A MECHANISTIC ANALYSIS AND DESIGN SYSTEM FOR
EVALUATION AND REHABILITATION OF FLEXIBLE PAVEMENTS
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
'UNIVERSITY OF FLORIDA LIBRARIES
It is almost impossible for the author to express her appreciation
to all who have contributed to the success and completion of this disser-
First of all, the author is deeply indebted to her former adviser,
Prof. Zhao Guofan, for his understanding, generosity and continuing sup-
port, without which her studying abroad would not have been possible in
the first place.
The author considers herself'fortunate to have had Dr. Byron E. Ruth
as adviser and chairman of the supervisory committee. His professional
expertise, encouragement and delightful personality have made this
research a challenging but enjoyable experience.
Thanks are given to Dr. Mang Tia, Associate Professor in Civil
Engineering Materials, Dr. Frank C. Townsend, Professor in Geotechnical
Engineering, Dr. Fernando E. Fagundo, Associate Professor in Structural
Engineering, and Dr. Andrawus I. Khuri, Professor in the Department of
Statistics, for their time and acceptance of serving on the supervisory
committee. The author has benefited substantially from their invaluable
expertise, guidance and constant encouragement throughout her three-year
The Florida Department of Transportation (FDOT) is gratefully ac-
knowledged for providing the financial support. The technical assistance
extended by personnel at the FDOT Materials Office, particularly Mr.
William G. Miley and Mr. Ron McNamara, is sincerely appreciated.
Special thanks go to Dr. Mark I. Hoit for his time, patience, and
generous consultations on computer-related problems.
Deep appreciation is given to Candace Leggett for her warmth, dili-
gence, skillful editing and printing of this dissertation. Thanks are
also expressed to other individuals, in the Department of Civil Engineer-
ing, who have helped in putting everything in perspective for the author's
study in this University.
This acknowledgment will not be complete without a mention of the
author's family. The author wishes to thank her husband, George (Zhihao)
Gu, for his important mental as well as technical support during the
course of this study. His constant reassurance, sound mathematical knowl-
edge and programming experience have all helped in facilitating the
research. The author's parents, parents-in-law, sisters and brothers have
all contributed indirectly to the completion of her overseas Ph.D. pro-
gram. Their kindness, love and affection are highly valued.
TABLE OF CONTENTS
ACKNOWLEDGMENTS . . . . . . . . ... ........ .ii
LIST OF TABLES . . . . . . . . ... .... . .ix
LIST OF FIGURES . . . . . . . . ... .. ..... .xi
ABSTRACT . . . . . . . .. . . . . . . xiv
1 INTRODUCTION . . . . . . . . ... . . 1
1.1 Research Need . . . . . . . .... 1
1.2 Study Objectives . . . . . . . . . 2
1.3 Scope of Study . . . . . . . . . 2
2 LITERATURE REVIEW . . . . . . . . . 8
2.1 Introduction . . . . . . . . ... .. 8
2.2 Life Pattern of Flexible Pavements . . . . . 9
2.3 Pavement Distresses and Causes . . . . .... .10
2.4 Mechanism of Pavement Distress . . . . .... .12
2.4.1 Mechanism of Cracking . . . . .... .12
2.4.2 Mechanism of Permanent Deformation . . .. 17
2.4.3 Mechanism of Surface Wear . . . . .. 19
2.5 Current Status of Pavement Evaluation and
Rehabilitation Design Research . . . . .... .20
2.5.1 Pavement Management . . . . . .... .21
2.5.2 Pavement Evaluation . . . . . .... .24
2.5.3 Pavement Rehabilitation Design . . ... 32
3 DEVELOPMENT OF A SIMPLIFIED MECHANISTIC
PAVEMENT EVALUATION SYSTEM (MEAPS) . . . . .... .53
3.1 Introduction . . . . . . . . ... . 53
3.2 Elastic Layered Model . . . . . . .... .53
3.3 Material Characterization . . . . . . 55
3.3.1 Validity of Linear Elastic Model ...... 55
3.3.2 Modulus Determination . . . . .... .59
3.4 Description of Dynaflect Testing System ...... 61
3.5 Backcalculation of Pavement Layer Moduli . . .. 62
3.5.1 Prediction Equations and Their Limitations .62
3.5.2 Computerized Tuning of Layer Moduli . . .. 66
3.6 Problems Associated with Backcalculation Procedures 68
3.7 Load Induced Stress Analyses (BISAR) . . . .. 72
3.8 Projection of Future Pavement Condition . . .. 76
3.9 Advantages and Limitations of MEAPS . . . .. 76
4 DEVELOPMENT OF A DETAILED MECHANISTIC PAVEMENT
EVALUATION SYSTEM FOR COMBINED THERMAL AND LOAD
EFFECTS . . . . . . . . . . . 78
4.1 Introduction . . . . . . . . . 78
4.2 Microcomputerization of CRACK3 . . . . . . 78
4.3 Basic Assumptions and Equations Used in CRACK3 (PC) 79
4.3.1 Basic Assumptions . . . . . . . 79
4.3.2 Basic Equations . . . . . . . .. 80
4.4 Advantages and Limitations of CRACK3 (PC) . . .. 85
4.5 Pavement Future Condition Projection and
Life Estimation . . . . . . . . 86
4.6 Prediction of Temperature Profiles Under
Paved Surfaces . . . . . . . . . 89
4.6.1 Introduction . . . . . . . .. 89
4.6.2 Problems in Current Analytical Models .... .89
4.6.3 Heat Transfer Problem and Exact Solution . 90
4.6.4 Description of the HTM Program . . . .. 92
4.6.5 Determination of Pavement Surface Temperature .98
4.7 Typical Temperature Regions in Florida . . . .. 104
5 IDENTIFICATION OF PAVEMENT SECTIONS WITH
SIMILAR STRUCTURAL RESPONSE . . . . . . .. 108
5.1 Introduction . . . . . . . . . 108
5.2 Problems with Multiple Comparison Procedures . .. 108
5.3 Problems with Cluster Analysis Procedures . . .. 110
5.3.1 Description of Cluster Analysis . . . .. 110
5.3.2 The Power of the Procedure . . . . 112
5.4 Development of the SORT Procedure for REDAPS . .. 114
5.5 Possible Violations of Assumptions . . . . .. 116
5.5.1 Outliers . . . . . . . . .. 116
5.5.2 Nonnormality . . . . . . . . .117
5.5.3 Dependence . . . . . . . . . 117
6 DEVELOPMENT OF A MECHANISTIC REHABILITATION
DESIGN SYSTEM FOR FLEXIBLE PAVEMENTS . . . . .. 119
6.1 Introduction . . . . . . . . . . 119
6.2 Simplified Rehabilitation Design . . . . .. 120
6.3 Detailed Rehabilitation Design . . . . . .. 124
6.3.1 Pavement Model . . . . . . . . 125
6.3.2 Material Characterization . . . . .. 127
6.3.3 Traffic Considerations . . . . .. .128
6.3.4 Environment Considerations . . . . .. 129
6.3.5 Design Distress Criteria . . . . .. 129
6.3.6 Life Estimation for a Given Design . . .. 130
6.3.7 Summary of Assumptions . . . . . .. 131
6.4 Design Procedure Summary . . . . . . .. 133
7 DESCRIPTION OF THE REDAPS PROGRAM . . . . . .. 137
7.1 Program Structure . . . . . . . . .. 137
7.2 Subroutine TRSLATOR . . . . . . . .. 139
7.3 Subroutine SORT . . . . . . . . .. 140
7.4 Subroutine MEAPS . . . . . . . . . 144
7.4.1 Program Structure . . . . . . .. 146
7.4.2 Input Information for MEAPS . . . . .. 148
7.4.3 Output from MEAPS . . . . . . .. 150
7.5 Subroutine PLOTQ . . . . . . . . .. 151
7.6 Subroutine CRACK3 (PC) . . . . . . . .. 151
7.6.1 Program Structure . . . . . . .. 153
7.6.2 Input and Output Information . . . .. 153
7.7 Subroutine STRATEGY . . . . . . . .. 156
7.8 Subroutine OVLR . . . . . . . . .. 160
7.8.1 Program Structure . . . . . . .. 160
7.8.2 Input and Output Information . . . .. 162
7.9 Subroutine OVLR2 . . . . . . . . .. 162
7.9.1 Program Structure . . . . . . .. 162
7.9.2 Input and Output Information . . . .. 165
8 CASE STUDY USING THE REDAPS PROGRAM . . . . .. 167
8.1 Pavement Evaluation . . . . . . . .. 169
8.1.1 Simplified Evaluation . . . . . .. 169
8.1.2 Detailed Evaluation . . . . . . .. 172
8.1.3 Regional Effect . . . . . . . .. 174
8.2 Rehabilitation Design . . . . . . . . 175
8.3 Parameters Influencing Pavement Life . . . .. 176
8.3.1 Effect of Age Hardening Rate . . . .. 177
8.3.2 Effect of Cooling Rate . . . . . .. 177
8.3.3 Effect of Cooling Time and
Minimum Temperature . . . . . . .. 177
8.3.4 Effect of Traffic Volume . . . . .. 180
8.4 Summary . . . . . . . . . . . 181
9 CONCLUSIONS AND RECOMMENDATIONS . . . . . .. 182
9.1 Overview . . . . . . . . . . 182
9.2 Summary of Program Capabilities . . . . .. 183
9.3 Conclusions . . . . . . . . . . 186
9.4 Recommendations . . . . . . . . .. 188
A OUTPUT FILES FOR COMPARISON OF THE INTERACTIVE EFFECT
BETWEEN THERMAL AND VEHICULAR LOADS . . . . . .
A.1 File 1 US441.016 . . . . . . . . .
A.2 File 2 US441.017 . . . . . . . . .
B ASPHALT BINDER AGE HARDENING STUDY . . . . . .
B.1 Introduction . . . . . . . . . . .
B.2 General Hardening Trend .......
B.3 Age Hardening Trend for Florida Pavements ...
B.3.1 Slope Intercept Relations . . . . .
B.3.2 Viscosity Temperature Relations . . . .
B.3.3 Critical Viscosity Temperature Relation . .
C USER'S MANUAL FOR THE REDAPS COMPUTER PROGRAM (Version 2.0)
Introduction . . . . . .
Required Hard/Software . . . .
Operation Procedures . . . . .
Pavement Evaluation . . . . .
C.4.1 Simplified Pavement Evaluation
C.4.2 Detailed Pavement Evaluation
C.4.3 Life Estimation . . .
C.5 Rehabilitation Designs . . .
C.5.1 Simplified Design Procedure
C.5.2 Detailed Design Procedure .
C.6 The Capacity of the REDAPS Program
D LIST OF OUTPUT FILES FOR THE CASE STUDY PRESENTED
IN CHAPTER 8 . . . . . . . . .
D.20 File 20 US441.012
D.21 File 21 US441.013
D.22 File 22 US441.014
D.23 File 23 US441.015
. . . . . . . 284
. . . . . . . . 286
. . . . . . . 288
. . . . . . . 290
REFERENCES . . . . . . . . . . . . . . 293
BIOGRAPHICAL SKETCH . . . . . . . . ... ...... 308
LIST OF TABLES
2.1 Pavement Distress and Possible Causes . . . . .. 11
2.2 Summary of Existing Analytically Based (Mechanistic) Overlay
Design Procedures . . . . . . . . . . . 33
3.1 Comparison of the Computer Tuned Result With That of
the Prediction Equations . . . . . ... .. ... 69
3.2 Nonuniqueness of Solutions in Deflection Matching Procedure 70
3.3 Minimum Regional Pavement Temperature . .. ...... 72
4.1 Comparison Between CRACK3 Analysis and the Independent
Analysis Approach . . . . . . . .. . 88
4.2 Comparison Between Predicted and Measured Pavement
Temperatures at Different Depths . . . . . .... .97
4.3 Characteristics of the Air Temperature Regions in Florida 106
7.1 Criteria for Selection of Rehabilitation Strategies .... .159
8.1 Results of Dynaflect Tests on US 441 (Columbia County) .. 169
8.2 Pavement Structure of US 441 (Columbia County) ...... 169
8.3 Constant Power Viscosity-Temperature Relation
(US 441--Columbia County) .. . . . . . .. . .170
8.4 Effect of Temperature Regions . . . . . . .... 175
8.5 Effect of Hardening Rate on Life . . . . . ... 178
8.6 Effect of Cooling Rate on Life . . . . . ... 179
8.7 Effect of Cooling Hours . . . . . . . ... 180
B.1 Summary of Asphalt Characteristics from Various Sources .. 212
B.2 Age Hardening Slope-Intercept Relationships . . ... 213
B.3 Summary of Slope and Intercept Relations for Florida Data 219
B.4 Summary of Regression Analyses for Slope Prediction
(Florida) . . . . . . .. . . . . 221
D.1 Index of Output Files . . . . . . . . . . 248
LIST OF FIGURES
2.1 Typical Pavement Life Cycle . . . . . . . .. 10
2.2 General Overlay Design Flow Chart . . . . .... .34
3.1 Idealized Pavement Structure in MEAPS . . . . .. 54
3.2 Standard Dynaflect Configuration . . . . .... .63
3.3 Modified Dynaflect Configuration . . . . .... .64
3.4 Typical Temperature Regions in Florida . . . ... 73
3.5 Indirect Tensile Test Failure Values . . . . .. 75
4.1 Stress-Strain Curve for Illustration of Energy
Computation . . . . . . . ... .... . .82
4.2 Predicted Pavement Temperatures at Various Depths
by Program HTM . . . . . . . .. . .94
4.3 Measured Pavement Temperatures at Various Depths . .. 94
4.4 Comparison Between Measured and Predicted Temperatures
at Depth of 0.25 Inch . . . . . . . . . 95
4.5 Comparison Between Measured and Predicted Temperatures
at Depth of 1.00 inch . . . . . . . . . 95
4.6 Comparison Between Measured and Predicted Temperatures
at Depth of 2.00 Inches . . . . . . . .... 96
4.7 Predicted and Measured Air Temperatures for I-10,
December 9-11, 1974 . . . . . . . ... . 100
4.8 Predicted and Measured Air Temperatures for I-10,
March 3-5, 1975 . . . . . . . .. . . 100
4.9 Comparison Between Measured and Predicted Hourly
Air Temperatures for I-10, March 1975 . . . . .. 101
4.10 Comparison Between Measured and Predicted Hourly
Air Temperatures for 1-10, December 1974 . . . ... 101
4.11 Difference Between Pavement Temperatures
(at 0.75-inch depth) and Time . . . . . .
4.12 Measured and Predicted Pavement Temperatures
at 0.75-Inch Depth with Time . . . . . .
4.13 Comparison Between Measured and Predicted
Pavement Temperatures at 0.75-Inch Depth . . .
4.14 Typical Air Cooling Curves in Florida . . . .
5.1 Resemblance Tree from Cluster Analysis . . .
6.1 Pavement Model for Simplified Design . . . .
6.2 Idealized Pavement Structure at Design Life
(tO > 1.5 inches) . . . . . . . . .
6.3 Idealized Pavement Structure at Design Life
(tO < 1.5 inches and tO + tl > 1.5 inches) . .
7.1 Interrelations Between Subprograms of REDAPS . .
7.2 Flow Chart of Subroutine SORT . . . . . .
7.3 Flow Chart of the MEAPS Subprogram . . . .
7.4 Flow Chart of Subroutine PLOTQ . . . . .
7.5 Flow Chart of CRACK3 (PC) Subprogram . . . .
7.6 Flow Chart of Subroutine LCHG . . . . . .
7.7 Flow Chart of Subprogram OVLR2 . . . . .
8.1 Cracking Pattern of US 441 (Columbia County) in 1986
8.2 Effect of Binder Age Hardening Rate on Pavement Life
8.3 Effect of Cooling Rate on Pavement Life . . .
8.4 Effect of Cooling Time on Pavement Life . . .
B.1 Slope Intercept Relationship for Log Absolute
Viscosity at 60 C Versus Log Day . . . . .
B.2 Slope Intercept Relationship for Log Viscosity
at 25 C (0.001/sec) Versus Log Day . . . .
B.3 Slope Intercept Relationship for Log Viscosity
at 25 C (0.05/sec) Versus Log Day . . . . .
. . 103
. . 104
. . 107
. . 111
. . 121
. . 126
. . 127
. . 138
. . 145
. . 149
. . 152
. . 154
. . 164
. . 179
. . 180
B.4 Slope Intercept Relationship for Log Penetration
Versus Log Day . . . . . . . . .
B.5 Slope Intercept Relation for Florida Data
(Log V60 Versus Log Day) . . . . . . .
B.6 Slope Intercept Relation for Log PEN (25C) Versus
Log Day (Florida Data) . . . . . . . .
B.7 Slope Intercept Between Log V25 (J=100 w/m3) Versus
Log Day (Florida Data) . . . . . . . .
B.8 Viscosity Temperature Trends for Asphalt Recovered
from US 98, Panama City . . . . . . . .
B.9 Viscosity Temperature Trends for Asphalt Recovered
from Lab Samples Processed in 60 C Forced Draft Oven
B.10 Illustration of the Critical Viscosity Temperature
Concept for Temperate Climates
Flow Chart of the REDAPS (Version 2) Program . .
Introductory Message from REDAPS (Version 2) . .
Main Menu of REDAPS (Version 2.0) . . . . .
Sub-Menu < Pavement Evaluation > . . . . .
Sub-Menu < Rehabilitation Design > . . . .
The First Level Menu of Simplified Pavement Evaluati
Menu of Simplified Evaluation . . . . . .
Sub-Menu < MEAPS Interactive > . . . . .
Attention Message from REDAPS (Version 2.0) . .
Sub-Menu Before Executing MEAPS . . . . .
Sub-Menu of Detailed Pavement Evaluation . . .
Sub-Menu Before Executing CRACK3 PC . . . .
Sub-Menu for Thickness Design . . . . . .
Sub-Menu for Detailed Design Procedure . . .
. . 215
. . 218
. . 218
. . 219
. . 222
. . 222
. . . 225
. . 227
. . 231
. . 231
. . 232
. . 232
on . 234
. . 234
. . . 237
S. . 237
. . 239
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. . 241
. . 244
. . 245
Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
A MECHANISTIC ANALYSIS AND DESIGN SYSTEM FOR
EVALUATION AND REHABILITATION OF FLEXIBLE PAVEMENTS
Chairman: Byron E. Ruth
Major Department: Civil Engineering
Prior and current investigations into various areas relating to pave-
ment structural performance have led to the development of a microcompu-
terized mechanistic analysis and design system for flexible pavements
using nondestructive testing techniques. This computer program, namely
REDAPS (REhabilitation Design of Asphalt Pavement Systems), is based on
the Critical Condition (State) Concept rather than the conventional
fatigue failure criterion. It utilizes a multilayered linear elastic
pavement model and incorporates material properties, distress criteria,
combined effects of temperature, asphalt binder age hardening and vehic-
ular loads into a system that should minimize the effort required in
routine pavement evaluations and rehabilitation designs.
The program sorts Dynaflect data into categories using the
statistically based clustering technique developed in this research and
then backcomputes the pavement layer moduli by matching the predicted and
measured (Dynaflect) deflection basins. It assesses the structural
condition of in-service pavements at either the present time or five years
in the future utilizing two alternative approaches: 1) the simplified
analysis of vehicular induced stresses at the minimum regional pavement
temperature using a stress ratio criterion; and 2) the detailed analysis
of the combined effects of thermal and vehicular loads employing the
applied energy ratio criterion. Suitable rehabilitation strategies are
recommended after the simplified evaluation.
Two similar approaches were subsequently developed for use in reha-
bilitation design, namely the simplified and the detailed design proce-
dures. The former gives a quick assessment of the thickness requirement,
whereas the latter has the capability of both determining the thickness
and estimating the life of either an existing or a rehabilitated pavement.
The REDAPS program has been shown to give reasonable predictions of
the existing pavement condition, the required rehabilitation thickness,
life and potential cracking locations and directions, through comparisons
of the analytical results with the field performance of US 441 in Columbia
In addition, a heat transfer program (HTM) was developed to predict
temperature profiles of the pavement based on the exact solution of the
1-D Fourier transient heat flow equation. This program has been verified
with excellent agreement to the test data.
1.1 Research Need
Pavement maintenance and rehabilitation work is of key importance to
those highly industrialized countries who began construction of their
modern highway networks more than thirty years ago. Because needs greatly
exceed the budgets, funds provided for maintenance and rehabilitation of
pavements must be used as effectively as possible. One method to accom-
plish this is through the use of a pavement management system which inte-
grates design, material properties, testing techniques, rehabilitation
along with maintenance, and life cycle economics to maximize pavement life
and benefits. This comprehensive system can not be established before the
development of the following three major subsystems: 1) pavement evalua-
tion or diagnostic monitoring system; 2) design system, i.e., technical
selection of design strategies for rehabilitation and determination of
required thickness; and 3) economic analysis. In order to accomplish this
goal, it is essential that an integrated, time-efficient, and reliable
pavement monitoring system be developed to evaluate the deterioration of
pavement structural conditions and serviceability on a routine basis and,
when necessary, followed by the rational selection of design alternatives
for rehabilitation and the required pavement thickness.
1.2 Study Objectives
The primary purpose of this research was to develop a microcompu-
terized mechanistic analysis and design system for flexible pavements
using data from nondestructive testing techniques. The research was aimed
at providing the Florida Department of Transportation with computer pro-
grams adaptable to their operational system which will facilitate routine
pavement evaluation and the establishment of rehabilitation needs. This
includes the development of two subsystems, the pavement monitoring (eval-
uation) system and the rehabilitation design system.
The pavement monitoring system is a mechanistic analysis model based
on the multilayered linear elastic theory, which incorporates material
properties, vehicular loadings, and environmental factors, such as temper-
ature and age hardening of the asphalt binder. It evaluates existing
pavements based on routinely collected nondestructive testing deflection
data (e.g., Dynaflect data) and predicts whether or not rehabilitation is
necessary in the near future.
If rehabilitation or maintenance needs have been identified, the
design system will serve as the second step and provide the decision
making process for the selection of suitable rehabilitation methods and
thickness requirements to achieve adequate structural behavior of the
1.3 Scope of Study
The research was carried out in six major phases. Phase one included
the development of the computer program MEAPS (Mechanistic Evaluation of
Asphalt Pavement System) starting in January 1989. This program backcal-
culates the layer moduli of existing asphalt pavements based on in situ
Dynaflect data, layer thicknesses, testing temperatures, and asphalt
material properties (optional). It iterates either automatically or
interactively upon the user's request for tuning of the layer moduli.
Then it performs a load induced stress analysis to rate the structural
adequacy of the pavement sections. The first version of MEAPS together
with subroutine SORT, was developed on a main frame computer (1). It was
adapted to the FDOT main frame in April 1989.
In July 1989, the program was revised and made operational on a per-
sonal computer (PC). The subroutine SORT was completely rewritten using
a newly developed statistically based clustering technique, which not only
reduced memory requirement substantially but more importantly enabled the
program to better identify the pavement segments with similar structural
In phase two of the research, emphasis was placed on the development
of a simplified design program for selection of suitable rehabilitation
strategies and determination of required overlay or recycled pavement
thicknesses. Subroutine DESIGN was developed at this stage along with the
development of some other supplementary subprograms, such as TRSLATOR,
INPUT, and PLOTQ. When integrated with MEAPS, these subprograms, arranged
in a sequence, made up the basic software for the new program, REDAPS
(REhabilitation Design of Asphalt Pavement System).
As pointed out by Ruth (2, p. xi), "the REDAPS program constitutes
the first attempt," in the state of Florida, "to combine all key elements
in the process of pavement evaluation and rehabilitation design into a
system which should minimize the effort required to evaluate all necessary
data and generate pavement thickness requirements for rehabilitation
designs." This program, operational on 640K RAM PC's, reads input of
Dynaflect deflection data directly from the floppy disks on which the data
were originally collected in situ. It analyzes the pavement's structural
response in terms of layer moduli using subroutine MEAPS, and then com-
putes the maximum stress ratios in the asphalt concrete layer as produced
by heavy truck loads (24 kip single axle). Once the moduli have been
obtained, REDAPS suggests the suitable course of action for rehabilitation
using subroutine STRATEGY and determines from subroutine OVLR the rehabil-
itation thickness design requirements based on the design stress ratio.
The stress results and the deflection data can be plotted on the screen
and copied by the printer to serve user's needs. The REDAPS program has
been in operation on the FDOT PC since October 1989 (2).
The third phase involved the development of a PC-based detailed
analysis program for evaluation of the cracking potential of asphalt pave-
ments under the combined effects of thermal and vehicular loads. Although
MEAPS provides a quick, simplified method for assessing the potential for
cracking, it is applicable only when stress levels are very low or
extremely high indicating a satisfactory or unsatisfactory pavement struc-
tural condition. When the stress levels are intermediate, however, ther-
mal influence may be crucial to pavement failure (cracking). A detailed
analysis program for the combined effects of temperature change and heavy
truck loads is essential in this case to better define the cracking poten-
tial of the in-service pavements.
For this purpose, the main frame version, CRACK3, originally written
by R. Roque (1) and debugged by the author during the fall of 1988, was
completely revised to supplement the PC-based REDAPS program. This
revised version, namely CRACK3 (PC), reduced about one third of its
original memory requirement without affecting the computational capacity.
The basic principles, equations, and the critical condition (state) con-
cept used in the main frame CRACK3 were retained in the CRACK3 (PC).
CRACK3 (PC) was then successfully incorporated into REDAPS which was
renamed as REDAPS (version 2.0) in November 1989, for detailed analysis
under the main menu of PAVEMENT EVALUATION.
The fourth phase of the research concentrated on the determination
of the temperature information required by CRACK3 (PC). As the first step
in this phase of the research, the HTM computer program was developed to
compute hourly change in pavement temperatures at different depths. This
program was written based on an exact solution, expressed as an integral
to infinity, of one dimensional transient heat flow in an elastic medium.
The program overcomes the disadvantages of most close form solutions as
well as those of numerical models. It is not only applicable to any type
of pavement surface temperature variations but also time efficient and
highly reliable. This program has been verified, with excellent agree-
ment, by temperatures measured in an earlier full-scale pavement testing
As the second step, a supplementary program HEAT was developed to
predict pavement surface temperature variations with time in the state of
Florida. Although temperature has been generally recognized as the most
influential factor on asphalt concrete properties and numerous thermal
analysis models have been developed, little has been done to predict the
hourly pavement surface temperature variation often required as essential
input into these models. An attempt was made in this phase of the
research to estimate pavement surface temperatures based on hourly air
temperatures which are in turn predicted according to a segmentally linear
model. This model was established upon limited field data and was found
to predict satisfactorily the continuous change in air temperatures in the
state of Florida.
The fifth phase of the research was aimed at the development of an
improved design system (namely detailed design procedure) which would
determine the required pavement layer thickness for rehabilitation under
a critical set of temperature change conditions, vehicular loading, and
asphalt binder age hardening based on the applied energy and combined
stress criteria. In order to achieve this goal, a comprehensive study of
the field age hardening data for various states was conducted in January
to mid-February 1990. Several relationships relating material properties
to binder age hardening were established based on the analyses of nearly
two thousanddata points comprised of four different parameters (viscosi-
ties at different shear rates, testing temperatures, and penetrations)
over the age span up to 20 years. Some findings from this study were then
used in the improved design program to determine the overlay or recycle
layer thicknesses at critical states under thermal and wheel loads using
the bisection root searching technique. This detailed design program was
completed in the latter half of February, 1990.
Two conditions are considered in the design of overlay: the present
condition and the future condition at the end of the design life. In the
present condition, the stress and applied energy at the bottom of the old
asphalt layer covered with unaged material might be critical under the
given combination of thermal and vehicular loads. In the future condi-
tion, the age hardening of the surface layer may shift the critical point
to the top or at the interface of the overlay and the underlying old
pavement layer. Only the top 1.5-inch layer is considered to harden with
age unless the entire asphalt layer is less than 1.5 inches. This top
1.5-inch layer may be composed of new asphalt material only or both new
and aged asphalt concrete depending on the required thickness to be reha-
The final portion of the program, completed by the end of February,
1990, was developed for pavement life estimation. If an overlay or a
recycled layer thickness is given, the life of the pavement after
rehabilitation can be estimated using this subroutine based again on the
bisection root searching iteration procedure. The user is provided with
the flexibility of estimating the life of either an overlay or a recycled
layer individually or estimating both design alternatives and then
comparing the economic benefit. Life of the existing pavement may also be
estimated using this subroutine.
Additional efforts were made in the formulation of the pavement
evaluation segment of the program to provide the capability for a five
year projection of the structural condition for in-service asphalt con-
crete pavements based on the results of the age hardening investigations
for both simplified and detailed analysis options.
Today, highway engineers are facing the major challenge of maintain-
ing and preserving highway networks. Pavements which were built about
forty years ago in industrialized countries are deteriorating at an alarm-
ing rate. In the United States, for example, approximately 45% of the
pavement mileage on arterial routes needs some level of restoration. In
1987, over 11% of this mileage required major improvement. Nearly 170,000
miles of the over 2 million miles of paved roads in the U.S. are in need
of attention (3).
It was projected that the accelerating deterioration of federally
aided highways would require a 44% increase over the 1981 funding level to
$13 billion annually to meet the repair and rehabilitation costs through
1990 (4). The Federal Highway Administration (FHWA) reported that mainte-
nance expenditures have increased 195% from 1972 to 1985. Fifteen billion
dollars were spent on maintenance in 1984 with a predicted increase of
about $300 million per year. Even so, in 1985 42% of the total road mile-
age was still in some level of deteriorating condition (5). In 1987, it
was estimated that $40 to $45 billion were spent annually and some $400
billion would be required by the year 2000 to replace and rehabilitate
worn-out pavements (6).
Similar situations are being encountered in developing countries.
A quarter of the paved roads outside urban areas are in need of recon-
struction and an additional 40% require strengthening either now or in the
next few years (4).
Because of the worldwide need for extensive rehabilitation and main-
tenance programs in the 1980s and 1990s, increasing research efforts are
being made to develop and refine theories and models for pavement evalua-
tion and maintenance management. The success of these research activities
lies in the understanding of the mechanisms of pavement deterioration.
2.2 Life Pattern of Flexible Pavements
Investigations of over 3100 miles of interstate pavements revealed
that few if any of the pavements can last 30 to 40 years without rehabili-
tation. Percentage failures usually increase rapidly after about 16 years
of age or after experiencing 6 million total equivalent axle loads (7).
Bituminous surfacings tend to crack at some stage of their life under
the combined actions of traffic, environment, and material aging. The
crack, as a defect in the surface, reduces the pavement structural capa-
bility and at the same time allows water to penetrate into the base and
subgrade soils to weaken the underlying support. The lack of support in
turn intensifies the stress condition in the bituminous surface layer and
thus causes further cracking under the same traffic loading.
Even if there was no further weakening of the underlying support due
to water penetration, cracking would still increase very rapidly in
extent, severity, and intensity after initiation. This is because severe
stress concentrations will develop at crack tips leading to rapid crack
propagation. According to fracture mechanics, the stresses at the crack
tips under the same external loading can be over three times higher than
those before cracking. These deteriorating cycles will eventually lead to
disintegration or complete failure of the pavement surfacings. The rate
of pavement deterioration therefore accelerates after the appearance of
cracking, exhibiting a life pattern as shown in Figure 2.1 (4).
Figure 2.1 Typical Pavement Life Cycle
2.3 Pavement Distresses and Causes
The major types of pavement surface defects and their possible causes
are summarized in Table 2.1.
These types of pavement distress develop interactively with each
other at different stages of a pavement life. The short range cracking,
commonly referred to as premature cracking, is usually caused by poor
construction, poor mix design, unsuitable climate during construction or
opening for traffic too early. Middle range cracking is initiated under
Table 2.1 Pavement Distress and Possible Causes
Type of Distress
alligator (in wheel path)
3. permanent deformation
skid resistance (wear)
4. layer slippage
Main Possible Causes
traffic + environment
thermal + aging
heavy trucks + high temp.
the combination of traffic loading, environment and asphalt age hardening.
Long range failures (such as alligator cracking at wheelpaths, and rutting
due to shear failures of the subgrade) are often the result of material
fatigue due to repeated traffic loading and cyclic environmental changes
Once initiated, cracking progresses rapidly under traffic and allows
water to ingress into the underlying layers. The presence of water re-
duces the shear strength of unbound materials and weakens pavement sup-
port. This, accompanied by stress concentrations at crack tips, results
in further cracking and deterioration of pavement layers which may be
accelerated by the cyclic actions of traffic and environment. Starting
from cracked areas, the bituminous concrete pavement spelling and potholes
may develop, which constitutes a major hazard to vehicular traffic. Dete-
rioration can continue until complete disintegration of the pavement sur-
facing occurs. If no maintenance action is undertaken, deterioration of
the pavement can excessively reduce serviceability and incur greater costs
for users and subsequent reconstruction (4).
2.4 Mechanisms of Pavement Distress
2.4.1 Mechanism of Cracking
Cracking has long been recognized as the most important pavement
distress which governs pavement life. Cracking can be caused by many
different mechanisms, most of which interact under field conditions. In
general, the majority of flexible pavement cracking can be categorized
into four types, namely fatigue cracking, cracking due to excessive age
hardening, thermal cracking, and reflection cracking.
Fatigue cracking. Bituminous material will fracture under the cumu-
lative effect of repeated loading when the environmental condition is kept
constant. This type of cracking, namely fatigue cracking, is believed to
be the major contributor of alligator cracking in the wheelpaths, though
in reality it is generally the result of combined loading and environ-
Although much effort has been concentrated on fatigue studies, the
fatigue mechanism is still unclear. Marchionna et al. (9) assumed that
the deterioration of moduli from an initial value to the final value under
repeated load was caused by the growth of the microcracks within the mate-
rial. The modulus will remain unchanged until the first crack appears.
From this point on, the modulus will start to reduce as the cracks tend to
interconnect and propagate.
Age hardening. Through exposure to air, a bituminous binder hardens
over time primarily due to thermal oxidation, sometimes due to evaporation
of plasticizing oils by overheating during construction. The hardening
increases the stiffness and fracture susceptibility of asphalt binders.
Once the binder becomes so brittle that it can no longer sustain the
strains induced by the combined actions of traffic and environment, crack-
ing will occur. Research has shown that there exists a critical viscosity
beyond which the binder will crack under certain loading conditions. This
apparent viscosity, when measured at 45 C of extracted bitumen at shear
rate of 0.005/s, was reported in reference 10 as 5.01E5 Pa.S in temperate
climates and 3.16E6 Pa.S in tropical regions. (More details on the criti-
cal viscosity concept is presented in Appendix B, Section B.3.3). At this
stage, the pavement surfacings are usually nine years old although it may
range from six to fifteen years depending on binder composition (4).
The rate of age hardening depends on binder properties and film
thickness. Hardening rate, therefore, varies with asphalt type and envi-
ronment, especially temperature. Age hardening has the effect of limiting
the life of flexible pavement surfacings to about 8 to 20 years from the
time of construction to the initiation of cracking depending on the
asphalt type and mix properties under normal traffic and environment
Cracking due to aging was observed to have initiated from both the
top and bottom of the asphalt concrete pavement but crack propagation was
primarily from bottom upwards (11). This can be explained by the load
induced stresses superpositioned upon the original stresses at crack tips.
Since traffic loading induces compressive stress at the surface of the
asphalt concrete layer under and close to the wheel loading, the resulting
stresses are most likely compressive or at least the tensile stresses are
substantially reduced which retard the crack propagation towards the bot-
Thermal cracking. At low temperatures, asphalt becomes very hard and
brittle. Cracking will occur when the thermal contraction strain exceeds
the maximum fracture strain of the material. No single reasonable temper-
ature exists above which cracking will not occur (8). It depends on
binder properties and the effect of the range and rate of temperature
variation. Low temperature cracking usually starts in the transverse
direction at regular intervals. Initially, these intervals are relatively
large. Further cracking then occurs in the middle of each previous inter-
val until the length of the segment reduces sufficiently so that the
effect of cumulative friction can no longer induce tensile strains greater
than the tensile strength of asphalt concrete (8). Thermal cracking can
also occur in the longitudinal direction if the above condition is met.
The end result therefore could be map or block cracking.
Unlike cracking due to age hardening, thermal cracking is generally
believed to start from the surface and propagate downwards (4). The
extent and severity of thermal cracking depend on the rate of temperature
reduction and the range of temperature change. However, longitudinal and
transverse cracking are often the result of the combined effects of load-
ing and temperature.
Reflection cracking. Asphalt overlays, which are often used to
correct a cracked rigid pavement surface or a hardened flexible pavement
surface, are frequently found to have cracked in a relatively short time
after construction of the new surface. This type of cracking is commonly
referred to as "reflection cracking" since the cracks are, in most cases,
reflected from the old cracks in the underlying pavement layer. Reflec-
tion cracks are most frequently encountered in semi-rigid or composite
pavements (e.g., asphalt overlays on Portland concrete pavements) and are
identified as the major contributor to the deterioration of overlaid
The mechanism of reflection cracking is still a controversial issue.
Some believe reflective cracking results from cyclic stresses induced by
movements in the underlying pavement (13, 14). It was observed that
nearly 98% of the reflection cracking occurred over the transverse joints
of the concrete pavements and cracks often appear during the first
freezing season (15). Others believe the cracking is caused by the incom-
patibility of relative stiffness during construction of overlay and thus
recommend a new type of rolling equipment (16, 17). Recently, fracture
mechanics has been used in explaining the mechanism of reflection crack-
ing. This opinion demonstrates that reflective cracking is caused by
stress concentrations at crack tips (14,18,19). By comparing stresses and
strains at crack tips with those obtained by multilayer elastic analysis
of uncracked pavements, it was found that the higher the bending stiffness
(product of thickness and modulus) ratio of the old pavement over the new
overlay, the higher the strains at the crack tips (19). So far no methods
have been found to totally eliminate reflection cracking (20).
Other types of cracking. Freezing and thawing cycles can cause
severe damage to the pavement surface layer. Even a slight frost may
result in a series of disturbances to the pavement surface course. Alli-
gator cracking due to frost action was found to be proportional to the
amount of fines in a granular base course. Little cracking was observed
when the base had less than 5% to 6% fines (11). Longitudinal cracking
near the pavement edges commonly results from moisture movement through
the shoulder due to poor drainage or lack of a waterproof surface (4).
Chemicals from moving vehicles and de-icing salt also play a very impor-
tant part in the development of surface distress. A lack of bond and
presence of horizontal forces can result in friction course tearing, a
form of cracking when the asphalt mixture is hard and stable.
Cracking can also result from differential soil collapse in founda-
tions when the pavement is subjected to traffic and water. Houston
explained the mechanism of soil collapse in arid climate as follows (21,
As the soil dries by evaporation, capillary tension causes
the remaining water to withdraw into the soil grain interfaces,
bringing with it soluble salts, clay and silt particles. As
soil continues to dry, these salts, clays and silts come out of
solution and tack-weld the large grains together. This leads
to a soil structure that has high apparent strength at its low,
natural water content.
However, collapse of the cemented structure may occur upon wetting
because the bonding material (clay and silt) softens. Such soil is
unstable at any stress level that exceeds that at which the soil had been
previously wetted. The triggering for collapse is the addition of water
while load aggravates the condition.
2.4.2 Mechanism of Permanent Deformation
Permanent deformation or unrecoverable deformation in flexible pave-
ments includes rutting, shoving, heaving, and small depressions. Rutting
and shoving are considered to be the major types of permanent deformation
mostly encountered in practice. Rutting is defined as accumulated perma-
nent deformation of pavement layers in the wheelpaths which results from
the repeated application of heavy wheel loads (22,23). The term rutting
is often used in practice to refer to the vertical consolidation or densi-
fication under traffic. It occurs as a result of either densification of
one or more pavement layers or shear failure of the underlying base or
It was reported that rutting suddenly occurred on asphalt concrete
pavements that were in the range of 5 to 15 years old (22). This type of
middle life rutting is most likely caused by shearing failures or soften-
ing of the underlying material layers due to water damage after the ini-
tiation of surface cracks and delayed maintenance.
Field data have shown that asphalt concrete materials are more sus-
ceptible to rutting than other pavement materials (24). After 7 years in
service, pavements with sand asphalt base were observed to have rutted 50%
more than those with limerock bases. About twice as much rutting occurred
in the full depth bituminous sections as that in the unstabilized gravel
base sections (24).
These observations suggest that the major amount of rutting develops
in the asphalt concrete layer. This type of rutting is believed to be
mainly the result of poor asphalt concrete mix design and improper con-
struction, and usually occurs at the early stages of a pavement life. In
Italy, for example, the problem of rutting has been solved by the choice
of high performance mixtures in the asphaltic concrete layers (25). Texas
data show that 90% of the pavement will be free of rutting in 10 years
using the current mix design specifications (8). In France, the 'anti-
rutting' mix design procedure and tests have been very successful for 20
years despite hot summers and a 13-ton-maximum legal axle weight for
vehicles (26). These researchers found that the two important causes of
rutting which occurred in asphalt concrete layers were excessive asphalt
content due to poor mix design and low air voids due to densification from
traffic, though temperature frequently serves as a direct triggering
Laboratory research has indicated that a 5% reduction in the density
achieved can increase plastic strains by over 100% in individual layers
and may increase rut depth by 15% or more (4). Low initial density means
lower shear strength which would also increase the potential for shoving.
In Florida, however, densification rutting appeared to be a minor problem
compared with transverse shoving which generally occurred immediately
following construction (22).
Shoving involves lateral distortion or plastic flow as a result of
a combination of vertical and horizontal forces applied to the asphalt
concrete mixture. This type of permanent deformation is closely related
to the volume of heavy trucks, the tire types and the presence of hori-
zontal forces. Poor mix design, such as high asphalt content, soft
asphalt, excessive fines and low air voids, and poor construction are
usually the direct cause of the distress (27). It was concluded by most
investigators that proper mix design and construction can provide suffi-
cient asphalt concrete layers to support today's traffic without rutting
There is a balance between permanent deformation and cracking resis-
tance of the asphalt concrete mix. From the viewpoint of improving crack-
ing resistance, it may be desirable to use a softer asphalt and a higher
asphalt content. On the other hand, harder asphalts and lower asphalt
contents may be necessary to produce a stable mix (rutting resistant) at
relatively high temperatures when subjected to heavy traffic. Therefore,
different mix design specifications should be used in different climatic
2.4.3 Mechanism of Surface Wear
Ravelling. Ravelling is defined by some authors to be the loss of
stone particles from pavement surfaces either by mechanical fracture of
the binder film or by loss of adhesion between binder and stones (4).
Mechanical fracture of the binder occurs when the asphalt material
becomes very brittle due to age hardening or low temperature. It can also
occur due to excessive cracking in that the weakly attached particles are
torn away by vehicle tires and suction effect at high speed.
Loss of film adhesion to stone particles is usually caused by water
stripping or dust contamination. Hydrophilic aggregates are particularly
susceptible to debonding in the presence of water (4). Dust can prevent
full bond between aggregate particles and asphalt binders during construc-
Potholes. Potholes are open cavities in the surfaces of flexible
pavements. They are the most visible and severe form of distress. It is
a more severe type of ravelling both in extent, depth and intensity. Pot-
holing is the result of disintegration (severe cracking, spelling and
ravelling) of the surfacing and underlying materials. Potholes may
develop through lack of bond between surface and base course (4).
The diameter of potholes depends on the conditions and properties of
the surrounding surfaces. In thin, brittle surfaces, it progresses rap-
idly with generally a dish shape. Its depth depends on volume of traffic
and the presence of water which induces a scouring action to accelerate
the formation of holes. Potholing is, therefore, usually the ultimate
form of distress due to delayed maintenance, which is hazardous to
Lack of skid resistance. The surface texture of the aggregates tend
to polish under repeated friction from traffic tires. The rate of reduc-
tion in skid resistance depends on the mineral type and degree of surface
wear. Lack of skid resistance can also be caused by asphalt bleeding at
hot weather and the wetting of the surface by water. Binder bleeding can
result in stone embedment and water can yield hydroplaning (4). Both can
produce unsafe driving conditions when the skid resistance is reduced
below acceptable levels.
Roughness. Surface unevenness or irregularities in the wheel paths
often develop from different types of pavement distress which has a great
impact on vehicle ride and user costs. The relative influence of distress
mechanisms is distinguishable in most cases. Roughness is regarded by
some researchers as the end result of surface disintegration (4).
2.5 Current Status of Pavement Evaluation and
Rehabilitation Design Research
Research pertaining to maintenance and rehabilitation of in-service
pavements has generally developed into four major areas: pavement evalua-
tion, evaluation or characterization of materials, analytically based
rehabilitation design and pavement management.
2.5.1 Pavement Management
A pavement management system is defined as an integrated system of
design, material properties, testing techniques, maintenance and rehabili-
tation, together with life cycle economics to maximize pavement life and
benefits (30,31). For in-service pavements, this system involves
1) pavement evaluation or diagnostic monitoring system; 2) design system--
technical selection of design strategies for rehabilitation; and 3) eco-
nomic analysis for timing, priority sorting, and optimization of strate-
gies at network or project level.
In recent years, pavement maintenance management has received
increasing attention because of the fact that accelerating maintenance
needs are far beyond budgets. As described previously, new paved roads
deteriorate very slowly in the first ten to fifteen years of their life,
and then deteriorate much more rapidly unless timely maintenance is
undertaken (4). A recent study estimates that much of the $90 billion
cost of the current maintenance work could have been saved by spending $12
billion on earlier preventive actions (4). According to one researcher,
if structural work is delayed for 2 years, the thickness of the overlay
will have to be increased 50% in order to avoid excessive fatigue in the
base course (26). It was reported that corrective rehabilitation being
done after failure develops in a pavement may cost in excess of four times
more than preventive maintenance undertaken before failure (3). Con-
versely, a 1% reduction in life cycle costs can lead to savings of $100
million per year. These savings can easily be achieved by improving the
reliability of performance or extending the effective life cycle of a
pavement by as little as two months (6).
The worldwide need for the establishment of a comprehensive pavement
maintenance management system has become a great driving force pushing the
progress of research in this field. Most of the effort has been made in
developing models for prediction of pavement performance and life cycle
cost, and the selection of proper techniques for optimization. It is
widely agreed that at network level, more simplified models are preferred
since they are often used in the analysis for planning and decision making
from an economic point of view. At project level, more detailed technical
analysis is necessary in diagnosing the actual deficiencies, the probable
causes for the defects, and alternative corrective methods. This may
include a preliminary design of what needs to be done and when action
should be taken based on the cost-effectiveness of alternatives.
A great deal of emphasis has been placed on the development of empi-
rical models for pavement performance (4,32,33). Some use a unique index
such as pavement serviceability index or roughness as the measure of pave-
ment condition (33-38). Others strongly urge that the structural response
and functional performance of the pavement should not be combined into one
index (4,32). These models together with the optimization techniques,
such as linear programming or dynamic programming based on life cycle cost
analysis (39-41), are important contributions in the development of a com-
prehensive pavement management system.
However, many questions still remain unanswered due to the complexity
of the problem. The most controversial issue is the method of quantifying
user's costs. Since the most economical pavement is not always the one
which costs the least but rather the one that yields the maximum benefits,
user's cost plays a vital role in the life cycle cost analysis. However,
it is the most difficult one to be converted into monetary values and is
attitude dependent (32). In addition to this, many other problems also
exist in a complete comprehensive pavement management model. They include
1) inaccurate methods for quantifying traffic uncertainties and
2) inaccurate considerations of environmental factors;
3) inaccurate material characterization;
4) lack of a reliable functional performance models; and
5) lack of sound criteria for design and decision making.
Despite the difficulties involved, pavement management has saved the
highway administrations a considerable amount of money and has brought
greater confidence in decision makings for highway maintenance agencies
In recent years, research in pavement management has been directed
toward the development of an expert system using the concept of artificial
intelligence (5,43-46). Expert systems are computer programs designed to
include a simulation of the reasoning and decision making process of human
experts. The only system available so far for maintenance and rehabilita-
tion of flexible pavements is named as SCEPTRE (44). Developed in Wash-
ington state, this program evaluates 24 possible rehabilitation alterna-
tives based on the pavement surface conditions at the project level. It
makes a specialized body of knowledge accessible to a much broader range
of potential engineering users. Another program, ROSE, was developed by
the Ontario Ministry of Transportation and Communication for routing and
sealing of in-service pavements in cold areas. For concrete pavements,
EXPEAR was developed by Federal Highway Administration, University of
Illinois at Urbana-Champaign. A different system, PAMEX, is also in the
developing stage (5).
While the application of high technology, such as artificial intelli-
gence, in pavement maintenance management has provided a valuable tool for
highway administrators and engineers, its limitations must also be under-
stood. First of all, the computerized expert system can not substitute
human experts completely. The computerized knowledge base is relatively
limited as compared to the knowledge of highway experts at all levels of
agencies. Secondly, the human knowledge which was gained through experi-
ence can not cover all types of loading and environmental conditions
encountered in the field. A rule obtained in one area may not be appli-
cable to another area or to slightly different situations. It is there-
fore essential that any research system be used as an aid in decision
making in which careful engineering judgement is always exercised.
2.5.2 Pavement Evaluation
One of the most important elements of a pavement maintenance and
rehabilitation system is pavement evaluation which requires improvement in
field testing techniques and analysis methods. Pavement evaluation con-
sists of two parts: structural evaluation and functional condition sur-
vey. The functional condition of a pavement usually includes riding
quality (roughness), skid resistance, rutting, driving visibility, noise
emission, and tire wear, etc., which describe the road condition in terms
of comfort, costs, and safety at a given point in time. Structural condi-
tion determines the road response in terms of bearing capacity, structural
adequacy, and its change in condition over time. In fact, the surface
distresses are often closely related to both functional and structural
condition of a pavement.
Surface condition survey. Surface condition surveys have tradition-
ally used visual inspection methods for many years. Recently, increasing
efforts have been made to improve and automate the process of pavement
surface condition surveys. The High Speed Road Monitor is probably the
most recent type of equipment that was available commercially for use in
1989 (47). It measures the surface profile or evenness, cracking, and
rutting conditions at normal driving speed with no interruption of traffic
daily flow. Research on the automation of pavement surface distress eval-
uation is underway at the Texas Department of Highways and Public Trans-
portation (48). Although the equipment, namely Motorola with lasers and
portable computer, is still of limited use so far, it has proved to be
promising. Another surface cracking measuring device is the cost-
effective, 70mm format non-metric camera based data collection system
(49). This system can be mounted on a road vehicle, combined with digiti-
zation using an analytical stereoplotter and analysis software, and is
shown to be effective in analyzing pavement cracking and rutting. It has
two major advantages: 1) allowing for fast collection of data without
significant interference with traffic, and 2) providing permanent records
of road surface condition history. Further feasibility and economic anal-
ysis will be needed before it can be adopted for practical use. Similar
equipment suitable for daylight use at highway speed is also under devel-
opment in research projects funded by the Federal Highway Administration
Testing equipment and analysis methods for structural evaluation of
pavements have been better developed than those for surface condition sur-
vey. In recent years, research in the structural evaluation of in-service
pavement performance has been directed towards the combination of
mechanistic models with nondestructive testing (NDT) techniques primarily
because the advantages of both methods have been well recognized.
Nondestructive testing. As its name implies, nondestructive testing
preserves the integrity of in-service pavement structures by eliminating
the trenching, repairing, and termination of traffic involved in destruc-
tive testing which is relatively expensive and time-consuming. Nonde-
structive structural testing generally involves application of some type
of dynamic load to the surface of the pavement and measurement of the
responses in terms of deflection, wave propagation through the media, etc.
Among the various types of the NDT equipment developed, surface deflection
measuring devices, such as Dynaflect, Road Rater, and Falling Weight
Deflectometer (FWD), have gained widespread popularity because they are
not only simple to operate, time-efficient, and relatively inexpensive,
but also capable of modeling more closely the actual traffic load intensi-
ties and durations. One of the main objectives/advantages of NDT of flex-
ible pavements is to provide a quantitative basis for evaluating the pave-
ment's structural condition at any stage of its life. A more detailed
description of these techniques can be found in reference 51.
Recently, a new nondestructive testing technique has been devised
which measures both the undeflected profile before loading and the
deflected profile at the same points after loading (52). The difference
between the two readings is considered to be capable of better defining
the deflection basin induced by wheel load; the capability all other NDT
devices do not have.
Deflection analysis. Among the currently used NDT devices, the wave
propagation method has not gained widespread application because of the
relative sophistication involved in field operation and data
interpretation (51,53). The development of the analytical methods has
therefore been concentrated on interpreting the deflection measurements to
relate them to the structural properties of the pavement, namely equiva-
lent elastic layer moduli.
As pointed out by Bonnot (54), the methods for analyzing the shape
of the deflection basin are currently very much in favor because the shape
provides greater definition of the pavement structural characteristics
than maximum deflection alone. The principle of interpreting the shape of
the deflection basin lies in the fact that the thickness and moduli of
pavement layers and subgrade determine the shape of the deflection bowl.
Hypothetically the layer moduli can be determined from the deflection
basin by solving an inverse problem.
Although empirical methods have been traditionally used in pavement
analysis for decades, their limitations have been widely recognized in
recent years. One of the important weaknesses of the empirical methods,
which establish a relationship between one dependent variable and several
other independent variables by regression, is that the conclusion may not
be transferable. The result obtained quite expensively may represent only
a thread of the local situation and not necessarily identify the true
underlying relationship between the variables. The extrapolation of empi-
rical relationships to any other circumstance will be very risky unless
the failure mechanism is fully understood. Because the mix properties,
traffic, and environmental condition will change with time and place, the
use of mechanistic analysis methods has, therefore, become increasingly
popular in recent years.
The mechanistic analysis procedure integrates material properties,
traffic information, environmental conditions, and the analysis of the
pavement's structural response (stresses, strains and deflections). Three
kinds of mechanistic analyses are currently in use or development. They
are Finite Element Method (FEM), layered elastic theory, and dynamic anal-
ysis which will be discussed in more detail in the subsequent sections.
Layered elastic theory. The most widely used mechanistic method at
present time is the linear elastic or viscoelastic theory of a multi-
layered halfspace subjected to uniform pressure acting on a finite area at
the surface boundary (55-64). A complete literature review of the devel-
opment of layered elastic theory is presented in reference 51 and will not
be repeated here.
The validity of the layered elastic theory has been verified by many
investigators (51,65) although there are still some disagreements on mate-
rial characterization and the dynamic loading effect. In pavement evalua-
tion, layered elastic theory is often used to compute the equivalent
elastic modulus values by matching the predicted with the measured deflec-
tion basin. This is known as the backcalculation procedure in the litera-
ture. Because of the iterative nature of the computation, several com-
puter programs have been developed for this purpose (66,67). Among these
programs, the program VESYS, developed by FHWA, is so far the only program
designed to account for the viscoelastic behavior of asphalt materials.
The backcalculation method determines the pavement layer moduli iter-
atively based on the linear elastic program (54). This method provides a
mechanistic approach which incorporates material properties along with
environmental factors into a pavement analysis system.
Although the use of linear elastic layered theory has provided high-
way engineers with a mechanistic approach for the design and evaluation of
asphalt concrete pavements, it has been challenged by the engineers
because of nonlinearity and inelastic behavior of pavement materials,
especially the granular base and subgrade soils. Tests have revealed that
the behavior of asphalt concrete is primarily influenced by temperature
and the rate of loading. Asphaltic materials will become stiffer as the
rate of loading increases and as the temperature decreases. The granular
base course and subgrade properties are dependent upon more complicated
parameters, such as moisture content, density, stress history, soil
fabric, etc. This made it extremely difficult, if not impossible, to
establish quantitative relationships of pavement and subgrade layer moduli
in terms of these parameters which could be conveniently used in routine
pavement evaluation and design methods.
Finite element methods. Because of the capability of simulating the
nonlinearity and the stress dependency of pavement materials, several
Finite Element Methods (FEMs) have been developed (68-70) based on mate-
rial characteristic relationships established in laboratory testing. One
such program is ILLI-PAVE (68,69). This program considers the stress
dependent and nonlinear resilient modulus together with the failure crite-
ria of the granular materials and soils. Although the program was found
to give reasonable values, the computations are too costly and complex to
be used in routine pavement design (69).
Another FEM program namely Mechanolattice Analysis simulates the
unbound behavior of the granular materials and soils (70). It was con-
cluded ironically that having an unbound layer (base and subgrade) in
certain cases apparently extended the fatigue life of the asphalt concrete
by giving it a greater plastic behavior. Rutting appeared to be less at
the surface when the unbound option was used but much greater at the top
of the subgrade leaving an increasing gap between the asphaltic concrete
layer and the subbase as each wheel load passes. In all cases, greater
rutting was obtained when the layers were composed of bound materials than
with a bound surface underlain by an unbound layer.
Dynamic analysis. In recent years more emphasis has been placed on
research in the field of dynamic simulation of NDT techniques (71-78). It
is argued that since almost all the NDT devices apply some type of dynamic
loading to approximate moving wheels, it is questionable to interpret the
measurements by static analysis in which inertial force plays no part.
Sebaaly et al. (73) concluded that in the backcalculation procedure,
static analysis of FWD measurements overestimated pavement stiffness 25%
to 30%, which is unconservative. Because of the wave propagation nature
of the dynamic response, the pavement surface profile differs in several
aspects from the stationary deflection basin assumed in the static analy-
sis. Davies et al. (74) pointed out that the dish shaped deflection basin
is valid only at low frequencies or with a static loading. Otherwise, the
instantaneous deflection is wave amplitude and frequency dependent. In
the current static analysis, the envelope of the peak to peak instanta-
neous deflection wave is often used, which may be quite different from the
static deflection basin.
Mamlouk (75,76) also emphasized the difference between the term dyna-
mic modulus and the resilient modulus. He pointed out that the former was
frequency dependent whereas the latter represented the slope of the
stress-strain relationship after many load repetitions.
In dynamic analyses, the pavement structure is usually assumed to
have laterally infinite layers underlaid by a rigid bedrock or incompres-
sible layer at a finite depth. The layers are fully bonded with each
other and the viscoelasticity of the material is considered through the
use of the dampening ratio. The major dissipation of energy in the con-
tinua results from radiation (geometric) dampening rather than material
dampening. Geometric dampening is the dispersion of energy from the
source of excitation to the far field.
It was concluded that when testing frequencies of the NDT devices
coincide with one of the fundamental frequencies of the pavement system,
a resonance condition will occur. In this case, the deflections predicted
by static analysis can be only about half of those obtained by dynamic
analysis. The readings of the furthermost sensor (i.e., the responses of
the subgrade) are most affected in amplitude by resonance (75). However,
if the depth of bedrock is greater than 60 ft or more, or if the resonance
condition can be avoided, the dynamic responses of the pavement are very
close to the static responses (75-77).
Mamlouk found that for the pavement sections they tested, the first
fundamental natural frequencies of the pavement are in the range from 13
to 16 Hz while the secondary frequencies are between 30 and 42 Hz which
are all higher than the operating frequency of the Dynaflect, i.e., 8 Hz
(75). However, these frequencies may change with temperature, moisture
condition, and pavement structural compositions, and could be as low as 8
to 10 Hz (79). It is therefore urged that the Dynaflect be used with
greater caution since it can not operate over a range of frequencies to
detect the resonance. Other investigators found that Dynaflect deflec-
tions for pavements in Texas region were independent of the operating
frequencies in the range of 6 to 10 Hz (80).
The dynamic analysis results indicated that FWD appeared to be the
most suitable NDT device because it not only simulates more closely the
shape and nature of the moving wheel loads but also covers a range of
testing frequencies. If resonance occurs at any single frequency, its
effect is essentially eliminated by the averaging of deflections at reso-
nant and nonresonant frequencies when the impact load is simulated by the
Fourier series expansion (76).
2.5.3 Pavement Rehabilitation Design
General framework. The design of a new or rehabilitated pavement
system differs in some important aspects from other civil engineering
design problems. First, it is not an either/or problem, i.e., either a
fail or no-fail condition. Pavements deteriorate gradually over time.
The design thus is not aimed at predicting a sudden failure but a slow
progress towards failure before a given time or expected number of traffic
loadings is reached, with no major structural safety concerns (25,32).
When a pavement needs rehabilitation or corrective maintenance, the
major strategies used are reconstruct (i.e., remove and replace--recycl-
ing) or overlay. In the case of reconstruction, the original design fea-
tures, such as elevation and subbase material, are usually preserved. In
the case of overlay, however, the thickness of the new surface layer needs
to be determined.
It is generally agreed that the NDT surveys are an important part in
the evaluation of existing pavements for overlay design. These surveys
usually provide information on layer thickness and moduli based on deflec-
tion measurements and other techniques, and information on pavement sur-
Table 2.2 summarizes the general features of the current analytically
based (mechanistic) procedures and their differences. These procedures
generally follow the same steps as shown in Figure 2.2 and the same
Summary of Existing Analytically Based
Overlay Design Procedures
Procedure NDT Layer Moduli Analysis Pavement Distress Ref
Determination Computer Model Criteria
Field Lab Program
Shell FWD Yes No BISAR EML* fatigue
FHWA- Dynaf. fatigue
ARE Benk. No Yes ELSYM EML rutting 81
RII others Yes Opt. ELSYM EML fatigue 81
Rater Yes No CHEVRON EML fatigue 81
FHWA- Dynaf. EML for fracture
ODE FWD No Yes ODE Ei beam due to 82
Road on elas- underlying
Rater tic foun- movements
South RSD No Yes graph ELT fatigue 83
Africa NITRR rutting
Alaska FWD opt Yes ELSDEF EML fatigue 84
Note: *, EML stands for Elastic Multilayer system
ELT is Equivalent Layer Thickness (Odemark's concept)
Pavement model and
Adjust Ei -- Compute deflection basin
No Pred. and meas.
Adjust material properties
Input design loads
Figure 2.2 General Overlay Design Flow Chart
assumption that the pavement structure responds to traffic loading as a
multilayered elastic half space.
Although the general frame work appeared to be similar, a tremendous
amount of difference exists among all the present methods in almost every
aspect of the procedure, such as the methods for the consideration of the
influence of traffic, environment, design criteria, etc., which will be
discussed in more detail hereafter.
Pavement models. At the present time, analytically based overlay
design methods rely very heavily on elastic layered theory although other
methods, such as FEM, dynamic analysis, fracture mechanics and probabilis-
tic approaches, are receiving increasing attention (85,86). The main rea-
son for the popularity of the layered elastic theory is the simple, conve-
nient and time efficient nature of the procedure. Most layered elastic
programs can run on a microcomputer in a short time. Conversely, the FEM
requires not only a mainframe but also a considerably amount of time and
cost due to the iterative nature of the nonlinear problem. Because of
this, some design charts have been developed from the finite element pro-
grams for use in routine designs to simplify the procedure. However,
these charts can only represent limited loading and environmental condi-
tions and depend on the criteria used in developing the charts.
As compared with layered elastic programs which need three input
variables namely modulus, Poisson's ratio and layer thickness for each
layer, the dynamic analysis requires two more input parameters for the
materials in each individual layer, i.e., density and material dampening
ratio. This increases the complexity of material characterization and
time for computation. On the other hand, the dynamic analysis was
reported to yield results very close to those by the static analysis when
the resonant condition is avoided. It therefore appears that improving
the testing technique to ensure a nonresonant condition during testing
would be better than simply discarding the static theory for pavement
Fracture mechanics has been proven to be a very powerful and unique
tool in explaining the crack propagation mechanism in a pavement struc-
ture. However, its application in routine design is limited by the com-
plex nature of cracking and loading situations. Even for very simplified
special cases, such as a few cracks aligned in a line perpendicular to the
uniform loading direction, it is quite difficult mathematically to find
the exact solutions. Besides, crack propagation models, which usually
have to rely on a finite element program, inherit the previously mentioned
disadvantages of the FEM analysis.
Recently, probability theory has been used in pavement rehabilitation
design (87). This approach emphasizes the fact that when a very precise
set of data obtained by a careful analysis of the materials and control of
the loads was used, the elastic layered programs yielded strain values
very close to the computed values. The deviation of the theoretical
results from the measured field data could therefore be caused by the
random nature of the variation in the material properties, traffic, envi-
ronment, etc. The uncertainties of load, material and environment can
only be better estimated by probabilistic description of the parameters,
the distribution of which should be used as input for the layered pro-
grams. Similar to other methods, the probabilistic method also needs more
computer time. It computes, many times instead of just once, the values
of stress, strain and deflection results, based on a group of randomly
selected input parameters from the distribution curves. As a result, the
distribution curve of the pavement fatigue life is obtained. A great deal
of effort will be necessary before this approach can be used in practical
All these difficulties and the research work of Maree et al. (88),
Ullidtz (32), Brown and Pappin (89), and Ruth et al. (90) suggest that the
simplest way for design or evaluation of asphalt concrete pavement system
involves the use of linear elastic layered theory provided that the equiv-
alent elastic moduli of the material are properly characterized. Field
measurements have indicated that elastic theory provided a reasonable
estimate of pavement response to moving loads (91).
Nevertheless, the limitations of the layered theory have been well
1. Unique solution of layer moduli may not be guaranteed in the
backcalculation procedure. Several combinations of layer moduli may yield
almost identical deflection basins. It is difficult to identify which is
the one actually encountered in the field.
2. Stress dependency, nonlinearity and inelasticity of subgrade
soils are not characterized in a linear elastic model.
3. The assumption of homogeneity within layers may not apply when
asphalt concrete layers are cracked.
4. Variation of layer thickness is interpreted as variation of layer
moduli. Unless layer thickness can be more precisely detected by in situ
technique, such as radar, the computed stresses or strains may be in
5. When pavement upper layers are thick or when their stiffnesses
are high, the furthermost sensor position of the NDT devices may not be
far enough to represent only the response of the subgrade.
6. The currently used sensor positions may not be the most appro-
priate configuration. Further research is necessary on sensitivity analy-
sis of those sensor readings. Pronk found that the moduli of the asphalt
surface layer and base course are independent of the deflection basin
defined by the current FWD sensor positions (92). The backcomputed layer
moduli can therefore be in large error for the current FWD geophone con-
7. When resonance occurs, the analysis of layer properties based on
the static layered theory can be in substantial error (71-78).
Traffic considerations. There are many variables associated with
traffic, such as the magnitude of load, the number of repetitions, the
vehicle speed, the vehicle type, tire type and pressure, and contact area.
All these have a great influence on the structural responses of a pavement
and its service life.
Traffic loading. Full-scale pavement tests have revealed that the
traffic data can be simplified into equivalent load or loads having the
same damaging effects (8). The load equivalence law has the form of
(Ni/Nj) = a (Pj/Pi)n, where N represents the number of load application and
P denotes the load, and subscripts i and j refer to the equivalent and
actual cases respectively. The destructive power n was found to be asso-
ciated with traffic load, pavement material, pavement structure and dis-
tress type. Constant a is used to account for dynamic effect. A n-value
of 4 was found to be generally true for flexible pavements under normal
traffic and environmental conditions.
The concept of load equivalence allows the complicated real traffic
information to be replaced by a single load (standard load Ps) repeated Ns
times, leading to an equivalent traffic that is much easier to handle in
mechanistic analysis of pavements. Most existing design methods use the
load equivalence concept. Frequently, a standard dual wheel 18 kip axle
load is used ( 1). Multiple wheel loads may be simulated using superposi-
tion in linear elastic layered program. However, it is not valid when
nonlinear material properties are considered. This suggests another
important practical limitation when employing nonlinear methods into mech-
anistic design procedures (11).
Tire type and pressure. Design methods utilizing layered elastic
theory generally express traffic in terms of standard design loads which
are assumed to be uniformly distributed over one or more circular areas.
However, it has long been recognized that the actual contact area is not
circular nor the contact pressure uniform. The nonuniform pressure as
produced by real tires can cause significantly higher strains and subse-
quently produce premature cracking of the pavement (93). Roberts (94)
discovered that when asphalt concrete layer thickness was less than 2
inches, nonuniform tire pressure could produce 100% more strain than
uniform pressure. Better pavement performance was observed when the
asphalt layer was thicker.
Uzan and Sides (95) studied the effects of contact area and pressure
distribution by numerical integration of the theoretical point load solu-
tion to simulate any pressure distributions with any contact area. They
concluded, based on the results for a rectangular contact area with non-
uniform pressure, that the assumption of circular contact area with uni-
form pressure is slightly conservative and adequate for design purposes
when asphalt concrete layer thickness is in the range of 1.8 to 4.0
inches. Chen et al. (96) also found similar results, i.e., the uniform
pressure model appeared to be on the conservative side in most cases.
Another study also appeared to support the conclusion that the response of
the conventional pavements (i.e., asphalt concrete layer thickness greater
than 2 inches) as measured by maximum tensile stress was affected more by
load than by tire pressure (97). Monismith et al. (98) found that wheel
load is more influential than contact pressure for thick asphalt layers
whereas the opposite is true for thin asphalt layers. Saraf et al. (99)
concluded that uniform pressure with circular contact area overestimates
the tensile strain at the bottom of an asphalt layer but underestimates
the surface tensile strains due to an increase in wheel load. The
vertical compressive strain at top of the subgrade is underestimated and
more influenced by load than by pressure.
Kim (100) found that a 25% increase in tire pressure resulted in a
40% to 60% increase in equivalency for a dual tired single axle of 18 kips
and a tandem axle of 34 kip load as far as the stability of the asphalt
mix is concerned.
Vehicle type and speed. Ceban (101,102) has made a quite extensive
theoretical study on the modeling of a vehicle's dynamic effect and its
interaction with pavements. In one study, a truck was modeled as a two
dimensional, 7 degrees of freedom system with variable contact areas and
wheel lift-off capability. The bogie suspension system was idealized by
a rigid beam with leaf spring elements at each end. Stiff bump stops were
included on all axles. The road surface response was modeled by a two-
dimensional Euler beam supported by a dampened, elastic (Winkler) foun-
dation. The pavement was assumed semi-infinite, linear, continuous system
subjected to moving random impulsive loads. The typical responses of the
road surface model at a vehicle speed of 30 meter/second were found to be
in agreement with the experimental results reasonably well (101).
In the other study, a trailer was modeled to have a four leaf suspen-
sion in which the four spring elements were jointed by two light beams and
a massless load leveller. The sprung mass effects were modeled by rigid
11 ton mass for each half of the vehicle. The tires were simulated by
linear springs and parallel viscous dampers with facilities for departure
from the road surface and simple contact patch averaging of short wave-
length roughness. The research has demonstrated that the nonlinearity,
such as tire, leaf spring properties, smoothing of the surface profile by
tire footprint, have a significant effect on the transient response of the
pavement surface (102). Based on the existing design criteria (rutting,
fatigue) and dynamic force criteria, the road damage was found to increase
steadily with vehicle speed. There are certain speeds at which pitch cou-
pling between axles resulted in a significant increase in the damage at
particular points along the road.
Another study on pavement dynamic response concluded that when the
vehicle speed was greater than 40 km/h, the rubber suspension yielded
dynamic loads substantially higher than the air suspension (103). Several
researchers have shown that pavement surface deflections decrease with
increasing vehicle speed (102,104) due to application of the dissipation
equation. The change of deflection with speed was not largely affected by
tire pressure, axle spacing, and pavement stiffness. The vertical stress
pulse at a point within the pavement was found to increase duration and
decrease amplitude with increasing depth due to the spread of load over a
larger area. The peak stress varied only slightly with speed. However,
the degree of skewing of the shape of the stress pulse with depth intensi-
fied when vehicle speed increased, especially at high speeds due to iner-
tial effect (104). Radial stress was found to be more critical when
wheels were moving. The peak stress indicated a significant increase as
the vehicle speed increased.
All these results are still in research stage. Few mechanistic con-
sideration of these factors are available in current design methods.
Environment and climate. Climatic factors, such as temperature, wind
velocity, humidity, solar radiation, etc., have a significant effect on
the characteristics of pavement materials, but are probably the least
understood of the design variables. The deterioration of materials
because of environment influence has not been presently taken into
account, in any detail, in either mechanistic or empirical design methods
(11). Asphalt concrete is known to be more sensitive to temperature
whereas subgrade soils are more susceptible to moisture changes.
Temperature effect. Most existing mechanistic design models consider
the temperature effect through its influence on asphalt stiffness. In
order to predict the thermal stress and cracking potential, accurate pave-
ment temperature prediction is necessary. This includes the magnitude and
variation of temperature with time and position within the pavement. The
best model so far for predicting pavement temperature is the Heat Transfer
Model based on the meteorological data, such as percent sunshine, wind
velocity, and air temperature, and the material thermal properties, such
as thermal conductivity, specific heat capacity, etc. (105-107). This
model predicts the temperature distribution within the pavement structure
as a multilayered elastic system. The governing Fourier equation for heat
aT(z,t) k 2T(z,t)
at pc az2
where T(z,t) pavement temperature at depth z and time t;
k thermal conductivity
c specific heat capacity
a partial derivative
Some use different thermal parameters for different layers. Most
prefer using thermally homogeneous media. Studies show that this approxi-
mation is justified from practical point of view (8). The boundary condi-
tion at the pavement surface must be known to define the solution of the
transient heat flow equation.
Two types of solutions for the one-dimensional Fourier equation have
been used. One is the exact solution for the thermal homogeneous block by
assuming the temperature circles in the following form (8):
T(z,t) = Tm + A sin (2n t/P Bz) exp (-Bz)
where Tm = mean surface temperature
A = (Tmax Tmin)/2
amplitude (mean) of temperature cycle T(0,t)
P = period (1 day, a month, 1 year, etc., same unit as t)
where factor B = (nxct/P) is the degree of damping of temperature with
This solution uses the sine boundary condition, i.e.,
T(O,t) = Tm + A sin (2i -)
The other solution uses the finite difference solution to compute
pavement temperatures as a function of time and depth based on a boundary
condition defined by meteorological data. Energy balance procedures have
been used to relate pavement surface temperature to climate parameters,
such as percent sunshine, wind velocity, etc. (106).
Good agreement between predicted and measured pavement surface tem-
peratures have been reported (8,108).
Water content. Water can cause many types of distress in flexible
pavements, such as stripping, localized upheaving, separation of layers,
and maybe the most dangerous of all, reduction in the strength of the base
and/or subgrade. It was reported that 80% to 90% of major pavement fail-
ures are attributable primarily to the presence of water (23). When free
water is present, each wheel application can cause at least forty times
the structural damage that would occur when the pavement is relatively dry
(11). Freeme et al. (109) have clearly demonstrated the rapid deterio-
ration of pavements when water enters a granular base.
Water has a much greater detrimental effect on the performance of the
subgrade materials than on the asphalt layer even though stripping can
also cause damage to the bituminous surface. Field investigation revealed
that after 7 years more alligator cracking was observed in granular base
pavement than in full depth asphalt concrete base pavement (23) partially
because asphalt pavement layers are less susceptible to water. Excessive
moisture will cause a loss in subgrade's bearing capacity and induce fur-
ther cracking of the surface layer due to weakened support.
At the present time, the models accounting for moisture effect are
mostly empirical and not valid for different types of climate. The sea-
sonal variations in moisture are usually handled by varying the equivalent
elastic modulus of the unbound layers and soil with the season of the
year. The spring thawing period is generally regarded as the worst season
of the year (110). The problems of water damage are commonly solved by
improving drainage rather than by mechanistic designs.
Very recently, an one-dimensional nonlinear numerical analysis method
has been developed for the prediction of moisture distribution in the
unsaturated soils (111). However, the model is limited to studying the
effect of nonlinearity of material thermal parameters on the moisture
distribution and in its present stage of development is of very little
practical value for use in pavement design.
Dempsey et al. (106) proposed an equilibrium moisture model in 1986
with the following assumptions:
1) temperature of subgrade is constant, uniform, above freezing;
2) subgrade cannot receive moisture by infiltration through pavement
or by migration from adjacent soil masses with higher pore water pressure,
nor can it give up moisture by evaporation or migration to adjacent soil
which have lower pore pressure;
3) a relation exists between pore water pressure in the soil and the
suction of the soil at a given level; and
4) a relation exists between the suction and the water content of
A coupled heat and moisture flow equation model is currently being
developed by the Federal Highway Administration, which should provide a
much better simulation of the environmental conditions of pavements by
taking into account the interactions between the two flows in both time
As far as damage due to water stripping is concerned, no mechanistic
model has been developed even though a lot of research have been conducted
in studying the causes of stripping. The emphasis has been placed on the
testing techniques and the effectiveness of antistripping additives and
other engineering measures (112,113).
Design distress criteria. A number of design criteria have been pro-
posed for use in overlay design using NDT devices. The maximum deflection
was one of the criteria used in early days. As mentioned previously,
increasing efforts have been made in recent years to use information
provided by deflection basin measurements. At the present time, almost
all analytically based (or mechanistic) design methods use fatigue and
rutting as the two basic design criteria for determination of overlay
thickness (85). It has been generally recognized, however, that an
adequate overlay design method should consider both the structural and
functional performance of the pavement and relate the overlay thickness to
various types of pavement failures during the useful life of the overlay
Fatigue. Fatigue cracking of an asphalt concrete overlay has been
regarded as the most important type of cracking by many investigators. It
has long been chosen as a necessary criterion but has been handled in a
number of different ways (25,83,101,113-116).
The traditional method of dealing with fatigue cracking in designs
is to use a relationship between the tensile strains at bottom of asphalt
concrete layers and the number of load applications N. Extensive research
in the past two decades has established well-defined relationships for the
fatigue failure law of bituminous materials, which take the general form,
Nf = Ket"n (2.1)
where Nf =.number of load repetitions in flexure to the
initiation of fatigue cracking;
Et = maximum horizontal tensile strain in the bituminous
material under the applied load; and
K,n = constants depending on material stiffness and binder
Although this fatigue model has been successfully backed up by labo-
ratory experiments, field data demonstrate large discrepancies of scale
and the strong effects of weathering. Because fatigue life is not only
influenced by loading but also affected by asphalt concrete mix propor-
tions and environment, considerable scatter was common in the experimental
results, with fatigue lives ranging typically over an order of magnitude,
or by a factor of three each side of the mean, even under controlled
One of the shortcomings of the fatigue hypothesis is believed to be
the lack of understanding of the fatigue mechanism in conventional materi-
als (25). Although Khedr (117) has made an effort in explaining the mech-
anism of cumulative deformation under repeated loading, the fact remains
that all asphaltic materials can not be represented by a single fatigue
law even under the same environmental conditions (54). This makes it
difficult to establish an analytical model for the general purposes of
routine design, despite the fact that energy methods have been recently
proposed in an attempt to eliminate the difference between stress and
strain controlled fatigue analysis so that less data scatter may be
Furthermore, the fatigue laws currently used in analytical models
were often obtained through lab investigation on uncracked specimens.
Therefore, its use in estimating remaining life of cracked pavements in
practice is questionable (54).
Questions have also been raised on whether fatigue cracking is the
primary type of pavement failure, as many have assumed. The usual fatigue
analysis assumes that the maximum tensile strains occur at the bottom of
asphalt layers. In practice, however, increasing incidents of cracking
from the exposed surface downwards have been reported (118,119). Cracks
were found almost invariably in Britain to originate at the top surface of
the asphalt concrete layer and extended downwards according to the cores
taken from the field (102). This could be attributed to combined thermal,
age hardening and load effects. Surface layer thickness also has an
Elastic layered analyses show that when the surface layer thickness
is less than 1.6 inches, the maximum tensile strains at the surface
occurring between dual wheels or outside the tire contact area exceeds the
tensile strains at the bottom of the surface layer (4).
Since very complicated variables interact to contribute to pavement
damage, simplified fatigue models based on regression of a few factors
inevitably contains large errors or scatter (120).
Permanent deformation. Permanent deformation has been chosen as
another important criterion by many researchers (25,114,115). They assume
that rutting would occur in the layers underlying the asphalt surface,
usually in the subgrade. The rutting, which occurs in asphalt concrete
layers, has generally been considered as a mix design problem and thus not
considered in thickness design.
Most design methods consider rutting indirectly by limiting the ver-
tical strains at the top of the subgrade based on empirical correlation
(11). More rational approaches are apparently needed because of the
untransferable nature of the empirical relationships.
Various mathematical models have been proposed to predict rutting
depth or permanent deformation in the asphalt layer of pavements. These
include linear elastic, nonlinear elastic, viscoelastic, and nonlinear-
viscoelastic models (25,28,117,120). Some investigators have tried to
establish models for rut depth prediction based on number of repeated load
applications (117) for all pavement layers. Others are studying permanent
deformation based on creep tests (25,28). However, large scatter between
measured and predicted values has been observed (120).
Although the mechanistic rut prediction models may seem more scien-
tific and desirable, the various systems appeared complex and required a
series of detailed information on material characteristics (121). First,
their nonlinear nature requires a large computer capacity for iteration.
Secondly, the input material parameters, such as those in the plastic
strain law, can only be determined by performing a series of complicated
tests. Third, the relationships between lab results and field performance
are unknown. Fourth, the important influence of tire type, contact pres-
sure and wheel load distribution on rut depth and profile has greatly
challenged the use of the equivalent load in rutting analysis (122,123).
Finally, the simulation of actual traffic and temperature which are very
closely related to rutting is very difficult.
Field data and laboratory investigation have shown that rutting is
primarily the result of poor mix design and/or improper construction
(4,8,22,23,28,29). In practice, rutting problems in granular base and
subgrade are usually controlled by specifying a required compaction
density and a gradation band, whereas rutting in bituminous layers is
dealt with by specifying a given mix design which has a known history of
satisfactory performance (11).
Age hardening. Although many studies have established the general
relationships of age hardening over time, few have used the concept of
constant power viscosity as the reference for comparison (10,108,124-127).
Tia and Ruth (128) have pointed out that the viscosities at a fixed shear
rate should not be used as a reference parameter for comparison of the
influence of other factors whenever the shear susceptibility is also
influenced by those factors such as temperature or age hardening. They
recommended that the concept of constant power viscosity established by
H. E. Schweyer be used for this purpose. At the constant power, the same
amount of external energy was applied to the specimens at different states
of stiffness. This minimizes the influence of loading on both the
viscosity parameter and the shear susceptibility C from the measurements
during testing. Page et al. (127) found relationships between the con-
stant power viscosity and asphalt age of a pavement exposed to normal
traffic and environmental conditions to be log linear.
Only some indirect consideration of age hardening has been incorpo-
rated in overlay design models which are still in research stage (107).
Thermal cracking. Asphalt cracking at low temperatures has been
modeled in several ways. The COLD program (129), for example, is based on
the heat transfer model. In a similar manner, the TDHC program (110) was
developed based on two-dimensional finite element heat conduct model. The
CRACK program (130,131) was developed by Ruth et al. (1) from static anal-
ysis and strain relationships of a viscoelastic system under dynamic load-
ing. The crack initiation potential predicted by CRACK was found to be in
good agreement with field observations.
Most of these programs, however, are for thermal analysis only. The
combined effects of thermal and load are usually obtained by superimposing
the two independent analysis. For example, some use the multilayer theory
for load induced stress analysis (130) while others employ the fracture
mechanics principles (108).
Full-scale pavement tests demonstrated that even when a pavement sur-
face is cooled for only a short period of time, it could undergo cracking
when subjected to traffic (11). This implies that combined thermal and
load effects can be much more detrimental than the thermal or load effect
alone. In other words, thermal effects and loading need to be considered
interactively rather than independently to ensure the adequacy of pavement
Ruth et al. (1) have probably made the first effort to interactively
analyze the combined effects of loading and temperature.
Different from the above methods, the CRACK3 program, developed by
Ruth et al. (1) uses the elastic layer program BISAR as a subroutine to
compute the elastic portion of the strains induced by load with the con-
sideration of change in asphalt concrete stiffness with temperature. The
thermal strains are computed based on a fixed boundary assumption (a rea-
sonable approximation for uncracked pavement) and different temperatures
corresponding to pavement depth. The creep strains are computed at each
time interval on the input cooling curve or curves under the combined
thermal and load induced stress level. These three types of strains are
then superpositioned within each time interval to obtain the total
strains, stresses and fracture energy.
Reflection cracking. Current overlay design practice does not gener-
ally specify crack reflection criteria (132). There are several submodels
in current research literature on the subject of reflection cracking.
Fracture mechanics and finite element techniques are often used in these
analytical models (14,17,19).
Because of the uncertainties involved in the actual mechanism of
reflection cracking, it is felt to be impractical to incorporate a
rational approach in routine overlay design. The most effective way
available so far is to use stress absorbing interlayers during construc-
Layer slippage. So far the effect of layer slippage has not been
considered in overlay design procedures. However, a theoretical study
based on elastic layered analysis shows that in a zero bond case, the most
critical point is at the bottom of the overlay instead of the bottom of
the old asphalt concrete surface layer (133,134). It is suggested that
the overlay slippage can only be effectively corrected by replacing the
old overlay with a new one (133).
DEVELOPMENT OF A SIMPLIFIED MECHANISTIC
PAVEMENT EVALUATION SYSTEM (MEAPS)
As part of the research project sponsored by the Florida Department
of Transportation, a main frame computer program for simplified pavement
evaluation was developed in April 1989 (1). This computer program
referred to as MEAPS (Mechanistic Evaluation of Asphalt Pavement Systems),
estimates the structural condition of the in-service pavement sections
using in situ nondestructive testing (NDT) deflection measurements, mate-
rial properties, regional minimum temperatures and traffic conditions
based on the linear elastic multilayer pavement model. The program was
revised in July 1989 to operate on a personal computer and its subroutine
SORT was completely rewritten using the newly developed clustering tech-
nique which will be presented in detail in Chapter 5.
3.2 Elastic Layered Model
As mentioned earlier in Chapter 2, many attractive features have made
it increasingly popular to use the linear elastic layer theory to model
highway and airfield pavements for design and evaluation. Among the vari-
ous computer programs developed, the program BISAR (BItumen Structures
Analysis in Roads), originally developed by the Shell Oil Company (135),
was chosen for use in the MEAPS computer program. BISAR is an extension
of Burmister's work (55) that permits the analysis of a linear elastic
structure consisting of multilayers supported by a semi-infinite subgrade
under various loading conditions. The program (BISAR) has been generally
regarded as one of the most commonly used elastic layer programs for the
analysis of flexible pavements. Many investigators have confirmed that
the linear multilayer model is highly reliable for the analysis of asphalt
concrete pavements if the material properties are properly characterized.
Research has shown that the BISAR predicted pavement strains for a dual
wheel loading under controlled temperature conditions were found to be
almost identical to the measured strains at numerous test temperatures
The BISAR analysis in the MEAPS program considers a typical asphalt
concrete pavement as a four-elastic layer system: the asphalt concrete
surface course, the base course, the stabilized subgrade and the semi-
infinite soil subgrade as shown in Figure 3.1.
Circular loaded area radius = a
i 111 I I I _111
Asphalt concrete layer El p1 tl
Base course E2 g2 t2
Stabilized subgrade E3 p3 t3
Granular subgrade E4 44 t4 = oo
Figure 3.1 Idealized Pavement Structure in MEAPS
The following assumptions are made with the use of BISAR to compute
the state of stress and deformation within the MEAPS program:
1. Pavement materials are homogeneous, isotropic, and linearly elas-
tic within each layer.
2. Each layer is horizontally continuous and has finite thickness
except for the lower layer. The horizontal dimension of a pavement is
3. Pavement layers are regarded as being fully bonded at the inter-
faces so that they act together as an elastic medium of composite nature
with full continuity of stresses and displacements. Although the program
BISAR itself is capable of modeling the slippage effect between layers,
the MEAPS program analyzes pavements uncracked so that the stress levels,
a primary indicator of cause or potential for cracking, before failure may
4. Surface loading is represented by uniformly distributed stresses
over a circular area. Inertial forces are negligible.
5. Thickness and Poisson's ratio of each layer are assumed to be
3.3 Material Characterization
3.3.1 Validity of Linear Elastic Model
A flexible pavement typically consists of four types of materials:
bituminous concrete mixture, cement bound granular soils, unbound granular
soils and fine-grained soil. Each type of these materials has its unique
behavior and therefore should be treated as separate layers commonly
referred to as surface course, base, stabilized subgrade and subgrade.
Although these materials are in reality very complex both in composition
and behavior, linear elastic theory has shown to be a reasonably good
approximation in most cases.
Bituminous materials, in the surface layer of a pavement, are influ-
enced primarily by time, rate of loading, and temperature because of its
theological nature. Asphaltic material will become stiffer as the rate of
loading increases and as temperature decreases. Creep strains are gener-
ally involved. However, reasonably good agreement has been obtained
between the measured strains at the bottom of asphalt concrete layers in
the full-scale testing pavements and the strains predicted by the multi-
layer elastic theory even though the viscous behavior was not considered
The stabilized subgrade consists of Cement-Bound materials or other
types of stabilized materials which are often used in practice to provide
a stiff layer for compaction of the overlying asphalt concrete and granu-
lar base layers during construction. These lime or cement bound materials
will usually crack prior to traffic loading as a result of thermal and
shrinkage effects which generally yield well spaced transverse cracking
(primary cracking). Under the action of traffic, further cracking (secon-
dary fatigue cracking) will occur if the stress in the slab between trans-
verse cracks is sufficiently high. Although these cracks induce non-
linear, inelastic behavior, the material may still be approximated with
satisfactory accuracy by the equivalent elastic parameters.
The base and subgrade of a pavement are usually constructed with
unbound granular material and fine grained soils respectively.
Subgrade soil is generally not only nonlinear, stress dependent, but
also density and moisture dependent. The uncertainties in climate and
seasonal variations make it more difficult to characterize these mate-
In the case of good quality rock or overconsolidated stiff clays,
however, elastic theory can be used as a fairly close approximation. The
most typical case is extensive, homogeneous deposits of saturated, or
nearly saturated cohesive soils, under moderate stress levels below the
preconsolidation pressure. In these cases, linear elastic theory is often
used to estimate immediate settlement for four reasons. First, they
roughly satisfy the assumption of continuity, homogeneity and isotropy.
Secondly, overconsolidated soils tend to have an approximately linear con-
stitutive relationship when the stress levels are below the preconsolida-
tion pressure. Most importantly, the deformations are primarily recover-
able and thus elastic. Finally, the elastic parameters in this case can
be easily determined. The settlements generally occur very quickly so
that the loading can be regarded as being similar to the undrained condi-
tion. The Poisson's ratio of an incompressible material, i.e., 0.50, is
often assumed in this case because there is no volume change. The modulus
of elasticity can be determined by triaxial isotropically consolidated
undrained shear (CU) test with the measurement of pore water pressures.
If the stiff clay is not fully saturated, however, there is no lab
technique presently available to measure the pore water pressure during
the test. The direct determination of the modulus of elasticity will
therefore be very difficult although the Poisson's ratio has been shown to
be of relatively little influence (e.g., the value of 0.30 to 0.38 have
been often recommended for use in practice).
For normally consolidated cohesive soils, their behavior may depart
considerably from the elastic linear stress-strain response because of the
yielding or the great amount of plastic deformation which occur within the
range of working stresses. For this case, a plastic model should be more
appropriate. However, normal consolidation of the subgrade soil is not
likely to occur during the service life of a pavement because traffic
loads are spread by the stiffer overlying layers and stresses are greatly
reduced before reaching the subgrade soil.
In the case of cohesionless soils (unbound granular soils), which
constitute the pavement base, the value of modulus of elasticity E is
stress dependent. It is a function of confining pressure, and thus depth.
It also varies horizontally, greater under the center of loaded area and
its magnitude decreases towards the edge. Such granular materials are
often referred to as elastoplastic materials for which nonlinear models
are often recommended (85). Because of the time-consuming, iterative
nature of the nonlinear models, however, their applications have been
Based on the results obtained by theoretical and experimental inves-
tigations, Perloff et al. (136), have made the following conclusions,
which is also the philosophy behind this research for pavement modeling:
1. Surface displacements predicted by linear elastic analysis, using
a proper "equivalent" elastic modulus and Poisson's ratio, are sufficient-
ly accurate for most soil engineering applications involving saturated
cohesive soils, even though they fail to account for certain time-
2. For other subgrade soils, the variability of natural deposits
combined with the difficulty of obtaining and testing appropriate samples
of the material to yield representative results for the material param-
eters introduces uncertainties, the effect of which exceeds the difference
in the stresses computed using viscoelastic rather than elastic constitu-
3. Material parameters are generally not obtainable with the degree
of accuracy required to justify a sophisticated analysis.
3.3.2 Modulus Determination
In the multilayered linear elastic model, the structural behavior of
a material are characterized by two parameters, namely the resilient
modulus (E) and Poisson's Ratio (p). Poisson's ratio has a negligible
effect on pavement responses as compared to the effect of layer moduli E.
A great deal of effort has been contributed to the evaluation of the
elastic moduli of pavement materials using laboratory and field testing
procedures. Among the various tests presently used, nondestructive test-
ing (NDT) has been widely recognized as one of the most valuable testing
methods for routine monitoring of a pavement's structural condition. A
comprehensive review of these techniques is given in reference 51.
The wide spread use of NDT devices has brought about the development
of the analytical methods for relating the measured deflections to the
equivalent pavement layer moduli. The methods analyzing the shape of the
deflection basin are currently very much in favor because the shape, as
Bonnot (54) put it, provides greater definition of the pavement structural
characteristics than maximum deflection alone. The principle of estimat-
ing the equivalent moduli of a pavement from the measured shape of the
deflection basin lies in the fact that the thickness and layer moduli of
a pavement determine the shape of the deflection basin, and hypothetically
the layer moduli can be determined from the deflection basin by solving an
inverse problem. This has been known in the literature as the backcalcu-
lation procedure which employs the multilayer linear elastic model with
computer iteration. In addition, factorial studies have also been carried
out based on regression and elastic models to establish the prediction
equations of pavement layer moduli from the NDT deflection readings
Because asphalt materials are more susceptible to temperature
changes, the elastic or resilient modulus of asphalt concrete was charac-
terized, in the MEAPS program, by its relationship with asphalt constant
power viscosity which varies with temperature. This relationship was
found, by Ruth et al. (128,130,131), to be linear on a log scale conform-
ing to a power law equation (1) as presented in equations (3.1) through
1) Asphalt viscosity temperature relationship
log(q0oo) = BO + Bl log(K) (3.1)
where qi10 (in Pa.S) is the viscosity of the asphalt concrete
layer at a constant power of 100 Watt/m3, and mean
pavement temperature in degree K.
These coefficients, BO and Bl, should be determined by the Schweyer
Rheometer tests described in reference 130.
2) Asphalt concrete layer modulus
A) when the viscosity temperature relationship is known
a) when q100 g 1.87E4 Pa.S
El = 90 ksi (3.2)
b) when 1.87E4 rqloo 8.31E6 Pa.S
log(El) = 7.960 + 0.195 log(ql00) (3.3)
c) when 8.31E6 qi10 o 9.19E8 Pa.S
log(El) = 7.18659 + 0.30677 log (Tq,0)
d) when 9.19E8 q 1t0 s 2.07E10 Pa.S
log(El) = 9.51354 + 0.04716 log(nl00) (3.5)
e) when qio > 2.07E10 Pa.S
El = 1453 ksi (3.6)
where El (Pa) is the resilient modulus (sometimes
referred to as dynamic modulus) of asphalt
concrete, q (Pa.S) is determined by
B) when the viscosity temperature relation is unknown
a) if pavement has no cracks
log(El) = 6.4147 0.0148 T (3.7)
where El is in psi and T in degree C.
b) if pavement has considerable cracking (i.e., medium
frequency class 2 and 3)
log(El) = 6.4167 0.01106 T (3.8)
where El is in psi and T in degree C.
Equations (3.7) and (3.8) are approximations applicable only for aged
3.4 Description of Dvnaflect Testing System
As one of the most commonly used nondestructive testing equipment,
the Dynaflect is an electro-mechanical device for measuring the dynamic
deflections on the pavement surface. It exerts oscillatory loading of
1000 lb with a frequency of 8 cycles per second through two wheels spaced
20 inches apart. The pavement responses to the dynamically applied load
is measured by five geophones, the location of which can easily be changed
to a desired pattern.
The configuration of the standard Dynaflect which is commercially
available is shown in Figure 3.2. The first sensor measures the deflec-
tion at a point midway between the rigid wheels while the remaining four
sensors measure the vertical deflection along the center line of the
trailer with a sensor spacing of one foot.
The standard sensor positions were modified by Ruth et al. in 1986
(51) in an attempt to separate the deflection responses contributed by the
subgrade, the stabilized subgrade and the combination of the base and the
asphalt concrete layers for flexible pavements typical of Florida. The
furthermost sensor position remains unchanged with the others rearranged
as shown in Figure 3.3. This is referred to as modified Dynaflect in the
3.5 Backcalculation of Pavement Layer Moduli
3.5.1 Prediction Equations and Their Limitations
The method of generating theoretical deflections and using multiple
regression analyses to establish predictive equations is a straightforward
and simple method for layer moduli prediction. The prediction equations
presented in (51) based on the modified Dynaflect sensor configuration
with improved sensitivity give reasonably good estimates of pavement layer
moduli when the deflections are within the specified range. Because of
the wide variations of the field deflection data, however, there are some
cases when the deflections are not within the range specified for the
equations to be applicable. Once the data fall outside the range, the
moduli estimated by the equations may not be representative of the actual
layer moduli. For this reason, a computerized iteration procedure for
tuning the layer moduli was incorporated into the MEAPS program.
Housing and Tow Bar
Loading Wheels \ No-.No.5
(a) The Dynaflect System in Operating Position (Ref 26).
10" No.1 No. 2 No. 3 No. 4 No. 5
10" -12" -j-12" -J4j-12" -.j-12"
(b) Configuration of Load Wheels and Geophones.
(b) Configuration of Load Wheels and Geophones.
Figure 3.2 Standard Dynaflect Configuration
-12" ------------32" ------------
Figure 3.3 Modified Dynaflect Configuration
In the case of an asphalt concrete pavement tested by the modified
Dynaflect, the modulus of the asphalt layer (El) is computed using the
asphalt viscosity-temperature relationship as shown in equations (3.1)
through (3.8). The moduli for other layers (E2, E3, and E4) are initially
estimated from modified Dynaflect deflections by the following prediction
1) Prediction equations for estimating E2, E3, E4 (Ei in ksi, Di
is in mils)
A) composite moduli
E12a = 60.611 (D1-D3)-0o831 (3.9a)
E12b = 59.174 (D1-D3)-0.805 (3.9b)
E12 = (E12a+E12b)/2 (3.9c)
where D1 is the average of D1 and D2 if they are not equal.
B) base modulus
E2a = (E12(tl+t2)-Eltl)/t2 (3.10a)
(tl+t2)(E12)1/3 tl(E)1/3 3
E2 = (E2a+E2b)/2 (3.10b)
C) modulus of stabilized subgrade
E3 = 8.7541 (D3-D4)-1.0919 (3.11)
D) modulus of subgrade
E4 = 5.40/05 (3.12)
2) Limitations for layer moduli (ksi)
The following range of layer moduli are specified in the
program to avoid unrealistic predictions.
90 El 1453
20 s E2 250
15 E3 s 250
3.5 E4 s 105 (3.13)
The predicted deflections corresponding to the modified Dynaflect
sensor positions are computed by subroutine BISAR based on these initially
estimated layer moduli and are compared against the measured deflections.
If they do not match each other within the given tolerances, the compu-
terized iteration will start. In the case of standard Dynaflect, similar
equations are used for automatic seed modulus estimation except that D3
and D4 were replaced by D2 and D3.
3.5.2 Computerized Tuning of Layer Moduli
In order to iterate effectively for the pavement layer moduli from
the measured deflection data, it is necessary to know how the change of
layer moduli influences the surface deflections corresponding to certain
Dynaflect sensor configurations. When the thicknesses of the pavement
layers are fixed, it was found by BISAR analyses that the stiffness of
each of the four pavement layers contributes differently to the shape of
the deflection basins in the longitudinal direction of the pavement along
the center line of the dual wheel loadings.
BISAR analyses (51) indicate that a change in the modulus of the
subgrade modulus (E4) tends to produce a parallel shift of the entire
deflection basin, whereas E3, tends to rotate the basin about the fifth
sensor. The change of the base course modulus E2 primarily influences the
central portion of the deflection basin within 15 to 20 inches from the
axis of the wheel, (i.e., the deflections of sensors 1, 2 of the conven-
tional Dynaflect and sensors 1, 2 and 3 of the modified Dynaflect).
Based on these findings, the criteria for computerized layer moduli
adjustment which have been found to be effective for fast convergence in
the process of iteration were established as follows:
i) El will not be changed unless adjusted by user. El can be
changed by an operator only in the case of inputing layer
moduli directly, such as when the surface course is composed
of nonasphaltic materials (e.g., granular base), or when the
option is selected which allows the user to adjust moduli under
the option of interactive tuning.
ii) The moduli of the other layers are adjusted simultaneously for
every iteration based on the following criteria.
a) All adjustable Ei will be changed according to
Ei(new) = Ei(old) (1+CORR) (3.14)
where CORR is a correction factor, whose value
is selected differently for different
b) E4 is changed according to the percentage difference of
deflections at the fifth sensor, or 50% whichever is less.
CORR = AD5/D5 (3.15)
where AD5 = D5 (pred.) D5 (meas.) in mils.
c) E3 is adjusted based on the following criteria:
CORR = [max(ADi,ADj)-AD5]/D5 (3.16)
where ADi or ADj is the difference between measured
and predicted deflection at the intermediate
sensors (i.e., i=2, j=3 for standard Dyna-
flect, and i=3, j=4 for modified Dynaflect)
d) E2 is adjusted by the percentage difference at sensor 1.
CORR = (AD1-AD5)/D3 (3.17)
iii) In special cases when the moduli of certain layer can not be
adjusted due to the boundary limit set in equation (3.11), the
following expressions are used instead:
CORR = max(AD1,AD2,AD3,AD4)/D5 (3.18)
In these equations, the max stands for the maximum absolute value
which goes with its original sign. When CORR is positive, the stiffness
will be increased to reduce the predicted deflection or vice versa.
As shown in Table 3.1, the deflection matching precision has been
greatly improved with just a few iterations after input of the seed moduli
estimated from the prediction equations.
3.6 Problems Associated with
Several problems are often encountered with iterative methods in many
of the backcalculation procedures used to compute tuned layer moduli from
the deflection data. First, a unique solution can not be guaranteed since
more than one combination of layer moduli can produce essentially the same
deflection basin. Secondly, if not controlled, most of the iterative pro-
grams yield questionable base course and stabilized subgrade moduli.
Third, the programs usually require a set of initial moduli, the choice of
which depends greatly upon the expertise or experience of the individual.
Seed moduli that deviate excessively from those of the pavement layers may
result in significant discrepancies in layer moduli even though the itera-
tion process has simulated the measured deflection basins.
Table 3.1 Comparison of the Computer Tuned Result
With That of the Prediction Equations
Pavement SR-26B (Modified Dynaflect Data)
Test Sensor Measured By Prediction Computer Tuned
Station Deflection Equations Results
milss) ADi Ei ADi Ei Iteration
milss) (psi) milss) (psi) No.
D1 1.31 -0.13 396131 0.01 396131
D2 1.31 -0.13 250000* 0.01 200100
1 D3 1.30 -0.19 41587 -0.06 15820 5
D4 1.06 -0.07 7826 0.04 8170
D5 0.69 -0.01 0.01
Dl 1.28 -0.12 396131 -0.03 396131
D2 1.28 -0.12 250000* -0.03 202430
2 D3 1.23 -0.14 41587 -0.05 25100 3
D4 0.99 -0.02 8060 0.05 8180
D5 0.67 -0.01 0.01
D1 1.15 -0.07 396131 -0.02 396131
D2 1.15 -0.07 250000* -0.02 239960
3 D3 1.12 -0.11 64749 -0.06 56410 1
D4 0.96 -0.05 8182 -0.01 7870
D5 0.66 -0.03 -0.00
D1 1.25 -0.07 396131 -0.02 396131
D2 1.25 -0.07 250000* -0.02 241120
4 D3 1.21 -0.10 53671 -0.05 48300 1
D4 1.02 -0.02 7397 0.03 7120
D5 0.73 -0.03 -0.00
Because the deflection data fell outside the range
specified by the prediction equations, the predicted
moduli were far off. This is not the predicted modulus
but rather the boundary values set in equation (3.13).
ADi = Di(pred.) Di(meas.) in mils.
Ei values listed in sequence El, E2, E3 and E4.
The MEAPS program overcomes the problem of arbitrary selection of
initial moduli by utilizing the prediction equations. Also, the predic-
tion equations were restricted by setting limits for the layer modulus
equations (3.13) to eliminate unrealistic values.
Many tests have
confirmed that El and E4 can be predicted fairly accurately using these
As reported by many other investigators, the nonuniqueness of solu-
tions was also observed in this research. When using the elastic layered
program to compute deflections, many different combinations of layer
moduli can produce essentially the same deflection basin. As shown in
Table 3.2, even when the predicted modulus of the asphalt layer and that
of the subgrade were fixed, the E2 and E3 values can change tremendously
while keeping the shape of the deflection basin almost unchanged.
Table 3.2 Nonuniqueness of Solutions in Deflection Matching Procedure
Pavement SR-715 (at Milepost 4.732)
Measured deflections milss) (Modified Dynaflect)
D0=1.29 D2=1.29 D3=1.13 D4=0.95 D5=0.70
ADi = difference = pred. measured
Solution 1 2* 3 4 5 6 7
El (ksi) 141.58 141.58 141.58 141.58 141.58 141.58 141.58
E2 (ksi) 167.00 139.18 115.00 96.00 83.00 79.00 73.00
E3 (ksi) 6.00 15.64 30.00 50.00 70.00 79.00 90.00
E4 (ksi) 6.77 6.77 6.77 6.77 6.77 6.77 6.77
ADI milss) -0.01 -0.01 0.00 0.01 0.02 0.02 0.04
AD2 milss) -0.01 -0.01 0.00 0.01 0.02 0.02 0.04
AD3 milss) -0.04 -0.06 -0.06 -0.07 -0.07 -0.07 -0.06
AD4 milss) 0.04 0.00 -0.01 -0.04 -0.05 -0.06 -0.06
AD5 milss) 0.04 0.01 -0.01 -0.02 -0.04 -0.04 -0.05
Stress 0.29 0.33 0.38 0.42 0.45 0.46 0.48
Note: A solution refers to a combination of layer moduli
values which yield the measured deflection basin
within satisfactory tolerances.
Stands for the particular solution found by MEAPS during
iteration. Other solutions were estimated by Odemark's
equation and then verified by MEAPS/BISAR.
Seven different E2 and E3 combinations are presented in Table 3.2 as
a typical example. Although all these combinations give about the same
deflection basin, the modulus of the stabilized subgrade can increase from
6 to 90 ksi with a corresponding decrease in the base modulus from 167 to
73 ksi with a change in stress ratio at the bottom of asphalt layer almost
doubled. This demonstrates that a proper identification procedure is
necessary in using the backcalculation method to ensure reliable solutions
of layer moduli which are representative of the actual pavement.
In order to achieve this goal, an attempt was made to see whether a
relationship exists among these solutions. It was found that all the
solutions satisfy the same equivalent thickness (as given by the Odemark's
E2(1-p22) 1/3 E3(1-p23) 1/3
te = t2 ( 2 )- + t3 ( )13
Based on this finding, the option of estimating layer moduli for
other possible combinations of E2 and E3 was added to the REDAPS program
so that a user can get a quick and convenient estimation of other possible
E2 and E3 values if he inputs the particular solution found by the simpli-
fied evaluation (MEAPS). One more unknown needs to be defined before the
correct solution can be identified. For example, if the stiffness ratio
between E2 and E3 or between E3 and E4 is known from other in situ tests,
or if the typical modulus value for a particular type of material is
known, then only one solution will satisfy most closely all the criteria.
This particular solution, if verified by rerunning the MEAPS deflection
matching option, should be representative of the structural properties of
the actual pavement. This process will be illustrated in the case study
presented in Chapter 8.
3.7 Load Induced Stress Analyses (BISAR)
Once the layer moduli are determined, the MEAPS program will perform
the load induced stress analysis at the minimum regional temperature. Two
options for load induced stress analysis are used in the MEAPS program,
namely the standard case and the nonstandard case. The standard case
refers to a 24 kip single axial loading (12 kip dual tires) with a tire
pressure of 105 psi and a wheel spacing of 13 inches. The Poisson's ratio
values used for the standard case are 0.35 for the upper three layers and
0.40 for the subgrade. The standard position on the pavement for BISAR
analysis of stresses and strains is at the bottom of the asphalt concrete
layer beneath one of the dual tires. The standard minimum pavement tem-
peratures that were selected to be characteristic of climatic regions
within the State of Florida are given in Table 3.3. These temperatures
are approximately 5C higher than the minimum regional air temperatures.
The locations of the regions are illustrated in Figure 3.4. In the
nonstandard case, these corresponding parameters need to be specified by
the user in the input file before running the program.
Table 3.3 Minimum Regional Pavement Temperature
Pavement stresses are computed at the bottom of the asphalt layer
beneath a tire and the maximum tensile stress will be selected. The
stress ratio is defined as the maximum stress over the asphalt tensile
Region No. Temperature (C)
REGION 1 (-10 C)
E (-5 L)
C7 T-r K -P _
SA(SANTAI A LMEE'jACK
%M\ROSAI L I *
B 0 VALTg'.A>'1-
F-(10 (WAKULLA ~SUWANEB IBAKERr '0
" l \ b. TAYLOR) -, I L ,t -- ,
FRAN LIN LAFAYETTE.. 4RAD. ST.
: "--'HRI FORk., JOHNS
/ '-- \ \ FLAi
GLF Of" LEVY r
Mr MARION r\l
o b Y ---- WOL
CITRUS' ; LAKE
I 1 ORAN
/- ,\ OSCl
L' A NA-
L MANATEE HARDEEI
A' g ----IHL
\S -TDE SOTO
REGION 4 TELA
(+5 C) ( I
Typical Temperature Regions in Florida
strength. As shown in Figure 3.5, the tensile strength of asphalt con-
crete is a function of temperature. It increases when temperature
decreases with a reduction in ultimate tensile strain. At high tempera-
tures, there is little potential for cracking because the material exhib-
its a sufficient amount of creep to relax the stresses regardless of load
repetitions. At low temperatures, however, cracking potential increases.
The lower the temperature, the more brittle the asphalt binder and the
lower its capability to accumulate strains and deformations. The highest
cracking potential exists at the lowest possible regional temperature.
Ruth et al. (130) have experimentally related the tensile failure limits
as shown in Figure 3.5. These tensile strengths were obtained from the
indirect tensile tests which were conducted using a fast rate of loading
(2.68 in/min). The strength reaches a maximum value at the glass transi-
tion temperature (below which the bituminous material behaves essentially
as an elastic solid). This maximum tensile strength, 400 psi, was
selected as the denominator (base value) of the stress ratio.
According to the research conducted by Ruth and his co-workers for
the Florida Department of Transportation over the past 10 years, two
levels of stress ratio were selected as an approximate indication of the
structural conditions of the asphalt concrete pavements in the State of
Florida. When the maximum stress ratio, obtained by MEAPS under the
minimum regional pavement temperature and the standard design load, is
less than 0.30, the pavement is considered to be in good structural condi-
tion. If the stress ratio exceeds 0.55, immediate rehabilitation may be
necessary. When the obtained stress ratio is between these values, the
pavement will require detailed analysis by the program, CRACK3, which
analyzes the combined thermal and load effects interactively (1).
O ORIGINAL MIX
* O WEATHERED MIX
BITUMEN GLASS TEMP.
Figure 3.5 Indirect Tensile Test Failure Values [after Ruth et al. (130)]
2. The analysis is mechanistic, therefore, it is adaptable to the
development of a mechanistic rehabilitation design program for Florida's
flexible pavement systems.
3. The analysis uses the BISAR elastic layer program which is
regarded as being highly reliable for evaluation of pavement response
4. The program provides pavement engineers with a simplified and
reliable approach for the evaluation of existing flexible pavements in the
State of Florida using nondestructive testing measurements.
5. It minimizes the possibility of getting unrealistic layer modulus
values, which are often encountered in uncontrolled iteration (backcalcu-
lation) methods, by having El and E4 essentially fixed and limiting the
total number of iterations for E2 and E3.
6. The program is user friendly and built with many flexible op-
tions. The interactive tuning option, for example, allows the user to
adjust layer moduli during iteration for testing stations that are of
particular interest. The automatic tuning option, on the other hand, is
more time efficient in analyzing large quantity of data.
Although the MEAPS program provides a quick, simplified analysis for
assessing pavement structural conditions, the rating conclusions based on
stress criterion alone can be obtained only when the stress ratios are
extremely low or high. In other words, MEAPS is capable of identifying
only satisfactory or badly deteriorated pavement conditions. When the
stress ratios are intermediate, more detailed analysis involving more
comprehensive parameters will be necessary. This led to the development
of the CRACK3 (PC) program described in Chapter 4.
3.8 Projection of Future Pavement Condition
An error in predicting the pavement future condition may result from
an error in estimating the binder hardening rate. This error can be mini-
mized if a shorter period, such as five years, is considered instead of 20
or even 40 years. An option for a five-year projection of the pavement's
condition was developed for the simplified evaluation. This option
assesses the structural condition of the pavement after the asphalt bin-
ders harden for an incremental age of five years. The asphalt hardening
rate was defined as the coefficient B in log~10o (Pa.s) = A + B log age
(days) relationship and the average value (B = 0.70) was used as the
default hardening rate for the state of Florida. The same layer moduli
and other parameters as used in the present condition analysis will be
used in the future condition analysis to compute the stress level induced
by heavy truck traffic at the regional minimum pavement temperature. The
empirical stress ratio criteria will be used to rate the structural
condition of the pavement in five years.
3.9 Advantages and Limitations of MEAPS
The key advantages of MEAPS are summarized as follows:
1. Built into the MEAPS program, the relationships for material
properties established by Ruth and his co-workers, greatly reduce the
amount of laboratory work required in routine pavement evaluation. These
include: a) asphalt concrete resilient modulus, static modulus, mix
viscosity and fracture stress, strain and energy relationships with con-
stant power viscosity and pavement temperature; and b) layer moduli rela-
tionships from the two types of Dynaflect.
DEVELOPMENT OF A DETAILED MECHANISTIC PAVEMENT
EVALUATION SYSTEM FOR COMBINED THERMAL AND LOAD EFFECTS
A PC-based detailed analysis program is essential, as discussed at
the end of Chapter 3, for evaluation of asphalt pavements under the com-
bined effects of thermal and vehicular loads to identify more definitively
their cracking potential, especially when the pavement stiffnesses are
moderate. For this purpose, the main frame version, CRACK3, originally
written by R. Roque (1), was revised and microcomputerized to supplement
the REDAPS program. In addition, two independent programs, HTM and HEAT,
were developed for determination of the temperature information required
by CRACK3 (PC). This chapter will describe in detail the principles,
assumptions and equations used in the development of these three programs.
Among these programs, CRACK3 (PC) was incorporated into REDAPS (Version 2)
whereas the HTM and HEAT are retained as separate programs for more
general temperature related predictions.
4.2 Microcomputerization of CRACK3
The original CRACK3 program (operational on a main frame) was written
by Roque (1) based on the critical condition concept established by Ruth.
The program determines the cracking potential of asphalt concrete pave-
ments subjected to a given combination of temperature changes and applied
Based on the same principles and essentially the same computation
procedures and output format, the original CRACK3 program was completely
revised in structure to reduce computer memory requirement so that it
could be incorporated into the REDAPS program which operates on PC's.
Some of the major changes made in the new version of the program, CRACK3
1. The program structure has been completely altered. As a result,
the size of the main source program was reduced from originally 52599
bytes to 37916 bytes.
2. Approximately 100 nonessential arrays were replaced by simple
variables. Consequently, the size of the executable program was reduced
from originally 321094 bytes to 186914 bytes (in which subroutine BISAR
alone occupies 105950 bytes that were untouched).
3. The subroutine INPUT2 was developed to make the input for CRACK3
(PC) interactive and user friendly. A user no longer needs to read an
input guide and prepare an input file before starting the program.
4. The CRACK3 (PC) has been incorporated, as a subprogram, into
REDAPS which is operational on 640K RAM PCs.
5. At low temperature, the upper limits for dynamic modulus (equa-
tions 4.21 and 4.24) are established as function of air void content to be
consistent with the limits used in the simplified (MEAPS) analysis.
4.3 Basic Assumptions and Equations Used in CRACK3 (PC)
4.3.1 Basic Assumptions
The assumptions used in the CRACK3 (PC) program are basically the
same as those used in the original CRACK3. They are summarized as fol-
1. The pavement structure is a multilayered elastic half space.
2. The properties of the asphalt layers are defined by the visco-
sities of the mix at the given temperatures, coefficient of thermal con-
tractions and the Poisson's ratios.
3. The properties of the foundation layers are described by the
elastic moduli and Poisson's ratios.
4. The interfaces between adjacent layers are defined by the coeffi-
cient (percentage) of layer slippage for vehicular induced stress analy-
sis. For thermal analysis, full bond between layers is assumed.
5. Both horizontal and vertical loads can be considered.
6. The last layer was regarded as semi-infinite in depth. If the
bottom layer is bedrock, it can be modeled as the semi-infinite layer with
an exceptionally high elastic modulus.
7. Failure (cracking) limits of asphalt concrete material follow the
empirical relations established by Ruth et al. (130).
8. The pavements are analyzed in uncracked condition in which the
boundary of the pavements is assumed to allow no horizontal movement.
9. No thermal rippling occur before cracking.
4.3.2 Basic Equations
The basic equations used in the program are summarized below:
1. Strain equations under combined thermal and load effects
In a small incremental time At at time step i, the amount
of thermal contraction strain, AEconi, under the fixed boundary
condition consists of two components, i.e., the thermal elastic
strain, AEthei, and creep strain expressed as follows:
Aconi = aATi = AEthei + AEthcri + Aedcri
where Aethcri = thermal creep strain increment during time
increment i, AEdcri = dynamic creep strain increment during time
increment i, a = thermal coefficient of contraction of asphalt
concrete (/C), and ATi = temperature change (C) during time
increment i. The tensile strains and stresses are positive.
The thermal elastic strain increment can be expressed in
terms of thermal stress increment, i.e.,
Aothi Othi Othi-1
Ethei = (4.2)
where the Esi is the static modulus (1) of the asphalt mixture
at time increment i, othi and othi.- are thermal stresses at the
end of time increment i and i-1, respectively.
According to the definition of the pseudo-viscosity of the
asphalt mixture at a constant power of 0.01 W/m3
l.oi = (4.3)
where 6cr is the creep strain rate under the constant stress o.
The thermal creep strain increment can be expressed as
Ethcri =thi At (4.4)
Similarly, based on equation (4.3), dynamic creep strain
increment induced by the dynamic load-induced stress, odi, is
Edcri = (0.1Ni) (4.5)
where the haversine load applied at a duration of 0.1 second/
wheel load at 0.4 second interval in the laboratory is con-
sidered equivalent to 40 MPH moving vehicle in the field. The
number of load repetitions occurring over time increment i is
2. Thermal stress equation under combined thermal and load effects
The total thermal stress at the end of time step i can be
obtained by substituting equations (4.4) and (4.5) into (4.2)
and then equating (4.2) with (4.1)
Esi aATi + othi-1 Es,i di (0.1Ni)
Othi = 0o.oi - (4.6)
Esi At + l0.o0i Es At + qo.01i
3. Energy equations under combined thermal and load effects
The energy equations used in the original main frame CRACK3
(1) were modified slightly according to the areas illustrated
in Figure 4.1.
-- iathi = (athi-l+
Wthi dei Wdcri
A their A thcri A dei dcri
Figure 4.1 Stress-Strain Curve for Illustration of Energy Computation
Wthi = E thi l(AEthei + AEthcri) (4.7)
Wdcri = (O Adcri) (4.8)
where ,ci = l|di + othi
Wdei d= (ldil Adei)/2 + lOthil AEdei (4.9)
(210thiJ + Iodil) Aedei
W = Wthi + Wdri + Wdei (4.10)
where Wthi = accumulated thermal energies at time step i, Wdcri =
accumulated dynamic creep energies at time step i, Wdei = dynamic
elastic incremental energies induced at time step i, and Wi =
total applied energies at time step i.
In all of the above equations, di, Edei are elastic stress
and strain induced by wheel loads determined by BISAR analysis
with an equivalent elastic modulus of the asphalt concrete layer
of Eo.1 (sometimes referred to as dynamic modulus, which is
obtained by indirect tensile tests under dynamic loading at 10 Hz
(0.1 sec loading time) (1) at temperatures below 25 "C.
4. Failure (cracking) limits
a) Stress criterion
Tensile strength of asphalt concrete is approximately 400
psi at low temperatures when asphalt becomes very brittle
(see Figure 3.5).
b) Incremental strain criterion
When Io100 s 2.60E8 Pa.S
log (AEf) = -2.17889 0.02574 log (1lio)
When l1oo > 2.60E8 Pa.S
log (Aes) = 3.43053 -0.70252 log (qoo) (4.12)
c) Fracture energy criterion
If air voids known, then
log (Wf) = 6.5879 0.32767 log (loo,) 0.6059 log (AV%)
If air voids unknown, then
log (Wf) = 6.32438 0.32767 log (T0oo) (4.14)
5. Asphalt concrete properties
a) Asphalt Constant Power Viscosity-Temperature relation
log (ti00) = BO + Bl log (*K) (4.15)
b) Pseudo-constant power viscosity of the mix r0.01 asphalt
cement 10oo relation
log (qo.oi) = 9.25549 + 0.36647 log (t0oo) (4.16)
c) Static modulus relation
If o.o01 2.70E12 Pa.S
log (Es) = -9.12911 + 1.47951 log (0.o01) (4.17)
If 0o.01 > 2.70E12 Pa.S
log (Es) = 1.62850 + 0.61409 log (o.o01) (4.18)
d) Dynamic modulus relation
If air voids known, then
If I1oo < 1.00E9 Pa.S
log (Eo.1) = 3.4984 + 0.30667 log (9100) 0.3120 log (AV%) (4.19)
If 1.00E9 Pa.S < i10oo 2.07E10 Pa.S
log (Eo.0) = 5.8349 + 0.04716 log (,00o) 0.3120 log (AV%) (4.20)
If qioo > 2.07E10 Pa.S
log (Eo.1) = Log 1453000 0.312 log (AV%) 0.312 log (3)
= 6.0134 0.312 log (AV%) (4.21)
When air voids unknown, then
If r0oo : 9.19E8 Pa.S
log (Eo.1) = 7.18659 + 0.30667 log (i10oo) (4.22)
If 9.19E8 Pa.S < rloo < 2.07E10 Pa.S
log (Eo.1) = 9.51354 + 0.04716 log ('ioo) (4.23)
If rioo > 2.07E10 Pa.S
Eo.1 = 1453 ksi (4.24)
The development of most of these equations, the pavement model, the
design environmental and loading conditions were discussed in detail in
4.4 Advantages and Limitations of CRACK3 (PC)
The CRACK3 (PC) subprogram has the following major advantages as com-
pared to the original CRACK3 program:
1. Its memory requirement has been greatly reduced without reducing
its capability. It can now operate on a personal computer not only alone
but even as a subroutine of the fairly large and comprehensive program