Description of the HDM-III Model

THE HIGHWAY DESIGN AND MAINTENANCE .STANDARDS SERIES

9951 VOL. 1

1t'

I S7'

0

Volume 1 Description of the HDM-III Model Thawat Watanatada, Clell G. Harral, William D. 0. Paterson, Ashok M. Dhareshwar, Anil Bhandari, and Koji Tsunokawa

*

...............

______

AWorldBank Publication

_

~

7-

g

0~

...

-

H 4

:4'-

_

THE HIGHWAYDESIGNAND MAINTENANCESTANDARDSSERIES

The Highway Design and Maintenance Standards Model Volume 1. Description of the HDM-III Model

Thawat Watanatada William D. 0. Paterson Anil Bhandari

Clell Harral Ashok M. Dhareshwar Koji Tsunokawa

in collaboration with Wee-Beng Aw Jonathan Rich Per E. Fossberg Theodora Underhill Edward Holland Sujiv Vurgese

Published for The World Bank

TheJohns HopkinsUniversityPress Baltimore and London

© 1987 The International Bank for Reconstruction and Development / The World Bank 1818 H Street, N.W., Washington, D.C. 20433, U.S.A. All rights reserved Manufactured in the United States of America The Johns Hopkins University Press Baltimore, Maryland 21211 First printing December 1987

The findings, interpretations, and conclusions expressed in this study are the results of research supported by the World Bank, but they are entirely those of the authors and should not be attributed in any manner to the World Bank, to its affiliated organizations, or to members of its Board of Executive Directors or the countries they represent.

Libraryof Congress Cataloging-in-PublicationData The Highway design and maintenance standards model. The Highway design and maintenance standards series) Bibliography:p. Contents: v. 1. Description of the HDM-IIImodelv.2. User's manual for the HDM-II model. 1. Roadsi-Design-Mathematical models. 2. RoadsMaintenance and repair-Mathematical models. 3. RoadsDeterioration-Mathematical models. 4. Motor vehiclesCost of operation-Mathematical models. I. Thawat Watanatada. II. World Bank. IlI. Series. TE175.H54 1987 625.7 87-22733 ISBN 0-8018-3591-7(v. 1) ISBN 0-8018-3592-5(v. 2)

Foreword An effective road transportation network is an important factor in economic and social development. It is also costly. Road construction and maintenance consume a large proportion of the national budget, while the costs borne by the road-using public for vehicle operation and depreciation are even greater. It is therefore vitally important that policies be pursued which, within financial and other constraints, minimize total transport costs for the individual road links and for the road network as a whole. To do this meaningfully, particularly when dealing with large and diverse road networks, alternatives must be compared and the tradeofffs between them carefully assessed. This in turn requires the ability to quantify and predict performance and cost functions for the desired period of analysis. Because of the need for such quantitative functions, the World Bank initiated a study in 1969 that later became a large-scale program of collaborative research with leading research institutions and road agencies in several countries. This Highway Design and Maintenance Standards Study (HDM) has focused both on the rigorous empirical quantification of the tradeoffs between the costs of road construction, road maintenance, and vehicle operation and on the development of planning models incorporating total life-cyclecost simulation as a basis for highways decisiomnaking. This volume is one in a series that documents the results of the HDM study. The other volumes are: v

Vehicle Operating Costs Evidence from Developing Countries VehicleSpeeds and Operating Costs Models for Road Planning and Management Road Deterioration and Maintenance Effects Models for Planning and Management The Highway Design and Maintenance Standards Model Volume 2. User's Manual for the HDM-III Model

The Highway Design and Maintenance Standards model resulting from the HDM study is now in its third version, HDM-III. It incorporates the relationships described in the other volumes of this series, as well as a road construction submodel, into interacting sets of costs related to construction, maintenance, and road use. These are added together over time in discounted present values, in which costs are determined by first predicting physical quantities of resource consumption and then multiplying these by unit costs or prices. HDM-mI is designed to make comparative cost estimates and economic evaluations of different construction and maintenance options, including different time-stagingstrategies, either for a given road project on a specific alignment or for groups of links on an entire network. The user can search for the alternative with the lowest discounted total cost and can call for rates of return, net present values, or first-year benefits. If the HDM is used in conjunction with the Expenditure Budgeting Model, the set of design and maintenance options that would minimize total discounted transport costs or maximize net present value of an entire highway system under year-to-yearbudget constraints can be determined. Adequate analysis of the many possible combinations of alternatives is too large a task for manual calculation. Even when analysts have had access to computers of sufficient capacity, they have been hampered by the lack of two essentials: an efficient simnulationprogram embodying an appropriate model and with procedures for using it and an adequate body of empirically established relationships among the relevant variables. The HDM-III model fiDlsboth of these needs. It is not only a readily usable program for handling the voluminous computations automatically, it is also a repository of the most extensive and consistent set of empirical data on the subject. The information includes the qualitative structure and

iii

quantitative parameters of relationships among construction standards, maintenance, traffic characteristics, road deterioration, and vehicle operating costs. This volume describes the HDM-III model and its constituent components and provides a comprehensive discussion of the submodels, their interaction, and the operational parameters involved. A companion volume, User's Manual for the HDM-III Model, is essentially for computer mainframe uses, but it also provides the basis for the currently available PC versions. Clell G. Harral Principal Transport Economist

Per E. Fossberg Highways Adviser

iv

Contents 3

Chapter 1. Introduction 1.1 The Problem 3 1.2 The Highway Design and Maintenance Standards Model (HDM) 5 1.3 Empirical Quantification of the Basic Relationships 10 1.3.1 Road construction costs 10 1.3.2 Vehicleoperating costs andotheruser costs 11 1.3.3 Road deterioration and maintenance effects 20 1.3.4 International Road Roughness Experiment 26 1.4 Conclusions 29 1.4.1 Validation of the models 29 1.4.2 Applicabilityof the HDM model in diverse physical and economic environments 31

Chapter 2. Model Operations and the Traffic Submodel 2.1 2.2 2.3 2.4 2.5 2.6

35

Basic Operations 35 Data Input and Diagnostics 35 Simulation Phase 36 Economic Evaluation and Reporting Phase 40 Interface with Expenditure Budgeting Model 41 TheTraffic Submodel 41 2.6.1 Trafficvolumes 41 2.6.2 Axle loadings 43

Chapter 3. Road Construction Submodel

47

3.1 Basic Computational Procedure 47 3.2 Predicting Road Construction Quantities 51 3.2.1 Site preparation 51 3.2.2 Earthwork 52 3.2.3 Drainage 54 3.2.4 Bridges 57 Appendix 3A. Forrnulation and Estimation of Relationships for Predicting Road Construction Quantities 59

Chapter 4. Road Deterioration and Maintenance Submodel 4.1 Paved Road Concepts and Logic 68 4.1.1 General concepts 68 4.1.2 Computational logic 71 4.1.3 Pavement structural characteristics 75 4.1.4 Pavement classification 80 4.1.5 Trafficcharacteristics 80 4.1.6 Environment and geometry 82 4.1.7 Variabilityanduncertainty 83 4.1.8 Local adaptation (deterioration factors) 84 4.2 Paved Road Deterioration Prediction 85 4.2.1 Variablesat beginning of analysis year 85 4.2.2 Cracking initiation and progression 87 4.2.3 Ravellinginitiation and progression 98 v

67

4.2.4 Potholing initiation and progression 101 4.2.5 Surface damage at the end of the year before maintenance 4.2.6 Rut depth progression 104 4.2.7 Roughness progression 107 4.3 Paved Road Maintenance Intervention 109 4.3.1 Classificationand hierarchy 109 4.3.2 Routine-miscellaneousmaintenance 110 4.3.3 Patching 113 4.3.4 Preventive treatments 115 4.3.5 Resealing 118 4.3.6 Overlay 122 4.3.7 Pavement reconstruction 125 4.3.8 Pavement parameters after maintenance 126 4.4 Unpaved Road Logic 128 4.4.1 Classification,concepts and logic 128 4.4.2 Material properties 129 4.4.3 Trafficloadingmeasures 130 4.4.4 Road geometry measures 130 4.4.5 Environment: climate and drainage 130 4.4.6 Basic computational procedure 133 4.4.7 Initialization of variables 134 4.5 Unpaved Road Deterioration and Maintenance 135 4.5.1 Road roughness 135 4.5.2 Material loss 142 4.5.3 Passability 142 4.5.4 Grading maintenance options 144 4.5.5 Spot regravelling 145 4.5.6 Gravel resurfacing maintenance 146 4.5.7 Routine-miscellaneousmaintenance 148

104

Chapter 5. Vehicle Operating Cost Submodel 5.1 General Outline 149 5.1.1 Operation of the submodel 149 5.1.2 Choiceofrelationships 150 5.2 The Brazilrelationships 153 5.2.1 Vehiclespeeds 153 5.2.2 Fuelconsumption 166 5.2.3 Tirewear 170 5.2.4 Maintenanceparts 176 5.2.5 Maintenancelabor 181 5.3 Relationships Used with AllOptions 185 5.3.1 Lubricants consumption 185 5.3.2 Crew requirements 185 5.3.3 Vehicledepreciation and interest 186 5.3.4 Overhead 191 5.3.5 Passenger delays 191 5.3.6 Cargo holding 191 5.3.7 Miscellaneous costs 194 5.4 Unit Costs 196 Appendix 5A. Comparative Vehicle Characteristics and Input Requirements for Alternative VehicleOperating Cost Models 197

vi

149

Chapter 6. Alternative Vehicle Operating Cost Relationships

201

6.1 Selectionof the Relations 201 6.2 The Kenya Relationships 202 6.2.1 Vehiclespeed 202 6.2.2 Fuel consumption 204 6.2.3 Alternative Kenya fuel consumption relationships 207 6.2.4 Tire wear 207 6.2.5 Maintenance parts 208 6.2.6 Maintenance labor 210 6.3 The Caribbean Relationships 211 6.3.1 Vehiclespeed 211 6.3.2 Fuelconsumption 212 6.3.3 Tire wear 213 6.3.4 Maintenance parts 214 6.3.5 Maintenance labor 215 6.4 The India Relationships 215 6.4.1 Vehiclespeed 215 6.4.2 Fuel consumption 216 6.4.3 Tirewear 218 6.4.4 Maintenance parts 219 6.4.5 Maintenance labor 221 Appendix 6A. Modificationsof TRRL-KenyaRelationships 222 Appendix 6B. Modificationsof India Relationships 230

Chapter 7. Benefits, Costs and Economic Analysis

233

7.1 RoadBenefitsandCosts 233 7.2 VehicleBenefitsandCosts 234 7.3 Exogenous Benefits and Costs 236 7.4 Economic Analysisand Comparisons 236

241

Chapter 8. Expenditure Budgeting Model 8.1 Multiple-period,Multiple-ConstraintExpenditureBudgeting 242 8.2 Single-periodExpenditure Budgeting: Economic Interpretations 248 Appendix 8A. Dynamic Programming Method 253 Appendix 8B. Effective Gradient Method 256

Glossary of Terms

259

References

275

vii

Acknowledgments This book is the result of a collaborativeeffort between many individualsand organizations who have contributed directly or indirectly to the various phases of development of the model and to the writing of the book. First of all, thanks are due to those who established the first model for rigorous analysis to optimize road policies and to minimize total transport cost: F. Moavenzadehand B. Brademeyer of Massachusetts Institute of Technology.We also thank those who contributed to the viabilityof the concept and the model through empirical validation: S.W. Abayanayaka, H. Hide, J. Rolt, R. Robinson, and many others at the Transport and Road Research Laboratory in UK; C.G. Swaminathan, L.R. Kadiyali and E. Viswanathan of the Central Road Research Institute in India, as well as the Governments of Kenya and India. Particular thanks are due to the United Nations Development Programme and the Government of Brazil for their sponsorship of the large highway research project which laid the basis for the empirical and theoretical work underlying the major set of relationships in HDM-III. In addition to the numerous contributors to this basic work, special thanks in the context of the HDM-III model are due to T. Lustosa, J. Swait and P.R.S. Resenda Lima of the Brazilian transport planning agency (GEIPOT),and to R. Hudson, B. Butler, R. Harrison, H. Orellana, and L. Moser of Texas Research and Development Foundation; and A. Chesher of Bristol University. In the writing of the book we have enjoyed the continuous suppot of all the above, as well as many others too numerous to mention. Within the World Bank, we appreciate the continued support of Christopher Willoughby and Louis Pouliquen, respectively the former and present directors of the Transportation Department. Thanks are also due to our numerous Bank colleagues, who over the years have used the various versions of the HDM model, with great patience and understanding for the difficulties encountered in setting up and using a complex model, and who have contributed with suggestionsand positive critiques. Finally,we want to express our thanks to S. Lo and R. Archondo-Callao for the excellent research and programming assistance and to E. Danowski, R. Bensky and M. Wu for their great skilland unfailing patience in producing the many drafts that the manuscript went through.

viii

The Highway Design and Maintenance Standards Model Volume 1. Description of the HDM-III Model

CHAPTER1

Introduction

1.1 THE PROBLEM More than 10,000millionsdollarsare spent each year on highway construction,maintenance,and administrationby governments in the developing countries of Africa, Asia, and Latin America. In the industrialized economiesof Europe,NorthAmerica,and Japan the total is but somethingmore than 10 timesas great. These numbersare impressive, it must also be noted that the costs borne by the road-usingpublic for vehicle operation and depreciationare of a much larger magnitude, typically-8-to 10-foldthose borne by the government. Moreover,travel time constitutesan additionalcost which can assume paramountimportance economies. in high-income In Europeand North America,from which until recentlymany of the road design and maintenancepracticesof the whole world have been derived,one sees that factorssuch as high trafficvolumes,high values abundantcapital attachedto motorists'traveltime savings,and relatively resourceshave dictated high standardsof road design and maintenance. With several thousandvehiclesper day, even minute savings in vehicle on road operatingcostsand traveltime can justifyvery largeexpenditures alignmentsand pavements. But even in the wealthy countriesbudgetary of economic are now forcinga re-examination pressureson road authorities priorities. which are the focusof The situationin the developingcountries, World Bank activities,is much differentand, of course,far more severe. Relative endowmentsof capital and labor are much different,traffic volumes are typicallymuch lower, incomesand values attachedto travel time savingsare far lower,and above all there is an acute shortageof financialresourcesin general,and foreignexchangein particular. These differencessuggestthat optimaldesignand maintenancestandardscould be quite differentin the developingcountries.Competingdemandsfor limited resourcesdictate that low-incomecountriesmust search for the most economicdesign of highwaysand maintenanceprograms,taking into account also the much largercostsof vehicleownershipand operationborne by the well-justified road users. And even then therewill be many economically projectswhich cannotbe undertakenbecauseof budgetaryconstraints,so that it becomes imperative to develop a system for assessing the priorities. But how are we to decide priorities? What is the benefit to societyof anotherdollar spent on maintenance,comparedto anotherspent of existingalignments?Is it more economical on new roadsor improvements to spend a bit more money to constructa strongerpavement initially,

3

4

INTRODUCTION

thereby permittingthe use of larger,more economicvehiclesand saving future outlays on road maintenanceor, alternatively, should we follow a stage constructionstrategy,economizingon the initial construction, vehicleaxleloadsand payingmore in the way of maintenance butrestricting and upgradingcosts later on, when possibleuncertainties about traffic growthwill have been resolved? How much, or how little,shouldwe spend to maintain paved roads, and how much to maintainand upgradeearth and gravelroads? And does it mattermuch if maintenance outlaysare postponed duringyears of financialstringency? To address these and similar issues the World Bank in 1969 initiated the Highway Design and Maintenance Standards study which ultimatelybecame a major program of collaborativeresearch involving in severalcountriesto developa new quantitative basis for institutions decisionmaking in the highwayssector. In PhaseI of the study,completed in 1971, a team at the MassachusettsInstitute of Technology, in conjunctionwith the BritishTransportand Road ResearchLaboratory,the French LaboratoireCentraledes Ponts et Chaussees,and the World Bank, developed a conceptual framework and a first prototype model for interrelating the life-cyclecostsof highwayconstruction, maintenance and vehicleoperation(Moavenzadeh et al., 1971). While the conceptualframeworkwas felt to be promising,the accompanyingsurvey of previous research revealed an absence of sound empiricalevidencefrom which the fundamental cost relationships could be quantitativelyestablished. Consequently,subsequent phases of the research have concentratedon empiricalquantificationinvolvingfield collectionof new primary data on the underlyingphysicaland economic to ensure that the theoreticalmodels conform to the real relationships world as closelyas possible. Four such studieshave been carriedout up to the present time -- in Kenya, the Caribbean,Brazil,and India -- as describedbelow. As the empiricalvalidationprogressedand experiencewas gained in applyingthe earlierversionsof the model in highwayplanningin more than 30 countriesworldwide,the Highway Design and MaintenanceSeries (HDM) model has undergoneextensivefurtherdevelopmentand a companion ExpenditureBudgetingModel (EBM) has also been developed(Harralet al., 1979; Watanatadaand Harral, 1980a;Watanatadaand Harral, 1980b). The current third generationversionof the model, HDM-III,draws on all of this researchand experienceand is the focusof this book. In the remainderof this chapterwe providea simple conceptual overview of the model: its scope, structure,and operation,a summary description of its theoretical underpinnings and empiricalvalidation, and, in the final section,a brief evaluationof the range of validityof the to diversephysicaland economicenvironmodel and its transferability ments. In Chapters2-6, we providea more detaileddescription of the model, its varioussubmodels(traffic,construction, roaddeterioration and maintenance, and vehicleoperatingcosts)and the interactions among them. Finally,Chapter 7 delineatesthe economicanalysisfeaturesof the HDM model, while Chapter8 discussesthe ExpenditureBudgetingModel (not an integralpart of the HDM itself)and the interfacebetweenthe two. The comprehensive Volume2: HDM-III User's Manual guides the user on model

INTRODUCTION

5

and everydayusage. For users interestedin studyingthe implementation program structureof the model with a view to altering the code to Guide (Rich incorporateresultsof their furtherresearch,a Programmer's and Underhill,1987) is available. The readerwho wishes to examinethe theoreticaland empiricalfoundationsof the model in greater depth is referred to the other volumes in the Highway Design and Maintenance 1 StandardsSeries. It is importantto note at this point five importantlimitations of the presentHDM model: first,the vehicleoperatingcosts submodelhas not yet been validatedfor congestedtrafficconditions.Second,the road submodelhas not been validatedfor freezingclimates,nor deterioration third, does it encompassrigid pavements. The readerwho must deal with any of these conditionsmust recognizethat the HDM model at its current stage of development,if used at all, must be used with cautionto avoid misleadingresults. (Indeed,in usingany suchmodel outsidethe specific physicaland economiccontextin which it was estimatedrequirescaution a point to whichwe returnin the final and attentionto localcalibration, address sectionof this chapter.) Fourth,the model does not endogenously impactssuch the issueof road accidentsnor, fifth,broaderenvironmental as air or noise pollution,although these costs, where known, can be exogenouslyincorporated.Thus the model in its presentform will be of littleinterestto the analystwho is primarilyconcernedwith the analysis interventions.Nor safetyor environmental of rigidpavements,congestion, design,ratherit is is the model intendedto be used for finalengineering a tool for economic analysis of alternativestandards,either at the projector networklevel. 1.2

MODEL (HDM) THE HIGHWAYDESIGNAND MAINTENANCE

To constructand maintainthe road networkhighway,authorities must choose from a wide range of options,involvingthe initialstandards of pavement and roadway alignmentand the frequencyand standardsof and subsequentroutine and periodic maintenance,pavement strengthening size on vehicle policies public related Closely improvements. geometric and weight limitsmust also be determined. These choices,in turn,have a strong influenceon the cost of vehicleoperationand therebythe cost of freightand passengertransport. The numberof alternativedesign/policy combinationsis very large and decisionstaken today will influence operationsand costsfor years to come.

1 VehicleOperatingCosts: Evidencefrom DevelopingCountries,Chesher and Harrison(1987). VehicleSpeedsand OperatingCosts: Modelsfor Road Planningand Watanatadaet al. (1987). Management, Effects: Modelsfor Planningand and Maintenance Deterioration Paterson(1987). Management,

INTRODUCTION

6

Thus, the basic task is to predicL total life-cyclecosts -construction, maintenance and road user costs -- as a functionof the road design, maintenancestandardsand other policy options which may be 2 considered. To have a generallyapplicabletool, one must know the effects of different environments(terrain,climate, traffic, driver behavior,economicconditions)on the differentcost relationships. To search over many alternativestrategiesto determinethe most economic, there must be a capabilityfor the rapid calculationand comparisonof alternative cost streamswhichmay extendovermany years. The broadconceptof the HDM model,as illustrated in Figure1.1, is quite simple. Three interactingsets of cost relationships are added togetherover time in discountedpresentvalues,where costsare determined by first predictingphysicalquantitiesof resourceconsumption which are thenmultipliedby unit costsor prices:

1

1terrain,soils,rainfall; geometricdesign;

Construction costs =

f1 pavementdesign;unit costs

Maintenance costs =

Road user costs

J

roaddeterioration (pavementdesign,climate, f2 time,traffic);maintenance standards; unit costs

=

geometricdesign;road surfacecondition; f3 vehiclespeed;vehicletype;unit costs

Vehicle speed, which is a major determinantof vehicle operatingcosts, itself relatedthrough a complex set of probabilistic functionsto road geometricdesign,surfacecondition,vehicletype and driverbehavior. The HDM model is used to make comparativecost estimatesand economicevaluationsof differentpolicyoptions,includingdifferenttime stagingstrategies, eitherfor a given roadprojecton a specificalignment or for groups of links on an entirenetwork. It can quicklyestimatethe total costs for large numbersof alternative projectdesignsand policies year by year for up to thirty years, discountingthe future costs if desiredat differentpostulatedinterestrates,so that the user can search for the alternativewith the lowest discountedtotal cost. Or, if he prefers,the user can call for comparisons in terms of rate of return,net present value, or first year benefit. Another capability,using the ExpenditureBudgetingModel, is findingthe set of design and maintenance options that would minimizetotal discountedtransportcosts or maximize 2 In certain circumstances an even broaderdefinitionof societalcosts is necessary,e.g., where the costs of air pollutionfrom road use sufferedby non-road-users is significant.Such externalcosts,may, if known,be enteredinto the model throughthe exogenousbenefitsand costs facility.

INTRODUCTION

7

Figure1.1: The HON Model: Interactionof Costs of Road Construction Maintenance and Use

CONSTRUCTION Envirola eent(climate, terrain, materials) Technology

M AEEMESTR STANDARDS

rDesign, OualIityControl: Unit Cot

I~~~~~

s

M4AINTEN COSTS

COSTSJ

/ Maintenance Pan,| Execution: Unit

_DeTRIOR _ tOD sION & MAIUTENANCE Envlronmeni (climate and malerials) Technologyl

FMAINTENANCE STANAD

\Condition:

_.yolue,

\ Vehle~~~~~~ile Speeds andl Journey Times _ Operating Costs

RoughnessJ__ TRAFFIC Sz WeGhoth Vlm,Got

TRAFFICREGULATIO~NS

8

INTRODUCTION

net present value of an entire highway system under multi-yearbudget constraints.In additionto comparingalternatives, the model can analyze the sensitivityof the results to changes in assumptionsabout key variablessuch as unit cost, trafficgrowth rates,the discountrate,and the valueof passengers' time. A generalsummaryof the scopeof the model in terms of input requirements, their limitsand the outputsthat can be generatedis providedin Table 1.1. As seen from the table, in a single computerrun, the model can evaluateup to twentydifferentroad links,each havingup to ten sections with differentdesign standardsand environmental conditions. Each link can have a differenttraffic volume. Further, differentmaintenance standardscan be implementedon differentsections. At any time, any section can be upgraded (e.g., from earth to gravel or from gravel to paved)and the road can be realignedor widened. Altogether,up to fifty pairs of alternatives can be comparedin one run. In order to make these comparisons, of course,the model must be given detailed specificationsof the various alternative sets of construction programs,designstandards, and maintenance and otherpolicies to be analyzed,togetherwith unit costs,projectedtrafficvolumes,and environmental conditions. Since there is always the possibility of error in coding these inputs,the model includesan extensivecheckingprogram which examinesthe inputsfor formalerrorsand internalinconsistencies. Warning messages are automaticallyproduced when such errors or inconsistencies are found,or when the programis requestedto extrapolate relationships beyondtheirempirically validatedrange. Once the apparentinput errors have been corrected,the model estimatesspeedsand resourceconsumption of the vehiclesas well as road deterioration and resourcesfor maintenance for all the combinations.The resourcerequirements for road construction for each design optionmay be endogenouslyestimatedin the model or may be directlyspecifiedby the user if he has more specificinformation or local data. After physical quantitiesinvolvedin construction, maintenance, and vehicleoperationare estimated,user-specified pricesand unit costs are applied to determine financialand economiccosts. Comparisonsin terms of relativebenefits, presentvalue,and rate of returncalculations then follow. The user has a wide range of optionsin specifyingwhat resultshe wants includedin the printedreport. Because some of the model relationshipshave highly complex non-linear forms, simulation, rather than any formal optimization technique,is employed in the HDM model itself,and the "optimization" which takes place in that model is merely the selectionof the group of alternatives with the highestdiscountednet benefitsamong thosespecified by the user. There is the possibilitythat an untriedpolicycombination couldexistwhich would providesuperiorresultsto any of those specified for analysis. However,the ease of specifyingand analyzinglargenumbers of alternativesreducesthe practicalimportanceof this limitation-- and the alternativeapproachof simplifyingthe relationships to a form more amenableto formaloptimization could constitutea criticaldeparturefrom the complex realitiesof the physicalworld. When the user comes to

INTRODUCTION Table 1.1:

9

HDM-III Model Inputs and Outputs Inputs

Input limits

o Link characteristics (existing roadand envirormentalfactors)

20 links

o Constructionprojects ard costs (wideningor nemconstruction standardsfor assigningto links)

50 projects with maxinmu duration of 5 years for any oneproject

o Maintenance standardsandunit costs (intervention criteria, properties andcosts for assigningto Tinks)

30 standards

o Vehicle fleet characteristics andunit costs (ccmnon to all link-groups)

9 vehicle types

o Traffic volunes, distribution ard growth (sets for assigningto links)

20 traffic sets

o Exogenous costs andbenefits (sets for assigningby link)

20 sets

o Link alternatives (assign to links the above construction andmaintenance standards, traffic andexogenous C-8sets)

100

o Groupalternatives (assign link-alternatives to link-groups)

100 group alternatives involving not more than 20 groupsor 100link-alternatives

o NuT,erof studies, econcmiccarparisonsand sensitivity analysis (defines groupsto be caTpared and type of analysis)

Up to 5 studies with raximungroupcarparisons of 50 with the numberof alternatives caypared not to exceed200; 5 discount rates (in addition to zero) per study

o Reportrequests(unifonmper run)

MaxiniLm of 500 reports

o Analysis period (uniformper run)

Upto 30years with the productof link alternatives andnuTberof analysis years not to exceed800 Outputs

o Roadmaintenance sumry (by link or group) o Annualroadmaintenance costsand physical quantities (by link or group) o Annualtraffic (link only) o Annualroadconditions (link only) o Annualroaduser costs andphysical resourcesconsunption (link only) o Financial costs of alternative (link or group) o Econanicand foreign exchange costs of alternative (link andgroup) o Cacparison of costs of alternatives (link andgroup) o Surmaryof caTparisonof alternatives by discount rate (link andgroup) o Sumaryof costs andcaoparisonsby discount rate (link alt vtimsonly)

10

INTRODUCTION

considerthe impactof expenditureconstraintson the compositionof the best feasiblegroup among the alternativesspecified,formal optimization techniques,in the fom of dynamicprogramning or heuristicapproximations thereto,are availablein the Expenditure BudgetingModel. 1.3 EMPIRICALQUANTIFICATION OF THE BASICRELATIONSHIPS Of the three basic sets of relationships -- construction,road deterioration/maintenance and road user costs -- it was evident at the conclusionof the firstphase of the researchthat most of what was needed was alreadyknown about estimatingconstruction costs,but far too little was known about the relationships of user costs, road deterioration and maintenancecosts to road designand maintenancepolicies. Consequently, only limitedresearcheffortwas devotedto fillingcertainspecificneeds with respect to constructioncosts, and, since vehicle operatingcosts constitutemuch the largestcomponentof total life-cyclecosts (typically 70-90percentof totalcosts in low-incomecountries), the greatesteffort was devotedto that subject. Largeeffortswere also made to establishthe road deteriorationrelationships which are the major determinants of both road maintenancecostsand vehicleoperatingcosts. We deal with each of thesein turn. 1.3.1 Road Construction Costs Constructioncost estimationis one of the oldest and best established branchesof engineering, and earlierversionsof the HDM simply provided for construction costs for different alternatives to be exogenously specifiedby the user -- which is still retainedas one option in HDM-III. However,as comprehensive highwaysector (or network)level planning assumed Increasingimportance,the need for an additional, endogenousfacilityfor estimatingconstruction costs was perceived. At the stage of highway sector planningand resourceallocationwhere the range of investmentoptions to be examinedis the widest, policy-makers need a method of constructioncost predictionthat requires minimal information inputsand yet producescost estimatesproperlysensitiveto a broadspectrumof designstandardsand terraincharacteristics. After realizingthat no suchmethodexistedin suitableform,the WorldBank and the Massachusetts Instituteof Technologyinitiatedin 1980 a small-scalecollaborative study to developa set of relationships for predictingroad construction costs that would meet the broad requirements above. As detailedin Aw (1981),roadconstruction data were compiledfrom 52 road projectslocatedin 28 countriesin Asia, Africa,and Centraland South America. The regionsin which these road projectswere constructed covera broad spectrumof topographic, climaticand soil characteristics -from flat plainsin the Sudan to extremelymountainous areas in Nepal,from the abundanceof monsoon rainfallin Pakistanto the dryness of inland Africa,and from areas of good soilmaterialsto landsof poor road-making volcanicash. The types of constructionvaried from feeder roads to four-lanefreeways,from earth roads to concretepaved roads,and from 30 to 100 km/h design speeds. The first productas reportedin Aw (1981, 1982) and Markow and Aw (1983)essentiallyconsistedof a comprehensive data base and a set of preliminaryrelationships with heavy relianceon

INTRODUCTION

11

engineeringprinciplesin their formulation. These relationships were furtherrefinedintoa form suitablefor generalapplications, as reported of the in Tsunokawa(1983). Chapter3 belowprovidesa summarydescription data base as well as the resultingmodelsand their functioning within the HDM model. 1.3.2 VehicleOperatingCostsand OtherUser Costs A decision was made early in the program to concentrate user-costsresearchon vehicleoperatingcosts relationships rather than the value of time and accident costs. Three factors entered this decision. First, not only are vehicle operatingcosts the largestcost component in low-incomedevelopingcountries,but there was already considerableevidenceto suggest that they were relativelysensitiveto variationsin road design and surface condition-- yet none of these relationswere then well quantifiedover a wide range of conditions. Second, as to the value of time, a great deal of complex (but not altogetherfruitful)researchhad already been conductedin high-income and a review countries,where time savingscan assumedominantimportance, of this literature(Yucel,1975)indicatedthat simplermethodscouldyield approximations to these values that were probablyno more unsatisfactory methods in than those yielded by any of the more "sophisticated" use -- and, in any case, in developingcountries,which are characterized the issue is by low incomesand often extensiveun- or under-employment, estimate much less important. (TheHDM model does,of course,endogenously specifiedby the travel times, but the value of time must be exogenously model user.) Third, with respect to accidents,a complicatedset of among driver behavior and causalitiesprevails,with interdependencies and it was felt that within the HDM importantthan road characteristics, beyondthe much larger-scale researchprogram littlecouldbe contributed researchefforts already underwayworldwide. Moreover,accidentcosts, althoughquite large in the aggregate-- as much as 1 percent of GNP in some developingcountries(Jacobsand Sayer, 1983) -- are quite small in relationto vehicleoperatingcostsand are in generalnot as sensitiveto accidentcosts are not variationsin road characteristics.Consequently, endogenouslymodeled in the HDM, but may be specifiedexogenouslywhere estimatesare available. With respectto vehicleoperatingcosts,major primary research studies were conductedby various institutionsin Kenya (1971-75),the Caribbean(1977-82),Brazil (1975-84)and India (1977-83). In this field of researchcertainkey variablescan be measuredquickly,e.g., vehicle speeds and fuel consumption,while other variables, e.g., vehicle maintenance, can only be observed over longer periods of time. each of these studiescontainedthree differentcomponents: Consequently, (1) observationsof vehicle speeds under normal usage for a stratified sample of the road network;(2) controlledexperimentsto establishfuel and (3) consumption speed relationsas a functionof road characteristics; a user cost survey collectingrecordsover time from large numbers of vehicleoperators,for all operatingcost components,stratifiedby road characteristics.Table 1.2 providessummary descriptorsindicatingthe in eachof thesestudies. size and rangeof observations

12

INTRODUCTION

Kenyaand the Caribbean The first of these studieswas the Kenya study conductedby the BritishTransportand Road ResearchLaboratory(TRRL)in collaboration with the KenyaMinistryof Works and the World Bank (Hide et al., 1975). This pioneeringstudy began developmentof basic measurementmethodologies (Abaynayaka, 1976) and was able to establish simple statistical relationships -- mostly in linear forms -- betweenthe variousoperating cost components(fuel,tires,vehiclemaintenance,driver'stime, vehicle depreciation and interest)and the principalroad characteristics (surface type, roughness,vertical and horizontalalignment)for the somewhat limited range of conditionstypical of Kenyan roads. A particularly importantdiscoverywas that of the large effect of road roughnesson vehicleoperatingcostsfor both pavedand unpavedroads-- althoughin the case of paved roads the rangeof roughnesswas limitedto a value of 4.5 m/km IRI due to the relativelygood conditionof paved road surfaceswhich prevailedin Kenyaat the time of the study. Similarlythe range of vertical and horizontalgeometry was necessarilylimitedbecauseof the essentiallyrollingterrainof Kenya. Consequentlythe relationshipsfor estimatingvehicle performancewere limitedto maximumgradientsof 8 percentand maximumhorizontalcurvatures of 250 degrees per kilometer,and it was not possible to isolate the effectsof road geometryon any operatingcost componentotherthan fuel. Moreover,sincethe linearcorrelation modelsdo not incorporate any of the underlyingphysicaland behavioralprocesses,and all effectsare additive, extrapolationcan produce unreasonableresults. Indeed, if the Kenya models are extrapolatedover higher ranges of vertical and horizontal geometries,as requiredfor the null (or 'baseline') case in incremental benefit-costanalysesof alternativealignmentsin more severe terrain, they predictnegativespeeds. Thereforethe smaller-scaleCaribbeanstudy was designed and undertakenby the TRRL as a complementary effort to further study the effectsof geometryand to extendthe rangeof the relationships for hilly and mountainousterrain and for very rough paved roads. (Hide, 1982; Morosiukand Abaynayaka,1982). Becausethey were conductedby the same team using the same methodologies, observingsimilarvehicletypes (except that buseswere not includedin the latterstudy),the Kenyaand Caribbean studiesprovidea good basisfor comparisonand an opportunity to evaluate how different physical and economic environmentsaffect the basic relationships. The speed observationsand controlledfuel experimentswere conductedonly on the island of St. Lucia, with rollingto mountainous terrain,where verticalgradientsup to 11 percentand horizontalcurvature up to nearly 1,100 degrees per kilometerwere observed. The user cost surveyencompassed also the islandsof Barbados,Dominica,and St. Vincent, with varyingterraincharacteristics, permittingsome stratification in the sample. All are small islands,so that the trip lengthand averageannual kilometersutilization by the vehiclesare quite low in comparisonto other countries.

INTRODUCTION

13

Table 1.2: Scopeof PrimaryStudies on Vehicle Operating Costs Kenya

Caribbean Brazil

India

A. Usersurvey Typesof vehicles 5 4 5 3 Totalvehicles 289 68 1675 939 Largest truckGVW 26 12 40 28 Comfpanies/operators NAV NAV 147 121 Lengthof observations (yr.) 2 2 4 3 Sizeof roadnetwork monitored (km) 9,300 NAV 36,000 40000 Rangeof routeaverage Roughness (m/kmIRI) 3.3-9.0 3.5-11.4 1.8-14.9 5.4-12.9 Averagerise+ fall(m/km)14.8-69.4 8-68 10-49 5.8-41.3 Horizontal curvature (deg/km) 1.5-49.7 90-1040 6-294 25.6-675.3 B. Speedobservation studies Sites Typesof vehicles No. of observations Rangeof specific links Roughness (m/kmIRI) Vertical gradient (%) Horizontal curvature (deg/km) Roadwidth(m)

95 5 NAV 2.1-22.1 0.1-8.6 0-198 3.5-7.9

28 4 38,000

108 6 76,000

102 6 14,000

2.0-14.6 1.6-12.2 2.8-16.9 0-11.1 0-10.8 0-9.1 0-1099 0-2,866 4.3-8.5 5.5-12.9

1-1243 3.5-7.0

C. Controlled experiments: Fuel Testsections Typesof vehicles Vehicle type Observations Rangeof specific links Roughness (m/kmIRI) Vertical gradient (%) Horizonal curvature (deg/km)

95 82 51 NAV 3 3 9 5 1 1 1 or 2 1 NAV 1,161-2,296 1,192-5,344 104-411 2.1-22.1 1.0-8.6

2.0-14.6 0-11.1

.0-198

0-1099

2.1-13.3 2.9-11.7 0-13 0-5 0-340

NAY

Sources:Kenya:Hide et al. (1975);Caribbean: Hide (1982);Morosiukand Abaynayaka (1982);Brazil:GEIPOT(1982); Watanatada et al. (1987); India:Central RoadResearch Institute (1982).

14

INTRODUCTION

Several important conclusionsemerge from the comparisons. First, the major influenceof road roughnesson operatingcosts noted in Kenyawas confirmedin the Caribbean, where it was furthershownthat these effectsare generallylargeron very badlydeteriorated paved roads (> 4.5 m/km IRI) than would be indicatedby a linearextrapolation of the Kenya relationships.Indeed,the rate of spareparts consumption and tire wear on badlydeteriorated bituminousroads in the Caribbeanwas higherthan on gravelroadswith the same measureof roughnessin Kenya (a fact which may be attributableto differencesin the exact profile of the surface irregularity which are not discernedby the bump-integrator instrumentused for measurement). Second, with respect to vehicle speeds, the linear models estimatedin St. Lucia predictfree speeds under ideal conditions(i.e., level,tangentroads)markedlylowerthan in Kenya,while the reductionsin speed from those already lower levels caused by poorer road geometric characteristics are far less substantial, most coefficientsrangingfrom less than 20 percentto just over 40 percentof the Kenyan coefficients. This may be due to actual behavioraldifferences--that in severe terrain where severalfactorsexist to suppressspeed,driversare less sensitive to an improvementin one factor alone. This type of physical and behavioralphenomenoncannot be captured by simple linear forms which assumeconstantsensitivity as reflectedin additivecoefficients. These resultscall into questionthe applicability of the model forms employedin both the Kenyanand Caribbeanstudies. While the TRRL team (Morosiukand Abaynayaka, 1982)proposeda simplelinearinterpolation of the Kenya and Caribbeanspeedequationsto deal with applications of the modelsin thirdcountrieswhere terrainconditionslie betweenthe extremes observedin Kenya and the Caribbean,other researcherssoughtalternative approaches, as discussedbelow,which incorporate theoretical modelsof the complexphysicaland behavioralmechanismsinvolvedin determiningvehicle speeds. Brazil

By far the largestof the fourmajor fieldstudieswas the Brazil study,conductedbetween1975 and 1984 by a joint team of specialists from 3 Braziland nine other countries. With the full advantageof the results of the Kenya study,and real resourcesmore than five times as large,the Brazil study employed more advanced theoretical and statistical methodologiesand generateda far larger data base covering in most respectsa broaderrange of road characteristics and vehicletypes better stratifiedacross the factorialdesign. Moreover,advanceswere made in measurement methodsfor the key variableof road roughness, as discussedin Section 1.3.3 below. Finally, this data base was most intensively exploitedwith successiveroundsof analysesover severalyears leadingto successivereformulation of models,and new experiments were undertakento 3 Financedprimarilyby the Governmentof Brazil and the United Nations DevelopmentProgram,the studywas executedby the EmpresaBrasileira de Planejamento de Transportes(GEIPOT)jointlywith a team from the World Bank and the TexasResearchand Development Foundation.

INTRODUCTION

15

address issues generated from the earlier analyses, as greater was gained. Substantialgains were made, both in model understanding formulationand statisticalestimation(GEIPOT,1982; Watanatadaet al., 1987). One of the major advances in the Brazil research was the modelsfor predictingvehiclespeedsand fuel of new non-linear development consumptionbased on mechanisticand behavioralconcepts,in contrastto the simple linear correlationforms employed in both the Kenya and the physicalmechanismsand Caribbeanstudies. By explicitlyincorporating governingbehavioralconstraintsin the models through a probabilistic in predictingvehiclespeeds limitingvelocityapproach,their performance which need to be over the wide rangesof alternativeroad characteristics much improved. By analysis is examinedin any incrementalbenefit-cost they providea realisticarray of formulations, relyingon probabilistic modelled by either of two actual outcomesin any specificsituation--as micro methodswhich mimic detailedspeed behavioralong the heterogeneous road alignment. The statisticalmethodologiesemployed also provide propertieswhich permit the same theoretical aggregatemodels incorporating thus furnishing the use of less detailed average road characteristics, predictionsof average speeds and fuel consumptionwhich are still sensitiveto the alternativeroad standardsnormally consideredat the et al., 1987). The latterhave been stageof economicanalysis(Watanatada model. the HDM-III into incorporated to comparethe speedpredictionsresultingfrom It is instructive the Brazilian,Caribbeanand Kenyan models. We draw on the normalized resultsgiven by Chesherand Harrison (1987). We adopt the supposition that for free speed under ideal conditionsand for average speeds each model is the respectivebest predictorfor the specificcountryin which it to note that was estimated. With respectto free speeds it is interesting speeds in Kenya and Brazil were generallynot too different,generally within ± 5 percent except in the case of buses, where Brazilianbuses (often long distance express services)travelledat speeds nearly 12 percent higher. Free speeds in the Caribbean,as already noted, were substantiallylower. With respect to the effect of different road characteristicstwo aspects are particularlynoteworthy. First, the non-linearBrazilianequationsyield slopes with respect to geometric which are not too differentfrom thoseof the Kenyanmodels characteristics over the rangeof the Kenyanmodelsand slopeswhich are not too different from the Caribbeanmodels over the range of poorer geometricconditions in Figure1.2, which graphspredicted observedthere. This is illustrated speeds of passengercars against horizontalcurvaturefor all of the models,but only over that rangefor which each was estimated; a similar though somewhat more mixed pattern holds for other vehicle types on horizontalcurvatureand for all vehicleson verticalalignment. Thus the Brazilmodels tend to supportthe conclusionfrom the Kenya studythat the first deviationsfrom the ideal conditionhave very large effectsand to supportthe conclusionof the Caribbeanstudy that furtherworseningof road geometry,once geometryis alreadybad, has greatlyreducedeffects. However,as a country of vast land area, free speeds observedon level higherthan those tangentroadsin Brazilwere observedto be significantly in the Caribbeanwhich comprisesonly small islandson which trips were

16

INTRODUCTION

necessarilyshort. Thus the model estimatedin Brazil would overpredict the responseof speedto smallchangesin curvaturefor betterroadsin the Caribbean(or India,as shown in Figure1.2 and discussedbelow),and some calibration, especiallyof desired speeds,to local conditionswould be necessary. Second,the estimatedeffectof road roughnesson vehiclespeeds, as illustratedin Figure 1.3, is quite similarfor all vehiclesfor the Kenyan, Caribbeanand Brazilianmodels over the lower to middle ranges (lessthan 5 mrkm IRI), but over the higherrangesof roughnessthe Brazil modelsestimatemuch sharpereffects,which are similarto the estimatesof the Indian models. Thus, once again the non-linearforms, reflecting theoretical properties, of the Brazilian models were deemed most appropriate for generalized model formulation. Given the success in estimatingthese mechanistic-behavioral models for vehiclespeedsand fuel consumption, and the strongpresumption that other cost componentsmay be physicallycloselyrelatedwith vehicle speedsand operatingpower requirements, the Brazilteam was encouragedto extend the same modellingprinciplesto the estimationof tire wear and vehicle maintenancecosts. Fortunately,significantresearch into the physicaltheoriesof tire performancehad been developedelsewhereby the early 1980swhich provideda firm basis for estimation. Despitethe fact that the data base in Brazil was ill-structured for such modelling,the resultingmechanisticmodels for tire wear developed in Brazil yield plausibleresults. They were deemed to be a significant advanceover the earlier linear correlationmodels, providinga better basis for both present use and future research. However,further researchto provide improvedmodels of tire consumptionwould be desirable,particularlyin isolatingthe respectiveeffectsof verticaland horizontalgeometryand superelevation,for policy-analysis purposes,and of tire construction type, rubbermaterial,road surfaceabrasiveness, ambienttemperature, and otherfactorsfor localadaptationpurposes. Unfortunately, the absenceof an acceptedbody of theoryrelating the physical wear and tear of vehicles to road characteristics, plus limitations in the data base, prevented any success in estimating mechanistic-behavioral models for that cost component. Consequently, for prediction of vehicle maintenance costs resort had to be made to correlationmodels. Fortunately,plausibleresultswere obtained with simplemodel forms for this component,with coefficients with respectto road roughnessnot too dissimilarto thosefoundin Kenyaand the Caribbean (Chesherand Harrison,1987). India Thereare severaluniquecharacteristics of roadsand trafficin Indiawhich argue againstthe applicability of models estimatedelsewhere. First,much of the Indiannetworkis stillsingle-lane with two directional flows. Second,the trafficmix, althoughvery limitedin termsof normal road vehicletypes and designs,is extremelyheterogenous when accountis takenof the multitudeof slow-moving vehicletypes (agricultural tractors, bullock carts, donkey carts, horse carts, bicycle rickshaws,bicycles,

INTRODUCTION

17

Figure1.2: Vehiclespeedversuscurvature for cars Speed (km/h) 807060

-.

50-

'

*

~

-

~ ~ ~

-- S

K ~~~~

30-

-S.---

---------

~ ~ ~ ~~

-----------

--------

20. '10-

0

200

400

600

800

1,000

1,200

Curvature(deg/km) Equations: B K C I

Brazil: Medium cars Kenya: Cars - Caribbean: Cars - India: Cars = =

UnLits:V RF C R

= Speed = = =

(km/h) Rise plus Fall (in/kin) Curvature ('/km) Rouighness(mm/kmn)

Variables not Plotted: RS = 15 rn/km FL = Fall - 15 rn/km R = Roughness = 5,500 mm/kmn M = Moisture Content (Kenya only) = 2.6% RD - Rut Depth (Kenya only) 18.9 mm W - Width (India only) = 7 in ASE = Average Superelevation (Brazil only) =0.01 (fraction) ALT = Altitude (Brazil only) -0 GVW = Gross Vehicle Weight (Brazil only) = 1.4 tonnes

Source:AdaptedfromChesher and Harrison, 1987

18

INTRODUCTION

Figure 1.3: Vehiclespeedversusroughnessfor cars Speed(km/h) 100 90 80

N.

70

.

K

60_ 50

B (paved)

-

B (unpaved) 40 30 20 10 I

Oil

0

2

4

I

6

8

10

12

14

16

18

Roughness (m/km IRI) Equations:

B K C I

Variables

-

not

Brazil: Medium cars Kenya: Cars Caribbean: Cars India: Cars

Plotted:

RS

Units:

FL R

- 15 m/km - Fall - 15 m/km - Roughness - 50°/km

M

=

RD

- Rut Depth

V RF C R

-

Speed (km/h) Rise plus Fall (m/km) Curvature ('/km) Roughness (mm/km)

Moisture Content (Kenya only) (Kenya only)

=

=

2.6%

18.9 mm

W - Width (India only) - 7 m ASE - Average Superelevation (Brazil only) - 0.01 (fraction) ALT - Altitude (Brazil only) - 0 GVW - Gross Vehicle Weight (Brazil only) - 1.4 tonnes Notes:

Results are graphed only for the range covered by the respective field studies.

Source: AdaptedfromChesherand Harrison,1987.

INTRODUCTION

19

thus etc.), each with different speed performance characteristics, of trafficflow analysis. Third,the wearing the complexities compounding surfaces of paved roads (reflectingindigenoustechnologiesoften with insufficientquality controls)tend to be unusually rough, even when relativelynew (althoughnormallynot as extremeas the badly potholed paved roadsobservedin the Caribbeanstudy). In order to address the very different road and traffic conditionsin India,the CentralRoad ResearchInstitute(CRRI-NewDelhi) in December1976 by the Governmentof Indiaand the World was commissioned Bank to undertakea Road User Costs Study. This projectencompassednot on only the three basic studiesof vehiclespeeds,controlledexperiments fuel-speedrelations,and a comprehensiveuser cost survey, but also includedpilot studieson simulationmodelingof congestedtrafficflows, road accidentcosts,and the value of time savings(CRRI,1982). A rich data base was collected,but, althoughextensiveanalyseswere performed, it was not possiblewithin the resourcesand time availableto the project instability in the to exploitthis data base fully. There is considerable coefficientsfor given factors across alternativemodel forms, which results in ambiguitiesand contradictions. Moreover, further data collectionis needed to extend the range of validationof the very promising traffic flow simulationmodels which have been developed. Consequentlythe results obtained so far must be viewed as highly tentative,and furtherresearchis deemedessential. Indeed,it is hard to and modellingthe avoid the conclusionthat the processof understanding under of vehiclespeed-flowand operatingcost relationships complexities Indianconditionshas only just begun. Nonetheless,some importantaspects are already quite clearly established. First, road roughnessis once again shown to be a major and determinantof vehicleoperatingcosts;the importanceof establishing good ridingsurfacesis unquestionable.Second,even underthe maintaining best free-flowingconditionsIndian vehiclestravel at very low speeds, ratiosfor all presumablyat least in part due to the very low power-weight vehicles. Despitethe alreadyvery low free speedsof motorizedvehicles, vehiclesseverelyreducesthe speedsof the the presenceof non-motorized averagemotor vehiclespeedson motorizedtraffic,so thatas a consequence amongstthe lowest rural highwaysin Indiaare extremelylow, undoubtedly in the world. To bring roadtransportserviceup to higherstandardswould probablyrequirea combinationof measures includingtraffic separation, vehicle designs and road geometry and surfaces to achieve a new equilibrium; improvementsin any one dimensionalone may yield little indeed, improvements in vehicle performance without advantage -the otherdimensionswouldprobablyresultin a significant in improvements worseningof roadaccidents.Third,buildingon earlierresearchin Sweden et al., 1977)and India (Marwah,1976),an 1966;Gynnerstedt (Gynnerstedt, Indo-SwedishTraffic Flow SimulationModel has been developed which incorporatesboth the single-lane,two-directionalroad (as well as mixture of traffic two-laneand four-laneroads) and the heterogenous typical of India (Marwah, 1983; Palaniswamy,1983; Gynnerstedt,1984; calibratedfor et al., 1985). The model has been successfully Palaniswamy a limitedrangeof trafficvolumesand terraintypesand offersa promising basisfor futuredevelopment.

20

INTRODUCTION

1.3.3 Road Deterioration and Maintenance Effects AASHO IllinoisRoad Test In the initialversionof the HDM model, the predictionof how road conditiondeterioratesover time under the action of traffic and weather was based very largely on the results of the AASHO Road Test conductedin Illinois,1960-61,in a partiallyfreezingclimate. That test was by far the largesteffortever undertakento quantifysystematically the complex interactionsamong road deterioration,traffic (comprising severalvehicletypes,severalaxle loadingsand axle configurations), and compositionof the pavement (in several layers of varying material strengthsand varyingthicknesses).The primaryobjectivewas to determine the relationshipsbetween the numbers of axle transits of different loadingsand the performanceof flexibleand rigid pavementsfor the dual purposeof developingsatisfactory pavementdesign proceduresto meet the growingdemandsof trafficand to aid legislators in settinguser taxation and controlsfor vehicle size and weight. The test was also the first occasionwhen the many facets of pavementconditionand its progressive change over time, which we term "road deterioration," were defined and quantifiedin a comprehensivestatistic,the "pavement serviceability index"(PSI). That indexembracedengineers'subjectiveevaluations of the remaininglife of a pavementand its need of maintenance,and was highly correlatedto the roughnessand, to lesserdegrees,to the rut depth and the area of crackingand patching. However,the applicability of the AASHO test resultsto roads in developingcountriesis severelylimitedby severalfactors. First, the freezing environmentof the test, which had a major influence on deterioration, is distinctlydifferentfrom the tropicaland subtropical climates of most developingcountries. Second, the range of pavement types, which was limited primarilyto heavy asphalt concreteand rigid of the thin surfacingson one weak subgrade,was not representative surface treatments)and range of material and surfacings(predominantly tropicalsoils)which are commonin developing subgradetypes (particularly countries;nor was any gravelor earth roadsurfaceincluded. Third,it is uncertain how applicable the relationships-- based on accelerated, experimentally controlledloading-- are to roads with mixed light and heavy trafficand roadswith low trafficvolumes. Fourth, in order that criteriaand standardscouldbe differentmaintenanceactions,intervention evaluated,it is desirableto predictthe trends of roughness,rut depth and crackingseparatelyratherthan in the compositeserviceability index; this has been encouraged also by more recent developmentsin the mechanistictheoryof pavementbehaviorand in pavementmanagement.Fifth, were not the effectsof alternative maintenancepolicieson deterioration consideredin the AASHO test. Kenya and Brazil The roaddeterioration studiesthatwere conductedin Kenya,1971 to 1974, and in Brazil, 1977 to 1982,were designedthereforeto collect data on the changesof roughness,crackingand rut depth of paved roads in non-freezing climates,over a wide range of pavementstrengthsand mixed

INTRODUCTION

21

traffic loadings,and under differentmaintenancestandards. By nature, the rate of change in paved road deterioration over time is both small, because road pavementsare usually designed to remain in serviceable conditionfor 15 to 20 years, and variable,becausematerial properties have high variability. Thus, the four-yearstudy periodswere at best the minimum necessaryto achieveadequateresolutionin the data for the development of predictive modelsfor paved roads,evenwhen the combination of cross-section and time-series methods,as discussedbelow,is used. The deterioration of unpavedroads,which constitutea large and importantshareof the networkin developingcountries,had receivedlittle researchattentionprior to the Kenyaand Brazilstudies. The inclusionof wide rangesof both graveland earthroads in the two studiesprovidedthe firstbasis for an economicevaluationof upgradingto a paved road,and of alternativegradingand gravel resurfacing strategies.Since unpavedroad deterioratemuch faster, resultscan be obtainedmore quickly,and both studiesextendedover periodsof approximately two years, encompassing a rangeof maintenancestrategies. The scope of the two studiesis comparedin Table 1.3. In the Kenya study,most of the pavementsstudiedwere of cement-stabilized base construction and covereda rathernarrow rangeof strengthsof 2.7 to 3.7 modifiedstructuralnumber. The volumesand loadingof traffic,however, were sufficientlyhigh on eight of the sections so that almost completedeterioration historieswere obtained. The studyon crushed-stone base pavementswas hamperedby the loss of seven sectionsdue to drainage rates observedagreed reasonably difficulties. While the deterioration well with currentpavementdesign criteria,the data base was very narrow well beyondthe base, did not extrapolate and the resultingrelationships particularly for thin pavements. In the Brazil paved road study, the number of sections and pavementtypeswas more thandoublethat of Kenyaand the rangeof pavement strengthcoveredvirtuallythe whole rangecurrentlyused in all developing countries, with the exceptionof very heavilytraffickedpavementscarrying more than one million equivalentstandard axles per lane per year. Excludedfrom the studywere thickbituminouspavementsand inverted-design pavements which are commonly used for very heavily cemented-subbase to observewater bound traffickedpavements;therewas also no opportunity macadams and bituminouspenetrationmacadams. In the Brazil study the rangesof pavementage, of roughnessand of observedroughnesschangewere also double those of Kenya. Axle loadingsper vehicle were generally lower,however. The climatesof the two study regionsare more different than suggestedby the rainfallranges,Brazil'sbeing classedas humid to wet-humidand Kenya'sbeing classedas arid to dry sub-humid. Neitherthe Kenya nor Brazil studies encompassedeither very low or very high rainfall. Horizontalcurvaturewas varied in Kenya but not Brazil. Verticalgradientrangedfrom 0 to 8 percent in both studies. Pavement width was not varied in Brazil (constant7.0 m), and variedonly slightly in Kenya (6.0to 7.5 m). For unpavedroads, the two studies includedsimilarnumbersof sections. Both studiesincludedlateriticand roundedquartziticgravels,

22

INTRODUCTION

Table 1.3: Scope of primarystudieson roaddeterioration and maintenancein non-freezing climates

Kenya

Brazil

Paved roads Sections 49 Granular-base sections 10 Cemented-base sections 39 Overlaidsections 0 Lengthof sections(m) 1,000 Periodof observations (year) 4 Observations NAV Trafficvolume(veh/day) 323-1,618 Equivalentaxles (million/lane/year)0.012-3.6 Equivalentaxlesper heavyvehicle 0.2-40 Cumulativeequivalentaxles (million) 0.004-3.3 Annual rainfall 400-2,000 Pavementage 0-14 Modifiedstructuralnumber 2.5-5.1 Deflection(Benkelman Beam) (mm) 0.18-1.12 Road roughness(m/kmIRI)' 2.9-6.0 Changeof roughness(m/kmIRI) 0.3-1.7

116 74 11 33 720 5 500,000 73-5,700 0.0003-1.7 0.08-14 0.003-18 1,200-2,000 0-24 1.5-7.0 0.20-2.02 1.8-10.2 0-4.9

Unpavedroads Sections Gravelroads Earth roads Lengthof sections(m) Trafficvolume (veh/day) Truckvolume (veh/day) Annual rainfall(mm/year) Periodof observation(years) Road roughness(m/kmIRI)1/

46 37 9 1,000 42-403 12-136 400-2,000 2 4-17

48 37 11 320-720 18-608 5-477 1,200-2,000 2.5 1.5-29

Roughnessconversionis given by QI(counts/km) = 13 IRI fm/km) BI (mm/km) = 630 IR *12 (m/km) (Seeconductingpart of Section1.3.4for furtherdetailson road roughness measures.) Sources: Brazil,GEIPOT (1982);Paterson(1987);Kenya,Hodgeset al. (1975).

INTRODUCTION

23

and in addition the Kenya study includedvolcanic and coral angular gravels;sedimentarygravelswere not includedin either study,and only nine to eleven sectionsof earth roadswere includedin each. The Brazil study includeda slightly greater range of traffic volumes, and much greater range of truck volume. The Kenya regionwas drier but covereda slightlywider rangeof rainfallthan in Brazil,as notedfor paved roads. Research methodology for road deterioration. The road perfomance studiesin Kenya and Brazilhad a commonobjective,namely,to of paved and developmodels to describethe perfomance and deterioration unpaved roads with structuralcompositionstypical of the respective countries,as functionsof regionaldesign and constructionstandards, environmentalfactors, traffic loading and maintenancepolicies. Both studiesaddressedthe problemin a similarfashion,althoughthe detailsof derivedturnedout to be quitedifferent. the relationships Excludingcontrolledload tests (as in the AASHO study)-- which were not attemptedin eitherthe Kenya or Brazil studies-- there are two primary methods which can be used to study the performanceof existing roads (Hodges,Rolt and Jones, 1975). First, the completedeterioration historyof a sampleof road test sectionscan be obtainedby monitoringthe test sectionsfrom the initialconstructionto their ultimate "failure" in usingthis method (time-series analysis). The main problemencountered to study the performanceof paved roads designed to carry low traffic volumes,or indeed any existingroad which has been designedfor a long need to be made over a periodof many years if life, is that observations historiesof the roadsare to be obtained. A second completedeterioration methodof studyis to samplethe roadpopulationat any instantof timeand collectionof roadsat different to includein the samplea representative analysis). The advantageof such stages of their lives (cross-section analysesis that resultscan be obtainedmuch more quickly; cross-section of this methodis thatthe data are more scatteredbecause the disadvantage and detailsof the differentstandardsachievedduringinitialconstruction the subsequent deteriorationhistories of the roads are invariably of the two methodswas used in both the difficultto obtain. A combination Kenyaand the Brazilstudies. A major principleof both studieswas to study road performance under normal operating conditions,rather than through experimental testing. This has severalimportantadvantages. First,roadsas normally constructedare more representativeof the network than experimental sections,which tend to be more closelycontrolledand, hence,are unlikely of the actual road networkwhich is to be modelled. to be representative analysis to be Second, it permits both time-seriesand cross-sectional carried out as outlined in the paragraphabove, which permits obtaining resultsin a reasonabletime,withoutresortto acceleratedloading(where a very important the time effect on pavement deterioration-aspect -- tends to be distorted). Third, it is much cheaper to use existing roads with nomal traffic than to build separateexperimental sections,an importantpracticalconcern. On the other hand, the chosen methodologyputs very strict data treatment-- the study design demands on analyticaland statistical

24

INTRODUCTION

has to be well defined and it has to allow for adequatereplicatesfor variationsthat will occur within each matrix cell. Also, it means a largernumber of sectionsunder study,which impliesmore data collection for establishingroad and pavement technicalparametersand climatic environment, as well as for monitoringpavementperformance and traffic(to determinevehicleflow and equivalentaxle flow). And this, in turn,calls for a well designed data handlingsystem,which will permit easy data retrievaland effectiveanalysis. In both Kenya and Brazil,an initial step was to measure the permanent characteristicsof each test section. These included the geometriccharacteristics such as width, rise, fall and curvature. More importantly, the propertiesof the pavementlayerswere determined. These included measurement of strength, layer thickness, particle size distribution,density, moisture content, and plasticity. The basic pavementstrengthindicatorin both studiesis the structuralnumber,SN, as conceptuallyderived during the AASHO study. There were slight differences in the evaluationof SN in the Kenyaand the Brazilstudy-- in the latter, structuralcoefficientsfor bound materialswere based on compressivestrength (for cement-stabilized materials),or on stiffness (e.g., resilient modulus for asphalt concrete and asphaltic bound materials). In both studies,however,layercoefficients for naturalsoils and gravel,as well as subgradecontribution to SN, are based on the CBR test. The conditionof each test sectionwas regularlymonitoredduring the respectivestudies. Again, both studiesassessedthe same type of parameters,namely cracking,potholingeffects, rut depth, roughnessand deflection. But in this respect, there was a notable divergenceof instrumentation and of modellingconcepts,particularlyin regard to the definitionand analysisof crackingand potholes,and in the definitionof road roughnessand instrumentation for measuringit (as furtherdiscussed below in connection with the International Road RoughnessExperiment). This eventually led to considerable differences in the formulationof performancepredictionequations. The Kenya equationsare characteristically of a continuousfunctiontype, each distressfunction being independentof other distress types, in other words, a parallel development in all distress modes. This makes for relatively straightforward functionalforms, but it misses some of the causalities involvedin road deterioration.The Brazilstudy buildson the causality of events,but in so doing,introducesformulational discontinuities, which increasethe computational effort,as the readerwill see in Chapter4. Resultson roaddeterioration and maintenance.Both studieshave advancedour abilityto predictroaddeterioration under normalmaintenance regimes,and in particularhave providedquantitative relationships that give reasonableresultswhen extrapolating over the life of a road. The effectsof alternative maintenancepolicieshave been well quantifiedfor unpavedroads, and reasonablyqualifiedfor paved roads, except that the longer term effects of repeatedmaintenanceon subsequentdeterioration need furtherresearch,a pointto whichwe returnbelow.

INTRODUCTION

25

The largesize of the data base and the wide rangesof the major of parametersgive us confidencethat the relative,or marginal,influences For example,on paved roads, thoseparametershave been well-represented. the predictedeffectsof pavementstrengthand trafficloadingcomparewell and refinedovermany with pavementdesigncodesthat have been implemented years. Dominatingthe studies,however,is a large degree of scatter in of primarilyfrom the inherentvariabilities the observeddata originating materialbehaviorand, partly, quality,materialproperties, construction measurementerror. This, in additionto the need to condensethe many system variablesinto a few manageablesummaryparameters,causes rather which is typicallyof the wide confidenceintervals. The variability, order+ 50 to 100 percentof the predictedchangein conditionfor a given road section,will be of no surpriseto the highwayengineer. Of greater importanceto the plannerevaluatinga road networkis the resultthat the predictionintervalsof the mean, that is the averagefor the network,are closerthan that,on the orderof + 20 percent. considerably have been developedfrom For paved roads, strong relationships the Brazil study for original pavements under normal maintenance. are their incrementalform and Importantfeaturesof the relationships inclusionof both trafficand time variables. This permitsevaluationof the marginaleffectsof a vehicletransit,and of time and climatewhich are importantissuesin user taxation. The roughnesspredictionrepresents a particularlyimportantadvance and has been well verified within experimentalerror on five other data bases (Kenya,three in USA, and southernAfrica). From the Brazil study, both roughnessand cracking predictions have developed beyond simple correlation models, and effects. In the crackingand ravelling most major mechanistic incorporate practicesand materialpropertiesnot however,construction relationships, easily quantifiedfor networkanalysiswere found to have strongeffects, of thesemodels is recommended.Nevertheless, and locallinearcalibration for the crackingof cemented the predictionsof the Brazil relationships base pavementsfor example comparedcloselywith observeddata in Kenya. In Brazil as in Kenya, road gradientwas not found to have significant effectson paved road deterioration.The effectsof road width were not quantified,although in both Kenya and Brazil the highest levels of distresswere sometimesobservedin the outerwheelpath. A usefulmeasure of the relativedamagingeffectsof different axle loads was deduced from the analysesof the Brazil data, which is importantbecausethe effectsare those undermixed loadingand long-term controlled aging,unlikethe AASHORoad Test and variousrecentaccelerated load studies. The power applied to axle load in the relativedamage functionwas found to vary with the distresstype: for roughnessand modes)a powervalue of 4 was foundto be valid rutting(i.e.,deformation 4.2), for cracking (in agreementwith the AASHO power of approximately lower powersin the order of 2 to 4 were found, initiationand progression and for ravelling(whichis distinctlysurfacewear) a powerof near 0 was for the stronglysignificant.Theseeffectswere generallywell-determined fulldata set, exceptin the cases of crackingand ruttingwhere they were slightly less distinct,and in the cases of a few individualsections. of past and present Overall,they serve as a very valuablecorroboration

26

INTRODUCTION

controlledstudies on load-damagingeffects, and add new evidence of reducedload-effects on crackingand no load effectson ravelling. The effectsof maintenanceon the rate of paved road deterioration,and its initialeffecton condition,are as yet only moderatelywell quantified.In the Brazilstudy,the major differencesin behaviorbefore and after maintenancewere in crackingbut, apart from initial effects quantifiedin the models,any significant differences in roughnessprogression were well quantifiedthrough the change in strength parameters. Recent follow-onstudiesin Kenya,however,have shown very strong reductions in the progressionof roughnessfollowingmultiple resealapplications under apparentlynegligiblechangesof strength. Furtherstudy is thus requiredon long term effects over several successivemaintenance phases. For unpaved roads, sound relationships have been developedfor the predictionof roughnessand materialloss,based on materialproperties (ratherthan materialtypesas in Kenya),geometry,rainfalland traffic. There is, however,an even higher degree of variability of behaviorthan for paved roads both across sections,and also acrossmaintenancecycles within a section. Roughnessis treatedas part of a cyclic processof deterioration under trafficand weather,and maintenancegrading,so that is predicted. An the average roughnessunder a long-term'steady-state' importantinnovationin the Brazil relationshipsis the estimationof minimum and maximum potentialroughnesslevels from material (including particlesize), geometricand climaticfactors. These levelsaffect the rate of roughnessprogression as a functionof trafficand also the effectivenessof gradingmaintenance. Both gradientand horizontalcurvature affect unpavedroad deterioration.The predictionshave been verifiedon independent data basesfrom Kenya,Ethiopia,Ghanaand southernAfricawith acceptableresults. The effectsof the limitedrangeof observedrainfallin both the Kenyaand Brazilstudieswere negligibleon paved roads. On unpavedroads the Kenya study showedsmall effectson gravel loss,but the Brazilstudy showed small effectson both roughnessand gravel loss. The relatively small rainfalleffect in the paved road relationships may not extend to high rainfall,or low-intensityrainfallclimates and requires further study. An importantrelatedeffectwas that the amount of crackingwas foundto affectrut depthand roughnessprogression, but the effectsmay be understated for situations where the pavementlayersbecomesaturated. 1.3.4 International Road RoughnessExperiment One of the most importantfindingsof the researchin Kenya, sustainedby the subsequentstudiesin the Caribbean,Braziland India,was or "roughness," on vehicle the major effect of road profileirregularity, operatingcosts. Road roughnessis thus the key variable linkinguser coststo road surfacecondition,and the magnitudeof theseeffectsis such that they have been foundgenerallyto dominatedecisionsconcerningchoice of surfacetype,pavementdesignand maintenance policies. Becauseof this discoverythe importanceof developinga standardreferencescale for road roughnessand standardized proceduresfor fieldmeasurementsbecameclear. Consequently,the InternationalRoad Roughness Experiment (IRRE) was

INTRODUCTION

27

of leading research organizedin Brazil in 1982 with the participation institutesfrom six countriesand the World Bank (Sayers,Gillespieand Queiroz,1986). As a resultof the IRRE,which encompassedsevenmajor typesof roughness has now been defined in an International instrumentation, RoughnessIndex (IRI). The IRI is a time-stable, transferable, absolute measure of the road profile in a wheeltrack,a dimensionlessslope statistic(expressedin unitsof m/km IRI) which representsthe effectof that profileon the axle-bodymotion of a moving vehicle,idealizedin a quarter-carsimulationtermed RARS80 (Sayers,Gillespie and Paterson, 1986). The IRI is similar in conceptto, and an improvementon, the QI scale developedin the Brazilstudy. The roughnessdata on which all the model relationshipsin HDM-III are based are the calibratedMaysmeter estimates (denoted QI* in the Brazil study reports) of a reference and this Quarter-carIndex of profilemeasuredby a dynamicprofilometer, is the measure referred to as QI throughoutthis volume. The Bump Integrator'scale'used in the otherstudiesis different,being basedon a is inherentlysubject to mechanicaldevice which, although standardized, smallmechanicalvariations. The IRRE experimentalso providesa sound basis for converting betweenthe differentscalesused in the variousstudies,an exercisethat is considerablycomplicatedby surfacetype frequencyeffectswhich are introducedby the differencesin standardmeasuringspeeds. The Bump Integrator(BI)valuestend to vary the most in relationto the IRI in this respectas also do some of the indicesfrom the French APL Profilometer. Typically,road profilesthat have high amplitudesin the shortwavelength for examplecorrugatedsurfaces rangetend to exaggeratethesedifferences, and roughearth roads. A summaryof suitableroughnessconversionsbased on IRRE data due given in Figure1.4 from Paterson(1987);variationsin the conversions to the frequencyeffectsmentionedaboveare indicatedby the rangelimits shown on the chart. Guidelinesfor conductingand calibratingroughness measurementsto IRI, which is the referenceroughnessin this volume,are availablein Sayers,Gillespieand Paterson(1986). However,here and in is generallyexpressed the model, roughnessin the individualrelationships study, namelyQI for the in the scaleadoptedin the relevantoritinating Brazil-UNDPstudy and BI for the Kenya and India studies. The main coversionsare: QI = 13 RI BI = 630 RI1 .12 = 55 Q1 m where

RI = roughness,in m/km IRI; QI = roughness,in counts/kmQIm; and BI = roughness,in man/kmBIr (BumpIntegratorTrailer).

The model will accept roughnessexpressedin variousunits providedthe coefficientsof a linear conversioncan be supplied,as indicatedin Volume2 HDM-IIIUser'sManual(Chapter2, SeriesK, Card K-104).

28

INTRODUCTION

Figure1.4: Chart for Approximate Conversions betweenthe International RoughnessIndex(IRI)and MajorRoughnessScales 61 IRI Q Br (m/km IRI) (count/km) (mm/km)

0

0

0 20

20 2014.01020 1 40 2.000 40 40

WSCAI 5 WSW

140

,SI (PSI)

2

CAPt25

0

5.0

1.000

1

' 12

CP2 5 (0.01 mm)

4

4

4 /

~

184

6

80~~~~~~~ 4,000 801

12

16 14

~~

160'

3.0 80

~~~~80 80~ 100

12' 20 220_28 2816

600 1004 120 28 8 ________________ ________ 120 6,000 1000 120 140 10 ________ 140 160 36 160~~~~~6 _ __ 36 __ ~ ~ 6.0 140 100,000' 12000

2.0.

36

12~20

________

0 4.0

0 00 '

2.0

)~~~~~~~~~~~~1.5 300 1.0

_

__

_

__

_

12.000_1

_

-

1

)0.5

.

600+__

120

714

20012.00014,000 16

~~1

800

0

_16__6_1

6

~~~~~~~~~~~~~~~~~~~~~~~~500 ~ 81

15

__

2

004

________

~~~~~~~~ 6 _

IRI mR/km

30

108120 2600

4

IMr (in/mile)

9001,00001

______

200 t24014,00016.0 N18

18 16,000

~~~~~~~~~~~~~~~20~

20 240 Other

IRI

Notes: Notes:

On the 3-line scales, the center line represents the estimated value, and the left and right margins represent the low (15th percentile) and high (85th percentile) limits of Individual values about the estimated value.

ESTIMATNG IRISCALE

~~~~~~~~~~~~~~~~~~~~~~Low valuevalue ~~~~~~~~~~~~~~~~~~~~~~~Estim High Value ESTIMATINGOTHERSCALE

LowValue Estimated value High value NOTES: Conversionsestimated

on data from the Internationol

1. IRI

- Intemational

2. Qlm

-

3. Bl,

-

4. CP 2 t

-

5. Wsw

Road Roughness Experiment, (Sayers. Gillespie and Queiroz, 1986) asfollows:

Roughness Index (Sayers, Gillespie and Paterson. World Bank Technical Paper 46, 1986)

Quarter-car Index of calibrated Maysmeter, Brazil-UNDP Road Costs Study RI= Qlr/13 ± 0.37/AE IRK17 Bump Integrator trailer at 32 km/h, Transport and Rood Research Laboratory. UK: 0 89 RI =0.0032 B1r-. +0.31iARi IRI<17

Coefficient of planaritYover 2.5m boselength for APL72 Profiometer, Centre de Recherches Routiers, Belgium: IRKII IRI = CP 2 5 /16 ±0.27iiAi: - Short Wavelength Energy for APL72 Profilometer, Laboratoire Central des Ponts et Choussees. France IRI =0.78 Ws,0 -±0.69 IRI: IRI<9

6. CAPL 2 5 - Coefficient of APL25 Profilometer. Laboratoire Central des Ponts et Chaussses. France: IRI =0.45 k CAPL 2 5 ±16%; IRI<11 where k = 1 for generaluse.k =0.74 for asphalt concrete surfaces. k =1. I1 for surface treatment, earth or gravel 7. SI - Serviceability Index. American Association of State Highway and Transportation Officials: IRI =5.5 In (5.0/SI) ±25%; IRK12 8. IMr - Inches/mile equivalent of IRI from Reference Quarter-Car Simulation at 50 mile/hr (see HSRI-reference' in Gillespie, Sayers and Segel NCHRP report 228.1980; and 'RARS8 0 ' in Sayers, Gillespie and Quelroz. World Bank Technical Paper 45,1986): 6 3 36 IRI = IMr/ .

Source: Paterson(1987).

INTRODUCTION

29

1.4. CONCLUSIONS The studies in Highway Design and MaintenanceStandardsSeries were undertakento develop and validateempiricallyproject and sector planningmodels to permit quantitativeanalysisof the life-cyclecost tradeoffs in highway construction,maintenanceand utilization,and to assesseconomicpriorities. Prior to the initiationof the HDM Series in 1969, and the series of field studieswhich followed,very little hard scientific evidence was available on the physical and economic maintenance,and user among road characteristics, inter-relationships most of the large researcheffort over the past costs. Consequently, quantifyingthose relationships fifteenyears has focussedon empirically modelsconformas closelyas possibleto the to ensurethat the theoretical realworld. Major strideshave been made toward this goal, and HDM-IIIhas formwhich can be usedwith some confidence been developedin a generalized over a fairly wide range of circumstancesto analyze a number of the decisionswhich face road authorities importantinvestmentand maintenance and stronger around the world. Becauseof theirmore generalformulation the Brazil models have been chosen as the statisticalquantification, primary basis for HDM-III. Based on mechanisticprinciplesas far as of most of the major possible,with explicitincorporation statistically causal factors, they are deemed to provide the best basis for to diverseenvironments.For and transference extrapolation interpolation, as describedin Chapter only the Brazil relationships, road deterioration 4, have been incorporatedin HDM-III, since they provide the best of time and traffic interactionsand are also the most representation suitedto studiesof marginaleffects. For vehiclespeeds and operating are similarly costs,as discussedin Chapter5, the Brazil relationships but the Kenya, Caribbeanand Indian recommendedfor most applications, (presentedin Chapter6) are also includedin HDM-IIIfor relationships purposes. in thoseparticularcountriesfor comparative applications In addressingsuch a broadand complexset of phenomenaover the worldwidediversityof conditionsit must be recognizedthat some factors are betterdetermined,than are betterunderstood,and.somerelationships its infancy,and further still in others. Life-cyclecost modellingis and strengthenthe (1) to refine researchwill be needed, inter alia: and to encompassother models, validationof the various prediction (2) to evaluate and traffic congestion, particularly importantphenomena, broaden their and further forms general model of the transferability We environments. economic and diverse physical for empiricalvalidation concludethis chapterwith a briefdiscussionof each of theseissues. The readerwho is interestedin a more detaileddiscussionis referredto the othervolumesof this series. 1.4.1 Validationof the Models is that the vehicle The most importantoverall generalization and the effects of conditions), operatingcost models (for free-flowing road conditionsthereon, are better determined,and their predictive accuracyis rathergreaterthan is the case for the modelsfor predicting

INTRODUCTION

30

road deteriorationand particularlythe effects of maintenancethereon. are touchedupon below. Variousfacetsof thisgeneralization Road user costs The effects of road characteristics on vehicle operatingcosts under free-flowing conditionsare generallywell establishedfor most road conditionsand vehicletypes in currentuse. Aside from furtheranalysis of the India data, which merits attention,additionalbasic researchin this area (as distinctfrom localcalibration) is thereforenot considered of high priority,although further improvements should be possiblewith respectto betterestablishing: 1. The effectof narrowroadwidths (under6 m) on speed,fuel consumption, tire and partswear, and accidents-- an issue of considerableimportancein those developingcountries wheremajor extensionsof the roadnetworkare stillneeded; 2. The effect of small changes in roughnesson very smooth paved roads (less than 2.7 m/km IRI) -- an issue of importance primarilyin countrieswhere the conditionof the networkis at very high standards; 3. The effectsof superelevation and horizontalalignmenton tirewear -- factorswhose effectswe have not been able to disentangle due to limitations in the data base; 4. The longer-termeffects of highway improvementson the utilizationand adaptationof the vehicle fleet -- the present models, consistentwith traditionalpractice in highway planning,reflect largely shorter-termimpacts on utilization and the model user is left to specify exogenouslyanticipated longer-termadaptations of the vehiclefleet,a point to whichwe returnbelow. With respectto predictionof the effectsof roadcharacteristics very little on vehicleoperatingcostsunder congestedtrafficconditions, is yet establishedother than for speeds and time-relatedcomponents. congestedconditions. A promisingstart has been made on this problem throughcollaboration of Swedish,Indian,and Australianresearchers using micro-mechanisticbehavioralmodels for traffic flow simulation (as referencedabove),and it can be anticipatedthat further researchalong these lines will yield satisfactory results in the near future for fuel mechanisticmodels for consumptionand possiblytire wear. Satisfactory vehiclemaintenancecostsdo not appearon the immediatehorizon,however, in the basictheoryof and probablywill have to await furtherdevelopments vehicledynamics. In the meantime,sincevehiclemaintenancecosts can be presumedto be sensitiveto trafficflow impedance,furtherresearchusing alternative approachesappearsto be warranted. Road deterioration and maintenance Performancemodels to predict the network average behaviorof asphaltconcrete,bituminoussurfacedressings,and a rangeof unpavedroad

INTRODUCTION

31

types have advancedconsiderably and have now achieveda reasonabledegree of accuracyfor the subsetof worldwideconditionstypifiedby Braziland Kenya. However,a greatdeal remainsto be done: 1. To improvepredictions of the long term effectsof alternative maintenance policiesfor paved roads-- only the immediateeffects(e.g.,reductionof roughness,cracking,etc.) are reasonably well quantified,and the longer-term effects on retardingsubsequentdeteriorationare quantifiedfor strengtheningactivitiesbut less well for resurfacings which have had to be adapted from the primarymodels in HDM-III,with engineering principlesand judgmentappliedto the limiteddata available. Fortunately, however,it is the immediateeffects which are most critical in determining optimalmaintenance policieswhere socialdiscountratesare high (more than 10 percent per annum), and the existing models are expectedto yield reasonableanswers for such importantquestionsas the choice between resealingand strengthening options,timingof theseactions,etc.; 2. To extend the models to a wider range of diversephysical environments, e.g.,encompassing very high moistureregimes, high temperatureregimes,freezingconditions,etc. This factor has largelybeen achievedthroughthe environmental values for roughness,but these need verification,and additionalparameters may be requiredin some cases; 3. To extendthe modelsto a wider rangeof pavementtypesand methods,e.g., to gap-gradedmaterialssuch as construction water bound macadams and bituminouspenetrationmacadams (typicalof SouthAsia), to inverteddesigns,thick asphalt and rigidpavementstypicallyused for very heavily loaded pavements,and, at the oppositeextreme,to a wider rangeof unpavedroad types -- although,with respectto the latter, the generalizedmodel form specified in HDM-III, which encompassesmaterial gradationand standardgeo-technical well; and parameters, can be expectedto transferreasonably 4. To delineate better the relative damaging effects of and loadingsfor the purpose differentaxle configurations of allocatinguser charges amongst vehicle classes and improvingvehicle design. With the advantage of the experienceof the HDM studiesas well as the AASHO test, further researchcould usefully now be addressedto this question. of the HDM Model in DiversePhysicaland Economic 1.4.2 Applicability Environments The developmentof HDM-IIIhas been guided by the objectiveto with limited local develop a general model which could be transferred, calibration, to diversecountriesaround the world. While extensivework empirically undera relatively to quantifythe variousmodel relationships

32

INTRODUCTION

wide range of conditionshas been done -- in the case of vehicleoperating coststhroughstudiesin Kenya,the Caribbean,Braziland India,and in the case of road deterioration relationships throughthe studiesin Kenya,USA and Brazil-- the questionremainsto what extentcan the modelsbe trusted to give accurate answers over the worldwidediversityof physical and economicenvironments.Essentiallythe same questioncan be posed as to the effect of changes over time in the technologicaland economic circumstances of the countrieswhere the modelswere originallyestimated. In addressingthis issue it is essentialto distinguishbetween the model forms and the model parameters(or coefficients).It is also importantto distinguishbetweenthe physicaland economicenvironments. Finally, it must be recognizedthat the ultimateconcern is to predict accuratelythe changesin vehicleoperatingcostswith respectto changes in road characteristics, rather than total operatingcosts, and cost differentials due to differentroad conditionsare expectedto vary much less than total operating costs in response to different economic environments (Chesherand Harrison,1987). Where model forms are based on well establishedtheories of physicaland behavioralphenomenaand incorporateall (or most) of the major determiningfactorsand mechanismsin sufficientdetail,such model forms (as distinct from model parameters) should in principle be transferableacross diverse environments. The fact that the various studies in Kenya, the Caribbean,Brazil, and India have separately establishedessentiallythe same factors playing similar roles -- and generallywith the same relativeorderof magnitudeeffects-- supportsthe view that most of the major factorshave been incorporated.An important exceptionis the effect of wider extremesin moisture and temperature, which were not observed in any of the particularlyfreezingconditions, primarystudiesuponwhich the HDM model is based,and whichare knownfrom both theoreticalprinciplesand other researchto have major effects. Thus, the road deterioration model is not expectedto be applicablein freezingclimateswithout further theoreticalelaborationand empirical validation-- although the vehicleoperatingcost models could still be utilizedwith onlyminor recalibration. In the HDM model cost componentsare, with few exceptions, predicted as the product of a predicted physical quantity and an exogenouslysupplied resource price or unit cost. This separationof physical quantities and prices is obviously essential to permit transferability of the models eitheracrossdifferenteconomiesor across time in a given economy. But it is not sufficientto ensure the transferability of the model acrossdifferenteconomicenvironments.That is becausecertainof the model's coefficients were themselvesdetermined in part by the broader economic circumstances, market conditionsand governmentalpoliciesprevailingat the time and place of the original and relativecost of capitaland studies. For example,the availability laborhave a major impactin determining vehiclereplacement decisionsand mix used for vehicle maintenance-- and it is not the technological surprisingthat in Indiavehiclesare maintainedover longerlivesand that than that in the other vehiclemaintenanceis much more labor-intensive countries. Also governmentalpolicies on vehicle manufacture and

INTRODUCTION

33

on importsof new vehiclesand spare parts,as well as other restrictions specificmarket conditions,have a major impacton the choice of vehicle policies. and maintenance type, replacement The manner in which these various issuesare dealt with in the contextof the HDM-IIImodel is throughthe user'sexogenousdetermination of a relativelylarge numberof vehicleattributesand and specification model parametersas inputs. Several of the model coefficientsare, of course, expected to vary across differentenvironments. Certain data averagevehicle (e.g.,resourceprices,vehicletechnicalcharacteristics, life and annual utilization,road subgradebearing strength,etc.) are easilyobtainedand are routineinputrequirements.Othermodel parameters desiredspeedand other driverbehaviorcoeffi(e.g.,rollingresistance, will requiresome small-scalespeed cients requiredfor speed predictions) 4 for a properlocalcalibration. and experimentation observations The user must also bear in mind that over the longerrun vehicle operatorshave a proclivityto adapt their vehiclesand operatingrulesto changes in road conditionsin order to maximize profit and/or minimize vary a numberof variablesto minicosts. They can, within constraints, mize transportcost, e.g., the number, type and make of vehicles,the enginesize,age and tires. Of thesevariables,in keepingwith traditional practicein highwayplanning,only vehicleutilization(or the numberof 5 are endovehiclekilometersdrivenper year) and, implicitlyfleet size, in HDM-III. The genous within the vehicleoperatingcost relationships and fleetsize as endogenousvariableshas arisen treatmentof utilization as well as their considerable from their sensitivityto road improvements influenceon vehicleoperatingcost via the sizablecomponentsof depreciation and interest. The other vehicle attributes,once specified,are regardedas constantsby the model. When the user has reason to believe that the changes in road conditionsor policiesbeingmodelledwill lead to other importantadaptaan exogenousestimate he can incorporate tions of vehiclecharacteristics, of the vehiclefleet in the of these by specifyinga changingcomposition of trafficprojections.Not to do so would result in an under-estimation the benefits of an improvementof road conditionsor policies,and, since of the lossesdue to a deterioration, an over-estimation conversely, road users' adaptationswill be oriented to improve their position vis-a-viswhateverconditionsthey face. This is probablynot a significant issue in most applications,particularlywhere the proposed road 4 For guidelineson calibrationof vehicle speeds and operatingcost models see Chapter13 of Watanatadaet al. (1987)and for roaddeteriomodelssee Chapter10 of Paterson(1987). rationand maintenance 5 Fleet size (numberof vehiclesemployedin a company) is implicitly tied to utilizationin the predictionof depreciationand interest costs per kilometer: when the averagespeed is changedby changes in the numberof trips a vehiclecan make each year road characteristics, is changed, thereby resultingin a change in the number of vehicles necessaryto haula given volumeof transport.

34

INTRODUCTION

changesare marginalor highly localized,but it could be of some importance where major changes in the road network as a whole or in broad policies,such as axleloadlimits,were being considered. In the latter casesthe model usermust give particularly carefulattentionto specification of the changingcharacteristics of futuretraffictypesand volumes.

CHAPTER 2

Model Operations and the Traffic Submodel

2.1

BASICOPERATIONS

The operationsof the HighwayDesignand Maintenance Model take place in three phases; what amounts to a fourth phase is possible by transfering outputsfrom thismodel into anothermodel. The first is the data inputand diagnostics phase,in which the inputdata are examinedfor possibleformat and numericalerrors and internalinconsistencies.Any seriousinputerrorsdetectedin this phasewill stop the executionof the remainingphases. The secondphase is the simulationof the trafficflows and of the changes in the roads as they go from initial construction through annual cycles of use, deterioration,and maintenance,with possible constructionprojects to upgrade them. This phase generates information from which, at the user'soption, reportsmay be printedout for specifiedperiods or annually,giving road conditionsas well as physicalquantitiesand costs for road construction, roadmaintenance, and vehicleoperation. Benefitsto generatedtrafficand exogenousbenefits and costs my be incorporated. The quantitiesand costs may be broken down, if desired,into components. The third phaseencompasses economicanalysesand comparisons of alternativeconstruction and maintenancepoliciesfor selectedgroups of road links. Reports are generatedto give differencesbetween the financial,economic,and foreignexchangecosts of pairs of alternatives, and comparethem in termsof net presentvalueat variousdiscountrates, internalrate of return,and firstyear benefit. The other model,with which the HDM may be interfaced,is the Expenditure BudgetingModel (EBM),which selectsthe optimalcombination of projectsand maintenance policiesunderbudgetconstraints. Each of the threeHDM phasesand the budgetingmodel is briefly describedin turn below. Followingthat, the first of the simulation phasesubmodel-- traffic-- is describedin detail. The other submodels are fullydescribedin succeedingchapters. 2.2

DATA INPUTAND DIAGNOSTICS

In order to do all the calculations and comparisonsdescribed above,the modelmust be givendetaileddata on the roadsand vehiclesand detailedspecifications of the variousalternativesets of construction programs,design standards,and maintenancepoliciesto be compared,as well as unit costs,projectedtrafficflows,and other data. All these data and specifications are punchedon cardsor codedas card imagefiles,

35

36

MODELOPERATIONS

accordingto the detailed instructionsin Chapter 2 of the Volume 2: HDM-IIIUser'sManual. To help eliminateerrorsthat may have occurredin codingsuch large amountsof information, the model checksall the input data against built-in criteria to identifydeparturesfrom prescribed format,inconsistencies, and numericalvaluesoutsideof expectedranges. Some errorswill preventexecutionof the simulation, while othersare not "fatal". Both typesof errorscausemessagesto be printedout describing the problem encountered. Chapter 3 of the Volume 2: HDM-III User's Manuallistsand explainsthe errormessagesthatmay occur. 2.3

SIMULATIONPHASE

The sequenceof operationsof the simulationphase is shown in Figure2.1. For eachyear of the analysisperiod,the submodelsshownare applied in succession to each road link with various alternative constructionprogramsand maintenancepoliciesthat have been specified for it. (A combination of construction optionsand maintenancepolicies that have been designatedas a case for analysison a particularlink are referredto as a "link-alternative.") The trafficsubmodelsimplytakesdata that have been specified by the user in abbreviatedform and uses them to calculatethe flow of each type of vehicle in each year on each road link. For link-alternativesin which improvementsattract additional traffic (relativeto the "baselinecase") the additionalor "generated"traffic must also be specifiedby the user and addedby the model to the "normal" or baselinetraffic. The user may specifythe time profileof flow of a given vehicletype on a given link eitherby specifyingflow volumesto take effect in particularyears and remainconstantuntil changed,or by specifyingan initial volume and a rate of growth -- either a fixed incrementor a proportionof the current volume each year. Another option,for generatedtraffic,is to specifyit as a fixed ratio to the normaltrafficin the sameyear. The time profileof a normal (i.e.,equal to baseline)traffic flow is specifiedto begin in a definite calendar year, while the generatedtraffic is on a relativescale so that it may be initiatedby the completionof a construction project,whichmay be in differentyears for differentalternatives. for each link-alternative, The trafficsubmodelalso calculates, the number of vehicle axles and the number of equivalentsingle axles going over the road each year. These valuesare used in determiningthe deterioration of the roadsurface. For the road constructionsubmodel, the user specifies a baseline schedule of constructionprojects and as many alternative schedulesas he wishes to investigate. A projectmay be scheduledto begin in a specificyear or may be initiatedby the volume of traffic reaching a specified level. The duration of each project is also specifiedby the user and may be from one to five years. Construction projectsmay include the building of new road links or the widening, and upgradingof the pavementof existinglinks. realignment,

MODELOPERATIONS

37

Figure2.1: Simulationof a link-alternative

For each year of the analysis period

TRAFFIC SUSNODEL

A

Computes this year's traffic for each link

ROAD CONSTRUCTIONSUBHODEL

IInitiates road constructionbased on thresholdtraffic of calendar year; computescosts for road construction and changes road characteristics

I

_____

ROAD DETERIORATIONAND MAINTENANCESUBKODEL

Predicts road deteriorationand quantitiesand costs of maintenancework in terms of existingpavement conditions, maintenancestandards,traffic loading and environmentalconditions

I

EHICLE OPERATING COSTSUUMODEL Predictsvehicle operating costs in terms of geometric standards,surface type and conditions Predicts

EOGENOUS

COSTS/]BENEFITSSUBKODEL

Assigns this year's exogenous costs and benefits

l l l

~~~~~~~Store results for ~~~~~~~EVALUAXION AND tE~~~~RPORTID P&&SE

38

MODELOPERATIONS

For the baseline case and each alternative, the road constructionsubmodel computes the quantitiesof work and materials required in each year for the constructionprojects that have been specifiedand determinestheir financial,economic,and foreignexchange costs. Upon completion of a project it changes the physical characteristics of the link involved,and on or before completionit assigns the corresponding generatedtraffic to it and accountsfor any prespecified exogenouscostsand benefits. The totalcost per kilometerof a projectis made up of various components,and each component cost -- except overhead and "other costs"-- is the productof a physicalquantityand a unit cost. One of several optionalways that the model can be used is for the user to specify,on the basis of separateanalyses,all of the physicalquantities per kilometerand all of the unit costs,as well as overheadand "other." Or, if the multiplications have alreadybeen carriedout, he can put in the resultingcost per kilometerfor each componentor even the totalfor all components, either for an entire link or for separatesectionsof a link. Another option makes use of endogenousrelationsderivedfrom the empiricalstudiesfor estimatingthe quantitiesinvolvedin certain aspects of construction. These built-in relations,combined with user-suppliedunit costs, provide preliminarycost estimates in case engineeringhas not yet been done. They are particularlyuseful in analyzingtradeoffsamong construction, maintenance, and vehicleoperating costs for the investigation of constructionstandardsand maintenance policiesat the highwaysectorlevel. The road deterioration and maintenancesubmodelis the key to analyzingthe effectsof designand maintenance policyon the conditionof roads and hence on vehicleoperatingcosts as a componentof the total costpicture. This submodelpredicts,for each year,the deterioration of the road surfacecausedby trafficand climateand the extentto which it is offset by work done under the prescribedmaintenancepolicy. It calculatesthe quantitiesinvolvedin the maintenancework, and applies unit costs to determinetotal maintenancecost for each year. The physicaleffectsof deterioration and maintenanceare simulatedon the basisof empiricalrelationsderivedmainlyfrom the Brazilstudy (GEIPOT, 1982;Paterson,1987). The statistical and engineering analysesare fully documentedin the lattersource. The submodelaccounts for deterioration of paved roads in the form of cracking,ravelling,potholeformation,and rut deepening,all of which affect the progressionof roughness,which is the measureof road surfaceconditionused in the vehicleoperatingcost submodel. Unpaved roads deteriorateby becoming rougher and by losing gravel surfacing material. Road deteriorationis a function of the original design, material types, traffic volume and its axle load characteristics, environmentalconditions,age of pavement,and the maintenancepolicy pursued. In addition,as shown by the Brazilstudy,the lossof material from unpavedroadsis affectedby horizontalcurvature,and erosiondue to

MODELOPERATIONS

39

rainfall is affected by vertical alignment,which also affects the development of roughnessfrom othercauses. of paved roads Maintenanceoptionsto offset the deterioration include patching, preventive treatment, resealing, overlaying, and reconstruction.For unpavedroadsthe optionsare grading,spot graveling (patching),and gravel resurfacing. In addition,maintenanceincludes routineattentionto drainage,shoulders,and roadsidevegetation. For paved roads, the deteriorationand maintenancesubmodel includesrelationsdealing with seven differentpavementsurface types (some of which result from maintenanceprocedures)and three base climates,but have types. The relationsapply to tropicaland subtropical not yet been extended to freezing conditions. Two types of unpaved roads -- gravel and earth -- are differentiatedby specifyingtheir genericphysicalattributes. The vehicle operating cost submodel computes road users' financialcosts,economiccosts,and foreignexchangecosts for each road sectionfor each year. The quantitiesof resourcesconsumedand times spent in transitare calculatedfirst and then multipliedby prices or unit costs to obtain operatingcosts and travel time costs. Vehicle speeds and resources consumed -- fuel, tires, vehicle maintenance, etc. -- are related to the volume and compositionof traffic,to the surface type and geometric charactristicsof the road section (as initiallyspecifiedor as alteredfrom time to time by the construction program),and to the currentroughnessof the surface(as determinedfrom submodel). and maintenance the roaddeterioration The analystchoosesamong four differentsets of relationships which were developedin the separatestudiesdone in Kenya,the Caribbean, India,and Brazil. Each set of relationsreflectsto some extentthe road conditions, the vehiclefleet,and the economicenvironmentof the study region. For each study a somewhat different scheme of vehicle to the range of vehiclescommonly was used, corresponding classification used in the differentcountries.The studiesalso differedin the variety of independentvariables observed and in analyticalmethodology,as discussedin Chapter1. for the Having specifiedone of the four sets of relationships study, the user must provide data on the rise and fall, horizontal width, and surfaceroughnessfor each section of curvature,carriageway also requirespecifying each link. Some of the sets of relationships surface type, altitude, and other factors. Characteristicsof the differenttypes of vehiclesin the fleetmust also be provided,such as ratedpower,gross weight,and vehicleservicelife,annual utilization, so on. the model first calculates For each year of each alternative, operatingspeed for each type of vehicle on each road link. This is of dependenton the road geometryand roughnessand on characteristics

40

MODEL OPERATIONS

the vehicle. From the speed, hilliness,roughness,and some other factors,fuel and lubricantconsumption and tire wear are determined,as well as parts and labor required for maintenance. For commercial vehicles,crew time on the road is inverselyproportionalto vehicle speed. For calculatingdepreciationand interest as proportionsof vehiclecosts,one is given optionsof treatingvehicle life as constant or varying,and differentmethodsare availablefor calculating the number of kilometersdrivenper year and overheadcosts. All of these elements, having been calculatedin physicalor "real" terms, are convertedinto monetary,economic,and foreignexchangecosts by multiplyingthem by the user-specified unit costsor prices. For some comparisons of alternatives, it is desirableto account for differencesin the time spent by passengersin transit and for differencesin the time that cargoestake to reach their destinations. Therefore,the model computesthose times and, if the user specifies appropriate unit values,will includethesetime costs in the analysis. 2.4

ECONOMICEVALUATIONAND REPORTINGPHASE

After all the time streamsof physicalquantitiesinvolvedin the baselineand each alternative for each road link have beenmultiplied by the appropriateunit costs or prices,detailedreportsand economic comparisonsare prepared. Some reportsare standardand are produced automatically; others are selectedby the user from a larger number of programsof construction options. Resultsmay be comparedfor alternative and maintenanceon individuallinks. In addition,for comparingpossible overall programs,alternativesfor differentlinks are usually bundled togetherinto "groupalternatives". in the HDM model can be summarized The analysisof alternatives in the followingsteps: 1.

For each link-alternative, the model separatelyassembles financial,economic and foreign exchange annual cost streams includingthe costs of: capital investment, recurrentspending,vehicleoperation,passengerand cargo see delays, as well as exogenouscosts. For illustration in the computer reports type 7 (for link-alternatives) printoutof the sample run. (Volume2: HDM-III User's Manual,Chapter5.)

2.

The annualcost streamsfor link-alternatives from step (i) are aggregated for each group-alternative. For see reportstype 7 (forgroup-alternatives) in illustration the samplerun printoutreferredto above.

3.

For each pair-wisecomparisonof link-alternatives the annual benefit and cost streams are computed for one alternativerelativeto the other in terms of: increases in roadcapitaland recurrentcosts;vehicleoperatingcost and travel time cost savings due to normal traffic;

MODEL OPERATIONS

41

benefitsdue to generatedtraffic;exogenousbenefits,and total economicbenefits. The savings in foreign exchangeare also For illustrationssee reports type 8 (for computed. in the samplerun. link-alternatives) 4.

The cost and benefitstreamsfor step (iii)are summarizedfor comparison. For illustration,see each group-alternative in the samplerun. reportstype8 (forgroup-alternatives)

5.

The model then computes for each pair-wise comparisonof link-alternatives:the net present value for five discount for the zero rates as specifiedby the user and automatically discountrate, the internalrate of return,and the first year benefits. For illustration see reportstypes 9, 10 and 11 in the samplerun.

6.

Step 5 is repeated for each pair-wisecomparisonof groupsee reportstypes 9 and 10 in alternatives.For illustration, the samplerun.

For sensitivitystudies,steps 3 through6 above are repeated factors. with certaincost streamsmultipliedby user-specified 2.5

BUDGETINGMODEL (EBM) INTERFACEWITH EXPENDITURE

When using the HDM model to predictthe total transportcosts for relativeto a base alternative and net presentvaluesof alternatives individuallinks,the user can, if desired,maximizethe net presentvalue for the highway sector under both capital and recurrentexpenditure constraints. This is accomplishedby interfacingHDM-III with the ExpenditureBudgeting Model (EBM) through a special output file as describedin Chapter8. This output file containsfor each alternative the annual net economicbenefitsrelativeto the base case as well as the annualcapitaland recurrentfinancialroad costs. 2.6

THE TRAFFICSUBMODEL

The simulationphase of the model operationbegins,as seen in Figure 2.1, with the operationof the traffic submodel. The traffic submodelemploysdata enteredby the user to derive,for each year of the analysis,the volume of traffic of each vehicle type, the number of vehicleaxles, and the number of equivalentsingle axles on each paved road link under analysis. For unpavedlinks,only total trafficvolumes are calculated. 2.6.1TrafficVolumes The data are entered in the form of "trafficsets," defined below, for normaland for generatedtraffic. Normaltrafficon a link is the average daily two-way traffic volume (ADT) of each vehicle group

42

MODELOPERATIONS

1 on the link in each year of the baselineor "withoutproject" case. Generatedtrafficis the additionalvolume (of each group in each year) that is inducedor divertedfrom other routesas a resultof improvedroad conditionsrelativeto the base case. Thus in the base case the total traffic is the normal traffic and there is no generatedtraffic. In alternative cases,the total trafficis the normaltrafficplus generated traffic,if there is any.

For any link in a given model run, there is only one base case and thereforeonly one set of normaltraffic,which is the same for all alternatives. Several sets of generatedtrafficmay be availablefor a link -- differentsets, e.g., associatedwith alternativeconstruction projects. Normal traffic is present at all times; generatedtraffic usually starts at some time later than the first year -- either in a definiteyear or at the time of completionof a particularproject,which may be differentin differentalternatives.If, as a resultof sequential improvements, more than one generatedtrafficset is applicableto a link in the sameyear, the volumesare simplyadded together. A trafficset definesa volume of flow for each vehiclegroup, includingits variationover a seriesof years. A set is made up of one or more "growthperiods"in sequence,and the parametersspecifiedfor a growthperiod remainin effectuntilanothergrowthperiodbeginsor until the end of the run. For a normal traffic growth period, an initial calendaryear must be specified. If it is the firstgrowthperiodin the set, this will usually be the first year of the run (althoughit is permissibleand sometimesconvenientto designatean earlieryear). The startingyear for the first growth period in a generatedtrafficset is Year One, and subsequentgrowth periods in the same set are timed from that point. Puttinggeneratedtrafficon a relativetime scalemakes it convenientto start a generatedset at differenttimes under different alternatives, or to make its initiationcontingenton other eventsin the run. Within each growth period, traffic -- either normal or generated-- may be specifiedin any of the followingthreeways: 1.

The user may specifyfixed volumesfor each vehiclegroup for particularyears. Each such amount will remain constantfor succeedingyears until supersededby a new amountor by the beginningof a new growthperiod.

2.

After initialtraffic volumeshave been established,the user may specify an annual incrementfor each vehicle group. The fixedamountswill be added eachyear untilnew values for the incrementsare called for or a new growth periodbegins.

1 When used in the roaddeterioration model,the total two-waytrafficis divided,in the model, by the effectivenumber of lanes, and half of the total is assumedto be goingeach way.

43

MODELOPERATIONS 3.

After initial volumes have been established,an annual percentagegrowth rate may be specifiedfor each vehicle group. Traffic volumes will be incrementedby these percentageseach year until new rates are put into effect or a new growthperiodbegins.

For generated traffic only, a fourth option is available. Generatedtraffic in each group may be specifiedas a percentageof the will be applieduntil group's normal traffic. The specifiedpercentages superseded. 2.6.2 Axle loadings For simulatingthe effectsof trafficon the roads, the model makes use of two differentmeasures of axle load -- vehicle axles and equivalentstandardaxle loads. The lattercombinesthe damagingeffects unit. The of the full spectrumof axle loadingin a commondamage-related measuresare computedin the trafficsubmodeland passedalong for use in and maintenancesubmodel(seeChapter4). the roaddeterioration The term "vehicleaxles" is definedas the total numberof axles of all vehicles. The numberof vehicleaxles traversinga given link in a given year is computedas the volumeof trafficin each group multiplied by the numberof axlesper vehicleof the type involved. standardaxle For each vehiclegroup,the numberof "equivalent loads"traversinga given link in a givenyear is computedas the product of the annual traffic volume of the group and the group's "equivalent standardaxle load factor,"specifiedby the user or computedfrom axle load information.These numbersare summedover all groups to obtainthe total number of equivalentstandardaxles traversinga link in a given year. The equivalentstandardaxle load factor, AF, is defined as of a standard80 kN dual-wheelsingleaxle load the numberof applications which would cause the same amount of damage to a road as one of the axle load beingconsidered. application The equivalentstandardaxle load factors (AF4k) are computed (and damage-reducing) as as follows, for the differentload-spreading by effectsof groupedaxles, singlewheels, etc. which are incorporated varying the standard load, SAXLj, used in determiningthe loading ratio:

AF4-k =

AF2k =

Ik ki Zki i=1 100 j=1

Ikpk kA 0

] XLkij SAXL.

ki [AXLk k [

i=1 100 j=1

1

SAXLj

2.0

44

MODELOPERATIONS AF4k = the equivalentstandardaxle load factorbased on the equivalency exponentof LE=4.0for vehiclegroup k, in ESA per vehicle; AF2k = the equivalentstandardaxle loadfactorbased on the equivalency exponentof LE=2.0for vehiclegroup k, in ESA per vehicle; LE = the axle load equivalency exponent; Pki = the percentageof vehiclesin subgroupi of the vehiclesin groupk; Ik = the numberof subgroupsin vehiclegroup k; Jki = the numberof singleaxlesper vehiclein subgroupi of vehiclegroupk (a tandemaxle is treatedas two separatesingleaxles); AXLkij = the averageloadon axle j of load range i in vehiclegroupk (tons);and SAXLj = standardsingleaxle load of axle grouptype,j: = 6.60 ton for single-wheel singleaxle, = 8.16 ton for dual-wheelsingleaxle, = 15.10/2= 7.55 ton for dual-wheeltandemaxle, = 22.90/3= 7.63 ton for dual-wheeltripleaxle. (Note: 1 ton = 1,000kg - 9.8 kN)

The i-th subgroupof a vehicletype k comprisesall thoseaxles of group type j (single or tandem, etc.) carrying loads AXLkij in the i-th range. The standardaxle load SAXLj is determinedsolelyon the basis of the axle group type j. In the classicalformulation derivedfrom the AASHO Road Test, the pavement structuralnumber (unmodified) and the initial and final values of the serviceability index are used in computingthe equivalent standardaxle load factor, which differs for single and tandem axles (AASHTO,1974). For the purposes of simplificationand because the economicanalysisshouldnot be restrictedto pre-determined initialand terminallevels of serviceability, the computational method specifiedin here includesthe average power value of 4 on the axle loading in the relativedamage function. Given the much greater inaccuracies usually associatedwith traffic volume forecasting,the high variabilityof pavementbehavior,and the varietyof approachespossiblefor derivinga value from performance data, such an averagevalue is highlyappropriate and the most representative of the pavementdamagingeffectwhich leads, ultimatelyto roughnessprogression. Analysisof the Brazil-UNDP studydata (Paterson,1987) in fact providedstrongvalidationof this value,basedmoreoveron an evaluation of pavement performanceunder mixed traffic on pavementswith a wide age-range,and under in-serviceconditions.The analysisshowedevidence that the exponent,LE, has a lowervalue of approximately 2 in some cases for crackinginitiation and such a tendencyis supportedfrom theoretical mechanistic considerations(Paterson,1987; Rauhut, et al., 1984). Provisionhas been made in the input forms thereforefor entry of an equivalent standard axle load factor, AF2k, computed with LE=2 as definedabove. In this HDM-IIIversion,however,the coefficients in the

MODELOPERATIONS

45

performancepredictionequationshave been standardized to valuesof LE=4 and LE=O (in the trafficflow variablesYE4 and YAX respectively), because the values of LE were not always consistentacross pavementtypes and distressmodes (see Paterson,1987). The exponentLE=O attributesequal damaging effect to every vehicle axle (including light-vehicles) independent of axle load. The numberof vehicleaxles, i.e. for LE=O, is definedas equal to the number of axles of the vehicle if it is classifiedas heavy (3,500kg grossweight or more),and two otherwise. If the user choosesto enter vehicleaxle loads throughcards D-203, the endogenouscomputationassumesSAXLj to be a constant,fixed value of 8.2 ton. This assumptionregards every axle as a single dual-wheelaxle and is validonlywhen the pavementdepth is thin relative to the loadmagnitude(as a rule of thumb,when axle spacingexceedshalf the pavementdepth or axle loads exceed 3 times the modifiedstructural number). The defaultvaluefor lightvehicleaxle loads is providedsuch that: AF4k = 0.14 AF2k = 0.12 The user should note that the factor AF4k is an average applying across all vehicles of type k, loaded and unloaded,in both directionson the given link.

CHAPTER 3

Road Construction Submodel

The main purposes of the road constructionsubmodel are: to computeand allocateconstruction costs by component(financial, economic, and foreign exchange)on a year-by-yearbasis over the durationof the construction period;to modify the physicalcharacteristics of the link as the constructionis completed;and to activate generatedtraffic (see Chapter2) and generatedexogenouscosts and benefits(see Chapter7) for the link, if any, upon the construction completion. Construction may be scheduledfor any year in the analysisperiod and may consist of new constructioneither on new or old alignmentand widening. Construction may also be scheduledsequentially, as in staging; that is, a linkmay be constructed to a low standardinitially,followedat a futuredate by widening,realignment, or some otherform of upgrading. Major road construction quantities,namely,earthwork,drainage, site preparation and bridges,can, if desired,be endogenously predictedas a functionof terrainseverityand geometricstandards. The relationships projectsfrom 28 used have been developedfromdata of 52 roadconstruction countriesin Africa, Latin America and Asia (Aw, 1981). While these providepreliminarycost estimateswhere local data are not relationships available,they are particularlyuseful in analyzing tradeoffs among road construction, maintenance, and vehicleoperatingcostsat the highway quantitiespredictedare sector level. This is becausethe construction sensitive to geometric standards,especiallyfor severe terrain (see Section3.2 for graphicalillustrations). However,the model user can often gain more preciseestimatesof of projectshas advanced constructioncosts where engineeringpreparation beyond the preliminarystage. In this case, the user simply specifies as describedbelow. construction costsexogenously, PROCEDURE 3.1 BASICCOMPUTATIONAL Construction may have a durationof one to fiveyears,and may be initiatedin any year during the analysis period by specifyingeither a startingcalendaryear or a thresholdtrafficlevel. In eitherway the constructionis assumed to be completedat the end of the effective completionyear specifiedby the user. The effectivecompletionyear, period,is which is less than or equalto the lastyear of the construction employedto handle cases in which some portionsof the road have already

of the entire and open to trafficbeforethe completion been completed construction. 47

48

ROAD CONSTRUCTION SUBMODEL

For instance, constructionscheduledto start in 1984 with effectivecompletionin year 2 will be initiatedat the beginningof 1984, and effectivelycompletedat the end of 1985. It will be availableto go into servicewith new physicalcharacteristics at the beginningof 1986. The road construction submodelmay be dividedinto the following stages: 1.

During the construction.For each year of the construction period, the cost incurredduring the year is computed in financial,economic,and foreignexchangeterms.A detailed descriptionof cost computationis provided in the next section. Salvage values are also computed by cost component. They are entered as percentagesof total financial,economic and foreign exchange costs, and are recordedas benefitsin the lastanalysisyear.

2.

In the openingyear. For the year followingthe effective completion year, the physical characteristicsof the affected link are changed to those of the new road. A detailed description of the requirements for road characteristics data is given in Chapter2 of the Volume2: HDM-IIIUser'sManual

In addition, if the user specifies generated traffic and exogenouscosts and benefitsassociatedwith the road construction,the generated traffic set and the exogenous costs and benefits set are activatedand assignedto the link startingin the year followingeffective completion. As schematicallyillustratedin Figure 3.1, road construction costsmay in generalbe brokendown into eight components: right-of-way, site preparation, earthwork,pavement,drainage,bridges,other costs,and overhead. Exceptfor other costsand overheadthesecomponentsmay further disaggregateinto physicalquantitiesand unit costs. For example,site preparationcosts can be obtainedas a productof the site clearancearea per unit lengthof road and the cost per unit area. Similarly,earthwork costscan be decomposedintoearthworkvolumeper unit road lengthand the costper unit volume. Taking this structureinto account,HDM-IIIprovidesa flexible input routinewhich allows the user to specifythe constructioncosts in differentways (see Table 3.1). Specifically, the user can specifythe costs as either total costs (level 1 or 2) or costs of each of the components(level3). The totalcosts can be enteredeitheras the costs for the entire link (level1) or separatelyfor the affectedsectionsin the link (level2). The user has a furtheroptionto enter someor all of the componentcosts (exceptother costs and overhead)by the physical quantitiesand the unit costs (level 4). As mentionedearlier, the quantitiesof road construction (exceptthe right-of-way area, the pavement volume,and in the case of widening,the floorarea of bridges)can either be exogenouslyspecifiedby the user or estimatedendogenouslyby the model. In the latter case, using the relationships describedin Section

ROAD CONSTRUCTION SUBMODEL

49

costsand availability of modelsfor predicting Figure 3.1: Construction quantities construction Link or section totalcosts

Component costs

Quantities& unit costs

Availability of prediction models

Area (m2 /km)

Right-ofway cost (perkm)

H

Unit cost (perm2)

Site preparation cost (perkm)

Area (m2/km)

Earthwork cost

Volume (m3/km)

New construction & widening

Unit cost (perm2) New construction & widening

(perkin) ( Total costs (perkm)

Volume(m3/km)

Pavement cost (per km)

Drainage cost _ (perkm)

Unit cost (perm3)

l 3) Unitcost(permn

_ _

_ Pipe culvert length(m/km)

H

Bridge cost _ (perkm)

Other _costs (perkm)l

(perm2)| ntcost

_ _ Box culverts(no.of culverts/km)

New construction & widening

- Unit cost (perculvert) - Floorarea of small | bridges(m2 /km)

lOverhead l L-cost (% or per km)

New construction & widening

Unit cost (perm2)

New construction & widening

50

ROAD CONSTRUCTION SUBMODEL

Table3.1: Structureof Cost Data for Road Construction Submodel

Level

Details

Level 1: Link total cost

The user providesa lump sum total cost for the entire link. The use of this level precludesthe use of more detailedlevels (2, 3 and 4) for all sectionsaffected.

Level2: Section totalcost

The user providesa lump sum total cost for an affected sectionon the link. The use of this levelprecludesthe use of levels3 and 4 for the link,but stillpermitsthese levelsto be appliedto the otheraffectedsections.

Level3: The user providesthe cost per km of a construction cost Component componentfor an affectedsection. The use of this level cost precludesthe use of level 4 (unit cost and quantity)for ("costper km"' this cost componentand section,but still permits "unit cost and quantity"to be providedfor the other components where applicable. Level4: The user providesthe unit cost (per unit quantity)and Component quantity (per km) for a component, for an affected cost section. Among the eight cost components,the following ("unitcost are applicable: and quantity") Right-of-way Pavement Site preparation Drainage Earthwork Bridges Of the above components,site preparation,earthwork, drainageand bridgeshavebuilt-informulasin HDM-IIIfor endogenously predictingthe physicalquantities.

3.2, they are computedas a functionof the geometriccharacteristics of the road sectionand the terrain. "Other costs" are all those which are not otherwiseincluded. The latter may include major structuressuch as large bridges, large culverts,side drains and so on. "Other costs" are specifiedon a per kilometerbasis. Overheadcostsare often represented as a fixedpercentageof the sum of the othercomponentcosts. Thus the user can specifyoverheadcosts eitheras a lump sum cost per km or as a fixedpercentageof the sum of the othercomponentcosts.

ROAD CONSTRUCTION SUBMODEL

51

Costs of construction, whether total costs, componentcosts or unit costs, are input by the user in financial,economic,and foreign exchangeterms (thoughfinancialand foreignexchangecostsare optional). They are distributedover the construction periodaccordingto the annual percentagesspecifiedby the user. The salvage value -- i.e., value remainingto be realizedafter the end of the analysis period -- is specifiedby the user as a fixed percentageof the total construction costs. 3.2 PREDICTINGROAD CONSTRUCTION QUANTITIES The empiricalrelationships used to compute the quantitiesof road construction, viz., the area of site preparation, volumeof earthwork, lengthof pipe culverts,numberof box culverts,and floorarea of bridges are describedin Appendix3A. The followingparagraphsprovidea summary of these relationships.The recommendedrange of the input variablesin Table 3.2 should be observed as departurefrom the range implies an extrapolation and couldproduceunreasonable results. 3.2.1 Site Preparation Site preparationinvolves creating site access and removing trees,stumps,bushes,and obstacles. Dependingon whetherit is for new construction or widening,the area of site preparationcan be estimated accordingto the relationships describedbelow. New construction In the case of new construction on new alignment,the area of site clearingand grubbingper unit lengthof road is givenby: ACG = 1770 exp(0.0278GRF) + 1610exp(-0.0114 GRF) RW where

ACG = the averagearea of site clearingand grubbingper unit lengthof road,in m2 /km; GRF = the ground rise plus fall, in m/km (see definition below);and RW = the roadwaywidth, in meters,definedas: RW = W + 2 WS; W = the width of the carriageway, in meters;and WS = the width of one shoulder,in meters.

The ground rise plus fall is definedas the sum of the absolute values of total vertical rise and total verticalfall of the originial ground,in meters,alongthe roadalignmentover the road sectionin either direction divided by the total section length, in km. Figure 3.2 illustrateshow this value is computed for a given road section. The predictedarea of site clearanceis plottedagainst the roadwaywidth in Figure3.3.

52

ROAD CONSTRUCTION SUBMODEL

Table 3.2: Recommended rangeof variablesfor road construction quantityprediction" Variable

Units

Recommended range

1 RW Roadwaywidth,

m

2 Road riseplus fall, RF Groundriseplus fall,GRF

m/km m/km

0-75 0-100

2 G Rise plus fall differential,

m/km

0-50

5-25

1 Not used in the drainagerelationships. Used only in the earthworkvolumerelationships. Source: Authors'recommendation basedon data fromAw (1981;1982). 2

Widening In the case of widening,ACG may be estimatedby the following incremental formula: ACG = 1610exp (-0.0114GRF) [RW(after)- RW(before)] where the subscripts"after"and "before"representthe values beforeand afterwidening,respectively. 3.2.2. Earthwork The earthworkof a road construction projectis that portionof materialzrequiredto convertthe originalgroundfeaturefrom its natural conditionor configurationto the prescribedsectionsand grades. It includesthe quantitiesof soil, gravel, rock, and unsuitablematerials resultingfrom the excavation, borrow,embankmentconstruction, spoil,and gradingoperations.Among the major cost components, earthworkis the one which is the most sensitiveto geometricstandardsand terrainconditions. New construction (newalignmentand existingalignment) The followingrelationshipis used to estimate the earthwork volumein the model: EWV = 1000 (RW + 0.731H) H where

EWV = the volumeof earthworkper unit lengthof road, in m3 /km (includescut, fill,borrowand waste materials); H = the effectiveheightof earthwork,in meters,given by

ROAD CONSTRUCTION SUBMODEL

53

Figure3.2: Illustration of groundrise+ fall

F1

F

A~~~~~~~~~~~~~~~~ A

Ground profile

~~~~~~~~~~~~~~~~

',

-

Road profile

Groundrise+ fall =

+ R3 + F1 + F2

+

L ab

Figure 3.3:

Predictedarea of site clearanceversusroadwaywidth Area of site clearance 2 (m /km)

40,000

GRF=0

30,000 -

GRF= 30 GRF = 70 GRF = 50

20,000 -

10,000 _ . 0

S

| a 10

| 15

I 20

Roadway I 25

~~~~~~width (m)

Source: Based on analysisin Tsunokawa(1983). See also Aw (1981;1982) and Markowand Aw (1983).

54

ROAD CONSTRUCTION SUBMODEL H = 1.41+ 0.129G + 0.0139GRF; and G = the rise plus fall differential, in m/km,given by G = GRF - RF

where

RF = the road riseplus fall, in m/km.

The road riseplus fall is definedin the sameway as the ground rise plus fall exceptthat the verticalprofileof the road is used instead (as elaboratedin detailin Chapter5). The sensitivityof the predicted earthworkvolume to the roadwaywidth and the road rise plus fall for variousvaluesof the groundrise plus fall (representing terrainseverity) is shown in Figures3.4 and 3.5. Widening For widening,the earthworkvolumeis givenby EWV = 1000 H ERW(after) - RW(before)] where the variablesand subscripts are as definedabove. If GRF fallswithin the range0 < GRF < 10, i.e., flat terrain, the user has the option of inputtingthe embankmentheight (in meters) directlyas the value for the effectiveearthworkheight,H, in the above expression. 3.2.3 Drainage Pipe and box culvertsare major componentsof drainage costs. Empiricalrelationships for predictingthe physicalquantitiesof culverts are availablefor regularpipe culverts(thosehavingdiametersbetween0.1 and 1.5 m) and box culverts(thosehavingspan lengthsunder1.0 m). Since the costsof largerpipe and box culvertsand side drains,if any, are not estimatedby theserelationships, they shouldbe includedin "othercosts." New construction (newand old alignment) Pipe culverts. The followingrelationship is used to estimate the aggregatelengthof regularpipe culvertsper unit lengthof road:

1.97ALPC if 0 < GRF < 10 (flat) DRL =

1.74ALPC if 10 < GRF < 40 (rolling) 2.02ALPC if 40 < GRF

where

(mountainous)

DRL = the aggregate length of regular pipe culvertsper unit lengthof road, in m/km; and

ROAD CONSTRUCTION SUBNODEL

55

Figure3.4: Predictedearthworkvolumeversusroadwaywidth Predicted earthwork volume 3 1m /km)

250,000

-

225,000

-

GRF = 100

RF = 160 GRF = 140 200,000

/RF

175,000

-

150,000

-

=0

GRF = 100 RF = 80

GRF = 20

125.000

RF = 0

100,000 G=40t

75,000

GRF = 100 RF = 100

50.000 G=20{

GRF = 0 RF = 0

25,000

G= 0 I 0

5

10

I

I

15

20

Roadway, width

I-25

(m)

Source: Based on analysisin Tsunokawa(1983). See also Aw (1981;1982) and Markowand Aw (1983). Figure3.5: Predictedearthworkvolumeversusroad rise+ fall Predicted earthwork 3 volume (m /km) 250,000

-

225,000

-

Legend C = RW = 21 m B = RW = 15 m A=RW=9 m

200,000

C 175.000BC

G

150,000

125,000

-C AA

1

0

0

0

A4

75,000B C

C~~~~~~~~~

A

A5

50.000

C

25,000

A-

RF25A A

0

10

20

F1

10 A

30

40

50

Road rise plus tall 60

70

50

90

100

(rn/kin)

Source: Based on analysisin Tsunokawa(1983). See also Aw (1981;1982) and Markowand Aw (1983).

SUBMODEL ROAD CONSTRUCTION

56

ALPC = the average length of regularpipe culverts,in meters, givenby: ALPC = 2.57 exp (-0.00313 GRF) RW0O 895 The predictedaverage lengthof regularpipe culvertsis plottedagainst the roadwaywidth in Figure3.6. Box culverts. The average number of regularbox culvertsper unit lengthof road is estimatedas follows:

0.27 if 0 < GRF < 10 ANBC =

0.15 if 10 < GRF < 40 0.62 if 40 < GRF

where ANBC = the averagenumberof regularbox culvertsper unit length of road,in culvertsper km. Widening For widening,the pipe culvert length and the number of box culvertsare estimatedaccordingto the followingrelationships: Pipe culverts.

1.97[ALPC(after) - ALPC(before)]if 0 < GRF < 10 - ALPC(before)]if 10 < GRF < 40 1.74 [ALPC(after)

DRL =

2.02 [ALPC(after) - ALPC(before)]if 40 < GRF

where ALPC(after l and ALPC(before) are computed using the above expressionfor ALPC basedon the "before"and "after"valuesof the roadway width,respectively. Box culverts. 0.27 if 0 < GRF < 10 ANBC

=

0.15 if 10 < GRF < 40 0.62 if 40 < GRF

57

SUBMODEL ROAD CONSTRUCTION Figure3.6: Predictedaveragepipe culvertlengthversusroadwaywidth Predictedaverage length of pipe culvert (m/km) 50GRF= 0 40 /

GGF = 30 G~~~RF = 50 R~~~~GF=

/G

70

30

20

10.

0. 5

0

10

15

20

25

Roadway width (m)

Source:

Based on analysisin Tsunokawa(1983). See also Aw (1981;1982) and Markowand Aw (1983).

where variablesand subscriptsare as definedabove. Althoughthe number and widening,unit costs of box culvertsis the same for new construction per culvertmay be differentand thereforeshouldbe reflectedin the input data. 3.2.4

Bridges

(newand old alignment) New construction The relationshipfor predictingthe total floor area of small bridges(thosehavingspan lengthsof less than 60 m) is givenby:

4.35 RW if 0 < GRF < 10 AB =

2.09 RW if 10 < GRF < 40 1.83RW if 40 < GRF

SUBMODEL ROAD CONSTRUCTION

58 where

AB = the averagefloorarea of bridgesper unit lengthof road, in m2 /km.

Widening is available. No relationship

ROAD CONSTRUCTION SUBMODEL

59

APPENDIX3A FORMULATION AND ESTIMATIONOF RELATIONSHIPS FOR PREDICTINGROAD CONSTRUCTION QUANTITIES At the stage of highwaysectorplanningand resourceallocation where the range of investmentoptions (e.g.,with respectto the location and standards)to be examinedare the widest,policy-makers need a method of constructioncost predictionthat requiresminimal informationinputs and yet producescost estimatesproperlysensitiveto a broad spectrumof design standardsand terrain characteristics. These requirementsare essentialto enablecost trade-offsamong roadconstruction and maintenance and vehicle operatingcosts to be made at the sector level. After realizingthat no such method existedin suitableform, the WorldBank and MIT initiatedin 1981 a small-scale collaborative studyto developa set of relationships for predictingroad constructioncosts that would meet the broad requirements above. The firstproductas reportedin Aw (1981,1982) and Markowand Aw (1983)essentially consistedof a comprehensive data base and a set of preliminary relationships which,becauseof the heavy reliance on engineering principlesin their formulation, represented a considerable improvementover their predecessors. These relationships were further refined into a form suitable for general applications,as reported in Tsunokawa(1983). This appendixprovidesa summarydescription of the data base and the development of the final relationships. 3A.1 Data Base As detailedin Aw (1981) road constructiondata were compiled from 52 road projectslocatedin 28 countriesin Asia, Africa,and Central and South America. These countriesinclude: Indonesia,New Guinea,the Phillipines, Taiwanand Thailandin the East Asia and the PacificRegion; Nepal and Pakistanin South Asia; Syria and Turkey in the Middle East; Ethiopia,Kenya, Malawi, Somalia,the Sudan, Swaziland,Uganda and Upper Volta in East and West Africa;Honduras,El Salvadorand Panamain Central America;and Argentina,Bolivia,Chile,Columbia,Equadorand Peru in South America. The regionsin which theseroadprojectswere constructed covera broad spectrumof topographic, climaticand soil characteristics -- from flatplains in the Sudan to extremelymountainous areas in Nepal,from the abundanceof monsoon rainfallin Pakistanto the drynessof inlandAfrica, and from areasof good soil materialsto landsof poor road-making volcanic ash. Of the 236 observations(roadsections)investigated, 42, 24 and 34 percentwere in mountainous,rollingand flat areas, respectively. The typesof construction variedfrom feederroadsto four-lanefreeways,from earthroadsto concretepaved roads,and from30 to 100 km/h designspeeds. 3A.2 Formulation and Estimationof FinalRelationships The original relationships developedby Aw and Markow provide

60

ROAD CONSTRUCTION SUBMODEL

separateestimatesfor "flat,""rolling"and "mountainous" areas basedon a satisfactorybecause although the predictedconstructionquantitiesare sensitiveto terraintype,it is difficultto determinein borderlinecases whether the terrain is "flat"as opposed to "rolling"or "rolling"as opposed to "mountainous". To overcome this problem, the revised relationshipsreported herein employ only a continuousdescriptionof terrain severity which can be measured on an objectivebasis. This objectivedescription, called the ground rise plus fall and devisedby Aw (1982),will be definedlaterin thisappendix. Several of the relationshipsformulatedare non-linear in parametersand were estimated using a special non-linear statistical procedure (NLIN) provided in the commerciallyavailable Statistical AnalaysisSystem (SAS) package. The followingparagraphsprovidea brief descriptionof the model formulationand estimationresults for the individualrelationships. Area of site clearance The area of site clearanceper unit road length (ACG) is hypothesizedas a linear function of the roadway width in which the coefficients are, in turn, exponentialfunctionsof the ground rise plus fall. The statisticalestimationusing this model form yielded the followingresults: ACG = 1770 exp [0.0278GRF] + 1610exp [-0.0114GRF] RW (0.8) (1.5) (6.2) (1.2) R2 = 0.51 Numberof observations = 35 where the variablesare as defined in the text and the figures in the parenthesesare asymptotict-statistics. The goodness of fit of this relationship is illustrated in Figure3A.1 in which the observedvaluesof the area of site clearanceis plottedagainstthe predicted. As shown graphicallyin Figure 3.3, this relationshipseems to indicatedifferentpracticesin settingup the site clearancearea under differentterrainconditions.First,the sensitivity of the site clearance area to the roadwaywidth is at its maximumfor flat terrain(GRE= 0) and decreasesas the terrain becomesmore severe (GRE approaches100 i/km). Second, for relativelynarrow roads (RW = 5 m) the site clearancearea increaseswith terrainseverity,which is as expected;however,the reverse is indicatedfor relativelywide roads (RW = 25 m). There is no clear explanation for the latterobservation, althoughthere might be a greater tendencyto economizeon relativelyexpensiveconstruction in mountainous terrain. Earthworkvolume Among the formulasattemptedfor predictingthe earthworkvolume,the followingwas selectedfor use in HDM III:1 1 This relationship is a revisedversionof the one reportedin Tsunokawa (1983).

61

SUBMODEL ROAD CONSTRUCTION Figure3A.1: Area of site clearance;observedversuspredicted area of (half-Pagefig Observed site clearance

(m2/km)

s0,000

Line of equality

40,000

30,000

20,000

_

*

10,000

10.000

0

30,000

20,000

40,000

area of site clearance

Predicted

2

1m /kml

Source: Based on analysisin Tsunokawa(1983). See also Aw (1981;1982) and Markowand Aw (1983). Figure3A.2: Earthworkvolume: observedversuspredicted Observed

(halfpa earthwork volume (m3/km) Line of equality

15,000

150,000

125,000

100,000 _ 0~~~~

75,000

*--

50,000-*

20,000

-

3

0

20,000

_

40

-

40,000

60,000

80,000

100,000

120,000

140,000

3

Predicted earthwork volume Im /km)

Source: Adapted from Tsunokawa(1983). Markowand Aw (1983).

See also Aw (1981; 1982) and

62 where

ROAD CONSTRUCTION SUBMODEL H = 1.41+ 0.129G + 0.0139GRF (7.5) (3.7) (1.3) G = GRF-RF R2 = 0.55 Numberof observations = 123

and the figuresin the parentheses are asymptotict-statistics.A plot of the observed against the predictedvalue of the earthworkvolume is providedin Figure3A.2. This specificationis based on the followingsimple physical constructof the road's cross-section.In a simplecase of zero ground crossfall,which typicallyoccurs in flat terrain,the cross-section of a fill section is assumed to be representedby a trapezoid,as shown schematically in Figure3A.3(a). The volume of earthworkper unit road length(m3/km) is givenby: EWV = 1000 (RW + cot m H) H where

m = the angleof the embankmentslope,in radians; H = the heightof the embankment, in meters.

The same derivationapplies to a cut section (see also Figure 3A.3)with the termsm and H now referringto the cut volume. In the case of medium and large ground crossfalls, which can be found in rollingand mountainous terrain,the volumeof earthworkmay also be represented by the same mathematical formula, but the physical construct is somewhat different.As depictedin Figures3A.3(b)and 3A.3(c),the cross-sectional area of earthworkcan be representedby an imaginarytrapezoidwith the shorterbase equalto RW, but now with the base angle equal to the cut or fill slope and the height to an imaginaryheight. When this formula is suppliedover an entire road stretchwith cross-sections of varyingshape and size, the term H is interpreted as the averageof the heightsof the real or imaginarytrapezoidsthat representthese cross-sections.At this levelof generalization, H is calledthe "effectiveearthworkheight". It is furtherhypothesized that the averageeffectiveheightH is a functionof terrainseverityand the designstandardof the road section; for simplicity, H is assumedto be a linearfunctionof G and GRF. The expectationthat the earthworkvolume is relativelylarge for a road sectionof high standardrelativeto terrainseverity(i.e.,largeG) is supportedby the significantpositivecoefficientfor G (0.129). The positive coefficientfor GRF (0.0139),although not significant,is consistentwith the expectation that the earthworkvolumetendsto increase with terrainseverityfor a given "relative"standard(G). Althoughwith small t-ratio(1.6),the estimatedvalue of cot m of 0.731appearsto be reasonable.The valuesof G and GRF shouldbe close to zero for flat terrain. When both G and GRF are zero, the predicted effectiveearthworkheight,H, equals 1.41 meters. The height of a fill section in flat terrain is generallya functionof the hydrologicand drainage conditionsof the area. However, this value appears to be representativeof the constructionprojects for which the data were

ROAD CONSTRUCTION SUBMODEL

63

Figure3A.3: Typicalearthworkcross-sections and equivalenttrapezoids 14 RW

(a) Zero groundcrossfall

LECEND RW: roadwaywidth H: effectiveearthworkheight e: angleof cut on fill slope

(b) Mediumgroundcrossfall

bc) large g

(c)

largeground

crossfflll

SUBMODEL ROAD CONSTRUCTION

64

collected. In HDM-III, however,an option is providedto overridethe endogenously predictedvalue of H by a user-specified inputwhen GRF is between0 and 10 m/km. Pipe culvertlength The relationshipfor predictingthe aggregatelength of pipe culvert was constructedas a product of two relationships,one for predictingthe averagelengthof a pipe culvertand anotherfor predicting the numberof pipe culvertsper unit lengthof road. An attemptto derive a relationship which directlypredictsthe aggregatelengthof pipe culvert per unit road lengthwas also made, but the formerapproachwas preferred on the basis of betterfit to the data. Among the various specificationstested, the following was selectedfor predictingthe averagelengthof a pipe culvertin HDM-III: 0.895 ALPC = 2.57 exp (-0.00313GRF) RW (5.20) (1.84) R2 = 0.705 Numberof observations = 75

(10.82)

where the figures in the parenthesesare asymptotict-statistics. As illustrated graphicallyin Figure 3A.4,ALPC is an increasingfunctionof RW; this is because the exponentand the multiplicativeterm are both positive. The negative coefficientof GRF indicatesthat for a given roadwaywidth (RW), the average pipe culvertlength decreasesas terrain severity(GRF) increases.A plausibleexplanationfor this is the greater tendencyto minimizeconstruction cost in steepterrain. the were testedfor predicting Althougha numberof relationships numberof pipe culvertsper unit road length,no significantimprovements were obtainedover the followinggroupaverages: Averagenumberof pipe culverts per km of road

Standard errorof estimate

Numberof observations

1.97 1.74 2.02

0.19 0.18 0.23

27 23 25

Rangeof ground rise + fall (m/km) 0 < GRF < 10 10 < GRF < 40 40 < GRF < 100

Source: Adaptedfrom Aw (1981). Thus the aggregatelength of pipe culvertsper unit length of road (m/km)is predictedin HDM-IIIas follows: DRL

=

1.97ALPC if 0 < GRF < 10 1.74ALPC if 10 < GRF < 40 -2.02 ALPC if 40 < GRF.

ROAD CONSTRUCTION SUBMODEL

65

Figure3A.4: Pipe culvertlength: observedversuspredicted Observed pipe culvert length (mikm)

Line o1 equality

50

40

30

20

10

o

10

20 Predicted

30

40

pipe culvert

50

length lm/kml

Source: Basedon analysisin Tsunokawa(1983). See also Aw (1981;1982) and Markowand Aw (1983). Other quantitiesof road construction Other quantitiesof the road construction, namely, the average numbers of box culverts (ANBC) and bridges (ANBR) per unit length of road are generally influenced by the terrain and climatic characteristics of specificlocations. However,because of the lack of data for these explanatoryvariables,the quantitiesare predictedas groupaveragesin HDM-III(shownwith standarderrorsin parentheses): Rangeof groundriseplus fall (m/km) Variable

Description

ANBC

Numberof smallbox culvertspert km (spansunder 1.0 m)

0.27 (0.04)

0.72 (0.15)

0.62 (0.20)

ANBR

Numberof small bridgesper km (spansunder60 m)

0.217 (0.027)

0.104 (0.016)

0.091 (0.027)

Numberof observations

O
43

10
26

40
16

Source: AdaptedfromAw (1981). Assuming that the average width of bridges is equal to the roadwaywidth (RW),the averagefloor area of bridgesper unit road length (m2/km) is given by: AB = 20 ANBR where 20 is the averagespan lenghtof smallbridgesfound in the data (in meters).

I

CHAPIER 4

Road Deterioration and Maintenance Submodel

The road deteriorationand maintenancesubmodel performs the importantfunction of linking constructionstandards(and costs), road maintenancestandards(and costs),and road user costs through the road deteriorationrelationships.The HDM model considersthese relationships of road condition,ultimatelymanifest in detail becausethe deterioration increasesin road causessignificant surface, in the roughnessof the road of maintenance and the effectiveness user costs. The rateof deterioration in investments of future and costs timing, nature togetheraffect the costs. rehabilitation and the magnitudeof returnsin savingson user The submodel estimates the combined effects of traffic, environmentand age on the conditionof the road, given data on its and materials,and proceedsyear by year to predictthe change construction of surface condition under specified maintenanceand rehabilitation policies throughoutthe course of the analysis period. Conditionis predicted by distress mode; for paved roads: cracking, ravelling, potholes,ruttingand roughness;for unpavedroads: roughness,material loss and passability. Parametersinclude the volume and loading of traffic,rainfalland moisturebalance,initialroad conditions,material the variabilityof materialbehavior strengthpropertiesand thicknesses, and construction quality,and a range of maintenanceoptions. They cover paved roads with flexiblepavementsof bituminoussurfacingsand either granularor cementedbase (but excludeportlandcementconcreteand thick asphalt base pavements),and unpaved roads of either gravel or earth surfacing. They apply mainly to engineeredroadswith adequatedrainage, crossfalland foundationstability (below the subgrade),though some roads that do not conformin all guidanceis given on how to parameterize climatesand respects. The models are applicabledirectlyto non-freezing may apply in some freezingclimates. with adjustments in this submodelare structuredon incorporated The relationships mechanistic concepts of pavement behavior and are empirical models (Paterson,1987) from an extensivedata base statistically-quantified study (GEIPOT,1982). Some are probabilistic collectedin the Brazil-UNDP in nature,predictingan array of outcomes. Some ratherthan deterministic models from other sourcesare includedand in minor models, supplementary where an adequateempiricalbase was lacking,engineeringprinciplesand have been verified judgmenthave been applied. The primaryrelationships on independentdata sets (Paterson,1987). Only a single set of is includedin the submodelbut provisionis made for the relationships user to adapt these to local conditionswhere quantitativestudies are available. Road roughnessthroughoutthis chapterhas been expressedin QI with the restof the model specification. units for the sake of consistency

67

68

ROAD DETERIORATION

The relationships and all supportingdocumentation in Paterson(1987)are expressedin International RoughnessIndex (IRI)units. (Note:1 m/km IRI = 13 counts/kmQIm.) 4.1 4.1.1

PAVEDROAD CONCEPTSAND LOGIC GeneralConcepts

In keepingwith the structureof HDM III, road deterioration is computed as the incrementalchange in pavement conditionduring each analysisyear due to traffic,environment and maintenance, and the current pavement conditionis updated each successiveyear during the analysis period. This computational sequenceis shown diagrammatically in Figure 4.1. The empirical relationshipsare compatiblewith this and are primarilyrecursiveincremental models in which the predictedchange in conditionis a functionof currentcondition,the cumulativetrafficand rainfall,and various pavementparameters. This model form is able to acconmodate pavements in any initial state of condition and age, facilitates the handling of environmentaleffects and interactive maintenancecriteria, is particularlyapposite to both validationand application in pavementmanagementsystems,and is appropriateto marginal cost evaluation.Historicaldata on trendsof pavementconditionare not a required input although where these are available they can be used indirectly to calibrate the relationshipsas discussed under local adaptation(Section4.1.8). Road pavementsdeteriorateover time under the combinedeffects of trafficand weather. Trafficaxle loadingsinducelevelsof stressand strainwithinthe pavementlayerswhich are functionsof the stiffnessand layer thicknesses of the materialsand which under repeatedloadingcause the initiationof cracking through fatigue in bound materialsand the deformationof all materials. Weatheringcauses bituminoussurfacing materialsto become brittleand thus more susceptibleto crackingand to disintegration(which includes ravelling,spalling,and edge-breaking). Once initiated,crackingextends in area, increasesin intensity(closer spacing)and increasesin severity(or width of crack)to the pointwhere spallingand ultimatelypotholesdevelop. Open cracks on the surfaceand poorly maintained drainage systems permit excess water to enter the pavement,hasteningthe process of disintegration,reducing the shear strengthof unboundmaterialsand thus increasingthe rate of deformation underthe stressesinducedby trafficloading. The cumulativedeformation throughoutthe pavementis manifestedin the wheelpathsas ruts and more generallyin the surfaceas an unevennessor distortionof profiletermed roughness. Apart from, and interactingwith, traffic, environmental effectsof weatherand seasonalchangescausedistortions which also result in roughness. The roughnessof a pavementis thereforethe result of a chain of distress mechanismsand the combinationof various modes of distress. Maintenance is usually intended to reduce the rate of deterioration, but certain forms such as patchingmay even increasethe roughnessslightly. Roughnessis thus viewed as a compositedistress,

ROAD DETERIORATION

69

Figure4.1: Logicsequenceof roaddeterioration and maintenance submodel: paved roads

INPUT pavement strength, condition, age for initial analysis year TRAFFIC| |

Jl____

l_____________(

SUBMODEL~

INPUT

local

l

adaptation factors COMPUTE TRAFFIC LOADINGS Increment in analysis year by damage functions COMPUTE SURFACE DISTRESS Increment in analysis year by mode: cracking, ravelling, potholes, rutdepth by pavement type classi fication by probability sublink

COMPUTE ROUGHNESS Increment in analysis year by

components: traffic, surface distress, age/environment by sublink

COMPUTE MAINTENANCE EFFECTS & QUANTITIES

NTENAN E

for Reconstruction or else Overlay or else Reseal or else Preventive according to specified CODTIONRESPONSIVEaoepiort MATNTENAN(

/

criteria

in

?

~~~~~~~~COMPUTE VCONDITION & ROUTINE ~~~~~MAINTENANCE QUJANTITY __

HICby

patching

COMPUTE POST-MAINTENANCE Condition, strength, age

l,

OUTPUTAVERAGE ROUGHNESS

to

Source: This study.

applied

VOC submodel

OUTPUTMAINTENANCE

~~~QUANTITIES to COSTS submodel

70

ROAD DETERIORATION

comprisingcomponentsof deformationdue to trafficloadingand rut depth variation,surfacedefectsfrom spalledcracking,potholes,and patching, and a combination of agingand environmental effects. These concepts of pavement behavior are reflected in the interactivenature of the relationshipsfor each distress mode and determinethe sequenceof computationshown in Figure 4.1. The pavement strength(whichis summarizedin an index,the modifiedstructuralnumber), the condition,and the age of the pavementat the beginningof the year are given, and the volume of traffic per lane is computedusing two damage functionsto reducethe spectrumof axle loadingto a numberof equivalent 8OkN standardaxle loads (ESA). The ages predictedfor the initiation of crackingor ravellingvary with surfaceand base type,and when the current surfacing age exceeds those, the areas of cracking and ravelling progression are predicted.Potholingbeginsbeyonda thresholdof the area and severityof crackingand ravelling,and progressesby volume. The by estimatingthe expected variability of materialbehavioris incorporated timesof early failures,medianfailuresand late failuresfor equalthirds of of the link lengthwhich are then treatedas sublinks. The increments rut depthand of roughnessdue to deterioration are then computedfor each sublink. Local adaptationof the predictionrelationshipsis effected factors"which multiplythe predictedvalues. throughinput "deterioration The averagevalues of roughnessfor each sublinkover the year are output to the VehicleOperatingCost submodelafter routinepatchingmaintenance, effectsare computed. but beforemajormaintenance, Maintenanceis applied at the end of the analysisyear if the specifiedinterventioncriteria are met. Maintenanceinterventionis specifiedas either "scheduled"(i.e., at specific time intervals)or 'conditionresponsive'(i.e.,at specifiedthresholdlevelsof condition). There are five categoriesof maintenance, in order of descendingpriority: reconstruction, overlay, resealing,preventivetreatment,and patching. criteria The prioritization ensures,for example,that if the intervention and overlaywere satisfiedin a givenanalysisyear for both reconstruction would be applied. Routinepatchingmaintenanceis thenonly reconstruction thereforeonly appliedwhen no major maintenanceis applied in that year. It is regardedas havingbeen appliedcontinually during the year, unlike majormaintenancewhich is appliedat the end of an applicableyear. The policy for each maintenancecategoryspecifieseither the unit quantities to be applied,for examplethe thicknessof overlayor reseal,the annual and maximumquantitiesof patching,etc., or the conditionto be achieved, e.g., the strength after reconstruction. The quantitiesare neither "designed" nor optimized,and are computedsolelyon the basis endogenously of the specifiedcriteria. Following the application of maintenance, the maintenance quantitiesand costs are computed and output to the benefits-costs submodel. The values of the road conditionparametersafter maintenance (i.e., cracking,ravelling,potholingand patchingareas, rut depth and roughness)are computedand become initialvalues for the next analysis year. The cycle continuesthroughsuccessiveyears to the final analysis year.

ROAD DETERIORATION

71

4.1.2 Computational Logic Road deteriorationis predictedthrough five separatedistress modes, i.e., cracking,ravelling,potholing,ruttingand roughness,as defined in Table 4.1 and illustratedin Figure4.2. Surfacingdistress, namely cracking,ravellingand potholing,is characterized by two phases, i.e., 1. Initiationphase- the periodbeforesurfacingdistressof a givenmode or severitydevelops; 2. Progressionphase - during which the area and severityof distressincreases. Separatesets of equationsare providedfor initiationand progression.In addition, cracking is characterizedby two degrees of severity,"all cracking"(narrowand wide) and "wide cracking,"which are subsequently combinedin a compositeindex. Deformation distress,namelyrut depth and roughnessare continuous,and representedby only progressionequations. As they are partlydependentupon the surfacingdistress,theyare computed after the change of surfacingdistress in the analysis year has been computed. As an aid to keepingtrack of the many variablesused in this chapter,some conventions have been adoptedas follows: Subscripts a b d m

[condition] at beginning of analysis year (after maintenance of the previousyear); [condition] at end of analysisyear (beforemaintenance); [changeof condition]due to deterioration; [changeof condition]due to maintenance.

Prefixes P A

previous value, before maintenance(e.g., PCRA in Table 4.2); changeof conditionvariableduringanalysisyear.

Also, in general,the letterA usuallystands for "area" (exceptin the word "AGE"),T is for "time,"and Y for "yearly" or "years." Other mnemonicswill be apparentas the presentation progresses. The primary variablesused from one analysisyear to the next to define pavement condition,history and strengthare defined in Table 4.2 and may be classifiedintogroupsas follows: [CONDITION]5 [HISTORY] 5 [TRAFFIC] = [STRUCTURE]5

[ACRA,ACRW,ARAV,APOT,RDM, RDS, QI] [AGE1,AGE2,AGE3] [YE4,YAX] [SNC,DEF, HS..,PCRA, PCRW,CRT, RRF]

72

ROAD DETERIORATION

Figure4.2: Primarymodes of pavementdistressestimatedin road deterioration and maintenance submodel Areasof Cracking & Potholes(%) Limit 100%_ //ACRW ACRA

*APOT Limit 30%

intiation

~

-4-

Progression

Time

Areasof Ravelling Limit 100%

ARAV

Initiation .. Rut Depth Mean & Standard Deviation (mm)

|

-

Progression

Time

Limit50mm RDM

Time Roughness Limit

150 Ql Ql

Time

Source: This study.

ROAD DETERIORATION

73

Table 4.1: Definitions of distressmeasures Measure

Definition

Area (of distress)-

Sum of rectangularareas circumscribingmanifest distress (linecracksare assigneda width dimension of 0.5m),expressedas percentageof carriageway area and sectionlength;

All cracking

-

Narrowand wide crackinginclusive;

Narrowcracking

-

Interconnected or line cracks of 1-3 mm crack width (equivalent to AASHTOClass 2);

Wide cracking

-

Interconnected or line cracksof 3 mm crackwidth or greater,with spalling (equivalentto AASHTO Class 4);

Indexedcracking -

Normalizedsum of AASHTO Classes 2 to 4 cracking weightedby class,i.e.: CRX = 2 ACRi/Ei, i = 1,4 and estimatedby (Paterson1987):

CRX = 0.62 ACRA + 0.39 ACRW. Ravelling

-

Loss of materialfromwearingsurface;

Rut depth

-

Maximum depth under a 1.2 m straightedgeplaced transversely acrossa wheelpath;

Pothole

-

Open cavity in road surface with at least 150 mm diameterand at least25 mm depth;

Roughness

-

Deviationsof a surfacefrom a true planar surface with characteristic dimensionsthat affect vehicle dynamics,ride quality,dynamic loads and drainage (ASTME-867-82A)- typicallyin rangesof 0.1 to 100 m wavelengths and 1 to 100 mm amplitudes;

IRI

-

International RoughnessIndex,the referencemeasure expressing roughness as a dimensionlessaverage rectifiedslopestatisticof the longitudinal profile and defined in Sayers, Gillespie, and Paterson (1987);

QI

-

Quarter-carIndex, roughnessmeasure of the main Brazil-UNDPstudy data base, an average rectified slope statistic,where 13 counts/kmQIm - 1 m/km IRI.

Source: This study.

74

ROAD DETERIORATION

Table 4.2: Definitionof primaryvariablesfor pavementcondition, historyand strength Variable

Definition

ACRAa, ACRAb

Thetotal areaof allcracking, inpercent of thetotal carriageway area ACRWa, ACRWb Thetotal areaofwidecracking, inpercent of thetotal carriageway area ARAVa, ARAVb Thetotal arearavelled, inpercent ofthetotal carriageway area APOTa, APOTb Thetotal areaofpotholing, inpercent of thetotal carriageway area AGE1 Thepreventive treatment age,defined as thetimesincethelatest preventive treatment, reseal, overlay, reconstruction standard axleloadand520kPatirepressure) of thesurfacing AGE2 The surfacing age defined as the timesincethe latestreseal, overlay, reconstruction or newconstruction activity, inyears AGE3 Theconstruction age,defined as thetimesincethelatest overlay, reconstruction or newconstruction activity, inyears CMOD Theresilient modulus of soilcement, inGPa(required forcemented basepavements only) COMP Therelative compaction in thebase, subbase andselected subgrade layers, inpercent (seenotein4.2.6) CQ Theconstruction quality indicator forsurfacing, whereCQ = 1 if thesurfacing hasconstruction faults, = 0 otherwise CRT The cracking retardation timedue to maintenance, in years(as elaborated in4.3.3) CRXa, CRXb The totalareaof indexcracking area,in percent of the total carriageway DEF ThemeanBenkelman Beamrebound deflection of thesurfacing in both wheelpaths under80kNstandard axleload, 520kPatirepresure, and 30eCaverage asphalt temperature), inmillimeters HBASE Thethickness of thebaselayerin theoriginal pavement (required only for cemented basepaveients), in millimeters HSNEW Thethicknessof the mostrecent surfacing, in millimeters HSOLD The total thickness of previous, underlying surfacing layers, in millimeters MM4P Meanmonthly precipitation, inm/month PCRA Theareaof allcracking before the latest reseal or overlay, in percent of thetotal carriageway area PCRW Thearea of wide cracking before the latest reseal or overlay, in percentof the total carriagewayarea QI a, Qlb The road roughness,in QI units (see Figure 1.4 for conversion relationships, andnotethat the modelaccepts alternate units with linear conversion) RDMa, RDMb Themeanrutdepthinbothwheelpaths,in mm RDSa, RDSb Thestandard deviation of rutdepth(across bothwheel paths), in rmm RRF Theravelling retardation factor duetomaintenance (dimenssionless - as elaborated In4.3.3)

RH SNC YAX YE4

Therehabilitation indicator, where RH = 1 forsurface types asphalt concrete overlay (OVSA) or open-graded cold-mix (OCMS) overlays, =0 otherwise Modified structural number of thepavement, corputed as defined in Section 4.1.3. ThetotalnuTber of axlesof allvehicle classes fortheanalysis year,inmillions/lane Thenumber of equivalent standard axleloadsfortheanalysis year based on anaxleloadequivalency exponent of4.0,inmillions/lane

Source: This study.

ROAD DETERIORATION

75

The computational logichas the followingsequence(seealso Figure4.1): 1. The pavementconditionat the beginningof the analysisyear is initialized eitherfrom inputdata if it is the firstyear of the analysis or the first year after construction, or otherwisefrom the result of the previousyear's condition aftermaintenance(seeSection4.2.1): [CONDITION]a= initialized, or updatedaftermaintenance of previouscycle (see (v) below). [HISTORY]a = [HISTORY]b+ 1 [TRAFFIC)a = updatedfrom trafficsubmodel [STRUCTURE] = updatedas resultof previousmaintenance 2. The surface conditionsbeforemaintenanceat the end of the year are predicted(seeSections4.2.2-4.2.5): [ACRA,ACRW,ARAV, APOT]b = [ACRA,ACRW,ARAV,APOT]a + ACACRA,ACRW,ARAV, APOT]d 3. The rut depth and roughnessconditionsbeforemaintenanceat the end of the years are predicted (see Sections 4.2.6-4.2.7):

[RDM,RDS, QI]b = [RDM,RDS, QI]a + A[RDM,RDS, QI]d 4. Maintenanceinterventioncriteriaare applied to determine the natureof maintenanceto be applied,if any (seeSections 4.3.3-4.3.7), Conditionresponsive: if [ACRW,ARAV,APOT,QI]b >= [ACRW,ARAV,APOT, QIJintervention or Scheduled: if [AGE1,AGE2,AGE3lb>= [AGE1,AGE2,AGE3 ]intervention 5. Highest-ranking applicablemaintenanceis applied and the effects on pavement condition computed (see Sections 4.3.3-4.3.7): [CONDITIONJa(next year)= ECONDITION]b+ A[CONDITION]m 4.1.3 PavementStructuralCharacteristics In performance predictionmodels it is necessaryto use measures of pavement strength which summarizethe complex interactionsbetween material types and stiffnesses,layer thicknessesand depths, subgrade stiffnessand surfacecondition. Measureswhich have provedeffectiveor popularin the past have included,interalia:

76

ROAD DETERIORATION Structuralnumber (AASHO)with soil support value (AASHTO)or modifiedstructuralnumber(TRRL); Surfacedeflectionundercreep loading(BenkelmanBeam); Surface deflectionand curvatureunder dynamic cyclic loading (Dynaflect, Road Rater,etc.);and Surface deflectionand curvatureunder dynamic impact loading (FallingWeightDeflectometer).

In the empiricalresearch(Paterson1986b,1987),the modified structural number (SNC)was found to be the most statistically significant measureof pavementstrengthaffectingthe deterioration of pavements,and is thus the primary strengthparameterin the predictionrelationships.Surfacepeak deflection measurementsunder standard loadings were generally weak predictorsof perfomancewithoutsupplementary strengthparameters, though BenkelmanBeam deflection(DEF)enterssome relationships.A fair degree of correlation existsamongststrengthand deflectionmeasureshowever,and the user may estimate SNC or DEF for input, either directly or from alternative measuresas follows. The modified structuralnumber, SNC, is defined as a linear combinationof the layer strengthcoefficients ai and thicknessesHi of the individuallayers above the subgrade,and a contributionfrom the subgradedenotedby SNSG, i.e.:

n SNC = 0.0394

I

ai Hi + SNSG

i1=1 where

ai Hi n

= the strengthcoefficient of the ith layeras defined in Table4.3 and shownin Figure4.3(a),(b); = the thicknessof the ith layerprovidedthat the sum of thicknesses, Hi is not greaterthan 700 mm, in mm; = the numberof pavementlayers;

SNSG = the modifiedstructuralnumbercontribution of the subgrade,givenby: 2 SNSG= 3.51Qog1o CBR - 0.85(Qog 1o CBR)

-

1.43;and

CBR = the CaliforniaBearingRatioof the subgradeat in situ conditionsof moistureand density,in percent. The strengthvariablesare updatedfollowingmaintenanceto take accountof changes in pavementstrengthdue to overlaying,resealingand cracking. The models are sensitiveto these variables,and input values shouldbe selectedcarefully. The user is requiredto specifyonly one of the primary variables,SNC or DEF, but predictionscan be improvedby specifyingboth values. When only one value is supplied, the other

ROAD DETERIORATION

77

Table 4.3: Pavement layer strength coefficients

Pavement layer

Strength coefficient ai

Surface course Surface treatments 0.20 to 0.40 Asphalt mixtures (cold or hot premix of low stability) 0.20 Asphalt concrete (hot premix of high stability), MR30 = 1500 MPa 0.30 MR3 0 = 2500 MPa 0.40 MR3 0 = 4000 MPa or greater 0.45 Base course Granular materials 2 CBR = 30% 3 CBR = 50% CBR = 70% CBR = 90% CBR = 110%

Max. axle load > 8OkN 0. 0. 0.10 0.12 0.14

Max. axle load < 8OkN 0.07 0.10 0.12 0.13 0.14

Cemented materials UCS = 0.7 MPa UCS = 2.0 MPa UCS = 3.5 MPa UCS = 5.0 MPa

0.10 0.15 0.20 0.24

Bituminousmaterials 6

0.32

Subbase course and selected subgrade layers (to total pavement depth of 700 mm) Granular Materials 6 CBR = 5% CBR = 15% CBR = 25% CBR = 50%

CBR = 100% Cemented materials UCS > 0.7 MPa

0.06 0.09 0.10 0.12

0.14 0.14

(See footnotes on next page.)

78

ROAD DETERIORATION Applicableonly when thicknessHI > 30 mm. MR30 = resilientmodulusby indirecttensiletest at 300 C.

2

3

4

ai = (29.14CBR - 0.1977CBR2 + 0.00045CBR3 ) 10-4; the coefficient ai may be increasedby 60 percent if CBR > 70 and the subbase is cement-or lime-treated.Note: ai = 0 for CBR < 60 when maximumaxle loadingexceeds80 kN. CBR = CaliforniaBearing Ratio (in percent) determinedat the equilibrium in situ conditionsof moisturecontentand density. ai = 0.075 + 0.039 UCS - 0.00088 UCS2 ; where UCS = Unconfined Compressive Strengthin MPa at 14 days. 'Cemented'impliesdevelopment of tensile strengththroughportlandcement or lime-treatment, or the use of certainflyash,slag, lateriticor ferricretematerialsthat are self-cementing over time.

5

Dense-graded bitumen-treated base of high stiffness,e.g., MR20 = 4000 MPa, resilientmodulusby indirecttensiletest at 200C.

6

ai

=

0.01

+

0.065 logioCBR.

Source: Adaptationof TRRL ReportLR673 (Hodgeset al., 1975),TRDF Final ReportV Brazil(GEIPOT,1982),and NITRRmanualTRH4, 1978,South Africa.

variable value is computed endogenouslyby the followingapproximate relationships (Paterson,1987)shownin Figure4.3(c): 6 if base is not cemented 6.5 SNC-1-

DEF

SNC

=

={

6 3.5 SNC-1. if base is cemented

63 3.2 DEF-0-

if base is not cemented

63 2.2 DEF-0.

if base is cemented.

Note: The standarderror (S.E.)and valid rangeof theseestimations are: for DEF: S.E. = 0.34mm; range= 0.13 to 2.0 mm; and for SNC: S.E. = 1.24;range= 1.5 to 7.7. The alternative, dynamic,deflection measuresmay be used to estimatethese inputs, but the relationshipsdepend upon pavement configurationas discussedin Paterson(1987),and the user may need to generatea specific conversionappropriate to the circumstances.

ROAD DETERIORATION

79

Figure 4.3: Charts for estimatingpavement strength and deflection parameters values (a) Layer strength coefficientsbituminous and cemented materials

(b) Layer strength coefficients for unbound materials and estimationof subgrade su port

0.5

0.25

25 a (BaseOverCemented Subbase)

0.4

Bituminous

0.20

Ma2erials / (Scale A.) / [J

r.)

t'D

0.02

0

1

/

_

< 0.3 / Ceffmnt_ous . ~~~~~~~~~~~~Materials ,- I*',/

/

1

/ .0

/

0.3

(Subbase)

3

4

0.0a

~~~~~~~~~~~~~~005 0_10 | ,'a____' (Base:Mcodmum Lood > 8_kN)

_

2

~~~~~~~~~~~~~~~~~~~Subgrade

/

5

0.5 1.0

hInstuCBR(%s)

A. ResilientModulus at 30 C (GPa) Bl Unconflned Compressive9rentath (MPa)

(c) Estimation of Benkelman BeamDeflection (C~EF) or Modified StLructural Numbers(SNC) BenkelmanBeam Deflection/mm)

0.01~~

... XGranular Base

$

\5 2.0

=

\

Cemented

Y

..

. T..

...

T .

D

r2

=

0.56

\S.E. = 0.34 mm

391 abs.

a\ oO 'Do

0

2

4

..

..

..

..

.

RDEF

0DEF=_3 . SNC-1.C°

t

B

Modified Structural Number, SNC

Source: This study.

~ ~~~~~

6.5 SNC-''

8

80

ROAD DETERIORATION

4.1.4 PavementClassification For the predictionof surfacingdistress(cracking,ravellingand potholing),neitherSNC nor DEF are sufficientpredictorsfor all pavement types. Thus, pavementsare classifiedby seven surface types and three base types,totallingtwentydifferentpavementcategories(onecombination is not used in practice). Within each category,the greater number of surfacingand base combinations used in practicehave statistically similar behavior, distinguishedotherwise through the explanatory variables appearingin a specificdistressequation. The seven surfacetypesare: 1. 2. 3. 4. 5. 6. 7.

Surfacetreatment(ST); Asphaltconcrete(AC); Slurryon surfacetreatment(SSST); Resealon surfacetreatment(RSST); Resealon asphaltconcrete(RSAC); Open gradedcoldmix on surfacetreatment(OCMS);and Asphalt overlay or slurry seal on asphalt concrete,and asphaltoverlayon surfacetreatment(OVSA).

Two of the surfacetypes,surfacetreatmentand asphaltconcrete, apply to original,new or reconstructed pavements. The other typesdefine surfacesafter a full-widthmaintenancetreatmentor rehabilitation of an existing pavement, as illustratedin Table 4.4. Slurry on surface treatmentand cold mix on surfacetreatmentare types which may be either original surfacings or the result of certain maintenanceoperations (resealingwith slurry and overlayingwith cold mix, respectively).The othersurfacetypesresultfrom othercombinations of reseals,overlaysand originalsurfacings. Note that the categorization groups together the combinationshaving similarbehaviorin order to restrictthe number of categories. The three base types are: granular, cement stabilizedand bituminous.These base typesare established as originallyconstructed or by pavement reconstruction and assumed to be unchangedthroughoutthe pavement life unless reconstruction takes place. In the classification that used herein,pavementreconstruction includesall major rehabilitation changesthe classification or strengthof the base. 4.1.5 TrafficCharacteristics For paved roads, traffic is defined by two variableswhich representboth the volumeand loadingaspectsof mixed vehiculartraffic. These are the flow of all vehicleaxles (YAX)and the flow of equivalent 80 kN standardaxle loads (YE4),both expressedon an annual,millionsper lanebasis as definedin Table4.2. In HDM-III,the road link or subsectioncomprisesthe full road width. Directionalsymmetry is assumed in the traffic flow and road deteriorationsubmodelsso that the variablesin this submodelexpress average pavement condition,average traffic flow and average equivalent axle loadingacrosslanesand directions.

81

ROAD DETERIORATION Table 4.4: Surfacetype classification afterrnaintenance treatment after Classification indicatedmaintenance before Classification maintenance

Surface 'ilurry Coldmix overlay treatseal (CM) ment(RS) (SS)

Asphalt concrete (OV)

Surfacetreatment(ST)

RSST

SSST

OCMS

OVSA

Slurryon surfacetreatment (SSST)

RSST

SSST

OCMS

OVSA

Resealon surfacetreatment (RSST)

RSST

SSST

OCMS

OVSA

Cold mix on surfacetreatment (CMST)

RSAC

SSST

OCMS

OVSA

Asphaltconcrete(AC)

RSAC

OVSA

OCMS

OVSA

Resealon asphaltconcrete (RSAC)

RSST

OVSA

OCMS

OVSA

Asphaltoverlayon asphalt concrete(OVAC)

RSAC

OVSA

OCMS

OVSA

Note:Only surface types ST, SSST, OCMS and AC can be treated as new in the model. construction Source: This study. To computeYAX and YE4, the total numbersof vehicleaxles and equivalent standard axles applicable during the analysis year are determinedin the trafficsubmodel(Chapter2) and dividedby the effective number of lanes, denoted by ELANES. The ELANES variablemay either be specifiedby the user or take a defaultvalue expressedas a functionof roadwidth, i.e.:

ELANES

where

=

1.0 1.5 2.0 3.0

if W if 4.5 < W if 6.0 < W if 8.0 < W

4.0

if 11.0 < W

< < < <

4.5 6.0 8.0 11.0

width,in meters. W = carriageway

82

ROAD DETERIORATION

4.1.6 Environment and Geometry Environmentalfactors are incorporatedin the deterioration models throughtwo variables,the modifiedstructuralnumber (SNC)and the mean monthlyprecipitation (MMP). The effectsof aging and weatheringare represented throughtime variablesincorporated in the predictionmodels. The modifiedstructuralnumber(SNC)includesthe contribution of the subgrade (SNSG) and the strength coefficientsof the material properties(a1 ) under the in situ conditionsof the local environment of the pavement. The combined effects of drainage and rainfall on the behavior of the pavement are thus representedthrough the effects of moistureon the strengthpropertiesand stiffness(e.g.resilientmodulus) of the materialsin each pavement layer. An increase in the moisture contentof a materialabove the optimumassociatedwith its densitycauses a decreasein the shear strength,and oftena decreasein the stiffness, of the material. Thus it usuallycausesa decreaseof the modifiedstructural numberand increaseof the deflection. Such increasesin the moisturecontentof a pavementlayerabove its optimum can be caused by poor drainage,the rise of a shallow watertabledue to seasonalincreasesin rainfall,or the ingressof water througheithercrackingin the pavementor pondingon the shoulders.Such effectsare particularly noticeablein cuttings,and on gradeswhere water enteringthe pavementin the upper part coursesdown the grade along the layers. The equilibrium moisturecontentof a pavementmaterial,which is the field moisture content when the above transientinfluencesare not present,is a functionof the soil moisturesuction,and is influencedby the depth of watertable,soil type and evapotranspiration potential. The equilibriummoisture content (EMC) in pavement layers can be estimated usingthe followingrelationship (Paterson,1987): EMC = 0.26 P075 + 0.019 IM + 2.10 where

EMC = the equilibrium moisturecontent,in percentby mass; P075 = the amountof materialpassing0.075mm sieve,in percent by mass; and IM = Thornthwaite's moistureindex,in the 1955classification where -100 < IM < +100.

When the watertableis stable but shallow, i.e., within the regionof influenceof the pavementlayers,the moisture contentwill be higher than estimatred by the above. Only under conditionswhere the material properties change significantlywith season, for example a fluctuating shallowor perchedwatertableor poor drainage,is it necessary to estimate different seasonal states (one of which may representa saturatedstate). Under these circumstances, the structuralnumbershould be an appropriate weightingof the seasonalstatesas follows(basedon the contribution to roughnessprogression):

ROAD DETERIORATION

83 SNCa SNCb

SNC =a

E

_

SNC5

where

_ ~~~~0.2 + b SNC5

SNCa = the modifiedstructuralnumberapplyingfor season"a"; SNCb = the modifiedstructuralnumberapplyingfor season"big; a, b = the durationof the applicableseason (fractionof 1 year) where a + b = 1.

If the seasonalvaluesof structuralnumbercannotbe determined directly from materialproperties,then use can be made of the seasonal deflectionsto estimate the seasonal structuralnumber as describedin Section4.1.3. In additionto the above generaleffectsof climateand drainage on pavement behaviorthrough the structuralnumber, water entering the pavement through a permeableor cracked surf'acecan cause significant shallow-seated distressin the base and surfacing. This effectis evident though the rainfalland crackingparametersin the ruttingpredictions (Section4.2.6),thoughit may be understated for a poorly-drained base or highlymoisture-susceptible basematerial. In othermodesof distress,the effectwas not statistically significant in the Brazil-UNDP empiricalbase (Paterson,1987). As this may have been due to the high intensity,short durationnature of tropicalrainfall,fairly high standardsof pavement crossfall and drainage, and moderately free-draining soils, some adjustmentsmay need to be made in respectof adverse conditions,e.g., poor drainage, suscrptiblesoils and high rainfall in subtropicaland temperateregions,throughthe deterioration factors(Section4.1.8). For example,the factor for crackingprogression, Kcp (but not for cracking initiation), and possiblyfor rut depth,Krp,may need to be increased. The environmental-age componentin the roughnesspredictionmodel takes acount of more generalclimaticeffects,and provisional values for the coefficient have been established throughcross-validation of the model on data in variousclimates(Paterson,1987),as given in Table 4.5. The coefficient quantifiesthe time-dependent proportional changein roughness, and the user adjusts for this through the deteriorationfactor, Kge (Section4.1.8). No geometriceffectson deterioration are present. Gradientwas not found to have significant effectsin the empiricalstudy but can give rise to drainageproblemson short sections. Road width effectshave not yet been studiedsufficiently and an adaptationof the submodelto include them is underdevelopment(seeHoban,1987). 4.1.7 Variability and Uncertainty Road segmentswhich have identicalmean values of pavement strengthindicatorssuchas modifiedstructuralnumber,surfacetype,etc., are often observed to deteriorateat different rates. Structural

84

ROAD DETERIORATION

and constructionquality vary along properties,drainage characteristics the road lengthand betweenroads of the same type. Uncertaintyin the predictionsof a statisticalmodel arise through the limitationsof the variablesthat can be practicallyincludedand the inferencespace of the model'sderivation. The model automatically dividesthe roadsection(partof a link) into three "subsections"of equal length, identifiedas (relatively) "weak,""medium,"and "strong"before startingsimulation. Althoughall the three subsectionsare assumed to have identicalnominal pavement characteristics, the "weak" subsectiondeterioratesthe fastest and the "strong"subsectionthe slowest. This assumptionis expressedin the HDM in terms of the occurrencedistributionfactor, F, appearing in each to predict the time at which crackingor ravellingstarts. relationship That is, thesesubsections employthe same basicdistressinitiation models but with occurrencedistribution factorsto accountfor the differentrates of deterioration.The factorsare not appliedto any distressprogression factorsused in the HDM models. The values of the occurrencedistribution model are predeterminedand representequal thirds of the probability analysisconductedin the of failurebased on the statistical distribution Brazil-UNDP study (Paterson,1987). They are listedin subsequentSections (4.2.2-4.2.3).

4.1.8 LocalAdaptation(Deterioration Factors) It is not practicalto includecertainmaterial propertiesand environmental conditionswhich may be specificto a regionor countryin the road deteriorationrelationships. These include,for example, the sourceand type of binderor aggregate,rainfallintensity,level of solar radiation, specific construction practices, equipment or material specifications, etc. The user may take account of these effects for factor,"which is a specificsets of links by specifyinga "deterioration for each mode of distresson the input linearmultiplierof the prediction, form. In addition to the deteriorationfactor, an integer (CQ) qualityof surfacetreatments(0 = good, 1 = the construction representing poor)has been providedto permitthe user to evaluatethe valueof quality specifications. of construction controland effectiveness Local adaptationof the HDM relationships throughthe exogenous of the deteriorationfactor should preferablybe based on specification balanced,quantitativestudiesof specificdistressfunctionsunder local conditions.Care shouldbe taken to avoid the bias often associatedwith small samples. A representative samplewould includea rangeof pavement age from young to old, a range of trafficvolumesfrom low to high, and (whenpossible)a rangeof pavementstrengthwithina given trafficvolume betweenage and trafficvolumeshouldalso and loadingclass. Collinearity be avoided(e.g.,low volume,old age; high volume,young age). Where such a studyis not available,use can be made of averagerepresentative values of performanceindicatorsthat might be determined. For example, the expectedlife of a surfacetreatmentbefore resealingmay be 12 years in the localregionbut the predictionof the HDM model for the same volumeof factor, traffic is 9 years, which suggestsa value of the deterioration Kci = 12/9 = 1.3.

ROAD DETERIORATION

85

Table4.5: Recomnended valuesof environmental coefficient 'm' in roughnessprogression model,for variousclassesof climate Temperature classification 2 Moisture classification

Moisture index'

Arid Semiarid Subhumid Humid

-100 to 61 -60 to -21 -20 to +19 20 to 100

Tropical Subtropical nonfreezing nonfreezing 0.005 0.010 0.023 0.030

0.010 0.016 0.030 0.040

Temperate freezing 0.025 0.035 0.050 0.070+

Note: In the HDM-IIImodel,m = 0.023Kge. ' AfterThornthwaite (1955). 2 Definition of these classesis as yet uncertain: Tropicalmeans warm temperatures 15 to 400C and small range;Subtropical includeswarm, high range (5 to 600C) and cool, moderaterange (--10to 30°C) temperatures; Temperatefreezingincludesclimateswith annualpavementfreezing(this last classmay requireeithersubdivision or reformulation of the model). Source: Paterson(1987). It is expectedthat the cracking,ravellingand potholingmodels are the most likelyto requirelocal adaptation. For example,in regions other than Brazil, the predicted life before cracking initiationfor asphalt concretemay need to be lengthenedby specifying,say, Kci = 1.2 may have to to 1.5, and likewisethe predictedrate of crackingprogression be retardedby specifying,say, Kcp = 0.7 to 1.0. The predictorsfor other surfacing types will usually need less adjustment. Potholing progression may need suppressionfor good qualitybase materials,densegraded with good cohesion,e.g., KPD = 0.2 (see 4.2.4). The factorKge term in the roughnesspredictionmodel, for the environmental roughness-age should be derivedas a ratio of the coefficient"mi"from Table 4.5, as follows: Kge = m/0.023 PREDICTION 4.2 PAVEDROAD DETERIORATION 4.2.1 Variablesat the Beginningof the AnalysisYear At the beginningof the analysisyear the trafficloadingvariables (YAX and YE4) are computedfor the year based on the user-specified (Series0). trafficdata (SeriesE) and vehicleaxle loadcharacteristics The valuesof the variablesthat describethe environment(MMP), (SN, SNC, SNSG, road geometry (ELANESand W), pavementcharacteristics

ROAD DETERIORATION

86

DEF, HSNEW,HSOLD,HBASE,CQ, RH, CMOD,COMP) are providedin one of three ways: 1. When the analysisyear is neither the first year of the analysisperiod nor a construction openingyear, definedas the year immediately followingthe effectivecompletionyear of a constructionoption affectingthe section,values are providedfrom the precedinganalysisyear; 2. When the analysisyear is the first year of the analysis period, valuesare providedfrom the input data of existing link characteristics (SeriesA); or openingyear, values 3. When the analysisyear is a construction are provided from the input data of construction characteristics (SeriesB). The variablesthat describe pavement history (AGE1, AGE2 and AGE3) and pavement condition (ACRAa, ACRWa, ARAVa, APOTa, RDMa, RDSa, QIa, CRT, RRF, PCRA and PCRW) are initializedin different mannersas follows: 1. When the analysisyear is neithera construction openingyear nor the first analysisyear, values are provided from the precedingyear, i.e., [AGE1,AGE2,AGE3 1after= [AGE1,AGE2,AGE3 1before+ 1 maintenance of previousyear [CONDITION]a = [CONDITION]after 2. When the analysisyear is the first year of the analysis period,values are providedfrom the inputdata of existing linkcharacteristics (SeriesA); [AGE1,AGE2,AGE3 1after= [AGE1,AGE2,AGE3 ]input+ 1; [CONDITION]after

= [CONDITION]input

3. When the analysisyear is a constructionopeningyear, the variablesare initializedto reflect a new pavement,as follows: [AGE1,AGE2,AGE3] = 1 [ACRAa, ACRWa, ARAVa, APOTa] =

0

[RDMa,RDSa, PCRA,PCRW] = 0 QIa = CRT =

where

QIIo 0, RRF

=

1

QIIo = the initialroad roughnessafterpavementconstruction or reconstructionspecifiedby the user or

ROAD DETERIORATION

87 providedas a defaultvalue accordingto the surface typesshown below (notethat surfacetype RSAC is not permittedin the construction optiondata): 25 QI for AC or OVSA; 35 QI for ST, SSST and RSST;and 45 QI for OCMS.

4.2.2

CrackingInitiationand Progression

Cracking initiation and progressionare predicted for two classes,all crackingand wide cracking (definedin Table 4.1), through separatesets of relationships.Theseare ass'igned to differentsurfacing and base types followingthe classification of Section4.1.4,as shown in Table 4.5. These are based on empiricalresultsfor each type, with the exceptionof the cemented-base maintenancesurfacingsand all bituminous base types which have been assignedthe most appropriaterelation. The crackingpredominantly comprisescrocodileand irregularcrackingrelated to traffic and oxidationeffects. For cemented base pavements,the predictions includelinearcrackingfrom shrinkageeffects. Howeverlinear crackingfrom subsidenceand edge moisturemovements,and cold temperature cracking,are not included. The uncertainties involvedin predictingcrackinginitiationare representedby the values of the occurrencedistributionfactors Fc in Table4.6. The factorsmultiplythe mean predictions and yield the ages at which the cracking of the three subsectionsof each link representing early,medianand latefailures(or weak,medium,strong)are expected. Crackinginitiation Initiationis definedby distressextendingover 0.5 percentof the subsectionarea. The meaning of the variablesused is illustrated in Figure 4.4. The relationships for predictingthe time to initiation (which is the surfacingage) for all cracking(TYCRA)and wide cracking (TYCRW)are given in Tables4.8 and 4.9. The supplementary variablesused here are definedas follows: TYCRA = the predictednumber of years to the initiationof narrowcrackssince last surfacingor resurfacing (when the surfacingage AGE2 = 0); TYCRW = the predictednumber of years to the initiationof wide cracks since last surfacingor resurfacing(when the surfacingage AGE2 = 0). Kci = the user-specified deteriorationfactor for cracking initiation(defaultvalue= l); Fc = the occurrence distribution factor for cracking initiationfor the subsection (the values used in HDM-III are listedin Table 4.5);

88

ROAD DETERIORATION

Table4.6: Crackingpredictionrelationships by pavementtype Base type Surfacetype Granular Cemented Bituminous Surfacetreatment(ST)

A

B

Asphaltconcrete(AC)

C

B

Slurryon surfacetreatment(SSST)

D

F

Resealon surfacetreatment(RSST)

E

F, H

2

Resealon asphaltconcrete(RSAC)

H

F, H

2

Coldmix on surfacetreatment(OCMS)

D

F

G

Asphaltoverlayon asphaltconcrete on surfacetreatment(OVSA)

G

F

G

C G

'

H H

Notes: Pavementtype is definedby surfacetype and base type. The charactersin the table representthe relationships described in the text to be employedfor each of the pavementtypes. In HDM-III (1987), relationshipF has been disabled and replacedby 2 relationship B. Relationship F for initiation and H for progression. Source: This study.

Table 4.7: Valuesof the occurrencedistribution factors,Fc for crackinginitiationrelationships, applyingto one-third subsections of each section. Subsection Relationships

Weak

Medium

Strong

A, D, E B, F

0.55 0.74

0.98 1.01

1.48 1.25

C, G, H

0.51

0.96

1.53

Source: Paterson(1987).

ROAD DETERIORATION

89

HSE = the effectivethicknessof the surfacinglayersdefined as HSE = min [100;HSNEW+ (1 - KW) HSOLD] (seeFigure4.4); KW = a variablefor indicatingthe presenceof wide cracking in the old surfacinglayers,definedas KW = min [0.05max (PCRW- 10; 0); 1]; and KA = a variablefor indicatingthe presenceof all cracking in the old surfacinglayersdefinedas KA = min [0.05max (PCRA- 10; 0); 1]. The relationshipsfor cracking initiationin original asphalt concrete and double surface treatment surfacings of granular base pavements,and all surfacingsof cemented-base pavementsare illustrated in Figures4.5 and 4.6 respectively.The curves in Figures 4.5 and 4.6(a) between the time to crackingand the equivalentaxle load flow, show an interactionbetween aging and traffic effects. At very low traffic volumes,aging has a dominanteffectand, as the trafficvolumeincreases, the trafficand pavementstrengthhave strongereffects,with the strongest trafficeffects (steepestgradient)on the weakestpavements. In the case of surfacetreatments, crackingdue to aging with very little traffic is indicatedto occurafter 13 years which,given (a67 percentprobability of with ± 50 percent(seeTable4.7), is consistent beingwithinapproximately practicalexperience. The greaterthicknessof asphaltsurfacingsand the stiffbase supportof surfacingson cementedbase pavementsmean that those surfacingsare less susceptibleto 'punching'shear than thin surface treatments, and thus at low trafficvolumespavementstrengthor deflection providesan intercepteffectwhich is not presentfor surfacetreatments. RelationshipsD through H for maintenancesurfacingsare not determinedbecauseof a limiteddata base. They relate fullystatistically for originalsurfacings(A to C), the predictedtime to the relationships and to the extent of previouscrackingwhich can appear by reflectionin the new surfacingunder certain conditions. For asphalt overlays on cementedbase, the coefficients(KA and KW) of previouscrackingassume reflectionof cracking at propagationrates of 20 to 50 mm of layer thicknessper year. Crackingprogression of crackedareawas found in the empiricalstudy The progression to be a non-linear,S-shapedfunction,the rate of progressiondepending primarilyon the area of crackingand the time since crackinginitiation, effectsof eithertrafficloadingor pavementstrength withoutsignificant (Paterson,1987). The empiricalevidencethus indicatedthat the rate of of the materials,with was a processrelatedto the variability progression only the initiationof cracking. trafficand pavementstrengthinfluencing with the followinggeneralderivativeform: The functionis symmetrical 1-b 1 dt dAt = a; SAt

90

ROAD DETERIORATION

Figure4.4: Diagrammatic definitionof primaryvariablesin and progression predictionof crackinginitiation variables (a) Initiation Area of Cracking. ACRA(%)

TYCRA ATCRA ACRAb

_

_…

0.5 ___-_y AGE2 0

Time Analysis Year

(b) Progression variables

(c) Effectivesurfacingthickness

Area of Cracking. ACRA (%)

Surfacingthickness(mm)

HSE(Case 2)

(HSNEWt HSOLD) 2 - - - - -

ACRAb

100

/se1)

AACRA, ACRA, -

L

(HSNEW+ HSOLD),

AACRAnv1ACA, , (After)

_ CRACRA 0

(

__

_

Time Analysis Year

+

_ HSNEWLC 2 0

10

20

30

PreviousWide Cracking, PVCRW (%)

Note: The definitionof othersurfacedistressvariablesis similar, substituting for ACRA and TYCRAas follows: Wide cracking: ACRW,TYCRW Ravelling: ARAV,TYRAV Source: This study.

ROAD DETERIORATION

91

Table 4.8: Models for predictingthe initiationof all (i.e., narrow) crackingin variouspavementtypes Relationship

Pavementtype

A

Surfacetreatments, granularbase TYCRA = Kci tFc RELIA+ CRTJ where 2] RELIA = 13.2 exp[-20.7(1 + CQ) YE4/SNC

B

All surfacinqs, cementedbase (withoutstress-absorbing membrane) TYCRA = Kci JFC RELIB+ CRTI where RELIB = 1.12 exp(.035HSE + .371Qn CMOD - .418in DEF - 2.87 YE4 DEF)

DC

Asphaltconcrete,granularbase 1 TYCRA = Kci tFc RELIC+ CRTJ where 2) RELIC = 4.21 exp(O.14SNC - 17.1YE4/SNC

D

Slurryseal on surfacetreatment, granularbase 2 TYCRA = Kci tFc RELID+ CRTj where RELID = max [RELIAmax (1 - PCRAl20,0), 1.4]

E

Resealon surfacetreatment,granularbase 2 TYCRA = Kcl tFc RELIE+ CRT3 where RELIE = max [RELIAmax (1 - PCRW/20,0), 0.22 HSNEW]

F

Resealson asphaltoverlay,cementedbase (withoutstress-absorbing membrane) TYCRA = Kci tFc [(0.8KA + 0.2 KW) (1 + 0.1 HSE) + (1 - KA) (1 - KW) RELIB]+ CRTJ

G

Asphaltoverlayon asphaltconcrete, granularor bituminousbase 2 TYCRA = Kci tFc RELIG+ CRTI where RELIG = max [RELICmax (1 - PCRW/30,O),, 0.025HSNEW]

H

Surfacetreatmentresealon asohaltconcrete, granularor bituminous base TYCRA = Kci [Fc RELIH+ CRTI where RELIH = max [RELICmax (1 - PCRW/20,O), 0.12 HSNEW]

Statistically derivedfrom Brazil-UNDP road cleterioration study. Empirically developedbasedon Brazil-UNDP studydata and judgment. Source: Adaptedfrom Paterson(1987). 2

92

ROAD DETERIORATION

Table 4.9: Modelsfor predictingthe initiation of wide crackingin variouspavementtypes Relationship A

Pavementtypeand model

Surfacetreatments, granularbase 1 TYCRW = Kci max(2.66+ 0.88 TYCRA,1.16TYCRA)

B

All surfacings, cementedbase (withoutstress-absorbing membrane) TYCRW = Kci (1.46+ 0.98 TYCRA)

C

Asphaltconcrete,granularbase l TYCRW = Kci (2.46+ 0.93 TYCRA)

D

Slurry sealon surfacetreatment TYCRW = Kci (0.70+ 1.65 TYCRA)

E, H

All surfacetreatmentreseals,granular'or bituminousbase 2 TYCRW = Kci (1.85+ TYCRA)

F

Resealsor asphaltoverlayon cementedbase (without stress-absorbing membrane TYCRW = Kci 1.78TYCRA

G

Asphaltoverlayon asphaltconcrete,granular'or bituminous base TYCRW = Kci (2.04+ 0.98 TYCRA)

Statistically derivedfromBrazil-UNDP roaddeterioration study. Empirically developedbased on Brazil-UNDP studydata and judgment. Source: Paterson(1987). 1 2

where At is the area distressedat time t; ai, bi are coefficients estimatedempiricallyfor pavementtype i (see Table 4.10) and SAt is a functionof At symmetricalabout an area of 50 percentas definedbelow for each relationship. The functions for each pavement type are illustratedin Figure 4. In the model the relationships have a general first-difference form as follows:

93

ROAD DETERIORATION Figure 4.5: Predictions of time cracking initiationfor original pavements with granular base (a) Asphalt concrete surfacing Time to Cracking (years)

Modified Structural Number. SNC

12 -

10

6 6

4 -

4

2

0.3

0.0

1.5

1.2

0.9

0.6

Traffic Loading (Million ESAfLaneNYear)

(b) Double surface treatment surfacings Time to Cracking (years) 15.0

Benkelman Beam Deflection

12.5\

0.2 mm 10.0

\ 7.5

"'.,

'\\

\

"\ \

'^-.

~~~~0.5 nmm

mm 0"l

2.0 mm

2.5

0.0 0.0

0.1

0.2

0.3

A 0.4

.5

Traffic Loading (Million ESA/LaneNYear)

Source: Paterson (1987).

0.6

07

94

ROAD DETERIORATION

Figure4.6: Predictions of time crackinginitiationfor original pavementswith cementedbase (a) Relatedto trafficloading Time to Cracking (years) '18-

15

=

12-

.-

-.--

…-------------

…

0.2

96-

6-

v _-_

_

0.5

- 1.0 O- 0

__________________________________________________________._ I i j ,~~---W- ------,----{l---

0.0

0.2

0.4

0.6

0.8

1.0

Traffic Loading (Million ESAILoneNYear)

Note: Modulusof base 20 GPa; Surfacingthickness20 mm. (b) Relatedto base stiffness Time to Cracking (years)

18-

15 Deflection,

E

12-

092/

--°?---------------------

0.5___

_

6-~~~~~~-

3

,, .........

-04

0

3

I 6

I 9

I

,

I

I

12

15

18

21

,

I

24

27

Base Modulus. CMOD (GPa)

Note: Traffic0.5 millionESA/lane/yr; Surfacingthickness20 mm. Source: Paterson(1987).

30

95

ROAD DETERIORATION area: 1. All-cracking b 1/b CRP Za {IZa a; bi ATCRA+ SCRAa

AACRAd=

SCRAa

2. Wide-cracking area: d. 1/d. 1 _ SCRWa

AACRWd= Kcp CRP Zw {[zw ci di ATCRW+ SCRWa1

where AACRAd= the predictedchangein the area of all cracking in duringthe analysisyear due to roaddeterioration, area; percentof the totalcarriageway ATCRA = the fractionof the analysisyear in which progression applies,in years,givenby: all-cracking

ATCRA =

and ACRAa= 0 if AGE2 < TYCRA O (AGE2- TYCRA)if AGE2 - 1 < TYCRA < AGE2 and ACRAa= 0 or ACRAa > 0 if TYCRA < AGE2 - 1 1

SCRAa = min (ACRAa,100 - ACRAa) SCRAa = max (SCRAa,.0.5)if ACRAa > 0.5

ACRA a

_

O 0.5 ACRAa

if ATCRA= 0 if 0 < ATCRA< 1 otherwise

the predictedchangein the area of wide cracking in duringthe analysisyear due to roaddeterioration, area. percentof the totalcarriageway ATCRW = fractionof the analysisyear in whichwide cracking applies,in years,givenby: progression AACRWd=

ATCRW =

and ACRWa= 0 O if AGE2 < TYCRW (AGE2- TYCRW)if AGE2 - 1 < TYCRW< AGE2 and ACRWa= 0 or ACRWa > O if TYCRW< AGE2 - 1 1

SCRWa = min (ACRWa,100-ACRWa)

> 0.5 SCRWa = max (SCRWa,0.5) if ACRWa 0 ACRWa a

0.5 LACRWa

if ATCRW- 0 ifotherwise 0 < ATCRW < 1 and ACRW <= 0.5

96

ROAD DETERIORATION

Table 4.10: Coefficients for predictionof cracking progression for all pavement types Relationship

Pavement type l

a

b

c

d

C

Asphalt concrete

1.84

0.45

2.94

0.56

A

Surface treatment

1.76

0.32

2.50

0.25

B, F

ST on cemented base

2.13

0.35

3.67

0.38

G

Asphalt overlays

1.07

0.28

2.58

0.45

E, H

Reseals

2.41

0.34

3.4

0.35

D

Slurry seals

2.41

0.34

3.4

0.35

Surfacing as indicated on flexible (granular or bituminous) base unless otherwise stated. Source: Paterson (1987).

ai, b1, c;, d. = coefficientsfor pavement type i given in Table 4.10 Kcp

= the user-specifieddeteriorationfactor for cracking progression (defaultvalue = 1); and

CRP

= the retardationof cracking progressiondue to preventive treatment,given by CRP = 1 - 0.12 CRT

za

= 1 if ACRAa < 50; za = -1 otherwise;

zw

= 1 if ACRWa < 50; zw = -1 otherwise.

In addition to the above basic definitions, the initiation of wide cracking is constrained so that it does not commence before the area of all cracking (ACRAa) exceeds 5 percent. In particular, this prevents wide and narrow cracking commencing simultaneously after patching, when both ATCRA and ATCRW equal 1. Furthermore, after the patching of wide cracking, the rate of progression of wide cracking is assumed to begin not at the low initial rate given by ACRWa = 0.5 but at a higher rate equivalent to its rate before patching, here simulated by defining a temporary value of wide cracking, X to be 5 percent less than ACRA, i.e.: ATCRW = 0 if ACRAa <= 5 and ACRWa <= 0.5 and MTCRW > 0. X

= ACRAa - 5

if ACRWa <= 1 and ACRAa > 11.

ROAD DETERIORATION Figure4.7:

97

Predictions of crackingprogression for original, reseal,and overlaysurfacings (a)

Original

surfacings

Area of Cracking [%)

100.

SurfaceTreatments 80-

-On Cemented

Base

-On Granular Base Concrete

"/Asphalt

/

60

4020

1

All Cracking

-,o

lIide Cracking

-----

20-

0

0

2

6

4

10

8

12

14

Time Since Cracking Initiation (years)

(b) Resealand overlay

sirfacings

Area of Cracking (%)

100i

j 80~n

Reseals and SlurrySeals

60

/

,1

/Asphalt Overlays

40

-;

0

2

4

/

/- All Cracking - WideCracking

6 8 10 Time Since Cracking Initiation (years)

Source: Paterson(1987).

12

14

98

ROAD DETERIORATION

where X is a temporaryvalue of ACRWa used only in the computationof AACRWdabove. 4.2.3 RavellingInitiationand Progression Ravellingis the lossof surfacingmaterialfrom pavements,which in thin surfacingsmay eventuallydevelop into potholes. Usuallyit is caused by weatheringof the binder,and except in very old pavementsis usuallylimitedto the upperlayerof doublesurfacetreatments. The empiricalmodels for predictingthe initiationand progression of ravellingderivedfrom the Brazilstudyrelateto both originaland maintenancesurfacingsof doublesurfacetreatments, slurrysealsand opengraded cold-mixasphalt,but not to asphaltconcrete. The relationships are definedin Table 4.11 and illustrated in Figure4.8. They have probabilisticand incremental forms similarto the crackingmodels. Structural propertiesare not significant, and the only explanatory variablesare the surfacingtype and construction quality. Major construction faultssuchas faulty binder distribution, contaminatedstone, strippingof the binder, etc.,causea 50 percentreductionin "life"beforeravelling. In progression, no variablesexcept time and area of ravellingwere significantin variablesare: the empiricalstudy. The supplementary TYRAV = the predictednumberof years to ravellinginitiationsince the last surfacingor resurfacing(when the surfacingage AGE2 = 0); deterioration factorfor ravelling Kvi = the user-specified initiation(defaultvalue= 1); factorfor ravellinginitiaFr = the occurrencedistribution tion for the subsection(the values used in HDM-III are 0.54,0.97 and 1.49 for the weak, mediumand strongsubsections,respectively); MARAVd= the predictedchangein the ravelledarea duringthe in percent;and analysisyear due to roaddeterioration, ATRAV = the fractionof the analysisyear duringwhich ravelling progression applies,in years,givenby: ATRAV =

and ARAVa = 0 O if AGE2 < TYRAV (AGE2- TYRAV)if AGE2 - 1 < TYRAV< AGE2 and ARAVa = 0 or ARAVa > 0 if TYRAV < AGE2 - 1 1

SRAVa= min (ARAVa,100-ARAVa) ARAVa =

r.5

if 0 < ATRAV < 1 and ARAVa <= 0.5

LARAVaotherwise

ROAD DETERIORATION

99

Table 4.11: Modelsfor predictingthe initiation and progression of ravellingof varioussurfacings

Relationship

Pavementtype and model

RAVELLINGINITIATION A

Surfacetreatmentsincludingreseals(ST,RSST,RSAC) 1 TYRAV = Kvi [Fr [10.5exp (- 0.655CQ - 0.156YAX)]RRF}

B

Slurryseal on surfacetreatmentor asphaltconcrete(SSST) TYRAV = Kvi [Fr [14.1exp (- 0.655CQ - 0.156 YAX)]RRF}

C

Cold-mixsurfacingor cold-mixoverlay(OCMS)l TYRAV = Kvj [Fr [8.0 exp (- 0.655CQ -. 0.156YAX)]RRFI

D

Asphaltconcreteand asphaltoverlays(P, OVSA) 2 TYRAV = 100

RAVELLINGPROGRESSION All surfacetreatments. reseals,slurryseal. cold-mix (ST, RSST,RSAC.SSST, OCMS

AARAVd= (KvyRRF) 1 Zr [[Zr1.560ATRAV+ SRAVa0 *352]2 .84

-

SRAVa)

Asphaltconcreteand asphaltoverlays(AC,OVSA) 2

AARAVd = 0 Statistically derivedfrom Brazil-UNDP roaddeterioration study. Default relationshipassumingsound specification and constructionof asphaltmixture. Source: After Paterson(1987). 1

2

100

ROAD DETERIORATION

Figure4.8: Predictions of ravellinginitiation and progression for variousthin surfacingson flexibleand semi-rigidpavements (a) Ravellinginitiation Time to Ravelling (years)

15-

SlurrySeal Cl-ip

Seal

Good Qality (Construction

Cold Mix 12"

Poor Quarif:

Chip Seal

Constructio

Col

i

0....

o

ea

-

I

* Iw -

1

-4

2

- -.

- I '..

3

....

5

5

4

Traffic Flow (million axles/lane yecar)

(b) Ravellingprogression AREA RAVELLEO (I)

40 so

30-

20,

0.0

0.5

1.0

.5

2.0 TtME

Source:

After Paterson (1987).

2.5

(y..r)

3.0

3.5

4.0

4.5

ROAD DETERIORATION

101

Zr = 1 if ARAVa < 50; Zr = -1 otherwise. 4.2.4 PotholingInitiation and Progression Potholingusuallydevelopsfrom the spallingof wide crackingor the ravellingof thin surfacetreatments, althoughin new surfacetreatment construction it can developfrom random localdlefects in the surfacingor base. In both cases the initiationand progression of potholesare highly dependenton the mechanicaldisintegration propertiesof the base. As theseare impractical to quantifyfor a networkanalysis,the base type and modifiedstructuralnumberare used as surrogatemeasures. The relationships are empirical,based on data from the Caribbean,Ghana, Braziland Kenya studies,because reliablestatisticalestimationwas impracticable (Paterson,1987). Initiationis expressedas a functionof the time (TMIN)since the initiationof triggeringdistressand trafficflow, and occurs typically 2 to 6 years afterwide crackingand 3 to 6 years after ravellingof thin surfacetreatments, as shown in Figure4.8 (a) and givenby: max [6 - YAX; 2] if base is cemented TMIN=

max [2 + 0.04 HS - 0.5 YAX; 2] otherwise

L

(HSNEW+ HSOLD) if base is granular HS=

(HSNEW+ HSOLD+ HBASE) if base is bituminous. The initiationindicatorINPOTis set to 1 eitherif the age of the oldest relevantdistress remainingafter maintenanceestimatedfrom the rate of progression is greaterthan TMIN,or if potholingis presentin the current conditionor if potholingwas presentin the firstanalysisyear and there has been no subsequentreseal,overlayreconstruction or construction, as follows: 1 if AGE2-TYCRW> TMIN and ACRWd > 20 or AGE2-TYRAV > TMIN + i(HSNEW + HSOLD)/10 and ARAVd > 30 INPOT=

or APOTa > 0 or APOTa(first analysisyear)>O and [AGE1- AGE1 (firstanalysisyear)= (analysis year - first: analysisyear) 0 otherwise.

102

ROAD DETERIORATION

The progression of potholingis computedfirstlyas a volume,in cubicmetersper lane-km,becausethe effecton roughnesshas been shownto be linearlyrelatedto potholevolume (Paterson,1987). For consistency with the accountingof otherdistresstypes,potholingis then convertedto an equivalentpercentagearea, assumingan averagepotholedepth of 80 mm, by the factor (0.8 W/ELANES)m3/lane-kmper percentarea. The potholing progressioncomprisesthree components,i.e., new potholescausedby wide cracking (AAPOTCRd),new potholes caused by ravelling (AAPOTRVd)and the enlargementof existingpotholes(AAPOTPd),as illustratedin Figure 4.9 (b) and (c) and definedas follows:

AAPOTd = min fAAPOTCRd + &APOTRVd+ AAPOTPd; 10} where

MAPOTd = the predictedchangein the totalarea of potholes duringthe analysisyear due to roaddeterioration, in percent; AAPOTCRd = the predictedchangein the area of potholesduring the analysisyear due to cracking,given by:

dAPOTCR = d

[KppINPOTmin [2ACRWaU; 6] if ACRWa > 20

Ootherwise U =

(1+CR)(YAX/SNC)/((HSNEW + NSOLD)0.8W/ELANES);

AAPOTRVd = the predictedchangein the area of potholesduring the analysisyear due to ravelling, given by: Kp INPOTmin [0.4ARAVa U; 6] AAPOTRV=

d if ARAVa > 30 0 otherwise AAPOTPd =

the predictedchangein the equivalentarea of potholesduring the analysisyear due to enlargement, givenby: AAPOTPd = min APOTa [KBASEYAX (MMP+ 0.1)];10}

KBASE

=

max [2 - 0.02 (HSNEW+ HSOLD);0.3] if base = granular 0.6 if base = cement-treated 0.3 otherwise

103

ROAD DETERIORATION

Figure 4.9: Parameter variationsfor predictionof potholing initiation and progression (b) Annual increment due to cracking

(a) Initiation

8 . SurfacingThickness20 m

1.0

76 ' r SudfociS Thicknein s s

/

01 _______________________ mm

0S2

4

"

_

6,

3\ me

80

__150

10

2/ ra

7g,,

i

47

8

-4

(d) Enlargement -S

|

7

§6-mrn

//

--

6 -~~~~~~~~~~~~~~

/I SNCf3/,,SNC0

SNC5

7

SudfocingiThlcknessi00 mrrr.'

/

/

TrafficFlo ( millionaxles/lane year)

7

/|

7

10

(c) Annual increment due to r:avelling

0.3-

6

_S_N=_

Traffc Row (million caxkBslaneyear)

2-

, 3

4-~

7.... 6

/_ SNC

ThiccikeThlcknew2mOOmm: Sur

23

F.ASNCS

0

4,," SNC3 ,

0

e:rfaclng Tckness 20 m:04

,. ike

/

42

--

30 mm 0llwlTrYruwTrrl7T°I1

rrlllrrrrTTlOxtlT

0

1

2

3

4

5

TrafficFlw (mililon axles/lane year)

6

7

0

Tr'

I I r-r

10

-T-I -

20 APOTa

-

r-1--T-

30

104

ROAD DETERIORATION

and 4.2.5

K

=

the user-specified deterioration factorfor pothole progression(defaultvalue= 1) (Section4.1.8).

SurfaceDamageat the End of the Year beforeMaintenance

Using the quantitiescomputedabove and appropriatelimits,the damaged areas at the end of the analysis year before maintenanceare predictedin the mannerdescribedbelow. For modellingpurposesthe road surfaceis assumedto consistof the areas potholed,cracked,ravelledand undamaged. The undamagedarea consistsof the originalroadarea which is still in intactconditionsince the last surfacingor resurfacingand the area which has been patched. These areas are assumed to be mutually exclusive,so the sum of the potholed,cracked,ravelledand undamagedareasmust equal100 percent. In devisinga logic that satisfiesthis constraintthe followingsimplifying assumptions are made: 1. Crackingdevelops first from the undamagedarea and then, after the latter is exhausted,from the ravelled area. Furthermore,an area once crackedcan developpotholesbut cannotravel. 2. Ravellingcan only developfrom the undamagedarea,and after an area is ravelledit also can crack,at which stage it is reclassified from ravelledto cracked. 3. Potholes can only develop from cracked, ravelled and undamagedareas (as reflectedin the formulasfor computing the change in potholedarea), and unless it is repaired,an area potholed cannot revert to cracking, ravelling or undamagedstatus. 4. An upper limitof 30 percentis imposedon the potholedarea because above this level the pavement surface becomes ill-defined and the roughnessfunctionbecomesinvalid. The above assumptionslead to the following equations for computingthe damagedareasbeforemaintenance: APOTb ACRAb ACRWb ARAVb

= = = =

min min min min

(30,APOTa+ AAPOTd) (100- APOTb;ACRAa+ AACRAd- AAPOTCRd) (100- APOTb;ACRWa + AACRWd- AAPOTCRd; ACRAb) (100- APOTb- ACRAb;ARAVa+ AARAVd- AAPOTRVd)

4.2.6 Rut Depth Progression All surface and base types employ the same relationshipsfor predictingrut depth progression. Mean rut depth is not used as a maintenanceintervention criterionin HDM-III,but is used as a means to estimatethe variationof rut depth (standarddeviation)which contributes directlyto roughness.

ROAD DETERIORATION

105

Mean rut depth The progression of mean rut depth is predictedby the following relationship (Paterson,1985):

RDM =

K

39800 [YE4 10 6ERM

rp SN0.502 cp2.30

SNC0

0

2 COMP

0

In the first year when RDMa = 0 the equationabove is used directlyto estimate ARDMd), but subsequentlythe incrementalchange in mean rut depth due to road deterioration during the analysisyear is derivedfrom this as follows. ARDMd = K

d

rp

0.166+ ERM + 0.0219MMP ACRXdQn [max

AE

(1; AGE3 YE4)]

where

RDMa

if RDMa >0

ARDMd= the predictedchangein the mean rut depthduringthe analysisyear due to roaddeterioration, in mm; Krp = the user-specified deterioration factorfor rut depth progression(defaultvalue = 1); ERM = the exponentwhich is a functionof surface characteristics and precipitation, givenby: ERM = 0.09 - 0.0009RH + 0.0384DEF + 0.00158MMP CRXa; CRXa = area of indexedcrackingat the beginningof the analysisyear, givenby: CRXa = 0.62 ACRAa+ 0.39 ACRWa;

and

ACRXd = the predictedchangearea of 'indexed crackingdue to roaddeterioration, givenby: ACRXd= 0.62 (ACRAb- ACRAa)+ 0.39 (ACRWbACRWa)

The mean rut depthat the end of the year,with a limitof 50 mm, is given by: RDMb = min (50;RDMa+ ARDMd).

106

ROAD DETERIORATION

in Fig. 4.10 which showsa The predictionof mean rut depth is illustrated diminishingrate of increasewith time and a slighteffectof rainfalland cracking. The level of compactionhas a strong influenceand the rapid rise in rut depth initiallyis probablydue to this influence. Unlessthe structuralnumberis very low for the trafficto be carried,ruttingis not usuallya major problemwith modern pavementconstructionspecifications. The problemof ruttingwhichmay developin thickor soft asphaltlayersin high temperatures is not coveredby the predictionmodel above. Standarddeviationof rut depth The variationof rut depthwhichdirectlyinfluencesroughnessis expressedby the standarddeviationand is a strong functionof the mean rut depth as follows(Paterson,1987): 4390 RDMd0 .532 (YE4 106)ERS

K RDS =

rp SNC0

422

COMP1.66

In the first year when RDMa . 0, the equation above is used ARDMd, and the predictionis directly to estimate ARDSd where RDM halved as an explicit suppressionof the sharp initial increase. Subsequently the incremental changein rut depth standarddeviationdue to roaddeterioration in the analysisyear is derivedfrom the above equation as follows

ARDSd

Krp

0.532 (RDMb- RDMa) ERS RDMa ++ 0.0159MMP ACRXd

tn [max (1; AGE3 YE4)]

j where

RDS

if RDMa > 0 and ROSa > 0

ARDSd = the predictedchangein the standarddeviationof rut depth during the analysis year due to road deterioration, in mm; and ERS = an exponent which is a function of the surface characteristics and precipitation, given by: ERS a

-0.0086RH + 0.00115MMP CRXa.

The standarddeviationof rut depthat the end of the year, with an upper limitequalto the mean rut depth,is given by: RDSb = min (RDMb;RDSa + ARDSd)

107

ROAD DETERIORATION

between the standarddeviationand mean The strong relationship in Fig. 4.10(b). of rut depth is illustrated 4.2.7

RoughnessProgression

Roughness progression is predicteclas the sum of three components: structuraldeformationrelated to roughness,equivalent standardaxle load flow,and structuralnumber;surfacecondition,related to changes in cracking, potholing and rut depth variation;and an roughnessterm. All flexiblepavementtypesemploy age-environment-related estimatedfrom the Brazil study,for predictingthe the same relationship, incrementalchange in roughness due to deteriorationbut excluding maintenance effects(seeSection4.3 later),givenby (Paterson,1987):

AQId = 13 Kgp 134 EMT (SNCK+ 1)-5.0 YE4 + 0.114 (RDSb- RDSa) + 0.0066ACRXd+ 0.42 &APOTd] + Kge 0.023Q a where AQId = Kgp = Kge = EMT = SNCK =

the predictedchangein road roughnessduringthe in QI; analysisyear due to roaddeterioration, factorfor roughness deterioration the user-specified (defaultvalue = 1); progression factorfor the deterioration the user-specified increasein roughness annual fractional environment-related (defaultvalue = 1); exp (0.023K e AGE3) 9 structural number adjustedfor the effectof the modified by: cracking,given SNCK = max (1.5;SNC - ASNK)

the predictedreductionin the structuralnumber due to cracking since the last pavement reseal, overlay or age, AGE2, equalszero), (whenthe surfacling reconstruction givenby: ASNK = 0.0000758[CRXaHSNEW+ ECR HSOLD] CRX' = min (63;CRXa);

ASNK =

a

ECR =

the predicted excess crackinc beyond the amount that existedin the old surfacinglayersat the time of the last givenby: pavementreseal,overlayor reconstruction, ECR = max [min(CRXa- PCRX;40); 0]

PCRX = area of previousindexedcrackingin the old surfacingand base layers,givenby: PCRX = 0.62 PCRA + 0.39 PCRW.

ROAD DETERIORATION

108

of the mean and standard of the progression Figure4.10: Predictions deviationof rut depth (a) Mean rut depth 22.5 ModfifedStructural Number.SNC - 2 Traffic= 05 M ESA/Lane/Year

20.0

.

17.5 Cracked <

2

Uracked

15.0

fo

E 125-/

X

10.0

f

SNC 6 Cracked Uncracked

/

7.5

2 5

x

;

~~

X~~---------*-o----2----

0.0 0

2

4

6

S

10

12

14

16

18

20

PavementAge (Years)

(b) Standarddeviationof rut depth

= 05 M ESA/La/Yr Trcffic

7

ModifSe/ Structura Nu.mter SNC =

6

2

E/. a 5. 6/,.<"""'

2

0

2

4

6

8,---

8

i

12

14

Rut DeDthMean (rrm)

Source: Paterson(1987)

16

18

20

ROAD DETERIORATION

109

Roughnessat the end of the analysisyear,beforemaintenance and imposingan upper limitof 150 QI, is givenby: QIb = min (150;QIa + AQId). Predictions from the model are illustratedin Fig. 4.11 for two pavements(SNC-values of 3 and 5) under six volumesof trafficloadingand minimalmaintenance comprisingthe patchingof all potholes. At the lowest trafficloadings,the roughnessprogression is a functionprimarilyof the last term in the model representing age-environment effects,whichamounted to 2.3 percent/year for the warm, subhumidto humid climateof the Brazil empiricalbase and may need adjustmentfor other climate and soil-type regions through the factor, Kge. Traffic loadingand pavementstrength effects are given by the explicittraffic-structural number-ageterm and also through the rut depth variationand cracking terms; adjustmentof these coefficientscan be made uniformlythroughthe factor Kgp although this is consideredunlikelyto be necessary. 4.3 PAVED ROAD MAINTENANCE INTERVENTION 4.3.1 Classification and Hierarchy Maintenance operationsare classifiedinto six primarycategories for the submodel,based on when they are to be appliedand their impacton pavementconditionand strength. These are listed in Table 4.12 together with a summary of the options availablefor interventioncriteria,the types of maintenancewithin each category,and the hierarchywith which they are applied in the model. Detaileddescriptionis given in the followingsections. The intervention criteriadeterminethe timing and type of maintenanceto be appliedand togethercomprisethe maintenance standardspecifiedby the user for each maintenancecategory. The timing of intervention is specifiedfor each type of maintenanceindividually as either: 1. Scheduled,that is a fixed amount per year (e.g.,m2/km) or at fixed intervalsof time (e.g.,every 3 years);or 2. Condition-responsive, that is intervening when the pavement conditionis predictedto reach a criticalthresholdlevel which is specifiedby the user. These two types representthe majority of rnaintenance policies,either explicitlyor implicitly, althoughin practicethere is often a blend of the two. Hence the condition-responsive olptionhas been extended to includeuser-specified limitson the minimumand maximum intervalsbetween successivetreatments.For example,it is possibleto specifyresealingto be appliedwhen the totaldamagedarea reaches30 percent,but to limitthe timing so that the resealingwould not be done any earlierthan, say, 4 years after the previousmajor maintenance(perhapsto minimize traffic disruptions),and no later than, say, 15 years (a possible preventive policy).

ROAD DETERIORATION

110

In order to simulaterealisticpoliciesfurther,it is recognized would normallypreclude the situationof that practicalconsiderations before a major overlayor periodicmaintenancebeing applied immediately were planned. Provisionis thereforemade to specify: reconstruction 1. The latesttime;and 2. The maximumapplicableroughnessat which each type of maintenancemight be performed. This also dictatesa naturalhierarchyin which lessertreatmentscannotbe performedin the sameyear as a major treatment. no or reconstruction, Thus, in the firstyear after construction are performed except the routine-miscellaneous maintenance operations operation. Routine-miscellaneous operationsare performed every year regardlessof otheroperations. In any analysisyear only one of the five operations,1 to 5 in Table 4.12, can be performedin addition to the routine-miscellaneous operation. An exceptionto that rule is that the resealingoperationincludesan option for preparatorypatching. Otherwise, preparatorywork such as preliminarypatching,crack sealing or a levellingcourse, are expectedto be includedin the unit costs of the operation. The hierarchical order simulatedin the maintenancedecisionis Pavementreconfrom 1 to 5 in the table,excludingroutine-miscellaneous. structionis performedin an analysisyear if its criteriaare satisfied irrespective of the criteriafor the remainingoperations.Otherwise,the criteriafor overlayingare considerednext, and if satisfied,overlaying of the criteriafor resealing,preventivetreatis performedirrespective ment, patching,etc. And so the hierarchycontinues. Except for routine-miscellaneous and patchingoperations,which are assumedto be performedregularlyduring the year, all periodic,major maintenanceis assumed for simplicityto be performedat the end of the analysisyear. It shouldbe noted that, in this version,all maintenanceoperadesign tions are specifiedexplicitlyby the user and that no endogeneous or selectionfrom alternativeoptionsis made by the submodel. For example, the user must specify the thicknessof overlay or reseal to be on pavementcondition,strengthand applied. The effectof the maintenance history,however,is computedendogeneously.Patchingareas for example are calculatedby applyingthe user's specifiedmaintenancepolicy to the damagedareaspredictedby the model. Maintenance 4.3.2 Routine-Miscellaneous levelsof The HDM model does not model the effectsof alternative routine maintenanceother than pothole patching. Rather for vital components, i.e.,drainagefeaturesand shoulders,the model assumeslevels

111

ROAD DETERIORATION

for flexibleand Figure4.11: Predictionof roughnessprogression of patching semi-rigidpavementsunderminimalmaintenance all potholes (a) AsphaltConcreteModifiedStructuralNumber3 12I

E&'tx 106/yeor ~~~~~Loading

,

--8 5 -.

0

10 Pavmet

15 Age(years)

20

25

6.

Number5 Structural Modified Concrete gb) AsDhalt 0.2~~~~~~.

12.

10

Loodig EsAx 1o6/year

2

u-u-u -r ITs r-rr-

0

Source: Paterson(1987).

5

,r-r-u-u-rr-r --u--u-u-u---r -u--,-r--r------nI u--rI-uu-yruu-r

20 15 10 Pavement Age(yers)

25

ROAD DETERIORATION

112 Table 4.12:

Class

Classification and hierarchyof maintenancefor paved roads

Hierarchy Frequency

Routine- 6 Annual, automatic miscellaneous

Intervention Criteria(IC) Nil

Type options Nil

Effects Nil; absence would indicate negative effects.

Patching 5 Periodic, 1. Scheduled a. Surface Distressand specifiedby if damaged, patching roughness. IC, % area, limitedarea fixedarea, 2. Condition a) all surface or limit b) potholesonly Preven- 4 Periodic, 1. Scheduled a. Fog seal Life,and tive specified fixed interval b. Rejuvena- (distressnot treatment by IC, type 2. Condition c. Slurry applicableat low cracking, seal high distress ravelling levels) Resealing Reseal- 3 Periodic, 1. Scheduled a. Surface Surfacetype, fixedinterval treatment all distress, ing specifiedby IC, type 2. Condition (i.e., roughness chip seal) (minor). thickness distress 3. Condition b. Slurryseal roughness c. Chip seal with shape correction a. Asphalt Surfacetype, 1. Scheduled Overlay- 2 Periodic, concrete distress, fixedinterval ing specifiedby IC, type, 2. Condition b. Openrut depth, thickness roughness graded roughness, cold-mix strength asphalt c. Auto-level control asphalt concrete Reconstruction

1. Scheduled 1 Periodic, fixedage specifiedby 2. Condition IC, new pavement roughness

Source: This study.

Any surface All pavement and base, characstrength teristics

ROADDETERIORATION

113

of maintenance adequate to assure a normal life for the pavement structure. These componentsare vital to normal pavement performance, (and,in the case of shoulders,safetyaspects)yet they constitutea minor proportionof total maintenancecosts. When adequate levels of routine maintenancedo not apply, the user should reflect this in the values specifiedfor the pavementstrengthparametersor deterioration factors. Other items of routine maintenance,e.g., safety installations, signs, vegetationcontrol (other than drainage areas) do not directly affect pavementperformance and are left to be determinedexogenously.Thus,the user simplyspecifiesa fixed sum per km per year as the basisfor costing routinemaintenance. 4.3.3

Patching

This operation,usually includedunder routine maintenanceby road authoritiesbecause it is an annual operationor recurrentcost, includes mainly surface patching and repair of surfacing distress. Includedare skin patchesof binderand stone or slurryseal on crackedor ravelledareas,the replacement of the surfacingin small severely-cracked areas, and the fillingof potholes. Crack sealingmight also be included in this categoryalthoughit has not beenmodelled. The relationshipspredictingthe effect of patching in the submodel representa mixture of the above forms, as it has not been feasibleto distinguish theireffects. In the Brazil-UNDP studybase, thin slurryseal skin patcheswere a dominantmethod of patching,althoughthey were rarelyeffectiveon areas of cracking. The user specifiespatchingin one of threeways: 1. In a scheduledpolicy, patchinc]is specifiedas a fixed maximum area per year (m2 /km), which might, for example, reflect the maximum resources available from the road authoritywhen averaged over all roads within the link category. The amountperformedis computedas the lesserof the specifiedamountand the unpatchedseverelydamagedarea, ADAMS. ADAMS is definedas the sum of the areas crackedwith wide cracks, ravelled,and potholed at the end of the analysisyear beforemaintenance. AASP = min

[

ASPS °; ADAMS] 10 W

where

AASP

=

the area of patchingperformed,in percent of totalcarriageway surfacearea;

ASPSo

=

the specifiedmaximumannualpatching,in m2 /km;and

ADAMS

=

ACRWb+ ARAVb4 APOTb;or

2. In one condition-responsive policy,the user may specifythe percentageof the severelydamagedarea, ADAMS,which is to

114

ROADDETERIORATION be patched in each year and impose a limit of the maximum area (m2/km) per year; or policy,the user may specify 3. In anothercondition-responsive the percentageof the potholingarea to be patched(thearea of potholepatchingcan be computedmanuallyby applyingan average depth of patchingof 80 mm to a desired patching volume),and a limit of the maximumannual area of patching (m2 /km)per year.

In both cases (2) and (3),the area of patchingis given by: AASP =

min [ASPS;AASPMAX} 10 W F

where

ASPS =

°AMQ ADAMS

if responsiveto severedamage;or

100 FPOT 0 ° APOTb

if responsiveto potholingonly.

100

FDAMo =

the percentageof the damagedarea to be patched in a year, specifiedby the user;

FPOTo =

the percentageof the potholingarea to be patchedin a year, specifiedby the user;and

AASPMAX =

the maximumapplicablearea of patchingin a year, in m2 /km.

The cost of patchingper km is computedby multiplyingthe user-specified unit cost (perm 2) with the area of patchingperformed,10 W AASP. When patchingis performed,the unpatcheddamagedarea is reduced by the amount of patching. It is assumed that potholing,wide cracking, and ravellinghave prioritiesin that order,and no patchingis performed to fix these individualdistressedareas until those of higherpriorities are completelyrepaired. As a result of these incremental changes in pavementcondition due to maintenance,the roughnessalso changes, as predicted by the following relationship,which forms part of the incrementalroughness predictionrelationship given in Section4.2.7: AQIm = min [0.130min (AASP;10) + 0.086ACRXm + 4.91AAPOTm;150 - QIb] where

AQIm = the predictedchangein road roughnessduringthe analysisyear due to maintenance, in QI; and

ROAD DETERIORATION

115

ACRXm = the predictedchangein crackingindex (weightedfor crackingseverity)due to maintenance given by:

ACRXM = 0.62 AACRAm+ 0.39 AACRWm. Note that the patchingdecreasesroughnessthrougha reductionof cracked area but usuallycausesa net slight increasein the roughnessundermost conditionswhen no potholesare present. The coefficientrepresentsan averagedepressionor protrusionof about 2 rm for skin patches;when the standardof workmanshipobservedin maintenancepatchingdiffers significantlyfrom this, a specificchangecould be made in the code (an individual deteriorationfactor is not available),adjustingthe coefficient 0.130 by the ratio of the observedaverageprotrusion/depression to 2 mm. Note also that the effecton roughnessis limitedto areas of patchingnot exceeding10 percent in any year; largerareas of patchingare likelyto have a net correctiverather than adverse impact on roughness. The patchingof potholesis takento be 90 percentefficientin correctingthe roughnessdue to potholes(i.e.,0.90 0.42 = 0.378 [for m/km IRI] or 4.91 [for QI]). 4.3.4 PreventiveTreatments Preventivetreatmentsare not widespreadpracticebut have been applied in some countriesover long periods and are receivingrenewed attentionbecauseof their low cost and the availabilityof new asphalt rejuvenating products. Their purposeis to extendthe life of bituminous surfacesby retardingthe effectsof weatheringand aging before significant amounts of distress have occurred. The followingtreatmentsare includedin the submodel. 1. Fog seal is a lightsprayedapplication of bitumenappliedon top of a bituminoussurfaceto reduce ravellingby binding the surfacestonesand to cover oxidizedbinder with fresh binder. Applications are usuallyin the rangeof 0.1 to 0.5 liter/m 2 . 2. Rejuvenationis a light applicationof solvents,oils or plasticizers(e.g., cut-backor fluxed bitumen, emulsified maltenes, etc.) sprayed on to the top of an existing bituminoussurface. Dependentupon the effectivedepth of penetrationof the rejuvenator,an oxidized binder is softened towards its original viscosityand becomes less susceptible to crackingand ravellling. Applicationratesare usually in the range of 0.3 to 0.9 liter/M2dependingupon dilution. 3. Slurryseal,which is a cold mixtureof bitumenemulsionand fine-graded aggregateof 3 to 10 nmnmaximumsize appliedin a single layer of approximately one stone-sizethickness,can be used as preventivetreatmentwhen it is appliedas a voidfilling coat on surfacetreatment. By filling the interstices of the surface, the slurry improvesdurabilityand retards ravelling,especiallywhen the original binder is

ROAD DETERIORATION

116

brittle or of inadequatefilm thickness. As a corrective treatmenton asphalt or cracking,slurry tends to be less effective(seeSection4.3.4). As statisticallyestimatedrelationshipswere not available, tentativerelationships have been incorporated in the submodelbasedon an engineering evaluationof the experiencewith similartreatmentsin several countries(Paterson,1987). In general,preventivetreatmentsare only expectedto be effectiveand economicon relativelylow-volumeroadswhere aging effects dominate traffickingeffects (for example, less than 1,000veh/day). The effectsof preventivetreatmentsare simulatedby: 1. The crackingretardation time,CRT, which is additiveto the predictedtime of cracking initiation(TYCRA, TYCRW), as illustratedin Figure 4.12. The change in CRT due to is denotedCRM which has the preventivetreatmentmaintenance assumedvalues for each treatmentgiven in Table 4.13. A maximum limit on the value of CRT due to multiple applicationsis imposed,defined by CRTMAX and the values is given in Table 4.13. The valueof CRT, aftermaintenance, definedby: CRT(after) = min [CRT(befOre) + CRM/YXK;CRTMAX/YXK; 8] where YXK = max (0.1;YAX). 2. The ravelling retardation factor, RRF, which is of the time of ravellinginitiation(TYRAV) multiplicative and a divisor of the rate of ravelling progression (AARAVd). The change in RRF due to preventivetreatment maintenance,RRM, takes the assumed values for respective treatmenttypes given in Table 4.13, subject to a maximum limit,RRFMAX,imposedon RRF for multipleapplications.The is definedby: valueof RRF aftermaintenance RRF = (after)

ll if the surfacetype is AC or OVAC

RRM; RRFMAX]otherwise. min [RRF(before)

Only one of the treatmentscan be applied in the analysisyear. treatmentpolicycan be definedeitherby:

The

1. A scheduledpolicy, in which the user specifiesa fixed intervalbetween successivetreatments,e.g., 3 years, and treatment is applied whenever the surfacing preventive treatmentage, AGE1, exceedsthis interval;or by 2. A condition-responsive policy,in which treatmentis applied at the firstsigns of crackingor ravellingdistressdefined by: 0 < ACRAb < 15 or 0 < ARAVb < 30

ROAD DETERIORATION

117

Table4.13: Parametersof preventivetreatment Parametervaluesfor preventive treatmentoptions Parameters

Pavementtype Slurry Rejuvenaseal tion Fog seal

CRM

ST on granularbase OCMS on granularbase Other combinations

1.0 0.25 0.5

3.0 0.75 1.5

1.6 0.4 0.8

CRTMAX

ST on granularbase OCMS on granularbase Other combinations

6.0 1.5 3.0

6.0 1.5 3.0

3.2 0.8 1.6

RRM

All combinations

1.5

1.15

1.3

RRFMAX

All combinations

4.0

2.0

3.0

ASNm

All combinations

0.05

0

0

Note: Valuesbased on availableengineering experience, not statistically estimated. Source: Paterson(1987). and is constrainedby the user-specified limitsof the minimum and maximumallowablepreventivetreatmentintervals,in years. Note that treatmentis not appliedif the distressexceedseither limit above, even if the maximum allowableinterval has been exceeded (as may occur in the first analysisyear of an old pavement). If performed,the amount of preventivetreatment,in m2 /km, is equal to 1,000 W where W is the width of the carriageway. The cost of preventivetreatmentper km is computedby multiplying this amountwith the 2 ). When preventivetreatment user-specified unit cost (per mi maintenance is performed,any surfacingdistress(whichis minimal)is nullified,and pavementstrengthis updatedby ASNm fromTable 4.13,as follows: A[ACRA,ACRW,ARAV,APOT]m = AGE1 =

0

-

[ACRA,ACRW, ARAV,APOT]b

118

ROAD DETERIORATION SNC(after)

=

DEF(after)

= DEF(before)

SNC + ASNm *

(aftr

4.3.5 Resealing Resealingmaintenancecomprisestwo thin resurfacingoperations which repairsurfacedistressbut cause littlechangeto the roughnessor structuralstrengthof the pavement;these optionsare surfacetreatment (i.e., chip seal) and slurry seal. A third option is surfacetreatment with shape correction, an alternativein which some reductionof roughness is achieved through the filling of depressionsand repair of damaged areas. The correctivematerial is assumed to be bituminous,with an averagethicknessof less than 50 m and placedto a qualityof less than that of automatic-levelling paver-finishers. The specification and effects are identicalfor all optionsexceptin the changeof roughnessand surface type after the application. One unit cost is used for all three but differencescan be incorporatedthrougha cost factor. The effects of resealing on subsequent pavement behavior are defined through the reclassification of surfacetype and adjustments to conditionand strength

Figure4.12: Illustration of effectsof preventivetreatmenton cracking initiationprediction Life RemainingBefore Cracking Initiation(Years) (AGE2-TYCRA)

9

\

v

C

>s

R~~~~~~~~CT

<

X~

~~~~CRTA

lime

Source: After Paterson(1987).

ROAD DETERIORATION

119

variables. In general,slurryseal is not an effectiveform of resealon cracked pavementsbecause reflectioncracking develops within 2 to 6 months,and the slurryhas an unquantified but probablynegligibleeffect on roughnessexcept for possiblebenefitsat high levels (above60 QI). The user specifies a reseal of fixed type, thickness and strength coefficient to be appliedunderone of threepolicies: 1. A scheduledpolicy,in which a fixed time intervalbetween successivereseals is specified,and the reseal is applied wheneverthe surfacingage, AGE2, exceedsthis interval;or 2. A condition-responsive policy,in which the resealis applied when the unpatcheddamagedarea, ADAMR,prior to maintenance exceedsa criticallevelspecifiedl by the user,where ADAMR = ACRAb + ARAVb + APOTb;cr 3. A condition-responsive policy,in which the resealis applied when the roughnessexceedsa criticallevel specifiedby the user. Underany policy,a resealwill not be performedif the surfacing age, AGE2, is less than the user-specified minimumapplicableinterval,or if the user-specified last applicableyear has been exceeded. Howevera resealwill alwaysbe performedif AGE2 exceedsthe user-specified maximum allowableintervalbetweenreseals. If performed,the amount of resealingin m2/km is equal to 1000 W. Under options 1 or 2, if the area of wide cracks is largerthan 20 percent,or the area of potholesis not zero at the end of the year before maintenance, preparatory patchingof the followingamount is assumedto be carriedout alongwith resealing:

AASP = max [0.1 (ACRWb- 20); 0] + APOTb. Underoption3 preparatory patchingis undertakenonly of potholes,i.e.,

AASP = APOTb. The cost of resealingper km is the user-specified unit cost of resealing (per m2 ) multiplied by 1000 W. The additionalarea of preparatory patchingis computedas 10 W AASP, and the cost is computedby multiplying this area by the unit cost of patching(perm 2). The areas and costsare reportedseparatelyunderresealingand patchingrespectively. Upon resealingthe surface type is changedto one of the four types (i.e.,RSST, RSAC, SSST or OVSA) as indicatedby Table 4.4 depending on the type of reseal (i.e., surfacetreatmentor slurry seal) and the previous surface type. This alters the applicable set of road deteriorationrelationships, as describedabove, to representdifferent deterioration behaviorafterperformingthe reseal.

120

ROAD DETERIORATION

The maintenanceeffect of resealingis to set the areas of cracking (for the new surfacinglayersonly), ravellingand potholingto zero,as follows: A[ACRA,ACRW,ARAV,APOT3m = -

[ACRA, ACRW,ARAV, APOT]b

The effects on roughness (QIS) of the first two options are not well-determined (Paterson,1987). Data from a numberof sourcesindicate step changesin roughnessdue to resealingwhich rangefrom small negative to small positiveincrements. Currently,it is thoughtthat the positive incrementsrepresenteitherthe transienteffectsof the early life of a surface treatment before stone embedment occurs, or the effects of roughnessmeasurementerror (whichcan be large on surface treatments). Thus, pending futureresearch,positiveincrementswere excluded,and the followingrelationshipwas adopted in the submodel,as illustratedin Figure4.13(a). It is given that patchinghas repairedall potholeswith an effectQIP. AQIm = min [0.086ACRXm+ QIP + QIS; 150 - QIb] where

QIP = max (4.91W AAPOTm; - 60)

min{O;max [0.3 (70 - QIb - QIP);- 6]} if resealwith surfacetreatment QIS = min{o;max [0.3 (60 - QIb - QIP);- 1.2 Ho]} if resealwith slurryseal

L

For resealwith shape correction, the roughnesschange is given by the following,as illustrated in Fig. 4.13(b):

AQIm= min [0,max [-0.0075HScQIb,- 0.0225HsCmax(QIb- 52, 0)]} where

Hsc = averagethicknessof resealincludingthe shapecorrection layer,in mm, = min (H0, 50);and

QIb = QIb + QIP. The crackingretardationtime, ravellingretardationfactor and preventivetreatmentand surfacingages are reinitializedto mark the beginningof the new deteriorationphase. The resealingoperationis assumed to be performedunder good quality control,so the construction fault code, CQ, is set to zero endogenously.To take accountof the net strengthening of the pavementdue to both maintenanceand cracking,the pavementstrengthparametersare updatedas follows:

ROAD DETERIORATION

121

Figure 4.13: Maintenance effect of resealingon roughness

(a) Surfacetreatmentand Slurryseal options 10

801 20

40

I0

120

1410

Roughress Befor Fesecl(Ql)

6

Sface Treolment In _

2~~~~~~~~~~~~~~~~~~~~~~~

-10~~~~~~

10(

_{

10mm

-15

(b) Surfacetreatmentwith shapecorrectionoption Roughness Change Dueto Maintenance,'hQlm

0-20

20

-40Average Thicknessof Reseal

-60

and ShapeCorrection(mm)

-80

0

20

,~~~.,,,

40

.............. .,,,,,,..

60

80

100

RoughnessBefore Reseal. Qlb

Source: This study.

....

,,,....,

120

140

160

ROAD DETERIORATION

122 SNC(after)

DEF (after)=

where

max [1.5;SNC(before) + 0.0394a0 H0 -ASNK] ~~~~~SNC iatr_-1.6 DEF(before)I (before)

ao = the strengthcoefficient of the reseal; Ho = the thicknessof the reseal,in mm; and ASNK = the predictedreductionin the structuralnumberdue to cracking since the last pavement reseal, overlay or (seeSection4.2.7). reconstruction

In updatingthe thicknessparametersthe resealthicknessbecomesthe new surfacingthickness,HSNEW,and the total thicknessof previoussurfacings becomesHSOLD. The areas of previouscracking(PCRA,PCRW)are updatedto equal the cracking in the current surfacingbefore resealing,and a weighting,w, of the crackingin the previoussurfacing,as givenby:

PCRA,af )

=

FACRAb

=

FCRWb if ACRWb > PCRW(before) ( ACRWb+ (1 - w) PCRW(before) if ACRWb< PCRW(before)

if ACRAb > PCRA(before) if ACRAb < PCRA(before) ( ACRAb + (1 - w) PCRA(before)

and

PCRW

where

w = the weightused for averagingthe crackingin the old and new surfacinglayers,as givenby the assumedrelationship: w = min (0.70+ 0.1 Ho; 1).

4.3.6 Overlay The overlayoperationin the submodelappliesonly to bituminous overlaysplacedby mechanicalpaver-finisher; otheroverlaysare dealtwith as describedbelow. Three optionsare provided: 1. Open-gradedcold-mixasphalt,regular or manual levelling control; 2. Hot-mixed asphalt concrete,regular or manual levelling control;and 3. Hot-mixasphaltconcrete,with long-baseautomaticlevelling (control(baselongerthan 5m).

ROAD DETERIORATION

123

The overlay operation in the model applies to single-layer overlays,but double-layer asphalticoverlaysof lessthan 125 mm thickness may be specifiedunder this operationby regardingthe two layersas one compound layer. Double-layeroverlays,such as granular overlay with bituminoussurfacing,or cementedlayers,or asphalticoverlaysof 125 mm thickness or greater, are best specified under the reconstruction operation. In that case, the overlayis modelledas a new pavementwith the top layeras the new surfacingand the lower layeras the new base. The effects of overlay on pavementdeteriorationare defined through the reclassificationof surface type and the associated deterioration predictionrelationships. An overlaypolicy comprisesan overlayof fixed type, thickness and strengthcoefficient specifiedby the user and appliedas follows: 1. Scheduled policy, in which the overlay of fixed specificationsis applied whenever the construction(or 'rehabilitation') age, AGE3, equals or exceedsa fixed time intervalspecifiedby the user,or 2. Condition-responsive, in which the overlay of fixed specificationsis applied when the roughness before maintenanceexceedsa maximumallowableroughnessspecified by the user. Under eitherpolicy,an overlayis not performedif the construction age, AGE3, is less than the user-specified minimumaipplicable overlay interval or if the last applicableyear has been exceeded. An overlayis also not performedif either the preventivetreatmentage, AGE1, or the surfacing age, AGE2, is less than the respectiveminimum preventivetreatmentor resealintervals. An overlayis performed,however,when the construction age, AGE3, exceeds the (optional)maximum allowable overlay interval specifiedby the user. If performed,the amount of overlay, in m2 /km, is equal to 1,000 W. The cost of the overlayper km is computedby multiplyingwith thisamountthe user-specified unit cost (perm2). When an overlay is performed,the surface type is changed to either of the two types: asphaltconcrete(OVSA) or cold mix (OCMS)as indicatedby Table 4.4, dependingon the type of overlay specifiedbut regardlessof the old surfacetype. This alters the applicableset of surfacing distress relationships,as described above, to represent different deterioration behavior after performing this maintenance operation. For the immediateeffectof overlay,the model sets to zero the amounts of cracking(for the new surfacinglayers only), ravelling,and potholingand the crackingretardation time, the constructionfault code; and resets the ravellingretardationfactor, the preventivetreatment, surfacingand construction ages. The rut depth is reducedby 85 percent, in recognition of the residualremainingafter the compactionof a single

ROAD DETERIORATION

124

valuespecifiedby layeroverlay. The roughnessis resetto the (optional) the user, QIIo, or to the defaultvalues dependentupon the quality of paving, as computed in the formulasfor AQIm below, and illustratedin Figure4.14: Option(a): Regularpaver QiiQ0 QIb

if QIIo is provided

ein {0; 20 + 10 kov + [28 max (QIl- 50; 0)/max(Ho;28)] - QIbj

long-basepaver Option (b):Automatic-levelling

Q1i1 0 -QIb AQIm =

if QII0 is provided

min 0o;max [(19.42- 0.78 QIb - 0.068Ho); (- 19.5- 0.008QIb max (Ho - 20; 0))flotherwise;

where QIIn

the initialroad roughnessafter overlayspecifiedby the user as an option,in QI:

QIb = max (13;QIb + 4.91 APOTm); Ho

= thicknessof the overlay,in mm.

Ho' = min (Ho;80); and Hov = 3 - [min (HO;80) + min (Ho;40)]/40. In additionthe pavementstrengthparametersare updatedto take accountof the net change in pavementstrengthdue to the new overlayand is the the underlyingcracks (if any). The procedurefor the modification same as that for reseal described in Section 4.3.4, except for the followingredefinitions: of the overlay;and ao = the strengthcoefficient Ho = as definedabove;and

w

max (HSNEW(before) /HSOLD(after); 0.6) if base type is not cemented a + HBASE);0.6] otherwise. /(HSOLD(after) ma [HSNEW(before)

ROAD DETERIORATION

125

overlaywith bituminoussecondlayer can be treated Double-layer in the same way as single layer overlayswith adaptationof the input of overlay valuesas follows. The thicknessand the strengthcoefficient in this case, are the sum and the weightedaverage of those two layers, respectively.The type of the overlay(asphaltconcreteor cold mix) is determinedby the top layerof the overlay. 4.3.7 PavementReconstruction appliesin the model to all works that Pavementreconstruction of the surfacingand base types, and pavement require re-specification thicknessesand strength parameters. This encompassesstrengtheningby overlaysthickerthan 125 mm, recyclingof the base and/or multiple-layer overlays. But it excludes surfacing layers, and membrane-interlayer widening,road realignment, and other geometricreshaping,which shouldbe specifiedas new constructionthrough the road constructionsubmodel (SeriesB). All surfacetypes and base types and combinations thereof listedin Table4.4 are permittedexceptfor surfacetype RSAC (resealon asphaltconcrete). The reconstructionoperation is defined by user-provided specifications for new surfacingand base layer thicknessesand material types, the constructionquality code for surface treatments,resilient modulus for cementedbase layers,and either the incrementin structural numberor the final structuralnumberafter reconstruction.(In order to specifya membraneinterlayeroverlay,in caseswhen the membraneis known the user can simplyspecify to be effectivein preventingcrack reflection, and redefinethe the new surfacingtype,thicknessand strengthcoefficient need not be specified base type if consideredappropriate. The mernbrane explicitly,as the reconstructionoperation automaticallyresets all policymay be historyand conditionvariablesto zero.) The reconstruction either: 1. Scheduled, in which the fixed reconstructionis to be performedwhenever the constructionage, AGE3, equals or maximumallowableage or exceedsthe user-specified is in which the fixed reconstruction 2. Condition-responsive, performed when the roughness before maintenance, QIb, equals or exceeds the user-specifiedmaximum allowable roughness. is not performedif the Again undereitherpolicy,reconstruction interval, age, AGE3, is less than the minimum reconstruction construction nor if the last applicableyear has been exceeded,nor if the preventive treatmentand surfacingages are less than their respectiveminimum intervals, nor if it is already a construction opening year. age, AGE3, exceeds is alwaysperformedif the construction Reconstruction interval,if specifiedby the user. the maximumallowablereconstruction in m2 /km, is If performed,the amountof pavementreconstruction, The cost per km is computed by multiplyingthe equal to 1,000 W. 2) with this amount. user-specified unit cost (permi

126

ROAD DETERIORATION

is performed,the surfaceand base When pavementreconstruction typesare convertedto the new types specifiedby the user, which can be identicalto the old types. The model sets to zero the amountsof cracking (for both new and old surfacinglayers), ravelling,potholingand rut depth;resetsthe preventivetreatment,surfacingand construction ages and the crackingretardationtime and ravellingretardationfactor;and sets the roughnessto the (optional) value specifiedby the user or the default value for the given surface type (see QIIo in Section 4.2.1). In addition,the constructionquality code is set to the (optional)value specifiedby the user or the defaultvalueof zero. The pavementstrengthparametersare updatedas follows:

if the user specifieda new structuralnumber SNC(before) + ASN if the user specifiedan increasein the structural number

SNo + SNSG SNC ft = (after)

65 (after) where

S

1(after) if new base is not cemented

3.5 SNC(after)

if new base is cemented

structuralnumberfor the SNo = the user-specified pavement;and reconstructed incrementin the structuralnumberdue ASN = the user-specified to the pavementreconstruction.

4.3.8 PavementParametersafterMaintenance Followingthe logic set out in Section 4.1.2, the submodel computesthe pavementconditionfor the beginningof the next analysisyear by adding the maintenanceeffectsto the conditionbeforemaintenanceas follows: [CONDITIONIa(next year) = [CONDITIONlb + A[CONDITION]m roughnessso that it is not A constraintis placedon the post-maintenance lowerthana practicalminimumof 15 QI or 1.2 mi/kmIRI, i.e., Qia(nextyear) = max (QIb+ tQIm; 15). As HDM-III uses the sectionas the smallestunit of road for computingvehicle operatingcosts, the average road roughnessof the section over the analysisyear is required,which is computed as the averagesfor the three subsections arithmeticaverageof the corresponding of weak,mediumand strongbehavior. The averageis given by:

127

ROAD DETERIORATION effectof asphaltoverlayson roughness Figure4.14: Maintenance (a) Regularand manualcontrolpaver-finishers Roughness Change Due to Maintenance. &Qim

0X 20 -20-

-40

-60

-80-

Overlay Thicknes(m

-100-

-120 20

0

40

60

80

120

100

140

160

Roughness Before Overlay. Qlb

(b)

paver-finishers

Long-base automatic-levellingi

Roughness Change Due to Maintenance, kQlm

-20

2

-40

40

-60

6

80

\

-80 Overlay Thickness (mm)

400

-400

-120 0

20

40

60

80

400

Roughness Before Overlay, Qlb

Source: This study.

420

140

160

128

ROAD DETERIORATION

QI avg

=

3 E (QIa

+ QI bj)/6

where QIaj and QIbj denote the roughnessof each subsectionj at the beginningand the end of the analysisyear before the road maintenance decision,respectively. 4.4 UNPAVEDROAD LOGIC 4.4.1 Classification, Concepts,and Logic Unpaved roads comprisethe lower classes of the road network hierarchy,and generallycarry low volumesof traffic rangingfrom a few vehicles to up to several hundred vehicles per day. The geometric standards vary considerablyand it is necessary to make a primary classificationof unpaved roads into engineered roads, which have controlledalignment,formationwidth,cross-section profileand drainage; and tracks,which are essentially ways formedby trafficking along natural contourswith or without the removalof topsoil. Unpavedroadsclassified in a country'snetworkare usuallyengineeredor partlyengineeredroads, and tracksare usuallynot classified. The analysis of deterioration and maintenanceeffects in this submodel is designed primarilyfor engineeredunpaved roads, of either gravel or earth surfacing,because the empiricalmodels are based on a variety of such roads. When necessary it is possible to use the relationship also for tracksas a firstestimate,but the user needsto be aware that the environmental effectsof drainageand rainfallmay be poorly represented. The deterioration of unpavedroads is characterized primarilyby roughnessand by material loss from the surfacing. The prediction relationshipsfor these are based on analysesof the Brazil-UNDPstudy (Visser,1981;Paterson,1987). Wheelpath rutsalso developundertraffic but the ruts are usuallydeviousor poorly definedand often mixed with water-induced surfaceerosion. Thus the conceptof rut depth is not used in HDM-III and is subsumed in the property of roughness; prediction relationships may be found in Visser (1981). The loosenessof surfacing material,which was analyzedin the Kenya study (Hodgeset al., 1975),was also observedin the Brazil-UNDPstudy (GEIPOT,1982) but as it was found to have no substantial effecton vehiclespeed,no predictionrelationships have been incorporatedin HDM-III. Finally, road passabilityis an importantcriterionfor upgradingtracksor earth roads to gravel roadsprovisionis made in the model for an increasein vehicleoperatingcosts (by a factor specifiedby the user, reflectingthe economiceffects of reducedpassability when the gravelthicknessdropsbelowa minimumlevelthis is discussedin Sections4.5.3and 5.3.7. The maintenanceof unpavedroadscomprises:

ROAD DETERIORATION

129

1. Periodic grading by motorizedor towed grader to restore surfacinggravel from the shouldersto the roadwayand to reduceroughness; to repairpotholes; 2. Spot regravelling to replaceor augmentthe gravelsurfacing 3. Gravel resurfacing layerin responseto materialloss;and maintenanceof drainage channelsand 4. Routine-miscellaneous verges. The periodicgradingof unpavedroads is usuallyundertakenon a more-orless regularbasisfor managementpurposes,eitherseasonallyor frequently enoughto keep the roughnesswithin tolerablelimits. The 'routine'tasks 2 and 4 above are oftenachievedat the same time as 1. These repeated cycles of roughnessdeteriorationand grading maintenanceare treatedas continualby the submodel. The averageroughness during each analysisyear is computedas a functionof the roughness at the beginningof the year, of material,traffic,geometryand rainfall parametersand the specifiedgrading frequency. Over a period of time dependingon the traffic volume and frequencyof grading, the annual averageroughnesstends towardsa long-termaverageroughnesswhich is also computed. Maintenanceof the gravel surfacingis accountedeach analysis year throughthe surfacingthicknessand the net changefrommaterialloss, maintenance. The material loss and gravel resurfacing spot regravelling from earth roads,althoughcomputed,is accountedonly for the purposeof quantitiesand is otherwiseignored. predicting"spotregravelling" The computationallogic describedabove is illustratedby the flow diagram in Figure 4.15 and detailed in Section4.4.6. In order to simplifythe logic,an unpavedroad is consideredto comprisetwo layers,a gravel surfacingand a subgrade. A gravel road has both layers,but an earth road has a zero thicknessof gravelsurfacingand its surfacecharacteristicsare thoseof the subgrade. When a gravel road loses all of its revertsto that of earth road. gravel surfacing,then its classification all unpavedroadsbecomegravel roads by definiUpon gravel resurfacing, tion of the new surfacinglayer. is predictedusing the propertiesof the surfacing Deterioration as it is defined for the layer,whether that be "gravel"or "subgrade," analysisyear. Thus the user must specifythe physicalpropertiesof both gravelsurfacingand subgradefor unpavedroads. 4.4.2 MaterialProperties by have been categorized relationships deterioration Previously, coral,volcanic,etc.),but from the quartzitic, materialtype (lateritic, Brazil-UNDPstudy it has been possible to replace these by material of the relationships. propertieswhich should improvethe transferability

130

ROAD DETERIORATION

The material properties which were found to affect the rate of deterioration in Brazil includethe maximum particle size, the particle size distribution and the soil plasticity(Paterson,1987). The specific soil properties, which are requiredinputsfor HDM-IIIas definedbelow, are used subsequently to define varioussummarynumericsof the particle size distributionwhich are parametersin the deteriorationprediction equations. The minimumand maximumlevelsof roughness,QIMINand QIMAX, are predictedendogenouslyfrom the soil propertiesbut the user may overridethoseby specifyinginputvalues. The soil propertiesare defined for both the 'gravel'and 'subgrade' layers(as describedin Section4.4.1) denotedby the subscriptj, where j = g for gravelsurfacinglayer,and j = s for subgrade(or earth roadsurfacing)layer,in Table4.14. 4.4.3 TrafficLoadingMeasures The traffic loadingvariablesused in predictingunpaved road deterioration are simplythose of two-waytrafficcountsfor all vehicles and for light (ADL)and heavy (ADH) vehicles,as defined in Table 4.14. Note that Table 5.1 providesdefault classifications for light and heavy vehicles. The variableADT, which equalsADL + ADH, is used in predicting materialloss,and the variablesADL and ADH in predictingroughness. 4.4.4 Road GeometryMeasures The geometric characteristics found to influence the deterioration of unpaved roads in the Brazil-UNDPstudy were horizontal by the rise plus gradient(here represented curvature(c) and longitudinal and in particularthe maximum fall variable,RF). Roughnessprogression, roughness,is influencedby both characteristics. In material loss predictionthe horizontalcurvatureaffects the rate of traffic-induced material whip-off and the gradient interactswith rainfall in causing Cross-sectionalgeometry, including crown, camber and erosion. were not measuredin the study and are discussedin the superelevation, followingsection. The averageshoulderwidth (WS) is used to computethe amount of gravel used in spot regravelling and gravel resurfacing. The variablesRF, C and WS are definedin Table4.14. 4.4.5 Environment:Climateand Drainage While the climateof the Brazil-UNDPstudy area is classedas humid to warm- or wet-humid,the rainfallpatternwas seasonal,ranging of lessthan 20 mm per monthand air humidityless than from precipitations 40 percent during a continuoussix to eight months of a year, to precipitations of 200 to 600 mm per month and air humidityin excessof 60 percent over four months of a year. The effectsof the full range of by highlyseasonalrainfallwere analyzedin the study,and are represented the average monthly rainfall in the deterioration prediction relationships.The predictionsof annual average roughnessand material loss transformthis to an annualaveragerainfalland thusmake no specific distinction betweenuniform-and seasonal-rainfall climates Geometriccross-sectional characteristics, particularlycrown, camber,table side-drainsand run-offpoints,have pronouncedeffectson

131

ROAD DETERIORATION and maintenance Figure4.15: Logicsequenceof roaddeterioratlion submodel:unpavedroads INPUT traffic, geometry material properties, envirornment, policy

-1

=~~~~~~~~

_i

COMPUTEAVERAGE ROUGHNESS given gravel properties

1

[

COMPUTE AVERAGE ROUGHNESSgiven subgrade properties

COMPUTE MATE in analysis year for subgrade

SuCOMPUTE MATERIAL LOSS in analysis year for gravel

l

l

COMPUTE QUANTITY of spot regravelling

_

r

t

>

K

COMPUTE QUANTITYi of spot reg:ravellingl (by subgrade material)l

UPUT

Ro~~~~~~~~ughness

~~~~~submodel/ K.

|COMPUTE GRAVEL THICKNESSl a7*fter so regravellingl

F OMPUTE GRAVEL THICKNESS|~~~~UTPU

Maintenance quantities to COST submodel

Source: This study.

.

ROAD DETERIORATION

132

Table 4.14: Definitionof primaryvariablesfor unpavedroads Variable

Definition

ADH =

the averagedaily heavyvehicletraffic(GVW >= 3,500 kg) in both directions, in vehicles/day.

ADL =

the averagedaily lightvehicletraffic(GVW < 3,500kg) in both directions, in vehicles/day; and

ADT =

the average daily vehiculartraffic in both directions, in vehicles/day;

C =

the averagehorizontalcurvatureof the road, in degrees/km (as definedin Figure5.1);

D95j =

the maximum particlesize of the material,definedas the equivalentsieve opening through which 95 percent of the materialpasses,in mm;

MGj

=

slope of mean material gradation,as defined in Section 4.5.1;

MGDj =

dust ratio of material gradation,as defined in Section 4.5.1;

PIj =

the plasticityindexof the material,in percent;

P075j =

the amount of materialpassingthe 0.075mm sieve (or ASTM No. 200 sieve),in percentby mass;

P425j =

the amount of material passing the 0.425 mm sieve (or ASTM No. 40 sieve),in percentby mass;

P02j =

the amount of material passing the 2.0 mm sieve (or ASTM No. 10), in percentby mass;

QIavg =

averageroughnessduringanalysisyear, in QI;

QI(after)=

roughnessaftergrading,in QI;

QI(before)=

roughnessbeforegrading,in QI;

QIMINj =

the minimumroughnessof the material (eitherestimatedin in QI; Section4.5.1or specified),

QIMAXj =

the maximum roughnessof the material (eitherestimatedin Section4.5.1or specified), in QI;

RF =

the averageabsoluterise plus fall of the road,in m/km (as defined in Figure 5.1) (note: RF = 10 times average absolutegradientin percent);and

WS =

averagewidthof shoulder,in meters;

ROAD DETERIORATION

133

drainage and deteriorationduring high rainfall. In the study area, roughnesslevelson level,tangentsectionsthat were poorlydrainedwere very high during wet periods due largely to the rapid developmentof potholes. On verticalgrades,roughnesslevelswere frequentlylow despite extensiveerosionby surfacerun-offbecausethe longitudinal profilewas affectedless than the transverseprofile. The study sectionsgenerally had moderatedrainagefacilitiesand maintenance, and positivecrowns. The predictionrelationsthereforeapply to unpavedroadswith moderateto good cross-sectional geometryand for dry to wet cond'itions but may not applyto 'bathtub'type roadswith negativecrown or lack of surfacedrainagein high rainfallconditions. 4.4.6 Basic Computational Procedure The model assumes that the grading operations and spot regravelling specifiedfor each year, both for graveland earth roads,are distributed uniformlythroughoutthe year. Howev,er, the gravel resurfacing operation,when it occurs,is assumedto be carriedout at the end of the year. Like the periodic paved road maintenanceoperations,gravel resurfacingis not permittedin an effectiveconstruction completionyear. The computational procedurefor road deterioration and maintenanceof the unpaved roads for each analysisyear followsthe flow diagram of Figure 4.15 and comprisesthe followingsteps: 1. Initializeroadcharacteristics and trafficloadingvariables at the beginningof the analysisyear. 2. If earth road skip to step 3. Otherwise,checkwhetherthe gravel thicknessis zero (i.e.,no gravel remaining)at the beginningof the analysisyear. If the thicknessis zero, resetthe road type to earth. 3. If grading is specifiedcompute the annual average road roughnessas a functionof the grading frequency,traffic volume, environmentalconditions,and attributes of the gravel (if gravel road) or the subgrade (if earth road). Otherwise,if no grading is specified,set the average roughnessequal to the predictedmaximum roughness(Section 4.5.1). 4. Computethe depth of materialloss during the analysisyear as a functionof the trafficvolume,monthly rainfall,and road geometryand the attributesof the gravel (if gravel road) or the subgrade (if earti,road) (Section4.5.2). Compute the average thicknessof spot regravellingto be providedduringthe analysisyear (Section4.5.3). 5. If earth road skip to step 6. Otherwise,computethe gravel thicknessat the end of the analysis year before gravel resurfacing decision. This is equal to the thicknessat the beginningof the year minus the depthof gravelloss plus the spot regravellingthickness. If the gravel thicknessis negative,resetit to zero.

134

ROAD DETERIORATION is to be carriedout (at 6. Determinewhethergravelresurfacing the end of the analysisyear) accordingto the criterion specified by the user as described below. If gravel resurfacingis performedset the road type to gravel road regardlessof the previous type and compute the gravel thicknessat the end of the analysisyear after resurfacing as equal to the thickness before resurfacingplus the resurfacing thickness. 7. Compute the correspondingroad maintenancequantitiesand costsby operation. 8. Store the resultsfor lateruse in the vehicleoperatingcost submodeland in the evaluationand reportingphase.

4.4.7 Initialization of Variables At the beginningof the analysisyear the trafficvariablesare trafficdata (SeriesE). The values computedbased on the user-specified of the environment,road geometry,and material property variablesare providedin one of threeways, in the samemanner as the similarvariables for paved roads,that is: 1. From the precedinganalysisyear, if the analysisyear is neither the first year of the analysis period nor a construction openingyear; 2. From the existinglink characteristics data (SeriesA) if the analysisyear is the firstyear of the analysisperiod;or optiondata (SeriesB) if the analysis 3. From the construction year is a construction openingyear. The only historyvariablefor unpaved roads is the gravel age, denotedby GAGE,which is relevantonly for gravelroads. It is definedas the number of years elapsed since the latest gravel surfacing or as follows: and is initialized resurfacing 1. When the analysisyear is not a constructionopeningyear, the value of GAGE is providedeither (a) from the preceding year (if the analysisyear is the secondor a subsequentyear of the analysis period) or (b) from the existing link characteristics data (if the analysisis the first year of the analysisperiod),and is increasedby one year; and 2. When the analysisyear is a construction openingyear (of a gravelroadproject),the valueof GAGE is set to one and the unpaved road surface type to gravel, irrespectiveof the previoussurfacetype.

ROAD DETERIORATION

135

4.5 UNPAVEDROAD DETERIORATION AND MAINTENANCE 4.5.1 Road Roughness The roughnessof unpaved roads increasesthrough the shear, mechanicaldisintegration, and erosionof the surfacingmaterialcausedby trafficand surfacewater runoff. Roughnesslevelsare usually4 to 15 m/km IRI (50 to 200 QI) althoughlower levelssometimesoccur with fine materials. Roughnessin excessof 13 m/km IRI (180 QI) is usuallyrelated to depressions, potholesor transverseerosiongullies,and levelsabove22 m/km IRI (300 QI), which correspondto numerouswheel-sizedpotholes,are very rare and usuallyapply only on shortsectionsor unclassified tracks. The roughnessmodelled for economic evaluationis the profile in the wheelpathsof the traffic, since this generatesthe vehicle operating costs. The locationof the wheelpathstendsto vary when roughnessreaches high levels as vehicles seek to minimizethe dynamic impact,hence the predictionof roughnessprogression must take this self-regulating tendency into account. On accountof the high variabilityof materialproperties, drainage,surfaceerosionand the high roughnesslevelsof unpavedroads, predictionerrorstend to be large,in the orderof 1.5 to 2.5 m/km IRI (20 to 32 QI) standard error, or equivalentto 95 percentileconfidence intervalsof 20 to 40 percent. A numberof differentmodel formshave been appliedto roughness progression and to the effectsof maintenance grading(Hodgeset al., 1975; Visser,1981;Paterson,1987). As the objectiveof policyanalysescan be satisfied by computationof the average roughness resultingfrom a specifiedpolicy, the model selectedfor predictingroughnesswas one which both represented the progression and gradingphasesof the roughnesscycle realistically and also permitteda closed-formsolution. The model form and its derivationare describedin detailelsewhere(Paterson,1987). The primaryprinciplesand parameterestimatesare as follows. Althoughthe IRI roughnessmeasure,or other compatiblemeasure, couldhave been used in the followingrelationships becausemany parameters are dimensionless, we have kept the nomenclature of QI for roughnessfor internalconsistency with the remainderof the model. Roughnessprogression In previousmodels,progressionfollowedeithercubic (Hodgeset al., 1975) or exponential(Visser,1981; Paterson,1987) concave curves which, unless restrained,led to unrealisticallyhigh predictionsof roughnessfor policiesof infrequentgrading. The model form adoptedhere constrainsthe roughnessto a high upper limit, or maximum roughness (QIMAX-),by a convex functionin which the rate of progression decreases lineary with roughnessto zero at QIMAX conformswell with practical observations.The predictionsof both forms differ significantly only at high levelsof roughness;at low levelsof roughnessthe concavecurve is often more realistic in shape, but quantitativelythere is little differencebetween the two. From the Brazil--UNDP study, the maximum roughnesswas found to be a functionof material propertiesand road geometry,and the rate of roughnessprogressionto be a functionof the

136

ROAD DETERIORATION

roughness,maximum roughness,time, light and heavy vehicle passes and materialproperties, as illustrated in Figure4.16 and given by (Paterson, 1987): QI (TG2)

= QIMAXj- b [QIMAXj- QI (TG1 )]

QI (TG1 ) = roughnessat timeTG1 , in QI;

where

QI (TG 2)

= roughnessat time TG2, in QI;

TG1, TG2

= time elapsedsince latestgrading,in days;

b

= exp [c (TG2 - TG1 )]; where 0 < b < 1;

c = - 0.001 (0.461+ .0174ADL + .0114ADH - 0.0287ADT MMP); QIMAXj = max [279- 421 (0.5- MGDj)2 + 0.220C - 9.93 RF MMP; 150]; MGDj = materialgradationdust ratio,definedas

1 if P425j= 0 MGD1

= f

P075j/P425j if P425j > 0; and other

variables = as definedpreviouslyin Section4.4.3 - 4.4.5. Note: The standarderror of this predictionon the originaldata basewas 19.8QI (1.5m/km IRI). Effectof compactionon roughnessprogression Observations on graveland earth roads in the first few grading cycles after construction or rehabilitation with full mechanicalshaping and compaction,indicate rates of roughnessprogressionthat are much slower than given by the model above,which was derivedfrom roadsunder repeatedgradingcycleswith no specialcompaction(Paterson,1987). Thus if "mechanical compaction" is specified in the model inputs, the coefficient c is reduced,initiallyto one quarterof its predictedvalue and risingto the full predictedvalueaftera few gradingcycles,but in a periodnot exceeding4 years,as follows c' = c min [1, 0.25 t max (1, n0 .33)] where t = time in years since regravelling or construction with mechanicalcompaction n = frequencyof grading,cycles/year. and thus

ROADDETERIORATION

137

Figure4.16: Predictions of maximumroughness and roughnessprogression for unpaved roads (a) Estimated maximumroughness forthe twogeometrics and threematerials MaximumRoughness[QI) 0.501 MGD: 0.75 HillyTerrain

-----

~ ~ ~ ~ ~

-

100-4

4

-

---

-

- -

-

---

-

- -

-

--

--

~0.50~ MGD:0,75 RollingTangent 1.00) Terrain

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Monthly Mean Rainfall,MMPfm/monith)

(b)

Roughness pro-gression for two traffic volumes

Roughness(QI) 200 -

QIMAX 16--

120-

0 0

~~~50

100

'150

200

250

Time SinceGrading (Days)

Source: Paterson(1987).

300

350

400

138

ROAD DETERIORATION b' = exp (c' 365/n)

where b', c' are the valuesof b and c abovewhen mechanicalcompactionis in effect. Effectof grading The effect of grading maintenanceon roughnesswas found to depend on the roughnessbefore grading,the materialpropertiesand the minimum roughness (QIMINj) (Paterson,1987). The minimum roughness, below which grading cannot reduce roughness,increasesas the maximum particle size increasesand the gradation of the surfacingmaterial worsens. The predictionof roughnessafter grading is expressedas a linearfunctionof the roughnessbeforegrading,dust ratioand the minimum as illustrated in Figure4.17 and givenby: roughness, QI(after) = QIMINj+ a [QI(before) - QIMINj] where

QI(after) = roughnessaftergrading,in QI; QI(before)= roughnessbeforegrading,in QI; a = 0.553+ 0.230MGDj; QIMINj = max {10;min [100;4.69 D95j (1 - 2.78 MGj]1; MGj = slopeof mean materialgradation,such that MGj = min (MGMj,1 - MGMj,0.36),where

MGM. =

MG075;+ MG425 + MG02 3

where

MG075j= [In (P075j/95)/In (0.075/D95j)if D95j > 0.4,

0o. 3

otherwise;

MG425j= [In (P425j/95)/tn (0.425/D95j)if D95j > 1.0,

.10.3

otherwise; and

MG02j = Qtn(PO2j/95)/9n (2.0/D95 j) MG425; otherwise.

if D95j > 4.0,

Note: The standarderrorof this predictionon the originaldata base was 31.6 QI (2.4m/km IRI). Averageroughnessin analysisyear The average roughnessduring the analysisyear is computedby and integrating relationships and grading-effect combiningthe progression (see Paterson 1987). The year's average is expressedin terms of the roughnessat the beginningof the year and the parametersin the previous as follows: expressions

ROAD DETERIORATION

139

Figure4.17: Predictionof minimumroughnessand roughnessafter grading for unpavedroads (a) Estimatedminimumroughnessfor variousmaterials MinimumRoughness (QI) 100X

80

60/0 /0.10

/O0.20

'0.25

40-/

0

.X

o

20

40

.- Grada.

80

60

MG

400

MaximumParticleSize.D95 (mm)

(b) Roughnessaftergradingas a functionof roughnessbeforegrading Roughness After Grading (QI)

3500

Li~~~~~~~~ne of Equolity

3001

200~~~~~~~~~~~~~~~~.

,15o= io-1

0

°~~~~~~~~De Ra.o,MG ,. -,

50

'°O

150

Roughness BeforeGrading (QI)

Source: This study.

200

250

300

140

ROAD DETERIORATION

Case 1 (t n > 1) The averageroughnessduringyear t, QIavg,is givenby: QIavg = QIMAX (1-y)+ SN yin where y = (b-1)n/365c SN = [n k + (1-(a b)n) QIa - k (1-(a b )n)/(l-ab)]/(l-a b).

k = (1-a)QIMIN+ a (1-b)QIMAX QIa = roughnessat beginningof year t where QIo = valuespecifiedby useror by default,in QI; if t = 1;

QIa =

or QIb = roughnessat end of year, t - 1, as given below in QI

QIavg= averageroughnessduringyear t, in QI a, b, c = as definedabove,exceptthat b, c take the valuesb' and c' when mechanicalcompactionhas been specifiedand the roughnessat the end of the year, QIb, is QIb = (ab)nQIj+ k (1-(ab) n)/(1-ab) Case 2 (t n < 1) QI avg = QIMAX - (QIMAX-QIa) [exp(365c) - 1]/(365c) QIb = QIMAX - (QIMAX- QIa)exp(365c) Roughnesscycle "steadystate" When gradingis performedregularlyat constanttime intervals, or a fixed roughnesslevel, or fixed traffic intervals,the process of roughnesschange describedby these relationshipswithout restriction eventuallyleads to a steady state, as shown in Paterson (1987). This steadystate is characterized by a saw-toothedpattern of roughness-time profile,in which the highs and lows representthe roughnessimmediately beforeand after grading,respectively.These highsand lows,denotedby QIH and QIL, are givenby: = [QIMAXj(1 - b) + QIMINj (1 - a) b]/(l - a b); QIL = [QIMINj (1 - a) + QIMAXja (1 - b)]/(1- a b); QIH

141

ROAD DETERIORATION

undervarioustraffic of roughnessprogression Figure4.18: Predictions roads unpaved for policies grading and volumes (a) Effectsof trafficvolumeunderregular90-daygradingpolicy Roughness(Ql) 250. ----25__J

-.

..

QIMAX IA

Long Term Averages, Qlita 200

_-';

______

A

._

.

._

'---,-1----L,

'-

-,

.

.

.

.

.

.

.

.

.

..

,--,

-,

veh/d

,500

,

/

150-

.

.

.

100veh1d

Qlo.QIMIN

50-

600

500

400

300

200

100

0

1000

900

800

700

Time (Days)

(b) Variousgradingpoliciesfor averagedaily traffic300 veh/dav Roughness (Ql) QIMAX

_

250

200

I

- -

| ',,

//,w

o

vCR

.........-

/

_

0

100

Grading Cycle ~~~~~~~~~30-dcay

_

Qlo.QIMIN

300

400

500 Time (Days)

Source: After Paterson(1987).

--

,I

,~

200

'''

'

~~~~~~90-dcay

|

100~-~7l0-~~~~~~~~~~~~~~~~~~~~~ 50

I

360-day

,.-

'

''

450

_

a

,

-

,

_

600

700

800

900

1000

142

ROAD DETERIORATION

where all parametersare as definedabove. The long-termaverage roughness,denoted by QIlta, at this steady state under a maintenancepolicy is dependent on the grading frequency (embodied in the parameter b above) and is obtained by integration over the roughness-timeprofile, so the annual average roughnesstendsto the following:

where

QIavg e

QIlta

QIlta =

QIMAXj+ (1 - a1 (1 - b) [QIMAXj- QIMINj]/ [(1- a b) In bJ.

The relationshipsare illustratedin Figure 4.18 where the long-term averageroughnessis superimposed on the cyclictrendsfor (a) a road under regular90-daygradingmaintenance and differentlevelsof traffic,and (b) a road underdifferent(30,90, 360-day)gradingpoliciesand one levelof traffic(300 veh/day: 200 light,100 heavy). The surfacingmaterialis a medium (20 mm) slightlyplasticgravel with high dust ratio (0.80) and moderategradation(MG = 0.20). 4.5.2 MaterialLoss From the Brazil-UNDPstudy the following relationshipfor predictingthe annual quantityof material loss as a functionof monthly rainfall,trafficvolume,road geometryand characteristics of the gravel (if gravel road)and the subgrade(if earth road)was obtained(Paterson, 1985): MLA = 3.65 £3.46+ 0.246MMP RF + KT ADT] where

MLA = the predictedannualmaterialloss, in mm/year; KT = the traffic-induced materialwhip-offcoefficient, expressedas a functionof rainfall,road geometryand materialcharacteristics: KT = max [0; (0.022+ 0.969

C + 0.00342MMP P075j 57300 - 0.0092MMP PIj - 0.101 MMP)];and

j = g if gravelroad;= s if earth road. The predictions are illustratedin Figure4.19 showingthe effectsof (a) trafficand rainfallfor flat terrainand (b) rainfalland geometryfor a traffic volume of 200 veh/day,and slightlyplastic, fine silty gravel surfacingmaterial. 4.5.3 Passability Passability is the qualityof the road surfacewhich ensuresthe safe passage of vehicles. In the vehicle operating cost submodel, provisionhas been made to determinethe economic impact of a partial

143

ROAD DETERIORATION of surfacingmaterialloss relatedto Figure4.19: Predictions traffic,rainfalland geometryfor unpavedroads 10010 807~~~~~~~~~~~~~~~~~~~~~~~~

Rainfali(rn/month)

0.20

~~~~~~0.10

E 0 0-

10-

Average DailyTraffic,ADT(vehicles/day)

-_

0

2

60-

~~~~~Geometry:-

-

-

Rolling-----

40E....-

~~~~~~~~~~~Flattangent

30 20-

100~ 0.00

0.05

0.10

0.15

Mean MonthlyRainfall,MMP(rn/month)

0.20

0.25

144

ROAD DETERIORATION

reductionin passability throughfactorsaugmentingthe operatingcostsof the various vehicle types (see Section 5.3.7). This augmentationcomes into effectwhen the gravelsurfacingthicknessdrops below a minimum,and relatesto the risk of the subgradematerialbeing impassable. The user howevermust determineexogenously whether passability will be a problemin the subgradematerial,becauseno physicalestimation of it is made within the model. The followingcriteriafrom Visser (1981) are adequatefor ensuringpassability and surfacestability: 1. Passability which is a functionof the shear strengthof the saturatedmaterial,is satisfactory when: SFCBR > 8.25 + 3.75 log1 o (ADT),and 2. Surfacing stability, which relates to looseness,is satisfactory when:

ravelling and

P075 > 14, where SFCBR = the (minimum)soakedCaliforniaBearingRatio at standardProctor laboratorycompactionfor ensuringpassability; and ADT, P075 = as definedpreviously. 4.5.4 GradingMaintenance Options The principalroutinemaintenancefor unpaved roads,other than the miscellaneous items coveredin Section4.5.7, is gradingwhich may be specifiedby the user in one of threeways, that is: 1. Scheduled: a fixedtime intervalin days betweensuccessive gradings; 2. Traffic-responsive:a fixed trafficintervalin number of vehiclepassesbetweensuccessivegradings;and 3. Roughness-responsive: a maximumallowableroughness. In all cases,the averageroughnessbetweensuccessivegradings, QIAVG, is computedas a functionof the numberof days betweengradings, DG, as describedin Section4.5.1. In the scheduledcase, DG is specified directlyby the user. In the trafficand roughness-responsive cases,DG is determinedas follows: DG =

DGMAX DG' DGMIN

if DGMAX< DG' if DGMIN< DG' < DGMAX if DG' < DGMIN

where DGMAX = the maximum allowabletime intervalbetween successive gradings,in days, specifiedby the user as an option or equal to the defaultvalueof 10,000;

145

ROAD DETERIORATION

DGMIN = the minimum applicabletime intervalbetween successive gradings,in days, specifiedby the user as an optionor equalto the defaultvalueof 5 days; DG' = the numberof days betweensuccessivegradingsdetermined from the trafficor roughnessparameter,as follows: VEHG

case for the traffic-responsive

ADT DG' = (1/c)Qn t(QIMAXj - QIMAXO)I/[QIMAXj - (1 - a) QIMINj- a QIMAX4]} for the roughness-responsive case

VEHG = the traffic interval between successivegradings, in vehicles,specifiedby the user;and QIMAXo = the maximum allowableroughnessspecifiedby the user, in QI. No grading If no grading is specified,the long-termaverage roughnessis as follows: equalto the maximumroughness, QI lta = QIMAXj over of the link has been nil-grading Note that if the historicmaintenance the of best estimate is the roughness severalyears, then the existing QIMAX by specifying this can provide average roughnessand the user with a valueequalto the existingroughness. exogenously 4.5.5 Spot Regravelling providesrepairto areas of severe depression Spot regravelling (gravelloss, rutting,etc.),and may be specifiedby the user eitherin a fixed numberof cubicmetersper kilometerper year or as a percentageof gravel or subgrade material loss in the current analysis year to be is replaced(subjectto a maximum limitper year). When spot regravelling performed,the added material is assumed to be the same type as the is computedas the productof the existing. The cost of spot regravelling unit cost of material per m3 and the volume of material added in m3 per

km. For gravel roads the thicknessof the gravel layer is increasedto reflectthe volume of materialadded, accordingto the followingformula rule): (trapezoidal ATHGS =

VGS W + WS

where

ATHGS = the increasein gravelthicknessdue to spot in mm; and regravelling,

146

ROAD DETERIORATION VGS = the in-placevolumeof graveladded due to the spot regravelling, in m3 /km.

The spot regravellingis predicted to reduce the average roughnesson the assumptionthat the gravel is applied in the major depressionsand potholesthat have appeared in the surface in the upper ranges of roughness. Roughnesslevels above 190 QI (15 m/km IRI) are invariably associated with the presence of visible birdbath type depressionsor potholes,which become larger or more frequent as the roughnesslevel increases,and thesecan be effectively patched,with high benefits,by spot regravelling.Over the roughnessrangeof 150 to 190 QI (11 to 15 m/km), such "patchable" birdbathdepressionsare frequentlybut not alwayspresentso that, in this range,spot regravelling may not always be effective. For example,spot regravelling is not effectivemaintenance on corrugationsor on runoff-induced surface erosion,which conditions commonlyinduce roughnesslevelswithin this range. At roughnesslevels below 150 QI (11 m/km IRI) spot regravellingis consideredto be ineffectiveon roughness. This logic is defined in the following algorithm,adoptingthe same roughness: volumeof depressionratioas for paved roadpotholesimulation(i.e.,2 QI per m3/lane/km),allowingfor the sgot regravellingto be only 60 percent effective(i.e., 1.2 QI per m /lane/km),and adoptingan averageeffective"lane"width of 3 m: Q1avg(after)= max150; QIavg(before) - min(1; (Qiavg(before) - 150)/40)VGS 3.6/W]}.

This is illustratedin Figure 4.20. It should be noted that spot regravelling affordsonly a temporaryrepairof depressions, and that the most effectivemeans is by grading,or in severe cases by scarifying, gradingand recompacting. 4.5.6 GravelResurfacing Maintenance A gravelresurfacing policyis specifiedeitheras: 1. Scheduled,in which gravel resurfacingis appliedwhen the gravel age, GAGE, equals or exceedsthe fixed time interval specifiedby the user;or 2. Condition-responsive, in which gravel resurfacingis applied when either (i) The current gravel thickness,THG, falls below the user-specifiedminimum allowable thickness, provided that the gravel age, GAGE, equals or exceeds the (optional) user-specified minimumapplicableresurfacing interval,in years;or

147

ROAD DETERIORATION Figure4.20: Effectof spot regravelling on averageroughness Roughness After Spot Regravelling (QI) 300-

0

,10 '20 Regrovelling Volume 3 (m lkmlyear)

250-

,-/E'

/,/

200

i/

7.

/

/

// /

50

//

1o

,/"

100~~~~~~~~~~~~~~~~~~~*0 150'

______________ .........

0 0

50

100

150

200

250

300

Roughness Before Spot Regravelling (QI)

Source: This study.

(ii) The gravelage, GAGE, equalsor exceeds the (optional) user-specified maximum allowableresurfacinginterval, in years. However, gravel resurfacingis not performed if the specified last applicableyear has been exceeded, or if the analysis year is a constructionyear, or if the final thicknessspecifiedin a scheduled policy is smallerthan the predictedthicknessat the end of the analysis decision. year beforethe resurfacing When gravel resurfacingis performedthe surfacetype is set to of the previoussurfacetype),the gravel age, GAGE, "gravel"(regardless is reset to zero, the existinggravelmaterialis changedto the material specifiedby the user (whichmay still be of the same attributesas the existing)and the thicknessof the gravelsurfaceis increasedaccordingto the formulabelow: THGF

if the finalgravelthickness + ATHG0 if specified an increasein the gravel TH(before) °thickness is specified

LHG

THG(after) =is THT(after)

148 where

ROAD DETERIORATION THGo = the user-specified finalgravelthicknessafter resurfacing, in mm; and ATHGo = the user-specified increasein the gravelthickness due to resurfacing, in mm.

The volume of gravel added per km is computedaccordingto the followingtrapezoidal formula: VGR = [THG - THG ] (W + WS) (after) (before) where

VGR = the in-placevolume of gravel material added due to gravelresurfacing, in m3/km.

Finally, the values of the gravel attributes(PO75 g, P425a, PO29, D959, PIg, QIMINg and QIMAXg), are replaced either by tge new values providedby the user, or by defaultvalues from the previous gravelattributes. 4.5.7 Routine-Miscellaneous Maintenance This includesdrainagemaintenance,vegetationcontrol,shoulder maintenance,safety installations, and other itemswhich are not modelled as affectingthe ridingqualityof the pavement. A lump sum cost per km per year is usedas the basisfor costingroutinemaintenance.Becausethe unpaved road deteriorationrelationshipsemployed are based on the assumptionof adequatedrainage,the cost of drainagemaintenanceshouldbe included,when it is normallydone; otherwise,some allowancedue to the lack of drainage,e.g., in the form of frequentroad closures,washouts, etc.,shouldbe incorporated in the economicanalysis.

CHAPTER 5

Vehicle Operating Cost Submodel

5.1

GENERALOUTLINE

5.1.1.Operationof the Submodel The function of the vehicle operating cost submodel is to simulatethe effectsof the physicalcharacteristics and conditionof a road on the operatingspeeds of various types of vehicles,on their consumptionof fuel and lubricants, on theirmaiintenance requirements, and so on, and to determinetheir total operatingcosts. The quantitiesof resourcesconsumed,such as litersof fuel,numbersof tires,man-hoursof labor,etc., are determinedtogetherwith vehiclespeeds as functionsof the characteristics of each type of vehicleand the geometry,surfacetype, and currentconditionof the road. Costsare then foundby multiplying the various resource quantities by user-specifiedunit costs and adding allowancesfor depreciation, interest,and overheadcostsand for the time valuesof passengerdelaysand cargoholding. The user may specifypricesor unit costs in both financialand economic terms and may specify the foreign exchange element of total costs. Financialcosts representthe actual Dostsincurredby transport operatorsin owningand operatingvehiclesover the road. Economiccosts representthe real costs to the economyof that ownershipand operation, where adjustmentsare made to allow for market price distortionssuch as taxes,foreignexchangerestrictions, laborwage laws,etc., and where the implicitcosts of passengers'time and cargo tholding are accountedfor. Foreignexchangecosts representthe costs which must be providedfor in foreigncurrenciesand, dependingon the use, can be interpreted as either financialor economic. The proceduresfollowedby the vehicleoperatingcost submodelin computingspeeds,resourceuse, and costs for the traffic using a given road sectionin each year may be summarized as follows: 1. Computethe averageoperatingspeedfor each vehiclegroup. 2. Compute the amountsof resourcesused per vehicle-kilometer by each group for the followingcomponents: a. Fuel b. Tire wear c. Maintenance parts d. Maintenance labor e. Lubricants f. Crew g. Depreciation h. Interest 149

150

VEHICLE OPERATING COST SUBMODEL i. J. k. 1.

Overhead Passenger time Cargo holding Miscellaneouscosts

3. Apply unit costs to the resource consumption amounts to obtain cost per vehicle-kilometerfor each vehicle group. 4. Multiply cost per vehicle-kilometerby the section length and by the year's traffic volume of each vehicle group to obtain the total road user costs for the year for each group. 5. Sum the group totals to obtain the overall total road user costs for the year. Throughout any computer run, the values of the parametersthat describe the environment, vehicle characteristics, and unit costs remain unchanged, while the variables that describe traffic flows, traffic composition, road geometry, and the type and condition of the surface may change from year to year according to the actions of the submodels described in previous chapters. In the HDM-III model there are actually four different sets of relationshipsfor estimating vehicle speeds and the consumption of some of the operating resources, based on four separate empirical studies by different agencies. The user must choose and specify which of these sets is to be employed in any given run. We give guidance on that issue in the next section. We then describe the relationshipsderived from the study conducted in Brazil. Also in this chapter, following the Brazil relationshipsfor certain components, are the relationships that are not differentiatedby the different studies or data sources and which are used regardlessof which of the four options is chosen. Relationshipsdeveloped by British Transport and Road Research Laboratory (TRRL) from studies in Kenya and the Caribbean, and by the Central Road Research Institute of New Delhi, (CRRI) from research in India, are presented in Chapter 6. 5.1.2 Choice of Relationships The principal set of relationshipsare those derived from the Brazil study by GEIPOT, the Texas Research and Development Foundation, and the World Bank. The alternative relationshipsare those from the Kenya and Caribbean studies by the British Transport and Road Research Laboratory, and those from the India study by the Central Road Research Institute-New Delhi. For brevity, the relationshipsderived from the Brazil studies are referred to as the Brazil relationships, and the alternative sets of relationships are referred to as the Kenya, Caribbean, and India relationships. Chapter 1 has already provided some discussion of the various sets of relationships,and certain further salient features are discussed here. For a more comprehensivediscussionof the four studies, includinga comparison of the resulting relationships, the reader is referred to Chesher and Harrison (1987).

VEHICLEOPERATINGCOST SUBMODEL

151

Appendix5A providescomparative information for the four studies concerning coverage of vehicle types (Table 5A.1) and the required informationfor utilizing the differentrelationships with respect to vehicle characteristics(Table 5A.2) and road characteristics(Table 5A.3). By examiningthesetablesone can gain some furtherappreciation of the differencesin the varioussetsof relationships. Vehicletypes. The vehicletypescoveredby the differentstudies differedsignificantly.In the Caribbeanstudy,only four categorieswere distinguished, and therewere no heavyor even medium trucksor buses. At the other extreme,the Brazil study used ten categories,includingthree classesof cars and five of trucks. Table 5A.L lists the characteristics of the differentvehicletypes includedin each of the four studies. Model formulation.The studiesalso differedconsiderably in the degreeof detailin the data and in the methodsof analysisand formulation used. The relationsusingthe most detailedsets of explanatory variables are those from Brazil. In that study the formulationof relationsfor vehiclespeed,fuel consumption, and truckand bus tire wear were based on generallyacceptedprinciplesof vehiclemechanicsand driver behavior. With that theoreticalbasis and the explicit accounting for many explanatoryvariables,the relationsshouldbe applicablein principleto many situationswhere combinations of conditionsdifferfrom thoseobserved in the field studiesin Brazil,althoughit must alwaysbe recognizedthat differences in economiccircumstances, not all of whichare encapsulated in the models,can affectthe relationships. The other studies used fewer explanatoryvariablesand relied more on statisticalcorrelationof associatedvariablesthrough linear multiple regression. This yielded simpler relationswhile implicitly assumingthat some of the detailsaccountedfor in the Brazilformulation couldbe safelyignored,either as being insignificant or as being highly correlatedwith,and thereforeaccountedfor by, variationsin the explicit variables. The different input data requirementsand options of the differentsets of relationships are indicatedin Tables 5A.2 and 5A.3. Comparedwith the other three sets, the Brazil relationsuse many more explanatoryvariables. Wherever possible the user should obtain local informationon these variables,as it will better calibratethe model to local conditions. For many of them, however,defaultvaluesbased on the empiricalstudywill be automatically suppliedif inputsare not entered, as indicatedin the tables by the letter "O" for "optional." For these items the user does not have to provideinputswhere there is not better localinformation or other basis for usingdiffierent values;in such case, however, the user should be aware that he is employingpotentially inaccurateassumptions. Since these parametersare already implicitly assumedin the Kenya, Caribbeanand India relationships, the user has no alternativebut to employthe same assumptions used in the originalstudy regardlessof whetherbetter localinformationis available-- and similar cautionsapply a fortiori.

152

VEHICLEOPERATINGCOST SUBMODEL

Other considerations. In considering all the various factors-- physical,economic,and behavioral-- which may affect vehicle operatingcost relationships, it is clear that the circumstances of India make it somewhatuniqueamong the four countriesstudied. Vehicledesigns are of oldervintagewith lowerhorsepower/weight ratios. Road and traffic flow conditions are much different, with generally poorer road characteristics and significanttraffic-interference even under nominally free-flowing conditions, and Indian drivers have adapted behavior accordingly. Even more striking is the contrast in general economic conditions,particularlythe relative costs of capital and labor and restrictions in the availability of new vehicles. These differenteconomic circumstancesundoubtedlyconstrain,and probably dominate, decisions concerningvehicle maintenanceand replacement. Circumstancesforce vehicleownersto maintainoldervehicles(withmuch higherexpenditures on laborand lowerexpenditures on sparepartsdue to the cheapnessof labor) for much longerperiods than they do in the other countries. Since for models, vehiclemaintenancecostswe do not yet have adequatetheoretical and are forced to rely on correlationrather than mechanistic-behavioral type models for this component,particularcare should be taken in local calibrationof this component,and under Indiantype conditionsthe India relationships may be preferred. Further researchis planned to compare predictiveabilitiesof the Brazilmodels calibratedfor Indian conditions againstthe CRRI Indiamodels. Conclusions on the choice of vehicle operating costs relationships.As indicatedin Chapter 1, because of their more general form and more extensiveempiricalvalidation,the user is advisednormally to use the Brazil relationshipswith as much local calibrationas possible. (SeeChapter13, Watanatadaet al., 1987,for guidanceon local calibration.) The principal exceptionswould be for applicationsin the Caribbean, Kenya and particularly India, where the alternative relationships were themselvesstatistically estimated. In these cases it is possible that local variationsin economic circumstances,traffic conditionsand driverbehaviormay be bettercapturedin the relationships estimatedfrom the substantiallocal researchstudies than by the more generalmodel formsdrawn from Braziland locallycalibrated. It should always be borne in mind, however,that the ultimate concern is to predict accuratelythe changes (or first differences)in vehicleoperatingcostswith respectto changes in road characteristics, rather than total operating costs over averaged conditions. Cost differentials due to differentroad conditionsare expectedto vary much less than total vehicleoperatingcosts in responseto differenteconomic environments (Chesherand Harrison,1987). At the presentstage of the research,we are unableto give more specificguidance,except to recommendthat an HDM model user in India, Kenya or the Caribbeanshouldapply the locallycalibratedBrazilmodelsas and compare the resultsto weli as the locallyestablishedrelationships gain a broader insight into probable effects of different road characteristics.

VEHICLEOPERATINGCOST SUBMODEL

153

5.2 THE BRAZILRELATIONSHIPS The Brazil portion of the vehicle operating cost (v.o.c.) submodel is made up of relationshipsbased on the Brazil-UNDPstudy (GEIPOT,1982; Chesherand Harrison,1985;Watanatadaet al., 1985). The vehiclesobservedin this studywere classifiedin the ten groupsshownin Table 5A.1 (in Appendix5A), where the representative characteristics of each vehicletype are tabulated.The formsof the relationsfor predicting vehiclespeed,fuel consumption, and bus and truck tire wear are based on principlesof vehiclemechanicsand driver behavior (Watanatada, et al., 1987),while thosefor predictingmaintenancepartsand labor requirements are based on econometricanalysis of user survey data (Chesher and Harrison,1987). These relationsare explainedin the followingsections. 5.2.1

VehicleSpeeds

The predictionof vehicle speeds is based on what may be described as an aggregateprobabilisticlimiting velocity approach to steady-statespeed prediction. The term aggregateconnotes that the predictionmethod works with aggregatedescriptorsof road geometryand surfaceconditionratherthan with detailedinformation about the roadway. The expressionsteady-stateimplies that transitionaleffects,that is, speed-change cyclesalong the roadway,are not modeled. The approachis termed a probabilisticlimitingvelocityapproach because the predicted speed is a probabilistic minimum of a numberof limitingor constraining speeds. These constrainingspeeds are functionsof such factors as characteristics of the vehicle (e.g.,enginepower,braking capacity)and of the roadway(e.g.,verticalgradient,roughness).Here we give a brief summarystatementof the model; for a more detailedpresentationof the methodology and its validationthe readeris referredto Chapters3 through 8 of Watanatadaet al. (1987). For the purpose of predicting the average vehicle speed for a round trip, it has proved satisfactory to represent the given roadway of various vertical and horizontalalignmentsby two idealizedhomogeneous segments-- one of positivegrade (uphill)and the other of negativegrade (downhill),both having the same length, roughness,average horizontal curvature,and averageriseplus fall. The steady-state speed for each type of vehicleis predictedfor each of these hypotheticalroad segments as a function of the road characteristics and the attributesof the vehicles. Then the averageround trip speed is computedto correspondto the space-meanspeed over the two segments(i.e.,the roundtrip distancedividedby the roundtrip time). The information on the roadwayneededfor the application of the speed predictionmethod is: the surfacetype cf the roadway,the average roughness, an aggregatemeasureof the verticalgradientof the roadway,an aggregatemeasure of its horizontalcurvatureand an average value of superelevation.The roughnessvalue is the averageof valuesmeasuredover short homogeneous subsections of the actualroadway. In HDM-IIIthis value is internallycomputedas describedin Chapter4. The aggregatemeasures of verticaland horizontalalignmentare definedas follows:

154

VEHICLEOPERATINGCOST SUBMODEL

The gradient is expressedas the average rise plus fall, RF, which is defined as the sum of the absolutevalues, in meters, of all ascents and all descentsalong a section,divided by the length of the sectionin kilometers. (This is numericallyequal to ten times the mean in Figure5.1. absolutegradientin percent.) The conceptis illustrated The averagehorizontalcurvature,C, is definedas the sum of the absolutevalues of angulardeviations(in degrees)of successivetangent linesof the roadalignmentwhen travelingin one direction,dividedby the section length in km. This concept is also illustratedin Figure 5.1. Note that the denominatoris the arc length(not the chord length)of the section. The average superelevation,SP, is defined as the weighted average of superelevations(in percent) of the curvy sections of the roadway,the weights being the proportionsof the lengths of the curvy sections. Note that the verticaland horizontalmeasuresare independent of directionalong the road section. The predictionof a vehicle'ssteady-state speedon a given road segmentmakes use of a set of limiting (or "constraining") velocities, corresponding to severaldifferentfactorsthat tend to limit the speed. We first define the variables,then give a diagrammatic discussion,and, finally,a formalmathematical statementof the model. Variables velocities,which are explainedin subsequent The constraining sections,are (all in meters/sec): VDRIVE = the limitingspeedbasedon verticalgradientand enginepower, VBRAKE = the limitingspeedbasedon verticalgradientand brakingcapacity, VCURVE = the limitingspeeddeterminedby road curvature, VROUGH = the limitingspeedbasedon road roughnessand associatedride severity,and VDESIR = the desiredspeedin the absenceof other constraints, economic,safety, and other based on psychological, considerations. speeds,viz. VDRIVEand VBRAKE,have The two gravity-related constraining a differentvalues for the uphilland the downhillsegmentsrepresenting speedshas the same given roadway. Each of the other three constraining value for both segments. Diagrammaticexposition. The three plots in Figure 5.2 speedon illustrate the constraining speedsand the resultingsteady-state

155

VEHICLEOPERATINGCOST SUBMODEL

of road rise plus fall and horizontalcurvature Figure5.1: Illustration (a) VerticalProfileof the roadsection

AB

R1 + R2 + R3 + F1 + F2

Average rise plus fall, RF=

(meters) (km)

Lab

(b) Plan view of the roadsection

B

Average horizontal curvature,C

=

1+

3

Lab

4

(degrees) (km)

156

VEHICLEOPERATINGCOST SUBMODEL

a segmentfor a heavytruck carryinga net load of 6,000kg, and traversing a paved segment. Each of the plots shows the responseof the steady-state speedas one of the three speed-influencing factors is variedholdingthe other two factorsconstant. Figure 5.2(a) shows the effect of surface irregularityon the steady-statespeed for a straightand downward-sloping segment. The steady-state speed (V) and the constraining speedbased on road roughness (VROUGH)are graphedusing continuouslinesand the other limitingspeeds usingbrokenlines. At any givenpointon the roughnessaxis,the limiting speed with the lowestvalue may be consideredthe "binding"speed as it exercisesthe predominantinfluenceon the resultingsteady-state speed at that point;other limitingspeeds have only marginaleffects. The higher the value of a limitingspeed, the more marginal its influenceon the predictedsteady-state speed. In this instance,over the lower range of road roughness(QI under about83), the desiredspeed (VDESIR)becomesthe binding speed. It may also be noted that roughnesshas no influenceon VDESIR and VCURVE, but has a slight influenceon the gravity-related constrainingspeeds, VDRIVE and VBRAKE through the rolling resistance coefficient. The effect of verticalalignmenton the steady-state speed for slightlycurvedand low roughnesssegmentsis shown in Figure5.2(b). The two constraining speedsmost closelyassociatedwith roadgradient,namely, VDRIVE and VBRAKE,as well as steady-statespeed, V, are shown using continuouslines. In this figure,threedifferentconstraining speedsare binding over the +10 percent range of the road gradient. On the one extreme,for negativegrades steeperthan 7.5 percent,the limitingspeed based on brakingcapacity(VBRAKE)is binding. At the oppositeend, the limitingspeedbased on enginepower (VDRIVE)becomesdominantfor slightly negative (-0.2 percent)and positivegradients. In the mid-rangethe steady-state speedis determinedby the desiredspeed (VDESIR). It may be noted that for slightlynegativeand positivegrades,the valueof VBRAKE is infinity,that is, it has no influenceon the resultingsteady-state speed over this range,while road gradienthas no influenceon VDESIR, VCURVE,and VROUGH. Figure 5.2(c) shows the effect of horizontalalignmenton the steady-statespeed for smooth and downward-slopingsegments. The steady-statespeed and the limitingspeed determinedby road curvature (VCURVE)are plottedusingcontinuouslines. In this case two constraining speeds are binding. The desired speed is the primary determinantover gentlecurvature(up to about250 degrees/km), beyondwhich the curve speed constraintprevails. VDESIR,VBRAKE,VDRIVEand VROUGHare all independent of horizontalalignment. Mathematicalsummary. Using the respectivevalues of the five limitingspeedsfor each road segment,the predictedsteady-state speedfor the segment is computed. The theory behind these computationsinvolves treatingeach of the limitingspeedsfor a segmentas a randomvariableand

157

VEHICLEOPERATINGCOST SUBMODEL

speed factorson predictedsteady-state Figure5.2: Effectof constraining (a) Surfaceirregularity

Speed (n/s) 300-

,~~~~~~~~~~~~~~~~~~~~~~~~~~~~

-

..

..

-..

-

-

-

..

- -

. - -

VCJRVF

250

200

VDRIVE

100 VDESIR

=-

V 50

n 125

109

75

50

25

0

0U5gtHss (Qll

(b) Verticalalignment

Speed (k,1h) 300

- --- -~ -O -__- ~~~~~~250 ~~~~~

~

~~~

r

200

100

100

50

10 __

e

2

-6

0

2

_

a

4_

IC

OldUierd%)Yo

(c) Horizontalalignment Speed (kelh) -

~~~~~300 VBAKEF P

u~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

XVCOOVE 200 UGH

200VR 150

100

=

N_

50

~

0 0

r-100

v------_ 200

300

400

500

600

-

-

700

ao

9oo

CuFvo,tre (deg-ee/km)

Source:

Bank highwayreseach project data Analysis of Brazil-UNDP-World 1987). al., et Watanatada 1982; (GEIPOT,

1000

VEHICLEOPERATINGCOST SUBMODEL

158

the resultingsteady-statespeed predictionas the average value of the minimum of these random variables. The probabilitymodel used is the Weibull distributionwhich is one of the standard "extreme value" distributions.The formulasare:

V

E°

-

1

u

1

1

VCURVE

VBRAKEu

VDRIVEu

Vd

1

VDESIR

VROUGH

-

{1

VDRIVEd

+

1

+

VBRAKEd

1

1

VCURVE

VROUGH

+

VDESIR

In the above formulas,the subscriptsu and d stand for the uphilland the downhillsegment,respectively.It may be noted that only the two constrainingvelocitiesinvolvingverticalgradientcarry these subscripts. The coefficient m determinesthe shape of the assumedWeibulldistribution and is a member of the set of parametersestimatedfor each type of of the vehicle. As the estimationinvolveda logarithmictransformation variables,the predictionformulasincludethe bias correctionfactor E°, equal to exp(O.5 02) where o is an estimateof the standarderror of residualsin the estimation.1 The numericalvalues of i and E° as estimatedfrom the Brazildata set and used in HDM are given in Table 5.1. From the uphill and downhill speeds, Vu and Vd, the average speedfor a roundtrip,usingboth segments,is calculatedas follows: s

where

(3.6)(2) LGTH LGTH LGTH

7.2 1

1

LGTH = Vu =

the lengthof the roadwayin km; the predictedvehiclespeedfor the uphillsedgmentin m/s; Vd = the predictedvehiclespeed for the downhillsegmentin m/s; 3.6 = conversionfactorfromm/s to km/h.

1 An explanationof the correctionof biases arising from non-linear of variablesin estimationis given in Chesher(1982). transformation

VEHICLEOPERATINGCOST SUBMODEL

159

Table 5.1: Parameterand defaultvaluesfor speeld prediction

Vehicletype Parameters

'iml1 car

Mediun Large Utili-

car

car

ty

Light truck

Bus

Mediun/Articu-

heavy lated truck truck 0.85 0.63

Dragcoefficient, CD

0.45

0.50

0.45

0.46

0.65

gas 0.70

Frontalarea, AR(m')

1.80

2.08

2.20 2.72

6.30

3.25

3.25

2.3

2.0

2.0

4.5/6.0213.0

diesel 0.70

5.20

5.75

Payload, LED (tons)

0

0

HPORIVE (netric

30.0

70.0

85.0 40.0

100.0

80.0

60.0

100.0 210.0

17.0

21.0

27.0

160.0

100.0

100.0

250.0 500.0

0

0.3

hp)"

WIRI (mretric hp)* Paved roads

30.0

0.268 0.268 0.268 0.221

0.233

0.253

0.253

0.292 0.170

FRATIO ef (ton-') lUpaved 0.124 0.124 0.124 0.117 roads

0.095

0.099

0.099

O.OB70.040

Paved roads FRATIO 1' { (ton') tUkaved roads mRmtX (mn(s)' Paved roads

0

0

0

0

0

0

0

0

0

0

0

0

212.8

194.0

194.0

259.7 259.7 259.7 239.7

0.0128 0.0128 0.00940.0023 0

0

177.7 130.9

98.3

98.3

98.3

94.9

93.4

81.6

81.6

88.8

VDESIR 0{ (kWh) Urpaved 82.2 roads

82.2

82.2

76.3

69.4

71.9

71.9

72.1 49.6

Bw

0.74

0 E

0.74

0.74

0.74

84.1

0.78

0.73

0.73

0.73

0.274 0.274 0.274 0.306

0.273

0.304

0.304

0.310 0.244

M1.003 1.003 1.003 1.004

1.012

1.008

1.008

1.013 1.018

0.73

Excludesthe weightof the twodrivers (150kg) whichis already includedin the tare weight. payloadis 4.5 tons for a nediuntruck ard6.0 tons for a heavytruck. 3These termsare defined in the followingdiscussionin the text. 2The

Source: Watanatada et al. (1987).

160

VEHICLEOPERATINGCOST SUBMODEL

Note that the lengthterm cancelsout and the averagepredictedspeedover of its length. the roadwayis independent Figures5.3 and 5.4 show predictedaveragespeedas a functionof highwaycharacteristics for a half-ladenheavytruckover pavedand unpaved roads,respectively. VDRIVE VDRIVE,the speed for a given road segmentas limitedby power and gradient,is arrivedat from the hypothesisthat the vehicleis driven at steady-state speed on a smooth,straightroad employinga high levelof power calledthe "useddrivingpower",HPDRIVE. The used powerhas been foundgenerallyto be less than the ratedpower of the engine,especially for gasoline engined vehicles. Reasons for the differenceare largely behavioral(unwillingness of driversto use full power)and perhapspartly mechanical (operation at less than rated rpm, power lost in the transmission and used by accessories).HPDRIVEhas been estimatedfrom the Brazil speed observations, and the resultsfor a number of vehicletypes are includedin Table 5.1.2 VDRIVEis relatedto HPDRIVEand the gradientthroughthe balance of forcesin the absenceof acceleration: jDrive

! force

Rolling

+

resistance2

Grade

+

Lresistance

+

Air

resistance

where the various terms, all measured in newtons, are given by the followingexpressions: Drive force = 736 HPDRIVE VDRIVE Rollingresistance= g 1000GVW CR Grade resistance= g 1000GVW GR Air resistance= 0.5 RHO CD AR VDRIVE where

= = = =

the numberof watts in one metrichp; the grossvehicleweight,in tons; constant,equalto 9.81 m/s2; the gravitational coefficient of rolling the dimensionless resistance; GR = the verticalgradientexpressedas a fraction; RHO = the mass densityof air, in kg/m3; drag coefficient of CD = the dimensionless aerodynamic or take the vehicle,which may be user-specified on a defaultvalueas shown in Table 5.1; and 736 GVW g CR

2 Guidelinesfor calibrating HPDRIVE,as well as HPBRAKEand variousother are given in Chapter13 of Watanatadaet al., 1987. parameters,

161

VEHICLEOPERATINGCOST SUBMODEL

half-ladenheavy Figure5.3: Speedas a functionof road characteristics: truck,paved road Speed (kmlh) 70

(a) Roughness 50

40

SteeP-CurVY--

20

10

125

100

75

50

25

0

[0) RoughnresstC (km/h)

Speea 70

(b) Rise plusfall

60

SO ------

~---

res;

iz

Smooth-cu,ry

-

----

------

--

Rough-curvy

0

-

30-

20

10

50

40

30

20

10

0

70

e0

S0

(b) Rlse plus toll fmktm) Speed (km/h) 70

(c) Curvature

60

-------

ve' -------

40

--30 Smooth-steep

--. =---.-.---- ---.--.

=_-_-_-=

---.--

20

10

°

.

0

7 --------

1OO

200

300

400

500

600

700

800

900

(C) Cv,votrrs (degreelkm)

Source:

Analysis of Brazil-UNDP-World Bank highway research project data (GEIPOT,1982;Watanatada et al., 1987).

1000

162

VEHICLE OPERATING COST SUBMODEL

Figure 5.4: Speed as a function of road characteristics: half-laden heavy truck, unpaved road Speed[kmlh) 70

60

(a) Roughness 50

40

--

-------------

30

__-_

----

_-_---

_,--

20

10

0

50

100

150 Rouwh.s

210

250

(4)

Speed (kn"h) 70

(b) Rise plus fall

60 50

40.

30

Ruhbgn,l~~-_ Rough

~-=--------

cunrs

_---_------

20

10

I_ I0

0

0

20

30

40

__ _ __-1 50

_

1_-_ 60

1-....-.1 70

80

Rlseplw fal (nIk,, 3Peed [krnih) 70

(c)

Curvature

60

40 30 _

&fOt

s__

__

__e_

Ro.gh-leveI 20 0050-sleep

40

O.I.

0

I.I.,.,. .,.,. .,

100

200

300

400

500

oO0

700

500

9700

4000

CunvOlor(d.uemr)

Source-

Analysisof Brazil-UNDP-World Bank highwayresearchproject data (GEIPOT,1982;Watanatadaet al., 1987).

VEHICLEOPERATINGCOST SUBMODEL

163

AR = the projectedfrontalarea of the vehicle,in m2, which may be user-specified or take on a default valueas shownin Table5.1. Substituting these valuesin the force balanceyields a cubicequationin VDRIVE. It may be shownthatwhen the left hand term of the forcebalance, drive force, is positivethe cubic equationalways has a singlepositive root. Thus, given valuesof HPDRIVEand the otlher variableslistedabove, a unique VDRIVE value may be computedfor a given vehicle type and road segment. The absolutevalue of the verticalgradient,GR, dependson the average rise plus fall, RF, for the roadwayand the sign of the gradient dependson whetherit is on the uphillor downhillsegment. Thus, solving the cubicequationwith GR =

+ RF 1000

would yield the valuefor VDRIVEu,and solvingit with GR =

_ RF 1000

would yield the valuefor VDRIVEd. The value of the gross vehicleweight may be specifiedby the useras an option. Alternatively, it is computedendogenously as follows:

GVW= TARE + LOAD where

TARE = LOAD

5

the vehicle tare weight, in tons, as given in Table 5A.1;and the vehicle payload, in tons, which may be userspecifiedor take on a defaultvalue as shown in Table 5.1.

The rolling resistance coefficient, CR, has been found empirically to be a functionof road roughness,as givenby:

CR = 10. 0 2 18 + 0.0000467 QI L0.0139 + 0.0000198 QI -

where

for cars and utilities for busesand trucks

QI = the standardroad roughnessmeasureused in the BrazilUNDP study,in Q1 units.

The mass densityof air, in kilogramsper cubic meter,' RHO, is a function of altitude,givenby (St.John et al., 1978): RHO = 1.225 [1 - 2.26 x 10-5 A]4 . 2 5 5

164 where

VEHICLEOPERATINGCOST SUBMODEL A

=

the road altitude,definedas the elevationof the road sectionabovethe mean sea level,in meters.

VBRAKE VBRAKE,the speed for a given road segmentas limitedby braking capacityand gradient,is arrivedat using the concept of "used braking power," which is a positive quantity,denoted by HPBRAKE, in metric horsepowerunits. The assumptionunderlyingthe concept is that the steady-state speedattainedon a long,smooth,straightdownhillsectionis limited by the braking capacity,HPBRAKE,which depends on the vehicle type. On an uphill segment the braking capacity constraintdoes not apply. Conceptually, when the brakesare not used the value of VBRAKEis infinityand 1/VBRAKEis zero. More generally,the constraintis not applicablewheneverpositiveenginepoweris neededto impartmotionto the vehicle. This would be the case on a downhillsegment if the rolling resistanceis greater in absolutevalue than the gradient-resistance; in symbols,whenverCR > RF/1,000. When the constraintapplies,VBRAKEand HPBRAKEare related,as before, through the force balance. However,since the braking capacity constraintis likelyto becomebindingonly for steep negativegradeswith low steady-statespeeds,the air resistanceterm may be ignoredwithout significant error. Thus the forcebalancemay be solvedas a firstdegree equationin VBRAKE. The above remarksare summarizedin theseexpressions: VBRAKEU VBRAKEd

736 HPBRAKE

if CR > RF/1000 if CR < RF/1000.

g 1000GVW (CR - RF/1000)

HPBRAKEwas estimatedas a parameterusingthe speedsobservedin the Brazil study. These values, appropriately modified,are given in Table 5.1 and may be used as defaults. Alternatively, the user has the optionof substituting suitablevaluesfor a givenpracticalapplication. VCURVE The curvature-limited speed, VCURVE, is arrived at from the postulatethat when curvatureis significantthe speed is limitedby the tendencyof the wheels to skid. A good indicatorof the tendencyto skid is the ratio of the side force on the vehicle to the normal force. The used valueof this ratiodependson the vehicletype and the surfacetype. It is called "perceivedfrictionratio",and is denotedby FRATIO. With some simplifications based on the facts that superelevation, SP, is small and that higher powers of small magnitudesare negligible,the ratio of forcesis expressedby:

165

VEHICLEOPERATINGCOST SUBMODEL 2 FRATIO = VCURVE g RC

whence

VCURVE =

SP

100

i(FRATIO + SP/100) g RC.

The value of FRATIOhas been derivedas a functionof the payload of the vehicle:

FRATIO = max(O.02,FRATIOo - FRATIO, LOAD) where FRATIOO and FRATIO 1 are parameterswhich depend on the vehicle type as well as the surfacetypeof the roadway. The valuesestimatedfrom the Brazil data set are given in Table 5.1 and may be used as defaults. Optionally,the user may calibratethe parametersusing the guidelines given in Ch. 13, Watanatadaet al. (1987). The radius of curvature,RC, is a simple functionof average horizontalcurvature:

RC iT

180,000 max(18/T,C)

If the user does not supply values for superelevation, SP, the model computesvaluesfrom the followingformulas: p

=r

0-012C for paved roads L0.017C for unpavedroads.

to suggesteddesignstandardsfor typical These formulasare approximations speedson these surfaces,and may be unrealisticfor actual conditionsin that whereverpossiblethe particularcases. Therefore,it is recommended user providevaluesbased on actualroad geometry. VROUGH VROUGH is the limiting speed correspondingto the "maximum allowable"suspensionmotion of the vehicle,which governsride severity. The ride suspension motion is measured by the rate of absolute displacementsof the vehicle rear axle relativeto the body, which, in turn, is related to vehicle speed and road roughnessby the following relationship: ARV = 0.0882V QI where

ARV = the average rectifiedvelocityof suspensionmotion of vehicletravellingat speed the standardOpala-Maysmeter V, in mm/s; V

= the vehiclespeed,in m/s; and

0.0882 = a constantfor unitconversion.

166

VEHICLEOPERATINGCOST SUBMODEL

The constrainingspeed due to ride severity,VROUGH,is assumed to be governedby the maximumallowableARV, calledARVMAX,as follows: VROUGH=

ARVMAX 0.0882QI

where ARVMAX is an estimatedparameter;estimatesof ARVMAX for various vehicleclassesare listedin Table5.1. VDESIR Finally,VDESIR is the desiredspeed,i.e., the speedat which a -vehicleis assumedto be operatedin the absenceof the constraints based on the verticalgrade, curvature,and ride severity. The desired speed resultsfrom the driver'sresponseto psychological, safety,economic,and other considerations. For each surface type (i.e., paved or unpaved), VDESIR was assumed to be constantfor each vehicletype in the original Brazilstudy. The originallyestimatedvaluesare listed in Table 5.1 as VDESIRo (in km/h). For narrow roads,however,VDESIR is assumed to be lower, and the followingmodified form, based on Indian data, has been adoptedfor use in HDM-III. VDESIRoB /3.6 if effectivenumberof lanesis 1.

VDESIR=

{

w

VDESIR 0 /3.6

where

if effectivenumberof lanesis more than 1 (thatis, 1.5 or 2)

VDESIRO= the unmodifiedvalueof VDESIRobtainedin the Brazil-UNDP study,in km/h; Bw = dimensionless widthparameterfor adjusting desiredspeed.

In using the Brazilspeed relationships the recomendedrangesof the input variablesshown in Table 5.2 should be observed to avoid extrapolating too far outsidethe rangeof the research.Local calibration of the model is alwaysdesirable,especiallyfor the VDESIRO,HPDRIVEand HPBRAKEparameters. Guidelinesfor adaptingmodel parametersare given in Chapter13 of Watanatadaet al. (1987). 5.2.2 Fuel Consumption Approachto fuel prediction The fuel consumption prediction model makes use of the conceptof the time-rateof fuel consumption or unit fuel consumption, denotedby UFC (in ml/s). Basic principlesof intervalcombustionengine suggestthat, under idealizedenvironmental conditions,the unit fuel consumptionis a functionof power output (HP, in metric hp) and engine speed (RPM, in rpm). Symbolically, we may write:

VEHICLEOPERATINGCOST SUBMODEL

167

UFC = UFC (HP,RPM). While it is not possibleto deduce the preciseform of the UFC function from theoretical considerations, the functionis knownto be convexin both arguments. In the Brazil study, a quadraticform was employed,with separate coefficientsfor positive and negaltivepower regimes. The estimated coefficientsare given in Table 5.3a following the formal presentation of the model. As in predictingvehiclespeed,it has been foundsatisfactory to employ the idealizedhomogeneousuphill and dlownhill road segmentsfor predictingfuel consumption.The power outputmay then be computedusing the respectivepredictedspeedsand the characteristics of the vehiclesand the homogeneous segments. In the Brazilexperimental study,it was found that satisfactory predictionof fuel consumptioncould be obtained by using a constant nominalenginespeed insteadof actual used engine speed. The values of nominalenginespeed (denotedby CRPM),as calibratedusing the validation data from the Brazilstudy,are used as defaultsin the fuelmodel. These are given in Table5.3a. The usermay supplyindividualvalues. Since the test vehiclesused in the Brazil study are makes and models typical in the mid-1970s,a "relativeenergy-efficiency factor," denotedby a,, has been introducedto allow thiemodel-userto incorporate changesin vehicletechnology.This factorhas a defaultvalue of 1.0 for makes and models close to the ones employedin the Brazilstudy. The user may specifylower valuesfor newer,more fuel-efficient makes and models. Some typicalvaluesare presentedin Table 5.3b. Finally, in order to account for the differences between experimental conditionsand real life drivingconditions,"fuel adjustment factors,"denoted by a2 , have been introduced. The valuesdeterminedby calibratingthe mechanisticfuel predictionmodielsto the road user cost surveydata are used as defaultsin HDM-III. They are 1.16 for cars and utilities,and 1.15 for buses and trucks. The user may specifyown values for a2. Full detailsregardingthe estimationand validationof the fuel model may be found in Chapter 9 and 10 of Watanatadaet al. (1987). Guidelinesfor localadaptationof CRPM,al. and a2 parametersmay be found in Chapter14 of the samework. Formalpresentation For a vehicle operating on any road section of specified geometric alignment,the average round trip fuel consumption,FL, in liters/1,000 vehicle-kmis given by:

FL = 500 a, a2

UFC + UFCd Vu

Vd

168

VEHICLEOPERATINGCOST SUBMODEL

where

UFCu = the predictedunit fuel consumption for the uphill segment,in ml/s; UFCd = the predictedunit fuel consumption for the downhill segment,in ml/s; and

a,, a2 are as explained earlier.

Table 5.2a: Recommendedrangeof variablesfor speed,fuel consumption and tirewear prediction:Brazilrelationships

Variable

Units

Recomended range

Road characteristics Altitude,A Rise plus fall,RF Horizontalcurvature', C Carriageway width,W Superelevation, SP Roughness,QI

m m/km degrees/km m % QI

0 0 0 3.0 0 15 -

5,000 120 1,200 8.0 20 300

0.8 1.1 7.5 3.0 5.0 6.0 13.0-

2.0 2.5 12.0 6.5 16.0 22.0 45.0

Vehiclefleet characteristics Gross vehicleweight,GVW Cars Utilities Largebuses Lighttrucks Mediumtrucks Heavytrucks Articulated trucks

Tons

Payload,LOAD

Tons

Cars

Utilities Large buses Light trucks Mediumtrucks Heavy trucks Articulated trucks See text on tire wear prediction. Source: Watanatadaet al. (1987).

0 0 0 0 0 0 0

-

0.4

-

1.4 4.5 3.5 11.0 16.0 32.0

VEHICLEOPERATINGCOST SUBMODEL

169

Table 5.2b: Recommendedrangeof variablesfor -speed, fuel consumption and tirewear prediction:Brazilrelationships Variable

Units

Recommended range

Vehiclefleetcharacteristics Maximumused drivingpower, HPDRIVE Cars Utilities Largebuses Lighttrucks Mediumtrucks Heavytrucks Articulatedtrucks Maximumused brakingpower, HPBRAKE Cars Utilities Largebuses Light trucks Mediumtrucks Heavy trucks Articulatedtrucks Projectedfrontalarea,AR Cars Utilities Largebuses Light trucks Mediumtrucks Heavy trucks Articulated trucks Aerodynamic drag coefficient, CD Wearablerubbervolume per tire,VOL Largebuses Lighttrucks Mediumtrucks Heavy trucks Articulatedtrucks Source: Watanatadaet al. (1987).

Metrichp 25 35 80 50 80 80 180 -

100 100 120 100 120 120 230

15 20 140 90 230 230 460 -

30 35 180 120 270 270 540

1.5 2.3 6.0 3.0 5.0 5.0 5.5 -

2.4 3.2 7.0 5.0 8.0 8.0 10.0

Metrichp

m2

Dimensionless

0.3 - 1.0

3 dmi

5.6 2.0 6.5 6.3 6.0 -

8.0 3.5 9.3 8.8 8.5

170

VEHICLEOPERATINGCOST SUBMODEL

The predictedunit fuel consumptionis given separatelyfor the uphilland downhillroad segments,as follows:

UFCU= [UFCo + as HPu + a4 HPu CRPM+ a, HP2 u

] x 10-5

~~~~uuu

[UFC0 + a. HPd + a4 HPd CRPM + as HP2] x 105 if HPd>O UFCd =

[UFCO+ a6 HPd + a, HP2] x 10 5

if NHo< HPd< 0

[UFCO+

if HPd < NH,

where UFCo=

a.

a6

+

NH, + a, NH2] x 10O5

a, CRPM + a2 CRPM2;

CRPM = the calibratedengine speed, in revolutionsper minute (defaultvalues of CRPM for the representativevehicles aregiven in Table 5.4, but the user may supply different values);and HPu, HPd = the vehiclepowerson the uphilland downhillroad segments,in metrichp, given by: HP, = [(1000CR + RF) GVW g Vu + 0.5 RHO CD AR Vu]/736 HPd = [(1000CR - RF) GVW g Vd + 0.5 RHO CD AR V;]/736 and ao through a, and NHO are the parametersof the mechanisticfuel predictionmodels estimatedusing the data from controlledexperiments. Their valuesare given in Table 5.3a. the In predictingfuel consumption usingthe Brazilrelationships recommendedrange of the input variablesshown in Table 5.2 should be observed. as a function Figures5.5 and 5.6 show predictedfuel consumption of highway characteristics for a half-ladenheavy truck over paved and unpaved roads, respectively. These curves have been drawn using the default values. Note that the fuel consumptioncurves incorporatethe associated changes in speed induced by variation of the road characteristics. 5.2.3 Tire Wear The HDM model employs two relationshipsobtained in the Brazil-UNDPstudy for predictingtire wear: one for cars and utilities, and another for trucks and buses. Because the tire data for cars and utilities obtained in the Brazil-UNDP study were inadequate, the relationshipconstructedwith the data for these vehicle types is

171

VEHICLEOPERATINGCOST SUBMODEL Table5.3a: Parametervaluesfor fuel consumption prediction

Lighttruck Medium/ArticuVehiheavy lated Small Medium Large Utility Large cle bus gats diesel truck truck type car car car CRPM 3,500 (rpm) al

3,000

3,300

3,300

2,300

31,300 2,600

1,800

1,700

-8,201 23,453-23,705 6,014 -7,276-48,381-41,803 -22,955-30,559

a1

33.4

40.6

100.8

37.6

a2

0

0.01214

0

0

a.

5,630

7,775

2,784

3,846

a4

0

0

0.938

1.398

a.

0

0

13.91

0

a6

4,460

6,552

4,590

3,604

a7

0

0

0

-10

-12

-15

NHt Source:

63.5 12;7.1 71.6 0

0

4,323 5,867

0

95.0 0

156.1 0

5,129

3,758

4,002

0

0

0

0

19.12

4.41

2,479 3,8343 2,653

2,394

4,435

0

11.50

0

0

13.76

26.08

-12

-50

-50

-30

-85

-85

0

0

8.64 43.70

Watanatadaet al. (1987).

data for trucks relativelycrude. On the other hand the more comprehensive principles and busespermitteda more elaborateanalysisbasedon mechanistic and idealizeduphill and downhill road segmentsas in the speed and fuel relationships.Detaileddescriptionof these analysesare found in Chapter for computingthe numberof 11 of Watanatadaet al., 1987. The relationships TC, for the equivalentnew tires consumed per 1,000 vehicle-kilometers, variousvehicletypesare givenas follows: 1. Passengercars (small,mediumand large)and utilities: NT (0.0114+ 0.000137QI)

for 0 < QI < 200

0.0388NT

for QI > 200

TC = 2. Light (gasolineand diesel),medium,helavy trucksand largebuses: and articulated

TC =

2IL) + 0.0075] NT [(1 + 0.01RREC NR) [Cotc+ CtcteCF

(1 + NR) VOL

172

VEHICLE OPERATING COSTSUBMODEL

Table 5.3b: Relative energy-efficiency factors

Vehicleclass

Relativeenergyefficiency factora,

Test vehicle

Comparable Modern design design

Possible range

Smallcar

VW-1300

1.00

0.85

0.70-1.00

Mediumcar

ChevroletOpala

1.00

0.85

0.70-1.00

Largecar

DodgeDart

1.00

0.95

0.80-1.00

Utility

VW-Kombi

1.00

0.95

0.80-1.00

Bus

Mercedes 0-326

1.00

0.95

0.80-1.00

Lightgasoline truck

Ford400

1.00

0.95

0.80-1.00

Lightdiesel truck

Ford 4000

1.00

0.95

0.80-1.00

Mediumtruck

Mercedes1113 (2 axles)

1.00

0.95

0.80-1.00

Heavy truck

Mercedes1113 (3 axles)

1.00

0.95

0.80-1.00

Articulatedtruck

Scania110/39

1.00

0.80

0.65-1.00

Source: Watanatadaet al. (1987).

where

NT = the numberof tiresper vehicle; RREC = the ratioof the cost of one retreadingto the cost of one new tire,in percent; per tire carcasspredictedby: NR = the numberof retreadings NR = NRoexp (-0.00248

QI - 0.00118 C)-1;

NR, = the base numberof recaps; Cotc = the constantterm of the treadwear model;and Ctcte= the wear coefficient;

173

VEHICLE OPERATING COST SUBMODEL

Figure 5.5: Fuel as a function of road characteristics: half-laden heavy truck, paved road Fuel (1itersl1000kmI 800

(a) Roughness K._ ....

-

SleP~c-

700 600

.

400 LevelOngenl

200

100

125

100

75

S0

25

0

Rouqghnffs (Q) Fuel[hiearsllOOO 61)

(b)

Rise plus fall

70-

600

200-

400 300-2

200

00

20

10

30

40

60

00

70

80

R15e plus fan (mkm) Fuel ;(FiVID61000kn.) 800

(c) Curvature

700

Rugh,tp - -- --

--

--

-- --

-

i ------

:.

--------

OmornIh-teep 600

5000

400 Rough-level

30D

A_

_-__

--

__-__

___-

-

_

--_

_-_-___-___ -

--

-

-

--

- _ -_

-__

_-

_--_ -

Sr60th-leuel

-

_

-

200

100

______-____-----_______

0 0

100

200

300

400

500

600

700

800

900

1000

Cunotlure )deWQreekmn)

Source:

Bank highwayresearchprojectdata Analysisof Brazil-UNDP-World (GEIPOT,1982; Watanatadaet al., 1987).

174

VEHICLEOPERATINGCOST SUBMODEL

Figure5.6: Fuel as a functionof road characteristics: half-ladenheavy truck,unpavedroad fuel ClitevsltwOO kmj] 800

(a)

Roughness

_

Ow' 5w -

4w

__________---

300

1-

200

0

80

100

I50

250

200

RougJhness(Q0| Fuel tIitess001O

km)

8w0

(b) Rise plus fall

700

600..

-

'

--

200

1w0

0 0

10

20

30

40

50

60

70

80

Riseplus foll (mAik) Fuel (llte,s/1000 km) Soo

(c)

Curvature

700

-

-

-

-.----.-

-.

Smnoolth -steep 600

t

~~~~~~~~~~~~~~~~~~5w Rought-levd 300 Smooth-btvel 2w

10w

.

01

0

10

300

4 Curte

Source:

I

I_._I_._-t_______________ 2w

5 1w

1w

700

81w

900

Iw

(dsgremA,,)

Bank highwayresearchproject Analysisof Brazil-UNDP-World data (GEIPOT,1982;Watanatadaet al., 1987).

175

VEHICLEOPERATINGCOST SUBMODEL

forceper tire,given CF2 = the average squared circumferential by: CF2 =

1

(CF2 + CF2);

d

2

CFu = the average circumferentialforce per tire (in the directiontangentialto the road surface)on the uphillroad segment,in newtons; CFd = the average circumferentialforce per tire (in the directiontangentialto the road surface)on the downhill road segment,in newtons; to L = the averageforceper tire in the directionperpendicular the road surface,in newtons,givenby: L = 1000GVW g NT VOL = the averagewearable rubber volume per tire for a given and nominaltire size, in vehicleaxle-wheelconfiguration dm'; and 0.0075 = the correctionterm for the predictionbias due to model nonlinearity. Among the variablesappearingin the formulas,NT, NRo and VOL are parametersspecificto vehicletypes. Their defaultvaluesare listed in Tables 5A.1 (for NT) and 5.4, but can be overriddenby the user as an option. The parametersCotc and Ctcte are specific,not to the vehicle class, but mainly to the materialpropertiesof the tire. The default (biasply) type of tires of the Pirelli valueswhich apply to conventional make are given in Table 5.4. RREC is a constantwhich has a defaultvalue of 15 percent representingthe average for Brazil, but can also be overriddenby the user. The circumferential forces CFu and CFd are computed as the vehicle drive force (on the uphill and downhillsegments,respectively) dividedby the numberof tiresof the vehicle: CFU =

u

[(1000CR + RF) GVW g + 0.5 RHO CD AR V2 ]

1

NT

u

1 CFd = -

d

[(1000CR - RF) GVW g + 0.5 RHO CD AR V2].

NTd

The above relationshipis intended for use with roads of alignment (C < 400 degrees/km) and well-designed moderateorizontal the effect of horizontal superelevation.It is expectedto underpredict Furthermorethe alignment when the above conditionsare not met.

176

VEHICLEOPERATINGCOST SUBMODEL

Table 5.4: Parameterand defaultvaluesfor tirewear prediction

NRo

VOL

Vehicletypes

Co tc

(dm3)

C tcte ( -102)

Large bus

3.39

6.85

0.164

1.278

Lighttruck (diesel and gasoline)

1.93

4.30

0.164

1.278

Mediumtruck

3.39

7.60

0.164

1.278

Heavytruck

3.39

7.30

0.164

1.278

Articulated truck

4.57

8.39

0.164

1.278

Source: Watanatadaet al. (1987).

recommendedrange of the input variablesshown in Table 5.2 should be observed. Figures 5.7 and 5.8 show predictedtire wear as a functionof highwaycharacteristics for a half-ladenheavy truckover pavedand unpaved roads, respectively. These curves have been plotted using the default values. It may be noted that the tire wear curves incorporatethe associated changes in speed induced by variation of the road characteristics shown in Figures5.3 and 5.4. 5.2.4 Maintenance Parts A convenientway of modelingpartsconsumptionis in termsof the ratio of the monetary cost of parts consumedper 1000 vehicle-kmto the price of a new vehiclein the same period. Under the assumptionthat the prices of spare parts and of a new vehicle vary togetherby the same proportions, data on their ratio from differentperiodsmay be includedin the estimationand the resultsmay be used to computethe monetarycostof spareparts consumedper 1000vehicle-kmfor any year. For example,if the currencyis Braziliancruzeirosand the analysisyear is 1990,then

where

MPC 1 990

= NVP1990 PC

MPC1 gg0

= monetarycostof sparepartsconsumed,in 1990 Brazilian cruzeirosper 1,000 vehicle-kmfor the givenvehicleclass;

177

VEHICLEOPERATINGCOST SUBMODEL

half-laden Figure5.7: Tirewear as a functionof road characteristics: road heavy truck,paved Tire weor tno

(a) Roughness

tIre9lOOW

-ehicle.k,n)

125

I 00 etCN

-~~~~

0.75

uy

0 25Lee

Lecel-lorigeril

0.00

,,__________'_'__'__'_'__'_'

______________

Roiighne0

125

100

75

50

25

0

9Q1)

Tire weor

(no fi,es110OOvehicle-kn,) 150

(b) Rise Plus fall 1.25

1.00

~~~rr 4

..

0.50

0.25

-

-

0

--

-

-

}

=

0.00 40

30

20

10

0

Rim plw

80

70

60

50

tatl (m/kmJ

Tire weco (no

(c) Curvature

Vmrer/1000 vehiCe-km,

50

1 25 I or.

1.00 -~~~~~~~~~~~~~~~~~~~_1.gh.p --

~~Smoott-steep

~~~~~~~~~~~~~

-

0.75

500

_Rooh-Ienel

0.25

0

Source:

10

200

300

400

500

Cuorvlu,e

(tgreeskm)

600

700

800

900

1000

Bank highwayresearchproject Analysisof Brazil-UNDP-World et al., 1987). Watanatada 1982; data (GEIPOT,

VEHICLE OPERATING COST SUBMODEL

178

Figure 5.8: Tire wear as a function of road characteristics: half-laden heavy truck, unpaved road Tire wear (no

eh,ie-1k,m)

tireO1000

I50

(a) Roughness

125

~

100-

----------

075

050

~~~~~~~~~~~~~~~~~Lev CUrvy njen

020

0 25

-------

000-..1I 250

200

150

100

50

0

-Soa4ness(QIJ Tire weor (no tIrenilO50 veb,ie.krn)

(b) Rise plus fall 1 25

1 00 0 75

~~~~ ~ ~ ~~~~~~~~7

0705

0

10

~~20

40

30

lure wecr (no tiresr1000

(c) Curvature

80

70

60

50

Plus ION (m/km)

Rts

veh,Cle-kmt

'-50 7-/

- Rough-R

teep

125 I~~~~~~~~~~~~~~~~~~~~~~I0

u

7/

_

----

0 50

0 28

t:

-

________________------------------------------

Smooth-level

0.00

0

10

20

0

3300 4000 Culw

00

8

'0

(Grkm)

Source: Analysis of Brazil-UNDP-WorldBank highway research project data (GEIPOT, 1982; Watanatada et al., 1987).

0

000

VEHICLEOPERATINGCOST SUBMODEL

179

NVP1990

=

expected average price of a new vehicle of the givenclass,in 1990Braziliancruzeiros;and

PC

=

the parts cost per 1,000 vehicle-kmfor the given vehicleclassexpressedas a fractionof the cost of a new vehicle.

The rest of this subsectionis devotedto discussionof the equationsto predictPC. PC has been found to be related to roughnessand vehicle age (Chesher and Harrison, 1987). The effects of these two factors are multiplicative.Holdingthe age constant,the relationship betweenPC and roughnessis generallyexponential, especiallyfor relativelylow valuesof roughness. However,the exponentialrelationtends to overpredictPC at higher values. Therefore,the recommendedequation is a compositeof exponential and linear-- exponential up to a transitional value of roughness, QIospn which is differentfor differentvehicle types, and then linearfor highervalues. The linearextensionis tangentto the exponential relationship at QIosp.3 Since the Brazil relationfor truck parts consumption was foundto be linearover all valuesof roughnessencountered in practice,QIosp is set to zero for all trucks. The averageage of the vehiclesin a regionbelongingto a given vehicle group is expressedby the average cumulativekilometrageof the group (denotedby CKM). The effectof CKM has been foundto be multiplicative with an exponent. The age exponent(denotedby "k") is remarkably stablefor a given vehicletype over environments as variedas Braziland India. Symbolically, PC is givenby: CKMkC0 sp exp(Cspqi QI) for QI < QIosp CKMk (a. + a1 QI) =

where

for QI > Q1osp

CKM

=

the averageage of the vehiclegroup in km, definedas the averagenumberof kilometersthe vehicleshave been drivensincetheywere built;

k

=

the age exponent-Table 5.5);

Cosp =

a fixedmodel parameter(givenin

the constantcoefficient in the exponential relationship betweenspare parts consumption and roughness-an optionaluser-inputmodel parameter(with default values);

3 The use of a tangentialextensionfor extrapolation of the log-linear modelwas Introducedby A. Chesher(GEIPOT,1982).

VEHICLEOPERATINGCOST SUBMODEL

180

Cspqi = the roughnesscoefficientin the exponentialrelationship between spare parts consumptionand roughness -- an model parameter(withdefaultvalues); optionaluser-input QIo

=

the transitionalvalue of roughness,in QI, beyond and betweenspareparts consumption which the relationship roughness is linear -- an optional user-inputmodel parameter(withdefaultvalues).

ao and a1 are coefficientsof the linear-tangential extensionof the exponentialrelationshipand may be expressed as functions of model parameters.The relationships are: ao

= CospexP(Cspqi QIosp)(l

al

= Cosp Cspqi exp(Cspqi QIosp)

-

Cspqi QIosp)

A convenientformulato arriveat a good estimateof CKM is CKM = min (1/2LIFEoAKMo,CKM1 ) where

LIFEO= the averagevehicleservicelife in years,inputby the user,and

Table 5.5: Parametersand defaultvaluesfor predictingspare parts spare partsconsumption

Vehicle classes Car and utility Largebus Light (gasoline and diesel)and medium truck Heavy truck Articulated truck (tractorand trailer)

k

cosp 6 (10)

Cspqi -3 (10 IQI)

QIosp

CKM'

(QI)

(km)

0.308 0.483

32.49 1.77

13.70 3.56

120 190

300,000 1,000,000

0.371

1.49

251.79

0

600,000

0.371

8.61

35.31

0

600,000

0.371

13.94

15.65

0

600,000

Source: Chesherand Harrison (1987),modifiedfor unit changes and the tangentialextension. The parametersfor utilitiesgiven there are not used becauseof the differencesin the associatedmakes and models.

VEHICLEOPERATINGCOST SUBMODEL AKMo

181

the average number of kilometersdriven per year per vehicleof the group,inputby the user,and

=

CKM' = the ceilingon average cumulativekilometeragegiven in Table5.5. The subscript'lo is used to emphasizethat the valuesof thesevariables are to be provided by the user and are not the same as the values calculatedin terms of speeds for depreciation and interestcalculations (Sec.5.3.3). The ceilingon averagecumulativekilometrageis introduced because high values of CKM could otherwiselead to unrealistically high predictions of parts consumption. The predictionof PC requires three parameters,namely Cosp, Cs?qi and QiOs?* These shouldbe providedby the user from local data, but default va ues will be used if inputsare not provided. The default values,basedon the Brazilstudyare given in Table5.5. The recommended ranges for the independentvariable QI, for use with the default parameters, are given in Table5.6. Figure 5.9 showsmaintenanceparts consumptionas a functionof roughnessfor differentvehicle classes. These curves have been drawn usingthe defaultvalues. 5.2.5 Maintenance Labor Maintenancelabor hours are related primarilyto maintenance parts requirements, and in some cases,to roughness.When significant, the latter has been found to be exponentialand the two effects are multiplicative.The relationship in its generalform is writtenas:

where

LH

=

CoQh pcCQhpc

exp(CthqiQI)

LH

=

the predicted number of maintenancelabor-hoursper 1,000vehicle-km;

PC

=

the standardizedparts cost per 1,000 vehicle-km expressedas a fractionof new vehicleprice;

Coth =

the constantcoefficient in thierelationship between labor hours and parts costs, which is an optional user-inputmodelparameter;

Cthpc =

the exponentof partscost in the relationship between labor hours and parts cost, which is an optional user-inputmodel parameter; and

C.hqi =

the roughnesscoefficient in the exponential relationship between labor hours and roughness,which is an optionaluser-input model parameter.

The predictionof LH requiresthree parameters,namely, Coths Cthpc, and Cthqi. These should be providedby the user, but default

182

VEHICLE OPERATING COST SUBMODEL

Figure 5.9: MaintenanceParts Consumptionas a Function of Road Roughness: Various Vehicles Maintlenance ports 1% vNdicIe

pnCeClOWO 051

Q. 120

3.0

(a) Cars and utilities

2.5

210

05

00-

,

,

.

, 50

1.S0

00

20i

250

OongonesstQII Moint.noce polls (% vNchk p0kei/Ow

611)

a . *90

035

(b) Largebuses

0..0

0.25

0 20

0 06 0.0

0.00....

3

40'0

t!i

9oJ0s

1tiO

250c

Z

(C)

Mointtonce pots (% venicie PACW/10W i) 1 25

(c) Heavy and articulated trucks' I100

.

0 10

O/5 s

;

>

t;

0

i~~~~~~~~~~~~~~

0 25

a 0(

0

50

10w

450

200

Reougn.h (0Q

Source:

Analysis of Brazil-UNDP-WorldBank highway research project

(GEIPOT,1982;Chesherand Harrison,1987,Watanatadaet al., 1987).

250

VEHICLEOPERATINGCOST SUBMODEL

183

Table 5.6: Recwomendedrange of variablesfor maintenance partsand labor prediction Variable Roughness,QI

Units

Recommended range

QI 25 - 120 25 - 190 25 - 120

Cars and utilities Largebuses Trucks Source: Basedon data from GEIPOT(1982,Volume5).

values will be used if inputs are not provided. The default values, estimatedfrom the Brazil data are given in Table 5.7. The recommended range for the independent variableQI is the same as for predictingparts requirements (Table5.6). Figure5.10 showsmaintenancelabor hoursneededas a functionof roughnessfor differentvehicle classes. These curves have been drawn usingthe defaultvalues. Table 5.7: Defaultvaluesof parametersfor computingmaintenance labor-hourprediction

Vehicleclasses

CO Qh

C Qhpc

Car and utility

77.14

0.547

Largebus

293.44

0.517

Light (gasolineand diesel)and medium truck

242.03

0.519

0

Heavytruck

301.46

0.519

0

Articulated truck (tractorand trailer)

652.51

0.519

0

C Qhqi (Qi1) 0 0.0055

Source: Chesher and Harrison (1985), modified for unit changes. The parametersfor utilitiesgiven there are not used becauseof the differencesin makes and models.

184

VEHICLEOPERATINGCOST SUBMODEL

Figure5.10: Maintenance laborhoursas a functionof road roughness: variousvehicles MaIntenance bbor Ch/1C00kml ¶00

(a) Cars and utilities 75

25

C

50

400

00

100

450

200

250

Mo.,,to.ea,,ceAobv, hl1000 km) 60

(b) Large buses 40

20

I30

20

0

150

200

250

200

250

RoughnOss (

M0/n¶ohle9elObo, th/1000 km)

(c)

Heavy and articulated trucks

6o

50-

40

___

20

10

0 0

50

100

450

ARu

Source:

(a)

Analysis of Brazil-UNDP-World Bank highway research project (GEIPOT,1982;Chesherand Harrison,1987,Watanatadaet al., 1987).

VEHICLEOPERATINGCOST SUBMODEL

185

5.3 RELATIONSHIPS USED WITH ALL OPTIONS The portionof the vehicleoperatingcost submodelexplainedthus far is the portionfor which differentformulations are availablefrom the four differentstudies. It includesrelationships from the Brazil-based option for vehiclespeed, fuel consumption, tire wear, maintenanceparts, and, maintenancelabor. The alternativeset'sof relationsfor these elementsfrom the other countrystudiesare presentedand explainedin the next chapter. Relationsfor other componentsinvolvedin vehicleoperatingcost are not differentiated accordingto the different: sources,but are the same regardlessof which option is chosenfor the elementslistedabove. These other componentsare lubricantsconsumption, crew,depreciation, interest, overhead,passengerdelays,cargoholding,and miscellaneous costs. Relationsfor these componentsare describedin the rest of this chapter. 5.3.1 LubricantsConsumption Lubricantsconsumptionis predictedas a functionof roughness using relationships modifiedby Chesherand Harrison(1985),based on the Indiastudy (CRRI,1982): 1. Passengercarsand utilities OC = 1.55+ 0.000211BI 2. Lighttrucks OC = 2.20 + 0.000211BI 3. Busesand mediumand heavytrucks OC = 3.07 + 0.000211BI 4. where

Articulated trucks OC = 5.15 + 0.000211BI

OC = the lubricants consumption, in liters/1,000 vehicle-km.

5.3.2 Crew Requirements In the HDM model the cost of crew labor is consideredto be a variablecost ratherthan a fixed cost. This means that the time the crew spends on non-driving activitiessuch as loading,unloading,and layovers is not chargedagainstthis cost category. Thus, the numberof crew hours requiredper 1,000vehicle-km, denotedby CRH, is inverselyproportional to speed: CRH =

-

0 S

VEHICLEOPERATINGCOST SUBMODEL

186 5.3.3 VehicleDepreciation and Interest

The amountof vehicledepreciation per 1,000 vehicle-km, denoted by DEP and expressedas a fractionof the averagecost of a new vehicle,is computedas: DEP = 1000ADEP AKM where

ADEP = the averageannualvehicledepreciation, expressedas a fractionof the averagecost of a new vehicle;and AKM = the averagenumberof kilometersdrivenper vehicleper year.

Similarly,the amountof interestchargeper 1,000 vehicle-km, denotedby INT and expressedas a fractionof the averagenew vehiclecost, is given by: INT = 1000AINT AKM where

AINT = the averageannualintereston the vehicleexpressedas a fractionof the averagecost of a new vehicle.

To calculate depreciation and interest costs per 1,000 vehicle-km,two steps are required:first, determinethe average annual depreciationand interest,and, second, determine the average annual kilometerage. Two optionalmethods are availablein the HDM model for (ADEP)and interest(AINT): computingthe averageannualdepreciation 1. de Weille'svaryingvehiclelifemethod. 2. Constantvehiclelifemethod. The above methods correspondto the DEPRECIATIONcodes in the input data (User'sManual,Chapter2, Form D-5). Similarly,three optionalmethodsare availablein the model for computingthe averageannualutilization (km): 1. Constantannualkilometerage method, method,and 2. Constantannualhourlyutilization 3. Adjustedutilization method; where the firsttwo methodsare, in fact,specialcasesof the more general codes in third method. These three methodscorrespondto the UTILIZATION UTILIZATION The DEPRECIATION and Chapter 2 (Form D-5). the User'sManual, methodscan be specifiedfor individualvehiclegroups in any combination. of thesemethods. The followingparagraphsprovidedetaileddescriptions

VEHICLEOPERATINGCOST SUBMODEL

187

Averageannualdepreciation and interest 1. de Weille's varying vehicle life method. This method, suggestedby de Weille (1966), is based on straight-line depreciation over a predetermined vehicleservicelife which is assumed to decreasesomewhatas vehiclespeed increases, so that lifetimekilometerageincreasesin less proportion than speed. Mathematically, de Weille'smethod is expressed as: Annualdepreciation factor: ADEP =

Annual interestfactor:

1 LIFE

AINT = AIN' * 1 2 100

where AINV = the annualinterest; chargeon the purchase cost of a new vehicle,in percent;and LIFE = the averagevehicleservicelife,in years. The vehicle service life is assumed to be related to the predictedvehicleoperatingspeed,S, as follows: LIFE = min t1.5LIFE.;[ --

S0 + 2]

S

LIFEo -

3

where LIFEo= the baselineaveragevehiclelife,in years, specifiedby the user;and SO = the baselineaverage! vehiclespeed,in km/h, givenby: AKMo So =

HRDo where AKMO = the user-specified tbaseline averageannual kilometerage (as def"ined before);and HRDo= the user-specified baselinenumberof hours drivenper vehicleper year. The maximum limit of 1.5 LIFEo is imposedin the model to eliminatethe possibility of computingunrealistically long vehicle lives. In addition to the method for estimating vehiclelife, de Weille (1966)also suggesteda method for estimatingthe averageannual kilometerage driven per year, called the "constant hourly utilizationmethod" to be describedsubsequently.

188

VEHICLEOPERATINGCOST SUBMODEL 2. Constant vehicle life method. This method also uses straight-linedepreciation,but differs from de Weille's method in that the vehicle life, LIFE, is assumed to be constant irrespectiveof vehicle speed and equal to the user-specified value,i.e., LIFE = LIFEo. The interestfactor,being independentof vehicle life, is the sameas in de Weille'smethod.

Averageannualutilization 1. Constant annual kilometerage method. This method assumes that for each vehiclegroup the averageannual kilometerage driven per vehicle, AKM, is constant and equal to the user-specified value,i.e.:

AKM = AKM9. The assumption of constant annual kilometeragemay be consideredappropriatefor non-commercial vehiclessuch as private passenger cars, of which the trip distancesand frequencies are usuallyassumedto be relativelyinsensitive to changes in average travel speed. However, commercial vehiclestend to be used for more frequentor longertrips if time for a given lengthtrip is reduced. 2. Constant annual hourly utilizationmethod. This method, which was also suggestedby de Weille (1966),assumes that the average annual number of hours driven per vehicle is constant. Thus the averageannual kilometeragedriven per vehicle, AKM, is computed as the product of the user-specified averagenumberof hoursdrivenper vehicleper

year,HRDo,and speed,S: AKM =

HRDO S.

It should be noted that the constant hourly utilization method tends to overpredicttime-relatedbenefits. As the average speed increasesthe number of trips a commercial vehicle can make in a year tends to rise. However, in addition to the driving time the total time needed to complete each trip also includes a large proportionof non-drivingactivitiessuch as loading,unloading,vehicle servicesand repairs,and layovers. This means that the number of trips per year does not increase in direct proportionto speed;doublingthe speed,for example,results in less than doubling the number of trips and annual kilometerage. The effect is particularlypronouncedfor shorttripswith many stopsfor pickupsand deliveries.

189

VEHICLEOPERATINGCOST SUBMODEL

3. Adjustedutilization method. This method aims to remedythe deficienciesin both of the othermethods. Each vehicleis assumed in this method to operate on the section under consideration as a fixed routeover the analysisyear, with the totaltime,per roundtrip,TT, given by: TT = TN + TD where TN = the time spenton non-driving activitiesas part of the round trip tour, includingloading and unloading,refueling,layovers,etc., in hoursper trip;and the drivingtime on the section,in hours per trip.

TD =

Letting RL denote the round trip drivingdistanceor route length,in km, the drivingtime on the section,TD, becomes: TD = RL

S It can be seen thatas the operatingspeed,S, increases,the driving time per trip decreases. Vehicle operatorsare assumedto try to make as many tripsas possiblewithin the total number of hours availableper year, denoted by HAV. The latter is an operatingconstraintwhich dependson the time allowed for crew rest, infeasibilityof vehicle operation (e.g., during early morning, vehicle repairs, of the vehiclespeed etc.). HAV is assumedto be indlependent and the route characteristics.Under this assumptionthe drivenper year is derivedas: kilometerage AKM =

(numberof roundtripsper year) x (routelength) HAV RL TT

HAV RL TN + RL S

HAV

TN + 1 RL

S

The term TN/RL, the number of non-driving hours per vehicle-kmof travel,can be expressedas follows: TN

HAV - HRD,

RL

AKMo

Substitutingthis expressioninto the above expressionfor AKM yields:

190

VEHICLEOPERATINGCOST SUBMODEL HAV

=

AKM

HAV - HRDO

1

AKMo

S

Thus if the values of HAV, HRDo and AKMo are available, the annual kilometerage driven,AKM, can be predictedas a functionof the predictedoperatingspeed,S. The baseline parametersHRDo and AKMo are to be provided directlyby the user. The HAV parameteris derivedfrom the

following formula: HRDo HAV

-

HURATIOO where HURATIOO = the "hourlyutilizationratio" for the baselinecase. Substitutingthis formulain the expression for AKM above yields the general formula for predicting vehicleutilization: AKM, HRDo AKM =

HRDo (1 - HURATIO) +

AKMO HURATIO 0 S

Basedon the data from the Brazil-UNDP study,Watanatadaet al. (1987) estimatedtypical values of hourly utilization ratio for variousclassesof vehicles. These resultsled to the followingdefaultvaluesof HURATIO,in the HDM model. Baselinehourly

Vehicle type

utilization ratio (HURATIOO)

Cars Utilities Buses

0.60 0.80 0.75

Trucks

0.85

These default values are based on the operating characteristics of typicalvehiclesin Brazil. However, since hourly utilizationratios are expectedto vary considerably acrosscountries, it is important to provide valuesappropriate to the localoperating conditions.

VEHICLEOPERATINGCOST SUBMODEL

191

The behaviorof the averageannualkilometerage driven,AKM, with respectto the hourlyutilization ratio,HURATIOo,is of interest. On one extreme,when HURATIOoequals zero, the abovegeneralformulareducesto: AKM = AKMo which is recognizedas the "constantannual kilometerage" method. On the oppositeextreme,when HURATIOOequalsone, the formulabecomes: AKM = HRDo S which is recognized as utilization" method.

the

"constant annual hourly

Figures5.11and 5.12 show deprecliation and interestcostsas a functionof highwaycharacteristics for a half-ladenheavy truck for paved and unpaved roads, respectively. These curveshave been drawn usingthe defaultvalues. The method used to predict vehicle utilization is the adjusted utilization method. 5.3.4 Overhead Two optionalmethods are availablefor computingthe overhead cost of vehicleoperationfor each vehiclegroup: 1. As a lump sum overheadcost per vehicle proratedover the annualkilometerage, AKM; and 2. As a percentageof the vehiclerunningcosts (consisting of the costs of fuel and lubricantsconsumption,tire wear, maintenanceparts and labor, depreciationand interestand crew). Only one methodmay be used for each vehiclegroup. 5.3.5 PassengerDelays The number of passenger-hoursspent 1000 vehicle-km, denotedby PXH, is givenby:

in

traveling per

PXH = 1000 PAX S where

PAX = the averagenumberof passengersper vehicle,inputby the user.

5.3.6 CargoHolding The numberof vehicle-hours spent in transitper 1000 vehicle-km, denotedby VCH, is givenby:

192

VEHICLEOPERATINGCOST SUBMODEL

Figure5.11: Depreciation and interestas a functionof road characteristics: half-ladenheavytruck,paved road DLep& WIl 1% vehlcle orceIlOOO ken o350

(a) Roughness

030

025

-.

Leep-cuvY

-

-,

OIeep4Qrngert

0 10

005

0 00

-

T

0

75

50 Romghoes-

Dep & Int 1% veh,cle p-0el100

r

____________I____T-rrr

25

100

125

(Q17

kml

035

(b) Riseplus fall

030 0 25

~--------

0 20

5vh--uw---------_: ------

-----

Rghcr

015

010

0 05

0.00

0

10

30

20

50

40

0

70

s0

9se plus foll (m/km)

Sep

(c) Curvature

& Int vehrle -%

p-ce/1100

km]

035 0 30

025

020

Rouo--eve

l----

----

, hle, el

0 0

015

040

000

000

I 0

100

200

,

, 300

,

__ - I __

,__

Cvrvolare

Source:

___

__ ,

S500

4

__,

___ , O

__

_

700

.___

__ 8X0

_.

__,

__

O0

(7dereelkm}

Analysis of Brazil-UNDP-World Bank highway research project (GEIPOT, 1982; Chesherand Harrison,1987,Watanatadaet al.,

1987).

_

r 1000

193

VEHICLEOPERATINGCOST SUBMODEL of road and interestas a fLunction Figure5.12: Depreciation road unpaved truck, half-laden characteristics: Dep. & ht. (% vehicle pflce/100O km) 0.35

(a) Roughness -- -- --

0.25

Level-Curv

0320

;e rel-rongen 0 15

0 10

0.05

0.00 250

200

150

100

50

0

RoUghnas (Q) Dep & MI (% vehicle pice/1000 km) 0.35

(b) Rise plus fall -----

0oughrTV

-_ _

0.30

-_

_-----------

---

_

_-

_

__…_

Oough-tovenC

U 25 020

0 10

0.05 0 00

80

70

O6

50

40

30

20

10

0

f1(rIkm) RlsePls toll Dep & rt. M%vehicle pWice01000km)

(c) Curvature

0.35

Rough-steeP

0.30

R-Uhlevel0.25

<

teeo ~ ~~~~~~~~~~~~~~~Sr-oclhv

-------

vth

020

ev.I

015

0 10

0.05

._ _

0.00 0

100

. _ _ 200

. _ _ 300

.

I

.

400 CVureo

Source:

I

500

.

I 600

700

. _

, _

. _

._

800

900

(d.geerkm)

Bank highwayresearchproject Analysisof Brazil-UNDP-World (GEIPOT,1982; Chesherand Harrison,1987,Watanatadaet al., 1987).

1000

194

VEHICLEOPERATINGCOST SUBMODEL 1000 VCH =

-

S

The cargo holding cost per 1000 vehicle-kmis defined as the productof VCH and the user-specified cargo holdingcost per vehicle-hour delayed. If time savingsor delays are perfectlydeterministic and there are no problemswith lumpinessin scheduling, the unit cargo holdingcost per vehicle-hour may be computedas equalto: (themonetaryvalueof cargo)x (theannualinterestrate,in fraction) 8760 hoursper year If time savingsor delaysare stochasticand schedulinglumpiness prevails(as is normallythe case at leastto some extent),the unit cargo holdingcost will generallybe higher,due to the need to build up extra inventories to avoid stockingout. In general,cargo holdingcost is much smaller than other vehicle operating cost componentsand therefore, although it is included in the HDM model, it is often ignored for simplicityin HDM applications. 5.3.7 Miscellaneous Costs In the preceedingdiscussionrelatingvariousvehiclesoperating cost componentsto road geometryand surface conditions,it was assumed that averageroughnessof the roadwaywas a sufficientstatisticfor all the road conditionfactorsaffectingthe cost of operatingvehicleson the because road condition roadway. It is obviouslyan over-simplification, factors -- such as, moisture, depth of loose material, and reduced due to gravel loss-- are relevantfor vehicleoperatingcosts, passability of an but are not capturedby roughness. Of such factors,impassability gravel "cover" is the most important. unpaved road due to insufficient the expected Hence, provisionhas been made in the model to incorporate rise in the vehicleoperatingcostsonce the gravelthicknessdropsbelowa minimumlevel. Increasein vehicleoperatingcostscan be attributedto: 1. Increasedtire slippagein loose(e.g.,sandy)or soft (e.g., muddy)materials; 2. Increaseddrag in losseor softmaterial; 3. Increasedtorque requirementsand consequentwear on the vehicledriveassembly;and 4. Reduced travel speed, includingprobablyforced stops where the vehiclemay partiallyor completelybog down; etc. None of these are reflecteddirectly in the measured roughness data.

VEHICLEOPERATINGCOST SUBMODEL

195

Rather than quantify these effects physically,their economic impact on the road user's selectionof vehiclemay be considered. For periods,the example,if the road is renderedimpassablefor significant road userwould selecta four-wheeldrivevehicleor truckat greatercosts in order to gain passability. These greater costs give a reasonable and thus the benefitsof passability. estimateof the cost of impassability The cost of marginal passabilityare modelled by a piecewise linear function,FPASS, of gravel thickness,which augments the unit vehicleoperatingcostsup to a limit,denotedby FPLIMIT. This limit is of the nature specifiedexplicitlyby the user based on an understanding (e.g.,by saturation,loss of cohesion[in and cause of passability-loss sands],etc.) The functionFPASS would beginwith a value of 1 when the gravel thickness(GH) equalledthe minimum thicknessrequired(GHMIN)and increase linearly to the limiting value (FPLIMIT)when the thickness reachednil. costs,for a given vehicleclass, The treatmentof impassability may be formalizedas follows: CPASS= VOC (FPASS- 1) where

in monetaryunitsper 1,000 CPASS= cost due to impassability, kim; VOC = totalunit vehicleoperatingcostscomputedas a sum of componentsdiscussedso far, in monetaryunits per 1000 km; factorderivedfromgravelthickness,given FPASS= dimensionless by

FPASS= 1 + (FPLIMIT- 1) max (0; 0 - GH/GHMIN); maximumvalueof FPASS, dimensionless FPLIMIT= vehicle-specific specifiedby the user; GH = mean gravelthicknessfor the year, in mm; and GHMIN = minimumgravelthickness,in mm, determinedas GHMIN= min (100.0;max (40.0;2.0 D95));where D95 = maximumparticlesize, in mm. Note that the physical explanationfor increasingFPASS for gravel thicknessless than the minimum is that there is greater risk of weak spots,and of increasedvehiclecosts, in this range than for roads with adequategravel"cover"thickness. The factorFPLIMITrangesin value from 1 for subgradematerials with soakedCBR greater than 10 percent (i.e.,fully passable)to 3 for heavy vehicleson soft soils. A defaultvalue of 1.0 is used which the CPASS is zero for a paved road,and GH usermay override. By definition, is zero for an earth road.

196

VEHICLEOPERATINGCOST SUBMODEL

5.4 UNIT COSTS Up to this point the analysishas dealt,whereverfeasible,with physical quantities of resources used, so that fundamentalphysical relationswould not be obscuredby pricevariations. Once determined, the physicalquantitiesare multipliedby unit costs or prices in a separate step. The unit costsor pricesmust be providedby the user. Physical conceptsproved difficultto define and quantify for maintenanceparts and for overheadand miscellaneouscosts, and are not relevantfor depreciation and interest, which are financialin nature. For threeof theseelements,i.e.,all exceptoverheadand miscellaneous costs, it was found convenientand valid to deal with the ratio of the element's cost to the price of a new vehicle,anothercost factorto be suppliedby the user. Overhead is treated,at the user's option, either as an exogenouslump sum or as a percentageof runningcosts. Miscellaneous costsare also treatedas a fractionof othercosts. Table 5.8 shows the units in which each element of resource consumptionis measured and the dimensionsof the price, unit cost, or other factor by which each has to be multipliedto obtain its value as a component of vehicle operating cost per 1,000 vehicle-kilometers. Multiplyingthese values by the number of thousand vehicle-kilometers traveledon the link in questionby each vehiclegroup in a year and adding the group totalsyields the total vehicleoperatingcost on the link for the year. Table 5.8: Costingof vehicleoperatingresources Component

Fuel consumption Tire wear

Unitsof measurement

Passengertime

liters/1,000 vehicle-km Equiv.new tires per 1,000vehicle-km Proportionof new vehicle cost per 1,000vehicle-km Labor-hours/1,000 veh.-km Litersper 1,000veh.-km Person-hrs./1,000 veh.-km Fractionof new vehicle cost per 1,000veh.-km Fractionof new vehicle cost per 1,000veh.-km 1. lumpsum + annualkm or 2. % of runningcosts Pass.-hours/1,000 veh.-km

Cargoholding

Vehicle-hrs./1,000 veh.-km

Miscellaneous costs

Fractionof above costs

Maintenance parts Maintenance labor Lubricantuse Crew time Depreciation Interest Overhead

Unit cost or other multiplyingfactor Cost per liter Cost per tire Cost of new vehicle Wage cost per hour Cost per liter Crew cost per hour Cost of new vehicle Cost of new vehicle No factorneeded: Sum of costsabove Valueper hr. of passengertime Cargo holdingcost per vehicle-hour Sum of costsabove

197

VEHICLEOPERATINGCOST SUBMODEL

APPENDIX5A AND IINPUT REQUIREMENTS FOR COMPARATIVE VEHICLECHARACTERISTICS VEHICLEOPERATINGCOST MODELS ALTERNATIVE

VEHICLE OPERATING COSTSUBMODEL

198 Table 5A.1: Vehiclecharacteristics

Engine

Vehicletype'

Approx. PWrox. rated We19ht tare gross classiweight weight fiaHeavyFuel (tons) (tons) tion Tires axles type

Maximm SAE rated Represenpower tative (mt- Cylin- test fleet ric hp) ders vehicle

Brazil' 1. Passenger cars

1.0

1.2

L

4

0

G

49

4

VW1300

2. Passenger cars

1.2

1.5

L

4

0

G

148

6

Opala

3. Passenercars (large) 4. Utilities 5. Buses 6. Light trucks (gasollne) 7. Light trucks (diesel) 8. Modtum trucks 9. Heavytrucks 10. Articulated tricks

1.7

1.9

L

4

0

G

201

8

Dodge Dart

1.3 8.1 3.1

2.1 11.5 6.1

L H H

4 6 6

0 2 2

G D G

61 149 171

4 6 8

W Katbi Merc.Benz0362 Ford,-4

3.3

6.1

H

6

2

D

103

4

Ford-400

5.4 6.6 14.7

15.0 18.5 40.0

H H H

6 10 18

2 3 5

D D D

149 149 289

6 6 6

Merc.Benz1113 Merc.Benz1113' Scania110/39

0.9

1.2

L

4

0

G

49

4

1.2

1.5

L

4

0

G

51

4

PreolerPadsini car Arbassador car

0.6 6.1 8.1 -

1.2 12.2 16.3 11.0 13.0

L H H H H

4 6 6 6 6

0 2 2 2 2

G D D D D

39 114 127 114 127

4 6 6 6 6

Nehindra jeep Tatatruck Ashoktruck None Ncne

4

(smil)

(nfeiun)

India 1. Passenger cars (s3ll) 2. Passenger cars (mediun) 3. Utilities 4. Mediun trucks 5. Heavytrucks 6. Buses(Tata) 7. Buses(Ashok) Kenya 1. Passerger cars

-

0.9

L

4

0

G

72

2. Utilities 3. Light trucks 4. Buses 5. Medium trucks

3.3 -

1.7 8.3 10.0 13.0

L H H H

4 6 -

0 2 2 2

G D D D

87 109 140 140

Caribean 1. Passenger cars

-

1.1

L

4

0

G

65

2. Utilities

1.6

2.6

L

4

0

G

71

3. Light trucks

4.0

8.4

H

6

2

D

115

FordCortina estate car 6 Lard-Rover 6 Bedfordtruck - None - NDre 4

FordCortina estate car 4 Ford Transit van 6 Fordtruck D1010

Figuresare thoseof representativevehicles. vehicle [rated rated gross weight under 3.5 [metric] tons; H = heavy L = light vehicle grossweightof 3.5 tons or mire]. Thenuiberof heavyaxles equalsthe nuyberof axles of the vehicle if it is a heavy vehicle andzero otherwise. G = gasolineengine; D = diesel engine. Tarewights of Brazil vehicles include150kg weightof tw drivers. Excludesthird rear axle. 7 Includesthird rear axle. Source: Kenya: Hide et al. (1975); Caribbean:Hide (1982); Morosiukand Abayanayaka (1982); et al.(1987); India: Central RoadResearchInstitute Brazil: GEIPOT (1982); Watanatada (1982).

VEHICLEOPERATINGCOST SUBMODEL

199

Table 5A.2: Vehiclefleetcharacteristics data for vehicleoperatingcost submodel Study region Variable

Brazil Kenya Caribbean India

Maximumratedpower (metrichp)' Gross vehicle weight (tons)2 Number of tires per vehicle'

0

0

0

0

0

0

0 0

0

Vehiclepayload(tons) 0 Used drivingpower (metrichp) 0 Used brakingpower (metrichp) 0 Aerodynamic drag coefficient(dimensionless) 0 Projected frontal area (m2 )

0

Calibratedenginespeed (rpm) Wearablerubbervolumeper tire (dm3)

0 0

4 Vehicle service life (years)

R

R

R

R

Annualnumberof km driven R 4 Annualnumberof hoursdriven R 5 Hourlyutilization ratio (dimensionless) 0

R R 0

R R 0

R R 0

Note: R = requiredinput; 0 = optional(a defaultvalue providedin the model for each vehicletype can be overriddenby user-specified value). 2

i

Relevantonly for trucksand buses. Not relevantfor cars and utilitiesin the Kenya, Caribbeanand India relationships. r Not relevantfor carsand utilitiesin the Indiarelationships. Generallyrequiredwith few exceptions. Definedas the ratio of the number of hours driven to the number of hoursthe vehicleis available.

Table 5A.3: Road and environmentalcharacteristicsdata for vehicle operatingcost submodel Study region Variable Environment Altitude(m) Road geometryand surfacetype and conditions Rise plus fall (m/km) Horizontalcurvature(degrees/km) Carriageway width (m) Superelevation (percent) Surfacetype (paved/unpaved) Roughness

Brazil Kenya Caribbean India 0

R

R R R 0 R R

R R R

R R R

R R R

R R

R

R

Note: R = requiredinput; 0 = defaultvalues are provided in the modelwhich can be overridden by the useras an option.

CHAPTER 6

Altemative Vehicle Operating Cost Relationships

6.1 SELECTIONOF THE RELATIONS The first two-thirdsof Chapter5 presentedthe principalset of relationsfor predictingvehiclespeed, fuel consumption,tire wear, and maintenanceparts and labor, which are based on data collectedin the GEIPOT-UNDP-IBRD study in Brazil. Exceptfor the maintenancecomponents, these were formulatedaccordingto mechanisticand behavioralprinciples. The present chapterpresentsseveralalternativesets of relationswhich were developedfrom data in Kenya, Caribbeanand India, respectively, and were analyzedby othermethods. As discussedin Chapter5, the user is advisednormallyto use the Brazil relationships with as much local calibration as possible. The principalexceptionswould be for applicationsin India, Kenya, and the Caribbeancountrieswhere the alternativerelationships were themselves statistically established, and even therethe user is encouragedto use the Brazil relationships also in parallelanalysesand to comparethe results in order to gain a more thoroughunderstanding of the likely effectsof alternativeroadpolicies. For a comparative evaluationof the alternative sets of relationships, includingtheir graphicalrepresentations, see the firstvolumein the HDM series(Chesherand Harrison,1987). All of the differentsets of relationsare included in the HDM-IIImodel,and the usermust specifywhich set is to be used. The same set will be used in its entiretythroughoutany run. Input data requirements differ somewhatfor differentsets, and the data requiredby the set chosen must, of course, be supplied. Appendix 5A presentscomparative vehicle characteristicsand input requirements for all sets of relationships.Regardlessof which set of relationsis chosenfor the cost componentsmentionedabove,the relationsfor other componentsof vehicle operatingcost -- lubricants, crew time,depreciation, interest,overhead, passengertime,cargo holdingand miscellaneous costs-- remainthe sameas thosepresentedin the lastpart of Chapter5. The alternativesets of relationships are essentiallyempirical in nature,and thus have limitedextrapolative validitybeyondthe rangeof the independent variablesin the estimationdata. These rangesare given for each components, based eitheron the recommendations in the respective study,as in the case of the Kenya and Caribbeanrelationships, or on the actual range in the data used for estimation, as in the case of the India relationships.As such, the rangesfor a given independent variableare not always consistentacrossdifferentcost componentsin the same study. It is recommendedthat the user pay close attentionto the ranges of independent variablesand discrepancies within them by greaterscrutinyof

201

202

ALTERNATIVE VEHICLEOPERATINGCOST RELATIONSHIPS

the detaileduser cost and resourceconsumptionreportsavailableas an outputoptionin applications of the HDM model. The rest of this chapterdescribesthe relationships derivedfrom the Kenya,Caribbean,and Indiastudiesfor estimatingvehiclespeeds,fuel consumption, tirewear, and maintenance partsand labor. 6.2 THE KENYARELATIONSHIPS The relationships describedin this sectionwere derivedfromthe TRRL study in Kenya (Hideet al., 1975)with the modifications describedin Appendix6A. 6.2.1 VehicleSpeed The average operatingspeeds of vehicles plying the road are required for estimating fuel consumption,the unit costs per 1000 vehicle-kmof crew,depreciation and interest,passengerdelays,and cargo holding. Speeds are calculatedas a functionof the average rise plus fall, horizontalcurvature,carriageway width, altitude,roughness,and, for trucksand buses,power-to-weight ratio. The round-tripjourneyspeed,S, in km/h, is definedas: s

where

2 1

1

Su

5d

Su = speedon the uphillsegmentof the trip, in km/h and Sd= speedon the downhillsegmentof the trip, in km/h.

The expressions for Su and Sd are as follows: Unpavedroads 1. Passengercars Su = max [20; 86.7 - 0.209RF - 0.118C - 0.00089BI - 0.00491 A - 4.32 max (0; 5 - W)]

Sd = max [20; 86.7 - 0.070RF - 0.118C - 0.00089BI - 0.00491 A - 4.32 max (0; 5 - W)]

2. Utilities Su = max [20; 80.3 - 0.317RF - 0.0966C - 0.00095BI - 0.00278 A - 4.32 max (0; 5 - W)]

Sd = max [20; 80.3 - 0.059RF - 0.0966C - 0.00095BI - 0.00278 A - 4.32 max (0; 5 - W)]

3. Buses Su = max [15;65.9 - 0.492RF - 0.0463C - 0.00036BI - 0.00417 A - 6.36 max (0; 5 - W)]

Sd = max [156 65.9 - 0.010RF - 0.0463C - 0.00036BI - 0.00417 A - 6.36 max (0; 5 - W)]

ALTERNATIVEVEHICLEOPERATINGCOST RELATIONSHIPS

203

4. Lightand mediumtrucks Su = max [15;44.1 - 0.433RF - 0.061C - 0.00060BI - 0.00042A + 1.10 PWR - 6.36max (0; 5 - W)] Sd = max [15; 44.1+ 0.00445RF - 0.061C - 0.00060BI - 0.00042A + 1.10 PWR - 6.36max (0; 5 - W)] Paved roads 1. Passengercars Su = max [20; 105.3- 0.372RF - 0.110 C - 0.00089BI - 0.00491A - 7.31 max (0; 5 - W)] Sd = max [20; 105.3- 0.0759RF - 0.110 C - 0.00089BI - 0.00491A - 7.31max (0; 5 - W)] 2. Utilities Su = max [20; 89.7 - 0.00278A Sd = max [20; 89.7 - 0.00278A

0.418RF - 0.0738C - 0.00095BI - 7.31max (0; 5 - W)] 0.0496RF - 0.0738C - 0.00095BI - 7.31max (0; 5 - W)]

3. Buses BI Su = max [15;73.4- 0.526RF - 0.0661C - 0.00036 - 0.00417 A - 3.29 max (0; 5 - W)] Sd = max [15;73.4 + 0.0666RF - 0.0661C - 0.00036 BI - 0.00417A - 3.29max (0; 5 - W)] 4. Lightand mediumtrucks Su = max [15; 49.8 - 0.519RF - 0.0581C - 0.00060BI - 0.00042A + 1.10 PWR - 3.29max (0; 5 - W)] Sd = max [15;49.8 + 0.030RF - 0.0581C - 0.00060BI - 0.00042 A + 1.10 PWR - 3.29max (0;5- W)] where

RF = the average rise plus fall, in mi/km(see definitionin 5.2.1); C = the average horizontalcurvature,in degrees/km (see definitionin 5.2.1); BI = the road roughness,in mm/km,as measuredby the TRRL Towed FifthWheelBump Integrator(Hideet al., 1975); in meters; W = the averagewidth of the carriageway, A = the road altitude,definedas the elevationof the road sectionabove the mean sea level,in meters;and ratio,givenby: PWR = the vehiclepower-to-weight PWR = HPRATED/GVW

where

HPRATED= the maximumratedpowerof the engine,in metrichp, or takeon the default whichmay be user-specified valueshown in Table5A.1;and GVW = the grossvehicleweight,in (metric)tons,whichmay be user-specified or take on the default value shown in Table5A.1 as ratedgrossvehicleweight.

Note that one metric hp is definedas equal to 75 kg-m/s; this makes one metrichp equalto 0.986Britishhp.

204

ALTERNATIVE VEHICLEOPERATINGCOST RELATIONSHIPS

In the TRRL's analysisof speed on paved roads,the effect of roughnesshad been found statistically insignificant.This is judgedto be the resultof an insufficiently wide rangeof roughnessin the test roads. Assumingthat a given changein roughnesswould have the same effectwith or withoutpaving,a term based on unpavedroad resultshas been added to the equationsfor speed on paved roads to account for roughness. The incorporationof this term and an offsettingconstantare explainedin Appendix6A, Section6A.1. Becauseof the linearform of the originalspeed equationsthe value of speed computed can possibly be unrealisticallylow or even negative. To circumventthis possibility, minimum limits,which roughly correspondto crawl speeds on very poor surfacesor alignments, have been imposed,i.e., 20 km/h for cars and utilitiesand 15 km/h for trucksand buses, for both paved and unpaved roads. The user should observe the recommendedrange of the input variables used in predicting speeds recommended by TRRL, as compiledin Table 6.1, as deviationfrom this range representsan extrapolation and couldproduceunreasonable results. 6.2.2

FuelConsumption

Two optionalsets of relationships are providedfor estimating fuel consumptionfor paved and unpaved roads, one set obtainedfrom the originalTRRL-Kenyastudy (Hideet al., 1975)and the other from subsequent work by Chesher(1977a)based on the same set of data. The originalTRRL-Kenyarelationships express fuel consumption, through multiple linear regressionequations,in terms of the vehicle Table 6.1: Recommended rangeof variablesfor vehiclespeedspredictions: Kenya relationships Variable

Units

Unpavedroads Rise plus fall,RF Horizontalcurvature,C Carriageway width,W Roughness,BI Altitude

m/km Degrees/km m mm/km m

0-120 0-250 3.0-8.0 2,000-14,000 0-2,500

Paved roads Rise plus fall,RF Horizontalcurvature,C Carriageway width,W Roughness,BI Altitude,A

m/km Degrees/km m mm/km m

0- 120 0- 200 3.0- 8.0 2,000-9,000 0-2,500

Vehiclefleetcharacteristics Power-to-weight ratio', PWR

Metrichp/ton

For lightand mediumtrucks. Source:Basedon data from Hide et al. (1975).

Recommended range

13 - 33

ALTERNATIVE VEHICLE OPERATING COST RELATIONSHIPS

205

speed, average rise and fall, gross vehicle weight, power-to-weightratio and, for unpaved roads, roughnessand loosenessof surface material. These relationshipswere slightlymodified, eliminating looseness as an explicit variable (by incorporatingthe mean value of 1.0 mm), and converting from British to metric horsepower. The predicted round-trip fuel consumption,FL, in liters/1000 km is defined as FLu + FLd FL = 2 where

FLu = fuel consumptionon the uphill segment of the trip, in liters/1,000km; and FLd = fuel consumptionon the downhill segment of the trip, in liters/1,000km

The expression for FLu and FLd are as follows: Unpaved roads 1. Passenger cars

FLU = 1.16 [47.7 +

6 14 /Su

+ 0.0079 S2 + 1.723 RF + 0.0011 BI]

FLd = 1.16 [47.7 +

6 1 4 /Sd

+ 0.0079 S2 - 1.066 RF + 0.0011 BI]

2. Utilities FLU =

1.16 [74.6 +

8 4 4 /S+u

FLd =

1.16 [74.6 +

8 4 4 /S+d

d

0.0137 S2 + 2.828 RF + 0.0011 BI]

- 1.306 RF d 0.0137 S2 ~~~~~~~~~u + 0.0011 BI]

3. Light trucks

FLu = 1.15 [124.0 + 796/S,

+

0.0150 Su + 4.176RF + 0.0014BI

- 2.58 min (PWR; 40)] FLd = 1.15 [124.0+ 796 /Sd + 0.01';0S2 + 2.216 RF + 0.0014BI - 2.58 min (PWR; 40)] 4. Medium trucks and buses FLU = 1.15 [-30.04 + 796/Sn + 0.0:150Su

-

4.176 RF + 0.0015 BI

+ max (-2.58 PWR + 69.2 1MVW; 0)]

206

ALTERNATIVE VEHICLEOPERATINGCOST RELATIONSHIPS 796 /Sd +

FLd = 1.15 [-30.04+

0.0150S2

-

2.216RF + 0.0015BI

+ max (-2.58PWR + 69.2IFVW ; 0)] Paved roads 1. Passengercars FLU = 1.16 [53.4+ 499/S + 0.0058S2 + 1.594RF + DFLRI FLU = 1.16 [53.4+

499 /Sd +

0.0058S2 - 0.854RF + DFLRI

2. Utilities FLU = 1.16 [74.7+ 1151/SU+ 0.0131S2 + 2.906RF + DFLR] FLd = 1.16 [74.7+ 1151/S + 0.0131S2 - 1.277RF + DFLR] 3. Light trucks FLU= 1.15 [105.4+ 903/SU+ 0.0143S2 + 4.362 RF - 2.37min (PWR;40) + DFLR] FLd = 1.15 [105.4+

903 /Sd +

0.0143S2 - 1.834RF

- 2.37min (PWR;40) + DFLRI 4. Mediumtrucksand buses

FLU = 1.15 [-48.6+ 903/S + 0.0143S2 + 4.362 RF + max (- 2.37 PWR + 69.2 AwVW; 0) + DFLRI FLd = 1.15 [-48.6+

903 /Sd +

0.0143S2 - 1.834RF

+ max (- 2.37 PRW + 69.2¶/VW;0) + DFLR] where

FL = the predictedfuel consumption, in liters/1,000 vehicle-km; and DFLR = the predicted increase in fuel consumptiondue to road roughness,in liters/1,000vehicle-km,to be describedsubsequently; and the other variablesare as definedbefore.

Multiple regressionrelationships were originallyobtainedfrom controlledfield experiments. To extend the resultingequations to real-worldoperatingconditions, the multiplicative factors,derivedfrom the Brazil study, 1.16 for cars and utilitiesand 1.15 for trucks and buses,are used.

ALTERNATIVE VEHICLEOPERATINGCOST RELATIONSHIPS

207

the effect of roughnesson fuel As in the speed relationships, consumptionon paved roads was found by TRRL to be statistically insignificant.Again it was assumedthat this,findingresultedfrom the narrownessof the range of roughness,and an adjustmentbased on unpaved road resultswas added to the fuel consumptionequations. As with the speed relationships, a constantwas includedto make the calculatedresult match that of the TRRL in the middle of the observed range. The expressions for the adjustment, DFLR,for differentvehicletypesare: D-3 .3 + 0.0011 BI for passengercars and utilities 4.2 + 0.0014BI for trucksand buses

DFLR

The constants3.3 and 4.2 have been chosen so that at the the mean roughness roughnesslevel of 3,000 mm/km,which is approximately value for the Kenya test paved road sections,the adjustmentDFLR becomes zero. In the equationsfor buses and trucks limitshave been imposedon the power-to-weight ratio (PWR) and gross vehicleweight (GVW) terms to do not becomenegative. predictions ensurethat fuel consumption In using the fuel consumptionrelationshipsthe user should rangeof the inputvariablesshownin Table6.2, as observethe recommended deviationfrom the rangerepresentsan extrapolation. Relationships Kenya FuelConsumption 6.2.3 Alternative Based on the same set of field data as the originalTRRL-Kenya equations,Chesher (1977a) developed a new set of fuel consumption relationshipswhich incorporatenon-lineareffects of the independent ratio variables,notablythe rise plus fall and the vehiclepower-to-weight of thesevariables. These and operatingspeed,as well as the interactions relationships, which are offeredas an option in the model, are described in detailin Appendix6A.2 6.2.4 Tire Wear Based on the road user surveydata with road roughnessranging from 2,500 to 7,500mm/km,TRRL (Hideet al., 1975)obtainedthe following for tire consumption: relationships 1. Passengercarsand utilities TC - [E-83+ 0.058BI] 10-3 0.03

BI > 2,000mm/km BI < 2,000mm/km

2. Lightand mediumtrucksand buses

TC where

T rGVW [83 + 0.0112BI] 10 4 BI > 1,500mm/km BI < 1,500mm/km GVW -0.01

TC = the numberof cost-equivalenit new tires consumedper 1,000vehicle-km.

208

ALTERNATIVE VEHICLEOPERATINGCOST RELATIONSHIPS

Table 6.2: Recommended rangeof variablesfor fuel consumption prediction: Kenya relationships Variable Unpavedroads Rise plus fall,RF Roughness,BI Speed,S Cars Utilities Light trucksand smallbuses Mediumtrucksand largebuses Paved roads Rise plus fall,RF Roughness,BI Speed,S Car Utilities Lighttrucksand smallbuses Mediumtrucksand largebuses Vehiclecharacteristics Power-to-weight ratio ', PWR Gross vehicleweight 2, GVW

Units

m/km mm/km km/h

Recommended range

0-120 2,000-14,000 20 - 110 10 - 100 5 - 90 5 - 90

m/km mm/km km/h

0-120 2,000-9,000 20-140 10-110 5-100 5-100

Metrichp/ton Tons

11-35 5.0-13.0

For trucksand buses. For medium trucksand buses. Source: Based on data from Hide et al., (1975). 2

In the above relationshipslower cut-off levels have been includedto avoid producingunreasonably low valuesof tirewear for roads smootherthan thosefromwhich the surveydata were collected.The cut-off levelshave been set to 0.03 tiresper 1,000vehicle-kmfor passengercars and utilitiesand to 0.01 tires per 1,000 vehicle-kmper ton of vehicle weightfor trucksand buses. In usingthe tire wear relationships the user shouldobservethe range of the inputvariablesshown in Table 6.3, as deviation recommended from the rangerepresentsan extrapolation. 6.2.5Maintenance Parts The consumption of vehiclespareparts is expressedas a fraction of the average cost of a new vehicleper 1,000 vehicle-kmof operation. The TRRL-Kenya study (Hide, et al., 1975) obtained the following relationships which relate spare parts consumptionto road roughnessand driven: and vehicleage expressedin termsof cumulativekilometerage

209

VEHICLEOPERATINGCOST RELATIONSHIPS ALTERNATIVE rangeof variablesfor tire wear prediction: Table6.3: Recommended Kenya relationships Variable

Units

Roughness,BI Gross vehicleweightGVW1

mm/km Tons

range Recommended 2,000-8,000 5.0 -26.0

Note: For trucksand buses. Source: Adaptedfrom Hide et al., 1975.

1. Passengercars and utilities PC = tCKM [-2.03+ 0.0018BI'] 10 13 200 [-2.03+ 0.0018BI'] 10 5

for CKM < 200,000km for CKM > 200,000km

2. Buses PC =

CRM [-67 + 0.06 BI'] 10i8 1.183 [-67+ 0.06 BI'] 10

1

for CKM < 1,400,000km for CKM > 1,400,000km

3. Lightand mediumtrucks PC = {CKM [0.48+ 0.00037BI] 10-a 500 [0.48+ 0.00037BI] 10 ' where

for CKM < 500,000km for CKM > 5009000km

per 1,000vehicle-km, PC = the predictedpartsconsumption expressedas a fractionof thieaveragenew vehiclecost; BI,

for BI > 1,500mm/km BI 11500 for BI < 1,500mm/km

CKM = the average cumulativekilometerage,defined as the drivenover the lifetimeof averagenumberof kilometers a vehicle. The followingequationis used to computeCKM: CKM where

= 1/2 LIFEOAKMO

LIFEO= the averagevehicleservicelife in years, inputby the user;and driverper vehicle AKMO = the averagenumberof kilometers by the user. group, input for the vehicle per year

The subscript"i," is used to emphasizethat the values of these variablesare to be provided by the user as opposed to the values calculatedin terms of speeds in Section 5.3.3 (on depreciationand rangeof roughness the recommended interest). In usingthese relationships

210

ALTERNATIVE VEHICLEOPERATINGCOST RELATIONSHIPS

and cumulativekilometerage compiledin Table 6.4, shouldbe observed. As high values of average cumulative kilometerage,CKM, can lead to unrealistically high parts consumption, cut-offlevels for CKM have been introducedin these relationships (i.e.,200,000km for passengercars and utilities,500,000km for trucksand 1,400,000km for buses). 6.2.6 Maintenance Labor The maintenancelabor-hourrequirements were foundby TRRL (Hide et al., 1975)to be relatedto partsconsumption and road roughness: 1. Passengercarsand utilities LH = tPC [851- 0.078B1] L383PC 2. Lightand medium trucks LH fPC [2975- 0.078BI] -2507PC

BI < 6,000mm/km BI > 6,000mm/km

BI < 6,000mm/km BI > 6,000mm/km

3. Buses LH = tPC [2640- 0.078BI] 2172 PC where

BI < 6,000mm/km BI > 6,000mm/km

LH = the numberof maintenance labor-hourper 1,000 vehicle-km; PC = the predictedsparepartsconsumption, as defined earlier. The recommendedrange of the input variablesfor predicting maintenance labor is the same as for maintenanceparts prediction ,(Table6.4).

Table 6.4: Recommended rangeof variablesfor maintenance partsand labor prediction:Kenya relationships Variable

Units

CKM Cumulativekilometerage, Cars and utilities Lightand mediumtrucks Buses

km

Roughness,BI

mm/km

Recormmended range 0- 100,000 0- 400,000 0-1,100,000

Source: Adaptedfrom Hide et al., (1975).

2,500-7,500

ALTERNATIVE VEHICLEOPERATINGCOST RELATIONSHIPS

211

6.3 THE CARIBBEANRELATIONSHIPS The relationships describedin this sectionwere obtainedfrom the study conductedby TRRL in Caribbean (Hide, 1982; Morosiuk and Abaynayaka,1982). In the TRRL-Caribbean study the data were collected from vehicleoperationson paved roads. Strictlyspeaking,therefore,the resultingrelationships shouldbe applicableonly to paved roads. 6.3.1 VehicleSpeed Using the findingsby Morosiukand Abaynayaka(1982),speedsare calculatedas a function of the average rise plus fall, horizontal curvature,roughness,and carriageway width,and, for trucks,power-to-weig ratio (with the minimum limitsof 20 km/h for cars and utilities,and 15 km/h for trucks. As in the case of the Kenya relationslhips, the round-tripspeed, S, in km/h, is definedas 2 1

+ 1

d

u

The expressions for Su and Sd are as follows: 1. Passengercars Su = max [20;67.6 - 0.078RF - 0.024C - 0.00087BI - 8.1 max (0; 5 - W)]

Sd

=

max [20; 67.6 - 0.067RF - 0.024C - 0.00087BI - 8.1 max (0; 5 - W)]

2. Utilities Su = max [20; 62.6 - 0.085RF - 0.022C - 0.00066BI - 7.0 max (0; 5 - W)]

Sd = max [20;62.6 - 0.067RF - 0.022C - 0.00066BI - 7.0 max (0; 5 - W)]

3. Lighttrucks Su = max [20;51.9 - 0.222RF - 0.017C - 0.00106BI + 0.552PWR - 6.2 max (0; 5 - W)] Sd = max [20;51.9 - 0.067RF - 0.017C - 0.00106BI + 0.552PWR - 6.2 max (0; 5 - W)] where the variablesare as definedfor the TRRL-Kenyarelationships. The user should observethe recommendedrange of the variables used in predictingspeeds recommended compiledin Table 6.5, as deviation from this range representsan extrapolation and could produceunreasonable results.

212

ALTERNATIVE VEHICLEOPERATINGCOST RELATIONSHIPS

Table 6.5: Recommendedrangeof variablesfor vehiclespeedsprediction: Caribbeanrelationships Variable

Units

Road characteristics Rise plus fall,RF Horizontalcurvature, C Carriageway width,W Roughness,BI

m/km Degrees/km m mm/km

Vehiclefleetcharacteristics Power-to-weight ratioPWR

Metrichp/ton

Recommended range 0 - 140 0 - 1,200 4.0 - 9.0 1,500-15,000 12 - 30

Note: For lighttrucks. Source:Based on data from Morosiukand Abaynayaka(1982). 6.3.2 Fuel Consumption The Caribbeanrelationships expressfuel consumption in terms of the vehicle speed, average rise plus f trucks gross vehicle weight (Morosiukand Abaynayaka,1982). As in the case of Kenya relationships, the predictedround-trip fuel consumption FL, in liters/1,000 km, is definedas:

FL

FLu + FLd =

2 The expressions for the FLu and FLd are as follows: 1. Passengercars FLu = 1.16 [24 +

969 /Su +

0.0076Su + 1.33RF ]

FLd = 1.16 [24 +

969 /Sd +

0.0076S2 - 0.63 RF + 0.0029RF2]

2. Utilities FLU = 1.16 [72 + 949/Su + 0.0048S2 u + 1.118GVW RF]

FLd = 1.16 [72 +

949 /Sd +

0.0048S2 - 1.18RF + 0.0057RF2]

3. Lighttrucks FLU = 1.15 [29 +

2219 /Su +

0.0203S2 + 0.848GYW RF]

FLd = 1.15 [29 +

2219 /Sd +

0.0203S2 - 2.60 RF - 0.0132RF2]

where the variables are as defined for Kenya relationships. The

ALTERNATIVE VEHICLEOPERATINGCOST RELATIONSHIPS

213

multiplicative factorsobtainedfrom the Brazil-IJNDP Study, i.e.,1.16 for cars and utilitiesand 1.15 for light trucks, are also applied to the Caribbeanrelationships to accountfor the differentconditionsbetweenthe controlledexperiments and realworld operations. Other than those variablesincludedas,explanatoryvariablesin the above relationships, there seem to be some other factorswhich affect fuel consumption such as roughness,curvatureand roadwidth. However,it is assumedin the Caribbeanstudythat the influenceof these factorswould be indirectlyreflectedthroughtheir influencecn speed. In using these fuel consumptionrelationships the user should observethe recommended rangeof the inputvariablesshown in Table6.6, as deviationfrom the rangerepresents an extrapolation. Table 6.6: Recommendedrangeof variablesfor fuel consumption prediction Caribbeanrelationships Variable

Units

Recommended range

Rise plus fall,RF Speed,S Gross vehicleweight 2, GVW

rm/km km/h Tons

0-120 15-80 4.0-8.5

Takento be the same as for the Kenya relationship. For lighttrucks. Source:Based on data fromMorosiukand Abaynayaka(1982). 1 2

6.3.3 Tire Wear Two relationships were derivedby the TRRL-Caribbean study (Hide, 1982),one for cars and utilities,and one for lighttrucks. They relate the total consumption of tiresper 1,000vehicle-kmto road roughnessand, for light trucks,the averagegross vehicleweight. These relationships are summarizedbelow: 1. Passengercars and utilities TC

=

60 .1 t[-

+ 0.0764BI] 10 3

0.03

BI > 1,200mm/km BI < 1,200mm/km

2. Lighttrucks TC = tGVw [70.6+ 0.0135BI] 10O4 0.01 GVW

BI > 2,200mm/km BI < 2,200m/km

In order to avoid producingunreasonably low valuesof the tire wear for smooth roads, the same cut-offlevelsof tire wear as those for the Kenya relationships are employedin these relationships.In using the tire wear relationships the user should observethe recommendedrange of the input variablesshown in Table 6.7, as deviationfrom the range representsan extrapolation.

214

ALTERNATIVE VEHICLEOPERATINGCOSTRELATIONSHIPS

Table 6.7: Recommended rangeof variablefor tirewear prediction: Caribbeanrelationships Variable

Units

Roughness,BI 1, Grossvehicleweight

GVW

Recommendedrange

mm/km Tons

3,000-8,000 4.0-11.0

1 For lighttrucks. Source: Based on data from Hide (1982).

6.3.4 Maintenance Parts As in the TRRL-Kenya counterpart,the parts consumption relationships in the TRRL-Caribbean study (Hide,1982)are expressedas a functionof road roughnessand vehiclecumulativekilometerage: 1. Passengercarsand utilities CKM [-5.50+ 0.00262BI'] 10 8 for CKM < 200,000km 200 [-5.50+ 0.00262BI'] 10

for CKM < 200,000km

2. Lighttrucks

CKM [-6.54+ 0.00316 BI' - 0.00000021 (BI)2]

10i8

for CKM < 500,000km PC=

{ 2] 105 500 [-6.54+ 0.00316B1' - 0.00000021(BI') for CKM > 500,000km

where 2,500 BI' = { BI 12,000

for BI < 2,500 for 2,500 < BI < 12,000 for 12,000< BI

and other variablesare as definedfor the Kenya relationships. As high valuesof averagecumulativekilometerage, CKM, can lead to unrealistically high parts consumption, cut-offlevelsfor CKM similar to the TRRL-Kenyarelationships have been introduced(i.e.,200,000km for passengercars and utilities,and 500,000km for lighttrucks.) In using these parts consumptionrelationships the user should observethe recommended rangeof the inputvariablesshown in Table 6.8, as deviationfrom the rangerepresents an extrapolation.

ALTERNATIVE VEHICLEOPERATINGCOST RELATIONSHIPS

215

Table 6.8: Recommended rangeof variablesfor maintenance partsand labor prediction:Caribbeanrelationships Variable

Units

Cumulativekilometerage, CKM Passengercars Utilities Lighttrucks

km

Roughness,BI

mm/km

Recommended range 0-100,000 0-100,000 0-200,000 3,000-7,500

Source: Basedon data from Hide (1982). 6.3.5 Maintenance Labor The data obtainedfrom the TRRL-Caribbean study (Hide,1982)were not sufficientfor estimatingelaborate relationshipsfor predicting maintenancelabor requirements.Therefore,the relationships found in the TRRL-Kenyastudyare used,as shown in section6.2.6above. 6.4 THE INDIARELATIONSHIPS The relationships describedin this sectionwere based on the study conductedin Indiaby the CentralRoad ResearchInstitute(CRRI,1982)and augmentedby subsequentanalysisby the WorldBank (Chesher,1983). 6.4.1 VehicleSpeed Vehiclespeedsare predictedas a linearfunctionof the average rise plus fall, horizontalcurvature,carriageway width, roughness,with minimum limits applied to the originalrelationships, i.e., 20 km/h for cars and utilitiesand 15 km/h for trucksand buses. As in the case of the Kenya and Caribbeanrelationships, the round-tripjourneyspeed,S, in km/h, is defineid as: 1 2

Su

Su

The expressions for Su and Sd are as follows: 1. Passengercars (smalland medium)and utilities: Su = max [20;60.6 + 1.046W - 0.192RF - 0.0078C - 0.0036BI] Sd = max [20;60.6 + 1.046W - 0.184RF - 0.0078C - 0.0036BI]

216

ALTERNATIVE VEHICLEOPERATINGCOST RELATIONSHIPS 2. Buses (Tataand Ashok) Su = max [15; 55.0+ 0.609W - 0.301RF - 0.0077C - 0.0022 BI]

Sd = max [15;55.0+ 0.609W - 0.228RF - 0.0077C - 0.0022 BI]

3. Trucks (mediumand heavy) Su = max [15; 47.3 + 1.056W - 0.269RF - 0.0099C - 0.0019 BI]

Sd = max [15; 47.3 + 1.056W - 0.265RF - 0.0099C - 0.0019 BI]

where the variablesare as defined for the Kenya relationships. The recommendedrange of the input variablesshown in Table 6.9 should be observed,as deviationfrom the rangecouldproduce unreasonable results. Table 6.9: Recomnended rangeof variablesfor vehiclespeedsprediction: India relationships Variable

Units

Riseplus fall,RF Horizontalcurvature,C Carriageway width,W Roughness,BI

m/km Degrees/km m mm/km

Recomnended range 0-150 0-1,200 3.5-7.0 2,000-7,000

Source: Basedon data from CRRI (1982). 6.4.2 Fuel Consumption Fuel consumption is predictedas a functionof the vehiclespeed, road roughnessand rise plus fall, based on the originalexperimentally obtainedrelationships adjustedto reflectactualoperatingconditions. As in the case of the Kenya and Caribbeanrelationships, the predicted round-trip fuel consumption,FL, in liters/1,000km, is determinedas:

FL=

FLu + FLd

u

d

2 The expressions for FLu and FLd are as follows: 1. Small passengercars FLU = 1.16 [49.8+ 319 + 0.0035S2 + 0.0019BI + 0.942RF] u u ~ ~~~ u FLd = 1.16 [49.8+ 319 + 0.0035S2 + 0.0019BI - 0.677RF] Sd

217

ALTERNATIVE VEHICLEOPERATINGCOST RELATIONSHIPS 2. Mediumpassengercars

FLU = 1.16 [10.3+ 1676+ 0.0133S2 + 0.0006BI + 1.388RF] U s~ ~ ~~~uU FLd = 1.16 [10.3+ 1676+ 0.0133Si + 0.0006BI - 1.032RF]

3. Utilities FLU = 1.16 [-30.8+ 2260 + 0.0242S' + 0.0012BI + 1.278RF]

S

Li

U

FLU = 1.16 [-30.8+ 2260 + 0.0242S" + 0.0012BI (1~~~s U d

-

0.565RF]

4. Mediumtrucksand buses (Tata) FLU = 1.15 [85.1+ 3900 + 0.0207S2 + 0.0012BI U Su + 3.328RF - 4.59min (PWR;30)] FLd = 1.15 [85.1+ 3900 + 0.0207S2 + 0.0012BI dSd -

U

1.777RF - 4.59 min (PWR;30)]

5. Heavy trucksand buses (Ashok) FLU = 1.15 [266.5+ 2517 + 0.0362S2 + 0.0066BI

Su + 4.265 RF - 4.60 min (PIWR; 30)]

FLd = 1.15 [266.5+ 2517 + 0.0362S2 + 0.0066BI + 2.737RF - 4.60min (PWR;30)]

where variablesare as defined for the Kenya relationships. In the equationsfor busesand trucksa floorvalue of 30 has been imposedon the predictions ratio (PWR)to make sure that fuel consumption power-to-weight factorsobtainedin Brazilare do not become negative. The multiplicative i.e., 1.16 for cars and utilities, also used in the India relationships, range of the input and 1.15 for trucks and buses. The recofnnended variablesshown in Table 6.10 should be observedas deviationfrom the results. rangecouldproduceunreasonable

218

ALTERNATIVE VEHICLEOPERATINGCOST RELATIONSHIPS

rangeof variablesfor fuel consumption Table6.10: Recommended prediction:Indiarelationships Variables

Units

Recommendedrange

Road characteristics Rise plus fall,RF Roughness,BI

m/km mm/km

0-100 2,000-10,000

Vehiclefleetcharacteristics Speed,S Passengercarsand utilities Mediumtrucksand buses (Tata) Heavytrucksand buses (Ashok) Power-to-weight ratio,'PWR

km/h 15-80 10-75 10-65 Metrichp/ton

7-19

l For trucksand buses. Source: Based on data from CRRI (1982). 6.4.3 Tire Wear Tire wear is predictedas a functionof the road rise plus fall, horizontalcurvature,width and roughness,and, in the case of buses, the cumulativekilometerage driven. The predictionemploysthe relationships estimatedby Chesher (1983),as discussedin Appendix6B.1, based on the representthe life data collectedby CRRI (1982). As these relationships of a new tire, definedas the numberof kilometersdrivenper tire, they have to be modifiedin two steps,as follows. First,they are invertedand then multipliedby the number of tires of the vehicleto representthe numberof new tires consumedper 1,000 vehicle-km. This involvesa bias as describedin Appendix6B. correctionfor the nonlineartransformation Second, a multiplicative factor equal to 0.727 obtainedby CRRI (1982, Volume2) is appliedto the numberof new tiresconsumedto accountfor the use of recaps; this resultsin the predictednumberof cost-equivalent new tiresper 1,000vehicle-km: 1. Passengercars (smalland medium)and utilities TC = [4000/(60020 - 5.86 BI) + 0.005]x 0.727 2. Buses (Tataand Ashok) TC = [1000NT/max (36100- 0.00434CKM - 241 RF - 10.54 C - 1.126BI + 1044W; 2000)+ 0.0022NT] x 0.727 3. Mediumand heavytrucks TC = [1000NT/max (23500- 117.5RF - 8.49 C - 0.609 BI + 2410 W; 2000)+ 0.0015NT] x 0.727

VEHICLEOPERATINGCOST RELATIONSHIPS ALTERNATIVE

219

In the equationfor buses and trucks,a floor value of 2,000 km has been imposed on the predictedtire life to ensure that tire wear do not becomenegative. predictions rangeof the inputvariablesshown in Table 6.11 The recommended should be observed, as departure from the range represents an extrapolation. rangeof variablesfor tirewear,maintenance Table6.11: Recommended labor prediction:Indiarelationships and parts Variable Road characteristics Rise plus fall,RF Cars and utilities Buses Trucks

Units

m/km 0-40 0-50 0-60

Horizontalcurvature,C Cars and utilities Buses Trucks

Degrees/km

width,W Carriageway Buses Trucks

m

Vehiclefleet characteristics CKM Cumulativekilometerage, Cars and utilities Buses Trucks Grossvehicleweight,GVW Trucks

Recomended range

0-700 0-1,000 0-1,200 3.5-7.5 3.5-7.5 km 12,000-250,000 20,000-1,000,000 -9,000-950,000 Tons 7.0-28.0

Source: Basedon data fromCRRI (1982). Parts 6.4.4 Maintenance were estimated for predictingpartsconsumption The relationships by Chesher(1983)usingthe data collectedin the Indiastudy(CRRI,1982); are discussedin Appendix6B.2. Since the estimation these relationships was done in log-linearform, the bias associatedwith the non-linear must be accountedfor, as describedin Appendix6B. As transformation expressparts costs in monetaryunits (in rupees,1978 these relationships by dividingthem by the averagecost prices),they have to be standardized of the vehicleclass in question. The new of a new vehiclerepresentative vehicleprices (in rupees,1978 prices)obtainedby Chesherand Harrison

220

ALTERNATIVE VEHICLEOPERATINGCOST RELATIONSHIPS

(1985) were used in the standardization, in the same manner as that employed in the Brazil parts consumptionrelationships. The resulting relationships expressparts consumption per 1,000vehicle-kmas a function of the road roughness,and, in the case of buses and trucks,the road rise the case of buses and trucks,road roughness. The relationships employed plus fall, horizontal curvature and width, and vehicle cumulative kilometeragedriven, and finally,in the case of trucks only, the gross vehicleweight: 1. Cars (smalland medium)and utilities PC where

= PCRPc/NVPc

PCRPc = the partscost of passengercars,in 1978 rupees as per 1,000vehicle-km, givenby: PCRPc= 42.0 exp (0.000169BI) NVPC = the averagepriceof a new car in 1978 rupees,equal to Rs 64,800which is the weightedaverageof the pricesof the PremierPadminiand Ambassador. 2. Buses (Tataand Ashok) PC

where

= PCRPb/NVPb

PCRPb= the partscost of buses,in 1978 rupeesper 1,000 vehicle-km, given by: 0 -358 exp (0.0000526 PCRPb= 0.691 (CKM) BI + 0.000282C +

0.00675RF + 2

00)

w

NVPb = the averagepriceof a new bus in 1978 rupees,equal to Rs234,000which is the weightedaverageof the pricesof the Tata and Ashok buses. 3. Trucks (mediumand heavy) PC where

= PCRPt/NVPt

PCRPt = the partscostsof trucks,in 1978 rupeesper 1,000 vehicle-km, givenby: 359 exp (0.0000618 PCRPt= 0.924 (CKM)0. BI + 0.000686C +

0.000545RF + 0.853+ 0.0765GVW) w NVPt = the averagepriceof a new truck in 1978 rupees, equal to Rs 180,700which is the weightedaverageof the pricesof the Tata and Ashok trucks

ALTERNATIVE VEHICLEOPERATINGCOST RELATIONSHIPS

221

In using the above relationshipthe recomended range of the inputvariablesshownin Table 6.9 shouldbe observedas departurefrom the rangerepresentsan extrapolation. 6.4.5 Maintenance Labor Maintenancelabor, expressedin the number of labor-hoursper 1,000 vehicle-km,is predictedas a functionof parts consumption, and in the case of buses and trucks,road roughness. The relationships employed representa modifiedform of those obtainedby Chesher(1983)basedon the data collectedin the India study (CRRI, 1982); these relationships are discussedin Appendix6B.3. The modifications made are corrections for the biases that resulted from exponentiatingthe original log-linear relationships. 1. Passengercars (smalland medium) 0 -584 LH = 1.799 (PCRPc)

2. Utilities 0 .445 LH = 4.42 (PCRPc)

3. Buses (Tataand Ashok) 0 .473 exp (0.0000426 LH = 1.839 (PCRPb) BI)

4. Trucks (mediumand heavy 654 exp (0.0000250 LH = 0.898 (PCRPt)0. BI)

where

LH = the numberof maintenance laborhoursper 1,000 vehicle-km; and PCRCC,PCRCb,PCRPt= the partscosts in 1978rupeesper 1,000vehicle-kmfor cars,busesand trucks,as computedpreviously.

In using the above relationships the recommendedrange of the inputvariablesshownin Table6.9 shouldbe observedas departurefrom the rangerepresents an extrapolation.

222

ALTERNATIVE VEHICLEOPERATINGCOST RELATIONSHIPS

APPENDIX6A MODIFICATIONS OF TRRL-KENYARELATIONSHIPS 6A.1 VEHICLESPEEDRELATIONSHIPS 6A.1.1 OriginalEquations The speed relationships originallyderivedby TRRL (Hideet al., 1975)consistof separateequationsfor unpavedand paved roads: Unpavedroads 1. Passengercars S = 84.2 - 0.210RS - 0.070F - 0.118C - 0.13 M - 0.186RD

0.00089BI

-

2. Utilities(lightgoodsvehicles)

S

=

81.2 - 0.317RS - 0.059F - 0.293M - 0.197RD

0.0966C

-

0.00095BI

-

3. Buses S = 62.6 - 0.492RS - 0.0102F - 0.163M - 0.0905RD

-

0.0463C - 0.00036BI

4. Lightand mediumtrucks S = 49.2 - 0.433RS + 0.00445F - 0.061C - 0.00060BI - 0.221M - 0.265RD + 1.10 PWR Paved roads 1. Passengercars S = 102.6- 0.372RS - 0.0759F - 0.110C

0.00491A

-

2. Utilities S = 86.9 - 0.418RS - 0.0496F - 0.0738C

-

0.00278A

-

0.00417A

3. Buses S = 72.5 - 0.526RS + 0.0666F - 0.0661C

ALTERNATIVE VEHICLEOPERATINGCOST RELATIONSHIPS

223

4. Lightand mediumtrucks S = 48.0 - 0.519RS + 0.030F - 0.0581C - 0.00042A +

where

1.10PWR

M = averagemoisturecontent,in percent; RD = mean rut depth alongthe wheel paths,in mm; and the othervariablesare as definedin Section6.2.1.

In the above equationsthe parametersfor PWR have been modified from those of the original relationships to account for conversionfrom British to metric horsepower. There were also two incompatibilities betweenthe pavedand unpavedspeedequationswhich had to be reconciledin orderto make these relationships more useful: 1. The paved speed equationsdo not have a coefficientfor the effect of road roughness. This makes predictedspeeds on paved roadsinsensitive to road surfaceconditions. 2. The unpavedroad speedequationsdo not have a coefficient for the effectof altitude,whereasthe pavedroad speedequations do. In Kenya the averagealtitudeof the speed test sections was about 1,300metersabovemean sea level. As altitudehas a negativeeffecton speed in the paved road equations,when these equationswere employed in predictingspeeds at high altitude,it was possible for predictedspeeds on unpaved roads to be greater than predictedspeedson paved roads of similar characteristics.Thus, these speed equationswere inadequatefor applications such as evaluatingthe upgrading of unpavedroadsin high altitudeareas. 6A.1.2 Modifications The followingparagraphsexplain Ihow roughnessand altitude coefficientshave been incorporatedin the paved and unpaved road speed equationsrespectively to overcometheseproblems. Roughnesscoefficient.A plausiblereason that road roughness was found to be statistically insignificant for paved roadswas that the analysiswas based on a narrow range of roughnessof the test sections (about 1,500 to 4,000 mi/km). On the other hand, roughnesswas indeed found to be statistically significantin the analysisof the unpavedroad speeds in which the roughnesscovereda much wider range (about3,500 to 14,000mm/km). Therefore,the effectof roughnesshas been incorporated in the paved road speed relationshipsby extrapolatingthe roughness coefficients for unpavedroads,as describedbelow. Assume that roughnessis a generic measure of road surface characteristics, meaning that paved and uinpavedroads with identical roughnessshould have the same roughnesseffect on speed. Thus, the

224

ALTERNATIVE VEHICLEOPERATINGCOST RELATIONSHIPS

followingroughnesscoefficients for unpavedsurface can be transferredto paved surfacesituations: Vehicletype

Roughnesscoefficient (km/hper mm/km)

Passengercars Utilities Buses Lightor mediumtrucks

-0.00089 -0.00095 -0.00036 -0.00060

The transferprocedureis describedas follows. For example,the original speed equationfor passengercarson paved road is givenby: S = 102.6- 0.372RS - 0.076 F - 0.111C - 0.0049A After the coefficient transferthe equationbecomes:

S

=

102.6- 0.372RS - 0.076F - 0.111 C - 0.0049A AS - 0.00089BI

+

where

AS = correctionterm to be added to the originalconstantterm (102.6),so that the new equationwill yield the same speed predictionwhen it is applied to the average roughnessin the Kenyasample.

From the TRRL Report (Hide et al., 1975), this average is approximately 3,000mm/km. Therefore,AS is computedas: AS = 0.00089x 3000 = 2.67 km/h The above procedureis applied to the speed equationsfor the remainingvehicletypes. The resultingequationsfor all vehicletypesare sunmarizedbelow: 1. Passengercars S = 105.3- 0.372RS - 0.00491A

-

0.0759F

-

0.110C - 0.00089BI

2. Utilities S = 89.7 - 0.418RS - 0.00278A

0.0496F

-

0.0738C - 0.00095BI

S = 73.4 - 0.526RS + 0.0666F - 0.00417A

-

0.0661C - 0.00036BI

-

3. Buses

225

VEHICLEOPERATINGCOST RELATIONSHIPS ALTERNATIVE 4. Lightand mediumtrucks S = 49.8 - 0.519RS + 0.030F - 0.0581C - 0.00060BI - 0.00042A + 1.10 PWR

That altitudewas not found to be a coefficient. Altitude statisticallysignificantvariable for unpaved roads can possiblybe attributedto the fact:that except for very few sections,the unpavedtest sectionswere at altitudeswithina relativelynarrowrangeof 1,000- 2,000meters. On the other hand, the altitudesfor the paved test sectionsspeed spread quite uniformlyover a considerablygreater range of 200 2,300meters. If this argumentis correct,then it would seem reasonableto use the paved road altitudecoefficientin the unpavedroad speedequations. To do this, the value of 1,300 meters (abovethe mean sea level)is takenas the mean value for the paved road section. Using a similar procedure to that for the roughness coefficient,the followingrevised speed relationshipsare obtainedfor unpavedroads: 1. Passengercars

S = 90.6 - 0.209 RS - 0.070 F - 0.118 C

-

0.00089 BI -

-

0.00095BI -

0.135M - 0.186RD - 0.00491A 2. Utilities

S = 84.8 - 0.317 RS - 0.059 F - 0.0966 C 0.293M - 0.197RD - 0.00278A 3. Buses

S = 68.0 - 0.492 RS - 0.0102F - 0.0463 C - 0.00036BI 0.163M - 0.0905RD - 0.00417A 4. Lightand mediumtrucksand buses S = 49.7 - 0.433 RS + 0.00445F - 0.061 C - 0.00060BI 0.221M - 0.265RD - 0.00042A + 1.10 PWR In addition to the modificationsdescribed above, the were furthermodifiedas describedbelow in the relationships HDM-III to keep the data requirementwithin a reasonable range: 5. Elimination of the variables M for unpavedroads. relationships

and

RD

from the

In the light of the relativelyinsignificantcontributions ofthesevariablesto speed prediction,they were replacedby the mean valuesto reducethe data requirement.The following mean valueswere listedin the TRRL report:

226

ALTERNATIVE VEHICLEOPERATINGCOST RELATIONSHIPS

Variable

Mean value

Moisturecontent(%) Rut depth (m)

2.6 18.9

6A.2 FUEL CONSUMPTION:CHESHERNON-LINEARRELATIONSHIPS Using multiple regressionanalysis, Chesher (1977a) first estimatedfuel consumption relationships for passengercars,utilities,and truckswith three levels of loading (viz.,empty, half-full,and full). The unmodifiedfuel consumptionprediction,FL,, in liters/1,000km is given by: FL1 u + FL1 d

FL,

U

2 where FLju and FL1d are direct predictionsof fuel consumptionfrom regressionequations,for the uphilland downhillsegments,respectively, (in liters/1,000 km). The expressions for FL,u and FLid are: 1. Passengercar FLiu = au + b RF FLid = ad + c RF 2. Bus and trucks FLju = exp (au + b RF) FLid = exp (ad + c RF) In the above equations, au, bd, b and c are functions of speed, roughnessand depth of loosematerial,givenby: au = ao + a, Su + a2 S2 + a. BI + a4 SL u

ad = ao + a, Sd + a2 S2 + a, BI + a4 SL b = bo + b1 Su + b2 S2; u c

where

Su

= co + C, Sd + C2 S2

Sd

,

BI = independent variablesas definedin the text; SL = depthof loosematerial,in mm; and

ALTERNATIVE VEHICLEOPERATINGCOST RELATIONSHIPS a1 a2 , a, , a4 bo , b, b2=

ao

coI

227

,

c,,

regressioncoefficients.

C2

The valuesof theseregressioncoefficients for pavedand unpaved roadsand differenttypes of vehicleare compiledinTable6A-1. The three relationships obtained using the testtruckwere intended for buses and lightand mediumtrucks. The variableSL in the expressionsfor au and ad is replaced with the value 1.0, the averagein the TRRL-Kenyastudyfor unpavedroads. (For pavedroadsSL is not definedand the parametera. takeson the value 0.) In addition,furthermodificationsare requiredto account for the effectsf: 1. 2. 3. 4.

The power-to-weight ratio; The paved road roughness; Speedchangecycles;and The gross vehicleweight.

The followingparagraphsdescribethe abovemodifications in some detail: 1. Power-to-weight ratio. The three fuel consumption obtainedusing the test truck under empty,half relationships ratios of and full loadscorrespondto fixed power-to-weight 40.6, 19.0 and 5.1 metric hp/ton,respectively.To estimate fuel consumption for busesand trucksof otherpower-to-weight ratiosthe followinglinearinterpolation formulais used: FL1 f + PWR - 5.1

[FL1h- FLlfjor PWR < 19.0

19.0-5.1 FL2 = FL,h +PR 6

h 40.6

19.0 [FL,e- FLIh]or PWR > 19.0

-19.0

where

computedwith the effect FL2 = the predictedfuel consumption, ratio accountedfor, in liters/1,000 of power-to-weight vehicle-km; ratioof the vehiclein metric hp/ton; PWR = power-to-weight and consumption, the predicted fuel FL,e,FLXh,FL,f = for the test truck under computedwith therelationships empty,half, and full loads, respectively, in liters/1,000 vehicle-km.

228

ALTERNATIVE VEHICLEOPERATINGCOST RELATIONSHIPS For passenger cars and utilities the effect of the power-to-weight ratiowas not consideredsignificant enoughto incorporate explicitlyand, therefore, we have:

FL2 = FL, 2. Paved road roughness. For paved roads and all vehicletypes the increasein fuel consumptiondue to roughness,DFLr, is added to FL2. For simplicity, the adjustmentDFLr isassumed to be that employed in the original TRRL-Kenyaequations, i.e., -3.3 + 0.0011 BI for passengercars and utilities

DFLr

=

{I -4.2 + 0.0014BI for busesand trucks

3. Speed changecycles. Basedon the findingsof the Brazil-UNDP study, to take account of the differencesbetween the experimentaland actual operatingconditionsthe values of fuel consumptioncomputedfor constantspeedsabove for both paved and unpaved roads are increasedby 16 percent for passengercars and utilitiesand 15 percent for buses and trucks. 4. Gross vehicleweight. As only one truck was employedin the field experimentsthe applicationof the fuel consumption equation obtained has to be adjusted for different gross vehicleweights. This is done by adding a correctionterm, DFLgvw, to the fuel consumptioncomputed for buses and trucks; DFLgvwis given by: DFLgvw = -179.4+ 80.8 IGVW where GVW = the gross vehicleweight,in tons. Summaryof relationships.Finally,with modifications(2), (3) and (4) incorporated, the updated fuel consumptionrelationships can be summarizedas: Unpavedroads 1.16 FL2 for passengercarsand utilities FL = { 1.15 FL2 - 179.4+ 80.8 JFVW for busesand trucks Paved roads FL

1.16 [FL2 - 3.3 + 0.0011 BI] for passengercarsand utilities ={

1.15 [FL2- 4.2 + 0.0014BI] -179.4+ 80.8 IGVW for busesand trucks where FL = the predictedfuel consumption, with all effects incorporated, in liters/1,000 vehicle-km.

Relationships for KenyaNon-LinearFuelConsumption Table6A.1: RegressionCoefficients

Coefficients

UnpavedRoads PassengerCars Utilities Trucksand buses Empty Half-full Full PavedRoads Passengercars Utilities Trucksand buses Empty Half-full Full r

ao

68.61 4.580

a1

a2

a4

a3

bo

bl

b2

co

cl

c2

-0.01568 0.00004032 0.00003496 -0.0380 -0.0111 0.0008902 0.04204 2.151 -.02019 0.0093 0.001275 0.00007562 0.00001026 0.008346 0.01541 0.0001 -0.00000199 0.005673 0.0006013 0.00000479

4.489 0.003373 0.0001143 0.00002515 0.01480 0.01989 0.0000 0.0000005 -0.03126 0.0004168 0.00001562 0.00345 0.01767 0.0004 0.00000502 -0.01970 5.114 0.02883 5.382 0.02568 0.0003415 0.00001582 0.03070 0.008792 0.0008 -0.00001069 -0.03386

0.00007993 0.00000328 0.0006130 0.00000671 -0.001797 0.00002141 0.00007821 -0.02075 -0.0008132 0.00000592

64.48 4.699 4.032 4.922 5.772

0.1330 0.00729 0.0004365 0.00009038

0 0

0 0

1.671 0.0047 -0.00008529 0.1072 0.01305 0.0001 -0.00000231 0.01229

0.01288 0.01822 0.05521

0 0 -

0 0 0

0.02029 0.0000 -0.00000189 -0.007446 -0.001021 0.02071 0.0003 -0.00000654 -0.009503 -0.001433 0.001965 0.0015 -0.00001554 -0.02161 -0.001507

So

Source:Chesher(1977a).

0.00001888 0.0003209 0.0006378

0.00000919 0.00001334 0.00001648

230

ALTERNATIVE VEHICLEOPERATINGCOST RELATIONSHIPS

APPENDIX6B MODIFICATIONS OF INDIARELATIONSHIPS 6B.1 TIRE WEAR RELATIONSHIPS The tire life relationshipsoriginally obtained by Chesher (1983a,1983b)are as follows: 1. Passengercars and utilities TL = 60020- 5.86 BI 2. Largebuses TL = 36100 - 4.34 CKM 1000 3. Trucks

241 RF - 10.54C - 1.126BI + 1044W

TL = 23500 - 117.5RF - 8.49 C - 0.609 BI + 2410 W TL = the predictedtire life, in km per physicallyequivalent new tire;and

where

the othervariablesare as definedin the text. The quantityused in the HDM-IIIfor tire consumption, i.e.,the number of equivalentnew tires per 1,000 vehicle-km,may be obtainedby dividing 1,000 NT by TL, where NT is the number of tires per vehicle. Since the inverseof TL is a non-lineartransformation, the associatedbias must be corrected.The Biasmay be approximated by aaiTLs, where 82 and TL are unbiasedestimatorsof the varianceof the regressionerror and the mean of the dependentvariable. The statisticsreportedby Chesherand Harrison(1987)neededto computethe bias correctionare as follows:

Vehicletype Car Largebus Mediumor largetruck where

TL 30,600 27,700 33,400

S2

S2

u

w

8.0 x 10' 11.2 x 10' 29.6 x 10'

28.3 x 106 34.6 x 10' 26.9 x 106

Su and Sw = unbiased estimators of the variances of the companyand vehicleerror terms,respectively.

ALTERNATIVEVEHICLEOPERATINGCOST RELATIONSHIPS

231

Using these figures,for example,the bias correctionterm for passengercars and utilitiescan be computedas follows: 02

bias = -

8.0 x 106+28.3 x 106 16 =-__ = 1.266 x

TL'

30,600a

Thus the modifiedrelationship for passengercars and utilitiesis givenas follows: TC = 4000/(60020 - 5.86 BI) + 4000 x 1.266x 10 6 = 4000/(60020 - 5.86 BI) + 0.005. The other relationships used in the HDM-III were obtainedin a similar manner. 6B.2 PARTSCONSUMPTION RELATIONSHIPS The parts consumption relationshipsoriginally obtained by Chesher(1983)may be expressedin HDM-IIIformatas follows:

1. Cars and utilities In

(

PCRPc ) = 1.264+ 0.000169BI 10

2. Largebuses

tn (P 10

b) =

-

0.309+ 0.358In _2LM)+ 0.0000526BI 10lD0

+ 0.000282C + 0.00675RF + 2.00 1 w 3. Mediumand heavytrucks in (PCRPt = 0.359Qn CKM)+ 0.0000618BI 10 1000 + 0.000686C + 0.000545RF + 0.853 1 w + 0.0765GVW where the variablesare as definedin the text. To use these relationships they must be exponentiated and then correctedfor the bias causedby the non-lineartransformation.

ALTERNATIVE VEHICLEOPERATINGCOST RELATIONSHIPS

232

LABORRELATIONSHIPS 6B.3 MAINTENANCE The maintenance labor relationshipsoriginally obtained by Chesherare as follows: 1. Passengercars

PCRP Qn (LH) = 1.896+ 0.584Qn

,a 10

2. Utilities PCRP Qn (LH) = 2.482+ 0.445Qn CRa 10 3. Largebuses

Qn (LH) = 1.652+ 0.473 In

PCRPb + 0.0000426BI 10

4. Trucks PCRPt Qn (LH) = 1.378+ 0.654In

+ 0.0000250BI 10

where the variablesare as definedin the text. To use these relationships and then correctedfor the bias caused in HDM-IIIthey were exponentiated by the non-lineartransformation (Chesher,1982).

CHAPIER 7

Benefits, Costs and Economic Analysis

The HighwayDesignand Maintenance Model (HDM-III) was designed to facilitate themakingof economic comparisons between manyalternatives, takingintoaccountthe interrelation betweenconstruction standards and maintenance operations in determining the qualityof a roadlinkand the interrelation betweenroad qualityand the operatingcosts of vehicles using the road. Link-alternatives may be definedby assigningto a particular linkdifferent construction and maintenance standards, traffic, and exogenous costsand benefitssets. The submodels thusfar described providethe costsof construction, maintenance, and vehicleoperation for any such link-alternative. Differences in thesecostsare part of the basisfor the economic evaluation of one alternative relativeto another, or of any alternative relativeto the "base"case. Also involvedare benefitsdue to increased volumesof traffic,and exogenous benefitsand costs. How theseelements are put togetherintoeconomic analysesis the subject of thischapter. 7.1 ROAD BENEFITSAND COSTS

For everyroadlinkand link-alternative, for everyyear of the analysis period, the physicalquantitiesinvolvedin construction and in maintenanceare calculatedand then multipliedby their unit prices. The resultingcosts for differentcomponentsare identifiedas eithercapital or recurrent,as explainedafter the equations. From the totals of componentcosts in these two categories,the cost differencesbetween alternatives for any link in a givenyear are calculatedas follows: Road capitalcost: Road recurrentcost: where

ACAP(mn)

CAPm

CAPn

(m-n)

RECm

RECn

ACAP(m-n) = the differencein road capitalcostof alternativem relativie to alternativen (fora given link in a givenyear); CAPj = the totalroad capitalcost incurredby alternativej; AREC(m-n) = the differencein road recurrentcost of alternativem relativeto alternativen; RECj = the totalroad recurrentcost incurredby alternativej. 233

234

BENEFITS,COSTS,AND ECONOMICANALYSIS

These differencesare calculatedseparatelyfor each year for each pair of link-alternatives that are to be compared. The total road capitalcost in any year comprisesall the costs incurredin that year for the construction option applied to the linkalternativeand all road maintenanceoperationsthat are classifiedas "capital." Similarly,the total road recurrentcost in the year consists of all that year's costs for maintenanceoperationsthat are classifiedas "recurrent."The HDM model providesa defaultclassification for capital and recurrentmaintenanceoperations. For paved roads the operations treated in the model as capitalare pavementreconstruction, overlaying, resealingand preventivetreatment.Patchingand routine-miscellaneous are treatedas recurrent. For unpavedroads,regravelling is the only capital maintenanceoperation;all othermaintenanceoperationsfor unpavedroads are treatedas recurrent. However,the user has the optionof overriding this classification with his own. 7.2 VEHICLEBENEFITSAND COSTS The annual economicbenefitsin terms of vehicleoperatingcost and travel time savingsare calculatedseparatelyfor normaland generated traffic. Normaltrafficis definedas equal to the total trafficin the baselinecase, and generatedtrafficas the trafficinducedor divertedto the roadby improvements relativeto the baseline. The baselinecase need not be either of the alternativesin the comparison. In evaluatingroad user benefitsthe model treatseach vehiclegroup as a demand entity or market segmentwhich is associated with its own unit price of travel. The benefitsare firstcomputedfor each vehiclegroup and then summedoverall vehicle groups to give total road user benefits. In the contextof the above definitionsof normaland generatedtraffic,the road user benefits of alternative m relativeto alternative n, for a given link in a given year, are calculatedusing the followingformulas: (a) Vehicleoperatingbenefitsdue to normaltraffic:

AVCN(m-n)

T TN I 1

=

EUCni- UCmi]

1 (b) Vehicleoperatingbenefitsdue to generatedtraffic

AVCG(M-n)

1

=

z

1/2 ETGmi+ TGnilEUCni- UCmil

If alternative n were the baselinecase, which is normallyalthough not necessarilyso, then TGni would be equal to zero, and the above equationswould reduceto the traditional fomulas. In other cases,for computational convenience, the divisionof benefitsbetween"normal"and "generated" as calculatedby the HDM variesfrom the usual definitions, but the totalbenefitsare identical.

235

BENEFITS,COSTS,AND ECONOMICANALYSIS (c) Vehicletraveltime benefitsdue to normaltraffic:

rCNm-n) =

XTN1

[UTni- UTmi]

(d) Vehicletraveltime benefitsdue to generatedtraffic2 ATCG (m-n)

where

AVCN(m-n)

TNi UCji

AVCG(m-n)

TG-i

ATCN(m-n) UTji

ATCG(m-n)

=

z

1/2 [TGmi + TGn][IUTni - UTm]

= the vehicleoperatingbenefitsdue to normal trafficof alternativem relativeto alternativen; = vehiclegroup i normaltrafficin numberof vehiclesper year in both directions; =

the averageoperatingcost per vehicle-trip group i under over the link for veh'icle alternativej (j = n or m);

=

the vehicleoperatingbenefitsdue to generated trafficof alternativem relativeto n; alternative

=

the generatedtrafficof vehiclegroup i due to alternativej, relativeto the baseline alternative(whichneed not be the same as either alternativen or m), in numberof vehiclesper year in both directions;

=

the traveltime benefitsdue to normaltraffic of alternativem relativeto alternativen;

=

the averagetraveltime cost per vehicle-trip over the link for vehiclegroup i under alternativej (j = n or m); and

=

the traveltime benefitsdue to generated trafficof alternativem relativeto alternativen on the given link in the given year.

, are overall the vehiclegroupsspecifiedby the user. The summations, of the aboveformulasthe user For the underlyingtheoryand assumptions may consult,interalia, van der Tak and Ray (1971),Walters(1968b),or Meyer and Straszheim(1971). 2 See footnote1.

236

BENEFITS, COSTS,AND ECONOMICANALYSIS

7.3 EXOGENOUSBENEFITSAND COSTS The savings in vehicle operating costs and travel time endogenouslycalculatedby the HDM model as describedabove normally constitutethe great majority of total benefits to society of road 3 improvements. The principalexceptionsare reductionsin accidents, environmental impacts(e.g.,noise and air pollution),and, under impeded trafficflow conditions,the increasedoperatingcosts due to congestion. Where these effectsare significant, they can be estimatedseparatelyand enteredas exogenousadditionsto the effectsthatare handledinternally. submodeluses parametersfurnishedby The exogenousbenefit-cost the user to compute,for each year of the analysis,the exogenousbenefits or costs and makes the results available for the model's economic analysis. Benefitand cost streamsmay be scheduledto begin at definite calendar years or to be triggeredby the completionof a construction project. For both benefitsand costs the user has the optionof entering valuesat particularyears relativeto the start of a streamor defininga streamgrowingfrom an initialvalue at eithera linearor compoundrate. With the first option, values put in remain constant every year until replaced. With the other option,the user specifiesan initialvalue and growth rate -- as a fixed incrementper year or a percentageper year -and the submodelcalculatesthe appropriate valueeach year. For each pair of alternatives beingcomparedon a given link in a givenyear, the differencein net exogenousbenefitsis as follows:

where

AEXB(m-n)

EXBm - EXCM - EXBn + EXC

AEXB(m-n) =

the differencein net exogenousbenefits relativeto of alternative m (benefits-costs) alternativen (fora given linkand year);

EXBj EXCj

=

exogenousbenefitfor alternativej, given by the submodelfor that linkand year; exogenouscost for alternativej, submodelfor that linkand year.

given by the

7.4 ECONOMICANALYSISAND COMPARISONS that are to be involvedin a For each pair of link-alternatives comparison,the formulasabove are used to calculate,year by year, the benefitsor costs of one relativeto the other, c6mbiningroad, vehicle, and exogenouscomponents,both capital and recurrent. The distinction 3 For theoriesand methodologyfor estimatingbenefitsand coststhat are not computedwithinthe model,the usermay consult,interalia,Walters (1968a),and Carnemarket al. (1976).

237

BENEFITS,COSTS,AND ECONOMICANALYSIS

betweencapitaland recurrentcosts is maintainedsolelyfor the purposeof in ciases where separatebugetary computingfinancialbudgetaryconstraints recurrent items. ceilingsare enforcedfor capitaland Usually it is convenientto groulpvarious link-alternatives rather than examine each alternativefor each link separately. This is done by grouping several links in one group and defining that are each of which is a set of link-alternatives "group-alternatives," to be treatedas a unit. In otherwords,each group of linkswith one set can be comparedwith the same group of links but havinga of alternatives differentset of alternatives. The time streams of relativebenefits are summedfor each and/orcosts of appropriatepairsof link-alternatives year to obtain the correspondingtime streams for designatedpairs of group-alternatives. k, in year y, the net Thus, for any link- or group-alternative, economicbenefitof alternative m relativeto alternative n, ANB(m.n), is computedas: ANBky(m-n)= AVCNky(m-nl AVCGky(m-ni AEXBky(m-nj ATCN ky(m-n) +

where ANBky(m-n)=

ATCGky(m-n)- ACAPky(m-n) - ARECky(m-n) the net economicbenefitof alternative m relative to alternativen in year y and the variableson the right-handside are as defined earlier, but with subscripts k and y added to indicatethe link or groupand year.

From the time streams of benefits or costs for the various comparativepairs of link and/or group alternatives,the model then computes net present values without discount and with up to five discountrates,as well as the internalrate of returnand user-specified first-yearbenefits. These conceptsare elaboratedbelow. costs in financialtermsand/or in foreign Savingsor incremental exchange are also computed if appropriateinputs have been given. are repeated Followingall this, if the user has so specified,comparisons with changes in selected parameters,prices, etc., to ascertainthe of the resultsthereto. sensitivity The net presentvalueof alternativem n, NPVk(m-n)is computedas: NPVk(mn) where

=

ANBky(m-n)= r Y

= =

relativeto alternative

ky(m-n) z y=1 [1 + 0.01r] the net economicbenefitof alternativem relativeto alternativen in year y; the annualdiscountrate,in percent; period,in years. anlalysis the user-specified

238

BENEFITS,COSTS,AND ECONOMICANALYSIS

The internaleconomicrate of return,denotedby r* in percent, is the discountrateat which the net presentvalueas definedaboveequals zero, i.e., y

ANBky(m-n) =

y=l [1 + 0.01 r*]y_1 The aboveequationis solvedfor r* by evaluatingthe net presentvalueat five percentintervalsof discountratesbetween-95 and +500 percent,and determining the zero(s)of the equationby linearinterpolation of adjacent discountrateswith net presentvaluesof oppositesigns. Dependingon the nature of the net benefitstream,ANBky(m-n),it is possibleto find one or multiplesolutionsor none at all. The first-yearbenefits,which can be used as a criterionin determiningthe optimaltimingof investments, is definedin the model as the ratio (in percent)of the net economicbenefitrealizedin the first year after construction completionto the increasein totalcapitalcost:

FYk(m-n) =

100 N

(mn

ATCCk(m-n) where

FYk(m-n) = the first-yearbenefitsof alternativem relativeto alternativen, in percent; ANBky*(m-n) = the net economicbenefitof alternativem relativeto alternativen in year y*, wherey* is the year immediately after the lastyear in which the capitalcost is incurredin alternative m; and ATCCk(m-n) = the difference in total capital cost (undiscounted) of alternativem relativeto alternative n.

Since it is neitherfeasiblenor even desirableto compareevery alternative with every other one, it is put up to the user to specifyone or more "studies." For each group alternativecomparisonthe model automatically producesall the componentlink alternativecomparisons.Up to 50 group alternativecomparisons may be specifiedin one run, provided that the total number of group and associatedlink comparisonsdoes not exceed200. If thereare severalalternatives for a givengroup of links,it is best to designateone of them as the "basecase"and compareeach of the otherswith it. Any one of the set may be so designated; it does not have to be a "do-nothing"or "no-project"case, although that is often convenient.

BENEFITS,COSTS,AND ECONOMICANALYSIS

239

For each group-alternative includedin a study,and for each of its componentlink-alternatives, the model will tabulateyear by year the economiccosts,brokendown into componentscorresponding to the terms of the equation for ANBky(m-n) given above. The foreign exchange requirementswill also be tabulatedyear by year. Each of these time serieswill be totaledwith no discountand with up to five discountrates. Then, for each Rair of group alternativesspecified,the model will tabulatethe differencesin componentcosits and benefitsyear by year accordingto the same breakdown,as well as the differencein foreign exchangerequirements, and will sum them with no discountand with up to five discountratesto get the corresponding net presentvalues. This will be done also for the pairs of link-alternatives that are includedin the group-alternative pair. The results of these comparisonsand relatedcalculationsare then summarizedlink by link and group by group in terms of net present value for each discount rate, internal rate of return, and first year benefits.

CHAPTER 8

Expenditure Budgeting Model

In recentyears,most highwayexpencliture programsin the World Bank borrowingcountrieshave containedconsiderablymore economically worthwhileprojectsthan can be implemented within availablefunds. The constraintsare becomingmore stringent,for many of these nationshave been forced to cut back their already small budgets as a result of the recentworldwideeconomicdifficulties since the late 1970s. The problem

thatfaces highway authorities evermore urgently is to findthe bestuse of the limited resources. This raisesa series of questionsalong the followingline: How should availablehighwayfundingbe allocatedamong new road construction,reconstruction, strengthening,and maintenance? What is the economically most productiveallocationof investmentamong differentfunctionalroad classes? How shoulda highwaynetworkrehabilitation program be scheduledso as to spread costs within the budgetary projectionover time while keepingthe network in reasonablyserviceable condition?And so on. Answers to questions of this type can be obtained through combineduse of HDM-IIIand the Expenditure BudgetingModel (EBM)alluded to earlier. The HDM model is employedto predict the discountedtotal transportcostsand consequently the net presentvaluesof differentalternativesrelativeto a base alternativefor each link in the network. The predictedeconomicbenefitsand associatedcostsare then transferred into the EBM,which, in turn,selectsthe set of alternatives thatmaximizesthe total net presentvalue for the entire networksubjectto user-specified budgetconstraints. A productof collaboration between ItheWorld Bank's Transportation Departmentand EconomicDevelopmentInstitute(EDI),the Expenditure 1 provides a formal mathematicaloptimizationframework BudgetingModel which is based on essentially the same economicprincipleas the HDM model, i.e.,that of maximizingof net benefits. While it is simpleto use, the model is still capableof analyzingall major economictradeoffs,particularlywith respectto the scaleand timingof investment, as well as handling the types of project interdependencies iiormally found among highway investmentprojects(in particular, mutualexclusivity).Togetherwith the HDM, the EBM is designedto assist highway authoritiesin determining short-to-medium range highwayexpenditureprograms(5-10years) entailing both recurrentand capitaloutlayson road maintenance, new construction, strengthening and rehabilitation.The methodologyunderlyingthe EBM has 1 A completeuser'smanualfor the Expenditure BudgetingModel is given in Chapter6, User'sManual. 241

242

EXPENDITURE BUDGETINGMODEL

been applied in part in preparing World Bank loans to developing 2 countries. Althoughthe present interfacebetween the HDM and EBM models allows for only recurrentand capital expenditureconstraintsto be considered, the EBM as such can handleother typesof resourceconstraints includingforeigncurrencyrestriction and the maximumcapacityfor maintenance or constructionby the local road authorityor road construction industry. A descriptionof the EBM model is provided in the following 3 paragraphs. While the discussionis generallyin the contextof highway sectorplanning,the model can be appliedto the othertransportsubsectors and the transportsectoras a whole. 8.1 MULTIPLE-PERIOD, MULTIPLE-CONSTRAINT EXPENDITURE BUDGETING In the course of developingthe model, various methods for handling multiple-period, multiple-constraint budgeting were reviewed, includingthose used by highwayauthorities and those describedin literature surveys (e.g., McKean, 1958; Beenhakker, 1976; Wilkes, 1977; Moavenzadeh et al., 1977). Thesemethodsmay be classifiedinto two broad groupings:intuitivemethodsand formalmethods. Intuitivemethods are generally simple, easy-to-useproject selectionrules. For example,using what we call the cut-off rate of return method, the rule is to set the discountrate and select only the projectsthat have positivenet presentvalues evaluatedat the discount rate (McKean,1958). The "optimal"solutionis obtainedwhen the project selectionexactlyexhauststhe budgetavailability.The rationaleof the method is that the tighter the budget the greaterwill be the discount rate,a parallelto the notionof higheropportunitycost of funds at the budgetmargin. This method is implicitly based on the assumptionthat the budget imposedis optimalwithin the contextof the nationaleconomy so that economicbenefitsfrom the projectselectioncan be reinvestedat the "optimal"discount rate. This assumptionis internallyconsistentonly when this discountrate turns out to equal the opportunitycost of capital in the economyat large. When budgetcutbacksare severethe formercan be severaltimes the latter. In thesesituations, the cut-offrateof return method tends to be myopic, i.e., biased in favor of projectswith relativelyshortlivesand smallcapitaloutlaysin earlyyears. In another intuitivemethod,projectsare selectedsequentially from the first budget period to the last in the descendingorder of 2 See Watanatadaand Harral (1980) for the developmentof a Costa Rica 5-yearroadmaintenance program. 3 This chapterdraws heavilyon an earlierpaper by Watanatadaand Harral (1980).

EXPENDITURE BUDGETINGMODEL

243

incremental benefit-cost ratios. This decisionruledoes not recognizethe fact that, becauseof scale-economies such as in pavementconstruction, it can be more advantageouseconomicallyto implementa few relatively high-standardprojects than a larger number of relativelylow-standard projects in a given year. Thus, intuitiveimethods, although appealing becauseof theirsimplicity, must generallybe usedwith caution. Formal methods are based on a mathematicalformulationof the problem as one of optimizationunder constraints. These include optimizationalgorithms,which guarantee a global optimum at least asymptotically(e.g., exhaustivesearch, integer programming,dynamic programming)and approximate algorithms, which rely on well-tested heuristic programmingconcepts where strict optimality is traded off againstefficientuse of computerresources(e.g.,the Shizuo-Toyoda-Ahmed algorithmbased on the conceptof effectivegradient,which we have used, as discussedbelow). Becauseof the relianceon propermathematical formulation of the objectivefunctionto be optimizedagainst resourceconstraints,formal methods lend themselvesto a systematicanalysisof economictrade-offs-in the same manner as trade-offanalysis in the absence of budget constraints. A commonexampleis the problemof the scale and timing of investment.Comparedto the intuitivemethods,formalmethodshaveprecise problem statements,and, with the availabilityof computers,are easy to use. Among the formal methods, the main drawback of optimization algorithmsis that, although in principlethieycan produce a globally optimal solution,the amount of computationcan be excessivefor large problems. Since the value of the objectivefunction(whichis generally the sum of net present values of individualprojects) can only be determinedapproximately, heuristicprogramlingl methods,which can handle much larger problemsand yield resultsclose to the global optimal (say, within5 percent),are consideredto be satisfactory.In usingthe EBM the user has a choice between an unconditionallyoptimal method, an asymptotically optimalmethodand an approximate method. Basicdefinitions We definean "investment unit"as a set of alternatives only one of which may be implemented.Differentinvestmentunitsare assumedto be mutuallyindependent.Let subscriptkm denotea physicalprojectwhich is alternativem for investmentunit k. Let K be the total number of investmentunits consideredfor implementationand Mk the number of alternatives for investmentunit k. In the contextof HDM, k representsa link,m a link-alternative, and K the numberof links in the network. A set of K projectsmade up of one alternativefor each of the investment units is calleda "programselection." For the projectkm, define NPVkm =

the presentvalue of net economicbenefits,expressed relative to a base case, and measured in terms of discountedfutureconsumption streamat an exogenously

244

EXPENDITURE BUDGETINGMODEL determinedsocial discount rate4 S (or interestrate r in HDM context);and Rkmqt =

the (undiscounted) amountof resourceof type q, q = 1 to Q, incurredby the sectoralagency in a budget period t, t = 1 to T, where Q = the total number of resource types, and T = the total number of budget periods(thedurationof t may be one or more years and need not be equal for differentbudgetperiods).

In the context of HDM, two types of resourcesare considered: capitaland recurrentexpenditures, as denotedby subscriptsq = 1 and 2, respectively.The amountsof these resourcesare givenby: Capital:

Rkmlt =

Z CAPFkmy yet

Recurrent:

Rkm2t =

E RECFkmy yet

the capital and where the terms CAPFkmx and RECFkmy are, respectively, recurrentexpenditureslexpressedin financialterms) incurredin year y by alternative m on link k; and the summationscover all years that fallwithinbudgetperiod t. Interpretation of investmentunits Defined as a set of mutually exclusive alternatives,an investmentunit can be interpretedin a varietyof forms,as describedin 5 the examplesbelow. 1. Independentprojects. An investmentunit may representa singlealternative projectindependent of otherprojects. 2. Scale of investment.A road construction project in which one of three different design standards representing alternative investment levels is to be implemented immediately. 3. Scale and timingof investment.The above road construction projectof three alternativeinvestmentlevelsmay have two alternativeconstructiondates (e.g., immediatelyand five years from now); this gives a maximum of six mutually exclusivecombinations. 4 The socialdiscountrate is basicallya policyparameterwhichmust be decidedat the policy level. Discussionsof the social discountrate and how it shouldbe determinedare given in Lind et al. (1982). Interpretations of mutually exclusivealternativeshave been made in Hirshleiferet al. (1960),Beenhakker(1976),and Juster and Pecknold (1976).

EXPENDITURE BUDGETINGMODEL

245

4. Staging strategies. Two alternativesare consideredin a road construction project: the first consistsof 10 unitsof lump sum investmentin the first year; and the second consistsof 6 units of lump sum investmentin each of the first and seventh years, where the seventh year is for upgradingto a higherpavementstandard. 5. Recurrent expenditure. An investment unit may involve recurrent expenditureon an existing facility such as alternative maintenance standardsfor a given road class. 6. Compound projects. An investmentunit may consist of the proposedmodernization of a sugarrefineryas one undertaking and the proposedupgradingof the access road to the plant site as another. The total benefitsof both undertakings when takentogetherexceedthe sum of the benefitsof each if taken alone. In this examplewe have three combinations or compoundprojects:modernizingthe refineryalone,upgrading the access roadalone,and doingboth. The notionof the investmentunitprovidesa convenientmeansfor organizingproject analyses. Physicalprojects in differentinvestment units are assumedto be independent whereasthose within each investment unit are assumedto be interdependent.In principleany type of project interdependency (mutualexclusivity,joint effect on benefitsand costs, etc.) can be handled. However, the number of feasible combinationsof interdependent projectsshouldnot in practicebecomeunmanageably large. Whileone may argue that all projectsare interdependent at least to some extentand that no projectshouldbe consideredin isolation, many projects can be assumed to be independentfor approximationpurposes without seriouslyaffectingproject selectionresults. The analystmust exercisejudgment to decide whether the projects should be analyzedas independentor interdependent.Also it is assumed that the analyst has sufficientunderstandingof the basic engineering-economic tradeoffsof investmentstrategiesin the sector so that only a few but meaningful alternatives are carefullyformulated. Problemstatement The publicexpenditure budgetingproblemfor multipleperiodscan be stated as an integerprogrammingproblem of maximizingthe total net 6 TNVP: presentvalue for the sector, Maximize TNPV [xkm] =

m

k

k=1m=1

NPVkkm Xkm

6 Other social welfare objectivessuch as income distributionare not addressed herein. However, it is possible to incorporateother objectives in the form of relative weights and constraintsin a mathematical programming formulation (Steiner,1969;UNIDO,1972;Major, 1973).

246

EXPENDITURE BUDGETINGMODEL

over the "zero-one"decisionvariablesXkm, m = 1 to Mk and k = 1 to K, where Xkm equals 1 if alternative m of investmentunit k is chosen for implementation, and equalszero otherwise;subjectto: 1. The resourceconstraints: K

M

X1mz1 RkmqtXkm < TRqt,q = where

TRqt =

1, ... , Q; t = 1, ... , T

the maximumamountof resourcetype q available for budgetperiod t; and

2. The mutualexclusivity constraints: Mk

I

Xkm < 1, k

= 1,

.s.,

K

m=1 i.e., for each investmentunit implemented.

k

no more than one alternativecan be

If we denote by M the average number of alternativesfor an investmentunit, the problemfomulated above has KM (= K x M) zero-one variablesand QT (= Q x T) resourceconstraintsand K interdependency constraints. The parameterswhich define the problemsize are K, M and QT. Depending on the solution method used, different problem-size parametersdeterminewhether the method is suitablefor the problem in effort(CE)needed. termsof comutational Solutionmethods Three methods for solving the above optimizationproblem are providedin the EBM: 1. Total enumeration (TOTE). This is the unconditionally optimalsolutionmethod in the EBM. It computesthe total net present values of all feasibleprogram selectionsand choosesthe one with the largestvalue. effort needed for the TOTE method may be The computational approximately expressedas follows: CE = C1 MK QT where C, is a constant. Thus the crucialparametersare K effort involved, and M. Becauseof the largecomputational the EBM permitsthe TOTE method to be employedonly when the number of program selections(MK) does not exceed a preset

EXPENDITURE BUDGETINGMODEL

247

limit (currentlyequalto 2 million). Thus, the TOTE method is feasibleonly for problemswhere the numberof investment units and the numberof the alternatives per investmentunit are relativelysmall. 2. Dynamic programming(DPGM). This is the asymptotically optimal solution method providledin EBM. It is an 7 of the traditionalsolution extensivelyrevised version methodoutlinedin Watanatadaand Harral(1980). The details of the methodare givenin Appendix8A. It involvesdividing the feasible space into a number of neighborhoodsor windows. The method is asymptotically globally optimal in the sense that as the number of windows is increasedthe solutionapproachesthe globaloptimum. If we divide each resourcefor each budget period into an averageof L intervals,the number of windowswould be LQT and the computational effortmay be expressedapproximately as:

CE = C. K M LQT where C2 is a constant. Thus the crucial problem-size parameterfor this method is QT. Past experiencewith the method indicatesthat L shouldbe of the order of 100 for a near-optimal solution. Currently,thereis a presetlimitof 1 millionon the numberof windows. Thus the DPGMmethodmay be consideredfor problems where the number of resource constraints, QT, is three or fewer. With the value of QT restrictedto three, practicalapplicationsof the DPGM method are in general confinedto problemswhich have one type of resourceconstraint(Q = 1), e.g., both capitaland recurrentcomponentscombined,and three or fewer budget periods(T < 3). Note: At thiswriting,the OPGMmethod is implemented only on Burroughsmainframesusingboth ALGOLand Fortran. It has been found that in some pathologicalcases with L equal to or smaller than 20, the "optimal"solution may changedependingon the orderingof the investmentunits. 3. Effective gradient (AHMED). This is the approximate solutionmethod provided in the EBM. It is a slightly modified version of the model for highway maintenance resourceallocationdevelopedby Ahmed (1983). Ahmed used the heuristic programmingconcept of effective gradient introducedby Shuizuo and Toyoda (1968) in the contextof investmentunits with singlealternatives and adapted it to the case of multiplealternatives.Appendix8B describesthe algorithmin detail. The revision is documentedin the EBM Programmer'sGuide (Rich and Vurgese,1987).

248

EXPENDITURE BUDGETINGMODEL The computational effortfor the AHMEDmethod is a polynomial functionof the problem-size parameters.Thus the method is not onlymuch faster,it can handlemuch largerproblemsthan the other methods. Currently,the method permitsproblems with up to 50 investmentunits,20 alternatives, 3 resource types and 25 time periods given that the total number of resourceconstraints does not exceed50 (i.e.,K < 50, Mk < 20, Q <3, T < 25 and QT < 50). The main disadvantageof the method is that it does not guaranteea global optimum (and, further, it occasionally fails to find an extantfeasiblesolution). However,Toyoda (1975)and Ahmed (op. cit.) reportthat algorithmsbased on effectivegradientconsistently yieldedsolutionswithin4-5 percentof the globaloptimal. For the purposesof highway sector planning,this degree of accuracymay be considered acceptable.Provisionhas been made in the EBM to deal with the problem of failureto find an extant feasiblesolution through pre-selectionof an alternativefor one or more investment-units. The details are given in the User's Manual,Chapter6.

Sensitivity analyses Executionof the EBM model using any of the above methods automatically providesinformation on the sensitivity of the optimaltotal net present value, TNPV*, to variationsin the resourcebudgets TRot. The sensitivityinformationcan be expressedin terms of resourceshadow pricesand cut-offeconomicrate of return(see Section8.3), and also in termsof the marginalprojectincrements.The marginalprojectincrements programif the resource may be added to or subtractedfrom the expenditure budgets, TRqt, themselvesare modified. The sensitivityinformation providesanswers to questionsof the followingtype: What would be the percentageloss (or gain) in the total net present value if the budgets were decreased (or increased)by, say, 20 percent? Are the existing budgets for road constructionand maintenanceeconomicallyoptimal? If not, how much additionalfunding allocationwill be required? How sensitiveare the road design and maintenancestandardsto the projected highwaydepartmentbudgetsover the next 5 or 10 years? And so on. EXPENDITURE BUDGETING: ECONOMICINTERPRETATIONS 8.2 SINGLE-PERIOD Section 8.1 above deals with general expenditurebudgeting problemsin whichmore than one type of resourcesare involvedand proposed improvementscan be postponedfor a few or several years, such as the pavingof gravelroadsor, more generally,roadconstruction projects. For these projects,expenditurescan be incurredin differenttime periods. However,for didactic purposes,it is easier if we consider relatively simpleproblemsinvolvingone aggregateexpenditure(Q = 1) and one budget period (T = 1). Two main types of investmentsituationsfall into this category.

EXPENDITURE BUDGETINGMODEL

249

The first type covers projectsthat iforone reason or another (e.g.,engineeringfeasibility) will either be implementedimmediately or not at all. The questionof investment timingand staged-construction does not arise for these projects. The second type involves recurrent expenditure(e.g., for road maintenance)which must be provided on a continuingbasiswithoutsubstantial year-to-year fluctuations.For these projects it is easier to estimate benefits for an entire recurrent expenditure program(4-5years in duration)than to isolatebenefitsdue to spendingin any individualyear. For such recurrentexpenditure projects the averageannualcost can be used for budgetingagainstan averageannual budgetceiling. Incremental benefit-cost ratiomethod Single-period budgetingproblemswith one resourcetypediscussed above may be solved using either the total enumerationmethod or the dynamic programming method to yield a globally optimal solution irrespectiveof the functionalrelationship betweenthe alternatives' net present values and resource requirements. However, when NPVkm is a convex functionof Rkmqt (q = 1 and t = 1), it is possibleto use a simpler solution technique alluded to earlier as the "incremental benefit-costratio"method,which still utilizesthe conceptof effective gradient(Shizuoand Toyoda,1968;Toyoda,1975). Since subscriptsq and t are always equal to one, we now drop them from Rkmqt yieldingRkm, which is interpretedas the requiredexpenditurefor alternative m of investmentunit k. For each investmentunit k, let the alternatives be so arranged

that Rkm increases monotonically with m, m = 1 to Mk. function NPVkmis convexwithrespect to Rkm if ANP

inm-1 >

ARk m-1 where

NPVki

Then, the

form = 1 to Mk

ARkm

ANPVkm = NPVkm- NPVk,m-1 ARkm = Rkm - Rk, m-1

8 and NPVko and Eko are definedas zero. A typical shape of the relationship betweenNPVkm and Rkm is illustrated in Figure8.1.9 In this figureif each straightline segmentol the curveis takenas a "project increment" m, thentheassumption of convexity ensuresthatfora given investmentunit the selectionof a project increment m automatically impliesselection of the earlierincrements (m-1,m-2, etc.)

8 The possibility thatARkm equalszero is ignoredfor simplicity since 9 it has no practical implications. The convexityassumptionis not applicable to projectswith joint positive benefits suchas in the sugarrefinery example, nor to projects with increasing returns to scale.

250

EXPENDITURE BUDGETINGMODEL

in the unit. Becauseof this "inclusive" propertyof the functionNPVkm, the expenditure increments ARkm can be treated as if they were independentprojects. For notationalsimplicity,a single subscript j will be made equivalentto subscripts k and m. Thus, we have ANPVkm and ARkm equivalentto ANPVj and ARj, respectively. For a project increment j definethe "incremental benefit-cost ratio,"Hj, as:

H

=

ANPV J AR,

Let N be the total numberof availableprojectincrements.We now rank these project incrementsin the descendingorder of the ratio Hj, yielding a new sequenceof project increments, i = 1, 2,..., N, w ere 0 H. > Hi+1

i = 1 to N.

Figure8.1: Net presentvalue versusexpenditure Net presentvalueof investmentunit k (at socialdiscountrateS) NPVkm ,ASRk1 ARk2

a Rk3

{ - _ |

s ANPVk 3

ANPVk 2

ANPVkl

________

Rkl

10 The possibility of a tie practical implications.

Rk2

Rk3

Rkm

Expenditure of investment unit k

has been ignored for simplicity,

as it

has no

251

EXPENDITURE BUDGETINGMODEL

to indicate is used instead of j The new subscript i randomnessof the old sequenceof projectincrementsindexedby j. In the B-C ratiomethodas many projectincrementsare selectedas the incremental budget TR (withsubscripts q = 1, t = 1 droppedfromTRqt) will allow by runningdown the sequencei, i = 1 to N. All projectincrementsi, i = 1 to nb are chosenwhere nb is such that nb

nbTRAR.

AR. < TR <

Rb+1

i=l

i=l1

Althoughoptimalityis not guaranteedthe incrementalB-C ratio method should be satisfactoryin most cases where convexityof the net 11 presentvaluefunctionapplies. B-C ratioat budgetmargin of incremental Economic interpretations are made in the contextof single The followinginterpretations to period expenditurebudgeting but can be extended straightforwardly multipleperiodbudgeting. B-C Definethe shadowpremiumof a budget,A, as the incremental ratio of the best project which is rejected because of the budget B-C method, duringthe givenbudgetperiod. In the incremental constraints we have A = Hn + 1

b Then, an equivalentproject selectioncriterionbased on the "budgetshadow premium"can be applied:each project increment j is selectedif ANPV. - A AR. > 0 Let r denotethe marginaleconomicrateof returnobtainablein the privatesector. If n is used for the socialdiscountrateS (S = n) and no budgetis imposed,we have A = 0 and the projectselectioncriterion reducesto the usual net presentvalue criterion. If S = n and the budget constraintis binding,we have A > 0, meaning that the incrementalnet by imposinga premiumon the incremental presentvaluemust be "penalized" (Note that the incrementalnet present value, investmentcost ARj. Because of ANPVj, already has ARj factored in at face value.) causedby the budgetconstraint, restrictedpublicinvestmentopportunities the cost of investmentin the sectoris valuedat 100 A percenthigherthan the cost of investmentin the economyat large.

There are cases where the solutionis not optimal. For example,the smallerthan TR so that a project may be substantially total expenditure incrementi' where i' > nb + 1 can be squeezedwithin the budget. But should not be serious if the investment problems of indivisibility incrementsare small relativeto the budget.

252

EXPENDITURE BUDGETINGMODEL

The shadow price of incrementalpublic expenditurebudget, defined as A + 1, can be interpretedas the present value of future benefits(for socialdiscountrate S) that must be sacrificedfor one unit of funding shortage. The future benefits can be representedby a hypotheticalannual benefit stream of y per year to perpetuity. Discounting the futurebenefitat socialdiscountrateS yields

A+1

=

i

Y

y=l (1 + S)y y =

or

(1 + A) S.

The term y may be,called the "marginal(or cutoff) imputed economicrate of return"for the budget. Similarly,the "imputedeconomic rate of return"or "imputedERR" for a given projectincrement j, IERRj, is definedas IERR

=

[

ANPV. J + 1] S.

AR, Using the abovedefinitions, anotherequivalentcriterionto the incremental B-C ratio rulecan be statedon the basis of the cutoffimputed ERR. That is, we selecteach projectincrementj for which IERRj> y. For S = n and where no fundingconstraintapplies,we have y = , i.e., the cutoff imputedERR equals the economicrate of return in the privatesector. Thus the cutoffimputedERR criterionis very similarto the more familiarinternalrate of returncriterion. For projectswith a relativelylarge initiallump sum cost, uniformfuture consumptionstream and long life, the imputedERR is expectedto be similarto the internal projects rateof return(IRR)computedin the regularway. For short-lived the with a relativelysmall initiallump sum cost (e.g.,roadmaintenance) imputedERR is expectedto be considerablysmallerthan the regular IRR. By definitionthe imputedERR is mathematically tied to the net present value which is taken as the correct measure of a project's worth. with the net presentvalue Therefore,the imputedERR is always consistent for project ranking purposes and does not discriminatein favor of projectsas does the regularERR. short-lived

EXPENDITURE BUDGETINGMODEL

253

APPENDIX8A DYNAMICPROGRAMMING METHOD One approachto solvingthe expenditurebudgettingproblemwith multipleconstraints presentedas an integerprogramming problemin Section 8.2 is dynamicprogramming.A reformulation of the problemusing dynamic programing is given first followedby a basic procedurefor implementing it. Since the basic procedurewas foundto be relativelyinefficient a new algorithmwas developedto implementthe dynamic prograrmming approach. This is describednext. DynamicProgramming Formulation For the sequenceof investmentunits, Q = 1, 2,..., K, let fk (ARkgt,t = 1 to T and q = 1 to Q) denote the maximum net presentvalue obtainablefrom the resourcesARkqt made available for the first k investmentunits in the sequence. Then, the availableresourcesARkqt (whereARkqt < TRqt) denote state variablesand subscript k stages. The function fk is related to fk-1 by the following recursive relationship: fk (ARkqt,t = 1 to T, q = 1 to Q) -

=max

maMk

+m!kR

NPVkmxkm + fk-1 [ kqt

IP

X]

kmqt km

over the zero-one variablesXkm, m = 1 to Mk; subject to the resource constraints: Mk = Rkmqt Xkm< ARkqt

for t = 1 to T and q = 1 to Q; and to the mutual exclusivityconstraint (thatno more than one alternative may be chosen): Mk

X

Xkm < 1

M=1

In this dynamic programmingformulationthe original complex integerprogramming problemis reducedto K smallersubproblems each having QT state variables(ARkqt,t = 1 to T and q = 1 to Q) and Mk "decision" variables(Xkm,m = 1 to Mk).

254

EXPENDITURE BUDGETINGMODEL

BasicDynamicProgramming Algorithm A basic procedurefor obtaininga solution to this dynamic programming problemis as follows: Step 1:

Divide each total resourcebudgetTRqt into INT equal intervals. This gives L = INT + 1 discrete budget levels (or grid points) for each state variable, ARkgt. This in turn gives LQT combinationsfor periodbudgetlevelsfor each stage k.

Step 2:

For each stage k, k = 1 to K, determinethe value of fk for each of the LQT combinationsof resource levels ARkqt. This is accomplishedby optimization over the zero-one decision variablesXkm, m = 1 to Mk. The optimizationis computationallyrather trivial since it involves linear search over Mk mutuallyexclusivealternatives. Store each value of fk-

Step 3:

The maximumtotalnet presentvalue for all investment units, TNPV*, correspondingto the total resource budgets, TRat, are obtained from the recursive functionat the last stage,k = K:

TNPV*= fk=K (ARKqt= TRqt, t = I to T, q = I to Q) The set of projectsselectedcorresponding to TNPV* is determinedby optimization over the zero-onedecision variablesXkm for each stage in the backwardorder, k = K, K - 1,...,1. Providedthat the numberof grid pointsper budgetperiod,L, is sufficientlylarge,the above algorithmyields the global optimumto the originalmultipleperiodbudgetingproblem. The globaloptimalityrequires no restrictive assumptions on the relationshipof NPVkm to Rqkmt (Bellman,1957). ModifiedDynamicProgramming Algorithm In implementing the DP methodthe basicprocedureabovewas found to be relativelyinefficient.Therefore,a new algorithmwas developedto take advantageof the structureof the multiple-constraint expenditure budgetingproblems. Instead of storingvalues Of fk evaluatedat grid points, the new algorithmstores values Of fk associatedwith actual programselectionsat each stage k. Feasibleprogramselectionscomprise all combinationsof Xim, m = 1 to M% and Q = 1 to k that satisfy the mutual exclusivityand resourceconstraints. As the total number of all possiblecombinations, equalto k ll [M9 +1] Q=1

255

BUDGETINGMODEL EXPENDITURE

would normallyexceed the computermemory capacity,it is necessaryto store only "superior"combinations.The rule for screeningout "inferior" combinations can be illustrated with the use of an example having one

resourcetype (Q = 1) and two budgetperiods. Supposethat the numberof intervalsinto which the resourcesTR1l and TR12 are divided equal 5. As shown in Figure8A.1,this impliesan array of grid pointswhich form 25 a range of resources. The screening squaresor windowseach representing rule statesthatwhenevertwo or more programselectionsfall into the same windowonly the one with the largesttotalnet presentvalue is kept in the storage array for stage k. The new algorithmmay be summarizedas follows: exampleof one resourcetype and two budget Figure8A.1 Illustrative periods window TR12

-

--

0

0)

TRll

Gridpoints Budgetperiod1

For each stage k. Within the total resource limits of TRqt. use the alternativesfor investmentunit k (m = 1 to Mk plus the base with the ones already alternative)to generateall feasiblecombinations for stage of combinations generatedfor stagek-1. (Whenk 5 1 the number and to zero expenditure 0 is definedas equal to unity which corresponds the with combination only the zero benefit). For each window, retain value. net present greatest with the For the last stage K. Take the program combination highestnet presentvalueas the optimalsolution. In contrastto the basicprocedurethe new algorithmrequiresno completelydefinesthe selected backwardphaseas each programcombination experienceindicates alternativefor each investmentunit. Computational of three (QT = 4) represents that the total numberof resourceconstraints the maximum practical limit for the dynamic programmingmethod to be efficient,given the numberof intervalsof one hundred(INT= 100) needed degreeof accuracy. to maintaina reasonable

256

EXPENDITURE BUDGETINGMODEL

APPENDIX8B EFFECTIVEGRADIENTMETHOD The effectivegradientmethod is a slightmodification of the one developedby Ahmed to solve multiple-choice resourceallocationproblems associatedwith highway maintenance planning. Ahmed's method is a generalization of the approximatemethod proposed by Shizuo and Toyoda (1968) and Toyoda (1975) to solve binary-choiceinteger programming problems. Although none of these methods guaranteeglobal optimality, these authorshave reportedthat the solutionsto the problemstestedare within4 percentof the corresponding exact solution,a degreeof accuracy consideredto be acceptablefor highwaysectorplanningpurposes. The effectivegradientmethod proceedsin two stages: first, find a feasiblesolutionbasedon the conceptof effectivegradient; and, second, search for better solutions. The computationalsteps are as follows: Stage I: Find feasiblesolution Step 1:

For each investmentunit k, considerthe alternative that has the maximumnet presentvalue. Check whether all the resourceconstraints are satisfied. If so, go to step 10. Otherwise,go to step 2.

Step 2:

For each investment unit rank the alternatives accordingto the rankingindex,RIkm,definedas:

NPVkm m = 1,

RIkm =

...

,

Mk

q=1 t=1 TRqt Step 3:

For each investmentunit select the alternativethat has the greatestrankingindex.

Step 4:

Add the resource requirementsfor the alternatives selectedand checkwhetherall the resourceconstraints are satisfied. If so, go to step 8. Otherwise,go to step 5.

Step 5:

Consider the investmentunits in step 4 with their correspondingalternatives. Compute the effective gradients EGk of the selected alternativesdefined as:

257

EXPENDITURE BUDGETINGMODEL NPVkm EGk

K

(q ' T)Rkmqt

(q,t

£

where k = 1, resources.

Stage II:

(XeRkmqt- TRqt) (E

Q' T') Rmtk=1

...

, K and Q'T' is the set of exceeded

Step 6:

Consider the investment unit with the smallest effective gradient and, if possible, exchange the current alternativewith the next best one for the investmentunit which satisfiesthe criterionthat it be not uniformlyworse in terms of requirementof exceeded resources. The next best alternativeis defined in terms of the next higher ranking index RIkm. If all the alternativesfor the investment unit are exhausted,go to step 7. Otherwise,go to step 4.

Step 7:

Consider the investmentunit with the next higher effectivegradient. Go to step 4.

Searchfor bettersolutions Step 8:

which unit, lookfor an alternative For each investment has the highest net presentvalue other than the one currentlychosen and which will be feasible if the currentlychosenone is droppedout. If at least one exists,go to step9. Otherwise,go to step 10.

Step 9:

From all the investmentunits that have at least one selectthe one that gives better feasiblealternativie, the maximum increasein the net presentvalue. Go to step8.

Step 10: Stop. A finalsolutionis obtained. betweenAhmed'salgorithmand the algorithmgiven The differences above are locatedin steps6 and 7. In step 6, Ahmed'salgorithmdoes not check whether the exchange is uniformlyworse. Further, in Ahmed's algorithmif the investmentunit with the lowesteffectivegradienthas no alternativewhich yields feasibilityit is droppedbefore moving to step 7. In the above algorithmit is retainedin order to increasethe chance of findinga feasibleprogramselectionwhen one exists. It is possiblethat the algorithmwould fail to find an extant that the feasiblesolutionin stage I. If this happensit is recommended user pre-selectan alternativefor one or more investmentunitsand re-run the EBM. The detailsare givenin AnnexA, ChapterA6.

Glossary of Terms

A

of the roadsection as the elevation defined roadaltitude, abovethe meansea level,in meters.

ai

coefficients of fuelconsumption model.

ai

of the spareparts extension of tangential coefficients consumption model.

ai

in structural numberof pavement layerstrength coefficients the roaddeterioration model.

AB

averagefloorareaof bridges per unitlengthof road,in m2 lkm.

AC

asphaltconcrete

ACG

average areaof siteclearing and grubbing per unitlengthof road,in m/km.

ACRAa ACRAb

totalareaof all cracking, comprising narrowandwide cracking, crocodile and irregular cracking of width1 mm and greater, in percent of the totalcarriageway area (subscripts a, b denoteafterand beforemaintenance, respectively).

AACRAd

changein the areaof all cracking duringthe predicted in percentof the yeardue to roaddeterioration, analysis area. totalcarriageway

MACRAm

predicted changein theareaof all cracking due to maintenance, in percent of totalcarriageway area.

ACRWa ACRWb

cracksand spalled comprising totalareaof widecracking, in percentof the total crackwidthsof 3 mm or greater, a, b denoteafterand before area(subscripts carriageway respectively). maintenance,

AACRWd

duringthe changein the areaof widecracking predicted in percentof the analysis yeardue to roaddeterioration, area. totalcarriageway

AACRWm

cracking duringthe changein theareaof widle predicted of totalthe in percent analysis yeardue to maintenance, carriageway area.

ADAMS

at the areaforpatching) damaged area (i.e.,damaged severely in percentof the total end of theyearbeforemaintenance, area. carriageway surface

259

260

GLOSSARY

ADEP

averageannualvehicledepreciation, expressedas a fractionof the averagecost of a new vehicle.

ADH

averagedaily heavytrafficin both directions, in vehicles/day (heavyvehiclesare definedas thosehavinggrossweightsof 3,500kg or more).

ADL

averagedaily lighttrafficin both directions,in vehicles/day (lightvehiclesare definedas thosehavinggrossweightsunder 3,500kg.).

ADT

averagedailyvehiculartrafficin both directions, in vehicles/day.

AF

equivalent80 kN standardaxle loadfactor.

AF2k

equivalent80 kN standardaxle loadfactorbased on the equivalency exponentof 2.0 for vehiclegroup k, in ESA per vehicle.

AF4k

equivalent80 kN standardaxle load factorbasedon the equivalency exponentof 4.0 for vehiclegroup k, in ESA per vehicle.

AGE1

preventivetreatmentage, definedas the numberof years elapsedsincethe latestpreventivetreatment,reseal,overlay, pavementreconstruction or new construction.

AGE2

surfacingage, definedas the numberof years elapsedsincethe latestreseal,overlay,pavementreconstruction or new construction.

AGE3

construction age, definedas the numberof years elapsedsince or new the latestoverlay,pavementreconstruction construction.

AINT

averageannualintereston the vehicleexpressedas a fraction of the averagecost of a new vehicle.

AINV

annualinterestchargeon the purchasecost of a new vehicle, in percent.

AKM

predictedaveragenumberof kilometersdrivenper vehicle,per year.

AKMo

baselineaveragenumberof kilometersdrivenper vehicleper year for the vehiclegroup,inputby the user.

ALPC

averagelengthof regularpipe culverts,in meters.

ANBC

averagenumberof regularbox culvertsper unit lengthof road, in culvertsper km.

ANBR

averagenumberof smallbridgesper km.

261

GLOSSARY APOTa APOTb

totalarea of potholing,in percentof the totalcarriageway a, b denoteafterand beforemaintenance, area (subscripts respectively).

AAPOTd

predictedchangein the totalarea of potholingduringthe in percent. analysisyear due to roaddeterioration,

AAPOTm

predictedchangein the totalarea of'potholingduringthe in percentof total analysisyear due to maintenance, area. carriageway

AAPOTCRd

predictedcomponentchangein the area of potholingduring the analysisyear due to cracking.

AAPOTd

predictedcomponentchangein the equivalentarea of potholingduringthe analysisyear due to enlargement.

AAPOTRVd

predictedcomponentchangein the area of potholingduring the analysisyear due to ravelling.

AR

projectedfrontalarea of the vehicle,in m2, whichmay be or take on a defaultvalueas shown in user-specified Table 5.2b.

ARV

motionof the standard averagerectifiedvelocityof suspension vehiclein responseto road roughness,in mm/s. Opala-Maysmeter

ARYMAX

speed maximumallowableARV, a parameterof the steady-state predictionmodel.

ARAVa ARAVb

totalarea of ravelling,in percentof the totalcarriwageway a, b denoteafterand beforemaintenance, area (subscripts respectively).

AARAVd

predictedchangein the ravelledarea duringthe analysis in percentof totalcarriageway year due to road deterioration, area.

MARAVm

predictedchangein the ravelledarea duringthe analysis area. in percentof totalcarriageway year due to maintenance,

AASP

in percentof total predictedarea of patchingperformeci, carriageway surfacearea.

AASPMAX

maximumapplicablepatchingin a year, specifiedby the user,

ASPSo

area of patchingspecifiedby the user, in m2 /km.

AXL

actualloadon the axle, in kgf.

AXLkij

load on axle j of a subgroupvehicle i in vehiclegroup k (metrictons).

in m2 /km.

262

GLOSSARY

Bw

magnitudeof the effectof roadwidthon speed reduction,in km/h per meter of width reductionbelow 5 m.

BI

road roughnessin mm/km,as measuredby the TRRL TowedFifth WheelBump Integrator(Hide,et al., 1975).

C

averagehorizontalcurvatureof the road,in degrees/km.

C0lh

constantcoefficient in the laborhoursmodel.

COSP

constantterm in the exponential relationbetweenspareparts consumption and roughness.

C0tc

constantterm of the tire treadwear model.

Clhpc

partscost exponentin the maintenancelaborhoursmodel.

Clhqi

roughnesscoefficient in the maintenancelaborhoursmodel, per QI.

Cspqi

roughnesscoefficient in the exponential relationbetween spareparts consumption and roughness,(perQI).

Ctctc

wear coefficient of the tire treadwear model.

CAPkyj

total road capitalcost incurredby alternativej analysisyear y for linkk.

ACAPky(m-n) increasein road capitalcost of alternativem alternativen in analysisyear y.

in

relativeto

CBR

CaliforniaBearingRatioof the subgradeat in situ conditions of moistureand density,in percent.

CD

dimensionless aerodynamic drag coefficient of the vehicle, whichmay be user-specified or takeon a defaultvalueas shown in Table 5.2b.

CFd

averagecircumferential forceper tire on the downhill segment,in newtons.

CFu

averagecircumferential forceper tire on the uphillroad segment,in newtons.

CQ

construction faultcode (1 if the pavementsurfacinghas construction faults;0 otherwise)specifiedby the user as an optionor equal to the defaultvalueof zero.

CKM

age of the vehiclegroupas proxiedby the averagenumberof kilometersthe vehiclesin the group have been driven,in km.

CKM'

upperlimiton CKM.

GLOSSARY

263

CMOD

resilientmodulusof soil cement,in GPa (relevantonly for pavementswith cementedbase and surfacetypesST or AC).

CMST

cold mix on surfacetreatment.

COMP

relativecompactionin the base, subbaseand selectedsubgrade layers,in percent.

CR

dimensionless coefficient of rollingresistance.

CRM

built-instandardcrackingretardation time due to maintenance, in years.

CRP

delay in crackingprogression due to preventivetreatment.

CRPM

calibratedenginespeed,in rpm.

CRX

crackingindexweightedfor severityof crackingat the beginningof the analysisyear.

CRX

crackingindexconstrained such that the strengthcoefficient of a crackedasphaltlayeris not less than that of an equivalentgranularlayer,min (63;MICRa).

ACRXd

predictedchangein crackingindex(weightedfor cracking severity)due to roaddeterioration.

ACRXm

predictedchangein crackingindex (weightedfor cracking severity)due to maintenance.

CRT

crackingretardation time due to ma'intenance, in years.

CRTMAX

built-inmaximumlimitfor CRT.

D95j

maximumparticlesize of the material,definedas the equivalentsieveopeningthroughwhich 95 percentof the materialpasses,in mm.

DEF

mean Benkelmanbeam deflectionover time,in mm.

DFLR

predictedincreasein fuel consumption due to road roughness, in liters/1000 vehicle-km.

DG'

numberof days betweensuccessive gradings,determinedfrom the trafficor roughnessparameter.

DGMAX

maximumallowabletime intervalbetweensuccessivegradings,in days, specifiedby the user as an optionor equalto the defaultvalueof 10,000days.

DGMIN

minimumapplicabletime intervalbetweensuccessivegradings, in days, specifiedby the user as an optionor equal to the defaultvalueof 5 days.

264

GLOSSARY

DRL

aggregatelengthof regularpipe culvertsper unit lengthor road,in m/km.

ECR

predictedexcesscrackingbeyondthe amountthat existedin the old surfacinglayersat the time of the last pavementreseal, overlayor reconstruction.

EMC

equilibrium moisturecontent,in percentby mass.

E4RS

exponentwhich is a functionof the surfacecharacteristics and precipitation.

EWV

volumeof earthworkper unit lengthof road, in m3 /km (includes cut, fill,borrowand wastematerials).

EXBkyj

totalexogenousbenefitsaccruedby alternativej in analysisyear y.

AEXBky(m.n)increasein net exogenousbenefitsof alternativem relativeto alternativen in analysisyear y. EXCkyj

total exogenouscosts incurredby alternativej in analysis year y.

Fc

occurrencedistribution factorfor crackinginitiationfor the subsection(thevaluesused in HDM-IIIare listedin Table 4.5).

f(e)

probability densityfunctionof E.

Fr

occurrencedistribution factorfor ravellinginitiationfor the subsection(thevaluesused in HDM-IIIare 0.54, 0.97,and 1.49 for weak,medium,and strongsubsections, respectively).

FDAMo

percentageof the damagedarea specifiedby the user to be patched,in percent.

FL

predictedfuel consumption, in liters/1000 vehicle-km.

FL1

predictedfuel consumption obtaineddirectlyfrom the regressionequations,in liters/1000 vehicle-km.

FLle FLlh

predictedfuel consumption, computedwith the relationships for the test truckunderempty,halfand full loads, respectively, in liters/1000 vehicle-km.

FL2

predictedfuel consumption, computedwith the effectof power-to-weight ratioaccountedfor, in liters/1000 vehicle-km.

FPDTo

percentageof potholingarea to be patchedper year, specifiedby the user,in percent.

FRATIO

dimensionless perceivedfrictionratio.

GLOSSARY

265

FRATIOO FRATIO 1

parametersof the relationbetweenFRATIOand vehicle payload.

FYk(m-n)

first-yearbenefitsof alternativem alternativen, in percent.

g

gravitationalconstant, equal to 9.81 m/s2 .

G

riseplus falldifferential, in m/km.

GR

verticalgradientof a roadsegment,expressedas a fraction.

GRF

groundrise plus fall, in m/km.

GVW

gross vehicleweight,in (metric)tons,whichmay be user-specified or take on the defaultvalue shown in Table 5.2a as ratedgrossvehicleweight.

GVWk

averagegrossvehicleweightfor vehiclegroupk, in metric tons.

GVWki

grossvehicleweightfor subgroup i in vehiclegroup k, in metric tons.

H

effectiveheightof earthwork,in meters.

Hi

thicknessof the ith pavementlayer,in mm.

HAXk

averagenumberof heavyvehicleaxles for vehiclegroupk.

HPd HPu

vehiclepowerson the downhilland uphillroad segments,in metrichp.

HPBRAKE

maximumused brakingpower,in metrichp.

HPDRIVE

maximumused drivingpower,in metrichp.

HPRATED

maximumratedpowerof the engine,in metrichp, whichmay be user-specified or take on the defaultvalueas shown in Table 6.1.

HRDO

baselinenumberof hoursdrivenper vheilce user-specified per year.

HSE

effectivethicknessof the surfacirglayers,in mm.

HURATIOO

ratio"for the baselinecase. "hourlyutilization

Ik

numberof subgroupsin vehiclegroup k.

IM

where moistureindex,in the 1955classification Thornthwaite's (-100< IM < +100).

relativeto

266

GLOSSARY

IRI

International RoughnessIndex,definingthe roughnessof a road profileby the RARS8 0 quarter-car simulationstatistic(see Sayers,Gillespieand Queiroz,1985).

Jki

numberof singleaxles per vehiclein subgroup i of vehicle group k (a tandemaxle is treatedas two separatesingle axles).

k

ratioof asphaltconcretedensityat full compaction; currently 0.85 is used by the HDM.

k

exponentof vehicleage in the maintenance partsconsumption model.

Kci

user-specified deterioration factorfor crackinginitiation, multiplyingtime (defaultvalue= 1).

Kcp

user-specified deterioration factorfor crackingprogression, multiplying area per year (defaultvalue= 1).

Kge

user-specified deterioration factor for age-roughness progression, multiplying annual fractional increment of roughness (default value = 1).

Kgp

user-specified deterioration factorfor roughness progression, multiplying total incrementof roughness(default value = 1).

KPP

user-specified deterioration factorfor potholeprogression, multiplyingeach componentincrementof potholing(default value= 1).

Krp

user-specified deterioration factorfor rut depth progression, multiplying incrementof rutdepth(default value = 1).

Kvi

user-specified deterioration factorfor ravellinginitiation, multiplying time (defaultvalue= 1).

KA

variablefor indicating the presenceof all crackingof the old surfacinglayers.

KT

traffic-induced materialwhip-offcoefficient, expressedas a functionof rainfall,roadgeometryand material characteristics.

KW

variablefor indicatingthe presenceof wide crackingof the old surfacinglayers.

L

averageforceper tire in the directionperpendicular to the road surface,in newtons.

LC

predictedmaintenancelaborcost, in Cr$/1000vehicle-km, in January1976prices.

267

GLOSSARY LE

exponent. axle load equivalency

LGTH

lengthof the roadway,in km.

LH

per 1000vehicle-km. labor-hours numberof maintenance

LIFE

predictedaveragevehicleservicelife,in years,using the varyingvehiclelifemethod.

LIFEo

baselineaveragevehicleservicelife in years,inputby the user.

LOAD

or vehiclepayload,in metrictons,whichmay be user-specified take on a defaultvalueas shown in Table5.2a.

M

averagemoisturecontent,in percent.

MGj

slopeof mean materialgradation.

MGDj

materialgradationdust ratio.

MLA

predictedannualmaterialloss,in mm/year.

MMP

in metersper month. annualaveragemonthlyprecipitation,

ANBky(m-n) economicbenefitof alternativem n in year y.

relativeto alternative

ANBky*(m-n)net economicbenefitof alternativem relativeto alternativen in year y*, where y* is the year immediately after the lastyear in which the capitalcost is incurredin alternativem. NPVky(m-n) net economicbenefitof alternativem alternativen in year y.

relativeto

NR

per tire carcass. predictednumberof retreadings

NRo

per tire carcass. base numberof retreadings

NT

numberof tiresper vehicle.

NVPb

averageprice of a new bus in 1978 rupees,equal to Rs234,000 which is a weightedaverageof the pricesof the Tata and Ashok buses.

NVPC

averagepriceof a new car in 1978 rupees,equalto Rs64,800 which is the weightedaverageof the pricesof the Premier Padminiand Ambassador.

NVPt

averagepriceof a new truckin 1978 rupees,equal to Rs180,700which is the weightedaverageof the priceof the Tata and Ashoktrucks.

OC

vehicle-km. in liters/1000 lubricantsconsumption,

GLOSSARY

268 OVAC

asphaltoverlayor slurrysealon asphaltconcrete,or asphalt overlayon surfacetreatment.

Pki

percentageof subgroup i vehiclesin vehiclegroup k.

P02

amountof materialpassingthe 2.0 mm sieve (or ASTM No. 10 sieve),in percentby mass.

P075

amountof materialpassingthe 0.075mm sieve (or ASTM No. 200 sieve),in percentby mass.

P425

amountof materialpassingthe 0.425mm sieve (or ASTM No. 40) sieve),in percentby mass.

PAX

averagenumberof passengersper vehicle.

PC

predictedparts consumption per 1000vehicle-km, expressedas a fractionof the averagenew vehiclecost.

PCRPb

parts cost of buses,in 1978 rupeesper 1000 vehicle-km.

PCRPc

parts cost of passengercars, in 1978 rupeesas per 1000 vehicle-km.

PCRPt

parts cost of trucks,in 1978 rupeesper 1000vehicle-km.

PCRA

area of all crackingbeforethe latestresealor overlay,in percentof the totalcarriageway area.

PCRW

area of wide crackingbeforethe latestresealor overlay,in percentof the totalcarriageway area.

PCRX

crackingindex (weightedfor severity)of the old surfacingand base layers.

PI

plasticityindexof the material,in percent.

PXH

numberof passenger-hours delayedper 1000vehicle-kmof travel.

PWR

vehiclepower-to-weight ratio,in metrichp/ton.

QIa QIb

roughnessof paved roadsafter previousmaintenance. (subscript a) or beforemaintenance(subscript b), in QI units.

QI(after) roughnessof unpavedroads (subscript after)or before QI(before)grading(subscript before),in QI units. Qld QIm

predictedchangein road roughnessduringthe analysisyear (subscript d), or due to due to roaddeterioration maintenance(subscript m), in QI units.

269

GLOSSARY QI(TG 1) QI(TG 2)

roughnessof unpavedroad at timeTG1 or time TG2, respectively, in QI units.

QIIo

initialroad roughnessafterpavementconstruction or reconstruction specifiedby the user or providedas a default valueaccordingto the surfacetype.

QIOsp

transitional valueof roughnessin the sparepartsmodel, in QI units.

QIMAXd

estimatedmaximumroughnessof unpavedroadssurfacing material,in QI units.

QIMAXo

maximumallowableroughnessspecifiedby the user, in QI units.

QIMINj

minimumroughnessof unpavedroad surfacingmaterial,in Q0 units.

r

annualdiscountrate,in percent.

r*

internaleconomicrate of return(thediscountrate at which the net presentvalueequalszero).

RD

mean rut depthalongboth wheelpaths,in mm.

RDMa RDMb

mean rut depth (alongthe wheel paths),in mm (subscripts a, be denotingafterand beforemaintenance, respectively).

RDSa RDSb

standarddeviationsof rut depth (alongthe wheel paths),in mm (subscripts a, b denotingafterand beforemaintenance, respectively).

ARDMd ARDMm

predictedchangein the mean rut depth duringthe analysis year due to roaddeterioration (subscript d) or due to maintenance(subscript m), In mm.

ARDSd ARDSm

predictedchangein the standarddeviationof rut depth duringthe analysisyear due to roaddeterioration (subscript d) or due to maintenance(subscript m), in mm.

ARECky(m-n)increasein road recurrentcost cf alternativem relative to alternativen in analysisyear y. RECkyj

total road recurrentcost of alternativej Ye

RF

road rise plus fall, in m/km.

RRF

ravellingretardation factordue to maintenance (dimensionless).

RH

rehabilitation indicator, value= 1 if the surfacetype is asphaltconcrete(OVAC)or cold mix (CMST)overlay;= 0 otherwise.

in analysisyear

270

GLOSSARY

RHO

mass densityof air, in kg/m3.

RL

roundtrip drivingdistanceor routelength,in km.

RREC

ratioof the cost of one retreadingto the cost of one new tire, in percent.

RRFMAX

built-inmaximumlimitfor RRF.

RRM

built-instandardravellingretardation factordue to maintenance(dimensionless).

RSST

resealon surfacetreatment.

RSAC

resealon asphaltconcrete.

RW

roadwaywidth, in meters.

S

predictedspeed,in km/h.

aS

correctionterm to be added to the originalconstantterm (102.6)so that the new equationwill yield the same speed predictionwhen it is appliedto the averageroughnessin the Kenya sample.

SO

baselineaveragevehiclespeedspecifiedby the user, in km/h.

SAS

Statistical AnalysisSystem.

SCRA,SCRW temporaryvariabledefiningsigmoidalfunctionof all cracking SRAV (SCRA),wide cracking(SCRW),and ravelling(SRAV). SL

depth of loosematerial,in mm.

SN

structuralnumberof the pavement.

SNo

user-specified structuralnumberfor the reconstructed pavement(the subscripto is used to emphasizethat the values of thesevariablesare to be providedby the user).

ASNo

user-specified incrementin the structuralnumberdue to the pavementreconstruction.

ASNm

incremental changein structuralnumberdue to maintenance.

SNC

modifiedstructural number.

SNCa SNCb

modifiedstructuralnumberapplyingfor season 'a' (subscript a), or for season'b' (subscript b).

SNCK

modifiedstructuralnumberadjustedfor the effectof cracking.

271

GLOSSARY ASNK

predictedreductionin the structuralnumberdue to cracking (when sincethe lastpavementreseal,overlayor reconstruction zero). the surfacingage, AGE2, equals

SNSG

of the subgrade. modifiedstructuralnumbercontribution

SP

of the road,in percent. superelevation

SSST

slurryseal on surfacetreatment.

ST

surfacetreatment.

TARE

vehicletareweight,in metrictons,as given in Table5A.1.

TC

new tiresconsumedper 1000 numberof cost-equivalent vehicle-km.

of alternative ATCCk(m.n) increasein totalcapitalcost (undiscounted) n. m relativeto alternative trafficof TCGky(m.n) traveltime benefitsdue to "generated" alternativem relativeto alternativen in year y. ATCNky(m-n)traveltime benefitsdue to "normal"traficof alternativem relativeto alternativen in year y. ATCRA

progression fractionof the analysisyear in which all-cracking applies,in years.

ATCRW

fractionof the analysisyear in whichwide cracking applies,in years. progression

TD

drivingtimeon the section,in hoursper trip.

TG1 , TG2

time elapsedsincelatestgrading,in days.

TGkyji

trafficin year y due to vehiclegroup i "generated" (which alternativej relativeto the baselinealternative need not be the sameas eitheralternativen or m), in number of vehiclesin both directions.

THGo

in mm. gravelthicknessafter resurfacing, user-specified

ATHGo

increasein the gravelthicknessdue to user-specified in mm. resurfacing,

TL

predictedtire life,in km per physicallyequivalentnew tire.

TN

activitiesas part of the roundtrip time spenton non-driving tour, includingloadingand unloading,refueling,layovers, etc., in hoursper trip.

TNkyi

vehiclegroup i "normal"trafficin year y on link k, in numberof vehiclesin both directions.

272

GLOSSARY

ATRAV

fractionof the analysisyear duringwhich ravelling progression applies,in years.

TYCRA TYCRW

predictednumberof years to the initiationof narrowcracking (TYCRA)or wide cracking(TYCRW),sincelast surfacingor resurfacing (whenthe surfacingage AGE2 = 0).

TYRAV

predictednumberof years to ravellinginitiationsincethe last surfacingor resurfacing (whenthe surfacingage AGE2 = 0).

UCkyji

averageoperatingcostper vehicle-trip over the link for vehiclegroup i underalternativej in year y (j = n or m).

UFCd UFCu

predictedunit fuel consumption for the downhillsegment (subscript d), or for the uphillsegment(subscriptu), ml/s.

UTkyji

averagetraveltime cost per vehicle-trip over the link for vehiclegroup i underalternativej in year y. (j = n or m).

V

vehiclespeed,in m/s.

Vd Vu

predictedsteady-state speedfor the downhillsegment (subscript d), or for the uphillsegment(subscript u), in M/s.

VBRAKE

limitingspeedbasedon verticalgradientand brakingcapacity, in m/s.

VBRAKEd VBRAKEu

limitingspeedbased on verticalgradientand braking capacityfor the downhillsegment(subscript d) or for the uphillsegment(subscript u), in m/s.

AVCGky(m.n) vehicleoperatingbenefitsdue to "generated" trafficof alternativem relativeto alternativen in year y. AVCNky(m.n) vehicleoperatingbenefitsdue to "normal"trafficof alternativem relativeto alternativen in years. AVDGky(m.n)vehicleoperatingbenefitsdue to "generated" trafficof alternativem relativeto alternativen in year VCURVE

limitingspeeddeterminedby roadcurvature,in m/s.

VDRIVE

limitingspeedbasedon verticalgradientand enginepower,in m/s.

VDRIVEd VDRIVEu

limitingspeedbasedon verticalgradientand driving capacityfor the downhillsegment(subscript d), or for the uphillsegment(subscriptu), in m/s.

VEHG

trafficintervalbetweensuccessivegradings,in vehicles, specifiedby the user.

273

GLOSSARY VGR

in-placevolumeof gravelmaterialadded to gravelresurfacing, in m /km.

VDESIR

basedon desiredspeed,in the absenceof otherconstraints economic,safetyand other considerations. psychological,

VDESIRo

study unmodifiedvalueof VOESIRobtainedin the Brazil-UNOP as referredto in Watanatada, et al., 1985, in km/h.

VROUGH

limitingspeedbasedon road roughnessassociatedride severity,in m/s.

w

weightused for averagingover the amountsof crackingareas in the old and new surfacinglayers.

W

width of the carriageway, in meters.

WI

widthbelow5 meters,in meters. reductionof carriageway

WS

width of one shoulder,in meters.

X

vectorof the explanatory variables.

Y

analysisperiod,in years. user-specified

YAX

numberof all vehicleaxles for the analysisyear, in million/lane.

YE2

numberof equivalent80 kN standardaxle loadsfor the analysis exponentof 2.0 in year based on the axle load equivalency million/lane(i.e.LE = 2.0).

YE4

numberof equivalent80 kN standardaxle loadsfor the analysis exponentof 4.0, in year basedon the axle loadequivalency (i.e.LE = 4.0). million/lane

a

predictedfuel consumption factorfor adjustingexperimentally to real-worldconditions. fi

o2

parameterof the steady-state speedpredictionmodel.

c

error term.

6

angleof the embankmentslope,in radians.

References

Costand Vehicle Operating for Measuring S.W. "SomeTechniques Abaynayaka, to Developing Reference -- WithParticular Parameters RoadDeterioration England: report193 UC. Crowthorne, TRRLsupplementary Countries." Laboratory, Research and Roacd Transport of the Environment, Department 1976. and and H. Hide. "TheEffectof Vehicle S.W.,G. Morosiuk, Abaynayaka, Speedsin Ethiopia."TRRL Vehicle on Commercial RoadCharacteristics Transport of the Environment, England:Department Report271. Crowthorne, 1975. Laboratory, and RoadResearch in Allocations Modelfor Resource Decision Ahmed,N.U. "AnAnalytical vol.17A,no. 2, Research, Transportation Management.' Maintenance Highway 1983. Officials.AASHTO and Transportation of StateHighway Association American D.C.,1972. Washington, Structures. Guidefor Designof Pavement Interim in DevelopCostModelfor SectorPlanning Construction Aw, W.B. "Highway of Institute Mass.: Massachusetts S.M.thesis.Cambridge, ing Countries." 1981. Technology, forUse in RoadConstruction Descripter Terrain , "TheGenerated -------for the WorldBank. paperprepared draftworking CostModel." Unpublished D.C.: WorldBank,1982. Washington, of CapitalInvestments. for theAnalysis H.L. Handbook Beenhakker, Press,1976. Conn.: Greenwood Westport, University N.J.: Princeton Princeton, R. DynamicProgramming. Bellman, Press,1957. of Rural Analysis and D. Bovet. The Economic C., J. Biderman, Carnemark, RoadProiects.WorldBankStaffWorkingPaperno. 241. Washington, D.C.: WorldBank,August1976. (CRRI).RoadUserCostStudyin India. Insititute CentralRoadResearch India,1982. New Delhi, FinalReport. 5 volumes. of Bus and TruckData." A. "IndiaRoadUserCostSurvey: Pooling Chesher, Washington, Department. for theTransportation reportprepared Unpublished D.C.: WorldBank,1983a. fromthe India Developed CostEquations Operating "Vehicle ----------.reportpreparedforthe TransporRoadUserCostSurveyData." Unpublished D.C.: WorldBank,1983b. Washington, tationDepartment.

275

276

REFERENCES

-----------."UnbiasedPredictionin Log-LinearModels." Unpublished projectmemorandum,ICR/AC/VLS/112/82. Washington, D.C.: World Bank, 1982. ----------. "Estimatesof the Effectsof VehicleSpeedand Highway Characteristics on FuelConsumption."Unpublished reportpreparedfor the Transportation Department.Washinaton, D.C.: WorldBank, 1977a. - -."Predicting the Fuel Consumption of Mediumand HeavyGoods Vehicles."Unpublished reportpreparedfor the Transportation Department. Washington, D.C.: World Bank,1977b. Chesher,A. and R. Harrison. HighwayDesignand Maintenance Standards Model (HDM-III), VolumeI, VehicleOperatingCosts:Evidencefrom DevelopingCountries. Washington, D.C.:WorldBank,Transportation Department, 1987. de Weille,Jan. Quantification of Road User Savings,World Bank Staff OccasionalPaperno. 2. Washington, D.C.: World Bank, 1966. Ellis,C.I. "PavementEngineering in DevelopingCountries."TRRL Supplementary Report537. Crowthorne, England: Departmentof the Environment, Transportand RoadResearchLaboratory, 1979. GEIPOT. Researchon the Interrelationships betweenCosts of Highway Construction, Maintenance and Utilization (PICR). FinalReport. 12 volumes. Brasilia,Brazil,1982. Harral,C.G. Preparation and Appraisalof TransportProjects. Prepared for the U.S. Departmentof Transportation.Washington, D.C., 1968. Harral,C.G., P.E. Fossberg,and T. Watanatada. "Evaluating the Economic Priorityof HighwayMaintenance:Some Exploratory Analyses." Paper presentedat the Pan AfricanConferenceon HighwayMaintenance and Rehabilitation.Ghana,November,1977. Gynnerstedt, G. "A Generalized Roadand HighwayTrafficSimulationModel." Indo-Swedish Road TrafficResearchProject. Stockholm,Sweden: Royal Instituteof Technology, 1984. --------------."Preliminary Model for DigitalComputerSimulationof Motor Trafficon a Two-LaneRoad' (in Swedish). Preliminary Reportno. 30. NationalSwedishRoad ResearchInstitute, TrafficDepartment,1966. Gynnerstedt, G., A. Carlson,and B. Westerlund."A Model for the Monte Carlo Simulationof TrafficFlow alongTwo-LaneSingleCarriageway Rural Roads." Meddelandeno. 43. NationalSwedishRoad and TrafficResearch Institute,TrafficDepartment, 1977. Hide, H. "An ImprovedData Base for EstimatingVehicleOperatingCosts in DevelopingCountries."TRRL Supplementary Report223 UC. Crowthorne, England: Departmentof the Environment, Transportand Road Research Laboratory, 1976.

REFERENCES

277

I. Sayer,and R.J. Wyatt. The KenyaRoad Hide, H., S.W. Abaynayaka, TransportCost Study: Researchon VehicleOperatingCosts. TRRL ReportLR Transportand England: Departmentof the Environment, 672. Crowthorne, 1975. Road ResearchLaboratory, HighwayResearchBoard. The AASHORoad Test. NationalResearchCouncil, D.C., 1962. no. 944. Washinglton, SpecialReport61E, Publication Hirshleifer, J., J.C. de Haven,and J.W. Milliman. Water Supply: and Policy. Chicago: The Universityof Chicago Economics,Technology, Press,1960. Hodges,J.W.,J. Rolt,and T.E. Jones. The KenYaRoad TransportCost Study: Researchon Road Deterioration.ReportLR 673. Crowthorne, Transportand Road Research England: Departmentof the Environment, Laboratory, 1975. Jacobs,G.D. and I.A.Sayer. "RoadAccidentsin DevelopingCountries." England: Departmentof the TRRL Digestof ReportSR 807. Crowthorne, 1983. Transportand Road ResearchLaboratory, Environment, Studyon UnpavedRoads." TRRL Jones,T.E. "TheKenyaMaintenance England: Departmentof the LaboratoryReport 1111. Crowthorne, Environment, Transportand Road ResearchLaboratory, 1984. the Processof Programming Juster,R.D. and W.M. Pecknold. "Improving ResearchRecord599. Transportation Investments."Transportation Research Washington, D.C.: NationalAcademyof Sciences,Transportation Board,1976. for Tine and Risk in Energy Lind,RobertC., and others. Discounting D.C.: Resourcesfor the Future,1982. Policy. Washington, WaterResourcePlanning.AmericanGeophysical Major,D.C. Multiobjective UnionWater ResourcesMonograph4. Reviewdraft,May, 1973. Criteria. London,England: GeorgeAllen Marglin,S.A. PublicInvestment and Unwin,Ltd. Cambridge,Mass.: MIT Press,1967. Costs for Sector Road Construction Markow,M.J. and W.B. Aw. "Estimating ResearchRecord898. Planningin DevelopingCountries."Transportation Research D.C.: NationalAcademyof Sciences,Transportation Washington, Board,1983. Marwah,B.R. "A SimulationModel of Two-Laneand Four-LaneHighwaysfor Instituteof IndianTrafficConditions."Kanpur,India: Inclian Technology,1983 (draft). …----. "Studiesin StochasticModellingand Simulationof Mixed VehicularTraffic." Ph.D.thesis. Kanpur,India: IndianInstituteof 1976. Technology,

278

REFERENCES

McKean,R.N. Efficiencyin GovernmentThroughSystemsAnalysis. New York: John Wiley & Sons, Inc.,1958. Meyer,J.R. and M.R. Straszheim.Pricingand ProjectEvaluation.Washington, D.C.: BrookingsInstitution, TransportResearchProgram,1971. Moavenzadeh, F., J.H. Stafford,J. Suhrbier,and J. Alexander. Highway DesignStandardsStudy PhaseI: The Model. World Bank StaffWorkingPaper no. 96. Washington, D.C.: World Bank,1971. Moavenzadeh, F., and B. Brademeyer.The Road Investment AnalysisModel: GeneralFrameworkfor Link Evaluation.Serieson Road TransportPlanning Programfor DevelopingCountries,vol. 2. TechnologyAdaptationProgram. Cambridge,Mass.: Massachusetts Instituteof Technology, 1977. Moavenzadeh, F., F. Berger,B. Brademeyer, and R. Wyatt. The HighwayCost Model: GeneralFramework.TechnologyAdaptationProgramReportno. 75-4. Cambridge,Mass.: Massachusetts Instituteof Technology, September1975. Moavenzadeh, F., E. Fernandez, and B. Brademeyer."TheRoad Investment AnalysisModel: GeneralFremeworkfor CapitalBudgetingand Programming." Serieson Road TransportPlanningProgramfor DevelopingCountries,vol. Develop4. TAP Report77-7. Preparedfor the Agencyfor International ment, UnitedStatesDepartmentof State,by the TechnologyAdaptation Instituteof Technology, 1977. Program. Cambridge,Mass.: Massachusetts Morosiuk,G. and S.W. Abaynayaka. "VehicleOperatingCosts in the Caribbean: An Experimental Studyof VehiclePerformance."TRRL Report 1056. Crowthorne, England: Transportand Road ResearchLaboratory, 1982. SimulationModel for VehicleBehavior Palaniswamy, S.P. "A Generalized underHeterogeneous TrafficConditions."Indo-Swedish Road Traffic ResearchProject. IndianInstituteof Technology, 1983. Road Palaniswamy, S.P.,G. Gynnerstedt, and Y.R. Phull. "Indo-Swedish TrafficSimulation(ISWERTS)Model: A Generalized TrafficSimulation." Paper presentedto the 64th AnnualMeetingof the TransportResearchBoard, Washington, D.C., 1985. Paterson,W.D.O. The HighwayDesignand Maintenance StandardsModel Effects: Models and Maintenance (HDM-III), VolumeIII, Road Deterioration for Planningand Management.Washington, D.C.:Transportation Department, World Bank, 1987. Rauhut,J.B.,R.L. Lytton,and M.I. Darter. "PavementDamageFunctionsfor Cost Allocation."4 volumes. ReportFHWA-RD-84/017-020. Washington, D.C.: FederalHighwayAdministration, U.S. Departmentof Transportation, June, 1984.

REFERENCES

279

Guideto the HDM Model Release Rich,J. and T. Underhill.A Programrer's 1987. Department, D.C.:The WorldBank,Transportation III. Washington, Budgeting Guide to the Expenditure Rich,J. and Vurgese,S. A Programmer's 1987. Department, D.C.:The WorldBank,Transportation Model. Washington, Robinson,R., H. Hide,J.W. Hodges,and J. Rolt. A Road Transport InvestmentModel for DevelopingCountries. TRRL ReportLR 674. Transportand Road England: Departmentof the Environment, Crowthorne, 1975. ResearchLaboratory, Experiment Sayers,M., T.D. Gillespie,and C.A.V.Queiroz. "International Methodsfor Road and StandardCalibration to EstablishCorrelation D.C.: RoughnessMeasurements."TechnicalReportno. 45. Washington, World Bank, 1986. for the Sayers,M., T.D. Gillespie,and W.D.O.Paterson. "Guidelines Report Technical Measurements." Roughness of Road Conductand Calibration 1986. D.C.: WorldBank, no. 46. Washington, with 0-1 Senju,S. and T. Toyoda. "An Approachto LinearProgramming 1968. 4. December, no. vol. 15, Variables."ManagementScience, Squire,L. and H.G. van der Tak. EconomicAnalysisof Projects. A World Bank, 1975. D.C.: iWorld Bank researchpublication.Washington, D.C.: Brookings Budgeting.Washington, Steiner,P.O. PublicExpenditure 1969. Institution, Solutionsto Toyoda,Y. "A SimplifiedAlgorithmfor ObtainingApproximate Problems. ManagementScience,vol. 21, no. 12. Zero-OneProgramming August,1975. Cost of Road Construction and Improvement Tsunokawa,K. "Evaluation draftworkingpaperpreparedfor the WorldBank. Models." Unpublished D.C.: WorldBank, 1983. Washington, (UNIDO). Guidelinesfor Organization UnitedNationsIndustrialDevelopment ProJectEvaluation.New York: UnitedNations,1972. van der Tak, H.G. and A. Ray. The EconomicBenefitsof Road Transport D.C.: Projects. World Bank StaffOccasionalPaperno. 13. Washington, World Bank, 1971. and Maintenance." Visser,A.T. " An Evaluationof UnpavedRoad Performance Ph.D. thesis. Austin,Texas: Universityof Texasat Austin,Departmentof Civil Engineering, February,1981.

280

REFERENCES

Walters,A.A. The Economicsof Road User Charges. WorldBank Staff OccasionalPaper no. 5. Washington, D.C.: WorldBank, 1968a. ------------."A Development Modelof Transport."AmericanEconomic Review. May, 1968b. Watanatada, T. and C.G. Harral. "Determination of Economically Balanced HighwayExpenditure ProgramsUnderBudgetConstraints:Case Study of Costa Rica." Paperpresentedto the RegionalSeminaron Road Maintenance.Asian Development Bank,Manila,1980a. ----------. "Determination of Economically BalancedHighwayExpenditure ProgramsunderBudgetConstraints, A PracticalApproach." Paperpresented at The World Conferenceon TransportResearch. London,1980. Watanatada, T., A. Dhareshwar, and P.R.S.Rezende-Lima.The HighwayDesign and Maintenance StandardsModel (HDM-III). VolumeII, VehicleOperating Costs: EvidencefromDevelopingCountries. Washington, D.C.: Transportation Department, WorldBank, 1987.

The World Bank The Highway Design and Maintenance Standards Series To provide road design and maintenance standards appropriate to the physical and economic circumstances of developing countries, the World Bank in 1969 instituted the Highway Design and Maintenance Standards Study, which developed into a major collaborative research project with leading research institutions and highway administrations in Australia, Brazil, France, India, Kenya, Sweden, the United Kingdom, and the United States. The aims of the study comprised the rigorous empirical quantification of cost tradeoffs between road construction, maintenance, and vehicle operating costs; and, as a basis for highway decisionmaking, the development of planning models incorporating total life-cycle cost simulation. Controlled experiments and extensive road user surveys were conducted to provide comprehensive data on highway conditions and vehicle operating costs in radically different economic environments on three continents. The five volumes in the series represent the culmination of the 18-year endeavor, along with a computerized highway sector planning and investment model, currently in its third version (HDM-III). The first three volumes in the series provide theoretical foundations and statistical estimation of the underlying physical and economic relationships. The other two discuss the model and its use and are essential references for applying HDM-III. Vehicle Operating Costs: Evidence from Developing Countries Andrew Chesher and Robert Harrison Presents an economic model of firms' management of vehicle fleets, which serves as a framework for the statistical analysis of vehicle operating cost data. Vehicle Speeds and Operating Costs: Models for Road Planning and Management Thawat Watanatada, Ashok M. Dhareshwar, and Paulo Roberto S. Rezende Lima Presents the theory and estimation of a comprehensive set of models to predict speeds and operating costs under free flow conditions for a wide range of vehicles on medium- and low-volume roads as functions of road geometry and condition. Road Deterioration and Maintenance Effects: Models for Planning and Management William D. 0. Paterson Contains an extensive analysis of the physical processes, causes of deterioration, and performance prediction relationships, as well as the effectiveness of maintenance practices on unpaved and paved roads. The Highway Design and Maintenance Standards Model Volume 1. Description of the HDM-III Model Volume 2. User's Manual for the HDM-III Model Thawat Watanatada, Clell G. Harral, William D. 0. Paterson, Ashok M. Dhareshwar, Anil Bhandari, and Koji Tsunokawa Volume 1 organizes relationships described in the first three volumes, as well as a road construction submodel, into interacting sets of costs related to construction, maintenance, and road use. Volume 2 provides guidance on the use of this model-including input data forms, inference ranges, and default values-and gives numerical examples.

ISBN 0-8018-3091-7 ISBN 0-8018-3668-9 (5-volume set)