Integrated Prioritization and Optimization Approach for Pavement Management · process, namely a...

INTEGRATED PRIORITIZATION AND OPTIMIZATION

APPROACH FOR PAVEMENT MANAGEMENT

FARHAN JAVED (B. Eng., National University of Sciences and Technology)

A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

DEPARTMENT OF CIVIL ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE

2011

ABSTRACT

Integrated Prioritization and Optimization Approach for Pavement Management

by

Farhan Javed

Doctor of Philosophy in Civil Engineering

National University of Singapore

Professor Fwa Tien Fang, Supervisor

This thesis proposes an improved methodology of incorporating priority preferences into

pavement maintenance programming to overcome these problems. Instead of applying

priority weights directly into the mathematical formulation of maintenance programming,

priority preferences are handled in two stages of post-processing of the optimal programming

process, namely a tie-breaking analysis and a trade-off analysis. The optimal programming

problem is first solved without applying priority weights to any parameters of the problem.

This ensures that the optimality of the solution is not disturbed. In the tie-breaking post-

processing, prioritized maintenance activities are identified to replace lower priority activities

in the solution, without affecting the optimality of the solution. Finally, a trade-off analysis is

performed to introduce more prioritized activities into the solution based on the willingness

of the highway agency to accept some loss in optimality. The entire framework is clearly

illustrated using examples.

Professor Fwa Tien Fang Dissertation Supervisor

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TABLE OF CONTENTS

TABLE OF CONTENTS .................................................................................................... i

ACKNOWLEDGEMENTS .............................................................................................. vi

SUMMARY ....................................................................................................................... vii

LIST OF TABLES .............................................................................................................. x

LIST OF FIGURES .......................................................................................................... xii

CHAPTER 1 INTRODUCTION .................................................................................... 1

1.1 PAVEMENT MANAGEMENT SYSTEMS .......................................................... 1

1.2 SIGNIFICANCE AND ISSUES OF PAVEMENT MAINTENANCE

MANAGEMENT .................................................................................................... 2

1.3 ORGANIZATION OF THESIS .............................................................................. 6

CHAPTER 2 LITERATURE REVIEW ........................................................................ 8

2.1 INTRODUCTION ................................................................................................... 8

2.2 PRIORITIZATION AND OPTIMIZATION APPLICATIONS IN PAVEMENT

MANAGEMENT .................................................................................................... 9

2.2.1 Prioritization Techniques for Pavement Management ................................... 9

2.2.1.1 Overview ............................................................................................ 9

2.2.1.2 Review Comments ........................................................................... 13

2.2.2 Optimization Techniques for Pavement Management ................................. 14

2.2.2.1 Overview .......................................................................................... 14

2.2.2.2 Review Comments ........................................................................... 19

2.2.3 Prioritization versus Optimization ................................................................ 19

2.3 REVIEW OF PMS MODELS AND SYSTEMS .................................................. 20

2.3.1 Implementation Status of Network Level Resource Allocation System ...... 20

2.3.1.1 Arizona PMS .................................................................................... 22

2.3.1.2 PAVER Pavement Management System ......................................... 25

2.3.1.3 PMS Model Developed at Purdue University .................................. 27

2.3.1.4 Singapore (PAVENET) .................................................................... 28

2.3.1.5 Caltrans PMS .................................................................................... 29

2.3.1.6 Indiana PMS ..................................................................................... 30

2.3.1.7 Georgia PMS .................................................................................... 31

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2.3.1.8 Washington State PMS ..................................................................... 34

2.3.1.9 Mississippi PMS ............................................................................... 35

2.3.1.10 Highway Development and Management Standards Model (HDM)

.......................................................................................................... 36

2.3.1.11 Japan PMS (MLIT-PMS) ............................................................... 42

2.3.2 Summary and Comments ............................................................................. 43

2.4 ISSUES IN PAVEMENT MANAGEMENT RESEARCH .................................. 44

2.5 OBJECTIVES OF RESEARCH AND PROPOSITION ....................................... 45

2.5.1 Objectives of Research ................................................................................. 45

2.5.2 Proposition .................................................................................................... 45

CHAPTER 3 IMPROVED PAVEMENT MAINTENANCE PRIORITY

ASSESSMENT: ANALYTIC HIERARCHY PROCESS .................. 51

3.1 NEED FOR RATIONAL MAINTENANCE PRIORITY ASSESSMENT .......... 51

3.2 SCALES OF MEASUREMENT ........................................................................... 52

3.2.1 Nominal Scale .............................................................................................. 53

3.2.2 Ordinal Scale ................................................................................................ 53

3.2.3 Interval Scale ................................................................................................ 53

3.2.4 Ratio Scale .................................................................................................... 53

3.3 CONCEPT OF ANALYTIC HIERARCHY PROCESS ....................................... 54

3.3.1 Distributive-Mode Relative AHP ................................................................. 56

3.3.2 Ideal-Mode Relative AHP ............................................................................ 57

3.3.3 Absolute AHP ............................................................................................... 57

3.4 METHODOLOGY OF STUDY ........................................................................... 57

3.4.1 Basis of Evaluation ....................................................................................... 57

3.4.2 Problem Formulation of Numerical Example .............................................. 59

3.4.3 Prioritization of Pavement Maintenance Activities ...................................... 60

3.5 ANALYSIS OF RESULTS OF PRIORITY RATINGS ....................................... 60

3.5.1 Results of Priority Ratings and Priority Rankings ....................................... 60

3.5.2 Analysis of Priority Rating Scores and Priority Rankings ........................... 60

3.5.2.1 Assessment of Priority Rating Scores .............................................. 61

3.5.2.2 Assessment of Priority Rankings ..................................................... 62

3.5.2.3 Assessment of Spread of Priority Assessments ................................ 63

3.5.3 Summary Comments on Applicability of AHP ............................................ 64

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3.5.3.1 Process of Pairwise Comparisons ..................................................... 65

3.6 SUMMARY .......................................................................................................... 67


ASSESSMENT: ANALYTIC HIERARCHY PROCESS FOR

MULTIPLE DISTRESSES ................................................................... 80

4.1 INTRODUCTION ................................................................................................. 80

4.2 CONVENTIONAL PRIORITY RATINGS .......................................................... 80

4.3 METHODOLOGY OF PROPOSED AHP PROCEDURE................................... 82

4.3.1 Choice of AHP Technique ........................................................................... 82

4.3.2 Hierarchy Structure for AHP Analysis ......................................................... 82

4.3.3 Prioritization and Synthesization .................................................................. 83

4.4 ILLUSTRATIVE APPLICATION OF PROPOSED AHP PROCEDURE .......... 83

4.4.1 Description of Example Problem ................................................................. 83

4.4.2 Prioritization Questionnaire Survey ............................................................. 84

4.4.3 Evaluation of the Proposed AHP Method .................................................... 84

4.4 ANALYSIS OF RESULTS OF PRIORITY RATINGS ....................................... 85

4.4.1 Results of Priority Ratings and Priority Rankings ....................................... 85

4.4.2 Analysis of Priority Rating Scores and Priority Rankings ........................... 86

4.4.2.1 Assessment of Priority Rating Scores .............................................. 87

4.4.2.2 Assessment of Priority Rankings ..................................................... 87

4.4.2.3 Statistical Testing of Rank Correlation ............................................ 88

4.4.3 Summary Comments on Applicability of AHP ............................................ 89

4.5 SUMMARY .......................................................................................................... 90


ASSESSMENT: MECHANISTIC BASED APPROACH ................ 101

5.1 INTRODUCTION ............................................................................................... 101

5.2 METHODOLOGY OF PROPOSED APPROACH ............................................ 103

5.2.1 Evaluating Remaining Life of Cracked Pavement Section ........................ 103

5.2.2 Concept of Cumulative Damage and Failure Risk ..................................... 105

5.2.3 Cumulative Damage and Priority Ranking ................................................ 106

5.3 DETERMINATION OF CUMULATIVE DAMAGE FACTOR AND PRIORITY

RANKING ........................................................................................................... 106

5.3.1 Step 1: Determination of Input Parameters ................................................ 107

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5.3.2 Step 2: Characterization of Loads .............................................................. 108

5.3.3 Step 3: Computation of Load Induced Strains εt ........................................ 109

5.3.4 Step 4: Computation of Cumulative Damage Factor Df ............................. 110

5.3.5 Step 5: Determination of Maintenance Priority of All Cracked Pavement

Sections ...................................................................................................... 111

5.3.6 Adjustments for Presence of Transverse Cracks or Cracks of Other

Orientations ................................................................................................ 111

5.4 ILLUSTRATIVE NUMERICAL EXAMPLE .................................................... 112

5.4.1 Problem Parameters and Data .................................................................... 112

5.4.2 Results of Analysis ..................................................................................... 113

5.4.3 Comparison with Traditional Prioritization Method .................................. 114

5.4.4 Computational Tool for Estimating Cumulative Damage Factor .............. 115

5.5 SUMMARY ........................................................................................................ 115

CHAPTER 6 INCORPORATING PRIORITY PREFERENCES INTO

PAVEMENT MAINTENANCE PROGRAMMING........................ 125

6.1 INTRODUCTION ............................................................................................... 125

6.2 FRAMEWORK OF STUDY METHODOLOGY .............................................. 126

6.3 PART ONE – PROGRAMMING INVOLVING PRIORITY WEIGHTED

PARAMETERS ................................................................................................... 128

6.3.1 Formulation and Analysis of Example Problem ........................................ 128

6.3.1.1 Analysis (i): Comparison of Different Priority Schemes ............... 129

6.3.1.2 Analysis (ii): Study of Effects of Changing Magnitudes of Priority

Weights ........................................................................................... 131

6.3.1.3 Analysis (iii): Study Effects of Changing Range of Priority Weights

........................................................................................................ 132

6.3.2 Summary Remarks ..................................................................................... 132

6.4 PART TWO – PROPOSED MAINTENANCE PROGRAMMING

FRAMEWORK ................................................................................................... 133

6.4.1 Step I – Tie-Breaking Analysis .................................................................. 133

6.4.2 Stage II – Trade-Off Analysis .................................................................... 136

6.5 COMPARISON OF PROPOSED METHOD AND CONVENTIONAL

PRIORITY WEIGHT APPROACH ................................................................... 138

6.6 SUMMARY ........................................................................................................ 139

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CHAPTER 7 OPTIMAL BUDGET ALLOCATION IN HIGHWAY ASSET

MANAGEMENT ................................................................................. 145

7.1 INTRODUCTION ............................................................................................... 145

7.2 FRAMEWORK OF PROPOSED APPROACH ................................................. 147

7.3 FORMULATION OF BUDGET ALLOCATION MODEL ............................... 149

7.3.1 Stage I – Asset System Number 1: Pavement Management System ......... 149

7.3.2 Stage I – Asset System Number 2: Bridge Management System .............. 150

7.3.3 Stage I – Asset System Number 3: Appurtenance Management System ... 152

7.3.4 Stage II – System-wide Budget Allocation ................................................ 153

7.4 ILLUSTRATIVE NUMERICAL EXAMPLE .................................................... 155

7.4.1 Problem Parameters and Input Data ........................................................... 155

7.4.2 Analyses and Results .................................................................................. 156

7.4.2.1 Stage I – Component Management Systems .................................. 156

7.4.2.2 Stage II – System-wide Budget Allocation .................................... 157

7.5 FRAMEWORK INVOLVING MULTIPLE DISTRICTS .................................. 157

7.5.1 Stage I – Budget Allocation within Districts .............................................. 158

7.5.2 Stage II – System-wide Budget Allocation ................................................ 158

7.5.3 Illustrative Example ................................................................................... 159

7.5.3.1 Formulation and Analysis of Example Problem ............................ 159

7.6 SUMMARY ........................................................................................................ 162

CHAPTER 8 CONCLUSIONS AND RECOMMENDATIONS ............................. 175

8.1 SUMMARY AND CONCLUSIONS .................................................................. 175

8.1.1 Improved Prioritization Methods for Pavement Maintenance Planning .... 176

8.1.1.1 Establishing Priority Preferences using the AHP ........................... 177

8.1.1.2 Establishing Priority Preferences using Mechanistic Approach .... 178

8.1.2 Incorporating Priority Preferences into Pavement Management Optimization

.................................................................................................................... 179

8.2 RECOMMENDATIONS FOR FURTHER RESEARCH .................................. 180

REFERENCES ................................................................................................................ 182

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ACKNOWLEDGEMENTS

The journey through postgraduate academic degree is ultimately a solitary one — a

dissertation bears only one name — but such a simplification conceals all of the people

who helped me, guided me, and taught me along the way.

Writing this dissertation has been fascinating and extremely rewarding, starting as

a vague idea, it evolved into its present form which is a result of years of interesting

research. I would like to thank a number of people who have contributed to the final result

in many different ways: My deepest gratitude first goes to my PhD supervisor, Professor

Fwa Tien Fang, for his valuable supervision, assistance and suggestions throughout the

duration of this research at the National University of Singapore. His passion and

enthusiasm in the research has profoundly assisted me in shaping my interest in academic

research, and nurtured creativity rather than stifling it.

I would also like to present my gratitude to Professor Meng Qiang for his words of

wisdom, and also to my colleagues Anupam, Fenghua, Santosh, Setiadji, Pasindu, Xiaobo,

and Xinchang for their encouragement and discussions on relevant topics. Xinchang was

my extraneous accomplice in crime for a great deal of research, our daily conversations,

knock-knocks, and collaboration underlie most of the motivations and dedications.

A special appreciation is expressed to my parents and siblings for their precious

devotion and understanding during the course of this program. Thanks for all the prayers

and encouragement, Mom. My mom has been amazingly patient and supportive, providing

a much needed counterpoint to my academic career. I do not think I could have foreseen

how auspicious my opportunities at the National University of Singapore were going to be:

I have been able to achieve more than what my wildest hopes held in year 2007.

vii

SUMMARY

Managing a pavement network is a highly complex and complicated task if it is to be

taken in its totality. The complexity of the problem derives from the need for reliable

pavement performance prediction models and extensive current and historical records of

pavement distress, maintenance and rehabilitation history, and traffic loadings of a large

number of pavement sections of non-uniform structural properties. Pavements develop

distresses due to internal and external causes, such as heavy traffic loading, inadequate

design, deficient paving mix, poor construction, weak subgrade and defective drainage

system, etc.

In order to find optimal strategies for providing, evaluating and maintaining

pavements at an acceptable level of service over a pre-selected period of time, an

efficacious pavement management program with sound resource utilization should be

identified in a pavement management system (PMS). The pavement program can be

planned using a priority or an optimization model

While optimization is preferred over prioritization, the pavement engineering

community has not completely addressed the crucial issues related to the applications of

optimization in pavement management. Traditionally, it has been a common practice to

apply priority weights, derived from prioritization process, to selected parameters in the

process of optimal programming of pavement maintenance or rehabilitation activities.

The form or structure of priority weights adopted, and their magnitudes applied vary from

highway agency to agency. For instance, pavement researchers and highway agencies have

applied priority weights to the following parameters in pavement maintenance planning

and programming: pavement distress, pavement condition, road class and traffic volume.

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It is a well known fact that artificially applying priority weights to selected problem

parameters could lead to a sub-optimal solution with respect to the original objective

function (such as minimal total maintenance cost or maximum pavement condition). Most

decision makers are not aware of this consequence and the magnitude of loss in optimality

caused by their choice of priority scheme.

This thesis has presented a study that examines the following two main aspects of

pavement maintenance planning: (i) rational prioritizing of pavement maintenance

planning involving multiple parameters such as highway class, distress type, distress

severity etc., and (ii) incorporation of priority preferences in PMS optimization. The

research demonstrated the issues associated with subjective judgments involving multiple

criteria and resolution of the same, and the implications of applying priority weights and

using them directly in the pavement maintenance programming analysis.

Two improved methods were introduced for prioritization of pavement

maintenance activities (i) analytic hierarchy process (AHP) and (ii) mechanistically based

prioritization approach.

The research concluded that by incorporating priority weights directly into the

mathematical formulation, a sub-optimal solution is obtained. Unfortunately, many users

of the approach are unaware this fact and do not know the magnitude of loss in optimality

caused by their choice of priority scheme. Recognizing the fact that highway agencies do

have the practical need to offer maintenance priorities to selected groups of pavement

sections, a suggested procedure has been proposed in this study to incorporate such

priority preferences into pavement maintenance planning and programming.

An improved procedure of incorporating a user’s priority preferences into the

pavement maintenance programming process has been demonstrated. It allows the

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highway agency to decide if they are willing to settle with a sub-optimal solution by

including more prioritized activities in the final maintenance program.

A two-stage approach to solve the budget allocation problem of highway asset

management involving competing asset systems in a district, each with its own multiple

operational objectives has been presented using the proposed improved procedure. Stage

I of the approach analyzed the individual multi-objective asset systems independently to

establish for each a family of optimal Pareto solutions. Stage II adopted an optimal

algorithm to allocate budget to individual assets by allowing interaction between the

overall system level and the individual asset level, and performing cross-asset trade-off to

achieve the optimal budget solution for the given overall system level objectives. The

approach was also extended to take into account multiple districts within each component

management system.

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LIST OF TABLES

Table 2.1 Comparison between different optimization techniques

Table 2.2 Network project selection practices

Table 2.3 Prioritization methods survey results

Table 2.4 Prioritization criteria survey results

Table 2.5 Review of PMS implemented in various regions

Table 3.1 Pavement sections considered in example problem

Table 3.2 Priority ratings of sections obtained using different methods

Table 3.3 Priority rankings of sections obtained using different methods

Table 3.4 Spearman’s rank correlation coefficient and student’s t-test for correlation with

Direct Assessment Method

Table 3.5 Number of comparisons required by different methods

Table 4.1 Pavement segment distress characteristics for example problem

Table 4.2 Pavement distress codes for table 4.1

Table 4.3 Priority ratings of sections obtained using different methods

Table 4.4 Priority rankings of sections obtained using different methods

Table 4.5 Spearman’s rank correlation coefficient and student’s t-test for correlation with


Table 5.1 Material parameters for numerical example

Table 5.2 Results of computation for numerical example

Table 5.3 Comparison of priority rankings by PCR method and proposed approach

Table 6.1 Pavement distress data for example problem.

Table 6.2 Cost data for the example problem.

Table 6.3 Priority preference scores for pavement maintenance activities.

Table 6.4 Results from analysis of different priority schemes.

Table 6.5 Results of trade-off analysis.

Table 7.1 Highway infrastructure facilities for example problem

Table 7.2 Cost data for example problem

Table 7.3 Pavement distress data for example problem

Table 7.4 Bridge element condition for the example problem

Table 7.5 Bridge element maintenance actions and costs for the example problem

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Table 7.6 Appurtenance existing service life for the example problem

Table 7.7 Appurtenance design service life and costs for the example problem

Table 7.8 Results of multi-asset budget allocation analysis for the example problem

Table 7.9 Highway infrastructure facilities for the example problem

Table 7.10 Results of multi-district budget allocation analysis for the example problem

xii

LIST OF FIGURES

Figure 2.1 Flow chart of basic genetic algorithm

Figure 3.1 Rating scale and instructions for Direct Assessment Method

Figure 3.2 Hierarchy structure for AHP analysis of example problem

Figure 3.3 Correlations between priority ratings obtained using Direct Assessment Method

and different AHP methods

Figure 3.4 Correlations between priority rankings obtained using Direct Assessment

Method and different AHP methods

Figure 3.5 Scatter plots of priority ratings against group mean ratings

Figure 3.6 Scatter plots of priority rankings against group mean rankings

Figure 3.7 Deviation of ratings between individual evaluators and group mean ratings

Figure 3.8 Deviation of rankings between individual evaluators and group mean rankings

Figure 4.1 Rating scale and instructions for Direct Assessment Method

Figure 4.2 Hierarchy structure for AHP analysis of example problem

Figure 4.3 Correlations between the priority ratings obtained using Direct Assessment

Method and absolute AHP method

Figure 4.4 Correlations between the priority ratings and rankings obtained using PAVER

System and Direct Assessment Method

Figure 4.5 Correlations between the priority ratings and rankings obtained using Absolute

AHP Method and PAVER System

Figure 5.1 Flowchart of proposed mechanistic crack prioritization approach

Figure 5.2 Schematic of the finite element model for pavement crack analysis

Figure 5.3 Variations of wheel load magnitude and load wander

Figure 5.4 Priority ratings of cracks for numerical example

Figure 5.5 Comparison between proposed and existing pavement condition rating

Figure 6.1 Framework of the proposed approach.

Figure 6.2 Loss in optimality versus employed priority scheme.

Figure 6.3 Illustration of the process of tie-breaking analysis.

Figure 7.1 Framework of the proposed approach

Figure 7.2 Pareto frontier from analysis of pavement management system

Figure 7.3 Pareto frontier from analysis of bridge management system

xiii

Figure 7.4 Pareto frontier from analysis of appurtenance management system

Figure 7.5 Results of optimal multi-asset budget allocation analysis

Figure 7.6 Framework of the proposed approach

Figure 7.7 Pareto frontiers from analysis of district-1 management system



Figure 7.10 Results of optimal multi-district budget allocation analysis

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CHAPTER 1

INTRODUCTION

1.1 PAVEMENT MANAGEMENT SYSTEMS

The American Association of State Highway and Transportation Officials (AASHTO,

1985) defines pavement management as “…the effective and efficient directing of the various

activities involved in providing and sustaining pavements in a condition acceptable to the

traveling public at the least life cycle cost.” This concept of providing pavements and

maintaining them in acceptable condition is as old as the first pavement. As a pavement

network covers many kilometers of roads, it cannot be effectively managed by simple

procedures or experiences of individuals. Instead, a more holistic systems approach is

needed.

Originally described as “a systems approach to pavement design”, the term “pavement

management system (PMS)” came into popular use in the late 1960s and early 1970s to

describe decision support tools for the entire range of activities involved in providing and

maintaining pavements (OECD, 1987). Hudson et al. (1979) described a “total pavement

management system” as “…a coordinated set of activities, all directed toward achieving the

best value possible for the available public funds in providing and operating smooth, safe,

and economical pavements.”

Haas and Hudson (1978) expanded on this by defining “activities” as those actions

associated with pavement planning, design, construction, maintenance, evaluation and

research. Haas et al. (1994) described pavement management system as “…a set of analytical

tools or methods that assist decision makers in finding optimum strategies for maintaining

pavements in a serviceable condition over a given period of time.” In the operations research

2

terminology, pavement management is considered as a decision support system, and finding

the optimum maintenance strategy is one of the major problems being faced by transport

agencies around the world. Decision makers are required to select a maintenance strategy

which closely meets their requirements or criteria.

1.2 SIGNIFICANCE AND ISSUES OF PAVEMENT MAINTENANCE MANAGEMENT

In pavement management, the purpose of maintenance is to execute protective and

repair measures in order to slow down the pavement deterioration process, thereby extending

the useful life of a pavement. The efficacy of pavement maintenance is highly increased, if

action is taken at an appropriate time in a preplanned manner (AASHTO, 2004; NCHRP,

2004). Lack of adequate funding has always been a problem for the management of

pavements. With the introduction of prioritization techniques, engineers and managers are

able to schedule maintenance of pavement sections according to their relative urgency of

needs for maintenance. Therefore, every pavement management system consists of decision-

making models to prioritize or select pavement projects or pavement maintenance activities

for implementation. These models range from simple ranking to complex optimization

models. The quality of pavement management process, which in most cases depends

primarily on the judgment of the decision maker, can directly influence the effectiveness of

the handling of available resources (Sharaf, 1993).

Depending on the funding levels, location, and specific conditions of a transportation

agency, several methods ranging from a simple subjective ranking of projects based on

judgment to comprehensive optimization by mathematical programming models, are being

employed for pavement maintenance prioritization.

A common practice adopted by highway agencies is to express pavement maintenance

priority in the form of priority index computed by means of an empirical mathematical

3

expression (Fawcett, 2001; Broten, 1996; Barros, 1991). Though convenient to use,

empirical mathematical indices often do not have a clear physical meanings, and could not

accurately and effectively convey the priority assessment or intention of highway agencies

and pavement engineers. This is because combining different factors empirically into a

single numerical index tends to conceal the various contributing effects and actual

characteristics of the distress (Fwa and Shanmugam, 1998). Furthermore, not all of the

factors and considerations involved can be expressed quantitatively and measured in

compatible units.

It is common to apply priority weights to selected parameters in the process of

optimal programming of pavement maintenance or rehabilitation activities. The form or

structure of priority weights adopted, and their magnitudes applied vary from highway

agency to agency. For instance, pavement researchers and highway agencies have applied

priority weights to the following parameters in pavement maintenance planning and

programming:

• Pavement distress -- Priority weights of different magnitudes are applied to

different distresses based on either distress type, distress extent or distress

severity (Abaza and Ashur 1999, Fwa et al. 2000).

• Pavement condition -- Priority weights are applied to pavement sections according

to an aggregate measure of pavement condition, with higher magnitude

assigned to pavement sections of poorer condition (Evdorides et al. 2002,

Abaza et al. 2004).

• Road class -- Priority weights are assigned to pavement sections in accordance

with their highway classifications. Higher priority weights are given to

pavement sections of higher functional classification (e.g. expressways) or

4

functional importance (e.g. designated snow routes or emergency routes)

(Fwa and Sinha 1988, Wahhab et al. 2002).

• Traffic volume -- Priority weights are applied to pavement sections based on the

traffic volumes they carry. Usually pavement sections carrying higher daily

traffic volume will receive higher maintenance priority (Wahhab et al. 2002,

Wang et al., 2003).

The rationale of applying priority weights, in a manner such as those listed above, is

easy to understand and it often represents the intention or pavement maintenance

management policy of the highway agency concerned. However, there are several questions

and issues involved as highlighted below:

(a) For a given objective function (e.g. maximizing overall pavement network

condition under a given budget, or maximizing the number of pavement sections

repaired for a given budget, etc), would the parameters selected to receive priority

weights lead to a satisfactory end result (i.e. maintenance program) that meets

with the original intention of the highway agency? The answer to this question,

unfortunately, is not always affirmative. This is because pavement maintenance

programming is a complex nonlinear process involving different forms of

operational considerations and constraints. Upon receiving the computed

maintenance program, the highway agency that applies the prioritization scheme

would in most cases not know exactly how the chosen scheme has affected the

outcome of the programming analysis.

(b) For a given prioritization scheme, how would the magnitudes of the priority

weights affect the final results of maintenance programming? The magnitudes of

weights applied to prioritized parameters in relation to non-prioritized parameters,

and the relative magnitudes of weights assigned to the sub-categories of a

5

prioritized parameter could have major effects on the results of maintenance

programming analysis. Most highway agencies that apply priority weights in their

pavement maintenance planning would not know how the relative magnitudes of

priority weights can affect the computed maintenance program, and how they

could change the relative or absolute magnitudes of the priority weights to make

adjustments to the final maintenance program.

Some use integer goal programming (e.g., Cook, 1984), some linear goal

programming (e.g., Benjamin, 1985), some linear programming (e.g., Karan and Haas, 1976;

Lytton (1985)), some linear integer programming (e.g., Mahoney et al. (1978); Garcia-Diaz

and Liebman (1980); Fwa and Sinha (1988); Li et al. (1998); Ferreira et al. (2002); Wang et

al. (2003)), some dynamic programming (e.g., Feighan et al. (1987); Tack and Chou (2002)),

some Markov decision analysis (Abaza and Murad (2007)), and some genetic algorithms (e.g.,

Chan et al. (1994), Fwa et al. (1994a, 1994b, 1996, 2000); Pilson et al. (1999)).

This research presents a study that examines the two issues above by demonstrating

the implications of applying priority weights, and using them directly in the pavement

maintenance programming analysis. Recognizing the fact that highway agencies do have the

practical need to offer maintenance priorities to selected groups of pavement sections, a

suggested procedure is proposed in this research to incorporate such priority preferences into

pavement maintenance planning and programming. The proposed procedure presents an

integrated prioritization and optimization approach, applying genetic algorithm (GA) and the

Analytic Hierarchy Process (AHP), to incorporate priority weights into pavement

maintenance programming analysis with the intention of eliminating or minimizing

unnecessary interferences to the optimal programming process, and allowing the highway

agency to know how the computed maintenance program can be changed by their choice of

priority scheme in maintenance planning.

6

1.3 ORGANIZATION OF THESIS

This thesis consists of eight chapters. The introductory chapter (Chapter 1) provides

the background of the proposed research along with the issues required to be addressed, and

the specific objectives of the study. Chapter 2 contains the literature review of the

prioritization and optimization techniques used in pavement management, and the objectives

of current research.

Chapter 3 presents a proposed rank based priority model for pavement maintenance

programming based on the Analytic Hierarchy Process (AHP). The implementation of the

proposed model is illustrated by considering pavement segments with a single distress each.

For each case, the results are assessed by comparing with the priority assessments obtained

from the Direct Assessment Method in which the raters make the evaluation by comparing all

the maintenance activities together directly.

Chapter 4 describes an extension of the approach presented in Chapter 3 to consider

maintenance programming of pavement segments each containing multiple distresses.

Instead of the approach based on subjective judgment, some distresses can be

prioritized using mechanistic analysis. Chapter 5 presents a mechanistically based approach

to assess the urgency of maintenance needs of cracks. The maintenance priority of a crack is

evaluated based on its adverse impact on the structural capacity of the pavement section. The

proposed approach expresses the severity of a crack in terms of the remaining life of the

cracked pavement section.

Chapter 6 proposes an integrated prioritization and optimization approach for

maintenance programming. It applies genetic algorithm (GA) and the Analytic Hierarchy

Process (AHP) to incorporate priority weights into the pavement maintenance programming

analysis with the intention of eliminating or minimizing unnecessary interferences to the

optimal programming process.

7

Chapter 7 presents the framework for the implementation of the proposed approach in

Chapter 6 to the system wide budget allocation problem for highway asset management of a

district. The framework consists of a two-stage approach with the first stage addressing the

optimal plans for subsystems, each with its own multiple operational objectives, while the

second stage handles the overall optimization of the entire system.

Finally, Chapter 8 concludes and summarizes the major conclusions elicit from this

research, as well as recommendations for further research.

8

CHAPTER 2

LITERATURE REVIEW

2.1 INTRODUCTION

Managing a pavement network is a highly complex and complicated task if it is to be

taken in its totality. The complexity of the problem derives from the need for reliable

pavement performance prediction models and extensive current and historical records of

pavement distress, maintenance and rehabilitation history, and traffic loadings of a large

number of pavement sections of non-uniform structural properties (Golabi et al., 1982;

Shahin, 1994; Fwa et al., 1994a; Pilson et al., 1999; Ferreira et al., 2002). Pavements develop

distresses due to internal and external causes, such as heavy traffic loading, inadequate design,

deficient paving mix, poor construction, weak subgrade and defective drainage system, etc.

In order to find optimal strategies for providing, evaluating and maintaining

pavements at an acceptable level of service over a pre-selected period of time, an efficacious

pavement management program with sound resource utilization should be identified in a

pavement management system (PMS). The pavement program can be planned using a

priority or an optimization model (Haas et al., 1978). Some PMSs employ rank based priority

models to derive the resources allocation for a selected maintenance program, and some

PMSs employ network optimization models to identify the optimal maintenance program,

while other PMSs are developed using a combination of the two types of models.

A review of existing PMS prioritization and optimization approaches is presented and

possible future developments are discussed. The chapter closes with an outline of the

proposed research and the significance of the research in this area.

9

2.2 PRIORITIZATION AND OPTIMIZATION APPLICATIONS IN PAVEMENT MANAGEMENT

Prioritized resource allocation is imperative given the fact that there is rarely enough

funding with highway agencies to address all the pavement sections, as discussed earlier.

Traditionally, the two most basic techniques for network level decision making are the

prioritization approach and the optimization approach. Prioritization involves ranking

competing pavement sections requiring maintenance using subjective judgment. In contrast to

prioritization, an optimization approach involves evaluation of all possible repair strategies,

on a network level, and selection of the optimal strategy to meet predefined objectives. The

literature review in this chapter aims to achieve the following,

i. Review existing prioritization and optimization methodologies.

ii. Draw a comparison between prioritization and optimization in general.

iii. Review practices of pavement maintenance programming adopted by highway

agencies.

iv. Identify specific issues related to pavement maintenance programming.

v. Explain the proposition for the present research and its significance in the domain of

pavement maintenance programming.

2.2.1 Prioritization Techniques for Pavement Management

2.2.1.1 Overview

Due to the complexity involved in the decision making process, subjective evaluation

based on experts’ judgments has been used in practice since the sixties when Delphi method

was proposed (Dalkey, 1967). Subsequently other methods such as Pugh Method (Pugh,

1981), Direct Rating Scale Methods (Wendt et al., 1973), Outranking Approaches (Brans,

10

1982; Roy, 1996), and Analytic Hierarchy Process (AHP) (Saaty, 1980, 1990, 1994) were

developed.

Prioritization is essentially performed in a sequential manner by first enlisting the

pavement maintenance projects required to be executed. Once projects are identified, the next

step is to prioritize the projects based on their relative perceived urgency of needs for repair.

The projects having the highest priority are executed until all the finances are expended. Any

projects left are re-prioritized together with the new projects upon availability of funds.

A common practice is to rank projects and treat those pavement sections in the worst

condition first regardless of the effect on the network-wide pavement condition and

maintenance cost. Such approach is known as “worst first” ranking approach. The “Worst

first” approach seems to be logical in a sense that pavements which are in the worst condition

will lead to the highest user cost, and the most complaints from the road users. However, it

fails to account for the level of change in benefit for the funds expended.

As widely known among pavement engineers, the “worst first” approach does not

consider the rates of deterioration of pavement sections and the incremental effectiveness of

repair treatments. It often does not produce a cost effective solution (Bemanian, 2007).

Some highway agencies have adopted a “reverse prioritization” strategy to overcome the

problems encountered with the “worst first” strategy (Broten et al., 1996). The highest rank is

assigned to pavement sections in a state where repair is cost effective, and thus it will

produce the effect of executing pavement repair while reducing the repair cost. However,

since pavement management involves conflicting and multiple objectives, this revised

approach of maximizing effectiveness may not necessarily optimize other objectives such as

safety and condition.

Various priority rating and ranking models to prioritize pavement sections according

to their maintenance needs have been reported by Mercier (1986). Reddy and Veeraragavan

11

(2002) put forward a Priority Index (PI) as a function of Pavement Distress Index (PDI) and

prioritization factor for ranking the pavements on a network level. Chen et al. (1993) and

Sharaf (1993) employed a Composite Index (CI) method for prioritization. However,

empirical mathematical indices often do not have a clear physical meaning, and could not


and pavement engineers. Furthermore, not all of the factors and considerations involved can

be expressed quantitatively and measured in compatible units.

Fwa et al. (1989) presented the “Direct Assessment Method” using a card approach to

prioritize routine maintenance activities by highway class, distress condition and level of

distress severity. The Direct Assessment Method is intuitively the method a normal person

would use in making priority assessment. In theory, to rank and rate n number of items, the

Direct Assessment Method would involve ( ) 21−nn number of comparisons. Hence, for a

network consisting of only 27 sections to be ranked, the number of comparison required to be

made will be 351. The major demerit of this methodology comes out to be the large number

of comparisons required to be made even for a small problem consisting of 27 sections, and

its inability to quantify the exact difference between the alternatives which dominates the

outcome in certain situations.

Fwa and Chan (1993) described an application of artificial neural networks to the

priority rating of pavement needs to mimic the decision making process of humans. Zhang et

al. (2001) presented a study applying neural networks in conjunction with GA to analyze the

implications of prioritization in pavement maintenance management. However as the

individual relations between the input variables and the output variables are not developed

through engineering judgment in neural networks, the model tends to be a black box or

input/output table without providing any physical relationship useful for practical decision

making.

12

Application of fuzzy logic to pavement management problem, demonstrated by Zhang

(1993), Fwa and Shanmugam (1998) and Chandran et al. (2007), tries to represent uncertainty

involved in human judgments. However, the three demerits associated with fuzzy logic are:

(1) it is difficult to estimate membership functions, (2) there exist many ways of interpreting

fuzzy rules, combining the outputs of several fuzzy rules and defuzzifying the output, and it

is difficult to assess the physical meanings of such operations, and (3) fuzzy assessments

made on individual alternatives may not provide any information about the relative

importance of alternatives.

The Analytic Hierarchy Process (AHP) was developed by Saaty (1980) to facilitate

decision makers in selecting the best alternative. The application of Analytic Hierarchy

Process (AHP) has been found valuable in decision making problems relevant to

transportation in general. Saaty (1995) presented the application of the AHP in transportation

analysis, and illustrated it with the aid of five examples. Tsamboulas and Yiotis (1999)

presented a comparative analysis of five multicriteria methods, inclusive of the AHP, for the

assessment of transport infrastructure projects. El-Assaly and Hammad (2001) presents a

decision support system for prioritizing pavement maintenance activities using the AHP for

the transport infrastructure in Alberta, Canada.

Kinoshita (2005) in his paper described the AHP as the most effective way of

selecting the best alternative based on pairwise comparisons. Furthermore, by making

pairwise comparison amongst the criteria and the alternatives, a common problem of

discarding the most favorable alternative is eliminated. He emphasized that the idea of

pairwise comparison is completely in line with the human behavior, and it reduces decision

maker’s reliance on his intuition. Moreover, he claimed that the AHP eases the load on the

brain in case of large number of alternatives. Cook and Kress (1994) developed a multiple

criteria composite index for evaluating a set of alternatives relative to a combination of

13

ordinal (qualitative) and cardinal (quantitative) criteria. This model has also been

incorporated in a software package known as multi-attribute ranking system (MARS).

Larson and Forma (2007) described the use of the AHP to facilitate the VDOT’s

(Virginia Department of Transportation) Asset Management Division in deciding the amount

of video logging and pavement condition data in terms of highway mileage. Ortiz-Garcia et al.

(2005) discussed the evolution of highway maintenance standards, and performed

multicriteria analysis is to determine the highway maintenance standards. Furthermore, it is

concluded in the paper that AHP is the most appropriate method, in view of its operational

advantages.

Cafiso et al. (2002) consider the AHP to be more appropriate, for integration with a

pavement maintenance management, than other multicriteria prioritization methods. Smith

and Tighe (2006) employed the AHP in infrastructure management, and concluded that the

AHP is a complimentary tool for evaluating alternatives, especially when constraints prohibit

field study.

2.2.1.2 Review Comments

Based on the merits of the AHP over other prioritization techniques as reviewed in the

preceding section, the AHP is included for evaluation in this research as a prioritization

scheme in pavement management problems. In the literature, there exist several variations of

the AHP. In the present study, the following three methods are analyzed for their

appropriateness for maintenance prioritization in pavement management: (a) distributive-

mode relative AHP, (b) ideal-mode relative AHP, and (c) absolute AHP. An in-depth

assessment and analysis of all the three variants of the AHP will be presented in Chapter 3.

14

2.2.2 Optimization Techniques for Pavement Management

2.2.2.1 Overview

Optimization involves maximizing or minimizing an objective function of several

binary, integer or real valued decision variables while satisfying equality or inequality

constraints. A problem involving single objective function is termed as single objective

problem, which is rarely the case for pavement management problems in the real world.

In pavement management, the role of optimization is not restricted to solving a

mathematical programming model, but to address engineering, socio-economic, political and

environmental concerns. The objectives required to be achieved are often multiple and

conflicting, necessitating the simultaneous maximization or minimization of several objective

functions.

Since the early 1980s, many optimization techniques have been adopted for

maintenance programming in PMS, such as integer goal programming (Cook, 1984), linear

goal programming (Benjamin, 1985), linear programming (Karan and Haas, 1976 and Lytton

(1985)), linear integer programming (Mahoney et al. (1978), Garcia-Diaz and Liebman

(1980), Fwa and Sinha (1988), Li et al. (1998), Ferreira et al. (2002) and Wang et al. (2003)),

dynamic programming (Feighan et al. (1987) and Tack and Chou (2002)), and genetic

algorithms (e.g., Chan et al. (1994), Fwa et al. (1994a, 1994b, 1996, 2000) and Pilson et al.

(1999)). Most of the approaches either maximized pavement performance subject to

maintenance and rehabilitation budget constraints, or minimize maintenance and

rehabilitation cost subject to performance constraints (Abaza and Ashur, 1999; Abaza et al.,

2004, 2006; Abaza and Murad, 2007; Haas et al., 1994; Shahin et al., 1994; Harper and

Majidzadeh, 1991; Hill et al., 1991).

One the major demerits in solving pavement maintenance resource allocation problem

through optimization is the presence of a large number of maintenance and rehabilitation

15

decision variables (Harper and Majidzadeh, 1991; Pilson et al., 1999; Abaza et al., 2001,

2004; Ferreira et al., 2002). Therefore, some of the developed pavement management systems

adopted a macroscopic approach rather than a microscopic approach in order to significantly

reduce the number of maintenance and rehabilitation decision variables (Abaza and Ashur

1999; Abaza et al. 2001, 2004).

In the macroscopic approach, the decision variables are introduced for each pavement

class and they represent the proportions of pavement that should be treated by the applicable

maintenance or rehabilitation activities (Grivas et al. 1993; Chen et al. 1993; Liu and Wang

1996). However, the exact segments of the pavement network selected for maintenance and

rehabilitation treatments are not identified. In contrast to the macroscopic approach, the

microscopic approach associates maintenance or rehabilitation activities with each pavement

segment, thus resulting in a much larger number of variables, and making the optimization

process extremely complicated (Shahin 1994; Pilson et al. 1999; Ferreira et al. 2002).

In a network level approach, only the total budget projected for the entire pavement

network is specified. Due to the complex nature of the pavement management problem, not

all techniques are considered feasible in certain situations (Fwa et al., 1994b; Pilson et al.,

1999).

Chan et al. (1994) developed the PAVENET model which deals with a single-

objective, segment based pavement management problem. It was the first PMS model to

incorporate genetic algorithm (GA) (Goldberg, 1989) as the optimization tool. The authors

successfully formulated multiyear road-maintenance planning problem on the operating

principles of GA, and illustrated special characteristics of the PAVENET model. The use of

heuristic made it possible to analyze the entire pavement network, and attain an acceptable

solution within a practical period of time.

16

Fwa et al. (1994a) analyzed road-maintenance planning problem using the developed

PAVENET model. Furthermore, Fwa et al. (1994b) compared solutions obtained using

PAVENET with solutions obtained through branch and bound algorithm, and found that

PAVENET was able to produce acceptable solutions with very little computational

complexity. Fwa et al. (1996) integrated rehabilitation planning into the PAVENET model,

and called it PAVENET-R. However, PAVENET being a single-objective model model, and

its variants could not be applied to solve the multi-objective problems commonly encountered

in the real world.

Acknowledging the fact that pavement management problems involve multiple

conflicting objectives, multi-objective GA approach was applied to solve such problems

(Pilson et al., 1999; Fwa et al., 2000). Furthermore, subjective ranking, in the form of

prioritized pavement maintenance activities based on predefined criteria related to the overall

objective function of the optimization process, was applied in order to direct the optimization

process on a certain expected course, and to promote solutions placed in the region of interest,

while neglecting the others during the search process. Incorporating subjective judgment in

the optimization model can be viewed as a form of interference to the resource allocation

process. It is likely to produce biased pavement maintenance strategy deviating from the

optimal strategy.

Chan et al. (2003) introduced a two-step genetic algorithm process for the allocation

of budget for PMS at regional level involving several sub-districts. It solves a single-

objective problem and unable to handle multiple and conflicting objectives. Wang et al.

(2003) used a weighted sum approach to scalarize two objectives instead of simultaneously

optimizing all the objectives. In the case of synthesization, the weight of an objective is

selected based on the relative importance of the objective in the considered problem.

17

The major obstacle in solving the pavement management problem is the need to

consider a large number of pavement sections and the associated maintenance and

rehabilitation decision variables covering multiple time periods. This makes the problem of

searching for a global optimum solution a highly complex and challenging issue (Harper and

Majidzadeh, 1991; Pilson et al., 1999; Abaza et al., 2001, 2004; Ferreira et al., 2002).

Therefore, some pavement management systems adopted a macroscopic approach rather than

a microscopic approach in order to significantly reduce the number of maintenance and

rehabilitation decision variables (Abaza and Ashur, 1999; Abaza et al., 2001, 2004).

In the macroscopic approach, the decision variables are introduced for each pavement

class and they represent the proportions of pavement that should be treated by the applicable

maintenance or rehabilitation activities (Grivas et al., 1993; Chen et al., 1993; Liu et al.,

1996). The exact segment of the pavement network cannot be identified for maintenance and

rehabilitation activities to be executed. In contrast to the macroscopic approach, the

microscopic approach associates maintenance or rehabilitation activities with each pavement

segment. This gives rise to a much larger number of variables, thus making the optimization

process extremely complicated (Shahin, 1994; Pilson et al. 1999; Ferreira et al. 2002).

In view of the scale and complexity of the pavement management problem, instead of

using conventional optimization algorithms, more and more researchers are employing

metaheuristics to solve the problem. Metaheuristics are generally applied when no problem-

specific algorithm is available or when it is not practical to implement conventional

algorithms. These approaches include simulated annealing (SA), and genetic algorithms (GA).

Simulated annealing is one of the stochastic search algorithms, which is designed

using a spin glass model by the Kirkpatrick et al. (1983). The name and inspiration come

from annealing in metallurgy, a technique involving heating and controlled cooling of a

material to increase the size of its crystals and reduce their defects. However, the genetic

18

algorithms outperform simulated annealing when the problem size and the epistatsis (the

degree of parameter interaction) become large (Nam and Park, 2000). The disadvantage of

SA is, as is well known, the long annealing time.

Genetic algorithms are the prominent class of evolutionary algorithms exploiting the

idea of the survival of the fittest or natural selection. The framework of GA is presented in

Fig. 2.1. GA has been found to produce satisfactory results in problems related to pavement

management, and has been employed by several researchers (Fwa et al., 1994a, 1994b, 2000;

Tack and Chou, 2002; Ferreira et al., 2002).

Ferreira et al. (2002) presented a probabilistic pavement management single objective

optimization model. The proposed methodology employed Markov decision analysis and

mixed-integer optimization model. However, because of the computationally intensive nature

of mixed-integer optimization model, genetic algorithms were recommended and employed

to solve the programming model. GA solutions were compared against branch-and-bound

solutions and were found to produce satisfactory results.

Dynamic programming (DP) (Bellman, 2003) is considered to be the most accurate of

the optimization techniques, but difficult to implement and it requires new formulation each

time an objective or constrained is added (Tack and Chou, 2002). Tack and Chou (2002)

implemented DP and GA to four pavement management problems with different network size

and concluded that the solutions obtained through GA are satisfactory compared to those

rendered by DP. The solutions yielded by GA were in excess of the 95th percentile accuracy

for all the four considered problems, and were near optimum.

The detailed comparison of various conventional optimization and artificial

intelligence approaches as presented above is summarized in Table. 2.1.

19

2.2.2.2 Review Comments

The insignificant difference in the final results rendered by GA and conventional

techniques, while requiring less computational effort, is the main reason of GA being selected

in solving complex pavement management problems. Based on the review of the

conventional and GA optimization techniques, GA was employed in solving pavement

management problems in the present research.

2.2.3 Prioritization versus Optimization

In pavement maintenance optimization, the timing of maintenance treatment is

considered as well as the selection of pavement sections. This makes it more complex, but it

also allows consideration of the benefits of delaying, or advancing the maintenance treatment

of pavement section compared to another. The advances in computational power makes it

possible for highway agency’s to employ optimization tools like the GA heuristic as their

resource allocation decision-making tool. Optimization allows multiple objectives to be

optimized simultaneously, can develop multi-year repair programs and maintenance plan

while capturing the effect of deferring a pavement maintenance activity on the pavement

condition. Unlike optimization, prioritization involves subjective ranking of pavement

sections based on the “worst first” principle. Prioritization fails to account for the change in

benefit for the funds expended, and produces a maintenance strategy which can be far from

optimal.

The optimization analysis selects a maintenance strategy to optimize the agency’s

goals. It has been identified that pavement priority ranking approach is 20 to 40 percent more

effective than subjective project selection approach, and further 10 to 20 percent

effectiveness can be achieved by using optimization approach (NCHRP, 1995). An ideal

optimization approach is one that evaluates all possible repair strategies on a network level

without imposing unnecessary constraints or subjective judgment.

20

2.3 REVIEW OF PMS MODELS AND SYSTEMS

This section summarizes the implementation status of network level pavement

maintenance resource allocation practice by various transportation agencies. The Intermodal

Surface Transportation Efficiency Act (ISTEA), passed into law by the U.S. Congress in

1991, mandated the development of pavement management system for each State Department

of Transportation (DOT). This has boosted the development and implementation of PMSs in

the United States (USDOT, 1997). As a result of ISTEA, pavement management has become

part of every transportation agency’s operation systems in the United States.

The first project-level pavement management system was implemented by the

Washington State Department of Transportation (WSDOT) in 1974 (Finn, 1997). The system

identified rehabilitation treatment methods for the projects in its highway network. By 1980,

five states, Arizona, California, Idaho, Utah, and Washington, were reported to be in various

stages of development of systematic procedures for managing their pavement systems (Finn,

1997). The first network-level PMS with optimization model was implemented by the

Arizona Department of Transportation (ADOT) in 1982 (Golabi et al., 1982).

2.3.1 Implementation Status of Network Level Resource Allocation System

NCHRP Synthesis 222 (NCHRP, 1995) investigated the network-level pavement

project selection systems used by highway agencies in the United States, Puerto Rico, and the

twelve Canadian provinces. Forty-six out of the 52 surveys sent to the State Departments of

Highway/Transportation in the United States and its territories, and 10 out of 12 surveys sent

to Canadian provinces transportation agencies were returned.

Table 2.2 presents the survey results. 29 of 62 responses (47 percent) indicated

pavement condition analysis approach to selecting projects and treatments. The pavement

conditions, used for ranking analysis included, pavement condition rating (PCR), rutting, and

21

cracking. 13 (21 percent) agencies reported the use of either a systematic methodology or no

formalized approach, while 10 (16 percent) and 12 (19 percent) agencies reported the use of

priority assessment models and network optimization models respectively. One or more

constraints were usually considered in the optimization models. The common constraints

were limits on the budget levels and limits on the overall network pavement conditions. The

total number of responses in the analysis methods is greater than 62 because some agencies

selected more than one analysis method.

Compared with NCHRP Synthesis 222, the survey performed by Gao and Tsai (2003)

concentrated on network-level needs analysis methods used by the state DOTs in the USA.

The survey by Gao and Tsai was sent to 50 state DOTs, and 22 states responded. Nine

questions in the survey were related to the organization, prioritization, and planning of

network-level maintenance needs analysis. In the questionnaire, agencies were asked to

identify the approach that best described the prioritization criteria used. Multi-year cost

effectiveness was the most common approach (10 out of 22) as shown in Table 2.3. Four

agencies reported using worst-first approach, and one reported using an optimization model.

Similar to the NCHRP Synthesis, some agencies indicated that more than one approach was

used.

Most of the agencies responding to the survey indicated that they considered multiple

years in their maintenance needs analysis. Seven agencies used a 2-to-5-year analysis period,

7 agencies used 6 to 10 years, and 5 agencies used 11 and more years. Many agencies use

different periods for performing maintenance needs analysis and for funding allocation.

Usually, a fund allocation period is shorter than the needs analysis period. No agency used

more than 12 years in fund allocation. Mississippi and Virginia are the only two agencies that

indicated using one year as the analysis period. Among all the agencies that responded, 5

agencies reported using individual-year composite ratings i.e. average pavement condition

22

weighted by traffic and/or pavement project length, to define network-level performance

requirements; two agencies used a multiple-year composite rating; three agencies used

minimum individual project ratings or a condition index; three agencies did not use any index;

and 9 indicated other measurements were used.

Regarding the criteria used for selecting pavement projects for rehabilitation, the most

common factor used was surface distresses, followed by the International Roughness Index

(IRI) and skid resistance as shown in Table 2.4. The other physical factors mentioned

included structural integrity, age, time of last rehabilitation treatment, etc. Traffic and

capacity improvement were reported by five and seven agencies, respectively. Six agencies

considered safety in determining multi-year funding, and five agencies included user costs in

determining multi-year funding.

To further understand the network-level pavement maintenance needs decision-

making systems used by highway agencies, the following section presents an overview of the

developed and implemented pavement management models and systems.

2.3.1.1 Arizona PMS

Markov-chain models are employed in the state of Arizona for predicting the

performance of infrastructure facilities because of their ability to capture the uncertainty of

pavement deterioration process. However pavement historical data are difficult to be included

in the Markov model because the future state of pavement is only based on its current state.

The Arizona network level pavement management procedure is known as Network

Optimization System (NOS) (Wang et al., 1993). It was subsequently implemented in Alaska,

Kansas, Holland, Finland, Hungary, Australia (Golabi and Pereira, 2003) and Saudi Arabia

(Harper and Majidzadeh, 1991). The Arizona pavement management system was structured

as a single objective cost minimization linear programming model (Wang et al., 1994),

expected to minimize agency discounted costs of pavement maintenance and rehabilitation

23

(M&R) actions over a given planning time span, while keeping the network within given

quality standards in terms of the proportion of roads.

The model is applied separately to each of 15 road categories defined according to

their traffic loadings and climate conditions. The deterioration of pavements over time is

described by a set of Markov chains, one for each road category. The probability of transition

between any two condition states was specified. Initially, four factors, roughness, cracking,

cracking change, and index to first crack were taken into account to define a condition state.

Each factor was assigned a severity level such as low, moderate and high. This results in 180

possible condition states. NOS considered 17 maintenance and rehabilitation actions for each

potential pavement to be treated.

Subsequently, it was observed that the rate of distress development does not increase

as the pavement deteriorates, and therefore crack change per year may not be an appropriate

indicator of the acceleration of pavement deterioration. Based on the revised condition state

structure, the total possible condition states were reduced to 45. The number of maintenance

and rehabilitation actions was also reduced to 6.

NOS possesses the capability to conduct steady-state and multi-period analysis. The

solution from steady-state analysis represents the uniform rehabilitation strategy to keep the

pavement at the required condition level. Under steady state the proportion of pavement in

each state becomes constant, and the essential M&R actions are fixed for every year.

However, budget needs based on steady-state runs are higher than a multi-period runs, and

the multi-period runs should be used in actual pavement preservation program (Wang et al.,

1994).

The Arizona Department of Transportation (ADOT) uses NOSLIP, a specific native

32-bit OS/2-based code developed at the civil engineering departments of the Universities of

Arizona and Arkansas to solve the linear optimization model. It has been noted that once

24

network grows larger it becomes virtually impossible for any supercomputer to solve the

linear programming problem to unique optimality (Pilson et al., 1999).

NOS employs a macroscopic approach to determine the proportion of pavement in

each condition state to receive M&R treatments. The specific locations of the pavement are

not identified, and additional work is needed to develop a maintenance and rehabilitation

schedule.

One of the major demerits of NOS is that it employs Markov chain in which the future

state of a pavement is only based on its current state. It is difficult to include pavement

historical data in the transition probability matrix (TPM). For example, if a pavement is in a

certain condition state due to some treatment performed 1 year ago, now the decision to

transit to a new state or staying at the current state is independent of the kind of action

performed in the past to bring the pavement to a current state. Hence, Markov chain cannot

take into account pavement maintenance history and the life expectancy of the performed

treatment.

Furthermore, pavements are classified into several categories based on functional

class, traffic level and region within the state so as to identify the category of road requiring

maintenance. A paradox in creating categories is that many disparate pavement sections have

to be grouped into a limited number of approximate homogenous categories, based on a set of

predetermined criteria, to obtain enough samples for meaningful statistical analysis. The

larger the number of categories, the larger the amount of uniformity each category possess.

As TPM is generated for each M&R action under each category of pavements, the

homogeneity of a category determines the accuracy of performance prediction of pavements

in that category after each M&R action. However, a large number of categories imply fewer

pavement samples in terms of the number of miles of pavements in each category which

compromises the reliability of the TPM. Moreover, a large number of categories will result in

25

a large number of TPMs. For instance, for 15 categories and 6 maintenance actions, ( )615×

90 TPMs have to be generated.

Pavement management involves multiple and conflicting objectives or alternatively

considers single objective to be optimized, while adding others as constraints as in NOS, and

has the main disadvantage that it requires a decision maker to know beforehand the ranges of

variation of each constrained objective in order to establish coherent goals. Moreover, the

kind of solution obtained using the above method largely relies on the constraint limits.

Setting constraints may be viewed as interference to the process of optimization by creating

artificial boundaries. This interference issue will be further explained under Section 2.4 in

detail.

ADOT is in the process of changing the pavement resource allocation system after

using the original system for about 20 years. The changes include not using Markov chain

models and incorporating certain capabilities to allow the generated M&R requirements from

network optimization analysis to be connected with specific pavement sections (Li et al.,

2006). However, the system will still only address single-objective problems.

2.3.1.2 PAVER Pavement Management System

The PAVER pavement management system is designed to optimize the use of funds

allocated for pavement maintenance and rehabilitation (M&R). It was developed at the U.S.

Army Construction Engineering Research Laboratory (USACERL) for predicting pavement’s

M&R needs many years into the future. It uses the Pavement Condition Index (PCI) with a

rating from zero (failed) to 100 (excellent). The PCI for airports became an ASTM standard

in 1993 (D5340-98). The PCI for roads and parking lots became an ASTM standard in 1999

(D6433-99).

The PAVER procedure requires the identification of the type of pavement distress, its

extent and severity. These values are then used to calculate an overall PCI for the pavement

26

section. The pavement distress, extent and severity are combined using “deduct value” curves

to establish the impact of the individual distress on the overall condition of the pavement.

PAVER has been implemented by several agencies as an airport pavement

management system worldwide from O’Hare International Airport in Chicago to Inchon

International Airport in South Korea. The Micro PAVER has been used to manage their

general aviation airports by many states including Arizona, California, Colorado, Georgia,

Illinois, Maryland, Ohio, Pennsylvania and South Carolina. Furthermore, the US Air Force,

US Army and the US Navy use Micro PAVER to manage their airfield pavements. Micro

PAVER is a pavement maintenance management system originally developed in the late

1970s to help the U.S. Department of Defense (DOD) manage M&R for its vast inventory of

pavements.

In the condition survey phase, distresses can be recorded using tablet computers or

paper forms. Inspections can also be carried out using digital imaging where data can be

imported into Micro PAVER using the Condition Data Import application. Inspection is

performed for smaller areas called sample units (e.g. for asphalt roads, a sample unit is

approximately 2500±1000 sq ft.).

Pavement performance prediction modeling is a critical element in the determination

of Maintenance & Repair (M&R) requirements for pavement sections. Micro PAVER

employs the Family Method for pavement condition prediction (Shahin, 2005). The method

consists of the following steps,

i. Pavement sections with similar construction and similar traits that affect pavement

performance (traffic, weather, maintenance, etc.) are identified and grouped together;

ii. Filter the data;

iii. Conduct data outlier analysis;

iv. Generate the family model;

27

v. Assign pavement sections to the family model.

The method was designed to be used with Micro Paver to predict PCI versus time.

The M&R work planning, over a specified number of years, is achieved through

utilizing basic inventory data, maintenance cost, and predictions about future pavement

condition. The repair work can be executed based on the “Worst First” approach (Shahin and

Kohn, 1982).

PAVER though widely implemented by highway agencies still suffers from issues

needing attention. One such issue is the combination of different factors empirically into a

single numerical index which tends to conceal the various contributing effects and actual

characteristics of the distress (Fwa and Shanmugam, 1998; Zimmerman and Peshkin, 2004).

Furthermore, treating according to the “worst first” procedure fails to account for the change

in benefit for the funds expended (Bemanian, 2007).

2.3.1.3 PMS Model Developed at Purdue University

Fwa and Sinha (1988) presented an integer programming optimization model for

pavement maintenance programming. An integer programming model is an optimization

model in which all decision variables can only have the values of integers. The ultimate goal

for performing the network-level pavement maintenance needs analysis under the integer

programming method is to determine a set of equivalent workload units in number of

workdays for different classes of highway with specific maintenance activity, and needs

urgency level to achieve the optimum results. The integer programming is also called

combinatorial optimization, because the model is concerned with finding answers to

questions such as “Does a particular arrangement exist?” or “How many arrangements of

some set of discrete objects exist to satisfy certain constraints?”

The concepts of integer programming models are quite simple and easily understood

by the engineers involved in developing maintenance needs analysis, as the decisions facing

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most transportation agencies are typically either to apply a treatment or not to apply a

treatment. The integer programming model proposed by Fwa and Sinha (1988) was solved

using the branch and bound algorithm.

The difficulty in employing integer programming optimization comes from its

computational intensive nature, especially when the number of variables is large. It is called

the “combinatorial explosion” of the possible solutions (Fwa et al., 1994a; Pilson et al., 1999).

It will take a very high-speed computer many years to obtain the solutions.

The proposed model is a single-objective, and the formulation includes priority

weighting factors to incorporate priorities for specific distress type and associated severity

level for each class of highway. The incorporation of priority factors can be seen as

interference to the optimization process, and might result in producing sub optimal

maintenance strategies.

2.3.1.4 Singapore (PAVENET)

Chan et al. (1994) developed the PAVENET model at the National University of

Singapore. PAVENET is a single-objective, pavement segment based model, and it is the first

optimization model in PMS that applies GA to solve PMS programming problem. The model

successfully formulated multiyear road-maintenance planning problem on the operating

principles of GA, and illustrated special characteristics of the PAVENET model. Fwa et al.

(1994a) analyzed road-maintenance planning problem using the developed PAVENET model.

Furthermore, Fwa et al. (1994b) compared solutions of PAVENET with the solution

obtained using branch and bound algorithm, and established that PAVENET renders

acceptable solutions. Fwa et al. (1996) integrated rehabilitation planning into the existing

model, as it is an important component of pavement management program, and called it

PAVENET-R. Like PAVENET, PAVENET-R also deals with single-objective problems.

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The ability of PAVENET-R to search solution in a solution space efficiently for

specific pavement segments gives it an advantage over the Arizona model (Ferreira et al.,

2002). Acknowledging the fact that pavement management problem involves multiple

conflicting objectives, Fwa et al. (2000) further improved the PAVENET model by

incorporating the capability to solve the multi-objective pavement management problems.

However, a rank based priority model, in the form of priority weights assigned to individual

maintenance activities, was employed to direct the optimization process.

2.3.1.5 Caltrans PMS

Since the late 1970s, the California Department of Transportation (Caltrans) has been

using a resource allocation system, based on pavement distress conditions, to perform its

pavement M&R needs analysis for managing its highways (Caltrans, 1978). The objective of

Caltrans’ pavement resource allocation system is to develop a list of candidate pavement

projects with associated repair strategies for rehabilitation. The rehabilitation plan is

developed solely based on the current year’s pavement conditions.

The Caltrans’s resource allocation system consists of a pavement condition rating and

evaluation system. The pavement condition rating system is used to collect pavement

condition data for its highway network on a 2-year cycle. The rating system identifies the

severity and extent for each of the six pavement distresses on flexible pavements and eight

distresses for rigid pavements. Ride quality data is also collected.

With these data, the central office uses pavement condition evaluation system to

correlate pavement distresses for feasible repair strategies based on a series of decision trees

for each of the distresses collected. Trigger values are established for all severity/extent

combinations of each distress type for identification of appropriate timing at which various

M&R strategies should be selected. Once all triggered strategies for various distresses of a

30

pavement project have been identified, the dominant M&R strategy is selected considering it

could best address all the distresses identified for that project.

Based on this system, Caltrans’ central office identifies and issues a list of distressed

pavement locations, recommended dominant M&R strategies, expected service life, and

anticipated project costs for each of the districts. The list is reviewed by the districts and a

final prioritized program is selected based on the factors such as pavement age and condition,

traffic levels, expected future plans, as well as available funding and agency policy (Shatnawi

et al., 2006).

The primary limitations of the system include the lack of pavement performance

models and predictive capabilities, the absence of prioritization or optimization programming.

Furthermore, the system is unable to perform multi-year repair needs analysis.

2.3.1.6 Indiana PMS

The Indiana Department of Transportation (InDOT) initiated the development of a

pavement management system in 1991 with an objective of maintaining its existing pavement

network at a specified level of service for the least possible cost.

The Indiana Pavement Management System (IPMS) included a roadway referencing

system (RRS), a computerized maintenance database for storage and retrieval of pavement

condition and inventory data, and a software program dROAD/dTIMS for developing the

M&R strategies. Pavement condition data collected by InDOT included International

Roughness Index (IRI), rutting, Pavement Condition Rating (PCR), and Pavement Quality

Index (PQI) (Flora, 2001). PCR is a composite rating incorporating various pavement

distresses, excluding rutting. The Pavement Quality Index (PQI) is a composite index based

on IRI, PCR, and Rutting.

The dROAD/dTIMS program has been used also by 17 other US State DOTs

(Deighton, 2004). The dROAD/dTIMS program consists of two programs: the dROAD

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program and the dTIMS program, both installed in the personal computer in the Pavement

Management Section. The dROAD program is used to download and store relevant

information for the identification of M&R projects and treatments, while dTIMS program is

used as the analysis tool for developing the pavement M&R strategies. The dTIMS program

uses an incremental benefit/cost analysis based on selected pavement deterioration models,

and the current and predicted pavement condition levels to prioritize all the projects over a 5-

year horizon. The prioritized candidate project list obtained from dTIMS is then used as the

first-cut list to be assessed by the field committee.

The synthesization of all the distress related information into a single composite index

may not be able to effectively identify feasible repair alternatives (Zimmerman and Peshkin,

2004). Furthermore, the use of benefit/cost analysis is not preferred in PMS because not all

the benefits can be conveniently and rationally converted into dollar value. The prioritization

process employed prioritized pavement repair alternatives based on incremental benefit/cost

analysis and subjective judgment. This system is not able to generate optimized repair

strategies based on the analysis of all the possible alternate strategies.

2.3.1.7 Georgia PMS

The GDOT has been maintaining its 18,000-centerline-mile highway pavement

system using the pavement rehabilitation needs analysis procedure. Pavement condition

evaluations were performed annually using the Pavement Condition Evaluation System

(PACES), developed by GDOT, from 1986 to 1997; and using the Computerized Pavement

Condition Evaluation System (COPACES), implemented since 1998. The system prioritized

resources based on condition index and subjective judgment of engineers. However, the

inherent deficiencies in the system made GDOT realize the need to develop a system that

could perform tasks more efficiently, incorporate more consistent decision criteria, satisfy

various specified requirements, utilize accumulated historical pavement survey data, and have

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the ability to maximize the pavement performance at the network level subject to various

balancing constraints (Tsai, 2005).

The newly developed pavement management system consists of two pavement project

selection programs, one each for flexible and rigid pavements. Each program contains two

modules: (1) District Pavement Rehabilitation Prioritization System (D-PREPS) and (2)

Pavement Rehabilitation Funding Allocation System (REFAS). A project is a length of

roadway with similar pavement geometries, structural conditions, and logical beginning and

ending points. The D-PREPS is employed by district level offices to prioritize pavement

projects based on selected prioritization factors/criteria, while the REFAS is employed by

central office to select candidate projects submitted by district offices for annual

rehabilitation and to allocate funding required based on certain prioritization criteria. The

factors used at district level include safety concerns, current performance rating, forecast

performance rating, and annual average daily traffic (AADT).

The Central Office collects the lists of the plans submitted from all GDOT District

offices and develops a statewide yearly pavement rehabilitation program. The annual

preservation program included candidate projects, types of preservation treatment methods

for each candidate project, total funding required, and distributions of projects. When

developing the program, decision maker could choose either “Worst First” or “Optimization”

as the initial criteria for funding allocation. In “Worst First” approach fund allocation can be

performed by using balancing constraints such as balancing the number of projects in each

district, distribution based on percentage of total route length, balance funding by GDOT

districts or balancing performance by GDOT districts. “Optimization” can be performed by

selecting an objective of maximizing pavement performance subject to the given total budget

constraint. However, the exact optimization technique employed is unknown.

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Apart from the annual pavement preservation program, GDOT has a GIS enabled

recurrent annual or multi-year program. The program is not a true multi-year as the effect of

deferring a pavement repair activity is not taken into account. At project level, it can perform

multi-year, project-linked network pavement preservation need analyses subject to funding

availability, minimum performance requirements, and other constraints. The program first

utilizes the current and historical project-level pavement condition evaluation information to

predict future project performance ratings and distresses, then determines appropriate

preservation treatment methods and costs, and finally calculates life-cycle cost effectiveness

ratios for all the projects at the district level. The cost effectiveness is defined as the ratio of

the averaged annual performance rating improvement to the annualized pavement

construction costs for a pavement project.

Based on this information from all the districts, the program performs various

analyses at network level to determine the multi-year minimum funding required to meet

prescribed pavement performance requirements and constraints, and to determine optimum

pavement rehabilitation plans subject to funding availability and other requirements, such as

balancing funding distribution or future pavement performance among various districts.

Balancing constraints include balancing performance or funds among various districts under

the jurisdiction of GDOT. If no balancing constraints are specified then the system follows

the “Worst First” approach, and prioritizes projects based on priority, cost effectiveness or

subjective judgment (Tsai, 2005).

Pavement ratings are the primary indicator for assessing pavement performance.

Pavement distress conditions, as expressed in terms of deduct values for different types of

distresses, together with pavement ratings, are used for determining rehabilitation treatment

methods through the use of pavement performance function. If more than one treatment

satisfies the prevailing performance rating, priority criteria for treatments within the program

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are used to break the tie. The primary criteria adopted include highest service year to cost

ratio, lowest cost or highest service life. Appropriate rules have been created to prevent the

same treatment to recur within a 2 to 3 year interval for a particular pavement project.

The system lacks true multi-year optimization because it adopts the “Worst First”

approach for fund allocation at the project level. Furthermore, when the optional individual

project rating requirement is imposed, all the pavement projects with ratings less than the

specified minimum individual project rating requirement will be selected for rehabilitation

actions first, regardless of their priority rankings in the network.

The pavement performance models incorporated into the system are based on

subjective rating from raters, and should be subject to rigorous calibration and validation to

ensure that the models used in the system, such as the rehabilitation treatment method

determination and the rehabilitation treatment costs, do accurately represent the engineering

judgment and the results generated by the system are accurate.

The priorities of projects are determined based on individual project rating constraints,

the life-cycle cost effectiveness ratio, and balance constraints. However decision makers are

allowed to interfere by employing subjective judgment to modify the priorities of the projects.

The feasible set for optimization consists of projects identified at the district level. The

optimization process does not consider all the possible projects to optimize the maintenance

and rehabilitation activities.

2.3.1.8 Washington State PMS

The formal implementation of a pavement management system in the Washington

state (WSPMS) took place in 1982. The current WSPMS is a Microsoft Windows based

program that incorporates annual pavement condition data, roughness data, and detailed

construction and traffic history data for the 28,800 lane-km (17,900 lane-miles) of the road

network. The WSPMS uses an empirical index, known as structural condition PSC, as a

35

trigger value to identify candidate pavement projects. The score of PSC 100 corresponds to a

distress-free situation, and a lower limit of 0 indicates the worst case with extensive distresses.

WSPMS aims to achieve PSC 50 for its pavement rehabilitation program (USDOT, 2008).

For example, if a pavement section is expected to reach a PSC equal to 50 in 2008, then the

pavement section will be included in 2008 rehabilitation program. Besides PSC, WSPMS

also takes into account the volume of traffic in prioritizing candidate sections.

Besides adopting the prioritization methodology adopted based on parameters such as

empirical index values and traffic volume, WSPMS also employs subjective judgment when

a trade-off between PSC and traffic volume is required. In addition, the highway agency

acknowledges that there is a need to consider multiple objectives, and trade-off between them

is imperative.

2.3.1.9 Mississippi PMS

The State of Mississippi Department of Transportation (MDOT) currently has four

congressional districts. District 2 covers an area of approximately 275 miles (443 km) long,

180 miles (290 km) wide and borders the Mississippi River. In 1986 MDOT contracted with

the University of Mississippi to implement a pilot pavement management system in District 2.

A basic database was developed, which included distress and roughness data collected on the

entire state-maintained roadway system in District 2. MDOT used the product developed in

the pilot program to launch a statewide pavement management system in 1989 (MDOT,

2001).

According to MDOT (2001), pavement condition and distress data have been

collected every two years beginning in 1991, which included roughness, rutting, faulting, and

texture indices. The International Roughness Index (IRI) is converted to Roughness Rating

with a lower and upper bound of 0 and 100 respectively. A distress evaluation (covering

cracking, potholes, etc.) is then performed. The distress evaluation is not performed on the

36

entire highway system. Rather, a sampling technique is used for approximately 20% coverage

of the state-maintained system.

MDOT has developed a procedure to quantify the overall health of a section of

pavement. The distress data, including severity levels and extent, are used to calculate a

Distress Rating of the pavement. This Distress Rating is combined with the International

Roughness Index (IRI) to calculate MDOT’s Pavement Condition Rating (PCR). The

calculation of the PCR involves deduction points from a perfect score of 100 for distresses,

roughness, etc. These algorithms were developed using a team of experts who rated the

interstate system, as well as statistical analyses.

The PCR is a number from 0-100 which reflects the overall condition of the pavement,

with 100 being new pavement with no defects. This number can be used to aid in

prioritization of pavement. For PCR < 72 or rut > 0.25in., selected sections are the worst first

until all the funds are expended.

Based on the review of existing system, it is evident that the system prioritizes

pavement maintenance projects based on empirical indices such as PCR. The current system

employs the “worst first” approach, which is known to produce sub-optimal results.

2.3.1.10 Highway Development and Management Standards Model (HDM)

The development of the HDM Model can be traced back to 1968 (Kerali, 2000). The

first model was produced in response to a highway design study initiated by the World Bank

in collaboration with the Transport and Road Research Laboratory (TRRL) of U.K. and the

Laboratoire Central des Ponts et Chaussees (LCPC) of France. Subsequently, the World Bank

funded the Massachusetts Institute of Technology (MIT) to continue the study and the

Highway Cost Model (HCM) was developed from the study (Kerali, 2000). This model was

used to study the relationship between roadwork costs and vehicle operating costs.

37

In 1976, based on a study in Kenya done by TRRL in collaboration with the World

Bank to investigate the deterioration of paved and unpaved roads as well as the factors

affecting vehicle operating costs in a developing country, the first prototype version of the

Road Transport Investment Model (RTIM) was produced by TRRL (Cundill and Withnall,

1995). Through World Bank funding, HCM was further developed at MIT, and the first

version of Highway Design and Maintenance Standards (HDM) was produced. Further work

resulted in releasing the RTIM2 model in 1982 and HDM-III in 1987 (Kerali and Mannisto,

1999; Kannemeyer and Kerali, 2001). RTIM3 was released in 1993 (Cundill and Withnall,

1995), and the development of the improved version, HDM-4 was initiated in 1993. The first

version of HDM-4 was released in 2000, and the development is still continuing.

HDM-4 was developed at the University of Birmingham in cooperation with the

World Bank, the Asian Development Bank, the UK Department for International

Development, the Swedish National Road Administration, the Finnish National Road

Administration, the Inter-American Federation of Cement Producers and other organizations.

The World Road Association (PIARC) has promoted HDM-4 development with other

organizations and now is supporting its worldwide dissemination and use (PIARC, 2008).

The features contained in the first version of HDM-4 are described below.

HDM-4 utilizes a prioritization method based on the concept of benefit-cost analysis

(BCA) over the pavement life cycle. The economic indicators can range from NPV (Net

present value), ERR (External rate of return), NPV/Cost (Return per unit investment) to

FYRR (First year rate of return).

The highway agencies in the United States predominantly employ Life Cycle Cost

Analysis (LCCA) which is a subset of BCA (FHWA, 2002). It has attracted more attention in

the pavement maintenance needs analysis practice (Geoffroy, 1996; Labi et al., 2003; Hall et

al., 2003; Ozbay et al., 2004). The main difference lies in the fact that LCCA does not

38

incorporate benefits in the analysis and assumes all the alternatives being compared to carry

equal benefits. BCA is the appropriate tool to use when design alternatives will not yield

equal benefits, such as when disparate projects are being compared or when a decision is

required on whether or not to undertake a project. The reason behind LCCA being adopted by

highway agencies is that the benefits of maintenance and rehabilitation in terms of condition

and safety over the life-cycle of that infrastructure are relatively consistent. Life-cycle cost

analysis uses a common period of time to assess cost differences between these alternatives

so that the results can be fairly compared.

In HDM-4 pavement network performance is predicted as a function of wheel loads,

pavement structural strength, maintenance standards, and environments in the network.

Benefits are quantified from savings in vehicle operation cost (VOC), reduced road user

travel times, a decreased number of accidents, and improved environmental effects.

The optimization is performed using the Expenditure Budgeting Model (EBM-32)

which computes the NPV of all feasible options, yielding an unconditional optimal solution

(Archondo-Callao, 2008). This method can be applied to very small networks, with less than

400 road classes or road sections at one time to render optimal solution with respect to the

programming model. If more that 400 road classes are defined in HDM-4, the model will still

perform the optimization, but with a less precise algorithm. EBM-32 is argued to be

particularly useful when used in tandem with the HDM-4 model, because of its ability to read

the network data generated by these programs. It must be noted that the set of investment

options to be optimized is user defined and is not the set of all possible options for a

particular network. Hence not all the possible solutions are evaluated to optimize the

objective function.

Using the concepts above, HDM-4 can perform three levels of analyses: strategy

analysis, work programme analysis, and project analysis. Strategy analysis is used to

39

determine funding needs and/or to predict future performance, under different budget

scenarios for the entire road network. A pavement network is first divided into different

categories, such as bituminous, unsealed, concrete, and block. For each pavement category,

representative traffic volume and loading and rehabilitation standards are defined. Then

benefits are calculated for each corresponding rehabilitation treatment to be used. Finally,

long-term funding needs and/or future performance under different budget constraints are

determined based on the prioritization of benefit/cost ratio of the pavements in a road

network. The output of the strategic analysis includes funding requirements and long-term

performance trends, such as average network conditions and performance indicators.

The objective of work programme analysis is to prioritize candidate road projects in

each year for a single or multi-year period within the annual budget constraint obtained from

strategic maintenance plan. Similar to the strategy analysis, prioritization of benefit/cost ratio

is used to select projects in each year within the analysis period. A list of feasible projects

within budget period is provided as the results of work programme analysis.

Project analysis of HDM-4 is concerned with the evaluation of one or more road

projects or investment options. Different treatment and investment alternatives are evaluated

for one or more road projects based on road-user costs and benefits, life cycle predictions of

road deterioration, road works effects and costs, etc.

HDM-4 has been implemented by highway agencies in several countries including

Armenia, Australia, Bangladesh, Brazil, Czech, Republic, Estonia, Fiji, Finland, Ghana, India,

Lebanon, Malaysia, Namibia, New Zealand, Papua New Guinea, Russia, Scotland, Slovenia,

South Africa, Sweden (benchmark), Tanzania, Thailand, Zimbabwe and Ukraine.

The second version of the HDM-4 has been recently released and it includes the

following improvements,

i. Improved Analysis Models

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ii. Sensitivity Analysis

iii. Budget Scenario Analysis

iv. Multi-Criteria Analysis (MCA) using the AHP (Saaty, 1980)

v. Estimation of Social Benefits

vi. Asset Valuation

The Multi-Criteria Analysis (MCA) in HDM-4 project analysis provides a means of

comparing projects using criteria that cannot easily be assigned an economic cost. MCA is

only supported for the Project Analysis and supports the following 10 criteria to evaluate

projects: Economic (Road agency cost, Road user cost and Net present value), Safety

(Accident analysis), Functional (Comfort and Delay), Environment (Air Pollution), Energy

(Energy efficiency), Social (Social Benefits) and Political Concerns.

Several issues limit the implementation of HDM-4. First, since most highway

agencies are government organizations and are not paid by the users of the pavement network

for their work, any attempt to attach a dollar value to highway agency’s pavement

rehabilitation activities would be speculative since there is little or no supportive data

available (FHWA, 2002). Although extensive literature on the value of traveler time exists,

much of this time (other than business and professional travel) does not have a traded market

value. This fact, combined with the uncertainty regarding actual values, may incline

transportation decision makers to give less credence to user costs than to their own agency

cost figures. HDM-4 tends to assign benefits to most indirect costs, such as reduced accident

costs, VOC, live costs, and economic benefit to agencies. When calculated, user costs are

often so large that they may substantially exceed agency costs, particularly for transportation

investments being considered for high-traffic areas.

Second, the use of benefit/cost analysis is not preferred in PMS because not all the

benefits can be conveniently and rationally converted into dollar value, and realization of this

41

discrepancy tempted the developers to incorporate the Analytic Hierarchy Process (AHP) in

HDM-4. However, relative AHP is employed which has the demerit of requiring large

number of pairwise comparisons once the number of alternatives become larger.

Third, the main difference between strategy analysis, programme analysis and project

analysis is in the details at which data are defined. Strategy analysis employs macroscopic

approach while programme analysis microscopic approach. For example, at project level

analysis data are specified in terms of measured defects such as IRI for roughness whereas

the specification for strategy and programme analysis can be more generic such as good, fair

or poor for roughness. Thus the funding requirement at strategy level involves uncertainty

and is not the true representation of what the pavement network requires.

Fourth, although HDM-4 does have several levels of analysis as presented above for

allowing management at different levels to make appropriate decisions, it does not link them

dynamically. For example, the budget determined based on strategic analysis can be used in

programme analysis to select projects; however, the effects of project selection process in

programme analysis on network performance cannot be evaluated. As such many authors

have stressed upon the need to integrate project level and network level pavement

management (Zimmerman and Peshkin, 2004).

Lastly, Multi-criteria Analysis (MCA) is employed as an alternative to single

objective (NPV maximization) optimization. HDM-4 being an economic optimization tool,

only considers a single objective of optimizing the Net Present Value (NPV), and other

objectives such as Safety (Accident analysis), Functional (Comfort and Delay), Environment

(Air Pollution), Energy (Energy efficiency), Social (Social Benefits) and Political Concerns

cannot be incorporated even if they are quantifiable, and as such it requires an alternative

methodology to deal with these.

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The reason for MCA to be incorporated in HDM-4 is reported as the need for a

representation of elements that are non-quantifiable, in terms of dollars ($), in the decision

making process (Cafiso et al., 2002). However, the results rendered from that will be highly

dependent on the subjective assessments, and will not be optimum with respect to the

pavement network. MCA is employed to prioritize investment alternatives, keeping in view

the consequences of each of the alternative. The consequences of each investment alternative

on pavement network are derived from the HDM-4.

It must be noted that HDM-4 is merely a tool for economic assessment of road

investment projects defined by the user, and should not be regarded as a pavement

management system. By exchanging data with a pavement management system, HDM-4 can

utilize existing data to perform an analysis, and as such calibration of pavement deterioration

models is imperative to fit the local conditions such as traffic characteristics, soil types,

climatic conditions, terrain type, and pavement composition. Some of the parameters

included in the model may not be appropriate for some highway agencies.

2.3.1.11 Japan PMS (MLIT-PMS)

The Ministry of Land, Infrastructure and Transport of Japan provides a pavement

management system (MLIT-PMS), composed of a pavement databank, a short-term repair

plan system at project level and a long-term repair plan at network level. The short-term

repair plan system is a core model of MLIT-PMS able to make judgment about repair

locations and work types, using the information from the pavement data bank (Taniguchi and

Yoshida, 2003).

According to Taniguchi and Yoshida (2003), it also has a sub-system for establishing

priorities with which to determine repair priority for each pavement section, and a repair

process-determination system. The purpose of the system for determining repair priorities is

to classify roads from 1 to 3 in terms of PINDEX (priority index), which is the scored level of

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repair priority. This index is determined from the maintenance control index (MCI) of MLIT-

PMS, after being corrected with road category and roadside conditions. Score 1 indicates

roads needing urgent repair, score 2 for those repair is desirable, and score 3 for those not

needing immediate repair.

The long-term repair plan system is provided in order to create an optimized repair

plan through the systematic combination of pavement management level, MCI-measured

pavement serviceability, repair cost and user benefits (Taniguchiand Yoshida, 2003). It

covers not only prediction of the demand for repair, estimate of investment effects (macro

evaluation), but also selection of repair locations, repair methods and repair timing (micro

evaluation).

The system employs the empirical index MCI for pavement serviceability prediction,

and prioritizes pavement sections based on the “Worst First” approach for short-term repair.

However, long-term resource allocation is carried-out through the aid of linear programming

optimization model. The disadvantages of the “Worst First” approach and conventional linear

programming solving techniques have already been stated in earlier sections. The program

also lacks tie breaking capability to resolve ties between alternate strategies having equal

strength.

2.3.2 Summary and Comments

Although all of the pavement management systems have been used in supporting

decision-making practices in the road sector, it is noted that none of the packages can

effectively deal with multiple and conflicting objectives. Most highway agencies considered

different objectives or criteria to identify the pavement maintenance strategy which

appropriately addresses their issue of maintaining pavements at an acceptable level of service.

The objectives range from maintenance cost, pavement condition, level of safety, traffic

volume, pavement age to agency policy. Furthermore, there is also an issue of integrating

44

policy issues with resource allocation process for the pavement management program to be

more effective. Most of the PMS employs the “Worst First” approach to prioritize pavement

repair alternatives. Table 2.5 presents a summary of all the pavement management systems

discussed earlier.

Agencies which employed prioritization have not incorporated multiple objectives or

integrated different issues effectively to produce optimal solutions. Therefore, it is of

practical significance to evaluate the degree of sub-optimality associated with the existing

approaches. As optimization is preferred over prioritization, it is imperative to develop an

approach which could incorporate multiple and conflicting objectives, while keeping in view

the policy and requirements set by the agency without causing unnecessary interference to the

optimization process. Another issue is that the tie breaking ability of a pavement management

program is often overlooked. For a pavement management system to serve as an effective

decision support system, it is essential that it contains a tie breaking procedure that will

produce results consistent with the strategy and policy of the highway agency concerned.

2.4 ISSUES IN PAVEMENT MANAGEMENT RESEARCH

While optimization is preferred over prioritization, the pavement engineering community

has not completely addressed the crucial issues related to the applications of optimization in

pavement management. Traditionally, it has been a common practice to apply priority

weights, derived from prioritization process, to selected parameters in the process of optimal

programming of pavement maintenance or rehabilitation activities. The form or structure of

priority weights adopted, and their magnitudes applied vary from highway agency to agency.

For instance, pavement researchers and highway agencies have applied priority weights to the

following parameters in pavement maintenance planning and programming: pavement

distress, pavement condition, road class and traffic volume.

45

It is a well known fact that artificially applying priority weights to selected problem

parameters could lead to a sub-optimal solution with respect to the original objective function

(such as minimal total maintenance cost or maximum pavement condition). Most decision

makers are not aware of this consequence and the magnitude of loss in optimality caused by

their choice of priority scheme. There is a need to examine meticulously the consequences of

incorporating priority preferences into pavement maintenance programming.

2.5 OBJECTIVES OF RESEARCH AND PROPOSITION

2.5.1 Objectives of Research

This research has two main objectives:

(i) Propose a rational prioritization approach for pavement maintenance planning to;

- handle conflicting requirements which cannot be measured quantitatively in

the same unit,

- break ties between alternatives producing identical benefits,

- overcome the limitations associated with empirical indices.

(ii) Integrated prioritization and optimization approach to;

- minimize unnecessary interferences to the optimal programming process,

- allow highway agencies to break ties between identical maintenance strategies

using rational prioritization approach,

- allow highway agencies to incorporate preferences based on certain criterion

into the pavement maintenance strategies with an anticipated loss in optimality.

2.5.2 Proposition

The research aims to introduce an integrated prioritization and optimization approach

to minimize artificial interferences in the PMS optimization. In the proposed approach,

priority ranking is only introduced in breaking a tie between analogous solutions in objective

46

space, and in making trade-off among multiple objectives. Unfortunately, many users of

optimization approaches are unaware of this fact and do not know the magnitude of loss in

optimality caused by their choice of priority scheme. Recognizing the fact that highway

agencies do have the practical need to offer maintenance priorities to selected groups of

pavement sections, the proposed procedure is able to incorporate such priority preferences

into pavement maintenance planning and programming.

47

TABLE 2.1. Comparison between different optimization techniques

Method Features Advantages Disadvantages/ Limitations

Linear Programming (Karan and Haas, 1976) and (Lytton, 1985)

Objective functions and constraints are formulated as linear equations Decision variables are continuous Most common method used in PMS

Relatively simple Suitable at project level for optimal solution

Cannot handle large number of decision variables Suffers from combinatorial explosion problems

Non-Linear Programming (Abaza et al., 2006)

Objective functions and constraints are formulated as non-linear equations

Suitable at project level for optimal solution

Same as linear programming, but complex as difficult to insure that the global optimum is found rather than a local optimum

Integer Programming (Mahoney et al., 1978), (Garcia-Diaz and Liebman, 1980), (Fwa and Sinha, 1988), and (Ferreira et al., 2002)

Objective functions and constraints are formulated as linear or non-linear programming Decision variables are bound to take only integer values 0 or 1.

Suitable at network level using macroscopic approach and project level problems for optimal solution More realistic in PMS as do or do-nothing approach

Same as linear programming

Dynamic Programming (Feighan et al., 1987) and (Tack and Chou, 2002)

No existing standard formulation equations The problem is divided into stages, where decision has to be taken at each stage Each stage has a number of states associated with it The solution procedure is to find an overall optimal policy

Can be used to optimize a multiyear pavement management problem Renders optimal solution Used when a number of decisions must be made in sequence

Every time new formulation is required once a problem changes Too many stages for large problems

Artificial Neural Networks (Fwa and Chan, 1993) and (Zhang et al., 2001)

The model is composed of large number of nodes Each node is associated with a state variable and an activation threshold Each link between node is associated with a weight State of node is determined by an activation function

Capable of solving combinatorial problems Can handle large number of decision variables Reduced computational complexity

Slow during training phase Difficult to interpret what network learns

Genetic Algorithms (Chan et al., 1994), (Fwa et al., 1994a, 1994b, 1996, 2000), (Pilson et al., 1999) and (Ferreira et al., 2002)

Based on natural selection Works with a pool of solutions, while performing crossover and mutation between parent and child population to search for a better strategy.

Capable of solving combinatorial problems Can handle large number of decision variables Flexible in defining objective functions and constraints Reduced computational complexity

Renders near optimal solutions

48

TABLE 2.2. Network project selection practices

Method Number of Responses Ranking based on Pavement Conditions 29

Benefit-cost (or incremental benefit/cost) 12

Life cycle costs 6 Costs and timing 4 Initial costs 4 Other 1

(Source: NCHRP, 1995)

TABLE 2.3. Prioritization methods survey results

Prioritization Method Number of Responses

Worst First 4 Multi-year Prioritization 10 Optimization 1 Other 7

(Source: Gao and Tsai, 2003)

TABLE 2.4. Prioritization criteria survey results

Physical Functional Safety Surface Distress IRI Skid Others Traffic Capacity

Improve Others Safety User Cost Others

20 14 9 7 5 7 3 6 5 4 (Source: Gao and Tsai, 2003)

49

TABLE 2.5. Review of PMS implemented in various regions

Region Features Disadvantages Interference Arizona (Golabi et al., 1982), (Wang et al., 1993) and (Li et al., 2006)

Minimizes agency discounted costs Employs Markov chain at macroscopic level

Not possible to include pavement historical maintenance data Single objective No tie breaking

∈-constrained approach

PAVER (Shahin and Kohn, 1982)

PAVER uses the Pavement Condition Index PAVER has been implemented by several agencies

Composite index may not be able to identify feasible repair alternatives Single objective No tie breaking

Employs worst first and ∈-constraint method

Purdue University (Fwa et al., 1988)

Integer programming Single objective

Computationally complex Single objective No tie breaking

∈-constraint method Priority factors assigned to maintenance activities

PAVENET (Chan et al., 1994) and (Fwa et al., 1996)

Segment based model First model in PMS which incorporates GA at search level Computationally efficient

Single objective No tie breaking

Subjective ranking in the form of prioritized pavement maintenance activities Unnecessary budget constraints

Caltrans (Caltrans, 1978) and (Shatnawi et al., 2006)

Employs pavement condition rating system Prioritization based on factors/criteria

Lack of predictive capabilities No optimization No pavement performance model involved.

Worst first approach

Indiana (Flora, 2001)

Pavement Quality Index (PQI) is a composite index based on IRI, PCR.

Incremental benefit/cost analysis and subjective judgment

Subjective judgment

Georgia (Tsai, 2005)

Prioritization based on Pavement Rating and Distress deduct values GIS enabled multi-year program

Lacks multi-year true optimization. Single objective Performance models are not calibrated

Worst first approach can be employed Priorities of projects can be modified causing interference Tie breaking capability not structured

Washington (USDOT, 2008)

Empirical index, known as structural condition (PSC)

Prioritization based on PSC and Traffic volume

No optimization Worst first and subjective judgment

Mississippi (MDOT, 2001)

Prioritization based on empirical index (PCR)

No optimization Worst first approach

HDM (Kerali and Mannisto, 1999) and (Kerali, 2000)

Prioritization method based on the concept of benefit cost analysis

User cost attached to agency’s cost Not a PMS Not all the benefits can be converted into dollars

∈-constraint method No tie breaking

Japan (Taniguchi and Yoshida, 2003)

Prioritization based on empirical index (MCI) and optimization

Single objective Linear Programming Model

Worst first approach for short-term repair needs

50

FIGURE 2.1. Flow chart of basic genetic algorithm

Selection

Recombination

Stopping criteria met?

End

Randomly Generated Initial Population

Crossover Probability (Pc) 1-Pc

Yes

No

51

CHAPTER 3

IMPROVED PAVEMENT MAINTENANCE PRIORITY ASSESSMENT: ANALYTIC HIERARCHY PROCESS

3.1 NEED FOR RATIONAL MAINTENANCE PRIORITY ASSESSMENT

A primary function of pavement maintenance is to retard pavement deterioration

process, thereby extending the useful life of a pavement. The efficacy of pavement

maintenance activities is greatly enhanced if they are performed at an appropriate time in a

preplanned manner (AASHTO, 2004; NCHRP, 2004). The appropriate or optimal timing of

maintenance for a pavement is a function of a host of different factors, including pavement

distress characteristics, pavement structural properties, climatic and environmental factors,

traffic loading, traffic and highway operational considerations, effects on road users, cost

implications, and maintenance policy and strategy of the highway agency (NCHRP, 2004;

Cechet, 2004; Fwa, 1989). Thus the urgency of the need for maintenance varies from distress

to distress.

This has led to the use of either priority ratings or priority rankings for pavement

maintenance by many highway agencies in planning their pavement maintenance programs.

Although, optimization is preferred over rating and ranking as explained in Chapter 1, many

agencies still prefer to employ the latter due to the difficulty encountered in formulating a

maintenance optimization problem (Broten et al., 1996) in addition to the computational

complexity associated with large number of decision variables.




52



and engineers. This is because combining different factors empirically into a single

numerical index tends to conceal the various contributing effects and actual characteristics of

the distress. Furthermore, not all of the factors and considerations involved can be expressed

quantitatively and measured in compatible units.

Sometimes absolute priority rating and ranking is applied in pavement maintenance

planning to prioritize pavement maintenance activities. However, it is the relative priority

ratings rather than the absolute priority ratings that matters in pavement maintenance

planning and moreover direct assessment method suffers from inconsistency in judgments.

In an attempt to overcome the above mentioned limitations associated with common

subjective priority rating methods, there is a need to identify a rational procedure to assess

maintenance priority rating. The use of analytic hierarchy process (AHP) (Saaty, 1994, 1990,

1980), is explored in this chapter, for prioritization of pavement maintenance activities. The

main aim is to identify an approach that can reflect the engineering judgment of highway

agency and engineers more closely. Three different forms of AHP are examined, and their

applications are illustrated with an example problem. The results are assessed by comparing

with the priority assessments obtained from a Direct Assessment Method in which the raters

make the evaluation by comparing all the maintenance activities together directly. One of the

major differences between the AHP and the Direct Assessment Method is that the former

uses ratio scale, and the latter uses ordinal scale. To explain the significance of ratio scales

over ordinal scales, it will be worthwhile to discuss the scales of measurements.

3.2 SCALES OF MEASUREMENT

There are four scales of measurement as follows: (1) Nominal scale, (2) Ordinal scale, (3)

Interval scale, and (4) Ratio scale.

53

3.2.1 Nominal Scale

In nominal measurement, scores are assigned in such a manner that only equality of

scores has meaning for the alternatives being measured. A nominal scale is really a list of

categories to which objects can be classified. For example, each distress type can be scored as

pothole, rutting or cracking.

3.2.2 Ordinal Scale

In ordinal measurement ordinality of scores also has a meaning in addition to equality.

Hence, ordinal scale assigns scores to objects based on their ranking with respect to one

another. For example, on an ordinal scale from 1 to 10, pothole is assigned a score 9, rutting

as 6, and cracking as 3 resulting in a final conclusion that pothole has the highest rank

followed by rutting and cracking. However, there is no implication that a 6 is twice as good

as a 3. Nor is the improvement from 3 to 6 necessarily the same "amount" of improvement as

the improvement from 6 to 9.

3.2.3 Interval Scale

In interval measurement, interval of scores has a meaning in addition to equality and

ordinality, but where "0" on the scale does not represent the absence of the thing being

measured. Hence, on an interval scale from 1 to 10, the improvement from 3 to 6 necessarily

has to be the same as the improvement from 6 to 9.

3.2.4 Ratio Scale

Ratio scale measurement not only has all the characteristics of the three scales

discussed, but has an added advantage over others by having a meaning in the ratios of the

scores, and where "0" on the scale represents the absence of the thing being measured. Thus,

a 6 on such a scale implies twice as good as a 3.

54

Hence, in the output from the AHP, preference between two alternatives can be

quantified such that one alternative is k times as preferred as the other, where k is any number

obtained by dividing priority rating of two alternatives being compared. As pavement

management problem consists of multiple and conflicting criteria, hence to make a trade-off

between alternatives it is essential that the preference be measured on a ratio scale.

3.3 CONCEPT OF ANALYTIC HIERARCHY PROCESS

The Analytic Hierarchy Process (AHP) is a mathematical technique for multicriteria

decision making developed by Saaty (1980) in the 1970s to facilitate decision makers in

selecting the best alternative. AHP has been used to compare between alternatives on a ratio

scale, and permits qualitative data to be included in addition to quantitative data (Saaty, 1994,

1990). AHP involves the following phases: (a) structuring of a hierarchy, (b) prioritization

based on pairwise comparison, (c) synthesis of pairwise priorities to form a priority vector,

and (d) checking for consistency of the preference judgments.

A hierarchy decomposes a problem into individual independent elements. According

to Saaty (1980), a hierarchy is “an abstraction of the structure of a system to study the

functional interactions of its components and their impacts on the entire system.” It consists

of an overall goal at the top or first level, a set of alternatives, at the bottom or last level, for

reaching the goal, and a set of criteria, at mid-level, that relate the alternatives to the goal.

Normally, the criteria are further broken down into sub-criteria, sub sub-criteria, and so on,

depending on the complexity of the problem.

The next phase is pairwise comparison of criteria. Findings from psychological

studies by Miller (1956) have shown that individuals are unable to effectively apply a rating

scale of more than seven (plus or minus two) points. AHP as recommended by Saaty (1980)

uses a nine-point scale to determine the comparative difference in a pairwise comparison of

two elements. The preference judgment is made by assigning a value of 1 to the elements if

55

they are of equal importance, 3 to a weakly more important element, 5 to a strongly more

important element, 7 to a very strongly important element, and 9 to an absolutely more

important element.

The outcome of each set of pairwise comparisons is expressed as a positive reciprocal

matrix )( ijaA = such that 1=iia and jiij aa /1= for all i, j ≤ n,

=

1.../1/1......

...1/1

...1

21

212

112

nn

n

n

aa

aaaa

A (3.1)

where n denotes the number of alternatives being compared within one set of pairwise

comparisons, ija denotes the importance of alternative i over alternative j, and jia denotes the

importance of alternative j over alternative i.

Synthesis is the next step that translates the priorities, assigned to each pair of

elements, in the matrix A into a priority vector w, that contains the priority weight of each

element. Several methods for deriving the priority vector w from the matrix A exists such as

Saaty’s eigenvector method (EM) (Saaty, 2000) and Logarithmic Least Squares Method

(LLSM) (Crawford, 1987). Saaty’s eigenvector method (EM) is often employed to derive the

priorities of the alternatives, and computes w' as the principal eigenvector, a vector that

corresponds to the largest eigenvalue called the principal eigenvalue λmax of the matrix A.

'max

' wAw λ= (3.2)

where n≥maxλ , and [ ]Tnwwww ...' 21= , the superscript T refers to transpose of a matrix.

The priority vector w is obtained by normalizing the principal eigenvector w', and is

also called the normalized principal eigenvector. The priority vector is the normalized

principal eigenvector of the pairwise comparison matrix. It is established for each criterion,

56

sub-criterion, as well as the alternatives under each sub-criterion. The overall priority weight

of alternatives is computed as follows (Belton, 1986),

∑=j

ijji XWV (3.3)

where Vi = overall priority weight of alternative i, Wj = weight assigned to criterion j, and Xij

= weight of alternative i given criterion j.

AHP allows for 10 percent inconsistency in human judgments (Saaty, 1980). To

check for consistency in judgments of a decision maker, Saaty (1994) defined the consistency

ratio CR which is a comparison between Consistency Index CI and Random Consistency

Index RI as follows,

RICICR = (3.4)

where CI is given by

1max

−−

=n

nCI

λ (3.5)

where n is the size of the matrix. RI is obtained by computing the CI value for randomly

generated matrices. A matrix is considered consistent, only if 1.0≤CR (Saaty, 1980).

In the literature, there exist several variations of AHP. In the present study, the

following three methods are considered: (a) distributive-mode relative AHP, (b) ideal-mode

relative AHP, and (c) absolute AHP. A brief description of each is given below.

3.3.1 Distributive-Mode Relative AHP

This is the original AHP method presented by Saaty (1980) and it involves relative

comparisons using the so-called “distributive mode”. In this mode, the priority vectors as

obtained in Eq. (3.2) of the criteria are used directly to arrive at the overall priorities of

alternatives. Elements are compared in pairs using a common comparison criterion and a

preference judgment is made. This method has several drawbacks. The number of pariwise

57

comparisons increases rapidly as the problem becomes bigger, and it becomes very time

consuming and difficult for an evaluator to make pairwise comparisons in a consistent

manner. It is also known that rank reversals may occur, leading to illogical assessments.

According to Millet and Harker (1990), the effort required to make all pairwise comparisons

is a major demerit of the method.

3.3.2 Ideal-Mode Relative AHP

This method was introduced by Belton and Gear (1983) to solve the rank reversal

problem in the distributive-mode relative AHP. The main modification is in the derivation of

the priority vectors by dividing each column of the reciprocal matrix by the maximum entry

of that column, creating the so-called idealized priority vectors. Saaty (1994) accepted the

revised procedure and called it the Ideal-Mode AHP.

3.3.3 Absolute AHP

This method was proposed by Saaty (1986) to overcome the problem of having too

many pairwise comparisons in the AHP computation. The computation of the priorities of

criteria or sub-criteria remains the same as in the relative AHP. The main difference occurs

at the last level during the evaluation of alternatives. The alternatives are each assigned a

degree of intensity under each covering criterion. By doing so, the number of pairwise

comparisons involved in the AHP computation is reduced substantially. It is noted that

intensities are still required to be compared pairwise.

3.4 METHODOLOGY OF STUDY

3.4.1 Basis of Evaluation

The main aim of this study is to evaluate the practical suitability and effectiveness of

the three AHP methods in determining the priorities of maintenance activities for formulating

58

a pavement maintenance program. As there does not exist any analytical technique or tool

that permits one to make comparison on a theoretical basis, it is necessary to resort to the use

of numerical examples to evaluate the relative merits of different methods.

There is also the issue of the need to establish a reference against which the practical

suitability and effectiveness of the three AHP methods can be made. Once again, because of

the presence of qualitative factors and the involvement of subjective judgmental assessment

required from the pavement engineers and highway agency concerned, there is no theoretical

procedure that one could rely on to obtain the “real” set of priorities. It is practically logical

to say that the “real” set of priorities must come from the engineers and the highway agency

involved in formulating maintenance strategies that lead to the final maintenance program.

In this study, it is considered that the “real” set of priorities of an expert is represented

by the priorities produced by the expert when he or she is presented all the alternatives

together, and is given all the time needed to rank the alternatives, and make adjustments until

he or she is fully satisfied. The “Direct Assessment Method” using a card approach as

employed by Fwa et al. (1989) is adopted for this purpose. The card approach was designed

to facilitate the ranking process and to allow convenient adjustments to the ranks by the

evaluator.

A set of cards with a maintenance activity written on each, was given to the evaluator.

The evaluator was first asked to place the cards in rank order according to the respective

urgency of the need to perform the maintenance activities. Next, they are required to move

the cards into relative positions above or below each other along a linear scale of 1 to 100

(see Fig. 3.1). The end results of this survey will provide the priority rating of each

maintenance activity ranked on a scale of 1 to 100. Also shown in Fig. 3.1 are the rater

instructions. Other researchers have employed similar direct assessment methods with slight

modifications under different names, such as the Successive Ratings technique and the

59

Alternate Ranking method described by Shillito and De Marle (1992), and the satisfaction

rating approach adopted by Elliott et al. (1995) in evaluating patient satisfaction.

It may be reasoned that card approach represents a decision making by an individual

expert in arriving at his or her final decision regarding the priorities of the alternatives. It can

also be argued that each of the three AHP methods could be taken as an expedient procedure

to simulate the actual decision making process by not going through the full process of

ranking and adjustments. In this sense, it is meaningful to use the results of the card

approach of Direct Assessment Method as the basis for evaluating the relative suitability and

effectiveness of the three AHP methods.

3.4.2 Problem Formulation of Numerical Example

For illustration purpose, three road functional classes, three distress types, and three

level of distress severity are considered. This gives 27 possible combinations of maintenance

treatments. The three road functional classes are expressway, arterial and access road. The

three types of distresses are pothole, rutting and cracking, and the three levels of distress

severity associated with each of these distresses are high, moderate and low.

For easy presentation, only 27 pavement sections are considered, each with a different

maintenance activity corresponding to one of the 27 possible combinations of maintenance

treatments. These 27 pavement sections to be prioritized for maintenance treatments are

tabulated in Table 3.1, each with the road classification, type of distress, and distress severity

level indicated.

Fig. 3.2 shows the hierarchy structure used for the AHP analysis of the example

problem. The overall objective is to prioritize pavement sections for maintenance, and is

placed as the top level in the hierarchy. The three factors influencing maintenance activities

are represented as the criteria for maintenance rating. Road function class is taken as the

main criterion at level 2, followed by distress type and the level of distress severity as the

60

sub-criterion at level 3 and the sub sub-criterion at level 4 respectively. The 27 pavement

sections are the alternatives which are the candidates for pavement maintenance activities,

and are placed at the bottom or the fifth level in the hierarchy.

3.4.3 Prioritization of Pavement Maintenance Activities

Five pavement engineers were asked to provide priority ratings for the 27 pavement

sections using the three AHP methods and the Direct Assessment Method. Each expert was

approached independently 4 times over a period of 4 weeks, each time to perform a rating

survey using one of the four methods. For the three AHP methods, all pairwise comparison

matrices were checked for consistency using the consistency ratio defined by Eq. (3.4).

Some of the matrices were found to be inconsistent, and the experts concerned were

requested to revise their judgments by redoing the survey.

3.5 ANALYSIS OF RESULTS OF PRIORITY RATINGS

3.5.1 Results of Priority Ratings and Priority Rankings

As the scale used in AHP is different from that used in the Direct Assessment Method,

the AHP scores are transformed linearly for the purpose of comparison. The final results of

priority ratings for the 27 pavement sections are recorded in Table 3.2. The priority rankings

derived from these priority ratings are shown in Table 3.3.

3.5.2 Analysis of Priority Rating Scores and Priority Rankings

The average priority ratings and ranks obtained from the 5 experts are used in the

analysis. The suitability and effectiveness of the three AHP methods are assessed using the

following analysis:

(a) Assessment of priority rating scores by comparing the statistical correlations with

scores obtained using the Direct Assessment Method;

61

(b) Assessment of priority rankings by comparing the rank correlations with rankings

obtained using the Direct Assessment Method;

(c) Hypothesis testing of consistency of priority rankings with the Direct Assessment

Method;

(d) Comparison of the spread in rating results by individual raters.

3.5.2.1 Assessment of Priority Rating Scores

Fig. 3.3 presents the plots of priority rating scores obtained using the three AHP

methods against those by the Direct Assessment Method. Also indicated in the two figures

are the Pearson correlation coefficients (Neter, 1990) between each of the three AHP methods

and the Direct Assessment Method. Pearson correlation coefficient r gives the strength of a

linear relationship between the Direct Assessment Method and the AHP methods evaluated.

It is given by (Neter, 1990),

∑∑∑∑∑∑∑

−×−

−=

2222 )()()()(

))(()(

iiii

iiii

yynxxn

yxyxnr (3.6)

where xi = value from observation i on variable X , yi = value from observation i on variable

Y , =n number of values in each data set, =i 1,…,n.

It is noted from Fig. 3.3 that the rating values of the three AHP methods were quite

different from the corresponding values by the Direct Assessment Method. These

discrepancies are believed to be reflective of the differences in the basic approach of survey

adopted by the AHP methods and the Direct Assessment Method, and the different rating

scales employed by them. Basically, AHP requires raters to assess pairwise differences

quantitatively on a ratio scale, while the Direct Assessment Method only asks raters to rank

different alternatives in relative order on a linear scale. Nevertheless, it is noted that there

exist rather strong positive correlation between each of the AHP methods and the Direct

Assessment Method.

62

The distributive-mode relative AHP has the highest correlation of 0.7, followed by the

ideal-mode relative AHP method having a correlation of 0.68, and the lowest correlation of

0.65 is with the absolute AHP method. Since it is the relative magnitudes of ratings of

different maintenance activities, rather than the absolute differences in their rating scores, that

matters in pavement maintenance planning, a more appropriate evaluation would be to base

on the relative rankings of the maintenance activities, as presented in the next section.

3.5.2.2 Assessment of Priority Rankings

Fig. 3.4 presents the plots of priority rakings obtained using the three AHP methods

against those by the Direct Assessment Method. The plots show strong positive correlations

between each of the three AHP methods and the Direct Assessment Method. The absolute

AHP has the highest correlation of 0.91, followed by the ideal-mode and the distributed-

mode relative AHP methods each with a correlation of about 0.82. These results suggest that

the AHP methods were able to produce priority rankings of pavement maintenance activities

in good agreement with the Direct Assessment Method. A statistical testing of the degree of

this agreement is presented in the next section.

The strength of association of each of the three AHP methods with the Direct

Assessment Method can be evaluated using statistical hypothesis testing based on the non-

parametric Spearman rank correlation test (Lehmann and D'Abrera, 1998). The test

parameter is the Spearman rank correlation coefficient ρ defined as follows,

)1n(n

d61 2

n

1i

2i

−−=

∑=ρ (3.7)

where di = difference between the ranks of pavement section i by the Direct Assessment

Method and the AHP method being evaluated, and all other variables as defined in Eq. (3.6).

63

The test was performed with the null hypothesis H0: ρ ≤ 0.6, against the alternative

hypothesis H1: ρ > 0.6. A correlation coefficient exceeding 0.6 indicates very strong degree

of correlation (Franzblau, 1958). When n > 10, the significance of Spearman’s correlation can

be tested by the Student’s statistic t given below,

)2/()1(6.0

22−−

−=−

ntn

ρ

ρ (3.8)

where ρ is given by Eq. (3.7).

The results of the hypothesis tests are summarized in Table 3.4. It can be seen from

the results that while all the three AHP methods produced priority rankings that are

statistically consistent with the Direct Assessment Method, the absolute AHP method shows

much better correlation with the Direct Assessment Method than the two relative AHP

methods.

3.5.2.3 Assessment of Spread of Priority Assessments

Fig. 3.5 plots the individual experts’ rating scores against the mean for each of the

four methods. The corresponding plots for priority rankings are shown in Fig. 3.6. For each

method, the degree of spread of the individual assessments can be measured by means of the

root-mean-square of the deviations RMS(d) from the respective mean values. The RMS(d) of

priority ratings are 2.37, 3.25, 2.50 and 16.82 for the distributive-mode relative AHP, the

ideal-mode relative AHP, the absolute AHP, and the direct assessment method, respectively

as shown in Fig. 3.7. The corresponding RMS(d) of priority rankings for the four methods

are 1.05, 1.42, 1.82 and 3.78 as shown in Fig. 3.8.

It is believed that the relative magnitudes of the spread of the four methods reflect the

nature of the four assessment processes more than the quality of the individual assessment

methods. The two relative AHP methods received the most number of “follow-up”

corrections to the original assessments by the raters because of the need to satisfy the AHP

64

consistency check. The absolute AHP received much less “follow-up” corrections, and there

were no such corrections for the case of the Direct Assessment Method.

3.5.3 Summary Comments on Applicability of AHP

The following observations may be made based on the results of the analysis

presented in the preceding section:

(a) All three AHP methods were found to produce priority ratings in strong positive

correlation with the Direct Assessment Method, although there were substantial

differences in the absolute magnitudes of the rating scores that reflect the different

approaches and scales employed in the AHP and the Direct Assessment Method. The

performances of three AHP methods were about equal with respect to the Direct

Assessment Method.

(b) All three AHP methods produced priority rankings in very strong positive correlation

with the Direct Assessment Method. This conclusion was statistically significant at

95% confidence level. In comparison with the two relative AHP methods, the

absolute AHP method produced the best consistency with the Direct Assessment

Method in terms of priority ranking assessment.

(c) The two relative AHP methods had the least internal variations of the priority

assessments by the individual raters. The absolute AHP gave somewhat higher

variations, while the Direct Assessment Method produced the highest variations.

However, these variations are believed to be related to the degree of corrections made

in the assessment process of each method, and not indicative of the quality of the

assessments.

With regard to the suitability of each method for priority assessment in practice, it is

appropriate to consider the number of pairwise comparisons required in arriving at the final

priority assessment. The Direct Assessment Method is intuitively the method a normal

65

person would use in making priority assessment. In theory, to rank and rate n number of

items, the Direct Assessment Method would involve ( ) 21−nn number of comparisons. For

the example problem analyzed in the preceding section, the number of comparisons would be

351. For the same example, the numbers of comparisons required were 129 and 21 for the

relative AHP and the absolute AHP respectively.

For a practical problem at the road network level, the number of pavement

maintenance alternatives involved would be much more than 27=n considered in the

example problem. The size of the problem can also be increased if more factors are added in

the priority assessment process. For instance, besides the three factors considered in the

example problem (i.e. road function class, distress type, and distress severity level), more

factors such as the level of traffic loading and climatic condition can be included. Taking the

example problem as an illustration, by adding these two additional factors, the number of

preference judgments needed would be 29403, 9759 and 39 for the Direct Assessment

Method, the relative AHP and the absolute AHP respectively, as shown in Table 3.5. The

algorithm of the process of pairwise comparison for relative and absolute AHP is as follows,

3.5.3.1 Process of Pairwise Comparisons

(a) Define a Problem.

Relative AHP

(b) Enter objective O, criteria E and possible mutually exclusive alternatives A.

(c) 1=O , ),...,2,1( nE = , ),...,2,1( nA = .

(d) Structure a hierarchy.

(e) iO denotes objective at level i, ni E denotes criterion n at level i, n

i A denotes

alternative n at level i and inn )2)1(( − denotes number of pairwise comparisons at

level i.

66

(f) Enter number of levels ),...,2,1( ni = in a hierarchy

(g) For objective 1O at 1=i , make 1)2)1(( +− inn pairwise comparisons among

criteria ni E1+

, where =n number of criteria.

(h) For each nE2 at 2=i , make 1)2)1(( +− inn

pairwise comparisons among criteria ni E1+

or alternatives ni A1+

under each criterion nE2, where =n number of criteria or

alternatives.

(i) The process will continue until 1−= ni .

(j) Total pairwise comparisons in the problem will be equal to the sum of pairwise

comparisons at each level ni ,...,2,1= under each criterion ni E

.

Procedure for absolute AHP is the same as relative AHP from (a) to (g).

Absolute AHP

(h) At 1−= ni , define intensities ni I1+ for each criterion n

i E and move alternatives to

level 1+= ni

(i) If )3,...,1(=i , for each nE2 define intensities nI3 and shift alternatives to next level

4=i .

(j) Make 3)2)1(( −nn pairwise comparisons among intensities nI3

under each

criterion nE2

(k) Score alternatives nA4 by checking off their respective intensities nI3

under each

criterion nE2.

(l) The process will continue until 1−= ni .

(m) Total pairwise comparisons in the problem will be equal to the sum of pairwise

comparisons at each level ni ,...,2,1= under each criterion ni E

.

67

It is clear by considering the number of comparisons required in Table 3.5, the

absolute AHP is the most suitable and manageable in terms performing priority assessment

for network level planning and programming of pavement maintenance activities. The

absolute AHP is also most suitable in terms of its ease and flexibility in handling increased

complexity of the problem when more factors are added into the maintenance management

process.

3.6 SUMMARY Three AHP methods have been evaluated for their suitability and effectiveness in

priority assessment of pavement maintenance activities. The evaluation was performed with

reference to the Direct Assessment Method in which the raters make their assessments by

comparing all the maintenance activities together directly. It was found that because of the

different survey approaches and scale employed, the priority rating scores obtained from the

AHP methods and the Direct Assessment Method differed significantly in their absolute

magnitudes. However, AHP generated priority ratings were positively correlated with those

obtained by the Direct Assessment Method. This strong association was supported by the

very high correlations found based on the ranking assessment. The strong correlation in

rankings was confirmed through statistical hypothesis testing performed at a confidence level

of 95%. As it is the relative priority ratings rather than the absolute priority ratings that count

in pavement maintenance planning, the findings suggest that the AHP approach is suitable for

the purpose of pavement maintenance prioritization.

The analysis also found that the AHP methods showed less variation among the

judgments of experts in contrast to the Direct Assessment Method. More importantly, the

number of comparisons necessary in the priority assessment increases dramatically for the

Direct Assessment Method. Even among the three AHP methods, the two relative AHP

68

methods would also require very large number of comparisons for a typical size problem in a

real-life road network level pavement maintenance problem.

Based on the operational advantage of the Absolute AHP in handling a large number

of items to be evaluated, and its ability to generate priority assessment in good agreement

with the Direct Assessment Method, the Absolute AHP method is considered to be the

preferred method for use in pavement maintenance prioritization. Hence, in the subsequent

Chapter, Absolute AHP is employed in the proposed integrated prioritization and

optimization approach.

69

TABLE 3.1. Pavement sections considered in example problem

Section Description

Highway class Distress Distress Severity 1 Expressway Pothole High 2 Expressway Pothole Moderate 3 Expressway Pothole Low 4 Expressway Rutting High 5 Expressway Rutting Moderate 6 Expressway Rutting Low 7 Expressway Cracking High 8 Expressway Cracking Moderate 9 Expressway Cracking Low

10 Arterial Pothole High 11 Arterial Pothole Moderate 12 Arterial Pothole Low 13 Arterial Rutting High 14 Arterial Rutting Moderate 15 Arterial Rutting Low 16 Arterial Cracking High 17 Arterial Cracking Moderate 18 Access Cracking Low 19 Access Pothole High 20 Access Pothole Moderate 21 Access Pothole Low 22 Access Rutting High 23 Access Rutting Moderate 24 Access Rutting Low 25 Access Cracking High 26 Access Cracking Moderate 27 Access Cracking Low

70

TABLE 3.2. Priority ratings of sections obtained using different methods

Sect-ion

Priority ratings (Distributive-Mode Relative AHP)

Priority ratings (Ideal-Mode Relative AHP)

Priority ratings (Absolute AHP)

Priority ratings (Direct Assessment Method)

Expert 1

Expert 2

Expert 3

Expert 4

Expert 5

Expert 1

Expert 2

Expert 3

Expert 4

Expert 5

Expert 1

Expert 2

Expert 3

Expert 4

Expert 5

Expert 1

Expert 2

Expert 3

Expert 4

Expert 5

1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

0.248 0.066 0.024 0.132 0.026 0.011 0.033 0.012 0.004 0.106 0.036 0.016 0.063 0.017 0.009 0.030 0.009 0.004 0.056 0.019 0.010 0.031 0.008 0.005 0.016 0.005 0.003

0.288 0.061 0.027 0.138 0.022 0.008 0.030 0.011 0.003 0.113 0.029 0.012 0.065 0.013 0.006 0.032 0.006 0.003 0.051 0.016 0.007 0.028 0.006 0.003 0.015 0.004 0.002

0.262 0.083 0.029 0.121 0.030 0.010 0.035 0.013 0.004 0.099 0.039 0.014 0.053 0.019 0.007 0.026 0.009 0.003 0.054 0.020 0.008 0.028 0.008 0.004 0.014 0.005 0.002

0.256 0.068 0.023 0.137 0.026 0.009 0.036 0.011 0.003 0.113 0.035 0.013 0.068 0.018 0.006 0.025 0.007 0.003 0.057 0.018 0.008 0.031 0.007 0.003 0.014 0.004 0.002

0.210 0.061 0.023 0.125 0.034 0.013 0.055 0.021 0.008 0.108 0.042 0.017 0.053 0.016 0.008 0.022 0.007 0.003 0.069 0.026 0.012 0.034 0.009 0.005 0.013 0.005 0.002

0.263 0.070 0.029 0.117 0.027 0.014 0.031 0.010 0.005 0.100 0.033 0.017 0.067 0.018 0.011 0.035 0.011 0.006 0.045 0.015 0.009 0.027 0.008 0.005 0.017 0.005 0.002

0.326 0.065 0.028 0.128 0.020 0.007 0.027 0.008 0.003 0.113 0.024 0.010 0.071 0.012 0.006 0.037 0.005 0.003 0.039 0.012 0.005 0.024 0.005 0.002 0.016 0.003 0.002

0.290 0.094 0.031 0.106 0.031 0.010 0.035 0.012 0.003 0.093 0.037 0.013 0.053 0.020 0.006 0.029 0.009 0.003 0.045 0.016 0.006 0.025 0.007 0.004 0.014 0.005 0.001

0.278 0.073 0.025 0.126 0.026 0.009 0.036 0.010 0.003 0.113 0.031 0.011 0.075 0.019 0.006 0.026 0.007 0.003 0.047 0.013 0.005 0.029 0.007 0.003 0.014 0.004 0.002

0.214 0.060 0.018 0.118 0.038 0.012 0.064 0.023 0.008 0.110 0.041 0.013 0.054 0.016 0.006 0.022 0.007 0.003 0.071 0.026 0.009 0.035 0.009 0.004 0.014 0.004 0.005

0.302 0.078 0.033 0.101 0.026 0.011 0.045 0.020 0.009 0.123 0.032 0.014 0.054 0.014 0.006 0.023 0.010 0.004 0.027 0.007 0.003 0.027 0.007 0.003 0.013 0.006 0.003

0.385 0.073 0.032 0.176 0.045 0.019 0.040 0.010 0.004 0.082 0.015 0.007 0.022 0.006 0.002 0.010 0.003 0.001 0.032 0.006 0.003 0.005 0.001 0.001 0.014 0.004 0.002

0.354 0.117 0.038 0.117 0.037 0.015 0.038 0.013 0.004 0.101 0.033 0.011 0.022 0.007 0.003 0.015 0.005 0.002 0.036 0.012 0.004 0.004 0.001 0.001 0.007 0.002 0.001

0.352 0.092 0.030 0.156 0.040 0.017 0.029 0.012 0.005 0.106 0.028 0.009 0.027 0.007 0.003 0.012 0.005 0.002 0.034 0.009 0.003 0.011 0.003 0.001 0.005 0.002 0.001

0.402 0.105 0.034 0.109 0.047 0.012 0.037 0.009 0.005 0.086 0.022 0.007 0.023 0.010 0.003 0.011 0.003 0.001 0.037 0.010 0.003 0.010 0.004 0.001 0.006 0.001 0.001

0.070 0.066 0.054 0.068 0.059 0.051 0.065 0.058 0.044 0.056 0.044 0.032 0.054 0.037 0.027 0.051 0.041 0.030 0.021 0.011 0.002 0.020 0.010 0.001 0.018 0.008 0.001

0.076 0.070 0.064 0.072 0.061 0.057 0.045 0.030 0.044 0.068 0.048 0.049 0.065 0.038 0.051 0.036 0.026 0.023 0.017 0.015 0.011 0.012 0.005 0.006 0.008 0.001 0.003

0.071 0.069 0.059 0.051 0.045 0.040 0.028 0.024 0.018 0.064 0.062 0.058 0.050 0.042 0.037 0.025 0.021 0.013 0.055 0.030 0.052 0.034 0.003 0.033 0.008 0.001 0.006

0.095 0.085 0.066 0.062 0.057 0.043 0.024 0.019 0.014 0.076 0.052 0.047 0.043 0.038 0.028 0.014 0.009 0.003 0.066 0.062 0.025 0.033 0.028 0.002 0.005 0.003 0.001

0.055 0.047 0.043 0.052 0.046 0.041 0.049 0.044 0.038 0.044 0.041 0.035 0.043 0.040 0.034 0.042 0.038 0.030 0.037 0.032 0.026 0.033 0.028 0.025 0.029 0.027 0.001

71

TABLE 3.3. Priority rankings of sections obtained using different methods

Sect-ion

Priority ratings (Distributive-Mode Relative AHP)

Priority ratings (Ideal-Mode Relative AHP)

Priority ratings (Absolute AHP)

Priority ratings (Direct Assessment Method)

Expert 1

Expert 2

Expert 3

Expert 4

Expert 5

Expert 1

Expert 2

Expert 3

Expert 4

Expert 5

Expert 1

Expert 2

Expert 3

Expert 4

Expert 5

Expert 1

Expert 2

Expert 3

Expert 4

Expert 5

1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

1 4

12 2

11 18 8

17 26 3 7

15 5

14 21 10 20 25 6

13 19 9

22 24 16 23 27

1 5

11 2

12 18 8

17 26 3 9

16 4

15 21 7

22 24 6

13 19 10 20 25 14 23 27

1 4

10 2 9

18 8

17 25 3 7

15 6

14 22 12 19 26 5

13 20 11 21 24 16 23 27

1 4

12 2

10 18 7

17 25 3 8

16 5

14 22 11 21 26 6

13 19 9

20 24 15 23 27

1 5

12 2

10 18 6

14 21 3 8

15 7

16 22 13 23 26 4

11 19 9

20 24 17 25 27

1 4

10 2

12 17 9

20 26 3 8

14 5

13 18 7

19 23 6

16 21 11 22 25 15 24 27

1 5 8 2

12 18 9

17 25 3

10 16 4

14 19 7

20 23 6

15 22 11 21 26 13 24 27

1 3 9 2

10 18 8

17 25 4 7

16 5

13 21 11 19 26 6

14 22 12 20 24 15 23 27

1 5

12 2

11 18 7

17 24 3 8

16 4

13 21 10 19 25 6

15 22 9

20 26 14 23 27

1 6

14 2 9

18 5

12 21 3 8

17 7

15 23 13 22 26 4

11 19 10 20 25 16 24 27

1 4 7 3

11 17 6

13 19 2 8

14 5

14 22 12 18 24 9

20 25 9

20 25 16 22 25

1 4 7 2 5

10 6

13 19 3

11 15 9

16 23 13 21 25 7

16 21 18 25 25 12 19 23

1 2 5 2 7

11 5

13 19 4 9

15 10 16 22 11 18 23 8

14 19 19 25 25 16 23 25

1 4 7 2 5

11 8

12 18 3 9

15 10 17 21 12 18 24 6

15 21 14 21 26 18 24 26

1 3 8 2 5

11 6

16 19 4

10 17 9

13 21 12 21 24 6

13 21 13 20 24 18 24 24

1 3 8 2 5

10 4 6

12 7

12 16 8

15 18 10 14 17 19 22 25 20 23 26 21 24 26

1 3 6 2 7 8

12 16 13 4

11 10 5

14 9

15 17 18 19 20 22 21 25 24 23 27 26

1 2 5 9

11 13 18 20 22 3 4 6

10 12 14 19 21 23 7

17 8

15 26 16 24 27 25

1 2 4 6 8

11 18 19 20 3 9

10 11 13 15 20 22 24 4 6

17 14 15 26 23 24 27

1 4 8 2 5

11 3 6

14 6

11 17 8

13 18 10 14 21 16 20 25 19 23 26 22 24 27

72

TABLE 3.4. Spearman’s rank correlation coefficient and Student’s t-test for correlation with


Statistic Distributive-Mode Relative AHP

Ideal-Mode Relative AHP Absolute AHP

Observations 27 27 27

Degrees of freedom 25 25 25

α 0.05 0.05 0.05

Correlation 0.81 0.81 0.90

Student’s T-test ( 2−nt for 10>n ) 1.79 1.79 3.44

Critical 1-sided T-value )( 2, −ntα 1.708 1.708 1.708

Result 2,2 −− > nn tt α 2,2 −− > nn tt α 2,2 −− > nn tt α

Conclusion Accept H1: 6.0>ρ Accept H1: 6.0>ρ Accept H1: 6.0>ρ

TABLE 3.5. Number of comparisons required by different methods

Description and Size of Problem

Number of Comparisons Required


Relative AHP (Ideal-Mode or

Distributed-Mode)

Absolute AHP

Three levels of criteria, 1. Road functional class; 2. Distress type; 3. Distress severity

Total number of maintenance alternatives = 27

351 129 21

Five levels of criteria, 1. Road functional class; 2. Distress type; 3. Distress severity; 4. Traffic loading; 5. Climatic condition

Total number of maintenance alternatives = 243

29403 9759 39

Note: Each criterion has three sub-criteria

73

Step 1

You are given 27 pavement sections requiring routine maintenance activity types. The attributes of each section, consisting of class of pavement, type of distress and distress severity, are written on a small card. Read the attributes carefully. Step 2 Rank the cards on your desk in accordance with the importance of each pavement section requiring maintenance in order to keep it at a required level of service. Place the most important section at the top, followed by other sections in the order of decreasing importance to rate the absolute and relative position of each section. Ties are permissible. Step 3 Carefully review the ranking in step 2. Make changes if required. Step 4 Move the top priority card to the top (i.e. a score of 100) of the scale on this instruction sheet. Next move one card at a time, in sequence of decreasing importance, to the score and assign a score to each by comparing with the activity immediately above it. Continue until all the cards are placed on the scale. Step 5 If the last card does not have a score of 1, adjust the scores (except the top score) so that the lowest priority section has a score of 1. Step 6 Carefully review the priority scores assigned. Make changes if necessary.

FIGURE 3.1. Rating scale and instructions for Direct Assessment Method

100

90

80

70

60

50

40

30

20

10

1

74

FIGURE 3.2. Hierarchy structure for AHP analysis of example problem

Alternatives (Level 5)

Sub sub-criteria (Level 4)

Selection of a Pavement Section for Maintenance

Expressway Arterial Access

Pothole Rutting Cracking

High Moderate Low

Section 1 Expressway

Pothole High


Pothole Moderate


Pothole Low


Rutting High


Rutting Moderate


Rutting Low


Cracking High


Cracking Moderate


Cracking Low

Section 10 Arterial Pothole

High


Moderate


Low

Section 13 Arterial Rutting High

Section 14 Arterial Rutting

Moderate

Section 15 Arterial Rutting

Low

Section 16 Arterial

Cracking High

Section 17 Arterial

Cracking Moderate

Section 18 Arterial

Cracking Low

Section 19 Access Pothole

High


Moderate


Low

Section 22 Access Rutting High

Section 23 Access Rutting

Moderate

Section 24 Access Rutting

Low

Section 25 Access

Cracking High

Section 26 Access

Cracking Moderate

Section 27 Access

Cracking Low

Objective (Level 1)

Criteria (Level 2)

Sub-criteria (Level 3)

75

Rating by Direct Assessment Method

Rat

ing

by D

istr

ibut

ive-

Mod

e R

elat

ive

AH

P

100806040200

100

80

60

40

20

0


Rat

ing

by I

deal

-Nod

e R

elat

ive

AH

P

100806040200

100

80

60

40

20

0


Rat

ing

by A

bsol

ute

AH

P

100806040200

100

80

60

40

20

0

FIGURE 3.3. Correlations between the priority ratings obtained using Direct Assessment


Methods Coefficient of correlation

Distributive-Mode Relative AHP and Direct Assessment

Method

0.70

Ideal-Mode Relative AHP and Direct Assessment

Method

0.68

Absolute AHP and Direct Assessment

Method 0.65

(a) Scatter plot of priority rating by Distributive-Mode Relative AHP and


(b) Scatter plot of priority rating by Ideal-Mode Relative AHP and


(c) Scatter plot of priority rating by Absolute AHP and


76

Ranking by Direct Assessment Method

Ran

king

by

Dis

trib

utiv

e-M

ode

Rel

ativ

e A

HP

302520151050

30

25

20

15

10

5

0


Ran

king

by

Idea

l-Mod

e R

elat

ive

AH

P

302520151050

30

25

20

15

10

5

0


Ran

king

by

Abs

olut

e A

HP

302520151050

30

25

20

15

10

5

0

FIGURE 3.4. Correlations between the priority rankings obtained using Direct Assessment


Methods Coefficient of correlation

Distributive-Mode Relative AHP and Direct Assessment

Method

0.81

Ideal-Mode Relative AHP and Direct Assessment

Method

0.82

Absolute AHP and Direct Assessment

Method 0.91

(a) Scatter plot of priority ranking by Distributive-Mode Relative AHP and


(b) Scatter plot of priority ranking by Ideal-Mode Relative AHP and


(c) Scatter of priority ranking by Absolute AHP and


77

Mean Rating

Indi

vidu

al R

atin

g

100806040200

100

80

60

40

20

0

Mean Rating

Indi

vidu

al R

atin

g

100806040200

100

80

60

40

20

0

Mean Rating

Indi

vidu

al R

atin

g

100806040200

100

80

60

40

20

0

Mean Rating

Indi

vidu

al R

atin

g

100806040200

100

80

60

40

20

0

FIGURE 3.5. Scatter plots of priority ratings against group mean ratings

RMS(d) = 2.37 RMS(d) = 3.25

RMS(d) = 2.50 RMS(d) = 16.82

(a) Distributive-Mode Relative AHP

(c) Absolute AHP (d) Direct Assessment Method

(b) Ideal-Mode Relative AHP

78

Mean Ranking

Indi

vidu

al R

anki

ng

302520151050

30

25

20

15

10

5

0

Mean Ranking

Indi

vidu

al R

anki

ng

302520151050

30

25

20

15

10

5

0

Mean Ranking

Indi

vidu

al R

anki

ng

302520151050

30

25

20

15

10

5

0

Mean Ranking

Indi

vidu

al R

anki

ng

302520151050

30

25

20

15

10

5

0

FIGURE 3.6. Scatter plots of priority rankings against group mean rankings

RMS(d) = 1.05 RMS(d) = 1.42

RMS(d) = 1.82 RMS(d) = 3.78

(a) Distributive-Mode Relative AHP

(c) Absolute AHP (d) Direct Assessment Method

(b) Ideal-Mode Relative AHP

79

FIGURE 3.7. Deviation of ratings between individual evaluators and group mean ratings

-50

-40

-30

-20

-10

0

10

20

30

40

50

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

Alternatives

Dev

iatio

ns

-50

-40

-30

-20

-10

0

10

20

30

40

50

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

Alternatives

Dev

iatio

ns

-50

-40

-30

-20

-10

0

10

20

30

40

50

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

Alternatives

Dev

iatio

ns

-50

-40

-30

-20

-10

0

10

20

30

40

50

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

Alternatives

Dev

iatio

ns

Relative AHP (DM) RMS(d) = 2.37

Relative AHP (IM) RMS(d) = 3.25

Absolute AHP RMS(d) = 1.82

Direct Assessment Method RMS(d) = 3.78

(a) (b)

(c) (d)

80

CHAPTER 4

IMPROVED PAVEMENT MAINTENANCE PRIORITY ASSESSMENT: ANALYTIC HIERARCHY PROCESS FOR

MULTIPLE DISTRESSES

4.1 INTRODUCTION

In pavement management, the purpose of maintenance is to execute protective and

repair measures in order to slow down the pavement deterioration process, thereby extending

the useful life of a pavement. The efficacy of pavement maintenance is highly increased, if

action is taken at an appropriate time in a preplanned manner. Practically all pavement

management system consists of priority models to prioritize pavement projects or pavement

maintenance activities. The quality of prioritization process can directly influence the

effectiveness of available resources that are, in most cases, the primary judgment of the

decision maker. The prioritization approach based on the analytic hierarchy process (AHP),

presented in Chapter 3, was developed based on the premise that each pavement section only

experience one distress type, and therefore is unable to take into account a situation where

pavement segment experiences multiple distress types. Hence, this chapter proposes an

approach based on the AHP, which enables prioritization of pavement section given multiple

distresses and associated severity level. As concluded in Chapter 3, absolute AHP is

employed to establish priority ratings and rankings of pavement sections.

4.2 CONVENTIONAL PRIORITY RATINGS

Conventional pavement priority rating procedures involve converting pavement

distress information into a condition index, which aggregates information from all of the

distress types, severities, and extent into a single numeral. The condition index may represent

81

a single distress such as alligator cracking or multiple distresses which is usually referred to

as a composite index.

One of the earliest pavement condition indices was the Present Serviceability Rating

(PSR) developed at the AASHO Road Test, which was later used to develop the new index

based on the values of pavement smoothness, rutting cracking and patching called the Present

Serviceability Index (PSI) (10). Chen et al. (1993) and Sharaf (1993) employed Composite

Index (CI) method for prioritization, however there is a paradox inherent in composite index

such as on one hand it has to be comprehensive to present an accurate picture in the mind of a

decision maker, and on the other hand merging excessive information may render the index

meaningless as too many different things are being measured at the same time.

The Pavement Condition Index (PCI) (ASTM, 2007), for the pavement condition

assessment, assigns PCI values to cracks on a scale from 0 to 100 based on crack type,

density and severity. Crack severity is determined based on the width of crack or visual

comparisons with established benchmarks and is classified into three categories such as low,

medium and high. The rating procedure requires the identification of the type of pavement

distress, its extent and severity. These values are then used to calculate an overall PCI for the

pavement section. The pavement distress, extent and severity are combined using “deduct

value” curves to establish the impact of the individual distress on the overall condition of the

pavement. The deduct values are determined from predefined deduct value curves for each

distress type and severity.

Pavement Condition Rating (PCR) (FHWA, 2009) is developed to describe the

pavement condition ranging from 0 to 100; a PCR of 100 represents a perfect pavement with

no observable distress and a PCR of 0 represents a pavement with all distress present at their

high levels of severity and extensive levels of extent. To determine PCR, the deduct points

are first calculated and PCR is equal to 100 minus the total deduct points. For each distress,

82

the deduct point is equal to (Weight for distress) x (Weight for severity) x (Weight for

Extent).

4.3 METHODOLOGY OF PROPOSED AHP PROCEDURE

4.3.1 Choice of AHP Technique

The Absolute AHP method was found to be the preferred method for the purpose of

establishing pavement maintenance priorities in the study presented in Chapter 3. The main

reasons for selecting the Absolute AHP technique are the significantly smaller number of

pairwise comparisons required to be made, and the insignificant loss of accuracy in the final

results. Therefore, this study employs Absolute AHP to establish maintenance priority

ratings. The primary aim of this study is to propose a methodology based on the Absolute

AHP method for determining the priorities of pavement segments in formulating a pavement

maintenance program.

4.3.2 Hierarchy Structure for AHP Analysis

Once a list of pavement segments requiring maintenance, along with the necessary

distress information, has been identified, the next step is to decompose the problem into

individual independent elements by developing a hierarchy. Placed at the top level in the

hierarchy, as shown in Fig. 4.1, is the overall objective to prioritize pavement segments for

the execution of pavement maintenance activities. Next, the factors influencing maintenance

are translated as criteria. “Distress type” is selected as the main criterion and is placed at the

second level. For ease of illustration, only three distress types (i.e. pothole, rutting, and

cracking) are considered, as shown in Fig. 4.1.

The next level is represented by the severity of distress as the sub-criterion to the

distress type. For each distress type, three levels of distress severity are identified and

designated as high, medium, and low. The final level gives all the alternatives available for

83

maintenance prioritization. These alternatives are all the pavement segments to be

considered for the purpose of pavement maintenance programming. The distress state of

each pavement segment, which is the criterion for maintenance priority assessment, is

quantitatively represented by the conditions of all the distresses present in the segment. In

Fig. 4.1, it is assumed that the pavement maintenance problem covers 30 pavement segments.

4.3.3 Prioritization and Synthesization

Prioritization involves pairwise comparisons between elements residing at the same

level in the hierarchical structure. It is recognized that currently there does not exist any

theoretical or analytical method that can make pairwise comparisons and determine the

relative maintenance priorities that precisely represent the opinion of the pavement

maintenance agency concerned. As such, questionnaire survey of the maintenance decision

makers is the only practical means for this purpose. In the proposed procedure of this study,

a prioritization questionnaire was prepared for the Absolute AHP procedure.

Once the priorities are established, the collected data is entered into spreadsheet files,

prepared following Saaty’s eigenvector method (Saaty, 2000) explained earlier, for

synthesization and analysis according to Eqs. (3.1) to (3.3). All pairwise comparison

matrices were checked for consistency using the consistency ratio defined in Eq. (3.4).

4.4 ILLUSTRATIVE APPLICATION OF PROPOSED AHP PROCEDURE

4.4.1 Description of Example Problem

For illustration purpose, thirty pavement segments, three distress types, and three

levels of distress severity are considered. The three types of distresses are pothole, rutting

and cracking; and the three levels of distress severity associated with each of these distresses

are high, medium and low. The distress states of the 30 pavement segments are given in

84

Table 4.1. In Table 4.1, the condition of each distress present in a pavement segment is

described by a distress code defined in Table 4.2. For this example problem, the hierarchy

structure shown in Fig. 4.1 is applicable.

4.4.2 Prioritization Questionnaire Survey

Based on the hierarchy structure of Fig. 4.1, a prioritization questionnaire was

prepared. Five pavement engineers were asked to provide priority ratings for the 30

pavement segments using the Absolute AHP method. Altogether there are 12 pairwise

comparisons to be made by each engineer in completing the questionnaire. All pairwise

comparison matrices were checked for consistency using the consistency ratio defined by Eq.

(3.4). It was to be noted that some of the pairwise comparison judgments made in the

questionnaire survey were inconsistent according to the Saaty’s criterion. The engineers

concerned were requested to revise their judgments accordingly.

4.4.3 Evaluation of the Proposed AHP Method

In order to assess the validity of the AHP approach as a method for establishing the

maintenance priorities of pavement segments, the results produced using the Absolute AHP

method were evaluated in two ways. First, the results of the Absolute AHP method were

compared with those obtained by the PAVER method, which is currently one of the most

widely used methods for the purpose. Next, it is proposed that a reference set of priority

assessments be developed so that reasonableness of the results of both the Absolute AHP and

PAVER methods can be examined. Hence, there is the need to establish a reference against

which the two methods can be evaluated.

Because of the presence of qualitative factors and the involvement of subjective

judgmental assessment required from the pavement engineers and highway agency concerned,

there is no theoretical procedure one could rely on to obtain the “real” set of priorities.

85

Therefore, it is practical and logical to say that the “real” set of priorities must come from the

engineers and the highway agency involved in formulating maintenance strategies that lead to

the final maintenance program.

In this study, it is considered that the “real” set of priorities of an expert is represented

by the priorities produced by the expert when he or she is presented all the alternatives

together, and is given all the time needed to rank the alternatives, and make adjustments until

he or she is fully satisfied. The “Direct Assessment Method” using a card approach as

employed by Fwa et al. (1989) is adopted for this purpose. The card approach was designed

to facilitate the ranking process and to allow convenient adjustments to the ranks by the

evaluator.

A set of cards with an alternative (i.e. a pavement distress state) written on each, was

given to the evaluator. The evaluator was first asked to place the cards in rank order

according to the respective urgency of the need to perform the needed maintenance treatment.

Next, they are required to move the cards into relative positions above or below each other

along a linear scale of 1 to 100 as shown in Fig. 4.2. Also indicated in Fig. 4.2 are the rater

instructions. The end results of this survey will provide the priority rating for each of the 30

alternatives (i.e. the 30 distress states in Fig. 4.1) ranked on a scale of 1 to 100.

In the present study, the five engineers were asked to do the Direct Assessment survey

two weeks after the AHP questionnaire survey, and they were not given access to the results

of the earlier AHP survey. This was to ensure that they were not in any way influenced by

the answers they provided in the AHP survey.

4.4 ANALYSIS OF RESULTS OF PRIORITY RATINGS

4.4.1 Results of Priority Ratings and Priority Rankings

The maintenance priority rating results by the three methods, namely the Absolute

AHP method, the PAVER method, and the Direct Assessment Method, are presented in Table

86

4.3. The ratings by the PAVER method were computed in accordance with the procedure of

the ASTM Standard D6433 (2007). The ratings by the other two methods are the results of

the surveys with the five engineers. As the scale used in AHP is different from that used in

the Direct Assessment Method, the AHP scores are transformed linearly for the purpose of

comparison. The priority rankings derived from these priority ratings are shown in Table 4.

These results of priority ratings and priority rankings are plotted in Figs. 4.3, 4.4, and 4.5.

Fig. 4.3a plots the priority ratings obtained using the Absolute AHP Method against those by

the Direct Assessment Method; Fig. 4.4a plots the priority ratings obtained using the PAVER

method against those by the Direct Assessment Method; while Fig. 4.5a presents the plot of

priority rating scores using the Absolute AHP Method against those by the PAVER method.

The corresponding plots for priority rankings are found in Figs. 4.3b, 4.4b and 4.5b.

4.4.2 Analysis of Priority Rating Scores and Priority Rankings

The average priority ratings and ranks obtained from the 5 experts are used in the

analysis. The suitability and effectiveness of the proposed prioritization approach based on

the absolute AHP is assessed using the following analysis:

(a) Assessment of priority rating scores by comparing the statistical correlations with

scores obtained using the Direct Assessment Method;

(b) Assessment of priority rankings by comparing the rank correlations with rankings

obtained using the Direct Assessment Method;

(c) Hypothesis testing of consistency of priority rankings with the Direct Assessment

Method;

For the purpose of establishing the merit of the proposed Absolute AHP method for

maintenance priority assessment, the three analyses above are also performed on the priority

rating results by the PAVER method. This offers a basis to compare the relative quality of

the two methods in handling the pavement maintenance prioritization problem.

87

4.4.2.1 Assessment of Priority Rating Scores

Fig. 4.3 presents the plots of priority rating scores obtained using the three AHP

methods against those by the Direct Assessment Method. Also indicated in the two figures

are the Pearson correlation coefficients (Neter, 1990) between each of the three AHP methods

and the Direct Assessment Method. Pearson correlation coefficient r gives the strength of a

linear relationship between the Direct Assessment Method and the AHP methods evaluated,

and is given by Eq. (3.6).

It is noted from Fig. 4.3a that although the rating values obtained using the proposed

AHP approach have a strong correlation coefficient of 0.77 with the results by the Direct

Assessment Method, there are some differences in the rating values by the two methods.

These discrepancies are believed to be reflective of the differences in the basic approach of

survey adopted by the AHP method and the Direct Assessment Method, and the different

rating scales employed by them. Basically, AHP requires raters to assess pairwise

differences quantitatively on a ratio scale, while the Direct Assessment Method only asks

raters to rank different alternatives in relative order on a linear scale. Nevertheless, the rather

strong positive correlation of 0.77 is considered to be sufficiently strong.

In the case of priority ratings by the PAVER method, a positive correlation the ratings

by the Direct Assessment Method is also observed as shown in Fig. 4.4a, although a lower

correlation coefficient of 0.61 was obtained. Fig. 4.5a indicates that although there are some

discrepancies between the values of priority ratings of the Absolute AHP method and the

PAVER method, statistically there is still a strong positive correlation of 0.75 between the

priority ratings by the two methods.

4.4.2.2 Assessment of Priority Rankings

As it is the relative magnitudes of ratings of different maintenance activities, rather

than the absolute differences in their rating scores, that matters in pavement maintenance

88

planning, a more appropriate evaluation would be to base on the relative rankings of the

maintenance activities, as presented in this section. Correlation of two sets of ranks is

evaluated using the non-parametric Spearman rank correlation coefficient (Lehmann and

D'Abrera, 1998) using Eq. (3.7).

In Fig. 4.3b, the plot comparing the Absolute AHP and the Direct Assessment Method

shows a strong positive rank correlation of 0.86 between the priority rankings obtained from

the two methods. Fig. 4.4a indicates that the corresponding rank correlation between the

PAVER method and the Direct Assessment Method is equal to 0.73, which still demonstrates

a strong positive correlation although it is comparatively less so than that between the

Absolute AHP method and the Direct Assessment Method. On other hand, as shown in Fig.

4.5b, there is a very high rank correlation of 0.89 between the priority rankings of the

Absolute AHP method and the PAVER method. These results suggest that the AHP method

was able to produce priority rankings of pavement maintenance segments in excellent

consistence with the PAVER method, and in the mean time achieving a rather good

agreement with the Direct Assessment Method as compared to the PAVER method.

4.4.2.3 Statistical Testing of Rank Correlation

The correlation relationships examined in the preceding sub-sections can be further

examined by means of statistical hypothesis testing. The test parameter is ρ as defined in Eq.

(3.8). The test was performed with the null hypothesis H0: ρ = 0, against the alternative

hypothesis H1: ρ > 0. When n > 10, the significance of Spearman’s correlation can be tested

by the Student’s statistic t given below,

The results of the hypothesis tests are summarized in Table 4.5. It can be seen from

the results that the priority rankings from the absolute AHP method are statistically consistent

with the rankings from the Direct Assessment Method.

89

4.4.3 Summary Comments on Applicability of AHP

With regard to the suitability of the Absolute AHP method for network level

maintenance priority assessment in practice, it is appropriate to consider the number of

pairwise comparisons required in arriving at the final priority assessment. The Direct

Assessment Method is intuitively the method a normal person would use in making priority

assessment. In theory, to rank and rate n number of items, the Direct Assessment Method

would involve number of comparisons. The number of pairwise comparison required for

the Absolute AHP method is many times smaller, depending on the hierarchy structure of the

problem. For the example problem analyzed in the preceding section, the number of

comparisons would be 435 and 12 for the Direct Assessment Method and the Absolute AHP

Method respectively.

For a practical problem at the road network level, the number of pavement

maintenance alternatives involved would be much more than considered in the example

problem. The number of distress types will also be more than the three considered in the

example problem. In addition, the size of the problem can also increase significantly if more

factor levels are added in the priority assessment process. In view of the very large number

of pairwise comparisons required by the Direct Assessment Method, it would not be

practically feasible for its adoption in practice. In comparison, the Absolute AHP offers a

practical alternative for the purpose.

The results of analysis presented in this study show that the Absolute AHP method

and the PAVER method produce maintenance priority assessments (either priority ratings or

rankings) in good agreement with one another. In addition, both methods were able to

generate priority ratings and priority rankings that are strongly consistent with those obtained

from the Direct Assessment Method, although the Absolute AHP tended to produce better

results.

90

It is apparent that a major strength of the PAVER procedure is the ease of application.

Other than the distress data, no additional questionnaires or other forms of survey are

necessary to perform the analysis. However, this same strength can become a limitation in

some applications. For instance, the PAVER procedure generates a fixed set of priority

ratings and ranking for a given set of input distress data, regardless of climatic and

geographic locations. In reality, maintenance priority setting policy or practice may vary

from highway agency to highway agency, arising from differences in maintenance strategy,

policy preference, pavement design and climatic considerations. In other words, the

pavement maintenance prioritization based on the PAVER procedure is unable reflect the

different maintenance strategies and preferences of different highway agencies. Under such

situations, the proposed Absolute AHP method would be a suitable alternative.

4.5 SUMMARY

The Absolute AHP method has been evaluated for its suitability and effectiveness in

network level maintenance priority assessment of pavement segments containing multiple

distresses. The evaluation was performed with reference to the PAVER method and the

Direct Assessment Method. The proposed Absolute AHP method and the PAVER method

were found to produce highly consistent results with one another. In comparison with the

reference ratings and rankings established by the Direct Assessment Method, it was found

that because of the different survey approaches and the scale employed, the priority rating

scores obtained from either the absolute AHP method or the PAVER method differed from

those by the Direct Assessment Method in their absolute magnitudes. However, both the

Absolute AHP method and the PAVER method generated priority ratings and ranking in very

strong positive correlation with those obtained by the Direct Assessment Method. The strong

correlations among the three methods were confirmed through statistical hypothesis testing

performed at a confidence level of 95%. As it is the relative priority ratings and rankings

91

rather than the absolute priority ratings that count in pavement maintenance planning, the

findings suggest that the proposed Absolute AHP approach and the PAVER are suitable for


In comparing the applicability of the PAVER method and the proposed Absolute AHP

method, the ease of application of the PAVER procedure was recognized as a major

advantage. However, the PCI values generated by PAVER are fixed values for a given set of

distress data and cannot vary to reflect the exact maintenance strategy and preferences of

highway agencies. The proposed Absolute AHP method is able to overcome this limitation.

Priority ratings, determined as described in the preceding paragraphs, are used for the

purpose of pavement maintenance planning at a network level.

This practice can be unsatisfactory because there are a number of factors, other than

the physical characteristics of distresses, which can significantly influence how a particular

distress would affect the structural performance of the distressed pavement section. To

overcome the above-mentioned limitation in current practice, the following chapter presents a

mechanistically based approach to assess the urgency of maintenance needs of a crack based

on its adverse impact on the structural capacity of the pavement section.

92

TABLE 4.1. Pavement segment distress characteristics for example problem

Pavement Segment Distress State* Segment 1 (D2, D4, D9) Segment 2 (D1, D4, D8) Segment 3 (D3, D6, D8) Segment 4 (D1, D5, D8) Segment 5 (D1, D5, D7) Segment 6 (D2, D4, D8) Segment 7 (D3, D4, D7) Segment 8 (D3, D6, D9) Segment 9 (D2, D6, D7) Segment 10 (D3, D5, D8) Segment 11 (D1, D4, D7) Segment 12 (D3, D4, D8) Segment 13 (D2, D5, D8) Segment 14 (D1, D6, D9) Segment 15 (D2, D4, D9) Segment 16 (D2, D5, D9) Segment 17 (D3, D5, D7) Segment 18 (D2, D6, D9) Segment 19 (D1, D6, D7) Segment 20 (D4, D9) Segment 21 (D4, D8) Segment 22 (D6, D8) Segment 23 (D5, D8) Segment 24 (D5, D7) Segment 25 (D4) Segment 26 (D3) Segment 27 (D6) Segment 28 (D8) Segment 29 (D1, D8) Segment 30 (D4, D7)

*Note: See Table 4.2 for definitions of distress codes D1 to D9.

TABLE 4.2. Pavement distress codes for Table 4.1

Distress Code Definition D1 High severity pothole D2 Medium severity pothole D3 Low severity pothole D4 High severity rutting D5 Medium severity rutting D6 Low severity rutting D7 High severity crack D8 Medium severity crack D9 Low severity crack

93

TABLE 4.3. Priority ratings of sections obtained using different methods

Seg-ment

Priority Ratings (Absolute AHP Method)

Priority ratings (Direct Assessment Method) Priority Ratings

(PAVER Method) Expert

1 Expert

2 Expert

3 Expert

4 Expert

5 Expert

1 Expert

2 Expert

3 Expert

4 Expert

5 1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

46.14 100.0 20.70 86.59 89.68 47.06 39.99 19.42 33.96 23.48 86.59 36.90 33.64 82.53 45.78 32.36 26.57 29.58 86.90 28.95 30.23 14.04 16.82 19.91 28.07 16.43 11.88 11.93 81.70 33.33

46.02 99.66 29.00 91.35 98.99 48.31 43.94 26.36 48.65 27.99 91.35 36.30 40.00 89.72 45.67 37.36 35.64 38.37 100.0 24.30 26.94 19.64 18.64 26.28 22.99 20.10 15.69 14.69 87.41 34.59

48.42 100.0 20.00 86.51 92.33 49.49 42.67 18.54 38.45 23.37 86.51 36.86 36.01 81.69 48.04 34.55 29.19 31.18 88.96 29.24 30.69 13.83 17.21 23.02 28.53 16.19 11.67 12.19 81.49 36.51

48.88 100.0 21.22 85.60 89.30 50.02 41.63 19.69 37.00 23.53 85.60 37.93 35.62 81.76 48.49 34.09 27.23 31.78 86.98 29.39 30.92 14.21 16.52 20.22 28.34 16.96 11.62 12.53 81.61 34.62

50.28 100.0 20.71 80.37 83.27 51.19 47.30 19.40 30.39 24.78 80.37 44.41 31.56 75.00 49.88 30.25 27.67 26.18 79.20 37.72 39.03 15.33 19.40 22.29 36.68 15.29 12.99 12.25 73.22 41.92

80 100 65

100 100 95 95 50 85 75

100 85 85 75 80 70 85 60

100 50 65 45 55 65 40 20 30 20 55 75

70 99 30 80 85 50 70 10 60 50

100 60 50 90 60 50 70 30 80 80 70 40 50 60 40 20 30 5

30 80

85 90 25 80 95 85 95 15 70 70

100 85 80 50 85 75 80 65 90 45 55 45 60 70 35 10 30 5

60 80

55 95 10 75 85 65 50 85 1

10 75 45 25

100 50 75 40 50 50 55 25 85 40 35 20 15 10 10 25 55

55 90 10 80 85 65 50 1

45 25

100 45 25 50 60 55 40 50 70 35 40 30 40 45 20 15 10 10 35 55

79.83 89.25 53.09 89.25 89.40 79.99 73.71 51.24 72.57 61.49 88.20 68.24 74.25 88.20 79.83 73.64 67.41 70.90 89.40 4.840 12.79 12.79 12.79 23.23 47.24 44.10 21.53 12.79 87.57 23.23

94

TABLE 4.4. Priority rankings of sections obtained using different methods

Seg-ment

Priority Ratings (Absolute AHP Method)

Priority Ratings (Direct Assessment Method) Priority Ratings

(PAVER Method) Expert

1 Expert

2 Expert

3 Expert

4 Expert

5 Expert

1 Expert

2 Expert

3 Expert

4 Expert

5 1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

9 1

23 4 2 8

11 25 13 22 4

12 14 6

10 16 21 18 3

19 17 28 26 24 20 27 30 29 7

15

10 2

19 4 3 9

12 22 8

20 4

16 13 6

11 15 17 14 1

24 21 27 28 23 25 26 29 30 7

18

9 1

24 4 2 8

11 25 12 22 4

13 15 6

10 16 20 17 3

19 18 28 26 23 21 27 30 29 7

14

9 1

23 4 2 8

11 25 13 22 4

12 14 6

10 16 21 17 3

19 18 28 27 24 20 26 30 29 7

15

9 1

24 3 2 8

11 25 18 22 3

12 17 6

10 19 20 21 5

15 14 27 26 23 16 28 29 30 7

13

12 1

18 1 1 6 6

24 8

14 1 8 8

14 12 17 8

21 1

24 18 26 22 18 27 29 28 29 22 14

9 2

24 5 4

17 9

29 13 17 1

13 17 3

13 17 9

24 5 5 9

22 17 13 22 28 24 30 24 5

6 4

27 10 2 6 2

28 15 15 1 6

10 22 6

14 10 18 4

23 21 23 19 15 25 29 26 30 19 10

10 2

26 6 3 9

13 3

30 26 6

17 21 1

13 6

18 13 13 10 21 3

18 20 24 25 26 26 21 10

8 2

27 4 3 6

11 30 14 23 1

14 23 11 7 8

17 11 5

20 17 22 17 14 25 26 27 27 20 8

9 3

19 3 1 8

12 20 14 18 5

16 11 5 9

13 17 15 1

30 26 26 26 23 21 22 25 26 7

23

95

TABLE 4.5. Spearman’s rank correlation coefficient and Student’s t-test for correlation with


Statistic Absolute AHP vs. Direct Assessment

Method

PAVER vs. Direct Assessment

Method

Absolute AHP vs. PAVER Method

Observations 30 30 30

Degrees of freedom 28 28 28

Confidence level tested 95% 95% 95%

Correlation 0.86 0.73 0.89

Student’s T-test ( 2−nt for 10>n ) 8.90 5.65 10.32

Critical 1-sided T-value )( 2, −ntα 1.70 1.70 1.70

Result 2,2 −− > nn tt α 2,2 −− > nn tt α 2,2 −− > nn tt α

Conclusion Accept H1: 0>ρ Accept H1: 0>ρ Accept H1: 0>ρ

96

High Severity High Severity

Selection of pavement Segment for maintenance

Pothole

Rutting

Cracking

High Severity

Objective (Level 1)

Criteria (Level 2)

Sub-criteria (Level 3)

Alternatives (Level 4)

Segment 1

Distress

state

Segment 2

Distress

state

Segment 3

Distress

state

Segment 4

Distress

state

Segment 5

Distress

state

Segment 6

Distress

state

Segment 7

Distress

state

Segment 8

Distress

state

Segment 9

Distress

state

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

Segment 22

Distress

state

Segment 23

Distress

state

Segment 24

Distress

state

Segment 25

Distress

state

Segment 26

Distress

state

Segment 27

Distress

state

Segment 28

Distress

state

Segment 29

Distress

state

Segment 30

Distress

state

Medium Severity

Low Severity

Medium Severity

Low Severity

Medium Severity

Low Severity

FIGURE 4.1. Hierarchy structure for AHP analysis of example problem

97

Step 1 You are given 27 pavement sections requiring routine maintenance activity types. The attributes of each section, consisting of class of pavement, type of distress and distress severity, are written on a small card. Read the attributes carefully. Step 2 Rank the cards on your desk in accordance with the importance of each pavement section requiring maintenance in order to keep it at a required level of service. Place the most important section at the top, followed by other sections in the order of decreasing importance to rate the absolute and relative position of each section. Ties are permissible. Step 3 Carefully review the ranking in step 2. Make changes if required. Step 4 Move the top priority card to the top (i.e. a score of 100) of the scale on this instruction sheet. Next move one card at a time, in sequence of decreasing importance, to the score and assign a score to each by comparing with the activity immediately above it. Continue until all the cards are placed on the scale. Step 5 If the last card does not have a score of 1, adjust the scores (except the top score) so that the lowest priority section has a score of 1. Step 6 Carefully review the priority scores assigned. Make changes if necessary.

FIGURE 4.2. Rating scale and instructions for Direct Assessment Method

100

90

80

70

60

50

40

30

20

10

1

98


Rat

ing

by A

bsol

ute

AH

P

100806040200

100

80

60

40

20

0


Ran

king

by

Abs

olut

e A

HP

302520151050

30

25

20

15

10

5

0

FIGURE 4.3. Correlations between the priority ratings and rankings obtained using

Absolute AHP method and Direct Assessment Method

(b) Scatter plot of priority rankings by Absolute AHP and


(a) Scatter plot of priority ratings by Absolute AHP and


r = 0.77

ρ = 0.86

99


Rat

ing

by P

AV

ER

Sys

tem

100806040200

100

80

60

40

20

0


Ran

king

By

PAV

ER

Sys

tem

302520151050

30

25

20

15

10

5

0

FIGURE 4.4. Correlations between the priority ratings and rankings obtained using PAVER

System and Direct Assessment Method

(a) Scatter plot of priority ratings by PAVER System and


(b) Scatter plot of priority rankings by PAVER System and


r = 0.61

ρ = 0.73

100

Rating by PAVER System

Rat

ing

by A

bsol

ute

AH

P

100806040200

100

80

60

40

20

0

Ranking by PAVER System

Ran

king

by

Abs

olut

e A

HP

302520151050

30

25

20

15

10

5

0

FIGURE 4.5. Correlations between the priority ratings and rankings obtained using Absolute AHP Method and PAVER System

(a) Scatter plot of priority ratings by Absolute AHP Method and

PAVER System

(b) Scatter plot of priority rankings by Absolute AHP Method and

PAVER System

r = 0.75

ρ = 0.89

101

CHAPTER 5

IMPROVED PAVEMENT MAINTENANCE PRIORITY ASSESSMENT: MECHANISTIC BASED APPROACH

5.1 INTRODUCTION

Instead of subjective assessment, there are instances where maintenance priority of

pavement distresses can be determined analytically using mechanistic theory. This Chapter

illustrates the mechanistic approach by demonstrating how maintenance priority of cracks can

be determined mechanistically. Traditionally in performing pavement maintenance planning,

which is an essential activity of a pavement management system, pavement distresses are

assigned priority ratings so that those distresses that deserve earlier maintenance treatments

will receive higher maintenance priority. In the case of cracks, condition indices or priority

ratings are typically assigned based on their physical characteristics such as crack width,

length, depth, density and extent (ASTM, 2007; FHWA, 1998; British Columbia MOT, 2009)

that are obtained from pavement condition surveys. The procedures for determining such

indices or ratings are often based on engineering judgment or some empirical relationships

derived from practical experience. For instance, the Pavement Condition Index (PCI), which

is an ASTM standard for the pavement condition assessment (ASTM, 2007), assigns PCI

values to cracks on a scale from 0 to 100 based on crack type, density and severity. Crack

severity is determined based on the width of crack or visual comparisons with established

benchmarks and is classified into three categories such as low, medium and high.

It is a common practice that pavement condition indices or priority ratings,

determined as described in the preceding paragraphs, are used for the purpose of pavement

maintenance planning at a network level. This practice can be unsatisfactory because there

are a number of factors, other than the physical characteristics of cracks, which can

Relative AHP (IM) RMS(d) = 1.42

102

significantly influence how a crack would affect the structural performance of the cracked

pavement section. These other factors include the following:

(a) Pavement structural design and material properties. Cracks with identical

physical characteristics will have different effects on the performance of

pavements having different structural designs and material properties. For

example, all other things being equal, a crack in a thinner and weaker pavement

will require maintenance treatment more urgently than an identical crack in a

thicker and stronger pavement.

(b) Traffic loading. A pavement section carrying heavier traffic loading would have

higher maintenance priority than another lightly trafficked pavement section if

there are identical cracks in both.

(c) Location within roadway. A crack within a wheel path is likely to receive higher

traffic loading and experience faster deterioration than a similar crack in the

shoulder or a non-wheel path location of the same pavement. This implies that

these cracks, even though they have identical physical characteristics, should be

given different maintenance priorities. The same argument also applies to

identical cracks found in different lanes of the same roadway.

(d) Variation in subgrade condition. Pavement subgrade condition can vary from

location to location of a given pavement. Pavement sections with identical cracks

will behave differently if their subgrade conditions are not the same.

(e) Pavement location and environmental factors. For a road network that covers a

relatively large geographical region, differences in climatic, drainage and other

environmental factors may occur and these could have a direct impact on how

cracks would affect the structural performance of pavements.

103

It is clear from this discussion that cracks with identical dimensions, density and

extent can have significantly different impacts on pavement performance and remaining life

if there are differences in one or more of the factors listed above. In other words, the

common practice of priority rating based on physical characteristics of cracks may not be

appropriate and it could result in incorrect priority setting in pavement maintenance planning.

To overcome the above-mentioned limitation in current practice, this research

proposes that a mechanistically based approach be adopted to assess the urgency of

maintenance priority of a crack based on its adverse impact on the structural capacity of the

pavement section. The proposed approach expresses the severity of a crack in terms of the

remaining life of the cracked pavement section. This involves a mechanistic analysis taking

into account the location of the crack, structural design and material properties of the

pavement, subgrade properties, expected traffic volume and loading characteristics, as well as

the prevailing environmental conditions. Knowing the remaining life of the cracked

pavement section, a damage factor can be defined using Miner’s rule (Miner, 1945) to

provide a rational basis for assigning maintenance priorities. The detailed procedure for

conducting the mechanistic analysis is presented in this chapter.

5.2 METHODOLOGY OF PROPOSED APPROACH

The methodology presented in this section applies to multilayered asphalt pavements.

The general framework and steps of analysis will be similar for Portland cement concrete

pavements, although the pavement structural response formulas would be different.

5.2.1 Evaluating Remaining Life of Cracked Pavement Section

Pavement maintenance planning in a pavement management system is usually made

on the basis of the pavement distress report derived from pavement condition surveys. Most

condition surveys in pavement management systems are performed manually or with

104

automated devices to identify distresses occurring in pavement surface. Pavement cracks

identified in this process are thus top-down cracks. Therefore, the methodology presented

deals with cracked pavement sections with one or more visible cracks in the pavement

surface. However, the same methodology is also applicable should the condition survey

report also contain pavement sections with bottom-up cracks.

A pavement section with a surface crack can fail structurally in two ways under the

action of external forces. It can fail through top-down cracking when the surface crack

propagates downward. It can also fail when a bottom crack develops at the weakened

cracked section and propagates upward. Of particular interest to pavement maintenance

planning is the number of additional traffic loadings a cracked pavement section can still take

before the end of its useful service life. This additional traffic loading is commonly known as

the remaining life of the pavement (Yeo et al., 2008, AASHTO, 1993). For the purpose of

this study, the following general fatigue failure model is adopted for the analysis (Al-Qadi et

al., 2008; El-Basyouny and Witczak, 2005; Molenaar, 2007),

( ) ( ) 32 kkt1f EkN −−= ε (5.1)

where Nf is the remaining life measured in terms of the number of loading cycles to failure, εt

is the critical tensile strain (microstrain), E is the stiffness modulus of the asphalt layer, and k1,

k2, and k3 are material coefficients. For instance, in a model suggested by the Asphalt

Institute (1982), k1 = 0.00432, k2 = 3.291 and k3 = 0.854. It is assumed that the same

expression of Nf is applicable to both top-down and bottom-up crack developments, although

the values of the coefficients and calibration parameters may be different. Other forms of

expression different from Eq. (5.1) can be used if appropriate. Whatever the case, the

methodology and procedure proposed in this study are still applicable.

105

5.2.2 Concept of Cumulative Damage and Failure Risk

The strain value tε in Eq. (5.1) is computed using layered elastic theory for any given wheel

loads. For a given cracked pavement section, the magnitude of the strain varies with the

points of application and magnitudes of the wheel loads, and structural properties of the

pavement system. Since a pavement section is likely to receive a wide range of vehicular

loadings from the traffic stream comprising vehicles of different wheel and axle

configurations, and of different wandering characteristics, the traffic-induced strains

experienced by the pavement section are expected to cover a wide range of values each with

a different number of repetitions. All of these will contribute to accumulation of damages in

the pavement section concerned according to fatigue theory (Al-Qadi et al., 2008; El-

Basyouny and Witczak, 2005; Molenaar, 2007). Based on the cumulative damage concept of

Miner’s rule of linear cumulative fatigue damage (Miner, 1945), the overall cumulative

damage factor (Df) caused to the pavement section by the entire load spectra of the traffic

stream is given by Eq. (5.2),

∑=

=k

1i fi

if N

nD (5.2)

where ni is the number of repetitions of load-induced strain level i expected in the analysis

period, Nfi is the total number of repetitions of load-induced strain level i needed to fail the

pavement section, and k is the total number of load types.

In accordance with Miner’s rule, Df can have any real values equal to or greater than 0.

The pavement section is said to reach failure when Df = 1 while a value of Df = 0 means that

there is no damage at all and the pavement is structurally intact like a newly constructed

pavement. On the other hand, a value of Df greater than 1.0 means that failure will occur

before the end of the analysis period. In other words, a pavement section with a higher Df

106

will require a lower number of load applications to reach failure. This means that the higher

the Df value, the sooner failure will occur, and the higher is the failure risk.

5.2.3 Cumulative Damage and Priority Ranking

It has been noted in the preceding section that the Miner’s cumulative damage factor

Df can have values equal to or greater than 0. A pavement section with a higher Df value has

a higher risk of failure, thus requiring maintenance treatment more urgently. Therefore, Df

can serve as a basis for priority ranking of cracked pavement sections for the purpose of

pavement maintenance planning. In establishing this link, it is necessary to select

appropriately the analysis period used for computing the cumulative damage factor Df .

It is appropriate to equate the analysis period for Df to the length of maintenance

planning period. By so doing, a meaningful time dimension becomes relevant in the

interpretation of the cumulative damage factor Df . A value Df = 1.0 means that failure will

occur at the end of the maintenance planning period. When Df < 1.0, failure will not occur

before the end of the maintenance planning period; and when Df > 1.0, failure will occur

within the maintenance planning period. On the reasoning that a cracked pavement section

that is expected to fail earlier (i.e. having a higher Df value) should be given maintenance

treatment sooner, it should thus be assigned a higher maintenance priority than another

cracked pavement section that has a lower Df value. This leads to the conclusion that Df

values can be considered as a measure of priority ratings to be used directly to form the basis

for performing priority ranking of cracked pavement sections for the purpose of maintenance

planning.

5.3 DETERMINATION OF CUMULATIVE DAMAGE FACTOR AND PRIORITY RANKING

107

Fig. 5.1 shows a flowchart that depicts the steps involved in the determination of

cumulative damage factor and priority ranking for use in pavement maintenance planning. A

detailed description of the steps is given in this section. It is noted that this procedure is

applicable to the case of longitudinal cracks. Some minor adjustments to the procedure are

necessary for computing the cumulative damage factor of transverse cracks. These

adjustments are mentioned at the end of this section.

5.3.1 Step 1: Determination of Input Parameters

For the purpose of performing mechanistic analysis of the stresses and strains in a

cracked pavement section, the following three groups of input data are required: crack related

data, traffic loading related data, and pavement structure related data. Specifically, the

following data items are necessary for the analysis proposed in this study:

Crack related data: crack width, length, depth, orientation and location.

Pavement related data: number of pavement layers, layer thicknesses, elastic modulus and

Poisson’s ratio of each layer, including subgrade.

Traffic loading related data: daily traffic flow volume by lane, traffic mix composition of

vehicle types, axle and wheel configurations, tire inflation pressure, statistical distributions of

vehicular and wheel loads, and wheelpath distribution (or lateral wander distribution).

Compared with crack and pavement related data, the traffic loading related data are

slightly more complex. While the former two groups of data items can be considered as

constant in values, the latter group comprises parameters with either discrete distributions

(e.g. mix composition of vehicle types) or continuous distributions (e.g. wheel loads, lateral

wander). The procedure of handling these statistical variations of these traffic loading related

data is described in the subsequent section.

Another input parameter needed for the analysis is the analysis period. Since the aim

of the analysis is to determine the maintenance priorities of different pavement cracks for the

108

purpose of maintenance planning, the analysis period is set equal to the maintenance planning

period.

5.3.2 Step 2: Characterization of Loads

For a given cracked pavement section with known crack- and pavement-related data,

the finite element method is employed to compute the pavement tensile strains for both top-

down and bottom-up modes of cracking under various applicable traffic loading conditions.

Crack dimensions and pavement properties being given, the critical strain induced by each

pass of a load is essentially a function of the magnitude of applied loads, and their position

with respect to the crack, as indicated in Fig. 5.2. i.e.,

εti = f{Wi1, Wi2, …. WiK; (xi1 - xc1), (xi2 - xc1), .... (xiK - xc1)} (5.3)

where εti is the critical tensile strain caused by one pass of vehicle type i having wheel loads

Wij each positioned at xij from lane centerline; K is the total number of wheels of vehicle type

i; and xc1 is the location of the crack.

If the magnitude of wheel load distribution is normal, the probability that the wheel

load will have a magnitude Wij is given by

−−

=2Wij

2wijij

2)W(

Wijij e

21)W(p σ

µ

σπ (5.4)

where µwij and σwij are respectively the mean and standard deviation of wheel load Wij.

Similarly, if the wheelpath of the vehicle type i is normally distributed (i.e. a normally

distributed lateral wander), the probability that the wheel load is positioned at a distance xij

from the lane centerline is

−−

=2xij

2xijij

2)x(

xijij e

21)x(p σ

µ

σπ (5.5)

109

where µxij and σxij are respectively the mean and standard deviation of distance xij. It is noted

that should the frequency distribution of either wheel load or lateral wander be not normal,

the probability of each can be obtained directly from their respective distributions. For

wheelpath distribution, normal distribution has been considered to be appropriate (NCHRP,

2002; Buiter et al., 1989). Buiter et al. (1989) suggested an average standard deviation of

0.29m in their study.

For the ease of computation, it is proper to discretize each wheel load distribution into

a suitable number of finite load groups each with a known frequency (number of load

applications). For each load group, a lateral wander distribution is considered, and can also

be discretized into a convenient number of intervals.

5.3.3 Step 3: Computation of Load Induced Strains εt

The general availability of efficient finite element software and computers today has

made the finite element method a suitable analytical tool for an application such as that

described in this study. A 3-dimensional finite element program (Simulia, 2007) could be

employed for this purpose or alternatively, since cracks are linear and the main aim of the

present study is to compute the maximum tensile strain under a pass of a given vehicle, a 2-

dimensional plain strain finite element analysis (Geo-Slope, 2009) will suffice too. Fig. 5.2

shows the finite element mesh design adopted in this study.

For a given vehicle type, the total number of finite element analysis runs required is

equal to (MA x MW x MP), where MA is the number of axle per vehicle, MW is the total

number of discretized wheel load groups, and MP is the total number of discretized wheelpath

intervals. If there are MV number of vehicle types in the traffic stream, then the total number

of computer runs required for the finite element analysis is equal to (MA x MW x MP x MV).

For each finite element run, the respective critical tensile strains for top-down and bottom-up

cracking failures are obtained. Therefore, there are (MA x MW x MP x MV) number of critical

110

strain values for top-down cracking failure, and another (MA x MW x MP x MV) number for

bottom-up failure.

5.3.4 Step 4: Computation of Cumulative Damage Factor Df

The calculation of cumulative damage factor Df, according to Eq. (5.2), requires the

knowledge of ni and Nfi, respectively the number of repetitions of load-induced strain level i

expected in the analysis period, and the total number of repetitions of load-induced strain

level i needed to fail the pavement section. For each critical strain computed in Step 3, the

corresponding value of Nfi, is computed from Eq. (5.1). On the other hand, the determination

of ni is more tedious and involves the following steps:

(i) For the wheel load that generates the strain concerned, identify the vehicle type j

and its total flow passes (designated as nTi) in the lane analyzed over the entire

analysis period.

(ii) Let the wheel load group that generates the strain concerned be m, the number of

passes of this wheel group is given by

−−

=2Wjm

2wjmjm

2)W(

Wjm

TijmTi e

2n)W(pn σ

µ

σπ (5.6)

where p(Wjm) is as defined earlier in Eq. (5.4).

(iii) Let the wheelpath interval that generates the strain concerned by r, the final ni is

then computed as

ni = nTi p(Wjm) p(xjr) (5.7)

where nTi p(Wjm)is given by Eq. (5.6), and p(xjr) is computed according to Eq. (5.5).

The procedure described can be repeated for all the strain levels εt computed in Step 3

to obtain the corresponding ni and Nfi values. A practical way is to divide the entire range of

strains into a convenient number of intervals, and compute the ni and Nfi values accordingly.

111

Two sets of answers for the εt-ni-Nfi values would be obtained, one for top-down failure and

another for bottom-up failure.

As explained in Step 3, there are altogether (MA x MW x MP x MV) number of

computed strains. Hence there is an equal number of (ni/Nfi) ratios for top-down failure, and

also for bottom-up failure. According to Eq. (5.2), summing up the (MA x MW x MP x MV)

number of (ni/Nfi) ratios will give the total Df for top-down failure. The Df for bottom-up

failure is obtained in a similar fashion. The higher Df value of the two will be taken as the

governing cumulative damage factor of the cracked pavement section considered.

5.3.5 Step 5: Determination of Maintenance Priority of All Cracked Pavement

Sections

For each of the cracked pavement sections, Steps 2 to 4 are repeated to compute the

governing cumulative damage factor Df. As explained earlier, the values of these governing

cumulative damage factors directly convey the relative maintenance priorities of the cracked

pavement sections. Cracked pavement sections with higher Df values will have higher

priorities. That is, the cracked section having the highest Df value will be assigned the

highest priority, and the section with the lowest Df value will be given the lowest priority.

5.3.6 Adjustments for Presence of Transverse Cracks or Cracks of Other

Orientations

When transverse cracks or cracks of other orientations are present, an additional step

to the procedure is necessary. Considering the full length of the crack, it is first divided into

equal segments of suitable length. Each segment is then analyzed by applying Steps 1 to 4 to

obtain the cumulative damage factor. The maximum cumulative damage factor of all

segments of the crack analyzed is taken as the cumulative damage factor of the crack, and

112

this cumulative damage factor is used in Step 5 for the determination of its maintenance

priority.

5.4 ILLUSTRATIVE NUMERICAL EXAMPLE

5.4.1 Problem Parameters and Data

A simple example is presented to illustrate the computation of the cumulative damage

factor and maintenance priorities of cracks. The structural properties of the asphalt pavement

analyzed are given in Table 5.1. Longitudinal cracks along a wheelpath are considered. For

easy explanation, the locations of cracks in this example are given with respect to the

centerline of the wheelpath. The problem parameters considered are as follows:

• Crack location from wheelpath centerline (cm): 0, 10, 20, 30, 40, 50, 60.

• Crack width (mm): 10, 40.

• Crack depth (mm): 30, 60, 90, 120.

• Axle load type: Single axle load with load magnitude distribution given by Fig.

5.3(a).

• Analysis period: One year.

• Lane annual traffic: 90,000

There are altogether (7 x 2 x 4) = 56 cracks to be analyzed in this example. It is

assumed that the traffic consists of only one load type, and that is a single axle load with one

wheel at each end of the axle. The axle load has an axle width (i.e. distance between the

centers of the wheels at the two ends) of 1.80 m. The wander distribution of the axle load is

shown in Fig. 5.3(b), expressed in terms of the normalized AADT (annual average daily

traffic) and the distance between load center (i.e. center point of the axle) and lane centerline.

The lane has a width of 3.70 m. The distance between the wheelpath centerline and lane

113

centerline is 0.9 m. The Asphalt Institute’s fatigue cracking model (1982) given by the

following equation is adopted for this example,

( ) ( ) 854.0291.300432.0 −−= EN tf ε (5.8)

where all variables are as defined in Eq. (5.1).

5.4.2 Results of Analysis

The computed cumulative damage factors for all the 56 cracks are summarized in

Tables 5.2. As explained earlier, the values of these cumulative damage factors can be used

directly as priority rating values to represent the relative maintenance priorities of the cracked

pavement sections. For easy comparison, the relative priority rankings of the 56 cracks are

also indicated in the table. A priority ranking of 1 is assigned to the crack with the highest

cumulative damage factor value, and the priority ranking of 56 is assigned to the crack with

the lowest cumulative damage factor value.

The relative priority rankings represent the combined effects of the following three

trends:

• Cracks with wider width tend to have higher priority;

• Cracks with deeper depth tend to have higher priority;

• Cracks that are located closer to the center of the wheelpath tend to have higher

priority because of the higher number of loading repetitions received.

The effects of these trends could be seen from some straight-forward cases. For instance, for

the extreme case of the crack located at 0 cm from lane centerline with the maximum crack

width of 40 mm and the maximum crack depth of 120 mm, the priority ranking of 1; and for

the crack located at 60 cm from lane centerline with the minimum crack width of 10 mm and

the minimum crack depth of 30 mm, the priority ranking is 56. However, the ranking of

intermediate cases would not be easily decided by intuition because of the interaction of the

114

various factors. This is especially so due to the presence of the two wheel loads spaced at 1.8

m apart. Their interaction would produce a complex distribution of stresses and strains that

are not linearly related to the location of cracks. Fig. 4.4 presents graphically the pattern of

priority ranking distribution of the 56 cracks.

5.4.3 Comparison with Traditional Prioritization Method

A typical method of maintenance prioritization of cracks in practice is to assign

priorities to cracks according to their severity classification, density, extent and location for

some. The severity classification is often made based on crack dimensions of width, length,

and depth. Most traditional methods classify crack severity into three broad classes: severe,

medium, and slight. For comparison with the computed results, the PCR method of

pavement condition rating by FHWA (1998) is used.

PCR is developed to describe the pavement condition ranging from 0 to 100; a PCR

of 100 represents a perfect pavement with no observable distress and a PCR of 0 represents a

pavement with all distress present at their high levels of severity and extensive levels of

extent. To determine PCR, the deduct points are first calculated and PCR is equal to 100

minus the total deduct points. For each distress, the deduct point is equal to (Weight for

distress) x (Weight for severity) x (Weight for Extent). For the example, the weight for

extent is the same for all 56 cracks. The only difference will come from the weight for

distress contributed by location, and the weight for severity. Based on the PCR guidelines,

for cracks at locations within 0 to 50cm of wheelpath centerline, the weight of the distress

type is 15 and beyond wheelpath it is 5. The weights of the severity levels associated with

each distress types are 0.4, 0.7, 1 for high, medium and low severities respectively. The low,

medium and high severity of longitudinal cracks correspond with crack width less than 6mm,

between 6mm-25mm, and greater than 25mm, respectively.

115

The comparison of priority ranking by PCR and those computed by the proposed

method in this study is made in Table 5.3. As it turns out, there are only 4 different PCR

ratings for the 56 cracks, leading to many cracks having tied ranking (i.e. same priority

ranking). This situation is undesirable for maintenance planning as no differentiation is made

between cracks which are actually different in both dimensions and performance under traffic

loading. The same results from the two methods are plotted in Fig. 5.5 to show the

differences graphically. It highlights the ability of the proposed approach in differentiating

the different urgency levels of needs for maintenance of the 56 cracks.

5.4.4 Computational Tool for Estimating Cumulative Damage Factor

To facilitate the computation of cumulative damage factor, computer software can be

developed for calculating the cumulative damage factor of a crack. Since all the input

information needed for the computation are data already in the pavement condition survey

reports and pavement maintenance management system, the inclusion of the computer

software into any existing pavement management computer system should not present any

major problem. Alternatively, a regression prediction model could be developed to expedite

the calculation.

5.5 SUMMARY

This Chapter has proposed a mechanistically based methodology to assess the

maintenance priorities of pavement cracks. The concept of cumulative damage and

remaining life was introduced. Miner’s rule was applied to compute a cumulative damage

factor to form the basis for maintenance prioritization. It was reasoned that a crack with a

higher cumulative damage factor (i.e. having a shorter remaining life) has a higher urgency of

needs for maintenance, and hence is assigned a higher maintenance priority. In the

computation of cumulative damage factor of a crack, the proposed mechanistic approach

116

considers crack dimensions (including crack orientation, crack width, depth and length),

crack location, and traffic loading characteristics (including statistical variations in traffic

composition, loading magnitude and loading frequency due to wander distributions).

Although for simplicity in explanation, only single cracks have been analyzed in the

presentation of this Chapter, the proposed mechanistic approach is also applicable to more

complex distress situations such as those involving multiples cracks. Overall, this approach

helps to reduce the uncertainty associated with the subjective or judgmental element involved

in many maintenance prioritization methods currently in use. It also helps to lessen the

problem of having many maintenance priority ties arising from classifying crack severity into

three very broad classes. It makes available a prioritization procedure that produces a more

rational priority ranking in support of pavement maintenance planning in a pavement

management system.

Furthermore, use of conventional priority ranking methods based on crack severity in

terms of its width leads to many cracks having tied ranking (i.e. same priority ranking). This

situation is undesirable for maintenance planning as no differentiation is made between

cracks which are actually different in both dimensions and performance under traffic loading.

Hence, the effectiveness of the proposed procedure is highlighted from its ability to

differentiate the different urgency levels of needs for maintenance of cracks.

117

TABLE 5.1. Material parameters for numerical example

Pavement Layer

Elastic Modulus

(MPa)

Poisson's ratio

Thickness (mm)

Asphalt Concrete 5500 0.35 150

Base 300 0.35 300 Subbase 140 0.35 300 Subgrade 31 0.4 --

118

TABLE 5.2. Results of computation for numerical example

Crack Description Cumulative Damage

Factor (Df)

Priority Ranking

Crack Description Cumulative Damage

Factor (Df)

Priority Ranking Location*

(cm) Width (mm)

Depth (mm)

Location* (cm)

Width (mm)

Depth (mm)

0 10 30 0.1138 37 0 40 30 0.1428 15 10 10 30 0.0908 49 10 40 30 0.1058 46 20 10 30 0.0892 50 20 40 30 0.1055 49 30 10 30 0.0808 51 30 40 30 0.0999 45 40 10 30 0.0794 53 40 40 30 0.0997 39 50 10 30 0.0710 55 50 40 30 0.0971 44 60 10 30 0.0704 56 60 40 30 0.0968 40 0 10 60 0.2525 13 0 40 60 0.2876 4 10 10 60 0.2221 25 10 40 60 0.2292 22 20 10 60 0.1967 18 20 40 60 0.2021 31 30 10 60 0.1275 50 30 40 60 0.1297 41 40 10 60 0.1176 35 40 40 60 0.1207 30 50 10 60 0.0800 51 50 40 60 0.1085 37 60 10 60 0.0780 53 60 40 60 0.0987 38 0 10 90 0.5450 5 0 40 90 0.5905 2 10 10 90 0.4101 10 10 40 90 0.4547 11 20 10 90 0.3917 12 20 40 90 0.4220 14 30 10 90 0.1890 26 30 40 90 0.2395 24 40 10 90 0.1764 23 40 40 90 0.2154 21 50 10 90 0.1134 36 50 40 90 0.1372 29 60 10 90 0.0990 43 60 40 90 0.1201 33 0 10 120 0.6762 3 0 40 120 0.7453 1 10 10 120 0.4569 7 10 40 120 0.4946 6 20 10 120 0.4176 9 20 40 120 0.4464 8 30 10 120 0.2180 20 30 40 120 0.2263 16 40 10 120 0.1940 19 40 40 120 0.2133 17 50 10 120 0.1217 32 50 40 120 0.1476 27 60 10 120 0.0990 42 60 40 120 0.1197 34

* Note: Location of crack is measured from wheelpath centerline in the direction towards lane centerline.

119

TABLE 5.3. Comparison of priority rankings by PCR method and proposed approach

Crack Description Priority Ranking Crack Description Priority Ranking Crack

Dimensions Location

(cm) PCR

Method Proposed Approach

Crack Dimensions

Location (cm)

PCR Method

Proposed Approach

10 mm crack width &

30 mm crack depth

0 25 37

40 mm crack width &

30 mm crack depth

0 1 15 10 25 49 10 1 46 20 25 50 20 1 49 30 25 51 30 1 45 40 25 53 40 1 39 50 25 55 50 1 44 60 53 56 60 49 40

10 mm crack width &

60 mm crack depth

0 25 13

40 mm crack width &

60 mm crack depth

0 1 4 10 25 25 10 1 22 20 25 18 20 1 31 30 25 50 30 1 41 40 25 35 40 1 30 50 25 51 50 1 37 60 53 53 60 49 38

10 mm crack width &

90 mm crack depth

0 25 5

40 mm crack width &

90 mm crack depth

0 1 2 10 25 10 10 1 11 20 25 12 20 1 14 30 25 26 30 1 24 40 25 23 40 1 21 50 25 36 50 1 29 60 53 43 60 49 33

10 mm crack width &

120 mm crack depth

0 25 3

40 mm crack width &

120 mm crack depth

0 1 1 10 25 7 10 1 6 20 25 9 20 1 8 30 25 20 30 1 16 40 25 19 40 1 17 50 25 32 50 1 27 60 53 42 60 49 34

120

FIGURE 5.1. Flowchart of proposed mechanistic crack prioritization approach

Load magnitude distribution

Load wander distribution

Finite element analysis to compute governing tensile strain for each

crack

Compute the fatigue damage (Df) for each

crack using Miner’s rule

STEP 1

STEP 2

STEP 3

STEP 4

STEP 5

Loading characterization for each crack

Input crack attributes such as crack orientation,

length, width, depth and location

Input traffic

loading data and analysis period

Input pavement geometric and material data

Priority ranking of

cracks

121

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 5.8

1.92.02.12.22.32.42.52.62.72.82.93.03.13.23.33.43.53.63.73.83.94.04.14.24.34.44.54.64.74.84.95.0

FIGURE 5.2. Schematic of the finite element model for pavement crack analysis

Distance (m)

Asphalt layer Shoulder Base

Subbase

Subgrade

20.3cm

1.8m

31.8cm

Ele

vatio

n

Tire Contact

Crack

Fine Mesh

Boundary Fixed in X/Y

20mm

x2

x3

Tire

x1

C L

122

0

2

4

6

8

10

12

14

16

18

20

0 5000 10000 15000 20000 25000 30000 35000 40000 45000

Single axle loads (lbs)

Freq

uenc

y (%

)

Vehicle class 9

(a) Distribution of axle load magnitude

0

0.2

0.4

0.6

0.8

1

-1.5 -1 -0.5 0 0.5 1 1.5

Distance between Wheel Load Center and Wheelpath Centerline (m)

Nor

mal

ized

AA

DT

(b) Wander distribution of wheel load

FIGURE 5.3. Variations of wheel load magnitude and load wander

1lb = 0.454kg

123

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 10 20 30 40 50 60Location of Crack in Distance from Wheelpath Centerline (cm)

Prio

rity

Rat

ing

Crack width=10mm, depth=30mmCrack width=40mm, depth=30mmCrack width=10mm, depth=120mmCrack width=40mm, depth=120mm

(a) For cracks with depth of 30mm and 120mm

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 10 20 30 40 50 60Location of Crack in Distance from Wheelpath Centerline (cm)

Prio

rity

Rat

ing

Crack width=10mm, depth=60mmCrack width=40mm, depth=60mmCrack width=10mm, depth=90mmCrack width=40mm, depth=90mm

(b) For cracks with depth of 60mm and 90mm

FIGURE 5.4. Priority ratings of cracks for numerical example

124

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 10 20 30 40 50 60

Location of Crack in Distance from Wheelpath Centerline (cm)

Prio

rity

Rat

ing

Crack width=10mm, depth=30mm




Crack width=10mm, depth=30mm (PCR)Crack width=40mm, depth=30mm (PCR)

Crack width=10mm, depth=120mm (PCR)


(a) For cracks with depth of 30mm and 120mm

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 10 20 30 40 50 60

Location of Crack in Distance from Wheelpath Centerline (cm)

Prio

rity

Rat

ing









(b) For cracks with depth of 60mm and 90mm

FIGURE 5.5. Comparison between proposed and existing pavement condition rating

125

CHAPTER 6

INCORPORATING PRIORITY PREFERENCES INTO PAVEMENT MAINTENANCE PROGRAMMING

6.1 INTRODUCTION

In pavement management the objectives required to be achieved are often multiple

and conflicting such as minimizing environmental, societal, and economic impacts, as well as

maximizing safety, level of service, and pavement condition, etc. Trade-off among the

various objectives is unavoidable, and is often made based on priority requirements,

subjective judgment, or preferences.

This chapter presents an approach that integrates multi-criteria ranking and multi-

objective optimization models to handle competing objectives and criteria in pavement

management. It is a Non-Dominated Sorting Genetic Algorithm (NSGA-II) (Deb et al., 2002)

centered optimization framework augmented with a tie breaking capability using priority

ranking concept. The aim is to minimize unnecessary interferences of subjective priority

ranking in the optimization process of maintenance activity programming and resource

allocation.

In the proposed approach, priority ranking is only introduced in breaking a tie

between analogous solutions in objective space, and in making trade-off among multiple

objectives. Owing to the inherent advantages of the absolute AHP approach over other

methodologies as illustrated in the preceding chapters, multi-criteria ranking scheme is

applied in the present analysis using the absolute AHP approach.

This chapter consists of two parts: part one provides a demonstrative analysis using an

example problem to illustrate how different priority weighting schemes would affect the

results of an optimal pavement maintenance programming analysis; and part two presents a

126

proposed methodology to incorporate priority weights into pavement maintenance

programming analysis with the intention of eliminating or minimizing unnecessary

interferences to the optimal programming process, and allowing the highway agency to know

how the computed maintenance program can be changed by their choice of priority scheme.

6.2 FRAMEWORK OF STUDY METHODOLOGY

Part one of the study deals with an optimal pavement maintenance programming

problem which is solved using the simple genetic-algorithm (SGA) method (Goldberg, 1989)

for the following eight different prioritization schemes:

(1) Zero priority weights are assigned. This scheme serves as a baseline case for

comparison purpose;

(2) Priority weights are assigned according to types of pavement distress;

(3) Priority weights are assigned according to the severity level of each distress;

(4) Priority weights are assigned according to highway class;

(5) A scheme that contains the priority weights of schemes (2) and (3) combined;



(8) A scheme that contains the priority weights of schemes (1), (2) and (3) combined.

Besides comparing the effects of different priority schemes, further analyses are conducted to

assess the effects of (i) changing the ratios of priority weights within a given scheme; and (ii)

changing the range of priority weights of a given scheme.

Part two presents the proposed framework to incorporate priority preferences into

pavement maintenance planning and programming. Instead of assigning weighting factors

directly to parameters, it first solves the optimization problem without applying any priority

weights. Next, two post-processing stages are executed to implement the desired priority

preferences as explained below:

127

• Stage I is a tie-breaking procedure. It first identifies if any of the selected pavement

sections in the maintenance program has one or more “tied” unselected pavement

sections. Two or more pavement sections are said to be “tied” if the selection of

any of the pavement sections over the others will not have any effect on the final

maintenance program in terms of the value of objective function. The tie-breaking

process will replace the selected pavement section by a “tied” unselected pavement

section if the latter has a higher priority weight.

• Stage II begins by first establishing the amount of loss in optimality that the highway

agency is willing to accept in order to include additional prioritized maintenance

activities (i.e. those prioritized maintenance activities not selected for the optimal

maintenance program) in the final maintenance program by replacing some non-

prioritized or lower-priority activities. Once this willingness level has been

established, a trade-off analysis is performed to include as many prioritized

maintenance activities into the maintenance program as possible, subject to the

maximum loss of optimality that the highway agency is willing to accept.

Fig. 6.1 presents a graphical representation of the proposed framework. Stage I of the

framework does not affect the optimality of the computed solution, but Stage II does. The

main difference between the proposed framework and the conventional approach of applying

priority weights to parameters is that the proposed approach permits decision makers to know

precisely the effects of introducing prioritization on the final pavement maintenance program,

while this is not possible when the conventional approach is adopted.

128

6.3 PART ONE – PROGRAMMING INVOLVING PRIORITY WEIGHTED PARAMETERS

6.3.1 Formulation and Analysis of Example Problem

A network of 150 one-km pavement sections, each with three possible forms of

distresses: raveling, rutting and cracking. Table 6.1 lists the highway class and distress

characteristics of the 150 pavement sections. To facilitate illustration, only 4 possible

maintenance options are considered for each pavement section: (1) No action, (2) patching, (3)

premix leveling, and (4) crack sealing. Table 6.2 gives the cost data for the maintenance

treatments. The sample problem is analyzed to minimize maintenance cost with the only

constraint of maintaining individual pavement section and average network PCI (ASTM,

2007) level above 55 and 70 respectively. The problem formulation can be represented

mathematically as follows:

Objective function: Minimize ∑=

N

1iiiCw (6.1)

Subject to: (i) PCIj ≥ 55 j = 1, 2, …, 150 (6.2)

(ii) Network average PCI ≥ 70 (6.3)

where wi is the priority weight assigned to distress i, Ci is the cost for repairing distress i, N is

the total number of pavement distresses, and PCIj is the Pavement Condition Index of

pavement section j. The PCI of a pavement section is computed by the following equation in

accordance with ASTM (2007):

PCIj = 100 - (TDV)j (6.4)

where TDV is total deduct value and is the sum of individual deduct values (DV) for each

distress type. If two or more individual deduct values are greater than two, the corrected

deduct value (CDV) is used instead of the total deduct value (TDV) in determining the PCI as

follows,

PCIj = 100 - (CDVm)j (6.5)

129

where CDVm is the maximum corrected deduct value. Pavement condition index lies within

the range of 0-100. The lower the PCI value, the worse the condition of the pavement is.

Any suitable optimization technique could be employed to solve the above example

problem for the purpose of the present study. In this chapter, the genetic-algorithm

optimization method, which has been shown by pavement researchers to be an efficient tool

to solve pavement programming problems (Chan et al., 1994; Fwa et al., 1994a; Ferreira et al.,

2002; Tack and Chou, 2002), is adopted. A population size of 300 was adopted for the simple

genetic algorithms analysis, with a replacement proportion of 0.10. The crossover and

mutation rates were 0.85 and 0.05 respectively.

6.3.1.1 Analysis (i): Comparison of Different Priority Schemes

To study the effects of adopting different priority schemes, the example problem is

solved for the following schemes of priority weights:

• Scheme A (No priority weights are applied) -- wi in Equation (6.1) is set as 1.0 for

all pavement distresses. wiCi in this case is equal to Ci.

• Scheme B (Priority weights based on distress type) -- Multiply the maintenance

cost of a distress by the assigned priority weight to obtain wiCi in Equation (6.1).

• Scheme C (Priority weights based on distress severity level) -- Multiply the

maintenance cost of a distress by the assigned priority weight to obtain wiCi.

• Scheme D (Priority weights based on highway class) -- A value of wi is given to

pavement distress i depending on the highway class it is located in. Multiply the

maintenance cost of a distress by this priority weight to obtain wiCi.

• Scheme (B+C) – wiCi of a distress is calculated as the product of its maintenance

cost and its aggregated priority weight wi for distress type and severity level. The

aggregated priority weight wi is computed as the sum of the distress’ priority

weight for distress type and its priority weight for severity level.

130

• Scheme (B+D) – wiCi of a distress is calculated as the product of its maintenance

cost and its aggregated priority weight wi for distress type and highway class. The

aggregated priority weight wi is computed as the sum of the distress’ priority

weight for distress type and its priority weight for highway class.

• Scheme (C+D) – wiCi of a distress is calculated as the product of its maintenance

cost and its aggregated priority weight wi for distress severity level and highway

class. The aggregated priority weight wi is computed as the sum of the distress’

priority weight for severity level and its priority weight for highway class.

• Scheme (B+C+D) -- wiCi of a distress is calculated as the product of its

maintenance cost and its aggregated priority weight wi for distress type, severity

level and highway class. The aggregated priority weight wi is computed as the sum

of the distress’ priority weights for distress type, severity level and highway class.

Table 6.3 gives the priority preferences assigned and the corresponding priority weights wi ,

respectively, for Schemes B, C, D and E. Since the optimization process aims to minimize

the objective function, a priority weight wi is expressed as (101 – priority preference score).

The total maintenance cost for each of the 5 schemes analyzed is listed in column 2 of Table

6.4. The following observations can be made:

(1) The most optimal solution (i.e. solution with the lowest total maintenance cost) is

obtained with Scheme A in which no priority weights are applied to any of the

problem parameters.

(2) Comparing the solutions of Schemes A, B, C and D, it is seen that applying

priority weights to any of the problem parameters will cause the final solution to

become sub-optimal. For the example problem analyzed, the magnitude of sub-

optimality is of the order of 11.09 to 40.36%.

131

(3) The solution will become increasingly sub-optimal when priority weights are

applied to a larger number of problem parameters (see Fig. 6.2). For the present

problem, the magnitude of sub-optimality varies from 58.20 to 69.36% when two

parameters are prioritized, and equals to 70.58% when three parameters are

prioritized in the analysis.

6.3.1.2 Analysis (ii): Study of Effects of Changing Magnitudes of Priority Weights

This analysis is performed to illustrate the differences in solutions caused by changing

the magnitudes of priority weights. For Scheme C in Table 6.4, instead of having a priority

preference score of 45 for medium severity of distresses, two additional cases with the scores

for medium severity of 15 (Scheme C1) and 85 (Scheme C2) respectively, as given below are

considered:

Scheme C: 1 for low severity, 45 for medium, and 100 for high severity.

Scheme C1: 1 for low severity, 15 for medium, and 100 for high severity.

Scheme C2: 1 for low severity, 85 for medium, and 100 for high severity.

The results of analysis as shown in column 3 of Table 6.4 indicate the following effects:

(1) Comparing the total maintenance costs of Schemes C, C1 and C2, Scheme C2

suffers the highest loss (44.12%) in optimality, while Scheme C1 has the least

loss (27.33%) in optimality. However, the magnitudes of loss in optimality are

not linearly proportional to the changes made in priority weights.

(2) Using the non-prioritized Scheme A (i.e. the case without priority weights, or all

parameters having the identical weights of 1) as the reference, among the three

priority schemes C, C1 and C2, the priority weights of Scheme C2 has the largest

deviation from Scheme A, while Scheme C1 has the smallest deviation. This

suggests that larger the priority weights deviate from the non-prioritized scheme,

132

the larger is the difference of the solution from the optimal solution (i.e. larger

loss of optimality).

6.3.1.3 Analysis (iii): Study Effects of Changing Range of Priority Weights

This analysis illustrates the effects of changing the range of priority weights in a given

priority scheme. Again, two variations of Scheme C are analyzed by setting the range from 1

to 100 to 1 to 50 (Scheme C3) and 1 to 10 (Scheme C4) respectively, as given below are

considered:

Scheme C: 1 for low severity, 45 for medium, and 100 for high severity.

Scheme C3: 1 for low severity, 22.5 for medium, and 50 for high severity.

Scheme C4: 1 for low severity, 4.5 for medium, and 10 for high severity.

From the results presented in column 3 of Table 6.4, the following trends are noted:

(1) Scheme C with the widest range and the largest maximum priority values has the

largest loss (40.86 %) in optimality, while Scheme C4 with the narrowest range

and smallest maximum priority value produces the least loss (27.33%) in

optimality. The losses are neither linearly proportional to their ranges nor

maximum priority values.

(2) The results suggest that a scheme having priority weights with a larger deviation

from the non-prioritized Scheme A (with all parameters having the identical

weights of 1) will suffer a higher loss in optimality.

6.3.2 Summary Remarks

The numerical examples presented in the preceding sections analyzes the effects of

several common priority weighting schemes in pavement maintenance programming, and

serves to highlight some interesting effects of such schemes on the final computed

maintenance program as summarized below:

133

(1) The optimality of the computed maintenance program will be affected regardless of

the form of priority scheme applied. The magnitude of loss in optimality varies

depending on the parameters chosen to be prioritized.

(2) Having decided on the parameters to receive priority weights and the form of priority

scheme structure, the magnitude of loss of optimality will also change with the range

of priority weights selected, and the relative magnitudes of the priority weights

assigned.

(3) The results of the analyses indicate that the variations in the losses of optimality are

not linearly related to the changes made in the priority weights. There does not

appear to be a straight-forward way by which the variations in the loss of optimality

can be predicted or estimated.

6.4 PART TWO – PROPOSED MAINTENANCE PROGRAMMING FRAMEWORK

As explained earlier under Section 6.2 on the Framework of Study Methodology, the

proposed procedure to overcome the issues highlighted in Part One of this chapter involves

first solving the optimal maintenance programming problem without applying any priority

weights, followed by two post-processing stages: tie-breaking analysis and trade-off analysis.

6.4.1 Step I – Tie-Breaking Analysis

Once the optimization programming has generated the optimal pavement maintenance

strategy, the tie-breaking analysis is performed to probe for “ties” and replace maintenance

activities in the optimal strategy by suitable “tied” unselected maintenance activities with

higher priority values. This post-processing of the optimal maintenance strategy does not

change the optimal objective function value of strategy. The detailed execution of tie-

breaking is as follows:

134

(1) Pick a maintenance activity Xi in the optimal strategy and identify all its “tied”

unselected maintenance activities.

(2) Rank the unselected “tied” maintenance activities according to their priority values.

(3) Starting from the highest ranked “tied” activity, replace activity Xi in the optimal

strategy with the “tied” activity and check if any of the constraints in the problem

formulation (i.e. Eq. (6.2) and (6.3) for the example problem in this chapter) is

violated. If none of the constraints is violated, then this “tied” activity will replace Xi

to become a new selected activity in the optimal strategy, and move to Step (4). If

one or more of the constraints are violated, abandon this “tied” activity and move on

to consider the next higher ranked “tied” activity. Move to Step (4) when a successful

“tied” activity in the list is found. If no feasible “tied” activity can be found in the list,

then keep Xi in the optimal strategy and move to Step (4).

(4) Move to Step (1) to examine the next Xi. The tie-breaking process ends when all

maintenance activities in the optimal strategy have been examined.

The above process can be executed using dynamic programming (Bellman, 1957) with the

following mathematical formulation:

Maximize ∑=

n

1ii )Yactivity of scores(Priority (6.6)

Subject to: (i) Total maintenance cost = CT (6.7)

(ii) PCIj ≥ 55 j = 1, 2, …, 150 (6.8)

(iii) Network average PCI ≥ 70 (6.9)

where Yi refers to a maintenance activity which is not within the original optimal

maintenance program but is chosen to enter the maintenance program by replacing a tied non-

prioritized or lower priority activity in the original optimal maintenance program; n is the

total number of Yi selected to enter the maintenance program; CT is the original optimal

135

maintenance cost (which is equal to S$1,534,441 for the example problem, see Table 6.4);

PCIj is the pavement condition index of pavement section j; and PCI is as defined by Eq.

(6.4).

Using the example problem presented earlier in this chapter, a tie-breaking analysis is

performed to implement priority Scheme C (i.e. priorities are assigned according to distress

severity levels). As explained earlier, the tie-breaking analysis is performed on the optimal

solution of the baseline case Scheme A (i.e. the case without no priority weights, see Table

6.4). An illustration of the tie-breaking analysis is given in Fig. 6.3 where the tie-breaking

process for two non-prioritized maintenance activities is shown. Activity ID-463 is a non-

prioritized treatment to a medium severity rutting with a cost of S$10,159. There are two tied

activities: ID-503 and ID-812 with priority preference scores of 45 and 100 respectively. It

turns out that none of the three activities can replace Activity ID-3 because in each case, one

of the two PCI constraints in Eqs. (6.2) and (6.3) will be violated. Hence, Activity ID-463

will stay in the optimal maintenance program. Next, for Activity ID-104, there are three tied

activities: ID-183, ID-24 and ID-344 with priority preference scores of 45, 1 and 1

respectively. Activity ID-183 is selected to replace Activity ID-104 because it has higher

priority than the latter, and the replacement does not violate either of the two constraints of

the problem.

The tie breaking analysis is performed for every maintenance activities in the optimal

maintenance program, including prioritized maintenance activities. Prioritized maintenance

activities have to be checked for tie-breaking too because they might have tied unselected

prioritized activities with higher priority than them. As shown in Table 6.5, for the example

problem, the tie-breaking analysis phase leads to 12 non-prioritized or low-priority

maintenance activities being replaced by higher priority activities, with no change in the

optimal total maintenance cost.

136

It should be mentioned that it is possible for tied prioritized activities to have the same

priority score. Under such situation, further tie-breaking is necessary by seeking

differentiating preferences from the highway agency based on other parameters. For instance,

for Scheme C prioritized activities with identical priority scores based on distress severity, a

secondary tie-breaking parameter (or more parameters) can be chosen. A database for such

priority preferences can be obtained in advance from the highway agency concerned by

means of the analytic hierarchy process (AHP) (Saaty, 1980) as illustrated by Farhan and

Fwa (2009).

6.4.2 Stage II – Trade-Off Analysis

After making adjustments to the optimal maintenance strategy by the tie-breaking

analysis, a trade-off analysis is next performed to select additional prioritized maintenance

activities to replace some of the lower priority maintenance activities in the optimal strategy.

Each of such replacements will cause some loss in optimality. A trade-off analysis is thus

necessary to determine which prioritized activities are to be included, and which non-

prioritized or lower-priority activities are to be replaced. The outcome of the analysis is

directly dependent on maximum loss in optimality the highway agency is willing to accept.

The trade-off analysis can thus be performed by solving the following optimization problem:

Maximize ∑=

n

1ii )Yactivity of scores(Priority (6.10)

Subject to: (i) Total maintenance cost ≤ {1 + (δ/100)}CT (6.11)

(ii) PCIj ≥ 55 j = 1, 2, …, 150 (6.12)

(iii) Network average PCI ≥ 70 (6.13)

where Yi refers to a maintenance activity which is not within the original optimal

maintenance program but is chosen to enter the maintenance program either as an additional

maintenance activity or by replacing a non-prioritized or lower priority activity in the original

137

optimal maintenance program; n is the total number of Yi selected to enter the maintenance

program; CT is the original optimal maintenance cost (which is equal to S$1,534,441 for the

example problem, see Table 6.4); δ is the maximum accepted percent increase in

maintenance cost over CT, and is equal to the maximum loss in optimality acceptable by the

highway agency concerned; PCIj is the pavement condition index of pavement section j; and

PCI is as defined by Eq. (6.4).

The trade-off optimization problem formulated above is solved by means of dynamic

programming. The objective function has been selected so that as many high priority

maintenance activities as permissible will be selected to enter the maintenance program. The

proposed trade-off analysis can be illustrated by continuing the example problem that has

been solved in the preceding section up to the stage of tie-breaking analysis. The input to the

trade-off analysis phase includes the optimal maintenance program revised by the tie-

breaking analysis, and the percent loss of optimality acceptable by the highway agency

concerned.

For illustration, the trade-off optimization for the example problem is solved for 5%,

7.5% and 10% loss of optimality respectively. Table 6.5 shows that 22 new prioritized

activities enter the maintenance program if the acceptable loss of optimality is 5%. The

revised total maintenance cost becomes 4.32% higher than the original optimal total

maintenance cost. For 7.5% acceptable loss in optimality, the corresponding new prioritized

activities in the revised maintenance program and extra maintenance cost percentage are 28

and 7.48%; and for 10% acceptable loss in optimality, the corresponding values are 33 and

9.56%. The results show that a higher acceptable loss in optimality will bring more

prioritized activities in the maintenance program at the price of having to increase the

maintenance budget.

138

6.5 COMPARISON OF PROPOSED METHOD AND CONVENTIONAL PRIORITY WEIGHT APPROACH

The proposed methodology to incorporate highway agency’s maintenance priority

preference has the following advantages over the conventional priority weight approach:

• The conventional approach produces a sub-optimal solution and the highway agency

concerned does not know how much loss in optimality has been caused by their

choice of priority scheme. In contrast, with the proposed approach, the highway

agency knows the loss in optimality associated with the priority scheme adopted.

• The proposed approach allows the highway agency to examine how changes in the

magnitudes of priority weights as well as the form of priority scheme structure would

affect the optimality of the solutions. This feature and flexibility for effective

maintenance planning is not available to the user of the conventional priority

approach.

• The tie-breaking post-processing in the proposed approach ensures that as many of the

prioritized maintenance activities as possible are included in the maintenance program,

without affecting the optimality of the solution. The highway agency could end the

programming process with this optimal solution (i.e. not proceeding with the trade-off

analysis) if they do not wish to compromise the optimality of the solution. This

option is not available in the conventional approach.

• The trade-off analysis offers a choice to the highway agency if they are willing to

accept some loss in optimality in order to include more prioritized activities in the

maintenance program. The user could vary the level of acceptable maximum loss and

make an informed decision accordingly. Such in-depth trade-off analysis cannot be

performed in the standard solution format of the typical conventional approach.

139

6.6 SUMMARY

This chapter has highlighted the issues associated with the conventional priority

weighting approach in optimal pavement maintenance programming. By incorporating

priority weights directly into the mathematical formulation, a sub-optimal solution is obtained.

Unfortunately, many users of the approach are unaware of this fact and do not know the

magnitude of loss in optimality caused by their choice of priority scheme.

An improved procedure of incorporating a user’s priority preferences into the

pavement maintenance programming process has been demonstrated. It allows the highway

agency to decide if they are willing to settle with a sub-optimal solution by including more

prioritized activities in the final maintenance program. If the user is not willing to

compromise on the optimality of the solution, the proposed procedure will produce the

optimal solution while having as many prioritized activities in the final program as possible

through the tie-breaking analysis. It is believed that the proposed procedure helps to improve

the effectiveness of pavement maintenance planning and management by allowing the

highway agency to know the effects of their decision in setting priorities, and putting them in

a better position to make informed decisions. In the following chapter, the proposed

approach is applied to a budget allocation problem in highway asset management.

140

TABLE 6.1. Pavement distress data for example problem

PAVEMENT SEGMENTS 1-50 51-100 101-150

Ravel Rut Crack Ravel Rut Crack Ravel Rut Crack L-19 M-24 L-21 M-4 M-2 M-24 M-29 M-12 M-21 L-26 L-8 L-13 L-28 L-15 L-26 M-2 M-21 M-13 M-13 M-14 M-1 H-19 M-18 H-20 H-23 H-25 H-1 M-1 L-34 M-17 H-30 H-20 H-28 H-1 H-18 H-17 M-29 M-6 M-18 M-29 M-22 M-18 M-19 M-27 M-18 H-4 M-7 H-28 M-21 L-36 M-6 M-16 H-6 M-28 L-7 M-39 L-1 L-22 L-2 L-6 L-6 L-22 L-1

L-22 L-33 L-25 M-25 M-38 M-22 H-3 M-26 H-25 H-24 L-23 H-21 H-21 M-36 H-13 M-4 L-10 M-21 H-13 L-32 L-13 M-4 L-24 M-5 H-17 H-34 H-13 L-5 L-20 L-16 H-27 M-9 H-24 M-8 L-3 M-16 H-9 M-23 H-12 M-23 L-39 M-12 M-2 M-3 M-12

M-13 L-28 M-1 M-1 H-14 M-13 L-24 M-3 L-1 L-21 L-39 L-16 M-2 M-20 M-5 H-10 M-27 H-16 M-19 M-19 M-27 H-6 H-40 H-25 H-20 H-10 H-27 H-26 M-30 H-8 M-29 M-16 M-20 M-7 M-34 M-8 L-26 M-18 L-5 L-22 L-3 L-16 H-25 L-28 H-5 H-12 M-35 H-29 L-8 M-6 L-25 M-21 L-6 M-29 M-27 L-24 M-19 M-6 L-34 M-9 H-12 M-28 H-19 M-6 L-6 M-8 H-9 M-12 H-30 H-17 L-32 H-8 H-25 L-35 H-24 H-13 L-31 H-12 M-16 M-1 M-24 H-24 M-6 H-23 M-9 L-16 M-3 L-12 H-16 L-23 M-7 M-1 M-6 M-26 H-18 M-17 M-23 L-29 M-6 M-2 M-27 M-20 M-11 L-30 M-29 L-28 M-13 L-20 M-25 M-29 M-23 M-12 L-8 M-20 M-20 M-23 M-23 L-16 M-21 L-25 M-28 M-32 M-23 M-9 L-6 M-25 M-20 L-15 M-25 L-17 H-22 L-2 M-4 L-34 M-25 H-23 M-23 H-13 H-12 L-8 H-26 M-29 L-25 M-13 M-4 L-8 M-12 H-12 H-14 H-16 L-8 M-24 L-12 L-28 M-19 L-19 L-1 H-18 L-28 M-15 H-13 M-19 M-15 M-21 M-20 H-37 L-5 M-22 L-22 L-31 L-20 L-6 H-22 L-15 L-29 L-19 L-16 M-28 M-8 M-15

M-14 M-3 M-23 M-18 M-18 M-13 H-17 M-21 H-23 L-29 L-13 L-13 L-19 L-17 L-19 L-9 H-18 L-13 M-23 L-7 M-16 H-23 M-15 H-19 L-3 M-24 L-16 M-29 L-12 L-13 L-25 M-38 L-11 L-21 L-39 L-13 M-29 H-5 M-23 M-29 L-31 M-15 H-27 L-35 H-23 M-24 L-28 M-6 L-30 L-37 L-15 H-9 M-21 H-6 H-12 L-28 H-7 H-24 M-28 H-22 H-6 H-22 H-7 M-11 L-32 M-1 L-25 M-10 L-1 L-23 H-10 L-1 H-8 L-22 H-3 H-13 L-33 H-8 L-16 H-27 L-3 L-7 M-14 L-25 H-27 L-29 H-25 L-19 L-19 L-25 M-5 L-32 M-5 L-11 M-6 L-30 H-16 M-19 H-5 L-18 L-29 L-29 L-27 L-33 L-11 L-27 M-22 L-29 M-18 L-36 M-9 M-28 L-22 M-8 M-8 L-18 M-9 M-18 L-35 M-27 L-7 L-25 L-21 L-23 L-10 L-27 H-7 M-23 H-23 H-6 L-33 H-21 H-21 L-32 H-23 M-4 M-13 M-6 M-21 L-16 M-26 L-23 L-35 L-6 L-25 M-4 L-16 M-28 L-40 M-6 M-5 M-32 M-16 M-30 M-31 M-2 H-1 L-23 H-3 M-1 H-9 M-2

Note: Each cell in the table contains a two-part code A-B, where A represents distress severity with H, M and L denoting high, medium and low severity respectively; and B is a numerical value delineating the distress extent with the unit of percentage area affected.

141

TABLE 6.2. Cost data for the example problem

Distress Type Maintenance Cost

Maintenance cost per unit in Singapore dollars (S$)

Distress Severity Level

Low Moderate High

Raveling (S$/m2) 1.00 1.85 2.75 Rutting (S$/m2) 2.00 2.20 3.85 Cracking (S$/m) 6.00 6.00 6.00

Note: S$ represents Singapore dollar

TABLE 6.3. Priority Preference scores for pavement maintenance activities

Parameter Preference Score

Scheme D -Highway Class Expressway 100 Arterial 65 Access 1 Scheme B -Distress Types Raveling 100 Cracking 60 Rutting 1 Scheme C -Distress Severity High 100 Medium 45 Low 1

142

TABLE 6.4. Results from analysis of different priority schemes

Description Actual Cost (S$)

Loss in Optimality (%)

Scheme A 1,534,441 0 Scheme B 1,939,729 26.41 Scheme D 1,704,665 11.09 Scheme C 2,161,460 40.86 − Scheme C1 2,042,460 33.11 − Scheme C2 2,211,440 44.12 − Scheme C3 2,098,040 36.73 − Scheme C4 1,953,840 27.33 Scheme (B+C) 2,598,680 69.36 Scheme (B+D) 2,427,460 58.20 Scheme (C+D) 2,508,660 63.49 Scheme (B+C+D) 2,617,440 70.58

TABLE 6.5. Results of trade-off analysis.

Description

Acceptable Loss in

Optimality (%)

Total Maintenance

Cost (S$)

Number of Lower

Priority Activities Replaced

(Nos.)

Number of Prioritized Activities

Added without Replacing

Lower Priority Activities

(Nos.)

Total Number of

New Prioritized Activities in Maintenance

Program (Nos.)

Analysis A 0 1,534,441 -- -- -- Tie-Breaking

Analysis 0 1,534,441 12 0 12

Trade-off Analysis

5 1,595,698 18 4 22

7.5 1,644,139 21 7 28

10 1,675,860 22 11 33

143

Problem Input-Pavement section data (location, highway

class, section length, geometric data)-Pavement distress data (location, distress

type, distress severity, distress extent)

State objective and constraints and establish mathematical formulation

Perform optimal maintenance programming using genetic algorithm

Perform tie-breaking using dynamic programming

Perform trade-off using dynamic programming

Output revised pavement

maintenance program

Output optimal pavement

maintenance program

Input priority scheme

Input acceptable

loss in optimality

Loss in optimality acceptable for preference

incorporation?

No

Yes

FIGURE 6.1. Framework of the proposed approach

0.0E+00

5.0E+05

1.0E+06

1.5E+06

2.0E+06

2.5E+06

3.0E+06

3.5E+06

4.0E+06

A B D C (B+C) (B+D) (C+D) (B+C+D)Priority Scheme

Tot

al M

aint

enan

ce C

ost (

S$)

0

20

40

60

80

100L

oss i

n O

ptim

ality

(%)

Total Maintenance Cost (S$)Loss in Optimality (%)

FIGURE 6.2. Loss in optimality versus employed priority scheme

Three prioritized parameters

No prioritized parameters

One prioritized parameters

Two prioritized parameters

144

Note: * Unselected prioritized activities are ranked in decreasing magnitude of priority scores ** Infeasible means that the replacement cannot be carried out because entering the

unselected prioritized activity into the maintenance program will violate one or more of the constraints of the problem.

FIGURE 6.3. Illustration of the process of tie-breaking analysis

Activities in Optimal Maintenance Program

Ranked Unselected Prioritized Activities*

Tie-Breaking Decision

•

Activity ID-463 Rutting, Low

Severity, S$10,159

Infeasible**

Infeasible**

Decision : Activity ID-463 stays in maintenance program.

•

Feasible

Decision : Activity ID-183 replaces

Activity ID-104 in

•

Activity ID-104 Cracking, Low

Severity, S$11,480

Activity ID-183 Rutting, Medium Severity, S$11,480


Severity, S$11,480


Severity, S$11,480

Activity ID-503 Rutting, Medium Severity, S$10,159

Activity ID-812 Raveling, High

Severity, S$10,159

•

•

• •

•

•

145

CHAPTER 7

OPTIMAL BUDGET ALLOCATION IN HIGHWAY ASSET MANAGEMENT

7.1 INTRODUCTION

This chapter presents an example application of the proposed integrated prioritization

and optimization approach to the optimal budget allocation problem of highway asset

management. In highway asset management, the objectives required to be achieved for each

individual asset system, as well as the overall highway asset system, are often multiple and

sometimes mutually conflicting. To achieve the best results at both the individual asset

system and the overall system levels when a given overall budget is available, an optimal

scheme for fund allocation to individual assets needs to be identified. This necessitates the

simultaneous maximization and/or minimization of more than one objective, while satisfying

all the necessary constraints.

The conventional practices of fund appropriation among competing highway asset

components within a certain district can be grouped broadly into 5 approaches as described

below:

(A) Appropriation based on historical allocation proportions -- The funds allocated to the

individual asset items are based on the proportions adopted historically, with minor

adjustments made to allow for special projects or requirements (Barber and Bland,

2008; OECD, 2001). This approach does not optimize at the overall system level.

Although optimal programming can be performed at the individual asset level based

on the fund allocated, the allocated fund may not be sufficient to meet the

maintenance needs to maintain a desired level of service for some asset items.

146

(B) Formula-based appropriation – Funds are allocated according to a predetermined

formula consisting of selected parameters from the various assets (Behrens, 2006;

MnDOT, 2006). Although relatively simple and convenient to implement, this

approach also suffers from the same drawbacks of approach (A) of not achieving

optimality at both the individual asset and overall system levels.

(C) Asset value-based appropriation -- This approach implicitly assumes that the

maintenance needs of each asset component is proportional to its asset value (Jani,

2007, Sirirangsi et al., 2003). Since this assumption is unlikely to hold for different

highway asset items that deteriorate at different rates, optimality at both the individual

asset and the overall system levels cannot be guaranteed.

(D) Needs-based appropriation – This approach involves funds appropriation in

accordance with the maintenance needs for each asset component (Ekern, 2006;

AMATS, 2008; NDOR, 2008; Flintsch and Bryant, 2006). It presents an

improvement over the previous two approaches by allocating the available funds in

proportion to the maintenance needs of each individual asset. However, the

proportions so determined do not address optimality for the overall asset system.

(E) Performance-based appropriation – This approach ties fund appropriation with the

desired performance level of each asset component. Some studies developed a

common performance indicator for all asset items, and allocated funds in proportion

to their performance indicator values (Gharaibeh et al., 1999 and 2006; Cowe Falls et

al., 2006). As in the case of approach (D), this approach does not address the

optimality of the overall asset system specifically. Another approach adopted by

some agencies is to convert various parameters or performance measures into a

system-wide multi-attribute utility function that is used for fund allocation to various

assets. Though convenient to use, such empirical indices do not have a clear physical

147

meaning, and could not accurately and effectively represent the maintenance needs or

performance levels of individual asset systems. As such, it is difficult to assess how

well optimality at the individual asset systems and the overall system levels has been

achieved using this approach.

In highway asset budget allocation, it is desirable to allocate the available fund to individual

asset systems in a certain district so that the following outcomes could be obtained: (i) the

maintenance needs of each asset component can be adequately addressed such that the pre-

determined desired performance level for each asset component can be achieved or exceeded;

(ii) the objectives (often more than one for each asset) of the various component systems are

optimally satisfied in an equitable manner; and (iii) the combined performance of all asset

components would contribute to achieving the overall highway asset level objectives in an

optimal manner. The conventional approaches as described above do not address adequately

the various issues required for achieving these three desirable outcomes.

To overcome the limitations of the conventional approaches, this chapter presents a

two-stage approach to solve the budget allocation problem of highway asset management

involving competing asset systems in a district, each with its own multiple operational

objectives. Stage I of the approach analyzes the individual multi-objective asset systems

independently to establish for each a family of optimal Pareto solutions using the approach

presented in Chapter 6. Stage II adopts an optimal algorithm to allocate budget to individual

assets by allowing interaction between the overall system level and the individual asset level,

and performing cross-asset trade-off to achieve the optimal budget solution for the given

overall system level objectives. The framework and execution of the proposed approach is

demonstrated through an analysis of a 3-asset highway network system.

7.2 FRAMEWORK OF PROPOSED APPROACH

148

For ease and clarity of presentation, the explanation of the proposed approach is

presented in this chapter based on a 3-asset highway network system. The three asset

components are pavements, bridges, and highway appurtenances of a given road network. As

depicted in Figure 7.1 which shows the framework of analysis of the proposed approach, the

overall highway asset management system comprises three sub-management systems as

follows: pavement management system (PMS), bridge management systems (BMS), and

appurtenances management system (AMS).

Figure 7.1 indicates that Stage I of the approach basically represents the currently

prevailing practice of having independent individual asset management systems, each

addressing operational and service objectives unique to itself but also having a common

objective in minimizing maintenance costs. The multi-objective optimization for each asset

management system will produce a family of Pareto optimal solutions. By having

maintenance cost optimization as an objective common to the three asset management

systems, it offers a convenient basis for performing cross-asset trade-off analysis to compare

the outcomes of different fund allocation strategies.

In Stage II, making use of these Pareto optimal solutions of the individual asset

systems, an optimal budget allocation analysis is carried out with the following inputs: (i) a

known overall amount of maintenance budget available for the entire road network, and (ii)

pre-determined network level objectives for the optimization analysis. The Stage I Pareto

optimal solutions of the individual asset systems offer the links for interaction with the

optimization analysis in Stage II. For any trial plan of funds allocated to individual asset

systems, these links provide feedback on asset performance information to the Stage II

optimization process where cross-asset trade-off analysis is conducted to arrive at the optimal

budget allocation strategy.

149

In Figure 7.1, although genetic algorithms are identified as the optimization tool for

Stage I analysis, and dynamic programming for Stage II for optimization analysis in this

chapter for illustration purpose, other suitable optimization tools can be used without

affecting the validity of the proposed conceptual framework.

7.3 FORMULATION OF BUDGET ALLOCATION MODEL

As indicated earlier, the formulation of the proposed budget allocation model will be

illustrated using a 3-asset highway network system. This section presents the mathematical

formulation of the optimization models for the three asset management systems, as well as

that for the overall highway system.

7.3.1 Stage I – Asset System Number 1: Pavement Management System

In this formulation, the pavement condition of a pavement section is represented by

the Pavement Condition Index (PCI), which is an ASTM standard for the pavement condition

assessment (ASTM, 2007). PCI values are assigned to distresses on a scale from 0 to 100

based on distress type, density and severity, for any pavement section j, is computed by the

following equation:

PCIj = 100 - (TDV)j (7.1)

where TDV is the total deduct value equal to the sum of individual deduct values (DV) for

each distress present in the pavement section, computed according to the procedure set out in

ASTM (2007). The PCI value varies from 100 for a perfect pavement condition to 0 for the

worst condition.

The model formulation is developed for the pavement management system (PMS)

with two objectives, namely maximization of the pavement network average PCI and

minimization of the total pavement maintenance cost. It has the constraint that the PCI of

150

each pavement section must fall below a pre-defined level. Thus, the Stage I optimization

model for PMS can be represented mathematically as follows:

Objective function:

(i) Minimize maintenance cost: Minimize ∑=

N

jjC

1 , and (7.2)

(ii) Maximize network average PCI: Maximize ∑=

N

jj NPCI

1 (7.3)

Subject to: PCIj ≥ α1 j = 1, 2, …, N (7.4)

where Ci is the maintenance cost for pavement section j, N is the total number of pavement

sections, and PCIj is the Pavement Condition Index of pavement section j. α1 represents the

required minimum pavement condition threshold for each pavement section.

Solving the formulated problem given by Eq. (7.2) to (7.4) will provide a family of

Pareto optimal solutions. Each solution in the Pareto family gives the optimal maintenance

program and the resultant network average PCI for the corresponding amount of the

maintenance cost spent (i.e. the budget amount allocated).

7.3.2 Stage I – Asset System Number 2: Bridge Management System

For illustration, the AASHTO (1997) guidelines are adopted to define five discrete

“condition states” for each bridge element, ranging from 1 to 5 where 1 and 5 represent the

best and the worst condition states respectively. Bridge elements consist of structural

members of bridge deck, superstructure, and substructure. The overall condition of the

bridge is measured in terms of Bridge Health Index (BHI) as proposed by Shepard and

Johnson (2001). BHI ranges from 0% in the worst state to 100% in the best condition. The

health index of an element is determined as follows,

151

100

1

1 ×=

∑

∑

=

=M

ss

M

sss

e

q

qkH (7.5)

where He denotes the health index of element e, s is an index that denotes the condition state

of the element, M is the total number of condition states, qs represents the element quantity in

sth condition state, and ks is a health index coefficient computed by Eq. (6) for the sth

condition state:

1−−

=n

snks (7.6)

where n represents number of the number of applicable condition states. According to the

procedure by Shepard and Johnson (2001), the number of applicable condition states varies

from 1 to 5, where 1 and 5 represents perfect and worse condition state respectively.

The health index of the entire bridge is given by

∑

∑

=

== M

see

M

seee

WQ

WQHBHI

1

1 (7.7)

where BHI, Qe, and We denotes the bridge health index, total quantity of element e and

weighting factor of element e of a bridge respectively.

In the present study, the optimization model formulation is developed for the bridge

management system (BMS) with two objectives, namely maximization of the pavement

network average BHI and minimization of the total pavement maintenance cost, subject to the

constraint of having to maintain the BHI of each individual bridge at a pre-defined level. The

problem can be mathematically represented as follows:

Objective function:

(i) Minimize maintenance cost: Minimize ∑∑∑= = =

P

i

K

j

M

sijsC

1 1 1 and (7.8)

152

(ii) Maximize network average BHI: Maximize PBHIP

jj∑

=1 (7.9)

Subject to: BHIj ≥ α2 j = 1, 2, …, n (7.10)

where Cijs is the cost for repairing element j in condition state s of bridge i, P, K and M are

the total number of bridges, bridge elements, and condition states respectively, and BHIj is

the Bridge Health Index of bridge j. α2 represent the minimum bridge health threshold

specified for each bridge in the network.

Solving the formulated problem given by Equations (8) to (10) will provide a family

of Pareto optimal solutions. Each solution in the Pareto family gives the optimal maintenance

program and the resultant network average BHI for the corresponding amount of the

maintenance cost spent (i.e. the budget amount allocated).

7.3.3 Stage I – Asset System Number 3: Appurtenance Management System

Highway appurtenances such as guardrails, signs, and luminaries are facilities

important for safe and efficient traffic operations. The condition state of these facilities can

be approximately expressed as a function of the accumulative length of their service time

(NCHRP, 2007). Similarly, their probability of failure usually increases as the length of

cumulative service time becomes longer. In other words, the level of service of these

facilities is positively related to the length of their remaining service lives. Therefore, it is

acceptable to represent the condition of each highway appurtenance element in terms of its

remaining life expressed as a percentage of its design service life.

Taking the remaining service life as a performance indicator, the optimal management

model of highway appurtenances can be formulated as one that simultaneously maximizes the

network average performance of all highway appurtenances, and minimizes the total

maintenance cost. Mathematically it is given by the following formulation:

Objective function:

153

(i) Minimize maintenance cost: Minimize∑=

N

iiC

1 (7.11)

(ii) Maximize network average percent remaining life (RSL):

Maximize { }∑∑= =

N

i

L

jiij

i

LRSLN1 1

1 (7.12)

Subject to: RSLij ≥ α3 ∀ i = {1,2,…,N}, j =1, 2, 3. (7.13)

where Ci is the cost for maintaining appurtenances in pavement section i, N is the total

number of pavement sections, RSLij denotes the average percent remaining service life of

appurtenance type j in pavement section i, and α3 represents the minimum average percent

remaining service life specified for each of the appurtenances.

Solving the formulated problem given by Eq. (7.11) to (7.13) will provide a family of

Pareto optimal solutions. Each solution in the Pareto family gives the optimal maintenance

program and the resultant network average percent remaining service life of appurtenances

for the corresponding amount of the maintenance cost spent (i.e. the budget amount

allocated).

7.3.4 Stage II – System-wide Budget Allocation

The Stage I Pareto families of optimal solutions for the three component systems offer

ready inputs to Stage II budget allocation analysis to identify an allocation strategy that will

satisfy the pre-determined system objectives and operational constraints. The forms of

preferred systems objectives and operational constraints vary from highway agency to agency.

For instance, a highway agency may opt to achieve comparable levels of performance of all

the component systems with respect to their respective minimum threshold performance

levels. This budget allocation strategy can be formulated mathematically as follows:

Objective function:

154

Minimize [Max {|(NPCI - α1) – (NBHI - α2)| , |(NPCI - α1) – (NRSL - α3)| ,

|(NRSL - α3) – (NBHI - α2)| }] (7.14)

Subject to: ∑=

−3

1iTiCB ≤ α4 and α4 ≥ 0 (7.15)

where NPCI, NBHI and NRSL represent the network level performance of the following

component systems respectively: Pavement Management System in level of PCI, Bridge

management System in level of BHI, and Appurtenance Management System in level of RSL;

CTi is the total budget allocated to component management system i, and B is the total

available budget for the system-wide asset maintenance program. α1, α2 and α3 are the

minimum threshold performance levels of the corresponding sub-systems as defined earlier in

Eq. (7.4), (7.10) and (7.13). α4 is the maximum difference allowed between the total budget

allocated and available, which is chosen to define the minimum amount of budget the agency

would like to allocate.

The three levels of performance can be compared directly because they have been

defined in such a way in Stage I formulations to facilitate the allocation analysis in Stage II.

Their respective ranges of valid values cover the common range from 0 to 100, and have the

same performance definition that 100 represents the perfect condition, and 0 the worst

condition.

Depending on the preference and requirements of the highway agency concerned,

other forms of system objectives and constraints can be defined and formulated accordingly.

155

7.4 ILLUSTRATIVE NUMERICAL EXAMPLE

7.4.1 Problem Parameters and Input Data

A network of 150 one-km highway sections is considered. For easy illustration, only

three possible forms of distresses are assumed to occur in the pavement in each highway

section: raveling, rutting and cracking. Tables 7.1 and 7.2 list the respective highway class

and maintenance cost data. The distress characteristics data is provided in Table 7.3. The

following 4 possible maintenance options are considered for each pavement section: (1) Do

nothing, (2) patching, (3) premix leveling, and (4) crack sealing.

There are a total of 6 bridges in the highway network. In the Bridge Management

System, a bridge is segregated into three separate elements: deck, superstructure, and

substructure. Bridge element condition is evaluated in terms of up to five discrete “condition

states” ranging from 1 to 5 where 1 and 5 are the best and the worst condition states

respectively. For each bridge element the quantity in each condition state is given in Table

7.4. The maintenance costs are shown in Table 7.5. The overall condition of the bridge is

expressed in terms of bridge health index as explained in Eq. (7.7).

In the present study, three appurtenances namely guardrail, luminaries, and road signs

are considered for the Appurtenance Management System. The condition state of an item is

defined in terms of its remaining service life, and it is assumed that only two actions can be

undertaken at any time over the planning horizon: (1) Do-Nothing, (2) Replacement. The

condition states of the items of an appurtenance type are given in the form of normal

distributions (see Table 7.6), and the costs of replacement are delineated in Table 7.7.

156

7.4.2 Analyses and Results

7.4.2.1 Stage I -- Component Management Systems

In the first stage, the procedure outlined in Fig. 7.1 is applied to each of the three

component systems independently. Any suitable optimization technique could be employed

to solve the above example problem. In this approach, the genetic-algorithm optimization

method, which has been shown by pavement researchers to be an efficient tool to solve

pavement programming problems (Chan et al., 1994; Fwa et al., 1994; Ferreira et al., 2002;

Tack and Chou, 2002; Jha and Abdullah, 2006), is adopted. A population size of 300 was

adopted for the genetic algorithms analysis, with a replacement proportion of 0.10. The

crossover and mutation rates of 0.85 and 0.05 respectively have been found suitable for the

problem.

The performance threshold values selected are α1 = 70 for PCI (see Eq. 7.4), α2 = 70

for BHI (see Eq. 7.10), and α3 = 50 for RSL (see Eq. 7.13) in Stage I analysis; α4 = 10 for Eq.

(7.15) in Stage II analysis. It can be seen that the Pareto frontier of Fig. 7.2 covers a range of

PCI from slight above 70 (the minimum PCI threshold) to about 95; that of Fig. 7.3 from BHI

of slightly above 70 (the minimum BHI threshold) to about 85; and that of Fig. 7.4 from RSL

of slightly above 50% (the minimum RSL threshold) to about 90%. These three plots show

the minimum budget required to meet the maintenance needs in order to maintain the

conditions of the various assets above the minimum threshold. The minimum budget needed

for PMS, BMS and AMS are respectively S$819,770, S$418,210 and S$928,550. These

represent the minimum budgets needed for each of the assets systems to meet their respective

basic maintenance needs (i.e. to meet the minimum condition thresholds). The results also

indicate the high-end budget to be the order of S$1,815,200, S$945,520 and S$4,305,200 for

PMS, BMS and AMS respectively. Hence, the total highway asset management budget for

157

the entire network of the three asset systems should lie between S$2,166,530 and

S$7,065,920. This sets the range of possible budget for Stage II analysis.

7.4.2.2 Stage II – System-wide Budget Allocation

The relationship between condition state and allocated budget for each of the three

component management systems established in the Stage I optimization analyses offer a

convenient database for stage II budget allocation analysis. Dynamic programming, which

has been shown to be a promising tool to solve resource allocation problems (Tack and Chou,

2002; Jiang and Sinha, 1989), is adopted to solve system-wide budget allocation problem.

The optimal shares of budget for the three component systems so determined are presented in

Table 7.8 and plotted in Fig. 7.5 for four different levels of available budget.

The results show the intended outcomes of budget allocation that the overall network

performance levels of the three component asset systems are kept within a comparable

magnitude with respect to their respective minimum threshold levels (i.e. PCI = 70, BHI = 70,

and RSL = 50%). It is also clearly seen from the results that as the available budget increases,

the performance levels of all the component asset systems can be raised correspondingly.

7.5 FRAMEWORK INVOLVING MULTIPLE DISTRICTS

The problem analyzed in Sections 7.2, 7.3 and 7.4 considered only one single central

district administration. A multi-goal multilevel fund allocation problem involving multiple

districts can also be solved by means of a two-stage optimization approach. For the sake of

illustration, the presentation of the proposed approach in this section considers a bi-level

decentralized multiple-district road management structure with two goals per district. The

general concept of the proposed procedure can easily be extended to incorporate multiple

levels of decision making. The proposed method consists of a two-stage optimization process

to determine the budget required system-wide to ensure the serviceability of the asset above a

158

certain level. At the first stage, each district generates optimal strategies with clearly defined

objectives and performance constraints using NSGA-II. At the second stage, the strategies

determined in the first stage would form mutually exclusive alternatives under their

respective districts. The system-wide management strategy is determined using dynamic

programming with the objective of achieving a consistent improvement in the performance

across all districts while keeping available budget as a constraint. An overview of the

proposed methodology is presented in Fig. 7.6.

7.5.1 Stage I - Budget Allocation within Districts

The process begins with defining a set of pavement management system objectives

and performance indicators for each district. The system goals at district levels can be

represented as objective functions of the optimization analysis, and include but are not

limited to:

(i) Maximizing the performance level of road network pavements;

(ii) Maximizing safety;

(iii) Minimizing user costs;

(iv) Minimizing the total manpower required;

(v) Maximizing the number of distressed road segments repaired; and

(vi) Minimizing the total pavement maintenance expenditure.

A mathematical optimization model, given a set of goals, is developed for each district level

management system for a certain analysis period, and is solved using NSGA-II resulting in a

number of Pareto solutions.

7.5.2 Stage II – System-wide Budget Allocation

A mathematical model is developed for the system-wide strategy selection with the

number of decision variables equal to the number of districts. The consistency in performance

159

across districts and expected budget are the objective and constraint respectively. The set of

pareto solutions generated in stage I under each district level pavement management system

will be classified as mutually exclusive alternatives against each decision variable. Hence, the

input to this stage of the analysis consists of mutually exclusive pavement maintenance

strategies corresponding to each district, and the available total system-wide budget.

Dynamic programming provides a straightforward solution to the problem and is employed to

solve for the overall system-wide pavement maintenance strategy.

7.5.3 Illustrative Example

7.5.3.1 Formulation and Analysis of Example Problem

For simplicity, three districts are considered for illustration and each district has

different pavement management goals and resource constraints. The analysis deals with

allocation of the available pavement maintenance budget at the central agency level to the

three district agencies. It addresses the system-wide network level pavement management

goal of the central agency, as well as pavement maintenance budget constraints, and

pavement distress conditions at the district level. The pavement maintenance management

objectives of each of the three district level agencies are as follows:

(i) Maximizing the condition of the road segments; and

(ii) Minimizing the maintenance cost.

At the central level, the overall available budget and the overall pavement

performance improvement of the entire road network are the primary concerns. Hence, the

goal of the central agency is to maximize the usage of available maintenance budget of the

entire road network covering the three district road networks, while having a consistent

improvement in pavement performance across all districts as the constraint.

Stage I: District Level Budget Allocation

160

A network of 150 one-km asphaltic pavement sections is considered, each with three

possible forms of distresses: raveling, rutting and cracking. Table 7.2 and Table 7.9 list the

cost data for the repair of different distresses and highway class respectively. The distress

characteristics data varies across 3 districts, and is provided exogenously. To facilitate

illustration, only 4 possible maintenance options are considered for each pavement section: (1)

Do nothing, (2) patching, (3) premix leveling, and (4) crack sealing. The sample problem is

analyzed to minimize maintenance cost, and maximize network average PCI with the only

constraint of maintaining individual pavement section PCI level above α1. The problem can

be represented mathematically as follows:

Objective function:

(i) Minimize maintenance cost: Minimize ∑=

N

jjC

1 , and (7.16)

(ii) Maximize network average PCI: Maximize ∑=

N

jj NPCI

1 (7.17)

Subject to: PCIj ≥ α1 j = 1, 2, …, N (7.18)

where Ci is the maintenance cost for pavement section j, N is the total number of pavement

sections, and PCIj is the Pavement Condition Index of pavement section j. α1 represents the

required minimum pavement condition threshold for each pavement section.

Any suitable optimization technique could be employed to solve the above example

problem. In the present study, the genetic-algorithm optimization method is adopted. A

population size of 300 was employed for the simple genetic algorithms analysis, with a

replacement proportion of 0.10. The crossover and mutation rates are 0.85 and 0.05

respectively.

Stage II: System-wide Budget Allocation

161

The system-wide budget allocation strategy takes as part all the Pareto optimal results

from the district level management systems and the overall available budget as constraint.

The process begins with collecting all the Pareto optimal results from each component system

and selecting the most suitable strategy out of each set of Pareto solutions in formulating the

system-wide pavement maintenance and rehabilitation strategy. The objective is to maximize

the utilization of the available budget for a certain analysis period while maintaining

consistency in terms of performance improvements across districts. The problem can be

represented mathematically as follows:

Objective function:

Minimize [Max {|(NPCI1 - α1) – (NPCI2 - α1)| , |(NPCI1 - α1) – (NPCI3 - α1)| , |(NPCI3 -

α1) – (NPCI2 - α1)| }] (7.19)

Subject to: ∑=

−3

1iTiCB ≤ α4 and α4 ≥ 0 (7.20)

where CTi is the total budget allocated to component management system i, and B is the total

available budget for the system-wide asset maintenance program. M is the total number of

districts. PCI1, PCI2, PCI3, and B denote pavement condition index for the three districts and

available budget respectively. α4 is the maximum difference allowed between the total budget

allocated and available, which is chosen to define the minimum amount of budget the agency

would like to allocate.

Dynamic programming, which has been shown to be a promising tool to solve

resource allocation problems (Tack and Chou, 2002; Jiang and Sinha, 1989), is adopted to

solve system-wide budget allocation problem.

Results of Stage I Optimization Analysis

In the first stage, the procedure outlined in Fig. 7.6 is applied to each of the three

district management systems independently to establish the Pareto frontiers given

162

maintenance cost and condition measure as the objectives. To facilitate illustration, the Pareto

frontiers from the three analyses are shown in Figs. 7.7, 7.8, and 7.9, respectively.

Results of Stage II Optimization Analysis

The relationship between condition and allocated budget for each of the three districts

established in Stage I optimization analyses offers a convenient database for Stage II analysis.

Following the procedure delineated in Fig. 7.6, the optimal shares of budget for the three

districts are determined and are presented in Table 7.10.

Sensitivity Analysis

A sensitivity analysis is carried out with respect to the available for budget which is

an essential factor in maintenance and rehabilitation programming. The analysis is performed

by varying the available budget level for a particular analysis period, and the impact of

changes on the condition or performance related aspects of the assets are recorded in Table

7.10 and visualized in Fig. 7.10.

7.6 SUMMARY

This chapter presented a holistic multi-dimensional highway asset budget allocation

optimization approach which considers individual asset optimization with multiple objectives,

equity in distribution of resources, and global cross asset trade-off at network level while

integrating assets with different objectives and performance measures in a manner to avoid

subjectivity in appropriation of funds and resources.

A two-stage analysis technique is employed to account for possible different goals in

the various highway management structures. The Stage I analysis considers the needs and

funds requirements of the various component management systems, while the Stage II

analysis determines the system-wide optimal budget allocation strategy with appropriate

constraints. The proposed procedure was illustrated with two example problems: (1) for

allocating funds to three component management systems involving single district, (2) for

163

allocating funds across multiple districts. The results suggest that the proposed procedure is

able to optimally and consistently allocate funds to meet maintenance needs and achieve the

desired improvement in overall network conditions of the various component asset systems.

164

TABLE 7.1. Highway infrastructure facilities for example problem

Infrastructure Type Quantity Pavements Asphaltic 150 (km)

-Expressway 4 lanes 50 segments

-Arterial 3 lanes 50 segments

-Access 2 lanes 50 segments

Bridges

Concrete 6

-Deck (ft2) 22074

-Superstructure (ft2) 2857

-Substructure (ft) 598

Appurtenances

Signs

-Regulatory (24”x 30”) 42 (Nos.)

-Informational (384”x 80”) 30 (Nos.)

-Warning (36”x 36”) 18 (Nos.)

-Medical (120”x 66”) 2 (Nos.)

Guardrails

-Galvanized steel W-beam 88 (km)

Street lightings

-Luminaire 3488 (Nos.)

-Lamps 3488 (Nos.)

-Pole 1744 (Nos.)

TABLE 7.2. Cost data for example problem

Distress Type Maintenance Cost

Maintenance cost per unit in Singapore dollars (S$)

Distress Severity Level Low Moderate High

Raveling (S$/m2) 1.00 1.85 2.75 Rutting (S$/m2) 2.00 2.20 3.85 Cracking (S$/m) 6.00 6.00 6.00


165

TABLE 7.3. Pavement distress data for example problem

PAVEMENT SEGMENTS 1-50 51-100 101-150

Ravel Rut Crack Ravel Rut Crack Ravel Rut Crack L-19 M-24 L-21 M-4 M-2 M-24 M-29 M-12 M-21 L-26 L-8 L-13 L-28 L-15 L-26 M-2 M-21 M-13 M-13 M-14 M-1 H-19 M-18 H-20 H-23 H-25 H-1 M-1 L-34 M-17 H-30 H-20 H-28 H-1 H-18 H-17 M-29 M-6 M-18 M-29 M-22 M-18 M-19 M-27 M-18 H-4 M-7 H-28 M-21 L-36 M-6 M-16 H-6 M-28 L-7 M-39 L-1 L-22 L-2 L-6 L-6 L-22 L-1

L-22 L-33 L-25 M-25 M-38 M-22 H-3 M-26 H-25 H-24 L-23 H-21 H-21 M-36 H-13 M-4 L-10 M-21 H-13 L-32 L-13 M-4 L-24 M-5 H-17 H-34 H-13 L-5 L-20 L-16 H-27 M-9 H-24 M-8 L-3 M-16 H-9 M-23 H-12 M-23 L-39 M-12 M-2 M-3 M-12

M-13 L-28 M-1 M-1 H-14 M-13 L-24 M-3 L-1 L-21 L-39 L-16 M-2 M-20 M-5 H-10 M-27 H-16 M-19 M-19 M-27 H-6 H-40 H-25 H-20 H-10 H-27 H-26 M-30 H-8 M-29 M-16 M-20 M-7 M-34 M-8 L-26 M-18 L-5 L-22 L-3 L-16 H-25 L-28 H-5 H-12 M-35 H-29 L-8 M-6 L-25 M-21 L-6 M-29 M-27 L-24 M-19 M-6 L-34 M-9 H-12 M-28 H-19 M-6 L-6 M-8 H-9 M-12 H-30 H-17 L-32 H-8 H-25 L-35 H-24 H-13 L-31 H-12 M-16 M-1 M-24 H-24 M-6 H-23 M-9 L-16 M-3 L-12 H-16 L-23 M-7 M-1 M-6 M-26 H-18 M-17 M-23 L-29 M-6 M-2 M-27 M-20 M-11 L-30 M-29 L-28 M-13 L-20 M-25 M-29 M-23 M-12 L-8 M-20 M-20 M-23 M-23 L-16 M-21 L-25 M-28 M-32 M-23 M-9 L-6 M-25 M-20 L-15 M-25 L-17 H-22 L-2 M-4 L-34 M-25 H-23 M-23 H-13 H-12 L-8 H-26 M-29 L-25 M-13 M-4 L-8 M-12 H-12 H-14 H-16 L-8 M-24 L-12 L-28 M-19 L-19 L-1 H-18 L-28 M-15 H-13 M-19 M-15 M-21 M-20 H-37 L-5 M-22 L-22 L-31 L-20 L-6 H-22 L-15 L-29 L-19 L-16 M-28 M-8 M-15

M-14 M-3 M-23 M-18 M-18 M-13 H-17 M-21 H-23 L-29 L-13 L-13 L-19 L-17 L-19 L-9 H-18 L-13 M-23 L-7 M-16 H-23 M-15 H-19 L-3 M-24 L-16 M-29 L-12 L-13 L-25 M-38 L-11 L-21 L-39 L-13 M-29 H-5 M-23 M-29 L-31 M-15 H-27 L-35 H-23 M-24 L-28 M-6 L-30 L-37 L-15 H-9 M-21 H-6 H-12 L-28 H-7 H-24 M-28 H-22 H-6 H-22 H-7 M-11 L-32 M-1 L-25 M-10 L-1 L-23 H-10 L-1 H-8 L-22 H-3 H-13 L-33 H-8 L-16 H-27 L-3 L-7 M-14 L-25 H-27 L-29 H-25 L-19 L-19 L-25 M-5 L-32 M-5 L-11 M-6 L-30 H-16 M-19 H-5 L-18 L-29 L-29 L-27 L-33 L-11 L-27 M-22 L-29 M-18 L-36 M-9 M-28 L-22 M-8 M-8 L-18 M-9 M-18 L-35 M-27 L-7 L-25 L-21 L-23 L-10 L-27 H-7 M-23 H-23 H-6 L-33 H-21 H-21 L-32 H-23 M-4 M-13 M-6 M-21 L-16 M-26 L-23 L-35 L-6 L-25 M-4 L-16 M-28 L-40 M-6 M-5 M-32 M-16 M-30 M-31 M-2 H-1 L-23 H-3 M-1 H-9 M-2

Note: Each cell in the table contains a two-part code A-B, where A represents distress severity with H, M and L

denoting high, medium and low severity respectively; and B is a numerical value delineating the distress extent

with the unit of percentage area affected.

166

TABLE 7.4. Bridge element condition for the example problem

Component Quantity

Condition State 1 2 3 4 5

Deck (m2) 673 807 1884 1547 1817

Superstructure (m) 61 122 543 139 0

Substructure (m) 18 60 66 37 0

Note: Value in each cell represents bridge element quantity of given condition state. For deck, quantity is measured in area; for superstructure and substructure, it is measured in linear meter.

TABLE 7.5. Bridge element maintenance actions and costs for the example problem

Component Condition State

Maintenance Actions Cost (S$)

Deck

1, 2 Do nothing 0 3 Minor maintenance 10% of replacement 4 Major maintenance 60% of replacement 5 Element replacement $549/m2

Superstructure

1, 2 Do nothing 0 3 Minor maintenance 10% of replacement 4 Major maintenance 60% of replacement 4 Element replacement S$1253/m

Substructure

1, 2 Do nothing 0 3 Minor maintenance 10% of replacement 4 Major maintenance 60% of replacement 4 Element replacement S$7165/m


167

TABLE 7.6. Appurtenance existing service life for the example problem

Component Service Life (Yrs.) Regulatory N(5,1.7)

Informational N(5,1.7) Warning N(6.8,2.3) Medical N(5,1.7)

Post N(11.5,4) Overhead Post N(25,6)

Galvanized steel W-beam N(5,1) *Failed: 48Nos.

W-beam post N(5,1) *Failed: 89Nos.

Luminaire N(12,2) Lamp N(3.5,0.5) Pole N(16,4)

Note: N(µ,σ) represents normal distribution with µ and σ as mean and standard deviation. * Predicted failure based on accident rate

TABLE 7.7. Appurtenance design service life and costs for the example problem

Appurtenance Type Component Design Service

Life (Yrs.) Replacement Cost

(S$)

Road Sign

Regulatory 7 135.48 per m2 Informational 7 135.48 per m2

Warning 10 169.35 per m2 Medical 7 135.48 per m2

Post 16.3 2128 per item Overhead Post 35 18144 per item

Guardrail

Galvanized steel W-beam 30 63 per 7.6m panel

W-beam post 30 19.25 per item

Luminaries Luminaire 17 921 per item

Lamps 4.5 140 per item Pole 25 1890 per item

168

TABLE 7.8. Results of multi-asset budget allocation analysis for the example problem

Budget (S$)

PMS BMS AMS

PCI Cost (S$) BHI Cost (S$)

Average Remaining Service Life

Cost (S$)

4000000 72.534 865000 72.129 446600 54.432 1188100 3500000 77.886 970000 77.689 614690 57.686 1341050 3000000 80.584 1030000 80.858 762530 61.201 1543400 2500000 85.152 1160000 83.564 937730 65.817 1803800


TABLE 7.9. Highway infrastructure facilities for the example problem

Infrastructure Type Quantity Pavements Asphaltic 150 (km)

-Expressway 4 lanes 50 segments

-Arterial 3 lanes 50 segments

-Access 2 lanes 50 segments

TABLE 7.10. Results of multi-district budget allocation analysis for the example problem

No. Budget (S$) Cost (S$) District 1 (PCI)

District 2 (PCI)

District 3 (PCI)

1 2600000 2588430 69.164 72.752 73.842 2 2800000 2695350 74.765 74.643 74.794 3 3000000 2928400 77.886 77.841 77.858

169


Pavement Management System

(PMS)

Bridge Management System (BMS)

Appurtenance Management System

(AMS)

STAGE I

Condition and Maintenance Cost Data, Performance

Indicator, Objectives

Mathematical Formulation of Objectives and

Constraints

Optimization using Dynamic Programming

STAGE II

State-wide Budget for M&R

Network-level Objectives






Constraints


Constraints

Inventory of Facilities of Analyzed Highway Network

System-wide Multi-Asset Budget Allocation Strategy

170

0.00E+00

6.00E+05

1.20E+06

1.80E+06

2.40E+06

60 65 70 75 80 85 90 95 100

Pavement Condition Index (PCI)

Pave

men

t Mai

nten

ance

Cos

t (SG

D)

FIGURE 7.2. Pareto frontier from analysis of pavement management system

2.00E+05

3.80E+05

5.60E+05

7.40E+05

9.20E+05

1.10E+06

60 65 70 75 80 85 90 95 100

Bridge Health Index (BHI)

Bri

dge

Mai

nten

ance

Cos

t (SG

D)

FIGURE 7.3. Pareto frontier from analysis of bridge management system

171

0.00E+00

1.00E+06

2.00E+06

3.00E+06

4.00E+06

5.00E+06

0 20 40 60 80 100

Average Remaining Service Life (%)

App

urte

nanc

e M

aint

enan

ce C

ost (

SGD

)

FIGURE 7.4. Pareto frontier from analysis of appurtenance management system

40

50

60

70

80

90

100

2.5 Million 3 Million 3.5 Million 4 MillionAvailable Total System-wide Budget (S$)

Ove

rall

Ave

rage

Mai

nten

ance

Con

ditio

n (N

PCI,

NB

HI o

r N

RSL

)

NPCI for Pavement Management SystemNBHI for Bridge Management SystemNRSL for Appurtenance Management System

FIGURE 7.5. Results of optimal multi-asset budget allocation analysis

172


DISTRICT 1 Pavement

Management System

• • •

DISTRICT M Pavement

Management System

Single-objective Optimization using

Dynamic Programming

STAGE I

STAGE II

Inventory, Condition Data, Performance

Indicators, Objectives

• • •

•

Multi-objective Optimization using Genetic Algorithm

• • •

•

List Candidate Strategies

• • •

Central Highway Agency

System-wide Pavement Management Strategy

Overall Budget for M&R of

Pavements

Feasible Strategies for Each MGT.

System

List Candidate Strategies

173

0

600000

1200000

1800000

2400000

60 65 70 75 80 85 90 95 100


Pave

men

t Mai

nten

ance

Cos

t (SG

D)

FIGURE 7.7. Pareto frontiers from analysis of district-1 management system

0

600000

1200000

1800000

2400000

60 65 70 75 80 85 90 95 100


Pave

men

t Mai

nten

ance

Cos

t (SG

D)


174

0

600000

1200000

1800000

2400000

60 65 70 75 80 85 90 95 100


Pave

men

t Mai

nten

ance

Cos

t (SG

D)


6062646668707274767880

2600000 2800000 3000000Available Budget (S$)

Net

wor

k Pa

vem

ent C

ondi

tion

Inde

x (N

PCI)

NPCI (District 1) NPCI (District 2) NPCI (District 3)

FIGURE 7.10. Results of optimal multi-district budget allocation analysis

175

CHAPTER 8

CONCLUSIONS AND RECOMMENDATIONS

8.1 SUMMARY AND CONCLUSIONS

Network level pavement management is a highly complex and complicated task if it is

to be taken in its totality. In order to find an optimal strategy for providing, evaluating and

maintaining pavements at an acceptable level of service over a pre-selected period of time, an

efficacious pavement management program with sound resource allocation should be

identified in a PMS. Traditionally, it has been a common practice to apply priority weights to

selected parameters in the process of optimal programming of pavement maintenance or

rehabilitation activities. The form or structure of priority weights adopted, and their

magnitudes applied vary from highway agency to agency. However, optimization is

preferred over prioritization, and many agencies currently either employ rank based priority

models or incorporate priority preferences based on subjective assessment in optimization

process. The reason to employ rank based priority models is due in-part to the mathematical

complication of formulating a pavement maintenance optimization problem at network level,

and in-part to the practical needs for prioritizing different maintenance activities. The

rationale of incorporating priority preferences in optimization is easy to understand, and it

often represents the intention or pavement maintenance management policy of the highway

agency concerned.

This thesis has presented a study that examines the following two main aspects of

pavement maintenance planning: (i) rational prioritizing of pavement maintenance planning

involving multiple parameters such as highway class, distress type, distress severity etc., and

(ii) incorporation of priority preferences in PMS optimization. The research demonstrated the

176

issues associated with subjective judgments involving multiple criteria and resolution of the

same, and the implications of applying priority weights and using them directly in the

pavement maintenance programming analysis. The research concluded that by incorporating

priority weights directly into the mathematical formulation, a sub-optimal solution is obtained.

Unfortunately, many users of the approach are unaware this fact and do not know the

magnitude of loss in optimality caused by their choice of priority scheme. Recognizing the

fact that highway agencies do have the practical need to offer maintenance priorities to

selected groups of pavement sections, a suggested procedure has been proposed in this study

to incorporate such priority preferences into pavement maintenance planning and

programming.

8.1.1 Improved Prioritization Methods for Pavement Maintenance Planning






and engineers. This is because combining different factors empirically into a single

numerical index tends to conceal the various contributing effects and actual characteristics of

the distress. Furthermore, not all of the factors and considerations involved can be expressed

quantitatively and measured in compatible units.

Sometimes absolute priority rating and ranking is applied in pavement maintenance

planning to prioritize pavement maintenance activities. However, it is the relative priority

ratings rather than the absolute priority ratings that matters in pavement maintenance

planning and moreover direct assessment method suffers from inconsistency in judgments.

177

In an attempt to overcome the above mentioned limitations associated with common

subjective priority rating methods, there is a need to identify rational procedure to assess

maintenance priority rating. In this research two improved methods were introduced for

prioritization of pavement maintenance activities (i) analytic hierarchy process (AHP) (Saaty,

1994, 1990, 1980), and (ii) mechanistically based prioritization approach. A brief overview

of the findings associated with the introduced methodologies is presented in subsequent

section.

8.1.1.1 Establishing Priority Preferences using the AHP

Three AHP methods have been evaluated for their suitability and effectiveness in

priority assessment of pavement maintenance activities. The evaluation was performed with

reference to the Direct Assessment Method in which the raters make their assessments by

comparing all the maintenance activities together directly. It was found that because of the

different survey approaches and scale employed, the priority rating scores obtained from the

AHP methods and the Direct Assessment Method differed significantly in their absolute

magnitudes. However, AHP generated priority ratings were positively correlated with those

obtained by the Direct Assessment Method. This strong association was supported by the

very high correlations found based on the ranking assessment. The strong correlation in

rankings was confirmed through statistical hypothesis testing performed at a confidence level

of 95%. As it is the relative priority ratings rather than the absolute priority ratings that count

in pavement maintenance planning, the findings suggest that the AHP approach is suitable for


The analysis also found that the AHP methods showed less variation among the

judgments of experts in contrast to the Direct Assessment Method. More importantly, the

number of comparisons necessary in the priority assessment increases dramatically for the

Direct Assessment Method as the size of the problem increases. Even among the three AHP

178

methods, the two relative AHP methods would also require very large number of

comparisons for a typical size problem in a real-life road network level pavement

maintenance problem. Based on its operational advantage in handling a large number of

items to be evaluated, and its ability to generate priority assessment in good agreement with

the Direct Assessment Method, the absolute AHP method is considered to be the preferred

method for use in pavement maintenance prioritization.

8.1.1.2 Establishing Priority Preferences using Mechanistic Approach

Traditionally in performing pavement maintenance planning, which is an essential

activity of a pavement management system, pavement maintenance activities are assigned

priority ratings so that those distresses that deserve earlier maintenance treatments will

receive higher maintenance priority. In the case of cracks, condition indices or priority

ratings are typically assigned based on their physical characteristics such as crack width,

length, depth, density and extent that are obtained from pavement condition surveys. The

procedures for determining such indices or ratings are often based on engineering judgment

or some empirical relationships derived from practical experience.

However, the mechanistic approach helps to reduce the uncertainty associated with

the subjective or judgmental element involved in many maintenance prioritization methods

currently in use. It also helps to lessen the problem of having many maintenance priority ties

arising from classifying crack severity into three very broad classes. It makes available a

prioritization procedure that produces a more rational priority ranking in support of pavement

maintenance planning in a pavement management system. Considering the constraint in the

available research in the area of mechanistically based prioritization, it is recommended to

employ prioritization process based on the AHP whenever mechanistic approach is

inapplicable.

179

This thesis has proposed a mechanistically based methodology to assess the relative

urgency of maintenance needs of pavement cracks. The concept of cumulative damage and

remaining life was introduced. Miner’s rule was applied to compute a cumulative damage

factor to form the basis for maintenance prioritization. It was reasoned that a crack with a

higher cumulative damage factor (i.e. having a shorter remaining life) has a higher urgency of

needs for maintenance, and hence is assigned a higher maintenance priority. In the

computation of cumulative damage factor of a crack, the proposed mechanistic approach

considers crack dimensions (including crack orientation, crack width, depth and length),

crack location, and traffic loading characteristics (including statistical variations in traffic

composition, loading magnitude and loading frequency due to wander distributions).

8.1.2 Incorporating Priority Preferences into Pavement Management

Optimization

The proposed framework to incorporate priority preferences into pavement

maintenance planning and programming involves assigning weighting factors directly to

parameters. It first solves the optimization problem without applying any priority weights.

Next, two post-processing stages are executed to implement the desired priority preferences

as explained below:

(i) Stage I is a tie-breaking procedure.

(ii) Stage II performs Trade-off analysis to include as many prioritized maintenance

activities into the maintenance program as possible, subject to the maximum loss of

optimality that the highway agency is willing to accept.

An improved procedure of incorporating a user’s priority preferences into the pavement

maintenance programming process has been demonstrated. It allows the highway agency to

decide if they are willing to settle with a sub-optimal solution by including more prioritized

activities in the final maintenance program. If the user is not willing to compromise on the

180

optimality of the solution, the proposed procedure will produce the optimal solution while

having as many prioritized activities in the final program as possible through the tie-breaking

analysis. It is believed that the proposed procedure helps to improve the effectiveness of

pavement maintenance planning and management by allowing the highway agency to know

the effects of their decision in setting priorities, and putting them in a better position to make

informed decisions.

This thesis has presented a two-stage approach to solve the budget allocation problem

of highway asset management involving competing asset systems in a district, each with its

own multiple operational objectives. Stage I of the approach analyzed the individual multi-

objective asset systems independently to establish for each a family of optimal Pareto

solutions. Stage II adopted an optimal algorithm to allocate budget to individual assets by

allowing interaction between the overall system level and the individual asset level, and

performing cross-asset trade-off to achieve the optimal budget solution for the given overall

system level objectives.

The approach was extended to take into account multiple districts within each

component management system. The proposed procedure was illustrated with an example

problem for allocating funds to three component asset systems. The results suggested that the

proposed procedure is able to optimally and consistently allocate funds to meet maintenance

needs and achieve the desired improvement in overall network conditions of the various

component asset systems.

8.2 RECOMMENDATIONS FOR FURTHER RESEARCH

In this research, two approaches of arriving at improved assessments of priority

preferences in pavement maintenance planning have been introduced, and an improved

procedure of incorporating a user’s priority preferences into the pavement maintenance

programming process has been demonstrated. It allows the highway agency to decide if they

181

are willing to settle with a sub-optimal solution by including more prioritized activities in the

final maintenance program. If the user is not willing to compromise on the optimality of the

solution, the proposed procedure will produce the optimal solution while having as many

prioritized activities in the final program as possible through a tie-breaking analysis.

Nevertheless, there are several improvements that can be made to further enhance the

proposed maintenance planning approach as follows,

1. The mechanistically based prioritization approach for single crack can be extended to

multiple cracks.

2. The mechanistic approach for priority setting can be explored for other types of

pavement distresses such as rutting, depressions, and potholes etc.

3. Multi-agent systems, a group of problem solvers that work collectively to solve

problems, can be employed to integrate individual asset systems within each district

and further to cover multiple districts.

182

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