Description of the HDM-III Model

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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

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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 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


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


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

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
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.

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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)