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[114229. LIBRARY
3, Michigan State
25W University

 

This is to certify that the
dissertation entitled

EFFECT OF HEAVY MULTl-AXLE TRUCKS ON FLEXIBLE
PAVEMENT RUTTING

presented by

Hassan Kamal Salama

has been accepted towards fulfillment
of the requirements for the

 

 

 

 

 

Ph. D. degree in Civil and Environmental
Engineering
A Mk3;
/ j Major Professor’s Si --—
‘i //7 #70057
’ I
Date

MSU is an Affirmative Action/Equal Opportunity Institution

 

.-.----~--—n— —

pn-.--a---a-----n--------o-o-o-.-‘--..

 

 

PLACE IN RETURN BOX to remove this checkout from your record.
TO AVOID FINES return on or before date due.
MAY BE RECALLED with earlier due date if requested.

 

DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2/05 p:/ClRC/DateDue.indd’p.1

 

 

EFFECT OF HEAVY MULTI-AXLE TRUCKS ON FLEXIBLE
PAVEMENT RUTTIN G

By

Hassan Kamal Salama

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of requirements
for the degree of

DOCTOR OF PHILOSOPHY
Department of Civil and Environmental Engineering
2005

ABSTRACT
Effect of Heavy Multi-Axle Trucks on Flexible Pavement Rutting
By
Hassan Kamal Salama

In this study, heavy axle and truck configurations were investigated to determine their
influence on flexible pavement rutting. Several approaches were considered: 1) analysis
of State of Michigan, in-service pavement data to investigate the effect of multi-axle
trucks on total pavement rutting damage; 2) laboratory simulation of multiple axle and
truck configurations to study their effects on asphalt concrete rutting; and 3) mechanistic
analysis of rutting damage due to multiple axle and truck configurations using a newly

calibrated mechanistic-empirical rutting model.

The analysis of in-service pavement data showed that damage caused by multiple-
axle truck configurations is more significant, showing higher [3 values than single- and
tandem-axle truck configurations. This indicates that rutting is most influenced by
axle/truck gross weight. In calibrating the VESYS rutting model, time-series, in-service
pavement data were used from the SPS-l experiment. This important methodological
improvement over previous studies permits more accurate determination of the
permanent deformation parameters (PDP) that lead to better agreement with results from
accelerated loading facilities. Analyses of layer rutting contribution of in-service
pavement data showed that, on average, the total amount of rutting breaks down as

follows: 57% HMA rutting, 27% base rutting, and 16% subgrade rutting. These results

suggest that accounting for subgrade rutting only is no longer valid for designing flexible

pavements .

The laboratory investigation indicates that the rutting damage due to different axle
configurations is approximately proportional to the number of axles. Calculating truck
rutting damage by simply summing the vertical permanent deformation corresponding to
its constituent axle groups result in erroneous predictions. Using Miner’s rule to
determine truck rutting damage from its constituent axles does improve the prediction,
although there are still variations among the damage values corresponding to different

axle and truck configurations.

The results from mechanistic analyses showed that there is little to no interaction
between axles in the vertical strain within the HMA layer. For the vertical strain within
the base layer, the interaction between axles increases with increasing HMA layer
thickness. On the other hand, there is always high interaction between axles in the
subgrade layer (vertical strains). Despite the interaction between axles, the mechanistic
analysis in this study confirmed the laboratory findings related to the proportionality of
axle and truck factors for the HMA layer. Moreover, it extended this same result to

include both the base and subgrade layers.

This dissertation is dedicated to my country

Egypt

iv

ACKNOWLEDGEMENT

Thanks to Allah Almighty for providing me with the opportunity to undertake and
complete this task. Special thanks to my advisor Dr. Karim Chatti for his constant
guidance and encouragement throughout this research study. Many thanks for the
doctoral committee members: Dr. Gilbert Y. Baladi, Dr. Neeraj J. Buch, Dr. Ghassan
Abu-Lebdeh, and Dr. Dennis Gilliland.

I would like to extend thanks to the Egyptian Ministry of Higher Education for
sponsoring me and my family during this study. Special thanks to the Michigan
Department of Transportation, MDOT for funding this research study.

I offer my special thanks to Steven Forbes Tuckey in the Writing Center at
Michigan State University for editing this dissertation and his proof-reading. I am
grateful to him for the countless hours of constructive discussion and his informative
revisions of my work.

I would like to thank my colleagues at Michigan State University, especially Syed
Waqar Haider and Hung Suk Lee for their help during this research. Also, many thanks
go to the laboratory manager Siavosh Ravanbakhsh and the equipment technologist
James C. (JC) Brenton for assisting me during the experimental work.

Last but not the least, many thanks go to my parents who keep praying for me, my
wife (Mona Zhran), without whose love, care, encouragement and continuous support I

could not complete this work.

TABLE OF CONTENTS

TABLE OF CONTENT ............................................................................. vi
LIST OF FIGURES .................................................................................. x
LIST OF TABLES .................................................................................. xii
CHAPTER 1 - INTRODUCTION ........................................................................ 1
1.1 INTRODUCTION .................................................................................................... 1
1.2 PROBLEM STATEMENT ....................................................................................... 3
1.3 RESEARCH OBJECTIVES ..................................................................................... 3
1.4 RESEARCH APPROACH ....................................................................................... 4
1.4.1 Analysis of in service data ................................................................................. 4
1.4.2 Laboratory experiment ....................................................................................... 5
1.4.3 Mechanistic analysis .......................................................................................... 5
1.5 THESIS STRUCTURE ............................................................................................. 7
CHAPTER 2 - LITERATURE REVIEW .......................................................... 8
2.1 INTRODUCTION .................................................................................................... 8
2.2 ANALYSIS OF IN-SERVICE PAVEMENT DATA .............................................. 8
2.3 LABORATORY STUDIES .................................................................................... 10
2.3.1 Fatigue .............................................................................................................. 10
2.3.2 Rutting ....................................................................... i ....................................... 15
2.4 MECHANISTIC ANALYSIS ................................................................................ 17
2.4.1 Fatigue .............................................................................................................. 17
2.4.2 Rutting .............................................................................................................. 19
2.5 SUMMARY ............................................................................................................ 31
2.5.1 Analysis of in-service pavements .................................................................... 31
2.5.2 Laboratory investigations ................................................................................. 32
2.5.3 Mechanistic analysis ........................................................................................ 32
CHAPTER 3- ANALYSIS OF FLEXIBLE PAVEMENT RUTTING
FROM IN-SERVICE DATA ................................................................................. 34

vi

3.1 INTRODUCTION .................................................................................................. 34

3.2 SITE SELECTION PROCEDURES ...................................................................... 34
3.3 PERFORMANCE DATA ....................................................................................... 36
3.4 TRAFFIC DATA .................................................................................................... 37
3.4.1 Vehicle Travel Information System, VTRIS ................................................... 40
3.4.2 Raw Traffic Data .............................................................................................. 41
3.5 ANALYSIS ............................................................................................................. 47
3.5.1 Regression Analysis ......................................................................................... 47
3.5.2 Standardized Regression Coefficients ............................................................. 50
3.5.3 Multicollinearity .............................................................................................. 52
3.5.4 Remedies for the Multicollinearity Problem .................................................... 52
3.6 RESULTS AND DISCUSSION ............................................................................. 56

CHAPTER 4 - CALIBRATION OF MECHANISTIC-EMPIRICAL

RUTTING MODEL .................................................................................................. 59
4.1 INTRODUCTION .................................................................................................. 59
4.2 SPS-l EXPERIMENT ............................................................................................ 60

4.2.1 SPS-l data used in the analysis ........................................................................ 61
4.3 VESYS MODEL ..................................................................................................... 62
4.4 BACKCALCULATION OF PAVEMENT LAYER MODULI ............................. 63

4.4.1 MICHBACK computer program ..................................................................... 63

4.4.2 Quality control of the backcalculation procedures .......................................... 65

4.4.3 Combination /separation of pavement layers ................................................... 69

4.4.4 Modulus variation in the longitudinal direction ............................................... 72

4.4.5 Summary of the backcalculation procedure ..................................................... 72

4.4.6 HMA modulus temperature correction ............................................................ 74
4.5 FORWARD ANALYSIS ........................................................................................ 75
4.6 MESURED RUT DATA FROM IN -SERVICE (SPS-l) PAVEMENTS .............. 77

4.6.1 Filtering the measured rut data ........................................................................ 77

4.7 BACKCALCULATION OF PERMANENT DEFORMATION PARAMETERS 78

vii

4.7.1 Backcalculation parameters constraints ........................................................... 81
4.7.2 Transverse surface profile ................................................................................ 82
4.7.3 Transverse surface profile analysis criteria ...................................................... 85
4.7.4 Unique solution for backcalculation of permanent deformation parameters... 86
4.7.5 Advantages of using backcalculated parameters ............................................. 89

4.7.6 Summary statistics for backcalculation of permanent deformation parameters

................................................................................................................................... 90
4.7.7 Comparison of obtained a, u, and rutting percentage with previous work ..... 96
4.8 PREDICTION OF PERMANENT DEFORMATION PARAMETERS ................ 98
4.8.1 Available material properties ........................................................................... 98
4.8.2 Regression analysis ........................................................................................ 101
4.8.3 HMA layer regression analysis ...................................................................... 102
4.8.4 Base layer regression analysis ....................................................................... 110
4.8.5 Subgrade regression analysis ......................................................................... 119
4.9 SUMMARY .......................................................................................................... 126
4.9.1 Conclusion ..................................................................................................... 128
4.9.2 Future research ............................................................................................... 129
CHAPTER 5- LABORATORY INVESTIGATION ................................... 130
5.1 INTRODUCTION ................................................................................................ 130
5.2 SAMPLE PREPARATION .................................................................................. 131
5.2.1 Samples coring, sawing, and capping ............................................................ 134
5.2.2 Air voids before and after coring ................................................................... 136
5.3 UNCONFINED UNIAXIAL COMPRESSION STRENGTH TEST ................... 137
5.4 UNCONFINED CYCLIC COMPRESSION LOAD TEST ................................. 138
5.5 TESTING PROCEDURES ................................................................................... 140
5.5.1 Typical test results ......................................................................................... 142
5.6 EXPERIMENTAL TEST RESULTS ................................................................... 145
5.6.1 Effect of interaction level ............................................................................... 145
5.6.2 Axle Factors ................................................................................................... 147
5.6.3 Truck factors .................................................................................................. 149
5.7 PERMANENT DEFORMATION DAMAGE CURVES ..................................... 157

viii

5.7.1 Last peak strain curve .................................................................................... 159

5.7.2 Dissipated energy-based curve ...................................................................... 161
5.7.3 Strain area-based curve .................................................................................. 163
5.7.4 Stress-based curve .......................................................................................... 165
5.8 CALIBRATION OF PERMANENT DEFORMATION DAMAGE MODELS. 166
5.8.1 Peak method ................................................................................................... 166
5.8.2 Peak-midway method ..................................................................................... 168
5.8.3 Integration method ......................................................................................... 169
5.8.4 Strain rate method .......................................................................................... 171
5.9 PREDICTION OF PERMANENT STRAIN ........................................................ 174
5.10 CONCLUSION ................................................................................................... 178
5.11 FUTURE RESEARCH ....................................................................................... 179
CHAPTER 6 — MECHANISTIC ANALYSIS ............................................... 180
6.1 INTRODUCTION ................................................................................................ 180
6.2 FORWARD ANALYSIS ...................................................................................... 181
6.3 RELATIVE COMPARISON OF RUTTING DAMAGE CAUSED BY
MULTIPLE AXLES ................................................................................................... 184
6.3.1 Calibrated mechanistic-empirical rutting model ............................................ 184
6.4 RESULTS AND DISCUSSIONS ......................................................................... 186
6.4.1 Rutting prediction using the new mechanistic-empirical design guide ......... 192
CHAPTER 7 — CONCLUSIONS AND RECOMMENDATIONS ......... 195
7.1 CONCLUSIONS ................................................................................................... 195
7.2 RECOMMENDATIONS FOR FUTURE RESEARCH ....................................... 198
APPENDIX ....................................................................................... 200
REFERENCES ................................................................................ 209

ix

LIST OF TABLES

Table 1-1 Michigan truck configurations ........................................................................... 2
Table 2-1 Comparison of applicable test methods for flexible pavement fatigue (Mathews

et. al., 1993) .............................................................................................................. 14
Table 2-2 Candidate test methods and responses for the SPT (Witczak et al., 2002) ...... 16
Table 2-3 Permanent deformation parameters .................................................................. 22
Table 2-4 Field calibration factors for the new mechanistic-empirical design guide ....... 23
Table 2-5 Percent layer distribution of rutting (U llidtz, 1987) ......................................... 24
Table 2- 6 Limitations of the existing flexible pavement rutting models ......................... 25
Table 2-7 Variables affecting the permanent deformation parameters ............................. 28

Table 2-8 Independent variables included in different models (Simpson et. al., 1995) 30

Table 3-1 Descriptive statistics of rut depth and pavement age ....................................... 39
Table 3-2 Axle/Truck Count and Weight for Station Number 26183049 East Direction
(Michigan Road, M-61) ............................................................................................ 45
Table 3-3 Proportions and Average Weights for FHWA Truck Classes .......................... 46
Table 3-4 Number of weigh stations and projects ............................................................ 47
Table3-5 Regression coefficients and collinearity statistics for all truck classes ............. 53

Table 3-6 Regression coefficients and collinearity statistics for all truck classes excluding

truck class 9 ............................................................................................................... 54
Table 3-7 Total variance explained by each component .................................................. 54
Table 3-8 Component matrix ............................................................................................ 55
Table 3-9 Effect of different truck/axle configurations on pavement rutting ................... 58

Table 4-1 Descriptive statistics for SPS-l experiment (LTPP database release 18) ........ 61

Table 4-2 Descriptive statistics for final backcalculation procedures (109 sections) ....... 74
Table 4-3 Backcalculation of PDPs using different seed values for section 1-0105 ........ 83
Table 4- 4 Number of point locations with corresponding failed layer-section 1-0105 88
Table 4-5 descriptive statistics of PDPs and rutting percentage ....................................... 92
Table 4-6 Climatic variables considered ......................................................................... 100
Table 4-7 ANOVA for aHMAand uHMA ........................................................................... 104
Table 4- 8 Model Summary for OLHMA and mum ............................................................ 104

Table 4-9 Model coefficients for OHMAand uHMA ........................................................... 105

Table 4-10 Descriptive statistics of (XHMA, “HMA, and their independent variables ........ 110
Table 4-11 ANOVA for abasc and phase ........................................................................... 113
Table 4-12 Model summary for abasc and phase ............................................................... 113
Table 4-13 Model coefficients for abasc and phase ........................................................... 114
Table 4-14 Descriptive statistics of abasc, phase, and their independent variables ........... 117
Table 4-15 ANOVA for use and Hso .............................................................................. 120
Table 4-16 Model summary for ass and usg .................................................................. 120
Table 4-17 Model Coefficients for (1.50 and um ............................................................. 121
Table 4-18 Descriptive statistics of ass, ”so, and the independent variables ................ 124
Table 5-1 Aggregate gradation of the mix ...................................................................... 131
Table 5-2 Volumetric properties of the asphalt mix ....................................................... 131
Table 5-3 Gyratory compactor setup .............................................................................. 132
Table 54 experimental test factorial for axle configurations ......................................... 139
Table 5-5 experimental test factorial for axle configurations ......................................... 140
Table 5-6 Possible combinations of the truck damage from its constituent axles .......... 155
Table 5-7 Experimental test results ................................................................................. 158
Table 6-1 Pavement cross-sections and moduli .............................................................. 181
Table 6-2 Calculated permanent deformation parameters .............................................. 185

xi

LIST OF FIGURES

Figure 1-1 Flow diagram of research plan .......................................................................... 6
Figure 2-1 Transverse strain versus time for different truck configurations .................... 12
Figure 2-2 Fatigue curve for multi-axle configurations (El Mohtar, 2003) ...................... 13

Figure 2-3 Axle factors per tonnage for different interaction levels (El Mohtar, 2003) .. 13

Figure 2—4 Transverse surface profile for various rut mechanism (Simpson et al., 1995) 27

Figure 3-1 Variation of the traffic along CS # 18024 ....................................................... 35
Figure 3-2 No variation of the traffic along two consecutive control sections (CS # 22023

and 55021) ................................................................................................................ 36
Figure 3-3 Rutting versus Time ........................................................................................ 37
Figure 3-4 FHWA vehicle class definitions ...................................................................... 42
Figure 3-5 Comparison between 2001 and 2002 total average daily truck traffic ............ 43
Figure 3-6 Axle/truck configurations extracted from raw data ........................................ 44
Figure 3-7 Weight and percentage of FHWA truck classes ............................................. 44
Figure 3-8 Normality plot ................................................................................................. 48
Figure 3-9 Predicted versus residual plot .......................................................................... 49
Figure 3-10 Cook’s distance ............................................................................................. 49
Figure 3-11 Ridge trace .................................................................................................... 56
Figure 4-1 Location of the SPS-l sites ............................................................................. 61

Figure 4-2 Flow chart of calibration of mechanistic-empirical rutting model (VESYS)
using SPS-l experiment ............................................................................................ 64
Figure 4-3 Distribution of RMS (%) for all point locations within SPS-l experiment 66

Figure 4- 4 Equivalent pavement modulus versus the distance from the center of the load

at different point locations within the section. .......................................................... 68
Figure 4-5 Pavement layer thicknesses for conventional pavement ................................. 70
Figure 4-6 pavement layer thicknesses for full depth asphalt ........................................... 71
Figure 4-7 Modulus variations for the pavement layers along the longitudinal direction 73
Figure 4-8 Division of the subgrade layer into several sub-layers ................................... 76
Figure 4-9 Strain at the middle of pavement layers for 5 different SPS-l sections .......... 76
Figure 4-10 Rutting with time for SPS-l pavements - All sections ................................. 77
Figure 4-11 Measured time series rutting data for section 1-0105 ................................... 79

xii

Figure 4-12 Transverse surface profile for HMA layer rutting— Section 31-01 13 ......... 84

Figure 4-13 Transverse surface profile for base rutting—Section 20-0102 ..................... 84
Figure 4-14 Transverse surface profile for subgrade rutting—Section 32-0110 .............. 85
Figure 4-15 Definition of positive and negative area in transverse surface profile .......... 86
Figure 4-16 Definition of maximum rut depth (White, et al., 2002) ................................ 86
Figure 4-17 Transverse profile section 1-0105 ................................................................. 89
Figure 4-18 measured versus predicted rut depth for sections used in the backcalculated
PDPs .......................................................................................................................... 89
Figure 4-19 time series rutting data for three layers system ............................................. 91
Figure 4-20 oc-value histograms ....................................................................................... 93
Figure 4-21 u-value histograms ........................................................................................ 94
Figure 4-22 Rutting percentage histograms ...................................................................... 95
Figure 4-23 Comparison of permanent deformation parameters ...................................... 97
Figure 4-24 Comparison of rutting contribution of pavement layer ................................. 98

Figure 4-25 Ranking the importance of the independent variables for aHMAand uHMA . 106

Figure 4-26 Relationship of aHMA versus strain at the middle of the HMA, % passing

sieve number 10, VFA% and Max AT ................................................................... 107
Figure 4-27 Relationship of pHMA versus (.XHMA and F I .................................................. 108
Figure 4-28 Actual versus predicted (1 and p for HMA layer ........................................ 109
Figure 4-29 Sieve analysis of HMA layer ...................................................................... 111
Figure 4-30 Sieve analysis of base layer ......................................................................... 111
Figure 4-31 Relationship between chase and base modulus, base thickness, % passing

sieve number 200, and GI ....................................................................................... 115
Figure 4-32 Relationship between phase and abuse, base thickness, and base strain ........ 116

Figure 4-33 Ranking the importance of the independent variables for came and phase 117

Figure 4-34 Actual versus predicted a and p. for base layer ........................................... 118
Figure 4-35 Sieve analysis of subgrade layer ................................................................. 119
Figure 4-36 Relationship between use and strain at the middle of the top 40 inches of SO,

GI, PI, and D32 ....................................................................................................... 123
Figure 4-37 Relationship between (130 and F I and wet days .......................................... 124

xiii

Figure 4-38 Relationship between use and modulus, strain at the middle of the top 40

inches of SO, GI, and PI ......................................................................................... 125
Figure 4-39 Ranking the importance of the independent variables for abasc and phase 126
Figure 4-40 Actual versus predicted a and u for subgrade layer ................................... 127
Figure 4-41 Measured, calculated, and predicted total rut depth for section 50113 ....... 128
Figure 5-1 Compacted test specimen (6-inch diameter, 7-inch height) .......................... 133
Figure 5-2 Coring of test specimens ............................................................................... 135
Figure 5-3 Sawing operation ........................................................................................... 135
Figure 5-4 Cored sample ................................................................................................. 136
Figure 5-5 Air voids before and after coring .................................................................. 137
Figure 5-6 Stress versus strain for unconfined compression strength tests at 100°F ...... 138
Figure 5-7 Loading and unloading time for axle and truck configurations .................... 141
Figure 5-8 Unconfined cyclic compression load test set up ........................................... 142

Figure 5-9 Typical experimental results from uniaxial cyclic compression load tests

(single axle-sample number 10) .............................................................................. 144
Figure 5-10 Distribution of wheel load (Deen, et al., 1980) ........................................... 145
Figure 5-11 Interaction levels for the quad axle configuration ....................................... 146

Figure 5-12 Effect of the interaction level of different axle configuration on pavement

rutting ...................................................................................................................... 146
Figure 5-13 Axle factors for different axle configurations and interaction levels .......... 148
Figure 5-14 Rut damage per axle for two replications of each axle '

configuration/interaction level pair ......................................................................... 149
Figure 5-15 Truck factor vs. total number of axles within truck .................................... 150
Figure 5-16 Relationship between total number of truck axles, maximum axle group, and

truck factor (two replications each) ........................................................................ 151
Figure 5-17 Prediction of the truck rutting damage from its constituent axle

configurations ......................................................................................................... 1 52
Figure 5-18 Damage distribution for different truck configurations .............................. 156
Figure 5-19 Average and standard deviation of the rutting damage for different truck

configurations ......................................................................................................... 157
Figure 5-20 Examples of the last peak of the initial strain pulse .................................... 160

xiv

Figure 5-21 Last peak strain rutting curve ...................................................................... 161

Figure 5-22 Example of Dissipated energy versus number of load repetitions for one

sample (two LVDT) ................................................................................................ 162
Figure 5—23 Dissipated energy-based rutting damage curve ........................................... 163
Figure 5-24 Strain area-based rutting damage curve ...................................................... 164

Figure 5-25 Stress level versus number of cycles to failure (S-N curve) for single and

tridem axles ............................................................................................................. 165
Figure 5-26 Peak and peak midway strain for 4-axle group ........................................... 167
Figure 5-27 Axle factor from calibrated peak method versus laboratory axle factor ..... 168

Figure 5-28 Axle factor from calibrated peak-midway method versus laboratory axle
factor values ............................................................................................................ 169

Figure 5-29 Axle factor from the integration method versus laboratory axle factor values
................................................................................................................................. 171

Figure 5-30 Depiction of variables from strain rate method ........................................... 172

Figure 5-31 Axle factor from strain rate method versus laboratory axle factor values .. 173

Figure 5-32 Summary of the developed and calibrated rutting damage methods .......... 174

Figure 5-33 Example of normalized cumulative strain with the initial last peak strain
versus number of cycles .......................................................................................... 177

Figure 5-34 Values of u and on for all tested axle and truck configurations ................... 178

Figure 6-1 Vertical compression strain at the middle of each pavement layer due to an 8-

axle group on thick pavement (profile 1) ................................................................ 182
Figure 6-2 Vertical compression strain at the middle of each pavement layer due to an 8-

axle group on thin pavement (profile 2) ................................................................. 183
Figure 6-3 Strain values underneath and outside the axle group .................................... 186

Figure 6-4 Rut depth for pavement layers and their axle factors at one million repetitions
— procedure 1 ........................................................................................................... 188

Figure 6-5 Rut depth for pavement layers and their truck factors at one million repetitions
— procedure 1 ........................................................................................................... 189

Figure 6-6 Rut depth for pavement layers and their axle factors at one million repetitions

- procedure 2 ........................................................................................................... 190

XV

Figure 6-7 Rut depth for pavement layers and their truck factors at one million repetitions
- procedure 2 ........................................................................................................... 191

Figure 6-8 Rut depth for single and tandem axles and tandem axle factor using new ME
guide ........................................................................................................................ 194

xvi

CHAPTER 1 — INTRODUCTION

1.1 INTRODUCTION

Truck traffic is a major factor in pavement design because truck loads are the primary
cause of pavement distresses. Different truck types with varying axle configurations may
contribute differently to pavement distresses. The American Association of State
Highway Transportations Officials (AASHTO) pavement design guide converts different
axle load configurations into a standard axle load (where one Equivalent Single Axle
Load, or ESAL, is 18 kips) using the Load Equivalency Factor (LEF) concept. These
LEFs are based on decreases in the Pavement Serviceability Index (PSI), and were
developed for a limited number of pavement cross-sections, load magnitudes, load
repetitions, and for a single subgrade and climate. The PS1 is based on the limited
“functional” performance of the road surface, and accounts only to a low degree for other

key performance measures such as fatigue and rutting for flexible pavements.

Moreover, the AASHTO procedure for pavement design only accounts for single
and tandem axle types based on AASHO road test results, and uses extrapolation to
estimate the damage due to tridem axles. Truck axle configurations and truck weights
have significantly changed since the AASHO road study was conducted in 1962. There
remain concerns about the effect of newer axle configurations on pavement damage,
which still are unaccounted for in the AASHTO procedure. Several researchers have
investigated the pavement damage resulting from different axle and truck configurations,
yet these researches were limited only to single, tandem, and tridem axles. The state of

Michigan is unique in permitting several heavy truck axle configurations that are

composed of up to 11 axles, sometimes with as many as 8 axles within one axle group, as
shown in Table 1-1. Thus, there is a need to identify the relative pavement damage
resulting from these multiple axle trucks, which are unaccounted for in current pavement

design. This thesis is concerned with only rutting as a pavement distress.

Table 1-1 Michigan truck configurations

 

1 #1,? 2

 

 

 

3 fw 4
5 fig}? 6
7 figfl 8

 

 

11 flak—Fm 12

 

13 fl 14

 

 

15 SEW ‘6

 

17 fl 18

 

 

 

19 fl . 20

 

 

21 firm

 

 

 

 

 

 

1.2 PROBLEM STATEMENT

The state of Michigan hosts several trucks that have unusual axle configurations, up
to eleven axles and 164 kips in gross weight and 8 axles within an axle group. The
relationship between these trucks and flexible pavement rutting has not been determined,
since previous research did not address the damage caused by multiple axle/truck
configurations. Therefore, there is a need to examine the relative effect of these heavy
vehicles on pavement rutting using field data from in-service pavements, laboratory
experimentation, and mechanistic analyses.

The Michigan Department of Transportation (MDOT) has very comprehensive
pavement surface distress data files. MDOT also has been collecting rutting data, as well
as traffic count and weight data, along its road network. The traffic and weight data
collection was recently upgraded by using new weigh-in-motion (WIM) technology. This
will allow for a more accurate representation of the distribution of truck axle weights and
configurations along MDOT's trunk-lines. In addition to in-service data, simulating the
effect of these Michigan multiple axle trucks using mechanistic analysis and in the
laboratory will farther explain their relative effect on rutting damage. The conclusions
and recommendations of this research can be accomplished by combining the findings

using in-service data with those from mechanistic analysis and the laboratory experiment.

1.3 RESEARCH OBJECTIVES

The overall objective of this research study is to investigate the relative effects of

different axle/truck configurations on flexible pavement rutting. Several axle

 

configurations including single, tandem, tridem, quad, S-axles, 7-axles, and 8-axles as
well as twenty different truck configurations are considered in this study, as shown in

Table 1-1. This research will also address the following items:

0 Developing a Load Equivalency Factor (LEF), and Axle and Truck Factor (AF,

TF) for rutting using laboratory data.

- Calibrating a mechanistic-empirical rutting model (VESYS) for flexible

pavements using field data from the SPS-l experiment.

0 Developing regression equations to predict permanent deformation parameters

based on pavement cross-section, material properties, and climatic condition.

0 Comparison the finding from the statistical analysis of in —service data, laboratory

test results, and mechanistic analysis.

1.4 RESEARCH APPROACH

The research problem was approached from three different angles 1) field investigation,
2) laboratory experimentation, and 3) mechanistic analysis. Figure 1-1 shows the Flow
diagram of research plan for the three different research approaches. A brief description

of each approach follows:

1.4.1 Analysis of in service data

The field investigation relates different axle/truck configurations that are common in the
state of Michigan (Table 1-1) to rutting. Several regression analyses were performed to
examine the relative effect of these axle/truck configurations on flexible pavement

rutting.

1.4.2 Laboratory experiment

The unconfined compression cyclic load test with loading cycle that simulate different
axle/truck configurations was used to examine their relative effect on permanent
deformation of an asphalt mixture. The specimens were prepared according the new
procedure from the simple performance test for permanent deformation. Five different

axle configurations and five different truck configurations were studied.

1.4.3 Mechanistic analysis

In this analysis, the KENPAVE computer program was used to calculate the vertical
compression strain at the middle of each pavement layer caused by various axle and truck
configurations for different pavement cross-sections. The mechanistic-empirical rutting
model (VESYS), calibrated using field data from SPS-l experiment, was used to predict

the rutting in the various layers within the pavement structure.

 

 

 

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1.5 THESIS STRUCTURE

This thesis is divided into seven chapters including this introductory chapter. Chapter 2
highlights the most relevant literature related to this research. Chapter 3 details the field
investigation of truck traffic and flexible pavement rutting. In this chapter, several
regression analyses are performed to examine the relative effect of different axle/truck
configurations on the total pavement rutting. Due to the lack of information on permanent
deformation parameters in the literature, chapter 4 addresses the calibration of a
mechanistic empirical rutting model. Chapter 5 outlines the laboratory experiment
designed to study the relative effect of different axle/truck configurations on permanent
deformation of an asphalt mixture. This chapter describes the sample preparation as well
as the results of unconfined compression cyclic load tests due to different axle/truck
configurations. Chapter 6 employs the calibrated rutting model along with the laboratory
results to facilitate the mechanistic analysis of the effect of different axle/truck
configurations on pavement rutting. Chapter 7 provides the conclusions and

recommendations for future research.

CHAPTER 2 — LITERATURE REVIEW

2.1 INTRODUCTION

Several factors such as traffic, environment, material and design considerations affect
pavement damage over time. Traffic loads play a key role in pavement deterioration.
This deterioration can take several forms of distress in flexible pavements, such as fatigue
(alligator cracking), and rutting. In the past, a small number of researchers investigated
the effect of some truck configurations on pavement damage empirically (using field and
laboratory data) and mechanistically (using theoretical models) (Ilves and Majidzadeh
1991, Saraf and Ilves 1995, Witczak et al. 2002, Gillespie et 01.1993, and Hajek and
Agarwal 1990). The majority of these previous works used one approach to investigate a
single type of damage caused by a limited number of axle/truck configurations. This
chapter establishes the connection between the three different approaches and emphasizes
the need for a more inclusive study of multiple damage forms caused by several

axle/truck configurations.

2.2 ANALYSIS OF IN-SERVICE PAVEMENT DATA

Analysis of in-service pavements is crucial since it represents the actual behavior of the
pavement, while laboratory and mechanistic investigations are simulations of the real
world. There were minimal field investigations related to the relative effect of multi-axle
trucks on pavement rutting. Chatti et al., 2004 used field data from the General Pavement
Study (GPS-l) in the Long Term Pavement Performance (LTTP) program to investigate

the relative damage (fatigue and rutting) to asphalt pavements by various axle and truck

configurations. There were no conclusive results from the analysis about the effect of
axle/truck configurations on fatigue and rutting damage.

In examining their special overload permits, the Ohio Department of Transportation
(ODOT) recognized that trucks traveling from Michigan to northern Ohio cities were
substantially heavier than those in Ohio (Ilves and Majidzadeh, 1991, Saraf and Ilves,
1995). Therefore, a field study was conducted to investigate the effect of Michigan
heavy vehicle weights on pavement performance. The following field data were collected
for this study: traffic, rutting, faulting, cracking, roughness, and deflection measurements.

Regression analysis of rutting data produced the following equation:
RUTF = 0.035 + 0.984 (C13) +0.03(B + C) + 0.0007 (months) (2-1)

where RUTF is rutting (in inches) in flexible pavement,

C13 is the number of FHWA class 13 vehicles in the lane per day in thousands,

B is the total number of trucks in FHWA classes 8—12 in thousands,

C is the total number of trucks in F HWA classes 4-7 in thousands,

months is the number of months of testing with January 1986 as month =1.
They concluded that heavy axle loads affected rutting of flexible and composite
pavements; however, the field traffic and performance data used in the study were from

only four roads linking Ohio and Michigan. In addition, the analysis did not compare the

relative damage resulting from various axle/truck configurations.

 

2.3 LABORATORY STUDIES

2.3.1 Fatigue

Several methodologies exist to measure the fatigue life of flexible pavements such as the
repeated flexural test, direct tension test, diametral repeated load test (Indirect Tensile
Cyclic Load Test, ITCLT), dissipated energy method, fracture mechanics test, repeated
tension or tension and compression test, triaxial repeated tension and compression test,
and wheel track test (Rao et al., 1990 and Matthews et al., 1993). Matthews et al., 1993
ranked these methods, incorporating the advantages, disadvantages and limitations, as
shown in Table 2-1. They also listed the laboratory fatigue tests (simple fracture, support
fracture, direct axial, diametral, triaxial, fracture tests, and wheel tracking tests) and the
basic concept of each test. Some of these tests were stresses-controlled while others were
strain-controlled. However, all of these tests have been performed using either a single
pulse with rest period or a continuous sinusoidal load. When a vehicle travels over the
pavement, a given point in the pavement is subjected to multiple pulses depending on the
trucks and their axle configurations as shown in Figure 2-1. To determine the fatigue life
under multiple axle loads, Miner’s hypothesis is commonly applied to accumulate the
damage resulting from the different axles within an axle group. This relation is given by

(Miner, 1945).

 

 

n1 n2 n, n, nm
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le sz st Nif Nmf

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where “i” is the ith level of applied strain/stress at the point under consideration. In is

(6'99
1

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10

6",,
l

the number of applications at strain level expected to cause fatigue failure if

applied separately.

Hence, the actual fatigue life of flexible pavements resulting from multiple
axle/truck loads has not been considered directly. Recently, Chatti and El Mohtar, 2004
studied the fatigue life of an asphalt mixture in the laboratory under different truck axle
configurations (single to 8-axles) using the ITCLT by applying load pulses that are
equivalent to the passage of an entire axle group or truck. A unique fatigue curve relating
the number of repetitions to cause failure in the laboratory, and the initial dissipated
energy for various axle configurations was found (see figure 2-2). The results indicated
that multiple-axle groups were less damaging in fatigue per tonnage carried as compared
to single axles (see Figure 2-3). The increased number of axles carrying the same load
resulted in less damage due to the decreased, evenly distributed weight at any given point
on the pavement. This decrease in damage was found to be more significant between
single, tandem and tridem axles, while it starts to level off at higher axle numbers, as
shown in Figure 2-3. Similar results were obtained for trucks with larger axle groups,

which had lower truck factors per tonnage than those with single and tandem axles.

11

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l4

2.3.2 Rutting

Similar to pavement fatigue, several trials have been made to predict pavement rutting
based on laboratory experiments (Leahy, 1989, Ayres, 2002, and Kaloush and Witczak,
2000); however all of these trials were based on single load pulse. In reality, the
pavement is subjected to multiple load pulses due to the passage of large axle groups as
shown before in Figure 2-1. The permanent deformation parameters can be predicted
from laboratory experimental data. Qi and Witczak, 1998 used the unconfined cyclic
creep load test to develop a permanent deformation model that considered not only the
effects of stress level and temperature but also that of loading time and rest period for

asphalt mixtures. They developed predictive equations for the permanent deformation
parameters on as a function of loading time and rest period and p as a function of loading

time, rest period, temperature and stress level as follows:

# = 000237082 ”100651478 .. td—o. 107480 .. T101843 .. 00.320862

0: = 0.751629 + 0.0438023 * log(t1) — 0.0231006 * log(td) (2-4)
where

t1=loading time (sec) td= rest period (sec)

T = test temperature (°F) 0' = stress (psi)

Even though these equations were based on a reasonable number of samples (72) they
were only for a single asphalt mixture. Moreover, this laboratory investigation did not
account for different load configurations (single, tandem, tridem, ect.).

Recently, the National Cooperative Highway Research Program (N CHRP) sponsored a
study to identify a simple test for confirming key performance characteristics of

Superpave volumetric mix designs (Witczak et al., 2002 and Bonaquist et al., 2003). In

15

this study, candidate simple performance tests for permanent deformation, fatigue

cracking, and low-temperature cracking were identified and validated. Table 2-2
identifies the test methods and the response variables measured in each test that was
evaluated for their correlation to permanent deformation performance.

The principal selection criteria for these candidate tests were 1) accuracy 2) reliability 3)
ease of use, and 4) reasonable equipment cost. The confined or unconfined repeated load
test was one of the recommended candidate tests as a simple performance test for
characterizing the permanent deformation.

Table 2-2 Candidate test methods and responses for the SPT (Witczak et al., 2002)

 

 

 

Test method Mixture response parameters
Dynamic modulus Dynamic modulus
test Phase angle

 

SST shear modulus

Dynamic modulus

 

Phase ang

 

Quasi-Direct shear
(field shear test)

Dynamic modulus

 

Phase angle

 

Triaxial repeated
load

Slope and intercept of accumulated permanent and total strains

 

Plastic to resilient strain ratio

 

Resilient modulus, total and instantaneous

 

Plastic and resilient strains

 

Number of cycles to plastic flow

 

SST repeated shear,
constant-height

Slope and intercept of accumulated permanent and total shear strains

 

Plastic to resilient strain ratio

 

Resilient shear modulus, total and instantaneous

 

Plastic and resilient shear strains

 

Number of cycles to plastic flow

 

Triaxial and uniaxial
creep

Angle of internal friction

 

Cohesion

 

Compressive strength

 

Percent strain recovery

 

 

Triaxial compressive
strength

Angle of internal friction

 

Cohesion

 

Compressive strength

 

 

Fracture energy

 

l6

 

2.4 MECHANISTIC ANALYSIS

Heavy trucks have been recognized as a source of pavement damage due to the stresses
and strains imposed by heavy multi-axle loads. Analytical models have been used to
calculate generalized pavement response. These responses ultimately cause the major

pavement damage manifestations such as fatigue and rutting.

2.4.1 Fatigue

Fatigue is one of the main distress types in flexible pavements. Numerous fatigue models
have been formulated based on laboratory testing and calibrated with the field
performance and accelerated pavement testing. Some of the well-known equations

include those developed by Asphalt Institute (AI) and Shell:

-—3.291 -—0.854
N f = 00796 * 8t *Eac (AI) (Shook, 1982) (2-5)

—5.671 -2.364
N f = 0.0685 * 8t * Eac (Shell) (Claussen, 1977) (2-6)

where
N f = the number of load repetitions to failure,

8; = the horizontal tensile strain at the bottom of the HMA layer,

Eac = the dynamic modulus of elasticity of asphalt concrete.
For the future mechanistic-empirical design procedure being developed under the

NCHRP l-37A project the following equation is proposed:

5.5/2

i E—1.4,Bf3

Nf :fllenKla

’ (SHRP) (ARA, Inc., 2004)(2—7)

where

17

1Vf= number of repetitions to fatigue cracking,
8, = tensile strain at the critical location,

E = material stiffness,

K10 = laboratory calibration parameter,

Bfl: [39, BB = field calibration factors.

Gillespie et al., 1993 provided the most comprehensive mechanistic analysis of heavy
trucks within the NCHRP study titled “Effects of Heavy-Vehicle Characteristics on
Pavement Response and Performance.” In this study, analytical models of truck and
pavement structures were developed to allow a systematic study of the pavement
responses to moving, dynamic loads of various truck configurations. The truck

characteristics included in this study were:

0 Truck type (straight trucks, tractor-semi-trailers, and multiple-trailer
configurations),

Axle loads,

Number of axles,

Spacing between axles,

Suspension type (single axle with leaf and air spring and tandem axle with leaf
spring, air spring, and walking beams), and

0 Tire parameters (single/dual configurations, radial/bias construction, and inflation

pressure).

The response was determined in both rigid and flexible pavements for various designs
and properties, with variations in road roughness and vehicle speed. Pavement responses
(stresses, strains, and deflections) were evaluated throughout the pavement. The main

conclusions of the study were:

0 Static axle load was found to be the unique vehicle factor that has a significant
effect on fatigue damage.

0 Fatigue in flexible pavements vary in a ratio of 1:20 over a range of axle loads
from 10 to 22 kips because fatigue damage is related to the fourth power of the
loads.

0 Fatigue damage was not directly related to vehicle gross weight but varied with
maximum axle loads on each vehicle configuration.

18

Axle spacing has little effect on flexible pavement fatigue.

Static load sharing in multiple axle groups has a moderate effect on the fatigue of

flexible pavements.

0 Flexible pavement fatigue remained fairly constant with vehicle speed.

Hajek and Agarwal, 1990 highlighted the factors to be considered in calculating the USPS
of various axle configurations for flexible pavements and developed factors using
different strain criteria. It was concluded that pavement response parameters such as
deflections and strains have considerable influence on LEFs. Moreover, axle weight and
their spacing also contribute to the flexible pavement fatigue damage significantly.
Sebaaly and Tabatabaee, 1992 studied the effect of tire parameters on flexible pavement
damage and LEFs. They compared single and tandem axles of similar per-axle load
levels, and concluded that the passage of one tandem axle produced less fatigue damage
than the passage of two single axles. Chatti and Lee, 2004 studied the effects of various
truck and axle configurations on flexible pavement fatigue using different summation
methods (peak strain, peak-midway strain, and dissipated energy) to calculate the fatigue
damage. The results indicate that the peak-midway strain method agrees reasonably well
with the dissipated energy method. Moreover, Chatti and Lee recommend using the

dissipated energy method because it captures the totality of the stress-strain response

during the passage of the loads.

2.4.2 Rutting

Rutting is a major failure mode for flexible pavements. Two mechanistic modeling
approaches have been developed to predict rutting. The first approach is referred to as the
subgrade strain model, while the second approach considers permanent deformation

within each pavement layer.

19

The two most widely used equations related to the subgrade strain model are the Asphalt

Institute (AI) model (Shook, 1982) and the Shell Petroleum model (Claussen, 1977).

_ —4.477
Np 21.365*10 9*8c (AI) (2-8)
_ -4
1Vp 26.15*10 7*EC (Shell) (2-9)
where

N p = Number of load repetitions to failure

8c = Vertical compressive strain at the top of subgrade.
Failure is defined as the development of 13-19 mm (0.5 to 0.75 in) rut depth in the AI

model and 13 mm (0.5 in) rut depth in the Shell model.

Kim (1999) developed a rutting model related to the second approach—permanent
deformation within each layer—which accounts for the total rutting in all pavement

layers as follows:

RD = (—O.016HAC + 0.033 1n(SD) + 0.01 Mama, -0.011n(KV))*

 

/ 0.097 0.883
_2'7O3+0'657(8v,base) +O°271(8V,SG) +
E (2-10)
O.2581n(NESAL) — 0.034 In [41—51]
K ESG
where:
RD = Total rut depth (in)
SD = Surface deflection (in)
KV = Kinematic viscosity (centistoke)
Tannual = Average annual ambient temperature (°F)
H AC = Thickness of asphalt concrete (in)
N = cumulative traffic volume (ESAL)
EAC = Resilient modulus of HMA
ESG = Resilient modulus of subgrade

20

8 = Vertical compressive strain at the top of the base (103)

v ,base

8 v,SG = Vertical compressive strain at the top of the subgrade (103)

This model is limited to using the ESAL, and therefore can not handle different axle
configurations. Also, the model was calibrated for specific sections in the state of

Michigan (50 sections).

The VESYS rutting model (Moavenzadeh, 1974) was derived so that each term of the
equation corresponds to one pavement layer with two unique permanent deformation
parameters (0t and u). The form of the model is more applicable for use in this research

as shown below [Ali and Tayabji, 2000 and Ali et al. 1998].

 

K 1- K 1_
pp = hAC #AC ( Z (ni) “AC (Eei,AC )j'i' hbase—gm—( E (ni) abase (gei,base))

1“CI’AC i=1 1"Jl'base i 1
#so K 1-a
+hso (2 (”i) 36 (Eei,so)]
l—aSG 1:]
(2-11)
where:
'0 P =tota1 cumulative rut depth (in the same units as the layer thickness),

i = subscript denoting axle group,

K = number of axle group,

h = layer thickness for HMA layer, combined base layer, and subgrade layer, respectively,
n = number of load applications,

5,, = compression vertical elastic strain at the middle of the layers,

= permanent deformation parameter representing the constant of proportionality
between plastic and elastic strain, and

= permanent deformation parameter indicating the rate of change in rutting as the
number of load applications increases.

Moreover, Ali etal., 1998 calibrated the new form of the model using 61 sections from
the Long Term Pavement Performance (LTPP) General Pavement Study 1 (GPS-l) by

backcalculating the permanent deformation parameters for each layer. Ali and Tayabji,

21

2000 also proposed using a transverse profile to backcalculate permanent deformation

parameters, and reported one set of values obtained from only one LTPP section (see

Table 2-3).

Kenis (1997) used the Accelerated Pavement Tests (APT) performance data to validate

and calibrate the two flexible pavement-rutting models used in VESYS 5. In their study,

they suggested a range for the permanent deformation parameters for the pavement layers

as shown in Table 2-3.

Table 2-3 Permanent deformation parameters
(Ali et al., 1998, Ali and Tayabji, 2000, Kenis, 1997, and Bonaquist, 1996)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Calibration Pavement layer p a
HMA 0.701 0.7
LTPP Base 0.442 0.537
(Ali et al., 1998) Subbase 0.333 0.451
Subgrade 0.021 0.752
HMA 0.000103 0.1
Transverse profile
.. Base 1.163 0.95
(Ali and Tayabj1,2000)
Subgrade 0.0008 0.644
HMA 0.6 to 1.0 0.5 to 0.75
APT
_ Base 0.3 to 0.5 0.64 to 0.75
(Kenis and Wang, 1997)
Subgrade 0.01 to 0.04 0.75
Asphalt concrete 0.1 to 0.5 0.45 to 0.9
APT Granular base/subbase 0.1 to 0.4 0.85 to 0.95
(Bonaquist, 1996) Sandy soil 0.05 to 0.1 0.8 to 0.95
Clay soil 0.05 to 0.1 0.6 to 0.9

 

 

22

 

The future mechanistic-empirical design procedure being developed under NCHRP 1-
37A (ARA, Inc., ERES division, 2004) provides a rutting model for the HMA layer

(equation 2-12) as well as unbounded layers (equation 2—13).

5 1.734 ,6 0.39937 ,6

—P = 0.0007 arr ’2 "3 (2-12)
8 r

where:

8 p = plastic strain 8 = resilient strain

T = layer temperature N = number of load repetitions

[3”, [3,2, [3,3 = field calibration factors

8. 1.3—1”

 

6a(N ) : flslgvh

e (2 13)
8 r
where:
6" = permanent deformation for the layer N = number of load repetitions
8 v = average vertical strain h = thickness 0f the layer
. a, . . .
80 a pa 18 = material parameters = re3111ent strain
1631 = field calibration factor

The field calibration factors for those two models are shown in Table 2-4.

Table 2-4 Field calibration factors for the new mechanistic-empirical design guide

 

Optimization B“

BrZ

fir3

Boa

Bsc;

 

Method one

0.551

0.900

1.200

1.050

1.350

 

 

Method two

 

0.509

 

0.900

 

1.200

 

1.673

 

1.350

 

 

As mentioned previously, there are several rutting models available in the literature

(more literature in Kim, 1999). However, each rutting model has specific limitations, as

23

listed in Table 2-6. Ullidtz’s, 1987 literature review shows that the subgrade strain
models (AI and Shell models) are based on unreasonable assumptions, since they only
account for subgrade rutting while neglecting upper pavement layer rutting. He also,
reported that the subgrade rutting in the AASHO road test was only 9% of the total
rutting as shown in Table 2-5.

Table 2-5 Percent layer distribution of rutting (Ullidtz, 1987)

 

 

 

 

 

Pavement layer Percent observed rutting
Asphalt concrete 32
Base 14
Subbase 45
Subgrade 9

 

 

 

 

The rutting model form of Ali et al. (1998) is more appropriate to apply in this study;
however the calibration of the permanent deformation parameters is the weakest point.
The previous calibration process of that model has several limitations as shown in Table
2-6. Hence, a calibration procedure for this model is suggested in this study using the
LTPP Special Pavement Study-l (SPS-l) data. This experiment provides rut data for
various combinations of layer thickness and base types with fine as well as coarse grained

subgrade soils and for different climatic zones (Hanna et al., 1994).

24

 

 

 

 

 

 

 

 

30m 0: 3 .0808
$28: 000825 0:0 000 .8 02805000 00xE A :00 00 200023 000% .9000 m2 0
._0008 05 2 00300 00 0000 >05 0000000 022800 32 .280M m>mm> m
80> 00 800080000 0005 .8 0800 00.630: 800080000 000080800 80:08.80 05 .8 080.. 002.3 A
0022080
00:86 000:: 200208 00:86 02 8 808028 0800 05 8.“ 00m: 00 b8 :00 800080000 002:. A
.0020> 8: 808808 ooom m>mm> v
05 was: 000.0 80¢ 8000.220 3000—0800 0003 80.080000 020088000 80:08.80 02002.00 05. A 230.3% 0:0 :<
8002008 80 030000008: 002w 82800 80000.20 8.2 8008 25 9203 A
028: .8 80080 082 0022.08 :20? 82800 080 8.“ 38 003 000008 8:05:00 05. A
.800 02000 080 005 0050.. 5000 8.. 8000— 05 8.“ 300 03 0.500008 00:08:00 05. A
0802008 8080002 00022» 800 02002—00 05 02080 20008 25 mama: A $2 ._0 00 =< m>mm> m
05000 8.. 0080008 080 0002008 8003000 000000 0804 A
500 82800 809022 8.2 000002—00 003 _0008 25. A
00>0_ 0000 2505 chE 02008 8: 0000 2 $28: .08. 20 $2008 _0008 05 0:03 A 000— 8Q DmE N
38mm 2 00 9 00: 050;. A
.0005
-m 008098 05 30:8 8: 020 0:00 0w0800 wage 0:0 wage 030030 8003000 020000200 05. A :9 0000005 :05 0:0 2 _
000082 82.02800 002 .8 0008.8 05 00 8280000: 0.00 8m 800000 8: 020 20008 0005. A mmwe xoonm
80.90— 0050 800 must: 05 8080: 0:0 mafia 00082.0 .80 >08 800000 20008 000.; A
08200283 0853‘ 0800 B002 0 .0002

 

 

 

 

 

20008 watt: 808300 0.28G 8028 05 .8 8200285 0 -N 0300.

25

2.4.2.1 Contribution of pavement layers to rutting

Rutting is the load-induced permanent deformation of a flexible pavement. According to
the magnitude of the load and the relative strength of the pavement layers, permanent
deformation can occur in the subgrade, the base, or hot mix asphalt (HMA) layers.
Susceptibility of pavement layers to rutting varies according to pavement material
properties and climatic conditions. For example, rutting of HMA layers is more common
during hot summer seasons than it is during the winter, and permanent deformation is
more likely in unbound sub-layers during wet spring seasons. Suitable rehabilitation of
existing rutting requires knowledge of the relative contributions of the layers (i.e.,
subgrade, base, and HMA) to the total permanent deformation in the pavement. There are
two main ways to identify the layers primarily responsible for the rutting of a flexible
pavement: l) trenches and 2) transverse surface profile. The rut depth measurements are
not precise in the trenched unbounded layers (base, subbase, and subgrade) due to the
inconsistency of layer thicknesses and noise caused by individual particles at the surface.
Moreover, digging trenches is expensive and difficult to maintain. On the other hand,
measuring a transverse surface profile is easier, less hazardous, and far less costly than
cutting a transverse trench to examine underlying layers. Therefore, great effort has been
made to investigate and analyze the transverse surface profile in order to determine
rutting within the pavement layers (White et al., 2002, Harvey and Popescu, 2000, and
Chen et al., 2003).

Simpson et al., 1995 introduced a technique in which the area under the transverse
surface profile can be used to determine whether rutting can be attributed to the effect of

heave, or changes in the subgrade, base, or asphalt layer. This technique is based on a

26

, linear elastic model to predict the shape of the surface profile. A single line, representing
the original pavement surface, was drawn between the two end points of the profile. They
used the total area bounded by the original and the current road surfaces and the ratio
between the amount of area above and below the original pavement line to determine the
possible main contributing layer to rutting. Figure 2-4 shows the variation of transverse
profile shapes and indicates for each where the rutting originated within the pavement

structure based on the area technique.

 

 

 

d- Heave

Figure 2-4 Transverse surface profile for various rut mechanism (Simpson et al., 1995)

White et al. (2002) indicated that Simpson’s technique did not accurately differentiate
rutting caused by asphalt or base layers. Their argument suggests that the discrepancies

were created because Simpson used a linear elastic theory to estimate the shape of the

27

surface profiles. White has extended Simpson’s method using a nonlinear visco-elastic
finite element model to predict pavement deformation. The FEM analysis matched
Simpson’s predictions and in addition, it was able to separate the effects of the base from
those of the HMA layer. However, the authors noted that the rut depths on all of the
sections analyzed in their research were greater than 5 mm (0.2 in). The rut depth has to
be well defined to accurately determine the reference line between the two end points of
the surface profile. White’s procedure required that the transverse profile measurements

be greater than 3.6 meters (12 ft), especially when a shoulder was present in the section.

2.4.2.2 Variables affecting permanent deformation parameters

There are several variables affecting permanent deformation parameters or and u (see
equation 2-11) . These variables can be divided into four groups 1) environmental, 2)
material properties, 3) cross sections, and 4) construction quality. Simpson et al., 1994
developed a rutting model to predict the total rut depth for LTPP data (GPS-l and GPS-
2). The model uses a multiplicative regression equation and includes several variables as

shown in Table 2-7.

Table 2-7 Variables affecting the permanent deformation parameters
(Simpson et al., 1994)

 

 

Environmental Material properties Cross sections Construction
gality

Freeze index Air voids in HMA HMA thickness Base compaction

Annual precipitation % passing sieve 200 in Base thickness

Average annual minimum subgrade

temperature % passing sieve 4 in HMA

Number of days above 90 °F Asphalt viscosity

 

 

 

 

 

 

28

In a further study, Simpson et al., 1995 distinguished the rutting contribution from each
pavement layer using the same LTPP data. A general model for the total surface rutting,
subgrade rutting, base rutting, HMA rutting, and heave was generated using neural
network analysis. The variables that were considered in each model are listed in Table 2-

8.

29

 

0A<mm

 

 

0008—25 000m
008003 a 8m 0 0:080 .x.

08088 000803

0.200 30.00 0305 000020

0170mm .0000 0800 0x00 .8 000802 0008000 2 com 0 w20008 .x. 020.8 305 0802

0008000 2 com 0 w20008 .xo mooEmuU 2200003 2080.4. 012mm 080088 000825 mooa 0>0n0 0%00 .8 000802
008088 000826 <35 2 v n w20008 .x. 02808800 000m 0005 2200—8 020022008 _0000<

0002 5220008 80800008 008> 2< 0005—22 000m 00—000 302 0000.5 moo: ® 200003 208000.

02020 305 000008 000800 2083.. moom 0800 0000 .8 000802 "Pom 0800 00900 .8 000082 80800008 008> 0?.
000022008 8082 0005—28 <35 000022008 ~0=00< 020022008 _0000< 0005—000 <22
02003 w2§c <35 w2§c 000m w2§0 000822 w2§= 000.080 388.

 

 

 

 

 

 

@00— 98 .00 0008828 20008 8000.020 2 000202 00320000 800008005 w-~ 0308.

30

2.5 SUMMARY

The main goal of this research is to investigate the relative effects of different axle/truck
configurations on rutting of flexible pavements. Although some research has been
conducted on the subject, there is still a need to extend this research to include new,
heavy, multi-axle trucks. This section will detail the research approach based on the
literature review presented above for analysis of in-service pavements, laboratory

investigation and mechanistic analysis.

2.5.1 Analysis of in-service pavements

It appears that previous field investigations were very limited and did not answer the
research question. Therefore, in the present study, actual field data from the state of
Michigan were analyzed to study the effects of various axle and truck configurations on
rutting. The Michigan Department of Transportation (MDOT) has very comprehensive
pavement performance data as part of their Pavement Management System (PMS).
MDOT also collects rutting and roughness data, as well as traffic count and weight data,
throughout its network. Collection of traffic and weight data has been recently upgraded
by using new Weigh In Motion (WIM) technology. This allows for a more accurate
representation of the distribution of truck axle weights and configurations along MDOT's
trunk-lines. The details of the truck traffic and pavement rutting data, as well as the

analyses conducted, are explained in the following chapter.

31

2.5.2 Laboratory investigations

2.5.2.1 Fatigue
The relative effect of different axle/truck configurations on fatigue cracking has been
extensively investigated in the laboratory at Michigan State University (Chatti and El

Mohtar, 2004).

2.5.2.2 Rutting

Based on the literture review, the most suitable rutting test that can characterize the
relative permanent deformation damage for asphalt mixture was the unconfined cyclic
creep test. The unconfined cyclic creep test will be utilized according to the new
procedure for sample preparations (coring, sawing, and capping). Different axle/truck
load configurations will be simulated as a series of different load pulses, and the

cumulative permanent strain and flow number will be used for relative comparisons.

2.5.3 Mechanistic analysis

The mechanistic analysis will consider the relative effect of different axle/truck
configurations on the entire pavement system (HMA, base, and subgrade layers). This

analysis will be compared with the field investigations.

2.5.3.1 Fatigue

The relative effect of different axle/truck configurations on fatigue cracking has been
extensively investigated mechanistically by Gillespie et al., 1993 and Chatti and Lee,
2004. Based on the results, fatigue is greatly affected by individual axles (as opposed to
gross weight of the truck), and large axle groups cause less damage per tonnage carried

than smaller axle group.

32

2.5.3.2 Rutting

The study of relative effects of different axle/truck configurations on permanent
deformation was limited to single and tandem axles only. Based on the literature review,
the most suitable rutting model for calculating the permanent deformation in each
pavement layer due to different axle/truck configurations is the VESYS model. Even
though several trials have been made to backcalculate the permanent deformation
parameters, they yield a wide range for these parameters. Therefore, this research will
consider calibration of the VESYS rutting model using in-service data from the LTPP

SPS-l experiment.

33

CHAPTER 3- ANALYSIS OF FLEXIBLE PAVEMENT
RUTTIN G FROM IN-SERVICE DATA

3.1 INTRODUCTION

The Michigan Department of Transportation (MDOT) has very comprehensive pavement
surface distress data files. The data include flexible pavement rutting as well as traffic
count and weight data. Therefore, these data can be utilized to investigate the relative
effect of Michigan multi-axle trucks on actual pavement rutting. In addition, investigating
the relationship between truck traffic and pavement rutting from in-service pavements

can be used to verify mechanistic and laboratory findings.

3.2 SITE SELECTION PROCEDURE

The following summarizes the steps that have been done for the site selection:

0 Extract the stations rut data that have available traffic for the years 2000 and 2001
from the FHWA program (VTRIS).

0 Match those stations rut data with the control sections using the Permanent Traffic
Recorder, PTR, file provided by MDOT.

0 Locate the stations in each county using the control section in the 2001 Physical
Reference/Control Section, PR/CS atlas and determine exactly the location of the
weigh stations on the control sections.

0 Traffic data in the sufficiency rating book and Michigan annual average 24-hour

commercial traffic volumes maps were used to examine the variation of the traffic

34

relative to the weigh station segment. The variation on the considered length of the
control section was limited to a maximum of 10%.

In some cases, the truck traffic data were valid only for a small portion of the control
section (the weigh station segment), especially when there are several main exits and
entrances on the road as shown in figure 3-1.

In other cases, the traffic data were valid for two consecutive control sections where

there are no main exits or entrances on the road as shown in Figure 3-2.

 

 

Beginning of the CS Location of the Ending of the CS
18024 weigh station 18024

 

 

 

 

 

 

 

 

 

 

 

'TUSTIN
500
650
312%.)- GORME -.
OSC EOLA
520 520
ED 0
Y EVART ,
20 270
. . . ,, . 610 990
J 190 L. I ‘ ,
27 ‘ 1:.
“ECOSTA ' Segment taken into 0 35 00“
consideration

 

 

 

Figure 3-1 Variation of the traffic along CS # 18024

35

“0 DICKINSON

. Iv gaps-«v.10?» .‘

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

220
t s.
" 380 ‘
-E ‘9 . kaflmmam fin. Hf
® FOSTER '- 3a
, Cfl' Y . é
. i.
Location of the :0- J. 1 . ® 4—
-. 1000 weigh station
1 z ,5. , \Q@ . é;
- 1000 .. End of cs # 22023
' NORWAY 91 l and beginning of CS #
:~' afi' WA EDAH; 55021
230 fl. BARI
180 a 910“ 5 CUNARD 910 RNEI
HARRIS
Q
POWERS ' 670 ~ 0
Beginning of CS
# 22023 M ADE
. AU End of CS #
390 55021
IVE NO M N EE
Figure 3-2 No variation of the traffic along two consecutive control sections (CS # 22023
and 55021)
3.3 PERFORMANCE DATA

Great effort has gone into selecting sections with different pavement type, age, cross—
sectional design, and traffic loading. The same control section was divided into several
sections that have similar Average Daily Truck Traffic (ADTT) so that if pavement age

varies, the cumulative control section traffic will reflect each subsection’s age. MDOT

36

surveys flexible pavement rutting for half of their network every year. The distress survey
includes only outside (slow) lane where most trucks travel.

Rutting is a main load-related distress in flexible pavements. It is the permanent
deformation in the transverse profile under the wheel path, starting at zero rut depth and
increasing with the number of heavy load repetitions. Rutting is cumulative over time
unless major rehabilitation is applied to the pavement. MDOT consider a rutting
threshold of 0.5 inch (12 mm) to be the boundary for poor pavement conditions as shown
in Figure 3-3. Table 1-1 shows the descriptive statistics for rut depth and corresponding

age for pavement sections used in the analysis.

Rut depth, m

A

 

 

 

 

Poor
12mm
/ Fair
6 mm
{ Good
>
Time, year
Figure 3-3 Rutting versus Time
3.4 TRAFFIC DATA

The Federal Highway Administration (FHWA) assembles highway traffic information all
over the United States and provides it in its Vehicle Travel Information System (V TRIS),
which is available as public domain software. The F HWA classifies truck traffic into nine

categories according to the number of axles and number/type of truck units. Most of the

37

truck categories include different truck configurations. The program provides the count of
each FHWA truck class without differentiating between different configurations or
providing the proportion of each configuration under a given category. Not all needed
traffic counts/proportions and the average weights of each truck configuration are
available in the VTRIS program. It was therefore necessary to analyze raw traffic data

provided by MDOT in order to extract all essential truck information.

38

000000 8:050:08 05 2 0:800 2 002088038 .

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

m 0 0 _ 8.0 E .0 2.0 E .o 0 0008 $0522
0 m 0m 0 00.0 0N0 00.0 0 8 .0 .2 0000083
0000 00802 308
m 0 N. _ 00.0 m~.0 0m.0 0 8 .0 0 000000002
0 m cm 0 00.0 mN.0 00.0 3 .0 0m =000>O
w 0 0m _ 00.0 S .0 3.0 00.0 0N 00000 0082022
m m 0N 0 8.0.0 mad 00.0 0_ .0 mm 0000083
mm88>
m w n _ 00.0 0N0 0m.0 E .0 0 000000002
0 0 0m 0 00.0 0N0 00.0 00.0 mm =000>O
.>0Q .00m 08000>< .082 .22 .>0Q .05 080003.. .082 .22 0000.88 800
083 2020.008 .
0w< 8200.8 .«0 000202 0502 80 0888.

 

 

080 00020208 000 2800 0:0 80 00000000 020800028 Tm 0308.

39

3.4.1 Vehicle Travel Information System, VTRIS

The FHWA traffic data are classified intol3 classes. Classes 5 to 13 are for truck traffic,
reported as the ADTT count per class type. Figure 3-4 shows the class definition, axle
groups (number of axles within an axle group), and examples of truck configurations for
classes 5 through 13. Axle spectra are also available from F HWA data but only for
single, tandem, tridem, and quad axles (FHWA website). The program does not have the
count for large (2 5) axle groups, which are of interest in this research. Using the F HWA
data (from “W-Z” tables at the website), the ADTT for classes 5 through 13 were
extracted for the control sections corresponding to the outside lane. The improvement
year of the control section was also obtained from MDOT’s sufficiency-rating books. The
improvement year represents the most recent year the segment received significant work
that improved the pavement condition or extended the life of the pavement. The

Cumulative Truck Traffic, (CTT) for classes 5 through 13 was calculated as follows:

CTT of class = ADTT of class x pavement age x 365 (3-1)

where:

ADTT = average daily truck traffic of a given class
Pavement age = year of improvement — distress survey year.

The consistency of weigh station traffic data from year to year was examined for total
ADTT and individual truck classes. Figure 3-5 shows a comparison of ADTT in 2001
and 2002 traffic data for all weigh stations in the State of Michigan. No significant
change can be seen in the traffic data. Therefore, the 2001 traffic data were used for truck

classes’ analysis.

40

3.4.2 Raw Traffic Data

Since VTRIS does not provide some essential data needed for this research, raw truck
traffic data for 2000 were analyzed to determine the distribution of axle and truck
configurations for all axle groups including those with a large number of axles for each
weigh station. Trucks were categorized according to their largest axle group. For
example, a quad axle is an axle group that has four axles that share the same weight, so
that trucks with a quad-axle are all trucks that have quad axle as the largest axle group.
Figure 3-6 shows the axle and truck categories used in the analysis. Table 3—2 shows an
example of the extracted axle/truck information. The analysis of raw traffic data also
allowed for determining the proportions of each truck type within each F HWA truck
class. Table 3-3 shows the proportions, average truck weight, and the percentage of truck
configurations within each class. FHWA truck class 13, which is the heaviest truck class,
includes many different configurations with most having very small numbers. Figure 3-7
shows that truck classes 7 and 12 have very small percentages (less than 0.4 %) and truck
class 5 has the lowest overall average weight (6.0 tons). These trucks will not
significantly contribute in explaining the pavement damage; therefore they were excluded

from the analysis.

Table 3-4 shows the number of weigh stations for raw traffic and VTRIS analysis
as well as the number of projects corresponding to each one of them. A more details
information about where these stations located on the roads, the beginning and ending,
the length of each project can be found in Table A-1 (appendix). Also, rut depth and

traffic count for each project are shown in Table A-2 (appendix).

41

 

 

 

 

 

 

 

 

 

 

 

 

 

 

fl

 

 

 

111W). Aile
Class Definition Example truck configurations
Class Type Group
Two-axle, six-tin,
5 0.319.011: mm 1 32“"
6 Three—axle single- 1 and 2 fl
unit trucks "
Four or more axle 1, 3 -.. ..
1 aimlumit trucks and 4 “a” N
Four or fewer axle ' Q :l
3 0010mm: trucks "”1 2 39h fir—w
£10.00 single- ._ 4 - ..... ‘
9 mm mm land 2 far-1:0 SE". ‘00
10 Si: or more axle l, 2, 7
single-trailer trucks and8 ‘3
mar—Fm
Five or fewer axle f?
11 mum-trailer trucks 1 ‘3'" ' ' '
12 50.0.1. mum. 1 and 2 EN .. ,j I 1
trailer' trucks 0 ‘ <3 ’5 5
l 2, 3
Seven or more axle ' ' .
13 mum-trailer bucks 7:31, i“ fur-rut REM

 

Figure 3-4 FHWA vehicle class definitions

42

 

0080b 0.00.0 8:00 08000>0 00000 N00N 000 _00N 0003000 000008200 m-m 028E

2.000 00:0 8000.500 30

EPA—.1 .0008.

800 800 800 80.. 080 800 08. 0
, .IIIITI IIITIIII T ,- IIIIIIII; 088.0

............................ I. : .. I 0880

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. .......... , 3 208.0

g ............ , ....... 088.0

_, I Ii : ; ; - ,. .. ........... 0800.0
,

4.1:... ~OONI.|.I NOONI ...................................... . ..... ._ omoood
,.-II I! - I .. [I |.Il-I.I. IIIIII lilli- ll II II III! [L 2000.0

 

000000 000 00 000 A00

000200000000
000000080800oommommvovmmommwommwor

 

0

(X1!

0

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TI... 0 0 0 l lLIIllIlT o
_

 

 

 

 

 

 

 

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3. E III 83

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000.0

 

 

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1.10

43

 

Axle/ch Example truck configurations Axle configurations

 

Single Igl o

 

Tandem g! M

 

 

Tridem #-

 

Quad

 

Five

 

Six

 

Seven

 

 

Eight

 

 

 

 

Figure 3-6 Axle/truck configurations extracted from raw data

k
01

F_.__,__-__ ______.._.___.___.____ _____.____0.__.——4——__—.—_

 

.b
o
7
J
I
D
'0
0
q
0
m
2-
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to
0
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52.
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01

 

 

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(DUI

 

01

 

 

 

 

 

 

Traffic Percentage and weight, tons
N
O

0

Truck class

Figure 3-7 Weight and percentage of FHWA truck classes

44

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.0m 0.00 052 0.00 08 N 0_x<-w
00w 0.: 0.2 N00 5 m 002-8.
mAN 0.; 0.: _._m 00 0_x<-0
0.00 Qwh 0.: 0&0 N00 0206
0.0m 0.0x. N.» ”mm 00.0.— 0200 00—000.:
0.0m W00 0.m 0.NN wonm 0_x0-m
mdm Numw Wm w.m_ 0.05 008020.
0.08 0.008 0.m 0.x 38— 08x0;
m.mN 0.00 0.0 0.0M 05 002.0
0.08 N60 0.0 0.0m : m 0020-0
w.: 0.0m 0.0 0.0.0. 00 002:0
m.m~ 0.00 Wm m.w_ N00 020:0
:2 mdm MIN 02 009 0000 00_x<
0.2 0.0m 0.0 N08 momm 200:8.
N08 0.0m 0.0 0.0 Nwmf E00008.
0.x 10m m0 8.0 N8 M08 082m
0.0 NBN w; m0 Nhnmm 00008
A0000 08203 02 00 .>00 0m 0000 28203 .082 00000 08203 .22 A0000 08003 0800020., 00000 0000280000 0831

 

00-2 .080 0000220 000800 000 0000060 00:52 8030 80 £003 05... 05.00 003.0202 0-0 200.0

45

Table 3-3 Proportions and Average Weights for FHW A Truck Classes

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

FHW A class Truck configuration Truck count Total count Proportions, % Awfgfite, $165k
511‘ 892451 98.5 6.0
5 5F12 10635 905700 1.2 7.0
5F11 1405 0.2 6.8
SH“ 1209 0.1 7.7
6 6F2 91657 91657 100.0 13.3
7 7F3 6096 6975 87.4 19.8
7F21 879 12.6 25.6
8F11 149141 64.9 30.7
8 8F12 65798 229718 23-6 15.3
8F21 7880 3-4 16.1
8F! 1 1 6899 3.0 14.6
9 9F22 631743 738310 35-6 21.4
9F21 1 106567 14.4 23.0
10F23 35972 69-3 24.4
10 10F2111 10657 51930 20-5 37.1
10F212“ 5234 10.1 32.6
10F221 67 0.1 29.2
11 111:1111 37790 37790 100.0 21.8
12 12F2111 1323 1323 100.0 31.2
Trucks with 8-axIe‘” 6987 4.4 58.3
Trucks with 7-axle 5753 3.6 68.7
Trucks with 6-axle 4284 2.7 66.5
13 Trucks with S-axle 31383 158305 19.7 61.7
Trucks with 4-axle 52190 32.8 58.5
Trucks with 3-axle 33914 21.3 51.1
Trucks with 2-axle 23794 14.9 53.8

 

 

FHWA class 5 front and single axle

 

.. FHWA class 10 front, tandem, single, and tandem
... Trucks with 8-axle group as the largest group

46

 

Table 3-4 Number of weigh stations and projects

 

 

 

 

 

 

 

 

 

 

 

Traffic Year Number of Number of ro'ec ts Source of the

configuration weigh stations p J data
Raw traffic

Axle type 2000 12 29 data
Raw traffic

Truck type 2000 12 29 data

FHWA “CR 2001 20 52 VTRIS

classes

3.5 ANALYSIS

The analysis was conducted using three different independent variables: 1) axle
configuration (29 subsections); 2) truck configuration (29 subsections); and 3) F HWA
truck class (52 subsections). The effects of these on pavement rutting were investigated

using simple, multiple, and stepwise linear regression.

3.5.1 Regression Analysis

A series of simple univariate linear regressions was used to investigate the effect of each
axle/truck configuration on rutting. The simple linear regression provides the value of the
slope and the correlation coefficient of the relationship between the independent variables
(axle/truck configurations) and dependent variable (rutting). Univariate analysis can only
partially explain pavement rutting since it does not account for other variables. It was
primarily used to gain insight into the data.

Multiple linear regression takes into account all specified variables at the same
time. The multiple linear equations produced herein are not intended to be a universal
model to predict pavement rutting. The regression parameter ([3), coefficient of

determination (R2), and test statistic (p-values) were utilized to compare the effect of

47

different axle and truck configurations on pavement rut damage. The analysis included
checking the normality assumption (Figure 3-8) and constant variance of the residual

(Figure 3-9), as well as deleting the influential points based on Cook’s distance as shown

in Figure 3-10.

1.0

 

0.8—

.0
a:
l

0

Expected Cum Prob
i
I
O
O

0.2-1 0 °

 

 

0.0

 

l l
0.0 0.2 0.4 0.6 0.8 1.0
Observed Cum Prob

Figure 3-8 Normality plot

48

 

 

 

 

 

 

 

'3 o
,3 o
"a; o
e
m 1— o
'8 o
..N. o
E o o o
'8 c o 0 °
8 8 ° ° °
0) oo 0
.5 -1 ° °
8 7 o
2
8’ o
a: -2-
o
-3—
l l l l
-1 0 1 2
Regression Standardized Predicted Value
Figure 3-9 Predicted versus residual plot
0.50— .l
0.40fi
e
3 o 30—
5 .
.9
D
.m
X
3 0.20-
0
0.10-
O
O
O
O O O O O
o o
0.00- o oo°°oo 00000 c O o oo
1 l 1 l l l l
0 5 10 15 20 25 30

Project number

Figure 3-10 Cook’s distance

49

 

 

Stepwise regression was also used to confirm the results from simple and multiple
linear regressions. Stepwise regression is a technique for choosing the variables to
include in a multivariate regression model. Forward stepwise regression starts with no
model terms. At each step, it adds the most statistically significant term (the one with the
highest F statistic or lowest p-value) until the addition of the next variable makes no
significant difference. An important assumption behind the method is that some input
variables in a multiple regression do not have an important explanatory effect on the

response. Stepwise regression keeps only the statistically significant terms in the model.

3.5.2 Standardized Regression Coefficients

The value of the slopes (BS) in simple, multiple, and stepwise linear regression depends
on the unit of measurement (number of truck repetitions). This slope represents the
change in rutting (dependent variable) due to a unit increase in the number of axle or
truck repetitions (independent variables). Axle/truck configurations with fewer
repetitions will have a larger slope value, while those axle/truck configurations with more
repetitions will have a very small slope value, which does not represent the actual effect
regardless of the number of repetitions. Moreover, the intercept for each independent
variable will be different from each other, which may not help in comparing the relative
effects. The standardized slope has been documented as a measure to compare the
relative importance of different independent variables (Dillon, W. and M. Goldstein,
1984, and Allen, J .C., 2001). Standardized slope values are determined by converting all
variables (dependent and independent) into Z-scores. Having the variables in Z-score

form will convert the distribution mean to zero and standard deviation to one, such that

50

all variables will have a common measurement scale and one can determine which
independent variable is relatively more important. The following equation represents the

non-standardized simple linear regression.
Y=a+,6X (3-2)

where:

Y = dependent variable (rutting)
a = intercept
B = non-standardized slope

X = independent variable (for example, single-tandem or multiple axle repetitions)

The following equations represent the standardized simple linear regression.

Y' =fl’X’ (3-3)

 

 

t Y— X
X = Z. = (3-4)
0.x
a 37— Y
Y = Z. = (3-5)
0.)”
where:

Y. = standardized dependent variable,
[3' = standardized slope,
= average value of dependent variable,

7
X = standardized independent variable, and
Y = average value of independent variable.

The same procedures were used to standardize the regression coefficient parameters in
multiple and stepwise regression. The standardized slope was used to compare the
relative effect of the axle/truck configurations in all regression analyses presented in the

following sections.

51

3.5.3 Multicollinearity

In multiple linear regression analysis, having several independent correlated variables in

the model will affect the values of the regression coefficients and in some cases cause the

signs to switch to counter-intuitive values. There are several outcomes that result from

multicollinearity in the data (Neter, and Wassennan, 1996):

l.

Disagreement between the F-test in the overall ANOVA table and the marginal t-
tests.

Inaccurate estimation of the regression parameters ([35) where some of the B
values are negative in multiple linear regression while they are positive in simple
linear regression.

Large standard errors for the regression parameters.

A large Variance Inflation Factor (VIF), which measures how much the variance
of a coefficient is increased because of multicollinearity. A VIP 2 10 indicates a
serious multicollinearity problem.

Correlations of the independent variables. An examination of the correlation
matrix showed that the weigh station traffic data for different truck types were

highly correlated with each other (p > 0.7).

3.5.4 Remedies for the Multicollinearity Problem

There are several methods suggested in the literature (Belsley, 1980) to remedy the

multicollinearity problem. Some of these methods are outlined below:

1.

Remove one or several predictor variables from the model in order to reduce the

multicollinearity and standard error of the regression parameters as shown in

52

Table 3-5 and 3-6. These tables show that truck classes 9 and 13 should be

excluded from the analysis to reduce the multicollinearity; however truck class 13

is one of the heaviest trucks and truck class 9 represents 33 % of the total truck

populations. Therefore, this method is not preferred since keeping all truck

classes in the model is desirable.

Table3-5 Regression coefficients and collinearity statistics for all truck classes

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Unstandardized Standardized Collinearity

Independent . . . .

Coefficrents Coefficrents t Sig. Statistics
Variable

B Std. Error Beta Tolerance VIP
(Constant) .21 1829 .021 l 10 10.034 .000
Class 5 .000000 .000000 -.010 -.O60 .953 .522 1.914
Class 6 -.000001 .000001 -.645 -1.996 .052 .134 7.467
Class 7 .000000 .000002 -.024 -.162 .872 .622 1.607
Class 8 -.000002 .000001 -1.603 -2.015 .050 .022 45.300
Class 9 .000001 .000000 3.241 2.508 .016 .008 119.480
Class 10 -.000002 .000001 -.667 -2.367 .023 .176 5.680
Class 11 -.000008 .000004 -1.158 -2.147 .038 .048 20.808
Class 12 -.000124 .000050 -1.432 -2.502 .016 .043 23.441
Class 13 .000001 .000000 1.614 3.138 .003 .053 18.938

 

 

 

 

 

 

 

 

53

 

Table 3-6 Regression coefficients and collinearity statistics for all truck classes excluding

 

 

 

 

 

 

 

 

 

 

 

 

 

truck class 9
Unstandardized Standardized Collinearity
F333;?“ Coefficients Coefficients t Sig. Statistics
Toleran
B Std. Error Beta ce VIF

(Constant) . 1864365 .0196320 9.497 .000

Class 5 .0000000 .0000000 -.012 -.O68 .946 .522 1.914
Class 6 -.0000007 .0000007 -.324 -1.032 .308 .159 6.301
Class 7 -.0000002 .0000019 -.015 -.O93 .926 .623 1.605
Class 8 .0000003 .0000004 .247 .781 .439 .157 6.379
Class 10 -.0000008 .0000007 -.306 -1.193 .240 .238 4.202
Class 11 .0000010 .0000011 .139 .850 .400 .589 1.697
Class 12 -.0000163 .0000262 -.188 -.621 .538 .171 5.855
Class 13 .0000006 .0000003 .862 1.947 .058 .080 12.504

 

 

 

 

 

 

 

 

2. Principal component analysis can be used to form one or several composite

indices based on the highly correlated predictor variables. The principal

components method provides combined indices that are uncorrelated. However,

this method also is not preferred since it can lump totally dissimilar truck

configurations together as shown in Tables 3-7 and 3-8. As can be seen in the

tables each component is composed of all truck classes. Also this method is not

desirable for meeting the objective of this research.

Table 3-7 Total variance explained by each component

 

 

 

 

 

 

 

 

 

 

 

 

 

Component Initial Eigenvalues
Total % of Variance Cumulative %
1 4.537 64.819 64.819
2 1.303 18.608 83.427
3 0.761 10.870 94.297
4 0.213 3.047 97.343
5 0.119 1.694 99.037
6 0.051 0.724 99.761
7 0.017 0.239 100.000

 

 

54

 

Table 3-8 Component matrix

 

 

 

 

 

 

 

 

 

 

 

 

 

Component

1 2
Class 6 .886 .350
Class 7 .528 .806
Class 8 .897 .284
Class 9 .953 -.211
Class 10 .870 -.293
Class 11 .694 -.503
Class 13 .721 -.257

 

3. Ridge regression is one of the remedies for such a problem. Ridge regression
introduces bias to the diagonal of X'X matrix (where X is n 4 k matrix of
independent variables, and X' is the inverse of X matrix) for calculating the
regression coefficients, shrinks the coefficient values toward zero, and decreases
the standard error of the coefficients.

Ridge Regression, R, has been suggested in the literature as one of the remedy methods
that deal with multicollinearity data (Belsley, 1980). RR introduces biasing coefficient,
theta, into the regression equation, thereby reducing the estimated coefficient error. The
resulting coefficient estimates are biased, but are often more precise than those obtained
from standard multiple regression analysis. The desirable theta value can be determined
from ridge trace graphs, as shown in Figure 3-11. The appropriate theta value is 0.1 at
which the majority of coefficient estimators (13’s) are positive except for classes 6, 10,
and 12. The coefficient values cannot be negative since it is impossible to have the total
number of trucks increasing while the pavement surface distress decreases. Having the
precise regression coefficient estimates will assist in ranking the truck classes/types

correctly according to their relative damage to the pavement. However due to the high

55

collinearity in the data the regression coefficients become positive at higher value of theta

which require more bias.

 

 

 

Standardized parameters

 

 

+ Class 5 -0— Class 6 + Class 7 —x- Class 8 -x— Class 9
-0— Class 10 —1— Class 11 —- Class 12 ——- Class 13

Figure 3-11 Ridge trace

4. Based on engineering judgment, combine similar truck configurations.

The final analysis was done using the last method.

3.6 RESULTS AND DISCUSSION

As mentioned above, the most logical way to compare the effect of different correlated
axle/truck configurations and truck classes was to group similar configurations together.
Therefore, axles/trucks were categorized into two groups: 1) single-tandem, and 2)
multiple axles/trucks. F HWA truck classes have nine different truck types (classes 5
through 13). Classes 7 and 12 were excluded based on their low percentage and class 5

was excluded due to the insignificant effect caused by its light weight. Trucks with single

56

and tandem axles can be found in classes 6, 8, 9, 10, and l 1, while trucks with multiple
axles are only in class 13. A given weigh station can be the source of traffic data for
several subsections based on their age; while the level of traffic is the same for these

subsections, their different ages will make their cumulative traffic different.

The results from the analyses are summarized in Tables 3-9. The results show that
multiple axles/trucks are significant and show higher [3 values than single-tandem
axles/trucks, which are not significant. This indicates that rutting is more influenced by
heavier loads (axle/truck gross weight), this also agrees with the analytical results of

other researchers (Gillespie et al., 1993).

Similar analysis for Distress Index, DI (pavement cracks) and Ride Quality Index, RQI

(pavement roughness) are shown in Tables A-3 and A-4 (appendix).

57

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58

CHAPTER 4 - CALIBRATION OF MECHANISTIC-
EMPIRICAL RUTTIN G MODEL

4.1 INTRODUCTION

Since rutting is a major failure mode in flexible pavements, researchers have been trying to
predict rut depth for future rehabilitation and budget allocation. There are two main
approaches for the prediction of rutting: l) subgrade strain model (i.e. AI and Shell models)
and 2) permanent deformation within each layer. The first approach assumes that most of the
rutting results from the subgrade layer only, and is no longer valid based on observations
from the field. The second approach considers the rutting contribution from all pavement
layers, and is not widely used due to the difficulties of determining the elasto-plastic
characteristics of pavement materials. Due to increased tire pressures and new axle
configurations as well as observations from the field, researchers began to investigate the
rutting contribution from all pavement layers. This approach is also implemented in the new
mechanistic-empirical (ME) pavement design guide.

One of the main models related to this approach is the VESYS rutting model that
relates the plastic strain to the elastic strain through the permanent deformation parameters

(PDPs) u and or as follows:

8,901) =#*8e ”VI—a (4-1)

The most essential task in using this model is to accurately calculate PDPs (u and a) for each
pavement layer within the pavement system. As mentioned earlier in chapter 2 (section
2.4.2), several attempts have been made to estimate these parameters; however agreement
between studies varies. Yet, the previous research provides a common, but wide range for

these parameters. As can be seen in Equation 4-1, or is an exponent and therefore prediction

59

of rutting is very sensitive to small changes in the ct-value. In this research, PDPs were
backcalculated by matching the rut time series data from the SPS-l experiment in the LTPP
program. The most novel aspect of this backcalculation process involved the application of
the approach developed in NCHRP 468 (White et. al., 2002), which uses transverse surface
profiles to locate the layer causing most of rutting. Using this process, a unique solution for
these parameters was attained for each pavement section within the SPS-l experiment— a
result that was empirically unattainable from previous approaches. PDPs were then related to
pavement material properties, climatic conditions, and particular pavement cross-sections

through regression analysis of SPS-l experiment data.

4.2 SPS-l EXPERIMENT

The Specific Pavement Study-1 (SPS-l) experiment includes eighteen sites with twelve
pavement sections each, for a total of 216 sections located in all four LTPP climatic regions:
Wet Freeze (W F), Wet-No-Freeze (WNF), Dry Freeze (DF), and Dry-No-Freeze (DNF). The
locations of SPS—l sites within the United State are shown in Figure 4-1. The SPS-l
experiment includes a wide range of pavement structures (different HMA/base/subbase
thickness and base types) in various site conditions (traffic level, subgrade type and climate).

Table 4-1 shows the descriptive statistics for the SPS-l variables.

60

 

 

 

i.“ .F

 

 

 

 

 

 

 

Figure 4-1 Location of the SPS-l sites

Table 4-1 Descriptive statistics for SPS-l experiment (LTPP database release 18)

 

 

 

 

 

 

 

 

Variables Minirmun Maximum Average St. dev. COV %
HMA thickness, in 3.4 9.5 5.75 1.5 26
Base thickness, in 7.1 17.9 11.14 2.88 25.8
Rut depth, m 3 30 8.62 5.31 61.6
KESAUyear 1 13 524 279 126 45.2
Age, year 0.83 10.2 6.5 2.34 36
F1‘, °C-day 0 988 226 276 121.7
AARF‘, mm 221 1539 846 402 47.5

 

 

 

 

 

 

 

 

" Freezing index
"”" Average annual rain fall
1 inch = 2.54 cm

4.2.] SPS-l data used in the analysis

The SPS-l data used in this research are as follows:

0 Initial Falling Weight Deflectometer ( FWD) data for backcalculation of pavement
layer moduli,

0 Time series rutting data for minimizing the error between predicted and measured rut
depth,
Transverse profile data to locate rutting within individual pavement layers,
Traffic data for rutting prediction,

61

o Pavement layer thicknesses for backcalculation of material properties and regression
analysis to predict permanent deformation parameters,
- Climatic data for regression analysis to predict permanent deformation parameters,

and
0 Material properties for regression analysis to predict permanent deformation
parameters.
4.3 VESYS MODEL

The original form of VESYS rutting model is based on the assumption that the permanent

strain is proportional to the resilient strain so that:

_ —a
8 p (n) — ,uaen (4_2)
where
5p (n) = the permanent or plastic strain due to a single load application,
8 = the elastic or resilient strain at 200 repetitions,
e
n = the number of load applications,
a = permanent deformation parameter indicating the rate of decrease in
permanent deformation as the number of load applications increases
(hardening effect),
lu = permanent deformation parameter representing the constant of

proportionality between plastic and elastic strain.

The total permanent deformation can be obtained by integrating Equation 4-2 as follows:

.11 genl—a

1 — a (4-3)

 

n
-a
Sp z Lugen dn =
O

The cumulative permanent deformation, P p in all pavement layers from all load groups can

be calculated from the following equation:

k .
Ill]. 2 Se. .nil—aJ

:2 h]-
1’1 “1' i=1 "1 (44)

j— =1

where

81"] = the vertical compressive strain at the middle of layer j due to load group i,

62

aj and Iuj =PDPs for layer j.

Determining the actual values for the PDPs for each pavement layer is the most challeng g
task to achieve an accurate rutting prediction. The flow chart in Figure 4-2 shows the process

used to predict the values of or and u from in-service pavements in the SPS-l experiment.

4.4 BACKCALCULATION OF PAVEMENT LAYER
MODULI

In this analysis, the initial layer moduli for each SPS-l pavement section were backcalculated
using Falling Weight Deflectometer (FWD) data obtained after the initial construction of the

test sections. The MICHBACK computer program was used for the (static) backcalculation.

4.4.1 MICHBACK computer program

There are several computer programs that can be used for backcalculation of the pavement
layer moduli such as MICHBACK, MODCOMP, MODULUS, and EVERCALC.
Backcalculation analysis was performed for two pavement sections, which have known layer
moduli (from the forward analysis), using the four backcalculation programs (Svasdisant,
2003). The MICHBACK computer program produced similar, and in some cases better
results over other backcalculation programs. Moreover, each SPS-l section has 11 or more
FWD measurements, and each point location requires backcalculation of the layer moduli.
The MICHBACK computer program can carry out backcalculation of all these point

locations at once, which simplifies the analysis and makes it more efficient.

63

 

Extract layer information
and initial FWD data for
SPS-l experiment from
LTPP database

 

 

 

 

 

Backcalculate pavement layer
moduli using MICHBACK

 

 

 

 

 

Calculate the strain at the
middle of each layer using

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

KENLAYER
3 5 Assume PDPs, or _’ Predict rutting 5 Traffic data
g E & u (seed values) over time (’5’) l (ESAL)
g s l g
g E Backcalculate PDPs, or & u by ,5 Extract rut data
E : m1n1m1z1ng RMS (r and r) : with time (r)
t 5 using Excel solver :
.9. : 1' 5
‘6 E l
5 i Calculate layer rutting : Extract transverse
E contributlon : surface profile
I ................................... T""""""""":
Compare and exclude solutions A l White’s
that did not agree with White’s ppcziteria
criteria

 

 

 

 

 

 

 

 

Select solution with minimum
RMS (most likely solution)

 

 

 

Figure 4-2 Flow chart of calibration of mechanistic-empirical rutting model (VESYS) using

SPS-l experiment

64

In this study, the backcalculation of layer moduli for all SPS-l sections was

conducted in order to calculate the vertical compressive strain at the middle of each

pavement layer. The process of layer moduli backcalculation yields a variety of possible

values, some of which are highly improbable (i.e. sub-layers with higher moduli than the

HMA layer). Therefore, the following section will highlight the procedures used during the

backcalculation to insure accurate estimation of pavement layer moduli.

4.4.2 Quality control of the backcalculation procedures

Several steps were used to ensure accurate and reliable backcalculation of pavement layer

moduli as follows (Schorsch, 2003):

The solutions converge, which means the difference between two consecutive
solutions is smaller than a specified tolerance limit. This criterion was used to
eliminate any unacceptable results. If the solution did not converge several trials
were made to combine or separate (subgrade) layers and/or introduce a stiff layer.
The sections with convergent moduli values were used in the later analysis of this

research, while all others were eliminated.

Low RMS values provide high accuracy backcalculation results and assure close
matches of the measured and calculated deflection basins. Figure 4-3 shows the
distribution of RMS (%) for all point locations within the SPS-l experiment.
Though all data were initially included, later procedural steps eliminated those with
unacceptable RMS% values.

HMA layer moduli > base layer moduli > roadbed soil moduli. This criterion is
based on the principles of pavement design which call for decreasing the pavement
modulus with depth. This was held as a general rule, but if the solution did not meet
this criterion other trials with pavement layer combinations or stiff layers were
introduced.

A roadbed modulus criterion of < 60000 psi was employed to eliminate

unreasonable moduli for natural subgrade soil.

65

 

 

 

 

 

 

 

 

 

 

700-
600— 7 Mean = 2.0653
' Std. Dev. = 2.13245
. N=2,328
500—
5400— H
3
U"
2
“-300— _
,.
200—
100—
° _ 1 ‘r *1 l l
0 2 4 6 810121416182022
RMS%

Figure 4-3 Distribution of RMS (%) for all point locations within SPS-l experiment

In parallel with the above criteria, examining the presence of a stiff layer for each
SPS-l section was taken into consideration to improve the backcalculation procedure. The
deflection data can be utilized to calculate the surface modulus which represents the
weighted mean modulus of the half space. The surface modulus calculated using

Boussinesq’s equations [Ullidtz, 1987].

 

E0(0)=2*(1"#2)*0’0*

 

61(0) (4-5)
2 ‘12
E0(r):(l—,u )*00*(r*d(r)) (4-6)

where

E0(r) = surface modulus at a distance r from the center of the FWD loading plate
11 = Poisson’s ratio
0- : contact stress under the loading plate
0

66

d(r) = deflection at a distance r

Figure 4-4 shows an example of the relationship between the equivalent modulus and
the distance from the center of the FWD loading plate at different point locations within the
section. If the equivalent modulus value at the tail of the curve remains constant with
increasing distance, it indicates a deep or non-existent stiff layer and linear elastic behavior
of subgrade as shown in Figure 4—4 (a) . If the equivalent modulus value at the tail of the
curve increases with increasing distance, it indicates the presence of a shallow stiff layer
and nonlinear elastic behavior of subgrade as shown in Figure 44 (b). If the equivalent
modulus value at the tail of the curve decreases with increasing distance, it indicates no
presence of stiff layer and nonlinear elastic behavior of subgrade as shown in Figure 4-4 (c).
Taking into account an existing stiff layer helps the solution to converge; however the exact
' depth of the stiff layer was determined by trials according to the minimum RMS. In this

study, only linear elastic backcalculation analyses were considered (Ullidtz, 1987).

67

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4.4.3 Combination /separation of pavement layers

MICHBACK computer program can backcalculate the layer moduli for 3 to 5 layers,
however the backcalculation for 5 layers is less accurate. Also, increasing the number of
layers will increase the number of PDPs since each layer has two unknown parameters. In
most cases, the SPS-l sections have more than 4 pavement layers. Therefore, the
combination of similar pavement layers or division of the subgrade into two layers was
taken into consideration in order to treat the pavement structure as a 3- layers system. This
allowed the highest accuracy backcalculation and minimized the number of unknown
permanent deformation parameters. Figure 4-5 shows an example of pavement section with
(a) as constructed layers and (b) pavement layer thicknesses used in the backcalculation
procedure. The HMA layers and the treated base layer were combined together as one HMA
layer (as shown in Figure 4-5 (b)) and an average modulus was used for forward analysis.
On the other hand, when no granular base existed in the design the treated base layer was
used as a separate layer in the backcalculation. If this solution did not converge, the treated
base was assumed to be part of the overall HMA layer and a 24-inch layer of the subgrade
was treated as a base layer, with the rest of the subgrade below considered as the third layer

as shown in Figure 4-6.

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71

4.4.4 Modulus variation in the longitudinal direction

The length of each SPS-l pavement section is 500 ft with 11 or more point locations for
collecting FWD data. Sometimes, the inconsistency of pavement layer thickness, material
variability, and computational quality among other factors cause large variations in the
backcalculated moduli between point locations. Hence, the layer moduli variability in the
longitudinal direction of each section was tested. All pavement layer (HMA, base,
subgrade) moduli were normalized to the first point location, and other point locations were
checked against this point for all pavement sections. Figure 4-7 shows two example
modulus variations for the pavement layers along the longitudinal direction of two sections.
Figure 4-7 (a) shows the modulus variations for section 50113 where there are acceptable
modulus variations along the longitudinal direction. Figure 4-7 (b) shows huge variations in

the base modulus which might be due to inconsistency in the base thickness.

4.4.5 Summary of the backcalculation procedure

As explained above, there are many steps in determining layer moduli that extend beyond
the simple backcalculation output. The results of the backcalculation procedure as output
from programs ofien require additional attention and discrimination. Great effort went into
the backcalculation procedure through several trials and checking steps to ensure the
backcalculated moduli are the most suitable ones. After applying all the quality control
steps, the number of sections reduced from 216 to 159 sections. All sections with HMA,
granular base, and subgrade layers (conventional pavements) were categorized as one group
(120 sections). These sections should have a common set of 6 unknown PDPs (two for each
layer). Sections with HMA and subgrade layers (full-depth asphalt pavements) were
categorized as another group (39 sections). This group should have a common set of 4

unknown PDPs (2 for the HMA layer and 2 for the subgrade layer). Table 4-2 shows the

72

descriptive statistics of HMA and base thicknesses as well as layer moduli for the final 109

sections that used for backcalculating the PDPs.

 

 

 

 

20 .——-—'~ ~~~~~~~~ — _- -~—~ -—————— —~— — —A—A— ”24
g : —<>—AC —o—Base +Subgrade :
8 1 - - - - - - _ - , _. __ ____.,-______ . W -_ __ _ “-1
E 15 1 1
a». 1 1
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.8 10 ‘r ‘
g 1 1
(U 1 1
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2 1

‘ a ‘ 4' a W4 W

0 L.-- _1 __
0 4 6 8 10 12

Point location

(a) section 5-0113

 

Normalized layer moduli

 

 

 

 

 

Point location

(b) section 30-0123

Figure 4-7 Modulus variations for the pavement layers along the longitudinal direction

73

Table 4-2 Descriptive statistics for final backcalculation procedures (109 sections)

 

 

 

 

 

 

Variables Minimum Maximum Average St. dev. COV %
HMA thickness, in 4.0 22.2 11.56 4.27 36.94
Base thickness, in 3.5 46.1 18.77 11.62 61.91
HMA modulus, psi 69,201 2,778,015 686,030 567,971 82.79
Base modulus, psi 4,599 2,499,710 118,191 345,501 292.32
Subgrade modulus, psi 15,099 57,984 29,980 8,757 29.21

 

 

 

 

 

 

 

 

4.4.6 HMA modulus temperature correction

The FWD test temperature varies with time and space even between point locations within
the same section. Therefore, the backcalculated HMA modulus needs to be corrected for the
standard temperature of 68°F (20°C). The following equation was used (Park, 2000):

CF = 100.0224(T—T,.)

where

(4-7)

CF = Temperature correction factor
T = Mid-depth temperature (°C)
Tr = Reference temperature of 20°C

The backcalculated HMA modulus is multiplied by CF to normalize the modulus to the
reference temperature. Park (2000) developed an empirical equation to predict the

temperature at the mid-depth of the HMA layer from the measured surface temperature.

Th = Tsutf + (-O.345 1h — 0.0432112 + 0.00196h3) * sin(—6.3252t + 5.0967) (4-8)
where

T1. = HMA temperature at depth h in °C
Tmf = HMA temperature at the surface in °C

h = mid-depth of HMA at which temperature is to be determined in cm

t = time when the HMA surface temperature was measured in days (0<t<1, e. g.,
1:30 pm = 13.5/24=0.5625 days)

74

4.5 FORWARD ANALYSIS

The VESYS model relates the plastic strain occurring in each pavement layer to the vertical
elastic compressive strain in that layer. There are several computer programs for conducting
the forward analysis such as ELYSYMS, VESYS, MICH-PAVE, ILLI-PAVE, and DAMA.
The KENLAYER computer program was developed by Huang (1993). He compared the
forward analysis of all of these computer programs with KENLAYER results. The solution
of the KENLAYER program gave similar or better results for all types of analyses.
Therefore, the KENLAYER computer program was used to calculate the vertical
compressive strain at the middle of each pavement layer, assuming that the mid-depth strain
represented the average layer strain.

To calculate the total rut depth resulting from all layers, it is essential to calculate
the strain in the sub-layers until the strain is no longer detectable. Based on the assumption
that there is no deformation beyond a certain depth in the subgrade, the subgrade was
divided into six 40-inch layers and the calculation of vertical compressive strain performed
until the strain approached zero. Figure 4-8 shows the division of the subgrade layer into six
40-inch sub-layers. Also, Figure 4-9 shows the strain values at the middle of each pavement
layer for 5 different SPS-l sections caused by one standard lS-kips single axle. As shown in

the figure the strain at the middle of the sixth layer has a very small value, as expected.

75

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

 

. 8base/subbasa Base/subbase

Figure 4-8 Division of the subgrade layer into several sub-layers

 

 

 

 

 

 

 

 

 

 

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5.015435 2 . 222422.21 2 _ -.1- _ 1.1

0.051-00 ’Mm 122— 2— 1 1
Base SG1 SGZ SGB SG4 SGS SGG

 

Middle of the layers

Figure 4-9 Strain at the middle of pavement layers for 5 different SPS-l sections

76

4.6 MEASURED RUT DATA FROM IN-SERVICE (SPS-l)
PAVEMENTS

The Long Term Pavement Performance (LTPP) database includes time series rutting data
for all SPS-l sections. Figure 4-10 shows the progression of rutting with time for all SPS-l
sections. As shown in the figure some of these sections showed premature rutting due to
material- or construction-related problems. These sections were excluded from the
proceeding analysis since the VESYS model can not predict premature rutting. More details
analysis regarding to premature rutting due to material- or construction-related problems

and structure rutting can be found in NCHRP 20-50 (10/ 160) report (Chatti et al., 2005).

 

35 2222 22 22 222 222

1

Rut Depth (mm)

 

 

 

 

 

0 1 2 3 4 5 6 7 8 9 10 1
Age (years)

Figure 4-10 Rutting with time for SPS-l pavements - All sections

4.6.] Filtering the measured rut data

Due to the inconsistency of field measurements with time, there was some variability of the
measured rut depth. Therefore, in order to have a consistent time series trend, the rut depths
which were believed to be caused by the measurement variability/error were removed from

the original data, especially where no maintenance action was carried out. Making the time

77

series trend smoother helped in achieving a better optimization (minimizing the RMS
between measured and predicted) as explained in the proceeding section. Figure 4-11 (a)
shows an example of a pavement section (1-0105) where only two points at year 8 and 10
have shown a lower rut depth compared to the existing time series trend. However, no
maintenance was performed at that time; therefore, these two points were considered as
faulty measurements and were deleted for this section. Figures 4-11 (b) and (0) show the
cleaned rut data with time and load with the time series trend. A similar procedure to clean
the time series rut depth data was adopted for all the pavement sections in the SPS-l
experiment. The VESYS rutting model was used to determine the PDPs for each section by
minimizing the error between the actual field data and the predictions. This is explained in

detail in the following sections.

4.7 BACKCALCULATION OF PERMANENT
DEF ORMATION PARAMETERS

The backcalculation was performed based on three layers, HMA, base, and subgrade. Each
layer has two PDPs (a and 11); therefore a total of six parameters need to be backcalculated
for each SPS-l section. The parameter or represents the rate of decrease in permanent
deformation as the number of load applications increase (hardening/densification effect).
The parameter 1.1 represents the constant of proportionality between plastic and elastic strain
due to the repetition of each load. As shown in equation 4-2, the number of load repetitions
(n) is raised to the power -01, therefore a is site-specific and has to be backcalculated by
changing the number of load repetitions (i.e. using time series rutting data for each section).
Rutting can be predicted by using seed values for a and n, such as those provided in

Chapter 2 (Table 2-1).

78

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Age (years)
(a) original rut data versus time
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KESALS
(a) cleaned rut data versus load
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0.00 2.00 4.00 6.00 8.00 10.00 12.00
Age (years)

(b) cleaned rut data versus time

Figure 4-11 Measured time series rutting data for section 1-0105

These six PDPs were backcalculated for each pavement section using Microsoft

Excel “Solver,” by minimizing the Root Mean Square (RMS) difference between the

79

measured and the predicted rutting. The following equation shows the optimization

procedure:

3
minimize F = 2(101' —RD,-)2

49
1:1 ( )

where:
F = function to be minimized by changing or and 1.1,

Pi = predicted rut depth fi'om equation 44,

RD,- = measured rut depth in the field,

5 = total number of rutting measurements in the field over time.

For backcalculating the six parameters simultaneously, a good agreement (small RMS)
between measured and predicted rutting can be achieved; however the solution is not
unique. In other words, the backcalculated parameters are dependent on the seed values.
This was due to the various possible distributions of rutting throughout the multiple
pavement layers which still match the total surface rutting, and yet did not match the actual
rutting percentage for each individual layer. Table 4-3 shows the backcalculation of PDPs
using different seed values. In the first ten solutions, the same seed values were used for all
six parameters, while the remaining solutions have different seed values (according to
results from previous research, see Table 2-1) for each parameter. The RMS values, after
the third solution, were very small (less than 1%) and close to each other which indicate
good agreement between the measured and predicted rut depth. However, each solution
gives completely different rut percentage for each pavement layer, yet the total rutting for
all layers matches well with the measured surface rutting. The question now is which

solution is closest to the actual pavement behavior?

80

The most logical way to solve this problem involves knowing the rut percentage within

each pavement layer, such that only two parameters can be calculated at one time. There are

several ways to determine the percent rutting for each pavement layer:

Assume the percent rutting within each pavement layer based on other studies.
However these percentages are section-specific and depend on the pavement
material properties, load, and climatic conditions. Therefore, it is not suitable to
generalize this assumption for different pavement sections,

Cut trenches and measure the rutting contribution from each layer. However, the
inconsistency of the pavement layer thicknesses along with the noise caused by the
erratic sub-layer boundary make the measurement of layer contribution difficult to
determine (Chen et al., 2003).

Install Linear Variable Differential Transformer (LVDT) instruments (e.g., a device
such as the Multi-Depth Deflectometer, MDD). However, these instruments are very
expensive and not suitable for long-term investigation due to durability issues (they
may be suitable for accelerated pavement tests) (Zhou and Scullion, 2002 and
Huang, 1993).

Measure the transverse surface profile of the pavement. Using transverse surface
profiles, the contribution of each pavement layer can be identified as a percentage of
the total rutting. The required data are available for each section, require less
complicated and non-destructive procedures to collect, and can be easily monitored
over time while the pavement is in-service. The LTTP database includes transverse
surface profile data for all SPS-l sections as part of the monitoring data. In addition,
agencies are increasingly collecting transverse surface profiles instead of measuring
only the maximum rut depth. Therefore, this extensive data were used as a means

for solving the problem of unique parameter solutions.

Though a method for determining percentage of rutting within each layer is available, there

remain constraints on the possible values for each parameter.

4.7.1 Backcalculation parameters constraints

Investigating the VESYS rutting model (Equation 44) showed that or represents the rate

@rogression) of permanent deformation and operates within the exponent of the number of

load applications as (l-a). Increasing the number of load applications will increase the

81

rutting rate, meaning the exponent must be a positive value. So or is constrained to a range
of values between 0 and 1. Lower values of on indicate higher rutting rates, and vice versa.
The parameter 1.1 represents the constant of proportionality between plastic and elastic
strains in Equation 4-4. Since rut depth is defined as a positive value, the value of u has to
be positive. Low values of p. indicate low initial rutting while higher p values (>1) indicate

premature rutting. These constraints were taken into consideration in the optimization

procedure that involved choosing seed values from the transverse surface profiles.

4.7.2 Transverse surface profile

Several researchers have analyzed the transverse surface profile (Simpson, et al., 1995,
White, et al., 2002 and Villiers, et al., 2005). The shape of the transverse surface profile is a
good indication of where the rutting originated within the pavement structure. Simpson, et
al., 1995 developed criteria for analyzing the transverse surface profile such that one can
locate the individual failed layer (the most probable contributor to the rutting).

Furthermore, White et al., 2002 refined these criteria by applying finite element analysis.
Based on the refined criteria, Figures 4-12, 4-13, and 4-14 show examples of transverse
surface profiles for failed HMA, base, and subgrade layers, respectively. The criteria used

for this research are discussed in the following section.

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Rut depth (m)

 

Distance from the edge (mm)

Figure 4-12 Transverse surface profile for HMA layer rutting— Section 31-0113

Rut depth (mm)

 

Distance from the edge (mm)

Figure 4-13 Transverse surface profile for base rutting—Section 20-0102

84

         

.__,____,, _k , ,_ , __ 7 ;¥___, _ .1 _ _ ,._.A __ g; # 7-: y 7_. 7L...__

1000 1500 2000 2500 300

            

Rut depth (m)
'5

Distance from the edge (nun)

Figure 4-14 Transverse surface profile for subgrade rutting—Section 32-0110

4.7.3 Transverse surface profile analysis criteria

The following equations represent the criteria developed by White, et. al to determine the

failed layer identity using transverse surface profile data:

 

 

A=AP+A,, (4-10)
A

R .—_ _& (4-11)
An

C1 = (—858.21)D + 667.58 (4-12)

C2 = (—1509)D - 287.78 (4-13)

C3 = (-2,120.1)D — 407.95 (4-14)

where:

A = total area
Ap = positive area (see Figure 4-15)
A" = negative area (see Figure 4-15)
R = area ratio
C1 = theoretical average total area for HMA failure, mm2

C 2 = theoretical average total area for base/subbase failure, mm2

85

C2 = theoretical average total area for subgrade failure, mm2

D = maximum rut depth, mm (see Figure 4-16)

/_\

   

 

Positive area ' 3 : 1 Negative area

 

 

 

 

 

Figure 4-15 Definition of positive and negative area in transverse surface profile
(White, et al., 2002)

W
V

Maximum rut depth

Figure 4-16 Definition of maximum rut depth (White, et al., 2002)

Based on the characteristics of a given surface profile and the criteria described above, the
following outcomes can be predicted:

(a) Failure will occur in the HMA layer if:

R > 0.05 and A > (C;+C2)/2

(b) Failure will occur in the base/subbase layer if:

R < 0.05 and A > (C 2+C 3)/2

(c) If none of the above criteria are satisfied, that suggests subgrade layer failure.

4.7.4 Unique solution for backcalculation of permanent deformation parameters

The problem of parameter uniqueness described previously can be dealt with by combining
backcalculation strategies with transverse surface profile analysis. This combination of

procedures overcomes the uniqueness problem for the backcalculation of the PDPs by

86

limiting the number of realistic candidates. In applying this technique to section 1-0105 (as

shown in Table 4—3), the following steps are required:

Backcalculate the parameters using different typical seed values (as shown in Table
2-2).

For each solution calculate the RMS error and the percent rutting from each layer as
shown in Table 4-3. Since the RMS error is minimized when there is a good match
with the field measurement, solutions 1, 2, 3, and 4 are excluded because they have
higher RMS compared to other solutions.

Assume that each layer will share some portion of the total rutting, unless premature
rutting occurred due to construction-related issues. Based on this assumption, one
can exclude solutions 1, 3, 4, 5, 6, 7, 9 and 10, since they have negligible detected
rutting in at least one layer.

Apply the criteria from section 4.6.3 for available transverse surface profiles at
different times (with more consideration for the latest available data) and point
locations within the pavement section to determine where the rutting originated.
Figure 4-17 shows the transverse surface profile for section l-OlOS at one point
location from the latest observation. The shape suggests that the rutting originated in
both HMA and base layers (see discussion in section 4.6.3).

To further verify this initial visual assessment, Table 4—4 shows the frequency of
layer failure over 9 years along the 11 point locations (making a total of 99 surface
profiles available for analysis). Based on this, solutions 8, ll, 12, 13, and 14 are
probable candidates; however the most likely solutions are 13 and 14. This is based
on their close agreement with the transverse surface profile analysis and relatively
low RMS errors. Furthermore, a solution with minimal RMS error comes closer to

representing the actual pavement behavior in the field. In this case, solution number

87

l4 satisfies all of these criteria, and can therefore be considered as the most likely
solution for the permanent deformation parameters.

0 A point of caution: Any rutting within the pavement will show on the surface,
though it is logical that rutting percentages should be in sequential order through the
different layers (e. g. if the HMA layer fails, it should have the highest rutting
percentage, with the second highest rutting percentage in the base, and the lowest in

the subgrade).

This same procedure was applied to the surface profiles for all sections in order to
backcalculate the unique permanent deformation parameters; out of 120 three-layer
sections, 109 sections (91%) had a most likely solution. In the remaining 11 sections,
rutting measurements were too low for layer-identification. Figure 4-18 shows the measured
(from the field) versus predicted rut depth for all sections included in the backcalculation of
PDPs (109).

The ability to obtain a unique solution for each section’s PDPs allows for many

advantages in rutting prediction. These will be discussed in the following section.

Table 4- 4 Number of point locations with corresponding failed layer-section 1-0105

 

 

 

 

 

Number of surface profiles Failed layer
56 HMA
37 Base
3 Subgrade
3 NA‘

 

 

 

 

' White’s criteria failed to recognize them

88

      
 

     

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5 _2 Q 1500 20 0 3000 3500 4 1 0

a 1 1

.0 1

3 '41 1
-61 1
81 '
-101 f-f-‘---_ _ _,_~_fi___ _ 3___-”-

Distance fi'om the edge (mm)

Figure 4-17 Transverse profile section 1-0105

 

 

 

 

 

 

 

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o 5 1o 15 20 25 30

Actual rut depth, mm

Figure 4-18 Measured versus predicted rut depth for sections used in the backcalculation

4.7.5 Advantages of using backcalculated parameters

There are several advantages of using the obtained PDPs as follows:

0 Determine precise parameters for pavement layers, since they are specific for each
section,

0 Determine the contribution (percentage) of each layer to the total pavement rutting,

89

o Characterize existing rutting as either premature or structural,

- Based on the above information, a correct remedial action can be taken for pavement
rehabilitation,

0 These procedures also can be used as diagnostic/prediction tools for rutting,

o Non-destructive rutting test to calculation the layer rutting contribution,

0 Compare these parameters as well as the rutting percentage with the previously
developed parameters of accelerated loading facilities, ALFs to describe the

difference in behavior between the actual field performance and ALFs,

0 These parameters can be predicted based on the material parameters, cross sections,
environmental conditions (from actual field data) of each section,

0 These procedures can be incorporated into a spreadsheet such that from the
transverse surface profile data the layer rutting contribution can be calculated in a

cost-effective manner.
4.7.6 Summary statistics for backcalculation of permanent deformation parameters
By applying the above procedures to distinguish the most likely solution, the backcalculated
PDPs and the rutting contribution of each pavement layer were determined for all (109)
sections. Excluding the sections that have:

0 p. >1 which represents high initial rutting (premature rutting),

o a = 0.99 which represents no progression of rutting with time because the majority
of the rutting occurred at the initial stage,

0 100% of the rutting in the HMA layer, in order to eliminate any rut failure due to
specific material problems within the HMA layer,

The number of sections with normal structural rutting reduced from 109 to 43 sections.
Figure 4-19 shows the time series rutting data for both categories, and Table 4-5 shows their
respective descriptive statistics. Also, the distribution of a and ,u as well as the rutting
percentages for both categories are shown in Figures 4-20, 4-21, and 4-22, respectively.
Figures 4-20 and 4-22 show that excluding the abnormal sections, a-values and the rutting
percentage become normally distributed. On the other hand, u-values showed either

uniform or lognormal distribution even afier excluding the abnormal sections.

90

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4.7.7 Comparison of obtained or, p, and rutting percentage with previous work

There were several trials in the past to backcalculate the permanent deformation parameters,
some of them from field data and the others from ALF. The first study predicted overall
average parameters for GPS-l sections and was not based on time series rutting data to
predict the parameters for each section (Ali et al., 1998). The second study predicted the
parameters for only one section using the transverse surface profile (Ali and Tayabj i, 2000).
Other researchers used ALF (FHWA and TxMLS) data to backcalculate the permanent
deformation parameters. Figure 4-23 shows comparison of the average predicted PDPs with
the previous studies. A good agreement exists between this study’s SPS-l predicted
parameters with those of the ALF studies especially the a values.

Also, there were several methods to measure the rutting contribution from each
pavement layer. The results from the above developed procedure for predicting the rut
percentages from each layer was compared with the measured rut depths from previous
studies (AASHO and ALFs). Figure 4-23 shows the average rut percentage of the normal
behavior group (43 sections) with AASHO and ALF. The results showed a good agreement
between the predicted rutting percentages of the SPS—l sections and the ALF-TxMLS. It is
important to note that the developed procedure (a non-destructive method for analyzing
rutting by layer) compares quite favorably with the trenching technique for measuring the

same rut layer contribution used in the other studies (Zhou and Scullion, 2002).

96

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Rutting percentage
4)
O

   

Subgrade

Pavement layers

Figure 4-24 Comparison of rutting contribution of pavement layer

4.8 PREDICTION OF PERMANENT DEFORMATION
PARAMETERS

A majority of the previous studies give a wide range of values for the permanent
deformation parameters. Compared with the multiplicative constant, u, even slight changes
in the exponential constant, or, produce enormous differences in predicted rutting over the
lifetime of the pavement (see Equation 4-1). Moreover, these parameters are section-
specific according to material properties, layer cross section, and even climatic condition. In
the past, there were some trials to predict these parameters in the laboratory for HMA-layer
material, yet predicted values need to be shifted to account for actual field behavior. The
proceeding sections will explain the regression analysis used to predict the PDPs for in—
service pavements (considering material properties, layer cross section, and climatic

conditions) in the SPS-l experiment.

4.8.1 Available material properties

The LTPP database provides information for the pavement layers of all SPS-l experiment

sections, structural, material as well as climatic variables. Several data elements were

98

extracted for each pavement layer from release 17 of the LTPP database (Datapave.com) as

follows:

0 HMA layer

The gradation of the fine and coarse aggregate,

Bulk specific gravity of fine and coarse aggregate,

Bulk specific gravity of the asphalt mixture from field cores,
Maximum theoretical specific gravity of the mix,

HMA binder content,

Kinematic and absolute viscosity of the asphalt binder
Indirect tensile strength of the mixture,

Resilient modulus of the mixture.

00000000

0 Base layer
0 The gradation of the fine and coarse aggregate.
o Atterberg limits (liquid and plastic limits)

0 Subgrade layer

0 Gradation,

0 Moisture content and dry density,

0 Atterberg limits (liquid and plastic limits)
0 Unconfined strength test.

Using the HMA layer data, the voids in total mix (VTM), voids in mineral aggregate

(VMA), and voids filled with asphalt (V FA) were calculated as follow:

 

VTM=[1— Gm” ]*100 (4-15)
Gmm
G l—P
VM=[1——'l”—£—L)]*loo (4-16)
Gsb
VFA=[KM—’47;fl]*1oo (4-17)

Bulk specific gravity of the combined aggregate, Gsb, can be calculated from the

following equation:

F+ C

___ P P 4-18

GS!) PF PC ( )
61“ 6C

where

VTM = voids in total mix
VMA = voids in mineral aggregates

99

VFA = voids filled with asphalt

Gmb = bulk specific gravity of the cores

Gm", = maximum theoretical specific gravity

Gs], = aggregate bulk specific gravity

percent asphalt content

PF = weight percentages of fine aggregates (percent passing sieve # 4)

PC = weight percentages of coarse aggregates (1- percent passing sieve # 4)
G F = bulk specific gravity of fine aggregate

CC = bulk specific gravity of coarse aggregate

:0
ll

Several climatic variables were extracted from the SPS-l data, and Table 4-6 explains those

that are considered in the regression analysis.

Table 4-6 Climatic variables considered

 

Climatic variables Description

 

Mean annual temperature Average of daily mean air temperatures for year, °C

 

Maximum annual temperature Average of daily maximum air temperatures for year, °C

 

Minimum annual temperature Average of daily minimum air temperatures for year, °C

 

 

 

 

 

 

Days above 32 °C Number of days where daily maximum air temperature is
above 32.2 °C for year

Days below 0 °C Number of days where daily minimum air temperature is
below 0 °C for year

Freeze index Calculated freezing index for year

Freeze thaw cycle Number of freeze/thaw cycles for year.

Total annual precipitation Total precipitation for year

Wet days Number of days for which precipitation was greater than
0.25 mm for the month.

 

Intense precipitation days/year Number of days for which precipitation was greater than
12.7 mm for year

 

 

 

 

The pavement layer thicknesses from the backcalculation procedure and the strain at the
middle of each pavement layer were considered as independent variables in the regression
analysis.

Since the independent variables are many, not all are introduced in the multiple linear
regression analysis. Based on the previous studies along with the simple univariate linear
regression of each variable, the independent variables that have reasonable relationships

with the PDPs were selected and introduced in the model. Additionally, the backward

100

regression analysis selects the most statistically significant variables for each permanent

deformation parameter.

4.8.2 Regression analysis

Possible forms of multiple linear regression models are shown in Equations 4-19 through 4-
23. Equation 4-19 shows the general form of multiple regression; Equation 4-20 is a
mathematical form for multiple linear regression; Equation 4—21 is similar to Equation 4-20
except that it includes additional interactive effects; Equation 4-22 is a multiplicative form
of regression which can consider the non-linear effects of the variables; and Equation 4-23

shows the log-linear regression form for multiple variables.
Y = f(x1,x2,x3, ........ ) + emode, (4-19)

I:
Y : :80 + Zflixi + gmodel (4'20)
i
n n n
Y = '50 + Zflixi + ZZflixix j + Emodel (4'21)
i i j
n ,0
Y : flOl—[xi lgmodel (4’22)
i

log Y = log ,60 + 2 ,6,- log x,- + amodc, (4-23)

The multi-linear regression analysis with variable selection offers two major advantages:

0 It provides relationships with explicit terms, and
o Allows for accuracy assessment of permanent deformation parameter predictions.

In this study, the multiplicative form of multiple linear regression (Equation 4-22) was
utilized to model the nonlinear relationship between the PDPs and the independent
variables. Several precautions were taken into consideration to ensure integrity of the
model as follows:

0 The signs of the multiple linear regression coefficients agree with the signs of the

simple linear regression of the individual independent variables,

101

o The signs of the multiple linear regressions for each independent variable agree with
intuitive engineering judgment. For example, higher annual temperature should
increase the rate of the rutting in HMA layer, and therefore create more positive
values for (l-a) and u.

0 There should be no multicollinearity among the final selected independent variables.
For example, two independent variables having the same effect (high bivariate
correlation) on the dependent variable should not be included in one model at the
same time.

0 One of several variable selection algorithms, such as stepwise, forward, and
backward regression analyses, is used in regression to eliminate the statistically
insignificant independent variables.

0 The model is selected with the smallest number of independent variables, minimum
standard error, and highest R2 value.

In addition, afier finalizing the model for each permanent deformation parameter, the
regression models were tested to ensure there were no assumption violations. These tests
are:

0 Normality distribution,

0 Constant variance,

0 Cook’s distance.

4.8.3 HMA layer regression analysis
The rutting in the HMA layer is characterized by dam and Hum. The parameter, can“,
represents the rate of decrease in HMA rutting as the number of load applications increases
(since there is a natural limit to the amount of permanent deformation) and as the material
becomes stiffer (the hardening effect due to environmental conditions). The parameter,
uHMA, represents the constant of proportionality between plastic and elastic strain within the
HMA layer.

There are several factors affecting HMA rutting. All available material and climatic
data used to explain HMA rutting were extracted from the LTPP database (section 4.7.1), as

per the existing literature (see chapter 2, section 2.2.1.3). Using simple linear regression,

102

these independent variables were regressed on aHMA and gum. The variables that have
reasonable relationships (relatively higher R2) were introduced into the multiple linear
regression models. The backward regression analysis was utilized to select the statistically
significant variables for the final model. A total of 15 sections were used for predicting
cum), and Wm. This is due to the limited amount of available data to calculate VTM,
VFA, and VMA, which are important for explaining the rate of the HMA rutting. Equations

4-24 and 4-25 show the final model for aHMA and pHMA.

0.555
)

(1% = 5105.124*(Strain *110‘1-013 «mm—058 *(Max A 730-732 (4-24)

pm“ = 6.746*aAC4'102 "'FI’O'213 (4-25)
where:
Strain = strain at the middle of HMA layer due to ESAL
P10 = % passing sieve number 10 of the most upper HMA layer
VFA = % voids filled with asphalt of the most upper HMA layer
Max A T = Average of daily maximum air temperatures for year, °C
F] = freezing index

It can be seen from the equations that aHMA is a function of P10 and VFA (both
material-related properties), strain (structure-related), and Max AT (environment-related),
while uHMA is a function of aHMA (rate of rutting) and F1 (environment-related). This
implies that, in order to predict uHMA, an estimate for calm must be predicted first.
Attempts were made to predict uHMA from variables other than aHMA (mainly those listed
below Equations 4—24 and 4-25), but all alternatives to using aHMA were found to have
much lower R2 values. Figures 4-26 and 4-27 show the individual relationship between
these independent variables and cum and uHMA, respectively. Table 4-7 shows the analysis
of variance of the multiple linear regression of cum and gum. The results show that the
overall models for a and u are statistically significant. Table 4-8 shows that 90% and 79 %

of the variance for calm and mum, respectively, is explained by the independent variable.

103

Table 4-7 ANOVA for aHMA and plum

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Variable Sum of Squares df Mean Square F Sig.
Regression 1.675 4 .419 33 .604 0.000
(1 Residual 0.125 10 0.012 - -
Total 1.800 14 - - -
Regression 16.675 2 8.338 26.065 0.000
p Residual 3.519 1 1 0.320 - -
Total 20.194 13 - - -
Table 4- 8 Model Summary for aHMA and “HMA
Variable R R2 Adjusted R2 Std. Error of the Estimate
or 0.965 0.931 0.903 0.11164]
p 0.909 0.826 0.794 0.565585

 

 

 

 

 

 

 

Table 4-9 shows the unstandardized and standardized model coefficients, t-test, statistical
significance, and collinearity statistics for both aHMA and “HMA. It can be seen from the
table that all independent variables included in the model for both aHMA and plum are
statistically significant. Also, there was no concern about the multicollinearity (small VIF).
Moreover, there is a good agreement between the multiple linear regression coefficient
signs and the univariate relationship of the individual variables as shown in Figures 4-26
and 4-27. The standardized regression coefficients show that:

o The higher the initial strain and/or the yearly average of daily maximum air
temperatures, the higher the dump, value, which means a lower rate of rutting
progression with time (the exponent is 1-0LHMA). In other words, if the HMA layer is
soft (higher initial strain) or the climatic region is hot (higher temperatures); the
majority of the rutting will occur at the initial stage and taper off with the remaining

life of the pavement.

104

o The higher the percent passing sieve number 10 and/or the percent of voids filled
with asphalt, the lower the aHMA value, which means a higher rate of rutting
progression with time. In other words, rutting will be more pronounced if the HMA
layer is composed of a finer mix or it contains more voids.

o The higher the aHMA, the higher the uHMA, as can be seen in Figure 4-27. This means
that pavements with lower initial rutting (lower uHMA value) will show rutting over a
longer period of time (lower aHMA value).

0 The higher the freezing index for a region, the lower its pHMA values. This indicates

that unlike hotter regions, pavements constructed in colder regions will show lower

initial rutting.

Table 4-9 shows the standardized regression coefficients used to rank the importance of the

independent variables to QHMA and plum values, as shown in Figure 4-25.

Table 4-9 Model coefficients for (rum and uHMA

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Unstandardized Standardized Collinearity
Variables Coefficients Coefficients t Sig. Statistics

Beta Std. Error Beta Tolerance VIF

Constant 8.538 1.220 - 6.997 0.000 - -
Strain 0.555 0.071 0.727 7.820 0.000 0.802 1.247
a % passing # 10 -l.013 0.156 -0.611 -6.485 0.000 0.781 1.281
VFA -0.580 0.238 -0.213 -2.439 0.035 0.907 1.103
Max A T 0.732 0.105 0.589 6.951 0.000 0.966 1.036

Constant 1.909 0.419 - 4.550 0.001 - -
p aHMA 4.102 0.658 0.786 6.229 0.000 0.995 1.005
F1 -0.213 0.066 -0.406 -3.219 0.008 0.995 1.005

 

 

 

105

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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l ; 'j . } T .
.,, 1 l i Max A T i 1, I
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L_, - -__ I - L _______ ___ _ _ 1;- __ -2 -.. ,-__, _ _ _ - _1________ _____
-0.9 -O.6 -O.3 O 0.3 0.6 0.9

Standardized regression coefficient

Figure 4-25 Ranking the importance of the independent variables for aHMAand uHMA

106

 

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1 o 1
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o 200 400 600 800 1000 1200
F1

Figure 4-27 Relationship of 11 HMA versus on HMA and F1

Figure 4-28 shows a reasonable prediction of aHMA and WW. in logarithmic (1n) and

arithmetic scales. A reduction in R2 (small for 0111114,, and quite large for pHMA) occurs due to

the transformation from logarithmic (In) to arithmetic scale. This dramatic reduction for

“HMA implies:

Prediction of 1.1mm, is very sensitive to aHMA (standardized [3 =0.786), so small
changes in (1.1—{MA prediction affect the predicted value of pump, to a great degree.
There is large scatter in the relationship between aHMA and Hum (Figure 4-26)
especially when uHMA is greater than 0.7.

Good prediction of plum at higher values (>1) is not expected since higher uHMA
values represent higher initial HMA rutting due to specific problems (material

and/or construction and/or environment).

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Table 4-10 shows the descriptive statistics for aHMA, pHMA and their independent variables
used in the regression analyses. It should be noted that Equations 4-24 and 4-25 should be
used within the range for each variable listed in Table 4-10 in order to obtain reasonable

predictions.

Table 4-10 Descriptive statistics of 01111141,, uHMA, and their independent variables

 

 

 

 

 

aHMA uHMA Strain P10 VFA Max AT Fl
Mean 0.589 0.649 6.35E-05 37 51.6 22 158
St. Dev. 0.173 0.675 2.73E-05 8 6.8 6 273
Minimum 0.207 0.010 2.69E-05 24 38.5 12 1
Maximum 0.844 2.059 1.03E-04 49 67.3 29 988

 

 

 

 

 

 

 

 

 

 

4.8.4 Base layer regression analysis

For base layer, the only data available were the gradation, base thickness used in the
backcalculation, and the calculated strain at the middle of the base due to one standard axle.
Unlike the HMA layer, in which the materials are highly controlled, the base and subgrade
layers of flexible pavements are frequently more dissimilar from one section to another.
This becomes evident when examining sieve analyses. Since the content of HMA material
is highly controlled, a particular sample can be uniquely identified by an individual sieve
measurement, that is, the percent material passing through one particular sieve (see Figure
4-29). This is not the case for the base layer material, since base materials from two
different sections might have the same percent passing through one sieve and different
gradations for the other sieves, as shown in Figure 4-30. Therefore, a new index termed,
Gradation Index (GI) is introduced in this analysis to represent the gradation of the base

layer such that using the GI alone or with the percent passing of any given sieve (such as

110

sieve 4, 10, or 200) will be more representative of an individual base layer’s material. The

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

    

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   

 

 

 

 

 

 

 

   

 

 

 

 

 

 

 

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111

Figure 4-30 Sieve analysis of base layer

100

For the base regression analysis, only sections that have base rutting of 10 percent or more

out of the total surface rutting and available base gradations were considered, these total 27

sections. The final regression equations for predicting the abase and phase are shown below:

“base = 2.724 "'10-5 * mod uluso' 102 * T hz'clcrzess0'066 * FIDO-0098 * 011-982

(4-27)

#base = 7.1977 "‘10—3 * (16256 * Thickness—0308 * strain—0809 (4-28)
where

Modulus = backcalculated base modulus, psi

Thickness = Thickness of base layer used in the backcalculation, in

P200 = % passing sieve number 200

GI = Gradation index

Strain = Strain at the middle of the base layer due to one standard axle

Table 4-11 shows the analysis of variance of the multiple linear regression for abase and
phase. The results show that the overall models for abase and phase are statistically

significant. Table 4-12 shows that 50.6 % and 68.7 % of the variance for abase and phase,

respectively, is explained by the independent variable.

Table 4-13 shows the unstandardized and standardized model coefficients, t-test, statistical

significance, and collinearity statistics for both abase and phase. It can be seen from the table
that all independent variables included in the model for both abase and phase are statistically

significant except for the base thickness in the abase model. Excluding the base thickness

from the model causes dramatic reduction of R2, therefore base thickness was kept in the
model. Also, there was no concern about multicollinearity (small VIF). Moreover, there is a
good agreement between the multiple linear regression coefficient signs and the univariate
relationship of the individual variables as shown in Figures 4-3l and 4-32. The standardized

regression coefficients show that:

112

o The higher the initial modulus, the higher the abase value, which means a lower rate
of rutting progression with time (the exponent is l-abase).

o The thicker the base with higher GI (coarser material), the higher the abase, which
means a lower rate of base rutting with time.

o The higher the percent passing sieve 200, the lower the abase, which leads to a
higher rate of rutting with time.

0 Similar to the HMA layer, there is a strong relationship between abase and 111,2,“(R2
= 0.5949); the higher the abase the higher the phase as can be seen in Figure 4-32.
This means that a pavement with lower initial rutting (lower phase value) will show
rutting over a longer period of time (lower abase value).

0 The thicker the base layer with higher initial strain value, the lower the phase, which

indicates that rutting will keep progression with time.

Table 4-13 shows the standardized regression coefficients used to rank the importance of

the independent variables in the abase and phase models, as shown in Figure 4-33.

Table 4-11 ANOVA for abase and phase

 

 

 

 

 

 

 

Variables Sum of Squares df Mean Square F Sig.
Regression 0.674 4 0.169 7.653 0.001
or Residual 0.485 22 0.022 - -
Total 1 . 159 26 - - -
Regression 59.63 1 3 19.877 20.000 0.000
p Residual 22.859 23 .994 - -
Total 82.490 26 - - -

 

 

 

 

 

 

 

 

 

Table 4-12 Model summary for abase and phase

 

Variables R R2 Adjusted R2 Std. Error of the Estimate

 

or 0.763 0.582 0.506 0.148
p. 0.850 0.723 0.687 0.997

 

 

 

 

 

 

 

 

113

Table 4-13 Model coefficients for abase and phase

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Variables Unstandardized Coefficients Standardized t Sig. Collinearity Statistics
Coefficients
Beta Std. Error Beta Tolerance VIF
Constant -10.51 1 3.519 - -2.987 0.007 - -
Modulus 0.102 0.037 0.447 2.75] 0.012 0.721 1.387
Thickness 0.066 0.051 0.205 1.303 0.206 0.771 1.297
or P200 -0.098 0.032 -0.462 -3.094 0.005 0.854 1.172
GI 1.982 0.715 0.429 2.774 0.011 0.794 1.259
Constant -4.934 2.083 - -2.369 0.027 - -
a 6.256 0.942 0.742 6.639 0.000 0.966 1.035
11 Thickness -0.808 0.355 -0.298 -2.280 0.032 0.707 1.415
Strain -0.809 0.254 -0.417 -3. l 82 0.004 0.700 1.428

 

 

Figure 4-34 shows the prediction of aHMA and Ill-[MA in logarithmic (1n) and arithmetic

scales. Similar to 0111114,, and uHMA, the figure shows a reasonable prediction of abase in the

actual scale. A reduction in R2 for phase occurs due to the transformation from In to actual

scale, similar to mm). (as mentioned previously).

Table 4-14 shows the descriptive statistics of abase, phase and their independent variables

used in the regression analysis. It should be noted that Equations 4-27 and 4-28 are used

within the range of the data in Table 4-14 to obtain reasonable predictions.

114

 

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1.0 4———v-—.#_ _..- __.____ __ _.._ __1_____,___W* fl.

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Base strain

 

 

 

Figure 4-32 Relationship between phase and abase, base thickness, and base strain

116

 

Modulus. 1 j 1

 

 

 

 

 

 

 

 

 

 

 

 

 

1 1 m1

1 1 1 1

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-0.6 -0.3 O 0.3 0.6 0.9

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Figure 4-33 Ranking the importance of the independent variables for abase and P-base

Table 4-14 Descriptive statistics of abase, phase, and their independent variables

 

Item “base 01 base modulus thickness Strain P200 GI
Mean 0.60 0.76 45058 21.7 1.3 85-04 29.1 106.59
ST. DEV. 0.77 0.16 41131 11.0 1.21E-04 31.5 4.86
Minimum 0.01 0.50 4599 3.6 1.29E-05 5.9 98.38
Maximum 2.44 0.99 178098 43 .3 5 .07E-04 91.3 1 15.99

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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118

4.8.5 Subgrade regression analysis

Similar to the base layer and even more pronounced, the percent subgrade material passing
through one sieve is not enough to characterize the subgrade materials, as shown in Figure
4-35. Therefore, the need for the GI (Equation 4-26) is at least as great for the subgrade

regression analysis as it was for the base layer.

 

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Figure 4-35 Sieve analysis of subgrade layer

For subgrade analysis, only those sections that show rutting in the subgrade and have (Isa
values less than 0.9 were considered, which totals 17 sections. The final regression

equations for predicting the age and use are shown below:

=1_385x10—5 ”fiat-"0.043 ... 011.89 ,P10.116 ... 0320.14 .. ”0.036 ,wet dayso'326

“50
(4-29)
,u S6 = 2.575 *10‘63 * mod ulus 2-41 * strain ‘0-764 * GI 22594 * P11‘304 (4-30)
where
Strain = Strain at the middle of the first 40 inches of subgrade layer due to one ESAL
G1 = Gradation index (as calculated fi'om equation 4-26)

119

P1 = Plasticity index of subgrade layer
D32 = Number of days where daily maximum air temperature is above 32.2 °C for year
Wet days = Number of days for which precipitation was greater than 0.25 mm for year.

Modulus = backcalculated subgrade modulus, psi

Table 4-15 shows the analysis of variance for use and use. The results show that the overall
models for use and use are statistically significant. Table 4-16 shows that 47.3% and 84.8%

of the variance for use and use, respectively, is explained by the independent variables.

Table 4-15 ANOVA for use and use

 

 

 

 

 

 

 

Variables Sum of Squares df Mean Square F Sig.
Regression 0.152 6 0.025 3.389 0.043
0t Residual 0.075 10 0.007 - -
Total 0.227 16 - - -
Regression 33.212 4 8.303 23 .344 0.000
p, Residual 4.268 12 0.356 - -
Total 37.480 16 - - -

 

 

 

 

 

 

 

 

 

Table 4-16 Model summary for use and use

 

 

 

R R2 Adjusted R2 Std. Error of the Estimate
0. 0.819 0.670 0.473 0.08660
14 0.941 0.886 0.848 0.59640

 

 

 

 

 

 

 

Table 4-17 shows the unstandardized and standardized model coefficients, t-test, statistical
significance, and collinearity statistics for both use and use. It can be seen from the table
that all independent variables included in the model for both use and use are statistically
significant except for the strain and F1 in the use model. Excluding either of these variables
from the model causes a dramatic reduction of the R2 value, therefore, similar to the base
layer, they were kept in the model since the backward regression analysis selects them.
Also, there was no concern about multicollinearity (small VIF). Moreover, there is a good

agreement between the multiple linear regression coefficient signs and the univariate

120

relationship of the individual variables as shown in Figures 4-36, 4-37 and 4-38. The
standardized regression coefficients as depicted in Figure 4-39 show that:

o The higher the PI, GI, D32, wet days, F1, and vertical compressive strain at the
middle of the first 40 in of the subgrade, the higher the use, which means a lower
rate of rutting progression with time (the exponent is l-use). This is what the
multiple linear regression analysis showed; however the univariate relationship of
these variables with use supports this result with a weak trend. Hence, the resulting

use relationships can not be generalized since the statistical evidence is not strong

enough.

0 The higher the PI, GI, and subgrade modulus, the higher the use, which means a

majority of the resulting rutting will occur at the first stage of pavement life with

very little progression with time. Similar to the base layer, higher initial strain value

in the subgrade indicates that rutting will keep progressing with time.

Table 4-17 Model Coefficients for use and use

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Unstandardized Standardized Collinearity
Variables Coefficients Coefficients t Sig. Statistics
Beta Std. Error Beta Tolerance VlF
Constant -1 1.187 3.965 - -2.822 0.018 - -
Strain 0.043 0.031 0.283 1.391 0.194 0.798 1.252
(31 1.890 0.805 0.955 2.348 0.041 0.199 5.020
or PI 0.116 0.035 1.271 3.342 0.007 0.228 4.387
D32 0.140 0.061 0.914 2.269 0.047 0.203 4.924
F1 0.036 0.020 0.656 1.796 0.103 0.247 4.047
Wet days 0.326 0.105 0.853 3.109 0.011 0.438 2.281
Constant -144. 12 21.825 - -6.603 0.000 - -
SG modulus 2.410 0.956 0.403 2.521 0.027 0.371 2.692
p Strain -0.764 0.274 -0.388 -2.786 0.016 0.490 2.043
01 22.594 5.006 0.890 4.513 0.001 0.244 4.096
PI 1.304 0.211 1.1 18 6.191 0.000 0.291 3.436

 

121

 

Figure 4-40 shows the prediction of use and use in logarithmic (1n) and arithmetic scales.
Table 4-18 shows the discriptive statistics of use, use and the independent variables used in

the regression analysis. Similar to the HMA and base layers, Equations 4-29 and 4-30 are
used within the range of the data in Table 4-18 to obtain reasonable predictions. Figure 4-41
shows the measured (field), calculated (backcalculated PDPs), and predicted (regression
equations) rut depth for one of the sections that have data for HMA, base, and subgrade
layers (section 50113).

Finally, it should be noted that, as shown in Figure 4-24, a majority of the total
rutting occurs within the HMA layer (on average, 57%), followed by the base layer
(27.5%), and the subgrade layer (15.5%). The decay in PDP prediction is justifiable when
correlated with the decay in successive layers’ overall rutting percentages. This is primarily
due to two analytical/data factors. First, with a smaller percentage of the total rutting to
predict, the base and subgrade models are more constrained by available data and the
smaller magnitude of the rutting effect measured within these layers. Secondly, the base and
subgrade layers have successively fewer variables available within the predictive models
than the HMA layer; therefore, it is more difficult to explain the rutting in these layers with
a decreased number of variables. The results of this analysis agree with the expectation that
prediction of the PDPs decays as the rutting percentage decreases. HMA regression analysis
showed that the overall model for uHMA and Hum are statistically significant, as are all
variables included. On the other hand, the overall models for ubase and um,c are statistically
significant, with only one insignificant variable (base thickness). Following the same pattern
of decreased significance with decreased rutting percentage, the overall models for use and
use are statistically significant, yet contain two insignificant variables (strain and F I). This
understandable pattern suggests the need for more study and further theorizing of variables

to explain rutting within the base and subgrade layers.

122

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4.9 SUMMARY

This chapter addresses several procedural difficulties that were major concerns within
previous PDP backcalculations such as: 1) PDPs are site specific rather than average values
that can be generalized, 2) the backcalculated PDPs are based on time series data of rutting
for each section instead of one rutting value, 3) a—values should be backcalculated based on
a varying traffic level (on is within the exponent of n, which is the number of load
repetitions) rather than one rut value which corresponds to one traffic level, 4) choosing the
backcalculated PDP values that match the sectional transverse surface profiles solves the
uniqueness problem. The resulting calibrated rutting model will be utilized in the
mechanistic analysis (Chapter 6) for relative comparison of different axle/truck
configurations and their effects on rutting. The following section summarizes the main

conclusions and the recommended future research related to this analysis.

126

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127

1 A Measured 0 Calculated :1 Predicted _ __ 0 _1 1 _ , 1

1
1 _ _ _ _ 0.91 __ _. 1

Rutdepth,mm
O A N (10 4:. 01 O) \1 oo
1
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3000 4000

0 1 000 2000
Traffic, KESAL
Figure 4-41 Measured, calculated, and predicted total rut depth for section 50113

4.9.1 Conclusion

Within this chapter, the following items were accomplished:

a Backcalculation of the PDPS from in-service pavement rut data;

0 A remedy for uniqueness of backcalculation of PDPs was developed by selecting the
solution that produces layer rutting percentages matching the individual transverse
surface profile;

0 A developed procedure allowing for calculation of the layer rutting contribution
through non-destructive means, which also can be used as a diagnostic/prediction
tool;

a A good agreement between the backcalculated PDPs, as well as layer rutting
percentage, with the previously developed parameters of ALF s; and

0 Parameters were predicted based on the material properties, cross sections,

environmental conditions (actual field data) of each section.

128

4.9.2 Future research

Though the improved methodology outlined in this chapter yields promising results, there

are several areas of the current study open for future improvement.

The same analysis can be conducted again when there are more material properties
available, such as V T M, VMA, and VFA for the HMA layer; compaction data
(moisture content and dry density) and unconfined compression strength for the base
layer; and more aggregate gradation for all pavement layers.

The same analysis procedures can be performed for ALFs where more data and
more controlled environments are available.

Further validation of the calibrated rutting model can be conducted using other data
sets outside of the SPS-l experiment, such as GPS-l and ALFs.

The rutting model was calibrated based on the calculated strain due to one standard
axle; however, either validation or calibration can be done based on axle load
spectra to eliminate the error due to converting the actual load distribution to ESALs
based on load equivalency factors, LEF.

In this analysis, the rutting model was calibrated for conventional flexible
pavements (three layer system); the amount of the data two-layer systems (full depth
pavements) was very small. So, similar procedures for full depth asphalt pavements
can be done wherever there are data for two layer pavement systems. Fortunately,
the uniqueness problem will be less severe since there will be four PDPs instead of

the six values in a three layer system.

129

CHAPTER 5- LABORATORY INVESTIGATION

5.1 INTRODUCTION

In the past few years, several research studies were conducted to select a fundamental—
based laboratory Simple Performance Test (SPT) for permanent deformation. The
candidate tests were evaluated and validated using three different experimental sites: 1)
the Minnesota Test Road (MnROAD), 2) the Federal Highway Administration’s
(FHWA) Accelerated Loading Facility (ALF) test sections, and 3) the West Track

F HWA test road facility. The candidate test parameters had good to excellent correlation
with actual measured rut depths. The test methods and their parameters were ranked as
follows: 1) the dynamic modulus measured through triaxial compression tests at high
temperature; 2) the flow time measured through triaxial creep tests; 3) the flow number
measured through confined or unconfined repeated load tests; and 4) the permanent shear
strain measured at 1000 loading cycles using repeated shear load tests (Kaloush and
Witczak, 2002).

The main purpose of the experiment in this research study is to investigate the relative
rut damage caused by different axle types (single, tandem, tridem, quad etc.) as well as
different truck configurations on hot mix asphalt (HMA). For this purpose, the
unconfined cyclic load test was used to determine the effect of multiple loading pulses on
the rutting performance of an asphalt mixture. The test enables a direct comparison of the

effect of axle/truck configurations on rut performance of HMA.

130

5.2 SAMPLE PREPARATION

This section details the sample preparation procedure including how to determine the
exact sample weight for the target air voids and gyratory compaction. Twenty 66-lb
asphalt concrete bags of 4E3-MDOT mix (Layer number four from the bottom, three
million ESAL repetitions) were obtained during the summer of 2004 from the Spartan
Asphalt mix plant (Lansing, Michigan), labeled and stored at room temperature. Table 5-
1 shows the aggregate gradation of the mix. The volumetric properties of the mix are

shown in Table 5-2.

Table 5-1 Aggregate gradation of the mix

 

 

 

 

 

 

 

 

 

 

 

Sieve Number (opening, mm) % passing
3/4 in (19.00) 100
1/2 in (12.50) 99.5
3/8 in (9.50) 88.6

4 (4.75) 58.7

8 (2.36) 35.2

16 (1.18) 23.7

30 (0.60) 17.3
50 (0.30) 11
100 (0.15) 6.5
200 (0.075) 4.7

 

 

 

 

Table 5-2 Volumetric properties of the asphalt mix

 

 

Value 2.487 2.386 2.714 2.641 14.7% 72.7% 1.028

 

 

 

 

 

 

 

 

 

 

where:
Gm, = maximum theoretical specific gravity Gmb = bulk specific gravity
G“ = effective specific gravity of aggregates Gsb = bulk specific gravity of aggregates
VMA = voids in mineral aggregate VFA = voids filled with asphalt

131

6,, = specific gravity of the bitumen
A 6-inch (diameter) by 7-inch (height) cylindrical sample required approximately 15.4 lb

of the mixture. Since there is no simple relationship between the sample weight and
percent air voids, the required sample weight for the target air voids (5.5 %) was
determined through trials. Initial calculations estimated the approximate sample weight to
be 15.84 lb. Knowing the target percent air voids (Va%) and the maximum theoretical
specific gravity of the asphalt concrete mixture (Gm), the bulk specific gravity of the
compacted sample can be calculated using the following equation:

Gmb = Gmm (100—Va%) (5-1)
Knowing the expected bulk specific gravity and volume of the sample, the approximate
required weight of the sample was calculated using the following equation:

W=Gmb*Pw*V (5-2)

where:
W = weight of the sample,
,Ow = the density of water, and

V = the final volume of the compacted specimen.
By using this approximated theoretical weight in the first compaction trial, the number of
trials to determine the targeted sample weight was minimized. The Superpave gyratory
compactor was used to compact samples in the laboratory with a target air voids content
of 5.5 %, as shown in Figure 5-1. Table 5-3 shows the specific gyratory compactor

parameters used during the compaction procedures.

Table 5-3 Gyratory compactor setup

 

 

 

 

 

 

 

 

Setup Value
Angle oftilt 1.25o
Loading ram 600 kPa
Rotation speed 30 rpm
Specimen height 7 inch

 

132

 

Figure 5-1 Compacted test specimen (6-inch diameter, 7-inch height)

For each sample, a specific gravity test (ASTM D-2726) was used to determine the actual
specific gravity, volume, and air void content. The bulk specific gravity of the mix, Gmb,
was calculated using the following equation:

Wd in air
Grub = ___—ry—*_ (5_3)
(WSSD _ WSubnierged ) pw
where:
W dry ,-,, air = dry weight of the specimen,
Wsso = saturated surface dry specimen weight,
WSubmmed = weight of the specimen submerged in water, and
Pw = density of water.

133

The volume of the specimen and its air voids content were calculated using the following

equations:
V sample z (WSSD _ WSubmerged ) * ,DW (5'4)
Va% = ELM—19% #100 (5,5)
Gm...
where:

Va% = the air voids content, and
Gm = the maximum theoretical specific gravity of the asphalt mix.

The air void tolerance for the test specimens was i0.5% variation from the mean air

voids content.

5.2.1 Samples coring, sawing, and capping

After gyratory compaction and the specific gravity test, the samples were cored from the
center to produce a 3.7-inch diameter specimen. Figure 5-2 shows the coring device used.
The sample holder shown in the figure was fabricated in house and used to restrain the
sample during the coring process. A 0.5 inch was trimmed from each side of the cored
specimen to achieve 6-inch height sample, using a saw as shown in Figure 5-3. Figure 5-
4 shows the final cored and sawed sample. The cored samples were capped with sulfur
capping compound according to ASTM 617-98(2003) standard. There are three main
reasons for using smaller capped test specimens obtained from larger gyratory specimens

in this experiment [Monismith, C.L. et. al. 2000 and Leahy, RB. et. a1. 1994]:

0 To obtain an appropriate aspect ratio for the test specimens — A minimum H/L
ratio of 1.5 was needed (6/3.7 = 1.62) in order to ensure that the response of a
tested sample using unconfined uniaxial compression test represents a
fundamental engineering property.

0 To eliminate areas of high air voids in the gyratory specimens — As numerous

studies have illustrated, gyratory compacted specimens of this size typically have

134

a large degree of non-homogeneity of air voids near the ends and the
circumference of the specimen.
0 To eliminate end friction and violation of the theoretical boundary effects —

Relatively smooth, parallel specimen ends were achieved in the testing.
. , 2. . ,

  

 

(a) Coring machine (19} Sample holder

Figure 5-2 Coring of test specimens

1

Figure 5-3 Sawing operation

135

 

Figure 5-4 Cored sample

5.2.2 Air voids before and after coring

The bulk specific gravities and air void contents for each test specimen were measured
before and after the specimens were cored. The air void tolerance used to accept or reject
the test specimens was a i0.5% variation from the mean air voids content for both before
and afier coring. Figure 5-5 shows the air voids content before and after coring. As
shown in the figure the average air voids percentage before coring was 5.47 with standard

deviation of 0.09 and after coring 4.22 with stande deviation of 0.15 respectively.

136

6.0 r-,--m--_-----h- -.----v-___‘___-_--_u“__fi WWW.”

 

 

i, o I
i o I
5.5 l‘—9VO‘°—O 0-0 O‘Qog'OB'bo 00 0'36 00000 0 ~50 0'°-—~O——o——36 I
I o l
| l
..\° 5.0 (~44- n—u -_ ——-— ~--~ ~~~ —— «u; ’ — —_. ~—"H_1
a) l 1
'16? 45 l o o_ l
. __ __ LL __ ,_ L _ L _¢__, _ _. L _.._3_____ ___ __L- L.-___._,_. ____,____ -___ —o—-— _
.2 log 0 Duo 0 D o D D o D a DU 0 D n |
< . a can 0 0° no a no 0° 0 o 0 ‘
4.0 rue; a - ---L , - 4}” u— _____-- , -_ _ ___- __ *1
l
I a
l |
35 ‘1”---5 , LL-,_# ~—f’—— —— ——- __w__~“fi___~____q‘
l 0 Before a After 1‘
30 !—_—.—+ ##__.‘7—**1 ... *________L_____ __J__.__._____;_. 1— 4 J
0 5 10 15 20 25 30 35 4O 45 50

Sample No.

Figure 5-5 Air voids before and after coring

5.3 UNCONFINED UNIAXIAL COMPRESSION
STRENGTH TEST
Unconfined uniaxial compression strength tests were conducted, at first, for two samples
at 100°F to determine the maximum compression strength of the asphalt concrete
cylinder. The vertical load and deformation were recorded during each test. The vertical
load applied in the uniaxial cyclic load test should be much lower than the peak vertical
force from the compression strength test (stress ratio from 0.3 to 0.1) to ensure that
failure is not due to shear. Figure 5-6 shows the relationship between the stress and strain
of samples 13 and 35. The maximum unconfined compressive strength at 100°F was 355
and 349 psi for samples 13 and 35, respectively. The stored energy (the area under the
stress-strain curve in Figure 5-6) until total failure was 22.16 and 20.98 psi for the

samples, respectively.

137

 

 

 

 
    

l

350 - — Hun---“ ----_-__-- _- ___-“q
300 ~ - ---, x
'32 “NH“... ---".--fiu --qu
$1 ————— ,-______m-_.._-i
l

100 —~__~- _e_-___l
....... ‘

._-___-_7

0.06 0.08 0.10 0.12 0.14

 

Strain, in/in

Figure 5—6 Stress versus strain for unconfined compression strength tests at 100°F

5.4 UNCONFINED CYCLIC COMPRESSION LOAD TEST

The objective of this experiment is to investigate the effect of different axle
configurations and truck types on the rutting of an asphalt mixture. The results of this
experiment provide a relative assessment of HMA rut damage from different axle/truck
combinations, and not a (universal) predictive rut model. The specimens were subjected
to cyclic pulses in an Unconfined Cyclic Compression Load Test (UCCLT). The series of
cyclic uniaxial compression tests were conducted using different multiple load pulses.
The pulses were designed to simulate different axle/truck configurations. The ratio of
loading/unloading duration to rest period was held constant at (1 :9). For single axles (as
an example), the loading duration was found to be 0.08 s to simulate a load moving at 30
mph; therefore a rest period of 0.72 s was used. For multiple axle configurations and
trucks, the loading time was taken as the time from the beginning of response due to the

first axle until the time when the response of the last axle dies as shown in Figure 5-7.

138

Laboratory testing of both axle and truck configurations were performed at
identical temperature (100°F) and average air void (4.22%) levels, and had the same
number (2) of replications. The experimental test factorial for axle configurations is
shown in Table 5-4. All axle configurations were tested at 25% and 75% interaction
levels and at high stress level (corresponding to trucks tire pressure), while single and
tridem axles were also tested at the 0% interaction level and the additional stress levels of

low and medium (corresponding to passenger cars and light weight trucks tire pressure).

Table 5-4 experimental test factorial for axle configurations

 

Level of treatment

 

 

 

 

 

Variable
(1) (2) (3) (4) (5)
Axles Single Tandem Tridem Quad 8-axles
. 25% and
Interactions 25% and 75% 25% and 75% 25% and 75% 25% and 75% 750/
0
Stress level. H, M, and L H H, M, and L H H

 

 

 

 

 

 

' Stress level: H =87.88 psi, M = 60.13psi, L = 32.38 psi

After testing axle configurations at variable interaction levels (25% and 75%), the
results (to be discussed in more detail later) showed no significant difference. This
influenced the subsequent design of the truck configuration testing. As a result, all truck
configurations were tested at the 0% interaction level and at the high stress level

(corresponding to truck tire pressure) (see Table 5-5).

139

 

Table 5-5 experimental test factorial for axle configurations

 

 

 

 

 

 

. Level of treatment
Variable
(1) (2) (3) (4) (5)
SS” SlT2 S1T2Tr2“ S3T2Ql S1T1E1**
Trucks“ . , . . .
Interactions 0% 0% 0% 0% 0%
Stress level H H H H H

 

 

 

 

 

 

* Trucks defined by their axle configuration
** S5 = Truck with five single axles, S1T2Tr2 = Truck with one single axle + 2 tandem axle + 2

tridem axles, and SIT1E1= truck with one single axle + one tandem axle + one eight axle
5.5 TESTING PROCEDURES

The unconfined cyclic compression load tests were conducted using an MTS electro-
hydraulic test machine, as shown in Figure 5-8. Since the pavements are more likely to
rut at higher temperature, the tests were performed at controlled temperature (100°F i 1).
The samples were raised to a temperature of 100°F inside the test chamber over the
course of 12 hours before starting the actual test to insure uniform temperature
throughout the mass of the specimen. Two steel plates (one at the top and another at the
bottom) were used to distribute the load evenly over the cross-sectional area of the
specimen. Two linear variable displacement transducers (LVDTs) were connected to the
sample to measure vertical deflection. The samples took from 4 to 5 hours until total
failure at high stress level for all axle and truck configurations, 9 to 11 hours at medium

stress level, and 45 to 50 hours at low stress level.

140

 

Stress

l l\ [l

u,
21,511, 91, 4|}? 91§ 4|}? 9% me

 

(a) Single axle
Interaction = 01/02

M il/Vlvé. /V\

Stress
4 L

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sustain stress :
11 N 11 9 IT u N l/ 9 1T 1, tr 0 9 t7 I, time
4 4 4 4 4 4 4
(b) Tandem axle
SltresstQJr
9‘0 1, 1, 1, EL 41, 9'0 timfi
4 4 4 4
(c) 4-axles
Stress
1517151 L 9 15mm 1’ tsms1 time
4 4 4 4
((1) Truck SlTlEl

Figure 5-7 Loading and unloading time for axle and truck configurations

141

 

Figure 5-8 Unconfined cyclic compression load test set up

5.5.1 Typical test results

A typical example of uniaxial cyclic compression load tests results is shown in Figure 5-9
(a). As shown in the figure, the cumulative vertical permanent deformation (CVPD) can
be divided into three major zones:
0 The primary zone—the portion in which the strain rate decreases with loading time;
o The secondary zone—the portion in which the strain rate is constant with loading
time; and
o The tertiary flow zone—the portion in which the strain rate increases with loading
time.
Ideally, the large increase in compliance occurs at a constant volume within the tertiary
zone. The starting point of tertiary deformation is defined as the flow number (Nf), which
has been found to be a significant parameter in evaluating an HMA mixture’s rutting

resistance (Kaloush and Witczak, 2002). The rate of change in C VPD was obtained by

142

calculating the incremental slope with respect to the number of load repetitions as shown

 

 

below:
A CVPD (CVPD)~,. ‘(C VP D)N,-_1
Slope = = N N (5'6)
1' — i—l
where:

C VPD = cumulative vertical permanent deformation at cycle N,- or NH
N = number of cycles

The slope of the C VPD curve first decreases (primary zone), reaches a valley or plateau
(at the end of the secondary zone), and then starts to increase (throughout the tertiary
zone). The decrease in the slope at the beginning of the test is due to densification and
sample seating. When cracks are initiated, the rate of C VPD increases. Hence, in this
procedure, the rutting life of a sample is defined as the number of load repetitions at

which the rate of accumulation of C VPD starts to increase, as shown in Figure 5-9 (b).

143

0.25 r—mm—w “I - A a —— ~— ——~-—-— -~- —-~ ,- —-——~~w—;— ~— — -~ _-__, ,

 

  
 
 

 

 

 

 

' l

0.20 l——_—4 — a. . _. ._ _ _ . _ _ _ , _ j
-E_ 0.15 . -

0

Q3, 0.10 I

0-05 ——-——~~—m———)—~—~——fl—-+RightLvoT-4

-°-Left LVDT :

0.00 -—‘r—-——--—~———1—7-———— __.__ __r.__‘.___ _____, 1_ r g

 

0 2000 4000 6000 8000 10000 12000 14000 16000 18000
Number of cycles

(a) Relationship between cumulative vertical permanent deformation and number of cycles

 

 

 

 

 

 

 

 

1E-03 ~~*—~A—f— 4—4— ~--A—~*—~—m—-——_~—*fl
i 0 Right LVDT i
5’ 0 Left LVDT I
A 1E-04 A,_Im__zfi____z__ — I- l
5’ o
r V
_ 0° 6
(D _ .*____.9_.-o___ M*__ _. ___ _._.__. ,__-.-___ _,__.___-.._____ __.6.__.B_ __ O—
1E05 0 60030130 3 a 6 3 at
l I N'
1E_06 L__n____ L..__ ___ _ 1* , r ,L____., i_ __ __L.______ __‘_J_ ___- ___; ____,____

0 2000 4000 6000 8000 10000 12000 14000 16000 18000
Number of cycles

(b) Rate of change in cumulative vertical permanent deformation vs. number of cycles

Figure 5-9 Typical experimental results from uniaxial cyclic compression load tests
(single axle-sample number 10)

144

 

5.6 EXPERIMENTAL TEST RESULTS

The main objective of this experiment is to study the relative effect of different axle and
truck configurations on asphalt pavement rutting. Several factors were included in the
experiment, and the following sections discuss these factors and show the experimental

results.

5.6.1 Effect of interaction level

The applied load from a truck axle group at the surface of the pavement is distributed
downward through the pavement over a triangular pattern, when viewed along a
longitudinal cross-section. At the tire-pavement interface, the stress is close to the tire
pressure value and there is no interaction between the responses caused by the individual
axles. The load from the axle tire is distributed over a larger area at increasing depth
within the pavement as shown in Figure 5-10. The amount of the interaction level
depends on the thickness and the stiffness of the asphalt concrete layer, among other

factors.

Wheel load
42 in

Pavement surface—7 /LJ l J
AC layer -------------------------- Approximate level of

response interaction

Basaayer /// 2&\\

Subgrade layer

 

Figure 5-10 Distribution of wheel load (Deen, et al., 1980)

145

All axle configurations used in this experiment were simulated at 25% and 75%
interactions. Figure 5-11 shows an example of the interaction levels for the quad axle
configurations. The number of cycles to failure (Nf) for all tested axles configurations
were determined. Figure 5-12 shows the effect of the interaction level of different axle
configuration on pavement rutting. The results show that there is no significant effect of
the interaction level on the number of cycles to rutting failure for different axle
configurations. These results indicate that the most important two factors that

characterize the sample failure are the stress level and the loading pulse duration.

   

 

 

 

 

 

 

100 4 w— ¢—— — -__ __—~#_#,
'«7» '65 — — —~ 4‘
g; 2 - —— ———i
3%; g 11:14
. _- , __ I 0 _.._._ __r..__.__--.. ___r,__ L I. -
93.6 93.7 93.8 93.9 94 94.1 93.9 94 94.1 94.2 94.3 94.4
Time, see Time. see
(a) 25% interaction (b) 75% interaction
Figure 5-11 Interaction levels for the quad axle configuration

4000 .... _,_,_ ._ ___ ..-. _ ___fl #3. __ __ ML __..___ LL”?

3500 L” "'0‘ T T * T" 7” T A W 4"“ o 25% o 75% "”1.

3000 r— °————4 497* w . +4 4w!” Fl

0

2500 f--,-__..__,____, --—— ivwfi A_ 7--., 1.- (_L,f_z:

l D l

2 2000 —~A —— 5—- — -— i ,_, _.,,____ LIIIAW, 73 __.l

1500 r * ¢ # ~- — —— i§—. -1 -fi 1. ,HJ #___,____*__fi_}

l..._ __________ _ _____‘ -_ .-..-__--._______.____ ‘ . F .‘

1000 _— 8 1

500 L- — - —~ -49 w .42 3-3.3. --- __ I “l

0 _ _.___-r _L __L _ l L; ___rz_ L_. n____ .r_ _ _J

1 2 3 4 5 6 7 8 9

Me configuration

Figure 5-12 Effect of the interaction level of different axle configuration on pavement
rutting

146

5.6.2 Axle Factors

The axle factor (AF) is defined as the damage of an axle group normalized to that of a
single axle carrying the same load as any of the individual axles within the axle group.

The AF can be calculated from the following equation:

1
= Damage of the axle group = N f axle group = N f single axle
Damage of the single axle 1 N f axle group
N f single axle

 

AF

 

 

 

(5-7)

 

Figure 5-13 shows the AF 5 for different axle configurations (single, tandem, tridem,
quad, and 8-axles). The results show that the AF 3 are approximately in proportion to the
number of axles within an axle group. In other words, rutting damage is proportional to
axle load. A similar mechanistic finding for rutting damage was reported by Gillespie et
al, 1993; however, the study was done for limited axle configurations. As a confirmation
of this finding, the rutting damage normalized per axle load is shown in Figure 5-14. The
results show that the rut damage per axle is constant for both interaction levels.

The results from this experiment provide evidence that multiple axles cause
rutting at the same relative rate as single axles. They produce similar or even slightly less
(the 8-axle result is 7.07 times the damage of a single axle) rutting damage than single
axle loads. Additionally, comparing AF 5 that were previously developed for fatigue
damage due to the same axle configurations at Michigan State University (El Mohtar,
2003), it appears that the multiple axles impose far less fatigue damage (the 8-axle result
is 4.5 times the damage of a single axle) relative to rutting damage. To compare the
results obtained from this study with those from the AASHO findings, when compared to

the l3-kip single axle configuration, the AF values of the 26-kip tandem and 39-kip

147

tridem configurations were calculated to be 1.38 and 1.49, respectively. The AF values
for the tandem and tridem configurations from this study were found to be 1.97 and 2.74,
respectively. It should be noted that the AF 5 from the AASHO study are based on
Pavement Serviceability Index (PSI) values from the AASHO road test and not from
laboratory rutting tests; therefore, a significant difference between the two is
understandable. The fact that the AASHO AF 8 fall between the AF 3 from this study and
those of the previously cited fatigue study, suggests that axle factors need to be
developed for each pavement distress rather than expecting a single axle factor to speak
for all distresses. Furthermore, since pavement fatigue and rutting rarely occur at
extreme levels within the same pavement, the environmental conditions of the site (i.e.,
average yearly temperature, seasonal variation in temperature and precipitation, etc.)
must be taken into consideration when selecting the most appropriate AF to use in

pavement design.

 

 

 

 

 

 

 

 

 

 

 

 

1o 3H__z__ — —e#—— __. — ~ *— ,_,“H_#~
3 SHIT—E“ _— _ldentity line—7 ‘
7 ___..-y=1.0428x°-9148 /° l
5 2 / 8
g e ~-—~——— R = 0.9788 /
E, 5 - y = 0.9743x0'9591“
if g __ *j': R2=0.985 l
2 ;- — —-—l
1: ~——~w1
O 4 __r_ r l

 

Axle configuration

Figure 5-13 Axle factors for different axle configurations and interaction levels

148

3E-04 5» 5 5 ~ + 5 5 5 5 ~ ~ ~ - ~ ~ «-——~—-~~--- » 5 7 7 - _-,________ u -55-,
[125% 675% '

 

 

 

 

 
     
      
 

    
 
 

 

    
       
    

 

 

 

     

 

 

 

    
    

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
   
   

 

l
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a) r" ,

— " V “:13:

7/ / 2?: I n l ~

3: 2E-04 4 Z .'. 5 rm; ii .
E, g Z :5: 5:: i w
to z x ~:~ 5
g 1E-04 g Z 3375:" — ‘ 5:3:5 ' r r jig-3 Er: . .::o
4'1: I :- 31: I 7:- 72:- x .°
° é Z '93:: ~i~-‘f‘E=i
g 5E—05 g g 55:": a 5 —— 5:55 ' — e - 2 5 i E;
Z 4 1:: a
0E+00 4 Z 5 5 . . 5 ..
1 1 2 2 3 3 4 4 8 8
Axle configurations
Figure 5-14 Rut damage per axle for two replications of each axle
configuration/interaction level pair
5.6.3 Truck factors

As mentioned previously, after testing axle configurations at various interaction levels
(25% and 75%), the results showed no significant difference between the two levels.
This influenced the subsequent design of the truck configuration testing. As a result, all
truck configurations were tested at 0% interaction and high stress levels. Similar to the

axle factor, the truck factor is calculated as follows:

 

 

 

 

__1______
_ Damage of the truck N f truck N f single axle
TF -— , = = (5-8)
Damage of the srngle axle 1 N f truck

N f single axle

Figure 5-15 shows the truck factors for the tested truck configurations. Though there are

only two values for the total number of axles, the scatter of the results within both is far

149

from the direct proportionality observed in the axle factor section. It is important to note
that, in both cases (5— and ll-axles), grouping of axles resulted in reduced damage. The
most likely reasons for this are:

0 The rest period between the truck axles is not the same as the individually tested

axles,

o The sequences of the axles are mixed which affects the total sum of the damage.

Rut damage per axle for trucks is not as constant as that axle groups (from Figure 5-13),
and a possible trend based on axle groups is detected. The results in Figure 5-16 suggest
that as the size of the maximum axle group within truck configuration increases, the
amount of rutting damage caused per load carried decreases. This result indicates that
larger axle groups cause less damage per axle load when compared to smaller axle
groups. It should be noted that the truck that has quad axle as a maximum axle group
shows similar or slightly higher T F because unlike the other trucks (SlT2Tr2 and

S lTlEl) this truck (S3T1Q1) has 3 single axles which create more rutting damage.

Truck factor

   

‘3 ‘3 a a r.
K '5. N N ‘-
|— :— l— l— l—
‘— \— m (‘0 ‘-
m u) (I) (I) U)

Truck configurations

Figure 5-15 Truck factor vs. total number of axles within truck

150

a, 3.0E-04 ‘ 5-axles 11-a)des
g 2.5E-O4 2 2 2 3
B 20E-04 2 2 2 - 2 2 2 2 2 2
0')
g 15E-04 - . 2 2 2 2
g 10E-04 2- -2 2 2
5 5.0E-05 ~ 2 ~ 2 2 .
0‘ 0.0E+00 - 2 2
a a E e S 9 5 a e 9
‘D U) :3 51' I93 E I— l—
‘— 1— 0'" m ‘— ‘—
a) a) (I) . (I) (D (D

Truck configurations

Figure 5-16 Relationship between total number of truck axles, maximum axle group, and
truck factor (two replications each)

Unlike fatigue damage, permanent deformation (rutting damage) can be
constantly measured in the laboratory during the testing. Trials have been made to
compose a truck’s cumulative vertical permanent deformation from the values of its
constituent axle configurations; however, such a sum does not match the actual values
resulting from the testing of specific truck configurations, as shown for an ll-axle truck
in Figure 5—17. This difference is the result of a simple addition of mismatched zone
values. For example, the 8-ax1e configuration and the truck depicted in Figure 5-17 reach
the tertiary zone at a cycle number that is well within the primary zone of both the single
and tandem axle configurations. Since the vertical deformation taking place within these

two zones is qualitatively different, it is unreasonable to consider summing them.

151

 

 

Number of cycles

- - 'Single — 'Tandem ——-8-a)des —Truck S1T1E1 -----Truck S1T1E1-sum

Figure 5-17 Prediction of the truck rutting damage from its constituent axle

configurations

Since prediction of the truck damage from the summation of its individual axle
rutting damage is erroneous, this study uses the most common method of summing
damage for a loading spectrum, Miner’s rule (Miner, 1924).

n.

D = z—L (59)
i

where:
"I. = Number of cycles to failure for the truck

N. = Number of cycles to failure for the individual axle

This method is widely understood and easy to implement and is the foundation for many
other cumulative damage theories that have been proposed. Ideally, the summation of
damage ratios would equal one at failure. The parameter D has been documented in the
literature; it is usually found in the range 0.7< D < 2.2 with an average value near unity

(Shigley and Mischke, 1989). Therefore, the truck damage was calculated from its

152

constituent axles that were tested separately. The following steps show the calculation

for truck S3T2Q1.

Using Equation 5-9, n: is the number of cycles to failure for the truck,

Each truck as well as its constituent axles has a duplicate,

Table 5-6 shows the possible combinations of summing the truck damage from its

constituent axles (from both axle replications); it shows 8 different possible

combinations to compose the truck from its axle groupings using the number of
cycles to failure from the first truck sample,

The same equations can be applied using the number of cycles to failure from the
second truck sample,

The above steps are applied at different values of C VPD (0.04, 0.05, 0.06, 0.07,
0.08, 0.09, 0.1, 0.11 inch) which are within the secondary zone of permanent
deformation,

These steps produce 8 (possible combinations) *2 (truck samples) *8 (values of
C VPD) = 128 possible combinations,

It should be noted that these are not all the possible combinations, however the
rest will give damage values within the range defined by the considered

combinations.

The distribution of the calculated damage for each truck is shown in Figure 5-18. The

average value of the damage and the standard deviation is illustrated in Figure 5-19. The

results show that damage is underestimated for trucks with smaller axle groups, and as

the size of the maximum axle groups increases, the rutting damage increases. The range

153

 

 

of the mean damage is 0.67 for the single axle truck (S5) to 1.075 for the eight-axle truck
(S lTlEl); however, the overall mean damage from all truck configurations is close to
unity (0.873). The accuracy of Miner’s rule in calculating the rutting damage depends on
the axle load spectra. In other words, if the axle loads are mixed and have all axle
configurations (single to eight axles) the damage predictions will be very close to unity.
Where as, if the majority of the axles are small axle groups, the predicted damage will be
underestimated. On the other hand, if the majority of the axles are within larger axle
groups, the predicted damage will be overestimated. There are two significant drawbacks
to using Miner’s rule that cause the damage values to have a wide range. First, the
influence of the order of application of various axle configurations is not considered.
Second, the damage is assumed to accumulate at the same rate (linear) at a given axle
configuration (Oh, 1991). Though both of these need further study, developing a non-

linear damage model is outside the scope of this study.

154

Table 5-6 Possible combinations of the truck damage from its constituent axles

 

1 D1:3-n_1_+2i+__nl_

Nsl NTl NQI

 

2 02:3—"‘ +2 "1 + "1

st N72 NQ2

 

 

n1

 

3 D3=3-’i+2 "1 +
Nsl er NQ2

 

4 D4=3£+2£+ "1

N32 NTl NQ2

 

5 DS:3_EI__+2__n_l_+_E_l__

st N72 NQi

 

6 D6=3_’:1_+2_’_11_+_r_11_

Nsl Nrr NQ2

 

7 D7=3l+2i+_n_l_

N51 NT2 NQi

 

8 Dg=3n_i+zn_n+_a_

st Nrr NQI

 

 

 

 

where:

n] = number of cycles to reach certain C VPD for truck S3T1Q1 for the first sample
N31 = number of cycles to reach certain C VPD for single axle for the first sample
N52 = number of cycles to reach certain C VPD for single axle for the second sample
NT, = number of cycles to reach certain C VPD for tandem axle for the first sample
er = number of cycles to reach certain C VPD for tandem axle for the second sample
NQ, = number of cycles to reach certain C VPD for quad axle for the first sample

NQ2 = number of cycles to reach certain C VPD for quad axle for the second sample

155

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Average and standard deviation of .
damage summation

$5 S1T2 S1T2Tr2 S3TZQ1 S1 T1 E1 Overall

Truck configuration

Figure 5-19 Average and standard deviation of the rutting damage for different truck
configurations

5.7 PERMANENT DEFORMATION DAMAGE CURVES

Several permanent deformation damage curves were developed in this study based on: (1)
last peak strain, (2) dissipated energy, (3) strain area, and (4) S-N rutting curves. The data
from which these rutting damage model curves are calculated are represented in Table 5-

7.

157

Table 5-7 Experimental test results

 

Last Peak

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Axle . # of Interaction Stress. AV ‘12:; r IDE, psi Strain 2:23:
configurations Axles level level %
(Nf) (80) area

l-axles 1 NA 4.2 6000 0.02572 0.00092 0.00025
l-axles 1 4.07 5750 0.02715 0.00092 0.00025
2-axles 2 4.2 2750 0.04182 0.001 18 0.00055
3-axles 3 4.19 2250 0.04950 0.00114 0.00109
4-axles 4 4.23 1750 0.06223 0.00148 0.00145
8-ax1es 8 25% 4.23 800 0.09877 0.00199 0.00415
2-axles 2 4.35 2750 0.04486 0.00130 0.00068
3-axles 3 4.36 2250 0.05594 0.00146 0.00112
4-axles 4 H 4.38 1375 0.06852 0.00183 0.00190
8-axles 8 4.39 875 0.09904 0.00203 0.00432
2-axles 2 4.1 3125 0.04836 0.00144 0.00078
3-ax1es 3 4.11 2250 0.05550 0.00162 0.00128
4-axles 4 4.1 1 1500 0.06374 0.00188 0.00191
8-axles 8 75% 4.12 750 0.07804 0.00205 0.00409
2-axles 2 4.3 3375 0.04305 0.00127 0.00066
3-axles 3 4.3 1875 0.05999 0.00175 0.00139
4-axles 4 4.31 1624 0.06465 0.00182 0.00196
8-axles 8 4.31 917 0.08345 0.00227 0.00484
l-axle 1 L 4.49 74500 0.00301 0.00028 0.00004
l-axle 1 4.5 57500 0.00351 0.00038 0.00008
l-axle 1 NA 4.4 13500 0.01267 0.00063 0.00017
l-axle 1 4.5 10500 0.01420 0.00072 0.00020
l-axle 1 M 4.45 7500 0.01349 0.00067 0.00016
3-axle 3 4.17 4500 0.02887 0.00098 0.00089
3-axle 3 4.17 3125 0.03050 0.00097 0.00075
3-axle 3 L 4.16 25000 0.00708 0.00049 0.00043
3-axle 3 4.14 19750 0.00773 0.00052 0.00046
Truck SlT2 5 4.08 933 0.11798 0.00190 0.00662
Truck SlT2 5 4.09 883 0.11086 0.00182 0.00629
Truck S5 5 4.1 800 0.11807 0.00180 0.00495
Truck 85 5 0% 4.1 750 0.14000 0.00162 0.00415
Truck S5 5 4.26 750 0.12449 0.00173 0.00916
Truck SlT2Tr2 11 H 3.91 450 0.21985 0.00226 0.03430
Truck S1T2Tr2 11 3.99 425 0.22077 0.00257 0.01756
Truck S1T1E1 11 4.01 575 0.18627 0.00208 0.01106
Truck S1T1E1 11 4.03 550 0.18959 0.00230 0.01281
Truck S3T2Q1 11 4.05 411 0.22742 0.00189 0.01573
Truck S3T2Q1 11 4.07 434 0.21491 0.00176 0.01441

 

' Stress level: H =87.88 psi, M = 60.13psi, L = 32.38 psi

158

 

5.7.1 Last peak strain curve

Strain-based damage curves are the most used curves for asphalt concrete. In this study,
the uniaxial compression cyclic load test runs in a stress controlled mode. When testing
specimens under a multi axle configuration, it was noticed that the strain peak value
increased significantly from the first peak, to the subsequent peaks. The last peak strain
has the advantage of representing and identifying the tested axle group or truck as shown
in Figure 5-20. The last peaks of the initial strains pulses were plotted versus the number
of load repetitions to failure. A strain-based rutting curve was generated based on the last
strain peak of the initial cycles for all tested axles and truck configurations, as shown in
Figure 5-21. The resulting last peak strain of the initial cycles can characterize the axle or
truck configuration which overcomes the need for a separate rutting curve for each axle
configuration. When considering the last peak strain instead of the first, the number of
axles and their spacing is taken into account leading to a unique curve for different axle
groups. All the different axle and truck configurations with the different interaction and
stress levels are presented in Figure 5-21. Therefore, using this strain-based rutting curve
allows for determining the number of repetitions until failure for any axle and truck
configuration in one step, without the need to conduct testing until the total failure of the

sample.

159

 

 

 

 

 

 

 

 

 

0.80:2

E § 80808
e 5 0.0006
a .. 88883
020000

 

93.9 94.4 94.9
Time, sec.

(0
p)
A

l

I

_ J

92.2 92.4 92.6 92.8 93 93.2
Time, see.

(a) single axle (b) Tandem axle

 

 

 

 

 

.E c
‘3 E
5 6
93.6 94.2 94.8 95.4 96 104 104.5 105 1055
Time sec. firm. sec
(C) Quad axle ((1) Truck S1T1E1

Figure 5-20 Examples of the last peak of the initial strain pulse

The last peak strain rutting damage model is as follows:
N f = 0.0002750'2-398 (5-10)
where:

80 = is the last peak strain of the initial cycle, and

N; = is the number of cycles to failure.
The developed strain-based rutting equation can be used to calculate the axle or truck

factor as follows:

 

2.398
N . g .
AF or TF = Damage of axle or truck _ f smglc axle :[ osmgle axle J (5_1 l)

Damage of the single axle — N f axle or truck goaxle or truck

160

 

1.0E-02 LL -..” “ — iii“ 3 TC'Z'TT’IZZ‘LTLZI ::":: 1:1 SL1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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:;:::;:,jmr':fL“:::;£-:t_u*;"1“+"—L:L TLW
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.3 - c c T. - -i- -1414-.- --._1_ a- _i 1- Nf = 0.0002750
,,_ ,-_,,___' .- 4.1 111 ‘ 2,__1_' Ha
a 1 his. [1 R2=0.9303 W i
1"“"“"—1_ _. ___-T ”LT ,
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1.0E-04 1.---L_ - tutu-41 ___l -_i_L¢1”l,iiL____l__u_1_ ‘
100 1000 10000 100000
N

 

- Individual axles (S, T, Tr, Q, E) - 25% and 75% Interaction - High stress level
a Single and tridem (0% interaction) axles-Low and Medium stress level
x Trucks - 0% interaction - High stress level

Figure 5-21 Last peak strain rutting curve

5.7.2 Dissipated energy-based curve

The dissipated energy (area within the stress-strain relationship) was calculated for all
tested samples as well as the number of cycles to failure (as mentioned earlier, Figure 5-
9). Figure 5-22 shows an example of the relationship between the dissipated energy and
number of cycles. For the dissipated energy rutting damage curve, the initial dissipated
energy density is plotted versus the number of load repetitions to failure. Figure 5-23
shows the dissipated energy rutting curve (for all individual axles, trucks, and individual

axles and different stress levels). Similar to the last peak strain rutting curve, the

 

dissipated energy-based curve is unique. All the different axle and truck configurations
with the different interaction and stress levels are presented. Therefore, using this rutting

curve would allow for determining the number of repetitions until failure for any axle and

161

truck configuration without conducting testing a sample to failure. In fact, considering the
stronger correlation between IDE and Nf, this may be a more precise model for predictive
purposes. Yet, the application of the dissipated energy model in mechanistic analyses
would require visco-elastic analysis, which is limited by existing software (especially for

larger axle groups). The dissipated energy rutting damage model is as follows:

N f = 64.935 1054-1902 (542)

where:
[DE = is the initial dissipated energy density in psi of the whole axle or truck group, and

N; = is the number of cycles to failure.

Equation 5-12 can be used to calculate the axle or truck factors as follow:

 

 

1.19
Damage of axle or truck _ N f single axle _[ IDEsingle axle J (5-13)

 

AF or TF = .
Damage of the srngle axle N f axle or truck [DEM]e or Wok
0.06 l _.-.7- -* fies—a— ——71rs v-F_11-E_W __ ___ __ _,_1
2. ‘
oos i_*L 1— w———w—~r_~—:_—u-__o.a.mm_l
1 «900 I
l__ii#i_m_i ° D--_._‘l
_ 004 0 vs. I
8. o O 0 l
g 003 if LL L L‘s—_.— in? 7 L": 3‘3”? 43“— “L“L‘j
D

 

”22 ___ ____l_ .______ _.-._ ___.— -._J_ _____,_._.___.-__.__.__

1 10 100 1000 10000 100000
Number of cycles

 

Figure 5-22 Example of Dissipated energy versus number of load repetitions for one

sample (two LVDT)

162

1.0E+00

 

::- : N, = 04.935101:"‘-‘902
R2 = 0.9828

105-01 '

IDE, psi

 

100 1000 10000 100000
N

- Individual axles (S, T, Tr, Q, E) - 25% and 75% Interaction - High stress level
A Single and tridem (0% interaction) axles-Low and Medium stress level
x Trucks - 0% interaction - High stress level

Figure 5-23 Dissipated energy-based rutting damage curve

5.7.3 Strain area-based curve

The area under the initial strain curves (Figure 5-20) were calculated for all tested axle
and truck configurations as well as different stress levels, and plotted against the number

of cycles to failure, as shown in Figure 5-24. The strain area-based rutting damage model

obtained from this procedure is as follows:

N f = 14.857 Ao'o'777 (514)

where:
A0 = is the initial area under the strain curve, and

Nf = Number of cycles to failure.

Axle and truck factors can be calculated using the area-based rutting damage as follows:

163

 

 

 

 

 

0.777
Damage of axle or truck = N f single axle =[ Aosingle axle J (5_15)

       
   
 

 
  

  
 
    

 

    
  

  
    

AF or TF = .
Damage of the smgle axle N f axle or truck A0 axle or truck
1-05'01 E:EE—_Z+_:::'::£3-EE"H:—’—=§E_—:—«; 5. __
Beta—"E $3— " ‘ L
i.-“i;;i’ N; = 14. 857A, “77‘
10592 5%:313? r R2 = 0.881
1 —, iii ‘ ——~
, t- ~——+—
< "05'0" his:
1:15:48: L _ _
r—~ —~- +1 +++++
11:81 3.: g: :1 H; “I“ :3: j:
10E-05 L , _Al-,L l _111 Li ____L LL _1
100 1000 10000 100000

N

- Individual axles (S, T, Tr, Q, E) - 25% and 75% Interaction - High stress level
A Single and tridem (0% interaction) axles-Low and Medium stress level
x Trucks - 0% interaction - High stress level

Figure 5-24 Strain area-based rutting damage curve

The dissipated energy method and the strain area method are recommended for
estimating pavement rutting damage, rather than the last peak strain method. This is
simply because the initial last peak strain in the laboratory includes not only the effect of
the individual axle load, but also the sample’s s“memory” of previous axle loads within an
axle group. Since all peaks are of equal strain value in a mechanistic analysis, especially
when elasticity of the pavement system is assumed, a mechanistic application of this
method can not adequately represent the system’s response to an entire axle group. Since
rutting damage depends not only on the discrete strain value, but also the duration of the

pulse, the additional advantage of the dissipated energy and strain area methods is that

164

both utilize a more complete representation of the values and duration of the axle group

response.

5.7.4 Stress-based curve

All axles and trucks were tested at high stress level except for single and tridem axles;
these were additionally tested at medium and low stress levels. Figure 5-25 shows the
relationship between the stress levels (H = 87.88 psi, M = 60.13 psi, L = 32.38 psi) and
the number of cycles to failure. The results show that the two relationships for single and
tridem are approximately parallel (slope of single = -2.45 and slope of tridem = -2.35)
with an average factor of 2.7 for high stress level, 3.2 for medium stress level, and 2.9 for
low stress level (overall 2.9) between them. These results confirm the proportionality,

even at different stress levels, of rut damage with respect to axle gross weight.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

100 -— .--— -‘——-——-~.—, .— . .7 - ___.._..__ _..33
i3 31‘: Hi i j~1= aoswoW
if; — T R2 = 0.980
LIL—— l ....D:\ \\
8 fflNf=7.20*107o'2-354 L N, _ 3, 0
° 5 R2=0.955 . l l l g l
L 'lLdL't-"l—i 13+, -—--—v—-- +1 l ,
I l i l i l l i l l IOSinglelo Tridelmi l
,01331-31-1411111-3; l l llllu
1000 10000 100000
Nr

Figure 5-25 Stress level versus number of cycles to failure (S-N curve) for single and
tridem axles

165

5.8 CALIBRATION OF PERMANENT DEFORMATION
DAMAGE MODELS

Characterizing the flexible pavement damage caused by multiple axle loads requires
quantification and summation of the pavement responses. Two different approaches can
be used: (1) discrete methods (Hajek and Agarwal, 1990) and (2) integration (Hajek and
Agarwal, 1990) or strain rate methods (Govind, 1988). The discrete methods are
applicable only for single pulses, so when it comes to multiple axles their usefulness is
debated within the research community since most do not account for the pavement

response rate due to the passage of multiple axles. On the other hand, the integration
method proposed with an arbitrary exponent, n,, is incompatible with the other methods.

Similarly, the strain rate method was developed for fatigue damage and there is not
enough information to apply it to rutting damage. In this research, axle factors for
pavement rutting due to multiple axle pulses were developed in the laboratory using
Uniaxial Compression Cyclic Load Tests (UCCLT). These axle factor were used to
facilitate the calibration of all of these methods in order to determine a suitable exponent

for each.

5.8.1 Peak method

This method was developed and used mainly for the mechanistic analysis of asphalt
pavement fatigue. This method relates the damage of single or multiple axles and truck
configurations to the damage of a standard axle based on peak strains (Figure 5-26) as

follows:

166

 

AF or TF =

 

 

Damage of axle or truck _ N f std. _ "E as“, "p (5 l 6)
Damage of the standard axle N f axle or truck [:1

where:

881d = peak strain caused by the standard axle,
8i = peak strain from multiple axle or truck,

M = number of axles in an axle group or truck, and
np = the exponent of the peak method.

Nf = number of cycles to failure

This method is calibrated by assuming an arbitrary exponent, n,,, and minimizing the sum

of the square error between the predicted and the laboratory axle factor using Excel
solver. The calibrated exponent (11,) was 0.2061 with a square error sum of 2.279. Figure

5-27 shows the axle factor from the calibrated peak method versus laboratory axle factor

for different axle configurations.

0.0014
0.0012
0.0010 -- --
0.0008
0.0006
0.0004
0.0002 -

0.0000
93.7

.s
13
(D

 

 

 

 

 

 

 

 

 

 

Time, see.

Figure 5-26 Peak and peak midway strain for 4-axle group

167

AF from calibrated peak method .

 

0 1 2 3 4 5 6 7 8
Laboratory AF

Figure 5-27 Axle factor from calibrated peak method versus laboratory axle factor

5.8.2 Peak-midway method

Similar to the peak method, the peak-midway strain method was developed and used
mainly for the mechanistic analysis of asphalt concrete fatigue. This method relates the

first peak and the subsequent valley-to-peak difference (Figure 5-26) to the peak of a

standard axle raised to the exponent, np-,,,, as follows:

 

 

n
N p p_m
AF or TF = Damage of axle or truck = f std. = X 3std
Damage of the standard axle N f axle or truck i=1 3i _ gmi_1
(5-17)
where:
3std = peak strain of the standard axle,
8i = peak strain of multiple axle or truck,
5'" = midway strain,
P = number of axles in an axle group or truck, and
”1M! = the exponent of the peak-midway method.
Nf = number of cycles to failure

168

The peak-midway method was calibrated using the laboratory axle factor values to
determine the exponent for rutting damage. The calibrated exponent (np-,,,) was -0.1069

with a square error sum of 2.47. Figure 5-28 shows the axle factor of the calibrated peak-
midway method versus the laboratory axle factor values for different axle configurations.

Both peak and peak-midway methods do not take into account the duration of the
strain pulse since both consider the discrete values of the peak or peak and midway
strains. However, rutting damage is highly influenced not only by the strain value but
also by the duration of the loading pulse. Therefore, the integration and strain rate

methods are examined in the following sections.

 

    
 

 

 

 

 

 

s. e (.---_--____.____3_3______33_3,__

E 7l——————w----—--_----w-..----.._-

E l

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5 . wwwwwzmil

L<L 0 - __1______;___.___L____. . __ - l
0 1 2 3 4 5 6 7 8

LaboratoryAF

Figure 5-28 Axle factor from calibrated peak-midway method versus laboratory axle
factor values

5.8.3 Integration method

The integration method was proposed by Hajek and Agarwal, 1990. Even though the

method takes into account both the magnitude and duration of the pavement response due

to multiple axles, the arbitrary nature of the exponent, n,, makes it incompatible with the

169

 

 

other methods. The developed laboratory axle factors facilitate the calibration of this
method, and allow for an empirical determination of a suitable exponent. The axle and
truck factor can be calculated from the integration method as follows:

I

 

 

 

 

N f std I aim dt
AF or TF= N ' =-?——— (5-18)
I n'
f axeortruck llas 1 dt
0
where:
at. = the strain values of an axle or truck within the strain time history as shown in
Figure 5-26,
as = the strain values of standard axle within the strain time history,
t = time if the strain is expressed in the time domain and distance if the strain is
expressed in the space domain,

n, = is the integration method exponent, and

Nf = number of cycles to failure.

The calibrated exponent for this rutting-oriented application of the integration method is
0.1303, compared to 3.8 for the fatigue discrete methods (peak and peak-midway). The
square error sum is 2.387. This large difference can be explained by the following
observations:

0 The pervious exponent (3.8) was not calibrated for the integration method; it was
borrowed from the discrete methods.

0 The previous exponent (3.8) was based on fatigue, which has a fundamentally
different failure mechanism than rutting (0.1303).

0 The exponent in the integration method is inside the integrand, which is expected
to require, even for fatigue, a dramatically different value due to its location in the
equation. Therefore, the usual “power law” explanation does not apply when the

exponent is within an integration.

170

The resulting exponent offers a promising solution to the problem of multi-axle damage
prediction, since the integration method accounts for not only the peak values but also for
the duration of the strain pulse. Figure 5-29 shows the relationship between the axle

factors of the calibrated integration method versus the laboratory axle factor values.

 

AF from calibrated integration
method
0 A N OD -§ 01 0') \I (I)

 

0 1 2 3 4 5 6 7 8
Laboratory AF

Figure 5-29 Axle factor from the integration method versus laboratory axle factor values

5.8.4 Strain rate method

The strain rate method was developed to determine the damage transform from stress
fields as shown in Equation 5-19 (Govind, 1988). The method was developed for fatigue
and calibrated using AASHO road test data. The calibration has an excellent agreement
with the AASHTO load equivalency factors. The strain rate method is adapted in this
study to the strain field as shown in Equation 5-20. Figure 5-30 depicts the elements of

the strain rate method.

171

 

 

 

 

 

t .
m m 1 1+1 do
2 Di": 2 —_ 1 ——dt (5-19)
i=1 i=1 ti+1-t,- t]. dt
Dama e of axle rou or truck N
AF or TF = g g, p = f 5“"
Damage of smgle axle N f axle 01. 0'1le
"s—r
m 1 P
z -————— 2 '81“ — 81-. (5-20)
_ i=1 9+1 ”ti H
1 p "s”
___.— Z 8 .+1 ._ 8 .
(,1 | . .1)
where:
m = number of axles (sub-event),
p = number of discrete points within one sub-event,

to = the starting time of the sub-event,
t 1 = the ending time of the sub-event l and starting time for sub-event 2, and
8 = the discrete strain values within the sub-event, and

n,., = is the exponent for the strain rate method.

Nf = number of cycles to failure

 

 

 

 

 

Strain Strain
u I}
81'” €j+1
J' 51'
to ‘71::F“ t, 0008 to -fl£§¢-t1 (2 fi0he
(a) Single axle (b) Tandem axle

Figure 5-30 Depiction of variables from strain rate method

The laboratory axle factor facilitates the calibration of the strain rate method.
Similar to the integration method, the strain rate method is calibrated by iteration of the

square error sum minimization process. Due to its computational complexity, an iterative

172

approach was used to minimize the difference between the axle factor of the strain rate

method and the laboratory axle factor values by changing the exponent n”. The

calibrated exponent, n5-" of the strain rate method is 0.8625 with square error sum of

9.032. Figure 5-31 shows the relationship between the calibrated strain rate method axle

factors and the laboratory axle factor values.

 

 

 

 

 

AF from calibrated strain rate
method
0 A N 00 #8 01 O) \1 00

Laboratory AF

Figure 5-31 Axle factor from strain rate method versus laboratory axle factor values

Figure 5-32 summarize the exponents and the square error sum of all developed rutting

damage models and the calibrated methods.

 

173

 

 

Exponent values

 

Developed and calibrated methods

Figure 5-32 Summary of the developed and calibrated rutting damage methods

The last peak initial strain, strain area, and dissipated energy methods were
calibrated for the laboratory axle factor values, and their exponent values (n’s) were
approximately the same as each of the power corresponding to their individual
permanent deformation damage curves (section 5.7). The relatively close agreement
between these two strategies for calculating each method’s n value is evidence of
consistency in the calibration procedure. However, the exponent of each permanent
deformation damage curve is more reliable, since it is based on a larger, more diverse
data set, containing not only all axle configurations but also the truck configurations and

stress levels.

5.9 PREDICTION OF PERMANENT STRAIN

It is well known that permanent deformation, whether in the field or in the laboratory,

obeys a fractional-power relationship (0<a<l); however when a laboratory sample

174

 

reaches the tertiary zone (failure) this relationship no longer applies (a>1). Therefore, the

permanent deformation power function within the first two zones can be expressed as

follows:
8
If 2 “Na (5-21)
r
where
5p = accumulated permanent strain,
gr = resilient strain,

= permanent deformation parameter representing the constant of proportionality
between plastic and elastic strain,
= permanent deformation parameter indicating the rate of decrease in permanent
deformation as the number of load applications increases, and
N = the number of load applications.

The cumulated vertical permanent strains were normalized with the value of the
initial last peak strain (as shown in Figure 5-20). As mentioned earlier, the last peak
strain has the advantage of representing and uniquely identifying the tested axle group or
truck. The normalized accumulated permanent strains with the values of the initial last
peak strain were plotted against the number of load repetitions within the primary and
secondary zones only, as shown in Figure 5-33. The figure shows samples of the u and 01
values for three different axle configurations and one truck configuration. It should be
noted that the initial last peak strain from the laboratory includes the resilient, visco-
elastic, and the plastic strain.

The p and or values for all tested axle and truck configurations were calculated
and are displayed in Figure 5-34. As can be seen in the figure the values of 01 (the rate of
change in permanent deformation as the number of load applications increases) cluster

tightly in a small range, from 0.35 to 0.61. The values of p. (the proportionality between

175

plastic and elastic strain) cluster more loosely in a wider range, from 0.12 to 0.56. This
means that once the sample is compacted and the aggregate is seated, the rate of the
accumulated plastic strain, when normalized with its initial strain, will be approximately
the same regardless of the load configuration. These results indicate that laboratory
samples follow a trend that is consistent with the behavior of field performance, but the
predictive power of the laboratory values for or and )1 depends upon more detailed

calibration from field data. Chapter 4 explains one such method that could be used for

field calibration of permanent deformation parameters in further detail.

176

 

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uvalues

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5.10 CONCLUSION

The main achievements of this laboratory experiment are as follows:

0 Axle and truck factors for rutting damage were established based on laboratory

data.

0 Using Miner’s rule to calculate the total damage for each truck by summing the
damage caused by its constituent axles is dependant on axle configuration.

0 Permanent deformation damage curves were developed using empirical data for
the following methods: last-peak strain, dissipated energy, strain area, and peak
stress.

0 Permanent deformation damage models (peak, peak-midway, integration, and
strain rate) were calibrated using laboratory axle factor values.

0 The need was established for field calibration of permanent deformation

parameters for the purpose of rutting prediction.

178

5.11 FUTURE RESEARCH

Though this study successfully accomplished its main goals, there is room to improve
and expand knowledge. Future studies may focus on the effect of temperature and
percent air void on laboratory axle and truck factors. These test variables, though held
constant during this experiment, most likely have significant effects on pavement
performance, and are therefore worthy of consideration. Further studies may also
investigate the effect of axle group on rutting damage using Miner’s rule and develop

a nonlinear damage model that takes axle grouping within truck configurations into

 

account. With the diversity of truck configurations on today’s highways, this further

investigation would be quite useful.

179

 

CHAPTER 6 — MECHANISTIC ANALYSIS

6.1 INTRODUCTION

In this chapter, the calibrated mechanistic-empirical rutting model (Chapter 4) as well as
laboratory results (Chapter 5) will facilitate the relative mechanistic comparison of layer
rutting damage for different axle and truck configurations. During the calibration of the
VESYS model, an investigation of the contribution of each pavement layer from SPS-l
experiment data showed that, on average, hot mix asphalt concrete (HMA) rutting is 57%
of the total, base rutting is 27%, and subgrade rutting is 16% (Figure 4-21). Moreover,
the laboratory investigations showed that the axle factors for rutting damage due to
different axle configurations follows a trend curve that is slightly below the identity line
relating axle factor and the number of axles within an axle group.

The conclusions from the field investigation and the laboratory experiment
chapters were further investigated using the mechanistic analysis of axle and truck
configuration effects on rutting damage in each individual pavement layer. Since a thick
HMA layer will account for a majority of the rutting damage in a pavement system
(Chapter 4), and the rutting within such HMA layer is roughly proportional to the number
of axles within an axle group (Chapter 5), remaining questions about the effect of axle
interaction on the sub-layers are the focus of this chapter. The selection of profiles in this
study is designed to further examine the effect of heavy axle trucks on a thick pavement,
where there is interaction in the base and subgrade layers (Figure 6-1), and a thin

pavement, where there is interaction in the subgrade layer only (Figure 6-2). Table 6-1

180

 

 

shows the layer thicknesses and moduli of the two pavement cross-sections that are used

in the mechanistic analysis.

Table 6-1 Pavement cross-sections and moduli

 

 

 

 

 

Cross- HMA Base Subgrade
section # Thickness, in Modulus, psi Thickness, in Modulus, psi Modulus, psi
1 8 450000 36 30000 10000
2' 4.1 551236 8.2 55283 23205

 

 

 

 

 

 

 

' Section 50113 SPS-l experiment

6.2 FORWARD ANALYSIS

The main goal of this research is to investigate the relative effect of multiple axle and
truck configurations on rutting damage. Since there is no available software that can
handle larger than tridem axle groups, the KENLAYER (Huang, 1993) elastic analysis
program was used with responses due to larger axle groups being calculated by
superposition. As shown previously in Figure 4—8, the vertical compression stress and
strain due to standard and single axles at the middle of the HMA, base, and six 40-inch
subsequent layers of subgrade were calculated. The standard axle load used in this
analysis is 18 kips with a tire pressure of 70 psi, while the single axle load is 13 kips with
a tire pressure of 100 psi. For the purposes of consistency, the responses of all multiple
axle and truck configurations were compiled from the superposition of the appropriate
number of single axles. As an example, Figure 6-1 and 6-2 show the vertical compression
strain at the middle of the HMA, base, and six subsequent subgrade (SG) layers due to an

8-axle group for cross-sections number 1 and 2.

181

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183

6.3 RELATIVE COMPARISON OF RUTTING
DAMAGE CAUSED BY MULTIPLE AXLES

The calibrated mechanistic-empirical rutting model (Chapter 4), along with the laboratory
results (Chapter 5) make it possible to mechanistically compare the resulting rutting

damage due to different axle and truck configurations for specific pavement profiles.

6.3.1 Calibrated mechanistic-empirical rutting model

In Chapter 4, The VESYS rutting model was calibrated using field data from the SPS-l
experiment. The calibrated rutting model is utilized in this mechanistic analysis to
compare the resulting rutting (HMA, base, and subgrade) from different axle and truck

configurations for different pavement profiles (Table 6-1). The calibrated rutting model is

 

 

as follows:

ClluAC )1— —aA .ub K l-a
pp= Call—a1 ("1) C‘6“(13131, AC ))+hbase age (,2 (”1) base (gei,base))

“A 1'abase 1:1

_fla__lso K
:—SG—[l(ni E107 G(sci, SG )]
(6-1)
where:
)0 P = total cumulative rut depth (in the same units as the layer thickness),

1 = subscript indicating axle group,

K = number of axle group,

h = layer thickness for HMA layer, combined base layer, and subgrade layer, respectively,
n = number of load applications,

5,, = compression vertical elastic strain at the middle of the layers,

= permanent deformation parameter representing the constant of proportionality
between plastic and elastic strain, and
= permanent deformation parameter indicating the rate of decrease in rutting as the
number of load applications increases.

184

The permanent deformation parameters for the two cross-sections were calculated from
the developed regression equations in Chapter 4 (Equations 4-24, 4-25, 4-27, 4-28, 4-29,
and 4-30). It should be noted that the pavement layer thicknesses and moduli shown in
Table 6-1 were inputs for these equations, whereas all other variables were assumed at
the mean values of the range used to develop the regression equations as shown in Tables
4-10, 4-14, and 4-18. Table 6-2 shows the calculated permanent deformation parameters

for these cross-sections.

Table 6-2 Calculated permanent deformation parameters

 

 

 

GHMA PHMA abasc llbasc use “so
Cross-Section 1 0.702 0.537 0.741 0.134 0.873 0.010
Cross-Section 2 0.594 0.271 0.716 0.129 0.910 0.037

 

 

 

 

 

 

 

 

 

As noted in Figure 6-1, the 8-axle responses (vertical compression elastic strain)
at the middle of the HMA layer have lower interaction levels, whereas the interaction
level increases with depth until the 8-axle response becomes one, wide pulse at deeper
sub-layers. To study the effect of the response pulse duration and the interaction on
rutting calculation for different axle and truck configurations, the strain value in the
calibrated rutting model is employed in two different procedures: 1) sum the rutting
damage due to only the strain values underneath each axle within an axle group, and 2)
sum the rutting damage due to the strain values underneath the axles (similar to previous)
and also include strain values outside the axle group (at the same intervals) until the
strain becomes negligible. A diagram illustrating these two procedures for calculating

rutting damage due to an 8-axle group is shown in Figure 6-3. The rutting due to one

185

million repetitions of different axle and truck configurations were calculated using both

procedures for each layer for both cross-sections.

 

 

 

 

 

 

 

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1.0E-04 ~—~—»——— [ _._
0.0E+00 “Mil ___... 1 _ -1. 1 1 m8 1 1

0 100 200 300 400 500 600 700 800
Distance, in

 

Figure 6-3 Strain values underneath and outside the axle group

6.4 RESULTS AND DISCUSSION

The calibrated mechanistic-empirical rutting model (Equation 6-1) is employed to
calculate the layer rutting for both thick and thin pavement sections. Figures 6-4 to 6-7
show the per-layer and total rut depth due to one million repetitions for different axle and
truck configurations using both procedures. The calculated rutting for the individual
layers as well as the total was normalized to the rutting due to a single axle (axle and
truck factors) to study the relative effect of these axle and truck configurations on
pavement rutting damage.

The results show that when there is no strain interaction between axles, both
procedures for calculating the rut depth show rutting damage proportional to the number
of axles. This is the case for HMA layer of cross-section 1 and HMA and base layers of
cross-section 2. On the other hand, when there is strain interaction between the axles, the

first procedure (accounting only for the strain values under the axles) shows that the

186

multiple axles are more damaging relative to the same number of single axles (Figures 6-
4, c and d (axles) and Figures 6-5, c and d (trucks)). This result is due to the fact that
procedure 1 ignores the strains outside the axles and the effect of these strain values
becomes more severe at higher levels of interaction. Yet, since unaccounted for strain
values still result in rutting damage, it is not logical to ignore strain values outside the
axles, as shown in Figure 6-3. Calculating the rut depth by accounting for all strain values
(strain underneath and outside the axles) shows that whether there is strain interaction or
not, the axle and truck factors are proportional to the number of axles. The results of
procedure 2 indicate that the interaction in the sub-layers is not important and does not . '
impose additional relative rutting damage. These results can be further confirmed from
the laboratory investigation of the HMA layer. Since interaction between pulses was not
significant for the visco-elastic material (HMA layer) it will be even less significant for
the granular sub-layers, as indicated by the mechanistic analysis in this study. This
conclusion suggests that procedure 2 is more accurate than procedure 1 for calculating
the rut depth due to multiple axle and truck configurations.

In a similar mechanistic analysis of the effect of heavy-vehicle characteristics on
pavement response and performance, Gillespie et al., 1993 calculated the rut depth for
different truck configurations by integrating the influence function, which resulted in
rutting damage that is proportional to the axle load. Though Gillespie’s analyses include
several truck configurations, the maximum axle group among all truck configurations
was limited to tandem. Therefore, this current mechanistic analysis, laboratory
experiment, and in-service pavement analysis extend these conclusions to a larger

number of heavy axle and truck configurations.

187

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6.4.1 Rutting prediction using the new mechanistic-empirical design
guide
The new mechanistic-empirical (ME) design guide (Witczak and El—basyouny, 2004)
predicts several forms of distress, including rutting. In particular, the document discusses
and predicts rutting for the individual layers as well as the total surface rutting. Unlike the
VESYS rutting model, the ME software has two independent equations for predicting
rutting: one for rutting within the HMA layer and one for rutting within granular
materials (base/subbase) and the subgrade. Moreover, the program can handle trucks
with single, tandem, tridem, and quad axle configurations. The rutting due to single and
tandem axle configurations was calculated in the present study using the new design
guide for a single SPS-l section. The predicted rutting for each individual pavement layer
and the total rutting were not proportional to the number of axles; that is, a tandem axle
produced less than twice the rutting damage of a single axle. Figure 6-6 shows the rut
depth and axle factor for tandem axles for two SPS-l sections, thin (50113) and thick
sections (190101). This prompted a further investigation of the methods and assumptions
that were incorporated into the new ME guide. The two major concerns about the ME
rutting models in the new design guide, and the solutions offered by the present study, are
summarized below:

0 Unlike the procedure described in the current study to calibrate the VESYS
rutting model—linking the shape of the transverse surface profile to the layer
rutting contributions—the ME guide research team bases layer rutting on an
assumed and statistically idealized percentage that is applied to all LTPP sections

equally. In the ME guide document, it states that a lack of trench data makes

192

section-based layer contributions impossible to calculate. The resulting lack of
variation on a section-by-section basis therefore becomes a matter of “practical,”
rather than statistical significance. By including the transverse surface profile as a
means of quantifying the layer contribution of each section to the total rutting, the
gap between assuming an individual section’s layer contribution and calculating it
has been bridged.

The most significant drawback is that the ME guide model uses only the
maximum strain value within a multiple axle group, as if the axle group can be
quantitatively represented by the superposition of the many axles into a single,
static pulse. However, this neglects the rutting damage due to those strain values
outside the maximum; of which, there are many in a large multiple axle group.
This, of course, can be partially accounted for in the calibration procedure, but
this adjustment is highly artificial and not representative of the damage that
occurs at an individual point in the pavement as the entire load (up to an 8-axle
group) passes over. The present study attempted to validate the ME guide model,
but found that, even with the calibration procedure adjustments, the predicted
rutting damage is not proportional to the number of axles within a group.
Therefore, the present study provides a more representative model for rutting
prediction, based on the summation of rutting damage throughout the entirety of
the passage of an axle group, not just the damage produced by the singular,

maximum strain value.

193

 

0.35 r
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AC Base SG Total
Pavement layers

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Rut depth, in

 

AC Base 86 Total
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(b) Rut depth due to tande axles

Axle factor

 

Pavement layers

(c) Tandem axle factor

Figure 6-8 Rut depth for single and tandem axles and tandem axle factor using new ME
guide

194

CHAPTER 7 — CONCLUSIONS AND
RECOMMENDATIONS

This study includes several approaches to investigate the effect of heavy, multiple axle
trucks on pavement rutting. The first approach is an analysis of in-service pavement data
from the State of Michigan to investigate the effect of multi-axle trucks on total pavement
rutting damage (Chapter 3). The second approach is a laboratory experiment designed to
simulate multiple axle and truck configurations and study their effects on hot mix asphalt
concrete (HMA layer) rutting (Chapter 5). The third approach (Chapter 6) is the
mechanistic analysis using the calibrated mechanistic-empirical rutting model (Chapter 4)
and applying models developed in the laboratory. Though each approach is different in
its methodology and design, overall agreement in results suggests a strong compatibility
that will prove useful in further research. Such recommendations for future research and

other conclusions from this work are the focus of this chapter.

7.1 CONCLUSIONS

Based on the field investigation of in-service pavement data, calibration of mechanistic-
empirical rutting model, laboratory investigations, and the mechanistic analyses, the
following conclusions are drawn:
0 Truck traffic analysis shows that the percentage of the heavy, multiple axle trucks
is less than 10%. Considering the increases in truck traffic and fuel prices,
demands for heavier gross truck weight with larger axle groups direct the

importance of this study toward policy—makers, as well as pavement designers.

195

 

The analyses of in-service pavement rut data show that multiple-axle trucks (with
higher gross vehicle weight) cause more rutting damage than single and tandem
axle trucks.

The common sense extension of the previous finding would be that the larger the
multiple axle group, the more rutting damage the truck causes. However,
laboratory results from this study indicate the opposite is the case. As the size of
the largest axle group within a truck configuration increases, the relative rutting
damage per axle caused by that truck decreases.

In calibrating the VESYS rutting model, time-series, in-service pavement rut data
was used from the SPS-l experiment. This important methodological
improvement over previous studies permits more accurate determination of the
permanent deformation parameters (PDP) that have good agreement with results
from accelerated loading facilities.

Analyses of in-service pavement layer data for rutting contribution showed that,
on average, total rutting breaks down as follows: 57% from HMA, 27% from
base, and 16% from subgrade. These results show that the total system rutting is
dependent upon more than just the subgrade layer. This is especially the case
when considering the many new, and heavier axle and truck configurations.
Prediction of permanent deformation parameters (a and p.) using layer-material
properties, pavement layer cross-sections, and climatic conditions showed
promising results for HMA and base layer predictions. However, due to the
limitation of material properties data, the subgrade permanent deformation

parameters showed poor predictions. Given the relatively small magnitude of the

196

 

subgrade layer contribution to the overall rutting and this reduced data
availability, a decayed predictive ability is expected.

The laboratory investigations indicate that rutting damage due to different axle
configurations is approximately proportional to the number of axles within an
axle group. In other words, rutting damage is proportional to the gross weight of
the load.

Calculating truck rutting damage by simply summing the vertical permanent
deformation corresponding to of its constituent axle groups results in erroneous
predictions. Using Miner’s rule to determine truck rutting damage from its
constituent axles does improve the prediction, although there are still variations
among the damage values corresponding to different axle and truck
configurations.

Regardless of the truck or axle configuration, as well as the variable stress level
and axle interaction within an axle group, the laboratory data in this study
followed unique curves for each of the three permanent deformation models used:
last peak strain, dissipated energy, and strain area. This result was for one
particular HMA mix at one target air void percentage, but the excellent
relationships show that this procedure can be used in the future for generating
similarly unique curves to predict the lifetimes of other mixes.

Quantifying pavement rut damage caused by multiple axles requires calibrations
of the summation methods. In this study, the exponents for various summation

methods were determined using laboratory-developed axle factors.

197

The mechanistic analysis in this study confirms the laboratory findings related to
the proportionality of axle and truck factors for the HMA layer. Moreover, it
extends this same result into both the base and subgrade layers, which suggests no
further laboratory experimentation is needed. This conclusion is based on the
following logic. There was initial assumption about the importance of interaction
between pulses in the pavement sub-layers. However, since the effect of
interaction between pulses was not significant for the visco-elastic material (HMA
layer), this interaction will be even less significant for the sub-layer, as indicated

by the mechanistic analysis in this study.

7.2 RECOMMENDATIONS FOR FUTURE RESEARCH

Though this study successfully accomplished its main goals, there is always room to

improve and expand knowledge.

Permanent deformation parameters prediction analysis can be conducted again
when there are more material properties available, such as VT M, VMA, and VFA
for the HMA layer; compaction data (moisture content and dry density) and
unconfined compression strength for the base layer; and more aggregate gradation
information for all pavement layers.

The same analysis procedures can be performed for ALFs where more data and
more controlled environments are available.

Further validation of the calibrated rutting model can be conducted using other

data sets outside of the SPS-l experiment, such as GPS-l and ALFs.

198

The rutting model was calibrated based on the calculated strain due to one ESAL;
however, either validation or calibration can be done based on axle load spectra to
eliminate the error due to converting the actual load to ESALs based on LEF.

The rutting model was calibrated for conventional pavements (three layer system)
and the amount of two layer system (full depth pavement) data was very small.
So, similar procedures for full depth asphalt can be done wherever there are data
for two layer pavement systems. Fortunately, the uniqueness problem will be less
severe since there will be four PDPs instead of the six values in a three layer
system.

Future laboratory studies may focus on the effect of temperature and percent air
void on laboratory axle and truck factors.

Also, further laboratory studies may investigate the effect of axle group on rutting
damage using Miner’s rule and develop a nonlinear damage model that takes axle
grouping within truck configurations into account.

Though the developed dissipated energy and strain area models were for one
HMA mixture, temperature, target air voids, similar to the calibrated rutting
model, these two models can be calibrated using field data to use them

universally.

199

APPENDIX

ANALYSIS OF FLEXIBLE PAVEMENT RUTTING
FROM IN-SERVICE DATA

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