Structural Mechanics of Buried Pipes

STRUCTURAL MECHANICS OF

BURIED PIPES Reynold King Watkins Utah State University Logan, Utah

Loren Runar Anderson Utah State University Logan, Utah

CRC Press Boca Raton London New York Washington, D.C.

©2000 CRC Press LLC

©2000 CRC Press LLC

GENERAL NOTATION Geometry A = cross sectional wall area per unit length of pipe, B = breadth of the trench D = pipe (tank) diameter, H = height of soil cover, h = height of water table, L = length of tank or pipe section, r = radius of curvature of the pipe (tank) cylinder, R = radius of a bend in the pipe, t = thickness of the wall, x = horizontal coordinate axis, y = vertical coordinate axis, z = longitudinal axis (with exceptions), β = angle of soil shear plane. Forces, Pressures, and Stresses P = external pressure on the pipe or tank, P' = internal pressure, p = vacuum in the pipe or tank, Q = concentrated force, W = surface wheel load, γ = unit weights, σ = direct (normal) stress, τ = shearing stress. Subscripts refer to directions of forces and stresses. Properties of Materials c = cohesion of soil, E = modulus of elasticity of pipe (tank) material, S = allowable stress (strength) of material, γ = unit weight of material, ν = Poisson ratio, ϕ = soil friction angle.

©2000 CRC Press LLC

CONTENTS Chapter 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

Introduction Preliminary Ring Design Ring Deformations Soil Mechanics Pipe Mechanics Ring Stresses Ring Deflection Ring Stiffness Non-circular Cross Sections Ring Stability Encased Flexible Pipes Rigid Pipes Minimum Soil Cover Longitudinal Mechanics Thrust Restraints Embedment Parallel Pipes and Trenches Special Sections Stress Analysis Plastic Pipes External Hydrostatics Buried Tanks and Silos Flotation Leaks in Buried Pipes and Tanks Long-Span Structures Non-circular Linings and Coatings Risers Analysis of Buried Structures by the Finite Element Method Application of Finite Element Analysis to a Buried Pipe Economics of Buried Pipes and Tanks Appendix A: Castigliano's Equation Appendix B: Reconciliation of Formulas for Predicting Ring Deflection Appendix C: Similitude Appendix D: Historical Sketch Appendix E: Stress Analysis Appendix F: Strain Energy Analysis

©2000 CRC Press LLC

PREFACE Buried pipes are an important medium of transportation. Only open channels are less costly to construct. On the average, pipelines transport over 500 ton-miles of product per gallon of fuel. Gravity systems require no fuel for pumping. Ships transport 250 ton-miles per gallon. Rails transport 125 ton-miles per gallon. Trucks transport 10 ton-miles per gallon. Aircraft transport less than 10 ton-miles per gallon of fuel. Buried pipelines are less hazardous, and less offensive environmentally than other media of transportation. They produce less contamination, eliminate evaporation into the atmosphere, and generally reduce loss and damage to the products that are transported. The structural mechanics of buried pipes can be complicated -- an interaction of soil and pipe each with vastly different properties. Imprecisions in properties of the soil embedment are usually so great that complicated analyses are not justified. This text is a tutorial primer for designers of buried structures -most of which are pipes. Complicated theories are minimized. Fundamentals of engineering mechanics and basic scientific principles prevail. "Science is understanding gained by deliberate inquiry."

-- Philip Handler

ACKNOWLEDGMENT Gratitude is expressed to Becky Hansen for her patient and expert preparation of manuscript.

©2000 CRC Press LLC

©2000 CRC Press LLC