at about the height of the large-diameter heater duct. Sifting through the rubble of the stack did not immediately reveal the cause of the failure. The top of the stack fell into the unit, destroying the heater, while the bottom portion fell into a pipeway running around the perimeter of the unit. The destroyed pipeway was heavily congested with © 2003 by CRC Press LLC
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piping from all over the refinery. Several months would be necessary to identify, isolate, and repair damaged piping in this area (Figure 29.22). One of the pipes broken by the stack collapse was a naphtha line from the original burning naphtha tank in the tank farm. A fire started when the collapse occurred and, although it was extinguished relatively quickly, it flared up several times because of the new fuel from the broken pipe. The supply could not be stopped because the two block valves were at the tank, inaccessible because of the fire and downstream from the crude unit.
29.2.7 Summary The accumulation of experience based on observations of the above events and others, which space does not permit discussing here, leads to the conclusion that the potential exists for large conflagrations following a major earthquake in an urban area, particularly in a region with a large wood-building stock. Under adverse meteorological and other conditions, these conflagrations could burn for several days, replicating the events of 1906 in San Francisco and 1923 in Tokyo. Extensive well-drilled mutual-aid systems are required to mobilize large resources in response, but the deployment of these resources will be hampered by transportation difficulties and, perhaps most tellingly, failure of firefighting water supplies. Improvements in planning and infrastructure are absolutely essential to forestall this potential.
29.3 Analysis This section presents a methodology for estimating fire losses following earthquake, developed by the author in the 1970s [Scawthorn, 1981] and extended via research and applications in a number of projects since that time. The basic methodology can be seen in Figure 29.23, the fire following earthquake process, which depicts the main aspects of the problem. Fire following earthquake is a process that begins with the occurrence of the earthquake. In summary, the steps in the process are: • Occurrence of the earthquake — This will presumably cause damage to buildings and contents, even if the damage is as simple as knocking things (such as candles or lamps) over. • Ignition — Whether a structure has been damaged or not, ignitions will occur due to earthquakes. The sources of ignitions are numerous, ranging from overturned heat sources to abraded and shorted electrical wiring, and from spilled chemicals having exothermic reactions to friction caused by things rubbing together. • Discovery — At some point, the fire resulting from the ignition will be discovered if it has not self-extinguished (this aspect is discussed further below). In the confusion following an earthquake, the discovery may take longer than it might otherwise. • Report — If it is not possible for the person or persons discovering the fire to extinguish it immediately, fire department response will be required. For the fire department to respond, a report to the fire department must be made. • Response — The fire department then must respond. • Suppression — The fire department then has to suppress the fire. If the fire department is successful, it will move on to the next incident. If the fire department is not successful, it will continue to attempt to control the fire. However, the fire spreads and becomes a conflagration. The process ends when the fuel is exhausted — that is, when the fire comes to a firebreak. This process is also shown in Figure 29.24, which is a fire department operations time line. Time is of the essence for the fire following earthquake problem. In this figure, the horizontal axis is time, beginning at the time of the earthquake, while the vertical axis presents a series of horizontal bars of varying width. Each of these bars depicts the development of one fire, from ignition through growth or increasing size (size is indicated by the width or number of bars).
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Earthquake
Ignition
Discovery
Report
FD Response
Suppression
Stop Y
N Spread / Conflagration
Firebreak / Fuel Exhaustion FIGURE 29.23 Fire following earthquake process.
Beginning at the left (that is, at the time of the earthquake) is the occurrence of various fires or ignitions (denoted by the number of the fire in a square box; see the legend at the bottom of Figure 29.24). Some of these fires occur very soon after the earthquake, while others occur some time later (due, for example, to restoration of utilities). The mechanism of these ignitions following an earthquake is no different from ignition at other times, although the earthquake can create unusual circumstances for ignition to take place. The primary difference due to the earthquake is the large number of simultaneous ignitions. Following this ignition, or fire initiation, phase, there is a period during which the fire is undiscovered but grows. A typical rule of thumb in the fire service is that the rate of growth of an unimpeded fire in this phase will double each 7 sec. In Figure 29.24, the size of the fire is denoted by its number of bars. That is, each bar for a particular fire represents one engine required for control or suppression. Thus, if a fire as charted in Figure 29.24 proceeds, with time, from one bar to two and then three, this denotes that the fire is growing and now requires three class A fire engines to control the fire (class A fire engines have approximately 1200 gpm of pumping capacity). The letter “D” denotes discovery of the fire. Discovery under the post-earthquake environment is often no different from other times, although discovery may be impeded due to damaged detectors or distracted observers. Upon discovery, citizens may themselves attempt to combat the fire and will sometimes be successful. We are concerned herein only with ignitions that citizens cannot or do not successfully combat,
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Earthquake EarthquakeOccurs Occurs
Phase
Fire Department Operations Timeline Ignition Discovery Report FD Arrival
3
?
R
1 D
D
2
R
?
DR
3
Fireground Operations
D
R
4
D
5
?
R
?
D R
6
D R
7
D R
8
Time Legend
7
Ignition
Fire Growth
D
Fire Discovery
Suppression
R Fire Report
Fire Response
Fire Growth (1~3 Engine fire)
FIGURE 29.24 Fire department operations time line.
and that require fire department response. The letter “R” denotes receipt of the fire report by the fire department. Under normal circumstances, fires are reported to the fire department by one of four methods: 1. 2. 3. 4.
Telephone Fire department street boxes (voice or telegraph) Direct travel to a fire station by a citizen (“citizen alarms”) Automatic detection and reporting equipment, usually maintained by private companies
With the exception of citizen alarms, these methods, under normal circumstances, communicate the occurrence of a fire within seconds, which is critical in the timely response and suppression of structural fires and in the size and “design” of modern fire departments. In the critical minutes following an earthquake, review of earthquake experience has indicated that, at present, in areas of strong ground shaking, citizen alarms are likely to be the only feasible method for reporting fires. The telephone system may or may not sustain damage, but almost definitely will be incapacitated due to overload. Fire department street boxes are generally no longer in use (in California, only San Francisco maintains street boxes). Automatic detection and reporting equipment account for only a fraction of commercial property. Such equipment may be damaged in an earthquake and will likely produce many false alarms, which leads to lack of response to real fires because of the inability to discriminate the real from the false alarms. Several other less conventional reporting methods may be employed. These include: • Amateur shortwave-radio operators • Helicopter observation • Ground reconnaissance by police or fire personnel © 2003 by CRC Press LLC
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With regard to the last of these methods, present post-earthquake damage reconnaissance planning on the part of several larger California fire departments has been reviewed and, in general, found to be unrealistic and inadequate for identifying fires at a sufficiently early stage to prevent conflagration. A fundamental flaw in most of these plans is the performance of the post-earthquake damage reconnaissance by the fire personnel themselves, employing fire apparatus (i.e., engines and trucks).3 The flaw lies in the fact that, following an earthquake, both personnel and apparatus will almost immediately be redirected from the reconnaissance to actual fires or other emergency response. Helicopter observation and amateur radio operators similarly will typically be able to identify and report fires only after they have reached greater alarm status (that is, when it is too late). Further, most fire officers have no special training in aerial observation or command. Following the fire department’s receipt of the fire report, apparatus will respond, if available (in Figure 29.24, arrival of apparatus at the fire is denoted by the engine number within a circle — note that herein we track only fire engines, because only engines can suppress serious fires). Response may be impeded by blocked streets due to collapsed structures or by traffic jams. Upon arrival, the fire may be combated according to normal procedures or, if the general situation is sufficiently serious, minimal tactics may be all that is possible. Minimal tactics may constitute: • Deluge (“flood and run” tactics) • Abandonment of the burning structure and protection of exposures only • Recognition that exposed structures cannot be protected, with fallback to a defensible line (e.g., abandonment of a city block, with attempt to stop the fire at a wide street) • Total abandonment, that is, recognition that either little or nothing can be done, that the fire will burn itself out at an identified firebreak with or without fire department intervention, or that other situations are more critical and demand the apparatus Water supply is a critical element and earthquake damage to the water system may reduce supply, thus altering tactics. Due to the interconnectedness of the elements of a water supply system, earthquake damage at some distance from a fireground may still result in reduced supply. In Figure 29.24, we denote increasing control of a fire by the reduction in the number of bars (i.e., engines required for control). As suppression progresses and control of the fire becomes near total, the incident commander will release engines for more pressing emergencies elsewhere. Movement of these released apparatuses is denoted by a diagonal arrow showing travel of an engine from one fire to another. As fires are controlled, engines eventually converge on one or several large fires, or conflagrations. The rate of growth and spread of conflagrations is a function of building materials, density, street width, wind, water supply, and firefighting tactics. In this methodology, the process depicted in Figure 29.24 can be coded in a computer program. An algorithm determines ignitions, assigns a number to each fire, and tracks fire growth. Algorithms also determine fire-reporting time and fire engine arrival. Each fire engine is tracked from location to location. Damage to the water supply is determined on the basis of available information and, in the case of reduced water supply, reduction in fire-suppression capability is estimated. Final burned area for each ignition is thus calculated as a function of fire growth and applied fire-suppression capacity. Each aspect of the problem is discussed in more detail next.
3 Basic fire service apparatus consists of two types: (1) engines (or pumpers), which typically carry a pump of about 1200 gpm capacity, 2000 ft of hose, 500 gal of water, some tools and small ladders, and several firefighters; (2) trucks (also termed ladders, aerials, hook and ladders, etc.), which carry large ladders of about 75 or 100 ft length, a much larger variety of tools and ladders and additional firefighters. A ladder truck by itself cannot pump water, so that the pumper is one basic measure of firefighting capacity. For typical non-earthquake structural fires, however, the limiting factor is more often manpower than pumping capacity.
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29.3.1 Ignition Available twentieth-century U.S. experience of fire following earthquake, provided in Table 29.1, has been reviewed so as to identify earthquake-caused ignitions requiring fire department response. (A detailed review of these data is beyond the scope of this chapter.) Based on this review, it has been determined that post-earthquake ignitions are typically a random event due to: • Excessive motions that result in overturning or breakage of building contents (e.g., ignitions due to open flames or chemical reaction) • Excessive structural deflections that result in abrasion or other damage to electrical wiring and consequent short-circuiting Building collapse is an extreme example of the first mentioned cause and will greatly increase the probability of ignition. Gas piping may be ruptured by either incident. For example, a water heater may overturn, thus breaking the connection, or a building may slide on its foundation and shear connections. Less typical but observed modes of ignition are heat due to friction or sparking due to pounding of structures. Post-earthquake fire ignitions have been normalized by building density and the data regressed against shaking intensity. Two equivalent measures of density and intensity are used: 1. For building density: • SFED (single-family equivalent dwellings = 1500 sq ft of floor area) are chosen as a measure that is readily understandable by laymen (they can be thought of as detached “houses”). A large building of 1.5 million sq ft, for example, would be 1000 SFED. • Millions of square feet of total building floor area. 2. For seismic density: • Modified Mercalli Intensity (MMI), which is a common measure of shaking intensity. • Peak ground acceleration (PGA), which is a measure more common in the technical community (see Chapter 4, this volume, for definitions of both MMI and PGA). SFED and MMI have been used by the author for several decades, for purposes of communication with laypersons and the fire service (whose jargon differs from that of engineers). Figure 29.25 shows normalized fire ignitions as a function of MMI vs. 1000 SFED, and PGA vs. a million square feet of building floor area. A clear trend of increasing ignitions with increasing intensity can be seen. This trend can be stated as shown in Table 29.8, which provides a simple rule of thumb for estimating the number of ignitions that a fire department will have to cope with. For example, for a town of population 20,000 subjected to MMI IX, the number of single-family-equivalent dwellings (SFED) in the town can be roughly estimated to be 20,000/3.5 = 5700 for residential. Total SFED is then about two to three times this (to account for commercial and industrial space), which equates to a total SFED of about 14,000. If the same town were to be subjected to MMI IX, one would expect about five ignitions. While only 1971 San Fernando and later data are employed in this relation, it would be about the same if all twentieth-century events had been employed. Interestingly, the trend is also quite similar to that observed in Kobe in the 1995 earthquake. Post-earthquake ignitions for a particular locality can thus be calculated as a random Poisson process with mean probability determined as a function of MMI or PGA and building inventory (i.e., SFED, or millions of square feet of building floor area). These rates of ignition do not account for possible intentional ignitions arising out of several motives (i.e., arson). It can be argued that arson will be a significant problem, because property owners are, in general, aware that while they may not be covered for shaking damage by their insurance, their fire coverage includes fire following earthquake. As will be seen, it takes relatively few additional ignitions to overwhelm fire department resources, with possible ensuing conflagration. Countering this is the © 2003 by CRC Press LLC
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Ign. per thous SFED
0.30 0.25 0.20 0.15 0.10 0.05 MMI
6
7
8
9
10
0.45 0.40
Ign. per MMsf
0.35 0.30 0.25 0.20 0.15 0.10 0.05 PGA 0
0.1
0.2
0.3
0.4
0.5
0.6
FIGURE 29.25 Post-earthquake ignition rate, based on San Fernando and later data: (A) ignitions per 1000 SFED vs. MMI and (B) ignitions per million square feet floor area vs. PGA.
TABLE 29.8 Approximate Number of SFED per Ignition vs. MMI
© 2003 by CRC Press LLC
MMI
1 Ign. per SFED
7 8 9 10
12,000 7,000 3,000 1,000
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point that, while past earthquakes have seen examples of arson, these appear to have been relatively few and did not occur immediately after the shaking but rather days or weeks later. That is, in the immediate post-earthquake period (the first minutes to hours) of injury, emotion, confusion, and multiple simultaneous ignitions potentially leading to conflagration, people will be too overwhelmed by events to consider arson. Later, when this occurs to the relatively few persons who would actually commit this crime, the fires they set will occur in a period when the fire departments are back on a more normal footing, have been reinforced from outside the stricken area, and presumably will be able to handle these fires. We estimate that the latter scenario is more relevant and hence have not included an allowance for arson in the methodology. Arson ignitions can be included, if one wishes to do so, by simply increasing the number of initial ignitions. The author has specifically investigated this aspect (i.e., intentional fires) following major earthquakes during the 1980s and 1990s and confirmed the above observations.
29.3.2 Fire Report and Response As discussed above, citizen alarms are likely to be the dominant — or only — method of reporting fires in the minutes following a major earthquake. This means that, following discovery, a fire will be reported by a citizen running or driving to the nearest fire station. Thus, we determine time of reporting as a period of delay (herein termed earthquake delay, which accounts for initial confusion, traffic difficulties, etc.) plus travel time from the location of the fire to the nearest fire station. In our model, travel time can be determined based on either direct or right-angle travel and vehicle speed is a variable. Time of fire engine travel to the fire following receipt of the report is similarly based on distance and vehicle speed. Under normal conditions, fire engines average between 15 and 20 mph in responding to a fire (i.e., if distance traveled is divided by total elapsed “roll time,” the result is in the range of 15 to 20 mph — of course, higher speeds are attained during certain portions of the travel). Delays are possible due to detours or traffic jams. Debris blockage of streets is a potential issue and was observed to be a significant factor in Kobe in 1995. This has been considered for typical U.S. urban situations, with the conclusion that typically this should not be a major impediment although it may occur in selected districts. Depending on the time of day, traffic jams may be a more critical factor. Based on a review of post-earthquake traffic conditions in U.S. earthquakes, typical delays can be accounted for by the abovementioned earthquake delay factor.
29.3.3 Fire Growth and Spread Fire growth is a particularly complex phenomenon. Most research in the United States has concentrated on fire growth within one room (so-called “compartment fires”) and only very limited research has been performed on U.S. interbuilding urban fire growth [Takata, 1968; Woycheese et al., 1999]. More work has been performed on wildlands fire spread [Rothermel, 1983], but this work is of limited applicability to the urban situation. Of available urban fire spread equations, the Hamada equations are most useful [Hamada, 1951, 1975; Horiuch, n.d.; Scawthorn et al., 1981; Terada, 1984]. These equations are based on Japanese experience in twentieth-century conflagrations, both during peacetime (e.g., following the 1923 Kanto earthquake) and wartime. The equations provide an elaborate model of fire spreading for urban Japan, accounting for buildup to a fully involved fire, which is too extensive to detail here. From Hamada’s model, conservatively using parameters for only a fully involved fire, a result that can be used [Scawthorn, 1981] is that:4
[
] [
N ( xt , V ) = (1.5 δ) a02 K s K d + K u
4
]
A similar form of the Hamada equations is provided in the HAZUS [2002].
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where N(xt , V) is the number of low-rise buildings destroyed by fire spread, per fire outbreak; xt is time in minutes; V is wind speed, m/sec; a0 is average building plan dimension, m; δ is total plan area of wooden buildings divided by (total area minus water area) of the subject regional subsection; and
[
]
K d = (a0 + d ) T4 × xt
(29.2a)
[
] [
]
(29.2b)
[
] [
]
(29.2c)
K s = (a0 2) + d + (a0 + d ) Ts ( xt − Ts ) K u = (a0 2) + d + (a0 + d ) Tu ( xt − Tu ) and
Ti =
(1 − fb )[3 + 0.375 a0 + (8d (c 4i + c 5iV ))] + fb [5 + 0.625 a0 + 16 d (c 4i + c 5iV )]
(
c1i 1 + c 2iV + c 3iV 2
)
(29.2d)
where d is the average building separation, m; T4 is the time in minutes required by the fully developed fire to advance to the next building in the downwind direction; Ts is similar in the side-wind and Tu is similar in the up-wind directions; fb is the ratio of fire-resistant buildings; i = 4,s,u and cji (j = 1 to 5), given in Table 29.9.
TABLE 29.9 Constants for Equation 29.2 (a–d) i
c 1i
c 2i
c 3i
c 4i
c 5i
4 s u
1.6 1.0 1.0
0.1 0.0 0.0
0.007 0.005 0.002
25.0 5.0 5.0
2.5 0.25 0.2
The Hamada equations are based on the hypothesis of an urban area being a series of equal blocks of structures with equal spacing between structures. The plan dimension of the average structure is denoted “a,” with average separation distance between structures “d.” The “built-upness,” or building density ratio δ, is defined above. Figure 29.26 shows fire spread as an irregular oval, which is typical of fires burning through a relatively uniformly distributed fuel load, with constant wind velocity. In actual urban conflagrations, patterns of fire spreading are more variable and are a function of wind speed and changes in direction, varying fuel availability in differing directions, and of fire suppression tactics. Burned area is approximately (Kd + Ku) * (2Ks). To explore the question of utility of these equations in the U.S. context, observed fire spread in various U.S. twentieth-century fires was compared with the fire spread predicted using these equations [Scawthorn, 1987] (see Figure 29.27). It was found that, with the exception of spread by branding among wood buildings under high winds, estimation using the Hamada equations agreed well with observation. Floor-to-floor fire spread in modern mid- and high-rise construction typically is slower, however, and we have modeled this by using the above equations reduced by a factor. Note that mid- and high-rise fire rate of resistance varies substantially by jurisdiction, depending on local fire codes and enforcement. These estimates are for fire spread within one city block or a built-up district and do not account for fire spread across firebreaks, such as streets. To develop estimates of the probability of a typical fully developed building fire crossing a firebreak under various wind speeds and with and without active fire suppression efforts (see Scawthorn, 1987 for details), World War II and other data were reviewed [Bond, 1946]. Fire growth and spread then is modeled using these equations, taking into account probability of © 2003 by CRC Press LLC
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10 mins Wind
1 hr
2 hrs
FIGURE 29.26 Typical fire spread. FIRE SPREAD: ESTIMATION VS OBSERVATION Method of Spreading B
40
35
B
OBS. FIRE SPREAD (fpm)
30
Branding among wood bldgs in high winds
SFb B
25 G 20
G
Line
15
ent
reem
B
Ag fect
er
of p
SFg SFg
10 G
SFg G G G SFg SFg SFg G G SFg G G SFg S GU S
5 0 0
2
SFg
4
6
SFg SFg D SFg
8 10 12 EST. FIRE SPREAD (fpm)
14
16
18
20
FIGURE 29.27 Fire spread estimated with Hamada equations vs. fire spread observed in U.S. non-earthquake conflagrations. (Source: Scawthorn, C. 1987. Fire Following Earthquake: Estimates of the Conflagration Risk to Insured Property in Greater Los Angeles and San Francisco, All-Industry Research and Advisory Council, Oak Brook, IL. With permission.) © 2003 by CRC Press LLC
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crossing a firebreak (with or without active fire-suppression capability being present). Fires are tracked and merged where they meet (i.e., areas are not “burned twice”).
29.3.4 Fire Response and Suppression As discussed above, fire growth and fire engine location are tracked concurrently. Under normal conditions, urban fire department response to a structural fire is usually a minimum of two fire engines and one ladder truck (additional apparatus responds in high-value or extra-hazard areas). These normal responses will not be possible following a large earthquake because fires may outnumber fire engines. Based on review of actual operations following earthquakes and discussions with senior fire department officials, it is likely that, following an earthquake, only one engine will respond to reported fires initially, to suppress the fire or size up the situation. Thus, initial response should be modeled in this manner, initially allocating one engine to each fire and additional engines as available. Where fires outnumber first-line engines, the difference is termed “excess fires.” A question arises whether fire department resources will initially be totally and primarily devoted to fire suppression, because it should be recognized that other demands (search and rescue, hazardousmaterial response, emergency medical treatment) will also be placed on these resources. For most analysis, it should be assumed that the fire department’s first priority will be fire suppression. Note that this assumption is optimistic, especially because building collapses and hazardous-material releases may involve large numbers of victims. This aspect has been reviewed with senior officials of several fire departments and their opinion is that some fire department resources will have to be diverted from firefighting to these other services. However, experience has shown that serious fires typically receive first priority for the following reasons: • Fire service training and tradition. • Fires are dynamic while building collapses are relatively static — that is, a fire situation will worsen if neglected, while the building collapse and rescue situation can often wait several hours (indeed often must await the arrival of heavy equipment). • Other services (police and others) can assist in building collapses, emergency medical treatment, and hazardous-material management (via isolation and evacuation), while only the fire service is equipped to handle serious fires. The impact of this assumption is to decrease total expected losses due to fire following earthquake. In addition to each jurisdiction’s fire-suppression resources (i.e., the department’s first-line and reserve engines, other equipment, and personnel), automatic and mutual aid need to be considered. These resources, of course, arrive somewhat later, from more distant locations. The size of the fire at first engine arrival time (in terms of actively burning SFEDs and water required for suppression) is the next parameter in the model and should be compared with that engine’s suppression capability. Engine-suppression capability should be modeled using guidelines appropriate for typical structural fires under non-earthquake conditions and modified to take into account reduced available water (due to earthquake damage to the water supply) and likely fire department use of minimal tactics (discussed above). That is, given a burning area, required fire flow under normal conditions can be computed on the basis of 4 gpm for each 100 cubic feet (cf) of occupancy directly involved in the fire or immediately exposed [Kimball, 1966]. For larger fires, this volumetric calculation is based only on perimeter defense. Depending on construction and available manpower, a fire engine typically can apply up to 1500 gpm (using the monitor or handlines — note, however, if 1500 gpm is to be applied entirely by handlines, additional personnel will be needed). This may be reduced depending on the post-earthquake condition of the water supply system. Thus, one engine can typically attack a maximum burning volume of 37,500 cf (typically, 3000 to 4000 sq ft of floor area) if the monitor can be efficiently used, or half of this (about one SFED) if handlines are used and additional personnel are not available. If minimal tactics are
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employed (i.e., no attacks, perimeter protection only), then the capacity of one engine can be considered to be increased (e.g., up to 300 or 400 linear feet of perimeter). Damage to the water supply was, of course, of prime importance in the 1906 San Francisco, 1989 Loma Prieta, 1994 Northridge, and 1995 Kobe earthquakes and will likely be critical in future earthquakes. As discussed above, although the main water transmission lines into San Francisco were severed by the earthquake, this was not critical — sufficient water for initial firefighting needs existed in reservoirs, etc., within the city itself. Rather, hundreds of breaks in the local distribution network, due to large ground displacements and liquefaction, resulted in the system hemorrhaging water and losing pressure. To account for damage to the water supply, two approaches can be employed: 1. A detailed hydraulic model of the system with estimated damage due to shaking, permanent ground displacements, etc., is preferred. This approach, however, may be beyond the scope of some investigations. 2. An alternative method is to review the regional water supply systems and likely areas of liquefaction and permanent ground displacement. Based on this review, for areas where permanent ground displacements are determined to severely impact the water supply system, remaining water supply functionality and reduction in fire-suppression capability can be estimated judgmentally. This approach is described in detail in ATC [1992]. At the time of first arrival, a fire (in terms of SFEDs) larger than the suppression capability (in terms of SFEDs) of the allocated (one or more) engines is termed a “large fire.” Large fires are assumed fought by available engines in a downwind perimeter defense, and to initially spread elliptically at down/up/ side wind rates through a uniformly spaced gridwork of buildings. This assumption of a uniform gridwork of buildings is reasonable, and has been used in all urban fire modeling to date. The spacing, story height, etc., of this gridwork are a function of building density and built-upness (the latter is the ratio of property devoted to buildings contrasted to the total area, including streets, parks, etc.). Firespreading rates are decreased and the initial elliptical shape is altered as the available firefighting capability increases. Eventually, for each fire, one of three things happens: 1. Fires are suppressed. That is, firefighting capability exceeds needs (either initially, or with build up of engines as other fires are suppressed and their engines redirected or mutual aid engines arrive) and the fire is surrounded, controlled, and suppressed. 2. The fire is too large and capability is exceeded by demand. The fire burns relatively freely within a city block. At each street or other (down/up/side wind) firebreak, the fire crosses, with crossing probability as discussed above. This probability is a function of firebreak width, wind direction, and, especially, suppression capability. If sufficient engines and water are available, many fires will typically be stopped at the first wide street. Note that strong winds have an important effect on downwind firebreak-crossing probabilities. In this context, branding (windborne transmission of flaming debris) is sometimes an important factor, especially where wood roofs are prevalent (these are banned in San Francisco, but are common in some other jurisdictions). In most cases, a fire is not expected to cross more than a few typical streets, so that most large fires will be stopped, or burn themselves out, within a few blocks. Again, moderate to strong winds will extend this stopping distance significantly. 3. The fire reaches an “ultimate” firebreak — that is, a large expanse of water, the edge of the urbanized area, etc. Available engines are sufficient to defend exposures along the remaining perimeter, and the fire is controlled and suppressed.
29.3.5 Final Burned Area The above method is followed for each fire. Fires need to be tracked and merged where they meet (i.e., areas should not be “burned twice”). Final burned areas are summed, to arrive at total final burned area.
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29.3.6 Example: Vancouver, B.C. The fire following earthquake methodology presented above has been applied in a number of localities for various purposes, including: • Assessing the adequacy of the fire service, in terms of the amount and location of resources, such as fire stations, firefighters, and equipment, as well as their earthquake planning. • Examining the reliability of water supply systems to provide firefighting water following a major earthquake. • Planning a metropolitan region, to examine whether major thoroughfares could serve as firebreaks and how building codes might be employed to reduce the fire following earthquake problem. • Examining the potential financial impacts a major earthquake may have on the insurance and finance industry. Note that in the United States and many other countries, fire following earthquake is covered under the fire insurance policy, not under the earthquake policy. Therefore, a major conflagration following an earthquake is virtually fully insured, as opposed to major building damage due to shaking, which may have little or no impact on the insurance industry (see Chapter 32, this volume). The fire following earthquake problem is a major concern to the insurance industry, which has supported research and studies in this area for several decades.
M6, M6.5 M7.5
1975 / 1997 epicenter M7.5
1909 epicenter M7.8
FIGURE 29.28 Scenario earthquake events; analysis of fire following earthquake, lower mainland, British Columbia. (From Scawthorn, C. and Waisman, F. 2001. “Assessment of Risk Due to Fire Following Earthquake, Lower Mainland, British Columbia,” Report prepared for the Institute for Catastrophic Loss Reduction, Toronto, by EQE International, Oakland, CA. With permission.)
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An example of analysis of fire-following-earthquake potential is a recent study performed by the author and colleagues for the Vancouver, B.C. (Canada) metropolitan region [Scawthorn and Waisman, 2001]. In summary, the analysis of potential property loss due to post-earthquake fires in the urbanized portions of the lower mainland of British Columbia included the municipalities and districts of Burnaby, Coquitlam, Delta, New Westminster, City of North Vancouver, District of North Vancouver, Port Coquitlam, Port Moody, Richmond, Surrey, Vancouver, and West Vancouver, which have a total population of 1.76 million, representing 96% of the Greater Vancouver Regional District (GVRD). The lower mainland of British Columbia is one of the highest earthquake risk regions in Canada. Seismological research indicates that there are several active seismic sources in the region that have caused destructive earthquakes in the past and are potential sources of future destructive shocks. The region is most affected by earthquakes originating (1) in the shallow crust, (2) on the Cascadia subduction zone, and (3) at depth under Vancouver Island and the Strait of Georgia. Based on the seismotectonics of the region, several scenario earthquakes were analyzed, including: • A magnitude 9.0 megathrust event on the Cascadia subduction zone • Three events of magnitude 7.5 to 7.8 occurring at various locations in the Strait of Georgia • Magnitude 6.0 and 6.5 events randomly placed central to the region of interest (i.e., located beneath the City of New Westminster)5 Shaking intensity due to the scenario events varies significantly across the region, ranging from MMI V in areas of good soil to MMI IX in areas of soft soils (e.g., around False Creek in the City of Richmond).6 Because each of these scenario earthquakes has a finite probability of occurrence and numerous other earthquakes with associated probabilities of occurrence can occur at other locations, all possible earthquakes were also analyzed in a probabilistic analysis, based on the seismotectonics of the region. The lower mainland of British Columbia is also one of the larger urban regions of Canada, with a high concentration of population and property. An estimate of total property values for buildings, vehicles, and infrastructure is approximately $260 billion.7 Wooden buildings represent approximately 58% of the building stock by value and 65% by total floor area. There are about 1200 high-rise8 buildings in the region, only about 20% of which are equipped with sprinkler systems. Of significant concern, however, is that very few of the high-rise buildings in the region have on-site firefighting water supply, in contrast to high-rise practice in the United States, where high-rise buildings in high seismicity areas typically have a 15,000-gallon or larger on-site dedicated water cistern. The analysis of potential losses due to fires following earthquakes in this example followed the methodology discussed above, in which the process of (1) earthquake occurrence, (2) resulting intensity of shaking at each location in the region, (3) structural damage and resulting probability of ignition, (4) fire discovery and reporting, (5) fire service response and effectiveness given damage to water supplies as well as other demands on the fire service, and (6) fire spread is treated as a stochastic process, with selected key variables treated as random variables. The uncertainty of these random variables is quantified on the basis of data from earthquake and non-earthquake events. The geographic unit of analysis for the region was three-character postal code (e.g., V6E xxx) — that is, the analysis treated each of the 80 three-character postal codes in the Greater Vancouver region as having uniform shaking intensity, building inventory, and other characteristics within that postal code area.
5
Magnitudes are measured on the moment magnitude scale. MMI is the Modified Mercalli Intensity scale, where VI is the initiation of damage to poorly built buildings and IX is collapse of such buildings, with significant damage to average to good buildings. Corresponding peak ground accelerations range from about 0.02 to 0.45 g. 7 Unless otherwise noted, all monetary amounts are 1999 Canadian dollars. 8 Definition of a “high-rise” building varies — in this analysis, high-rise was defined as seven stories or greater, which is a definition widely employed in the fire service. This estimate is conservative and there are quite possibly more than 1200 high-rises in the study region. 6
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To determine the availability and effectiveness of firefighting and water resources, data were collected from a variety of sources, including interviews with key fire service and water department personnel, Fire Underwriters Survey municipal grading summaries, and engineering analyses of water department seismic vulnerabilities, finding that: • Firefighting — The Greater Vancouver region is well protected under normal circumstances by a well-trained and equipped fire service, largely professional but in part volunteer, with a total firefighting staffing of about 2700, of whom about 400 are on duty at any one time. The total number of fire engines in the region is 120, housed in 77 fire halls or stations, a significant fraction of which may be seismically vulnerable. In addition to fire engines, additional pumping capacity is furnished by five “fast attack” fireboats sited around Burrard Inlet (equivalent to five fire engines) and, in the City of Vancouver, the recently constructed dedicated fire protection system (DFPS — discussed further below) and associated hose tenders and special pumps (from a pumping capacity perspective, DFPS can be equated to about eight fire engines, although its effectiveness is much greater). • Water — The region is almost entirely served by the Greater Vancouver Water District (GVWD, part of the GVRD), which has three supplies: Capilano, Seymour, and Coquitlam. The Capilano and Seymour supplies are north of the Burrard Inlet. They supply Vancouver, Burnaby, and other areas via transmission lines that cross the inlet via submarine crossings that, however, pass through areas subject to liquefaction. The Coquitlam supply is northeast of Vancouver and no major marine crossings are required to reach the City of Vancouver or a number of other areas. Since the early 1990s, GVWD has been implementing a program of seismic improvements and is currently conducting a major review of that program to assure that appropriate goals are being met. Within each municipality, water is distributed via a gridded network of smaller pipelines that are anticipated to break in a large earthquake, such that in a number of locations (especially in areas of softer soils), fire hydrants will initially be without adequate water pressure or supply. To prepare for such contingencies, the fire service typically identifies alternative water supplies and carries special hard suction hose and other equipment to access these supplies. Examples of alternative water supplies include water reservoirs, creeks, waterfront access to bays or lakes, and swimming pools. Among Burrard Inlet, the Fraser River, and other sources, the study region is generously supplied with opportunities for alternative supply. All fire departments interviewed had equipment for accessing alternative water supplies, but only five out of eight departments appeared to have adequately planned for such contingencies. As noted above, fireboats and Vancouver’s DFPS significantly enhance emergency water supply in Vancouver and around Burrard Inlet. However, there are no fireboats located on the Fraser River. For each scenario, the number of initial fires was estimated based on shaking intensity, and fire department response estimated taking into account effects of the earthquake on transportation, communications, water supply, and related factors (see Figure 29.29 and Table 29.10). Fire growth was estimated for each fire, taking into account fire suppression (or the lack thereof), to arrive at an estimate of final burned area for each fire and the sum of all fires. Loss is estimated as the monetary amount corresponding to this final burned area.9 Based on these data and analyses for the scenario events, it was estimated that the Greater Vancouver region would sustain fires and losses as indicated in Table 29.10. Uncertainty associated with these estimates is substantial, with coefficients of variation on the order of 0.5 to 1.0. Taking into account all possible earthquakes together with their associated probabilities of occurrence, it was found that the annualized loss for the study region was $88.3 million, representing 0.04% of the value at risk. These losses are of similar relative magnitude to previous estimates for other North American urban areas [Scawthorn and Khater, 1992].
9 Note that shaking damage was not quantified in this analysis, and that shaking loss and post-earthquake fire losses cannot be directly summed, as there may be some burning of the rubble.
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FIGURE 29.29 Mean number of ignitions, M9.0 subduction zone event. (Source: Scawthorn, C. and Waisman, F. 2001. “Assessment of Risk Due to Fire Following Earthquake, Lower Mainland, British Columbia,” Report prepared for the Institute for Catastrophic Loss Reduction, Toronto, by EQE International, Oakland, CA. With permission.)
TABLE 29.10 Scenario Events, Fires, and Losses (Loss in Year 2000 C$ millions, % of total value at risk) Georgia Strait M = 7.5 113 fires
1909 Epicenter M = 7.8 31 fires
Loss
%
Loss
%
Loss
%
Loss
%
Loss
%
Loss
%
$2,795
1.04%
$1,172
0.43%
$2,685
1.00%
$1,752
0.65%
$8,529
3.12%
$4,700
1.74%
1975/1997 Epicenter, M = 7.5 101 fires
New Westminster M = 6.0 66 fires
New Westminster M = 6.5 157 fires
Subduction Zone M = 9.0 155 fires
With regard to the conditions found in the Greater Vancouver region, it was found that reduction of post-earthquake fire risk could be accomplished via a number of measures, including: • Development of a regional earthquake plan with a detailed post-earthquake fire element, which would include procedures for rapid location and reporting of post-earthquake fires, mutual aid response to larger fires, identification of alternative water supplies, and related measures. • Improved provision for alternative water sources, including extension of the DFPS on the other side of False Creek, installation of saltwater hydrants along shorelines in higher density areas, provision of fireboats on the Fraser River, and acquisition of additional portable pumps by several of the region’s fire departments, similar to the HydroSub recently acquired by the City of Vancouver. • Installation of water cisterns in sprinklered high-rises and retrofitting of unsprinklered high-rises with sprinklers. • A regional effort at reducing post-earthquake fire ignitions — for example: • Vancouver’s central business district (CBD) is an enormous concentration of value, yet it is the only major North American city with overhead electric transmission lines. Wood polemounted transformers abound in the CBD, in many cases only inches from commercial buildings (this is discussed further below). In past earthquakes, pole-mounted transformers arced and exploded. Because these were typically in residential areas, few ignitions occurred, but it is expected that many ignitions would result in Vancouver’s CBD due to these electrical
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•
sources. Undergrounding of the electrical transmission in the CBD would significantly reduce post-earthquake fires. Fire departments could institute public education as to post-earthquake fires, the need for their rapid suppression, and, specifically, the need to brace residential water heaters.
29.4 Mitigation This section discusses mitigation of the fire following earthquake problem. Fortunately, numerous opportunities exist, although, unfortunately, their application is sparse. A framework for the discussion of mitigation opportunities is shown in Figure 29.23, which has been enhanced in Figure 29.30 to show opportunities for intervention in the fire following earthquake process. As indicated in the diagram, following the earthquake damage in the most general sense (even if it is only the overturning of a candle) is required for an ignition. Thus, reduction of damage is the first opportunity for mitigation of fires following earthquake. This ignition might be extinguished without human intervention if automatic sprinklers or other automatic suppression systems (e.g., Halon) are present, and if the automatic system is post-earthquake functional, and if the water, for example for the sprinklers, is available. If the ignition is not automatically extinguished, then the fire remains to be discovered, and the citizens so discovering it may be able to extinguish it, if water is available. If those persons are not able to extinguish the fire, they must report it to the fire department. For the citizens to report the fire, functional communications (i.e., telephones) are required (unless, perhaps, the fire department observes the smoke column and selfreports). For the fire department to respond, they must have available fire department assets, and the assets (i.e., apparatus) must be able to travel to the fire — that is, transportation, in the form of roads, etc., must be functional. Upon arrival, the fire department will be able to extinguish the fire, if water is available and if the fire is controllable, given the fire department resources reporting to the scene. If not, the fire will continue to grow (admittedly, perhaps at a smaller rate given the fire department’s efforts), until it meets a firebreak. The provision of firebreaks, via the urban planning process, is the last opportunity for mitigation of fire following earthquake. We discuss each of these aspects in turn.
29.4.1 Reduction of Damage In a general sense, reducing earthquake damage or effects due to shaking reduces the potential for ignitions following an earthquake. Obvious examples include restraining sources of ignition such as water heaters, lamps, and other heat sources, and containers holding potentially reactive chemicals. Many sources of information and products exist for bracing and anchoring of simple household and office goods (e.g., www.abag.org) — a simple search of the Internet will uncover many. Gas appliances in the home are a concern to many persons, because overturned water heaters or broken gas piping (due to excessive displacements of a seismically weak house) can result in gas leaks that, in a few minutes, can produce a life-threatening explosive mixture of gas and air. Figure 29.31 shows how to restrain a gas water heater. Mroz and Soong [1997] evaluated the method depicted as well as other methods of restraint, and found varying effectiveness — using only plumber’s tape provided resistance against falling away from the wall, but not toward the wall — thus use of rigid tubing is recommended. Similarly, Figure 29.32 illustrates the gas valve controlling service to a home, together with a “gas wrench,” affixed by the homeowner to the gas valve so as to be always available in the event of an emergency. Because persons may not be home when an earthquake occurs, and thus are unable to turn off the gas service in the event of a gas leak following an earthquake, automatic shutoff valves have been invented. These are of two types: (1) excess flow valves actuated by a change in gas pressure and (2) seismic valves actuated by motion or movement. Both are intended to actuate when subjected at the point of installation to an earthquake severe enough to cause damage to gas systems and appliances within the structures they protect. Figure 29.33 shows an example of an automatic gas shutoff valve installation. © 2003 by CRC Press LLC
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Earthquake Damage Reduction
Ignition Automatic Suppression (e.g., sprinklers)
Discovery Water
Citizen Suppression
Report
Communications FD assets / Transportation
FD Response
Suppression
Stop
Y
N
Spread / Conflagration Urban Planning
Firebreak / Fuel Exhaustion FIGURE 29.30 Fire following earthquake process, with mitigation opportunities.
The above precautions are appropriate assuming the structure is relatively safe; however, should the house slide off its foundation, the gas service line will be sheared off, allowing pressurized gas to escape to the atmosphere — one spark produces a gas “torch” of major proportions, which will quickly ignite the home. In such cases, if one can get to the pipe before the gas ignites, simply plugging the broken pipe with a tapered piece of wood effectively turns the gas off. Older homes with unbolted foundations or unbraced cripple walls are particularly common in the western United States and especially prone to sliding off their foundations. Figure 29.34 shows an example of how to bolt and brace cripple walls, while Figure 29.35 shows houses fallen off their foundations in the 1989 Loma Prieta earthquake. Another source of post-earthquake ignition is electricity, which can cause ignitions via a number of mechanisms, including wiring shorts, appliance damage, overhead line arcing, etc. A particularly egregious example of the latter is found in the CBD of Vancouver, which is the only major North American city with overhead electric transmission (see Figure 29.36).
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Strapping Your Water Heater 24″ Maximum
Sheetrock
″ 30
imum
24″ Maximum
2×4 Stud
M um im ax
Water heater
Max
Log screw with washer
4″ Minimum
30″
5/ ″×3″ 16
4″ Minimum
1/ ″ EMT (conduit) flattened at ends 2 Bolt (with nut and washers) 1 1 /2″×16 -gauge metal strap through strap and flattened end of EMT 5/ ″×11/ ″ Bolt (with nut and washers) 16 4 through bent ends of strap 5/ ″×3/ ″ 16 4
(A)
Locate center of studs with a small finish nail Wall sheathing 1/ ″ EMT (conduit) 2 flattened at ends
Water heater
11/2″×16 -gauge metal strap
Flexible gas pipe connection
2″×4″ Studs behind sheetrock (B)
(C)
FIGURE 29.31 Strapping water heater: (A) plan view, showing “plumber’s tape” strap around water heater and attachment to framing using rigid tubing; (B) elevation view; (C) photo of actual water heater — note “plumber’s tape” strap around “belly” of the water heater. (Courtesy EQE International and C. Scawthorn)
Finally, another major source of post-earthquake fires is chemical reactions. Glass and other containers containing chemicals can easily fall off shelves or tip over in an earthquake, spilling their contents and reacting with other spilled chemicals or materials such as flooring or furniture. The heat given off by the reaction (termed exothermic reactions) can be sufficient to ignite cloth or other materials, thus starting a fire. High-school chemistry laboratories are a source of fires in almost all major earthquakes. In California and other high-seismicity regions, it has become relatively common practice to put lips on © 2003 by CRC Press LLC
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Shutting of the Gas and Other Utilities GAS SHUTOFF
(Click on diagram for a detailed drawing) ON
OFF
Switch on gas Special Tool for turning off gas water on 3 gas and Gas Meter water (A crescent Wrench Switch off or on gas W’I’ Work.)
Switch off gas
1. Locate the main gas shutoff (usually outside the house) and all pilot lights. 2. Clear the area around the shutoff valve for quick and easy access in case of emergency. 3. A wrench (or specialty tool for turning off gas and water) should be attached to a pipe next to the shutoff valve or in another easily accessible but hidden location. 4. You may want to paint the shutoff valve with white or fluorescent paint so that it can be located easily in an emergency. 5. If you are concerned about your ability to turn off the main gas shuttoff valve, are unsure whether it is in proper working order (indication of rust, etc), or do not know how to relight your pilot lights, contact your local gas company. The gas company can send a service representative to your house to show you the proper procedure and check the valve and pilot lights to be sure that they operate properly. (A)
(B)
FIGURE 29.32 (A) EQE Web site explaining how to shut off gas valve and (B) actual gas service to a home, showing pressure regulator (flat, round, plate-like object) and valve, with “gas wrench” wired to pipe and writing on side of house showing location. (Courtesy EQE International and C. Scawthorn)
shelves in laboratories, restrain chemical containers, put door latches on laboratory cabinets, and take other precautions to prevent spillage of chemicals.
29.4.2 Automatic Suppression The fire hazard in non-earthquake conditions is such that automatic suppression systems have become a standard part of most larger buildings. These also serve the same purpose following an earthquake and, by stopping many ignitions at their initiation, can be very effective in reducing the overall post-earthquake © 2003 by CRC Press LLC
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TWINGATE ® SEISMIC VALVE
B-LINE B 437 CLAMP ON 1″ × 1″ STRUT
PLUG TEE
REMOVE EXISTING
GAS METER (A)
(B)
FIGURE 29.33 Example of automatic gas shutoff valve: (A) typical installation; (B) close-up of valve. (Courtesy Quake Defense, Inc.)
fire problem. Thus, an item of critical importance for the problem of fire following earthquake is the seismic performance of automatic sprinklers. Design and installation of automatic sprinklers in the United States are generally governed by NFPA 13,10 which includes provisions for seismic design of sprinklers. This design, which consists of 10
NFPA 13, Standard for the Installation of Sprinkler Systems (most recent edition), National Fire Protection Association. © 2003 by CRC Press LLC
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Framing clips Rim joint Floor joints Rim joint connecting top or blocking extenior plate and rim joint Plywood of grade at 16″ spacing plank subfloor structural 8d of nails at 8″ plywood spacing at Top infernediate plates studs
1/ ″ 2
Exterior stud wall
Anchor Bolt
Foundation grade beam 8d nails at 3″ spacing around the perimeter of each plywood sheet Sill plate 3/8″ from edge Nailing each side Holddown located of plywood joints or end of each 11/2″ dia. ventilation Reinforcing plywood wall panel less than 8″ holes top and bottom bars in length between studs © 1995 by EQE International Materials Needed
Tools Needed
1/ ″, STRUCTURAL I or C-DX plywood 2 8d common nails Simpson HD2A holddown or equivalent Simpcon A35 Framing clips with N8 nails or equivalent Anchor bolls (see project2)
Circular saw Jigsaw 1-1/2″ hole saw Framing square Hammer
Plywood blade Tape measure Chalk line Pencil
(A)
(B)
FIGURE 29.34 (A) Diagram and (B) example of cripple wall bracing using plywood. Note steel straps nailed through plywood into studs and horizontally bolted into concrete foundation. (Courtesy EQE International and C. Scawthorn)
lateral and longitudinal bracing for sprinkler mains at specified distances, is relatively simple. These provisions have generally proven to be adequate in most earthquakes [Fleming, 1998], although a flaw in the design is the general overlooking of situations where the sprinklers are restrained by the bracing on either side of a building temperature joint. Large buildings are often built with joints, intended to limit stresses due to normal heating and cooling of the buildings during the day. Where sprinklers cross these joints, flexible couplings have to be provided. Otherwise, in an earthquake, the two parts of the building on either side of the joint (effectively, that is, two buildings) will move differentially, thus © 2003 by CRC Press LLC
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FIGURE 29.35 Watsonville in 1989 Loma Prieta earthquake; examples of houses fallen off their foundations. (Courtesy EQE International)
FIGURE 29.36 Vancouver, B.C. central business district, with overhead electric lines — an obvious fire hazard, especially following an earthquake. (Photo: C. Scawthorn)
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FIGURE 29.37 Test of intumescent paint — both “buildings” had crib fires set at the same time. Building on the left is of bare wood and has flashed over and is fully involved at slightly less than 5 minutes following ignition, while building on the right, painted interior and exterior with intumescent paint, still has only a small fire on the interior, not yet flashed over. (Photo: C. Scawthorn) Shown as Color Figure 29.37.
rupturing the sprinkler. Differential movement of piping supports, in general, is a seismic design issue often overlooked. One or a few failures of sprinkler mains in this manner can drain the sprinkler system and prevent functional post-earthquake fire suppression. In addition to water-based sprinklers, other automatic suppression systems include halogenated agents (e.g., HALON), CO2, dry chemical, foam, and other systems, each of which can similarly be of great benefit in the post-earthquake environment, and each of which should be reviewed to assure postearthquake functionality. In addition to automatic suppression systems, the post-earthquake functionality of fire-detection and -alarm systems is vital following an earthquake, if for no other reason than to provide warning for evacuation. The author was involved in the development of an entire methodology for the assessment of such systems to assure post-earthquake functionality [Johnson et al., 1999], which is discussed in another chapter of this book. Finally, the application of intumescent paint, which is special paint for walls and other surfaces that is highly resistive to radiant heat, is emerging as a promising form of passive fire protection in general. This paint may have special application for fire following earthquake risk reduction. The resistance of intumescent paint is largely gained via chemicals in the paint that utilize the heat gain in expansion, resulting in a swelling or “blistering” of the paint rather than ignition, and the creation of a fire-retardant foam. Ignition is thus much delayed and, in certain cases, prevented (see Figure 29.37). San Francisco has approved intumescent coatings for application in a number of historical buildings as an alternative or adjunct to other fire-protection systems and is investigating its possible benefits with regard to fire following earthquake [Kobayashi and Kornfield, 2002].
29.4.3 Suppression by Citizens Because the essence of the fire following earthquake problem is the multiple simultaneous ignitions following an earthquake, which overwhelm fire department resources when they are most in demand, one approach to mitigating the problem is the use of additional personnel in the form of citizen volunteers. The concept of volunteers in fire departments is not new; in fact, the first fire departments were all volunteers. The United States today still has large numbers of volunteer fire departments outside the major metropolitan areas and many fire departments are part paid and part volunteer. In this regard, several of the larger fire departments in the United States have developed specialized training of citizen volunteers to be mobilized in the event of major disasters.11 San Francisco, for example, has trained 10,000 citizens in elementary firefighting and search and rescue (see Figure 29.38).
11 For example, the San Francisco FD Neighborhood Emergency Response Teams (NERT), (http://www.sfnert.org/), and the Los Angeles region’s Community Emergency Response Teams (http://www.cert-la.com/).
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San Francisco Neighborhood Emergency Response Teams
[ Home ] [ NERT Auxiliary ] [ Our Mission ] [ Calendar ] [ Contact NERT ] [ Help NERT ] [ Links ] [ Search ]
NERTNews Calendar Change....... The next Coordinators Meeting will be June 26th, Archive 1011 Turk Street, 6:30 pm .... NERT Auxiliary Annual Meeting will be held Class Schedule May 22nd, 1011 Turk Street, 7:00 pm .... Training Class Content NERT Fall Class Schedule updated - 5/13/03 NERT Manual Battalions April Drill Photos Staging Areas Add SFNERT.ORG to your favorites NERT Forms HAM Operators: HAM Cram MS-Internet Explorer users click here Disaster Registry Practice your skills during Siren Netscape users hit CTRL+D to bookmark our site. First Responder Net Pictures CCSF announces Fall 2002 Terrorism Click here if you would like e-mail Bay Net First Responder Training notification of updates to SFNERT.org click here for details New Ham Cram - July 20, 2002
NERT Shirts Now Available
Let the U.S. Geological Survey know if you feel an earthquake
NERTNews is the official voice of the San Francisco NERT organization and is published quarterly by the San Francisco NERT Executive Board. NERTNews Editor is Lynn Jacklevich. NERTNews - Online Editor is Bill Travis. San Francisco NERT is a non-registered San Francisco volunteer group, registered with the Office of Emergency Service of the State of California as Volunteer Disaster Service Workers, and dedicated to preparing citizens of the City and County of San Francisco for potential disaster. To contribute to NERTNews, contact the Editor. The deadline for submitted materials is the first Friday of February, May, August, and November. NERTNews is under no obligation to print materials received, and submitted materials may be subject to editing for style, content, and length. For permission to reproduce or distribute any of the content of this newsletter, contact the San Francisco Fire Department for conditions and approval. Last Modified : 05/14/02 07:01 AM Copyright © 1999-2002 SF NERT All rights reserved
Email webmaster
FIGURE 29.38 San Francisco Fire Department’s NERT (Neighborhood Emergency Response Team) home page. (Source: http://www.sfnert.org/)
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To quote the Los Angeles CERT (Community Emergency Response Team) Web site: Local government prepares for everyday emergencies. However, during a disaster, the number and scope of incidents can overwhelm conventional emergency services. The Community Emergency Response Team (CERT) program is an all-risk, all-hazard training. This valuable course is designed to help you protect yourself, your family, your neighbors and your neighborhood in an emergency situation. CERT is a positive and realistic approach to emergency and disaster situations where citizens may initially be on their own and their actions can make a difference. While people will respond to others in need without the training, one goal of the CERT program is to help them do so effectively and efficiently without placing themselves in unnecessary danger. In the CERT training, citizens learn to: • • • • • • •
Manage utilities and put out small fires Treat the three medical killers by opening airways Control bleeding and treat for shock Provide basic medical aid Search for and rescue victims safely Organize themselves and spontaneous volunteers to be effective Collect disaster intelligence to support first responder efforts
The CERT concept emerged in 1985 as part of observations on Japanese neighborhood preparedness made by the United States during a cooperative United States–Japan exchange of emergency response officials. The City of Los Angeles Fire Department under the leadership of Chief Frank Borden then developed a pilot program, which was so successful that, by 1993, the Federal Emergency Management Agency (FEMA) decided to make the concept and program available to communities nationwide. By 2002, 38 states and 6 foreign countries were using the CERT training.
29.4.4 Communications The foregoing discussion emphasized the need for rapid reporting of fires following an earthquake, and the fact that this is problematic due to saturation and possible damage to the telephone system, as well as overloading of the emergency dispatch (911) system. Fire department emergency dispatch centers have contingency plans for coping with a large number of calls in an emergency, but can still be overwhelmed at some point. An additional issue is damage to the emergency dispatch center itself, which should not only be structurally sound, but also have assured backup power and other resources.
29.4.5 Fire Department Assets The fire service is the first line of defense against fires following earthquakes. However, the fire service is both vulnerable to earthquakes itself and sometimes not as well organized for this specific issue as it might be. This section discusses actions the fire service itself can take to improve its preparedness for fires following earthquakes. 29.4.5.1 Fire Stations As noted above (in the discussion of the 1994 Northridge earthquake, where 35 fire stations sustained damage [Sepponen et al., 1997], fire stations themselves can sustain damage in an earthquake, potentially injuring and rendering the assets they house (i.e., firefighters and their equipment) useless in an earthquake. Many larger fire departments in high seismic areas have reviewed their fire stations’ structural seismic adequacy and subsequently strengthened inadequate premises. In the late 1980s, San Francisco, for example, undertook an analysis that found that, of 55 department facilities, 11 were collapse hazards and another 13 would sustain extensive damage in a major earthquake [EQE, 1989]. To strengthen and
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(A)
FIGURE 29.39 (A) Example of single-bay unreinforced masonry fire station, built in 1913. (Source: EQE, 1989. Report prepared for the San Francisco Fire Commission) (B) Fire station strengthened in the 1990s per indicated structural reinforcement scheme. (Source: C. Scawthorn)
replace fire stations, the city embarked on a sweeping program that has since been completed. Figure 29.39, for example, shows a 1913-vintage unreinforced masonry single-bay fire station that was analyzed by a team headed by the author and found to be a collapse hazard. A structural reinforcement scheme, also shown in the figure, was developed and constructed during the 1990s. In the Vancouver study discussed above, many fire departments were found to have quite new fire stations, or have reviewed and as required strengthened their fire stations. However, there still remained somewhere between 14 and 30 fire stations (i.e., 18% to 38% of the fire stations in the region) that were seismically questionable. Thus, a review of fire stations and other emergency facilities, for seismic © 2003 by CRC Press LLC
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Center Core North and South Walls, Full Height, East and West Parapets Install Steel Diaphragm Bracing Beneath Ceilings, 1st and 2nd Story, Anchor Walls to Bracing Brace East and West Parapets
Gunite Front and Rear Walls
Infill Selected Windows Install Moment-Resisting Frame and Foundation 2 Places
(B)
FIGURE 29.39 (CONTINUED)
structural adequacy and to assure post-earthquake functionality, should be undertaken by all fire departments in seismic areas. 29.4.5.2 Mutual Aid Fire departments regularly practice mutual aid and, based on their daily experience, are quite confident of their ability to respond to emergencies. However, a major earthquake is a very rare occurrence, one that few senior fire officers experience in their lifetimes. Earthquake planning for fire departments is thus mandated. All fire departments in a region should cooperate in the development of a regional earthquake plan with a detailed post-earthquake fire element that should include procedures for rapid location and reporting of post-earthquake fires, mutual-aid response to larger fires, identification of alternative water supplies, and related measures. 29.4.5.3 Post-Earthquake Damage Surveys Most fire services have a damage survey by fire companies as part of their earthquake plan. This is very unrealistic, in that fire companies self-dispatch or are dispatched immediately following the earthquake. An alternative to damage surveys by fire companies needs to be developed. One possibility is that damage surveys should be performed by the police department, because they are not equipped to deal with fires or building collapses, yet they know their neighborhoods, are mobile and reliable observers, and have reliable communications. Whether the damage survey is performed by police or others can be discussed, but tasking fire companies with this role is unrealistic.
29.4.6 Water Water for firefighting is obviously a vital aspect of the fire following earthquake problem. Earthquakes damage water systems and, thus, post-earthquake reliability of water supply is a necessary element of © 2003 by CRC Press LLC
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post-earthquake fire mitigation. Water supply systems in seismic regions should be assessed for their post-earthquake functionality. Several methodologies for this exist [Ballantyne and Crouse, 1997; ATC, 1992]. If the municipal water supply system cannot be made post-earthquake reliable, alternative water supplies are required. Alternative water supplies can be provided for in a number of ways, including: • Identification of alternative water sources, such as rivers, lakes, swimming pools, or other supplies. This is a normal part of fire department planning that is increasingly being overlooked as the fire department increasingly takes on emergency medical treatment (EMT) as part of its central mission. Los Angeles Fire Department, in the response to the North Balboa Boulevard fire, made excellent use of backyard swimming pools as an alternative source of firefighting water. Thus, fire officers need to be aware that the hydrant alone cannot be relied upon following a major earthquake, and they need to identify and regularly practice using alternative sources of water supply. It is remarkable that San Francisco burned down in 1906, despite being surrounded on three sides by the largest body of water on Earth. As part of its AWSS, San Francisco has installed saltwater hydrants (i.e., special connections to the bay for drafting) along its shorelines. It is even more remarkable that other similarly situated cities (e.g., Los Angeles, Tokyo, Osaka, Manila, Istanbul, etc.) have not done so. • Acquisition of specialized portable pumps and large-diameter hoses similar to the HydroSub system recently acquired by the cities of Vancouver, Oakland, Vallejo, and Berkeley. It is not well understood that water can be practicably drafted only a vertical distance of about 26 ft (8 m). If a bridge, seawall, pier, or other access point is more than this distance above the water, a fire engine cannot access the water — it must get closer, which is often difficult. To overcome this problem, several systems such as the HydroSub are designed to lower a powered pumphead to the water and push rather than draft the water through the hose. In this manner, the HydroSub, for example, can access water more than 100 ft (33 m) below its location. • In the United States, in recognition of the unreliability of municipal water supplies in earthquakes, high-rise buildings in higher seismicity zones are required to have on-site secondary water supplies. These requirements usually translate to a minimum of 15,000 gallons.12 Other high seismicity regions should adopt this requirement. • Consideration can be given to development of special auxiliary high-pressure water systems similar to San Francisco’s AWSS (discussed above) or Vancouver’s DFPS (discussed below). Such highpressure systems can be justified only for major metropolitan areas in high seismic regions, but there is no shortage of these. It is noteworthy that Vancouver undertook construction of the DFPS in the 1990s.
29.4.7 Dedicated Fire Protection Systems In the early twentieth century, as a result of major urban conflagrations, a number of U.S. cities built special high-pressure systems to protect their central business districts. The 1871 Chicago, 1904 Baltimore, and 1906 San Francisco fires are only the best known of many large urban conflagrations that plagued the United States at that time. A number of factors contributed to these conflagrations, but lack of reliable water supplies was a key factor that led to the construction of the high-pressure systems. For various reasons having to do with improved building stock and fire service capability, most of these cities have since abandoned these systems, with San Francisco being the one major exception. Due to its high seismic
12 “903.3.5.2 Secondary Water Supply. A secondary on-site water supply equal to the hydraulically calculated sprinkler demand, including the hose stream requirement, shall be provided for in high-rise buildings in Seismic Design Category C, D, E or F …. The secondary water supply shall have a duration of not less than 30 minutes.” (International Building Code, 2000 — note that the 1997 UBC has similar requirements.)
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Approved Layout Constructed to date Burrard Inlet
Coal Harbour Pump Station English Bay
False Creek Pump Station FIGURE 29.40 Dedicated fire protection system, City of Vancouver, B.C.
risk and the trauma of the 1906 fire, San Francisco maintains its AWSS. A key aspect of San Francisco’s ability to maintain and even extend this unique system is the fact that it is, by city charter, owned and operated by the fire department. Recently, the City of Vancouver, as a result of analysis of its water supply system’s seismic reliability (or lack thereof), embarked on the design and construction of a system similar to San Francisco’s that Vancouver called its Dedicated Fire Protection System (DFPS). This section briefly describes Vancouver’s DFPS. The City of Vancouver’s primary water supply is via the 1st and 2nd Narrows Crossings, which both cross liquefiable deposits and were identified a decade ago as seismically vulnerable [EQE, 1990]. The only in-city water storage is at Little Mountain Reservoir in the center of the city — the reservoir has been recently strengthened. Fully 77% of the domestic water distribution system in Vancouver is seismically vulnerable CI pipe more than 30 years old, while 30% of the larger steel trunk mains in the city are more than 70 years old and of highly vulnerable riveted construction [MTR, 1991]. The DFPS is a major asset for protection of the high-value district of Vancouver and consists of two seismically reliable pump stations (Coal Harbor and False Creek), each capable of 10,000 Igpm (see Figures 29.40 and 29.41). The two stations are connected by a loop around the CBD of 20-in.-diameter welded steel pipe (see Figure 29.41B). Special large-diameter hydrants connect to this loop, from which firefighters can receive high-volume, high-pressure flows. The Vancouver Fire and Rescue Service is acquiring special large-diameter hose that, together with the DFPS, can be used to protect a 1000-ft radius from any hydrant off of this loop, thus “blanketing” the CBD.
29.5 Conclusion The 1989 Loma Prieta and 1994 Northridge earthquakes, the 1991 Oakland Hills and 1993 Southern California fires, Japan’s 1994 Kobe earthquake, and Turkey’s 1999 Marmara earthquake all demonstrate the potential for fires following earthquakes and the current, real possibility of conflagration. In North America, all the elements that would hamper firefighting capabilities are present: density of wooden structures, limited personnel and equipment to address multiple fires, debris blocking the access of firefighting equipment, and a limited water supply. Large cities in the United States and those in other countries, such as Tokyo, Osaka, Vancouver, Istanbul, and Wellington, are at substantial risk of fire
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(A)
(B)
FIGURE 29.41 Vancouver, B.C. DFPS. (A) False Creek pump station (foreground, nearing completion in 1995); (B) welded steel pipe under construction, 1995; (C) False Creek station proof test, 1995. (Photos: C. Scawthorn) © 2003 by CRC Press LLC
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(C)
FIGURE 29.41 (CONTINUED)
following earthquakes. A number of proactive steps can be taken to reduce this risk. Awareness, assessment, and mitigation of the risk of fire following earthquakes are crucial if catastrophe is to be avoided.
Defining Terms Conflagration — Large destructive fire. In the fire service, in the urban context, conflagration usually denotes a large fire that spreads across one or more city streets, or a large fire destroying a complex of buildings.
References American Society of Civil Engineers. 1929. Report of the Special Committee on Effects of Earthquakes on Engineering Structures with Special Reference to the Japanese Earthquake of September 1, 1923, San Francisco. ATC (Applied Technology Council). 1992. A Model Methodology for Assessment of Seismic Vulnerability and Impact of Disruption of Water Supply Systems, Report ATC-25–1, funded by the Federal Emergency Management Agency. Prepared for Applied Technology Council by EQE International, C. Scawthorn and M. Khater, Applied Technology Council, Redwood City, CA. Ballantyne, D.B. and Crouse, C.B., Eds. 1997. Reliability and Restoration of Water Supply Systems for Fire Suppression and Drinking Following Earthquakes, Report NIST GCR 97–730, Building and Fire Research Laboratory, National Institute of Standards and Technology, Gaithersburg, MD. Bond, H. 1946. Fire and the Air War, National Fire Protection Association, Boston, MA. Bowlen, Fred J., S.F.F.D. n.d. “Outline of the History of the San Francisco Fire,” Original manuscript. Chandler, C.C. et al. 1963. Prediction of Fire Spread Following Nuclear Explosions, Pacific Southwest Forest and Range Experimental Station, U.S. Forest Service, Berkeley, CA. Earthquake Engineering Research Institute. 1995. The Hyogo-ken Nanbu Earthquake, January 17, 1995, Preliminary Reconnaissance Report, Earthquake Engineering Research Institute, Oakland, CA. EQE. 1989. San Francisco Fire Department Facilities, Summary Report, prepared by EQE/AGS under contract to Department of Public Works, City and County of San Francisco, for the San Francisco Fire Commission. EQE Engineering. 1990. Emergency Planning Considerations, City of Vancouver Water System Master Plan, prepared under subcontract to CH2M-Hill, for City Engineering Department, City of Vancouver, B.C. © 2003 by CRC Press LLC
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EQE International. 1995. “The January 17, 1995 Kobe Earthquake: An EQE Summary Report,” EQE International, San Francisco. Fleming, R. 1998. Analysis of Fire Sprinkler System Performance in the Northridge Earthquake, NIST-GCR98–736, Building and Fire Research Laboratory, National Institute of Standards and Technology, Gaithersburg, MD. Freeman, J.R. 1932. Earthquake Damage and Earthquake Insurance, McGraw-Hill, New York. Hamada, M. 1951. On Fire Spreading Velocity in Disasters, Sagami Shobo, Tokyo (in Japanese). Hamada, M. 1975. “Architectural Fire Resistant Themes,” No. 21 in Kenchiku-gaku Taikei, Shokoku sha, Tokyo (in Japanese). Hamada, M., Wakamatsu, K., and Yasuda, S. 1992. “Liquefaction-Induced Ground Deformations during the 1923 Kanto Earthquake,” in Case Studies of Liquefaction and Lifeline Performance during Past Earthquakes, Vol. 1, Japanese Case Studies, M. Hamada and T.D. O’Rourke, Eds., NCEER Technical Report NCEER 92–0001, National Center for Earthquake Engineering Research, State University of New York, Buffalo, NY. Hansen, G. and Condon, E. 1989. Denial of Disaster: The Untold Story and Photographs of the San Francisco Earthquake and Fire of 1906, Cameron and Company, San Francisco. HAZUS. 2002. HAZUS99 SR2 Technical Manual, National Institute of Building Sciences, Washington, D.C. Heubach, W. 1997. “The 1994 Northridge, California Earthquake Water Supply Effects,” in Reliability and Restoration of Water Supply Systems for Fire Suppression and Drinking Following Earthquakes, Report NIST GCR 97–730, D.B. Ballantyne. and C.B. Crouse, Eds., Building and Fire Research Laboratory, National Institute of Standards and Technology, Gaithersburg, MD. Horiuchi, S. n.d. Research on Estimation of Fire Disasters in Earthquakes, Disaster Prevention Section, Comprehensive Planning Bureau, Osaka Municipal Government, Osaka (in Japanese). Jensen, A. 1989. “Report to the Board of Supervisors Concerning the Water Supply,” Memorandum from acting general manager, San Francisco Water Department, to Public Utilities Commission, City and County of San Francisco, November 21. Johnson, G.S., Ascheim, M., and Sezen, H. 2000. “Performance of Industrial Facilities,” in The Marmara, Turkey Earthquake of August 17, 1999: Reconnaissance Report, MCEER Technical Report MCEER–00–0001, C. Scawthorn, Ed., Multidisciplinary Center for Earthquake Engineering Research, State University of New York, Buffalo, NY. Johnson, G.S., Sheppard, R.E., Quilici, M.D., Eder, S.J. and Scawthorn, C. 1999. Seismic Reliability Assessment of Critical Facilities: A Handbook, Supporting Documentation and Model Code Provisions, Technical Report MCEER–99–0008, Multidisciplinary Center for Earthquake Engineering Research, State University of New York, Buffalo, NY. Kanai, K. 1983. Engineering Seismology, University of Tokyo Press, Tokyo. Kimball, W.Y. 1966. Fire Attack! Command Decisions and Company Operations, National Fire Protection Association, Boston, MA. Kobayashi, M. 1979. “A Systems Approach to Urban Disaster Planning,” Ph.D. dissertation, Kyoto University, Kyoto, Japan (in Japanese). Kobayashi, M. and Kornfield, L.M. 2002. “Strategies for Reducing Post-Earthquake Fire Damage in Historic Wood Structures, in Proc. 7th National Conference on Earthquake Engineering, Boston, Earthquake Engineering Research Institute, Oakland, CA. Kobe Fire Department. 1995. Heisei 7 Hyogo ken Nanbu Earthquake — Regarding Kobe City Damage and Fire Department Activities, Kobe City (in Japanese). Los Angeles City Fire Department. 1987. Earthquake Emergency Operational Plan. Los Angeles City Fire Department. 1994. ’94 Earthquake After Action Report, March 9, 1994. Los Angeles County Fire Department. 1994. Northridge Earthquake Fact Sheet. Maher, T.J. 1933. Abstract of Reports Received Regarding the Earthquake that Occurred in Southern California on March 10, 1933, U.S. Coast and Geodetic Survey, Field Station, San Francisco.
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Manson, M. 1908. “Report on an Auxiliary Water Supply System for Fire Protection for San Francisco,” California Board of Public Works, San Francisco. Mohammadi, J., Alyasin, S., and Bak, D.N. 1992. “Investigation of Cause and Effects of Fires Following the Loma Prieta Earthquake,” Report to the National Science Foundation funded under research grant BCS-9003557, Department of Civil Engineering, Illinois Institute of Technology, Chicago. Mroz, M.P. and Soong, T.T. 1997. Fire Hazards and Mitigation Measures Associated with Seismic Damage of Water Heaters, Report NIST GCR 97–732, Building and Fire Research Laboratory, National Institute of Standards and Technology, Gaithersburg, MD. MTR. 1991. Pre-Design Report for Saltwater Pumping Stations and Dedicated Distribution Systems, prepared by MTR Consultants Ltd. and James M. Montgomery Consulting Engineers, for the Waterworks Engineer, City of Vancouver, B.C. National Fire Research Institute. 1995. “Report on the Hyogo Ken Nanbu Earthquake and Urban Fires in Kobe City,” Mitaka, Tokyo, Japan. Nawa, M. 1924. “Quake Damage to Water Supplies of Japanese Railways,” Engineering News-Record, 93(2.5), 986. NBFU (National Board of Fire Underwriters). 1905. “Committee of Twenty, Report of National Board of Fire Underwriters on the City of San Francisco, CA,” National Board of Fire Underwriters, New York. NBFU (National Board of Fire Underwriters). 1906. “The San Francisco Conflagration of April, 1906,” S. Albert Reed, Special Report to National Board of Fire Underwriters Committee of Twenty, May 1906, National Board of Fire Underwriters, New York. NBFU (National Board of Fire Underwriters). 1933. Report on the Southern California Earthquake of March 10, 1933, National Board of Fire Underwriters, New York. Okamoto, S. 1984. Introduction to Earthquake Engineering, University of Tokyo Press, Tokyo. O’Rourke, T.D., Pease, J.W., and Stewart, H.F. 1992. “Lifeline Performance and Ground Deformation during the Earthquake,” in The Loma Prieta, California Earthquake of October 17, 1989: Marina District, U.S. Geological Survey Professional Paper 1551-F, T.D. O’Rourke, Ed., Strong Ground Motion and Ground Failure, T.L. Holzer, Coordinator, U.S. Government Printing Office, Washington, D.C. Porter, K.A., Scawthom, C., Honegger, D.G., O’Rourke, T.D., and Blackburn, F. 1991. “Performance of Water Supply Pipelines in Liquefied Soil,” in Proc. 4th U.S.-Japan Workshop on Lifeline Earthquake Engineering, Los Angeles, August 19–23, National Science Foundation, Washington, D.C. Ree, A.C.D. 1941. “Fire Department Operations during the Long Beach Earthquake of 1933,” Bull. Seismol. Soc. Am., 31(1), 9–12. Rothermel, R.C. 1983. How to Predict the Spread and Intensity of Forest and Range Fires, General Technical Report INT-143, U.S. Forest Service, Ogden, UT. Scawthom, C. 1984. “Simulation Modeling of Fire Following Earthquake,” in Proc. 3rd U.S. National Conference on Earthquake Engineering, Charleston, SC, Earthquake Engineering Research Institute, El Cerrito, CA. Scawthorn, C. 1987. Fire Following Earthquake: Estimates of the Conflagration Risk to Insured Property in Greater Los Angeles and San Francisco, All-Industry Research and Advisory Council, Oak Brook, IL. Scawthorn, C. 1997a. “The 1923 Kanto, Japan, Earthquake,” in Reliability and Restoration of Water Supply Systems for Fire Suppression and Drinking Following Earthquakes, Report NIST GCR 97–730, D.B. Ballantyne and C.B. Crouse, Eds., Building and Fire Research Laboratory, National Institute of Standards and Technology, Gaithersburg, MD. Scawthorn, C. 1997b. “The 1989 Loma Prieta, California Earthquake Water Supply Effects,” in Reliability and Restoration of Water Supply Systems for Fire Suppression and Drinking Following Earthquakes, Report NIST GCR 97–730, D.B. Ballantyne and C.B. Crouse, Eds., Building and Fire Research Laboratory, National Institute of Standards and Technology, Gaithersburg, MD.
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Scawthorn, C. 1998. “Reliability-Based Design of Water Supply Systems,” in Proc. International Water Works Association Workshop on Anti-Seismic Measures on Water Supply, November, Japan Water Works Association, Tokyo. Scawthorn, C., Ed. 2000. The Marmara, Turkey Earthquake of August 17, 1999: Reconnaissance Report, MCEER Technical Report MCEER–00–0001, Multidisciplinary Center for Earthquake Engineering Research, State University of New York, Buffalo, NY. Scawthorn, C. and Donelan, J. 1983. “Fire-Related Aspects of the Coalinga Earthquake,” in Report on the Coalinga Earthquake of May 2, 1983, Earthquake Engineering Research Institute, Berkeley, CA. Scawthorn, C. and Khater, M. 1992. “Fire-Following-Earthquake: Conflagration Potential in the Greater Los Angeles, San Francisco, Seattle and Memphis Areas,” prepared for the Natural Disaster Coalition by EQE International, San Francisco. Scawthorn, C. and Khater, M. 1994. “Fires Caused by Earthquakes: A Greater Threat than Many Realize,” NFPA Journal, May/June, 82–86. Scawthorn, C. and O’Rourke, T.D. 1989. “Effects of Ground Failure on Water Supply and Fire Following Earthquake: The 1906 San Francisco Earthquake,” in Proc. 2nd U.S.–Japan Workshop on Large Ground Deformation, July, National Center for Earthquake Engineering Research, Buffalo, NY. Scawthorn, C. and O’Rourke, T.D. 1997. “The 1906 San Francisco, California Earthquake,” in Reliability and Restoration of Water Supply Systems for Fire Suppression and Drinking Following Earthquakes, Report NIST GCR 97–730, D.B. Ballantyne and C.B. Crouse, Eds., Building and Fire Research Laboratory, National Institute of Standards and Technology, Gaithersburg, MD. Scawthorn, C. and Waisman, F. 2001. “Assessment of Risk Due to Fire Following Earthquake, Lower Mainland, British Columbia,” Report prepared for the Institute for Catastrophic Loss Reduction, Toronto, by EQE International, Oakland, CA. Scawthorn, C., Yamada, Y., and Iemura, H. 1981. “A Model for Urban Post-Earthquake Fire Hazard,” DISASTERS, Int. J. Disaster Studies Practice, 5(2), 125–132. Scawthorn, C. et al. 1985. “Fire-Related Aspects of the 24 April 1984 Morgan Hill Earthquake,” Earthquake Spectra, 1(3), 675–685. Scawthorn, C. et al. 1995. “Fire-Related Aspects of the January 17, 1994 Northridge Earthquake,” Earthquake Spectra, 11C, 419–435. Scawthorn, C., Porter, K.A., and Blackburn, F.T. 1992. “Performance of Emergency Response Services After the Earthquake,” in The Loma Prieta, California Earthquake of October 17, 1989: Marina District, U.S. Geological Survey Professional Paper 1551-F, T.D. O’Rourke, Ed., Strong Ground Motion and Ground Failure, T.L. Holzer, Coordinator, U.S. Government Printing Office, Washington, D.C. Scawthorn, C., Cowell, A.D., and Borden, F. 1997. “Fire-Related Aspects of the Northridge Earthquake,” Report prepared for Building and Fire Research Laboratory, NIST-GCR-98–743, National Institute of Standards and Technology, Gaithersburg, MD. Schiff, A., Ed. 1997. Northridge Earthquake: Lifeline Performance and Post-Earthquake Response, Report NIST GCR 97–712, Building and Fire Research Laboratory, National Institute of Standards and Technology, Gaithersburg, MD. Schussler, H. 1906. The Water Supply of San Francisco, California, Spring Valley Water Company. Sekizawa, A. 1997. “Post-Earthquake Fires and Firefighting Activities in the Early Stage in the 1995 Great Hanshin Earthquake,” paper presented at 13th Meeting of the UJNR Panel on Fire Research and Safety, March 13–20, 1996, NIST Tech. Report NISTIR 6030, Building and Fire Research Laboratory, National Institute of Standards and Technology, Gaithersburg, MD. Sepponen, C. 1997. “Fire Department Emergency Response,” in Northridge Earthquake: Lifeline Performance and Post-Earthquake Response, Report NIST GCR 97–712, A. Schiff, Ed., National Institute of Standards and Technology Building and Fire Research Laboratory, Gaithersburg, MD, chap. 16. SFFD (San Francisco Fire Department). 1990. “Report on the Operations of the San Francisco Fire Department Following the Earthquake and Fire of October 17, 1989,” San Francisco Fire Department. © 2003 by CRC Press LLC
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Steinbrugge, K.V. 1982. Earthquakes, Volcanoes and Tsunamis, Skandia-America Group, New York. Takata, A. and Saizberg, F. 1968. Development and Application of a Complete Fire-Spread Model, Vols. 1 to 4, Office of Civil Defense, Illinois Institute of Technology Research Institute, Chicago. Usami, T. 1996. Nihon Higai Jishin Soran (List of Damaging Japanese Earthquakes), University of Tokyo Press, Tokyo. USGS. 1907. The San Francisco Earthquake and Fire of April 18, 1906 and Their Effects on Structures and Structural Materials, Bull. No. 324, U.S. Geological Survey, Washington, D.C. Woycheese, J.P., Pagni, P.J., and Liepmann, D. 1999. “Brand Propagation from Large-Scale Fires,” J. Fire Protection Eng., 10(2), 32–44. Youd, T.L. and Hoose, S.N. 1978. Historic Ground Failures in Northern California Associated with Earthquakes, Professional Paper 993, U.S. Geological Survey, Washington, D.C.
Further Reading Comprehensive works on fire following earthquake are rare. Steinbrugge [1982] provides a good qualitative discussion, while Scawthorn [1981] and the AIRAC report [Scawthorn, 1987] provide the first integrated model of the problem and probably still the best overall discussion, followed by HAZUS [2002]. Sekizawa and other Japanese researchers cited in the references are well worth reading.
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30 Hazardous Materials: Earthquake-Caused Incidents and Mitigation Approaches 30.1 Introduction and Significance of Earthquake-Caused Hazardous Materials Incidents 30.2 The Loma Prieta Earthquake 30.3 The Northridge Earthquake 30.4 The Hanshin-Awaji Earthquake Hazmat Storage Facilities · Gasoline Stations · LPG Leak · Chemical Releases and Fires
30.5 Earthquake-Caused HAZMAT Incidents at Educational Institutions and Laboratories The 1923 Great Kanto Earthquake · The 1948 Fukui Earthquake · The 1964 Niigata Earthquake · The 1968 Tokachi-Oki Earthquake · The 1978 Santa Barbara Earthquake · The 1978 Miyagiken-Oki Earthquake · The 1983 Coalinga Earthquake · The 1985 Chile Earthquake · The 1987 Whittier-Narrows Earthquake · The 1989 Loma Prieta Earthquake · The 1993 Kushiro-Oki Earthquake · The 1994 Northridge Earthquake · The 1994 Sanriku-Haruka-Oki Earthquake · The 1995 Hanshin-Awaji (Kobe) Earthquake
30.6 Damage and Corrective Actions at Japanese Petroleum Facilities The 1964 Niigata Earthquake · The 1978 Miyagiken-Oki Earthquake · The 1984 Nihonkai-Chubu Earthquake · Effectiveness of Hazard Mitigation at Japanese Petroleum Facilities
30.7 Lessons Learned Reluctance to Divulge Information · Reportable Quantities · Documentation · Mitigation Works · Laboratory Fires · Storage Areas · Laboratories · Asbestos · Biohazards · Compressed Gas Cylinders
30.8 Mitigation Approaches Inventory Reduction · Separation of Incompatibles · Anchoring of Storage Shelves and Cabinets · Reagent Vessels and Containers · Pressurized Gas Cylinders · Pipes and Piping Connections · Glass · Education
Guna Selvaduray San Jose State University San Jose, CA © 2003 by CRC Press LLC
30.9 Problem Areas That Must Be Addressed 30.10 Conclusions Acknowledgments References
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30.1 Introduction and Significance of Earthquake-Caused Hazardous Materials Incidents This chapter deals with hazardous materials (HAZMAT) release due to earthquakes, and the mitigation of this problem. Reports of earthquake-caused damage have tended to focus primarily on structural collapse, and HAZMAT incidents that occur during earthquakes have been reported only when they have resulted in major conflagrations, such as the petroleum fires that followed the 1964 Niigata earthquake. This lack of recognition reflected society’s general lack of awareness of the importance of HAZMATrelated problems until recently, and it is noteworthy that the first paper on HAZMAT incidents that occurred during earthquakes was not presented until 1982 [Reitherman, 1982]. The occurrence of HAZMAT incidents during earthquakes has special significance due to a number of factors. First and foremost, from an earthquake-response perspective, it is desirable to reduce the number of incidents that require response after an earthquake. The agencies that are trained to respond to HAZMAT incidents are not equipped for (and do not expect) a large number of occurrences within a relatively small geographic region, and within a very narrow time frame. In the event of an earthquake, however, far more than the usual number of hazardous materials incidents can occur, not only within a small geographic region, but also within a very short time frame. Approximately 75% of HAZMAT releases after an earthquake are addressed by the facilities owners and contractors, rather than publicagency responders who are overloaded at such times. A reduction in the number of HAZMAT incidents during an earthquake can therefore be expected to reduce the strain on response agencies that already will be heavily burdened. The occurrence of HAZMAT incidents during earthquakes has resulted in damage to the environment. The uncontrolled release of hazardous materials, at any time, poses a threat to the environment. Perhaps the most notable earthquake-related environmental incident was the oil spill at the Tohoku Petroleum Refinery outside Sendai, Japan, during the Miyagiken-oki earthquake of 1978. Approximately 770,000 gallons of petroleum flowed out from the damaged storage tanks into the bay adjacent to the refinery [Selvaduray, 1986]. Contamination of bodies of water also occurred during the Northridge and Kushirooki earthquakes. There is the potential for contamination not only of oceans and waterways but also of underground water sources and soils surrounding the facilities that contain the hazardous materials. There is an economic incentive for preventing the release of hazardous materials, especially when such a release can result in the contamination of the soil and underground and aboveground water sources. Cleanup efforts are extremely expensive; it is far more economical to prevent an uncontrolled release than to clean it up. The HAZMAT spill at the Coalinga High School chemistry laboratory resulted in cleanup costs of approximately $90,000 [Tierney, 1985]. A conservative estimate for the cleanup of the HAZMAT spill at the California State University, Northridge (CSUN) chemistry laboratories was between $5 and 7 million [Norton, 1997]. Implementation of hazard mitigation measures that could have prevented these spills would have cost significantly less. Another motivating factor to reduce the occurrence of earthquake-caused hazardous materials incidents pertains to the nature of the industries that either handle or use hazardous materials. With the progress of science and technology, there is a rapid emergence of new chemicals and reagents that are being used. The potential consequences of incidents involving these reagents and chemicals are not always fully known prior to the occurrence of spills or incidents. In some cases, the incidents involve a number of different materials, with varying properties and characteristics, and posing different threats, thus making response rather difficult. Also, a number of facilities that either manufacture or handle hazardous materials were constructed prior to the establishment of regulations requiring adequate safety measures, and thus may be particularly vulnerable. A worldwide listing of HAZMAT incidents that have been reported for earthquakes prior to 1996 is contained in Table 30.1. It should be noted that there is a significant disparity in the number of HAZMAT incidents between the Loma Prieta and Northridge earthquakes on the one hand, and all other earthquakes on the other hand. This is due to the fact that, for these two earthquakes, data pertaining to
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TABLE 30.1 Listing of Hazardous Materials Incidents That Have Occurred during Past Earthquakes Earthquake Name Long Beach Fukui Kern County Alaska Niigata Tokachi-oki Santa Rosa San Fernando Nicaragua Izuhanto-oki Peru Tangshan, China Izuoshima-kinkai Miyagi-ken-oki Santa Barbara Imperial Valley Livermore Chibaken Chubu Greece Urakawa-oki Coalinga Nihonkai-Chubu Nemuro-hanto oki Morgan Hill Nagano-ken Seibu Chile Mexico City Palm Springs El Salvador New Zealand Ecuador Whittier-Narrows Chibaken Toho-oki Quebec Loma Prieta Costa Rica Kushiro-oki Hokkaido Nansei-oki Northridge
Date
M (magnitude)
Incidents (#)
Mar 33 Jun 48 Jul 52 Mar 64 Jun 64 May 68 Oct 69 Feb 71 Dec 72 May 74 Oct 74 Jul 76 Jan 78 Jun 78 Aug 78 Oct 79 Jan 80 Sep 80 Feb 81 Mar 82 May 83 May 83 Jun 83 Apr 84 Sep 84 Mar 85 Sep 85 Jul 86 Oct 86 Mar 87 Mar 87 Oct 87 Dec 87 Nov 88 Oct 89 Mar 90 Jan 93 Jul 93 Jan 94
6.3 7.3 7.7 8.0 7.5 7.9 5.6 6.4 6.3 6.8 7.5 7.8 7.0 7.4 5.1 6.6 5.8 6.1 6.7 7.9 6.7 7.7 7.4 6.2 6.8 7.8 8.1 5.9 5.4 6.3 6.1 6.1 6.7 6.0 7.1 6.9 7.5 7.8 6.7
13 4 4 30 30 17 1 29 1 1 2 1 1 23 2 6 8 1 1 2 26 67 1 1 1 5 2 2 2 1 3 20 11 3 490 1 5 11 387
HAZMAT releases were specifically sought out; there were probably more HAZMAT releases during previous earthquakes, they simply were not recorded and reported. The Loma Prieta earthquake of October 1989 was the first earthquake in the United States (and perhaps in the world) to be specifically researched for HAZMAT releases and incidents. A total of 490 incidents were identified [Perkins and Wyatt, 1992]. The Northridge earthquake of January 1994 was also investigated for HAZMAT releases, and 387 HAZMAT incidents were identified [Selvaduray, 1997]. Urban earthquakes, such as the 1994 Northridge earthquake, have also caused fires. In some cases there were major conflagrations, some of which were associated with hazardous materials. The Four Corners pipeline break in the Northridge earthquake, at Huntington and Laurel Canyon Roads, resulted in petroleum vapors infiltrating the area. When the vapors were ignited, a major conflagration ensued, resulting in 14 automobiles and several homes being burned [LAFD, 1994]. In the chemistry laboratories of CSUN, three separate fires were ignited, due to gas leaks and chemical reactions. The fires destroyed, © 2003 by CRC Press LLC
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totally or in part, nine science laboratories, and burned for approximately 5 hours. One of the fires reignited several times, and was fully extinguished only after approximately 15 hours [Kupfer, 1994]. The more recent earthquakes in Turkey and in Taiwan have also resulted in HAZMAT releases and fires. In Turkey, the Tupras refinery was set ablaze, with its 700,000 tons of oil, resulting in air pollution due to the smoke; the toxic waste dump at Petkim sustained large cracks with potential leaks; and a factory producing synthetic fibers suffered chemical leaks [BBC, 1999]. The outbreak of several fires across Taiwan in the 1999 Chi-Chi earthquake was also reported [PBS, 1999]. The discussion of structural issues as they pertain to HAZMAT incidents is specifically not covered in this chapter. If a failure occurs in a structure that contains hazardous materials (e.g., a building in which a chemical laboratory is located), then there is bound to be release of hazardous materials. The obvious solution to such a problem is to address the structural integrity of the building, which is the purview of the structural engineering community, which has taken admirable steps toward addressing this issue. The focus of this chapter, therefore, is on the release of hazardous materials when there is no contributing structural damage. The vast majority of failures that have resulted in HAZMAT releases during earthquakes can be summarized as follows [Perkins and Wyatt, 1990]: 1. 2. 3. 4.
5.
6. 7. 8. 9.
10.
Failure of buildings and structures Dislodging of asbestos or encapsulated asbestos Breakage of underground pipelines due to soil movement Damage to aboveground pipelines, including process piping, due to: 4.1. Differential movement between pipes and structures or equipment 4.2. Impact from other structures or equipment 4.3. Damage from failing pipe supports 4.4. Damage/rupture at threaded connections Failure of cylindrical storage tanks due to: 5.1. Buckling of side walls 5.2. Sloshing 5.3. Corrosion Toppling of elevated tanks Shifting and overturning of horizontal tanks Sloshing from open tanks Falling containers and shelves, particularly in: 9.1. Hospitals 9.2. Laboratories 9.3. Retail stores 9.4. Storage warehouses Problems due to sliding, overturning, or internal failures of industrial equipment
Some examples of HAZMAT releases during past earthquakes are shown in Figures 30.1 through 30.5. In Sections 30.2 through 30.4 of this chapter, the occurrences of hazardous materials incidents during the Loma Prieta, Northridge, and Hanshin-Awaji earthquakes are described, as illustrations of the issues. These earthquakes are particularly important because they occurred in areas that are urban and industrialized. Section 30.5 describes the occurrence of earthquake-caused HAZMAT incidents at educational institutions. This topic is particularly relevant because the findings from the Loma Prieta and Northridge earthquakes indicate that approximately 50% of HAZMAT incidents occur in laboratories. Section 30.6 provides a description of incidents that occurred at Japanese petroleum facilities during the 1964 Niigata and the 1978 Miyagiken-oki earthquakes, the corrective actions that were taken as a result of these earthquakes, and how these mitigation approaches were effective in preventing similar incidents during the Hanshin-Awaji earthquake. Lessons learned (Section 30.7) and feasible mitigation approaches (Section 30.8) are then discussed, followed by a brief overview of problem areas requiring attention (Section 30.9). © 2003 by CRC Press LLC
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FIGURE 30.1 Chlorine cylinders in the process of being filled. Movement of the cylinders and subsequent rupture of pipe connections resulted in a chlorine leak during the Whittier-Narrows earthquake of 1987.
FIGURE 30.2 Photograph of chemicals storage area that burned during the Northridge earthquake of 1994. The fire started as a result of mixture of incompatible chemicals.
FIGURE 30.3 Collapse of 5-gallon lubricating oil containers during the Hanshin-Awaji earthquake of 1995 resulted in a spill of lubricating oils.
30.2 The Loma Prieta Earthquake A total of 490 HAZMAT incidents of all sorts were found to have occurred during the MW 7.1 Loma Prieta earthquake, which occurred on October 17, 1989. This total number does not include natural gas leaks in the gas distribution system, for which data were not available. An important observation is that © 2003 by CRC Press LLC
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FIGURE 30.4 A major fire engulfed portions of this building as a result of ruptured gas lines during the HanshinAwaji earthquake of 1995.
FIGURE 30.5 Photograph of gas distribution line that ruptured at a welded joint during the Hanshin-Awaji earthquake of 1995. The gas pressure blew out the ground around the point of rupture.
46.1% (226) of the incidents involved spills in laboratories. Many of these laboratories were not in the category of “permitted facilities” and had quantities below the threshold quantities that requires permits. The next highest rate of occurrence was release of asbestos, which accounted for 16.5% or 81 incidents. Other major occurrences involved releases from tanks, releases due to sloshing, releases from other containers, and releases from pipes. The data are summarized in Table 30.2. Of the 490 events, 43 were identified as being particularly large occurrences, i.e., these incidents resulted in the release of relatively large quantities of hazardous materials. The major problem was sloshing, with 19 events. Other causes for the large releases were releases from tanks, pipes, containers, and equipment.
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TABLE 30.2 Hazardous Materials Releases during the Loma Prieta Earthquake Type of Problem Laboratory Asbestos Tank Sloshing Container Pipe Equipment Cylinder Valve Indirect Transportation TOTAL
Number
Percentage
226 81 49 40 39 36 8 4 3 3 1 490
46.1 16.5 10.0 8.2 8.0 7.4 1.6 0.8 0.6 0.6 0.2 100.0
TABLE 30.3 Types of Hazardous Materials Released during the Loma Prieta Earthquake Material
Percentage of Total Number of Releases
Miscellaneous lab chemicals Asbestos Miscellaneous liquids Propane Plating solutions Fuels and petroleum products Acids Ammonia Pesticides Formaldehyde Paint Biohazards Solvents Other/unknown
41.6 16.1 11.1 6.9 5.6 5.6 3.0 2.4 2.2 1.2 1.2 0.8 0.6 0.8
The incidents were also classified in terms of the specific chemicals released, and the data are shown in Table 30.3. Laboratory chemicals were the materials most frequently released, followed by asbestos. This is not surprising given the finding that close to one half of the incidents occurred in laboratories. The next largest releases involved miscellaneous liquids, propane, plating solutions, fuel and petroleum products, and acids. It was possible to obtain information on containment of the releases for only 331, or 67.7%, of the releases. Of this total number, 188 (57%) were contained, 52 (15.7%) were partially contained, and 90 (27.3%) were not contained. Most of the gaseous releases went into the atmosphere. Some of the liquid releases ended up in the drains or directly into soil, although some evaporated into the atmosphere. When hazardous materials are released, they must be cleaned up. The majority of the cleanup effort was undertaken in-house; this accounted for 70.4% of the incidents. The local health departments were involved in 24.6% of the cases and the local fire departments in another 11.2%. Only in 19.6% of the cases was the cleanup performed by a private contractor. For a large proportion of the releases, there were two or more responding parties. Despite the relatively large number of releases that were identified and documented, there were no major HAZMAT-caused conflagrations or contamination of bodies of water.
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TABLE 30.4 Hazardous Materials Releases during the Northridge Earthquake Type of Problem
Number of Occurrences
Percentage
Laboratory Asbestos Containers Pipe Sloshing Tanks Equipment Transportation Valves Indirect damage Cause unknown TOTAL
232 4 21 9 7 4 2 2 1 9 96 387
59.95 1.03 5.43 2.33 1.81 1.03 0.52 0.52 0.26 2.33 24.81 100
TABLE 30.5 Types of Hazardous Materials Released during the Loma Prieta Earthquake Material
Number of Occurrences
Asbestosa Acids Medical/biological Crude oil Paint Petroleum Mercury Insecticides/fertilizers Organic gases Contaminated water Household agents Plating chemicals Various/mixed Miscellaneousb Unknown TOTAL
4 30 17 12 10 9 8 7 6 4 3 3 194 27 53 387
Percentage 1.03 7.75 4.39 3.10 2.58 2.33 2.07 1.81 1.55 1.03 0.78 0.78 50.13 6.98 13.70 100
a
A total of 48 asbestos releases were documented. However, only 4 of these were cases where only asbestos was involved. The other 44 involved incidents where asbestos release was combined with the release of other materials as well. b This category involves materials whose identities are known, but do not fit within one of the other categories.
30.3 The Northridge Earthquake The MW 6.7 Northridge earthquake of January 17, 1994 resulted in 387 hazardous materials incidents, not including those related to natural gas. The data were collected from Los Angeles and Ventura counties. The type of problem that led to the releases is summarized in Table 30.4, and the hazardous materials involved in each of these incidents is summarized in Table 30.5. In most cases, the material involved in the incident was identifiable; however, this was not possible for 53 (14%) of the incidents. In 50% of the incidents, more than one hazardous material was involved. In the case of incidents where only one material was involved, the most frequently released material was © 2003 by CRC Press LLC
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TABLE 30.6 Major HAZMAT Incidents That Occurred during the Northridge Earthquake Company Name HASA CSU Northridge Union Oil Southern Pacific Railroad ARCO Pumping Station Caltico Oil Co. Hillside Oil Partners Shell Oil Southern California Gas Co. ARCO (Four Corners Pipeline) Sylmar Convertor Station
Material Released
Quantity (gal)
Hydrochloric acid Sodium hypochlorite Various Crude oil Sulfuric acid Crude oil Crude oil Crude oil Gasoline Crude oil Crude oil
1,000 500 Substantial 700 8,000 214,000 1,100 1,000 2,000 8,000 21,500 68,800
Mineral oil
5,000
Cause of Release
Cleanup Organization HASA funded
Numerous Sloshing Train derailment Pipeline rupture Pipe shear failure Tank rupture Tank rupture Tank collision Pipeline rupture Pipeline rupture during pressure check Transformer valve failure
Contractor, Cal-EPA In-house Contractor Contractor In-house Contractor Contractor Contractor LADWP HAZMAT Team
acids, followed by medical/biological materials, crude oil, paint, and petroleum. There were also a total of 48 incidents where asbestos was released. Only four of these incidents involved the release of asbestos only; in the other 44 incidents, asbestos was released in addition to other hazardous materials. The most frequent releases of hazardous materials occurred at laboratories, primarily laboratories in educational institutions. Of the 387 total, 232 (60%) occurred in laboratories. It was also found that a total of 100 gas cylinders had failed in one manner or another, with all of these occurring in educational institutions. Two locations, namely CSUN and the University of California, Los Angeles (UCLA), had the largest number of occurrences, a total of 226 or 58%. There were 92 sites that had occurrences of single incidents, and 14 sites that had two incidents. The 387 incidents occurred at a total of 116 sites. While the total number of HAZMAT incidents identified is relatively large, not all of them had severe consequences. Several HAZMAT incidents that were called in entailed minor quantities, for example, of mercury from thermometers that had broken. However, there were several large incidents, and these are summarized in Table 30.6. Description of the incidents that occurred at educational institutions during the Northridge earthquake is covered in Section 30.5, which discusses earthquake-caused HAZMAT incidents at educational institutions and laboratories. There were several leaks from pipelines that convey petroleum products from the production sites to Los Angeles Harbor. The Four Corners pipeline no. 1 sprung a leak at a failed weld, and released 3500 barrels of crude oil, which flowed into Santa Clara Creek. Another Four Corners pipeline break, at Huntington and Laurel Canyon, resulted in a major conflagration. In this case, the leak resulted in petroleum vapors infiltrating the area and the fire subsequently started when the vapors were ignited. Several houses and 14 cars in this area were burned as a result of the fire. Overall, at least seven leaks from pipelines owned by Four Corners Pipeline were reported at various locations. Another major incident occurred when a Southern Pacific Railroad train was affected by the earthquake. Six cars containing sulfuric acid derailed. One of these cars leaked approximately 8000 gallons of sulfuric acid. One car containing ethylene glycol and one car containing petroleum wax also derailed, but there were no leaks. There was also a leak of approximately 400 gallons of diesel fuel from the locomotive engine that overturned. All of the spills were confined to the railroad right-of-way. A large variety of incidents occurred at several businesses and industries: release of acids from tanks, oil spills from ruptured tanks, asbestos releases, propane tank releases, and plating chemicals releases. Cleanup cost estimates, provided by the Los Angeles County Health Department HazMat Division, indicate that for incidents within the county, the cost was approximately $1.5 million. However, this number is most probably significantly lower than the actual cost involved.
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30.4 The Hanshin-Awaji Earthquake Despite its magnitude and the fact that it occurred in an urban industrial area, the MW 6.9 HanshinAwaji earthquake (January 17, 1995) was relatively devoid of HAZMAT releases. There was one major incident that involved the release of liquid propane gas (LPG) with the potential for a major conflagration; however, this was handled very capably by the fire departments involved. Despite the presence of a very large number of petroleum storage tanks, there were no major releases, as may have been anticipated. This is one of the success stories that this earthquake provided. Another success story was the effectiveness of the concrete block firewalls that are built around gasoline stations; despite the extensive fires that raged in the greater Kobe region, no gasoline station was affected by the fires because of the presence of these firewalls. This earthquake also showed the vulnerability of rack storage systems. The HAZMAT releases and fires that occurred during and immediately after the earthquake are described in Sections 30.4.1 through 30.4.4.
30.4.1 Hazmat Storage Facilities In the four prefectures (Osaka, Kyoto, Hyogo, and Kagawa) affected by the Hanshin-Awaji earthquake, there were a total of 60,259 facilities that handle hazardous materials, including 968 production facilities, 9,528 indoor storage facilities, 2,177 outdoor storage facilities 30,029 tank storage facilities, 8,804 gas stations, and 17,557 other HAZMAT handling facilities. In Hyogo Prefecture itself, there were a total of 21,953 facilities, including 3,085 indoor storage facilities, 967 outdoor storage facilities, and 2,945 gas stations. Of the total number of facilities in all four prefectures, there were 1,258 facilities that had damage due to the earthquake, including 7 fires and 157 leaks. Of the total, 1,172 or 93% of the damaged facilities were located within Hyogo Prefecture, which bore the brunt of the earthquake. Five of the seven fires and 75% of the leaks occurred within Hyogo Prefecture, a large proportion of the damage occurring in Kobe City. While there were seven fires at HAZMAT facilities, they were ignited by post-earthquake fires that spread, resulting in these facilities catching fire. Of the 157 leaks that occurred, 96 (61%) were at indoor storage facilities, followed by 16 (10%) at outdoor tank storage facilities, and 15 (9.5%) at general handling facilities. There were also 12 (7.5%) leaks at underground tank storage facilities. The primary cause of leaks in indoor storage facilities was damage to containers when they fell from storage racks and released their contents upon impact with the floor. Of the 16 leaks that occurred at outdoor storage facilities, none of them occurred at tanks constructed under the new design criteria that came into effect in 1977. There were seven cases of leaks due to sloshing, with minimal amounts leaked. Six leaks were due to damage to piping, two were due to damage to valves, and one leak was due to sidewall buckling. The largest leak resulted in a release of 40 kl. Many storage facilities sustained a variety of damage, including uneven settlement of tanks, buckling of sidewalls, damage to secondary containment walls, etc. What is noteworthy is that, unlike in the past, there were no major releases of petroleum and petroleum products during the Hanshin-Awaji earthquake, despite the close proximity of these facilities to the epicenter and the severe ground shaking that these facilities experienced. The problem area that remains to be addressed pertains to indoor storage, where 61% of the leaks occurred. At these facilities, drums, pails, and cans are stacked on pallets, racks, or organized in other ways, with no restraints. The storage mode is inherently vulnerable to ground shaking, and it is not surprising that damage to containers and leaks ensued. This damage pattern has been observed during prior earthquakes as well, in both Japan and the United States. Furthermore, this damage pattern is not unique to HAZMAT storage facilities but is common to all storage facilities that resemble warehouses. Rather than consider this problem as a situation that is unique to indoor HAZMAT storage facilities, it must be recognized that all indoor storage facilities, especially warehouses, are extremely vulnerable, and a broad-based solution that can have wide applicability must be developed. It is also interesting to note that the estimated damage cost for spills and releases was U.S. $26,537 million, indicating that the economic consequence due to spills and releases was quite severe. These data © 2003 by CRC Press LLC
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represent direct damage to physical facilities and do not include opportunity costs associated with business losses, which can further increase the total.
30.4.2 Gasoline Stations Of the total of 8,804 gas stations in the four prefectures, 383 sustained damage. Within Hyogo Prefecture, there were 2,945 gas stations, 357 (12%) of which sustained damage. Again, it is important to note that there were no fires, and only four cases of leaks, all minor. The damage was primarily to the structures and equipment. The leaks were due primarily to cracks or damage in the piping connected to the tanks, and were in the range of 5 to 20 liters. Current code requires construction of a firewall around gas stations, except on the side where it is open to the street. Even in areas of Kobe where conflagrations spread, the firewalls were very effective in stopping the spread of fire. There were several cases where the fires burned up to the firewall, but did not spread into the gas station. If the firewalls had not been constructed, a scenario where escaping vapors from underground storage tanks at gas stations fueled fires is conceivable. The Hanshin-Awaji earthquake occurred at 5:46 a.m., a time when the gas stations were closed. If the earthquake had occurred during normal business hours, it is conceivable that there would have been more releases. However, when one takes into account the manner in which gas stations are constructed, this scenario is not very likely.
30.4.3 LPG Leak The only HAZMAT release that could have had major consequences occurred at MMC Terminal in Kobe. A 20,000-ton LPG tank sprang a leak at the flange of the main valve. Because the leaking flange was on the tank side of the valve, the leak could not be shut off. The leak was detected shortly after the earthquake, and the employees who detected it made the first attempts to stop the leak by covering the flange with blankets and pouring water in an attempt to freeze it, thus stopping the leak. However, aftershocks and gradual settlement of the pipeline leading away from the tank resulted in the leak becoming worse. The secondary containment walls also had been damaged, thus increasing the risk posed. The Kobe Fire Department was informed of the leak at around 10:00 a.m. on January 17. In view of the possibility of a major conflagration, and even explosion, an evacuation warning was issued at 6:00 a.m. on January 18 (i.e., approximately 24 hours after the earthquake and leak). This affected approximately 70,000 residents, who had difficulty finding alternate housing in the post-disaster environment. All fire departments that were capable of responding to this incident did so. This facility had three 20,000-ton LPG tanks; fortunately, only one was damaged. Further, one of the neighboring tanks was practically empty so that the contents of the leaking tank could be transferred, a process that was completed on January 30 (i.e., approximately 2 weeks later). Despite being a hazardous material, LPG is regulated in Japan by MITI rather than the Fire Defense Agency. After the earthquake, a detailed analysis of the factors that contributed to the leak was undertaken and new design criteria developed. These include improved attachment of the main valve to the sidewall of the tank, and improved seismic design criteria for pipelines and secondary containment walls. Reconstruction of the damaged LPG tank began in July 1995 and was completed in December 1996, with product shipment beginning in April 1997. There was significant damage to this particular site, although there was only one release. The total cost for repair to physical plant facilities was estimated at U.S. $100 million. The opportunity cost associated with the inability to ship LPG for 27 months was estimated at approximately U.S. $750 million. Even after shipment began, between 10 and 15% of the pre-earthquake customers were permanently lost.
30.4.4 Chemical Releases and Fires A total of six fires related to chemicals were identified. Four of the six occurred at educational institutions, two at universities and two at secondary schools. These are described in greater detail in Section 30.5. One fire started at a rubber shoe company and another at a government laboratory. All of these fires are reported to have started shortly after the earthquake. © 2003 by CRC Press LLC
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The fire that began at the rubber shoe company become a major conflagration, resulting in 76,000 m2 being burned. This included 434 structures that were totally burned, 2 that were half burned, and 6 that were partially burned. It is suspected that the natural gas leak that followed the earthquake was ignited by some means. The real estate cost of this fire was estimated at U.S. $23 million. Equipment costs and business losses were not estimated. The fire at the government laboratory, located on the fourth floor, was due to mixing of chemicals, resulting in 133 m2 being burned. This fire did not spread, and the cost of the fire was estimated at U.S. $14,000, the cost to repair the space.
30.5 Earthquake-Caused HAZMAT Incidents at Educational Institutions and Laboratories Based on the foregoing discussion, several past earthquakes have shown that significant damage can occur in laboratories, especially chemical laboratories, during earthquakes. The uniqueness of laboratories arises from the fact that they are locations where new ideas are developed and tested. Equipment layout and arrangements are generally semipermanent, at best. In addition, laboratories at educational institutions are designed to demonstrate a very wide variety of ideas and concepts, and therefore must maintain flexibility to the constantly changing needs of the research and education community. In addition to flexibility, laboratories are also locations where a large number of highly reactive and toxic materials, albeit in small quantities, are stored and used. This is especially true of chemical laboratories. Damage to a laboratory can thus result not only in significant economic loss, but can also be a serious threat to life safety. Educational institutions also face the unique problem of having a transitory population, i.e., students. Laboratories are used by large numbers of students, with each group residing in the laboratory for relatively short periods of 3 hours or less. Students use the laboratories but do not necessarily have ownership of the facilities, which can result in poor housekeeping practices. Also, while many educational institutions have courses covering chemical safety, this component generally does not cover earthquake safety. The occurrence of HAZMAT incidents at educational institutions is not restricted to the United States. There also have been a significant number of incidents that have occurred at Japanese educational institutions during earthquakes. The remainder of this section contains a summary of HAZMAT incidents in educational institutions in Japan and the United States that have occurred as a result of earthquakes.
30.5.1 The 1923 Great Kanto Earthquake The chemical spills that occurred during this earthquake and the fires that resulted from these spills have been studied by several researchers and were recently summarized by Tadao Yoshida [Yoshida et al., 1994]. The schools and universities that are reported to have had major “chemical fires,” i.e., fires that ensued as a result of chemical spills, include the Tokyo Imperial University, Waseda University, Keio Medical University, Tokyo Technical College, Yokohama Technical College, the Military Academy Preparatory College, Japan Dental and Medical College, Meiji Pharmacological College, and Gakushuin University. The chemicals that were reported to have been involved include white phosphorus, sodium, sodium peroxide, volatile organics, and concentrated acids, among others.
30.5.2 The 1948 Fukui Earthquake A total of six elementary schools, five middle schools, and one high school were reported to have been burned down within Fukui Prefecture, due to chemical fires (Yoshida et al., 1994). Within Fukui City, a fire thought to have been started by chemicals in the science room of Haruyama Elementary School, resulted in a conflagration leading to 100 casualties. In a separate incident, a chemical fire occurred in a laboratory of Fukui Technical College but was extinguished before it spread.
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30.5.3 The 1964 Niigata Earthquake A fire broke out in the science room of the Higashi-Niigata Middle School, Niigata City, due to containers of phosphorus, metallic sodium, metallic magnesium, concentrated sulfuric acid, and other chemicals falling off their shelves and mixing with each other. Although desks started to burn, the teachers and pupils extinguished the fire within 30 minutes [Yoshida et al., 1994].
30.5.4 The 1968 Tokachi-Oki Earthquake There were two reported incidents of fires caused by chemical spills at high schools [Takayama, 1969]. At Misawa Shogyo High School, a fire started from the physics and chemistry preparation rooms, located on the second floor. During the ground shaking, the chemicals fell from the shelves onto the concrete floor, mixed, and resulted in the fire. There were medical supplies in the same room but because the shelves had been anchored to the wall, none of those chemicals fell. The fire was extinguished by the staff, who used dry-chemical fire extinguishers. At the Hachinohe-kita High School, there was an explosion inside the chemicals storage room 1 minute after the earthquake. The door of the storage room blew out and the gases released ignited, resulting in the fire. The chemicals had been stored on five-high shelves. Metallic sodium, which was on the third shelf, fell down and mixed together with hydrochloric acid and sulfuric acid, resulting in the explosion and fire. Ether and acetone that had been stored volatilized and also were ignited. The shelves had no restraints, and between 10 and 20% of the chemicals fell. This fire too was subsequently extinguished with dry-powder fire extinguishers before it could spread and become a major conflagration.
30.5.5 The 1978 Santa Barbara Earthquake At the University of California, Santa Barbara, there were numerous chemical spills in the laboratories in the Science Building [Reitherman, 1982]. Further details on these spills have not been available.
30.5.6 The 1978 Miyagiken-Oki Earthquake Several HAZMAT incidents occurred as a result of this earthquake, and have been documented by several researchers [Yoshida et al., 1994; Ikegami, 1979; Sakurai, 1978; Ogino, 1978]. The most serious incidents occurred at Tohoku University, where there were several spills and fires. In addition, there were also incidents at the Tohoku Pharmacological University and a technical high school. 30.5.6.1 Tohoku University Spills and fires occurred in the science, engineering, and medical science buildings. In the science building, three rooms were destroyed by fire, primarily due to failure of the fire extinguishing system at the beginning of the earthquake. In Room 403 (fourth floor), a bottle containing metallic sodium in ether, which had been placed on the lower level of the reagent shelf, slid off and fell onto the floor. Reagent jars from the higher shelves also fell, breaking the bottle containing the metallic sodium and releasing the sodium, which reacted with the moisture present, generating heat. This ignited the solvent vapors from the other broken jars, resulting in a fire that expanded rapidly. This fire spread to the adjacent room (Room 401) as well. A similar incident occurred in another room on the fourth floor, Room 410, where metallic sodium also reacted with water, resulting in a fire. This fire was initially extinguished by the students present, who closed the doors and windows and left. When the firefighters arrived and opened a window to evaluate the scene, the fire reignited, but was subsequently suppressed. On the seventh floor (Room 705), an experiment on distillation of diisopropyl benzyl alcohol, using an oil bath, was in progress when the earthquake occurred. The vibration caused the oil bath to tip and ignite the ether, benzene, and methanol that had been released from other reagent jars that fell and broke. This fire also spread to the adjacent room, Room 703.
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The science building was constructed of reinforced concrete, and damage to the first three floors was not too severe, but from the fourth floor upwards all laboratories were badly damaged. The chains restraining many compressed gas cylinders were broken. The horizontal acceleration on the fourth floor was reported as being 405 gal, and it was 710 gal on the seventh floor. Approximately 85% of all reagents on the seventh floor, 65% on the fourth floor, and 30% on the third floor fell from the shelves [Tokyo Metropolitan Government, 1986]. In the medical science building, there were two incidents of chromium trioxide spills, with ensuing fires. In one incident, the chromium trioxide mixed with other spilled reagents and ignited; the fire was extinguished by personnel present at the scene. In another incident, a restrained shelf fell, due to failure of the restraint, and chromium trioxide reacted with the floor tiles, resulting in a fire. This fire too was quickly extinguished by the personnel present at the scene. Two other incidents of reactive metal fires, one involving sodium and another involving lithium, also occurred. In both cases, the reactive metals lost their protective containment, reacted with moisture present, and ignited. There were also numerous spills on the fifth and sixth floors of the engineering building, where reagent jars fell from shelves, were broken, and their contents spilled. However, there were no ensuing fires. 30.5.6.2 Tohoku Pharmacological University Two laboratories in this university had fires that followed spills. In the environmental laboratory, chemicals fell from a shelf that had 1-cm-high lips installed. A seminar was in progress at the time of the earthquake, and the professor immediately tried to support the shelf containing the chemicals to prevent it from falling. However, the reagent jars fell around the professor’s feet, ignited, and caused him injury. In the organic chemistry laboratory, a solvent bottle fell and broke, and the vapors were ignited by a gas burner that was in use, resulting in the laboratory being burned. Approximately 60% of the reagent jars on the fourth floor fell from their shelves. It is reported that the horizontal acceleration on the fourth floor was 820 gal and on the fifth floor, it was 1050 gal [Tokyo Fire Department, 1985]. 30.5.6.3 Prefectural Technical High School In the analytical chemistry laboratory, acid containers stored in wooden cabinets fell and spilled the acid, which flowed onto the floor. The steel cabinets in the organic chemistry laboratory did not tip over but the reagent jars inside the cabinets did shatter, releasing their contents. All reagent jars and equipment on laboratory countertops also fell and were damaged or broke [Tokyo Fire Department, 1985]. 30.5.6.4 Miyagi Prefectural Environmental Health Research Laboratories In the chemistry laboratories of this prefectural facility, practically all of the reagent shelves tipped over and fell, with resulting chemical reactions and release of toxic fumes. There were also fires as a result of chemical reactions among incompatible reagents. Practically all foam fire extinguishers were damaged and could not be used. Fire extinguishment was problematic because access to the origin of the fires was difficult, due to the presence of fallen objects or hazardous fumes. While most of the equipment and shelving that had not been anchored fell, there was practically no damage to equipment that was anchored to laboratory benches or structural walls. Numerous pressurized gas cylinders were knocked down. Piping connections were found to be weak spots. In the case of plastic pipes, practically every joint and bend cracked, loosened, or was displaced.
30.5.7 The 1983 Coalinga Earthquake Chemical spills occurred at the Coalinga high school and also at the community college. In the high school chemistry laboratory store room, 1-gal glass jugs containing sulfuric acid fell to the floor, broke, and spilled their contents, which corroded through the floor of the laboratory, located on the first floor, and dripped on the floor of the basement. This resulted in the generation of hydrogen sulfide and other fumes [Scawthorn and Donelan, 1984]. The laboratory spill caused extensive damage, and the costs of cleaning up and restoring the laboratory totalled approximately $90,000 [Tierney, 1985]. At the community college, there was also a spill in the store room adjoining the chemistry laboratory. Despite 1-in.-high shelf lips © 2003 by CRC Press LLC
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having been installed, reagent jars fell, causing a spill, which was cleaned up by the fire department’s HAZMAT team. After the earthquake, the college installed an additional wire restraint at a height of approximately 3 in. above the shelf. In the high school chemistry laboratory, large glass jars containing reagents crashed onto the floor, spilling their contents. In the Coalinga Water Filtration Plant, many of the chemical containers on the testing laboratory shelves and benches toppled, spilling their contents [Isenberg and Escalante, 1985].
30.5.8 The 1985 Chile Earthquake The Oxiquim Chemical Plant, located in the northeastern part of Vina del Mar, had a fire in a laboratory due to chemical reagents falling off shelves, spilling, and mixing. The fire died due to lack of oxygen but started up again three separate times when the door to the laboratory was opened [Wyllie et al., 1986].
30.5.9 The 1987 Whittier-Narrows Earthquake Chemicals and supplies stored on the sixth, seventh, and eighth floors of the physical sciences building at California State University, Los Angeles were dislodged, with some of them reacting with each other. The spilled chemicals resulted in a fire in a laboratory on the eighth floor [SCEPP, 1987]. The cause of the fire is thought to have been organic solvent vapors ignited by potassium metal reacting with moisture. Though the fire was extinguished by the responding fire department, all the laboratory equipment was destroyed, and approximately one quarter of the eighth floor had smoke damage. Asbestos contamination on the eighth floor and penthouse of the building also was found to be at unacceptably high levels, forcing closure of both floors until repairs were completed. A fire, due to leaking toluene that was ignited either by an electric furnace or from the reaction of metallic sodium, in a laboratory at the University of California was also reported [Yoshida et al., 1994].
30.5.10 The 1989 Loma Prieta Earthquake A total of 135, or 27.6%, of the incidents during this earthquake occurred at educational institutions and involved laboratory chemicals and asbestos release and contamination. Fortunately, there were no major spills or conflagrations. The incidents occurred at all levels of the educational establishment, including middle schools, high schools, junior colleges, and universities. In most cases, the HAZMAT (chemicals) spills occurred due to reagent jars falling from the shelves and impacting with the floor. It is interesting to note that at many educational institutions, shelf restraints had been installed prior to the earthquake, despite which reagent jars fell off the shelves. At some institutions, the shelf restraints were found to be effective, with reagent jars only falling off shelves that had no restraints. One fire, at the University of California, Santa Cruz, occurred due to a Bunsen burner that was in use. A “near-fire” occurred at San Jose State University, where a custodian discovered smoke coming from one of the rooms in the old science building and contacted the university police, who in turn contacted the San Jose Fire Department. A heating unit that was being used to heat dimethylpolyroxane (Dow-Corning 200 Fluid) had been left on, causing the material to smoke. The largest number of incidents occurred at Stanford University (81 incidents), followed by San Jose State University (30 incidents). As stated earlier, all of these were relatively minor spills, and there were no major incidents.
30.5.11 The 1993 Kushiro-Oki Earthquake A fire occurred in one of the laboratories of the Obihiro Veterinary University and was investigated in detail by the Obihiro Fire Department. Total losses were estimated at ¥7 million [Obihiro Fire Department, 1993]. This fire occurred due to mixing of incompatible chemicals and the subsequent ignition of a container of n-pentane. The reagents had been stored on shelves that were anchored to the wall, and
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also had 3-cm-high shelf lips. Furthermore, the reagents also had been separated with a divider, in terms of incompatibles. The investigation report concludes that the reagents fell from the shelves onto the floor, despite the shelf lips. The chemicals thus released mixed, generating heat and igniting. A container of npentane in a corrugated box had been placed in front of the shelf. The fire burned the corrugated box, which in turn ignited the n-pentane, and thus the fire spread.
30.5.12 The 1994 Northridge Earthquake Of the total 387 incidents identified, 232 (60%) occurred in laboratories, not all at educational institutions. Hazardous materials incidents occurred at a variety of institutions, including K–12, junior colleges, and universities. While a large number of incidents occurred at K–12 institutions, they were all very minor. There was one relatively major incident at a junior college. Of the universities, CSUN and UCLA had a large number of occurrences. The incidents at CSUN were by far the most severe, and included three fires as a result of the hazardous chemical spills. 30.5.12.1 Junior Colleges Los Angeles Valley College and College of the Canyons both had chemical spills. At the College of the Canyons, despite shelf lips having been installed, the extensive vertical movement caused reagent jars to tip or topple over the shelf lips. This incident occurred in a three-story laboratory building that housed facilities for art, biology, and chemistry. 30.5.12.2 University of California, Los Angeles There were several spills, which occurred in 14 different buildings on this campus. Some of the spills were significant enough to require cleanup by HAZMAT teams. 30.5.12.3 California State University, Northridge This campus experienced perhaps the largest number of earthquake-caused HAZMAT incidents ever, probably due to its close proximity to the earthquake epicenter. The information here is summarized from a report written by William Kupfer to the California Chemical Emergency Planning and Response Commission [Kupfer, 1994]. Three separate fires were ignited, probably by gas leaks or chemical reactions, near the time of the earthquake. The fires burned until 9:30 a.m. and destroyed, totally or in part, nine science laboratories. One of the fires reignited several times and was not fully extinguished until later in the day. Approximately 100 compressed gas cylinders were damaged or exploded in the fires. After the fires were extinguished, there were 53 cylinders that had been badly damaged but were unexploded, and the gases contained in them could not be readily identified. A company that specializes in evacuating damaged cylinders and identifying and recontainerizing dangerous gases was retained for this task. Chemical spills occurred widely over the campus, at over 200 locations. Virtually every laboratory containing chemicals had some degree of spillage. Only one of the spills contained a chemical in excess of its “reportable quantity,” namely 800 g of bromine, which was dissipated to the air. While some of the spills occurred in isolated locations and it was possible to determine the material and quantity spilled, there also were many spills that were intermixed, with the result that labeling was lost. The cleanup crews, which consisted of a cleanup contractor, hazardous waste consultant, and in-house physical plant staff, operated for about 3 weeks. Over 30 buildings were contaminated with asbestos, as a result of the shaking. Asbestos contamination came from three primary sources: (1) structural fireproofing, (2) thermal and acoustic insulation on utilities and ceilings, and (3) floor and ceiling tiles. The engineering building and the main library presented the most significant problems here. Every room in the engineering building had to be cleaned, including several utility rooms. The entire fourth floor was so badly damaged that it required complete asbestos abatement. The main library required cleaning of approximately 200,000 books per floor. One particular difficulty encountered was with one of the science buildings, which contained human pathogens used for research and teaching. Due to the potential threat to human health, the entire building was first sealed completely, and imminent hazards in adjacent buildings abated. The floor on which the © 2003 by CRC Press LLC
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human pathogens were kept was then sealed separately, under negative pressure, and the exhaust filtered with a HEPA filter. A contracting epidemiologist was the first person to enter and assess the situation. After confirming that the pathogens had not been released, the chemical cleanup crews then entered and abated the chemical hazards in the building. Similar steps also were taken to survey and ensure that no radioactive materials had been released.
30.5.13 The 1994 Sanriku-Haruka-Oki Earthquake Spills occurred during this earthquake at Kitazato University and Misawa Commercial High School. At Kitazato University, there were six separate spills, involving a wide variety of chemicals including acetonitrile, in the laboratories of the Veterinary Sciences Department. In five of the six cases, chemicals that had been stored on shelves fell to the floor, broke upon impact, and spilled their contents. In one case which involved used chemicals, the bottles containing these chemicals had been placed on the floor. The glass containers collided with each other as a result of the ground shaking, and broke. As a result of this incident, the university now disposes of used chemicals immediately. The cleanup of the spills was done by university personnel, including graduate students. Total cost of the damage was estimated at ¥2.6 million. The spill at Misawa Commercial High School was similar in nature, i.e., spills due to reagent jars falling from shelves and breaking upon impact. After the earthquake, the school replaced all of the older wooden cabinets with steel cabinets that are anchored to the wall and floor. At Mutsudo High School, there were no spills due to some of the mitigation measures taken ahead of time. Containers with more hazardous reagents were placed on shelves, in sand, and sulfuric acid containers were provided with double containment.
30.5.14 The 1995 Hanshin-Awaji (Kobe) Earthquake While this earthquake had a major impact on the Kansai region of Japan, there were relatively few reports of HAZMAT incident occurrence at educational institutions and laboratories. 30.5.14.1 Universities There were several chemical spills in the School of Science at Osaka University but details of the spills are not available. Spills, including tipping over of shelves, were reported in laboratories and rooms where mitigation measures were not taken, such as anchoring of shelves and cabinets, and storage of hazardous materials in appropriate containers and cabinets [Umezaki, 1996]. However, in areas where mitigation measures had been taken, the damage was relatively light, though no mention of the extent of spills was made. A similar observation was made regarding compressed gas cylinders. Those that had not been adequately restrained, or had been placed in holders on the floor, tipped over, resulting in damage to the pressure regulator valves or adjacent equipment. At Kansei Gakuin University, metallic sodium reacted with water and resulted in a fire, which was extinguished by the fire department. Total damage cost was estimated at ¥8.5 million. At the university, there were two separate fires, in the chemistry lab and the biology lab on the seventh floor. The fire in the chemistry lab started shortly after the earthquake, while the fire in the biology lab started after 7:00 p.m. on January 17, 1995. The fire in the chemistry lab was confined to two rooms, and the fire doors and concrete walls were found to be effective in containing the fire. The fire department did not respond to this earlier fire. The fire in the biology lab, which started after 7:00 p.m., is thought to have been an electrical fire. Laboratory equipment had fallen on top of electrical wires, damaging them, resulting in short circuits when the power was turned on later. The cost for repairs to the building, due to fire damage, was approximately U.S. $1.5 million. The cost for replacement equipment was approximately U.S. $4.2 million, and the cost for equipment repair was approximately U.S. $6 million, bringing the total damage to the Faculty of Science to approximately U.S. $11.7 million.
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30.5.14.2 Secondary Schools Hazardous materials incidents at five high schools were identified. In all cases, reagent jars in laboratories fell from their shelves and broke, resulting in spills. At two high schools, the cabinets and shelves on which the reagent jars had been stored fell and the jars broke. One of the five incidents resulted in a fire, due to mixing of incompatible chemicals, which was extinguished by the fire department. The damage cost at this location was estimated at ¥38.5 million. In the case of the junior high school, the variety of reagents stored was actually quite minimal, despite which mixing of incompatibles appears to have occurred, resulting in a fire in a second-floor laboratory. This fire was left to burn itself out, primarily due to the lack of water for firefighting and the local fire department being overwhelmed with the total number of fires. A total of 1016 m2 of floor space was burned, including the gymnasium located on the third floor above. The building where the fire occurred also had structural damage. The total cost of the damage was estimated at U.S. $5.95 million. The cost for recovery and reconstruction of the building was estimated at U.S. $8.64 million. At the high school, where there was a relatively large inventory of chemicals that were used, the fire began in the chemistry laboratory storage room, located on the second floor. There was an explosion at some time after the fire began. In this case, too, the fire was left to burn itself out, due to lack of water supply. The fire burned a total area of 2359 m2, and the total building damage cost was estimated at U.S. $3.6 million. The cost of reagents, chemicals, and equipment was estimated at approximately U.S. $400,000. It is estimated that spills occurred at a large number of laboratories, both at educational institutions and otherwise. An exhaustive survey of chemical spills at laboratories has not been undertaken so far. At this time, there appears to be no reporting requirements in Japan for chemical spills if “hazardous materials” according to the Japanese definition are not involved. In some cases, chemicals, reagents, corrosives, toxics, etc., are not regulated by the fire agencies, but rather by the Ministry of Health and Welfare. Only if the release of chemicals results in a fire does it enter the fire department databases, and thus become available to researchers. Surveys conducted by this author and others indicate that spills were widespread in laboratories of high schools located in Kobe and other cities close to the epicenter. In all cases, it appears that school personnel did the cleanup themselves, typically washing away the spilled reagents with water.
30.6 Damage and Corrective Actions at Japanese Petroleum Facilities As was mentioned earlier, the Hanshin-Awaji earthquake was notable in its lack of spills and releases from petroleum storage tanks, despite the large number of tanks in the region that were affected. The lack of damage to petroleum storage tanks in Japan was first noted by this author when conducting postearthquake studies following the January 15, 1993 Kushiro-oki earthquake. A tank farm containing approximately 150 cylindrical petroleum storage tanks of varying sizes had no spills or damage. Interestingly, this tank farm had been newly constructed approximately 10 years prior to the earthquake. An older tank farm was demolished. The Japanese authorities have been very proactive in developing standards and regulations to minimize damage to petroleum storage and processing facilities, and the results of these efforts were apparent after the Kushiro-oki and the Hanshin-Awaji earthquakes. The damage to petroleum storage facilities during the Niigata, Miyagiken-oki, and Nihonkai-chubu earthquakes are described next, followed by the corrective actions taken.
30.6.1 The 1964 Niigata Earthquake Two fires occurred as a result of this earthquake. Based on the cause and time of ignition, these have been named primary and secondary fires. The primary fire occurred at 1:03 p.m., immediately after the earthquake, at Showa Petroleum’s new processing facility, which only had been completed in 1963. The conflagration was eventually extinguished at 5 a.m. on July 1, 1964, after it had burned for more than © 2003 by CRC Press LLC
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14 days. By the time the fire burned out, it had consumed three 30,000-liter crude oil tanks, two 45,000liter crude oil tanks (total crude lost was 122 million liters), and a portion of the processing equipment in the new 40,000 barrels per day multipurpose plant. Investigation of the cause of this fire led to the conclusion that friction and impact between the floating roof and sidewall of the storage tank led to sparking. The seal material between the roof and the sidewall was metallic, and it actually was the seal that led to sparking when it scraped against the side wall. These sparks ignited the petroleum vapors contained inside the tank, leading to a major conflagration. Five hours after the occurrence of the earthquake, at approximately 6:00 p.m. on June 16, 1964, another fire broke out at the site where a 5000 barrels per day line was operating. This secondary fire was caused by sparks carried over from a fire at another factory in the vicinity. Totally destroyed were 144 tanks containing a total of 32 million liters of assorted petroleum liquids and 69 structures having a total floor area of 13,828 m2, and the equipment contained therein. This fire was eventually extinguished at approximately 5 p.m. on June 20, 1964, i.e., 4 days later.
30.6.2 The 1978 Miyagiken-Oki Earthquake At the time of this earthquake, the Tohoku Petroleum plant had been shut down for planned maintenance, and only one package boiler was operating. As a consequence of this shutdown, all the storage tanks were filled to capacity. Five storage tanks, having a combined total capacity of 139 million liters, were damaged, and about 68 million liters of heavy oil were released. In all five cases, the bottom section of the tank was damaged, and in three of the five cases the bottom plate broke. The oil spill was not successfully contained within the dikes; some of it overflowed the dikes and some passed through under the dikes. The pipes running under the dikes were displaced sufficiently to create an underground passage through which the spilled oil passed. Approximately 2.9 million liters of oil actually found its way into Sendai Port via storm drains, despite shutting dampers and sandbagging. Fortunately, the oil spill was not ignited, and no fires resulted.
30.6.3 The 1984 Nihonkai-Chubu Earthquake The damage to petroleum facilities during this earthquake was primarily to storage tanks, with sloshing as the main problem. It was storage tanks with floating rather than fixed roofs that had sloshing problems. The tanks themselves, their foundations, and oil dikes were not damaged. Weather seals, foam dams, rolling rudders, and gage balls were also damaged. In particular, the tanks where sloshing occurred had natural frequencies (of the liquid) of 8 to 10 seconds.
30.6.4 Effectiveness of Hazard Mitigation at Japanese Petroleum Facilities The credit for the lack of major petroleum spills from storage tanks during the Hanshin-Awaji earthquake goes to the Japanese authorities who have investigated past releases in detail, and have instituted code changes to ensure improved safety during subsequent earthquakes. The fact that the effort to minimize spills, releases, and fires from petroleum storage tanks has been so far successful was proven by the lack of major incidents during the Hanshin-Awaji and the Kushiro-oki earthquakes. Some of the code and practice changes that have been implemented in Japan, beginning from 1964 right after the Niigata earthquake, include the following: 1. Plant and equipment design criteria emphasize choice of materials that are corrosion-, impact-, and fire-resistant for construction of equipment and tanks. 2. Plant and equipment layouts emphasize minimization of fire spread. 3. Storm drain shutoff valves were installed at all points from which water is discharged to prevent occurrences similar to what happened after the Miyagiken-oki earthquake. 4. A perimeter water curtain was installed to prevent spreading of fires to surrounding regions. Pumps were provided with standby generators in case of power failures. © 2003 by CRC Press LLC
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FIGURE 30.6 Photograph showing effectiveness of improved foundation construction and flexible pipes in preventing petroleum spills. (Courtesy Professor K. Suzuki, Tokyo Metropolitan University)
5. Sand piles were required for storage tanks to counteract effects of soil liquefaction. 6. Spill prevention techniques were instituted, including installation of level indicators, limit on upper fluid level to prevent sloshing losses, installation of equipment for recovery of oil in waste waters, and primary and secondary containment walls. 7. Periodic inspections of storage tanks for weld failure and corrosion. Tanks above a certain capacity are emptied out periodically and inspected by competent authorities. 8. Synthetic rubber weather seals are used instead of metallic seals on floating roof tanks to prevent sparking. 9. Reduction of piping failure potential by addition of loops at suitable distances, redesign of pipecontainment wall joints, and installation of flexible pipe connections where piping is connected to equipment or storage tanks. One notable success story that was possible to document after the Hanshin-Awaji earthquake was the lack of damage due to the improved tank foundation construction practice and the requirement to use flexible pipe connections, as shown in Figure 30.6. Notwithstanding this, since February 1998 Japanese authorities have required petroleum storage tanks with capacities greater than 10,000 kl to be fitted with emergency shutoff valves on all incoming and outgoing pipes to further reduce the possibility of leaks from ruptured pipelines. The design criteria for tanks having a capacity greater than 500 kl but less than 1000 kl have also been improved, in a direction toward greater assurance that even if the tanks were damaged, the probability of a spill or release can be minimized. These undoubtedly are further steps toward minimizing the possibility of leaks from petroleum storage tanks.
30.7 Lessons Learned In looking back at the types of hazardous materials releases that have occurred during previous earthquakes, and the challenges faced in collecting the data necessary to analyze these incidents adequately, a number of lessons have been learned. These are reviewed here very briefly. © 2003 by CRC Press LLC
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30.7.1 Reluctance to Divulge Information There is a great reluctance to divulge information on the part of the owners of facilities where such incidents have occurred. The individuals willing to share the information have been the exception rather than the rule. There is a perception that if the occurrence of a HAZMAT incident is known, then the facility could be dragged into a bureaucratic nightmare, and owners and managers of facilities are eager to avoid this. This problem must somehow be solved, so that we can continue to learn from past mistakes, and at least make sure that we do not repeat the same mistakes in the future.
30.7.2 Reportable Quantities A large number of the incidents that have occurred have involved HAZMAT quantities below the reportable quantities set by regulatory agencies, such as the fire departments, as threshold quantities. Only spills involving material quantities greater than the designated quantities must be reported to local and state authorities. As a result, a large number of occurrences have tended to go unreported. After the Northridge earthquake, the Los Angeles Fire Department was most willing to share the information that it had about 65 reported HAZMAT incidents. Yet, by pursuing a strategy of directly contacting facilities that were thought to be high-risk areas, the author and his research team were able to identify a large number of incidents that occurred but had not been reported because they were below the reportable quantities. HAZMAT threshold quantities, above which a permit would be required, have generally been set with industries and other hazardous materials handlers in mind. Educational facilities and laboratories generally tend to use or store, at any one given site, a large variety of chemicals and reagents in relatively small quantities. Therefore, it is possible that the quantity for any one given chemical is below the threshold quantity, and does not require permitting. On the other hand, if the permitting process becomes too detailed, university personnel can be burdened with an inordinate amount of paperwork, which can easily become unmanageable. This issue is a double-edged sword, and a workable compromise must be developed.
30.7.3 Documentation Of the published records examined, it was noted that Japanese records are generally far more detailed than U.S. records. If past damage examples are to be utilized for improvement of earthquake safety in laboratories, then survey methodologies of damage must be improved, with the compiling of sufficiently detailed information that will be more directly useful in planning hazard reduction. The information thus gathered can also be disseminated to the safety and research communities, or at least be easily accessible by them.
30.7.4 Mitigation Works It was repeatedly found that the most damage occurred at locations where implementation of mitigation measures was insufficient or totally lacking. As can be seen from the various examples described in this chapter, whenever mitigation steps had been taken prior to the earthquake, damage was minimized or totally avoided. This was clearly the case with the petroleum storage tanks and gasoline stations in the greater Kobe area. There were at least two laboratories where HAZMAT incidents would most probably have occurred at the time of the Northridge earthquake, had not inventory reduction been practiced in advance. In both of these cases, the laboratory management had already contracted with cleanup companies to remove unwanted chemicals. At the time of the earthquake, the unwanted chemicals already had been removed from the shelves and packed in containers awaiting disposal. This timely action averted possible releases. Figures 30.7A and B are photographs that were taken at adjacent laboratories, one where compressed gas cylinders were not adequately restrained, and another where compressed gas cylinders had been properly stored in racks. © 2003 by CRC Press LLC
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(A)
(B)
FIGURE 30.7 (A) Photograph of compressed gas cylinders that fell due to inability of clamps to restrain the cylinders during the Northridge earthquake of 1995. (B) Compressed gas cylinders stored in well-secured racks did not fall during the Northridge earthquake of 1995.
Mitigation techniques that are appropriate for reducing the risk of HAZMAT releases during earthquakes are described in Section 30.8.
30.7.5 Laboratory Fires Two major causes of laboratory fires are (1) ignition due to mixing of incompatible chemicals and (2) ignition due to the presence of reactive metals such as sodium, magnesium, or lithium. It has been reported that when proper storage practices have been followed, especially in terms of separating incompatible chemicals, fires have not ensued, even when there have been spills. This was the case at several corporate facilities. When reactive metals have been involved in fire ignition, the cause of the ignition has been contact between the reactive metal and water or moisture. In several cases, fires that started in one room have spread to adjoining rooms. In some cases, the spreading has been even wider, with significant portions of the entire building being affected. Incidents of fires that were thought to have been extinguished reigniting, due to the reintroduction of oxygen when fire suppression personnel entered the area at a later time, have also been reported.
30.7.6 Storage Areas More incidents appear to have occurred in storage areas than in laboratories or processing plants. While this may appear counterintuitive, if one takes into account the actual time spans over which chemicals are used in laboratories, such a finding is not very surprising. Most laboratories are used for perhaps 6 hours or so during the day, 5 days a week. If proper housekeeping practice is followed, the chemicals and reagents are cleaned up and put away in storage areas, where they reside 24 hours a day, 7 days a © 2003 by CRC Press LLC
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week. If an earthquake occurs during times when a laboratory is not in session, then in theory at least, there would be no chemicals in the laboratory area to cause spills, whereas there are always chemicals in the storage areas. In the 1983 Coalinga earthquake, high school personnel indicated that the laboratories had chemicals on their shelves dating back many years, whose existence in many cases had literally been forgotten [Scawthorn, personal communication]. The post-earthquake investigation of the HanshinAwaji earthquake also revealed that the largest number of HAZMAT releases occurred in indoor storage areas, with large numbers of 55- and 5-gal containers damaged. Chemical and hazardous materials storage areas have thus been found to be high hazard areas, and it is important to implement appropriate hazard mitigation measures.
30.7.7 Laboratories The major cause of chemical spills in laboratories is reagent jars falling off shelves, impacting the floor, and releasing their contents. Almost invariably the reagent jars that break tend to be glass containers. Alternative containers must be considered. Some reagents, notably hydrofluoric acid, are shipped in polymeric containers, which are more impact resistant. In some cases, one has a choice between glass containers and polymeric containers. Where glass containers are unavoidable, it is possible to obtain glass containers with a protective polymeric coating, albeit at a higher cost. Although shelf lips are effective in reducing the potential for reagent jars to fall off shelves, there are several incidents where the bottles have fallen off despite the shelf lips. There is a need to critically assess the required height of shelf lips, and also to develop other, more positive means of restraint that would prevent reagent jars from falling off the shelves on which they have been placed. Even when reagent jars do not fall out of cabinets or off shelves, it has been found that collision between jars can also result in breakage and spills. While placing reagent jars in appropriate cabinets with secondary containment does reduce the risk of release, it must not be thought of as a guarantee that spills will not occur.
30.7.8 Asbestos Data from recent earthquakes have shown that asbestos release has become a major problem. While this does not result in an immediate threat to life safety, the monetary cost of subsequent cleanup and abatement procedures is extremely high. The first time asbestos was identified as a problem was after the 1987 Whittier-Narrows earthquake. There were no reports of asbestos releases from prior earthquakes because asbestos was not considered a hazardous material until approximately the mid-1970s. As society continues to evaluate the vast number of materials that are used, it is very likely that materials once thought benign will emerge as being hazardous.
30.7.9 Biohazards While there have been no recorded incidents of release of biohazards, this is an item that deserves special attention because any such release can have major consequences. With research in biotechnology and pharmaceuticals on the increase, hazard mitigation procedures far more stringent than for regular chemicals is perhaps called for, in order to avoid a major incident during future earthquakes.
30.7.10 Compressed Gas Cylinders There have been numerous reports of damage to compressed gas cylinders during all of the earthquakes that this author has investigated, beginning with the 1971 San Fernando earthquake. Fortunately, there have been no reports of a HAZMAT release directly due to the failure of these cylinders. However, the potential for such a release exists, especially where particularly toxic gases such as arsine, phosgene, chlorine, etc., are used. Proper securing of compressed gas cylinders must be addressed at all locations where they are used. Floor mounts and straps anchoring cylinders to laboratory countertops with clamps © 2003 by CRC Press LLC
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have been generally found not to be very effective. Properly designed steel frames, such as those shown in Figure 30.7B, which in turn are anchored to the floor or the wall, have been found to be effective in restraining these cylinders during ground shaking.
30.8 Mitigation Approaches This section provides a brief review of some practical hazard reduction measures that can be implemented at reasonable cost. A detailed treatise on mitigation approaches is too extensive to be covered here.
30.8.1 Inventory Reduction Probably the best means of avoiding the occurrence of HAZMAT releases is to have on hand the minimum quantities necessary. Most laboratories tend to have chemicals that are not currently being used but can nevertheless pose a hazard if released from containment. Periodic reviews of the materials and quantities needed must be carried out, and excess chemicals and reagents sent away for proper disposal.
30.8.2 Separation of Incompatibles Perhaps the most important lesson to be learned from past damage examples is that storage methods play a major role in determining whether or not a HAZMAT release will occur. Incompatible chemicals or reagents must not be stored in close proximity in laboratories; they must be divided into individual categories, such as flammables or corrosives, and stored appropriately so that they will not mix if a release occurs. The interaction between them, if containment is lost, must be determined first, and storage sites determined accordingly. Special reagent cabinets, especially for flammables and explosives, are highly recommended. Incompatible chemicals can be divided into two major categories: those that liberate gases upon mixing, and those that react exothermically, i.e., release heat. Chemicals that form gases upon mixing can be divided into groups, depending upon the toxicity of the gases released. For example, cyanide-bearing solutions when mixed with oxidizing acids will release cyanide gas, which is extremely toxic and life-threatening. Ethanol when mixed with nitric acid releases nitrous oxide, which by itself is not highly toxic. However, if this mixture occurs in a closed container, then the buildup of gas pressure can result in an explosion. A very good source of information regarding incompatible chemicals is the Materials Safety Data Sheets available from the manufacturers of individual reagents. Another reliable source is Manual 491M, published by the National Fire Protection Association [NFPA, 1986]. In the event that such information is not available, and there is reason to conclude that toxic gases may be released, it is strongly recommended that tests be performed according to standard procedures to determine the gases released, along with the quantity released. Large containers of liquid reagents, such as gallon jugs of acids or solvents, and heavy items, are best placed on the bottom-most shelves of cabinets because the acceleration experienced at higher shelves is generally greater. Cabinets in which liquid reagents are stored can be provided with secondary containment so that spills that may arise from breakage can be contained. This can be done by either constructing barriers or providing sandboxes on the bottom-most shelf.
31.8.3 Anchoring of Storage Shelves and Cabinets Cabinets, shelves, and racks in which chemicals and other hazardous materials are stored must be sturdy and well secured to structural members. The effectiveness of this approach has been proven several times during past earthquakes. It is impossible to prevent damage to reagent containers if the cabinets or shelves in which they are stored are themselves damaged. Properly designed hardware must be utilized to anchor these to the floor and walls or ceiling, as appropriate. Especially in the case of shelves with high aspect ratios (height greater than two times the © 2003 by CRC Press LLC
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smaller of the base dimensions), it is important to restrain the top of the shelf as well. Anchoring only at the base is effective in preventing the shelf from sliding but it may not be sufficient to prevent the top of the shelf from swaying. As far as possible, placing cabinets one on top of another (double decking) must be avoided. If this is unavoidable, the two cabinets must be connected with properly designed hardware so that they will perform as one unit. The cabinets must then be adequately anchored at the floor and wall. On open shelving, restraints must be provided to prevent reagent containers from falling out. This can easily be implemented by a variety of methods. One very common method is to use a lightweight, high modulus wire, such as piano wire, stretched across the shelf with coil springs at either end. The height of the restraining wire above each individual shelf is dependent on the size (height) of the jars, and must be determined accordingly in each case. Another approach is to install a lip on the shelf board. Lips can also be installed on laboratory counters and benches. If the lips are installed in a manner such that they are leakproof, then they will also serve the purpose of containing spills. In most laboratory furniture, the individual shelf boards are generally supported by cabinet walls but are not attached to them. The vertical component of earthquake-induced ground shaking can dislodge boards thus supported, resulting in damage to the reagents. Shelf boards must therefore be firmly attached to cabinet walls. Angle brackets and wood screws, both of which are available from hardware stores, are generally sufficient for this task. Another factor that frequently contributes to reagent spills is doors that do not lock positively. Cabinet doors must therefore be fitted with locks that do not permit the doors to open during an earthquake. When purchasing new laboratory furniture, cabinets with positive locks must be specified for minimal additional cost. In the case of retrofitting, there are several varieties available, such as touch latches, that can be installed at very little cost.
30.8.4 Reagent Vessels and Containers Reagents that are contained in glass jars are especially susceptible to loss of containment due to fracture of the glass. Where possible, it is best to use impact-resistant, plastic containers. Most acids and bases can be contained in plastic containers rather than glass. Plastic containers are also less likely to be damaged by falling objects. In cases where glass containers are mandatory, as might be the case with some solvents, it is advisable to coat the glass with a plastic material that is resistant to the solvent contained therein. Most of the major laboratory equipment suppliers have plastic-coated glass bottles, as an off-the-shelf item. However, when converting to plastic containers, it must be borne in mind that these are less resistant to heat than are glass containers. It is also important to prevent glass jars from impacting each other inside the cabinet. Where possible, storage areas inside the cabinet can be divided so that the jars in storage do not impact each other during an earthquake. Reagent containers must also be inspected periodically for cracks or other forms of damage. Cracked glass jars, for example, are more prone to disintegrate altogether when subjected to even minor impact.
30.8.5 Pressurized Gas Cylinders Use of pressurized gas cylinders in laboratories is extremely common. They are frequently strapped to laboratory benches, and gas lines are commonly made of polymeric materials. Damage to gas cylinders and their piping invariably results in gas leaks. If the cylinder contains hazardous gases such as chlorine, carbon tetrachloride, etc., the consequences can be disastrous. Where possible, it is preferable to store gas cylinders outside, and pipe the gas in. If there is damage to gas cylinders and a leak develops, the gas will be dispersed outdoors rather than contained indoors. It is important, in this case, to make sure that there are no ventilation intakes located adjacent to gas cylinder storage sites. The cylinders themselves must be restrained adequately. The most common method is to restrain them with chains or straps. Gas cylinders must be restrained at two locations along their vertical axis, © 2003 by CRC Press LLC
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one in the top one third of the cylinder, and another in the bottom one third of the cylinder. Restraining must be done to either a structural wall or the studs. Anchoring gas cylinders to dry wall is insufficient to prevent damage. When it is not possible to anchor gas cylinders to a structural wall, a properly designed rack with adequate structural strength must first be anchored to the floor, and the gas cylinders subsequently restrained to this rack. When securing gas cylinders, it must also be borne in mind that earthquakes have a vertical component, and possible vertical motion of the gas cylinder must be taken into account. Installation of automatic shutoff valves at the main valve of cylinders is usually the best means of shutting off supply when a leak develops. When selecting such shutoff valves, it is imperative to first ascertain that the materials of construction of the valve are compatible with the gas that is being piped. It is also very good practice to shut off the main valve when gases from a particular cylinder are not being used, both during the workday and during nonworking hours.
30.8.6 Pipes and Piping Connections Piping within laboratories must be installed according to existing standards. In the event that applicable standards are not available, adequate care must be taken to prevent leaks. Piping containing particularly hazardous liquids and gases must be provided with double containment. In the event of liquids that do not vaporize, a trough directly beneath the pipe may be sufficient. However, in the event of liquids that tend to vaporize, such as anhydrous ammonia, the pipeline must be covered completely with another pipe. One of the most common causes of pipeline failure is due to differential motion between the pipe and equipment to which it is connected. The use of flexible connections reduces the probability of such a failure. The effectiveness of this approach was documented during the Hanshin-Awaji earthquake, as shown in Figure 30.6. When the supply source is far away from the point of usage, and gases or liquids are being piped in, it is prudent to install a shutoff valve just outside the point of usage, in a location that would be easily accessible. In the event of a leak, this valve can be used to shut off supply.
30.8.7 Glass Another part of laboratories that can be damaged during earthquakes are windows and glass panes. Fracture of glass panes must be prevented for the simple reason that shards flying out can cause injury. Glass panes are also used to isolate one area from another. For instance, in a typical building, the windowpanes isolate the building from the outside environment, making it possible to have a comfortable work environment inside. In the case of a cleanroom environment, damage to glass panes can result in significant losses, with major cleanup requirements to remove microcontamination. Glass used for interior partitions can be replaced with other transparent, shatter-resistant materials such as polycarbonate. Where other materials cannot replace the glass, transparent adhesive films can be applied on the surface. Though these adhesive films will not prevent glass breakage, they will prevent the fragments from flying out. The film can also be effective in preventing microcontamination by atmospheric intrusion. In the case of new construction, use of wired glass can achieve the same effect, but wired glass is generally more expensive than sheet glass, and it is not effective in preventing microcontamination.
30.8.8 Education The most important factor in implementing safety measures is, beyond a doubt, people. It is extremely important that not only the related safety personnel but also the researchers and other laboratory personnel be provided adequate education in safety measures. Most researchers find safety measures a necessary evil that they have to live with. It is true that many safety measures result in procedures taking longer than they would otherwise require. Nevertheless, it is important that researchers realize that without adequate safety measures, the loss could be greater in © 2003 by CRC Press LLC
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terms of time, morale, and life safety. The best hazard-reduction program is undoubtedly one that is implemented by the laboratory personnel themselves, rather than one that is imposed upon laboratory personnel by safety personnel. While most universities conduct classes on safe procedures of handling chemicals, it has been found that the earthquake threat is generally not an integral part of such training. Especially in areas prone to earthquakes, such as the western United States, it is imperative that earthquake safety is included in any class on safety training. There is a critical need for educational institutions to accept the fact that they are located within earthquake zones, and educate not only their personnel but also their students in an appropriate manner.
30.9 Problem Areas That Must Be Addressed There are a number of issues that are still outstanding, the resolution of which will contribute toward further lowering the risk of HAZMAT releases and associated fires during earthquakes. The first such issue is one pertaining to regulations. Hazardous materials are regulated by myriad regulations, and navigating the field of HAZMAT-related regulations can sometimes be extremely nerve wracking, especially for the regulatory novice. Nevertheless, current regulations do contribute significantly toward the safe handling and usage of hazardous materials. Regulations that specifically address the issue of earthquake safety of hazardous materials, however, are still lacking. The Japanese have shown, by the example of how they have regulated petroleum storage tank design and construction, that regulations aimed specifically at earthquake safety can be very effective. The U.S. bodies that write codes must follow this excellent example set by our Japanese colleagues. As was mentioned previously, there continues to be tremendous reluctance on the part of facilities owners who experience HAZMAT releases during earthquakes to even admit that there was a release. The tendency is for the owners to clean up the incident as quickly as possible and then carry on with business as usual. Even internal documentation of the incident is frequently lacking. An effort is needed to assure facilities owners and cleanup companies that providing such data to researchers will in no way jeopardize their operations. Too much data have been lost thus far; we may not be able to afford such losses in the future. The Japanese, on the other hand, have been extremely thorough in their data collection methods, and these data have been used for the benefit of society as a whole. There is also an associated problem with reporting requirements. Hazardous materials releases are required to be reported to the local fire department only if threshold quantities are exceeded. If the quantity released is below the threshold, the reporting of such an incident is voluntary, and they are generally not reported, especially by industries and businesses. There is a need to dissociate the reporting requirements from the threshold quantities that are utilized in the permitting process. This can result in better information becoming available. The challenge in data collection lies in identifying the damage mechanism that led to the incident rather than just identifying the occurrence of an incident. In many cases the release is cleaned up, and no detailed records are kept. This is in sharp contrast to the case in Japan, where company and institutional personnel have maintained detailed records of incidents that occurred. The cost effectiveness of mitigation is very intuitive to those who believe in it. However, there is still a severe lack of implementation of mitigation, especially if codes or regulations do not require it. While a significant body of data on cost effectiveness is coming into existence, the data are still insufficient. Particularly lacking are data on cleanup costs, without which reliable cost-effectiveness calculations cannot be performed.
30.10 Conclusions At the present time, the technology and know-how necessary for mitigating the potential for HAZMAT releases and associated fires exist for the most part. What appears to be lacking is the awareness that © 2003 by CRC Press LLC
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mitigation is effective, and in some cases the will to implement is also lacking. The cost savings, especially when one takes into account the expenses necessary for cleanup after the fact, will more than pay for the hazard mitigation. The 1995 Hanshin-Awaji earthquake provided us not only with lessons learned but also with success stories. The efforts that the Japanese regulatory agencies put into developing appropriate design guidelines for HAZMAT storage and handling facilities bore fruit during that earthquake. Thanks to this effort, there were no major spills from petroleum storage tanks, especially outdoor storage tanks. These efforts are continuing in the wake of the Hanshin-Awaji earthquake, and further design improvements are now being implemented, based on lessons learned. An area deserving greater attention is the earthquake safety of indoor storage facilities. The damage pattern seen here is identical to that seen in warehouses in general, and has been observed in earthquakes throughout the world. Solutions for this area must be developed so that the safety of all indoor storage facilities, not just HAZMAT facilities, can be improved. The documentation and analysis of chemical spills and releases also needs to be undertaken with greater earnestness. Chemical spills have occurred during earthquakes since the 1923 Great Kanto earthquake. Recently, several of these have resulted in fires. Though the damage has not been extensive thus far, the potential for such incidents to result in casualties is extremely high, especially if the earthquake occurs during normal working hours.
Acknowledgments A large number of individuals and organizations, too numerous to mention individually, have provided invaluable help and assistance during the course of the numerous investigations that have led to the information summarized in this chapter. The author wishes to acknowledge a select few who have been especially critical to his efforts: The National Science Foundation, which provided several grants; Dr. William Anderson, formerly of the National Science Foundation, for his continued support; Ms. Jeanne Perkins of the Association of Bay Area Governments, Oakland, CA; Professor Osamu Hiroi of Tokyo University; Professor Y. Kumagai of Tsukuba University; and Professor K. Suzuki of Tokyo Metropolitan University.
References BBC (British Broadcasting Company) News Online Network. August 19, 1999. Earthquake Safety for Facilities Utilizing Chemicals (in Japanese). February 1982. Shizuoka Prefecture, Environmental Health Division. Ikegami, Y. 1979. “Chemical Laboratories and Earthquakes: Case Studies from the Miyagiken-oki Earthquake,” Kagaku to Kogyo (Chemistry and Industry), 31, 558. Isenberg, J. and Escalante, L.E. 1984. “Damage to Lifelines,” in Coalinga, California, Earthquake of May 2, 1983: Reconnaissance Report, EERI report No. 84–03, January, Earthquake Engineering Research Institute, Oakland, CA, p. 230. Kupfer, W.R. 1994. Letter Report Written to the California Chemical Emergency Planning and Response Commission. LAFD (Los Angeles County Fire Department). 1994. HazMat Emergency Incident Report, log # 940227, and Memo from Erlinda MacAlintal to Chief Jim Ryland, Los Angeles County Fire Department, January 24. NFPA (National Fire Protection Association). 1986. NFPA 491M Manual of Hazardous Chemical Reactions., National Fire Protection Association, Quincy, MA. Norton, R. 1997. Director, Office of Environmental Health and Occupational Safety, California State University, Northridge, personal communication to Richard Staley, Emergency Preparedness Coordinator, San Jose State University, January 6.
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Obihiro Fire Department. 1993. “Report on the Fire That Occurred at Obihiro Veterinary University during the 1993 Kushiro-oki Earthquake,” Unpublished report provided to author by the Obihiro Fire Department via the Kushiro Fire Department. Ogino, H. 1978. “The Miyagiken-oki earthquake and chemistry laboratories,” Bunseki (Analysis), 1978(9), 86. PBS (Public Broadcasting System) Online News. September 21, 1999. Perkins, J.B. and Wyatt, E.G. 1992. “Hazardous Materials Problems in the Loma Prieta Earthquake,” in National Earthquake Hazard Reduction Program report to the U.S. Congress: The Loma Prieta, California, earthquake of October 17, 1989, part of the chapter “Fire, Police, Transportation and Hazardous Materials.” Perkins, J.B. and Wyatt, E. 1990. “Hazardous Materials Problems in Earthquakes: Background Materials,” Association of Bay Area Governments, Oakland, CA, September. Reitherman, R.K. 1982. “Earthquake-Caused Hazardous Materials Releases,” Proceedings of the Hazardous Materials Spills Conference, Milwaukee, WI. Rihal, S. 1984. “Architectural (Nonstructural) Component Damage Caused by Coalinga Earthquake
of May 2, 1983,” in Coalinga, California, Earthquake of May 2, 1983: Reconnaissance Report, EERI report no. 84–03, January, Earthquake Engineering Research Institute, Oakland, CA, p. 206. Sakurai, H. 1978. “Earthquakes and Chemical Laboratories at Tohoku University: Damage and Lessons Learned from the Miyagiken-oki Earthquake,” Kagaku (Science), 48, 568. Scawthorn, C. and Donelan, J. 1984. “Fire-Related Aspects of the Coalinga Earthquake,” in Coalinga, California, Earthquake of May 2, 1983: Reconnaissance Report, EERI report no. 84–03, January, Earthquake Engineering Research Institute, Oakland, CA, pp. 273–276. SCEPP (Southern California Earthquake Preparedness Project). 1987. “The Los Angeles-Whittier Narrows Earthquake of October 1, 1987: Federal/State Hazard Mitigation Survey Team Report,” Southern California Earthquake Preparedness Project, Los Angeles, CA, p. 12. Selvaduray, G. 1986. “Earthquake Hazard Reduction Techniques at Petroleum Facilities in Japan,” in Proc. Third U.S. Conference on Earthquake Engineering, Charleston, SC, August, Earthquake Engineering Research Institute, Oakland, CA. Selvaduray, G. 1997. “Occurrence of Hazardous Materials Incidents during the Northridge Earthquake of January 17, 1994,” in Proc. Northridge Earthquake Research Conference, August 20–22, Consortium of Universities for Research in Earthquake Engineering (CUREE), Richmond, CA. Takayama, H. 1969. “Report on the Mechanism of Fire Outbreak during the 1968 Tokachi-oki Earthquake,” Tokyo Disaster Prevention Council, Tokyo. Tierney, K.J. 1985. “Report on the Coalinga Earthquake of May 2, 1983,” Report no. SSC 85–01, Seismic Safety Commission, Sacramento, CA, p. 25. Tokyo Fire Department. 1985. Unpublished data provided to author. Tokyo Metropolitan Government. 1986. “The Planning of Disaster Prevention in Tokyo,” Report prepared by the Department of Urban Planning, June, Tokyo Metropolitan Government. Umezaki. 1996. “Lessons from the Hanshin Earthquake: Record of Damage in Osaka University’s School of Science Rooms,” Gendai Kagaku (Modern Chemistry), (February), 27–30. Wyllie, L.A. et al. 1986. “The Chile Earthquake of March 3, 1985: Industrial Facilities,” Earthquake Spectra, 2(2), 373–390. Yoshida, T., Wada, Y., and Foster, N. 1994. “Safety of Reactive Chemicals and Pyrotechnics,” Pre-publication manuscript, Tokyo, Japan.
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31 Loss Estimation 31.1 31.2 31.3 31.4
Introduction and Overview Why Do We Need Loss Estimation? History of Loss Estimation Loss Modeling Define the Assets · Define the Hazard · Methodology · Correlation
31.5 The Hazard Module Seismic Sources · Ground-Motion Models · Site Soil Conditions
31.6 Seismic Vulnerability Models Structures and Buildings · Contents · Business Interruption · Fire Following Earthquake
31.7 Damage and Loss Estimation Damage Estimation · Loss Estimation · Probabilistic Loss Exceedance Curves · Modeling Uncertainty
Mahmoud Khater ABS Consulting Oakland, CA
Charles Scawthorn Consulting Engineer Berkeley, CA
James J. Johnson James J. Johnson and Associates Alamo, CA
31.8 HAZUS® Earthquake Loss Estimation Software 31.9 Applications of Loss Estimation Estimation of Earthquake Losses in Los Angeles · Estimation of Earthquake Losses in New York · Impact of Earthquake Losses on U.S. National Infrastructure · Estimation of Earthquake Losses in the 1994 Northridge Earthquake · Seismic Performance Evaluation of Fire Stations · California Earthquake Authority · Estimation of Building Earthquake Losses in the United States
Defining Terms References Further Reading
31.1 Introduction and Overview The purpose of this chapter is to provide an introduction to the concepts and the technical methodology employed in earthquake loss estimation, also known as loss modeling. Loss estimation consists of the employment of mathematical models of the constitutive contributing elements of the loss process (that is, modeling) to arrive at estimates and associated confidence bounds of the potential losses that might result from an earthquake. Loss estimation is essentially a quantitative science, consisting of basic elements shown in Figure 31.1, defined using tools drawn from the natural sciences, engineering, economics, actuarial science, regional science, sociology, and the medical profession, and linked by the mathematics of probability and statistics.
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Natural Phenomena – the earthquake, its intensity distribution and resulting effects, such as liquefaction, landslide, tsunami etc
Built Environment – buildings, structures, lifelines and other creations of humankind – their distribution, vulnerabilities, values and functions
Human Environment – People, their mortality and morbidity, organizations and their functions, the economy social institutions and society
Losses – Human injuries, cost of repairs, business interruption, dysfunctional organizations and institutions, social disruption
FIGURE 31.1 Constitutive contributing elements of the loss process.
Loss estimation is a basic first step in the mitigation of earthquake risk (see Chapter 2). As William Thompson observed: I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind: it may be the beginning of knowledge, but you have scarcely, in your thoughts, advanced to the stage of science whatever the matter might be. [William Thompson (Lord Kelvin), Popular Lectures and Addresses (p. 80)] Loss estimation, therefore, is the quantification of the problem of earthquake loss,1 as a first step to understanding what contributes most to the loss, how the loss might be reduced, what should be an appropriate resource dedicated to reducing the loss, and what is an acceptable loss. As a first step in discussing loss estimation, the next section asks the question of why do we need such models, and why do they take a probabilistic vs. deterministic form? The main part of the chapter discusses the probabilistic modeling methodology, reviewing the various modules, including the hazard and damage modules, defining the portfolio of risks, estimation of financial losses, and typical outputs. This is followed by a review of some applications of loss estimation.
31.2 Why Do We Need Loss Estimation? Loss estimation is needed because earthquakes in any specific location are fortunately relatively infrequent. The result is that, while we may recognize regions to be of high seismic hazard, we do not really know the precise impacts of future events, but we need to know these impacts in order to guide new construction, reduce existing hazards, plan for emergencies, and prudently manage insurance and other financial commitments. A simple example vividly highlights the need for catastrophe loss estimation models — the 1994 Northridge earthquake. At that time, catastrophe models were only beginning to be developed and were not generally available within the insurance industry [Scawthorn, 1995]. Instead, insurance rates, which
1It should be noted that loss estimation is employed for most natural and technological hazards, such as hurricanes, floods, fires, and explosions, although this chapter focuses on earthquakes.
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in part are based on the expectation of loss costs in the future, were based on extrapolating loss results from the past. In California, insurance companies were required by law to offer earthquake insurance to homeowners, if they offered homeowner’s insurance. Underlying this offer were implicit assumptions that the prior history was “normal,” population (and property) distributions were constant, construction quality was consistent, and that the market reasonably priced the insurance cover. A review of those assumptions, in hindsight, shows they were grossly in error. Following the 1857 and 1906 very large earthquakes in southern and northern California, respectively, seismicity in California was abnormally low, when viewed in the context of several hundred years of seismologic and paleoseismologic data. This resulted in an underestimation of loss frequency. Furthermore, the population surged, especially in the high-hazard Los Angeles and San Francisco areas. Insurers did not have accurate methods for tracking precisely where their insured properties were located so that, unknown to the insurers, an unusually high fraction of properties in the highest hazard areas were purchasing insurance (a phenomenon known as adverse selection). The loss severity potential also was significantly understated. The Northridge earthquake, in a single event, shocked the insurance industry out of its complacency towards catastrophic risk. In 1994, the MW 6.7 Northridge earthquake, not especially large by California standards, struck the San Fernando Valley portion of the Los Angeles metropolitan area. The result was the largest natural disaster in U.S. history, in monetary terms, with total losses estimated at approximately $40 billion. Several insurers became insolvent, and other major property insurers (principally personal lines companies) withdrew from the market, precipitating an insurance crisis and necessitating the creation of a government insurance pool (the California Earthquake Authority). The Northridge earthquake demonstrated a number of risk characteristics that were not being recognized by traditional actuarial methods, which rely on historical loss data. These included: • Insurance rates are based on future loss occurrences, but were developed on past experience. • Large-catastrophe events (i.e., low probability and high severity), since they fortunately occur infrequently, yield only limited loss data. • The Northridge event should not have been a surprise — it was almost an exact repeat of the 1971 San Fernando earthquake, not only with respect to location but even as to time of year and time of day. The corollary of this is that low-frequency events provide sparse information regarding future, scientifically credible events, especially when they have not occurred in the past. • The future loss vulnerability is a function of changing building and land use development practices (i.e., zoning), which historical information does not capture. Therefore, what is needed are models that are prospective in risk estimation, not retrospective. In addition, considerable scientific and engineering uncertainty is involved, partly due to the inherent randomness of the physical events and partly due to our lack of complete understanding of the precise nature of damage and loss. In addition, the numerous computational factors are not necessarily independent, i.e., correlation between factors may alter the loss severity expectations. Hence, a model using single-point parameters (i.e., deterministic) for simulation of future losses will not be able to adequately estimate the risk associated with these events, and the loss potential. Most earthquake loss estimation models have utilized a probabilistic construction, which treats many of the loss parameters as random variables. This permits simulating potential loss events over a wide range of parametric variations, which is characteristic of the underlying physical aspects of the phenomenon. Since the Northridge earthquake, the development of the insurance-linked catastrophe securities markets could not have occurred without the rigorous risk quantification provided by the use of such models, since investors and rating agencies place significant (but not total) reliance on modeled results in assessing risk of loss and required pricing. Hence, loss estimation models have become an essential ingredient in structuring these securities, and assisting ceding companies in managing their overall catastrophe risk positions. The resulting loss metrics from a probabilistic model include probabilities of losses (attachment probability), and expected losses to defined layers of risk. These metrics are very similar to the credit market parameters of default probabilities and expected loss recoveries. The models, © 2003 by CRC Press LLC
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in essence, provide the risk bridge between insurance-related risks and credit market risks, enabling insurance-linked securities to receive credit ratings that are so essential in the fixed income debt markets.
31.3 History of Loss Estimation Natural hazards loss estimation has a long history, which is only briefly reviewed here. Freeman [1932] was perhaps the first person to seriously treat the subject. His review of earthquake damage and its relation to insurance remains a landmark in the field. Steinbrugge and coworkers in the 1960s were next. Their impetus grew from the insurance industry, although the industry approached the problem from a deterministic “probable maximum loss” approach, influenced by a similar long-standing approach in the fire insurance area [Steinbrugge, 1982]. Beginning in the 1960s, Steinbrugge, Algermissen, Lagorio and others developed a series of scenario loss estimates for major U.S. high seismic metropolitan areas [e.g., NOAA, 1972], which formed the basis for national policy-making and local preparedness. In the late 1970s [e.g., Wiggins, 1979] and in the 1980s probabilistic loss estimation [e.g., Scawthorn, 1981a] emerged, was extended to related hazards [e.g., Scawthorn, 1981b], and was increasingly employed in policy-making [Petak and Atkinson, 1982]. In the late 1980s, well-founded loss estimation methods began to be employed in the insurance industry and, in the 1990s, gained support from the federal government with the development of the HAZUS earthquake loss estimation software by the National Institute for Building Sciences and the Federal Emergency Management Agency [Whitman et al., 1997]. There was substantial development of probabilistic earthquake loss models, directed primarily at the insurance and reinsurance industry, and focusing on regions of high insurance exposures to perils that had the potential of producing very large, Northridge-style losses. The first models logically focused on the United States, as the world’s largest single insurance market. California earthquake (and Florida/East Coast, for hurricane) generated the most catastrophe exposures and loss potential and hence was modeled first. Subsequently, models were developed for other high loss potential regions, including Japan earthquake (and typhoon, and also European windstorm and U.S. tornado). Over time, probabilistic models have evolved for the southern and eastern Mediterranean, the Middle East, Canada, and Latin America. Other modeled regions include Australia, New Zealand, Southeast Asia, Taiwan, and China. In most cases, insurance and reinsurance exposures have dictated the priority and robustness of the country/peril model. Model uses include underwriting and risk screening, portfolio risk management, claims management, solvency analysis (in conjunction with financial planning models), pricing, and risk transfer (reinsurance or retro covers). Finally, the models were naturally relied upon to provide the risk analysis necessary in the alternative risk transfer (ART) markets, especially insurance-linked securities. The next section of the chapter describes the methodology typically found in probabilistic earthquake loss models.
31.4 Loss Modeling 31.4.1 Define the Assets The first step in modeling catastrophe losses is to determine what is subject to loss. This can vary depending on the users and their needs, but typically involves life safety, property, and/or business or operational interruption. For any of these, methods and associated software can usually handle various levels of information, as illustrated in Figure 31.2, which is oriented toward insurance industry applications. This flexibility is usually needed because available information varies, depending on the users and the nature of their needs. For example, for insurance companies, some companies can provide detailed location and insurance information and others are only able to provide general information, such as premium collected by state. Data can be analyzed on an individual risk basis (e.g., every building) or aggregated in a number of ways, including by geographic locations (e.g., all houses in a zip code), by occupancy, and by structural type, to meet specific needs. But, as shown in Figure 31.2, increasing quality of exposure information reduces the level of uncertainty in the analysis. © 2003 by CRC Press LLC
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Increasing Quality of Data
Premium by country, etc. Cresta Zones
Postal Code Specific address Address, Log/Lat, etc.
Location
Decreasing Uncertainty
Occupancy Premium (Residential, or TSI Commercial)
Detailed Occupancy Codes Standard Structural Classification Material, age, height, engineering report, etc.
Structural
TSI/ Risk TSI, value, limits, etc. Value, limits, ded., etc.
Insurance
FIGURE 31.2 Data requirements (oriented towards insurance).
31.4.2 Define the Hazard Once the assets at risk have been identified, loss assessment methodology follows a general procedure, regardless of the kind of natural hazard being investigated (e.g., earthquake, tropical or extra-tropical cyclone, tornado, flood). First, the hazard phenomenon is modeled based on historical and scientific information, as discussed in Chapter 8 of this volume. The hazard intensity at the source (for earthquake, the earthquake fault) is then propagated to hazard intensities at different sites away from the event location using attenuation models, e.g., ground-motion attenuation models for earthquakes, as discussed in Chapters 5 and 6 of this volume. Once the intensity of the hazard (e.g., shaking intensity) is estimated at a site, the induced damage to the property is quantified using vulnerability models, discussed in detail in Chapter 20. A prerequisite for assessing damage is to have as much information as possible on the physical characteristics of the assets, i.e., appropriate inventory information. Losses are then computed based on the amount of damage and the characteristics of how loss inures from damage. For example, while a company’s factory may be heavily damaged, good emergency planning and preparedness can minimize business interruption, which may be the real source of loss. Similarly, in the case of insurance, while a structure may be heavily damaged, the loss to the insured party, and/or to the insurance company, can vary widely, depending on the deductibles and limits. Each step of the process involves dealing with stochastic or random variation associated with all aspects of the modeled phenomenon. Consequently, the estimated damage and losses are defined probabilistically, e.g., in terms of a probability distribution, moments, and/or probable maximum damages and losses. The process may be performed for a single event, i.e., a scenario event, or repeated to analyze the effects of all possible events in a given time period, such as 1 year. In the latter case, the individual damage and loss estimates for each possible event are probabilistically weighted and aggregated to estimate the overall loss exceedance probabilities, expected (annual) damage and loss, and associated variability in damages and losses between events.
31.4.3 Methodology When assessing the risk to which an asset, or a set of assets, is exposed due to a possible earthquake, a series of analyses is performed as shown in Figure 31.3.
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Hazard Source and Attenuation Models
Hazard Module
Historic and Scientific Hazard Information
Structure, Content, and BI Vulnerability Models
Damage Module
Inventory of Asset Attributes
Loss Module
Loss inuring Information
FIGURE 31.3 Natural catastrophe model components.
31.4.3.1 Hazard The first of these phases is the hazard module, which involves estimating the hazard potential. Historic information, such as the frequency, location, and magnitude of past events, is used together with scientific information. The hazard is estimated using either a semiprobabilistic or a full probabilistic definition of the earthquake event. In the first case, a given scenario (e.g., a repeat of a significant past event, a maximum possible event without consideration of its probability of occurrence, or an event with a certain probability of occurrence), or a series of scenarios, is selected and simulated. In the second case, a probabilistic analysis of all the major sources and magnitudes of the hazard is carried out, leading to a probabilistic description of occurrence of the hazard intensity through hazard curves. A hazard curve typically defines the probability of exceedance of a hazard intensity level in a given duration of time, usually 1 year. The effect of an event of a given magnitude and its attenuation or amplification as it propagates from the source to a particular site is estimated as a function of the distance between the site and the event location, i.e., the earthquake epicenter. These functions, called attenuation relations, are based on statistical studies, and are a function of the physical characteristics of the geology and terrain between hazard sources and sites. Local characteristics of the site are also accounted for in the attenuation relations, that is, local soil type and depth are included in ground-motion models. Probability distributions are derived for a hazard intensity variable at the site (e.g., peak ground acceleration in the case of earthquakes), which describes the variability of the hazard at the site. The mean and standard deviation of the hazard intensity at the site are derived from this distribution, as shown in Figure 31.4. 31.4.3.2 Vulnerability The second phase of the analysis involves two databases of input information and an estimation of the damage induced by the hazard at each site. One database is the inventory of asset attributes. It contains all the relevant information of the portfolio members, including location (street address, or latitude and longitude coordinates), values at risk, structure type (wood frame, reinforced concrete shear wall, etc.), condition (quantified by a quality factor), occupancy, or use. This information is used in determining the potential damage. Development of this information is very important, because the quality and accuracy of the information provided will have a significant effect on the level of uncertainty contained in the final loss estimate. For example, if the site address is known, the latitude and longitude coordinates of a portfolio member can be determined accurately, as can the soil characteristics at the site. On the other hand, if only the state location is known, more generic and less accurate soil conditions must be used. Between these two extremes, a range of data quality exists. Similarly, for the structural data, the best situation is when detailed information is available regarding material, age, design code, etc. However, © 2003 by CRC Press LLC
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Possible location of event
Medium and site conditions Property site
Event-site distance pdf
mean µ A
Site hazard intensity
FIGURE 31.4 Estimation of hazard potential.
DAMAGE FACTOR, D
VULNERABILITY FUNCTIONS
100%
Type B Type A
µ D(I)
Type C
0% I
HAZARD INTENSITY, I
FIGURE 31.5 Vulnerability functions for various structure types.
it may be that the only data available concern occupancy type. As the quality of the information increases, the accuracy and quality of the damage estimates increase. The second database provides inputs relevant to determining the relative vulnerability of buildings, contents, and/or operations to the hazard intensity at the site of the property. Vulnerability can be measured in many ways, such as in terms of the damage factor, D, which is the ratio of the repair cost to the total value. Depending on the type of structural system (e.g., frame or walls), the method and time of construction, the materials, and so on, specific vulnerability models are defined, as shown in Figure 31.5. A vulnerability model consists of a vulnerability function, describing the mean or expected vulnerability as a function of the hazard intensity, and a coefficient of variation (COV) or standard deviation, describing the variation of the vulnerability given the hazard intensity, which is generally also a function of the hazard intensity. It should be noted that in Figure 31.5 a Type C structure has the lowest expected damage factor or vulnerability, whereas a Type A structure has the highest vulnerability. Vulnerability functions typically have been developed on the basis of analysis of claims data from catastrophe events throughout the world, engineering-based analytical studies, expert opinions, testing, or a combination of all these. Vulnerability functions have been developed for structural damage, as well as for business interruption losses and damage to contents. 31.4.3.3 Damage The potential hazard, vulnerability models, and site attributes are combined in the damage module, the central module of Figure 31.3, to estimate the potential damage to individual properties and the portfolio. For a particular value of the intensity of the hazard, and the type of structural system, a damage factor © 2003 by CRC Press LLC
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DAMAGE FACTOR 100% PDF of damage D
Conditional PDF of damage,D, given I Vulnerability function
µD
PDF of site intensity I µ D(I) 0%
I
SITE HAZARD INTENSITY I
FIGURE 31.6 Computation of damage distribution for an individual property.
Loss L
Loss L =
l
d
d +l
TIV
0 D-d l
D
Damage D
FIGURE 31.7 Relation between damage and loss.
is derived for each individual property. This factor expresses the relative cost of repair that the structure is likely to need, with respect to its insured value, if the property is hit by a hazard of a given intensity. The hazard module yields a probability density function (pdf) of the hazard intensity at the site (e.g., the shaking intensity), as shown on the horizontal axis of Figure 31.6. For a given value of the hazard intensity I, a mean damage factor, µD(I), is obtained from the vulnerability function, with its corresponding standard deviation, σD(I), derived from the associated COV curve. Combining the vulnerability assessment over all values of hazard intensity results in a probability distribution for the damage factor described by the PDF on the vertical axis in Figure 31.6. From this distribution the mean value, µD, and standard deviation, σD, for the damage factor of a particular structure, contents, or business interruption can be obtained. The level of damage is calculated by adjusting the damage factor by a quality factor (to account for any specific structural characteristic of the site) and multiplying by the total insured value (TIV). The damage for the entire portfolio is the statistical combination of the damages for each individual property taking correlation into account, as discussed below. 31.4.3.4 Loss The fourth phase of analysis, the loss module in Figure 31.3, involves estimating the losses to the lossbearer. Losses are borne, or inure, in various ways. For example, if a house is heavily damaged, but insured for earthquake, the owner’s loss is significantly less than if it were not insured, although the damage is the same. In this case the insurance company now also has a loss. This aspect of the distribution of losses is especially important in the insurance industry, where socalled insurance information is at the heart of the matter. The insurance information, in general, is expressed in terms of deductibles (d), limits (l), and total insured value (TIV). The quality of the insurance data can vary from crude to detailed, which will affect the level of uncertainty in the estimation of losses. The gross loss at a property or group of properties is a function of damage and the insurance information, d, l, and TIV, relevant to the properties. Figure 31.7 shows a typical relation between loss and damage, d, l, and TIV, for any given property. Combining the insurance information with the probability distribution of damage using the loss relation is the analysis represented by the loss module © 2003 by CRC Press LLC
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in Figure 31.3. The probability distribution of gross loss is derived from the loss model (Figure 31.7) and the pdf for damage (Figure 31.6). The mean, standard deviation, and the loss exceedance curve are estimated from the loss distribution. Net loss to a primary insurer and losses to reinsurers are further calculated based on the appropriate insurance information relevant to facultative reinsurance and treaties. In all cases the relevant probabilistic information, e.g., the expected loss of a treaty layer, is based on the probabilistic information of the gross loss and the relation between the loss of interest, e.g., treaty layer loss, and gross loss.
31.4.4 Correlation An important element in the analysis process is the consideration of the inherent correlation associated with many of the stochastic variables characterizing potential losses due to catastrophic natural events. Correlation is a factor in the hazard due to a catastrophic event at various sites in a portfolio, as well as in the damage induced by the event at the sites. In the case of earthquake hazards, the shaking intensity at the various sites depends on the earthquake source variables, e.g., magnitude, depth, epicenter location; the geological conditions of the travel path of the seismic waves; and the local soil conditions. It can be expected that the travel path and the local soil conditions at sites in close proximity to each other will be similar. Thus, it can be expected that the variability (deviation from its expected value) in the stochastic shaking intensity, i.e., hazards, at sites close together will be more highly correlated then the ground motions at sites some distance apart, which may be geologically quite different. Correlation in the hazard between sites can be modeled in a probabilistic analysis by accounting for correlation in the development of sample vectors (across sites) of hazard intensities. For damage assessments, given a hazard intensity, it can be expected that the variability of the damage for similar structures, i.e., structures of the same type, material, age, etc., will be more similar than the variability of the damage for dissimilar structures. The same can be expected for damages between structures close to each other as compared to damages of structures that are some distance apart. For example, consider homes built by the same builder in the same housing development as compared to homes built by separate builders in widely scattered locations in different years. Correlation of damage will be a function of structure type, material, age, and distance between site locations. What is the affect of accounting for correlation in the assessment? Assuming a positive correlation, not accounting for the correlation, either in the hazard or the damage, results in underestimation of the standard deviation of losses aggregated over multiple sites, e.g., portfolio losses. Why? Suppose hazard correlation is not considered, e.g., the hazard intensities at multiple sites are assumed to be independent. The assessment process assumes that a relatively high hazard (relative to its expected value) at one site and a relatively low hazard at an adjacent site are just as likely as both relatively high and relatively low hazards at the two sites. On the other hand, with correlation considered, the latter two outcomes are more likely. When the losses are computed, the independent analysis assumption associates lower probabilities to the more extreme high and low losses. Thus, based on the independence assumption, the distribution of losses over all sampled ground-motion vectors will be less variable (a lower standard deviation) then the distribution based on the realistic correlation assumption. A similar effect occurs when the correlation of damage to structures of the same type, material, age, etc., is not considered. Again, the independent analysis associates lower probabilities with the extremes of the aggregated losses. In conclusion, correlated analysis results in higher exceedance probabilities for large losses.
31.5 The Hazard Module The peril of earthquakes has many potential agents of damage or hazards, including fault rupture, shaking, liquefaction, land sliding, fire, hazardous material release, tsunami, and inundation. The most important of these hazards is shaking, not only because of the potential for damage to a large number of properties, but also because it is the underlying initiator of the other hazards. A graphical description of the elements of the seismic hazard model is shown in Figure 31.8. The seismic hazard model, which © 2003 by CRC Press LLC
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PORTFOLIO DATA Construction Type Location Age Design Details Configuration Soil 3 1 d1 d3
d4 4 EARTHQUAKE M i
HAZARD CURVE d2
Frequency of Exceedance (per year)
2
GROUND MOTION DATA AT SITE PGA = f (M,d, regional geology) MMI = f (PGA, soil)
LENGTH OF FAULT RUPTURE
ALT
FIGURE 31.8 Summary of the seismic hazard model.
Seismotectonic Model
Ground Motion Model
Ground Motion Estimates
Site Specific Effects
FIGURE 31.9 Components of the seismic hazard model.
corresponds to the hazard module of Figure 31.3, consists of three parts (as shown in Figure 31.9), with each part contributing to the final ground-motion estimates.
31.5.1 Seismic Sources Depending on the information available regarding the tectonics of the region under consideration, point or area source models (to model thrust faults or zones of unknown geological structure), or a line source model (to model strike-slip faults) can be adopted to represent the regional seismotectonics, as shown © 2003 by CRC Press LLC
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Area Source
Possible Rupture Location
Fault
Possible Epicenter Location Site-Rupture Distance
Site-Epicenter Distance Site Location
FIGURE 31.10 Different earthquake sources and their relation to a site location.
Event of Magnitude M
d1 Soil Type Si
Site 1
Fault d2
Acceleration (g)
PGA1
Site 2
Soil Type Sj
Time (sec) Acceleration (g)
PGA2 Time (sec)
FIGURE 31.11 Ground-motion attenuation at different site locations.
in Figure 31.10. In a point or area source model the earthquake epicenter can be located anywhere in a given area, whereas in the line source model the seismic event is modeled as a fault rupture of a given length (the rupture in turn can be located anywhere along a given fault). In some models, faults can be modeled in three dimensions to accommodate nonvertical faults (dipping) and blind thrusts (dipping faults at depth). Earthquake models typically build in seismotectonic databases, which contain detailed information on all major active faults in the region of interest.
31.5.2 Ground-Motion Models The locations of the sites in a portfolio can be translated from street or postal code addresses to absolute geographic references (latitudes and longitudes) using internally developed and/or third party software. If a site street address is not known, the site postal code centroid can be used as an approximation. Using the site latitude/longitude, the distance from the site to the relevant earthquake faults or area sources is determined. Based on the event magnitude and the distance to the fault rupture or earthquake epicenter, attenuation relations are used to determine the ground motion, e.g., the peak ground-motion acceleration (PGA), or spectral acceleration at the site. Thus, for a given event magnitude, the distance of the site from the fault determines the magnitude of the shaking hazard at the site. This is illustrated in Figure 31.11. The attenuation relations are based on statistical studies of earthquake data. They differ from region to region. Most models contain a library of ground-motion attenuation models and use multiple models, as appropriate for each region. © 2003 by CRC Press LLC
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31.5.3 Site Soil Conditions Given a site latitude/longitude, soil databases are accessed to determine site soil conditions. The soil databases characterize soil stiffness at a location, with stiffer soils producing lower surface shaking than soft loose soils. A simple classification consisting of four soil types is listed in Table 31.1. For each site, for a given event magnitude and rupture location, the PGA and spectral acceleration obtained from the region’s attenuation relation are adjusted (increased or decreased) using local soil characteristics in terms of shear wave velocity, which is a physical measure of a soil’s stiffness. TABLE 31.1 Soil Types (Abbreviated List) Soil Type S1 S2 S3 S4
Description A rock-like stiff or dense soil (good soil) A soft to medium stiff soil (average soil) A saturated alluvium soil (poor soil) Non-engineered fill (very poor soil)
31.6 Seismic Vulnerability Models Vulnerability models have been developed from a number of sources, and are discussed in detail in Chapter 20. The primary sources are studies of past earthquakes and the damage they have caused to structural and architectural building systems, contents, equipment, stock and supplies, as well as the losses incurred due to loss of use or “business interruption.” Vulnerability models also can address other nonstructural loss sources, such as workers compensation and general liability. The vulnerability models also consider modern building codes and engineering analyses of numerous structures representative of common construction categories.
31.6.1 Structures and Buildings Specialized techniques have been developed for identifying differences in relative earthquake damage potential for similar or different types of buildings, in different parts of the same geographic areas [e.g., Porter et al., 2002; Kircher et al., 1997a; Scawthorn et al., 1981]. Relative damage potential is based on differences in building practices arising from different dates of construction and differing building codes. Models will usually rely on a database of buildings that have been analyzed in detail to estimate the structural vulnerability, as well as on externally published information. Based on the extent of available information, a specific building is characterized by its material, lateral-force-resisting system, geometry, height, and other measures of its size and complexity. The building is then assigned to a class for which a vulnerability function has been developed based on analysis of similar buildings. Models include vulnerability functions for a wide variety of building types representing occupancy, age, and type of construction. The vulnerability function is a measure of the expected cost of repairs of a structure belonging to a specific class (e.g., ductile moment frame mid-rise). The function is modified by a quality factor based on the value, age, complexity, and other specifics of the building. Figure 31.12 shows an example of a building vulnerability function for a particular type of reinforced concrete structure. Given the hazard intensity for a site, the vulnerability function provides an estimate of the mean damage factor for the structure. The damage factor is an estimate of the cost of repairs, expressed as a percentage of the total insured value of the building.
31.6.2 Contents Vulnerability functions, similar to the ones described above, exist to identify damage potential to the contents of buildings. These functions have been developed based on analysis of performance in past earthquakes [Federal Emergency Management Agency, n.d.]. © 2003 by CRC Press LLC
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10 2
Damage Factor (%)
10 1
0
high estimate
10-1
mean estimate
10
low estimate
-2
10
10-3 0.05
0.1
0.25
0.5
Peak Ground Acceleration (g) FIGURE 31.12 Typical vulnerability function and variation of damage factor.
31.6.3 Business Interruption A significant component of loss, for both commercial companies and the insurance industry, is business interruption (BI). Therefore, models need to have algorithms to estimate BI, which usually are based on damage to a structure. The business interruption is evaluated in number of days lost, as a function of the damage factor of the building (between 0 and 100%). For residential properties, this calculation yields the additional living expense portion of the loss settlement. Development of BI vulnerability functions is extremely difficult, as they are very dependent on the nature of the operations, as well as specifics of the emergency preparedness planning.
31.6.4 Fire Following Earthquake Very large insured losses from earthquake-induced fires, while rare, have the potential to result in losses many times greater than from the shaking damage. This was demonstrated by the large conflagrations in the Great Kanto earthquake in Tokyo in 1923 and the 1906 San Francisco earthquake. Therefore, loss algorithms for fire following are usually included in earthquake models [Scawthorn and Khater, 1992; Scawthorn, 1981b], and are based on the amount of shaking damage, building construction type, and building density, as well as the regional supply of water and fire department resources. In general, these estimates become quite important when considering very large events, since fire ignition probabilities rise as the impacted area grows, while the fire fighting resources are limited. This topic is discussed in detail in Chapter 29.
31.7 Damage and Loss Estimation The estimation of damage or loss follows similar algorithms:
© 2003 by CRC Press LLC
E(D) = ∫ E(D|H) p(H)
(31.1)
E(L) = ∫ E(L|D) E(D|H) p(H)
(31.2)
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where E(.) L D E(L|D) p(.) p(H)
= = = = = =
expected value loss to the assets of interest damage the expected loss given the damage the probability density function (PDF) the probability of the hazard; that is, the combined effect of the probability of the initiating earthquake occurring on the seismogenic fault, and the attenuation of the hazard (e.g., shaking) from the fault to the site of interest E(D|H) = the damage given the hazard; that is, the seismic vulnerability Each element of Equation 31.1 or 31.2 is uncertain to a varying degree and can be treated as a random variable. While exhaustive treatment of uncertainty is rare, insurance and actuarial applications require relatively complete treatment, with other applications permitting increasing relaxation of this requirement. We discuss aspects of the equations below.
31.7.1 Damage Estimation The seismic hazard model estimates the hazard of interest, usually shaking, typically measured in terms of PGA or response spectral acceleration at the site. Given the hazard intensity and the information specific to each property, the vulnerability model provides an estimate of the degree of damage for each individual asset. This is expressed in terms of an estimate of the mean and standard deviation of damage. To estimate the damage for a given property for each relevant earthquake scenario, a model typically recognizes two sources of stochastic or random variation associated with the damage calculation. Given a shaking intensity at a site, the damage sustained by a structure is subject to a number of sources of variation, such as variation in coupling of the ground motion to the structure, quality of construction, local soil conditions, etc. Thus, the damage at a site, given the shaking intensity, is modeled by a probability distribution. The shaking intensity at the site is also subject to random variation, as described by the hazard intensity distribution or hazard curve. The damage for a given property is calculated by combining the damage over all possible shaking intensity values, based on the distribution of the intensity. This calculation involves numerical integration to develop the probability distribution and/or moment propagation methods to calculate the mean and standard deviation of the potential damage at the property. Portfolio, or other aggregations of properties, and damage estimates, such as the portfolio normal expected damage (NED, the damage that the portfolio is expected to sustain on average), are calculated by aggregating the damage over all properties in the portfolio. The portfolio NED and standard deviation are based on combining the individual property mean and standard deviation, accounting for correlation between damages at various sites. Thus, the model provides a measure of the average or mean damage, as well as a measure of the variability of the damage in terms of the standard deviation of the damage, both for individual properties and for aggregations of properties.
31.7.2 Loss Estimation Given the damage estimates, the next step in the risk assessment process is to estimate the potential losses. The discussion herein is in the context of insurance loss estimation, and the reader can extend the concepts to other areas of loss. Estimation of insurance losses involves subjecting the damage estimates to the constraints imposed by the insurance loss model. Policy-level deductibles and limits, facultative reinsurance and treaty attachment points and layer amounts, and special catastrophic loss settlement factors are all considered in the loss calculations. The initial loss calculation involves estimating the gross loss, which considers the effects of policy deductibles and limits. The algorithm for calculating gross loss is based on the relation of loss to damage, as shown in Figure 31.7. Both site- and policy-level constraints are © 2003 by CRC Press LLC
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considered. The probabilistic information for gross loss is calculated using the damage–loss relation and the probabilistic information developed for damage. Similar calculations are performed to develop probabilistic information for the net loss (to the primary insurer) and ceded losses to reinsurers, based on the amount and layers of any reinsurance in place. The basic probabilistic information is based on deriving the probability distribution of the loss, given a hazard event (i.e., an earthquake). Losses are characterized in several ways: 1. Scenario — for a given hazard scenario, e.g., a repeat of a significant past event, or a series of specified hazard scenarios, the primary measures of loss are the normal expected loss (NEL), expected annual loss (EAL), and the loss distribution associated with each hazard scenario. 2. Probabilistic — for a probabilistic analysis, e.g., considering all possible hazard scenarios, the primary measures of loss are EAL, and the per-occurrence and aggregate loss exceedance curves (described below). The expected annual loss (EAL) reflects both the loss, given an event occurs, and the frequency per year of the event occurring. For a given hazard scenario, EAL measures the average aggregated loss, per year, associated with the given scenario. For a probabilistic analysis, EAL takes into account the losses and frequencies of occurrence of all foreseeable earthquake magnitudes on all faults and seismic zones. The primary reinsurance results are the expected annual losses, i.e., risk premiums, by treaty layer and by reinsurer. Additional results for each reinsurer include the EAL, standard deviation of the annual loss, and the probabilities of penetration and exceeding the limit, for each layer. Also, the damage and the gross loss (to the reinsurer) nonexceedance curves are developed for each layer.
31.7.3 Probabilistic Loss Exceedance Curves In addition to characterizing loss in terms of the expected and probable maximum losses, risk curves, or loss exceedance curves, are developed in the probabilistic analysis. A risk curve is a useful way of quantifying the variability of losses and the potential of significant losses. One such curve is the annualized per-occurrence loss exceedance curve shown in Figure 31.13. This curve quantifies the probability that the largest per-occurrence loss, per year, exceeds a value x, as a function of loss. The first curve, based on different time periods, is used to assess the probability that the annual per-occurrence loss exceeds specified loss thresholds in 1, 10, 25, 50, etc. years. 0.16
Exceedance Probability
0.14 0.12 0.10
Site-1
0.08 0.06 0.04
Site-2
0.02 0.00 0
100
200
Loss (Millions) FIGURE 31.13 Typical per-occurrence loss exceedance curve.
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Figure 31.13 shows the per-occurrence loss exceedance curves for two sites. The curve for site 2 has a longer tail than site 1, which indicates that site 2 is affected by high-severity, low-frequency events more than site 1. An alternate curve is the aggregate loss exceedance curve. This curve quantifies the probability that the aggregate loss, per year, i.e., the sum of the losses for all events per year, exceeds a value x , as a function of loss.
31.7.4 Modeling Uncertainty There are two types of variability that can be included in the probabilistic analysis: aleatory and epistemic. Aleatory variability is uncertainty in the data used in an analysis and generally accounts for randomness associated with the prediction of a parameter from a specific model, assuming that the model is correct. Specification of the standard deviation (σ) of a mean ground-motion attenuation relationship is a representation of aleatory variability. Epistemic variability, or modeling uncertainty, accounts for incomplete knowledge in the predictive models and the variability in the interpretations of the data used to develop the models. Aleatory uncertainty can usually be better estimated, but it cannot be reduced through advances in science. This contrasts with epistemic uncertainty, which arises from imperfect information and knowledge, which is potentially reducible through data acquisition. Aleatory variability is usually included directly in the probabilistic analysis calculations by means of simulation or mathematical integration. Epistemic uncertainty, on the other hand, is included in the probabilistic analysis by explicitly including alternative hypotheses and models. This uncertainty can be accounted for through the evaluation of multiple individual seismotectonic models or through the formulation of a logic tree that includes multiple alternative hypotheses in a single model (see Chapter 4). The logic tree allows a formal characterization of uncertainty in the analysis by explicitly including alternative interpretations, models, and parameters that are weighted in the analysis according to their probability of being correct. Logic tree models may be exhaustively evaluated, or adequately sampled through Monte Carlo simulation, which is computationally a more efficient procedure. Each alternative hypothesis, indicated by a branch of the logic tree, is given a subjective weight corresponding to its assessed likelihood of being correct. The proposed alternative hypotheses account for uncertainty in earthquake source zonation, maximum magnitude, earthquake recurrence rate, location and segmentation of seismogenic faults, style of faulting, distribution of seismicity between faults and area sources, and ground-motion attenuation relationships.
31.8 HAZUS® Earthquake Loss Estimation Software A major advance in earthquake loss estimation has been the development of the HAZUS® earthquake loss estimation software, by the National Institute of Building Sciences and the Federal Emergency Management Agency (FEMA) [Whitman et al., 1997]. The following vision statement and description of HAZUS® are excerpted and adapted from the HAZUS®99 SR2 Technical Manual (Federal Emergency Management Agency, n.d.): The earthquake loss estimation methodology will provide local, state and regional officials with the tools necessary to plan and stimulate efforts to reduce risk from earthquakes and to prepare for emergency response and recovery from an earthquake. The methodology will also provide the basis for assessment of nationwide risks of earthquake loss. The methodology can be used by a variety of users with needs ranging from simplified estimates that require minimal input to refined calculations of earthquake loss. The methodology may be implemented using either geographical information system (GIS) technology provided in a software package or by application of the theory documented in a Technical Manual. The HAZUS® earthquake loss estimation methodology attempts to more completely address regional impacts of earthquakes. Examples of these impacts are service outages for lifelines, estimates of fire © 2003 by CRC Press LLC
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FIGURE 31.14 Flowchart of the HAZUS® earthquake loss estimation methodology.
ignitions and fire spread, potential for a serious hazardous materials release incident, and indirect economic effects. In addition, a strength of this methodology is the ability to readily display inputs and outputs on GIS-based maps that can be overlaid. By overlaying maps the user is able to experiment with different scenarios and ask “what if ” questions. The HAZUS® methodology is modular, with different modules interacting in the calculation of different losses, as shown in Figure 31.14, which shows each of the modules and the flow of information among them. It can be seen that, because of the complexity of earthquake damage and loss estimation, the HAZUS® model is complex. One advantage of the modularity of the HAZUS® methodology is that it enables users to limit their studies to selected losses. The HAZUS® software is furnished gratis by FEMA, and comes with a national inventory for the built environment, termed the default data. Necessarily, this inventory is not very detailed, so that users will often wish to develop a local inventory that better reflects the characteristics of their region, such as building types and demographics. Three types of analysis are defined, as follows: • Default data analysis. This is the simplest type of analysis requiring minimum effort by the user, as it is based mostly on default data provided with the methodology (e.g., census information, broad regional patterns of seismic code adoption, and earthquake resistance of classes of construction, etc.). The user is not expected to have extensive technical knowledge. While the methods require some user-supplied input to run, the type of input required could be gathered by contacting government agencies or by referring to published information. At this level, estimates will be crude, and will likely be appropriate only as initial loss estimates to determine where more detailed analyses are warranted. © 2003 by CRC Press LLC
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• User-supplied data analysis. This is the most commonly used type of analysis. It requires more extensive inventory data and effort by the user than default data analysis. The purpose of this type is to provide the user with the best estimates of earthquake damage/loss that can be obtained using the standardized methods of analysis included in the methodology. • Advanced data and models analysis. This type incorporates results from engineering and economic studies carried out using methods and software not included in the methodology. The HAZUS methodology appears to depart slightly from the general process of loss estimation described above, in that vulnerability functions are not used, but rather a form of fragility functions. The overall building loss estimation process consists of the use of building capacity curves [Kircher et al., 1997b], described in Chapter 20 of this volume, to provide an estimate of building lateral displacements. These estimates are arrived at via a nonlinear iterative process involving successive analyses of the building capacity curve vs. response spectral ordinates, to arrive at a final displacement. This displacement is used to determine the probability of being in various damage states, which are reported by the HAZUS software, and used internally to determine mean dollar loss, shelter needs, and other measures of interest. The final dollar loss estimates in fact do not depart from the general process of loss estimation described above — the vulnerability functions that would “normally” be used are simply the weighted average of the damage state fragility functions employed in HAZUS. The process, however, is less transparent to the user than if vulnerability functions had been employed. HAZUS is a complex, powerful program and technology, providing the user gratis what hitherto had generally been unavailable. Even with perfect data, which can never be obtained, the HAZUS® methodology is not presented as being able to precisely estimate earthquake loss. Simply put, “predictive methods are approximate and will often have large amounts of uncertainty associated with damage and loss estimates.” A discussion of uncertainty and guidance for users performing earthquake loss estimation is provided in the HAZUS® Technical Manual. (Federal Emergency Management Agency, n.d.). Development of HAZUS® began in the early to mid-1990s, with deployment of version 1 in 1997. As of this writing, the most current version is HAZUS® 99 SR2, which remains an earthquake loss estimation model. A multi-hazard version of HAZUS, termed HAZUS®-MH and providing national flood, hurricane, and earthquake loss estimation capabilities, is scheduled to be released in early 2003.
31.9 Applications of Loss Estimation This section briefly reviews some examples of loss estimation, to illustrate variations in loss estimation methodologies, and how the results are used.
31.9.1 Estimation of Earthquake Losses in Los Angeles Three areas of earthquake research — ground response estimation, structural response estimation, and earthquake prediction — were investigated to determine which avenue of research might be most effective in reducing earthquake damage [Scawthorn and Gates, 1983]. Effectiveness was measured by the decrease in building damage in Los Angeles County for an M 8+ earthquake on the San Andreas fault, an earthquake similar to the 1857 Fort Tejon earthquake, which was considered at four different times: the present (1982) and 5, 10, or 20 years in the future (1987, 1992, 2002). Three levels of research funding were considered: the present level of funding continued in constant dollars, and the same level either halved or doubled. Progress in ground response and building response research was estimated by regressing past progress (in terms of reduced uncertainty), and projecting the progress through 2002, for the several levels of funding. For continued present levels of funding, ground and building response COV were estimated to be approximately halved from 1983 COV levels. For progress in earthquake prediction, the study postulated a certain level of progress vs. funding. In order to estimate seismic damage for Los Angeles County, the literature was reviewed for appropriate isoseismal distributions and building seismic performance © 2003 by CRC Press LLC
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functions. A Los Angeles building inventory was compiled and determined total building value in Los Angeles County to be about $275 billion (1982 $). Present (1983) building damage in Los Angeles County due to an M 8+ earthquake on the San Andreas fault was estimated to be about $4.77 billion (about 1.7% of total building value, 1982 $). About 68% of the damage occurred in one- and two-story wooden buildings. Under the assumptions of this study, earthquake prediction proved to be the most beneficial of the three avenues of research, due to a prediction meaning increased likelihood of an earthquake (false predictions were not considered in this study). The typical damage reduction for Los Angeles County for various scenarios of research progress was determined to be about $500 million, or about 10% of total building damage. Extension of this by simplified techniques for other faults in Los Angeles and the San Francisco area results in total building damage reduction of more than $3 billion (1982 $).
31.9.2 Estimation of Earthquake Losses in New York Earthquake damage and the number of fire ignitions due to earthquakes occurring in or near New York City were examined, as a first step towards quantifying the general importance of earthquake risk in the New York area [Scawthorn and Harris, 1989]. The five-borough building inventory of approximately $404 billion was categorized in terms of story height and structural material. Seismic intensity (MMI) was estimated using central United States (CUS) attenuation relations, accounting for soil conditions and earthquake magnitude. Three earthquakes of magnitude 6.0 were postulated: (1) 17 miles southeast of City Hall, at the location of the 1884 M 4.9 event offshore Rockaway Beach; (2) 11 miles southeast of City Hall; and (3) 5 miles southeast of City Hall, in Brooklyn. Building vulnerability was modeled using modified ATC-13 relations. For an M 6.0 event at the 1884 location, approximately 2.8% (or $11 billion) damage is sustained. Further, about 130 post-earthquake ignitions occur. Although several of these ignitions may grow into large fires, first-line fire department capability should in general be able to cope with the fire situation, if water supply is not impaired.
31.9.3 Impact of Earthquake Losses on U.S. National Infrastructure The U.S. national lifelines infrastructure (electric power, water, gas, and oil pipelines, highways, railroads, and several other lifelines of critical importance at the U.S. national level) were inventoried on a regional basis and analyzed, to estimate overall seismic vulnerability, impact of major earthquakes on their performance, and resulting economic consequences. The purpose was to assess the impacts of a large earthquake relative to other impacts on the national infrastructure. Innovative aspects of the project included compilation of a national level PC-format digitized inventory of lifelines, extensive development and discussion of lifeline component seismic vulnerability, use of graphical user interface seismic risk analysis PC-based software, assessment of economic and social impacts of lifeline interruption for major metropolitan areas of the United States, and identification of cost-effective mitigation measures for lifelines. The project concluded that electric power and water are the two most critical lifelines. Of eight scenario earthquakes considered in the study, the greatest lifeline-related impacts to the United States resulted from either a CUS (i.e., New Madrid) or Southern California M 8 event, resulting in direct transmission-level lifeline damage of approximately $10 billion, and indirect economic losses of approximately $12 to $14 billion (1992 $).
31.9.4 Estimation of Earthquake Losses in the 1994 Northridge Earthquake On the day of the January 17, 1994 Northridge earthquake, data and loss estimation models were employed to produce timely information that was used by state and federal officials to support key policy and program decisions. Estimates of dollar losses and ground shaking intensity were used by the California Office of Emergency Services to define the general regional scope of the disaster during the critical 24 to 48 hours after the event. The shaking intensity map was instrumental in approximating the locations of heaviest damage, used for briefing key officials including the California governor, and making decisions
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regarding shelter needs and fast-tracking disaster assistance. A total dollar loss estimate of $15 billion (1994 $), generated within 24 hours of the event, served as the basis for negotiation of a supplemental Congressional appropriation of $8.6 billion in federal disaster assistance [Wall Street Journal, January 21, 1994, p. A-3; Eguchi et al.1, 1997].
31.9.5 Seismic Performance Evaluation of Fire Stations The seismic performance of 71 fire stations in Shelby County, TN were assessed for several large CUS earthquakes. Results indicated that most of the fire stations would suffer moderate to heavy damage and would be expected to be out of operation after the earthquakes [Hwang et al., 1997].
31.9.6 California Earthquake Authority The 1994 Northridge earthquake and the attendant major losses to the insurance industry, estimated to be approximately $12 billion, prompted a general refusal by virtually all large insurance companies to provide earthquake insurance for homeowners. In 1996, as a result of this, the California Legislature established the California Earthquake Authority (CEA) as a privately financed, publicly managed entity to help California residents protect themselves against earthquake loss. As of this writing, the CEA is the world’s largest residential earthquake insurer ($7.5 billion initial capitalization), with 2.5 million policies representing over $500 billion of building and contents value. Acting through its participating insurers, the CEA sells earthquake policies to homeowners, mobile home owners, condominium owners, and renters throughout California and provides retrofit assistance to help people protect their houses against earthquakes. In order to rationally determine appropriate insurance rates, scenario and probabilistic loss estimates were performed for CEA [EQECAT, 1998]. Loss exceedance analysis for the entire portfolio was provided to over 100 reinsurers in the placement of $2 billion of earthquake reinsurance, the largest catastrophic reinsurance transaction ever undertaken. The analysis also provided expected annual loss cost at zip code levels, which formed the basis of a territorial rating plan. The territorial rating plan was the subject of controversy, and subjected to a 4-month administrative law hearing involving significant cross examination and scrutiny by intervenors and third-party experts. This resulted in the most rigorous examination of any earthquake loss model, and ultimately was deemed by the insurance commissioner to meet the “state-of-the-art” legislative requirements.
31.9.7 Estimation of Building Earthquake Losses in the United States FEMA estimated losses to buildings in the United States [Federal Emergency Management Agency, 2000), using the HAZUS loss estimation tool (Federal Emergency Management Agency, n.d.). The study was driven by the recognition that recent earthquakes around the world have shown a pattern of steadily increasing damages and losses, due primarily to two factors: (1) significant growth in urban areas that are prone to earthquakes; and (2) the vulnerability of the older building stock (even buildings that were constructed within the past 20 years). HAZUS is a GIS-based earthquake loss estimation tool, developed by FEMA in cooperation with the National Institute of Building Sciences (NIBS). The HAZUS tool provides an approach to quantifying future earthquake losses that is national in scope, uniform in application, and comprehensive in its coverage of the built environment. The study estimated seismic risk in all regions of the United States by using two interrelated risk indicators: 1. The annualized earthquake loss (AEL), which is the estimated long-term value of earthquake losses to the general building stock in any single year in a specified geographic area (e.g., state, county, metropolitan area) 2. The annualized earthquake loss ratio (AELR), which expresses estimated annualized loss as a fraction of the building inventory replacement value
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Pacific Northwest
CT, DC, DE, MA, MD, ME NH, NJ, NY, OH, PA, RI, VT
OR, WA 0.40 $B Northeast ID, NV, UT, AZ, MT WY, CO, NM
0.21 $B
ND, SD, MN, IA, MI WI, NE, KS, OK, TX
A CA 0.18 $B 3.26 $B 0.01 $B
MO, IL, IN, KY, LA AR, TN, MS, AL 0.19 $B
WV, VA NC, SC GA, FL 0.10 $B
Rocky Mountaim/ Basin and Range Southeast 0.04 $B
Alaska
Central Great Plains
0.03 $B Hawaii
FIGURE 31.15 Comparison of regional seismic risk in the United States by annualized earthquake losses (AEL). (From Federal Emergency Management Agency. 2000. Estimated Annualized Earthquake Losses for the United States, FEMA 366, Federal Emergency Management Agency, Washington, D.C.)
The analysis indicated that the AEL to the national building stock is $4.4 billion per year. The estimated losses are in two categories: 1. Capital losses ($3.5 billion), which include repair and replacement costs for structural and nonstructural components, building content loss, and business inventory loss 2. Income losses ($0.9 billion), which include business interruption, wage, and rental income losses The majority (84%) of average annual loss is located on the West Coast (California, Oregon, Washington), with 74% ($3.3 billion per year) concentrated in the State of California. The high concentration of loss in California is consistent with the state’s high seismic hazard and large structural exposure. The remaining 16% ($0.70 billion per year) of annual loss is distributed throughout the rest of the United States (including Alaska and Hawaii), as reflected in Figure 31.15. While the majority of economic loss is concentrated along the west coast of the United States, the distribution of relative earthquake risk, as measured by the AELR, is much broader and reinforces the fact that earthquakes are a national problem. There are relatively high earthquake loss ratios throughout the western United States, the central United States (states within the New Madrid Seismic Zone), and in the Charleston, SC area. Forty metropolitan areas, led by the Los Angeles and San Francisco Bay areas, account for 86% of the total annualized losses in the United States. Los Angeles County alone has about 25% of the total AEL. This observation supports the need for strategies to reduce the current seismic risk by focusing on rehabilitation of the existing building stock in our most vulnerable communities. Strategies to reduce future losses throughout the United States need to be closely integrated with policies
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and programs that guide urban planning and development. This loss study was an important milestone, and was useful in at least four ways: • • • •
Improving our understanding of the seismic risk in the United States Supporting the adoption and enforcement of seismic provisions of building codes Comparing the seismic risk with that of other natural hazards Providing a baseline for earthquake policy development and the comparison of mitigation alternatives
Defining Terms Aleatory — Uncertainty in the data used in an analysis — generally accounts for randomness associated with the prediction of a parameter from a specific model, assuming that the model is correct. Specification of the standard deviation (σ) of a mean ground-motion attenuation relationship is a representation of aleatory variability. Assets — Things of value, such as human lives, buildings, equipment, or revenue from an operation, such as a factory. Epistemic — Variability or uncertainty in modeling, accounting for incomplete knowledge in the predictive models and the variability in the interpretations of the data used to develop the models. Exposure — The quantity and quality of an asset. Inure — The manner in which losses are distributed to the loss-bearers, especially in the insurance industry. Loss estimation — The use of mathematical models of the constitutive contributing elements of the loss process (that is, modeling), to arrive at estimates and associated confidence bounds of the potential losses that might result from an event — in this context, from an earthquake. Loss exceedance curve — A curve of loss vs. the probability of that level of loss being exceeded. Risk curve — see Loss exceedance curve.
References Applied Technology Council. 1985. Earthquake Damage Evaluation Data for California, ATC-13, Applied Technology Council, Redwood City, CA. Eguchi, R.T. et al. 1997. “Real-Time Loss Estimation as an Emergency Response Decision Support System: The Early Post-Earthquake Damage Assessment Tool (EPEDAT),” Earthquake Spectra, 13(4), 815–832. EQECAT. 1998. “Earthquake Risk Assessment, Loss Cost Analysis,” prepared for California Earthquake Authority by EQECAT, Inc., Oakland. Federal Emergency Management Agency. 2000. HAZUS®99 Estimated Annualized Earthquake Losses for the United States, FEMA 366, Federal Emergency Management Agency, Washington, D.C. Federal Emergency Management Agency. n.d. Earthquake Loss Estimation Methodology HAZUS®99 Service Release 2 (SR2), Technical Manual developed by Federal Emergency Management Agency, Washington, D.C. through agreements with the National Institute of Building Sciences, Washington, D.C. Freeman, J.R. 1932. Earthquake Damage and Earthquake Insurance, McGraw-Hill, New York. Hwang, H.H.M., Lin, H., and Huo, J.-R. 1997. “Seismic Performance Evaluation of Fire Stations in Shelby County, Tennessee,” Earthquake Spectra, 13(4), 759–772. Kircher, C.A. et al. 1997a. “Estimation of Earthquake Losses in Buildings,” Earthquake Spectra, 13(4), 721–738. Kircher, C.A. et al. 1997b. “Development of Building Damage Functions for Earthquake Estimation,” Earthquake Spectra, 13(4), 663–682.
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NOAA. 1972. A Study of Earthquake Losses in the San Francisco Bay Area, Report prepared by the National Oceanographic and Atmospheric Administration of the Department of Commerce for the Office of Emergency Preparedness, Washington, D.C. Petak, W.J. and Atkinson, A.A. 1982. Natural Hazard Risk Assessment and Public Policy: Anticipating the Unexpected, Springer-Verlag, New York. Porter, K.A., Beck, J.L., Scawthorn, C.R., Seligson, H.A., Tobin, L.T., Boyd, T., and Cobeen, K. 2002. Improving Loss Estimation for Woodframe Buildings, Tasks 4.1 and 4.5, Report for the CUREECaltech Woodframe Project, California Institute of Technology, Pasadena. Scawthorn, C. 1981a. “Urban Seismic Risk: Analysis and Mitigation,” Ph.D. dissertation, Kyoto University, Kyoto. Scawthorn, C. 1981b. “A Model for Urban Post-Earthquake Fire Hazard,” Disaster: The International Journal of Disaster Studies and Practice (London), 5(2), 125–132. Scawthorn, C. 1995. “Insurance Estimation: Performance in the Northridge Earthquake,” Contingencies, the magazine of the American Institute of Actuaries, Washington, D.C. Scawthorn, C. and Gates, W.E. 1983. Estimation of Earthquake Losses in Los Angeles Damage Scenarios Under Varying Earthquake Research Effort, Final Technical Report, sponsored by U.S. Geological Survey Contract No. 14–08–0001–19822, Contractor: Dames & Moore, San Francisco. Scawthorn, C. and Harris, S.K. 1989. “Estimation of Earthquake Loss for a Large Eastern Urban Center: Scenario Events for One City,” in Earthquake Hazards and the Design of Constructed Facilities in the Eastern United States, K.H. Jacob and C.J. Turkstra, Eds., vol. 558, Annals of the New York Academy of Sciences, New York. Scawthorn, C. and Khater, M. 1992. “Fire Following Earthquake: Conflagration Potential in the Greater Los Angeles, San Francisco, Seattle and Memphis Areas,” prepared for the Natural Disaster Coalition by EQE International, San Francisco. Scawthorn, C., Iemura, H., and Yamada, Y. 1981. “Seismic Damage Estimation for Low- and Mid-Rise Buildings in Japan,” Earthquake Eng. Struct. Dyn., 9, 93–115. Scawthorn, C., Khater, M., and Rojahn, C. 1993. “Seismic Vulnerability and Impact of Disruption of Lifelines in the Conterminous United States,” in Proc. 1993 National Earthquake Conference, Memphis, TN. Steinbrugge, K.V. 1982. Earthquakes, Volcanoes and Tsunamis: An Anatomy of Hazards, Skandia America, New York. Thompson, W. (Lord Kelvin). 1891. Popular Lectures and Addresses, Macmillan, London. Whitman, R.V. et al. 1997. “Development of a National Earthquake Loss Estimation Methodology,” Earthquake Spectra, 13(4), 643–662. Wiggins, J. H. 1979. “Estimated Building Losses from U.S. Earthquakes,” in Proc. 2nd U.S. National Conference on Earthquake Engineering, Earthquake Engineering Research Institute, Berkeley, CA, pp. 253–262.
Further Reading There is an extensive literature on loss estimation, but Steinbrugge [1982], the ATC-13 publication [Applied Technology Council, 1985], a special theme issue of Earthquake Spectra (volume 13, number 4, November, 1997), and the HAZUS Technical Manuals [Federal Emergency Management Agency, n.d.] all provide an excellent introduction to the subject. There is still much to be learned from a careful reading of Freeman [1932].
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32 Insurance and Financial Risk Transfer 32.1 Introduction 32.2 Insurance and the Insurance Industry The Law of Large Numbers · Insurability Conditions · Types of Insurance · Reinsurance
32.3 Earthquake Insurance Insurance Supply and Insurers’ Decision Processes · Insurance Demand and Homeowners’ Decision Processes
32.4 Earthquake Insurance Risk Assessment California Department of Insurance Probable Maximum Loss · CRESTA Zonation · Probabilistic Earthquake Insurance Loss Estimation · Dynamic Financial Analysis
32.5 Government Earthquake Insurance Pools
Charles Scawthorn Consulting Engineer Berkeley, CA
Howard Kunreuther University of Pennsylvania Philadelphia, PA
Richard Roth, Jr. Consulting Actuary Huntington Beach, CA
California and the California Earthquake Authority · Japan and the Japan Earthquake Reinsurance Company · Turkey and the Turkish Catastrophic Insurance Pool · New Zealand and the Earthquake Commission
32.6 Alternative Risk Transfer Index-Based Cat Bonds · Other Types of Cat Bonds · Cat Bond Example · ART Summary
32.7 Summary Defining Terms References Further Reading
32.1 Introduction Earthquakes cause damage. It is usually considered not economically feasible to construct buildings and structures so as to completely eliminate the potential for any future damage. In fact, a certain amount of damage is predicated in the formulation of building codes, as exemplified in the first edition of the Recommended Lateral Force Requirements and Commentary [SEAOC, 1999]. This code proposed that structures are designed to meet the following multitiered performance capabilities: • Resist minor earthquake shaking without damage • Resist moderate earthquake shaking without structural damage but possibly with some damage to nonstructural features • Resist major levels of earthquake shaking with both structural and nonstructural damage but without endangerment of the lives of occupants © 2003 by CRC Press LLC
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In addition, modern buildings may sustain large losses beyond those anticipated in the building code because of the uncertainty associated with earthquakes and errors in the design process. Finally, until recently, earthquake codes only addressed the basic structure, and did not seek to prevent damage to contents, or prevent disruption of function,1 which can result in significant financial loss. Given that the potential exists for large losses even in well-designed buildings, individuals and organizations often protect themselves against this financial loss by purchasing insurance. In this chapter, we focus on how insurers approach the earthquake problem to set fair and reasonable rates of coverage against earthquakes. We additionally show under what circumstances a risk is insurable and how a company can develop new strategies for coping with catastrophic losses. We begin by explaining the basics of insurance and then examine specific risk assessment tools (exceedance probability curves and probable maximum loss estimates) used by insurers to measure earthquake risk, the insurer’s decision process in offering coverage against damage from earthquakes, and the risk bearer’s decision process in deciding whether or not to purchase coverage. We then discuss the typical earthquake insurance situation in high-risk regions, such as California, Japan, and Turkey, and conclude with a discussion of recent alternatives to traditional insurance.
32.2 Insurance and the Insurance Industry Insurance is a contract binding one party to indemnify a second party against specified loss in return for premiums paid. Insurance is one of the principal mechanisms used to manage risk. Insurance enables one to pay a relatively small premium today to protect oneself against an uncertain but potentially large loss in the future. Basically, the insurance contract is “the substitution of a certain small loss for the possibility of a large uncertain loss.” Insurance rewards those who take protection against a potential loss and provides funds to cover the cost after a disaster occurs. In the United States, some insurance is required while other coverage is voluntary. For example, new homeowners are often compelled to purchase homeowner’s coverage as a requirement for a mortgage. In this way, the bank or other financial institution protects its investment in case of a fire or other large loss. Also, automobile liability insurance is required in most states as a condition for operating a car. Our focus in this chapter is on earthquake insurance to cover losses to property. Property insurance has its origins in fire insurance and, in the English-speaking world, can be traced back to the Great Fire of London in 1666 [Kunreuther and Roth, 1998]. It is based on the collection of premiums from the members of the pool from which those suffering a loss are compensated. Property insurance works best when there is a significant number of randomly occurring, independent losses that are large for any individual in the pool but small relative to the total insured value covered by the pool. Although there may be considerable variability between individual claims, the variance of aggregate losses is small if the events are independent as a result of the central limit theorem, or law of large numbers, discussed later. The insurance industry is one of the largest industries in the United States and the world. It is divided into two major sectors: life/health and property/casualty (P&C). The P&C industry is divided into two major markets: personal lines and commercial lines. Personal lines are the types of insurance (e.g., homeowners, auto), referred to as lines of business, sold to individuals to protect their personal property. Commercial lines are the types of insurance offered to organizations, such as companies, corporations, municipalities, etc., and include fire, theft, business interruption (BI), loss of valuable papers, etc. Earthquake insurance, as well as fire and most kinds of insurance protecting real property, is written by the property/casualty sector of the industry. In 1998, the P&C sector accounted for 41% of the total U.S. insurance industry, with gross direct premiums of $368 billion [Insurance Information Institute, 2002], i.e., the property/casualty industry accounted for about 4% of the entire U.S. gross domestic product. 1 Function is the ultimate goal of a facility. For most normal buildings, the function is the housing of people and their goods. For example, if the function of a factory is disrupted, products cannot be manufactured and profits are therefore not made. In the insurance industry, these lost profits are covered under a business interruption (BI) policy.
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32.2.1 The Law of Large Numbers Ratemaking is the process of determining what premium (rate) to charge on a property. The premium that you pay is determined by an actuary at the insurance company. Ratemaking is normally based on the law of large numbers. Insurance markets can exist because of this. In simple terms, the law of large numbers states that, as a series of independent events under consideration increases, the distribution of the frequency of those events tends toward the normal distribution. Using fire insurance as an example, as long as the occurrence of a fire in one house is independent of the occurrence of a fire in a second house, then the average (mean) loss per year of a collection or portfolio of n houses can be estimated with increasing accuracy for an increasing number of houses. The mean is the sum of the means, and the variance is the sum of the variances, which implies that the mean increases linearly with n houses but the standard deviation σ increases with the square root of n: L=
∑ (l ) n
(32.1)
i
and σ ( L) =
∑ (L − l ) 2
n
0.5
(32.2)
i
where L = the expected value of loss for the n houses li = the expected loss for the ith house, equal to the value of that house times the probability of loss for the house σ = the standard deviation (a measure of the dispersion about the mean) Σn = summation over n Equation 32.2 is based on independence of loss between the risks. As n increases, it results in a lower standard deviation (i.e., a robust mean), or a statistical predictability that permits a limited amount of capital to insure (or protect) many properties simultaneously. This is illustrated in Figure 32.1, where the distribution of the probability of the loss (probability density function, pdf ) for a small portfolio is shown on the left. Note that it has a relatively broad shape, a large standard deviation. On the right in Figure 32.1 is the pdf for a large portfolio, the expected loss (i.e., the most likely value of loss) is larger but the shape is tighter, a relatively smaller standard deviation. The expected loss of the large portfolio is less uncertain; it is better known, more predictable (on average), and therefore a more known risk. It is a larger risk but more certain, and therefore more manageable. For example, if an insurance company has an amount of capital equal to the value of a house, and if on average one house in a thousand is destroyed by fire per year, then if one thousand homeowners each pay 0.1% of the value of their house per year to an insurance company, the company can use the collected payments (premiums) to pay the one homeowner whose house is totally destroyed by fire, and still have a surplus of capital (its initial capital) in case, unusually, a second house is destroyed by fire. The probability
Loss
FIGURE 32.1 Probability density function (pdf) of small portfolio (left) and large portfolio (right). © 2003 by CRC Press LLC
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determination of the average loss per year, or the loss or burning rate, is the province of actuaries, who base their estimates on loss statistics (when a large body of experience data is available), or on rational analysis and judgment (when insufficient data are available). This means that for a large number of claims, you can estimate the proper premium rate very accurately. It does not mean that the E[x] goes to zero or that insurance will become cheaper by the law of large numbers. Exactly the same principle is used in political polling to estimate the outcome of the next election, based on a sample poll. The sample does not have to be very large; a sample of 2000 is quite large. Similarly, an insurance company does not have to be very large to be able to predict the proper rate fairly accurately. The actuary estimates the average loss cost and then increases the number for future inflation and company expenses. This produces the needed rate that is charged to the public. As the number of houses in the company’s portfolio grows, the ratio of surplus required to protect against a greater than average number of losses in a year becomes smaller. In this manner, the company can accumulate more capital each year, a portion of which is retained to increase the surplus and thus permit growth of the company’s business. When a large number of properties are affected simultaneously by a common cause, such as a conflagration, flood, hurricane, earthquake, etc., then independence is lost, i.e., Equation 32.2 is not appropriate, and correlation between risks must be accounted for. This implies that many insureds must be indemnified simultaneously, leading to extraordinary demands on the company’s surplus. In the insurance industry, such events are termed catastrophes, and may result in insolvency. To avoid this, the actuarial and underwriting elements of an insurance company need to constantly monitor the potential for catastrophic occurrence, or portfolio risk. In addition to the problems of insuring such high-variance losses, there is the additional problem of estimating the parameters of the probability distribution of losses. Due to the frequency of these events, it takes an extraordinarily long history of past disasters to estimate the mean loss with an acceptable degree of predictability. This is why hazard experts and risk assessors would like to have databases of earthquakes and other hazards over thousands of years. Given the relatively short period of accurate history of hundreds of years, the mean loss and other parameters of the loss distribution are difficult to estimate with an acceptable degree of accuracy. Thus, most estimates of mean loss are supplemented by scientific estimates of the risk from such experts as seismologists, meteorologists, and structural engineers (discussed in other chapters of this volume).
32.2.2 Insurability Conditions What does it mean to say that a particular risk is insurable? We address this question from the vantage point of a supplier of insurance who offers coverage against a specific risk at a certain premium to a potential policyholder. The policyholder is protected against a prespecified set of losses defined in an insurance contract. Two conditions must be met before insurance providers are willing to offer coverage against an uncertain event: 1. The first condition is the ability to calculate expected losses to the insurer. This includes identifying and estimating the probability of uncertain events occurring and the associated losses when providing different levels of coverage. 2. The second condition is the ability to set premiums for each potential customer or class of customers. This requires some knowledge of the customer’s risk in relation to others in the population of potential policyholders. If conditions 1 and 2 are both satisfied, a risk is classified as insurable. But it still may not be profitable. In other words, it may be impossible to specify a rate for which there is sufficient demand and incoming revenue to cover the development, marketing, and claims costs of the insurance and yield a net positive profit. In such cases, the insurer will opt not to offer coverage against this risk.
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• Condition 1: To satisfy the first condition of insurability, probabilistic loss estimates must be calculated for various coverage levels. Such estimates can be based on historical data from previous events and on scientific forecasts of what is likely to occur in the future. Specifically, for earthquakes, hazard risk maps can be utilized. Such maps have been drawn in the United States but they only provide rough guidelines as to the likelihood and potential risk of certain events. Loss data for earthquakes are quite uncertain and cover a relatively short time horizon. Therefore, scientists have been working to reduce the uncertainty in the risk assessment process for earthquakes. Such analyses, aided by new developments in earthquake risk modeling, make it easier to estimate the risk facing insurers when they are considering how much coverage to provide in hazard-prone areas. • Condition 2: Once the risk has been identified, the insurer must determine a strategy to avoid an unacceptable level of earthquake loss while still making a profit. There are a number of factors that play a role in determining what premiums companies can charge for insurance coverage. State regulations often limit insurers in their rate-setting process, and competition may play a role in what they may be able to charge in the marketplace. In the ensuing discussion, however, we assume that insurers are free to set the premiums at any level they wish. Even in the absence of regulation and competition, there are two major problems that insurers face when deciding to provide coverage against earthquakes: ambiguity and highly correlated risks. Turning first to ambiguity, Kunreuther et al. [1995] conducted a survey of 896 underwriters in 190 randomly chosen insurance companies to determine what premiums would be required to insure a factory against property damage from a severe earthquake. The survey’s goal was to examine changes in pricing strategy as a function of the degree of uncertainty in the expected loss. Because the expected loss, E[L], of any event is defined as the probability of the event occurring multiplied by the resulting loss, probability and loss were the two variables considered. A probability is well specified when there is enough historical information on the event such that all experts agree that the probability of a given loss is p. When there is wide disagreement about the estimate of p among the experts, this ambiguous probability is referred to as AP. Similarly, L represents a known loss (i.e., there is a general consensus about what the loss will be if a specific event occurs). When a loss is uncertain, the experts’ estimates range between Lmin and Lmax, and this uncertain loss is denoted UL. Combining the degree of probability and loss uncertainty leads to four cases, which are shown in Table 32.1, along with a set of illustrative examples of the types of risks that fall in each category. The case of an earthquake falls within case 4, where the probability is ambiguous, Ap, and the loss is unknown, UL. As a further part of the survey, in order to see how underwriters might set premiums based on degrees of ambiguity and uncertainty, four scenarios were constructed for each participant to consider, as shown in Table 32.1. When the risk is well specified, the annual probability of the earthquake is either 1.0 or 0.5%; the loss, should the event occur, is either $1 million or $10 million. With the underwriter’s premium standardized to one for the nonambiguous case (i.e., p is well specified and L is known), one can examine how ambiguity affects pricing decisions. TABLE 32.1 Classification of Risks by Degree of Ambiguity and Uncertainty Loss Probability
Known
Unknown
Well-specified
Case 1 p, L (life, auto, fire) Case 2 Ap, L (satellite)
Case 3 p, UL (playground accidents) Case 4 Ap, UL (earthquake, bioterrorism)
Ambiguous
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TABLE 32.2 Ratios of Underwriters’ Actuarial Premiums for Ambiguous and Uncertain Earthquake Risks Relative to Well-Specified Risks Cases Scenario p = 0.5% L = $1 million E[L] = $5,000 p = 0.5% L = $10 million E[L] = $50,000 p = 1% L = $1 million E[L] = $10,000 p = 1% L = $10 million E[L] = $100,000
Case 1 (p, L)
Case 2 (Ap, L)
Case 3 (p, UL)
Case 4 (Ap, UL)
1
1.28
1.19
1.77
1
1.31
1.29
1.59
1
1.19
1.21
1.50
1
1.38
1.15
1.43
From Table 32.2, the pricing ratios of the other three cases relative to the nonambiguous case are presented. For the highly ambiguous case (i.e., Ap and UL), the premiums were between 1.43 to 1.77 times higher than if underwriters priced a nonambiguous risk. As expected, the pricing ratios for the other two cases were always above one but less than the highly ambiguous case. Correlated risk is also an important factor for insurers to examine in determining what premium to charge to make a risk insurable. Correlated risk refers to the simultaneous occurrence of many losses from a single event. As pointed out earlier, earthquakes produce highly correlated losses; many homes and buildings in the affected area are damaged and destroyed by a single event. If a risk-averse insurer faces highly correlated losses from one event, it may want to set a high enough premium not only to cover its expected losses but also to protect itself against the possibility of experiencing earthquake losses. An insurer will face this problem if it has many policies in one area, such as providing earthquake coverage to residences only in Los Angeles County rather than diversifying across the entire western region of the United States. To illustrate the impact of correlated risk on the distribution of losses, assume that there are two policies sold against a risk where p = 10% and L = $100. The expected loss for each policy is $10. If the losses are perfectly correlated, there will be either two losses with a probability of 10%, or no loss with a probability of 90%. On the other hand, if the losses are independent of each other, the chance of two losses decreases to 1% (i.e., 0.l * 0.1), with the probability of no loss equal to 81% (i.e., 0.9 * 0.9). In this case, there is also an 18% chance that there will be only one loss (i.e., 0.9 * 0.1 ± 0.1 * 0.9). The expected loss for both the correlated and uncorrelated risks is $20.2 However, the variance will always be higher for the correlated risk. Thus, risk-averse insurers will always want to charge a higher premium for the correlated risk. There are two other problems insurers face in setting premiums with respect to risks: adverse selection and moral hazard. Neither appears to be a major problem with respect to earthquake risks. Adverse selection occurs when the insurer cannot distinguish between the probability of a loss for good and poor risk categories. Moral hazard refers to an increase in the probability of loss or the magnitude of the loss itself caused by the behavior of the policyholder. With regard to earthquakes, adverse selection has been a problem for insurers until recently. Insurers can normally identify houses that are low and high risks with respect to potential losses from disasters but had not done so until the 1980s. Even then, several companies were rudely surprised by their losses
2
For the correlated risk, the expected loss is 0.9 * $0 + 0.1 * $200 = $20. For the independent risk, the expected loss is (0.81 * $0) + (0.18 * $100) + (0.01 * $200) = $20. © 2003 by CRC Press LLC
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$100
Value
Layer C ($56 p/o $70 xs $30)
Part D (retained)
80% $30
Layer B ($20 xs $10) $10 0
Layer A (typ. Deductible, eg, 10%) Fraction
FIGURE 32.2 Insurance diagram.
in the 1994 Northridge earthquake. If properties are priced to reflect risk, there cannot be adverse selection. Even if the property is located in an area of high seismic activity or on poor soil, if the earthquake insurance is priced properly, there cannot be adverse selection. However, pricing properties properly implies perfect knowledge, which is never possible, so that adverse selection in practice requires diligence on the part of insurers. An example of moral hazard is setting fire to a house that has been damaged by an earthquake; the house is insured for fire but may not be insured for earthquake, and thus the homeowner collects on the fire policy. Insurers do not like ambiguity and this is reflected in the premiums that they charge for events that fall into this category. Not surprisingly, the higher the uncertainty regarding the probability of a specific loss and its magnitude, the higher the premium will be. As shown by a series of empirical studies, actuaries and underwriters are generally averse to ambiguity and they tend to recommend much higher premiums for risks with high degrees of uncertainty surrounding them.
32.2.3 Types of Insurance There are many types of insurance, the broadest distinction being layered vs. coinsurance. This is illustrated in Figure 32.2, which is termed an insurance diagram. On the right is the pdf of loss for the property under consideration (note that the pdf in Figure 32.2 is turned on its side, vs. how the pdf is shown in Figure 32.1), while the large rectangle on the left illustrates the way the coverage is divided between the different types of insurance. On the bottom, layer A represents the risk up to the first 10% of loss of the value of the property because this example shows the total insured value (TIV) as $100, the deductible is 10% of $100 or $10. If the property sustains a $9 loss, the insurer of layer A sustains all of that $9 loss; if the property sustains a $12 loss, the insurer of layer A sustains a loss equal to 10% of the value of the property (i.e., $10), and the insurer of layer B sustains the next $2 of loss. Layer A is the first layer, and is typical of the deductible on ordinary building properties (in the case of the deductible, the insurer of layer A is the owner, who retains the risk). Layer B is the second layer, and represents a risk of 20% of the value in excess of the first 10%. Because the value of the property in this example is $100, this layer would be denoted $20 xs $10. There is no coinsurance in layer B. Layer C is divided (or has coinsurance) such that the insurer bears 80% of the risk (denoted $56 part of [p/o] $70 xs $30), while the owner bears (or retains) the remaining 14% of the value (denoted as Part D). Note that the higher the layer (for the pdf shown), the lower the probability of loss, so that the required premium (per unit value) for higher layers should be relatively lower.
32.2.4 Reinsurance Reinsurance is a transaction whereby the reinsurer, for a consideration, agrees to indemnify the ceding company (the primary insurer) against all or part of the loss which the insurer may sustain under the © 2003 by CRC Press LLC
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policy or policies it has issued. Basically, reinsurance is insurance for an insurer. Reinsurance is a very common practice and is employed, analogously to insurance, to permit the ceding company to spread its risk, and thereby better manage its total exposure and its cash flow. Reinsurance has two basic forms: pro rata and excess of loss. Pro rata reinsurance is sometimes called proportional reinsurance (analogous to coinsurance), because the reinsurer shares proportionately in risks and premiums. Pro rata reinsurance is often contracted on a treaty basis, such that it occurs automatically, where the reinsurer agrees to assume some part (e.g., 20% of all claims) of the ceding company’s risks of a predefined nature (e.g., all homeowner fire policies). In effect, the reinsurer becomes a financial partner of the primary company, lending its capital to support the primary insurer’s capital. In contrast, excess of loss (analogous to layer insurance) reinsurance provides for loss indemnification above a specified level (attachment point) up to a limit (exhaustion point), which defines a layer. The reinsurer will charge a premium for losses that occur within the layer ceded. Alternative to automatic reinsurance is facultative reinsurance where, case by case, a primary insurer transfers some portion of a specific risk to a reinsurer. A small reinsurer may have the opportunity to underwrite an unusually large risk, which its capital surplus would not normally permit it to insure. By ceding or laying off a major portion of the large risk to a reinsurer, the ceding company utilizes the reinsurer’s capital to appear to underwrite or assume the large risk, thus improving client relations, reputation, and (hopefully) profits. Determination of reinsurance risk and premiums is performed analogously to ordinary insurance, and diagrams similar to Figure 32.2 are developed for a ceding company’s portfolio, to determine the actuarial basis for the loss potential and associated premium. The development of the pdf of the ceding company’s portfolio risk is a specialized field, performed by only a few “modeling” companies. As noted previously, any insurer assuming a risk from another insurer is technically a reinsurer, and many primary companies have a reinsurance operation. Globally, however, reinsurance is dominated by a relatively few companies with access to the necessary capital. Traditional global reinsurers include several Lloyd’s syndicates, Munich Re, Swiss Re, SCOR, and in the United States, Gen Re and Employer’s Re. In the 1990s, a major and growing market for reinsurance also developed in Bermuda, competitive with the traditional reinsurers. Analyzing a ceding company’s reinsurance needs and efficiently accessing the reinsurance market is a complex task, such that several large reinsurance intermediaries play a major role, including Guy Carpenter (part of the Marsh McLennan group), Aon, and Benfield Blanche. Reinsurance plays a very significant role with respect to natural hazards catastrophic risks, such as earthquake. As noted previously, a prime distinguishing feature of large earthquakes is their simultaneous impact on thousands of properties, resulting in loss of independence between risks. The net result is that the losses due to large “cats” is far more uncertain than ordinary insurance risks, so that many primary companies utilize reinsurance to a significant degree in managing catastrophe risk. This reliance on reinsurance extends to large regional catastrophe pools, such as the California Earthquake Authority or New Zealand’s Earthquake Commission, which employ reinsurance in multibillion dollar programs of several layers.
32.3 Earthquake Insurance In the United States, earthquake insurance is typically offered to homeowners as an amendment to their fire or homeowner’s policy, and to commercial customers as an added peril or difference in condition (DIC) to whichever type of loss (i.e., fire, BI, etc.) they are concerned about. One important point should be noted: in the United States, the United Kingdom, Canada, Australia, New Zealand, and other Englishspeaking countries, fire following earthquake is covered under the fire policy, whereas in virtually the rest of the world, fire following earthquake is covered under the earthquake policy. Because conflagration following earthquake is a significant risk in regions with a large stock of wood buildings, such as California, New Zealand, and Japan, this distinction can be critical. Fire following earthquake is addressed in Chapter 29 of this volume.
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$60
Economic Losses ($ billions)
Median
Median Loss
0 Earthquake (5 events) Flood (21 events) Hurricane (25 events)
Type of Natural Disaster
FIGURE 32.3 Historical economic losses vs. type of significant U.S. natural hazards in 50-year period. (Courtesy Geoscience Division, American Re)
A considerable amount of historical data is utilized to estimate earthquake insurance premiums as a function of the type of building (e.g., steel vs. masonry). Premiums are fundamentally based on two factors: frequency (how often an event such as an earthquake occurs), and severity (what is the loss, when it occurs). With respect to earthquakes, given the low frequency of these events over time, historical data on which to base insurance premiums are limited. Hence, there is a need to supplement historical information with scientific data in order to improve the accuracy of the risk estimates and determine what premiums to charge. Because there may be considerable uncertainty surrounding these figures, insurers may charge relatively high premiums, reflecting their aversion to ambiguity and uncertainty. The important question is whether or not there is sufficient demand for coverage at the rates that insurers want to charge. Earthquakes pose a set of challenging problems for the insurance industry because they involve potentially high losses that are extremely uncertain. This ambiguity is best seen in a graphical representation of historical loss data. Figure 32.3 depicts the range of economic losses in the United States for three types of events: earthquakes, floods, and hurricanes. The natural hazards shown have corresponding frequencies of occurrence of 5, 21, and 25 events, respectively, over the past 50 years in the United States. The horizontal axis indicates the type of natural disaster3 and the vertical axis shows the range of economic loss and median value of loss. These natural hazards have a historically low median and a significant upper range of economic loss. In other words, while the historical losses have been relatively low for more than half of these disasters as shown by the median lines in Figure 32.3, the upper bound of the range of losses has been very high. More interestingly, the most infrequent type of natural disaster (earthquakes) and the most frequent type of natural disaster (hurricanes) have the greatest ranges of historical loss. Given this significant uncertainty, it is not surprising that earthquake models were initially developed to aid the insurance industry in the quantification of potential loss from these two types of disasters.
32.3.1 Insurance Supply and Insurers’ Decision Processes The above discussion suggests that, in theory, insurers can offer protection against any risk that they can identify and calculate the expected losses for, as long as they have the freedom to set premiums at any level. However, due to problems of ambiguity and highly correlated losses, they may want to charge premiums that considerably exceed the expected loss. For some risks, the desired premium may be so 3
A significant U.S. natural disaster is an economic loss (adjusted to year 2000 dollars) of at least $1 billion or more than 50 deaths, or both, attributed to the event. Also, these loss estimates, while adjusted for inflation, are not adjusted for population increases and increases in wealth in given locations. © 2003 by CRC Press LLC
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high that there would be very little demand for coverage at that rate. In such cases, even though an insurer determines that a particular risk meets the two insurability conditions discussed previously, it will not invest the time and money to develop the product because it believes that it cannot profitably market it. More specifically, the insurer must be convinced that there is sufficient demand to cover the development and marketing costs of the coverage through future premiums received.4 In addition, insurers must be convinced that they can manage the ambiguity of the risk so that premiums can be charged that will be attractive to potential policyholders. Insurers will limit their losses by restricting the amount of coverage in hazard-prone areas to avoid losses that may cause them to lose a considerable amount of surplus and possibly become insolvent. In his definitive study, which sheds light on insurers and their decision rules, Stone [1973] indicated that firms interested in maximizing expected profits are subject to two constraints representing the survival of the firm and the stability of its operation. The insurance underwriter satisfies the survival constraint by choosing a portfolio of risks with an overall expected probability of insolvency less than some threshold, p1 . The stability constraint focuses on the combined loss and expense ratio, LR, for each year. Insurers define a target level, LR*, which represents an upper limit on this ratio and requires that the probability that LR exceeds LR* is less than p2. A simple example illustrates how an insurer, in determining whether the earthquake risk is insurable, will utilize these two constraints. Assume that all homes in an earthquake-prone area are equally resistant to damage, so that the insurance premium on each structure is the same, denoted P. Further assume that the Down-to-Earth (DTE) Insurance Company has $A dollars in current surplus and wants to determine the number of policies it can write and still satisfy its survival and stability constraints. Then, the maximum number of policies, n1 , satisfying the survival constraint is: Probability [(Total Losses ± Expenses ≥ n1P ± A)] ≤ p1
(32.3)
In addition, the maximum number of policies, n2, satisfying the stability constraint is: Probability [(Total Losses ± Expenses)/n2P ≥ LR*] ≤ p2
(32.4)
Whether DTE will view the earthquake risk as insurable depends on whether the fixed cost of issuing policies in the area is sufficiently low so it can make a positive expected profit. This, in turn, depends on how large the values of n1 and n2 are for any given premium, P. Note that DTE also has some freedom to change its premium. A larger P will increase the values of n1 and n2 but will lower the demand for coverage. DTE will decide not to offer earthquake coverage if it believes it cannot attract enough demand at any premium structure to make a positive expected profit using the survival and stability constraints as restrictions on how many policies it is willing to offer. In a series of interviews conducted with insurers following Hurricane Andrew and the Northridge earthquake, it was indicated that a key factor that influences insurers’ decisions on how many policies to write is their probable maximum loss (PML) in the event a disaster occurs.5 Today, in many hazardprone regions, most insurers would like to reduce their current PML estimates. A.M. Best Company includes PML exposures as a part of its rating of insurer capability [BestWeek, 1996].
32.3.2 Insurance Demand and Homeowners’ Decision Processes Given that insurers provide residential coverage for earthquakes, how much interest does the potential policyholder have in purchasing this coverage at some prespecified price? The uncertainty associated with
4
We are assuming implicitly that there are no regulatory restrictions that force the insurer to keep the premium for certain types of coverage below a given value. If that value is too low, the insurer may decide not to offer such coverage simply because it will not be profitable. 5 These interviews were conducted by Jacqueline Meszaros as part of a National Science Foundation study, “The Role of Insurance and Regulations in Managing Catastrophic Risk.” © 2003 by CRC Press LLC
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earthquakes, coupled with the limited information-processing capabilities of individuals, lead homeowners to utilize simplified decision rules in determining whether or not they want to purchase coverage.6 Residents in hazard-prone areas often exhibit one of two reactions with respect to earthquake events. If they have not experienced a specific disaster and do not have friends and neighbors who have been affected by such an event, they often behave as if “it will not happen to me.” In other words, they treat the probability of an earthquake as essentially zero. These residents will have no interest in voluntarily purchasing insurance [Kunreuther, 1996]. Alternatively, individuals who have recently experienced a disaster are much more likely to purchase insurance voluntarily. With the recent event prominent in their minds, the perceived probability of occurrence triggers interest in protecting themselves. It is thus not surprising that demand for earthquake insurance in California increased significantly following the Loma Prieta earthquake in 1989 and the Northridge earthquake in 1994; in the 1970s, less than 10% of homes in the state were insured against earthquake damage. Similar behavior occurred in Japan following the 1995 Kobe earthquake. The individuals who are not concerned with the consequences of a future disaster often behave as if they have a threshold probability, p*, below which they will not purchase insurance. In their minds, the attention costs (i.e., the costs to think about the event) and the transaction costs (i.e., the costs to gather information about insurance coverage) are too high relative to the probability that the disaster will occur. The higher these perceived costs, the larger p* will be. Those who feel the probability of a disaster exceeds p* are likely to seek out friends and neighbors for information about where to buy coverage [Kunreuther et al., 1978; Weinstein, 1987].
32.4 Earthquake Insurance Risk Assessment The ambiguity and uncertainty associated with expected losses from earthquakes highlight the importance of understanding the risk assessment process and how it can potentially reduce the uncertainty associated with these earthquake events. The risk assessment process is most commonly probabilistic in nature, consisting of two primary components, hazard and vulnerability, both of which are covered in considerable detail in other chapters in this volume, and thus only summarized here. This section first reviews traditional methods insurers used to estimate their overall risk, and then discusses earthquake loss modeling, which built on earlier work [Hirschberg et al., 1978; Petak and Atkinsson, 1982; Scawthorn, 1981; Steinbrugge, 1982; Wiggins, 1981] to emerge in the 1990s as a powerful tool for the insurance industry, leading to innovations, such as catastrophe securitization (discussed later).
32.4.1 California Department of Insurance Probable Maximum Loss In the aftermath of the San Fernando earthquake in 1971, concern about the exposure of the insurance industry to earthquakes greatly increased, leading the California Insurance Department to issue Rule 226, which requires all licensed insurers to report each year their insured exposures for earthquake shake damage on residential and commercial structures in California. At that time, the percentage of homes and commercial structures insured for earthquake damage was less than 10%, and the insurance losses from the San Fernando earthquake were about $46 million. Since then, the demand for earthquake insurance has grown dramatically, along with a dramatic increase in housing and commercial building values. The insurance industry paid out about $1 billion after the Loma Prieta earthquake in northern California in 1989. The insurance industry has paid out more than $15 billion for the January 17, 1994 Northridge earthquake. While no insurers went out of business after the Northridge earthquake, the financial impact was severely constricting for insurers of all sizes.
6 These decision rules differ from normative models of choice, such as expected utility theory or cost–benefit analysis. For more detail on how they differ, see Camerer and Kunreuther [1989].
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As a result of Rule 226, the California Insurance Department developed a simple but useful method for insurers to estimate their probable maximum loss (PML). Definitions of PML vary widely within the industry but the methodology developed by the California Department of Insurance and its consultant K.V. Steinbrugge has been used by the State of California since about 1980 to monitor insurance industry exposure [Steinbrugge, 1982; Steinbrugge and Roth, 1994; Roth and Van, 1998; CDI, 2001]. In that methodology: • Building Class PML (i.e., for an individual building of a specific class, such as wood frame, see Tables 32.3 and 32.4) is defined as the expected maximum percentage of monetary loss which will not be exceeded for nine out of ten buildings, where the building is located on firm alluvial ground, subjected only to the vibratory motion from the maximum probable earthquake (i.e., not astride a fault or in a resulting landslide). • Aggregate PML is the sum of all of the PML values in a PML zone (see Figure 32.4), plus factored PML values for buildings located outside of the PML zone but still within the earthquake underwriting zone. A factored PML is a reduced PML value based on reduced intensity (i.e., damage) with increasing distance away from the causative fault. Using this methodology, insurance companies in California are required to report their aggregrate PML each year to the California Department of Insurance [CDI, 2001]. This is of interest to the department, as it wishes to assure adequate company surplus to assure payment of claims in the event of a large earthquake.
32.4.2 CRESTA Zonation A key system employed by reinsurers for tracking catastrophe exposure is the CRESTA (Catastrophe Risk Evaluating and Standardizing Target Accumulations) system,7 originally developed in the late 1970s in a joint project of several major reinsurance companies. CRESTA is a standardized method of exposure accumulation reporting by primary companies for reporting to reinsurance companies. Based primarily on the observed or expected seismic activity within a country, CRESTA zones permit accumulation of insured values within a country by administrative or political boundaries for easier assessment of risks. It is a simple but effective system that has permitted rational albeit approximate analysis of the potential exposure by the large, multinational reinsurance companies. Figure 32.5 shows examples of CRESTA accumulation zones; note that the California CRESTA zones are identical to the California Department of Insurance’s earthquake zones, which is typical in that the CRESTA system seeks to minimize the reporting burden on companies by using existing reporting formats wherever possible. CRESTA reports, for example, are utilized by a reinsurer to compare requests for reinsurance from two primary companies. The two primaries may be requesting catastrophe reinsurance for properties located in several countries. Such global programs can become very complex and difficult to analyze. TABLE 32.3 Building Classes, California Department of Insurance Class 1A 1B 1C
Type of Building Single- through four-family dwellings. No limitations on story height, area, and construction materials. Homeowners. Habitational: Wood frame and frame stucco habitational buildings that do not exceed two stories in height, regardless of area. Nonhabitational: Wood frame and frame stucco, except buildings: (1) > three stories and (2) > 3000 ft 2 in ground floor area. Wood frame and frame stucco buildings not qualifying under Class 1C. Mobile homes and contents.
1D 1E
7
The system’s name actually derives from the fact that the initial meeting was held at the Hotel Cresta.
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TABLE 32.3 (CONTINUED) Building Classes, California Department of Insurance All-Metal Buildings 2A 2B
All-metal buildings one story in height and 20,000 ft2 or less in ground floor area. Wood or cement-asbestos are acceptable alternatives to metal roofing and siding. Buildings that would qualify as Class 2A, except for exceeding area or height limitations. Steel Frame Buildings
3A
3B
3C
Buildings with a complete steel frame carrying all loads. Floors and roofs must be of cast-in-place (CIP) reinforced concrete (RC) or of concrete fill on metal decking welded to the steel frame (open web steel joists excluded). Exterior walls must be nonload bearing and of CIP RC or of reinforced unit masonry. Buildings having columnfree areas greater than 2500 ft2 (auditoriums, theaters, public halls, etc.) do not qualify. Buildings with a complete steel frame carrying all loads. Floors and roofs must be of CIP RC, metal, or any combination thereof, except that roofs on buildings over three stories may be of any material. Exterior and interior walls may be of any nonload-bearing material. Buildings having a complete steel frame with floors and roofs of any material (such as wood joist on steel beams) and with walls of any nonload-bearing materials. RC Buildings Combined RC and Structural Steel Buildings
Note
4A
4B 4C 4D
Class 4A and 4B buildings must have all vertical loads carried by a structural system consisting of one or a combination of the following: (1) CIP RC frame, (2) CIP RC bearing walls, (3) partial structural steel frame with (1) or (2) or both (1) and (2). Floors and roofs must be of CIP RC, except that materials other than RC may be used for the roofs of buildings over three stories. Buildings with a structural system as defined by the note above with CIP RC exterior walls or reinforced unit masonry exterior walls. Not qualifying are buildings having column-free areas greater than 2500 ft2 (auditoriums, theaters, public halls, etc.). Buildings having a structural system as defined by the note above with exterior and interior nonbearing walls of any material. Buildings having (1) a partial or complete load carrying system of precast concrete or (2) RC lift-slab floors or roofs, or both (1) and (2), and (3) otherwise qualifying for Class 4A and 4B. Buildings having an RC frame or combined RC and structural steel frame. Floors and roofs may be of any material (such as wood joist on RC beams), walls may be of any nonload-bearing material. Mixed Construction
5A
5B 5C Class
Buildings having load-bearing exterior walls of (1) CIP RC or (2) precast RC (such as tilt-up walls) or (3) reinforced brick masonry, or (4) reinforced hollow concrete block masonry or (5) any combination of (1)–(4). Floors and roofs may be of wood, metal, CIP concrete, precast concrete, or other material. Interior bearing walls must be of wood frame or any one of a combination of the aforementioned wall materials. Note: No class distinction is made between newer, highly earthquake-resistive buildings and older moderate earthquake-resistive buildings having these construction materials. ISO Classes 5A and 5AA shall be combined and considered as Class 5A. Buildings having load-bearing walls of unreinforced brick or other types of unreinforced solid unit masonry, excluding adobe. Buildings having load-bearing walls of hollow tile or other hollow unit masonry construction, adobe, and cavity wall construction. Also included are buildings not covered by any other class. Type of Building Earthquake-Resistive Construction
6
Any building with any combination of materials so designed and constructed as to be highly earthquake resistant and also with superior damage control features in addition to the minimum requirements of building codes.
7
Bridges, tunnels, dams, piers, wharves, tanks, tank contents, towers of all types, and the like. Time-element coverages for these structures to be included.
Miscellaneous
Source: http://www.insurance.ca.gov/RRD/RSU/Forms/Year2001/PML2001/pml2001.htm. © 2003 by CRC Press LLC
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TABLE 32.4 Probable Maximum Loss (PML) for Building Classes, California Department of Insurance CONSTRUCTION CLASSES, PML, AND DEDUCTIBLES Net PML (%) Class
Deductible
Zone A
Zone B
Zone C
Zone D
Zone E
Zone F
Zone G
Zone H
1A
1%
6.75
5.75
6.13
2.63
5.25
3.13
1.75
2.50
&
5%
3.63
3.00
3.13
1.19
2.38
1.88
1.00
1.50
1B
10%
2.13
1.63
1.75
0.56
1.13
1.13
0.63
0.88
15%
1.38
1.00
1.13
0.31
0.63
0.63
0.38
0.50
“Mini”
0.69
0.50
0.56
0.16
0.31
0.31
0.19
0.25
“Wrap”
2.94
2.50
2.56
1.03
2.06
1.56
0.81
1.25
1C
5%
3
3
3
3
3
3
3
3
1D
5%
10
10
10
10
10
10
10
10
1E
2%
5
5
5
5
5
5
5
5
2A
5%
2
2
2
2
2
2
2
2
2B
5%
10
10
10
10
10
10
10
10
3A
5%
15
15
15
15
15
15
15
15
3B
5%
25
25
25
25
25
25
25
25
3C
10%
25
25
25
25
25
25
25
25
4A
5%
20
20
20
20
20
20
20
20
4B
5%
35
35
35
35
35
35
35
35
4C
10%
50
50
50
50
50
50
50
50
4D
10%
45
45
45
45
45
45
45
45
5A
5%
25
25
25
25
25
25
25
25
5B
10%
60
60
60
60
60
60
60
60
5C
10%
75
75
75
75
75
75
75
75
6
5%
10
10
10
10
10
10
10
10
*7
0%
50
50
50
50
50
50
50
50
COC
**
**
**
**
**
**
**
**
**
* Includes special structures such as bridges, tunnels, dams, piers, wharves, tanks, tank contents, towers of all types, and the like. Time–element coverages for these structures are also to be included. **Buildings in the course of construction (COC) are to be placed in the completed building class, using 50% of the completed PML and the full value of the usual deductible (Fire Forms where insurance is written at 80% of value or higher). Buildings constructed of materials of more than one class shall be assigned to the Construction Class with the highest PML. Earthquake liabilities on buildings, contents, time element, and other location coverages shall be included under the building Construction Class. Source: http://www.insurance.ca.gov/RRD/RSU/Forms/Year2001/PML2001/pml2001.htm.
Because the two companies report in a standardized CRESTA format, the aggregate risks for the two companies can be compared on the same basis to allow the reinsurer to make appropriate pricing and other decisions. CRESTA was developed prior to the emergence of modeling for the global insurance industry, and is gradually being supplanted by probabilistic risk assessment but will continue to be useful for a significant period as a simple standardized reporting format.
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ZONE Del Norte
A Siskiyou
Humboldt
Alameda Contra Costa Del Norte Humboldt Lake Marin Mendocino Monterey Napa San Benito San Francisco San Mateo Santa Clara Santa Cruz Solano Sonoma
Modoc
H
Shasta
Trinity
Lassen
A
Tehama Plumas Butte
Glenn
Sierra
Mendocino
Nevada Yuba
r
Colusa
Sutte
Lake
G
Solano
Tuolumne
San Joaquin
Contra Costa
San Mateo
C
Kern San Luis Obispo Santa Barbara Ventura
D
San Diego
Alameda
Stanislaus
Alpine Imperial Inyo Mono Riverside San Bernardino
F
Fresno Kings Madera Mariposa Merced Tulare
G
Amador Butte Calaveras Colusa El Dorado Glenn Nevada Placer Sacramento San Joaquin Stanislaus Sutter Tuolumne Yolo Yuba
Santa Clara Sa nta Cr uz
H
Lassen Modoc Plumas Shasta Sierra Siskiyou Tehama Trinity
A
E
Madera
Merced
San Benito
Mono
Mariposa
F
Fresno
COUNTY
E
Calaveras
Marin San Francisco
Los Angeles Orange
Alpine Amador
Sa
cra
A
me
Napa
B
El Dorado
nto
Yolo Sonoma
Placer
ZONE
COUNTY
Inyo
Tulare
Monterey Kings
San Luis Obispo
Kern
C
San Bernardino
Santa Barbara Ventura
Los Angeles
B
E Riverside
Orange
D
San Diego
Imperial
E
FIGURE 32.4 California Department of Insurance earthquake zones. Source: http://www.insurance.ca.gov/RRD/ RSU/Forms/Year2001/PML2001/pml2001.htm)
32.4.3 Probabilistic Earthquake Insurance Loss Estimation The CRESTA system was critically important for insurers8 and reinsurers when these companies did not have the ability to accurately estimate the potential losses a catastrophe may cause to the properties they insure. By the 1990s, however, and building on earlier work [Hirschberg et al., 1978; Petak and Atkinsson,
8 Especially for large global primary companies, which used the system internally as well as for reporting to reinsurers.
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California, USA
Earthquake Accumulation Assessment Zones
5
5
6
4
H
6
7
3
8
2 12
13
7
1
A
10 9 8 8 14 11 7 15 6 5 9 10 11 4 12 San 4 3 Francisco 3 2 2 6 13 14
G
1 1
2
5 4
F
3
Fresno 3
15 16
1
2 2
1 3
E
C 2
4
4
B 1
Los Angeles
5
3
6
D 0
100
San Diego
200 miles
1 Detailed map of Zone SAITAMA
5
1
IBARAKI
Tokyo 5.2 Chiba YAMANASHI 5.3.3 5.1 KANAGAWA CHIBA SHIZUOKA
0–SHIMA
Sea of Japan Pacific Ocean
2.1 2.2
2
7
Kawasaki 5.3.1 Yokohama 5.3.2
0
3
HONSHU
8
9 9.4 9.1 9.2 9.5
11
10
KYUSHU
10
3.3
4.2 7.1 4.1 7.2 4.4 6.2 4.3 7.3 6.1 6.3
8.1 8.28.3
9.3
11
3.1
2.3 3.2
40 km 2.4
6.5 6.4
8.4 6.6 8.5 8.6
8
4 5
See detailed map
6
OKINAWA
SHIKOKU 0
100 200 300 km
FIGURE 32.5 CRESTA Zones for California and Japan. © 2003 by CRC Press LLC
HOKKAIDO
Naha
12 0 25 50 km
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Hazard Source and Attenuation Models
Structure, Content, and BI Vulnerability Models
Hazard Module
Historic and Scientific Hazard Information
Damage Module
Inventory of Asset Attributes
Loss Module
Loss inuring Information
FIGURE 32.6 Basic earthquake insurance loss estimation process.
1982; Scawthorn, 1981; Steinbrugge, 1982; Wiggins, 1981], the technology of earthquake loss modeling emerged as a powerful tool for the insurance industry. Earthquake loss modeling has applications in many areas, such as infrastructure planning and building-code development, and is covered in detail elsewhere in this volume. The discussion here is an overview only, limited to an insurance perspective. The basic earthquake insurance loss estimation process is shown in Figure 32.6, and begins with the hazard component, which calculates the probability of exceeding certain levels of event intensity based on the physical parameters that describe the earthquake. The vulnerability component deals with the nature of the damage to the built environment (e.g., structures and lifelines) and the resulting monetary cost of repairs or other losses. Due to the complexity of the hazard and the limited historical data on past events, both of these components have considerable uncertainty. When the potential hazard is determined, one needs to characterize the population and property at risk. One way to specify who is at risk is to construct a community or region consisting of homes, businesses, and other properties that are subject to future disasters. One needs to know the design of each structure, whether specific loss reduction measures are in place or can be utilized in the future, and the property’s location in relation to the hazard (e.g., distance from an earthquake fault line), as well as other risk-related factors. Using the estimates of probability that earthquakes of certain intensities or magnitudes will occur, the expected damage to a community or region (or portfolio of structures) is calculated. From this estimate, the resulting loss to the structures is estimated. The recent use of geographic information systems (GIS) for incorporating geologic, topographical, and property information for a region has enabled scientists to estimate potential damage and losses from different types of hazards much more easily. The data for the region are stored in the form of GIS maps of hazard estimation, maps of secondary hazards, and maps of damage to structures in the region [King and Kiremidjian, 1997]. These maps form the core of today’s earthquake models. A key tool utilized when undertaking an analysis for determining potential earthquake risk is the loss exceedance probability (EP) curve. The exceedance probability of loss (i.e., the probability of exceeding the loss) is the complement of the cumulative distribution function (CDF) of loss: EP (L) = 1 – CDF (L)
(32.5)
The use of loss exceedance curves has enabled the insurance industry to develop more accurate rate structures for coverage against losses from earthquakes. An example of an exceedance probability curve is shown in Figure 32.7. Typically, the exceedance probability curve has a continuous shape with the probability of exceedance on the y-axis and the measure of risk on the x-axis. The probability of exceedance is the probability that the measure of risk will be surpassed for a given period of time. Most often, the period of time is 1 year (i.e., an annual probability of exceedance). © 2003 by CRC Press LLC
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Probability of Exceedance, p
Earthquake Engineering Handbook
PML
Loss, L (in Dollars)
FIGURE 32.7 Exceedance probability curve.
Loss, L (in Dollars)
10%
$20
$10
80%
15%
$20
$10
Probability of exceedance, p
FIGURE 32.8 Examples: (left) insurance diagram and (right) loss exceedance probability curve with layer.
The measure of risk (x-axis) in Figure 32.7 is dollar loss. As expected, the probability of exceedance decreases as the risk measure increases. The events with the lowest probabilities of exceedance are the ones with the highest potential loss; typically, these are the events of greatest concern. As previously mentioned, developing exceedance probability curves for earthquakes has significant uncertainty, which plays a critical role in assessing natural disaster mitigation and financing the consequences of earthquakes. It is important to understand where the uncertainty lies, and how it can be captured and utilized in the risk assessment and risk management process. One way to capture this uncertainty is through a set of exceedance probability curves. In other words, values are calculated at various confidence intervals around the mean estimates of loss (or hazard or damage). Given the loss exceedance probability curve and an insurance diagram, the probability of sustaining a loss, per an insurance contract, can be readily determined. For example, referring to Figure 32.8), the insurance contract in this case is for a particular layer, specifically $10 excess of $10 (which could easily be $10 million but $10 is used as an example; note that this is a layer with an upper limit of $20 and a lower limit of $10, written 10 xs 10). Furthermore, as is typical in many contracts, the insurer will only cover 80% of this layer, requiring the insured to retain 20% (in part to limit the potential for moral hazard). If the property in this example sustains a loss of $8, for example, the insurer pays nothing. If the loss is $15, the insurer pays 80% of the excess of $10, or $4. If the loss is $25, the insurer pays 80% of the $10 xs $10, or $8. The maximum the insurer may pay is $8, no matter how high the loss. From the exceedance probability curve, we note that the probability of penetrating the layer is 15%, and of exhausting the layer is 10%. Therefore, the expected loss given these parameters is approximately © 2003 by CRC Press LLC
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capital
failure time
FIGURE 32.9 Example of dynamic financial analysis.
80% of (10% of $10 plus half of 5% × $10), or 80% of $1.25, or $1. This is the pure premium, given the hazard, vulnerability, values, and insurance contract. One dollar, or 10%, is therefore the rate on line for 80% coverage of $10 xs $10. Note that the insurance contract’s terms are a major determinant in the insurer’s expected loss, and that a high layer on a risky property can still have a low expected loss, and therefore may be a profitable contract for the insurer while still providing some protection to the insured.
32.4.4 Dynamic Financial Analysis An emerging technique for insurers and insureds is dynamic financial analysis (DFA), which is simply a forward-looking estimate of the financial condition of a risk or risk pool over a period of time (e.g., 50 years). DFA models are employed (1) by insurance companies, to calculate the capital required for an insurance pool, given a desired level of solvency;9 and (2) by insureds, to estimate what their risk is, and how it should be priced (i.e., to determine if the price available from insurers is a good buy). In actuality, DFA is a tool currently being employed only by larger, more progressive insurers, and by only the largest, most sophisticated insureds, such as multinational companies or government pools seeking reinsurance. The explanation of a DFA model provided here is a somewhat simplified version of a relatively complex model typically used in insurance company studies (for a detailed description of DFA modeling, see the DFA Research Handbook, Casualty Actuarial Society, http://www.casact.org/research/dfa/). Conceptually, a DFA model has three steps: 1. A set amount of capital is invested at the initiation of the insurance pool. 2. Premiums are collected, invested annually, with return on the investment. 3. The insurance pool pays out losses of claims for simulated events, finances mitigation efforts, and covers its own expenses. In order to estimate annual risk losses to the insurance pool, Monte Carlo simulations are employed to generate loss samples consistent with the loss exceedance distributions calculated as described previously. Each loss sample has an equal likelihood of occurrence. Because the annual aggregate loss distributions are used, the occurrence of more than one earthquake in a given year is accounted for. Schematically, the process is shown in Figure 32.9, where each simulation begins with an initial capital, and undergoes 50 years of premium and investment growth and risk claim losses. In most simulations, the pool performs well but occasionally an infelicitous combination of exposure growth and risk losses leads to exhaustion of capital, or failure (i.e., bankruptcy). Based on the risk loss sample, a “random walk” technique is used to generate 10,000 trials (or random walks) of 50 consecutive years of risk losses. In each trial, a sequence of 50 loss samples is selected from the loss distribution, resulting in one hypothetical set of occurrences, or random walk, for the 50-year period. This process is repeated 10,000 times to generate the 10,000 random walks of 50 years duration each for the analysis. The sampling is done in such a manner that each year has a unique and statistically
9 Put another way, a desired level of solvency is a desired low “probability or ruin,” i.e., probability of a catastrophic loss exhausting an insurance company’s capital.
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independent set of damage points; however, for each of the 50 years, all the 10,000 damage points are equally likely. The output of this model provides a probabilistic estimate of future claims, premiums, revenues, and profits (or losses) for each business strategy option that an insurance company may wish to consider.
32.5 Government Earthquake Insurance Pools The value of catastrophe insurance in the recovery process following major disasters has long been recognized, and in some countries this has led to the development of government-controlled natural disaster insurance schemes. This section first summarizes an overview of 15 government-controlled natural disaster insurance schemes listed in Table 32.5 [Scawthorn, 2001], not all of which protect against earthquake. Rather, a number of these schemes protect against flood, wind, or other natural hazards; in many cases, against all natural hazards. Nevertheless, many similarities exist irrespective of the hazard addressed, and much can be gained by reviewing their similarities and differences. The main trends in the programs surveyed may be summarized as follows: 1. Age. All of the programs dated from the 1960s or later, although the New Zealand Earthquake Commission’s predecessor dated from the 1940s. 2. National vs. regional. About half of the programs were national in scope, the other half regional. Only the United States, France, and New Zealand appear to have truly national catastrophe programs (United States for flood only, New Zealand for earthquake and volcano, and France for multiperil). 3. Perils. Eleven of the programs covered flood, and six were multiperil). 4. Residential vs. commercial-industrial. All programs covered residential risks, 11 also covered commercial risks. In many cases, the commercial participation is minor. 5. Buildings. Coverage always included buildings and usually contents, only about one third covered time element (i.e., additional living expenses [ALE] or BI). Two programs covered publicly owned buildings. 6. Voluntary vs. compulsory. More of the programs were voluntary, with only three being compulsory. Compliance rates for the compulsory programs, while not available, did not appear to be near 100%. About half the programs’ premiums were risk based, and none was subsidized. i.e., all programs appeared to attempt to operate on a basis such that premiums covered claims and expenses, on average.
TABLE 32.5 Natural Hazards Insurance Programs Surveyed No.
Country
1 2 3 4 5 6 7 9 10 11 12 13 14 15
U.S. U.S. U.S. U.S. New Zealand France Spain Japan UK Czech Republic Switzerland Switzerland Switzerland Hungary
© 2003 by CRC Press LLC
Program Name Florida Hurricane Cat Fund Hawaii Hurricane Relief Fund California Earthquake Authority National Flood Insurance Plan Natural Disaster Fund Cat Nat, Caisse Centrale de Reassurance Consorcio Compensación de Seguros Japan Earthquake Reinsurance Company
Interkantonaler Rückversicherungsverband Elementarschadenpool Schweizer pool für Erdbendeckung
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7. Mitigation. Five of the programs offered incentives or positively considered mitigation. However, only two of the programs actively used hazard maps in their underwriting or loss control (one of these, the U.S. National Flood Insurance Program (NFIP), has a very active hazard mapping program). 8. Deductible. Most programs had a deductible, which was typically 10% or less of TIV. Limits on coverage varied between a percentage of TIV, or a flat limit, but the limit was 100% replacement cost in about half the programs. 9. Management. About one third (six) of the programs were publicly (i.e., government) managed, while about two thirds (ten) were privately managed. It should be noted that in some cases the private management was by a nonprofit quasipublic board, independent of the government. Distribution and servicing of insurance policies were typically through the established distribution networks of private primary insurance companies and agents. 10. Primary vs. reinsurance: Four of the programs were insurance (i.e., primary) pools, and four were reinsurance pools. Virtually all programs covered second and subsequent losses. Only two programs were directly funded by the government. While there are a number of government pools in existence for natural hazards, there are four that dominate earthquake risk for government pools: the California Earthquake Authority, the Japan Earthquake Reinsurance Company, the Turkish Catastrophic Insurance Pool, and New Zealand’s Earthquake Commission. In large part, this is due to the combination of market size and earthquake hazard. The United States accounted for 32.35% of the world ’s total insurance premium volume in 1997, with nonlife premiums at U.S. $897 billion accounting for 42% of total premiums. The great preponderance of earthquake risk in the United States is in California. Japan’s share of world markets was 23.05%. In this section, we describe these programs; additional information is available in Guy Carpenter [2001].
32.5.1 California and the California Earthquake Authority In 1996, the California legislature established the CEA (California Earthquake Authority) as a privately financed, publicly managed entity to help California residents protect themselves against earthquake loss. Today, the CEA is the world’s largest residential earthquake insurer. Acting through its participating insurers, the CEA sells earthquake policies to homeowners, mobile-home owners, condominium owners, and renters throughout California, and provides retrofit assistance to help people protect their homes against earthquakes. This section discusses earthquake insurance in California, from early in the twentieth century to the creation of the CEA. 32.5.1.1 California: Early Earthquake Insurance Experience California is well known, especially to insurers, for having earthquakes. The 1906 San Francisco earthquake caused approximately $300 million in losses, about 80% of which was due to the fire that followed, and virtually all of the fire-related losses were insured. This was the largest insurance catastrophe up to that time, and remained so for many years. Many companies struggled to pay off their claims, in some cases taking years. Yet damage-causing earthquakes have not been common in California until recently. After 1906, the next damage-causing earthquakes occurred in Santa Barbara (1925) and in Long Beach (1933) but were not especially catastrophic for insurers. The modern era of earthquake activity began with the 1971 San Fernando earthquake, which caused substantial damage to homes, businesses, and public buildings. Insurance covered only a small portion of the losses because very few people had earthquake coverage, and there was very little fire damage. (In California, as well as other states, homeowner’s insurance covers any fire losses, even if caused by an earthquake.) The 1971 disaster caused several important changes in attitudes. It raised the consciousness of people with respect to the dangers of earthquakes, and it focused attention on the necessity of revising the building codes to require earthquake-resistive design and construction. The event also reinforced the insurance industry’s concern about the threat of earthquakes, and prompted the California Insurance
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Department to request private insurers to report annually on their earthquake exposures. This questionnaire, still in use today, is valuable to the department in monitoring the solvency of insurers. 32.5.1.2 The Northridge Earthquake Although a series of damaging earthquakes have occurred in California since the San Fernando earthquake, none compares to the January 17, 1994 Northridge earthquake. Next to Hurricane Andrew, it is the largest insured natural disaster ever, causing the most insured damage by far of any earthquake in the United States, with total insured losses of more than $12.5 billion. (In contrast, only a fraction of the damage caused by the Kobe, Japan earthquake in 1995 was covered by insurance.) To put the $12.5 billion figure in context, the population of Los Angeles County (where Northridge is located) is 9,244,646, with 1,565,862 single-unit dwellings and 1,402,997 apartment units (as of January 1, 1995). This works out to insurance company payments of $1352 for each man, woman, and child over a very large geographic area. The value of the total loss from the earthquake, including disaster assistance and uncompensated losses, is much greater. The insured loss amounts were about one third commercial and two thirds residential. The high peak ground acceleration of the earthquake was the primary cause of damage to building contents, chimneys, and garden walls. Building damage from landslide and liquefaction was not as common as in the Loma Prieta earthquake. While the insurance payments on this event exceed all of the earthquake insurance premiums collected in the twentieth century, this amount should only be compared to the current premium volume because so few structures were insured in past years, and so little premium collected. A typical earthquake policy insures for loss against structural damage, damage to contents, and loss of use (residential) or business income (commercial). Loss of use covers the cost of hotel accommodations and meals while the structure is being repaired, or it covers the loss of rental income on the house. Business income covers the loss of profits and the costs arising from shutting down the business (sometimes called business interruption). In the Northridge earthquake, for every $100 of insured residential damage, there was an average of $20 of content damage, and $10 of loss of use. It turned out that these ratios were the same for the 1989 Loma Prieta earthquake, even though the dollar amounts were much greater in Northridge. The insurance industry had great difficulty estimating the ultimate losses from the Northridge earthquake. Property Claim Services (PCS) collects statistics on disasters and runs training classes on catastrophe claims handling for member insurance companies. PCS was the designated insurance-industry collector of the estimates of the Northridge insured losses, as well as the media spokesperson for this catastrophe. It polled its members and announced estimates of the total industry-insured losses periodically. Table 32.6, which provides a summary of these figures, shows that estimates of total insured losses grow over time as more accurate damage figures become available.
TABLE 32.6 Estimates of Insured Losses Caused by the Northridgc Earthquake, January 17, 1994 Month of Estimation vs. Estimate of Total Losses (in billions of dollars) 1994 January April June August October
2.5 4.5 5.5 7.2 9.0 1995
January March May Source: Property Claim Services. © 2003 by CRC Press LLC
10.4 11.2 11.7
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The California Insurance Department conducted its own surveys. The first survey asked insurers to report their estimates as of October–November 1994, and the total reported was $8.8 billion. The survey conducted February–March 1995 reported that total losses were $10.6 billion, including loss adjustment expenses. Both of these surveys were consistent with the survey data shown in Table 32.6. A short, final survey made in 1996 confirmed that the final figure was $12.5 billion for industry-insured losses. Earthquake damage losses are difficult to estimate because the full extent of damage is not known until reconstruction and repair have been completed. This is why the initial estimates after the earthquake were about $2.5 billion and then grew monthly for more than 2 years [Scawthorn, 1995]. 32.5.1.3 The California Earthquake Authority (1996) In 1985, the California legislature passed a law requiring insurers writing homeowner’s insurance on oneto four-family units to offer earthquake coverage on these structures. There was no requirement that the owners had to buy earthquake insurance, only that the insurers had to offer it. This law was not instigated by consumers but was passed at the urging of the insurance industry to overcome a recent lower court decision that had required greatly expanded coverage under the homeowner’s policy, including earthquake damage. In other words, the lower court decision appeared to enable homeowners to collect for earthquake damage even though they had not purchased an earthquake endorsement, and the insurer had not received a premium for the earthquake coverage. The California Supreme Court eventually overturned the lower court case but the mandatory offer law remained in effect. Many people who were close to the drafting of this law believe that it was a poor solution to a legal problem that no longer existed. Furthermore, it took away from insurers the ability to manage their total earthquake exposure and forced them to insure structures that are so old or in such poor condition that they should not be provided with coverage. The insurance companies lived with this law until the 1994 Northridge earthquake struck. The insured damage was beyond expectations, and when homeowners across the state heard about the average insurance payments of $30,000 to $50,000 after the 10% deductible for homes in the Northridge area, earthquake insurance became a desirable commodity in the minds of many. The insurance companies reevaluated their earthquake exposures up and down the state and decided that they could not risk selling any more earthquake policies. In view of the mandatory offer law, the only legal response they had was to stop offering new homeowner’s policies, although in fact they did renew existing homeowner’s policies even at the risk of the policyholder’s opting to buy earthquake insurance. In view of the desire of homeowners to maintain their earthquake coverage in the future, there was no possibility that the mandatory offer law could be repealed by the legislature. The California Insurance Department surveyed insurers and found out that up to 90% of them had either stopped selling new homeowner’s policies or had placed restrictions on selling them. After extended discussions between the California Insurance Department and the large insurers, an advisory group of insurers and actuaries proposed the formation of a state-run earthquake insurance company, the CEA. The challenge from the start was to capitalize the CEA adequately. This challenge generated some innovative financing ideas. First, the department and the advisory group listed the possible sources of funding and chose these possibilities: (1) cash up front, (2) post-event assessments on insurers, (3) post-event assessments on CEA earthquake policyholders, (4) reinsurance, and (5) borrowing in the capital market. Next, each of these possibilities was designated as a block, then the blocks were put into various patterns to decide which one made the most sense. In 1995, the state legislature passed a law, referred to as Assembly Bill 13, authorizing the insurance commissioner to undertake a feasibility study of the CEA proposal. The final block pattern, which was incorporated in this law, is shown in Table 32.7, and totals $10.5 billion in start-up funding. The innovative features of this financing plan are the ability to pay for a large earthquake while committing relatively few dollars up front. At the time of the formation of the CEA, the capital market had never been used to back potential earthquake losses. In the proposed plan, capital markets were given the opportunity to cover the layer of losses from $7 to $8.5 billion. Before the markets had a chance to raise the full amount of capital, Warren Buffet of Berkshire Hathaway offered to cover the layer with his company’s funds, and the insurance commissioner accepted his offer. The excess-of-loss reinsurance © 2003 by CRC Press LLC
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TABLE 32.7 Capacity Participation in the CEA Layer
Source of Funding
Total (in $ billions)
Up to $1 billion $3 billion $2 billion $1 billion $1.5 billion $2 billion
Industry contingent assessment (to start the program) Industry contingent assessment (after the earthquake) Reinsurance (no reinstatement) Policyholder contingent assessment Capital markets Industry contingent assessment (after the earthquake)
1 4 6 7 8.5 10.5
commitment was $2 billion in excess of $4 billion. No reinsurance commitment this large has ever been made. A group of reinsurance brokers was chosen to determine if such a large placement was possible. Presentations were made to reinsurance companies in the United States and Europe. A long list of reinsurers agreed to commit small amounts, which added up to $1.7 billion. The reinsurance that was placed was a 2-year policy with an aggregate limit, a provision that there would be no coverage after the limit had been exceeded, and a provision that the rate would be just under 15% rate on line (that is, 15% of the $1.7 billion, or $255 million, per year). This translates to very expensive reinsurance but was the only choice, because the worldwide reinsurers were already heavily committed to reinsuring the commercial earthquake insurance market in California. The all-residential CEA program would have to be in addition to the reinsurers’ commitment to the commercial earthquake insurance market in California. The $10.5 billion total funding amount assumed that 100% of the current earthquake insurance policyholders would agree to buy coverage insured through the CEA, which would be limited coverage policies with a higher deductible (15% instead of 10%) and additional exclusions. If the CEA had been in business at the time of the Northridge earthquake, the CEA would have had to pay out about $4 billion. Therefore, the $10.5 billion figure was chosen so that the CEA would be able to pay for an earthquake two-and-a-half times the Northridge event.
32.5.2 Japan and the Japan Earthquake Reinsurance Company In Japan, earthquake insurance has only been available since the 1950s. Residential earthquake insurance tends to be regarded as poor value for money and has limited use. This was highlighted following the 1995 Kobe earthquake for which the estimated direct property losses were of the order of $100 billion, of which the insurance industry provided less than $5 billion.10 At the time of the Great Hanshin-Awaji earthquake, only 3% of the residents of Kobe had any form of earthquake insurance. This was due in part to the popular perception that Kobe was a low to moderate earthquake risk. Demand has increased since the 1995 earthquake and, as of 2000, it was estimated that 15% of residents in Japan have earthquake insurance. Residential earthquake insurance is only available as a special extension provided by the fire insurer but reinsured through the Japan Earthquake Reinsurance Company (JER). However, all policies include an earthquake fire expenses insurance (EFEI) extension, which pays an additional 5% of the total sum insured if more than 50% of the dwelling is destroyed by fire following earthquake or volcanic eruption. JER was formed in 1966 and is partly owned by the domestic insurance industry and partly by the government. JER’s sole function is to reinsure the government-sponsored earthquake protection scheme for residential risks. For residential earthquake coverage, an insured may elect to purchase a separate earthquake policy issued by the policyholder’s household insurer covering earthquake shock and fire, volcanic eruption, and tidal wave following earthquake. Under the latest revision of the scheme (January 1, 1996), the
10 Contrast this with Northridge, where total losses were estimated to have been $30 to $40 billion, and insurance payments were approximately $15 billion, or almost 50%.
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TABLE 32.8 Japanese Residential Earthquake Policy Terms Extent of Damage
Paid (%)
Buildings Damage > 50% of sum insured (or 70% of floor area) 20% < damage < 50% of sum insured (or 20% < floor area < 70%) 3% < damage < 20% Contents 80% sum insured < damage 30% < damage < 80% of sum insured 10% < damage < 30%
100 50 5 100 50 5
maximum insurance limits are ¥50 million on buildings and ¥10 million on contents. Within these monetary limits, Table 32.8 indicates the percentages of the actual sum insured that the policy pays. All household policies and most commercial fire policies, except warehouse risks, are automatically extended to include earthquake fire expenses insurance without additional premium. The EFEI extension pays an additional 5% of the sum insured in the event that 50% or more of the property is destroyed by fire following earthquake or volcanic eruption. The maximum EFEI indemnity is limited to ¥3 million with respect to domestic risks and ¥20 million with respect to industrial risks. Residential earthquake risks underwritten by insurance companies are reinsured exclusively with JER and shared with the Japanese government. Under the current arrangement, all residential earthquake business is reinsured 100% with JER, which retrocedes a certain portion of the portfolio back to the direct market. The remainder of the portfolio is guaranteed by the government. The aggregate limit of indemnity payable by all insurers and the government was increased to ¥4100 billion for any one occurrence with effect from March 31, 1999. Claims are scaled down pro rata if the insured losses from any one earthquake exceed the scheme limit.
32.5.3 Turkey and the Turkish Catastrophic Insurance Pool The Turkish Catastrophic Insurance Pool (TCIP) was established by the Turkish government in cooperation with the World Bank, as a result of the 1999 Marmara earthquake. TCIP objectives are to: 1. 2. 3. 4. 5.
Ensure most domestic dwellings have earthquake insurance Reduce government fiscal exposure Transfer most of catastrophe risk to international reinsurance and capital markets Build up TCIP’s capital base over time to insure against larger events Encourage risk mitigation and safer construction practices
In order to accomplish this, in summary, the TCIP program consists of: 1. Compulsory earthquake coverage for all registered residential dwellings and independent business offices in those same buildings 2. A stand-alone product, separate from fire (homeowner’s) insurance but covering fire, explosion, and landslide following earthquake 3. Coverage up to TL 20 billion (approximately $16,000 at year 2002 exchange rates) per dwelling (none for contents). Limits and sums insured valuations are expected to be adjusted annually based on TL inflation rates. Losses are to be settled on the basis of current replacement cost (in TL) at the time of loss, subject to policy limit 4. Coverage in excess of TCIP, obtainable from private insurers 5. Policies distributed by private insurers acting as agents, i.e., assume no risk of loss 6. Elimination of “penny claims” and reduced administrative and reinsurance costs of the pool, a deductible of 2% introduced 7. Online (Web-automated) policy underwriting, in addition to insurers’ own underwriting systems, employed together with a centralized, integrated data management © 2003 by CRC Press LLC
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8. Functions that are completely outsourced to the private sector 9. Independent (hired by TCIP) loss adjusters, used in claim settlement 10. Fifteen rating categories, based on hazard zone (not CRESTA zones) and the type of buildings, as shown in Table 32.9. TABLE 32.9 Turkish Catastrophic Insurance Pool Earthquake Insurance Rates Zone (%) Type of Construction Steel and reinforced concrete buildings Masonry buildings made of stone or brick Other buildings
I
II
III
IV
V
2.00 3.50 5.00
1.40 2.50 3.20
0.75 1.30 1.60
0.50 0.50 0.70
0.40 0.40 0.50
TCIP policy count and exposures were projected for October 2002 to be 2.5 million and total sums insured of $32 million, making it a rival of the California Earthquake Authority to be the largest earthquake insurance company in the world.
32.5.4 New Zealand and the Earthquake Commission In 1941, the New Zealand government set up a special war damages insurance pool funded by a levy of 0.25% of insured value on all fire insurance premiums. The government soon extended the scheme to cover earthquake, establishing the pool as the Earthquake and War Damage Fund. After the war, the levy was reduced to 0.05%. The scheme covered all property for indemnity value and, over time, was extended to other uninsured natural hazards. In 1993, it was restructured as the Earthquake Commission (EQC), and currently offers replacement coverage home insurance up to NZ $100,000 for buildings and $20,000 for contents, at a levy of 0.05% on all fire insurance premiums.
32.6 Alternative Risk Transfer This section discusses the use of earthquake modeling in a typical insurance-linked securitization, or alternative risk transfer (ART). In the second half of the 1990s, a major innovative alternative to traditional reinsurance emerged, which may be generically termed catastrophe securitization. A “cat bond” requires the investor to pay money up front that will be used by the firm if some type of triggering event occurs.11 In exchange for a high return on investment, the investor faces the possibility of losing either interest on the money in trust, or a portion or entire principal investment. The amount paid out to the firm (i.e., the ceding company) depends on how the cat bond is constructed, and this amount is specified in advance of the triggering event. Notably, the firm does not face any credit risk from the cat bond; the money to pay for the losses is already in hand. Initial insurance-linked securitizations were structured to mimic excess-of-loss reinsurance coverages. Thus, incurred monetary losses above an attachment point were paid out by the bondholders, i.e., the payment was indemnity-based. However, due to investor concerns related to moral hazard and data quality issues, the ceding company was required to retain a portion of the risk. So in some circumstances, the PCS industry loss became a more attractive loss trigger, especially if the ceding company did not have detailed policy information, or did not want to publicly disclose its book of business to competitors.
11
The investor’s up-front investment is generally placed in a trust, and paid to the ceding company in the case of a triggering event. This implies that the ceding company is only able to reinvest proceeds from cat bond premiums in liquid securities at approximately the risk-free rate. © 2003 by CRC Press LLC
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32.6.1 Index-Based Cat Bonds Most of the cat bonds issued today are tied to a disaster-severity index (e.g., covering damage from a certain earthquake magnitude event within a specified region) rather than to the firm’s actual losses.12 Because these indexed parameters are normally independent of the firm’s actual losses, payments can be made to the firm immediately after the disaster occurs rather than being subject to the time delay necessary to compute actual losses, as in the case of insurance or reinsurance. Hence, indexed cat bonds reduce the amount of moral hazard in loss estimation. On the other hand, such a cat bond creates basis risk. Basis risk refers to the imperfect correlation between the actual losses suffered by the firm and the payments received from the cat bond. Insurance sold to firms or excess-ofloss reinsurance to insurers has very little basis risk because there is a direct relationship between the loss and the payment delivered by the reinsurance instrument. In May 1999, a parametric-based contract to cover the loss from an earthquake was purchased by Oriental Land, a Japanese company that is best known as the owner and operator of Tokyo Disneyland. This cat bond provides $100 million to the company if an earthquake of a specific magnitude occurs in the vicinity of Tokyo. The Japanese Meteorological Agency determines the measurement of event magnitude. The magnitude that qualifies a given quake for payments to Oriental Land is higher as the location of its epicenter becomes more remote from Tokyo Disneyland. These bonds represent the first direct access of the capital markets by a corporation seeking catastrophe risk financing [Standard and Poors, 2000].
32.6.2 Other Types of Cat Bonds Further variations on nonmonetary loss triggers have also been introduced, including loss triggers based on modeled losses. When an event takes place, the loss to investors is calculated by inputting event parameters into the same model used to perform the risk estimate. (In order to protect the investor, the model is placed in escrow for the duration of the term of the security.) The model then calculates the payout to the issuer. A further variant of nonmonetary triggers has been recently introduced, called second generation parametric triggers, in which the loss trigger is defined by a specific physical parameter, such as peak ground velocity, and measured (or calculated) at a defined series of locations in the vicinity of the insured exposures. In many cases, the physical parameters are available on the Internet within minutes of the event, permitting investors and issuers to quickly determine if a payout is forthcoming. In summary, nonmonetary triggers rely on portions of the loss models to estimate the loss exceedance probabilities, thus creating a simple structure for investors to understand. This also reduces issues of moral hazard and uncertainty in damage and loss payments. Of course, the issuer then retains those risks in the form of basis risk. In conclusion, probabilistic loss models have become essential ingredients in ART earthquake insurance transactions, either for monetary or nonmonetary loss triggers.
32.6.3 Cat Bond Example A California earthquake transaction is used as an example. California represents one of the largest sources of earthquake risk in a reinsurer’s portfolio, and hence alternate risk market sources are appealing. Since 1997, five California earthquake securitizations totaling over $700 million have been placed. In addition, several more multiperil and multiregion deals that included California earthquake have also been completed. A typical transaction involves a reinsurer with excess California earthquake exposures. Such a company wishes to hedge some of that exposure to large events, such as a repeat of the 1906 California earthquake. Because their reinsurance portfolio is likely to derive from a large number of primary insurance com-
12
For more details on the structure of recent cat bonds, see Insurance Services Office [1999].
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Aggregate Probability (%)
0.8
Attachment Amount
0.7 0.6
0.5 Exhaustion Amount
0.4
0.3 21.5
23.5
25.5
27.5
29.5
31.5
Cumulative Insured Losses ($ in billions)
FIGURE 32.10 The aggregate loss exceedance curve for California-insured exposures.
panies with California earthquake exposures, their losses are expected to be highly correlated with reported industry losses. So instead of using their own portfolio, they select an index based on Property Claims Services,13 which regularly reports insured U.S. property losses from catastrophic events. In such a transaction, the ceding company retains the services of a risk-modeling consultant to perform the analysis on the portfolio, in this case earthquake-insured exposures in the State of California. The modeling company compiles an estimate of insurance in force, using data from the California Department of Insurance, California Earthquake Authority, private insurers, tax assessors, and census data. A portfolio of insured properties by zip code is created and input into the loss model. The portfolio defines the type of occupancy, location (zip code), and underlying insurance policy coverages such as deductibles, limits, sublimits, etc. The portfolio is analyzed using a probabilistic earthquake model, and the loss exceedance curve is output from the model. Based on the reinsurer’s desired level of protection and correlation with the industry loss, the reinsurer selects a level of coverage desired. from the curve. The resulting attachment and exhaustion probabilities are determined from the curve, and the expected loss for the layer is derived by integrating the area under the curve between those two points. Figure 32.10 shows the curve from a typical transaction. The expected loss to the layer becomes the base estimate for pricing the security. Moody’s Investor Service [1997] and other rating agencies have developed criteria to rate insurance-linked notes based on comparing model-based loss probabilities with historical credit default and loss. Following a series of stress tests by the rating agencies, the agency determines a bond rating, which then becomes the basis for pricing based on spreads over LIBOR (London Interbank Overnight Rate) for equivalent rated securities.
32.6.4 ART Summary By transforming cat risk into a security and trading it in the global capital markets (Wall Street, London, Tokyo), the total capital that can be accessed is one to two orders of magnitude larger (i.e., U.S. $5 to $50 trillion) [Froot et al., n.d.]. Additionally, cat bonds are relatively uncorrelated with normal stocks and bonds, which makes them attractive to investors. For these reasons, cat bonds have emerged as an increasingly attractive method for reinsuring natural hazards cat risks, such as flood, windstorm, and earthquake. Traditional reinsurers have recognized this, and are ready to assist their clients in the complexities of issuing a cat bond. One of the major complexities is the increased public scrutiny associated
13
Property Claims Services, a division of ISO Services, www.iso.com/AISG/pcs.
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with a publicly traded security. That is, in traditional reinsurance, the contract is of a traditional nature, well understood by both parties, and not normally subject to public scrutiny. In the case of cat bonds, security regulations in the U.S. and other capital markets require substantial disclosure, and investors require attractive rating by agencies such as Moody’s, Standard and Poors, and others, which closely review the details of the cat bond and its underlying analyses. Another form of ART, termed a swap, is available also for nontraditional financial risk transfer. A swap is a contract between two parties, specifying payments under certain conditions. Used for several decades for hedging foreign currency or interest risk, swaps are also now being used to hedge cat risk. Currently most cat risk swaps are private transactions, usually only between insurers.
32.7 Summary The insurance industry is a large, complex endeavor that, for several hundred years, has provided financial protection against common risks such as fire and theft. Insurance has also been an effective tool for loss prevention, via both the market as well as the institution of systematic loss prevention programs by companies such as the Factory Mutual system. Due to a clear understanding of earthquake causes and effects only emerging in the twentieth century, earthquake insurance for much of the century had a much softer foundation than more common forms of insurance, and the question was often asked, “Are earthquakes even an insurable risk?” In this context, Freeman’s little-known, pioneering work, Earthquake Damage and Earthquake Insurance [Freeman, 1932] deserves to be mentioned. In that treatise, Freeman not only collated existing knowledge on earthquakes but also analyzed and provided the basis for earthquake insurance rates for California and other locations, using sound underwriting principles. Today, earthquakes and their effects are better understood, and earthquake insurance is increasingly better founded, available and rationally priced using risk-based underwriting based on earthquake loss modeling. Finally, new techniques such as ART are also emerging, which should increasingly lower the cost of earthquake insurance.
Defining Terms Adverse selection — A situation in which an insured or group of insureds obtain insurance contracts with adverse facts being unknown to the insurer. In earthquake insurance, persons with wellconstructed houses know their houses to be low risk, and therefore are less likely to purchase earthquake insurance, while persons with houses likely to sustain a large loss are more likely to purchase insurance. If the insurer does not diligently determine the specific earthquake-related quality of the houses insured, the resulting portfolio will have a lower quality (higher loss) than that on which the insurance premiums are based, and adverse selection has occurred. ALE — Additional living expenses. Payments made to insureds for expenses associated with loss of use of their normal residence. Alternative risk transfer — New financial mechanism for transferring risk, employed as an alternative to traditional insurance. Examples include swaps and cat bond securitizations. Amortization period — Synonymous with payback period, this term is used in the rating of per occurrence excess coverage and represents the number of years at a given premium level necessary to accumulate total premiums equal to the indemnity. Assume — To accept all or part of a ceding company’s insurance or reinsurance on a risk or exposure. Attachment point — The amount at which excess reinsurance protection becomes operative; the retention under an excess reinsurance contract. Base premium — The ceding company’s premiums (written or earned) to which the reinsurance premium rate is applied to produce the reinsurance premium. Basis risk — The risk associated with the difference between the best estimate of a parameter (e.g., loss in an earthquake) and the actual value of the parameter.
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BI — Business interruption. Payments made to commercial entities for expenses associated with restoring normal operations.
Burning cost — The ratio of actual past reinsured losses to ceding company’s subject matter premium (written or earned) for the same period. Used to analyze past reinsurance experience or to project the future. The matching of all losses incurred within a given 12-month period, usually beginning on January 1, with all premium earned within the same period of time. Capacity — A company that is wholly owned by another organization (generally noninsurance), the main purpose of which is to insure the risks of the parent organization. Catastrophe — A form of excess-of-loss reinsurance that, subject to a specific limit, indemnifies the ceding company against the amount of loss in excess of a specified retention. This loss amount represents the accumulation of losses resulting from a catastrophic event or series of events. To transfer to a reinsurer all or part of the insurance or reinsurance written by a ceding company with the object of reducing the potential liability of the latter. Catastrophe reinsurance — In reinsurance, an allowance (usually a percentage of the reinsurance premium) made by the reinsurer for part or all of a ceding company’s acquisition and other costs. The ceding commission may also include a profit factor. Cede — A written statement issued by an intermediary, broker, or direct writer, indicating that coverage has been effected. Cession — The unit of insurance passed to a reinsurer by the primary company that issued a policy to the original insured. A cession accordingly may be the whole or a portion of single risks, defined policies, or defined divisions of business, as agreed in the reinsurance contract. Commercial lines — Types of insurance offered to larger organizations, such as companies, corporations, municipalities, etc., for protection against fire, theft, business interruption, loss of valuable papers, and other risks. DFA — Dynamic financial analysis. An analysis based on stochastic simulation of financial operations over time. In the insurance context, the premium income, claims paid, investment income, and other cash flows are stochastically simulated over a time horizon to determine risk adjusted return on capital (RAROC), probability of ruin, or other parameters of interest. Earned premium — The portion of a premium which is the property of an insurance company, based on the expired portion of the policy period. Excess-of-loss reinsurance — A generic term describing reinsurance that, subject to a specified limit, indemnifies the ceding company against all or a portion of the amount in excess of a specified retention. Exposure — The state of being subject to the possibility of loss; the extent of risk as measured by various standards such as payroll, gate receipts, and area. Facultative — The reinsurance of part or all of (the insurance provided by) a single policy in which each cession is negotiated separately. The primary company and the reinsurer have the option of accepting or declining each individual submission (as parties agree in treaty reinsurance). Frequency — Number of times an event such as a loss occurs. GIS — Geographic information system. Computer technology permitting relational database analysis of data with a geographic attribute. Commonly used to identify spatial trends, which are presented in mapped or statistical forms. Ground-up loss — The total amount of loss sustained before deductions are applied for reinsurance coverage that inure to the benefit of the cover being considered before the application of a deductible, if any, because that base theoretically reflects changes in exposure. Guaranty fund — A fund supported by assessments against solvent insurance companies to absorb losses of claimants against insolvent insurers. Incurred losses — In insurance accounting, an amount representing the losses paid plus the change (positive or negative) in outstanding loss reserves within a given period of time.
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Indemnity — The compensation owed by the insurer to the insured, per the terms of the insurance contract. Indemnity makes the insured whole but nothing more.
Insurance — Mechanism for contractually shifting burdens of a number of pure risks by pooling them. Law of large numbers — A mathematical concept that postulates that the more times an event is repeated, the more predictable the outcome becomes.
Leveraged effect — The disproportionate result produced by inflation on a reinsurer’s liability in excess of loss reinsurance compared with the ceding company’s liability. Inflationary increase in average claim costs of a reinsured usually produced even greater for its excess of loss reinsurer, because an increase affecting all losses multiplies itself when affecting the excess of loss portion above that retention limit. Liability insurance — Covers damage on behalf of an insured who becomes legally obligated to pay because of an actual or alleged negligent act and omissions. LIBOR — London Interbank Overnight Rate. A standard interest rate used in the financial industry. Line — Either the limit of insurance to be written which a company has fixed for itself on a class of risk (line limit), or the actual amount that it has accepted on single risk or other unit. Lines of business — Five primary sectors of insurance: life, health, annuity, property, and liability. Loss exceedance curve — A graph depicting the probability of exceeding a specified level of loss. Loss ratio — Losses incurred expressed as a percentage of earned premiums. Loss reserve — For an individual loss, an estimate of the amount the insurer expects to pay for the reported claim. For total losses, estimates of expected payments for reported and unreported claims. May include amounts of loss adjustment expenses. Loss reserve transfer — A type of reinsurance treaty through which companies can exchange certain types of liabilities. Also known as loss portfolio transfer. MFO — Most favored option. The option that appears most satisfactory, considering all aspects. Net loss — The amount of loss sustained by an insurer after making deductions for all recoveries, salvage, and all claims upon reinsurers with specifics of the definition derived from the reinsurance agreement. Such net loss may or may not include claim expenses. As provided in the reinsurance agreement, net loss can be confined to the amount paid by the reinsured within applicable policy damages in excess of applicable policy limits because of failure of the reinsured to settle within applicable policy limits. Net retention — The amount of insurance that an insurer keeps for its own account and does not reinsure in any way. Nonproportional reinsurance — Reinsurance under which the reinsurer’s participation in a loss depends on the size of the loss. Also known as excess-of-loss reinsurance. Occurrence — An event that results in an insured loss. In some lines of insurance, such as liability, it is distinguished from an accident in that the loss does not have to be sudden and fortuitous. It can result from continuous or repeated exposure. Parametric trigger — Catastrophe securitization in which payments are triggered by the occurrence of a parameter (e.g., of a specified magnitude event within a specified region), and not the ensuing monetary loss. Penetration — Also known as the buy rate, market penetration is defined as the percentage of insured vs. the maximum number of possible insured. Personal lines — Types of insurance (homeowners, auto) sold to individuals to protect their personal property. Pool — Any joint underwriting operation of insurance or reinsurance in which the participants assume a predetermined and fixed interest in all business written. Pools are often independently managed by professionals with expertise in the classes of business undertaken, and the members share equally in the premiums, losses, expenses, and profits. An association and a syndicate (excluding that of Lloyd’s of London) are both synonymous with a pool, and the basic principles of operation are much the same. © 2003 by CRC Press LLC
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Portfolio — A defined body of insurance policies in force. Premium — The monetary consideration in contracts of insurance and reinsurance. Primary — An adjective applied in reinsurance to these nouns: insurer, insured, policy, and insurance, referring to the parties involved in the initial insurance transaction with the property owner.
pdf — Probability density function. PML — Variously defined but usually intended to indicate an estimate of maximum loss which can be sustained under realistic situations.
Pure premium — That part of the premium that is sufficient to pay losses and loss adjustment expenses but not including other expenses.
Pure risk — Situation involving a chance of a loss or no loss but no chance of gain. For example, either one’s home burns, or it does not; this risk is insurable. Pure risk is also synonymous with pure premium. RAROC — Risk adjusted return on capital. The present value of capital, taking into account the stochastic character of risks to that capital, commonly determined via a dynamic financial analysis. Rate — The percentage or factor applied to the ceding company’s base premium to produce the reinsurance premium, or the percentage applied to the reinsurer’s premium to produce the commission payable to the primary company (or, if applicable, the reinsurance intermediary). Reinsurance — The transaction whereby the reinsurer, for a consideration, agrees to indemnify the ceding company against all or part of the loss that the latter may sustain under the policy or policies it has issued. Reinsurer — An organization that assumes the liability of another by way of reinsurance. Retention — The amount that an insurer assumes for its own account. In pro rata contracts, the retention may be a percentage of the policy limit. In excess-of-loss contracts, the retention is a dollar amount of loss. Retrocession — The transaction whereby a reinsurer cedes to another reinsurer all or part of the reinsurance it has previously assumed. Risk — The chance of loss. Also used to refer to the insured or to property covered by a policy. In reinsurance, each company makes its own rules for defining units of hazard or single risks. Ruin — Lack of solvency (i.e., bankruptcy), where liabilities exceed assets and ability to honor liabilities cannot be achieved. Securitization — The creation of a security, such as a bond. The security is issued in the capital markets, as a promise to pay a series of payments against the loss of principal and interest to the bondholder if a specified indemnity-based loss or parametric trigger occurs. Severity — Size of the loss used as a factor in calculating insurance premium. Surplus to policyholders — The net worth of an insurer as reported in its annual statement. For a stock insurer, the sum of its unassigned surplus and capital. Surplus-share reinsurance — A form of pro rata reinsurance indemnifying the ceding company against loss for the surplus liability ceded. Essentially, this can be viewed as a variable quota share contract wherein the reinsurer’s pro rata share of insurance on individual risks will increase as the amount of insurance increases in order that the primary company can limit its new exposure regardless of the amount of insurance written. Syndicate — A group of insurers or underwriters who join to insure property that presents high values or high hazards. Also see Pool. Time element — Refers to insurance coverage for additional living expense or business interruption. TIV — Total insured value. Treaty — A reinsurance agreement between the ceding company and the reinsurer, usually for one year or longer, which stipulates the technical particulars applicable to the reinsurance of some class or classes of business. Treaty reinsurance — A standing agreement between reinsured and reinsurer for the cession and assumption of certain risks as defined in the treaty. © 2003 by CRC Press LLC
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Underwriting capacity — The maximum amount of money an insurer or reinsurer is willing to risk in a single loss event on a single risk or in a given period. The limit of capacity for an insurer or reinsurer may also be imposed by law or regulatory authority. Unearned premium reserve — The sum of all the premiums representing the unexpired portions of the policies or contracts that the insurer or reinsurer has on its books as of a certain date. It is usually based on a formula of averages of issue dates and the length of term. Write — To insure, to underwrite, or to accept an application for insurance.
References BestWeek. 1996. “Earthquakes: A Major Paradigm Shift for P/C Insurers,” BestWeek: Property Casualty Supplement, P/C 1–18, March 25. Camerer, C. and Kunreuther, H. 1989. “Decision Processes for Low Probability Events: Policy Implications,” J. Policy Anal. Manage., 8, 565–592. Carpenter, G. 2001. The World Catastrophe Reinsurance Market, published by Guy Carpenter, New York. Report available on the Internet at http://www.guycarpenter.com/publications/pubmn.html. CDI (California Department of Insurance). 2001. California Earthquake Liability Questionnaire, California Administrative Code Title 10, Chapter 5, Subchapter 3, Article 3, Section 2307 General Instructions (Revised 10/2001), California Department of Insurance. http://www.insurance.ca.gov/ RRD/RSU/Forms/Year2001/PML2001/pml2001.htm. EQC (Earthquake Commission). 1998. Annual Report 1997–98, Earthquake Commission, Wellington, New Zealand. Freeman, J.H. 1932. Earthquake Damage and Earthquake Insurance, McGraw-Hill, New York. Froot, K. et al. n.d. The Evolving Market for Catastrophic Event Risk, Guy Carpenter, New York, www.guycarp.com. Heubner, S.S. and Black, K. 1995. Property and Liability Insurance, Prentice-Hall, New York. Hirschberg, J.C., Gordon, P., and Petak, W. J. 1978. Natural Hazards: Socio-Economic Impact Assessment Model, NSF/PRA-7509998/5, J.H. Wiggins and Co., Redondo Beach, CA. Insurance Information Institute. 2002. Available on the Internet at http://www.financialservicesfacts.org/ financial/insurance/overview/natureandsize. Insurance Research Council and Insurance Institute of Property Loss Reduction. 1995. Coastal Exposure and Community Protection: Hurricane Andrew’s Legacy, IRC, Wheaton, IL and IIPLR, Boston. Insurance Services Office. 1999. Financing Catastrophe Risk: Capital Market Solutions, Insurance Services Office, New York. King, S. and Kiremidjian, A. 1997. “Use of GIS for Earthquake Hazard and Loss Estimation,” in Geographic Information Research: Bridging the Atlantic, Taylor & Francis, London. Kunreuther, H. 1996. “Mitigating Disaster Losses through Insurance,” J. Risk Uncertainty, 12, 171–187. Kunreuther, H. and Roth, R.J., Eds. 1998. Paying the Price: The Status and Role of Insurance against Earthquakes in the U.S., Joseph Henry Press, Washington, D.C. Kunreuther, H. et al. 1978. Disaster Insurance Protection: Public Policy Lessons, John Wiley & Sons, New York. Kunreuther, H., Hogarth, R., Meszaros, J., and Spranca, M. 1995. “Ambiguity and Underwriter Decision Processes,” J. Economic Behav. Organ., 26, 337–352. Lecomte, G. and Gahagan, K. 1998. “Hurricane Insurance Protection in Florida,” in Paying the Price: The Status and Role of Insurance Against Earthquakes in the U.S., Kunreuther, H. and Roth, R., Eds., Joseph Henry Press, Washington, D.C., chap. 5. Long, J.D. and Gregg, D.W. 1965. Property and Liability Insurance Handbook, Dow Jones-Irwin, Homewood, IL. Moody’s Investor Service. 1997. Approach to the Rating of Earthquake-Linked Notes, September 1997, Moody’s Investor Service, New York.
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Palm, R. 1995. Earthquake Insurance: A Longitudinal Study of California Homeowners, Westview Press, Boulder, CO. Petak, W.J. and Atkinsson, A.A. 1982. Natural Hazard Risk Assessment and Public Policy: Expecting the Unexpected, Springer-Verlag, New York. Roth, R.J. Jr. and Van, T.Q. 1998. California Earthquake Zoning and Probable Maximum Loss Evaluation Program: An Analysis of Potential Insured Earthquake Losses from Questionnaires Submitted by Property/Casualty Insurers in California, per California Administrative Code, Title 10, Chapter 5, Subchapter 3, Section 2307. California Department of Insurance, Los Angeles. Scawthorn, C. 1981. “Urban Seismic Risk: Analysis and Mitigation,” Ph.D. dissertation, Kyoto University, Kyoto, Japan. Scawthorn, C. 1995. “Insurance Estimation: Performance in the Northridge Earthquake,” Contingencies, the magazine of the American Institute of Actuaries, Washington, D.C. Scawthorn, C. 2001. “National Programs for Natural Hazards Insurance,” First Annual IIASA-DPRI Meeting, Integrated Disaster Risk Management: Reducing Socioeconomic Vulnerability, International Institute for Advanced Systems Analysis, Laxenburg, Austria. SEAOC (Structural Engineers Association of California), Seismology Committee. 1999. Recommended Lateral Force Requirements and Commentary, Sacramento, CA. Standard and Poors. 2000. Sector Report: Securitization, June. Steinbrugge, K.V. 1982. Earthquakes, Volanoes and Tsunamis: An Anatomy of Hazards, Skandia America Group, New York. Steinbrugge, K.V. and Roth, R.J., Jr. 1994. Dwelling and Mobile Home Monetary Losses Due to the 1989 Loma Prieta, California, Earthquake with an Emphasis on Loss Estimation, U.S. Geological Survey Bulletin 1939-B. Stone, J. 1973. “A Theory of Capacity and the Insurance of Earthquake Risks, I and II,” J. Risk Insur., 40, 231–243 (Part I) and 40, 339–355 (Part II). Walker, G.R. 2000. Earthquake Engineering and Insurance: Past, Present and Future, Aon Re Australia, available on the Internet at http://www.aon.com.au/reinsurance/knowledge/quake_engineering.asp Weinstein, N., Ed. 1987. Taking Care: Understanding and Encouraging Self-Protective Behavior, Cambridge University Press, New York. Wiggins, J.H., 1981. “Earthquake Hazard and Risk Mitigation,” J.H. Wiggins Company, Report No. 80-1371-1, Redondo Beach, CA.
Further Reading The pioneering work by Freeman [1932] still offers much of value. Several standard references on insurance in general, such as Long and Gregg [1965] or Heubner and Black [1995], provide more detail on insurance contracts, underwriting, and related matters. Steinbrugge [1982] is a good overview of the California PML methodology and earthquake insurance prior to the innovations of probabilistic earthquake loss modeling. Paying the Price [Kunreuther and Roth, 1998] provides an excellent overview of the current status of natural hazards insurance.
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33 Emergency Planning 33.1 Introduction 33.2 Planning for Emergencies Deciding to Plan for Emergencies · Who Will Plan for Emergencies: The Team · Determining the Current Status · Approaches to Planning for Emergencies · Purpose of the Emergency Plan: The Mission · Mission-Critical Functions
33.3 Writing the Emergency Plan Outlining the Emergency Plan · Front Matter and Introduction · Situation and Assumptions · Concept of Operations · Declaring a State of Emergency · Emergency Management · Communications · Plan Maintenance and Training · References · Key Information · Facility Annexes · Hazard Annexes · Other Annexes
33.4 The Emergency Operations Center (EOC) 33.5 Training and Maintenance of the Emergency Plan Training · Maintenance
Charles Scawthorn Consulting Engineer Berkeley, CA
33.6 Summary: Developing an Emergency Plan Defining Terms References Further Reading Appendix A Appendix B
The plan is nothing. Planning is everything. —Dwight David Eisenhower
33.1 Introduction Earthquakes cannot be prevented, but the previous chapters have demonstrated that the potential for damage can be reduced or mitigated by strengthening of structures, bracing of equipment, and other measures. It is usually very difficult to eliminate the potential for all damage, so that some potential residual damage will always exist. Therefore, an organization should always have a plan for responding to some degree of damage and negative impacts due to an earthquake. Earthquake-specific plans are part of an organization’s overall emergency plan. Most emergency plans have a far wider scope than earthquakes — they also address fires, explosions, transportation accidents, etc. In this chapter, we discuss the development and content of a general emergency plan, with occasional comments specific to earthquakes. Note that both public (whether a city government, water department, school district, etc.) and private
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entities should have an emergency plan, although these plans generally differ in some significant ways, such as: • A private entity’s emergency plan is normally more narrowly focused on getting the business up and running. • A governmental emergency plan normally has varying degrees of police powers, i.e., the ability to force people to do things. Because there are many parallels between public and private emergency plans, this chapter treats public and private entities together, referring in the broad sense to both entities as the organization, with occasional distinctions being made when appropriate. Furthermore, the discussion in this chapter does not attempt to address emergency planning for very large organizations, such as a multinational corporation or the federal government, or very small entities, such as a “mom-and-pop” store. Rather, this chapter is written with a mid-sized corporation or governmental agency in mind, such as an organization with several hundred to several thousand employees. An emergency is any event, usually sudden and without much, if any, warning, that can cause deaths or significant injuries to employees, customers, or the public; or that can shut down an organization’s functions or business, disrupt operations, cause physical or environmental damage, threaten its financial standing or public image; or have other unwanted outcomes. Examples include any of the following, when they cannot be satisfactorily resolved by standard operating procedures (SOPs). • Natural hazards: Earthquake, wildland fire, flood or flash flood, hurricane, tornado, winter storm, etc. • Technological hazards: Explosion, fire, hazardous materials incident, communications failure, data loss, transportation accident, radiological accident, loss of key supplier or customer, etc. • Man-made hazards: Product tampering, cyber attack, bombing, theft, sabotage, kidnapping, assault, civil disturbance, industrial espionage, etc. Emergency planning is a relatively young field, having generally developed in the 1960s and 1970s out of the post-war civil defense function [DRC, n.d.], with many organizations not developing formal emergency plans until the 1980s or even 1990s. Terminology in the field is relatively elastic, with the term emergency plan being variously synonymous with disaster plan, emergency operations plan, emergency response plan, emergency preparedness plan, emergency recovery plan, business continuity plan, contingency planning, etc. Each of these terms is used to narrowly distinguish plans with specific goals or that specifically exclude certain aspects of a broader emergency plan. According to the Federal Emergency Management Agency [FEMA, 1996], while it depends to some extent on the organization and the situation, most emergency plans will be a document that: • Strives to maintain continuity of functions that are fundamental to the organization’s reason for being, through the duration of the emergency. • Assigns responsibility to organizations and individuals for carrying out specific actions at projected times and places in an emergency that exceeds the capability or routine responsibility of any one department or agency. • Sets forth lines of authority and organizational relationships, and shows how all actions will be coordinated. • Describes how people and property will be protected in emergencies and disasters. • Identifies personnel, equipment, facilities, supplies, and other resources available, within the organization or by agreement with other organizations, for use during response and recovery operations. • Identifies steps to address mitigation concerns during response and recovery activities. If the emergency plan is a public document, it also cites its legal basis, objectives, and assumptions. An emergency plan is not any of the following: © 2003 by CRC Press LLC
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• Safety plan: A plan by which normal day-to-day operations are performed safely, and consists of SOPs developed to allow safe operations, safety training, monitoring of accidents, etc. • Business plan: A plan by which a company operates under normal circumstances, defines the company’s mission, organization, products, strategy, finances, and operations under normal conditions. • Administrative plan: A plan that describes policies and procedures basic to the support of a governmental endeavor, analogous to a private firm’s business plan. • Mitigation plan: More typical of governmental agencies than of private sector companies, these typically consist of a policy statement and a series of steps designed to reduce a hazard’s damage potential. For example, a mitigation plan might consist of the decision to seismically retrofit a set number of buildings each year. • Preparedness plan: This plan covers maintaining existing emergency management capability in readiness, preventing emergency management capabilities from themselves falling victim to emergencies, and, if possible, augmenting the organization’s emergency management capability. • Recovery plan: This plan describes the process, responsibilities, resources, and other requirements for recovering from a disaster. Additionally, an emergency plan is not a collection of procedures [FEMA, 1996]. The basic criterion for what is in the plan is: What does the entire audience of the emergency plan need to know or have set out as a matter of public record? Information and “how-to” instructions needed only by an individual or smaller group can be left to SOPs, which may be annexed to the emergency plan or referenced as appropriate. Emergency management is the process of preparing for, mitigating, responding to, and recovering from an emergency. Emergency management is a dynamic process. Planning, though critical, is not the only component [FEMA, n.d.]. Training, conducting drills, testing equipment, and coordinating activities with the community are other important aspects of emergency management, which we will discuss next.
33.2 Planning for Emergencies Emergency planning consists of the development of the plan. Actually, emergency planning begins with getting the organization to decide to plan for emergencies, i.e., prior to the actual development of an emergency plan, there may be a need to convince an organization’s management that it needs an emergency plan.
33.2.1 Deciding to Plan for Emergencies For governmental agencies, this preliminary step is becoming less of a problem, in that agencies are increasingly being required legally or administratively to have an emergency plan. To some extent, private companies are being required also to have an emergency plan, although this is not yet a common occurrence, except in certain industries. To be successful, an emergency plan requires the support of upper management. If it is necessary to present a “case” for developing an emergency plan, focusing on the positive aspects will be more likely to lead to management support. Reasons for developing an emergency plan include (we focus here on earthquake): • Earthquakes are no longer “acts of God.” Their cause and likelihood in a general sense are well understood, and public and legal expectations are that a prudent person will take some reasonable precautions against an earthquake. If peer organizations have an earthquake emergency plan, your organization is remiss (and potentially liable) if it does not have one. • The public sees a key function of government as protecting them against or helping them recover from sudden, unforeseen disasters such as earthquakes. For governmental agencies, the public © 2003 by CRC Press LLC
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• •
• • •
expects elected leaders to take immediate appropriate action to deal with the problem. The government is expected to marshal its resources, channel the efforts of voluntary agencies and private enterprise in the community, and solicit assistance from outside of the jurisdiction, if necessary [FEMA, 1996]. Similarly, private companies have a moral responsibility to protect employees, the community, and the environment from processes and facilities within their purview. Whether a public or private organization, emergency response actions cannot be developed and properly executed in the confusion and stress immediately following an earthquake. To be effective, they must be planned, well thought out, and coordinated; responsibilities must be assigned; there must be adequate resources provided, and training to implement them. For industries such as banking, chemical, and nuclear, there are regulatory requirements of federal, state, and local agencies. An emergency plan enhances an organization’s ability to recover from financial losses, regulatory fines, loss of market share, damage to equipment or products, and business interruption [FEMA, n.d.]. An emergency plan reduces exposure to civil or criminal liability in the event of an incident. A good earthquake emergency plan enhances an organization’s image and credibility with employees, customers, suppliers, and the community. An earthquake emergency plan can reduce insurance premiums.
Each of these arguments carries different weight, depending on the organization and the audience. One or several of them will often make a sufficiently compelling case to at least begin determining the organization’s current status with regard to having an emergency plan.
33.2.2 Who Will Plan for Emergencies: The Team Once a decision has been made to develop an emergency plan, the next step is to form an emergency planning team. The team will consist of a core team and ancillary members. It is important to have senior management support for the planning effort and this should be achieved by having a member of senior management chair or sponsor the core team. The organization’s chief executive officer (CEO), having made the decision to develop an emergency plan, must set the tone by authorizing planning and directing senior management to become involved. Identification of members of the core planning team is specific to each organization and also to the personalities of the people involved. Some are better attuned to the creative aspects of the planning process, and can be used in the initial research, in brainstorming sessions, and thereafter as reviewers. Others are better with organizational issues, and can perhaps bear the brunt of managing and performing the plan drafting, scheduling, and budgeting tasks. This personality aspect must be considered in forming the core team. Core team members can be drawn from departments or branches of the organization having missioncritical functions (see Section 33.2.6). The core team can consist of: • Emergency planning sponsor: This is a member of senior management, reporting directly to the CEO, who lends knowledge and authority to the emergency planning effort. The sponsor does not make a major time commitment to the actual planning effort. Rather, the sponsor attends (most likely, chairs) key meetings of the core team, resolves questions, and assures that the core team has the cooperation of all groups in the organization and that it has the necessary resources to develop the plan. In a broad sense, the sponsor monitors progress and schedule, and is responsible to the CEO for the successful completion of the emergency plan, on schedule and within budget. • Emergency planning manager: This is the member of management who actually leads the development of the emergency plan, reporting to the CEO through the sponsor. The manager has sufficient knowledge of the organization and of general planning efforts for development of the emergency plan. The manager makes a significant time commitment and is quite involved in the © 2003 by CRC Press LLC
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TABLE 33.1 Example Core Team Composition
Team Member/Function Sponsor Emergency planning manager Knows inputs Knows process Knows output/delivery Knows facilities Risk manager Other/ancillary members
a b
Water Department
School District
ABC Widget Manufacturing Company
Deputy department manager Operations manager Transmission managera Treatment plant managera Distribution managera Maintenance managera Risk manager Billing managera Water quality managera Eng. managera Personnel/HR managera Data/IT managera
Deputy district director Safety manager Transp. managera Instructional managera Nutrition managera Facilities managera Risk manager Personnel/HR managera Special education managera Data/IT managera School vice principalb PTA representative
Vice president Facilities manager Purchasing managera Operations managera Sales managera Maintenance managera Risk manager Data/IT managera Eng. managera Personnel/HR managera Billing managera Accounting managera
Most likely, a deputy or a member of the department. One from each school.
actual planning effort. Except for very large organizations, the development of the emergency plan is not a full-time effort, and the manager’s time commitment typically will range from 10 to 25% during development. The manager attends all meetings of the core team, chairing them in the sponsor’s absence, monitors and directs plan content, resolves questions, directs resources, and monitors progress and schedule. Through the sponsor, the manager is responsible for the successful completion of the emergency plan, on schedule and within budget. Candidates for emergency planning manager can be the managers of operations, safety, facilities, or planning. • Other members of the core team usually include managers or their deputies drawn typically from the following key functions: operations, facilities, engineering, planning, human resources, and finance. Table 33.1 shows hypothetical examples of core team composition for a water department, a school district, and a private manufacturing company. The organization’s legal counsel can be a resource but not necessarily a member of the planning team. In some organizations, the role of emergency plan manager is outsourced to a consultant; however, this is not recommended because the consultant probably will not be available during an emergency. Consultants may be used as members of the core team (facilitators) because they bring experience and expertise to the planning process. Note that a natural development is for the core team to evolve into the emergency management team, with the emergency planning manager becoming the organization’s emergency manager. However, it should be recognized, and reflected in the emergency plan, that the CEO makes all final, critical decisions for the emergency management team in a real emergency. This is discussed in Section 33.3.4.
33.2.3 Determining the Current Status Prior to developing an emergency plan, a key step is determining the organization’s current status with regard to emergency preparedness and planning. Researching the current status must be the initial task for the core team. With regard to earthquakes, this research can involve several steps. 33.2.3.1 Current Earthquake Risk Even a cursory examination by a lay person of an organization’s locations and structures can be very revealing. Are any of the buildings in “earthquake country”? Reference to a U.S. Geological Survey (USGS) or a state geological survey can quickly determine whether the organization has a degree of earthquake risk. For example, Figure 33.1 shows a map of the United States with peak ground acceleration (PGA)
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values with 10% probability of exceedance in 50 years. If an organization’s facilities lie within areas with PGA values of 3% of g or greater, then there is at least some degree of earthquake risk. Ground shaking is one aspect of earthquake risk; another is the vulnerability of an organization’s buildings and equipment. These aspects are covered in detail in other chapters in this volume but a ready reference with ample illustrative photographs on the degree of seismic vulnerability for various kinds of buildings is FEMA 154 [2002]. 33.2.3.2 Current Plans, Documents, and Requirements Does any part of the organization have other plans, such as safety plans, fire and evacuation plans, security procedures, or insurance loss prevention reports, which may be useful to an emergency plan? Another issue is whether an emergency plan is required for the organization. If so, the specific requirements can be determined early in the planning process, so that the resulting emergency plan satisfies those requirements. 33.2.3.3 Insurance After life safety, an important goal of any emergency plan is to reduce the potential economic loss. Insurance is another method of protecting against potential economic loss. Determining the degree to which an organization’s insurance coverage protects it against potential economic loss indicates the urgency for an emergency plan. In the case of earthquakes, obtaining adequate insurance coverage is not always possible, and typically is expensive in high seismic hazard regions. Thus, it may be that the organization has little or no insurance for potential economic losses due to earthquake, in which case the need for an emergency plan is further validated. The more sophisticated insurance companies and brokers have extensive experience with earthquake risk and emergency planning, and may be able to assist the organization in its efforts.
33.2.4 Approaches to Planning for Emergencies There are several approaches to developing an emergency plan, which may be characterized as either “top-down” or “bottom-up.” Both methods begin by identifying the critical functions of the organization. Top-down is an approach derived from and more often employed by operations, management, or business-oriented planners concerned with business continuity in a private enterprise. The basic approach is to diagram the organization into business units and functions, and to ask what happens if one of these units is lost? The approach does not normally focus on why or how the unit is lost, nor on loss of multiple units simultaneously. Rather, it focuses on how vital the function performed by the unit is, and the consequences associated with the loss of the unit. The typical outcome of the top-down approach is an identification of an organization’s critically important units, a decision by management to protect against loss of these units, and implementation of measures responsive to that decision, e.g., developing redundant capability for the unit. Bottom-up is an approach derived from the natural hazards arena, and more often employed by technically oriented planners. The basic approach is to examine the universe of possible emergencies and to ask what happens if any of them occurs. The approach does not normally focus on units but on the likely physical effects of the causative agent, which much more often result in partial or temporary rather than total loss of a unit or function. The typical outcome of the bottom-up approach is an identification of critically important units, a decision by management to protect against loss of these units, and measures responsive to that decision. The measures derived from a bottom-up approach range from developing redundant capability for an entire unit to reducing the likelihood of loss of the unit, e.g., strengthening a building against earthquake. The top-down approach is more appealing to senior management, because their role is often continual examination of the value a unit brings to the organization. The bottom-up approach is more physically based, more intuitive for most people, and considers correlation of loss between units.
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Nov. 1996
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FIGURE 33.1 Map of peak ground acceleration (PGA) with 10% probability of exceedance in 50 years. (From U.S. Geological Survey, available online at http://geohazards.cr.usgs.gov/eq/hazmaps/usmap1r.gif.)
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33.2.5 Purpose of the Emergency Plan: The Mission Irrespective of the approach taken, a key issue for emergency planning is identifying the key functions the organization needs to maintain despite the emergency. Key functions derive from the organization’s mission. The mission is the organization’s reason for being. For example, the education of students is the mission of a school district; the delivery of good quality water in volume is the mission of a water district; and the making of profit via the manufacture of widgets is the mission of the ABC Widget Manufacturing Company. Mission statements are often somewhat more embroidered than these examples; usually the embroidery introduces additional values which should more properly be reserved for the organization’s value statement, rather than its mission statement. Recognition and continual reexamination of an organization’s mission is vital to its success.1 Most organizations believe they understand their mission. However, a mission all organizations have, which is often unstated (due to its being assumed), is the health and safety of employees and the public. This becomes a vitally important aspect of the organization’s mission in an emergency. Within each organization, there are subgroups, each of which has one or more functions supportive of the organization’s overall mission. For example, the mission of the water department is the delivery of good quality water in volume. Within that department, there is a water treatment plant whose function is the processing of raw water and production of good quality water but not the conveyance of that water. Conveyance of the water is the function of the transmission and distribution departments. Within the water treatment plant, there are various functions supportive of the function of the plant, such as the water quality laboratory, which assures water quality by monitoring and testing.2 Some of these functions are mission-critical, i.e., the organization’s mission fails if that function is not performed. Thus, a key step in developing an emergency plan is identifying the mission-critical functions, which must be maintained despite the emergency. Identification of these mission-critical functions follows from the organization’s mission statement and a high-level schematic of the organization’s processes. Using a water department as an example, mission-critical functions can include: • • • •
Continual supply of water from a source (e.g., the reservoir, groundwater wells) Transmission of the water to the water treatment plant Treatment of the water at the water treatment plant Distribution of the water from the water treatment plant to the customers
Note that mission-critical functions do not have to maintain their normal productivity during the emergency period; some reduction in water quality and quantity may be acceptable. Note also that other functions within the water department, such as payroll, maintenance, billing, and accounting, may be temporarily deferred during the emergency period (i.e., they are not mission-critical), and those human and other resources (e.g., vehicles, space) may be employed with other duties during the emergency period. For example, human resources peronnel can assist in recalling off-duty staff to deal with the emergency and assist overburdened staff in coping with stress, and public relations personnel can assure proper dissemination of urgent messages to the public, such as a “boil water” order. In summary, the purpose of the emergency plan is to assure continued fulfillment of the organization’s mission despite the emergency. A necessary step in developing an emergency plan is therefore to employ the organization’s mission statement for defining the purpose of the emergency plan. Successful 1
Consider, for example, the great railroad companies of the early twentieth century, who thought their mission was to move people and goods by rail. In fact, their mission was to provide transportation, and when the airplane emerged as a viable transportation mode, the railroad companies did not understand that it was simply a technological development supportive of their mission. Rather, they thought aviation was a “different business.” 2 Clearly, one can argue that mission and function as defined here are interchangeable. However, there is a distinction: the mission is the reason for being of the organization, and should be accomplished whether various functions are performed or not. © 2003 by CRC Press LLC
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fulfillment of the organization’s mission requires assuring performance of mission-critical functions. A next necessary step is therefore to identify mission-critical functions.
33.2.6 Mission-Critical Functions Identification of mission-critical functions is a complex process, requiring detailed knowledge of the organization, its normal operations, its inputs, and the needs of those the organization serves. The process is usually iterative, in that the operations of the organization are reviewed by the core team, and a preliminary list of mission-critical functions is identified, based on assumptions as to what emergencies can occur and what constitutes acceptable response to those emergencies. In the process of compiling this list, it is necessary to employ the expertise of various members of the organization, some of whom may become members of the core emergency planning team. As noted previously, a vitally important aspect of the organization’s mission in an emergency is the health and safety of its employees and the public. Thus, certain mission-critical functions, which may exist only in an emergency and often must be accomplished with the highest priority, are: • • • •
Communicating with and ascertaining the condition of all employees Communicating with and ascertaining the condition of key facilities Assuring the safe shut-down or operation (if needed) of hazardous processes Assuring the safe storage or handling of hazardous materials
The preliminary list of mission-critical functions can be reviewed with stakeholders and persons and organizations who are affected by the organization’s performance, including management, parent organizations, employees, customers, suppliers, regulators, and representatives of the public. Using a water department as an example, stakeholders can include senior department management, the mayor and relevant council members, employees’ unions, business customers (e.g., a brewery or process industry), the fire department and local hospitals (customers), the water wholesaler (e.g., U.S. Bureau of Reclamation), the state health board, the U.S. Environmental Protection Agency, and neighborhood associations. Consultation of stakeholders, especially for public agencies, is a very important issue. Stakeholders are not members of the core team, and most do not have a decision role in the formulation of the emergency plan; more typically, they are a source of data for the core team. However, because they are stakeholders, their participation must be carefully and respectfully solicited, and it must be recognized that they may have expectations as to feedback they will receive for their participation. Consultation of stakeholders can be accomplished via one-on-one interviews or in one or more workshops. Either method requires careful preparation and good communication. Development and careful framing of questions for the interview or workshop is necessary and can be tested prior to actual use. Testing of interview questions can be done via role-playing within the core team, or by conducting an interview with a person supportive of the emergency planning effort. For actual interviews, the interviewer must be carefully selected so as to have good communication and people skills. For a workshop, a trained facilitator is recommended. Taking the water department as an example again, an initial, mission-critical function the core team identifies is that some water volume and pressure (regardless of quality) must be supplied to a particular district because that district contains a large factory. The water is required for fire protection of the factory and surrounding properties. Interviews with the fire department and factory manager may indicate: • The fire department has identified adequate alternative water supplies (e.g., a nearby pond) • The factory has its own auxiliary water supply, equipment, and personnel for fighting fires (e.g., the pond, pumps, an in-house fire brigade, etc.) Therefore, that mission-critical function can be eliminated for that district. Review of the preliminary list in light of stakeholder input will result in amendment of the list and dimensions of mission-critical functions. The process may take several rounds until a reasonably complete set of mission-critical functions can be identified. © 2003 by CRC Press LLC
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33.2.6.1 Accomplishing Mission-Critical Functions Having identified mission-critical functions, the next step is identifying how they will be accomplished under emergency conditions. Clearly, this depends on the emergency. Most of the time, some planning assumptions, based on emergency scenarios, must be introduced at this point in the planning process. It is not realistic and neither can an organization afford to plan for accomplishing its mission-critical functions during an earthquake in which everything is destroyed, people are killed, no transportation is possible, etc. Some assumptions have to be made that certain facilities are likely to be partially functional, some communications will be possible, etc. These assumptions in the context of emergency planning for earthquakes must be based on reasonable, conservative analyses and assumptions as to the magnitude and location of the earthquake, its intensity at various points, the vulnerability of facilities, etc. Other chapters in this volume provide background, data, and references on these aspects. For earthquake-related emergency planning, the planning process takes a bottom-up approach. In this approach, earthquake impacts on facilities, people, and processes are estimated, allowing for some “negative coincidences” (in the example of a water department, both water treatment plants 1 and 2 are damaged) in order to develop one or more earthquake planning scenarios. These scenarios describe the impacts on mission-critical functions and resources that can be employed to respond to these impacts. The planning process then proceeds to identify alternative ways to restore or accomplish the missioncritical functions, taking into account post-earthquake conditions. A key aspect of the planning process is to carefully examine mission-critical functions to assure that their restoration or alternative accomplishment does not solely depend on one facility, person, or process, i.e., there are no single points of failure. To that extent, the emergency plan must identify backup measures for restoring or alternatively accomplishing the mission-critical functions. In the event that a missioncritical function cannot be assured of restoration or alternative accomplishment, the core team must communicate to the CEO that the emergency plan cannot assure the organization’s mission in an emergency. The CEO then must resolve the issue as to whether to commit more resources to assuring the organization’s mission in an emergency, or to relax the organization’s commitment to the performance of its mission under emergency conditions. Using the water department as an example again, it may be prohibitively expensive to assure potable water service to a district immediately following an earthquake, due to analysis indicating that there will be too many pipe breaks in the distribution system. The water department manager must then confer with the fire department (and probably the mayor and other decision-makers) and communicate the possible outcome: • Because the district will not have water service until the pipe breaks are fixed, the fire department will understand that hydrants will be dry following an earthquake, and it will be necessary to identify and practice (i.e., plan) using alternative water supplies. • Water will be brought in to the district for household use, the city will furnish portable toilets, and businesses will function without water service. Because this example concerns public matters, whether to communicate this decision and its consequences to the public and the business community is a political issue. In the example of a private firm knowing that its emergency plan cannot overcome the loss of a key facility, that decision must then be communicated to the CEO, the board, and disclosed to investors.
33.3 Writing the Emergency Plan Having gone through the above process, the core team has accomplished the following: • Understood that emergencies can happen and that coping with them is primarily the responsibility of the organization • Understood the organization’s mission and the way the organization functions to accomplish that mission, i.e., how it serves its customers or the public © 2003 by CRC Press LLC
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• Examined the organization from the point of view of a recovery effort • Gained senior management and organizational support, and necessary resources for developing the emergency plan • Identified mission-critical functions • Gained a head start in dealing with future emergencies While this is of enormous benefit, the knowledge is confined to the core team only. It must be recorded in a written emergency plan in order to preserve the knowledge, disseminate it to the rest of the organization, and provide a document for training and drill purposes and as a resource in the event of an actual emergency. This section discusses the writing of the emergency plan.
33.3.1 Outlining the Emergency Plan Emergency plans come in many formats specific to the needs of the organization. This section presents a generic emergency plan outline, that can be adapted on a case-by-case basis. In general, an emergency plan is typically organized as shown in Table 33.2. As an example of an actual emergency plan, Figure 33.2, shows the Table of Contents of the City of Seattle’s Disaster Readiness and Response Plan. A more-detailed Table of Contents is provided in Appendix A. In the following subsections, we discuss each part of a typical emergency plan. Organization of the emergency plan must be intuitive, and printing and formatting must be clear and uncluttered, with good illustrations and sufficient white space for marginal notes and sketches. The emergency plan must be clearly written in simple, jargon-free language. A nonspecialist editor can edit the plan for clarity, accuracy, and conciseness. Technically correct terms, such as dip-slip reverse bilateral faulting, special moment-resisting composite frame, and planning environment, should be avoided or relegated to technical appendices.
TABLE 33.2 Table of Contents of a Typical Emergency Plan 1. Introduction 1.1 Purpose 1.2 Organization mission statement 2. Situation and Assumptions 2.1 Organization 2.2 Situation 2.3 Risk assessment 2.4 Assumptions 3. Concept of Operations 3.1 Organization’s emergency response 3.2 Other responders 4. Declaring an Emergency 4.1 Activation 4.2 Notification 4.3 Mobilization 5. Emergency Management (see Section 33.3.6) 6. Communications 6.1 Internal 6.2 External 7. Plan Maintenance and Training 8. Authorities 9. References 10. Key Information 11. Facility Annexes 12. Hazard Annexes 13. Other Annexes
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Table of Contents Mayor’s Promulgation Memorandum Cover Letter to Public Safety Chair Requesting City Council Approval City Council Resolution 30041 Acknowledgments Record of Revisions INTRODUCTION Mission Purpose Scope Limitations Liability Substantive Plan Changes POLICIES Applicable Federal Laws, Regulations, and Executive Branch Orders Applicable State Laws and Regulations Applicable Municipal Laws Related Plans Governance Assignment of Responsibilities SITUATION Local Environment Emergency/Disaster Conditions and Hazards Planning Assumptions CONCEPT OF OPERATIONS General Emergency Management Concepts Direction and Control Emergency Support Functions Citywide Flow of Emergency Communications Government Emergency Operations Facilities ORGANIZATIONAL RESPONSIBILITIES Common Responsibilities for City Departments and Commissions Specific Responsibilities for City Departments Non-City Government Support Organizations MAYORAL PREROGATIVES Proclamation of “Civil Emergency” Emergency Powers Authority to Enter into Contracts and Incur Obligations Commandeering Services, Equipment, and Supplies Proclamation of “Termination of Civil Emergency” INTERGOVERNMENT RELATIONSHIPS Emergency Support Given by the City Emergency Support Received by the City TABS Tab A Glossary of Emergency Management and ICS Terms Tab B Generic Outline for Internal Emergency Preparedness Plans Tab C Disaster Recovery Plan Checklist Tab D Federal Disaster Recovery Programs Tab E Weapons of Mass Destruction Response Resources Tab F Plan Distribution FIGURE 33.2 Disaster Readiness and Response Plan, City of Seattle. Available online at http://www.ci.seattle.wa.us/ emergency_mgt/resources/plans.htm.
33.3.2 Front Matter and Introduction The type on the cover and binding of the plan document must be clear, and the document must be readily identifiable from a distance (e.g., bright orange cover). If possible, the back and inside covers should have organization charts or other useful ready-reference diagrams (e.g., an area-wide map with key facilities indicated, or a system diagram if appropriate). The title page indicates key specifics: title, organizational name, date, prepared by, and responsible person (i.e., the emergency manager). A revision © 2003 by CRC Press LLC
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page is the first page after the title page, followed by a distribution log, indicating who receives copies of the emergency plan. A one-page executive summary is next, followed by a one-page table of contents; if needed, a detailed table of contents follows. The introduction states the plan’s purpose, derived from the organization’s mission statement, which also is stated. If relevant, authorizing legislation or regulations, mandating the plan, and acknowledgments are stated in the Introduction. If the plan is required by law, a brief explanation of compliance is included. History of the emergency plan and special circumstances associated with its creation (e.g., this plan was created because of the terrible experience we had in the last earthquake) are included. The organization of the plan document is described. Associated materials that may have been distributed, such as wallet-sized phone cards or pocket-sized summaries of the emergency plan (for keeping at home, in a briefcase, or in the trunk of a key person’s car), are mentioned and described.
33.3.3 Situation and Assumptions This section presents the planning environment, a summary of the organization and its situation, potential risks that are known to exist, and key assumptions underlying the emergency plan. 33.3.3.1 Organization and Situation This section summarizes the organization and factors affecting its operation and location. Key facilities are identified, a map is provided showing their location, and readers are referred to the facility annex for detailed data sheets on each facility. The Everytown Unified School District (EUSD) provides K–12 public education for the incorporated towns of Everytown and Othertown, USA, which have a combined population of 250,000. Student population of EUSD is 25,000, served by six K–6 schools (Washington, Adams, Jefferson, etc.), three middle schools (Magnolia, Cedar, and Pine) and one high school (Founder H.S.), as well as an administration building and maintenance building. Transportation of students … EUSD exists by charter from the State Board of … or: The Widget Manufacturing Company was founded in 1880 in Everytown, USA by Mr. R. Widget Founder. Today, WMC is a publicly owned corporation with 40,000 employees in six countries, with its headquarters, R&D facility, and main manufacturing plant in Everytown, a key assembly plant in Othertown, two Regional warehouses in … An organizational chart is provided, as well as maps of the region and key facilities, and detailed maps of areas around each key facility (detailed maps may be provided in the facility annex). 33.3.3.2 Risk Assessment This section summarizes potential risks that are known to exist, provides key information on those risks, and references for additional information. For earthquakes, the tectonics and geology of the region are summarized in a few sentences; the earthquake history is discussed in more detail with a tabulation of all significant earthquakes; the location of all known major faults is provided in a map with discussion; the location is provided of poor soils, potential liquefaction, landslide, or other sites of possible ground failure. Key authorities, such as the local university or the state Geological Survey that provided earthquake information, are cited and references provided. Figure 33.3 shows an example of a map of liquefaction zones and landslide-prone areas, taken from the Disaster Readiness and Response Plan of the City of Seattle. 33.3.3.3 Assumptions The section states key assumptions made when developing the emergency plan, and the underlying risk assessment. For example, if the following are the planning assumptions, they must be stated: the © 2003 by CRC Press LLC
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Legend Liquefaction Zones Landslide Prone Areas
Puget
Elliolt Bay
L a k e Wa s h i n g t o
Lake Union
n
Green Lake
N W
E S
Scale in Miles
0
1
2
© 2000, The City of Seattle, all rights reserved. No warranties of any sort, including accuracy, fitness or merchantability, accompany this product.
FIGURE 33.3 Map of liquefaction zones and landslide-prone areas, Disaster Readiness and Response Plan, City of Seattle. Available online at http://www.ci.seattle.wa.us/emergency_mgt/resources/plans.htm. © 2003 by CRC Press LLC
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earthquake is assumed to occur when children are in school … or … at the period of highest water demand. If mutual aid is a key part of the emergency plan, the assumption of how the emergency affects the aiding entity must be stated: mutual aid is assumed to come from Faraway Township, because the scenario earthquake used for this emergency plan is also assumed to affect Othertown. Interdependencies must be stated here: it is assumed that Faraway Water Wholesaler, the supplier of raw water to Everytown Water District, is unaffected by the scenario earthquake. A key assumption for all emergency plans is the arrival of outside disaster assistance (e.g., state militia, mutual aiding utilities, etc). This must be clearly and unambiguously stated, as it forms the basis for many actions in the emergency plan. If the conditions on which this assumption are based change, this is clearly understood, and the emergency plan can be correspondingly revised.
33.3.4 Concept of Operations This section presents the overall concept of how the emergency response is organized. It is broken into three main sections: the organization of the emergency response, the response of other entities, and interaction with those responders. 33.3.4.1 Organization’s Emergency Response This section presents and describes the emergency organization and how it will respond. One or several charts, showing the emergency response organization and reporting arrangements, are a key part of this section (e.g., Figure 33.4). Key members of the emergency management team should be identified, and their roles and responsibilities clearly detailed (see examples in Table 33.3). For large organizations or complex situations, a matrix indicating primary and supporting responsibilities can be provided. 33.3.4.2 Other Responders In most emergencies, and especially in a large earthquake, many organizations will be responding. It is important that an organization coordinates and cooperates with these other responders. In many cases, cooperation is absolutely vital to handling the emergency. Examples of this include: • Breaks in water mains, where the water department must inform and support the fire department • Hazardous materials release, where a factory must inform and support the police and fire departments • Use of schools for emergency shelters, where the school district must support the Red Cross and other humanitarian organizations To the extent possible, these interactions should be foreseen, and working relationships should be developed with other responders. These interactions should be documented in this section of the emergency plan, along with appropriate actions. Because various agencies use their own jargon, and have different kinds of organizations, a common organizational concept of operations, called a standardized emergency management system (SEMS), is evolving in the emergency management community. SEMS was developed in California and has been adopted by that state for its emergency management. Currently, it is not universally accepted outside of California, but some version of it will likely evolve across the United States and in other countries. SEMS utilizes the Incident Command System (ICS). ICS was originally developed by the fire service for managing emergency response to wildland fires, and is now widely employed across the United States for a variety of emergencies, particularly those for which the fire service has lead responsibility. The basic structure of ICS is shown in Figure 33.5, and detailed information on SEMS and ICS can be found at www.oes.ca.gov.
33.3.5 Declaring a State of Emergency This section of the emergency plan defines the first steps taken during an emergency response, which consist of activation, notification, and mobilization, each of which is described next.
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GENERAL STAFF
COMMAND STAFF
MAYOR DEPUTY MAYOR FOR PUBLIC SAFETY OVERSIGHT ESF-5 EMERGENCY PUBLIC INFORMATION (DIRECTOR OF COMMUNICATIONS)
ESF-2 LAW ENFORCEMENT COORDINATOR (SPD)
ESF-3 PUBLIC WORKS COORDINATOR (SeaTran)
DMC CHAIRMAN (SPD)
ESF-4 FIRE, RESCUE, AND EMS COORDINATOR (SFD)
ESF-6 HUMAN SERVICES COORDINATOR (HSD)
ESF-8 HEALTH, MEDICAL, AND MORTUARY COORDINATOR (PUBLIC HEALTH)
OPERATIONS SECTION
ESF-1 EMERGENCY MANAGEMENT COORDINATOR (SPD)
ESF-7 LOGISTICAL SERVICES COORDINATOR (Fleets and Fac Dept)
ESF-9 LONG-TERM RECOVERY AND UNMET NEEDS COORDINATOR (BUDGET OFFICE)
PLANS/ADMIN SECTION
LOGISTICS SECTION
FINANCE SECTION
FIGURE 33.4 Disaster management committee organization, Disaster Readiness and Response Plan, City of Seattle. Available online at http://www.ci.seattle.wa.us/emergency_mgt/resources/plans.htm.
TABLE 33.3 Responsibilities of Key Members of Emergency Management Team Key Member CEO
Emergency manager
Public information officer
© 2003 by CRC Press LLC
Responsibilities • Sets policy for overall emergency management • Makes critical decisions during emergency • Monitors performance of emergency manager during emergency to assure satisfactory response • Manages overall emergency response, making all but critical decisions • Delegates responsibility and oversees key emergency functions, assures that operations, public information, facilities, and other managers are executing the emergency plan • Advises the emergency manager and CEO on matters of emergency public information (EPI) • Convenes and maintains the media briefing room during and after the emergency • Prepares a call-down list for disseminating EPI to groups that do not have access to normal media (e.g., schoolchildren) • Prepares EPI packets for release; ensures that information needs of visually impaired, hearing impaired, and non-English speaking audiences are met • Establishes and maintains a working relationship with local media
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Management (Incident Command System) Operations
Initiating a State of Emergency
Planning / Intelligence Logistics Finance / Administration
FIGURE 33.5 Incident command system (ICS).
33.3.5.1 Activation This step consists of deciding that an emergency exists. In some cases, such as an approaching hurricane, the damaging agent may not have occurred yet, but the emergency may have already occurred with significant actions such as evacuation underway. Deciding that an emergency exists requires recognizing that certain conditions exist, and that these conditions may prevent the organization’s mission from being accomplished under normal SOPs. Earthquakes fall into the category of self-declaring emergencies, i.e., if an earthquake occurs, people in the affected area know about it. However, persons outside of the affected area will not immediately know that an earthquake has occurred. The emergency management team, the Emergency Operations Center (EOC), and other relevant parts of the emergency management organization may be outside of the affected area. In such cases, preexisting arrangements should be made with local seismological observatories or emergency services for notification of possible activation if an earthquake has occurred in certain localities. 33.3.5.2 Notification This step consists of two parts: 1. Internal notification: Notifying the emergency management team and other relevant members of the organization that an emergency exists, so that they may begin to take appropriate actions. Specifics of how notification should occur depend on the organization and the situational context. Again, for persons in the affected area, earthquakes are self-declaring. Outside the affected area, communications should be such that notification is not totally precluded: pagers and telephones should still be functioning, generally speaking. This is not always the case, however. In the 1999 Marmara (Turkey) earthquake, the earthquake severed the main fiber-optic telephone lines between Istanbul, the Marmara region, and the national capital of Ankara. The Turkish head of state, the national emergency response agency, and other key persons did not know of the event, and then did not have adequate communication with the affected area for several critical hours. 2. External notification: Notifying others that an emergency exists. While earthquakes may be selfdeclaring, local emergency agencies in the affected area may not know of a specific emergency condition at your organization until you inform them. Similarly, your organization may be vulnerable to an emergency at another location, and will remain ignorant of the vulnerability until you are notified. The emergency plan should have a checklist of agencies with whom your organization must cooperate and coordinate.
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33.3.5.3 Mobilization This step consists of the execution of the initial emergency response actions, one of the first of which is the activation of the EOC, and the assembling of the emergency management team. In some cases, the emergency plan should include selected persons taking initial steps different than activating and assembling at the EOC (e.g., in the event of the earthquake, the water department’s dam keeper should immediately inspect the dam and report its condition to the EOC).
33.3.6 Emergency Management Also known as incident management, this consists of the actual steps taken to understand, respond to, and control the emergency. Depending on the organization, emergency management can be very simple or very complex. For earthquakes, for example, school districts typically have a relatively simple emergency management plan: they assume parents will rush to the school (because the earthquake is selfdeclaring). Thus, the school district’s emergency management tasks are: • Assembly of students in a safe location • Release of students to parents as they arrive • Damage assessment and isolation of damaged buildings if required Whether there are damaged buildings or not, reopening of schools is part of the recovery plan, not the emergency or incident management task. A detailed enumeration of all the possible tasks in the emergency management phase is beyond the scope of this chapter. Essentially, the tasks follow from the identification of the mission-critical functions discussed previously. However, there are certain emergency management tasks that are common to most organizations. These tasks are discussed largely in terms of the members of the emergency management team responsible for assuring their completion. Thus, the following discussion provides a general makeup of a typical emergency management team, and many of the tasks they must perform. Note that each member of the emergency management team should have a secondary or backup person identified for that role. 33.3.6.1 Personnel Safety This consists of assuring that all of the organization’s personnel are safe and accounted for. This can be accomplished by having a specific task in the emergency plan delegating a member of the emergency management team to contact and confirm the safety of all personnel. Therefore, the emergency plan must have lists of personnel on the job (job titles and actual names, if possible) at different times of day (e.g., in the middle of the night there may only be a few personnel on the job), how to contact them (telephone and pager numbers), etc. The member of the emergency management team must perform this task rapidly with procedures that eliminate or minimize errors in the confusion of an emergency. The member also needs to have instructions on what to tell those personnel to do when he contacts them (e.g., stay where they are, perform a damage assessment, evacuate, go home, go to the EOC, etc.), and actions to be taken if personnel are injured, in unsafe conditions, need to assure their family’s safety, or are unable to perform their job. The detail here is representative of what is required of an emergency plan: each step must be well thought out, contingencies anticipated, and decisions made and provided as guidance to those who will perform the emergency management. 33.3.6.2 Situation Assessment Concurrent with the personal safety assessment, other members of the emergency management team will be assessing the situation. This consists of determining the nature and dimensions of what caused the emergency, and the condition and possible damage of all mission-critical facilities. For an earthquake, the local seismological observatory or emergency agencies will provide preliminary data on the magnitude and epicentral location of the event within minutes; also within minutes, radio and television broadcasts
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TriNet Rapid Instrumental Intensity Map Epicenter: 26.2 mi SSE of Calexico, CA Fri Feb 22, 2002 11:32:41 AM PST M5.7 N32.32 W115.32 ID: 12456384 34°
33.5°
33°
32.5°
km
32°
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45
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-115°
PROCESSED: Sun Feb 24, 2002 05:43:19 PM PST, — NOT REVIEWED BY HUMAN PERCEIVED SHAKING POTENTIAL DAMAGE
Not felt
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Strong
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Severe
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none
none
none
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PEAK ACC (%g)
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PEAK VEL (cm/s)
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0.1 - 1.1 1.1 - 3.4
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INSTRUMENTAL INTENSITY
I
V
VI
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IV
FIGURE 33.6 Example of near real-time shaking intensity map (available online at http://www.trinet.org/shake/).
will be providing the same information. The USGS National Earthquake Information Center Web site (http://neic.usgs.gov/neis/bulletin/) provides near real-time information on significant earthquakes anywhere in the world (located in Denver, the telephone number is 303-273-8516). There are a number of Web sites that now provide rapid intensity information, such as the California Integrated Seismic Network (Figure 33.6). Also available are damage estimation tools, such as EPEDAT (Early Post-Earthquake Damage Assessment Tool) and GeoProtectSM, which permit rapid estimation of damage to guide the situation assessment and emergency responders prior to their acquiring hard information (Figures 33.7 and 33.8). Situation assessment is an ongoing task throughout the emergency. At first, it is broad and general, assessing the general situation; as the emergency progresses, situation assessment evolves into more detailed damage assessment. The emergency plan should call for situation reports (SitReps) to be made and distributed, according to a simple, concise, prearranged format, at regular intervals that correspond to the urgency of the situation. At first, SitReps can be issued every 30 minutes but as the emergency is brought under control, SitReps can be required only twice daily, then once daily, and so on.
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(a)
USC UNIVERSITY HOSPITAL
LONG BEACH MEMORIAL MEDICAL CENTER
(b)
FIGURE 33.7 Early Post-Earthquake Damage Assessment Tool (EPEDAT). (a) Earthquake shaking intensity map for selected event (M 7.0, Newport-Inglewood fault zone, Los Angeles). (b) Map showing major hospitals in affected zone. (Courtesy EQE International) © 2003 by CRC Press LLC
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(a)
(b)
FIGURE 33.8 (a) Utilizing toxic hazard plume modeling, real-time emergency response vehicle tracking, and automated evacuation route generation, GeoProtectSM provides emergency managers and first responders with an accurate depiction of the event scene that enhances crisis management decision-making. (b) Integrating accurate information about a water distribution system with GIS, GeoProtectSM enables disaster planners to predict the impact of a contamination or disruption of vital services. (From CH2MHILL, Inc. With permission.)
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33.3.6.3 Operations This consists of taking specific steps to restore mission-critical functions or respond to damage. Operations are the responsibility of the operations officer, who should initiate Ops only as the situation assessment clarifies the actions that are required, and these can be prioritized against the available resources. The emergency plan can assist the emergency management team in anticipating likely scenarios based on the risk assessment, and providing checklists for such situations. An example checklist is provided in Appendix B. 33.3.6.4 Resource Management Also termed the logistics function, this consists of a resource or logistics officer (the latter term is used in the ICS) who tracks, controls, and deploys resources at the request of the operations officer. As resources dwindle, it is the responsibility of the resource officer to find additional resources. Sources such as local contractors, emergency agencies, mutual aid organizations, and others must be identified in the emergency plan, with appropriate contact information. To the extent appropriate, soft or hard contracting arrangements can be prearranged. 33.3.6.5 Finance A member of the emergency management team handles finances. Cash may be required in certain cases, but authority to spend will definitely be necessary. This authority on the part of the emergency management team must be predefined, with special authorization required of the emergency manager or the CEO. For example, if a company must house and feed stranded workers, the finance officer of the emergency management team has the authority to approve that expenditure. 33.3.6.6 Communications The communications officer is the member of the emergency management team who has responsibility for communications, including hardware and content. Tasks include (1) assuring that the emergency management team has adequate communications in terms of telephone, radio, incoming broadcast, etc., and (2) assuring appropriate public information is being communicated. In the latter case, a public information officer (PIO) can report to the communications officer and have responsibility for understanding the need for information and how to appropriately transmit this information to the media and the public. The PIO both advises the emergency management team and CEO on public image and related matters, and convenes and maintains the media briefing room. 33.3.6.7 Human Resources The human resource officer (HRO) is the member of the emergency management team who has several responsibilities, including (1) assuring adequate human resources are available for the tasks, (2) assisting employees with family needs, including medical insurance and related aspects, and (3) monitoring and assisting with emergency-related stress. An emergency is a very stressful situation, and the HRO must be alert to employees or members of the emergency management team who are suffering undue effects from this stress. Stress management and relief techniques are well documented, and the emergency plan must provide for these, as well as for training the HRO in these techniques. This task does not have to fall entirely on the shoulders of the HRO; the emergency plan, for example, can prearrange for clergy, academics, or other resources helpful in this aspect to be part of the larger emergency management team. 33.3.6.8 Records The records officer (RO) is the member of the emergency management team who is present in the EOC and records all important events, including personnel arrivals and departures, incoming reports, questions, decisions, outgoing communications, and expenditures-related information. The RO does not necessarily record all of these events personally, but assures they are being recorded (e.g., expenditures are recorded by the finance officer) and that a record is provided to the scribe. However, a computer can be provided in the EOC for the use of the RO. The RO or an assistant can be stationed there during the initial phases of the emergency. © 2003 by CRC Press LLC
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33.3.6.9 Recovery/Reconstruction (R/R) The purpose of operations is to bring the emergency under control and stabilize the situation. Stabilize means that nothing is getting worse, and that processes, hazardous materials, and other potentially dynamic phenomena have been safely shut down, contained, or otherwise controlled. When the emergency is under control, the initial phase of the emergency is over. The next phase is the recovery, and then the reconstruction. Recovery refers to the restoration of seminormal operations of the organization, perhaps in temporary quarters or using temporary methods. Reconstruction refers to the restoration of normal operations of the organization, in permanent quarters using normal procedures. The R/R aspects may or may not be part of the emergency plan. 33.3.6.10 Stand Down This refers to the end of the emergency, return of the emergency management team members to their normal jobs, and closure of the EOC. This is not always a clear-cut process. In many cases, the EOC and emergency management team remain in a semiactive role and increasingly assume R/R responsibilities. However, it is healthy for the organization to declare the emergency phase over, and some criteria and procedures for doing this must be part of the emergency plan. 33.3.6.11 After-Incident Report (AIR) This consists of collation and interpretation of data from the emergency. Data to be collated include information on the damaging event (e.g., the earthquake), damage assessments, personnel debriefs, quantifiable impacts (e.g., lost production, drops in tank levels, student attendance drop-off), financial impacts, the emergency response, and an assessment of what worked well and what did not. The media, especially newspapers, are a valuable resource that should not be overlooked in this regard. The purpose of the AIR is to capture data while it is still available (i.e., before it is lost), to extract valuable lessons so as to reduce the organization’s overall vulnerability to the emergency, and to improve the emergency plan and the emergency management team’s performance. In the exhaustion of the post-emergency phase, it is all too easy to postpone or forego the AIR. The emergency manager and CEO must ensure this does not happen.
33.3.7 Communications This section of the plan details the responsibilities of the communications officer (described previously). Communications are divided into two fundamental aspects: 1. Internal: This involves assuring that the emergency management team has adequate communications capabilities in terms of telephone, radio, incoming broadcasts, etc. to perform its tasks. This also involves organization and dissemination of important information in the form of SitReps, discussed previously. Another aspect of communications is information display within the EOC: whiteboards, large projection, GIS-based maps, video, and other data and methods can all be considered, depending on the organization. 2. External: The PIO, reporting to the communications officer, has responsibility for understanding the public need for information and how to appropriately transmit this information to the media and the public. The PIO both advises the emergency management team and CEO on public image and related matters, and convenes and maintains the media briefing room.
33.3.8 Plan Maintenance and Training This section is not needed during the emergency period, but is a vital part of the emergency plan. It details how the maintenance of the emergency plan will be handled, and how individuals, the entire emergency management team, and the entire organization will train for an emergency. This is a key part of emergency management, and must be included in the emergency plan. Details of actual plan maintenance and training are discussed in Section 33.5. © 2003 by CRC Press LLC
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33.3.9 References This section contains proper and full citation of SOPs, materials, data, and other information and agencies referred to in the emergency plan.
33.3.10 Key Information This section contains key information, such as lists of emergency agencies, organization personnel, professional resources (e.g., a structural engineer for assessing structural safety), contractors, and other data that may be needed quickly in an emergency. Contact information can include office, home, cell and pager numbers, secondary contacts (e.g., neighbors, close relations), and alternates. The data must be clearly provided, preferably in a format that can also be provided on a wallet-sized card or for use in a Personal Digital Assistant (PDA, e.g., a Palm Pilot).
33.3.11 Facility Annexes Facility annexes are comprised of detailed descriptions of the facility, including photographs, maps, diagrams, schematics, specifications, capacities, and floor plans. Depending on the purpose of the facility, its operations, personnel, organization, and other operational aspects are also detailed.
33.3.12 Hazard Annexes Hazard annexes are comprised of detailed descriptions of the likely hazards affecting the organization, and their impacts. Maps, tables, and perhaps photographs and diagrams are all appropriate.
33.3.13 Other Annexes As appropriate, these can include information on other resources, more detail on procedures, etc. Examples of items that might be included here are: • Contractors and vendor resources • Mutual aid resources and agreements • Technical data, such as equipment weights, fuel or other logistic requirements, shelter capacities, etc.
33.4 The Emergency Operations Center (EOC) The EOC is a key part of the emergency plan. Having an identified EOC simplifies mobilization and communications enormously. Without an adequately equipped and staffed EOC, the emergency management team cannot do its job. EOCs vary widely depending on the organization’s size and needs, ranging from one room to an entire building. An adequate EOC has most or all of the following attributes: • Assured functionality in an emergency: The EOC must be located in a building that has been reviewed and is expected to survive most emergencies (in the context of this discussion, it must be functional immediately following an earthquake). This means it must have multiple redundant communications; backup power with adequate fuel; stores of food, water, bedding, and other necessities; secured access; and facilities for media briefing (separate from the actual operations area). Because absolute assured functionality is not achievable, the EOC must have a backup or alternative site and, depending on the organization, this can be backed up by a mobile EOC. • Dual purpose: Few, if any, organizations can afford a dedicated EOC; therefore, most EOCs serve a normal day-to-day purpose and are converted to the EOC in an emergency. Examples include (1) the board room and executive offices of a mid-sized company, (2) a conference or training center of a large corporation, and (3) the dispatch center, headquarters, or maintenance facility of a public agency. © 2003 by CRC Press LLC
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DORM
DORM
Office
Office Ops Ctr. Office
CEO office
Comm. EATING AREA Media Briefing Room
SEPARATE MEDIA ENTRANCE
MAIN ENTRANCE (SECURED)
Fence
FIGURE 33.9 A schematic example of an emergency operations center layout.
• Layout — for a medium- to large-sized organization — A typical EOC has a main operations center, typically a large room with a large table or U-shaped arrangement of tables or desks, at which the main members of the emergency management team sit, with the emergency manager at the head of the table. The walls of this room can have whiteboards and a large video projection display. A TV with low volume can be on at all times. One or several smaller rooms can be available for small secured conferences, telephone calls, or simple quiet rooms. A room, typically with a window overlooking the Ops Center, can be reserved for the CEO, in which he can function while visually monitoring the overall operation (simple body language can often keep the CEO informed as to how the emergency is progressing). Separated from the main Ops Center can be an eating area and one or two dormitories, restrooms, etc. • Security: The entire EOC must have secured access. • Media: Media should not be permitted in the EOC, but rather are briefed in a separate media briefing room. Figure 33.9 shows a schematic example of an EOC layout; Figure 33.10 shows an actual EOC in a mid-sized city.
33.5 Training and Maintenance of the Emergency Plan 33.5.1 Training Training is a vital part of the emergency plan and consists of two main parts: tasks and exercises. © 2003 by CRC Press LLC
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FIGURE 33.10 Example of an actual municipal emergency operations center.
33.5.1.1 Tasks This refers to identifying specific tasks in the emergency plan and the parties responsible for performing them, and assuring that the responsible parties have the understanding, skills, and resources to perform the tasks. For example, is the records officer appropriately informed, skilled, and equipped to assure adequate record-keeping during the emergency? Does that person have the computer literacy, organizational abilities, database proficiency, and other skills to process, archive, and retrieve a large mass of information in a short time? To assure this, the emergency plan must be reviewed for the hundreds of tasks that may be required of each member of the emergency management team. These tasks can all be compiled and reviewed for skills required, equipment needed, etc. Most of the tasks can be easily identified as within the normal skill set of the members of the emergency management team. Some fraction, however, may not clearly be so, and a training program can then be established to assure that the skills exist. These skills can then be maintained via periodic drills of individuals. 33.5.1.2 Exercises In an actual emergency, it is too late to begin to read the emergency plan. The methods and processes of the emergency plan must be inculcated in the team via task training and exercises. Exercises combine various tasks to simulate some or all aspects of the emergency management. Exercising of the emergency plan can start off by combining only a few of the emergency plan tasks, such as Situation Assessment and Communications. Simply bring these two officers together and have them try to perform selected tasks where interaction or support of one by the other is required. Gradually increase the combination of tasks until the entire emergency plan is being practiced in a tabletop exercise. Tabletop exercises consist of simply sitting around a table and discussing what each member of the emergency management team would be doing in response to various simulated situations. As tabletop exercises are successfully completed, a full exercise is then required, involving the activation of the EOC, assembling of the entire emergency management team (including the CEO), real-time simulation of emergency messages, some surprises, etc. Design and execution of tabletop and full exercises are a vital part of the overall emergency plan.
33.5.2 Maintenance Any emergency plan, if not maintained, will quickly become out of date. Maintenance involves periodic revision of information in the report, such as organization charts, contact information, monitoring of applicable regulations and requirements to assure compliance, and review of the overall emergency plan to assure it is updated with regard to best practices in the field.
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33.6 Summary: Developing an Emergency Plan In summary, the following steps are required for the development of an emergency plan: 1. Decide to develop an emergency plan: This involves cooperation with senior management — gaining support, identifying a sponsor, and allocating the resources required for development of the emergency plan, as well as for maintaining and exercising it. Reasons for developing an emergency plan were discussed previously. 2. Form a core team to write the plan. The core team is drawn from core functional areas of the organization; examples of core team members are provided in Table 33.1. Recognize that the core team will likely become the core emergency management team. 3. Determine the organization’s current capability for emergency response, and its emergency management needs. 4. Determine the purpose of the emergency plan by reviewing the organization’s mission statement. 5. Identify mission-critical functions essential to fulfilling the organization’s mission. 6. Outline the emergency plan. Example outlines are provided in this chapter. 7. Write each section of the report based on an outline. The outline provides the key elements of an emergency plan; in order to write each section, questions specific to the organization and its mission-critical functions must be asked. Therefore, writing the report is an analytical process, analyzing what needs to be done, by whom, when, and how, in order to identify and maintain mission-critical functions that are at risk of not being performed. 8. Establish an EOC. Having developed the emergency plan, the personnel, communications assets, and other resources necessary to execute it must become apparent. This forms the requirements for the organization’s EOC. Given these requirements, identify a suitable venue, obtain senior management approval of the site, and equip it to function as the EOC. 9. Move the written plan to a capability. Completing the written emergency plan is not sufficient; it must now be translated into an organizational emergency response capability. This is achieved by analyzing needed skills, assuring that members of the emergency management team have the skills, and welding the members into an emergency management team through increasingly realistic exercises. 10. Maintain the plan and the capability. The emergency plan is maintained via periodic review and update. The capability is maintained by regular skills renewal and exercise.
Defining Terms Disaster — This term is not used in this chapter as it is associated with a large-scale event, usually a natural disaster. More appropriately, each incident must be considered in view of the impact it has on the organization. What may constitute a nuisance to a large corporation can be a disaster to a small business. Emergency — Any unplanned event that can cause death or significant injury to employees, customers, or the public; shut down a business; disrupt operations; cause physical or environmental damage; threaten a facility’s financial standing or public image; or cause the loss of key supplier or customer. An emergency can be caused by explosion, fire, hazardous materials incident, flood or flash flood, hurricane, tornado, winter storm, earthquake, communications failure, radiological accident, or civil disturbance. Emergency operations center (EOC) — The location from which emergency operations are commanded and coordinated. Usually consists of a predesignated location with assured communications and logistics. The EOC must have a backup location. Emergency plan — An organization’s written description of how it will respond to an emergency, detailing the makeup of the emergency management team and the tasks it will perform.
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Function — Operations or purposes serving the organization’s mission. Mission — The purpose of the organization, why it exists. Mitigation — Actions taken to reduce the negative impacts of an event such as an earthquake. Organization — As used in this chapter, a rubric for the public or private agency for which the emergency plan is written.
Residual damage — Any damage that it is not feasible to mitigate. Standard operating procedures (SOP) — Normal, day-to-day procedures developed and approved by an organization on the basis that they are safe and efficient for the performance of a function.
References City of Seattle. 1999. Disaster Readiness and Response Plan, City of Seattle, WA. Available online at http:/ /www.ci.seattle.wa.us/emergency_mgt/resources/plans.htm. DRC (n.d.). Disaster Planning, Emergency Management, and Civil Protection: The Historical Development and Current Characteristics of Organized Efforts to Prevent and Respond to Disasters, Disaster Research Center, University of Delaware, Newark. Available online at http://www.udel.edu/DRC/ preliminary/227.pdf). FEMA (n.d.). Emergency Management Guide for Business and Industry: A Step-by-Step Approach to Emergency Planning, Response and Recovery for Companies of all Sizes, Sponsored by a public-private partnership with the Federal Emergency Management Agency, Washington, D.C. FEMA. 1996. Guide for All-Hazard Emergency Operations Planning, State and Local Guide (SLG) 101, Federal Emergency Management Agency, Washington, D.C. FEMA. 2002. Rapid Visual Screening of Buildings for Potential Seismic Hazards: A Handbook, 2nd ed., FEMA 154, developed for the Federal Emergency Management Agency by the Applied Technology Council, Redwood City, CA. Available from the Federal Emergency Management Agency, Washington, D.C.
Further Reading There are a number of good references on emergency planning. FEMA [n.d.] is appropriate for privatesector organizations, while FEMA [1996] is appropriate for state and local governments. Both are available free at www.fema.gov. The City of Seattle’s Disaster Readiness and Response Plan is available online, and is a good emergency plan model, whether public or private sector. The Disaster Research Center (University of Delaware, www.udel.edu/DRC) is an excellent resource for the more fundamental aspects of disasters and their impacts.
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Appendix A Everytown Water Department EVERYTOWN WATER DEPARTMENT EMERGENCY PLAN TABLE OF CONTENTS
Plan Organization Plan Revision Pagination Plan Distribution Abbreviations
INTRODUCTION Emergency Operations Plan Emergency Planning Group Mission Statement Response Objectives Response Priorities Authorities/References
Part I DISASTER PREPAREDNESS 1.0 Potential Hazards 1.1 Major Earthquake 1.2 Fire/Conflagration 1.3 Hazardous Material Incident 1.4 Transportation Accident 1.5 Imminent/Actual Dam Reservoir Failure 1.6 Civil Disturbance 1.7 Earthquake Prediction Advisory 1.8 Peacetime Nuclear Technological Incident 1.9 Tsunami/Seiche Inundation 2.0 Water System Earthquake Vulnerabilities 2.1 Water Supply and Transmission 2.2 Water Treatment Plants 2.3 City Distribution 3.0 Hazard Mitigation 3.1 Fire Safety 3.2 Building Contents and Employee Protection
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4.0 Testing, Maintenance, Training, and Employee Training 4.1 Plan Testing and Maintenance 4.2 Employee Training
Part II EMERGENCY RESPONSE 1.0 Response Activation 2.0 Emergency Management Organization 2.1 EMO Responsibilities 2.2 Concept of Operations 3.0 Emergency Operations Center(s) 3.1 EOC Locations 3.2 EOC Activation 3.3 EOC Physical Layout 3.4 Emergency Power Systems 3.5 EOC Forms and Status Boards 4.0 Communications 4.1 Telephone Communications Systems 4.2 Radio Communications 5.0 Mutual Aid Procedures 5.1 Local Mutual Aid Agreements 5.2 Water Agency Mutual Aid Agreements 5.3 Water Agency Emergency Resources Directory 5.4 Everytown City Personnel 5.5 City Emergency Helicopter Transportation Procedure 5.6 EWD Call-Up of Retired Personnel 6.0 Contractor/Vendor Resources 6.1 Proposed Emergency Contract Procedure 6.2 Contractor/Vendor Emergency Contact List 6.3 Everytown City Procurement Procedures 7.0 Water Supply and Treatment Division 7.1 Emergency Response Function 7.2 Water Supply 7.3 Operations Engineering, Operations Planning, and Project Engineering 7.4 Water Treatment and Operations 7.5 Coordination with Local Governments 7.6 Dam and Reservoir Emergency Response 7.7 Forms • Suburban Customer Contact List • Employee Emergency Contact List (North Division) • Emergency Equipment Materials List (North Division) • Employee Emergency Contact List (North Division, Buildings and Grounds) • Emergency Equipment Materials List (North Division, Buildings and Grounds) • Vehicle List (North Division, Buildings and Grounds) • Employee Emergency Contact List (Operations Engineering) • Emergency Equipment Materials List (South Division) • Employee Emergency Contact List (Water Treatment Plants) • Emergency Equipment Materials List (Water Treatment Division) © 2003 by CRC Press LLC
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• Vehicle List (Water Treatment Division) • Vehicle List (North Division) • Vehicle List (Operations Engineering) • Vehicle List (South Division) • Employee Emergency Contact List (South Division) 8.0 Water Quality Division 8.1 Emergency Response Function 8.2 Emergency Water Quality Policies 8.3 Coordination with Local Governments 8.4 Emergency Response Procedures 8.5 Forms • Notification of Unsafe Water Alert Sample • Cancellation of Unsafe Water Alert • Notification of Boil Water Order • Notification of Cancellation of Boil Water Order • Employee Emergency Contact List • Emergency Equipment/Materials List • Vehicle List • Emergency Chlorination Plan • Emergency Management Organization (EMO) • EMO Responsibilities • EOC Layout 9.0 City Distribution Division 9.1 Emergency Response Functions 9.2 Damage Assessment Procedures 9.3 Water Transfer Strategy Procedures 9.4 Coordination with Everytown Fire Department 9.5 Emergency Water Supply Procedures 9.6 System Repair Procedures 9.7 Dam and Reservoir Emergency Procedures 9.8 CDD Administration and Clerical Personnel 9.9 Forms • CDD Rendezvous Points and Staging Areas • Employee Emergency Contact List • Emergency Equipment/Materials List • Vehicle List • Emergency Management Organization (EMO) • EMO Responsibilities • EOC Layout 10.0 Customer Service Division 10.1 Customer Service and Commercial Division 10.2 Field Services Section 10.3 Forms • Employee Emergency Contact List (Customer Accounts and Customer Service) • Vehicle List (Customer Accounts and Customer Service) • Employee Emergency Contact List (Field Services Section) • Emergency Equipment Materials List (Field Services Section) • Vehicle List (Field Services Section) © 2003 by CRC Press LLC
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• Labor Pool Emergency Assignment List • Field Services Section Damage Assessment Report Form • Infirm Areas Map • Emergency Management Organization (EMO) • EMO Responsibilities • EOC Layout General Manager and Staff 11.1 Emergency Response Actions 11.2 Chain of Succession 11.3 Forms • Employee Emergency Contact • Emergency Management Organization (EMO) • EMO Responsibilities • EOC Layout Hazardous Materials Response 12.1 Response Categories 12.2 Immediate Threat to Water Supply or Life Safety 12.3 Reportable Event or Threat to the Environment 12.4 Not a Reportable Event, No Threat 12.5 Hazardous Materials Departmental Coordinator and Hazardous Materials Site Coordinators Media Plan 13.1 Key Audiences 13.2 Level of Response and Media Interest 13.3 Organizational Response Structure 13.4 Crisis Communications Responsibilities 13.5 Guidelines for Notifying and Informing Key Audiences 13.6 Policies for EWD Spokespersons 13.7 Guidelines and Policies for Employees 13.8 Guidelines for Conducting a News Briefing or Press Conference 13.9 Guidelines for Responding to External Inquiries Other Than News Media 13.10 Guidelines for Providing Information to Employees Employee Care and Welfare 14.1 Medical 14.2 Provisioning 14.3 Employee Self-Sufficiency 14.4 Shelter 14.5 Forms • Employee Questionnaire • Employee Roster • Emergency Supply Locations • Triage Tag • Injured Transport Record • Emergency Supply Inventory • Medical Treatment Log Emergency Response Team and Building Evacuation 15.1 Emergency Response Team 15.2 Building Evacuation Drill Guidelines
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15.3 Occupant Stairwell Safety 15.4 Disabled Employees 15.5 Forms • ERT Organization • ERT Membership Application • ERT Assignments • Floor Coordinator Evacuation Drill Checklist • Area Coordinator Evacuation Drill Checklist • ERT Evacuation Drill Summary Checklist • Building Evacuation Report • Floor Plans • Division Manager Evacuation Drill Checklist
Part III RECOVERY OPERATIONS 1.0 Essential Records 2.0 Facilities Restoration 2.1 Forms • Damage Assessment Inspection Report • Building Inspection Placards 3.0 Records Restoration 3.1 Forms • Office Restoration Log • Operational Damage Assessment Summary • Office Damage Assessment Summary 4.0 Management Information Systems 5.0 Emergency Pay and Financials 6.0 Federal I State Disaster Cost Reimbursement and Hazard Mitigation Grant Program (HMGP) 6.1 Forms • Labor Record • Force Account Equipment Record • Rented Equipment Record • Material Record 7.0 Disaster Application Centers 8.0 Post-Event Debriefing and Evaluation Report 8.1 Form Post-Event Evaluation Report
Part IV EMERGENCY ACTION CHECKLISTS 1.0 Emergency Operations Management 2.0 Water Supply and Treatment Division 3.0 City Distribution Division 4.0 Customer Service Division 5.0 Water Quality Division 6.0 Hazardous Materials Incident 7.0 Equipment and Supplies Procurement
Part V SYSTEM MAPS © 2003 by CRC Press LLC
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Appendix B Everytown Water Department
Rev. 1.0
EMERGENCY ACTION CHECKLIST CITY DISTRIBUTION DIVISION Response to Major Earthquake Primary responsibility for this checklist is assigned to the Operations Manager at the EWD EOC.
ACTION Report to EWD EOC. Activate EOC and ensure that the EOC is staffed and operational. Contact General Manager at Everytown EOC to confirm that EWD EOC is activated and provide briefing on current status.
DAMAGE ASSESSMENT Monitor radio traffic for initial information on system damage and city-wide damage areas. If telephones are operating, monitor and log calls from citizens reporting visible water system damage. Establish radio contact with CDD Gatemen and repair crews in the field and at staging areas. Dispatch crews to reservoirs and storage tanks for damage inspection. Receive damage information from Adopt-A-Main volunteers, Gatemen, and repair crews. Analyze damage information and provide recommendations for repair priorities to Operations Manager at EOC. Provide damage status report to General Manager at Everytown EOC, as needed. Maintain records of damage information and record activities on Activity Log.
REPAIR COORDINATION Determine repair priorities based on requirements to maintain water pressure to critical users. Contact and coordinate activities with Everytown Fire Department liaison. Dispatch Gatemen to assist EFD at critical locations for firefighting.
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ACTION Determine water transfer strategies and direct Gatemen to isolate main breaks and route water flow, as needed to maintain pressure. Dispatch repair crews to priority locations to begin repairs. Contact EOC Director (Deputy General Manager) or Operations Manager at Othertown EOC to provide periodic status reports and to coordinate activities, as needed. Determine need for mutual aid and contact Mutual Aid partners, as needed to supplement repair crews. Determine need for contractors and vendors, and contact, as needed to provide repair services, equipment, and supplies. Provide periodic status reports to General Manager at Everytown EOC.
DAM AND RESERVOIR EMERGENCY RESPONSE Dispatch personnel to inspect dams and reservoirs. Contact Everytown EOC to notify that inspections are underway. Receive and analyze damage information. Contact Everytown EOC to report damage and initiate emergency evacuation, if needed. Initiate notifications to state regulatory agencies, as required. Provide periodic status reports to the General Manager at the Everytown EOC.
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34 Developing an Earthquake Mitigation Program 34.1 34.2 34.3 34.4 34.5 34.6
Introduction Overview of an Earthquake Mitigation Program Phase 0: Pre-Program Activities Phase 1: Assessing the Problem Phase 2: Developing the Program Phase 3: Implementing the Program Retaining Seismic Retrofit Design Professionals · Funding the Program · Coordinating with Other Parts of the Organization · Perform Seismic Retrofit · Dealing with Residual Risk
Charles Scawthorn Consulting Engineer Berkeley, CA
34.7 Maintaining the Program Defining Terms References Further Reading
When schemes are laid in advance, it is surprising how often the circumstances fit in with them. — Sir William Osler (1849–1919)
34.1 Introduction Previous chapters of this volume have discussed the effects of earthquake and the potential resulting damage. This chapter provides guidance on how to go about developing and implementing an earthquake risk reduction program to reduce that potential damage — that is, this chapter discusses developing an earthquake mitigation program. An earthquake mitigation program has five basic aspects: 1. 2. 3. 4. 5.
Pre-program activities Assessing the risk Developing the program Implementing the program Maintaining the program
The next section first provides an overview of these aspects, and is then followed by sections providing a detailed discussion of each aspect.
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34.2 Overview of an Earthquake Mitigation Program Earthquakes are a problem and, in the most general sense, solving a problem has three basic phases: 1. Phase 1: Understanding the problem 2. Phase 2: Finding a solution 3. Phase 3: Putting the solution into effect Solving the earthquake problem — that is, an earthquake mitigation program — has these three basic phases, plus two more phases. These two additional phases are required because earthquake mitigation typically involves activities in large organizations over a prolonged period (years, if not decades), during which personnel changes are not uncommon. Therefore, the two additional phases are (1) a phase “zero,” which consists of actually getting a large organization to embark on an earthquake mitigation program, and (2) phase 4: putting in place the organizational mechanisms such that the earthquake mitigation program is maintained over the required period. Regarding the latter phase, maintaining the earthquake mitigation program over the required period is not actually sufficient; once the formal earthquake mitigation program has been completed, or during its implementation, conditions are likely to change such that the earthquake mitigation program should likewise change. Lastly, part of any comprehensive earthquake mitigation program is an emergency plan. As discussed in Chapter 33, maintaining an emergency plan is integral to that plan. Therefore, in the sense that the emergency plan is part of the earthquake implementation program, and that the program needs to be alert to changing conditions in the organization that may increase earthquake risk, maintenance of the earthquake mitigation program is an ongoing task which never ends. That is, once the formal earthquake mitigation program has been completed, earthquake mitigation should be an ongoing part of the organization’s normal risk management activities. Therefore, developing an earthquake mitigation program involves the following five phases: 1. Phase 0, pre-program activities, involving increasing awareness of the potential earthquake problem, and gaining authorization for an initial assessment of the problem. 2. Phase 1, assessing the risk, consisting of an initial review of life, property, and business or functional exposures, and the threat that earthquakes may pose to them, in order to determine the current seismic risk. That is, are earthquakes indeed a problem (i.e., does a problem exist?) and, if so, what is the magnitude and nature of that problem? 3. Phase 2, developing the program, which consists of determining the organization’s acceptable risk, the options that exist for reducing the current risk to an acceptable level, the costs of doing that, and how it should be accomplished. 4. Phase 3, implementing the program — that is, actually taking the actions that reduce the risk. 5. Phase 4, maintaining the program — so that the risk does not become unacceptable. These phases are shown in Figure 34.1, and discussed in more detail in the next sections.
34.3 Phase 0: Pre-Program Activities Pre-program activities may be very simple or very difficult, depending on geographic and organizational factors, such as the organization’s mode of decision-making. The fundamental driver is geographic — is there a potential for earthquakes in regions in which the organization operates? While earthquakes have the potential to occur almost anywhere, there are regions such as parts of California, Japan, and Mexico, in which they are clearly a problem. There are other regions in which the degree of earthquake risk is less clear — in the eastern United States, for example, where earthquakes have occurred, but their frequency is relatively low. The region to be considered, by the way, is not only the region in which the organization may be located, but also regions related to the organization, such as where the organization’s suppliers, or customers, are located. Chapters 1 and 4 of this volume should provide sufficient information, in a global sense, to obtain a broad understanding as to whether earthquakes are a problem for a © 2003 by CRC Press LLC
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Factors - Seismic environment? - Organization / decision-making - Responsibility / liability
Pre-program
Data - Seismic hazard - Exposure - life - property - business / function - revenue - data - market share - reputation / image - Vulnerability - Assessment
Assess the Risk
Stop
Y
Acceptable?
N
Develop the Program
Acceptable? N Y
Mitigation Options - Locational - Redundancy / backup - Move - Structural - Strengthen structures - Brace equipment / furnishings - Operational - Emergency Plan - Backup data - Transfer - Insurance - Contracts
Implement the Program
Maintain the Program
FIGURE 34.1 Earthquake mitigation program.
specific region. More detailed information can then be obtained from references cited in those chapters, as well as from expert sources, such as the U.S. Geological Survey or various seismological observatories. If earthquakes appear to have some potential for occurrence, the next issue is obtaining the authorization for assessing the risk they may pose to the organization. Depending on the organization and its decision-making, several arguments may be needed to authorize the expenditure involved in a seismic risk assessment. These arguments typically fall into the following categories: • Ethical — this is often the first argument to occur to a proponent of a seismic risk assessment. It typically takes the form of, “it is the organization’s responsibility to assess its earthquake’s risk, to be sure it is protecting life and property.” This argument may sometimes be sufficient, but often it is not, and it fails not because decision-makers are unethical, but rather because the argument is insubstantial in itself. That is, logically, for this argument to prevail, it is then true that it is “the organization’s responsibility to assess ALL risks, to be sure….” Organizations cannot be risk-free, and decision-makers are painfully aware of the limited resources they have available to deal with quite real, significant risks, whether those risks are hurricanes, worker safety, foreign exchange, competition, or others. Therefore, the argument needs to be accompanied by sufficient facts and initial analysis to substantiate that some ethical risk exists — the proponent must do some homework. © 2003 by CRC Press LLC
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• Good business — also known as enlightened self-interest, this is often the most effective argument. A bit of homework, consisting of assembling some facts on (1) earthquake history of the region; (2) how other organizations may have been affected in past earthquakes (see Chapter 1, this volume) or even other disasters, such as hurricanes, floods, or fires; and (3) the approximate exposure the organization has in the event of a structural collapse, loss of IT data, or other possible event, can go a very long way toward convincing a CEO that it is worth looking into the matter a bit further. Thus, the basis for a seismic risk assessment should be that it can be cost-effective, reduce potential losses greatly should an earthquake occur, and possibly reduce current insurance and other costs. • Liability — In the United States and many other countries today, an ignorance-of-risk defense is highly questionable, and this should be brought to the attention of decision-makers in a tactful manner. Decision-makers are responsible for protecting the welfare of their organizations and the public today, and are expected to understand the extent of this risk and to deal with it in a responsible manner. Questions such as, “Are you prepared?” are valid, and not inappropriate (Figure 34.2). After a disaster occurs, decision-makers are often held responsible for having made the wrong decision, especially if losses are seen as unacceptably high and all stakeholders were not involved in the decision process. Steps to understand the risk and share the information with the affected stakeholders can help to minimize post-event backlash, even if no action to mitigate is ultimately taken. Once disclosure is made, the stakeholders can either accept the risk or make it known that the risk must be addressed. In either event, the decision-maker who actively addresses earthquake risk and involves all stakeholders is better off than one who does not. • Feasible — Part of any argument for a seismic risk assessment should be that mitigation is feasible. Decision-makers may believe they need to greatly mitigate or even totally eliminate risks once they are discovered, relating this to issues of potential liability. Therefore, some decision-makers may prefer to adopt an “ignorance is bliss” approach to risk management, avoid having positive knowledge of a risk, and believe they have limited potential liability as a result. They believe that if an earthquake causes a building to collapse, it will be considered an act of God for which they will have no liability, particularly if no prior positive identification of the risk was available. Opposing this is that it is often possible to obtain incremental reduction in risk by performing limited mitigation as part of other programs. For example, if an existing building is going to be expanded, seismic upgrade of the building can probably be accomplished concurrently, at little additional cost. Similarly, if a major asbestos reduction program is going to be pursued, it may be possible at very little additional expenditure to perform concurrent seismic upgrades. Until the extent of seismic risk is understood and priorities set for mitigating this risk, the opportunities to embark on such incremental and cost-effective programs cannot be identified. Making the above arguments is not sufficient in themselves. A decision-maker will also want to know what the next steps are, if he or she wishes to proceed. We discuss this aspect next.
34.4 Phase 1: Assessing the Problem Assessing seismic risk, or risk screening, is discussed in some detail in Chapter 2 of this volume. Basically, the process is shown in Figure 34.3, and consists of the following steps: • • • •
Identifying the assets (people, property, functions) at risk Establishing (i.e., quantifying) the seismic hazard Developing performance objectives Performing first a risk screening and then, for selected structures, a more detailed review
Identifying the assets at risk should be relatively straightforward — most organization’s facilities department should have values, personnel counts, etc. readily available. More difficult is determining © 2003 by CRC Press LLC
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FIGURE 34.2 The cover and following page from Guide for Decision-Makers, prepared by the California Seismic Safety Commission, asks, “California’s Next Earthquake — are you prepared?” and states, “The public will want to know what you did to prepare.” (Courtesy California Seismic Safety Commission)
the value of business or functional operations in a particular facility, and this may take a team effort involving operations, the finance department, and perhaps others. Often, this aspect results in some surprises, where a specific facility is found to be more critical than previously believed, due to its housing high-value goods or operations. A classic example often encountered by the author is an organization’s data center, in which the equipment may be worth millions, and yet the building housing the data center has a book value only a fraction of the value of the equipment it houses. In this regard, the data itself may be “priceless” (e.g., it would cost tens of millions to replace, and would result in hundreds of millions in lost revenues if it could not be replaced), and therefore organizations have learned to back up the data offsite, and its value is less an issue. Developing performance objectives should normally be straightforward. A first priority is no loss of life, which normally translates into no significant collapse hazard, and dangerous processes should be able to safely shut down. Following in priority is normally preservation of value, which usually means limited property loss, no loss of essential equipment, and restoration of operations onsite, or at a backup site, within a period of time appropriate for the organization. These two aspects, identifying assets at risk and performance objectives, can be qualitatively assessed using a technique developed by Saaty [1980] termed the Analytic Hierarchy Process (AHP). At the core of the AHP lies a method for converting subjective assessments of relative importance to a set of overall scores or weights. It is a simple yet useful tool, and one of the more widely applied multi-criteria analysis methods. The fundamental input to the AHP is the decision-maker’s answers to a series of questions of © 2003 by CRC Press LLC
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Occupants Buildings Other Structures Equipment Infrastructure Operations Profits Market Share Reputation
Identify Assets at Risk Establish Seismic Hazard
Develop Performance Objective
Buildings/Structures
Equipment
Is it OK per FEMA154?
Is it OK per MLEER 99-0008?
Risk Screening
Stop
Yes
No
Yes
Stop
No
Detailed Review
Stop
Yes
Is it OK per FEMA310?
Is it OK per Equipment Assessment?
No
Yes
Stop
No
ALTERNATIVES
FIGURE 34.3 Earthquake risk assessment. (Courtesy California Seismic Safety Commission)
the general form, “How important is criterion A relative to criterion B?” These are termed pairwise comparisons. Questions of this type may be used to establish, within AHP, both weights for criteria and performance scores for options on the different criteria. In AHP, a very simple series of weights, such as: • “Much more” = 5 • “About the same” = 3 • “Much less” = 1 are applied in a matrix, such that off-diagonal terms are the complement of one another (i.e., if row 1 column 2 is “much more” = 5, then row 2 column 1 is “much less” = 1). A simple example suffices. Suppose a company has the following facilities: headquarters, factory 1, factory 2, warehouse, and R&D laboratory, and wishes to determine the relative value of these facilities on the basis of the number of personnel, the value of building and contents, and the revenues that can be assigned to each facility. This is a multi-criteria analysis (the criteria are lives, property, and revenues) problem. The first task is to determine the relative importance of the criteria. This is done as shown in Table 34.1. In this table, life is assigned a relative value “much more” than property, that is, a value of 5 (and, therefore, property is “much less,” 1). The relative weights of the three criteria are thus: • Life = 10 • Property = 4 • Revenue = 4 The same technique is then applied to each of the facilities, for the facility’s respective values of life, property, and revenue. For example, as shown in Table 34.2, headquarters contains 100 personnel, while factory 1 contains 600, so that headquarters personnel are “much less” than factory 1 personnel, and © 2003 by CRC Press LLC
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TABLE 34.1 AHP Results for Relative Weighting of Three Criteria
1 1
E
3
0
0
5 3
0
5
0
ENU REV
1 LIFE 2 PROPERTY 3 REVENUE 4 5 6 7
PRO
LIFE
PER TY
Criteria
SUM 10 4 4 0 0 0 0
“much less” than factory 2 personnel, “much more” than warehouse personnel, and “about the same” as the R&D laboratory personnel (in numbers of personnel). The sum of the “headquarters” row is thus 10, which is multiplied by the weight assigned to life (which was 10), so that the life-weighted product for headquarters is 100, for factory 1 is 180, and so on. This process is continued, and the final result is shown in Table 34.3, where factory 2 is seen to be the most important facility (highest criteria-weighted sum) and so on, to the least important facility (headquarters1). Although it is somewhat arbitrary, the AHP is a useful tool for obtaining a relative ranking of facilities during the risk assessment process. Quantifying the hazard and developing seismic vulnerabilities are technical aspects that require the expertise of specialist earth scientists, structural engineers, and related experts. Most organizations utilize specialist consultants for this aspect who employ methods detailed in other chapters of this volume. The methods can be highly quantified, although at a screening level of analysis such methods may not be justified. It may simply suffice for facilities to be identified as being on “good” or “poor” soils, from a seismic perspective, and the structures as being similarly “good” or “poor.” In the latter case, a structural engineer’s review in identifying a continuous lateral-force-resisting system (LFRS) is a powerful discriminant. The result of an earthquake risk assessment task is a statement of the potential damage and losses that can result under current conditions. An example is shown in Figure 34.4, which shows the findings for a hypothetical arena that was judged to be a high collapse hazard. The result of the screening is typically qualitative.
34.5 Phase 2: Developing the Program Having performed a risk screening, facilities may be usefully grouped into several categories, such as: I. Probable high risk II. Possible high risk III. Probable low risk with the benefit that the category III probable low risk facilities can be dropped from further consideration. The category I and category II facilities should then be subjected to a more detailed analysis, the product of which is not only a confirmation of their risk, but also the design of strengthening or 1
Author’s note: a result that perhaps many employees already suspected.
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TABLE 34.2 AHP Relative Weights for Facilities, for Two Criteria
1 1
3 5 5
5 5 3 5
5 1 3
1 1
Cr tt 1
0
0
1
SUM 6 14 20 8 12 0 0
3 5 5 3
3
3
1 3 5 3
Cr tt 2
0
R&D
ouse
1 1
SUM 10 100 18 180 18 180 6 60 8 80 0 0 0 0
0
3 1 1
R&D
Ware hous e
5 5 1 3
Ware h
2 Facto ry
5 5 5
y2
1 Facto ry
HQ
1 3
Facto r
PROPERTY 100 600 2000 200 400 0 0
1
y1
1 HQ 2 Factory 1 3 Factory 2 4 Warehouse 5 R&D 6 7
LIFE 100 600 900 25 50
Facto r
1 HQ 2 Factory 1 3 Factory 2 4 Warehouse 5 R&D 6 7
Criteria
HQ
Name of Facility
24 56 80 32 48 0 0
development of other mitigation measures, including the estimation of costs for the mitigation measures. Since this is not a final design, the estimate of costs for structural strengthening or other mitigation measures is necessarily approximate, and is often termed a “rough order of magnitude” (ROM) estimate of costs. An example of a Phase 2 more detailed analysis is shown in Figure 34.5, which shows results of a structural analysis of a San Francisco Fire Department fire station performed under the author’s direction, including a schematic of the structural retrofit scheme and a ROM cost estimate. All facilities falling into categories I and II should be the subject of similar analyses, for structural retrofitting or alternative mitigation measures, as appropriate. Based on analyses such as indicated in Figure 34.5, all category I and category II facilities can be ranked according to their risk, mitigation costs, or other criteria. Table 34.4 shows an example of a hypothetical seismic risk assessment performed for a municipality. Strengthening cost based on a Phase 2 structural analysis is indicated for each facility. Additionally, the facilities are ranked by their benefit-cost ratio (explained below), and the cumulative costs are indicated. The cumulative cost column indicates in what order a limited budget is best spent. In this example, if the organization (i.e., the city) has only $20 million, then it is best spent not on the Fine Art Museum, but on the North Police Station, Fire Station 2, and the Aquarium. This ranking is based on a benefit-cost ratio, developed on the basis of a set of rules created for assessing the benefits resulting from assured seismic functionality of each facility. Benefit is the loss © 2003 by CRC Press LLC
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1 HQ 2 Factory 1 3 Factory 2 4 Warehouse 5 R&D 6 7
0 0
100 80 180 60 80 0 0
24 56 80 32 48 0 0
Cr tt 7
Cr tt 6
Cr tt 5
Cr tt 4
Cr tt 3 E
16 56 80 56 32 0 0
0
0
0
0
ENU REV
Cr tt 2 PRO
PER TY
Cr tt 1
Name of Facility
LIFE
TABLE 34.3 Criteria-Weighted Sums and Final Ranking for Each Facility
SUM 140 292 340 148 160 0 0
RANK 5 2 1 4 3
avoided by mitigation, derived by investing the cost of mitigation. If a large loss can be avoided via a small investment, the benefit-cost ratio is high, and the investment is a good investment. If the required investment is large and only a small loss is avoided, then the mitigation action is not cost-beneficial — that is, it is not worth it. These rules can be as simple as assessing the cost of loss of functionality of the facility as the rent that would have to be paid to provide the same space, if that facility is lost. In the case of a fire station, the benefit should be this rent, plus perhaps some allowance for the fire department not being able to function in the earthquake disaster — that is, some allowance for losses due to fires which the fire department cannot respond to (and also, perhaps, some allowance for lost lives, although the latter are difficult to quantify). In the case of an art museum, some allowance might also be made for damage to the high-value contents — the works of art. While some works of art may be “priceless” (even though they are bought and sold), a good proxy for the allowance would be the insurance premium for the contents. Thus, for each facility, the benefit is determined on a consistent basis, and that benefit divided by the cost of mitigation. The facilities are then ranked by this ratio, as shown in Table 34.4. Such a ranking is meant as a guide for decision-makers and should not be rigidly adhered to — common sense may indicate that a particular facility, although ranked low, may actually be more important than indicated. The true meaning of this overriding of the ranking process is of course that the criteria employed in the process did not truly reflect the actual, usually intuitive, criteria of the decision-maker. The final decision as to what facilities to mitigate will depend on available budget or other resources and is, ultimately, the final expression of the organization’s acceptable risk. That is, the organization must balance what it wishes against what it can afford. The final program, arrived at iteratively, expresses what it can afford, and the allocation of resources is the indication of the risks the organization is willing to incur. This is an important point, in that it is emphasized that the organization’s acceptable risk cannot be decided a priori — it is arrived at in a give-and-take, once the potential losses, and the costs of reducing those losses to various degrees, are known. Much time and effort are wasted in organizations at the beginning of a risk reduction program, trying to decide what is their level of acceptable risk. Leave this decision until the facts are known. Trying to determine acceptable risk early in the process can adversely affect, even prematurely terminate, an earthquake risk reduction program.
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FIGURE 34.4 Example result of a seismic risk assessment.
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FIGURE 34.5 Example Phase 2 seismic risk analysis, with rough order of magnitude (ROM) cost estimate. (Courtesy EQE International)
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TABLE 34.4 Example Result, Seismic Risk Assessment Facility
Strengthening Cost
Cumulative Cost
North Police Station Fire Station 2 Aquarium Natural History Museum Thompson Fine Art Museum Fire Station 17 Justice Center Municipal Building Central library South Police Station Fire Department Headquarters Fire Station 29 Municipal Building Annex Fire Station 24 Downtown parking garage Jefferson Community Center Bayside library Lincoln Community Center
$82,600 $115,500 $6,047,300 $11,663,300 $17,725,000 $887,100 $6,960,300 $10,497,400 $4,178,800 $1,154,500 $2,149,900 $2,590,400 $4,239,600 $1,204,900 $1,018,700 $5,729,800 $1,428,400 $6,276,200
$82,600 $198,100 $6,245,400 $17,908,700 $35,633,700 $36,520,800 $43,481,100 $53,978,500 $58,157,300 $59,311,800 $61,461,700 $64,052,100 $68,291,700 $69,496,600 $70,515,300 $76,245,100 $77,673,500 $83,949,700
Highest
Benefit/Cost
Lowest
34.6 Phase 3: Implementing the Program Implementing the program consists of several key steps, including: • • • •
Retaining seismic retrofit design professionals Funding the program Performing final design Coordinating design and construction with other parts of the organization
We discuss each of the aspects in turn.
34.6.1 Retaining Seismic Retrofit Design Professionals Retaining engineers experienced in seismic retrofit is an important aspect of the retrofit process. One of the most important attributes to look for is experience and satisfactory performance on previous projects. As outlined above, the seismic retrofit professional will typically go about the assessment and mitigation in a three-phased approach, consisting of: • Initial investigation and screening • Detailed investigation and conceptual retrofit design and costing of alternatives • Final design and production of design documents and a “bid package” Step two is perhaps the most crucial from the decision-making viewpoint, since this is where the alternatives are evaluated for cost and effectiveness. In retaining an engineer, a clear and detailed scope of services should form the basis for the relationship. The scope of services must of course be specific to the particular situation, but may consist of the following tasks (services for all three phases are listed below). 34.6.1.1 Phase I: Initial Investigation and Screening 1. Review all available construction documents for the building, including structural and architectural drawings and specifications for the original construction, as well as similar documents for any significant modifications or upgrades. The purpose of this review shall be to determine the basic © 2003 by CRC Press LLC
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2.
3.
4.
5.
6.
7.
8.
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structural load-carrying systems and to identify seismic performance issues related to configuration and structural detailing. Review available geotechnical reports for the site to determine a site class for use in developing seismic hazards and to identify conditions that could lead to ground failure or other site instabilities. Where site-specific soils data are not available, reference should be made to available generalized geotechnical data, such as found on regional maps produced by the U.S. Geologic Survey and the California Division of Mines and Geology. Reference should also be made to the seismic safety element of local general plans. Perform a seismic hazard for analysis for the site to identify the location of the site relative to significant faults, and to estimate the probable intensity of ground acceleration as a function of return period (or probability of exceedance). Conduct a visual survey of the building to document the structure’s condition and to confirm that available construction documents are representative of existing conditions. To the extent that construction documents are unavailable, perform field investigation to develop sufficient information to identify the vertical and lateral structural load-carrying systems, and to quantify their strengths. Perform a preliminary structural evaluation to quantify the probable performance of the building structure to resist the effects of ground shaking having a 10% probability of exceedance in 50 years. (Note that either more or less probable levels of ground shaking may be specified, based on the importance of individual facilities. For facilities located within a few miles of major active faults, it may be more appropriate to specify that the evaluation be performed for a median estimate of the ground shaking resulting from a characteristic earthquake on that fault.) The evaluation should, as a minimum, conform to the requirements of FEMA-310 [Federal Emergency Management Agency, 1998] for a tier 1 evaluation. Alternative evaluations that quantify the adequacy of the seismic-force-resisting system considering strength, ductility, and configuration issues may be used. Develop an inventory of critical nonstructural components, including building utility equipment (power supply, HVAC systems), operating equipment, ceilings, building fascia panels, elevators, and fire protection systems. Identify the adequacy of installation of these nonstructural components to resist damage. Develop a preliminary opinion as to the probable performance of the facilities, in the event of the designated earthquake ground motion (see item 5 above) using the performance levels contained in FEMA-273 and FEMA-310 [Federal Emergency Management Agency, 1997, 1998]. Prepare a written report documenting the scope of study, the findings, and recommendations, with written documentation of the evaluation process (FEMA-310 checklists, calculations, etc.) included as appendices. If preliminary study indicates significant potential for earthquake-induced ground failure and sufficient site-specific soils data are not available to conclusively assess this, the report should include a recommendation for site-specific geotechnical investigation. If the existing construction of the structure is not sufficiently well defined to permit quantification of its structural characteristics, include recommendations for detailed field investigations to confirm the construction.
34.6.1.2 Phase II: Detailed Investigation and Conceptual Retrofit Design 1. Review the phase I evaluation report and available construction documents for the facility to develop an overall understanding of the building’s construction and its probable seismic performance. 2. Conduct a visual survey of the building to observe the building condition and note obvious deviations from the available documentation. Observe potential opportunities for introduction of seismic upgrade elements. Note sensitive areas of the building, such as historic spaces, traffic corridors, etc. that may not be impacted by seismic upgrade measures.
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3. Meet with the facility manager to discuss alternative performance criteria and to select an appropriate criterion, or set of criteria. Also discuss restrictions on placement of retrofit elements, relative to building appearance and functionality concerns. 4. If recommended in the phase I evaluation, perform field investigation of the building to confirm the details of its construction and material strengths. 5. If recommended in the phase I evaluation, obtain site-specific geotechnical data to evaluate potential ground failure and associated mitigation measures. 6. Perform structural engineering calculations to quantify seismic deficiencies in the building relative to the selected performance levels. As a minimum, the criteria of FEMA-310 for a tier 2 evaluation should be performed. Alternatively, the performance analysis procedures contained in the California Building Code, Division IIIR, in FEMA-273, or in the California Seismic Safety Commission’s SSC-96–01 may be used. 7. Review alternative potential methods for seismic upgrade for each specified performance criterion, to a level sufficient to confirm feasibility and to select a recommended approach. Meet with the facility manager to review the alternatives and to agree on the appropriateness of the recommended approach. 8. Develop conceptual-level upgrade designs for each specified performance criteria. Supporting calculations shall be performed to a sufficient level of detail to confirm that the overall size and scope of the recommendations are appropriate. The level of detail should be sufficient to permit an ROM cost estimate to be performed. Consideration should be given to collateral upgrades triggered by the seismic work, including disabled access, fire/life safety, and other code upgrades. 9. Prepare conceptual-level sketches showing recommended upgrades for nonstructural components. 10. Prepare preliminary cost estimates for the recommended seismic upgrade work, for each performance criterion, together with required collateral upgrades. 11. Prepare a report indicating the scope of the study, the findings with regard to building deficiency and performance, and the recommendations for alternative levels of upgrade, as well as any recommendations for additional investigation to be performed as part of final design. Include schematic drawings documenting the upgrade recommendations and cost estimating worksheets in an appendix. 34.6.1.3 Phase III: Construction Documents and Construction Support 1. Assemble a complete design team, including project management, structural engineering, architecture, mechanical and electrical engineering, and cost estimating, as required to support the development of construction documents. 2. Review all available documentation for the building as well as previous evaluation reports and supporting calculations in order to develop an understanding of the building deficiencies and recommended upgrade approach. 3. Meet with the building official as necessary to confirm the design criteria and proposed approach, as well as to confirm the extent of required collateral upgrades. 4. Develop construction documents, including drawings and specifications, together with supporting calculations, to implement the recommended structural upgrades, together with all required collateral upgrades. Submit copies of construction documents to client for review, at the 40% and 90% stages of completion. Final construction documents shall be suitable for obtaining building permits, competitive construction bids, and for executing the work. 5. Prepare an estimate of probable construction cost at each stage of document submittal and for the final construction documents. 6. Provide support to client in the development of bid packages for construction contracts. 7. Respond to comments from plan checkers and revise construction documents as necessary to obtain approval. 8. Respond to bidder requests for clarification.
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9. Provide support to client in evaluation of construction contract bids for completeness and consistency with the requirements of the construction documents. 10. Attend periodic meetings at the construction site, during the construction period, to coordinate construction progress. 11. Conduct periodic site visits to confirm that the work is generally being conducted in accordance with the design requirements. 12. Review contractor submittals and shop drawings. 13. Respond to contractor Requests for Information and assist client in negotiation of contractor change order requests. 14. Review special inspection and test reports. 15. Perform a walkthrough of the project site at 95% completion to develop a punchlist of items not completed by contractor.
34.6.2 Funding the Program Like all programs, earthquake risk management requires the investment of funds. The initial phases of the program, in which the risk is assessed and mitigation options explored, typically entails relatively modest cost. By spreading these tasks out over a period of one or two years, most organizations will be able to accommodate these costs within their normal operating budgets. However, major programs of capital improvement will typically require extraordinary sources of funding. The following sources should generally be considered when planning programs of seismic mitigation: • General operating and maintenance funds. Not all seismic upgrade projects are particularly costly and some seismic upgrades can be done at nominal cost. For example, most equipment items can be anchored or braced for seismic resistance at a per-item cost of a few hundred dollars or less. Many organizations will be able to cover significant seismic upgrade activities out of their general operating and maintenance funds. • Bond issues. If an organization understands its existing earthquake risk and is convinced that this is unacceptable, it may be willing to support additional bonded indebtedness as a means of raising the necessary funds. This is a particularly appropriate mechanism for the public sector. For example, the City of San Francisco obtained permission from its electorate to raise more than $100 million for earthquake safety retrofits of fire stations and other municipal buildings. From a strategic perspective, such bond measures are most successful in the period immediately following a major earthquake somewhere in the world, when the public’s attention is drawn to the issue of earthquake risk. • Special use fees. In some cases, it may be possible to support the cost of seismic upgrade through the establishment of special use fees. As an example, the State of California raised tolls on bridges crossing San Francisco Bay as a means of funding seismic upgrades of these structures. • Hazard mitigation grants. Occasionally, special grants become available from the federal and/or state government for partial funding of seismic mitigation work. These grants may be offered as (1) seed money for demonstration projects, to encourage and attract other sources of funding; or (2) in order to reduce risk of damage in future earthquakes and to help communities become more self-sufficient. These grants are usually available only for public or nonprofit organizations and often are restricted to, or give preference to, certain types of projects. For example, using funding obtained under the Proposition 122 bond program, the State of California made limited mitigation funding available to cities, counties, and similar agencies. Generally, projects to strengthen emergency response facilities, such as fire stations, police stations, and city halls, received priority over other types of projects. When mitigation grant programs are available, communities must typically apply for funding in competition with others. In addition, it is usually necessary for the enterprise to provide some co-funding of the project, often in the amount of 10 to 20% of total project costs. © 2003 by CRC Press LLC
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• Tax preferences and credits. Certain tax credit and tax preference incentives are available for the rehabilitation of facilities. Special facilities, such as qualified historic landmarks, are prime candidates for other tax incentives. These incentives are typically applicable only to private, for-profit enterprises. In order to qualify for these incentives, it is necessary to comply with certain historic preservation standards and to be subjected to a review and approval process for the design.
34.6.3 Coordinating with Other Parts of the Organization It is very important to include earthquake risk mitigation measures with other facets of an organization’s asset management program. Key issues related to this are the following: • Often, by performing seismic upgrade work concurrently with other planned projects, it is possible to reduce the cost and disruption of the upgrade work. For example, a common requirement of seismic upgrade programs for low-rise buildings with wood roof structures is to increase the nailing of the plywood roof sheathing. This can only be done upon removal of the roofing. Clearly, if such upgrade work is performed concurrently with routine replacement of the roofing system, it will be far more economical. • If an existing facility is assessed as incapable of providing adequate seismic performance for its current use, consider changing its mission to be more compatible with its seismic performance category. For example, if a critical care wing of a hospital is judged incapable of immediate postearthquake occupancy, and there is simultaneous need to develop new outpatient care at the facility, the best choice may be to build new critical care space and convert the existing space to use for outpatient care. • Consideration should be given to the length of time a facility is expected to remain in service. If a facility is scheduled for replacement or retirement in the near future, it makes little sense to invest in upgrade of the facility. • Construction for seismic improvements to a facility will often trigger mandatory requirements to perform other types of upgrades, such as disabled access improvements, hazardous material abatement, and fire/life safety improvements. These collateral upgrade requirements can have substantial impact on the implementation cost and, in some cases, the cost of collateral upgrades is higher than the seismic construction cost. It is important to account for these impacts when evaluating the cost of seismic mitigation. Earthquake risk cannot be managed effectively in a vacuum. The decision-maker and the risk manager must involve the facilities or asset manager in planning and implementing the mitigation program in order to assure that collateral issues are addressed and all capital improvements are coordinated. It is also important to ask professional consultants, who may be retained to assist in quantifying risk and suggesting mitigation alternatives, to be mindful of these needs.
34.6.4 Perform Seismic Retrofit Performing the seismic retrofit consists of the following steps: 1. Retaining a team of design professionals to develop construction documents, using the phased approach described above. Result: a series of specifications for performing the desired upgrade work and reliable estimates of probable construction cost. 2. Identifying funding sources for performing the work. Available funding sources were discussed in the previous section, and include: • General operating and reserve funds • Grant programs operated by HUD (Housing and Urban Development), FEMA, and other agencies • General obligation bonds © 2003 by CRC Press LLC
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Result: sufficient funds to execute the required construction work. 3. Hiring retrofit contractors. This is an important aspect of the retrofit process. As with hiring a contractor for any other purpose, one of the most important attributes to look for is experience and satisfactory previous performance. Generally, public agencies will have to use a competitive bid process for the selection of a contractor. It is recommended that a process of bidder prequalification be performed, prior to requesting construction bids, to assure that bidders have adequate resources and experience. Result: on-board contractor, ready to go. 4. Scheduling the work so as to minimize disruption, in coordination with tenants, managers, or operators, is another important aspect. Note that construction scheduling can have a significant impact on construction costs. Therefore, any scheduling requirements or constraints that will be imposed on the contractor, such as limiting work to certain periods of time or requiring that work in certain sections of a facility be staged, should be clearly included in the general conditions section of the specifications used to solicit contractor bids. The selected contractor should be requested to submit a detailed construction schedule, incorporating the client-specified milestones and indicating the specific timing of work by different trades. Result: schedule for construction. 5. Construction. Result: retrofitted facilities. 6. Maintaining the retrofitted facility. Retain as-builts, specifications, and engineer’s maintenance instructions in the retrofitted building or other archive. Use a plaque or other notice to ensure that these materials are not lost or overlooked. Result: complete record of retrofit.
34.6.5 Dealing with Residual Risk After the seismic upgrade work has been completed, the seismic risk associated with a facility will be greatly reduced from original levels. However, some residual risk will remain. Prudent risk management suggests that effective steps be taken to further minimize the residual risk, through the steps outlined below. 34.6.5.1 Emergency Plan Even relatively minor damage to a facility can result in extended interruption of service and loss of use, if no-one knows what to do about assessing its condition, securing potentially hazardous contents and utilities, and conducting repairs so that service can be restored. Emergency response plans that clearly designate the persons responsible for each of these actions, and how they can be contacted in the event of an emergency, can significantly reduce the amount of confusion and lost time when an earthquake actually occurs. In addition to basic information on who is responsible for specific actions when an emergency occurs, emergency response plans should include information on the critical equipment and systems within the building, the structural system, expected types and locations of damage, and checklists for specific postearthquake actions to be taken. For critical facilities, the emergency operations plan can also include provision for alternative work spaces, in the event that damage is so severe that reoccupancy of the facility within the short term is not feasible. 34.6.5.2 Risk Transfer Earthquake insurance can be an effective method of guarding against the direct financial losses associated with an earthquake and is commonly used in the private sector for this purpose. Earthquake insurance is very effective in reimbursing a property owner for the direct costs related to repair of damage. It is less effective with regard to reimbursement for business interruption costs, as often the quantification of these costs is difficult and therefore subject to dispute. It is also important to note that most earthquake insurance policies include significant deductibles and will not cover upgrades to the facility that may be triggered by the building official as part of damage repair work. The cost of earthquake insurance is highly variable and depends as much on the global financial markets and health of the insurance industry as it does on the actual risk associated with a facility. In some years insurance can be obtained at a fraction
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of its real value, while in other years, it may cost several times its actual value or may not be available at all. This is why it is prudent not to rely on earthquake insurance as the sole means of risk management. Another aspect of risk transfer involves an organization’s suppliers and customers. To the extent that provisions for special circumstances in the event of an earthquake can be written into contracts, then the earthquake risk has been transferred. For example, if obligations to purchase supplies or deliver product can be relaxed in the event of an earthquake, then additional time is gained by the organization during its crisis period. Keeping this aspect in mind during contract negotiations, as an ongoing aspect, can pay handsome dividends in the event of an earthquake, at little or no cost. 34.6.5.3 Physical Redundancy and Geographic Dispersion One of the most effective techniques for mitigation of earthquake risk is to disperse operations into independent locations at different sites. Although the effects of earthquakes can be widely dispersed over a region of many square miles, the most extreme earthquake effects are typically limited to a small fraction of the affected region. If all of the physical facilities associated with an operation are concentrated at a single site or location, there may be significant potential for damage to this physical facility to completely interrupt operations for an extended period of time. However, if the physical facilities are dispersed to multiple locations, it becomes much less likely that all of these facilities would be damaged to an extent that would limit operations at all of the locations. Thus, dispersion can become an effective tool to maintain at least partial operational capability following a major earthquake. To the extent that the dispersed facilities provide redundant capacity, it may be possible to provide full operational capability if some of the facilities become damaged. 34.6.5.4 Data Backup Redundant storage of critical records and data can be a highly effective risk mitigation technique. Following the 1989 Loma Prieta earthquake, the City of Oakland’s Building Department found itself displaced from City Hall, which had been severely damaged by the earthquake. The building department stored microfilm copies of the original construction drawings for private buildings in archives maintained within City Hall. The red-tagging of that building effectively made these records unavailable for many months following the earthquake, hampering the efforts of the community to assess and repair damage sustained by other buildings. Had a redundant set of microfilm records been maintained in another, offsite, location, it is highly unlikely that access to both sets of data would have been lost. Public agencies and private businesses can maintain their own off-site records storage or, alternatively, they can rely on any of a number of providers of this service. This may be particularly important for electronic records that are maintained on-line. There are a number of private data centers that provide stand-by electronic records storage, as well as data processing capability. 34.6.5.5 Retain Structural Engineers and Contractors Following the 1989 Loma Prieta earthquake, the City of San Francisco’s Building Inspection Department found itself overwhelmed by the demand to perform post-earthquake safety inspections of public and private buildings in the city. Even with the assistance of many volunteer inspectors, it took a period of months before all buildings were evaluated and their conditions determined. During this period of time, building owners and tenants were often at a loss to know whether it was safe to reoccupy damaged buildings, leading to extensive economic losses. In order to avoid these problems in future earthquakes, the City of San Francisco later established the voluntary Business Occupancy Resumption Earthquake Inspection Program (BOREIP). Under the BOREIP, building owners can retain qualified structural engineers to perform post-earthquake inspections of their buildings in the event of a future earthquake. These engineers must develop a post-earthquake inspection plan for the building and be certified by the city as deputy building inspectors for the specific building. Under the program BOREIP inspectors are obligated to perform post-earthquake inspections within 36 hours of the occurrence of an earthquake disaster. They then have the authority to post buildings, as inspected, following an earthquake, on behalf of the city.
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Building departments can develop similar programs to speed the post-earthquake recovery of their communities. In addition, even in the absence of such programs, individual public and private building owners and tenants can retain structural engineers to perform rapid post-earthquake assessments of buildings, to advise as to whether the buildings are safe for occupancy and to develop repairs in the event these are required. While these engineers would not have the power to officially “post” a building, they can provide assurance as to the condition of its structure and appropriate recovery actions. It is often beneficial to develop retainer agreements with engineers before the earthquake actually occurs. In the days and weeks immediately following a major earthquake, structural engineers are extremely busy and are unlikely to be available on short notice unless advance arrangements have been made. It may also be beneficial to develop similar retainer agreements with general contractors, so that there is assurance that in the event repairs are needed, construction capability to effect these repairs will be available.
34.7 Maintaining the Program In many ways, the actual earthquake mitigation program has been performed when the following actions have been carried through to completion: • Facilities have been strengthened, or otherwise dealt with such that their risk is acceptable. • Emergency response and business continuity plans have been developed and exercised. • Residual risk has been insured, transferred, or accepted. However, organizations are dynamic and facilities, operations, and personnel are constantly changing. Thus, documentation of the steps taken, including the process and criteria, is an important step to complete. As new facilities or operations are developed, the same or enhanced criteria can be applied to them, thus retaining the overall balance of the earthquake mitigation program. As new personnel join the organization, they can review the earthquake mitigation program documentation and maintain the overall goals. Finally, when (not if) the earthquake occurs, there are a number of important steps to be quickly performed, including: 1. Assessing the extent of damage. The first thing that should be done following an earthquake is to assess the extent of damage that has occurred. It is necessary to assess whether physical facilities that are relied upon for operations are functional and safe, as well as to estimate the amount of time they may be out of service. It is impossible to implement an effective response and recovery program until these data are known. For many public agencies, the responsibility for post-earthquake damage assessment may extend beyond the need to assess the performance of the physical facilities that the agency relies upon for operation, to include an assessment of the extent of damage and loss that has occurred community-wide. For example, if housing in a community is severely impacted, public agencies will be expected to provide for the temporary shelter and care of displaced families. If a number of building collapses have occurred, public agencies will be expected to assist in locating and extracting victims. In order to effectively respond to such needs, it is necessary to be able to rapidly assess the likely extent of damage and loss. These assessments can be made by performing rapid post-earthquake reconnaissance or, alternatively, by implementing one of several disaster simulation software packages that permit rapid estimation of losses. Regardless of the method an agency or business elects to pursue, a current emergency response plan and previously negotiated agreements with necessary engineering consultants and contractors can speed this phase of the recovery effort. 2. Implementing emergency operations procedures. As soon as an assessment of damage is made, and the extent of impairment of ability to provide service and the need for these services is ascertained, recovery operations should commence. In the period immediately following the earthquake, individual public agencies and private businesses will have to rely on their own resources. An © 2003 by CRC Press LLC
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effective emergency response plan can help to smooth the difficult immediate post-event recovery period. Within days to weeks, outside assistance will begin to become available from such sources as FEMA, the State of California Office of Emergency Services, the American Red Cross, and other volunteer agencies. In extreme emergencies, military assistance may also be made available. 3. Restoring normal operations. Over a period of days to weeks and, in the worst disasters, perhaps a period of years, normal operations will be restored. The length of time necessary for restoration of normal operations will be directly dependent on the severity of the event, as well as the extent to which risks were identified and mitigated, and emergency response plans developed prior to the event. It many cases, what is deemed to be “normal operations” after the earthquake is not the same condition that existed before the event. Earthquakes can have far-reaching economic and social impacts that can completely change the character of a community and the long-term profitability of individual businesses. For this reason, it is particularly important that public leaders view earthquake risk reduction not only as their responsibility with regard to protection of public facilities, but a responsibility that the entire community must share. One of the major benefits of proactive risk mitigation on the part of a public agency is that it sets a leadership example for the community at large. 4. Assessing the lessons learned. An important but often overlooked concluding step in the process is a carefully conducted review of the loss and recovery experience. No matter how well prepared a community or business is for an emergency, it will typically find that unanticipated problems developed and that preparation could have been better. Although severe earthquakes are rare events, it is possible for some communities in California, Japan, or other high seismicity regions to experience major damaging events several times during a typical lifetime. The San Fernando Valley, for example, experienced large-magnitude events in both 1971 and 1994, located within a few miles of each other. A careful assessment of what went wrong and what went right in the disaster can allow for better preparation for the next event, as well as serve as valuable learning tools for other communities that have not yet been affected by earthquake disaster.
Defining Terms Benefit — The loss avoided by mitigation. Benefit-cost ratio — Ratio of avoided losses to cost required to avoid those losses. Both amounts should be computed on the same basis. For example, if the mitigation cost is the current cost of retrofitting, then the benefit should be computed in present value dollars. Earthquake mitigation — Actions taken to reduce the effects or unwanted consequences of earthquakes, such as human casualties, structural damage, or business interruption. Actions can be taken prior to an earthquake (e.g., strengthening a building) or after the earthquake (e.g., activating a business continuity plan). Exposure — What is at risk — that is the total value of assets that could conceivably be lost due to a hazard such as earthquake. If 100 workers are employed in a company in or near one location, that company’s exposure at that location is 100 employees. Lateral-force-resisting system (LFRS) — The structural system in a building or structure that resists lateral forces, arising, for example, from an earthquake. In order to resist an earthquake, a structure must have a LFRS continuous to the foundation. Surprisingly, many pre-code structures may not have a demonstrable LFRS, and therefore are collapse hazards. Risk management — An integral activity of an organization, normally centralized in a risk management department headed by the risk manager and associated with the chief financial function. Ideally, risk managers monitor and manage all sources of risk to the organization aside from those associated with the organization’s central mission. For example, in a manufacturing company, the risk manager will deal with property, life, and health risk, but not market or foreign exchange risks or worker safety. In dealing with property risk, the risk manager will normally purchase
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property insurance, but will also examine alternatives to insurance, such as strengthening a building for earthquake so as to reduce the need for earthquake insurance. Rough order of magnitude (ROM) estimate of costs — ROM estimates are made at an early stage in the design or development of a project. By ROM is not meant, in the mathematical sense, variations on the order of powers of 10, but rather within a factor of ±2. Therefore, if the ROM cost estimate for strengthening a building is $1 million, it is anticipated that the final cost will not be less than $500,000 and not more than $2 million. ROM estimates are refined in later stages of the design or development process, such that final cost estimates are usually ±20% or less.
References Federal Emergency Management Agency. 1997. “NEHRP Guidelines for the Seismic Rehabilitation of Buildings,” FEMA 273, prepared by the Building Seismic Safety Council for the Federal Emergency Management Agency, Washington, D.C. Federal Emergency Management Agency. 1998. Handbook for the Seismic Evaluation of Buildings: A Prestandard, FEMA 310, prepared by the American Society of Civil Engineers for the Federal Emergency Management Agency, Washington, D.C. Saaty, T. 1980. The Analytical Hierarchy Process, John Wiley & Sons, New York.
Further Reading Earthquake Risk Management: A Toolkit for Decision-Makers, prepared by the California Seismic Safety Commission and available via their Web site (www.seismic.ca.gov), is a useful compendium of methods and tools for developing and implementing an earthquake mitigation program. The author was involved in the development of the Toolkit and drew on it for this chapter, but it contains much additional material and is highly recommended. Also recommended are two accompanying publications: A Guide for Decision-Makers and Earthquake Risk Management: Mitigation Success Stories, both also available via the Commission’s Web site.
© 2003 by CRC Press LLC
