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""1 “TERARY
Q 003 Michigan State
5592M 9 33 '-'.".."- :.";;I’.',-'

 

 

This is to certify that the
thesis entitled

The Effect of Different Axle Configurations on the Fatigue Life
of an Asphalt Concrete Mixture

presented by

Chadi Said El Mohtar

has been accepted towards fulfillment
of the requirements for the

Master of degree in Civil and Environmental
Science Engineering

 

 

 

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TM 25: 20033
L/ /

Date

MSU is an Affimafive Action/Equal Opportunity Institution

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

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6/01 o'JClRC/DateDuepescsz

THE EFFECT OF DIFFERENT AXLE CONFIGURATIONS ON
THE FATIGUE LIFE OF AN ASPHALT
CONCRETE MIXTURE
By

Chadi Said El Mohtar

A THESIS
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
MASTER OF SCIENCE
Department of Civil and Environmental Engineering

2003

ABSTRACT

THE EFFECT OF DIFFERENT AXLE CONFIGURATIONS ON THE FATIGUE
LIFE OF AN ASPHALT CONCRETE MIXTURE

By

Chadi Said E1 Mohtar

The Load Equivalency Factor (LEF) and the Truck Factor (TF) are defined as the relative
damage of an axle group or a truck to that of a standard axle. The AASHTO procedure of
pavement design only accounts for single and tandem axles based on AASHO road test
results and does not account for damage due to axle groups with more than three axles.
In the mechanistic—empirical pavement design approach, the procedures used to
determine these values consists of building up the truck or axle group from its axle
components and computing the damage based on Miner’s hypothesis using fatigue curves
obtained from single haversine or continuous sinusoidal load pulses. In this thesis, the
fatigue life of an asphalt mixture under different trucks and axle groups was determined
directly from the indirect tensile cyclic load test by using load pulses that are equivalent
to the passage of an entire axle group or truck. The dissipated energy approach was
adopted in analyzing the results and determining the number of repetitions to failure for
each case, and a unique fatigue curve that can be used for multi-axle configurations was
developed. Trucks consisting of up to eleven axles and axle groups of up to eight axles
were studied. The results showed that the normalized damage per load carried decreases
with increasing the number of axles within an axle group. Additionally, the fatigue lives
predicted using single load pulses were compared to the measured ones from the different

axle groups and trucks, and correction factors were developed.

TO MY PARENTS, FAMILY AND FRIENDS

iii

ACKNOWLEDGEMENT

The author would like to express his great appreciation to his major advisor Dr. Karim
Chatti, Assistant Professor of Civil Engineering, for his continuous support throughout
the author’s study as a graduate student at Michigan State University and while preparing
this thesis. The author would also like to thank the other members of the committee,
Dr. Gilbert Baladi, Professor of Civil Engineering, and Dr. Amit Varma, Assistant
Professor of Civil Engineering, for their continuous advice and support.

Thanks are also due to the Department of Civil and Environmental Engineering at MSU
for the financial support offered for most of the author’s study period, and to the
Michigan Department of Transportation for sponsoring this research.

Last but not least, the author would like to thank his Civil and Environmental
Engineering graduate student colleagues for their support and company throughout his

stay at Michigan State University.

iv

TABLE OF CONTENTS

 

 

 

 

 

 

LIST OF TABLES - vii
LIST OF FIGURES viii
Chapter 1 - Introduction and Research Objectives 1
1.1 Introduction .......................................................................................................... 1
1.2 Objectives ............................................................................................................ 2
1.3 Organization ......................................................................................................... 2
Chapter 2 - Literature Review 4
2.1 Introduction .......................................................................................................... 4
2.1.1 Critical Stresses in Pavement Analysis ........................................................ 4
2.1.2 Fatigue cracking ........................................................................................... 5

2.2 Fatigue Prediction Tests ....................................................................................... 6
2.2.1 Flexural Beam test: ...................................................................................... 6
2.2.2 Axial Load Test: .......................................................................................... 7
2.2.3 Wheel Track Test: ........................................................................................ 7
2.2.4 Rotating Cantilever Test: ............................................................................. 7
2.2.5 Triaxial Test: ................................................................................................ 8
2.2.6 Indirect Tensile Cyclic Load Test: ............................................................... 8

2.3 Fatigue Failure in the Laboratory ........................................................................ 9
2.3.1 Different Fatigue Failure Criteria ........................ 9
2.3.2 Fatigue Propagation Stages ........................................................................ 11
2.3.3 Fatigue Life of Multiple Axles .................................................................. 11

2.4 Fatigue Models .................................................................... 12
Chapter 3 - Sample Preparation - _ 15
3.1 Introduction ........................................................................................................ 15
3.2 Determining Mass Required For Each Sample .................................................. 15
3.3 Specimen Compaction ....................................................................................... 16
3.4 Specific Gravity Test ......................................................................................... 19
3.5 Specimen Surface Preparation ........................................................................... 20
Chapter 4 - Indirect Tensile Test - 23
4.1 Introduction ........................................................................................................ 23
4.2 Analytical Models .............................................................................................. 26
4.3 Indirect Tensile Strength Test ............................................................................ 29
4.3.1 Tensile Strength ......................................................................................... 30
4.3.2 Compressive Stress at Failure .................................................................... 30
4.3.3 Equivalent Modulus ................................................................................... 30
4.3.4 Stored Energy Density until Cracking ....................................................... 31

4.4 Indirect Tensile Cyclic Load Test ...................................................................... 32
4.4.1 Recoverable Deformations ......................................................................... 33

4.4.2 Permanent Deformation ............................................................................. 34

 

 

 

 

 

 

 

4.4.3 Resilient Modulus ...................................................................................... 34
4.4.4 Dissipated Energy Density ......................................................................... 35

4.5 Determining Load Pulse Magnitude and Shape ................................................. 35
4.6 Comparison between ITCLT and Field Conditions ..... ~ ...................................... 40
Chapter 5 - Dissipated Energy Concept and New Failure Criterion 43
5.1 Introduction ........................................................................................................ 43
5.2 Previous Studies on Dissipated Energy ............................................................. 45
5.3 Dissipated Energy Fatigue Models .................................................................... 48
5.4 New Suggested Failure Criterion ....................................................................... 50
Chapter 6 - Test Results and Corresponding Fatigue Curves 56
6.1 Introduction ........................................................................................................ 56
6.2 Preliminary Tests Results .................................................................................. 56
6.2.1 Specific Gravity Test Results ..................................................................... 57
6.2.2 Indirect Tensile Strength Test Results ................................................... ' ....57
6.2.3 Resilient Modulus ...................................................................................... 59

6.3 Fatigue Curves ................................................................................................... 60
6.3.1 Dissipated-Energy-B ased Fatigue Curves ................................................. 63
6.3.2 Stress Based Fatigue Curves ...................................................................... 68
6.3.3 Strain—Based Fatigue Curves ...................................................................... 69
6.3.4 Comparison between the Different Fatigue Curves: .................................. 72
Chapter 7 - Load Equivalency, Axle and Truck Factors: - 74
7.1 Introduction ........................................................................................................ 74
7.2 Axle Factors ....................................................................................................... 76
7.2.1 AF for Different AC Thickness ................................................................. 76
7.2.2 AF for Different Vehicle Speeds ............................................................... 77
7.2.3 Summary of Effect of Axle Groups ........................................................... 77

7.3 Load Equivalency Factors .................................................................................. 78
7.4 Truck Factors ..................................................................................................... 81
7.5 Evaluating Different Mechanistic Approaches for Determining AF and TF ....87
7.5.1 AF from Strain Fatigue Curve ................................................................... 87
7.5.2 AF from Dissipated Energy Fatigue Curve ............................................... 92
7.5.3 Summary of Mechanistic Approaches for Determining AF ...................... 97
7.5.4 TF from Dissipated Energy Fatigue Curves .............................................. 97
Chapter 8 - Conclusion and Recommendations 102
8.1 Conclusions ...................................................................................................... 102
8.2 Recommendations ............................................................................................ 104
APPENDIX A - Hysteresis Loops and Trucks 106
APPENDIX B - Fatigue and Specific Gravity Tests Results - 121
APPENDIX C - AF and TF Results 140
BIBLIOGRAPHY - 146

 

vi

LIST OF (TABLES

Table 3.1Gyratory Compactor Setup .................................... 18
Table 6.1 Volumetric Properties of Mix I ......................................................................... 56
Table 6.2 ITST Results. .................................................................................................... 57
Table 6.3 Resilient Modulus Results ..................... 60
Table 6.4 Fatigue Testing Matrix ...................................................................................... 60
Table 6.5 Fatigue Tests Results ........................................................................................ 63
Table 7.1 LEF Results ....................................................................................................... 79
Table 7.2 Truck Axles and Axle Groups ............................ 83
Table B.1 Specific Gravity Results for Tested Specimens of Mix I ............................... 121
Table B.2 Specific Gravity Results of Mix II ................................................................. 122
Table C.l Measured Truck Factors .............................................................. . ................... 140
Table C.2 Effect of Speed on AF .................................................................................... 140
Table C.3 Effect of Thickness (Interaction Level) on AF .............................................. 141
Table C.4 Calculated AF from Strain Fatigue Curve Using Peak Method ..................... 141
Table 05 Calculated AF from Strain Fatigue Curve Using Peak-Midway Method ...... 142

Table C.6 Calculated AF from Strain Fatigue Curve Using Peak Method (After
Correction) .............................................................................................................. 142

Table C.7 Calculated AF from Dissipated Energy Fatigue Curve Using Peak
Method .................................................................................................................... 143

Table 08 Calculated AF from Dissipated Energy Curve Using Peak-Midway
Method .................................................................................................................... 143

Table C.9 Calculated AF from Dissipated Energy Curve Using Peak Method
(After Correction) ................................................................................................... 144

vii

LIST OF FIGURES

Figure 2.1 General Flexible Pavement Cross-section ................... -. ..................................... 4
Figure 2.2 Critical Strains in Flexible Pavements .............................................................. 5
Figure 2.3 Stress Pulse from a Multiple Axle Groups ...................................................... 12
Figure 3.1 Gyratory Compaction Mold ............................................................................ 17
Figure 3.2 Patching Location ............................................................................................ 21
Figure 3.3 Specimen Patching .......................................................................................... 22
Figure 4.1 ITT Setup ......................................................................................................... 23
Figure 4.2 Stresses in ITT Specimen ................................................................................ 24
Figure 4.3 LVDT Configuration ....................................................................................... 25
Figure 4.4 Actual I'IT Setup ............................ 25
Figure 4.5 Stresses in a Circular Disk Subjected to a Frictionless Strip Loading

(Baladi, 1988) ........................................................................................................... 27
Figure 4.6 ITST Load Deformation Curve ....................................................................... 31
Figure 4.7 Stored Energy Density until Cracking ............................................................. 32
Figure 4.8 Load-Deformation Curve under Cyclic Loading ............................................ 33
Figure 4.9 SAPSI-M Analysis Model ............................................................................... 36
Figure 4.10 Local Shear Failure ........................................................................................ 38
Figure 4.11 Fatigue Cracking in lab Specimen at Early Stages ........................................ 38
Figure 4.12 Fatigue Cracking in lab Specimen at Intermediate Stages ............................ 39
Figure 4.13 Fatigue Cracking in lab Specimen at Final Stages ........................................ 39
Figure 4.14 SAPMSI-M vs ITCLT Pulses ........................................................................ 40
Figure 4.15 Longitudinal Stress Time History at the Bottom of AC Layer ..................... 41

viii

Figure 4.16 Transverse Stress Time History at the Bottom of AC Layer ......................... 42

Figure 4.17 Vertical Stress Time History at the Bottom of AC Layer ............................. 42
Figure 5.1 Stress-Strain Hysteresis Loop ...................................... . ................................... 43
- Figure 5.2 Dissipated Energy Density Per Cycle .............................................................. 44
Figure 5 .3 Cumulative Dissipated Energy Density ........................................................... 44
Figure 5.4 Dissipated Energy Density from Controlled-Stress and Controlled-Strain
Tests (Sousa, 1992) ................................................................................................... 45
Figure 5.5 Cumulative DE from Controlled-Stress and Controlled-Strain Tests ............. 46
Figure 5.6 Determining N f from Cumulative Dissipated Energy Density and SEC ......... 53
Figure 5.7 Dissipated Energy Density per Cycle Curve with Nf Superimposed on it ...... 54
Figure 5.8 Determining Nf from Cumulative Dissipated Energy Density and SEC ......... 54
Figure 5.9 Dissipated Energy Density per Cycle Curve with Nf Superimposed on it ...... 55
Figure 6.1 Output from ITST (specimen 154) .................................................................. 58
Figure 6.2 Stored Energy Density till Cracking (specimen 154) ................. V .................... 5 9
Figure 6.3 Different Interaction Levels ............................................................................ 61
Figure 6.4 Cumulative DE Curves for Different Axle Configurations ............................. 64
Figure 6.5 Dissipated Energy Fatigue Curve .................................................................... 65
Figure 6.6 Fatigue Curves at Different DE Levels ........................................................... 66
Figure 6.7 Continuous Load Pulse and Truck 13 Results ................................................. 67
Figure 6.8 Truck Number 13 ............................................................................................ 68
Figure 6.9 Stress Fatigue Curves ...................................................................................... 69
Figure 6.10 Typical Tensile Strain Response from I'IT Under Multi Axle Load
Configuration ............................................................................................................ 70
Figure 6.11 Fatigue Curves based on First Peak Strain .................................................... 71

ix

Figure 6.12 Fatigue Curve for All Axle Configurations based on Last Peak Strain ........ 72

Figure 7.1 Axle Factor for Different Interaction Levels ................................................... 79
Figure 7.2 Axle Factor per Tonnage for Different Interaction Levels .............................. 80
Figure 7.3 Nf Vs No. of Axles for Different Speed Values .............................................. 80
Figure 7.4 Axle Factor for Different Speed Values .......................................................... 81
Figure 7.5 Effect of Speed on Dissipated Energy of a Single Axle .................................. 84
Figure 7.6 Effect of Speed on Dissipated Energy of an 8-Axle Group ............................ 85
Figure 7.7 Truck Factors ................................................................................................... 86
Figure 7.8 Truck Factors per Tonnage .............................................................................. 86

Figure 7.9 Fatigue Lives under Different Axle Groups Using Peak—Midway
Method from Strain Fatigue Curve ........................................................................... 89

Figure 7.10 Percent Difference between Measured and Calculated Fatigue Lives
under Different Axle Groups Using Peak—Midway Method from Strain Fatigue
Curve ......................................................................................................................... 89

Figure 7.11 Fatigue Lives under Different Axle Groups Using Peak Method from
Strain Fatigue Curve ................................................................................................. 90

Figure 7.12 Percent Difference between Measured and Calculated Fatigue Lives
under Different Axle Groups Using Peak Method from Strain Fatigue Curve ........ 90

Figure 7.13 Fatigue Lives under Different Axle Groups Using Peak Method from
Strain Fatigue Curve (After Correction) ................................................................... 91

Figure 7.14 Percent Difference between Measured and Calculated Fatigue Lives
under Different Axle Groups Using Peak-Peak Method from Strain Fatigue
Curve (After Correction) ..................................................................... . ..................... 91

Figure 7.15 Fatigue Lives under Different Axle Groups Using Peak-Midway
Method from DE Fatigue Curve ............................................................................... 94

Figure 7.16 Percent Difference between Measured and Calculated Fatigue Lives
under Different Axle Groups Using Peak-Midway Method from DE Fatigue
Curve ......................................................................................................................... 94

Figure 7.17 Fatigue Lives under Different Axle Groups Using Peak Method from
DE Fatigue Curve ..................................................................................................... 95

Figure 7.18 Percent Difference between Measured and Calculated Fatigue Lives
under Different Axle Groups Using Peak Method from DEFatigue Curve ............. 95

Figure 7.19 Fatigue Lives under Different Axle Groups Using Peak Method from
DE Fatigue Curve (After Correction) ....................................................................... 96

Figure 7.20 Percent Difference between Measured and Calculated Fatigue Lives
under Different Axle Groups Using Peak Method from DE Fatigue Curve

(After Correction) ..................................................................................................... 96
Figure 7.21 Trucks Fatigue Lives Using Axle Groups and Individual Axles from

DE Fatigue Curve ..................................................................................................... 99
Figure 7.22 Percent Difference between Measured and Calculated Trucks Fatigue

Lives from DE Fatigue Curve ................................................................................... 99
Figure 7.23 Truck Fatigue Lives Using Axle Groups and Individual Axles from

DE Fatigue Curve (After Correction) ..................................................................... 100
Figure 7.24 Percent Difference between Measured and Calculated Trucks Fatigue

Lives from DE Fatigue Curve (After Correction) ................................................... 101
Figure A.1 Hysteresis Loop for Single Axle ......................... 106
Figure A.2 Hysteresis Loop for Tandem Axle 25% Interaction ..................................... 106
Figure A.3 Hysteresis Loop for Tandem Axle 50% Interaction ..................................... 107
Figure A.4 Hysteresis Loop for Tandem Axle 75% Interaction ..................................... 107
Figure A.5 Hysteresis Loop for Tridem Axle 25% Interaction ...................................... 108
Figure A.6 Hysteresis Loop for Tridem Axle 50% Interaction ...................................... 108
Figure A.7 Hysteresis Loop for Tridem Axle 75% Interaction ...................................... 109
Figure A.8 Hysteresis Loop for 4-Axle 25% Interaction ................................................ 109
Figure A.9 Hysteresis Loop for 4-Axle 50% Interaction ................................................ 110
Figure A.1O Hysteresis Loop for 4-Axle 75 % Interaction .............................................. 110
Figure A.11 Hysteresis Loop for 5-Axle 25% Interaction .............................................. 111

xi

Figure A.12 Hysteresis Loop for 5-Ax1e 50% Interaction .............................................. 111

Figure A.13 Hysteresis Loop for 5-Axle 7 5% Interaction .............................................. 112
Figure A.14 Hysteresis Loop for 7-Ax1e 25% Interaction .............................................. 112
Figure A.15 Hysteresis Loop for 7-Axle 50% Interaction .............................................. 113
Figure A.16 Hysteresis Loop for 7-Ax1e 75% Interaction .............................................. 113
Figure A.17 Hysteresis Loop for 8—Axle 25% Interaction .............................................. 114
Figure A.18 Hysteresis Loop for 8-Axle 50% Interaction .............................................. 114
Figure A.19 Hysteresis LOOp for 8-Axle 75% Interaction ............................................. 115
Figure A.20 Hysteresis Loop for Truck 0 ....................................................................... 115
Figure A.21 Hysteresis Loop for Truck 1 ....................................................................... 116
Figure A.22 Hysteresis Loop for Truck 10 ..................................................................... 116
Figure A.23 Hysteresis Loop for Truck 13 .................................................................... 117
Figure A.24 Truck 0 ........................................................................................................ 117
Figure A.25 Truck 1 ........................................................................................................ 117
Figure A.26 Truck 2 ........................................................................................................ 118
Figure A.27 Truck 3 ........................................................................................................ 118
Figure A.28 Truck 4 ........................................................................................................ 118
Figure A.29 Truck 10 ...................................................................................................... 118
Figure A.30 Truck 13 ...................................................................................................... 119
Figure A.31 Truck 14 ...................................................................................................... 119
Figure A.32 Truck 17 ...................................................................................................... 119
Figure A.33 Truck 19 ...................................................................................................... 119
Figure A.34 Truck 20 ...................................................................................................... 120

xii

Figure B.1 Single Axle Low Stress (Specimen 112) ...................................................... 122

Figure 3.2 Single Axle Low Stress (Specimen 157) ...................................................... 123
Figure B.3 Single Axle Medium Stress (Specimen 130) ................................................ 123
Figure B.4 Single Axle Medium Stress (Specimen 139) ............................................... 124
Figure B.5 Single Axle Medium Stress (Specimen 142) ................................................ 124
Figure B.6 Single Axle High Stress (Specimen 119) .................................................... 125
Figure B.7 Single Axle High Stress (Specimen 151) ..................................................... 125
Figure B.8 Tandem Axle Medium Stress (Specimen 122) ............................................. 126
Figure B.9 Tandem Axle Medium Stress (Specimen 124) ............................................. 126
Figure B.10 Tandem Axle Medium Stress (Specimen 128) ........................................... 127
Figure B.11 Tandem Axle High Stress (Specimen 145) ................................................. 127
Figure B.12 Tandem Axle High Stress (Specimen 137) ................................................. 128
Figure B.13 Tridem Axle Low Stress (Specimen 140) .................................. . ................ 128
Figure B.14 Tridem Axle Low Stress (Specimen 133) ................................................... 129
Figure B.15 Tridem Axle Medium Stress (Specimen 147) ............................................ 129
Figure B.16 Tridem Axle Medium Stress (Specimen 116) ............................................ 130
Figure B.17 Tridem Axle Medium Stress (Specimen 156) ............................................ 130
Figure B.18 Tridem Axle High Stress (Specimen 149) .................................................. 131
Figure B.19 Tridem Axle High Stress (Specimen 138) .................................................. 131
Figure B.20 4-Axle Medium Stress (Specimen 117) ...................................................... 132
Figure B.21 4—Axle Medium Stress (Specimen 144) ...................................................... 132
Figure B.22 4-Ax1e Medium Stress (Specimen 141) ...................................................... 133
Figure B.23 8-Axle Low Stress (Specimen 150) ............................................................ 133

xiii

Figure B.24 8-Axle Low Stress (Specimen 127) ............................................................ 134

Figure B.25 8-Axle Medium Stress (Specimen 111) ...................................................... 134
Figure B.26 8-Axle Medium Stress (Specimen 121) ...................................................... 135
Figure B.27 8-Axle Medium Stress (Specimen 109) .............................. .. ...................... 135
Figure B.28 8-Axle High Stress (Specimen 106) ........................................................... 136
Figure B.29 8-Axle High Stress (Specimen 118) ........................................................... 136
Figure B.30 8—Axle Medium Stress (75% Interaction) (Specimen 136) ........................ 137
Figure B.31 8-Axle Medium Stress (75% Interaction) (Specimen 114) ........................ 137
Figure B.32 Continuous Haversine Pulse Medium Stress (Specimen 110) .................... 138
Figure B33 Continuous Haversine Pulse Medium Stress (Specimen 152) .................... 138
Figure B.34 Truck 13 (Specimen 131) ........................................................................... 139
Figure B.35 Truck 13 (Specimen 120) ........................................................................... 139

xiv

Chapter 1 - Introduction and Research Objectives

1.1 Introduction

Determining the strength and fatigue life characteristics of asphalt based mixes has been
a major focus of research and testing since the early 1960’s. Many different accelerated
tests were developed and studied to determine the long term performance of the asphalt
mixes. Different test procedures ended up giving various results depending on the testing
setup and conditions and approaches used in analyzing the results. Tests such as the
Flexural Beam, Trapezoidal, Direct Tension, Tri-axial and Indirect Tensile tests have
been used to develop models for a new mechanistic approach in pavement design.

Some of these tests were performed under controlled stress mode while others were
conducted under controlled strain mode. This resulted in different approaches when
analyzing the results. One approach is to monitor the stresses in the tested specimens;
another involves monitoring the strains and permanent deformations. A new approach has
been proposed in the recent years in which the dissipated energy is used as the criterion
for failure. This method incorporates viscoelastic properties of materials and tries to
establish relationships between the repetitive IOad applications to the materials by
accounting for both stresses and strains simultaneously. The main purpose of this
research is to come up with an energy formulation for the indirect tensile test predicting
the performance of asphalt based mixtures under different axle configurations. By using
laboratory test results, energy based criteria and laws would be established for fatigue life
prediction and determining Load Equivalency Factors (LEFs) for different axles and

truck configurations.

1.2 Objectives

The objectives of this study are to:

i)

iii)

Determine a new fatigue failure criterion that is consistent, objective, and
compatible with the dissipated energy approach;

Determine fatigue curves for the indirect tensile test using dissipated energy
density and strains.

Study the effect of different axle configurations, interaction levels, load
duration, and stress levels on the dissipated energy fatigue curves.

Determine Load Equivalency Factors for the trucks with multi-axle groups (up
to 11 axles) using the dissipated energy approach and the results from the
indirect tensile cyclic load test.

Evaluate the mechanistic fatigue prediction methods for asphalt pavement

using laboratory results.

1.3 Organization

This thesis consists of eight chapters including this introductory one.

Chapter 2 includes a literature review on different fatigue testing procedures, laboratory

fatigue stages, different criteria used to define failure and fatigue models.

Chapter 3 is a summary of the lab procedures used specimen compaction, air void content

determination and sample surface preparation for testing.

In chapter 4, the indirect tensile test is explained in detail. Both the indirect tensile

strength and cyclic load tests are presented. The analytical solution for calculating

stresses and strains at the center of the specimen using two dimensional stress theory is

summarized.

Chapter 5 introduces the dissipated energy concept in more detail. Previous studies on
dissipated energy are summarized and their corresponding fatigue models are presented.
Also, the new failure criterion is introduced and explained.

Chapter 6 presents the preliminary test results from specific gravity and indirect tensile
strength tests. The different fatigue models developed are presented with a comparison
between the advantages and disadvantages of each one.

In chapter 7, the analysis of different axle configurations using both strain and dissipated
energy fatigue curves is presented. The effects of AC layer thickness and vehicle speed
on Axle Factors are also shown. In addition, the different mechanistic approaches for
determining LEF, AF and TF are evaluated based on the experimental results.

Chapter 8 summarizes the over all results of this study and lists the main conclusions.

Recommendations for future research are proposed.

Chapter 2 - Literature Review

2.1 Introduction

Distresses in pavements are the manifestation of surface degradation that reflect changes
in their structural capacity or functional and serviceability that would require
maintenance or rehabilitation action when exceeding certain thresholds. In flexible
pavements, the most common forms of distresses are longitudinal and fatigue cracking,

rutting and thermal/transverse cracking. The major focus in this study will be on fatigue

cracking under trucks with different axle configurations.

2.1.1 Critical Stresses in Pavement Analysis

Figure 2.1 shows a typical cross-section of a flexible pavement. The pavement structure

consists of a top Asphalt Concrete (AC) layer lying on an aggregate base and a granular

subbase. The structure lies on the natural soil called roadbed soil or subgrade.

 

 

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Subgrade

 

l Zone A: Area of Interest]

 

 

Figure 2.1 General Flexible Pavement Cross-section

 

Most of the traffic generally passes over a limited area within a lane called the Wheel
Path as shown in Figure 2.1 above. Due to the traffic concentration in the wheel path, the
major distresses in flexible pavements are located, or at least originate from the zone
directly under the wheel path area (Zone A in Figure 2.1).

Figure 2.2 shows the critical strains that are responsible for distresses. Fatigue cracks are
caused by the horizontal tensile strains at the bottom of the AC layer (at). The vertical
strains at the top of the subgrade (81) are the major strains resulting in the surface rutting

of the paVements in the wheel path. This study is focused on the fatigue life and thus the

tensile strain at the bottom at the AC layer.

 

 

 

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.-__..:__ ._\.:\Ix.. . ...... “'4
a. '01:... a . a: ’0: :.-...
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s'. c I o: .-. . ... '1 - . '._-Lo',.“

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Base/Subbase ‘. f 1. 8t

 

 

 

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Figure 2.2 Critical Strains in Flexible Pavements

2.1.2 Fatigue cracking

As mentioned in section 2.1.1 above, fatigue cracking is caused by the tensile strains at
the bottom of the AC layer under the wheel path. The tensile strains/stresses induced in

the pavement by the wheel loads are too small compared to the tensile strength of the

asphalt mixture; however, the large number of load repetitions will eventually cause the
initiation of fatigue cracks. The cracks propagate to the surface initially as one or more
longitudinal parallel cracks. After repeated traffic loading thecracks connect, forming
many-sided, sharp-angled pieces that develop an alligator skin like pattern called alligator

cracking.

2.2 Fatigue Prediction Tests

In the past few decades, different researchers have adopted different tests in an attempt to
predict the fatigue life of asphalt concrete mixes. Tests such as the flexural beam test
(center and third point loadings), the two point trapezoidal beam test, the rotational
cantilever test, the direct axial load test, the triaxial test, the wheel tracking test, and the
indirect tensile test have been used and different failure criteria were developed for each
test.

Overall, all the tests mentioned above can be divided into two major categories
depending on the loading mode: Stress-controlled and Strain-controlled. Strain controlled
tests are used to represent thin pavements, while stress-controlled tests represent material
behavior in thick pavements. For the same mix type, stress-controlled tests result in a
shorter life than strain-controlled tests. A summary of the most popular tests is listed

below [8, 9]:

2.2.] F lexural Beam test:

Specimens can be tested under different load pulse shapes with frequencies ranging
between 30 and 100 cycles per minute. This test allows for applying stress reversal, and

the calculations of the stresses and strains are very simple. It can be used to simulate both

thick pavements and thin pavements. On the other hand, the uniaxial state of stress, the

high cost and time consumption are the main disadvantages of this test.

2.2.2 Axial Load Test:

Specimens can be tested under sinusoidal or haversine pulses with loading durations
between 0.04 and 0.4 seconds and rest periods up to 1.0 second. Both tensile and
compressive wave patterns can be applied to the specimens leading to tensile or
compressive uniaxial state of stress. The calculations of the stresses and strains are very

simple and the test is inexpensive and quick, but it poorly represents field conditions.

2.2.3 Wheel Track Test:

This test can have a laboratory version as well as a full scale version. It is the best
representation of a wheel rolling on a pavement. The main disadvantage of this test is the
high initial as well as operational and maintenance cost, and its inability to measure the
mix properties at the same time as the fatigue test is performed. Van Dijk [5] has
compared results form the WTI‘ to the uinaxial lab bending tests in order to correlate the

lab results to actual response in the field for pavement design purposes.

2.2.4 Rotating Cantilever Test:

The specimens in this test are rotated causing a sinusoidal tension and compression under
specified points. The frequency of applied load cycles ranges between 80 to 3000 cycles
per minute. This test has not been extensively used for determining the fatigue life of

asphalt concrete mixes.

2.2.5 Triaxial Test:

The specimens are cylindrical with a diameter of 4 inches and a height of 8 inches.
Specimens are tested under sinusoidal axial stresses. To accommodate tension, end caps
are bonded to the specimens. Its main advantages are its ability to simulate field
conditions by applying compression and tension stresses and it represents the state of
stress in situ better than any other testing procedure. On the other hand, its main
disadvantages are the shear strains that might develop in the specimen in addition to the

high cost and specialized equipments.

2.2.6 Indirect Tensile Cyclic Load Test:

The specimens are in the shape of a disk with diameters of 4 or 6 inches and a thickness
ranging from 2.5 to 3 inches. Haversine/sine load pulses can be applied to the specimens
with no stress reversal. The load frequencies most commonly used are 60 and 120 cycles
per minute. The specimens experience a biaxial sate of stress, permanent deformations
and creep.

The presence of a relatively uniform tensile stress region where failure initiates, the
biaxial stress state and the simplicity of the test are the main advantages of the indirect
tensile test. On the other hand, the fixed stress ratio of 3 to 1 (3 vertical compression
stress to 1 horizontal tensile stress) and the absence of stress reversal that result in high
permanent deformations and under predictions of fatigue life are the main disadvantages
of this test.

In summary, the triaxial test can best simulate the field conditions. However, the high
cost, time consuming and specialized equipment over shadow this advantage. As for the

remaining tests, their main disadvantage is the uniaxial state of stress that does not

represent actual field conditions. Nevertheless, the stress reversal that can be imposed in

these tests is a good simulation of the stress patterns imposed by traffic load in the field.

2.3 Fatigue Failure in the Laboratory

The fatigue properties of a material are defined by the number of repetitions till failure
(Nf) and the stress, strain, or dissipated energy density corresponding to that Nf. The
fatigue curves, also known as SN curves, express the relationship between the initial
strain, stress or dissipated energy density at the beginning of the test and the number of

load repetitions to failure.

2.3.1 Different Fatigue Failure Criteria

The definition of failure varies from test to test depending on nature of the test and
analysis of results. For strain controlled tests, as the number of load applications
increases, the stresses in the sample decrease, while in stress controlled tests, the strains
increase as the test progresses. Different researchers came up with different failure
criteria, some of which are listed below. The fatigue life may be defined by [1, 2, 3, 4]:
i) The number of load cycles at which the resilient modulus loses 50% of its
original value (flexural beam test).
ii) The number of load cycles at which the horizontal tensile plastic deformation
reaches 0.1 inch (indirect tensile test).
iii) The number of cycles at which the slope of the plastic deformation ratio (the
ratio of the horizontal to vertical plastic deformations) increases rapidly

(indirect tensile test).

iv) The number of cycles at which the measured cumulative vertical plastic
deformation reaches a value between 0.28 and 0.36 inches (indirect tensile
test).

v) The number of cycles at which the cumulative horizontal plastic deformation
reaches a value equal to 95 percent of the total horizontal deformation at
failure of a compatible specimen tested to failure using the Indirect Tensile
Strength Test (indirect tensile test).

vi) The number of load cycles at which the ratio of the change in the dissipated
energy ADE between cycles “i” and “i+1” divided by the total dissipated

‘6",
1

energy of load cycle begins to increase rapidly (flexural beam test).

The most common failure criterion is the 50 percent reduction in the initial stiffness.
Unfortunately, the 50% threshold is an arbitrary value that is to correlate with actual
damage accumulation in the material. Moreover, this procedure is dependent on the
loading mode (whether stress or strain controlled) and thus, cannot be generalized. The
criterion suggested by Ghuzlan and Carpenter [4] uses the ratio of the change in the
dissipated energy ADE as defined in item (vi) above to determine failure. Although this
criterion overcomes the testing mode limitation, the failure point is still visually picked,
making it subjective, and its selectiOn can be difficult depending on the scatter in the
data. In this study, a new criterion based on equating the energy needed to fail the
specimen in the indirect tensile strength test and the cumulative dissipated energy in the
Indirect cyclic load test will be presented. This new failure definition should be valid for

any testing mode by using the dissipated energy approach as long as the strength and

fatigue tests use the same loading setup [5].

10

2.3.2 Fatigue Propagation Stages

Van Dijk suggested that there are three different stages of crack development in the
specimen [5]:

i) The number of load repetitions, N, at which strains (and dissipated energy)
start to increase. This stage is associated with the formation of hair cracks in
the sample.

ii) The number of load repetitions, N2, at which the strains reach their maximum
values. This stage is associated with the formation of the real or macro cracks.

iii) The number of load repetitions, N3, at which the strains do not change any
more. This is the total failure stage.

As a result of the wheel tracking tests that he conducted, Van Dijk [5] concluded that N2
is approximately three times higher than N, and N3 is three to five times higher than N2.
The failure criterion proposed in this study was found to provide a very consistent
method to determine the crack initiation in the specimen. Additionally, the behavior of

the samples at later stages was compared to the behavior at the time of crack initiation.

2.3.3 Fatigue Life of Multiple Axles

Most fatigue tests on asphalt based mixes were performed under single pulse loads or
continuous sinusoidal wave pulse. However, the pavement response to different axle
configurations, load durations and spacing is different. To determine the fatigue life
under multiple axles, Miner’s hypothesis is commonly applied to accumulate the damage

resulting from the different axles in an axle group. This relation is given by [7]:

 

 

"1
N1! N2! N3;

11

“ ,’

where “i” is the ith level of applied strain/stress at the point under consideration. ni is
the actual number of applications at strain level “i” that is anticipated, and “ if“ is the
number of applications at strain level “i” expected to cause . fatigue failure if applied
separately. A typical stress pulse from a multiple axle is shown in Figure 2.3. Typically,
either the damage caused by the peak strains (81, £2, 83, 84, and 85) or the damage frOm the
peak of the first axle (81) in addition to that of the intermediate strains (86, 87, £3 and 89)

are uSed to predict the total damage caused by the whole axle group [19].

 

5-axle Stress

 

A ll n I.

/\1{/ A AflAfl
File} file]
\lll

/ e, MlggLJ—EsleIé—‘ri‘j Es\

 

 

 

 

 

 

 

 

 

 

 

Stress (psi)
—\.J

 

 

 

 

 

 

 

 

 

 

Time (sec)

 

 

 

Figure 2.3 Stress Pulse from a Multiple Axle Groups

In this study, the fatigue life of the asphalt mix under different axle groups will be
determined directly using the dissipated energy approach and the new failure criterion.
The results will be compared to those obtained by summing up the damage from the

different axles individually.

2.4 Fatigue Models

The results of fatigue tests are presented as: 1) stresses versus the number of load

repetitions to failure usually known as S-N curves or 2) strain versus the number of load

12

repetitions to failure known as e-N curves. In a controlled strain test, the strains are taken
as the different strain levels the test is performed at, while in a controlled stress mode, the
strains are taken as the initial value of the strains (under low number of repetitions). A

very common model used for fatigue prediction is [10, ll]:

wwwm

where: Nf is the fatigue life,
a or a; is the applied tensile strain or stress respectively,

(n & k) or (n’ & k’) are material constants
To accommodate for air void content and mode of loading, Monismith et al. suggested
another fatigue model [8]:
Nf = a*eb'MF *ecv" *8: *5:

Where: MP is the loading mode factor, which equals 1 for strain
controlled and -1 for stress controlled tests,
V0 is the initial air void content in percent,
so is the initial strain,
So is the initial mix stiffness,

a, b ,c ,d, and e are regression coefficients.
Baladi [3] suggested a model that includes temperature, air void content, viscosity and
aggregate angularity as factors affecting the fatigue behavior.
Ln(Nf) = a + b*(T1‘) + c*Ln(CL) + d(AV) + e(KV) +f(ANG)

Where: TT is test temperature
CL is the magnitude of cyclic load
AV is the air void content
KV is the kinematic viscosity of the aspalt
ANG is the aggregate angularity _

13

a, b, c, d, and e are regression coefficients. .
Similar to the S-N and e-N curves, curves based on the initial dissipated energy versus
the number of repetitions to failure can be used to describe the fatigue behavior of asphalt
mixes [5]:
N f = A * (Wo)”
Where: W0 is the initial dissipated energy
A and B are material constants.

However, none of the models mentioned above can be used directly to estimate the
fatigue life of an asphalt-based mix under multiple axles or trucks. In this report, fatigue
curves based on dissipated energy and a new failure criterion will be generated for
different axle configurations in addition to the different stress levels. Theoretically, when
using the dissipated. energy approach, the fatigue curves for the different axle

configurations should coincide.

14

Chapter 3 - Sample Preparation

3.1 Introduction

This chapter details the specimen preparation procedure including compaction and
surface preparation prior to testing“. Four 30 Kg. asphalt concrete bags were obtained
from the asphalt mix plant for each mix. The bags were labeled and stored in the lab at
room temperature. To prepare a 4—inch diameter, 2.5- inch thick sample, it will require 1
tol.3 kg. of the mix. Thus each bag can be used to prepare around 25 samples. More

detailed calculations are presented later in this chapter.

3.2 Determining Mass Required For Each Sample

Knowing the target air void (Va) and the maximum theoretical specific gravity of the'
asphalt concrete mix (Gum), the bulk specific gravity of the compacted sample can be
calculated using the following equation: '

G4,, = Gm (1 —-Va) (3.1)
Knowing the expected bulk specific gravity and volume of the sample, we can calculate
the required mass using the following equation: I

M = Gmb *pw *V (3.2)

Where: pw is the density of water,
V is the final volume of the compacted specimen

First, a trial specimen is compacted. The actual specific gravity, volume and air void
content of the specimen are determined by running a specific gravity test (details on
specimen preparation and specific gravity test calculations are discussed later). Then the

actual height of the specimen is measured. The difference between the theoretical and

15

measured height, volume and air void content can be explained by looking at Figure 3.1A
and 3.1B. All the calculations, performed before the test, are based on Figure 3.1A. The
target air void includes the voids within the specimen only, and not those between the
asphalt and the mold, as shown in Figure 3. 13. Thus, the calculated mass is more than the
required one since the voids between the asphalt and the compaction mold occupy some
volume without using any of the asphalt mix. Therefore, the actual air void of the sample
is lower than the expected Va and the actual height is larger.

The volume of the sample calculated from specific gravity test does not include the
external voids. Knowing the actual height of the sample, the theoretical vOlume

(assuming a perfect disc without external voids) can be calculated from the equation:
V1,, =rr*R2*H (3.3)

From the theoretical volume and the actual specimen volume, the volume of the external

voids can be determined as follows:
VErremal Void: = VTh _ VSample (3’4)

A corrected mass can now be calculated by modifying equation (3.2):

i

M = Gmb * pw * [VT]! — (VfitemalVoid: *%5-):| (35)

3.3 Specimen Compaction

The following details the procedure for compacting the specimens:

i) The target air void content of each asphalt mix was set to 4%.

16

 

  

 

 

 

 

L A) Theoretical conditions of a corn cted sam le B) Actual conditions of a com acted 1e

 

Figure 3.1 Gyratory Compaction Mold

ii) Each bag is placed in a conventional oven preset at 90°C (194°F) for eight
hours. This would increase the workability of the mix, and allow easy
extraction from the bags.

iii) The asphalt is then extracted from the bag and inspected for any impurities or
asphalt and aggregate lumps. A11 impurities, such as threads from the bag or
any other materials, are taken out, and all the lumps of asphalt are broken
down. The loose asphalt is then remixed and distributed into mixing bowls
such that there is enough mix in each bowl for three specimens (since three
compaction molds were used). The samples are then covered with aluminum
foil and stored. (Note that the final weight required for each specimen was
determined as mentioned in the previous section after a first trial specimen).
The same steps used in this procedure apply to the first specimen preparation
with the exception that the amount of asphalt mix placed in the mixing bowl

was for one specimen instead of three.

vi)

vii)

viii)

One bowl at a time is placed in a conventional oven preset at 140°C (284°F)
for 3 hours.

The three sets of compaction molds (each set includes a compaction mold,
bottom plate and upper plate) are placed in a conventional oven preset at
140°C (284°F) one and a half hour before compaction.

One set of compaction mold and plates are moved from the oven. The bottom
plate is first placed in the mold and a paper disk is placed over it.

The mixing bowl is removed from the oven and the predetermined weight of
asphalt mix for one specimen is added to the mold. The mixing bowl is re-
covered with the aluminum foil and returned to the oven.

Another disk paper is placed on top of the asphalt mix in the mold and the
upper plate is placed over it. The mold is then placed in the gyratory

compactor, and compaction starts. The gyratory compactor is set as follows:

Table 3.1 Gyratory Compactor Setup

 

 

 

 

 

 

 

 

Setup , Value
Angle of tilt 1.25°
Loading ram pressure 600 KPa
Rotation speed - 30 rpm
Specimen height 2.5”

 

Once the compaction is complete, the mold is removed from the compactor
and the specimen is extracted from the mold. The disk papers are removed,
and the specimen is left to cool down.

Steps (vi) to (ix) are repeated twice for the second and third molds. The

remaining asphalt mix is thrown away.

18

xi) The samples are given 3 digit numbers. The first digit represents the mix type
where 1 stands for the 4E3 mix and 2 stands for the 4E10 mix. The second
two digits represent the order in which the sample was compacted. For
example, the fifth sample that was compacted using the 4E3 mix will have the

number 105.

3.4 Specific Gravity Test

The bulk specific gravity tests were performed according to ASTM D-2726 standard test
procedure [12]. The ASTM procedure defines the bulk specific gravity as the ratio of the
mass of a given volume of material at 25°C to the mass of an equal volume of water at
the same temperature. The bulk specific gravity of the mix, Gmb, is calculated as shown in

equation (3.6):

 

W
Gmb = dry in air * (3 .6)
(WSSD " WSubmerged ) pw

Where: Wdrymai, is the dry weight of the specimen .
W550 is the weight of the specimen saturated surface dry

WSubmerged is the submerged weight of the specimen

pw is the density of water

The volume of the specimen and its air void content are calculated as shown in equations

(3.7) and (3.8), respectively:
Vsample = (W550 " WSubmerged) * pw (3-7)

Va% = Elysium (3.8)

mm

Where: Va% is the air void content

Gm is the maximum theoretical specific gravity of the asphalt mix

19

3.5 Specimen Surface Preparation

This procedure is conducted on all samples that are to be tested using the Indirect Tensile
Cyclic Load Test (ITCLT). The purpose of this procedure is to provide a smooth surface
for the Linear Variable Displacement Transformer (LVDT) to reduce noise in the
monitored deformation signals.

i) Check the perimeter of the specimen along its thickness, and mark the two
smoothest diagonally opposite sides. These sides will be used as the seating
sides, and no patching would be applied to these areas.

ii) Seat the sample in a similar position to the one in the loading frame with the
two smooth surfaces lying on the vertical diameter. Draw a line along the
specimen vertical diameter and another one perpendicular to it on each of the -
specimen faces. Draw a line along the thickness of the specimen connecting
the ends of the horizontal lines on both faces.

iii) Apply plaster patching on the intersection of the two lines (described in item
(ii) above) on both faces of the specimen. Figure 3.2 shows the location of the
patching on a specimen.

iv) Let the patching set for at least 4 hours. Using a sand paper number 150,
remove all excess plaster over the patched area until there is no more plaster
thickness. The asphalt mix should appear inside the patch and the plaster will
be only filling the surface cavities

Figure 3.3a shows an actual specimen before patching with the smooth surfaces located at

the top and bottom. Figure 3.3b shows the specimen after the plaster was applied. Figure

20

3.3c shows the specimen in its final condition ready to be tested. The black dots inside

the plaster show that the thickness of the patch is just enough to fill the surface cavities.

 

 

 

 

 

 

Figure 3.2 Patching Location

21

 

 

 

b) Amythe plaster

a)Markthesmootliestsmface

 

 

c)Rexmvcextraplasterwithasandpapa

 

 

g

Figure 3.3 Specimen Pat

22

Chapter 4 - Indirect Tensile Test

4.1 Introduction

The Indirect Tensile Test (HT) is conducted by applying a vertical compressive strip
load on a cylindrical specimen. The load is distributed over the thickness of the specimen
through two loading strips at the top and bottom as shown in Figure 4.1. The strips are
curved at the interface with the specimen and have a radius equal to that of the specimen

to ensure full contact over the entire seating area.

 

 

 

 

 

 

 

 

 

 

 

Figure 4.1 ITT Setup

This combination of specimen geometry and boundary conditions induce tensile and
compressive stresses along both the vertical and horizontal diameters (Figure 4.2). The
tensile stresses, developed perpendicular to the direction of the load, have a relatively

constant value over a large portion of the vertical diameter. This would result in the

23

failure of the specimen by splitting along the vertical diameter as shown in Figure 4.1.

Note that under high vertical loads, local shear failure might occur near the loading strips.

 

y ch : Compressive
Vertical Stresses
along Y- axis

K O'yc O’fl : Tensile
Horizontal Stresses
along Y-axis

 

 

O'xc : Compressive
X X Horizontal stresses
Oyt alon X-axis

 

 

Vertical Stresses

\ O’xt : Tensile
along X-axis

 

 

Y

 

 

 

Figure 4.2 Stresses in ITT Specimen

The specimens tested are normally 4.0 inch or 6.0 inch in diameter with 0.5 or 0.75
inches wide loading strips respectively. The thickness of the specimen ranges between
2.5 and 3.0 inches. For this report, all the specimens tested have a 4.0 inch diameter and
2.5 inch thickness with a 0.5 inch wide loading strip.

Five LVDTs are used to measure the response of the specimen to the loading. Two
LVDTs are aligned horizontally along the thickness of the specimen (parallel to the
loading strip) and the summation of these two reading results in the Longitudinal
. Deformation (D1,). Another two LVDTs are set horizontally, but along the diameter of the
specimen (that is, perpendicular to the loading strip), and the summation of these two
readings gives the Horizontal Deformation (D1,). Note that (D1,) is along the tensile

stresses causing the specimen to fail. The final LVDT is used to monitor the vertical

24

deformation. Figure 4.3 shows the LVDT configuration. Figure 4.4 shows the actual test

setup.

 

Vertical LVDT

 

 

 

 

 

Longitudinal LVDT

 

Figure 4.3 LVDT Configuration

 

Figure 4.4 Actual ITT Setup

25

4.2 Analytical Models

The analytical models used to calculate stresses and strains in a cylindrical asphalt mix

are based on plane stress theory and thus, the stresses and strains along the thickness are

neglected. Additionally, these models assume that the asphalt concrete mix is

homogenous, isotropic, and behave according to the theory of elasticity. Vertical and

horizontal stresses and strains have a closed-form solution relating them to the applied

load, measured deformations, and Poison’s ratio [1, 13]. For all later calculations, a

Poison’s ratio of 0.35 is assumed as suggested by ASTM D4123 [14]. The tensile stress

(ox) and the compressive stress (0,) can be determined from the following equations

(Figure 4.5):

lb (cos62 )"‘[sin2 (¢- -62 )]d
r2

 

 

_-2___q__R*{I: (cos622)*[sin (¢+6)]

r1 d¢+ J1“

«b (cos62 )"‘[cos2 (¢- 62 )]d

 

 

-2 R 4b (cos622)*[cos (¢+6)]
0y: _fl—fl“ —*{Lb r1 d¢+ I40 r2
where q = -—P.—0—
2R(srn ¢o)

P0 = I: qR(cos ¢)d¢ = 24R sin ¢e

P0 = applied total load (lb)

 

 

r1=,[x2+(R—y)2, r2=,/x2 +(R+y)2

 

 

 

sin6 = x , cos6l = (R—y)
J(R- y) H x/(R-yfwc2
sin62=i , cos62= +y
r2 r2

L = thickness of specimen and R = radius of specimen

26

(lb

(iii—72'} (4-1)
__¢_"’_
61¢ R} (4-2)

 

I
I
I
17%

 

 

 

 

 

 

Figure 4.5 Stresses in a Circular Disk Subjected to a Frictionless Strip Loading (Baladi,
1988)

The stresses are maximrim at the center where x=0 and y=0. For a 4 inch diameter
specimen and a 0.5 inch wide loading strip, the maximum stresses can be' calculated from

equations (4.1) and (4.2) to be:

ox = 0.156241"‘-1;Jg (4.3)
ay = 4.475380“? (4.4)
From plane elasticity theory,
_ 1 at: * 4 5
E’_F (ax—v 0y) (.)
_ l :l: * 4 6
8.2—E (Cy—U 0") (~)

where: E is the elastic modulus of specimen

27

1.) is Poisson’s ratio

The horizontal tensile strain (8,) along the horizontal diameter of the indirect tensile

specimen under the strip loading can be written as:

 

 

 

 

 

 

2
2 0.501-1.984* 21 —O.496* 2"
£2=———*[-4*q*( ‘2” x +4—o.063)+
7t*L*E 1: +4
1 x2
O.501+l.984* 2 —0.496* 2
1,4*q*( x2+4 x +4—O.063)] (4.7)
x +4

The vertical compressive strain (8,) along the horizontal diameter of the indirect tensile

specimen under the strip loading can be written as:

 

 

 

 

 

 

2
2 0.501+1.984* 214—O.496* 2x 4
e =————* -4* * x + x + -0.063 +
y 7Z*L*E [ q ( x2+4 )
1- Jr2
o.501-1.9s4* 2 4+0.496* 2 4
1.4* * x + x + —0.063
q ( x224 )1 (4.8)

Integration of equations (4.7) and (4.8) along the horizontal diameter of the specimen

produces the equation for the horizontal and the vertical deformations:

 

 

D, = 0.6159 * L}: 0E (4.9)
D, = —l.0895 * L1: 0E (4.10)

The largest horizontal and vertical strains occur at the center of specimen, and are

obtained by replacing the variable x by zero.

28

P0

32, =1.0136*ET—;-Z (4.11)
7!
£2, = _1.6653*—E—*f£’ri- (4.12)
72' .

Combining Equations (4.5) and (4.6) with Equations (4.9) and (4.10) and (4.11) and
(4.12) produce the following equations:
82 =O.523"‘Dh (4.13)
82 = 0.487 * D, (4.14)

Therefore, the strains at the center of the specimen can be expressed uniquely as a

function of deformations.

4.3 Indirect Tensile Strength Test

The indirect tensile strength test (ITST) uses the same setup described in Section 4.1. A
ramp loading is applied to the sample at a constant rate of 2 inches per minute until
failure. The magnitude of the load resisted by the sample as a function of the vertical
deformation is directly obtained from the ITST machine. The horizontal and vertical
deformations are collected as a function of time by a separate data acquisition system. By
matching the vertical deformation from both graphs, the force versus time graph can be
obtained. The properties that can be determined from this test are:

> The tensile strength

> The compressive stress at failure

> The equivalent modulus

> The stored energy density until cracking

29

4.3.1 Tensile Strength

The Tensile Strength (TS) is the maximum tensile stress a sample can accommodate
before failure. A higher tensile strength results in higher resistance to cracking. TS is
determined by equation (4.15) where Pu is the ultimate vertical force resisted by the

specimen.

TS =0.156241*-E“— (4.15)

4.3.2 Compressive Stress at Failure

The Compressive Stress at Failure (CSF) is the maximum compressive stress the
specimen is subjected to during testing. A higher CSF results in better rut resistance. Note
that the specimens tested in IT ST fail in tension and not in compression, and thus, the
compressive strength determined in this test might not be the highest compressive stress
the asphalt mix can handle. The CSF is determined by equation (4.16) where Pu is the

ultimate vertical force resisted by the specimen.

CSF = -0.475386 * i:

 

(4. 16)

4.3.3 Equivalent Modulus

The Equivalent Modulus (EM) is an indication of the material stiffness. A higher
modulus results in higher resistance to deformation. Since the load deformation curve
remains linear for the first part of the curve (up till half the maximum load), the EM is

determined as the slope of that part of the curve (Figure 4.6).

30

1P
HM=—— an
25 ( )

Where: P is the ultimate vertical load at failure in pounds,

and 8 is the deformation corresponding to P/2 (in inches).

 

A Load

P/2

 

 

 

 

5 Deformation

 

 

 

Figure 4.6 ITST Load Deformation Curve

4. 3.4 Stored Energy Density until Cracking

The Stored Energy Density until Cracking (SEC) is the total energy density (pounds per
square inch) required to start the failure of the specimen. It is determined as the area
under the stress-strain curve starting from the origin until the peak, as shown in Figure
4.7. This value will be later used as part of the new failure criterion. The stresses and
strains used are the tensile ones in the horizontal direction and are calculated from the
monitored load, horizontal deformation (D1,) and vertical deformation (Dy) as shown in

equations (4.3) and (4.13) respectively.

31

 

A Stress

Stored

/€2.°’£.§“

 

 

 

/A >

Strain
Figure 4.7 Stored Energy Density until Cracking

 

 

 

4.4 Indirect Tensile Cyclic Load Test

The indirect tensile cyclic load test (ITCLT) uses the same setup described in Section 4.1.
With the MTS system used for this research, the load can be applied to the specimen as a
combination of sine, haversine, ramp, and constant level pulses. In addition to any load
pulse, a constant sustained load of 20 pounds is applied to the specimen to insure contact
between specimen and the loading strips. The horizontal, longitudinal and transverse
deformations are measured and recorded as a function of time. These deformations can be
divided into three components: elastic, viscoelastic and plastic deformations, as shown in
Figure 4.8.

The portion of deformation that is immediately recovered upon unloading is called the
elastic deformation. Another recoverable portion is the viscoelastic deformation;

however, this part is recovered after the unloading is over. Finally, the last portion of the

32

 

 

 

 

Load
A
, F
Deformation
Plastic Non- Viscoelastic Elastic
recoverable Recovery Recovery

 

 

 

 

 

 

 

Figure 4.8 Load-Deformation Curve under Cyclic Loading

deformation, the plastic deformation, is permanent and will not be recovered. The
properties that can be determined from this test are:

> Recoverable deformation

> Permanent deformation

> Resilient modulus

>

Dissipated energy density

4.4.1 Recoverable Deformations

The recoverable deformation is the summation of the elastic and viscoelastic
deformations. For elastic materials, the recoverable deformation is simply the elastic
deformation and the loading and unloading portions of the stress strain curve coincide.
However, for viscoelastic materials, the loading and unloading portions are different, thus

producing the hysteresis loop and the corresponding dissipated energy. The recoverable

33

deformation can be determined in both horizontal and vertical directions, and is

calculated per cycle to calculate the dissipated energy density and the resilient modulus.

4.4.2 Permanent Deformation

Permanent deformation, known also as plastic deformation, can be determined in both
horizontal and vertical directions. Both, the horizontal plastic deformation (HPD) and the
vertical plastic deformation (VPD) per cycle can be determined as a function of number
of load repetitions by calculating the difference between the deformation at the beginning
and end of each cycle. Additionally, VPD and HPD can be determined based on a
reference load cycle (second load cycle in this study) for obtaining the cumulative
permanent deformation directly. The cumulative PD is used as an indicator of the mix

resistance to rutting.

4.4.3 Resilient Modulus

The resilient modulus is calculated for each cycle and its reduction as a function of the
number of repetitions increases is recorded. The resilient modulus is calculated based on

the following equation [15]:

__ P(v + 0.2734)

M“ 6*L

(4.18)

 

where: P is the applied vertical load
5 is the recoverable deformation
v is Poisson’s ratio, and

L is the specimen width.

34

4.4.4 Dissipated Energy Density

Dissipated energy density is defined as the area within a stress-strain hysteresis loop and
represents the energy lost at a specific point due to a load application. The tensile stresses
and strains at the center of the specimen are used to calculate the dissipated energy
density. The dissipated energy density is calculated at each cycle where data collected,

The cumulative dissipated energy density is then determined by superposition.

4.5 Determining Load Pulse Magnitude and Shape

A tliree-layer pavement cross-section was analyzed using the SAPSI-M computer
program to get the field response under the wheel loads. The SASI-M program uses finite
layer analysis and a polar coordinates system (Figure 4.9). Knowing the radial distance
(R) to any point and the angle of inclination (0), two stresses are calculated first: the
radial stress (0,) and the tangential stress (0.). From these two stresses, all the critical
stresses mentioned in section 2.1.1 can then be calculated. The vaer of the elastic
.modulus for the asphalt layer was calculated from the resilient modulus obtained form the
lab. Based on an FHWA study in 1998 [16], it was concluded that the elastic modulus in
the field is approximately three times that from the lab.

The pavement response is obtained as a function of time at a specific point at the bottom
of the AC layer as the load (truck, axle group,..) passes over the pavement surface. Once
the pavement response is determined, these values can be converted into a load pulse

applied by the actuator on the specimen using either of the following equations:

P=6.4*0'2 *L (4.19)

P = 0.8031 * £2 * L (4.20)

35

Where: o, is the tensile stress in psi

8. is the tensile strain in micro-strain.

 

W

 

 

 

 

Figure 4.9 SAPSI-M Analysis Model

First, the tensile stresses at the center of the specimen were equated to the transverse
tensile stress at the bottom of the AC layer (equation 4.19); however, the obtained
vertical load was too high, and caused the sample to fail in local shear near the loading
strips as shown in Figure 4.10. A typical specimen failing under fatigue is shown in
Figures 4.11, 4.12 and 4.13. Additionally, the strains at the center of the specimen under
these stresses were much higher than the strains at the bottom of the AC layer. This can
be explained by the different confinement provided by the pavement structure in the field
(or from a computer modeling of the field) and that provided by the unconfined specimen
at its center. Clearly, the confinement in a pavement structure is much higher than that in

a cylindrical specimen, and thus, the high values of the strains. Given the above

36

considerations, the load pulse was determined by equating the transverse tensile strains at
the bottom of the AC layer to the tensile strains at the center of the specimen as shown in
equation 4.20. Equating the strains seemed to be the logical way to go, regardless of local
shear failure near the loading strips. After all, the strain value is what causes the asphalt
concrete to fail in tension and not the stress value. When comparing two identical
pavement structures with only the AC stiffness being different, the stresses at the bottom ‘
of both asphalt layers would be almost the same; however, the Strains at the bottom of the
stiffer layer will be much lower. Thus the difference in the fatigtre life between the two
pavements would show that strains are what cause the fatigue failure and not the stresses.
Figure 4.14 shows a comparison between the response at the bottom of the AC layer from
SAPSI-M modeling and the response at the center of the specimen under the load pulse
obtained from the procedure mentioned above.

As for the rest period, a constant ratio of 1 to 4 was used for loading and rest periods.
Since the effect of the rest period on the fatigue life is not a part of this study, the
constant ratio was used. For single axles, the loading/unloading duration was found to be
0.1 second using the response calculated from SAPSI-M due to a moving load at 40 mph;
therefore a rest period of 0.4 seconds was used. For the different axle configurations and
trucks, the loading time is taken as the time from the beginning of response due to the

first axle until the time when the response of the axle dies, as calculated from SAPSI-M.

37

 

    

Figure 4.11 Fatigue Cracking in lab Specimen at Early Stages

38

 

g in lab Specimen at Intermediate Stages

Figure 4.12 Fatigue Cra

 

Final Stages

lab Specimen at

gin

tigue Cra

Figure 4.13 Fa

39

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

160
140
120 x 2 2 - - - -SAPSI-M
100 ' , 2 2 - -——-ITCLT ’
l ' ' 2 2 2
g. 80 ' ' l—‘J
g 60 ' :2
40 i ll '
20 .
0 J I I I
O 0.1 0.2 0.3 0.4 0.5 0.6
'Iime(sec)

 

Figure 4.14 SAPMSI-M vs ITCLT Pulses

4.6 Comparison between ITCLT and Field Conditions

When considering a stationary wheel load on the surface of a pavement structure, three
strains/stresses are generated at the bottom of the AC layer. These are the longitudinal
strain and stress (81, & 01,: parallel to the traffic direction), transverse strain and stress (at
8; o“: perpendicular to the traffic direction) and vertical strain and stress (8,, & cry: in the
vertical plane). As the wheel moves on the surface along the road axis, the values of the
stresses and strains at a given point vary. Typical graphs A of longitudinal, transverse and
vertical stress time histories are shown in Figures 4.15, 4.16 and 4.17, respectively.

The peak values of the stresses are reached when the wheel is exactly above the point
where the response is measured. The positive values represent tensile stresses while
negative values correspond to compressive stresSes. As can be seen from these graphs,
the vertical stresses are not critical. Their magnitude is justabove 10% of the longitudinal

and transverse stresses. The following tensors show peak values of stresses and strains at

the bottom of the AC layer obtained from SAPSI-M analysis under a single load to

compare with the stresses and strains at the center of a lab specimen.

L 130.14 0 -—8.21 L 1.333 — 4 0 ' —1.33E - 5

t 0 133.26 0 t 0 1.4E - 4 0
v -8.21 0 —14.8 v -l.3£ - 5 0 —l.3SE — 4
Stress Tensor Strain Tensor

Recalling equations 4.3, 4.4, 4.11 and 4.12 from section 4.2, the stress ratio of the
compressive vertical stress to the tensile horizontal stress is 3 : l in the ITT specimen
compared to 1 to 8.8 in the field. Additionally, the longitudinal stresses are negligible in
the lab, while these stresses are the same as the transverse ones in the field. Thus, the
stress ratio between the lab and field are totally different and this should be always taken
into consideration when analyzing. lab results, or calculating load pulses that will be
applied to a specimen in the lab. Therefore, only the dissipated energy density from the

horizontal tensile stresses and strains was used in determining the fatigue life.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

140
120 |
100
f 80
5
g 60
in 40
20
o a - l x, ".7.
I “I“?! Law"
'20 I
1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2
Tlme (sec)

 

 

 

Figure 4.15 Longitudinal Stress Time History at the Bottom of AC Layer

41

 

 

Stress (psi)

8

 

‘s‘

 

8‘

 

8

 

8

 

8

 

 

 

 

l
.0 ,H
-1/

 

 

 

 

 

 

 

 

 

 

 

 

 

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9
Tlme(sec)

 

Figure 4.16 Transverse Stress Time History at the Bottom of AC Layer

 

 

Stress (98')

Time (sec)
1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 4.17 Vertical Stress Time History at the Bottom of AC Layer

42

 

Chapter 5 - Dissipated Energy Concept and New Failure Criterion

5.1 Introduction

Dissipated energy density is defined as the area within a stress-strain hysteresis 100p and
represents the energy lost at a specific point due to a load application. The tensile stresses
and strains at the center of a specimen are used to calculate the dissipated energy density.

Figure 5.1 shows a typical stress-strain hysteresis loop.

 

 

 

 

 

‘Stress
Dissipated Energy
/
- +
Strain

 

 

 

Figure 5.1 Stress-Strain Hysteresis Loop

Energy is dissipated with each cycle and accumulates as the load is repeatedly applied to
the specimen. The cumulative dissipated energy density up to a given cycle can be
calculated by summing up the dissipated energies in the previous cycles. Initially, the
dissipated energy density per cycle is constant for a number of load repetitions, after
which it starts to increase rapidly (Figure 5.2). As for the cumulative dissipated energy

density, it starts increasing gradually at the beginning, then it starts increasing

43

dramatically as cracking develops (Figure 5.3). Either of the two measures, cumulative

or cyclic, can be used as a failure criterion for fatigue testing.

 

 

0.0035 l

 

0.003

 

0.0025

 

0.002 I

 

l 0
0.0015 . ’ 0

DE (PSI)

 

0.001

 

0.0005
0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1 10 1 00 1 000 10000 1 00000
N

 

 

 

Figure 5.2 Dissipated Energy Density Per Cycle

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

:2, a.
"‘ 7
o
g 25
E 20
5

15

10 V1/

5 27/

l 0”)
o lot-l ’5
1 10 100 1000 10000 100000
N

 

 

 

Figure 5.3 Cumulative Dissipated Energy Density

5.2 Previous Studies on Dissipated Energy

The fatigue of viscoelastic materials subjected to repeated loads has been associated with

the energy loss due to these load cycles. Laboratory fatigue tests have showed a unique

relation between the fatigue life of an asphalt mixture and the cumulative dissipated

energy.

Figure 5.4 shows the values of dissipated energy density per cycle as a function of

number of load repetitions [17]. The dissipated energy density per cycle increases with

increasing load repetitions in a controlled stress test, while it decreases in a controlled

strain test. Additionally, it can be seen that for the initial cycles (before cracks initiation),

the values from both tests are equal.

 

0.04

 

O
p .
a Q

Dlsslpated Energy (psi)
0
8

 

 

 

 

 

 

 

 

 

0.02 ~ x
0.015 2 xControlled-Stress Test
oControlled-Strain Test
0.01 . .
100 1000 10000 100000
Number of cycles

 

Figure 5.4 Dissipated Energy Density

from Controlled-Stress and Controlled-Strain Tests
(Sousa, 1992)

45

 

Figure 5.5 shows the variation of the cumulative dissipated energy density as the number
of load repetitions increase. The cumulative dissipated energy density values obtained
from the stress controlled and strain controlled tests are different. However, the two

curves are very similar for the first portion (initial cycles).

 

 

.0
to

.0
on

.0
V
L

.0
or
1

 

Total Energy Dlsslpated (psi)
0
0|

 

 

 

 

 

 

 

0.4 1
0.3 .
022 2 xControtled-Stress Test
021 i OControlled-Straln Test
0 I I I I l I
O.E+OO 1 .E+04 2.E+O4 3. E+04 4. E+04 5.E+04 6. 51-04 7.5-+04
Number of cycles

 

 

 

Figure 5.5 Cumulative DE from Controlled-Stress and Controlled-Strain Tests
(Van Dijk, 1974)

Van Dijk [6] was one of the first researchers to apply the dissipated energy concept to
asphalt concrete fatigue testing. From tests conducted under both stress and strain
controlled modes, he concluded that the total amount of dissipated energy density to
failure is independent on the testing mode. However, the stress controlled tests dissipate
- energy much faster than strain controlled tests resulting in lower predicted fatigue life. In
another study, Van Dijk [6] reported that the cumulative dissipated energy versus the

number of load repetitions is dependent on the mix properties, but independent of test

46

methods (two and three point bending), temperature (50°F to 104°F), mode of loading
(stress controlled and strain controlled) and load frequency (10 to 50 Hz).

Monismith et al. [8] indicated that the uniqueness of the cumulative dissipated energyfor
different types and conditions of testing cannot be sustained. Further investigations
showed that the total dissipated energy varies depending on the testing mode, temperature
and mix type. Ghuzlan and Carpenter [4] introduced a new failure criterion using the
change in dissipated energy between two cycles divided by the dissipated energy per
cycle. This criterion is very similar to using the dissipated energy per cycle. They
reported that when using this failure criterion, the mode of testing is taken care of, and
the results from strain controlled, or stress controlled match well.

Tangella et al. [18] summarized the advantages and disadvantages of the dissipated
energy approach in fatigue analysis. The major advantages are:

i) According to Van Dijk, loading mode, temperature, frequency of loading and
occurrence of rest period do not have a significant effect on the cumulative
dissipated energy.

ii) This procedure is [based on a physical phenomenon: the accumulation of the
dissipated energy from the repeated load cycles causes the fatigue in a visco-
elastic material.

iii) Prediction of fatigue life is possible as a first “approximation if initial stiffness
and phase angles are known.

iv) For both stress controlled and strain controlled tests, there is a unique
relationship between the total dissipated energy and the number of load

repetitions to failure.

47

The major disadvantages of this method include:

i) Accurate prediction of fatigue behavior is not possible without conducting
detailed fatigue testing.
ii) The procedure proposed in this method can not be considered as a design

technique; rather, it serves to indicate the general magnitude of the fatigue life
of a given asphalt mix.
An additional advantage of the dissipated energy approach is its applicability to
simulating multi axles and whole trucks at once. This will be discussed later in detail in

the next chapter.

5.3 Dissipated Energy Fatigue Models

As mentioned in the previous sections, the dissipated energy density is determined as the
area inside the hysteresis loop. To calculate this area, the trapezoidal rule is used where
the area is calculated over a stress/strain interval corresponding to 0.005 seconds. And

thus, the dissipated energy density at a given cycle is determined as:

Wo = 22—”——'- (5.1)
l _(EH-l +81)

The cumulative dissipated energy density is determined as the integral of the dissipated

energy density per cycle:

Nf ,2
W = jw2d1= 2w, (5.2)
0 l

48

Van Dijk presented his fatigue model in terms of the cumulative dissipated energy per
unit volume (Wfafiguc) and number of load repetitions to [6] failure (Nf). The model is of

the form:

ANz

f (5.3)

fatigue =

Where A and z are material parameters. For asphalt concrete, Van Dijk suggested that 2
were equal to 0.63 and A was equal to 6.76 * 104 J/m3.

Sousa et al. [17] suggested two fatigue models, one for the stress controlled test and
another for the strain controlled test. The failure criteria were when the dissipated energy
reaches 2.1 times the value of the initial dissipated energy for the stress controlled test

and half the initial dissipated energy for strain controlled tests. The equations are:

Nf = Ln(2.1) / (0.0071 A1 '43 ) for controlled stress test (5.4)

N, = Ln(0.5) / (000247.043) for controlled strain test (5.4)
Where: A is the initial dissipated energy. I
Monismith et a1. [9] evaluated the performance of a thin pavement at the FHWA
Accelerated Loading Facility. Tests were run in a strain control mode under a continuous
sinusoidal loading with no rest period. The final model related the fatigue life (Nf) to the

initial dissipated energy per cycle.

Nf= 425.81 (WW-846 (5.5)

49

5.4 New Suggested Failure Criterion

Whether using the strain or dissipated energy approach in determining the fatigue life of
an asphalt concrete mix, an objective failure criterion based on the actual damage
occurring during a fatigue test needs to be established. The most common failure criterion
is the 50% reduction in the resilient modulus where failure is defined as the cycle at
which the resilient modulus value is half the initial value. However, this is an arbitrary
criterion with no exact relationship with the actual amount of damage occurring in the
sample. Additionally, this criterion is dependent on the loading mode.

Sousa et al. [17] performed a flexural beam test series that consisted of a V2 factorial
experimental design for mixtures composed of two aggregates, two asphalt binders, two
asphalt contents, two temperatures, two compaction levels and two loading modes. They
used the least squares technique to determine the value of the ratio (Rf) of energy
dissipated at failure to that of the first cycle. They reported an Rf [value of 2.1 for
controlled stress tests and 0.5 for controlled strain test. These results indicate that in a
stress controlled test, the failure occurs when the area of the hysteresis loop becomes
double the area of the first loop. While ina strain controlled test, the failure is defined
when the hysteresis loop area becomes half of the initial loop area. The same
disadvantages mentioned for the 50% reduction in the resilient modulus apply to this
failure definition.

Ghuzlan and Carpenter [4] defined fatigue life as the number of load cycles at which the
ratio of the change in the dissipated energy between cycles “i” and “i+1” divided by the

G‘i”

total dissipated energy of load cycle begins to increase rapidly. Although this criterion

overcomes the testing mode limitation, using this ratio (ADE / DE) might be misleading

50

when dealing with experimental results. A small change in the value of the DE will lead
to a large change in lepe and thus, a negligible noise in the results might be magnified
when calculating the slope. Additionally, the failure point when the plateau value starts to
increase is still visually picked, introducing a subjective assessment, which depends on
the scatter in the lab data. More importantly, the plateau value can not be used in any
mechanistic design.

The failure criterion should relate to the damage occurring in the tested specimen. As
shown in Figure 5.2, the dissipated energy density remains constant and then suddenly
starts increasing. The point when the dissipated energy density starts increasing is
basically the initiation of failure, and the corresponding cycle number is the number of
repetitions to crack initiation. This is very similar to what GhUzlan and Carpenter
presented with their plateau value and the point where it starts changing. However, it is
hard to visually determine the number of cycles at which the dissipated energy density
value starts to increase. To overcome the subjectivity in this process, the results obtained
from the indirect tensile strength test, and the fatigue test (both dissipated energy density
per cycle and cumulative dissipated energy density) were combined.

Figure 4.7 (showed below for convenience) shows the stress strain curve from an indirect
tensile strength test. The shaded area represents the stored energy density until cracking
(SEC). Previous studies showed that the dissipated energy until crack initiation is the
same regardless of the loading mode, and thus, a specimen tested under indirect tensile
cyclic load test should start cracking when the total dissipated energy density reaches the
same value as SEC. The new fatigue failure criterion is therefore defined by equating the

cumulative dissipated energy density under cyclic loading to the SEC value from the

51

indirect tensile strength test. It should be noted that this criterion can be applied to other
test modes provided the fatigue and strength tests are conducted under the same test
setup. For example, if one is to extend this criterion to flexural beam testing, then the
SEC value would be the flexural strength obtained by loading a beam to failure under a
constant rate of deformation.

To verify this, three samples were tested using the ITST and the average SEC was
determined. Then, triplets were tested under different load pulses and stress levels until
fatigue failure. The dissipated energy density per cycle was determined, and integrated to
obtain the cumulative dissipated energy density. From the cumulative dissipated energy

density, the number of load repetitions (Nf) required to reach the SEC was determined.

 

A Stress

Stored
Energy till
Cracking

 

 

 

Figure 4.7 (Repeated): Stored Energy Density till Failure

 

 

 

Figure 5.6 shows the SEC value plotted on the cumulative dissipated energy density
curve. The intersection of the SEC line with the cumulative dissipated energy density

curve is the fatigue life (Nf). The values of Nf was then plotted as a vertical line on the

52

dissipated energy density plot per cycle to check if it matches with the region where the
initial dissipated energy density value start to increase. Figure 5.7 shows the Ngvflue on
the dissipated energy density per cycle plot. As expected, the dissipated energy density
value starts to increase in the neighborhood of Nf. Figures 5.8 and 5.9 show the same '
trend from a sample tested at a lower stress level. The value of Nf increase by a ratio of
10, but the same failure criterion still applies. A total of 31 samples tested at three stress
levels (4.375, 8.75 and 17.5 psi) and 5 different load pulses (single, tandem, tridem, 4-

axles and 8-axles) were used to verify the applicability of this procedure for determining

.the fatigue failure.

 

30

 

 

20

 

N
15 '

 

10

 

Cumulative DE (PSI)

\/
"w.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

t—l- l—I- I_ —1- n I--_ —— -I HJ III—i 1-1- III——
0 ._*.Jl__--.: _qzqelfi-gfi i“ 1

1 10 1 00 1000 1 0000 1 00000
N .

 

 

 

Figure 5.6 Determining Nf from Cumulative Dissipated Energy Density and SEC
(Sample 1)

53

 

 

DE (PSI)

0.0035

0.003

0.0025

0.002

0.0015

0.001

0.0005

 

 

it.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

10

100

N

1000

1 0000

1 00000

 

Figure 5.7 Dissipated Energy Density per Cycle Curve with N; Superimposed on it

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(Sample 1)
30 I
25
G
O
5 20
“’ i
a
o
5 15
.9
= /
g 10
0 /
5 /
K
0 x x SL1 "'9'?
100 1000 10000 100000 1000000
N

 

Figure 5.8 Determining N: from Cumulative Dissipated Energy Density and SEC
(Sample 2)

54

 

 

 

0.0005

 

 

0.0004

0.0003

 

DE 1P")

0.0002 0

 

0.0001

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

100 1 000 1 0000 100000 1 000000
N .

 

 

 

Figure 5.9 Dissipated Energy Density per Cycle Curve with N; Superimposed on it
(Sample 2)

Due to equipment limitations, controlled strain tests were not performed to check whether
this criterion is dependent on the loading mode or not. However, from the previous study
by Ghuzlan and Carpenter [4] where a similar failure criterion was adOpted, it was found
to be independent of loading mode. Therefore, it is expected that this prOcedure should be
independent of loading mode as well. In their definition of failure, Ghuzlan and
Carpenter found out that using the change in the value of (ADE/DE) between two
consecutive cycles is an indicator of failure initiation. Since the dissipated’energy per
cycle was used in determining this ratio, the sudden increase (ADE/DE) corresponds
basically to the increase in the initial value of the dissipated energy. Thus, the only
difference between the failure point presented here and that of Ghuzlan and Carpenter is
the procedure used to determine this point. While Ghuzlan and Carpenter use the ratio
(ADE/DE) and visually pick the failure point, the procedure presented above use the
cumulative dissipated energy density and the SEC value from the indirect tensile strength

test.

55

Chapter 6 - Test Results and Corresponding Fatigue Curves

6.1 Introduction

Two asphalt concrete mixes were tested in this study: I) 4E3. mixiand II) 4E10 mix. The
mixes were obtained from actual batches that were used by the Michigan DOT on
projects in the summer of 2002. A total of 73 samples were compacted using the gyratory
compactor (57 from mix I and 16 from mix II). Forty samples were tested for fatigue (35
samples from mix I and 5 from mix 11). Three samples from each mix were tested under
the indirect tensile test.. Mix I was tested first, followed by mix 11. The results obtained
from mix II were very similar to those of mix I, and thus, the fatigue tests were stopped.
Checking results from a previous study at Michigan State University performed by Baladi
and Crince [20], their results also showed that there was no clear difference between the
two mixes. The mix used in this study was a super-pave 4E3 mix with a top aggregate
size of ‘6 inch and a target asphalt content of 5.9%. The volumetric prOperties of mix I
are presented in Table 6.1 below.

Table 6.1 Volumetric Properties of Mix I

Pmperty Gm, Gmb (3,, GS, VMA VFA Gs
Value ~ 2.487 2.388 2.731 2.661 15.6% 74.4% 1.026

 

 

 

 

 

 

 

 

 

 

 

 

6.2 Preliminary Tests Results

Several tests were performed before the actual fatigue tests started. Tests such as specific
gravity, indirect tensile strength and indirect tensile cyclic load tests were performed to
determine sample air void content, indirect tensile strength and stored energy density till

cracking, and resilient modulus respectively.

56

6.2.] Specific Gravity Test Results

After the samples were compacted using the gyratory compactor, a bulk specific gravity
test was performed on each specimen, and the air void content was determined. The
average air void content and its standard deviation for the samples used are 3.9 and 00.2
for mix I, and 3.74 and 0.24 for mix 11 respectively. Specimens with high or low air voids

were not tested. The detailed specific gravity results are included in the appendix.

6.2.2 Indirect Tensile Strength Test Results

Three samples (129, 143 and 154) were tested to determine the indirect tensile strength
and the stored energy density until cracking. The vertical force at failure was recorded to}
be used as a reference for the fatigue test vertical loads. The vertical load applied in the
fatigue test should be much lower than the peak vertical force from the strength test, or

else, the test performed cannot be considered a fatigue test. Results are summarized in

 

 

 

 

 

Table 6.2.
Table 6.2 ITST Results
fiecimen No 143 129 154 Average
Tensile Strength (psi) 170.4 167.9 174.2 170.9
Max. Compressive
Stress (psi) 511.3 503.8 522.6 - 512.6
ven' ”(383; mu“ 2677.2 ~ 2637.8 2736.2 2683.7
Stored Energy Density
Until Failure (psi) 1.547 1.553 1.568 1.556

 

 

 

 

 

 

 

Figure 6.1 shows a typical out put from the ITST. The vertical deformation is linear until

the test ends; this is due to the constant ramping'rate of 2 inches per minute at which the

57

test is performed. The test starts when both the load and horizontal deformation starts
picking up. All the vertical deformation before this point is neglected. The specimen fails
when the load reaches its peak. This is the point when cracks start to initiate. (Note that
the last portion of the load curve is extrapolated. The test is usually stopped after the load
starts decreasing. Figure 6.2 shows the stress strain curve and the stored energy density
until cracking calculated for the same specimen. (Refer to section 4.3 for details on

calculating the stresses and strains).

 

0.2 3000
Failure

 

0.15 1

0.1 4 Beginning of Test

 

.6 p
8:58
13.1
i
i
i
.T

 

 

 

Load (Lbs)

I
O
Q.‘
'0

 

Deformation (In)

0.1 i --1000
0.15 .

-0.2 .

 

 

 

 

-0.25 t

.a
d
.1
..
A
.4
.4
O

 

Time (sec)

 

 

 

Figure 6.1 Output from ITST (specimen 154)

58

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

180
160i 2”»?
/

1404
Z 1204
a 100 4 /
i /
g StoredEnergy
1- 6° ‘ Density until

40 ] Cracking

o A swipe-.. .
0 0.01 0.02 0.03 0.04 0.05 2 0.06
Tensile Straln

 

Figure 6.2 Stored Energy Density till Cracking (specimen 154)

6.2.3 Resilient Modulus

Two samples (12 and 146) were tested under Indirect Tensile Cyclic Load to determine
the “Lab” resilient modulus of the 4E3 mix. Three tests were run on eaCh sample, and the
average of the deformations measured at the 499, 500 and 501 cycles were used to
determine the resilient modulus. A sustained load of 50 pounds and a cyclic load of 300
pounds were used. The cyclic load was applied at a frequency of 2 hertz with 0.1 seconds
of loading and unloading and 0.4 seconds of rest period. The resilient modulus was

calculated from the equation (6.1) [1]:

_ P(3.58791— 0.062745 * V)

L*Dv (6.1)

MR

 

Where: P is the vertical load (Lbs)
L is the specimen thickness (in)
Dv is the vertical deformation (in)

Vis Poisson’s ratio.

59

The results are summarized in Table 6.3 below. The resilient modulus from the
laboratory is used to calculate the elastic modulus of the asphalt concrete layer used in
the SAPSI-M analysis for obtaining the response of a pavement structure under a given

load.

Table 6.3 Resilient Modulus Results

1
250906
23401 6

0
264571 252575 18706 7.41 /6

238582

 

6.3 Fatigue Curves

The main purpose of this study was to determine a fatigue curve that can be used to
determine the fatigue life of an asphalt mix subjected to a multi-axle load pulse. To do so,
specimens were tested under different load pulses representing different axle

configurations. Table 6.4 shows the fatigue testing matrix.

Table 6.4 Fatigue Testing Matrix

no.

Level 1

Low Medium 50%

Medium Medium 50%
5%

High Medium 50% xx

 

No. of 'x's represents the number of samples tested.

60

Three tensile stress levels where used: 4.375, 8.75 and 17.51 psi. The medium stress level
is the stress required to produce a strain at the center of the specimen equal to those at the
bottom of the AC layer modeled in SAPSI-M. The 5 axle configurations tested for fatigue
life are: single, tandem, tridem, 4-axles and 8 axles. The spacing between the axles is 3.5
feet and each axle carries 13 kips (medium stress). The interaction level is defined as the
ratio of the peak stress to that of the valley (also known as midway) and is shown in
Figure 6.3. The high interaction level represents a thicker asphalt concrete layer (around
10 inches) while the lower interaction level represents a thinner pavement (around 6

inches).

 

 

 

J J '

(a) Low (b) Medium (6‘) High

 

 

 

Figure 6.3 Different Interaction Levels

FOr all fatigue test load pulses, a twenty (20) pound sustained load was used to guarantee
contact between the loading strips and the specimens at all times. The twenty pound load
was applied first to the specimen, and a rest period of ninety (90) seconds was used
before the actual load cycles started. This rest period is applied to make sure that the
deformation due to the sustained load is not included in the response recorded for the first
cycle. The average of three consecutive cycles was taken as the value of the intermediate
one. Thus, the data presented as cycle number 5 is basically the average of cycles 4, 5 and
6. Collected data were filtered using the moving point average to reduce the noise. A

twenty point moving average correction was applied. This is acceptable given that the

61

data was collected at a rate of 2000 readings per second, meaning that in a 0.1 second
loading, 200 readings are taken.

the pavement response, under the actual axle configurations were obtained Using the
SAPSI-M program. A 6 inch AC layer with an elastic modulus of 700 ksi was used and
typical values for base thickness and modulus and subgrade modulus were input. The
load pulse is obtained by equating the tensile strains (time history) at the bottom of the
AC layer to the tensile strains at the center of the lab specimen.

The number of repetitions to failure was determined as mentioned in section 5.4. The
stored energy density until cracking (SEC) was calculated from the indirect tensile
strength test and was found to be 1.556 psi. For each tested specimen, the initial
dissipated energy density, initial strain and Nf were recorded for later use in developing

the fatigue curves. These results are tabulated in Table 6.5.

62

Table 6.5 Fatigue Tests Results

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

. Sample . Tensile strains Tensile
Axle Configuration No. Intlal DE Nf First Peak [ILast Peak Stresses (p51)
1 - axle Low 119 3.00E-05 46135 2.00E-05 4.062
Stress(25% lnt.) 157 2.00505 52137 2.50505 4.062
3 - axles Low 140 1.00504 15119 2.50505 3.50505 4.375
Stress(25°/o Int.) 133 1.10504 11725 3.00505 4.00505 4.375
8 - axles Low 150 1.80504 8267 2.80505 5.00505 4.375
Stress(25% Int.) 127 2201304 6983 3.00505 - 6.00505 4.375
. 139 1.10504 13378 3.30505 8.125
Aggggflm 142 1.30504 1209 4.0g05 8.125
' 130 1.00504 14867 3.30506 8.125
. 122 2.50504 6122 6.00505 8.749
ég‘gffig 128 2.50504 5770 6.00505 8.749
' 124 2.80E-04 5219 EDGE-05 8.749
. 116 3.75504 4316 4.00505 5.50505 8.749
5162053338 156 4.00504 3692 5.50505 7.30505 8.749
' 147 3.00504 4511 4.50505 5.70505 8.749
. 141 4.25504 3499 8.00505 8.749
Qgigcidlii'; 144 4.25504 3772 7.00505 8.749
' 117 4.50504 4097 6.50505 8.749
. 111 6.00504 3215 4.00505 7.50505 8.749
222:?Zggdfig 109 5.00504 2650 3.30505 6.50E-05 8.749
' 121 6.00504 2269 4.00505 7.001505 8.749
8 - axles Medium 136 7.50504 2052 1.20504 4.375
Stress(75% ihter.) 114 6.00504 2359 _ 1.00504 4.375
1 - axles High 112 5.25504 2692 8.005-05 15.624
Stress(25°/e Int.) 151 4.80E-04 3020 7.00505 15.624
2 - axles High 145 1.10503 1533 1.40504 16.874
Stress(25% lpt.) 137 1.60503 891 1.801304 16.874
3 - axles High 149 1.40503 1105 9.00505 1.30504 17.499
Stress(25%_lnt.) 138 1.50503 1020 8.40505 1.331304 17.499
8 - axles High 118 2.50503 620 8.00505 1.70504 17.499
Stress(25% Int.) 106 2.80503 568 8.00E—05 1.70504 17.499

 

 

 

 

 

 

 

 

 

6.3.1 Dissipated-Energy-Based Fatigue Curves

For the dissipated energy fatigue curve, the initial dissipated energy density is plotted
versus the number of repetitions to failure. Figure 6.4 shows cumulative dissipated

energy density curves for different axle configurations tested under the different stress

63

levels. The overall behavior is as expected: Higher stresses (HS) caused higher dissipated

energies, and more axles in a configuration lead to more dissipated energy as well.

 

 

 

 

 

 

50
45 .
o
40 - :A 3
35 I
.9
in 30 " 1'
° . x
g 25 « .- : A
:1 ' - .I
0 20.. E5 "I 0
.A ," I. I I
15 -1 x. 1' I
‘ . 4' fl , ’
10 'l .m' ”I 1". , I ’ ol
5 q .3 A ':._..axl.',.-_'_.. " ‘ya. I"
o 0",. . __,_,_,,._.-
100 1000 10000 100000 1000000
. N .
---A'°- B-HS ---i-:l-- 3-HS --->e 2-HS --0--1-HS —a—8-MS —e—4-MS
+3-MS —x—2-MS —-e—1-MS mama-LS --a--3-LS --e--1-LS

 

 

 

Figure 6.4 Cumulative DE Curves for Different Axle Configurations

Figure 6.5 shows the dissipated energy fatigue curve. It can be seenthat this curve is
unique. All the different axle configurations with the different interaction and stress
levels are presented. Thus, using this fatigue curve would allow for determining the
number of repetitions till failure for any axle configuration in one step without the need

to build up an axle group from its components. The fatigue model obtained is:

Nf = 2.12 we”55 (5.2)
where (W0) is the initial dissipated energy density in psi of the whole axle group.

However, with the failure criterion used, the failure is assumed when cracks initiate in the

specimen. This might not be the best representation of actual failure in the field, where

cracks have already initiated and propagated from the bottom of the AC to the top. So,
different failure criteria were assumed to check its effect on the dissipated energy fatigue
curves. Figure 6.6 shows the curves obtained when considering different dissipated

energy levels as the failure criteria.

 

 

 

 

 

 

 

 

 

 

1E-02 :
A 1503 -;
E- 5
Q in
Q s
E i
E 1E-04 '5
1E-05 A A A AAAAA: A A AAAAAA: A A, A AL...
100 1000 Nf 10000 100000
I 8-HS-25% A 3-HS—25°/o X 2-I'S'25% X 1+8 0 8-MS—25%
A 8-MS-75% + 4-MS-25% - 3-MS-25% O 2-MS-50°/o D 1-MS
O 8-LS-25°/e O 3-LS-25% + 1-LS

 

 

Figure 6.5 Dissipated Energy Fatigue Curve

The curves obtained are all parallel; thus, a shift factor is sufficient to make up for the
later cracking stages. Since this was not the main focus of the study, no further analyses
were performed to determine what each dissipated energy level corresponded to in terms

of crack development and propagation.

65

 

 

 

 

 

 

15-02
'DE=1
0138:1556
lB-O3"
IDE=2
g ADE=5
El
9
XDE=10
lBrO4-I:
p +DE=-20
CDE=30
+
1505 ‘ ““‘“§ (L ““'“C “ ““‘ ; ‘+ I
100 I” 10000 100000 1000000

 

 

N; at a Given Cumulative DE Level

 

Figure 6.6 Fatigue Curves at Different DE Levels

Two samples were tested under a continuous (i.e., without rest period) haversine load at
medium stress level. The same failure criterion was used to define failure, and the
dissipated energy density for one cycle corresponded to the load value going from 20
pounds (the sustained load value) to the peak, then back to the 20 pound level. The results
were plotted on the same graph with the dissipated energy fatigue curve and are shown in
Figure 6.7. The initial dissipated energy density and number of repetitions to failure from
this test was found to be matching with the dissipated energy fatigue curve.

Another two samples were tested under a load pulse simulating a whole truck The truck
used, truck number 13 in the Michigan Trucks table (check appendix), consists of a
steering axle, front tandem axle, a tridem axle, and a rear tandem and tridem axles

consecutively from front to end. The truck with its axle loads is shown in Figure 6.8. The

66

whole truck is treated as one load pulse, and the dissipated energy density is determined
for the whole truck. The rest period was determined based on the same ratio used for the
axle groups (1 loading to 4 rest period). The loading duration was taken from the point
when the influence of the steering axle started till the response due to the final axle died.
The results are presented in

Figure 6.7 below, and it can be seen that it matches with the dissipated energy fatigue
curve. Therefore, no further fatigue testing was performed for trucks or axle groups since
the dissipated energy fatigue curve was found to be unique regardless of the load pulse.
The procedure used to determine the truck factors of the rest of the trucks will be

presented later.

 

 

    

 

 

 

1.00E-02 =
. DEMasterFatigueCurve
6.

1005-03-5 (figure 5)
‘2 I
.2:
E b
Ill
.0

1'OOE.O4JE

1.00E-05 . - A‘.“-: L ‘ ““*‘: ‘ A AAA-AA It

100 1000 10000 100000
"1
I Continuous Pulse A Truck 13

 

 

 

Figure 6.7 Continuous Load Pulse and Truck 13 Results

67

 

 

: Loads in Pounds
9’ 3'6'v 9' , 3'6' 3’65 9’ v 3'6'v 9' , 3’6' 3'6'

16.400 16.000 16,000 ‘ 13.000 13,000 13,000 13.00013,000 13,000 13.000 13.000

 

 

 

 

 

 

 

 

 

 

 

Figure 6.8 Truck Number 13

6.3.2 Stress Based Fatigue Curves

Three axle configurations (single, tridem and 8 axles) were tested under three different
stress levels (Low, Medium and High). The stress fatigue curves were obtained by
plotting the stress level versus the number of load repetitions to failure. The number of
repetitions to failure was determined using the same failure criterion as that for the
dissipated energy fatigue curve (based on dissipated energy). As expected, at a constant
stress level, the number of single axle repetitions to failure was higher than that of a
tridem, which in turn, was higher than that of the 8-axle group. Note that for multi-axles
and truck analysis, a stress-based fatigue curve would need to be determined for each

configuration separately. The stress fatigue models are:

1- axle :Nf = 27.25 ( U )-2.I.?04 (6.3)
3 — axles : N, = 36.76 ( 0243457 (6.4)
8 — axles : N, = 27.875 ( arm” (6.5)

68

 

 

 

 
 
 

 

 

 

 

 

 

 

 

 

100 :

E 1-ax5:y=672.67x'°°“94-

- 3-axhs:y=774.81x'°'5418
‘5‘: ' 8-axles:y= 533.47x'0'5296i
E: -. ..

10 -: ‘‘‘‘‘
g t
1 1 I l l I I I I I I I I l I I I I I I I I J I I I I
100 1000 N 10000 100000
r
— Single —— Tridem ------- 8-aides
Figure 6.9 Stress Fatigue Curves

6. 3.3 Strain-Based Fatigue Curves

Stain fatigue curves are the most used fatigue curves for asphalt concrete. However, the
way failure is defined varies from researCher to another. In general, when using a strain
controlled test, the strain level is plotted versus the number of load repetitions to failure;
on the other hand, in a stress controlled test, the initial strain is plotted versus the number
of load repetitions to failure. In this study, the indirect tensile test performed runs in a
stress controlled mode, and thus the initial strains were plotted versus the number 'of load
cycles at which the value of the cumulative dissipated energy density reached the SEC
value.

When testing specimens under a multi axle configuration, it was noticed that the strain
peak value increased significantly from the first peak, to subsequent peaks (Figure 6.10).
This is due to the strain accumulation from one axle response to another and the fact that

the test is a stress controlled test. Two strain fatigue curves were generated based on: 1)

69

first strain peak fatigue curves, and 2) last strain peak fatigue curve. The single pulse load

results were the same for both fatigue curves since the response has only one peak.

 

 

9.E-05
8.E-05 -
7.E-05 " fi
5 6.E-05 -
a, 5.5-05 ' Last
'3 4.E-05 - . Peak
E" 3.E-05 - First
2.5-05 - Peak
1.E-051- NM
0.5+00 V .V a -

0 0.5 , 1 1 .5
Time (sec)

 

 

 

 

 

 

 

 

 

Figure 6.10 Typical Tensile Strain Response from ITT Under Multi Axle Load
Configuration

i) Fatigue Curves based on First Peak Strain: Figure 6.11. shows the fatigue
curves obtained from plotting the first strain peak (63;) versus the number of
repetitions to failure (same failure criterion used as above). For a constant
stress level, the first peak strain values are the same for single, tridem and 8
axles. This is expected since for the first peak, there is still no accumulation of
strains due to the multiple axles. Thus, at a constant strain level, the number of
repetitions to failure increases as the number of axles decreases. This means
that a fatigue curve needs to be established for each axle configuration. The

fatigue models obtained are:

l—axle :lvf = 0.0731 80,: )‘2342 (6.6)

70

3 — axles :N, = 0.0591 60,, )‘2’72 (6.6)

8 — axles :N, = 0.0616 80,. )‘2479 (6.6)

 

 

Strain

1 5-04

1 E-05

 

I V'rT

  
    

 

1-a1de: y = 0.0022x‘°‘427

3-axles: y = 0.0022x'°'46°5
8-axles: y = 0.001x‘°°‘°3‘

 

1 0000
------- 8-a1des

 

 

 

1 00 1 00000

—1-axle

 

 

ii)

Figure 6.11 Fatigue Curves based on First Peak Strain

Fatigue Curve Last Peak Strain: To overcome the need of a separate fatigue
curve for each axle configuration, the. last peak strains (801) were plotted

versus the number of repetitions to failure (Figure 6.12). 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, as

shown in Figure 6.12. The fatigue model obtained is:

N , =0.00003777 50L 24-92302 (6.9)

71

 

 

113-03

 

'T""

y = 000003777964"4903
’ R2 .'-= 0.94

 

 

E 1504-

S

 

 

 

1305 A A LAAAAJA A A LILJIII A_ A LAAAAA
T I

100 1000 10000 100000
Nf

- I 8-HS-25% A 3-HS-25% X 2-HS-25% X l-HS 0 8-MS-25%
A 8-MS-75% + ALMS-25% - 3-MS-25% O 2-MS-50% U l-MS
. 8-LS-25% 0 3-LS-25% + l-LS

 

 

 

 

Figure 6.12 Fatigue Curve for All Axle Configurations based on Last Peak Strain

6.3.4 Comparison between the Difi'erent Fatigue Curves:

The stress and the first peak strain fatigue curves are not the best prediction models when
analyzing multi-axle configurations or trucks since any axle configuration. would need to
have its own fatigue curve. On the other hand, using the last peak strain fatigue curve
dictates using stress controlled fatigue tests since in a strain-controlled test, there will not
be any accumulation of strains from the first axle to the following one (although a similar
stress curve might be obtained in a strain—controlled test, but since no strain controlled
tests were performed in this study, such curves could not be established). When using the
dissipated energy fatigue curve, all these problems can be overcome. Additionally, the

last peak strain fatigue curve cannot be used to determine truck factors because the

72

relatively long rest period between the axle groups in a truck reduces the interaction
between these groups, and therefore, under estimates the last peak strain. Moreover, there
is less scatter in the data when using the initial dissipated energy density versus using the
last peak strain. This can be visually seen when comparing Figure 6.5 to Figure 6.12. It is
shown as well in the “R2” values for both curves. (Note that when using the last peak
strain, the strain values used are still considered as initial strains). Therefore, the
dissipated energy fatigue curve is recommended to be used when analyzing multiple

axles and truck configurations.

73

Chapter 7 - Load Equivalency, Axle and Truck Factors:

7 .1 Introduction

In this chapter, the values of Load Equivalency (LEF), Truck (TF) and Axle Factors (AF)
values are determined using the fatigue curves established in the previous chapter, and
using the mechanistic prediction models mentioned in section 2.3.3. When calculating
LEFs, TFs and AFs from the fatigue curves, the initial values of dissipated energy and
strain were determined for the whole axle combinations, and used in the fatigue models
(based on DE or based or strain) to determine the fatigue life from the combination under
study. For the mechanistic prediction models, 1) the initial dissipated energy and strains
from single pulses representing peak and peak-midway values we obtained 2) these
values were used to determine the fatigue life, and 3) Miner’s hypothesis is applied to
determine the fatigue life of the whole axle configurations from their components. Some
of the terms used in this chapter are defined below:

The Load Equivalency Factor (LEF) is defined as the relative damage of an axle group or
a truck to that of a standard axle, where damage is the inverse of the number of

repetitions till failure.

LEF _ Damage (axle configuration) _ Nf (axle configuration)
Damage (I8 - kip standard axle) Nf (standard)

 

 

(7.1)

The Truck Factor (TF) is defined as the relative damage of an axle group or a truck to
that of a standard axle, where damage is the inverse of the number of repetitions till

failure.

74

The Axle Factor (AF) is defined as the relative damage of an axle group to that of a
single axle carrying the same load as any of the axle group components. For example, a
39-kip tridem AF is determined as:

AF _ Damage(39 - kip tridem) _ Nf(13 - kip single)

_ 7.2
Damage (13 - kip single) Nf (39 - kip tridem) ( )

 

 

The AF, TF and LEF per tonnage are defined as the AF, TF and LEF normalized by the
total load carried by the axle configuration, respectively. Using the per tonnage values
allow for a better understanding of the relative damage caused by the different axle
configuration while carrying the same total gross weight, and thus allow for determining
the most efficient configuration to carry a certain load.

The initial procedures used to determine these values consist basically of building up the
truck or axle group from its axle components and computing the damage based on
Miner’s hypothesis. However, in this study, the LEFs, AFs and TFs are calculated
directly by simulating the whole truck/axle group as one load pulse in an indirect tensile
cyclic test.

Both initial dissipated energies and strains were used with their corresponding fatigue
curves to determine the number of repetitions to failure. The main advantage of using this
approach is eliminating, or at least significantly reducing, the error in the results due to
the variability in specimen and testing conditions. The same specimen was used to
determine the initial dissipated energy density for all axle groups and trucks studied, and
thus eliminating the variability of air void content and the asphalt concrete internal
structure. Additionally, performing all the tests while the specimen was still in the same

position in the loading frame decreased any errors due to specimen misalignment with the

7S

loading strips. Trucks consisting of up to 11 axles and axle groups of up to 8 axles were
studied. Three samples from mix I were tested under different load combinations for 15
cycles each to determine the initial dissipated energy density and strains. The results

obtained are presented in the following sections.

7.2 Axle Factors

As mentioned previously, the Axle Factor (AF) is defined as the relative damage of an
axle group to that of a single axle carrying the same load as any of the axle group
components. The effects of thickness, and thus interaction level, and speed (load

duration) on the axle factors were studied using 13-kip axles.

7.2.1 AF for Different AC Thickness

Thin, intermediate and thick asphalt concrete layers were modeled through high (7 5%),
medium (50%) and low (25%) interaction levels between the axle components of an axle
group (see chapter 6 for proper definitions). Figure 7 .1 shows the AF for single, tandem,
tridem, 4- and 8-axles at the different interaction levels. The results showed that there is
no significant effect of the interaction level on the axle factor. Figure 7.2 show the axle
factors per tonnage. The AF/Tonnage is defined as the axle factors divided by the total
weight carried by all the axle group components. Similarly, there is no significant effect
of the interaction level on the AF/Tonnage. Therefore, it can be concluded that the
thickness of the AC layer has no effect on the relative damage between different! axle
configurations. Note that the number of repetitions to failure changes as the thickness

change for each of the axle groups.

76

7.2.2 AF for Different Vehicle Speeds

To simulate different axle speed values, the duration of the load cycles was modified.
However, the same ratio of the loading/unloading to rest period was maintained. Three
velocities were studied: 27 mph, 40 mph and 60 mph. Again, the AF and AF/Tonnage
were calculated. Figure 7.3 shows that the fatigue life of different axle configurations
increases as the speed increases. Figure 7.4 shows that the change in the AF is not as
significant as the change in the fatigue life. Figures 7 .5 and 7.6 show the effect of speed
on the hysteresis loop, and thus the value of dissipated energy density,for single and 8-
axles. This increase in the dissipated energy density explains the increase in the fatigue

life with an increase in the velocity.

7.2.3 Summary of Effect of Axle Groups

Figures 7.1, 7.2 and 7.4 show that using multi axles increases the total fatigue life of an
asphalt mix. The increase in fatigue life is much more significant when going from a
single to tandem and tridem axles; whereas the value of AF/Tonnage starts to even out as
the number of axles reaches 7 and 8. This implies that using an 8-axle configuration to
carry 104 kips is much better that using 8 separate axles carrying 13 kips each.

To compare the results obtained from this study with those from the AASHTO findings,
the LEF values of the 13-kip single, 26-kip tandem and 39-kip tridem were used to

calculate the corresponding axle factors. The AF was calculated as:

_ LEF(tandem or tridem)

. (7.3)
LEF(srngle)

 

77

The AASHTO AF values for the tandem and tridem axles were calculated to be 1.38 and
1.49, respectively. The AF values for the tandem and tridem from this study were found
to be 1.57 and 1.95, respectively. It should be noted that the LEFs from the AASHTO
study are based on Pavement Serviceability Index (PSI) from the AASHO road test and

not from laboratory fatigue tests; therefore, the difference between the two is expected.

7 .3 Load Equivalency Factors

The Load Equivalency Factor (LEF) is defined as the relative damage of an axle group to
that of a standard axle. The same results were obtained for the LEFs as the AFs. The only
difference is that the values of the AF and AF/Tonnage are lower since the standard 18
kip single axle will have a lower fatigue life than the 13 kip single axle. However, all the
results were presented in the form of AF inthis study since the effect of the usage of axle
groups would be more obvious when compared to a similar single axle instead of a single

axle with a different weight. The results are summarized in Table 7.1 below.

78

Table 7.1 LEF Results

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Nf LEF LEF/Tonnage

1 axle 18-kip 5388 1.00 1.00
1 axle 13-kip 7750 0.70 0.96
2 axles 4889 1.10 0.76
3 axles 3876 1.39 0.64
25% 4 axles 2889 1.87 0.65
Interaction 5 axles 2377 2.27 0.63
7 axles 1893 2.85 0.56
8 axles 1707 3.16 0.55
2 axles 5987 0.90 0.62
. 3 axles 4592 1.17 0.54
50% 4 axles ' 3577 1.51 0.52
Interaction 5 axles 2992 1.80 0.50
7 axles 2477 2.18 0.43
8 axles 2289 2.35 0.41
2 axles 5644 0.95 0.66

3 axles 4155 1.30 0.60 ‘
75% 4 axles 3431 1.57 0.54
Interaction 5 axles 3058 1.76 0.49
7 axles 2549 2.11 0.42
8 axles 2439 2.21 0.38

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

o 25% Interaction

I

4

5

Axle No.
:1 50% Interaction

A 7 5% Interaction

 

Figure 7 .1 Axle Factor for Different Interaction Levels

79

 

 

 

 

 

AF / Tonnage

p
8

p
8

8

 

 

 

 

 

 

 

O

Axle No.
0 25% Interaction CI 50% Interaction A 75% Interaction

 

Figure 7.2 Axle Factor per Tonnage for Different Interaction Levels

 

 

Nf

 

 

 

 

 

 

 

 

No. of Axles

 

Figure 7.3 Nf Vs No. of Axles for Different Speed Values

80

 

 

 

 

 

 

 

 

 

 

 

 

 

6
O
5...
€44
:1
is. 3~
0
E
2-
1..
0 l l l l l l l l
0 1 2 3 4 5 6 7 8 9
No.0foles
060MPH U40MPH A27MPH

 

 

 

Figure 7 .4 Axle Factor for Different Speed Values

7.4 Truck Factors

Truck Factor (TF) is defined as the relative damage of a truck to that of a standard axle.
ten trucks were selected for laboratory testing. The trucks were chosen to cover the all
axle configurations that are used in Michigan. The trucks used are: TrucksO, Truck 1,
Truck 2, Truck 3, Truck 4, Truck 10, Truck 13, Truck 14, Truck 17, Truck 19, and Truck
20. (Check Table 7.2 and the appendix for truck details). The initial dissipated energy
density for all the trucks and the standard axle was determined twice, each time from a
different sample. The fatigue life for each truck was determined using the dissipated
energy fatigue curve, and the corresponding truck factors and truck factors per tonnage
were calculated.

Figure 7.7 shows the truck factors, and Figure 7.8 shows the truck factors per tonnage.

From the latter figure, can be seen that Truck 1 is the most damaging per tonnage. Truck

81

1 is a 2-axle single body truck that consists of a 15.4 kip front steering axle and a single
18 kip standard axle in the rear. Trucks 13, 14, 17, 19, and 20 have very similar low truck
factors per tonnage because their total load is distributed over larger axle groups (Table
7.2). The decrease in the truck factor per tonnage when going from Truck 1 to Truck 4
emphasizes the same finding mentioned in section 7.2.3 that multi-axle groups are less
damaging than individual axles when considering the load they carry. Truck 20, which
has the most axles and least axle groups, is the most efficient between all the trucks

investigated.

82

Table 7 .2 Truck Axles and Axle Groups

 

No. of Axle No. of

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Truck No. groups Axles Truck Configuration
truck 0 3 5
truck 1 2 2
truck 2 2 3
truck 3 2 4
truck 4 2 5

truck 10 6 7

truck 13 5 11
truck 14 6 11
truck 17 3 10
truck 19 3 10
truck 20 3 11

 

 

 

 

 

83

 

 

 

Stress (psi)

 

8.4
60 MPHI
7-1

 

 

81
40MPH|
7—1

 

10 r v
9-

8....
7, 27MPH|

6...
5...
4-i
3-1
2..
l-l

 

 

 

O r r
0.E+00 l.E-05 2.E-05

l

3.E-05

l l l I

4.E-05 5.E-05 6.E-05 7.E-05
Strain

8. E-05

 

Figure 7.5 Effect of Speed on Dissipated Energy of a Single Axle

84

 

 

S tress (psi)

 

60 MPH

 

 

g.
7_ 27MPH

 

o _-__A *‘- J
I 1' ‘r I l 1 l l l

0E+00 213—05 413-05 6E-05 813-05 113-04 113-04 113-04 215-04 213-04

Strain

 

Figure 7.6 Effect of Speed on Dissipated Energy of an 8-Axle Group

85

 

 

 

 

 

 

 

 

I sample 135
I sample 125

 

 

 

 

    

 

 

8L

_ _ _ _ a
7 6 5 4 3 2 1 0

6.328 8.2% 3.55:.

o—x< Em

 

 

Figure 7.7 Truck Factors

 

 

 

 

 

 

 

I sample 135
I sample 125

 

 

 

 

 

 

 

 

   

 

 

ouEeEuSoah :95;

 

 

Figure 7.8 Truck Factors per Tonnage

86

7.5 Evaluating Different Mechanistic Approaches for Determining AF and TF

In the mechanistic fatigue prediction of asphalt pavements due to different axle groups
and trucks, the common practice is to build up the truck or axle group from its axle
components and compute the damage based on Miner’s hypothesis. Two approaches are
typically adopted for axle groups: (1) Using the peak values, and (2) using the difference
between the peak and midway values of the response. As for trucks, the damage is
calculated by summing up the damage from the individual axles. These approaches use
the fatigue curves obtained from single haversine or continuous sinusoidal load pulses to
determine the damage/fatigue life of the individual axles. In this study, the fatigue life of
an asphalt mixture under different trucks and axle groups was determined directly from
the indirect tensile cyclic load test by using load pulses that are equivalent to the passage
of an entire axle group or truck. Additionally, the fatigue life under individual axles was
determined for the purpose of predicting the damage based on the procedures mentioned
above. The predicted and measured fatigue lives were compared for the different axle
groups and trucks. Both dissipated energy and strain fatigue curves were used to
determine the axle factors, while only the dissipated energy fatigue curve was used for

determining truck factors.

7.5.1 AF from Strain Fatigue Curve

Single, tandem, tridem, 4-axle, 5-axle, 7-axle and 8-axle load pulses were tested to
determine their initial strains (last peak) on the same specimen. Additionally, single
pulses with peak magnitudes equal to 25%, 50% and 75% of the single peak stress were
applied on the same specimen and their corresponding initial strains were determined.

The strains from the latter pulses were used in the peak-midway method of building axle

87

groups. Details on calculating Nf of an axle group from its components (whether peak-
peak or peak-midway) were mentioned previously in section 2.3.3.
Figures 7.9 and 7.11 show the measured and calculated using peak-midway and peak

methods respectively for the six axle groups at three interaction levels. Figures 7.10 and
7.12 show the percentage difierence between measured and calculated Nf-values as well

as to this difference divided by the number of axles in each axle group, using peak-
midway and peak-peak methods, respectively.

It can be seen from these figures that the peak-midway method results vary widely
depending on the interaction level. While for 25% interaction, the peak-midway method
over estimates the damage, the same method under estimates the damage for higher
interaction levels. Additionally, the percentage difference per N does not follow any
obvious trend whether between the different axle groups within an interaction level or
between the interaction levels in general. Therefore, it is hard to correct for the error
resulting from using this method. On the other hand, the peak-peak method is more
consistent regardless of the interaction level. Moreover, there is an obvious trend between
the percentage difference and the number of axles. A linear correction factor of the form
shown in equation (7.4) below can be used to correct the calculated Nf using the peak-

peak method.

Cf: -0.0116 (N) + 0.1748 (7.4)

where: C; is the correction factor per axle.

N is the number of axles in the axle group

88

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2700 9
2400 \ \\ 8
2100 - -- 7
\ \ \ W
181]) — 5—1 —- T 6
\ \ 8
1500 4 -— — —— —~ 5 '53
e-r ,. <
Z \ ‘5
1200 \ —- a a. H —-—i 5— —~ 4 g
\ \M z
900 _ —— P —4 ——. L — H~ 3
\:' H\ Y
600 F —— —— H —"‘=" — ~‘>~...—- 2
mw—L— 040 —e_—4 _e—M
0 ‘r 1 O
25% 50% Interactionlevel 75%
12:] No of Axles + Measured -+- Calculated

 

Figure 7.9 Fatigue Lives under Different Axle Groups Using Peak-Midway Method from

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Strain Fatigue Curve

270% 9

240% I. 8

210% . __ 7

u 180% —— L / —— ~- 6
8 / 8
a 150% —— _ — ~~ 5 i
o <
E / “5
g 120% —— —— — — / — ~—- ——4 g
68 Z

60% -—— L i‘ — A —— — —— —-2

30% a — —— —- r— ITr—L—ii- 1

0., n H h o

25% 50% Interaction Level 75%
C23 No of Axbs + % Difference O % Difference / N

 

Figure 7.10 Percent Difference between Measured and Calculated Fatigue Lives under
Different Axle Groups Using Peak-Midway Method from Strain Fatigue Curve

89

 

 

 

 

 

 

 

 

 

 

”5° \\\ ‘x J\\\ l"
1500 \ *— \ ' 6

 

 

 

 

 

 

/
//
L l
Nofilf Axles

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

H 1250
z \ A
1000 V l— \ {l _' \ .r '
750 R34 —‘\L:"l‘ x>4 3V E ‘L :1 r-fl —- 3
500 __ k __ L\> _l _ ‘>ti%‘l _2
“‘9 ‘\e \»
2501————1———-——-—*—-—————-L——4~~1
0 r r 0
25% 50% Interaction Level 75%
:1 No of Axles + Measured -+- Calculated

 

Figure 7 .11 Fatigue Lives under Different Axle Groups Using Peak Method from Strain
Fatigue Curve

 

 

 

60.0% 8

52.5% / i _- 7
45.0% ll rd 5 6

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

37.5% — '—
3 / / \ 2" i
a 30.0% —-l — .d-R‘Id F-4<
D / f \ W } ii ‘5
e
a? 22.5% i F— — — / T“ ’— J ""‘ — F 7" 32
159% —‘ —‘ r * y=-0.0116x+0.1748 ‘7 “'7 — ‘1 r 2
J , , 2
7.5% 7 -— lfi. — 1— *— "*1
0.0% 7 l , r 0
25% 50% InteractionLevel 75%
1:1N0 of Axles + % Difference + % Difference IN

 

Figure 7 .12 Percent Difference between Measured and Calculated Fatigue Lives under
Different Axle Groups Using Peak Method from Strain Fatigue Curve

90

 

 

 

 

Nf

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2250 9

m x \ Ah 8

1750 \\ k\ \ "7

1500 \ \K i — x l—r — —-6
1250 \ _ ”’_ —' "h' 5:
Ian Ni __ ”S: __ ’3 _ 5-4:
A \ §‘ 2

750 ~ — ‘ — ><‘§. ~ .u‘»"'3

500 ~—-—~—-— +——~————-« r—i—i—«w—a-z

250--—-~—l——--~————%———--——--1
0 r 0

25% 50% Interaction Level 75%
:3 No of Axles + Measured + Calculated

 

Figure 7 .13 Fatigue Lives under Different Axle Groups Using Peak Method from Strain
Fatigue Curve (After Correction)

 

 

 

10

 

27%

 

24%

 

21%

 

 

 

18%

 

 

 

15%

 

 

 

% Difference

12%

 

9%

 

6%
3% r

l

 

 

 

 

 

 

 

 

 

 

/
I i __

—

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

l?

 

 

 

l\[

ll\a
[Tl

 

 

 

 

 

l\

 

 

r-6

l
U!
No of Axles

—-3
—-2

 

 

 

25%

T I

50% Interaction Level
[:1 No of Axles

75%

-'- % Difference

 

Figure 7.14 Percent Difference between Measured and Calculated Fatigue Lives under
Different Axle Groups Using Peak-Peak Method from Strain Fatigue Curve (After

Correction)

91

 

 

The final Nf can be calculated as:
(Nflfinal = ( Nflcalculated *(1 + N * Cf ) (75)

where: (Nficalculated is the calculated Nf using Miner’s Hypothesis.

Figure 7.13 shows the calculated Nf using peak-peak method with the correction factor
versus the measured ones from the fatigue curves for the six axle groups at the three
interaction levels. By comparing Figures 7.9, 7.11 and 7.13, the increase in the prediction
accuracy is very obvious. This can be also seen from Figure 7.14 where the percentage

difference was reduced to less than 16% for all axle configurations and interaction levels.

7.5.2 AF from Dissipated Energy Fatigue Curve

Single, tandem, tridem, 4-axle, S-axle, 7-axle and 8-axle load pulses were tested to
determine their initial dissipatedenergy on the same specimen. Additionally, single pulses »
with peak magnitudes equal to 25%, 50% and 75% of the single peak stress were applied
on the same specimen and their corresponding initial dissipated energies were
determined. The dissipated energies from the latter pulses were used in the peak-midway
method of building axle groups. The same procedure mentioned in the previous section

was used for determining Nf of an axle group.
Figures 7.15 and 7.17 show the measured and calculated eralues using peak-midway

and peak methods respectively versus the measured ones from the fatigue curves for the

six axle groups at three interaction levels. Figures 7.16 and 7.18 show the percentage

difference between measured and calculated Nf-V31UCS as well as this difference divided

92

by the number of axles in each axle group using peak-midway and peak-peak methods,
respectively.

It can be seen from these figures that the peak-midway method results vary widely
depending on the interaction level. For 25% and 50% interaction, the peak-midway
method over estimates the damage. The same method under estimates the damage for
75% interaction level for some axles and over estimates it for others. On the other hand,
the peak-peak method is more consistent regardless of the interaction level. Moreover,
there is an obvious trend between the percentage difference and the number of axles. A

linear correction factor of the form shown in equation (7.6) below can be used to correct

the calculated Nf-values using the peak method.

Cf: 0.137 (N) (7.6)

where: Cf is the correction factor per axle.
N is the number of axles in the axle group
It should be noted that when calculating the percentage difference to check accuracy of

the prediction models, it is calculated as the difference between the measured and
calculated Nf-values divided by the measured one. However, to calculate the correction
factor, this should be modified to: measured minus calculated divided by calculated since
when using the correction factor, the only known term is going to be the calculated Nf
only. This explains the difference between the average value of percentage difference per
N shown in Figure 7.18 and the correction factor shown in the equation. The final Nf can

be calculated as shown in equation (7.5) in the previous section.

93

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

41H) 8
3500 ‘ ——\ H7
3°°° \ r \ - \ —
2500 — ~— IN —— r-sg
zzooo\ __ \‘m___ \ '45
N i. e
1500 5— kxfi H‘Qifi —- —— >-—~3 z
e ‘7‘
\
1000 —— -\—— —-———-——~ —-~—————-2
ma“.
500-~——4~————————F—7—-—~——~————-1
0 ‘r i 0
25% 50% Interaction Level 75%
[:1 No of Axles + Measured + Cakmlated

 

Figure 7 .15 Fatigue Lives under Different Axle Groups Using Peak-Midway Method from

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

DE Fatigue Curve

60.0% 8

52.5% /\ p.7

45.0% 7 ”A. -—i — ”6
3 37.5% — _ __ .__ 5
i /l’ i
a 30.0% "—" "_‘ _ "_J — '_ —"4.5
e \ l 2
B‘22.5%. “‘1’“ —— —-Z———3

15.0% lL_— ._ ~~L ———— ——-~2

Ebb . NF,/ IR
7.5% -~ —— —— HBT —.~— —— — 7'5: —- ~ +1
0.0% , H p H, I y 1' fl 0
25% 50% 75%
Interactionlevel
:1No of Axles +96 Difference O % Difference/ N

 

Figure 7 .16 Percent Difference between Measured and Calculated Fatigue Lives under
Different Axle Groups Using Peak-Midway Method from DE Fatigue Curve

94

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4000 8
3500 —\ ~r7
3000 \ -— \ _. -_6
X \ j I \
25(1) \ "—1 \ l— \ ——* ”58
.. \\ \ \ \ 2
z 2000 —— —— — — — ~— ——4
in. \iL “5
X \ 2
1500 —- i— -— — =.. ~ —- fic-«3
\ ix. \‘ \
1000 ——~~q~— 4_.<_ —><—F52
~'.'\-~e Ne ‘N-le
500~aL———-—~L————————-~—~—— ——————~1
o 0
25% 50% Interaction Level 75%
:lNoof Axbs +Measured +Cahuhted

 

Figure 7 .17 Fatigue Lives under Different Axle Groups Using Peak Method from DE
Fatigue Curve

 

 

 

 

 

 

 

 

 

60.0%
52.5% a. ‘-
45.0% ~ — — —

.-

3 37.5% —— — — — -

a .

r ./

. / ‘ - / ” i “

a

39 .— —_ L ., _ e— 4 L

Ll—d y=0.137x — — — i
—— _ — &

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

_E'Hllli

 

 

 

 

 

 

 

 

 

 

 

 

No of Axles

 

 

25%

 

50% Interaction Level

I

75%

 

[:1 No of Axles -l- % Difference C % Difference IN —Linear (% Difference / N)

 

Figure 7 .18 Percent Difference between Measured and Calculated Fatigue Lives under
Different Axle Groups Using Peak Method from DE Fatigue Curve

95

 

 

 

 

Nf

 

4500

\O

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4000 8
3500 4\ e ‘ _X __7
3000 \ H J l \ ——l —-6
2500 —1 F" \ l— -- 5%
h
2000 J —3 —— —— \Ra ~ 543
WE N z
1500 ~— ‘N-e _ a —4 —-3
\“l
1000 —*—t—-—1 ——————-— ——rJ—fl~-2
0 0
25% 50% InteractionLevel 75%
DNoofoles +Measured +Calcuhted

 

Figure 7.19 Fatigue Lives under Different Axle Groups Using Peak Method from DE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Fatigue Curve (After Correction)
22.5% 9
20.0% 8
17.5% —— V7
g 15.0% ~— ~ — ~~ 6
E 125% — ._1 —- ”5%
Q L e.-
E 0.0% "1 —- “r -— r— ~~4§
2
517.5% "\ Zj—‘HWZE—h— /:i___...3
a _ _t __- a:_s
2.5%a——J—~————J— ——-~\rl ~~R51
0.0% r r 0
25% 50% ' 75%
Interactionlgvel
CJNoofobs +%Difference

 

Figure 7 .20 Percent Difference between Measured and Calculated Fatigue Lives under
Different Axle Groups Using Peak Method from DE Fatigue Curve (After Correction)

96

 

 

7. 5.3 Summary of Mechanistic Approaches for Determining AF '

The peak-peak method under-predicted the fatigue life regardless of the interaction level,
the number of axles and the fatigue curve used. Therefore, a correction factor was
calculated to reduce the errors obtained from this method and reach more reasonable
results. On the other hand, the peak-midway method results were inconsistent, and varied
with the interaction level, fatigue prediction model and number of axles, making it harder
to correct the results obtained. Therefore, whenever it is not possible to use the fatigue
curves to determine the damage of the whole axle at once, the peak-peak method is
recommended to predict the fatigue life of an axle group with the correction factors

mentioned in equations (7.4) and (7.6).

7.5.4 TF from Dissipated Energy Fatigue Curves

Load pulses equivalent to Trucks 0, 1, 2, 3, 4, 10, 13, 14, 17, 19, 20, single (13 kips, 15.4
kips, 16 kips and 18 kips), tandem (2-13 kips and 2-16 kips), tridem (3-13 kips), 4-axle
(4-13 kips), 5-ax1e (5-13 kips), 7-axle (7-13 kips) and 8-axle (8-13 kips) were applied to
the same specimen and- their corresponding initial dissipated energies were obtained.

Using the dissipated energy fatigue curve, the fatigue life was determined for all these
axle configurations. The Nts obtained for the trucks were considered as the measured
fatigue life, and thus used as a reference to check the accuracy of building up trucks. Two

procedures were used for calculating the Nf of a truck:
i) Using individual axles method. In this case, Nf of Truck 13, for example

(Figure 6.8), was calculated from Nf-values of a single 15.4-kip axle, a two

97

l6-kip single axles and eight 13-kip single axles. Note that this is the common
practice in Mechanistic Design Procedures.
ii) Using axle groups. In this case, N f of Truck 13. was calculated from Nf-values
of the single 15.4-kip axle, a 32-kip tandem axle, two 39-kip tridem axles and
a 26-kip tandem axle.
Figure 7.21 shows the measured and calculated Nf'VHlUCS using individual axles and axle
groups for the eleven trucks at three interaction levels. Figure 7.22 shows the percentage
difference between measured and calculated N pvalues from both methods. Additionally,
the percentage difference divided by the number of axles in each truck is also shown in
the same figure for the methods using axle groups.
It can be seen from these figures that the method using axle groups gives more accurate
results than the method using single axles. For Truck 1, the Nf calculated from both
methods coincide since this truck has only two single axles. AdditiOnally, as the ratio of
the number of axles to axle groups increases, the error obtained from the individual axles
increases as well. Figure 7.22 shows that there is an obvious trend between the
percentage difference from the method using axle groups and the number of axles. The
percentage difference per N is constant, and thus a correction factor can be applied when

using the method with axle groups. The correction factor is of the form:

cf: 0.038 (N) (7.7)

where: Cf is the correction factor per axle.

N is the number of axles in the axle group

98

 

 

 

 

1650 11
1500 10
1350 9 g.
1200 8 E
1050 .7 :9:
2 90° 6 E
' 750 5 g
61!) 4 4
450 3 ‘3‘
300 2 Z
150 1
0 . 0
truckO truckl truckZ truck3 truck4 truck 10 truck 13 truck 14 truck 17 truck 19 truckm
m Noofob Groups :Noofobs +Measured +Cabulated(Axbs) +Cabuhted(Axb group)

 

Figure 7 .21 Trucks Fatigue Lives Using Axle Groups and Individual Axles from DE Fatigue
Curve

 

._:
H

82.5%
75.0%
67.5%
60.0%
52.5%
45.0%
37.5%
30.0%
22.5%
15.0%

7.5%

0.0%

H
O

% Difference
No of Axles / Axle groups

=0.038 x

 

OHNUJ§MGQNU

uucko truckl truck2 truck3 truck4 truck 10 truck 13 truck 14 truck 17 truck 19 truck20

“NoofobGoups I:Noofoles +%Difl’erulce(fiornaxlegroups)
+ % Difference (fromaxles) O % Difi'erencemomaxh groups)/ N

 

 

 

Figure 7 .22 Percent Difference between Measured and Calculated Trucks Fatigue Lives
from DE Fatigue Curve

99

Figures 7.23 and 7.24 show the Nf obtained from the two methods after correction and

the percentage difference between these values and the measured ones. The reduction in
error is very obvious. It should be noted that for the method using individual axle, the

axle groups were calculated first using the peak-peak method and corrected using
equations (7.4) and (7.5), then these axle groups were used to determine the Nf-values for

the trucks using the correction factor presented in equation (7.7). Therefore, whenever
determining the Nf for the whole truck in one step is not possible, it is recommended to

use the method using axle groups with the corresponding correction factor, or else, use
individual axles to calculate Nf-values of axle groups and then calculate the trucks Nf-

values from these results with applying the corresponding correction factors at each step.

 

~
~

1650
1500
1350
1200
1050

p—e
O

750

450

No of Axles [Axle Groups

150

 

OHNW‘hMG‘lmVD

truckO truckl truck2 truck3 truck4 truck 10 truck 13 truck 14 truck 17 truck 19 truck20

- No of Axle Grorqas E No of Axks + Measured -9- Calculated (Axles) + Calculated (Axb groups)

 

 

 

Figure 7.23 Truck Fatigue Lives Using Axle Groups and Individual Axles from DE Fatigue
Curve (After Correction)

100

 

 

envoy—e
O"

Percent Difference
No of Axles I Axle groups

 

OHNM#MO\~IN\O

truckO truck 1 truck2 truck3 truck4 truck 10 truck 13 truck 14 truck 17 truck 19 truck20

-No of Axle G'oups :No of Axles + % Difference(frornaxle groups) —0— % Difference (fromaxks)

 

Figure 7 .24 Percent Difference between Measured and Calculated Trucks Fatigue Lives
from DE Fatigue Curve (After Correction)

101

 

Chapter 8 - Conclusion and Recommendations

8.1 Conclusions

Based on the experimental results from fatigue testing of asphalt concrete mixes in an

indirect tensile cyclic load test, the following conclusions were drawn:

0

iii)

The stored energy density criterion (SEC), developed in this study, was found to
be as a good failure criterion for fatigue life of asphalt concrete mixes when
using the dissipated energy approach. This failure criterion indicates crack
initiation in the specimen.

The fatigue curves obtained using the SEC value as failure criterion does not
represent field conditions where cracking at failure is at more developed stages.
Nevertheless, similar fatigue curves were obtained at higher dissipated energy
levels indicating that a shift factor might be enough to obtain fatigue

performance at later crack propagation levels.

The initial dissipated energy-based fatigue curve wass found to be unique for
different axle and truck configurations at different stress levels, making it useful
for predicting the fatigue life of an axle group or a truck at once without the need

for summing up the damage from individual axles.

Multi axles were found to be less damaging per tonnage compared to single
axles. Increasing the number of axles carrying the same load results in less
damage. 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

102

V)

vi)

vii)

viii)

numbers. Similar results were obtained for trucks where trucks having more
axles and axle groups had lower truck factors per tonnage than those with single

axles.

Both speed and AC thickness (expressed through the interaction level between
consecutive axles) had no significant effect on the axle factor values for the
different axle configurations investigated, although changes in either of them did

affect the fatigue life.

Using the peak-midway method for predicting the fatigue life of an axle group
was found to be inconsistent and the results varied depending on the interaction

level between consecutive axles and the number of axles in an axle group.

Using the peak method for predicting the fatigue life of an axle group was found
to be more consistent regardless of the interaction level and the number of axles.
A correction factor as a function of the number of axles was developed to correct

for fatigue life calculated from the peak method.

Summing the damage from the axle groups composing a truck was found to
yield a better prediction of truck fatigue life from trucks than using the
individual axles. A correction factor based on the number of individual axles in a
truck was developed to improve the results obtained from using axle groups. It
was also found that using the fatigue life from individual axle to determine the
fatigue life from an axle group then using the latter in determining the fatigue
life of a truck could be used if the corresponding correction factors were applied

in each stage.

103

8.2 Recommendations

The results of this study have led to many interesting conclusions. However, more mixes
need to be tested to be able to generalize the conclusions reached. Additionally, similar
tests should be performed at different temperatures to study its effect on the results.
Finally, it is highly recommended that a different testing setup (flexural beam preferably)
be used to check the consistency of the results under different loading modes and stress
states. The flexural beam test could allow for stress reversals, which are relevant for
longitudinal stresses and strains. This will allow for checking the peak and peak-midway

methods of predicting the fatigue life using longitudinal stress/strain.

104

APPENDIX

105

APPENDIX A - Hysteresis Loops and Trucks

 

 

Stress (psi)

 

 

 

 

0 I I l I T l l
0.E+(X) l.E-05 2E-05 3.E-05 4.13-05 5.E-05 6.E—05 7.E-05 8.E-05
Strain

 

Figure A.l Hysteresis Loop for Single Axle

 

 

Stress (psi)

 

 

 

 

0 l l T r l T l I

0.E+(X) l.E-05 213-05 3.E-05 4.E-05 5.E-05 6.E-05 7.13-05 8.E-05 9.E-05
Strain

 

Figure A.2 Hysteresis Loop for Tandem Axle 25% Interaction

106

 

 

 

 

Stress (psi)

 

 

 

 

O l I l l l l l l
0.E+00 l.E—05 2.E—05 3.E—05 4.E-05 5.E—05 6.E-05 7.E-05 8.E-05 9.E-05

Strain

 

 

Figure A.3 Hysteresis Loop for Tandem Axle 50% Interaction

 

 

Stress (psi)

 

 

 

 

O I — I i I I I i I
0.E+00 l.E-05 2.E-05 3.E-05 4.E—05 5.E-05 6.E-05 7.E-05 8.E-05 9.E-05
Strain

 

 

Figure A.4 Hysteresis L00p for Tandem Axle 75% Interaction ‘

107

 

 

Stress (psi)

 

 

 

 

 

 

 

6.E-05 8.E-05 l.E-04

Strain

4.E-OS

l.E-04

 

 

Figure A.5 Hysteresis Loop for Tridem Axle 25% Interaction

 

 

Stress (psi)

 

 

 

6.E-05
Strain

8.E-05 1.E-04

 

l.E—04

 

Figure A.6 Hysteresis Loop for Tridem Axle 50% Interaction

108

 

 

 

 

 

 

 

0.E+(X) ZE-OS 4.E-05 6.E-05 8.E—05 1.E-04

1.E-04

 

 

Figure A.7 Hysteresis Leap for Tridem Axle 75% Interaction

 

 

Stress (psi)

 

 

 

 

O I — i I i I
0.E+(X) ZE-OS 4. E-05 6.E-05 8.E—05 l.E-04
Strain

1.E-04

 

 

Figure A.8 Hysteresis Loop for 4-Axle 25 % Interaction

109

 

 

Stress (psi)

 

 

 

 

 

j j I j I

2.E-05 4.E-05 6.E-05 8.E-05 1.E-04
Strain

1.E-04

 

 

Figure A.9 Hysteresis Loop for 4-Axle 50 % Interaction

 

 

Stress (psi)

 

 

 

1 I I I I I

2.E-05 4.E-05 6.E—05 8.E-05 l.E-04 1.E-04
Strain

 

1.504

 

Figure A.10 Hysteresis Loop for 4-Axle 75% Interaction

110

 

 

 

Stress (psi)

 

 

_-
_‘___

 

 

I I I I I

2.E—05 4.13-05 6.E-05 8.E-05 l.E—04
Strain

l.E-04

 

 

Figure A.11 Hysteresis Loop for S-Axle 25% Interaction

 

 

 

u —A h!“

 

 

I r I I I I l

2.E-05 4.E-05 6.E—05 8.E-05 1.E-04 l.E-04 l.E—04
Strain

 

2.E-04

 

 

Figure A.12 Hysteresis Loop for S-Axle 50% Interaction

111

 

 

Stress (psi)

 

 

 

 

O I —
OBI-(X) 2.E-05

4.13-05

I

6.E-05

8.E-05 1.E-04

Strain

I I

1.E-04 1.E_-04 2.E—04

 

Figure A.13 Hysteresis Loop for 5-Axle 75% Interaction

 

 

Stress (psi)

 

 

A

I

/ It?”

I I

0.E+00 ZE-OS 4.E-05 6.E-05 8.E-05 1.E-04

Strain

I

1.E-04

 

 

I I

1.E-04 2.E-04 2.E-04

 

Figure A.14 Hysteresis Loop for 7-Ax1e 25% Interaction

112

 

 

 

 

Stress (psi)

 

 

 

O _‘A ‘_ ‘ ‘ - - -
I

I I r I I— I I

 

0.E-I00 2.E—05 4.E-05 6.E-05 8.E—05 1.E-04 l.E—04 1.E-04 2.E-04 2.E-04
Strain

 

Figure A.15 Hysteresis Loop for 7-Axle 50% Interaction

 

 

Stress (psi)

 

 

 

 

0 41—‘ I a r I I T I

0.E+00 2.E-05 4.E—05 6.E-05 8.E—05 1.E-04 1.E-04 1.E-04 2.E-04 2E-O4
Strain

 

Figure A.16 Hysteresis Loop for 7-Axle 75% Interaction

113

 

 

 

Stress (psi)

 

 

 

 

 

0'1 I_fi I I I I

0.E+(X) 2.E-05 4.E-05 6.E-05 8.E-05 1.E-04 l.E-04 l.E-04 2.E-04 2.E-04
Strain

 

Figure A.17 Hysteresis Loop for 8-Axle 25% Interaction

 

Stress (psi)

 

 

 

 

 

0 —— AA— A 4‘“—

I I I I I I I I I

0.1-3+0) 2.E-05 4.E—05 6.E-05 8.E-05 l.E-04 1.E-04 l.E-04 2.E—04 2.E-04 2.E-04
Strain

 

Figure A.18 Hysteresis Loop for 8-Axle 50% Interaction

114

 

 

 

. Stress (psi)

 

 

 

 

I I j I r I I T T

0.E+00 2.E-05 4.E-05 6.E-05 8.E-05 1.E-04 1.E-04 1.E-04 2.E-04 2.E-04 2.E—04

Strain

 

 

 

Figure A.19 Hysteresis Loop for 8-Axle 75% Interaction

 

 

Stress (psi)

 

16
144
124
10-

84

 

 

 

I I I I I

2.E-05 4.E-05 6.E-05 8.E-05 1.E-04 1.E-04
Strain

 

l.E-04

 

Figure A.20 Hysteresis Loop for Truck 0

115

 

 

 

 

 

 

 

 

F _T I l T 1

2.E-05 4.E-05 6.E—05 8.E-05 l.E-04 l.E-04
Strain

1.E—04

 

 

Figure A.2] Hysteresis Loop for Truck 1

 

 

 

 

 

 

 

I f I I I

2.E-05 4.E—05 6.E-05 8.E-05 l.E-04 l.E-04
Strain

1.E-04

 

Figure A.22 Hysteresis Loop for Truck 10

116

 

 

 

 

 

 

 

 

F I T

2.E—05 4.E-05 6.E-05 8.E-05 l.E-04

Strain

l.E-04

l.E-04

 

Figure A.23 Hysteresis Loop for Truck 13

 

 

/ I Loads in Pounds
[_— n
9. - 3.6., ... - 3.6.

7

15.41!) 16.1!” 16.01!) 13.01!) l3.(X)0

 

 

 

 

 

Figure A.24 Truck 0

 

 

 

Z Loads in Pounds

o '10?

‘1

15.400 18010

 

 

 

 

 

 

\13

 

Figure A.25 Truck 1

117

 

 

 

 

 

é Loads in Pounds
9 991‘
s 9- . 3’6'

15.4% 16.0% 16.0%

 

 

 

 

 

 

Figure A.26 Truck 2

 

é Loads in Pounds
9 99¢
, 9' 1 3’6' 3'6'

15.4% 13.%0 l3.%0 13.0%

 

 

 

 

 

 

 

Figure A.27 Truck 3

 

 

g LoadsinPounds
C? . 9999,.

15.400 13.1“) 13.0% l3.0%13,%0

 

 

 

 

 

~10

 

Figure A.28 Truck 4

 

 

 

é Loads in Pounds

 

 

 

 

 

 

 

15.400 16.0% 16.0%

 

Figure A.29 Truck 10

118

so to; o o 01
18.000 18.000 18.000 18.000

 

 

 

Loads in Pounds

15.4% 16%0 16.0% 13.1!» 13.11!) 13,%0 13.0% 13.0% 13.11!) 13.” 13.%0

 

 

 

 

 

Figure A.30 Truck 13

 

 

 

9H Loads in Pounds

“<2 9

15.4% 16.%0 16%0 1311!) 13.0% 13 .W 13 ,%0 l3 .%0 13 .(XX)

 

 

 

 

Figure A.31 Truck 14

 

 

 

 

 

G

13.0)) 13.0% 13.1XX113.%0 130!) 13 ,,%013 %0 13.%0 13,11!)

 

 

 

 

Figure A.32 Truck 17

 

 

 

16.11» 16.%0 13,W13.IXD13,...%013%013(XX)13%013.0%

 

 

Figure A.33 Truck 19

119

 

 

 

 

 

 

 

 

 

 

 

 

15.4% 16.0% 16.0% 13.11!) l3.%013.0%13.(XD13.0%l3.W13.%011W

 

Figure A.34 Truck 20

120

 

APPENDIX B - Fatigue and Specific Gravity Tests Results

Table B.1 Specific Gravity Results for Tested Specimens of Mix I

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Specimen # Gmm Wt '" °" W‘ s""' w‘ 55° "°'“';‘° se see so 811' Va %
(9r-) (9h) (9r-) (cm 2
104 2.489 1 141 .30 664.20 1 142.90 478.7 2.388 2.384 4.212
106 2.489 1 144.80 667.70 1 145.80 478.1 2.397 2.394 3.798
107 2.489 1144.80 868.50 1146.20 477.7 2.399 2.396 3.717
109 2.489 1144.80 867.10 1 145.40 478.3 2.395 2.393 3.838
110 2.489 1 142.90 665.30 1 144.50 479.2 2.388 2.385 4.178
111 2.489 1 142.60 888.80 1 144.50 477.9 2.395 2.391 3.942
112 2.489 1142.00 667.10 1143.60 476.5 2.400 2.397 3.711
113 2.489 1 144.40 669.00 1 146.70 477.7 2.400 2.396 3.751
114 2.489 1 143.20 665.80 1 145.00 479.2 2.389 2.386 4.153
118 2.489 1143.60 667.30 1145.00 477.7 2.397 2.394 3.818
117 2.489 1144.70 688.10 1146.90 478.8 2.395 2.391 3.947
118 2.489 1 143.90 887.80 1 145.40 477.8 2.398 2.395 3.773
119 2.489 1143.90 889.00 1148.30 477.3 2.402 2.397 3.712
120 2.489 1 143.90 685.80 1 145.70 480.1 2.388 2.383 4.274
121 2.489 1 143.90 887.00 1 145.40 478.4 2.394 2.391 3.933
122 2.489 1144.70 867.40 1148.00 478.6 2.394 2.392 3.908
124 2.489 1 144.80 888.20 1 146.70 478.5 2.396 2.392 3.878
125 2.489 1 143.80 885.40 1 145.20 479.8 2.387 2.384 4.222
128 2.489 1 144.30 888.10 1 148.20 480.1 2.387 2.383 4.240
127 2.489 1 145.40 667.10 1146.90 479.8 2.390 2.387 4.088
128 2.489 1 145.70 888.90 1 147.70 478.8 2.397 2.393 3.883
129 2.489 1 143.40 868.30 1 145.50 477.2 2.400 2.396 3.734
130 2.489 1143.30 686.90 _1 144.80 477.9 2.395 2.392 3.883
131 2.489 1 141.90 884.30 1143.80 479.3 2.386 2.382 4.282
133 2.489 1 143.40 685.90 1 144.90 479.0 2.390 2.387 4.098
135 2.489 1 145.80 667.00 1 147.60 480.8 2.388 2.384 4.231
138 2.489 1 143.80 888.50 1 145.40 476.9 2.402 2.398 3.840
137 2.489 1143.60 888.10 1145.00 478.9 2.401 2.398 3.857
138 2.489 1 144.10 887.90 1145.60 477.7 2.398 2.395 3.776
139 2.489 1144.00 667.90 1 148.10 478.2 2.397 2.392 3.885
140 2.489 1145.80 889.80 1 147.60 478.0 2.401 2.397 3.893
141 2.489 1 144.50 887.40 1 148.20 478.8 2.394 2.390 3.983
142 2.489 1 145.20 888.40 1 147.10 478.7 2.396 2.392 3.885
143 2.489 1142.10 888.10 1144.20 478.1 2.393 2.389 4.024
144 2.489 1 143.10 688.80 1 145.00 478.2 2.394 2.390 3.961
145 2.489 1144.00 888.40 1 145.80 479.4 2.390 2.388 4.126
147 2.489 1 143.80 867.20 1 144.90 477.7 2.397 2.394 3.818
148 2.489 1 144.90 889.70 1 148.70 477.0 2.404 2.400 3.587
149 2.489 1 144.40 888.40 1 148.20 477.8 2.399 2.395 3.771
150 2.489 1 145.20 889.40 1 147.20 477.8 2.401 2.397 3.704
151 2.489 1144.10 886.20 1145.10 478.9 2.391 2.389 4.017
152 2.489 1 143.20 887.30 1 143.90 476.6 2.400 2.399 3.830
154 2.489 1 144.70 868.20 1 145.90 477.7 2.399 2.398 3.725
155 2.489 1 142.40 888.80 1 143.70 477.1 2.397 2.394 3.798
156 2.489 1 145.70 888.20 1 147.60 479.4 2.394 2.390 3.983
157 2.489 1144.00 867.70 1145.00 477.3 2.399 2.397 3.704

 

121

 

Table B.2 Specific Gravity Results of Mix 11

Wt In air Wt sub. Wt SSD
Gmm

SG SSD SG alr Va %

 

 

 
   
 

Cum.DE(psl)
o N a a co

§

10000 1W 1000000

 

1000
Number dhpflflm

 

Figure B.1 Single Axle Low Stress (Specimen 112)

122

 

 

 

Cum. m: (pal)

0.00002

0.00001

 

10000 100000 1000000

1000
Number 11 Repetition-

 

Figure B.2 Single Axle Low Stress (Specimen 157)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ET‘ 4 .. _ 7 hr
204—. .
g 15 -1- ~ 7 9
a .
e 2
5 10 l v
s-—— 7%.
0 y . c c, 5
am- : %
l l ;
0.00015- 1 1 , . -
E 00001- *1 i . ’
i . . 1
0.00005- -: 1 1' 1 E
i 1
A A 1 1 ‘ z .
V v
1 10 100 1000 100011) 1000000
Nunhrotkepetluom

 

Figure B.3 Single Axle Medium Stress (Specimen 130)

123

 

 

 

 

 

.---_.,._-_ - ,
l

 

 

:.1 1 1 +1.1..1111 .

 

 

.
...—.-..._. ...—..-

 

 

. ......ll .. 1‘1.)

- 11-1. .

 

 

 

 

_
1 .1 v ..1...
: .

 

. . 'l1l:...|1\..l .11 ..

 

 

 

 

.. 13': 1‘11

 

 

.1111,.111.U

 

 

 

 

 

 

10'
5

an: HQ .390

 

0
0.0004 '

011113 -

g o.0002~

 

0.0001 1 ---. —----

“1-11.114
. . 1 a
.

1000 10000 100000 1000000
Plum:- a! luminous

1(1)

10

 

 

en 139)

peclm

Figure B.4 Single Axle Medium Stress (S

 

 

    

.fi,l.1.

 

O

11111111 [..11|.Il1\ .1 1.1.! 1 lltllrllllti

-7 .. .-.

._.__ ...-..
n

1111. ll: ..1.

__ .--- ..x_.
1
P

1.11111

 

 

 

 

 

: 1... . .. a 1 .1.. .1.;

 

 

 

 

 

 

 

 

.1..
. . ._ . -,
w.
. .11; ..- -1 ...--1 1
.
.2..

1—_ -..

 

l

0

it

..-4... .4.
l
l
i
l

1
K
t
I
l

. 3115.51! 1 L

1
1

l
1
.3
l

 

“4,...

'1 ‘ .
1 J ‘ .
.-. -- -..—...... 4.. . ..n... _ . -. .1.... - 1‘" g ‘_ .- __ g...
. 1 . ,1 1 .
1

 

 

 

 

 

 

00001 -.-

 

1000 10000 100000 1000000
mm: «11611811111111:

100

10

 

 

Figure B.5 Single Axle Medium Stress (Specimen 142)

124

 

 

Cum. DE (pd)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

35"""“”’:"“" 1’ "' "’1 ' '1'“ ' . 1 -
1 1 g 1 f 1'
so — -_ 1 4
- 1 1 - i ;
”.__,.- . , - 7 A -<~~—— 1 f i ~+—
1 1 : ‘ , i g .
20-»—*— 7 ~5~~ §---* "2- i 1
' v.‘ . I 1 i
10' 1 E ‘ 2' 2 ‘ 1
s. ~ 1} 5 ' f 1
. 1 % 2 1 f 1
o A J. L A A A A A I 1 1 j
v v V v v - : . y .
0.0012- 3 ; j 1 l .
i i ; 2 1'
00009- E 1 1 1‘ Q i E
E I 1 1 j ‘ ' 5
T F ‘ .. 1 1 1 . . ‘ .
011005» 1 1 -1 1 ~~I1M> -: 1 : 1
0.0000- i 1 3 -. —» ‘1- I
1 z i 1 1
3 3 " : i 1 1
‘ 100000

10 100 1G!) 10000

Numbr d Rapedtlun

 

Figure B.6 Single Axle High Stress (Specimen 119)

 

 

Cum. DE (psi)

DEW)

 

10 1(1) 1000 10000
Nunhr d Reptitlms

100000

1000000

 

Figure B.7 Single Axle High Stress (Specimen 151)

125

 

 

 

 

Cum. DE (pd)

DE (All)

10000 100000

 

 

10 100 1000
mm: or Reptitlal

 

Figure 13.8 Tandem Axle Medium Stress (Specimen 122)

 

Cum. m: (pal)

DEM)

 

 

Nunitr d Repllllms

Figure B.9 Tandem Axle Medium Stress (Specimen 124)

126

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

75'” " 1"; ‘— ' —‘ r—‘—“’
E r ‘ y
E- 15 .- _ 7 7 7.. ‘_7 7 7 7 7 7 7 7.7
an
a .
g 10- ‘ ‘
o ‘ ‘
5 u
0 c c g: c c c ‘ "
QN‘ f ' i
00005< E
A 0.000“
E am. ‘ Q ' .
a ‘ ’ ’ : . ' 3 . o o 0 o
nom- \ 2 s 9 '
:1 ’ ‘ t
0000M § ’
\ a ‘ j I
0 * ; ‘ L ;
1 10 100 1000
Nuduolkepeflum
Figure 3.10 Tandem Axle Medium Stress (Specimen 128)
H
a
o
3 0.002- ; ,
2 00015- g Y . . j
le.7._7.77.‘;-;_17_‘_t7 . ‘ O ,9 §__UAQ__A5_ .1 9 ._O ’ __ _7..7Z,. ; a 7 777777
' i 1 g ‘ 5 1
0.0005- ' ; i ;’ ‘:
a 1r . ’ ‘ . i i
1 10 100 1000 10000 100000

Numbn- 0l Repetitlan

Figure B.11 Tandem Axle High Stress (Specimen 145)

127

 

 

 

 

 

Cum. m: (psi)

DEM)

 

100 1000 10000 100000
mm (1 Repeat“:

 

 

Figure B.12 Tandem Axle High Stress (Specimen 137)

 

Cum. DR (pd)

0.01115

01!!)12

0.00m

 

10 100 11!!) 10000 100000 1000000
Nunim’ d mum.

Figure B.13 Tridem Axle Low Stress (Specimen 140)

128

 

 

 

 

Cum. DE (psi)

 

OIXXJZI ‘

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.M18-~_...77._’A7 ,4 A , ,_ f_, _ xx .11..” I , x
. 0.00015- f ‘ 1 g .0 . - I:
3 0.00012-—— 0- 9 7’7 . 77 i ‘ j , ,r _ _-,
0.000094 1 I 04> o .. .+
0.0u3064—77~--———v— i~~~~ 1 I 1 ~—— - A:
0.000034 " 1 ' :
c ii ‘ ' ' ‘

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

601~ 1 w —~
A, : . ‘ g
50+ V. 7 ‘;~ 77 I"?
:2: wJ—-~--- s 2 — . ; er
a ”J i i ii
0”“ 1: r1 ' a:
. , W : 4 . ,
. 1 ,. V g 0'
1°““"““'— ‘“‘ *A "T"? ‘- i 1 L , A ~——~«—~; ;‘
am 4x 1\ A A AA A x i AQ’AA ‘
UM": T V Vv v Y ,
00005-—v—v ~ "f‘*—* f f p '
000m< i .1 I ‘. . 'f:
A 1: E i ‘ «9 .
g 0111)“ O ‘ i {1‘1}0 .9 ..1 V
an 4» 'o 1‘ o f : V
a own-”v 0 o :0 .77. 1,.‘_o_._, I
army—~- 7- - — a — W, ~— 1%» L ' vvvvvv -— —— ~ -—~ v _j‘__,_.-
W ;

 

 

 

 

 

 

 

 

 

 

 

Nllllinl’ cl Repetition

Figure B.15 Tridem Axle Medium Stress (Specimen 147)

129

 

 

 

 

Cum. DE (psi)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

i
E
10 1(1) 1“!) 10000 100000 1000000
Nunilr ol' Repflflul
Figure B.16 Tridem Axle Medium Stress (Specimen 116)
3 2;
H i ' :
a.
5 I
U
3 9
5' a
1mm

 

 

Figure 3.17 Tridem Axle Medium Stress (Specimen 156)

130

 

 

 

 

 

 

 

 

0005-7777—7777-g7177 -

   

 

 

 

0.004-»—7777—~77 7 7 ~
0003- i
5
o. - , i ,
0m . .
0.(Dl- ‘ ; k
c ; ': ‘ ; é

 

Number otkepdtlms

 

Figure B.18 Tridem Axle High Stress (Specimen 149)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6°“‘ '" *T‘”? W“: ‘*‘*‘T‘ W— 7”" 2
3. §< J j ,g g ‘
50' . i i 7 : i
340‘7—77777 71' 7 3— +‘i7 5 g
i1 i . e ; I

H , l, ‘ '$ j 5

a sol J (a: ' : :i , .

I i F 1 ;
20' ‘ i :1 t 7.. i 7
10 —— 7 77L — 7 7 ‘ g E

l ? ‘H 1 ‘ ‘
I‘ ‘
o c :' ¢ c e :7? t , u

QW‘ ' ' ‘ ; i

0.005- % . I

0.004< % ’3; ‘ :

0.003‘

0002- i .

9 Y O O o 639‘ o o o 4» O i:

0.001- 2; u ; 31 ‘

 

 

100000
Numlzr o! Repdtions

 

Figure B.19 Tridem Axle High Stress (Specimen 138)

131

 

 

 

 

 

 

 

 

'1?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

,. -
7 : 7 .

7..., H 7 -. ...
7 7

w w, m m c

E
3.
s
U

:5 an

 

 

100000

10

mm cinematic-

 

 

117)

pecimen

Figure 3.20 4-Axle Medium Stress (S

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

: .H :31: .Myi . “in- i
. .e ...... a. .
: ::::: [AV . E . ...i : ,7.
.1: $.17», : ..7,. ..
, c O . 7
. . 7 . . 7 7: . 7 i 7 .L.
muwummmumsom m m m. m c
0 0 Q

100000

10000

I!!!)

100

Nlnflnr of Regalia:

 

 

Figure B.21 4-Axle Medium Stress (Specimen 144)

132

 

 

 

 

 

.. .... -. -_

l

l

y :
_——_ Qfl.-~' .2...

' C

.

 

 

 

 

 

i
l
!

 

 

.- 7-7 '. ..- ... .77

 

  

 

l
l
l
.’

 

: E 3 . -
7;__.__ _7——..._-._- y» >1 _-
. : -

l
l
7777.. . 7 77

 

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g i . i .
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I
:

 

i
1.

 

 

 

l
s
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l

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1 1'
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r
l
3
l
:

 

-..—.77—4

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. . . .
.7777. +...._. 47777....
. ; ‘
x

l
1
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l

l
r
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I
l
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Truck Specimen No. 135 Specimen No. 125
Number Nf kakips TF TF/tonnage Nf Nfikjps TF TF/tonnage
Std Axle 4267 76805 1.00 1.00 5388 96988 1.00 1.00
truck 0 881 64671 4.84 1.19 1197 87896 4.50 1.10
truck 1 1207 40328 3.53 1.90 1735 57946 3.11 1.67
truck 2 1131 53587 3.77 1.43 1518 71973 3.55 1.35
truck 3 1094 59524 3.90 1.29 1438 78209 3.75 1.24
truck 4 1053 70967 4.05 1.08 1482 99900 3.64 0.97
truck 10 635 75792 6.72 1.01 801 95636 6.73 1.01
truck 13 705 106742 6.05 0.72 807 122162 6.68 0.79
truck 14 691 111595 6.17 0.69 704 113659 7.65 0.85
truck 17 878 116304 4.86 0.66 923 122222 5.84 0.79
truck 19 851 117846 5.01 0.65 906 125391 5.95 0.77
truck 20 829 125584 5.14 0.61 831 125869 6.48 0.77
Table 0.2 Effect of Speed on AF
Wed Axlefionr. Nf AF_'
1 axle 7795 1.113
2 axles 4216 2.058
3 axles 3059 2.837
60 MPH 4 axles 2471 3.511
5 axles 2130 4.075
7 axles 1655 5.242
8 axles 1450 5.983
1 axle 5960 1.122
2 axles 3610 1.853
3 axles 2674 2.502
40 MPH 4 axles 2159 3.099
5 axles 1879 3.561
7 axles 1475 4.536
8 axles 1359 4.922
1 axle 4957 1.123
2 axles 2978 1.869
3 axles 2304 2.415
27 MPH 4 axles 2016 2.760
5 axles 1819 3.060
7 axles 1187 4.688
8 axles 1080 5.150

 

 

 

 

 

 

 

140

Table C.3 Effect of Thickness (Interaction Level) on AF

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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5 axles 2022 2.75 0.55

7 axles 1322 4.21 0.60

8 axles 1210 4.60 0.57

2 axles 3302 1.68 0.84

3 axles 2712 2.05 0.68

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7 axles 1494 3.72 0.53

8 axles 1436 3.87 0.48

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3 axles 2804 1.98 0.66

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. Level Axle No

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141

Table C.5 Calculated AF from Strain Fatigue Curve Using Peak-Midway Method

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Table C.6 Calculated AF from Strain Fatigue Curve Using Peak Method (After Correction)

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Level Meas_ured Calculated Measured Calculated Total per n
2 2072 2149 1.32 1 .2727806 3.7% 1 .8%
3 1800 1561 1.52 1 .7521349 13.3% 4.4%
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5 1410 1045 1.94 2.6178783 25.9% 5.2%
7 816 780 3.35 3.5073749 4.5% 0.6%
8 761 683 3.60 4.006492 10.3% 1 .3%
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50% 4 1448 1248 1.89 2.1917121 13.8% 3.5%
5 844 1045 3.24 2.6178783 23.8% 4.8%
7 661 780 4.14 3.5073749 17.9% 2.6%
8 640 683 4.28 4.006492 6.1% 0.8%
2 2032 2149 1.35 1 .2727806 5.7% 2.9%
3 1548 1561 1.77 1.7521349 0.8% 0.3%
75% 4 1186 1248 2.30 2.1917121 5.2% 1.3%
5 952 1045 2.87 2.6178783 9.7% 1 .9%
7 661 780 4.14 3.5073749 18.0% 2.6%
8 568 683 4.81 4.006492 20.1% 2.5%

 

 

 

 

 

 

 

 

142

 

Table C.7 Calculated AF from Dissipated Energy Fatigue Curve Using Peak Method

Level

Axle No

£L18

1148
2L75
4L21
4L60

2L05
2L29
1107
1172
1187

1.98
2L36
2173
1144

(3%th

Nat-hm

27U296
1%1096
lfii096
39£¥%
4£L596
15
31J696
4£L796
£ML696
4£L896
51.696
. 96
1§L996
4(L996
4£i396
SCL996

n

SL196
£1596
9lfi6
5&796
Ei396

1(1596
1(L796
76796
Ei796
£1496

11.396
1(L296
SL196
7K396

 

Table C.8 Calculated AF from Dissipated Energy Curve Using Peak-Midway Method

Level

Axle No

QVUI#OD

3
4
5
7
8

0040150:

143

2L18
2L48
£L75
1L21
4L60

2L05
£L29
1107
3L”?

1.98
£L36
£L73
1944

 

Table C.9 Calculated AF from Dissipated Energy Curve Using Peak Method (After Correction)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Interaction Axle No N f_ Axle Factor _ % de'feirence
Level Meas_u red Calculated Measured Calculated Total per n
2 3279 3543 1 .70 1 .5698587 8.0% 4.0%
3 2547 2616 2.18 2.1261517 2.7% 0.9%
25% 4 2241 2153 2.48 2.5839793 4.0% 1 .0%
5 2022 1875 2.75 2.9673591 7.3% 1 .5%
7 1322 1557 4.21 3.5732517 17.8% 2.5%
8 1210 1457 4.60 3.8167939 20.5% 2.696
2 3302 3543 1 .68 1 .5698587 7.3% 3.6%
3 2712 2616 2.05 2.1261517 3.5% 1.2%
50% 4 2426 2153 2.29 2.5839793 1 1 .3% 2.8%
5 1 81 1 1875 3.07 2.9673591 3.5% 0.7%
7 1494 1557 3.72 3.5732517 4.2% 0.6%
8 1436 1457 3.87 3.8167939 1 .5% 0.2%
2 3493 3543 1.519 1.5698587 1.4% 0.7%
3 2804 2616 1.98 2.1261517 6.7% 2.2%
75% 4 2352 2153 2.36 2.5839793 8.5% 2.1%
5 2035 1875 2.73 2.9673591 7.9% 1 .6%
7 1617 1557 3.44 3.5732517 3.7% 0.5%
8 1478 1457 3.76 3.81 67939 1 .4% 0.2%

 

 

 

 

 

 

 

 

144

 

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