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
CHAPTER 4 IMPROVED PAVEMENT MAINTENANCE PRIORITY
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
CHAPTER 5 IMPROVED PAVEMENT MAINTENANCE PRIORITY
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
vi
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.
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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
Direct Assessment Method
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 7.8 Pareto frontiers from analysis of district-2 management system
Figure 7.9 Pareto frontiers from analysis of district-3 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.
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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
accurately and effectively convey the priority assessment or intention of highway agencies
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.
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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
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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.
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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.
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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.
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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.
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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.
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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;
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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
28
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
32
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
34
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
40
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
43
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.
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
expression (Fawcett, 2001; Broten, 1996; Barros, 1991). Though convenient to use,
52
empirical mathematical indices often do not have a clear physical meaning, and could not
accurately and effectively convey the priority assessment or intention of highway agencies
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
Direct Assessment Method
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
Direct Assessment Method
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
Section 2 Expressway
Pothole Moderate
Section 3 Expressway
Pothole Low
Section 4 Expressway
Rutting High
Section 5 Expressway
Rutting Moderate
Section 6 Expressway
Rutting Low
Section 7 Expressway
Cracking High
Section 8 Expressway
Cracking Moderate
Section 9 Expressway
Cracking Low
Section 10 Arterial Pothole
High
Section 11 Arterial Pothole
Moderate
Section 12 Arterial Pothole
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
Section 20 Access Pothole
Moderate
Section 21 Access Pothole
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
Rating by Direct Assessment Method
Rat
ing
by I
deal
-Nod
e R
elat
ive
AH
P
100806040200
100
80
60
40
20
0
Rating by Direct Assessment Method
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
Method and different AHP methods
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
Direct Assessment Method
(b) Scatter plot of priority rating by Ideal-Mode Relative AHP and
Direct Assessment Method
(c) Scatter plot of priority rating by Absolute AHP and
Direct Assessment Method
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
Ranking by Direct Assessment Method
Ran
king
by
Idea
l-Mod
e R
elat
ive
AH
P
302520151050
30
25
20
15
10
5
0
Ranking by Direct Assessment Method
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
Method and different AHP methods
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
Direct Assessment Method
(b) Scatter plot of priority ranking by Ideal-Mode Relative AHP and
Direct Assessment Method
(c) Scatter of priority ranking by Absolute AHP and
Direct Assessment Method
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
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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
the purpose of pavement maintenance prioritization.
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
Direct Assessment Method
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
Rating by Direct Assessment Method
Rat
ing
by A
bsol
ute
AH
P
100806040200
100
80
60
40
20
0
Ranking by Direct Assessment Method
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
Direct Assessment Method
(a) Scatter plot of priority ratings by Absolute AHP and
Direct Assessment Method
r = 0.77
ρ = 0.86
99
Rating by Direct Assessment Method
Rat
ing
by P
AV
ER
Sys
tem
100806040200
100
80
60
40
20
0
Ranking by Direct Assessment Method
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
Direct Assessment Method
(b) Scatter plot of priority rankings by PAVER System and
Direct Assessment Method
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=40mm, depth=30mm
Crack width=10mm, depth=120mm
Crack width=40mm, depth=120mm
Crack width=10mm, depth=30mm (PCR)Crack width=40mm, depth=30mm (PCR)
Crack width=10mm, depth=120mm (PCR)
Crack width=40mm, 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
Crack width=10mm, depth=60mm
Crack width=40mm, depth=60mm
Crack width=10mm, depth=90mm
Crack width=40mm, depth=90mm
Crack width=10mm, depth=60mm (PCR)
Crack width=40mm, depth=60mm (PCR)
Crack width=10mm, depth=90mm (PCR)
Crack width=40mm, depth=90mm (PCR)
(b) For cracks with depth of 60mm and 90mm
FIGURE 5.5. Comparison between proposed and existing pavement condition rating
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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
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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;
(6) A scheme that contains the priority weights of schemes (2) and (4) combined;
(7) A scheme that contains the priority weights of schemes (3) and (4) 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:
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• 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.
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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)
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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.
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• 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%.
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(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,
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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:
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(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:
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(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
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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.
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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
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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.
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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.
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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.
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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.
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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
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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
Activity ID-24 Cracking, Low
Severity, S$11,480
Activity ID-344 Cracking, Low
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$/m) 6.00 6.00 6.00
Note: S$ represents Singapore dollar
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$7165/m
Note: S$ represents Singapore dollar
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$)
4000000 72.534 865000 72.129 446600 54.432 1188100 3500000 77.886 970000 77.689 614690 57.686 1341050 3000000 80.584 1030000 80.858 762530 61.201 1543400 2500000 85.152 1160000 83.564 937730 65.817 1803800
Note: S$ represents Singapore dollar
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
FIGURE 7.1. Framework of the proposed approach
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
Condition and Maintenance Cost Data, Performance
Indicator, Objectives
Condition and Maintenance Cost Data, Performance
Indicator, Objectives
Mathematical Formulation of Objectives and
Constraints
Mathematical Formulation of Objectives and
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$)
Ove
rall
Ave
rage
Mai
nten
ance
Con
ditio
n (N
PCI,
NB
HI o
r N
RSL
)
NPCI for Pavement Management SystemNBHI for Bridge Management SystemNRSL for Appurtenance Management System
FIGURE 7.5. Results of optimal multi-asset budget allocation analysis
172
FIGURE 7.6. Framework of the proposed approach
DISTRICT 1 Pavement
Management System
• • •
DISTRICT M Pavement
Management System
Single-objective Optimization using
Dynamic Programming
STAGE I
STAGE II
Inventory, Condition Data, Performance
Indicators, Objectives
• • •
•
Multi-objective Optimization using Genetic Algorithm
• • •
•
List Candidate Strategies
• • •
Central Highway Agency
System-wide Pavement Management Strategy
Overall Budget for M&R of
Pavements
Feasible Strategies for Each MGT.
System
List Candidate Strategies
173
0
600000
1200000
1800000
2400000
60 65 70 75 80 85 90 95 100
Pavement Condition Index (PCI)
Pave
men
t Mai
nten
ance
Cos
t (SG
D)
FIGURE 7.7. Pareto frontiers from analysis of district-1 management system
0
600000
1200000
1800000
2400000
60 65 70 75 80 85 90 95 100
Pavement Condition Index (PCI)
Pave
men
t Mai
nten
ance
Cos
t (SG
D)
FIGURE 7.8. Pareto frontiers from analysis of district-2 management system
174
0
600000
1200000
1800000
2400000
60 65 70 75 80 85 90 95 100
Pavement Condition Index (PCI)
Pave
men
t Mai
nten
ance
Cos
t (SG
D)
FIGURE 7.9. Pareto frontiers from analysis of district-3 management system
6062646668707274767880
2600000 2800000 3000000Available Budget (S$)
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
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
expression (Fawcett, 2001; Broten, 1996; Barros, 1991). Though convenient to use,
empirical mathematical indices often do not have a clear physical meaning, and could not
accurately and effectively convey the priority assessment or intention of highway agencies
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 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 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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