Citation
Development and propagation of surface-initiated longitudinal wheel path cracks in flexible highway pavements

Material Information

Title:
Development and propagation of surface-initiated longitudinal wheel path cracks in flexible highway pavements
Creator:
Myers, Leslie Ann, 1974-
Publication Date:
Language:
English
Physical Description:
xvii, 208 leaves : ill. ; 29 cm.

Subjects

Subjects / Keywords:
Base courses ( jstor )
Bituminous concrete pavements ( jstor )
Modeling ( jstor )
Pavements ( jstor )
Ribs ( jstor )
Stiffness ( jstor )
Stress distribution ( jstor )
Stress intensity factors ( jstor )
Stress ratio ( jstor )
Wheels ( jstor )
Civil Engineering thesis, Ph.D ( lcsh )
Dissertations, Academic -- Civil Engineering -- UF ( lcsh )
Pavements -- Cracking -- Florida ( lcsh )
Pavements, Bituminous -- Cracking -- Florida ( lcsh )
Genre:
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 2000.
Bibliography:
Includes bibliographical references (leaves 204-207).
Additional Physical Form:
Also available online.
General Note:
Printout.
General Note:
Vita.
Statement of Responsibility:
by Leslie Ann Myers.

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Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Resource Identifier:
025862312 ( ALEPH )
47122836 ( OCLC )

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DEVELOPMENT AND PROPAGATION OF SURFACE-INITIATED
LONGITUDINAL WHEEL PATH CRACKS IN FLEXIBLE HIGHWAY PAVEMENTS













By

LESLIE ANN MYERS














A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2000














.ACKNOWLEDGMENTS

I would like to acknowledge those individuals who were instrumental in the advancement of this research. Special thanks go to Dr. Reynaldo Roque for willingly sharing his knowledge and experiences through constant encouragement. I also appreciate the fun jokes and sound advice given to me by Dr. Byron Ruth who truly epitomizes the concept that "learning is fun." Acknowledgments should also be made to my graduate committee members, Dr. Mang Tia and Dr. Bjorn Birgisson, who were always available to discuss ideas and lend valuable advice. I would also like to acknowledge Dr. Bhavani Sankar for lending his technical support and advice and Dr. Marion Pottinger of Smithers Scientific Services, Inc. for generously providing me with measured truck tire-pavement interface stress data and technical advice.

Other individuals who assisted me in my graduate studies include Christos Drakos and Dr. Yusuf Mehta. I would like to acknowledge the everyday support of my best friend Roberto Vitali.

Finally, I acknowledge the unwavering support of my parents, Robert and Bonnie Myers, and brother and sister, Tom and Katie, who gave me the strength to conquer challenges that I faced along the way.



I dedicate this Ph.D. dissertation to the memory of my father.














TABLE OF CONTENTS


Page


ACKN OW LED GM EN TS .................................................................................................. ii

LIST OF TABLES ............................................................................................................. vi

LIST OF FIGURES ......................................................................................................... viii

ABSTRA CT .................................................................................................................... xvi

CHAPTERS

I INTRODU CTION ........................................................................................................... I
1. 1 Background .............................................................................................................. 1
1.2 Research Hypothesis ................................................................................................ 4
1.3 Objectives ................................................................................................................ 5
1.4 Scope ........................................................................................................................ 5
1.5 Research Approach .................................................................................................. 7


2 LITERATURE REV IEW .............................................................................................. 10
2.1 Overview ................................................................................................................ 10
2.2 Classical Fatigue Approach ................................................................................... I I
2.3 Continuum Dam age A pproach .............................................................................. 13
2.4 Fracture M echanics Approach ............................................................................... 15
2.5 M easurem ent of Tire Contact Stresses .................................................................. 18
2.6 Analysis of Surface Cracking ................................................................................ 28
2.7 Sum m ary ................................................................................................................ 32


3 AN A LYTICA L APPROA CH ....................................................................................... 33
3.1 Introduction ............................................................................................................ 33
3.2 V alidation of M easured Tire Contact Stresses ....................................................... 34
3.2.1 Developm ent of Tire M odel .......................................................................... 35
3.2.2 Selection of Pavem ent Structures For Analysis ............................................ 39
3.2.3 Results of Verification Analyses .................................................................. 43
3.3 Modification of Two-Dimensional Finite Element Model to Capture
Bending Response of A sphalt Pavem ent System .................................................. 61
3.3.1 Finite Elem ent M odel Types ......................................................................... 63


iii








3.3.2 Finite Element Modeling of Pavement System Using ABAQUS ................ 65
3.3.3 Evaluation of Predicted Stresses ................................................................... 68
3.3.3-1 Definition of Bending Stress Ratio ...................................................... 71
3.3.3-2 Relations Between Bending Stress Ratio and Structural
Parameters ........................................................................................... 72
3.3.4 Application of Bending Stress Ratio ............................................................. 79
3.3.5 Additional Observations ............................................................................... 81
3.3.6 Summary ....................................................................................................... 82
3.4 Description of Pavement M odel ............................................................................ 83
3.4.1 Structural Parameters of M odel .................................................................... 84
3.4.2 Crack Length ................................................................................................. 85
3.4.3 M odeling System .......................................................................................... 88
3.5 Selection of Fracture M echanics Theory For Analysis .......................................... 93
3.5.1 Description of Fracture Parameters .............................................................. 94
3.5.2 Application of Fracture M echanics ............................................................... 95
3.6 Summary ................................................................................................................ 98


4 PARAMETRIC STUDY PAVEMENT STRUCTURE ............................................. 99
4.1 Overview ................................................................................................................ 99
4.2 Factors Investigated for Structural Analysis ........................................................ 100
4.3 Effects of Pavement Structure on Crack Propagation .......................................... 104
4.3.1 Asphalt Concrete Thickness ....................................................................... 104
4.3.2 Asphalt Concrete-to-Base Layer Stiffness Ratio ........................................ 105
4.3.3 Results ......................................................................................................... 114
4.4 Effects of Loading on Crack Propagation ............................................................ 114
4.4.1 Determination of Appropriate Load Positions ............................................ 116
4.4.2 Load Position W ith Respect to Crack ......................................................... 119
4.4.3 Direction of Crack Growth ......................................................................... 130
4.5 Summary .............................................................................................................. 134


5 PARAMETRIC STUDY TEMPERATURE AND
ENVIRONM ENTAL CONDITIONS ......................................................................... 135
5.1 Overview .............................................................................................................. 135
5.2 Analysis Procedure For Evaluating Induced Stiffness Gradient .......................... 137
5.3 Analysis of Cracked Pavement With Induced Stiffness Gradient ....................... 147
5.3.1 Effect of Pavement Structure on Cracked Pavement With Stifffiess
Gradients ..................................................................................................... 153
5.3.2 Effect of Stiffness Gradient on Direction of Crack Growth ....................... 161
5.4 Summary .............................................................................................................. 162


6 POTENTIAL IMPLICATIONS FOR PAVEMENT DESIGN AND
PERFORM ANCE ....................................................................................................... 165
6.1 Overview .............................................................................................................. 165
6.2 Implications of Load Spectra ............................................................................... 166


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6.3 Implications of Rate of Cracking ......................................................................... 175
6.4 Summary .............................................................................................................. 182


7 FINDINGS AND CONCLUSIONS ............................................................................ 183
7.1 Findings ................................................................................................................ 183
7.2 Conclusions .......................................................................................................... 186

8 RECOMM ENDATIONS ....................................................................... 188

APPENDICES

A SAMPLE CALCULATION OF STRESS INTENSITY FACTORS ......................... 191

B STRESS INTENSITY FACTOR DATA .................................................... 195

REFERENCES ................................................................................................................ 204

BIOGRAPHICAL SKETCH ........................................................................................... 208
































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LIST OF TABLES

Table Pag

3.1 Pavement Structures Used for Analysis ....................................... 43

3.2 Parameters Used in Development of Pavement Finite Element Models...........66

3.3 Parameters Evaluated For Identification of Factors Critical to Development of
Surface Cracking Mechanism.................................................. 85

3.4 Boundary Conditions Applied to Model of Entire Pavement System............ 89

3.5 Boundary Conditions Applied to Refined Model of Surface Layer.............. 91

4.1 Transverse Stress Distribution Along Surface of Pavement For Each Pavement
Modeled, As Predicted in BISAR Elastic Layer Analysis Program............. 118

4.2 Example Calculation of Direction of Crack Growth For Thick Pavement (hl= 8 in)
With Low Base Stiffness (E1 :E2 = 800:20 ksi) ................. ............131

6.1 Rate of Crack Growth For Given K-value From Fracture Tests Performed on
Laboratory Specimens ........................................................174

B. 1 Stress Intensity Factors Predicted in ABAQUS For Uniform Stiffness 4-inch
Pavement Layer With Low Stiffness Base (E2=20 ksi)........................ 196

B.2 Stress Intensity Factors Predicted in ABAQUS For Uniform Stiffness 4-inch
Pavement Layer With High Stiffness Base (E2=44 ksi) ....................... 197

B.3 Stress Intensity Factors Predicted in ABAQUS For 4-inch Pavement Layer With
Stiffness Gradients and Low Stiffness Base (E2=20 ksi)....................... 198

B.4 Stress Intensity Factors Predicted in ABAQUS For 4-inch Pavement Layer With
Stiffness Gradients and High Stiffness Base (E2=44 ksi)...................... 199

B.5 Stress Intensity Factors Predicted in ABAQUS For Uniform Stiffness 8-inch
Pavement Layer With Low Stiffness Base (E2=20 ksi)....... ...... ....... 200

B.6 Stress Intensity Factors Predicted in ABAQUS For Uniform Stiffness 8-inch
Pavement Layer With High Stiffness Base (E2=44ksi) ......................201



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B.7 Stress Intensity Factors Predicted in ABAQUS For 8-inch Pavement Layer With
Stiffness Gradients and Low Stiffness Base (E2=20 ksi) ............................ 202

B.8 Stress Intensity Factors Predicted in ABAQUS For 8-inch Pavement Layer With
Stiffness Gradients and High Stiffness Base (E2=44 ksi) ............................ 203











































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LIST OF FIGURES

Figure Page

1. 1 Overall Research Approach Flowchart ........................................................................ 9

2.1 Stress Intensity Factor Plotted As a Function of Crack Length for a Surface Crack
Due to Vehicular Loading For Three Different Pavement Structures With Different
Modulus Ratios (after Collop and Cebon 1995) ...................................................... 17

2.2 Structural Characteristics of Bias Ply and Radial Truck Tires and Their Effects on
the Pavement Surface (after Roque et al. 1998) ....................................................... 20

2.3 Schematic of System Used to Measure Tire Contact Stresses (after Roque et al.
19 9 8 ) ........................................................................................................................ 2 1

2.4 Experimental Setup of Vehicle-Road Surface Pressure Transducer Array (VRSPTA)
System Used to Measure Tire Contact Stresses (after de Beer et al. 1997) .............. 22

2.5 Three-dimensional Vertical and Lateral Contact Stress Distributions Under Radial
(R22.5) Truck Tire at Rated Load (after de Beer et al. 1997) .................................. 23

2.6 Effect of Pavement Bending Due to a Bias Ply and Radial Truck
Tire on Surface Stress Distribution (after Myers et al. 1999) .................................. 25

2.7 Transverse Contact Shear Stresses Measured For a Bias Ply, Radial, and Wide Base
Radial Tire At the Appropriate Rated Load and Inflation Pressure (after Myers et al.
19 9 9) ......................................................................................................................... 2 6

2.8 Vertical Contact Stresses Measured For a Bias Ply, Radial, and Wide Base Radial
Tire At the Appropriate Rated Load and Inflation Pressure
(after M yers et al. 1999) ............................................................................................ 27

2.9 Predicted Transverse Stress Distribution Induced By Radial Truck Tire Near
Pavement Surface (after M yers et al. 1998 ............................................................... 30

3.1 Cross-Section of a Typical Radial Truck Tire .......................................................... 37

3.2 Finite Element Representation of Tire Tread Structure ............................................. 37

3.3 Measured and Predicted Vertical Stress Distribution at Surface of Steel Bed ......... 40

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3.4 Measured and Predicted Transverse Stress Distribution at Surface of Steel Bed ...41

3.5 Vertical Stresses Predicted at Surface of 4-in Pavement System: Stiffness Ratio of
4.6 (E1 = 200 ksi, E2 =44 ksi)............................................................. 44

3.6 Transverse Stresses Predicted at Surface of 4-in Pavement System: Stiffness Ratio
of 4.6 (B1 = 200 ksi, B2 = 44 ksi).......................................................... 45

3.7 Vertical Stresses Predicted at Surface of 4-in Pavement Systemn:. Stiffness Ratio of
39.4 (El1 800 ksi, B2 = 20 ksi) ......................................................... 46

3.8 Transverse Stresses Predicted at Surface of 4-in Pavement System: Stiffness Ratio
of 39.4 (Bl = 800 ksi, E2 =20 ksi) ........................................................ 47

3.9 Vertical Stresses Predicted at Surface of 4-in Pavement System: Stiffness Ratio of
10.0 (B1 = 200 ksi, B2 = 20 ksi)........................................................... 48

3.10 Transverse Stresses Predicted at Surface of 4-in Pavement System: Stiffness Ratio
of 10.0 (El 200 ksi, E2 = 20 ksi) ........................................................ 49

3.11 Vertical Stresses Predicted at Surface of 4-in Pavement System: Stiffness Ratio of
18.0 (Bl = 800 ksi, B2 = 44 ksi) ........................................................... 50

3.12 Transverse Stresses Predicted at Surface of 4-in Pavement System: Stiffness Ratio
of 18.0 (Bl = 800 ksi, B2 = 44 ksi)........................................................ 51

3.13 Vertical Stresses Predicted at Surface of 2-in Pavement System: Stiffness Ratio of
4.6 (El = 200 ksi, E2 =44 ksi) ............................................................ 53

3.14 Transverse Stresses Predicted at Surface of 2-in Pavement System: Stiffness Ratio
of 4.6 (B1 = 200 ksi, E2 = 44 ksi).......................................................... 54

3.15 Vertical Stresses Predicted at Surface of 2-in Pavement System: Stiffness Ratio of
39.4 (El = 800 ksi, B2 = 20 ksi) ......................................................... 55

3.16 Transverse Stresses Predicted at Surface of 2-in Pavement System: Stiffness Ratio
of 39.4 (E1 = 800 ksi, E2 = 20 ksi) ........................................................ 56

3.17 Vertical Stresses Predicted at Surface of 2-in Pavement System: Stiffness Ratio of
10.0 (E1 = 200 ksi, B2 = 20 ksi)........................................................... 57

3.18 Transverse Stresses Predicted at Surface of 2-in Pavement System: Stiffness Ratio
of 10.0 (E1 = 200 ksi, B2 = 20 ksi) ........................................................ 58




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3.19 Vertical Stresses Predicted at Surface of 2-in Pavement System: Stiffness Ratio of
18.0 (El = 800 ksi, E2 = 44 ksi) ........................................................... 59

3.20 Transverse Stresses Predicted at Surface of 2-in Pavement System: Stiffness Ratio
of 18.0 (E1 = 800 ksi, E2 = 44 ksi) ...................................................... 60

3.21 Schematic of Axisymmetric and 2-D Finite Element Pavement Models............. 64

3.22 Schematic and Detailed View of Pavement System Modeled Using the Finite
Element Program, ABAQUS .............................................................. 67

3.23 Transverse Stress Distribution Along Bottom of 4-in Asphalt Concrete Layer for
Stiffness Ratio of 4.6 (Ej = 203 ksi : E2 = 44 ksi) ....................................... 69

3.24 Transverse Stress Distribution Along Bottom of 8-in Asphalt Concrete Layer for
Stiffness Ratio of 59 (El = 1200 ksi : E2 = 20 ksi) ...................................... 70

3.25 Effect of Asphalt Concrete Thickness on Bending Stress Ratio ...................... 75

3.26 Effect of Stiffness Ratio (B1 / E2) on Bending Stress Ratio ........................... 76

3.27 Effect of Asphalt Concrete and Base Layer Stiffness on Bending Stress Ratio ....77

3.28 Effect of Subgrade Stiffness on Bending Stress Ratio at Various Stiffness Ratios
(BEl/E2) .................................................................................... 78

3.29 Application of Approach Parametric Study of a Cracked Pavement ............... 80

3.30 Typical Finite Element Model of Pavement Used In Parametric Study For
Determining Factors Critical to Development of Crack Propagation ................ 86

3.31 Detailed View of Crack in Finite Element Model of Pavement ....................... 87

3.32 System Used For Two-Step Approach to Finite Element Modeling of Pavement. ...90

3.33 Example of Spring Constant Computation Used For Application of Boundary
Conditions to 4-inch Finite Element Pavement Model From EXCEL Computer
Program ................................................................................... 92

3.34 Detailed View of Finite Element Mesh Surrounding Crack Tip ...................... 96

4.1 Determination of K1 For Two Different 4-inch Pavement Sections With a 0.5 inch
Surface Crack, and Load Centered 25 inches From Crack........................... 102

4.2 Determination of K11 For Two Different 4-inch Pavement Sections With a 0.5 inch
Surface Crack, and Load Centered 25 inches From Crack........................... 103



x









4.3 Effects of Asphalt Concrete Thickness: Distribution of K, Versus Crack Length For
Loading Position Centered 25 inches From Crack ................................................. 106

4.4 Effects of Asphalt Concrete Thickness and Base Layer Stiffness: Distribution of K,
Versus Crack Length For Loading Position Centered 7 inches From Crack ........... 107

4.5 Effects of Asphalt Concrete Thickness and Base Layer Stiffness: Distribution of K,
Versus Crack Length For Loading Position With Wide Rib Centered on Top of
C rack ....................................................................................................................... 10 8

4.6 Effects of Asphalt Concrete Thickness and Base Layer Stiffness: Distribution of K11
Versus Crack Length For Loading Position Centered 25 inches From Crack ......... 109

4.7 Effects of Asphalt Concrete Thickness and Base Layer Stiffness: Distribution of K11
Versus Crack Length For Loading Position Centered 7 inches From Crack ........... 110

4.8 Effects of Asphalt Concrete Thickness and Base Layer Stiffness: Distribution of K11
Versus Crack Length For Loading Position With Wide Rib Centered on Top of
C rack ....................................................................................................................... I I I

4.9 Comparison of Stress Intensity Magnitudes For K, and K11 At The Crack Tip For:
8-inch AC, I inch Crack, Load Centered 25 inches From Crack ........................... 112

4. 10 Effects of Asphalt Concrete and Base Layer Stiffness: Distributions of K, and K11
Versus Crack Length For Loading Centered 25 inches From Crack ....................... 113

4.11 Visual Example of Vertical and Lateral Load Application to Finite
E lem ent M odel ......................................................................................................... 115

4.12 Visual Example of Transverse Stress Distribution in Response to Loading:
Undeformed Pavement, Deformed Loaded Pavement, and Transverse Stress
Distribution Along the Pavement's Surface ........................................................... 117

4.13 Effects of Individual Layer Stiffness Values on Transverse Stress Distribution Along
Surface of Pavement From Center of Load For Layer Stiffness Ratio of 40 ......... 120

4.14 Effect of Load Positioning on Opening At the Crack Tip For a 4-inch Surface Layer
and Low Stiffness (EI/E2 = 800:20 ksi) Ratio ........................................................ 122

4.15 Effect of Load Positioning on Shearing At the Crack Tip For a 4-inch Surface Layer
and Low Stiffness (EI/E2 = 800:20 ksi) Ratio ........................................................ 123

4.16 Effect of Load Positioning on Opening At the Crack Tip For a 4-inch Surface Layer
and High Stifftiess (EI/E2 = 800:44.5 ksi) Ratio ...................................................... 124



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4.17 Effect of Load Positioning on Shearing At the Crack Tip For a 4-inch Surface Layer
and High Stiffness (EIfE2 = 800:44.5 ksi) Ratio ....................................... 125

4.18 Effect of Load Positioning on Opening At the Crack Tip For an 8-inch Surface
Layer and Lower Stiffness (E1/E2 = 800:20 ksi) Ratio................................. 126

4.19 Effect of Load Positioning on Shearing At the Crack Tip For an 8-inch Surface
Layer and Lower Stiffness (E1/E2 =800:20 ksi) Ratio ................................ 127

4.20 Effect of Load Positioning on Opening At the Crack Tip For an 8-inch Surface
Layer and High Stiffness (E1/E2 = 800:44.5 ksi) Ratio................................ 128

4.21 Effect of Load Positioning on Shearing At the Crack Tip For an 8-inch Surface
Layer and High Stiffness (EI/E2 =800:44.5 ksi) Ratio................................ 129

4.22 Example Field Section and Core Exhibiting Short Crack: Pure Tensile Failure
Mechanism ................................................................................ 132

4.23 Example Field Section and Core Exhibiting Intermediate or Deep Crack: Tensile
Failure Mechanism and Directional Change in Crack Growth ...................... 133

5.1 Temperature Gradient Cases Used to Determine Stiffness Gradients in the Asphalt
Concrete Layer to be Evaluated in ABAQUS .......................................... 138

5.2 Dynamic Modulus versus Temperature Plot For Unaged AC-30 Asphalt Cement
Mixture Used to Convert Temperature Gradients Into Stiffness Gradients ........ 141

5.3 Asphalt Concrete Sublayer Configuration Used For Analyzing Case 1 Uniform
Layer Stiffness Temperature Gradient.................................................. 142

5.4 Asphalt Concrete Sublayer Configuration Used For Analyzing Case 2 Temperature
Gradient.................................................................................. 143

5.5 Asphalt Concrete Sublayer Configuration Used For Analyzing Case 3 Temperature
Gradient.................................................................................. 144

5.6 Asphalt Concrete Sublayer Configuration Used For Analyzing Case 4 Temperature
Gradient.................................................................................. 145

5.7 Effect of Temperature-Induced Stiffness Gradients on Stress Intensity K, Predicted
At the Crack Tip For 8-inch Asphalt Concrete (Load Centered 30 in From Crack). 147

5.8 Effect of Temperature-Induced Stiffness Gradients on Stress Intensity K11 Predicted
At the Crack Tip For 8-inch Asphalt Concrete (Load Centered 30 in From Crack). 148




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5.9 Effect of Temperature-Induced Stiffness Gradients on Transverse Stress Distribution
Within 8-inch Asphalt Concrete with a 1.0 inch Crack (Load Centered 30 in From
C rack) ....................................................................................................................... 149

5. 10 Effect of Load Wander on Stress Intensity Within 8 -inch Asphalt Concrete
(Stiffness G radient C ase 3) ..................................................................................... 150

5.11 Illustration of Effects of Stiffness Gradients on Crack Propagation in 4-inch Asphalt
Pavement (Load Centered 25 in From Crack) ........................................................ 151

5.12 Illustration of Effects of Stiffness Gradients on Crack Propagation in 8-inch Asphalt
Pavement (Load Centered 30 in From Crack) ........................................................ 153

5.13 Effects of Stiffness Gradients and Base Layer Stiffness on Crack Propagation in
8-inch Asphalt Pavement (Load Centered 30 in From Crack) ............................... 154

5.14 Effects of Stiffness Gradients and Asphalt Concrete Layer Thickness on Crack
Propagation (Load Centered 25 in and 30 in From Crack) ...................................... 155

5.15 Effects of Stiffness Gradients and Asphalt Concrete Layer Thickness on Crack
Propagation (Load Centered 20 in and 25 in From Crack) ...................................... 156

5.16 Effects of Stiffness Gradients and Asphalt Concrete Layer Thickness on Crack
Propagation (Load Centered 15 in and 20 in From Crack) ...................................... 157

5.17 Effects of Stiffness Gradients and Asphalt Concrete Layer Thickness on Crack
Propagation (Load Centered 7in From Crack) ......................................................... 158

5.18 Effects of Stiffness Gradients and Asphalt Concrete Layer Thickness on Crack
Propagation (Wide Rib Load Centered on Top of Crack) ...................................... 159

5.19 Effects of Stiffness Gradient Case 2 on Direction of Crack Growth in 4-inch
Pavement (Angle Relative to Vertical) .................... : ............................................... 161

5.20 Effects of Various Stiffness Gradients on Direction of Crack Growth in 8-inch
Pavement (Angle Relative to Vertical) ................................................................... 163

5.21 Effects of Various Stiffness Gradients on Direction of Crack Growth: Photo of
Cracked Trench Extracted From Florida Highway 301 ........................................... 164

6.1 View of Lane Exhibiting Visible Surface-Initiated Longitudinal Cracks in the Wheel
P ath s ......................................................................................................................... 16 7

6.2 Transverse Distribution of Load Within Wheel Path and Critical Load Positions For
Pavements For a 4-inch Asphalt Concrete Layer of Uniform Stiffness ................. 170




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6.3 Transverse Distribution of Load Within Wheel Path and Critical Load Positions For
Pavements For an 8-inch Asphalt Concrete Layer of Uniform Stiffhess ................ 171

6.4 Effect of Temperature-Induced Stiffness Gradients on Transverse Distribution of
Load Within Wheel Path and Critical Load Positions For 4-inch Pavement ......... 172

6.5 Effect of Temperature-Induced Stiffness Gradients on Transverse Distribution of
Load Within Wheel Path and Critical Load Positions For 8-inch Pavement .......... 173

6'6 Example Field Section and Core Exhibiting Short Crack: Pure Tensile Failure
M echanism .............................................................................................................. 176

6.7 Example Field Section and Core Exhibiting Inten-nediate or Deep Crack: Tensile
Failure Mechanism and Directional Change in Crack Growth ................................ 177

6.8 Field Core Showing Longitudinal Wheel Path Crack Opened At Surface From
Florida Interstate 1-10 .............................................................................................. 178

6.9 Potential For Crack Growth and Time Available For Identification and
Rehabilitation For 8-inch Pavement and Given Load Spectrum ............................. 180

6. 10 Potential For Crack Growth and Time Available For Identification and
Rehabilitation For 4-inch Pavement and Given Load Spectrum .............................. 181

A. I Distribution of Transverse Stresses Computed At Increasing Vertical Distance From
0.5-in Crack: 8-in Asphalt Concrete, Stiffness Gradient Case 2, Load Positioned At 0, 7, and 20 inches From Crack ............................................................................... 192

A.2 Distribution of Shear Stresses Computed At Increasing Vertical Distance From 0.5in Crack: 8-in Asphalt Concrete, Stiffness Gradient Case 2, Load Positioned At 0, 7, and 20 inches From Crack ........................................................................................ 192

A.3 Distribution of Transverse Stresses Computed At Increasing Vertical Distance From
0.5-in Crack: 8-in Asphalt Concrete, Stiffness Gradient Case 2, Load Positioned At 25 inches From C rack .............................................................................................. 193

A.4 Distribution of Shear Stresses Computed At Increasing Vertical Distance From 0.5in Crack: 8-in Asphalt Concrete, Stiffness Gradient Case 2, Load Positioned At 25
inches From C rack ................................................................................................... 193

A.5 Distribution of Transverse Stresses Computed At Increasing Vertical Distance From
0.5-in Crack: 8-in Asphalt Concrete, Stiffness Gradient Case 2, Load Positioned At
30 inches From C rack ............................................................................................... 194



xiv








A.6 Distribution of Shear Stresses Computed At Increasing Vertical Distance From 0.5in Crack: 8-in Asphalt Concrete, Stiffness Gradient Case 2, Load Positioned At 30
inches From C rack ................................................................................................... 194
















































xv














Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy

DEVELOPMENT AND PROPAGATION OF SURFACE-INITIATED
LONGITUDINAL WHEEL PATH CRACKS IN FLEXIBLE HIGHWAY PAVEMENTS By

Leslie Ann Myers

December 2000


Chairman: Dr. Reynaldo Roque
Major Department: Civil Engineering

The primary distress mode of over 90% of high-type bituminous pavements

scheduled for rehabilitation in Florida is longitudinal wheel path cracking. This situation creates an immediate need for a clear definition of the growth mechanisms of this costly mode of failure. These cracks initiate at the surface of thick and thin asphalt concrete layers and propagate downwards in an opening mode, as evidenced by observations of trench sections and cores taken from field sites. Literature review has shown that several researchers have presented observations and/or hypotheses that attempt to explain the surface cracking phenomenon, but a complete identification for the crack propagation mechanism that considers factors found in the field does not exist.

Parametric study analyses performed were focused on predicting near-surface

crack tip stresses and determining which factors result in tensile crack growth downwards from the surface of the pavement. The finite element analysis program ABAQUS was



xvi








used along with other analytical models to compute stress intensity factors at the crack tip and to determine the propensity of effects such as pavement structure, crack length, load spectra (load magnitude and wander in wheel path), tire-pavement interface stresses, and temperature- or aged-induced stiffness gradients. Stress analyses were performed using actual measured radial truck tire-pavement interface stresses obtained from a tire research company in Ohio. Thermal analyses were conducted using temperatures measured by National Oceanic and Atmospheric Agency (NOAA) daily for several years in various north-central Florida locations. Furthermore, a sensitivity analysis of finite element model types indicated that modified 2D pavement models are suitable for representing 3D pavement bending.

The physical presence of a crack or discontinuity must be considered in pavement design in order to properly account for surface crack growth in asphalt concrete pavements. The load spectra, such as tire-pavement interface stresses produced under radial truck tires and load wander in the wheel path, in combination with stiffness gradients caused by seasonal temperatures and aging, will apparently result in tensile failure that is the primary mechanism of surface-initiated longitudinal crack propagation in the wheel paths.














xvii














CHAPTER I
INTRODUCTION


1. 1 Background


Longitudinal wheel path cracking that initiates at the surface of asphalt pavements is a relatively recent phenomenon that has major cost implications to highway departments. In Florida alone, over 90% of flexible pavements are scheduled for rehabilitation of surface cracking, making it the predominant mode of failure. Cores and trench sections taken from pavement sections that are found to have substandard crack ratings clearly show that cracks initiated at the surface and worked their way down. The surface cracking phenomenon has been reported in other areas of the United States and documented in Europe, which indicates the immediate importance of the scope of this study to be expanded to include environmental and geographical conditions other than those found in Florida. However, the development and mechanism for this mode of failure, as well as the conditions that make the pavement susceptible to crack growth, have not been clearly defined.

The aspects which define the traditional approach to pavement evaluation have been cited in numerous publications (e.g., Huang 1993; Yoder and Witczak 1975). The existing approach to performance prediction classifies pavement failure types that have been observed, studied and documented many times. However, until recently

1





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longitudinal surface cracking was not associated with damage propagating from the surface of the pavement. Therefore, the loading as defined in the existing performance analyses is not representative of field observations for longitudinal pavement surface cracking. As described in Huang's book, performance prediction is based on a collection of general data that is geared more specifically for traditional load-associated cracks that initiate at the bottom of flexible pavements. The loading included for these response predictions is a uniformly distributed vertical surface load with an average tire pressure. This loading is applied at only one position, in the location found to be critical for traditional cracking. No effort is made to distinguish between tire types nor to capture the possible effects of changing load positioning due to wander in the wheel paths.

The pavement structures analyzed using typical performance relationships are also not representative of those currently found in the field. For example, in order to capture the effects of temperature, a seasonally-averaged definition of the pavement structure is often made using a relationship developed by the Asphalt Institute (Huang 1993). This procedure has been used to find a uniform asphalt concrete stiffness, as based on the temperature computed at one-third of the depth of the asphalt concrete layer. Another key factor that is missing from pavement structures analyzed using the traditional approach is the presence of discontinuities or flaws. There is no allowance for the introduction or growth of cracks when analyzing a traditional pavement structure. Therefore, using the traditional approach to analysis is not only inconsistent with field observations, but also will not address the various conditions that lead to surface cracking.

Work done recently with measured contact stresses under radial truck tires (Roque et al. 1998; de Beer et al. 1997; Woodside et al. 1992; Bonaquist 1992) appears to define





3


conditions under which cracking initiates (Myers et al. 1999). However, because surfaceinitiated longitudinal wheel path cracking is a relatively recent phenomenon, as reported by some researchers (Myers et al. 1998; Jacobs 1995; Matsuno et al. 1992), failure theories that may apply towards addressing its development are not definitive at the present time. In fact, most failure theories do not address the possibility of a critical condition existing near the pavement's surface. The distortion energy approach has been used by some researchers (Center for Research and Contract Standardization in Civil and Traffic Engineering 1990) to analyze development of surface cracking; however, this approach will always compute the highest distortion energy at the bottom rather than at the top of the asphalt layer. Another approach currently in development incorporates continuum damage mechanics (Kim et al. 1997). Continuum damage mechanics may be used to create a reduced stiffness area within a continuum that approximates the presence of a discontinuity or flaw; however, the physical characteristics of a crack and crack tip stresses are not addressed in this method.

Several researchers have addressed the propagation of cracks in asphalt concrete by using the fracture mechanics approach. Unfortunately, the analyses presented in the studies were often limited to traditional pavement structures and loading conditions. The parameters used in the studies were often limited to either traditional bottom-up cracks (Ramsamooj 1993) or uniform and/or pneumatic truck tire loading (Collop and Cebon 1995; Merrill et al. 1998). Jacobs et al. (1996) applied an approach to characterize both surface and bottom cracking by calculating the stress intensity factors at the tip of cracks in the asphalt layer; however, the loading used in the approach was based on contact stresses measured from a bias ply truck tire. In a primarily laboratory study of cracking in





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the asphalt layer, Jacobs et al. (1996) described the continuously changing stress distribution during the crack growth process by applying linear elastic fracture mechanics principles such as Paris's Law and Schapery's theory, Because fracture mechanics can be used to describe the conditions ahead of the crack tip, it appears to be a suitable approach to describing surface crack development.

This study is part of a general investigation on the characteristics and generation of longitudinal wheel path cracking undertaken by University of Florida and supported by the Florida Department of Transportation (FDOT) and Federal Highway Administration (FHWA). Results from this study can be used to relate fracture behavior from the field to laboratory testing of asphalt concrete. Substantiating the cracking predictions would require additional field data on the characteristics of wander in the wheel paths and the frequency of critical temperatures (or gradients) in the pavement.



1.2 Research Hypothesis


The purpose of this investigation is to determine whether propagation will only occur under critical conditions by identifying the mechanisms, and the most critical factors, that lead to the development and propagation of surface-initiated longitudinal wheel path cracks. The effects of factors such as realistic tire contact stresses and load position, thermal gradients in asphalt layer, presence of discontinuities, and other certain critical conditions on cracking performance will be investigated. The implication would be that traditional approaches to pavement analysis, which typically include average





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conditions that do not capture these key factors, cannot properly describe this failure mode.



1.3 Obiectives


The primary objectives of this research study were as follows:

0 To identify the most likely mechanisms for the development and propagation of
longitudinal wheel path cracks that initiate at the surface of bituminous
pavements.

0 To investigate and identify critical conditions that result in surface crack
propagation, in order to capture the key factors that lead to this type of failure. 0 To evaluate the use of fracture mechanics for the analysis of surface-initiated
longitudinal crack growth.

0 To examine the critical conditions leading to failure, in order to assist in the
development of analysis and design tools for asphalt mixtures and pavements.



1.4 Scope


The research conducted in this study focused on identifying the critical conditions that contribute to the propagation mechanism of surface-initiated longitudinal wheel path cracking. A detailed literature review revealed that nontraditional approaches, including critical loading and pavement structural conditions, to evaluating longitudinal surface cracking have not been extensively investigated. Defining the conditions which propagate surface-initiated cracks may lead to ideas on how to best address the problem through remediation and/or prevention. It should be noted that the specific mixture





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characteristics (mixture type, gradation, etc.) that can help to alleviate this problem were

beyond the scope of this study.

The study primarily focused on analyses which predict the effects of near-surface

and crack tip stresses. The analyses necessary for developing the hypothesis on surfaceinitiated crack growth were not comparable to those of typical pavement response

models. Some characteristics and/or limitations of the analyses included in the study are

as follows:

" Two-dimensional (2D) finite element analysis was conducted for pavements with a
surface crack and complex surface loading conditions using the finite element
computer program ABAQUS. The primary focus was on using 2D modeling to evaluate the effects of different factors on crack propagation. As a first step, the
method of approximating three-dimensional (3D) pavement responses using modified
2D models was determined to be adequate for predicting the various effects.

" The evaluations and approach presented herein were designed to be suitable for nearsurface stress states and. most specifically, the development and propagation of
surface-initiated longitudinal wheel path cracks.

" Application of a single radial truck tire load was used on the pavement models. The
analyses were performed at one static load magnitude, as measured and provided by Dr. Marion Pottinger at Smithers Scientific Services, Inc. in Ohio. This magnitude
was deemed representative of a typical value for a radial tire found on a high-volume
highway.

" Conventional pavement structures were considered in the study (i.e., asphalt surface
on aggregate base and subgrade).

" Linear elastic fracture mechanics was utilized to predict stress intensity factors (KI,
K11) and fracture energy release rate (J). These parameters were descriptive of crack
tip stress states and conditions.


Some of the assumptions on which the analyses were based include:

" A study was conducted that indicated use of two-dimensional (2D) finite element
analysis was reasonable for approximating three-dimensional (3D) finite element
analysis, if certain modifications were applied to match pavement response.





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Plane strain conditions were assumed for 2D analyses and the stress-strain response of
the asphalt concrete layer was considered in the evaluation. The accuracy of the stress
distributions within the base and subgrade layers was not considered.

Linear elastic materials were used in the models, which allowed for the evaluation of
effects on pavement response, while reducing modeling time and computational effort. It also allowed for the evaluation of pavement models using linear elastic
fracture mechanics. However, it should be noted that using linear elastic
isoparametric elements in a model does not allow for the exact estimation of stress
concentrations under the edge of a concentrated loading. Likewise, linear elastic
materials are assumed to have infinite strength, which does not reflect the physical
reality of the pavement.


A range of factors was defined to represent critical structural or loading conditions for the pavement model. The values assumed to represent specific load and pavement structure include load positioning (wander) with respect to crack, realistic (vertical and lateral contact stresses) tire load application, crack depth, asphalt pavement thickness, surface and base layer stiffness, and stiffness gradients induced in asphalt concrete layer due to daily environmental and temperature fluctuations.




1.5 Research Approac


The research was mainly an analytical study supplemented by the acquisition of measured tire-pavement interface stresses and other specific truck tire data. The overall research approach for the development of an explanation for the propagation mechanism of surface cracking is presented in Figure 1. 1. The main purpose of the analyses was to identify different factors that determine the critical conditions that lead to the development and propagation of surface-initiated cracking. Studies conducted as part of the research are described in the following areas:





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" Literature Review: existing ideas and theories published on the subject of surfaceinitiated cracking in asphalt concrete pavements and traditional continuum mechanics
versus fracture or damage mechanics are examined. The findings in the literature
yielded different methods available for explaining crack growth such that selection of
the most plausible theory could be made.

" Tire Contact Stress Verification: finite element modeling was used to verify
measured tire contact stress use in pavement systems and to determine the effects of
tire type, loading, and inflation pressure.

" Pavement Analysis: pavement analyses were conducted and used in the development
of an approach to modify two-dimensional analyses to approximate three-dimensional
pavement response.

" Parametric Studies of Pavement System: analytical studies were conducted to discern
structural and temperature-related effects on pavement response. Evaluations were
conducted by predicting stress states in the process zone ahead of crack tip, as well as by evaluating different stages of crack length and various positions of loading relative
to crack location. Characterization of crack tip conditions was accomplished by predicting stress intensity factors and the fracture energy release rate parameter.

Identification of Critical Conditions For Surface Crack Propagation: analytical
studies were conducted to determine the factors that induce critical conditions near cracked pavement surface. The purpose was to distinguish which factors produced conditions most likely to result in the propagation of surface-initiated longitudinal
cracks observed in the field.

Final recommendations were made for the development of an analysis and design tool
for asphalt mixtures and pavements.






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Continuum Mechanics Theories on Surface-Initiated
versus Longitudinal Wheel Path Crackinjg
Fracture Mechanics


Selection of Methods for Analysis FRACTURE MECHANICS
of Crack Propagation in Asphalt Stress Intensity Factors
Concrete Pavement Fracture Energy Parameter


Verification of Tire Contact Stresses
Using Finite Element Tire Model


fAnalysis of Crack Growth in Asphalt Layer
Using Finite Element Model of Pavement
F ________________Prediction of Crack Tip Stresses Characterization of Crack Growth
and Stress Intensity Factors By Fracture Energy Parameter




Identification of Critical Conditions On Crack Propagation
-Measured lire Load and Wander
Varied Pavement Structures


Recommendations for Development of An Analysis and Design Tool For Asphalt Mixtures and Pavements









Figure 1. 1: Overall Research Approach Flowchart.














CHAPTER 2
LITERATURE REVIEW




2.1 Overview


A comprehensive literature search was conducted to identify existing publications dealing with the evaluation of surface-initiated cracking. Previous work had demonstrated that surface cracking was most likely initiated by near-surface lateral stresses induced by radial truck tires. The following subjects were examined:

Classical fatigue approach

Continuum damage approach Fracture mechanics approach

Measurement of tire contact stresses

Analysis of surface cracking

With the exception of the literature on tire contact stresses, until recently researchers had not focused on the possibility of critical stresses occurring at the surface of the pavement. The primary focus had traditionally been on the critical stress induced by pavement bending at the bottom of the asphalt concrete layer.






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2.2 Classical Fatigue Approac.


Longitudinal wheel path cracking has been observed in the field and cited in

publications as initiating at the pavement surface (Myers et al. 1998; Roque et al. 1998). This type of damage occurs in a situation not considered by classical fatigue approaches to pavement cracking. The aspects which define the traditional approach to pavement evaluation have been cited in numerous publications (Huang 1993; Yoder and Witzcak 1975). The existing approach to performance prediction is broad and classifies pavement failure types that have been studied and documented extensively; therefore in this way, it fails to account for recent damage found in the field (i.e., longitudinal surface cracking). For example, loading as defined in existing performance analyses is far removed from field observations. As described by Huang (1993), performance prediction is based on a collection of general data that is geared more specifically for traditional load-associated cracks that initiate at the bottom of flexible pavements. The loading included for these response predictions is a uniformly distributed vertical surface load with an average tire pressure. This loading is applied at only one position, in the location found to be critical for traditional cracking. No effort is made to distinguish between tire types nor to capture the possible effects of changing load positioning due to wander in the wheel paths.

The pavement structures analyzed using typical performance relationships are also not representative of those currently found in the field. For example, in order to capture the effects of temperature, a seasonally-averaged definition of the pavement structure is made using a relationship developed by the Asphalt Institute (Huang 1993). This procedure has been used to find a uniform asphalt concrete stiffness, as based on the





12


temperature computed at one-third of the depth of the asphalt concrete layer. Another key factor that is missing from pavement structures analyzed using the traditional approach is the presence of discontinuities or flaws. There is no allowance for the introduction or growth of cracks when analyzing a traditional pavement structure. Therefore, using the traditional approach to analysis is not only inconsistent with field observations, but also will not address the various conditions that may lead to-surface cracking.

Studies and pavement performance modeling conducted in the United States have usually concentrated on classical fatigue approaches that consider failure to start at the bottom of the asphalt surface layer (e.g., Asphalt Institute mechanistic-empirical design procedure (Huang 1993); and the performance models developed for Superpave in the SHRP program, (Lytton et al. 1990)). The Asphalt Institute method for pavement design is based on this approach. The number of cycles to failure (Nf) can be calculated as a function of the dynamic modulus and tensile strain at the bottom of the asphalt layer for the prediction of fatigue cracking for a standard mix with an asphalt volume of I I% and air void volume of 5%, although an adjustment for different mixture volumetrics is available (Huang 1993). The following fatigue equation was used as the failure criterion for cracking in the Asphalt Institute's design procedure:



Nf = 0,0796 (E;t)-1.291 JE*J -0.854

where Nf = allowable number of load repetitions to control fatigue cracking,
JE*J = dynamic modulus of the asphalt mixture (psi),

st = tensile strain at the bottom of the asphalt layer, computed by elastic layer theory (in/in).





13


Such predictions for failure are based on laboratory tests which are calibrated to the field and offer limited correlation to field occurrence in accounting for traffic load relaxation times and the subsequent crack propagation rates. Therefore, this elastic layer analysis approach will neither predict nor provide design input for the type of surface cracking found on Florida's interstate roads.



2.3 Continuum Damage Approach


An approach currently in development to explain damage growth incorporates

continuum damage mechanics (Kim et al. 1997). Continuum damage mechanics may be used to create a reduced stiffness area within a continuum that approximates the presence of a discontinuity or flaw. The method utilizes the work potential theory to model damage growth during both control led-strain and controlled-stress loading cycles and healing during rest periods. The research has primarily been applied to evaluation of classical fatigue cracking, which does not develop in the same manner as longitudinal surface cracking. Another limitation of the continuum damage approach is the inability to replicate the physical characteristics of a crack and the prediction of crack tip stresses and behavior.

Boundary element methods have been described in detail by Crouch and Starfield (1990). Boundary element methods have been widely used in the geomechanics field and offer a different computational technique for predicting damage in asphalt concrete pavements.





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Another theory which was a possibility for explaining the mechanism of surface cracking was the distortion energy approach. The distortion energy model was used by some researchers (CROW 1990) in an attempt to explain the development of surface cracking. This approach is based on the existence of a relationship between distortion energy and fatigue life. That is, fatigue of a viscoelastic material develops with the accumulation of distortion energy induced by load repetitions (Stulen and Cunnings 1954). It assumes that failure occurs by exceeding the energy tolerance of a material and the pavement has no crack present initially. The basic idea behind the distortion energy model is that repeated applications of a moving wheel results in an accumulation of distortion energy in a viscoelastic material that will eventually exceed the tolerance of the asphalt mixture.

But as the study pointed out, this approach will always compute the highest

distortion energy at the bottom rather than at the top of the asphalt layer, which may limit its usefulness in explaining crack development at the pavement surface. However, the study mentioned that the combination of tensile stresses at the surface (induced by horizontal contact shear forces) and high values of dissipated distortion energy could cause cracking in the wearing course. It should be noted that linear elastic multi-layer analysis programs cannot be used to compute dissipated energy values due to passing loads, although approximations are available in the literature.





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2.4 Fracture Mechanics Approach


The concept of crack propagation that proceeds downwards from the surface of the asphalt has not been fully analyzed using traditional pavement analysis tools. In fact, most failure theories do not address the possibility of a critical condition existing near the pavement's surface. Several researchers have addressed the general propagation of cracks in asphalt concrete by using the fracture mechanics approach. Unfortunately, the analyses presented in the studies were often limited to traditional pavement structures and uniform loading conditions. Nevertheless, existing solutions for uncracked pavements (uniform stress distribution) are not appropriate for use in evaluating pavements with a crack. Ramsamooj (1993) adopted existing solutions by employing the fundamentals of fracture mechanics to predict crack growth under dynamic loading. The stress intensity factors (SIF) at the crack tip were calculated at incremental stages of crack growth, from the initial crack at the surface, to a short through-crack and finally into a long throughcrack. Three different crack types were evaluated: transverse (across wheel path), longitudinal (parallel to wheel path), and semi-elliptical. Fracture was defined as occurring when the stress intensity factor computed at the crack tip under fatigue loading exceeds the fracture toughness of the material. The effects of temperature on fracture susceptibility were also considered. Closed-forin solutions were manipulated to predict stress intensity factors for various crack types at different stages of crack growth; however, a uniform vertical loading was used for the analyses which does not reflect a realistic loading case.





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Collop and Cebon (1995) also conducted a study on the use of fracture mechanics for analyzing surface crack growth in pavement systems. The authors sought to theoretically define the mechanisms of fatigue cracking in flexible pavements under different traffic and cyclic thermal loading conditions by using linear elastic fracture mechanics. An axisymmetric finite element model (FEM) was developed using the ABAQUS computer program (HKS 1997) to investigate stresses ahead of the longitudinal cracks in the surface layer. Loading data taken from work done by Jacobs (1995) for a bias ply truck tire were used in the analysis. A parametric study was conducted to evaluate the effects of pavement thickness and elastic modulus ratio and found that increasing the modulus ratio and reducing the asphalt thickness will tend to reduce the transverse tensile stress at the pavement's surface. The Mode I stress intensity factor (Broek 1982) was predicted ahead of the crack tip and it was shown that the crack propagates vertically downward to about 10 to 20 mrn and then stops. Also, increasing the asphalt thickness and decreasing the elastic modulus ratio will increase the magnitude of the stress intensity factor and the depth to which the crack propagates, as illustrated in Figure 2.1

Increasing temperature fluctuation also increased the stress intensity factor at the surface crack tip, which helped to explain longitudinal cracking that occurs in warmer climates where thermal cooling gradients are found to be high. The effects of other modes of fracture were not included in the study.





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A THEORETICAL ANALYSIS OF FATIGUE CRACKING IN FLEXIBLE PAVEMENTS
0.2
Structure C (350 mm)
S 0.15 .... Structure A (25 mm.


.. Etl E2 = 50
A 0.15
%' EI/E2 5 I0
C.C


0 .-..'

01E
10 -4 Io-, 0-2 to-I
Crack length .C
m



Figure 2.1: Stress Intensity Factor Plotted As a Function of Crack Length for a Surface Crack Due to Vehicular Loading For Three Different Pavement Structures With Different Modulus Ratios. (after Collop and Cebon 1995)


Using fracture mechanics principles, Jacobs et al. (1996) analyzed the crack

growth process. Specimens measuring 50-mm by 50-mm by 150-mm were subjected to tension-compression tests under repeated loading conditions. Analysis of crack opening displacement (COD) measurements yielded crack growth parameters n and A. Results of the study showed that Schapery's theoretical derivations for n and A for viscoelastic materials were valid and that the exponent in the Paris Law can be estimated by the slope of the compliance curve. They also concluded that the constant A from the Paris Law may be estimated from a combination of the fracture energy, mixture stiffness, and maximum tensile strength.





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2.5 Measurement of Tire Contact Stresses


Tire engineers have tried for many years to model the three-dimensional contact patch between a tire and the pavement. It should be noted that stresses predicted by automotive models were those of the pavement on the tire and were thus opposite the orientation of the pavement engineers. Also, because measuring pressure was so difficult and expensive, studies conducted were limited to tires run on steel plates rather than on actual asphalt or other viscoelastic materials.

It is important to understand how tire-pavement interface stresses are measured and where they come from. Work has been done in this area by various tire researchers. M.G. Pottinger (1992) has done considerable work in the area of contact patch stress fields for both truck and car tires. He explained that the effect of free rolling radial truck tires on a pavement is very different than that of bias ply truck tires. Two types of effects exist under truck tires. These are generally referred to as the pneumatic effect and Poisson's effect (Roque et al. 1998). Figure 2.2 illustrates the basic difference in contact effects. Although both fields exist under both types of tires, one effect will be more dominant for a given type of tire.

The overriding effect induced under radial truck tires is the Poisson effect. In

other words, the pneumatic effect is less, such that Poisson effect is dominant. This is a Direct result of tire construction. Radial tires are constructed to have stiffer treads and less stiff sidewalls, so that the tread does not defonn as much as the tire rolls. Thus, the lateral stresses induced on the road by the radial truck tire will tend to push out from center of the tire ribs, as shown in Figure 2.2. On the other hand, the pneumatic effect is





19


dominant under bias ply truck tires, such that lateral stresses pull the pavement surface toward the center of the tire.

By using triaxial load pin transducers inserted onto a flat steel test track, Pottinger was able to measure tire-pavement interface stresses and displacements for vertical, longitudinal and transverse axes. He also determined the rolling tire footprint shape. Figure 2.3 shows the test track configuration that was utilized.

Other researchers have developed measurement systems to capture the contact

patch between the tire and the underlying structure. In South Africa, de Beer et al. (1997) conducted a laboratory and field experiment on the development of the Vehicle-Road Pressure Transducer Array (VRSPTA) System that measures three-dimensional stresses induced under bias ply, radial and wide based radial truck tires at different loads and inflation pressures. The experimental setup consisted of 13 triaxial strain gauge steel pins (spaced 17mm transversely) mounted on a steel plate and fixed flush with the road surface. The setup is illustrated in Figure 2.4. The contact stress distributions measured by de Beer, although a less refined patch was captured, were comparable in both stress magnitude and pattern to those measured on Pottinger's steel bed device. As seen in Figure 2.5, both the nonuniform vertical load and transverse stress reversals were captured by the VRSPTA system.

Woodside et al. (1992) also developed a similar steel bed-transducer array device to measure the contact stress patch between the tire and underlying material in the laboratory. Normal and tangential contact stresses were measured under both static and dynamic radial car and truck tires. The steel plate system was fitted with 12 transducers and repeatedly measured a strip transversely every 5 mm over the entire contact patch. A





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Radial TieBias Ply Tire


Flexible Wall More Rigid
0( Wall
More Rigid UFlexible
T read Tread
M'




~ Pneumatic
Effect




Ld Poisson

Effect





~Nc Effect





Figure 2.2: Structural Characteristics of Bias Ply and Radial Truck Tires and Their Effects on the Pavement Surface. (after Roque et al. 1998)






21

















Bed Motion
16Transducers Tr



Tire Rolling Direction Bed


cry ,6x


OYz

Coaxial Load and Displacement Transducer Detail









Figure 2.3: Schematic of System Used to Measure Tire Contact Stresses. (after Roque et al. 1998)





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TYRE ON HVS (or Vehicle) Direction of travel


VRSPTA

123 56 Pavement Surface




Z CONDITIONER
RACM
1 2 3 4 5 6






z t I l a 7! .. ... .. : .." '

N~i! ii 4!i~i:?lMaster
L10




Slave 1


Slave 3 pro

Computer set-up Figure 2.4: Experimental Setup of Vehicle-Road Surface Pressure Transducer
Array (VRSPTA) System Used to Measure Tire Contact Stresses.
(after de Beer et al. 1997)






23

315/80 R22.5: TYPE IV, Table 1
Inflation Pressure =800 kPa; Load =40 kN

Q_ 1 5







-6


Longitudinal rear Lateral

Vertical Contact Stress Distribution












-01


LateralLongitudinal Lateral Contact Stress Distribution Figure 2.5: Three-dimensional Vertical and Lateral Contact Stress Distributions Under Radial (R22.5) Truck Tire at Rated Load. (after de Beer et al. 1997)





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total of 90 contact stresses were obtained for each test. The contact stresses were then used in the evaluation of durability of surface clippings on asphalt overlays. Results concluded that implementation of surface clippings of I mrn macro-texture may improve skid resistance on pavements.

A tire-pavement study was conducted by Bonaquist (1992) at the FHWA

Accelerated Loading Facility to determine the flexible pavement response to wide based single tires. The focus of the experiment was to capture the tensile strain at the bottom of the surface layer and the vertical strains in the asphalt concrete, base and subgrade layers. He reported that a wide base single tire results in higher vertical compressive strains in all of the pavement layers, generates increased tensile strains at the bottom of the asphalt concrete layer, and induces more rutting damage in less time than the traditional dual tire configuration. Responses near the surface of the pavement were not evaluated.

Work done recently by researchers in Florida focused on the effects of tire type, loading, and inflation pressure on measured contact stresses under various truck tires (Myers et al. 1999). The study showed that the contact stress distributions measured under radial truck tires appear to contribute to the prevalence in recent years of surfaceinitiated wheel path cracking and near-surface rutting. It was explained that tire structure has a significant influence on contact stresses; in fact, stress states induced by radial and wide base radial tires were determined to be potentially more detrimental to the pavement's surface than stress states induced by bias ply tires. The primary difference was found in lateral contact stresses, rather than in vertical stresses, that develop under each type of tire. The effect of tire structure is shown in Figure 2.6.





25


Radial Truck Tire

+ I

Near-Surface Stresses


Tension A AA Truck Tire
Compression Tread Effect

(+) Pavement
() "000 Bending Effect


(+) ., .'
G i 'x. % Overall Effect (0 4010




Bias Ply Truck Tire

+

Near-Surface Stresses

Tension 4 Truck Tire
Compression Tread Effect

(+) Pavement
(_) *@e* ** Bending Effect


(+)
Oxx ,Overall Effect





Figure 2.6: Effect of Pavement Bending Due to a Bias Ply and Radial Truck Tire on Surface Stress Distribution. (after Myers et al. 1999)






26


The research stated that vertical and lateral tire contact stresses must be considered in the

design and evaluation of asphalt pavements. Lateral stresses under radial tires appear to

result in stress states that are more conducive to surface cracking in asphalt pavements

(Figure 2.7). The vertical stresses for various tire types are different, as shown in Figure

2.8, but do not influence surface failure to the extent that the lateral






600
0 Bias Ply A- -Radial 400- -D- Wide Base Radial
14
0. 1

200 16
EP


0
cc 0

Eq
-200- fn
Nip
A
A

-400




-600
0 50 100 150 200 250 300 350

Transverse Location, X (mm)




Figure 2.7: Transverse Contact Shear Stresses Measured For a Bias Ply, Radial, and Wide Base Radial Tire At the Appropriate Rated Load and Inflation Pressure. (after Myers et al. 1999)






27






-2000
-Bias Ply
Radial
-1800 Wide Base Radial

-1600


-1400 -________CL
-1200 -___-O1000i-


o -800 _-





-400 U_ a a

-200
0 *I







(ate MyrItal 99





28


stresses do. It appears that lateral stresses induce tension at the pavement's surface and consequently may initiate cracking and/or reduce the mixture's confinement and resistance to shear and permanent deformation.

Wide base radial (Super-single) tires were observed to induce vertical contact stresses as high as 2.5 times the inflation pressure, as shown in Figure 2.8. The authors explained that this case represents a severe loading condition that, when combined with lateral stresses under the tire that reduce mixture confinement, greatly increases the potential for near-surface damage.




2.6 Analysis of Surface Cracking


Because surface-initiated longitudinal wheel path cracking has been cited as critical pavement damage in recent years, failure theories that may apply towards addressing its development are not yet definitive. In Europe, the effects of lateral stresses at the tire-pavement interface have been studied and published. The belief is that these lateral stresses initiate cracking at the pavement surface which somehow propagates downwards. It is recognized that these cracks are neither of the traditional fatigue nor reflective nature. Traditional fatigue is generally identified by the appearance of alligator cracking in the wheel paths and is typically assumed to be caused by large tensile stresses and strains at the bottom of the asphalt concrete surface layer. Hugo and Kennedy (1985) presented observations that allude to the phenomenon of surface-initiated cracks. They reported the initiation of cracks at the pavement's surface directly underneath the rubber pressure pads of the heavy vehicle simulator after the





29


pavement was subjected to repeated stationary cyclic loads. They attributed the cracks to the presence of horizontal shear stresses induced by the rubber pads on the pavement.

Analytical work in the Netherlands illustrated how inward radial (horizontal) stresses could lead to tension at the edges of a circular load (CROW 1990). This work prompted M.M Jacobs of Delft Institute of Technology (the Netherlands) to describe the occurrence of maximum tensile stresses at the surface of the pavement through analytical evaluation (Jacobs 1995). This study predicted tensile stresses at the edge of a truck tire on the pavement's surface which were sufficient to cause fracture. These tensile stresses were found to dissipate rapidly with increasing depth; that is, they typically existed in the top 10 millimeters of the asphalt layer. These tensile stresses were cited as the most probable cause for the initiation of longitudinal cracking found in flexible pavements. However, tensile stresses were generated at the edge of the tire load because measurements were obtained from a bias ply truck tire, since Jacobs did not use recently measured tirepavement interface stresses. The predictions provided by Jacobs suppor-ted the theory that lateral stresses in the surface may initiate cracking. However, the study was limited by the following factors:

" Lateral stresses were inferred from values published in the literature, not measured. Exclusion of dimensional (layer thickness) effects. Sources of tire-pavement interface stress data are considered outdated in comparison
to current tire characteristics.

" There did not appear to be access to measured tire-interface stresses for radial truck
tires.

Recent work (Myers 1997; Myers et al. 1998) has shown that longitudinal surface cracking appears to be initiated by significant lateral contact stresses that are induced






30


under radial truck tires. Measured contact stresses were obtained for a typical radial tire

from Pottinger's steel bed device and were analyzed in the BISAR program. Analyses

showed that a high magnitude of tension was induced under certain ribs of the tire tread

that are in contact with the pavement's surface, as presented in Figure 2.9.






10
9 Tension
8
7 Rib 1 Rib 2 Rib 3 Rib 4 Rib 5

6
5
IL
4 3

0 1
0
CO) -1

> -3
-4 Rated Load/Pressure
-5 Pavement Structure
-6 AC: d1=200 mm, E1=5500 MPa
-7 Base: d2=300 mm, E2=300 MPa
-8 Subgrade: d3=infinite, E3= 100 MPa
-9 Compression
-10 1 1
0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 Transverse Distance, X (mm)






Figure 2.9: Predicted Transverse Stress Distribution Induced By Radial Truck Tire Near Pavement Surface. (after Myers et al. 1998)





31

Tensile stresses were found to be more significant in thicker and stiffer asphalt concrete pavements. The study gave a viable explanation for longitudinal crack initiation; however, use of linear elastic layer analysis did not allow for analysis of crack growth or discontinuities in the pavement.

Researchers in Japan (Matsuna and Nishizawa 1992) indicated that longitudinal

surface cracks have been reported as a major problem in asphalt pavements. Results from a visual condition survey indicated that the cracks are due to large tensile strains that develop close to the tire shoulders at high temperatures. By using an axisymmetric finite element model, they explained that tensile strains are concentrated at the tip of a small crack that has been induced at the pavement's surface. The analysis work included a traditional uniform circular vertical loading, which is not representative of a realistic tire loading.

Finite element modeling was used by Merrill et al. (1998) to analyze a flexible pavement system modeled with a nonuniform tire load. An axisymmetric model was developed using the ABAQUS finite element analysis computer program (HKS 1997) and was loaded with lateral and vertical stress measurements taken from the South African VRSPTA (de Beer et al. 1997) device. Significant transverse tensile strains were predicted at the pavement surface under the tire's edges and were found to be more pronounced in thicker pavements. The authors stated that conventional pavement response models are inadequate for the prediction of surface crack initiation. The effects of temperature on the predicted strains near the pavement surface were not considered and discontinuities (i.e. cracks) were not introduced into the pavement system in the study. However, it was significant to find that other researchers found the concept of





32


critical condition (versus those included in traditional pavement analysis) essential to the initiation of surface cracks and recommend a move to utilizing more complex pavement analysis tools.



2.7 Summ


The discussion and review presented above indicate that there is an immediate need to more completely define the behavior of surface-initiated longitudinal wheel path cracking. Identification of the critical conditions that induce the cracking mechanism, as well as obtaining a clearer understanding of the effects of different factors involved, is essential for this problem to be addressed fully.













CHAPTER 3
ANALYTICAL APPROACH




3.1 Introduction


An analytical approach was formulated to identify critical factors on surface crack development. The purpose of the approach was multifaceted, ranging from detailed verification of tire load measurements to the development of a systematic pavement analysis method. The basic objective for analyzing a series of pavement systems was to establish the circumstances in which a critical condition that induces crack growth will occur. The study was restricted to the analysis of the asphalt concrete layer, particularly with respect to the portion immediately surrounding the initiated surface crack. For this reason, the approach that was developed concentrated on the validation, evaluation, and methodology applicable to near-surface response of the asphalt pavement. The validation segment of the research involved verifying the use of measured tire contact stresses in pavement analysis and calibrating the pavement model to approximate the bending response of a real pavement system. The evaluation section included the actual approach to modeling a cracked pavement system and analyzing the stress states that occur once a crack was induced and complex loading was applied. The selection of a method for



33





34


analysis incorporated fracture mechanics as an analysis tool for describing the characteristics of crack tip conditions and growth. Expanding these segments of the approach gave a comprehensive basis for analysis.



3.2 Validation of Measured Tire Contact Stresses


As discussed in Chapter 2, tire measurements were obtained from Smithers Scientific Services, Inc. for three different truck tire types at three load and inflation pressure levels. The tire contact stresses were measured on a steel bed device and were then presented in database form for use in analysis. However, there was a need to determine whether tire contact stresses measured on a rigid foundation are significantly different than contact stresses under the same tire on an actual pavement. Therefore, finite element modeling was used to verify measured tire contact stress use in pavement systems and to define the effects of pavement structure on contact stress distribution. A two-dimensional (21)) finite element tire model was designed and analyzed in the ABAQUS computer program (HKS 1997) to verify that tire contact stresses measured on sensors embedded in a steel foundation can be used appropriately for pavement analysis. The basic idea was to compare tire contact stresses measured on a steel bed with tire contact stresses for the same tire on typical asphalt pavement structures. A comparison between near-surface stresses in the asphalt concrete layer between the following two cases was made:

" Tire contact stresses measured on a steel bed, then applied to the pavement structure. The same tire applied directly to the pavement structure.





35

Since measured contact stresses were typically applied to the surface of a modeled pavement structure to evaluate pavement response and performance, the most important question to be answered was whether there is a significant difference between pavement stresses predicted by the application of these measured stresses and pavement stresses predicted when a tire structure of equivalent load is applied directly to the surface.

Therefore, the following steps were involved in the research:

I Development and validation of a tire tread model that adequately represented the
behavior of a real tire. The measured tire contact responses to inflation were used
to verify the reasonableness of the tire tread model.

2. Use of the tire model to predict tire contact stress distributions on a steel bed.
These predicted stresses then served as the "measured" contact stresses on the
steel bed.

3. Application of the "measured" contact stresses obtained in step 2 to a range of
pavement structures, and determination of the resulting pavement contact stresses.

4. Application of the tire model to the same range of pavement structures and
determination of the resulting pavement contact stresses.

5. Evaluation of the vertical and transverse pavement contact stresses predicted in
steps 4 and 5 to determine whether the use of contact stresses measured on a steel
bed were reasonable for the evaluation of pavement response and performance.



3.2.1 Development of Tire Model

A secondary objective of this study was to develop a reasonable tire model that represents the structural behavior and response of a typical radial truck tire tread. This was a critical step in this investigation. A tire model had to be used to make fair comparisons of contact stress distributions, since actual measurements of contact stresses under tires could not be made on real pavements.





36

The development of a comprehensive structural model of a truck tire was a major challenge. Furthermore, radial tires and bias-ply tires are totally different from a structural point of view (Myers et al. 1999) and the actual structural make-up of these tires is proprietary information not available to the general public. However, some basic response data regarding the behavior of typical radial truck tires and their structural makeup was provided by Smithers Scientific Services, Inc. and was used along with a basic knowledge of the structural behavior of radial truck tires to develop a two-dimensional model of a radial truck tire tread.

As discussed previously, the structural behavior of radial truck tires is governed by a wall structure of very low stiffness and a very stiff tread structure resulting from the steel strands used to reinforce the tread. A cross-section of a typical radial tire is illustrated in Figure 3.1 and shows a tread area that is 8.12 inches wide and 1.4 inches high. The steel reinforcement was concentrated in an area that is 0.33 inches high, approximately 0.96 inches above the outer surface of the tire.

Data provided by Dr. Pottinger indicated that the radius of curvature of the tread structure shown in Figure 3.1 was 20.32 inches at an inflation pressure of I 10 psi. This radius of curvature corresponded to a deflection of 0.4 inches at the center of the tread structure relative to the uninflated position of the tread. This measured structural response was used to develop a tire tread structural model by determining the structural characteristics (essentially, the amount of steel) required to match the measured response.





37












0.96in 1.i



8in





Figure 3.1: Cross-Section of a Typical Radial Truck Tire.






Inflation Pressure 110 psi

0.1in


1.4in 28 0 0.05in in



8in



Material Properties: Tire Part Material Elastic Modulus, E Poisson's Ratio, v

Reinforcing Beads Steel 29.0E6 psi 0.15

Tire Tread Rubber 1160 psi 0.48

Tire Grooves Air 9.8E-6 psi 0.4955



Figure 3.2: Finite Element Representation of Tire Tread Structure.





38


The ABAQUS finite element program was used to model the tire tread as shown in Figure 3.2, which is a reasonable representation of the actual tire tread shown in Figure

3. 1. The steel strands were modeled as a solid strip of steel, and the connection between the steel strands and the rim were modeled as a pin connection at either end of the steel strip used to represent the strands. Typical modulus values were used for tire rubber and steel, as presented in Figure 3.2. An inflation pressure of I 10 psi was used.

The height of the steel strip was determined by varying the height of the steel until the predicted deformation response of the tire matched the measured deformation response of the real tire. Thus, the overall stiffness of the tire tread was matched for the generation of a tire model. It was determined that a 0. 1 inch steel strip embedded in the tire tread resulted in the same structural response as the 0.34 inch high area of steel strand reinforcement in the actual tire.

In order to further assess the potential of the tire model developed, a comparison was made between contact stresses predicted by the tire model applied to a steel bed, and contact stresses measured under the actual tire on a steel bed. The ABAQUS finite element computer program was used to apply the tire model (Figure 3.2) to a steel bed and determine the resulting vertical and transverse contact stresses. Predicted stresses were captured under the tire model at the nodal points of a finely-graded finite element mesh. As stated previously, measured contact stresses for the tire modeled were provided by SWithers Scientific Services, Inc. for comparison purposes.

Figures 3.3 and 3.4 clearly indicate that the tire modeled on a steel bed predicted both vertical and transverse contact stresses similar to those actually measured under the real tire. Although some variation in magnitude was observed, the tire model captured





39


the patterns of both the vertical and transverse contact stress distributions, as well as predicted the maximum stress values, reported to exist under typical radial truck tires (Myers et al. 1999; de Beer et al. 1997). The model's ability to capture the transverse contact stress reversals under the individual tire ribs was particularly important (Figure

3.4).


3.2.2 Selection of Pavement Structures For Analvsis

The key question to be answered was whether there is a significant difference

between Pavement stresses predicted by the application of contact stresses measured on a rigid foundation, and pavement stresses predicted when a tire structure of equivalent load is applied directly to the pavement surface. The primary source of variation between the two cases was related to the degree of interaction that occurs between the tire structure and the pavement structure. Therefore, for a given tire structure, the answer to this question varied with the structural characteristics of the pavement system. However, a basic understanding of stress distributions within layered systems (Huang 1993; Yoder 1975) indicated that the greatest differences would occur in pavements with thinner asphalt concrete surface layers and in pavements with higher surface-to-base layer modulus ratios (E I /E2).

Boussinesq's theory (e.g., see Huang 1993) clearly indicated that stress

distributions caused by surface loads applied to a semi-infinite mass (i.e., one-layer






40
















Transverse Distance, x (in)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
0



-50



-100 4 r



in-150-A



-200
Rib 1 Rib 2 Rib 3 Rib 4 Rib 5


-250
--'-- Stresses Measured From Tire Tested on Steel Bed Device
Stresses Predicted Using Tire Model on Steel Bed
-300








Figure 3.3: Measured and Predicted Vertical Stress Distribution at Surface
of Steel Bed.






41







8O

Rib1 Rlb2 Rib3 Rib4 Rib5

60_



0




020-





40



-60._ __Stresses Measured From Tire Tested on Steel Bed Device '

--I-Stresses Predicted Using Tire Model on Steel Bed
-80 1....
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Transverse Distance, x (in)









Figure 3.4: Measured and Predicted Transverse Stress Distribution at
Surface of Steel Bed.






42


theory) are independent of stiffness. Thus the stress distribution induced by a uniformly distributed load applied to a steel foundation was identical to the stress distribution induced by a uniformly distributed load applied to a rubber foundation. On the other hand, multi-layer theory (e.g., see Huang 1993) clearly indicated that near-surface stress distributions are primarily governed by relative stiffness between the surface and the base layer. Consequently, near-surface stress distributions deviate most from one-layer theory* as the surface-to-base layer modulus ratio (EI/E2) increases and as the surface-to-base layer thickness ratio (h I /h2) decreases. Furthermore, base thickness and subgrade stiffness have almost no influence on the near-surface stress distribution of pavements, which made these factors of no consequence to this study (Huang 1993; Yoder and Witczak 1975).

Therefore, relatively thin asphalt surface layers having a range of ElI /E2 ratios

were targeted for this study. Analyses were first conducted using a 4-in surface layer with E1/E2 ratios ranging from about 4 to 40. As indicated below in the discussion of results, no difference in pavement surface stresses was observed, indicating there was no need to evaluate thicker surface layers. Therefore, analyses were then conducted using a 2-in surface layer with II/E2 ratios ranging from about 4 to 40 to determine if an effect would develop. A summary of the eight pavement structures analyzed is presented in Table 3. 1.





43




Table 3.1: Pavement Structures Used for Analysis. Parameter Pavement Structure
1 2 3 4 5 6 7 8
Surface Layer Thickness (in) 2 4 2 4 2 4 2 4
Base Layer Thickness (in) 12 12 12 12 12 12 12 12
Subgrade Thickness (in) 92 92 92 92 92 92 92 92
Surface Layer Modulus (ksi) 200 200 200 200 800 800 800 800 Base Layer Modulus (ksi) 44 44 20 20 44 44 20 20
Subgrade Modulus (ksi) 15 15 15 15 15 15 15 15
Surface-to-Base Layer Stiffness 4.7 4.7 10 10 18.3 18.3 39.3 39.3 Ratio (E I IE2)



3.2.3 Results of Verification Analyses

The vertical and transverse stresses at the surface of the pavement system were predicted for the following two cases:

I The tire model developed in this study was applied directly to the pavement structure. 2. Contact stresses predicted by applying the tire model to a steel bed were converted to
nodal point forces that were applied to the surface of the pavement structure. This corresponds to the case of using contact stresses measured on a steel bed to predict
pavement response.

Figures 3.5 through 3.8 show that there was little difference between either the

vertical or the transverse surface stresses predicted by these two cases for the 4-in surface layer over the range of stiffness ratios evaluated. Figures 3.5 and 3.6 show results for a stiffness ratio of 4.6, while Figures 3.7 and 3.8 show results for a stiffness ratio of 39.4. The analyses clearly indicated that use of contact stresses measured on a steel bed predicted pavement stresses adequately, in terms of both the pattern of the stress







44











Transverse Distance, X (in)
6 8 10 12 1




-50







0





>-200Rib i Rib 2 Rib 3 Rib 4 Rib 6


-U- Predicted Stresses Using Tire Model on Pavement System
-250
Predicted Stresses Using Contact Stresses From Tire Model
on Steel Bed

-300















Figure 3.5: Vertical Stresses Predicted at Surface of 4-in Pavement System:

Stiffness Ratio of 4.6 (E1 = 200 ksi, E2 = 44 ksi).







45












120


100

80

Rib I Rib 2 Rib 3 Rib 4 Rib 5
60

40 J~
"
20


0"
0 0 12

-20 ,
>
40
0 -40 __I-t

-60


-80
Predicted Stresses Using Tire Model on Pavement System
-100 --- ----___ _Predicted Stresses Using Contact Stresses From Tire Model on Steel Bed
-120

Transverse Distance, X (in)












Figure 3.6: Transverse Stresses Predicted at Surface of 4-in Pavement

System: Stiffness Ratio of 4.6 (El = 200 ksi, E2= 44 ksi).







46







Transverse Distance, X (in) 0
1)2 4 6 8 10 12 1



-50 --____________________ ________015


>-200
Rib 1 Rib 2 Rib 3 Rib 4 Rib 5


-5- Predicted Stresses Using Tire Model on Pavement System

Predicted Stresses Using Contact Stresses From lire Model
on Steel Bed

-300











Figure 3.7: Vertical Stresses Predicted at Surface of 4-in Pavement System:

Stiffness Ratio of 39.4 (El 800 ksi, E2 = 20 ksi).







47









120 100


80
Rib I Rib 2 Rib 3 Rib 4 Rib 5

60


. 40


-20


00


-20 -0







-too- Predicted Stresses Using Contact Stresses From Tire Model
on Steel Bed
-120

Transverse Distance, X (in)








Figure 3.8: Transverse Stresses Predicted at Surface of 4-in Pavement

System: Stiffness Ratio of 39.4 (El = 800 aci, E2 = 20 4-i).






48







Transverse Distance, X (in)

0
S2 4 6 8 10 12 14


-50-




-100 --
0.0





URibI Rib 2 Rib 3 tib 4 Rib 5

> -200-U1)- Predicted Stresses Using Tire IModel on Pavement System
-250
Predicted Stresses Using Contact Stresses From Tire IModel
on Steel Bed

-300







Figure 3.9: Vertical Stresses Predicted at Surface of 4-in Pavement System:
Stiffness Ratio of 10.0 (El = 200 ksi, E2 = 20 ksi).







49











120 100
Rib 1 Rib 2 Rib 3 Rib 4 Rib 5
80 -'60

q 40

0_20

c 0
01
-20 ----


---- Predicted Stresses Using Tire Model on Pavement System
-80
Predicted Stresses Using Contact Stresses From Tire Model
-to0 -- "o -Steel Bud

-120

Transverse Distance, X (in)











Figure 3.10: Transverse Stresses Predicted at Surface of 4-in Pavement

System: Stiffness Ratio of 10.0 (El = 200 ksi, E2 = 20 ksi).







50









Transverse Distance, X (in) 0
1)2 4 6 8 10 12 1


-50



-100 _________Rib 1 Rib 2 Rib 3 Rib 4 Rib 5



--Predicted Stresses Using Tire Model on Pavement System
-250 -___ ______________________Predicted Stresses Using Contact Stresses From Tire Model
on Steel Bed


-300














Figure 3.11: Vertical Stresses Predicted at Surface of 4-in Pavement System:

Stiffness Ratio of 18.0 (El = 800 ksi, E2 = 44 ksi).







51









120

100

80 Rib I Rib 2 Rib 3 Rib 4 Rib 5


60

CL


20 J1

0 0

0-2


I
-60


-80
Predicted Stresses Using Tire Model on Pavement System

-100
... Predicted Stresses Using Contact Stresses From Tire Model
on Steel Bed
-120

Transverse Distance, X (in)









Figure 3.12: Transverse Stresses Predicted at Surface of 4-in Pavement

System: Stiffness Ratio of 18.0 (El = 800 ksi, E2 = 44 ksi).





52


distributions and the magnitude of stresses. As expected, similar comparisons for the 4-in pavement structures at the intermediate stiffness ratios of 10.0 and 18.0 yielded similar results (Figures 3.9 through 3.12). Also, as explained earlier, pavements with surface layer thickness greater than 4-in would exhibit less difference between the two surface loading conditions and therefore do not require evaluation.

Figures 3.13 through 3.16 show similar comparisons for the 2-in surface layer with stiffness ratios of 4.6 (Figures 3.13 and 3.14) and 39.4 (Figures 3.15 and 3.16). As seen in Figures 3.13 and 3.15, the vertical stresses agreed almost exactly for the two loading cases, whereas Figures 3.14 and 3.16 show that there was slightly greater variation between the transverse stresses than there was for the 4-in pavement. However, the correspondence was still very good. As was the case of the 4-in pavement, in which intermediate stiffness ratios exhibited similar results, the same effect was observed for the 2-in pavement as indicated in Figures 3.17 through 3.20.

The findings from this study were summarized as follows:

The radial tire model developed in this study did a very reasonable job of
predicting both the vertical and transverse contact stresses measured under the real
tire. The ability of the model to capture transverse contact stress reversals under
individual tire ribs was of great importance.

Finite element analyses of a range of pavement structures indicated that the use of
contact stresses measured on a steel bed predicted vertical and transverse
pavement stresses very well, as compared to stresses predicted when the tire was
applied directly to the pavement system. Both the pattern of the stress
distributions and the magnitude of stresses were predicted well.







53








Transverse Distance, X (in)
0
2 4 6 8 10 12 1



-50---__________U-200- __I*-150



RibI Rib 2 Rib 3 Rib 4 Rib 6


-U-Predicted Stresses Using Tire Model on Pavement System
-250
4p.Predicted Stresses Using Contact Stresses From Tire Model
on Steel Bed


-300












Figure 3.13: Vertical Stresses Predicted at Surface of 2-in Pavement System:

Stiffness Ratio of 4.6 (El = 200 ksi, E2 = 44 ksi).






54










120 100

80 Rib I Rib2 Rib 3 Rib 4 Rib 5
-0 E -60



20



2 4 6 1 14
20
U


40 60 -80
Predicted Stresses Using Tire Model on Pavement System
-100
Predicted Stresses Using Contact Stresses From Tire Model on Steel Bed
-120

Transverse Distance, X (in)







Figure 3.14: Transverse Stresses Predicted at Surface of 2-in Pavement
System: Stiffness Ratio of 4.6 (E = 200 ksi, E2 = 44 ksi).






55











Transverse Distance, X (in)
0
2 4 6 8 10 12


-50




-100


06
0 -150




Rib I Rib 2 Rib 3 Rib 4 Rib 5


--- Predicted Stresses Using Tire Model on Pavement System
-250
Predicted Stresses Using Contact Stresses From Tire Model
on Steel Bed

-300











Figure 3.15: Vertical Stresses Predicted at Surface of 2-in Pavement System:
Stiffness Ratio of 39.4 (El = 800 ksi, E2 = 20 ksi).







56










120
Rib I Rib 2 Rib 3 Rib 4 Rib 5
100



60

60
40.W

20 0


0 2 4 6 8 10 1
S -20 S -40


-60

-80 Predicted Stresses Using Tire Model on Pavement System

-100 ..Predicted Stresses Using Contact Stresses From Tire Model

on Steel Bed
-120

Transverse Distance, X (in)












Figure 3.16: Transverse Stresses Predicted at Surface of 2-in Pavement

System: Stiffness Ratio of 39.4 (El = 800 ksi, E2 = 20 ksi).







57














0
2 4 6 8 10 12 1



-50




-100


-10




-20



Ribi1 Rib 2 Rib 3 Rib 4 Rib 5


--Predicted Stresses Using Tire Model on Pavement System
-250- _______-__________________ ________________** Predicted Stresses Using Contact Stresses From Tire Model
on Steel Bed


-300

Transverse Distance, X (in)















Figure 3.17: Vertical Stresses Predicted at Surface of 2-in Pavement System:

Stiffness Ratio of 10.0 (El = 200 ksi, E2 = 20 ksi).







58










120


100 ____Rib 1 Rib 2 Rib 3 Rib 4 Rib 5
80 -______ __60


S 40 pal
to
20

~ 0-- -_
(0
0 1
02


-4

06



I- 10



-10 Predicted Stresses Using Contact Stresses From Tire Model

-120 on Steel Bed

Transverse Distance, X (in)












Figure 3.18: Transverse Stresses Predicted at Surface of 2-in Pavement

System: Stiffness Ratio of 10.0 (El 200 ksi, E2 = 20 ksi).







59











0
2 6 8 10 12


-50





-100~

U-150 __U,)
(U
b
: -200Rib I Rib 2 Rib 3 Rib 4 Rib 5



-250 -- Predict Stresses Using Tire Model on Pavement System

Predicted Stresses Using Contact Stresses From Tire Model
on Steel Bed
-300
Transverse Distance, X (in)













Figure 3.19: Vertical Stresses Predicted at Surface of 2-in Pavement System:

Stiffness Ratio of 18.0 (El = 800 ksi, E2 = 44 ksi).







60










120


100__________ ______
Rib I Rib 2 Rib 3 Rib 4 Rib 5
80


600

CL 40 -~--_-____00
0 0
02

-4

-20


-80


--Predicted Stresses Using Tire Model on Pavement System

-100 Predicted Stresses Using Contact Stresses From Tire Model_-120 on Steel Bed

Transverse Distance, X (in)









Figure 3.20: Transverse Stresses Predicted at Surface of 2-in Pavement

System: Stiffness Ratio of 18.0 (El = 800 ksi, E2 = 44 ksi).





61




Some minor differences were observed for thin (2-in surface) pavements on weak
bases, but the correspondence in terms of both distribution and magnitude was
still very good.


Based on these findings, it was concluded that contact stresses measured using devices with rigid foundations are suitable for the prediction of response and performance of highway pavements.


3.3 Modification of Two-Dimensional Finite Element Model to Capture Bending Response of Asphalt Pavement System



Although three-dimensional FEM provides the most accurate representation of a pavement structure, it remains a relatively challenging and costly technique, particularly for pavement performance predictions that involve a continuously changing structure and thousands of load applications of varying magnitudes and positions. Axisymmetric and two-dimensional analyses provide simpler, more cost-effective solutions at the expense of accuracy. A study was undertaken to evaluate the discrepancies between two- and threedimensional analysis of pavement structures, and to determine whether a modified twodimensional analysis could be used as a reasonable approximation of the threedimensional bending response of asphalt pavements. Therefore, the primary objectives of this study were as follows:

To develop a procedure for using two-dimensional analysis to predict pavement
response at critical locations with respect to fracture propagation for several
structural and loading cases.
To evaluate and illustrate the differences between two- and three-dimensional
bending response of asphalt pavement structures.





62


To identify/develop an approach to calibrate two-dimensional analyses such that reasonable approximations of the three-dimensional response of asphalt pavements.

To illustrate how the modified approach may be used in practice for the analysis and
evaluation of pavement systems.

The evaluation conducted in this investigation was then restricted to the following

constrictions:

Only the stress-strain response of the asphalt concrete layer was considered in the evaluation. The accuracy of stress distributions within base and subgrade were not considered, such that the evaluation and approach were primarily suitable for loadassociated cracking within the asphalt surface layer.

A broad range of conventional pavement structures (i.e., asphalt surface on aggregate base and subgrade) were considered. However, overlays on rigid pavements were not
addressed.

" Well-establ i shed principles of pavement response (i.e., layered systems) indicated that
near-surface stresses within the asphalt concrete surface layer are almost exclusively
governed by surface thickness, surface stiffness, and base course stiffness. Therefore,
these were the three primary variables investigated and used to define the range of
pavement structures investigated. Limited analyses of the effects of subgrade
stiffness and base layer thickness on near-surface response were conducted.

" All two- and three-dimensional analyses were conducted using the ABAQUS finite
element computer program (HKS 1997). Plane strain conditions were assumed for
nonsymmetrical simulations and all analyses were conducted taking advantage of
symmetry.

The primary objectives of the research were met by comparing stresses from the threedimensional finite element analyses to stresses obtained from two-dimensional plane

strain analyses using the same contact stress and width of load on a broad range of

pavement structures. The observed differences were evaluated to identify characteristic

patterns in the differences, and to determine whether specific relationships could be

established between these solutions. Specifically, relationships were sought that would





63

allow reasonable estimates of the three-dimensional solutions based on the twodimensional analyses.


3.3.1 Finite Element Model Types

Axisymmetric and two-dimensional analyses provide simpler and more costeffective solutions, but often at the expense of accuracy. Axisymmetric solutions have long been used to analyze pavement structures; for example, it forms the core of the FEM program ILLIPAVE (1990). These solutions are generally limited to the application of a single symmetrical tire load, although recent work has been done that allows axisymmetric solutions to handle multiple loads and nonlinear analysis. In any case, discontinuities in the form of damage zones and/or cracks cannot be properly modeled using axisymmetric solutions. As shown in Figure 3.21, in an axisymmetric model, a crack would essentially be modeled a discontinuous ring around the symmetrical load, which would result in inaccurate stress distributions and/or stress concentrations at the crack tip.

Also shown in Figure 3.21 is a two-dimensional model that resulted in

considerably better representation of a continuous longitudinal crack in a pavement system. Multiple loads and cracks, as well as non-symmetrical tire contact stresses, can be represented in the two-dimensional model. Unfortunately, the analysis would be conducted by assuming either plane stress or plane strain conditions, and the load(s) would be considered essentially as strip loads, which then result in different bending patterns than a true wheel load applied in three-dimensional analysis. Therefore, before attempting to use two-dimensional analysis for the evaluation of pavement response and





64

performance, a thorough understanding of the differences in stress distributions between two- and three-dimensional analyses was developed. Furthermore, an approach was developed to determine stress distributions for pavement analysis using a twodimensional model that reasonably estimated the stresses predicted by a true threedimensional model. This modified approach was used for parametric studies to show the relative effects of different factors on pavement response and performance, as will be discussed in Chapter 4.







Dual Loading
Crack





Crack





Axisymmetric Model 2 -D Model





Figure 3.21: Schematic of Axisymmetric and 2-D Finite Element Pavement Models.





65

3.3.2 Finite Element Modeling of Pavement System Using ABAQUS

The range of pavement structures that were evaluated is summarized in Table 3.2. Asphalt concrete layer thickness was varied from 2 to 8 inches, which encompassed the range of surface layer thickness typically used on conventional pavements with aggregate base. Preliminary analyses indicated that the difference between two- and threedimensional analysis was found not to change for asphalt concrete thicknesses greater than 8 inches. Base course and subgrade thickness were held constant at 12 inches and 336 inches, respectively. As cited by Huang (1993) and others, it is common knowledge that base course thickness has a negligible effect on near-surface stress distributions.

Three levels of asphalt concrete modulus (200, 800, and 1200 ksi) and two levels of base course modulus (20 and 44 ksi) were used. These resulted in surface to base layer stiffness ratios (EI/E2) ranging from 4.6 to 59.0. The asphalt modulus values were selected to capture the asphalt concrete stiffness within the in-service temperature range. The base course values were selected to represent a poor and a good granular base course. Two subgrade layer modulus values were used (7.0 and 14.5 ksi) to verify that subgrade modulus has a negligible effect on near-surface stress distributions.

An applied contact stress of 115 ksi, which corresponded to a standard inflation pressure for a typical radial truck tire was used to conduct all analyses. Also, a contact width (two-dimensional) or diameter (three-dimensional) of 8 inches was used for all analyses, which corresponds to the width of a typical radial truck tire.

A general schematic of a typical finite element mesh used to model the pavement structures in ABAQUS is shown in Figure 3.22, which also shows a more detailed view






66




Table 3.2: Parameters Used in Development of Pavement Finite Element Models. AC Layer Stiffness Modulus (ksi)
Thickness
(in) Asphalt Concrete Layer Base Layer Subgrade Layer
2 200 800 1200 20 44 14.5
3 200 800 1200 20 44 7.0 14.5
4 200 800 1200 20 44 7.0 14.5
6 200 800 1200 20 44 7.0 14.5
8 200 800 1200 20 44 7.0 14.5
Note: Applied contact stress on models = 11 5 psi Base Thickness = 12 in Subgrade Thickness = 336 in





of the typical mesh structure used near the loading area. Since only one load was used to meet the necessary objectives of the study, an axisymmetric model was used to represent the three-dimensional loading case for comparison to the two-dimensional analyses. Therefore, the same mesh structure was used for both two-dimensional and threedimensional (axisymmetric) analyses.

The accuracy of the mesh structures used in the analyses was evaluated by

comparing the ABAQUS solutions to solutions obtained with the BISAR elastic layer computer program. Detailed results showed that excellent correspondence was obtained for stress distributions predicted by both of the programs. Thus, it was confirmed that the ABAQUS code was working well.





67







/


Nonuniform Vertical Load

AC
hl,Evariable

Base
h2,E2variable


Subgrade h3 constant
_I E3variable
x

ABAQUS Finite Element Detailed View of Model Near
2-D and Axisymmetric Model Loading Area






Figure 3.22: Schematic and Detailed View of Pavement System Modeled Using the Finite Element Program, ABAQUS.





68

3.3.3 Evaluation of Predicted Stresses

Figures 3.23 and 3.24 show that differences between two- and three-dimensional solutions were highly dependent upon the characteristics of the pavement structure. These figures show the transverse (horizontal) stress distributions beneath the loaded area at the bottom of the asphalt concrete surface layer, as predicted by two- and threedimensional representation of the pavement structure. This stress was selected because the tensile response immediately underneath the load traditionally has been considered as the critical response related to fatigue cracking in pavements (critical tensile stress). Figure 3.23 shows that for a pavement structure with a low stiffness ratio, the two- and three-dimensional solutions predicted almost exactly the same critical tensile stress. On the other hand, Figure 3.24 shows that the two-dimensional solution grossly overpredicted the tensile stress for a pavement with high stiffness ratio (EI/E2 = 59.0). Tensile stress at the bottom of the asphalt concrete layer was nearly a factor of four greater for the two-dimensional analysis than for the three-dimensional analysis (334 psi versus 87 psi). Figures 3.23 and 3.24 also indicate that significant differences were observed between the two- and three-dimensional stress distributions at distances further from the center of the loaded area. However, the accurate prediction of stresses in this region was less critical for two reasons: firstly, the stresses were compressive for pavements with low stiffness ratios (Figure 3.23); and secondly, even when the stresses were tensile (Figure 3.24), they were significantly lower than under the center of the loaded area.






69






-200
Compression
-150 Loaded
Area
-100 __

-50
-~~- -- .. .. ........

S50



0
0) 100

> 150
(U
200 -2-D Model

250 3-D (Axisymmetric) Model

300 ... n---- 2-D Model with Vertical Loading
Tension Modified by Bending Stress Ratio
350
2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38
400 1 1 1 1 1 1 ,

Transverse Distance Along Bottom of Surface Layer, x (in)










Figure 3.23: Transverse Stress Distribution Along Bottom of 4-in Asphalt
Concrete Layer for Stiffness Ratio of 4.6 (Ej = 203 ksi : E2 = 44 ksi).






70





-200
Compression

-150 Loaded
Area

-100

-50


0



'f 100

0
> 150
0

i- 200 A 2-D Model 250 -.- 3-D (Axisymmetric) Model

300 ------ 2-D Model with Vertical Loading
Tension Modified by Bending Stress Ratio
350
2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38
4 0 0 1 I .

Transverse Distance Along Bottom of Surface Layer, x (in)









Figure 3.24: Transverse Stress Distribution Along Bottom of 8-in Asphalt
Concrete Layer for Stiffness Ratio of 59 (El = 1200 ksi : E2 = 20 ksi).





71


An evaluation of similar comparisons for the range of pavement structures under investigation indicated that the difference between tensile stresses predicted by two- and three-dimensional analyses was related to the relative stiffness between the surface and base layers. That is, the relative difference between the two solutions appeared to be governed primarily by the stiffness ratio (EI/E2) and the thickness of the surface layer.

Based on these observations, analyses were conducted to determine whether a

structurally-dependent correction factor could be identified to estimate three-dimensional tensile stresses using results obtained from the two-dimensional analysis. The idea involved the determination of a factor that could be used to modify surface loads applied to the two-dimensional analysis, such that the predicted bending stress (specifically, the critical tensile stress) would closely approximate the bending stress predicted by threedimensional analysis.


3.3.3-1 Definition of Bending Stress Ratio

A ratio between the critical tensile stress predicted by three-dimensional analysis and the critical tensile stress predicted using two-dimensional analysis was defined to normalize the difference between the two stresses via calibration. The ratio was related to pavement structural characteristics to act as a modifying factor for two-dimensional loads (strip load), in order to obtain accurate three-dimensional stress predictions using twodimensional analysis.

The bending stress ratio was defined as follows:


BSR = CTXX(3-D) (3.1)
CFXX(2-D)





72





where, BSR = bending stress ratio
axx(3-D) = critical tensile stress based on three-dimensional analysis
(Yxx(2-D) = critical tensile stress based on two-dimensional analysis

A BSR was calculated for each of the pavement structures analyzed. For the

pavement structure used to obtain the results presented in Figure 3.23, the BSR computed from Equation 3.1 was approximately 1.0. A BSR of 3.8 was determined for the pavement structure used to obtain the results presented in Figure 3.24. Figures 3.23 and

3.24 also show modified stress distributions obtained by multiplying the two-dimensional results by the corresponding BSR. As shown in Figure 3.23, the modified twodimensional results for a low stiffness ratio case agreed well with the three-dimensional stress distribution immediately underneath the load, but the correspondence between the compressive stresses further from the load were not improved. Figure 3.24 shows that for the high stiffness ratio case, the correspondence was excellent immediately underneath the load, and was also improved significantly ftirther from the load. As previously mentioned, the area of tensile stress immediately under the load is generally considered the critical area for evaluating load-associated fatigue cracking of asphalt pavements. Therefore, it was logical to define the bending stress ratio such that response was matched most accurately in this zone.


3.3.3-2 Relations Between Bending Stress Ratio and Structural Parameters

As mentioned earlier, the relative difference in critical tensile stresses between the two- and three-dimensional solutions appeared to be primarily governed by the stiffness





73

ratio (EI/E2) and the thickness of the surface layer (h). Therefore, the bending stress ratio (BSR) should be related to EI/E2 and h. Figures 3.25 and 3.26 show the relationships between BSR and h, and BSR and EI/E2. The two figures show essentially the same data presented in two ways. The following general observations were made on the basis of the results presented in Figures 3.25 and 3.26: BSR increased as stiffness ratio or surface layer thickness decreased. BSR decreased at a decreasing rate as surface layer thickness increased or as stiffness
ratio increased.

For a given stiffness ratio, the BSR approached a constant value as the surface layer
thickness was increased. That is, beyond a certain surface layer thickness
(approximately 8 inches), the relative difference between the two- and threedimensional solutions did not change.

" For a given surface layer thickness, the BSR approached a constant value as stiffness
ratio was increased. In other words, beyond a certain stiffness ratio (approximately
40), the relative difference between the two- and three-dimensional solutions did not
change.

" For the majority of pavement structures, BSR was less than 1.0, indicating that twodimensional analysis over-estimated the critical tensile stress for most pavement
structures.

" BSR exceeded 1.0 (i.e., two-dimensional analysis under-estimated critical tensile
stress) for cases with thin surface layers and low stiffness ratios. However, a sharp reversal occurred, and even negative BSR's were observed, in cases of very thin (2inch) surface layers with low stiffness ratios. These results were explained by the fact that the bottom of a very thin surface layer may be in compression rather than tension,
particularly in cases where the stiffness ratio is low.

It should be noted that highway pavements, particularly those in relatively high-traffic areas, are rarely found to have a surface layer thickness less than 3 inches. Therefore, the observed reversal in the BSR relationship was of little or no practical significance.





74

Based on the observations from Figures 3.25 and 3.26 discussed above, the

following non-linear relationship was developed for BSR as a function of stiffness ratio (E1/E2) and thickness ratio (hj/h2) where h, was the thickness of the surface layer and h2 was the thickness of the base layer:


Iog(BSR) =-O.29655(E1 /E2 )0.29531 (h, /1h2)095659 (3.2)

R2 = 0.97


The following range of parameters was used to develop Equation (3.2): Surface layer thickness from 3 inches to 8 inches, which corresponded to surface to base layer thickness ratios (hj/h2) from 0.25 to 0.67. Stiffness ratios (E1/E2) from 4.6 to 59.0. In other words, pavement structures that resulted in reversals in the BSR trends were not included in the development of the equation.

It must be noted that the relationships presented in Figures 3.25 and 3.26 assumed that BSR was only a function of the stiffness ratio (E1/E2), and not of the magnitude of the stiffness of the individual layers (E1 or E2) used to determine the stiffness ratio. It was also assumed that BSR was independent of subgrade stiffness. Therefore, additional analyses were conducted to evaluate the validity of these assumptions. Figure 3.27 clearly shows that the magnitude of E, and B2 had no effect on the relationship between BSR and surface layer thickness. As shown in the figure, stiffness ratios of 10 and 40 were achieved by using two different levels of surface and base layer stiffness. Results of the analyses indicated that identical BSR's were determined regardless of how the stiffness ratio was achieved.







75








4.0- --Stiffness Ratio of 4.56 (El =203ksi E2-44ksi)

3.5--- Stiffness Ratio of 10.0 (El =2O3ksi :E2-=2ks).Stiffess Ratio of17.98 (E =80qsi :E2--44ksi) 3.0- A-- Stiffness Ratio of 28.0 (El = I20(ksi: E2--44ksi)
---- Stiffness Ratio of 39.41 (El1=8(Xksi E2-=20ki) S2.5 -e- Stiffness Ratio of600O (E1=1200ksi E2-=2Cks)



0

.0



'S 1.0 -Z~>~. o 0.5-20





Asphalt Corete Thicknss, h (in)
















Figure 3.25: Effect of Asphalt Concrete Thickness on Bending Stress Ratio.






76









4.0
4- Asphalt Concrete Thickness of 2" 35 ---x- Asphalt Concrete Thickness of 3"

3.0- Asphalt Concrete Thickness of 4"
---Asphalt Concrete Thickness of 6"

2.5 -Asphalt Concrete Thickness of 8"

=2.0
b /


IN 1.5' 0 ,---,



== 0 __ --



10
--------------------0.5
A~0.0
C*10 20 30 40 50 6








-2.0
Stiffness Ratio, El:E2









Figure 3.26: Effect of Stiffness Ratio (El / E2) on Bending Stress Ratio.






77
















4.0- ---- Stiffness Ratio of 10.0 (E1=203ksi: E2=20ksi)
3.5
SStiffness Ratio of 10.0 (E1 =440ksi : E2-44ksi) 3.0 --- Stiffness Ratio of 40.0 (El=800ksi: E2=20ksi)

--o- Stiffness Ratio of 40.0 (E1=1600ksi: E2=40ksi) S2.5 --

2 .0

a
1.5

0 1.0


0.5

S0.0

S1 2 3 4 5 6 7 8 9
-0.5


-1.0

-1.5 4

-2.0
Asphalt Concrete Thickness, h (In)











Figure 3.27: Effect of Asphalt Concrete and Base Layer Stiffness on Bending
Stress Ratio.






78


Similarly, Figure 3.28 shows that subgrade stiffness had a negligible effect on the


relationship between BSR and surface layer thickness for stiffness ratios ranging from 10


to 28. As shown in the figure, BSR's that were essentially identical were determined at a


given surface layer thickness and stiffness ratio for different values of subgrade modulus.







4.0
--- Subgrade Stiffness 7.0 ksi (El=203ksi: E2=20ksi) 3.5 -+- Subgrade Stiffness 14.5 ksi (E1=203ksi: E2-20ksi)

3.0- Subgrade Stiffness 7.0 ksi (El=800ksi: E2-20ksi)
3.0
-- Subgrade Stiffness 14.5 ksi (E1=800Dksi: E2-20ksi)
_2.5 ---a- Subgrade Stiffness 7.0 ksi (E1=1200ksi: E2-44ksi)
-o-- Subgrade Stiffness 14.5 ksi (E1=1200ksi: E2=44ksi)
2.0

M


1.0
10.5



0.0
1 2 3 4 5 6 7 8
-0.5
- 1.0






-1.5
(I,
0}





-2.0






Asphalt Concret Thickness, h (in)








Figure 3.28: Effect of Subgrade Stiffness on Bending Stress Ratio at Various
Stiffness Ratios (El / E 4 5 6 7 8
m
-0.5

-1.0

-1.5

-2.0
Aspul~t Concret Thckzuss, h (In)







Figure 3.28: Effect of Subgrade Stiffness on Bending Stress Ratio at Various
Stiffness Ratios (E1 / E2).





79

3.3.4 Application of Bending Stress Ratio

The bending stress ratio (BSR) described in the previous section provided a useful tool for predicting the three-dimensional bending stresses in asphalt pavement systems using two-dimensional finite element analysis. The benefits were particularly important for evaluating highly complex contact stress conditions, or for cases where a large number of computer runs are required to predict pavement performance. For example, the prediction of crack propagation using fracture mechanics, not only requires a large number of runs for a pavement structure and wheel loads that are continually changing, but also requires continually changing the finite element mesh as crack growth progresses. Using a two-dimensional model would be considerably beneficial, in terms of reduced complexity and computer run times. An example of the generalized twodimensional model that could be used to represent the longitudinal wheel path cracking situation is presented in Figure 3.29, showing a pavement surface with multiple cracks loaded using a realistic tire contact stress distribution involving non-uniform vertical and transverse stresses. An axisymmetric model was an unsuitable choice for this problem because it did not properly model the tire contact stresses or the discontinuities caused by the cracks. On the other hand, modeling this problem in three dimensions for a broad range of pavement structural characteristics, load positions, and crack lengths posed a formidable and time-consuming problem. The modified two-dimensional approach provided reasonable solutions comparable to those obtained using a three-dimensional model, but with considerably less complexity and cost.





80





Variable A----'-- Vertical Load Crack Magnitude
% 1 4-"
Variable
a

F Variable Variable
Distance hi El

A Variable
a


Crack

Variable h2 E2










Figure 3.29: Application of Approach Parametric Study of a Cracked Pavement.





81




The following procedure was used, including the BSR relationships presented earlier (Figures 3.25 and 3.26 or Equation 3.2), to obtain a modified two-dimensional solution that approximated the true three-dimensional bending response of typical pavement structures:

I Calculate the surface-to-base layer stiffness ratio (EI/E2) and the surface-to-base layer thickness ratio (hj/h2) for the pavement structure being analyzed.

2. Use these ratios to determine the BSR using either Figure 3.25, Figure 3.26, or
Equation 3.2. Only use Equation 3.2 if the pavement structural parameters are within
the range used to generate the equation.

3. Multiply only the vertical contact stresses by the BSR. The calculated stresses are
then considered the modified vertical contact stresses. The transverse tire contact
stresses were not modified for two-dimensional analysis.

4. Apply the modified vertical contact stresses and the transverse contact stresses to the
two-dimensional finite element representation of the pavement structure. The width of the wheel load(s) used in the two-dimensional analysis was equal to the width or
diameter of the actual tire.

Based on the analyses conducted in this investigation, the resulting tensile stresses within the asphalt concrete surface layer in the vicinity of the tire reasonably approximated the tensile stresses for the true three-dimensional loading condition. Furthermore, for cases similar to the one shown in Figure 3.29, the modified two-dimensional analysis could be used to determine realistic stress intensity factors and crack growth rates for variable loading conditions.


3.3.5 Additional Observations

The correspondence between two- and three-dimensional analysis was obtained for the case of linear elastic layered systems. Although the development of a similar





82

approach for a layered system composed of materials exhibiting non-linear behavior would need to be investigated, it was clearly shown that the assumption of a homogeneous, linear elastic layered material could be used to obtain reasonable predictions of measured field loading responses on typical Interstate flexible pavement systems (Chabourn et al. 1997). At first glance, it appeared that the number of structural and material parameters influencing the bending stress ratio between two- and threedimensional analysis was overwhelming, such that the development of a simplified approach would not be possible. However, earlier research work suggested that a modified version of the approach developed may be suitable for the case of predicting bending stresses within the asphalt concrete layer. Roque et al. (1992) showed that for a broad range of pavement structures and non-linear material properties, linear elastic analysis could be used to accurately determine the stress-strain response within the surface layer if suitable effective layer modulus values were included in the analysis. A procedure was presented for determining suitable effective layer modulus values of nonlinear layers that involved prediction of the non-linear deflection response of the pavement system, then back-calculation of effective layer moduli using the linear elastic layer model. Their work suggested that a stiffness ratio calculated using the effective layer modulus values determined in this manner could be used along with the surface-tobase layer thickness ratio to apply the bending stress ratio (BSR) concept. It is recommended that this approach be investigated further prior to full implementation.


3.3.6 SummM

Discrepancies between two- and three-dimensional analysis of pavement





83

structures were evaluated, and the question of whether a modified two-dimensional analysis could be used as a reasonable approximation of the three-dimensional response of asphalt pavements was addressed. Two- and three-dimensional analysis of a range of pavement structures typically encountered in highway pavements indicated that discrepancies between two- and three-dimensional analyses were highly dependent upon the structural characteristics of the pavement. A bending stress ratio (BSR) was defined as the ratio between the critical tensile stress from three-dimensional analysis and the critical tensile stress from two-dimensional analysis. It was determined that the BSR was primarily a function of surface-to-base layer stiffness ratio (EI/E2) and surface-to-base layer thickness ratio (hj/h2) and specific relationships were developed between BSR and these parameters. An approach was developed to use the pavement structural characteristics and BSR to modify two-dimensional loads such that two-dimensional analyses reasonably estimated the true three-dimensional pavement stresses.

Based on the comparisons presented, it was concluded that the modified twodimensional analysis developed reasonably approximated three-dimensional tensile stresses within the asphalt concrete surface layer for the typical range of conventional pavement structures encountered in highway pavements.



3.4 Description of Pavement Model


Longitudinal wheel path cracks have been observed in the field and the resulting core and trench sections have shown that they initiate at the surface and propagate downwards in the surface layer. Therefore, analysis of the problem involved replication




Full Text
DEVELOPMENT AND PROPAGATION OF SURFACE-INITIATED
LONGITUDINAL WHEEL PATH CRACKS IN FLEXIBLE HIGHWAY PAVEMENTS
By
LESLIE ANN MYERS
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
2000

ACKNOWLEDGMENTS
I would like to acknowledge those individuals who were instrumental in the
advancement of this research. Special thanks go to Dr. Reynaldo Roque for willingly
sharing his knowledge and experiences through constant encouragement. I also appreciate
the tun jokes and sound advice given to me by Dr. Byron Ruth who truly epitomizes the
concept that “learning is fun.” Acknowledgments should also be made to my graduate
committee members, Dr. Mang Tia and Dr. Bjorn Birgisson, who were always available to
discuss ideas and lend valuable advice. I would also like to acknowledge Dr. Bhavani
Sankar for lending his technical support and advice and Dr. Marion Pottinger of Smithers
Scientific Services, Inc. for generously providing me with measured truck tire-pavement
interface stress data and technical advice.
Other individuals who assisted me in my graduate studies include Christos Drakos
and Dr. Yusuf Mehta. I would like to acknowledge the everyday support of my best friend
Roberto Vitali.
Finally, I acknowledge the unwavering support of my parents, Robert and Bonnie
Myers, and brother and sister, Tom and Katie, who gave me the strength to conquer
challenges that I faced along the way.
I dedicate this Ph D. dissertation to the memory of my father.
11

TABLE OF CONTENTS
Page
ACKNOWLEDGMENTS ii
LIST OF TABLES vi
LIST OF FIGURES viii
ABSTRACT xvi
CHAPTERS
1 INTRODUCTION 1
1.1 Background 1
1.2 Research Hypothesis 4
1.3 Objectives 5
1.4 Scope 5
1.5 Research Approach 7
2 LITERATURE REVIEW 10
2.1 Overview 10
2.2 Classical Fatigue Approach 11
2.3 Continuum Damage Approach 13
2.4 Fracture Mechanics Approach 15
2.5 Measurement of Tire Contact Stresses 18
2.6 Analysis of Surface Cracking 28
2.7 Summary 32
3 ANALYTICAL APPROACH 33
3.1 Introduction 33
3.2 Validation of Measured Tire Contact Stresses 34
3.2.1 Development of Tire Model 35
3.2.2 Selection of Pavement Structures For Analysis 39
3.2.3 Results of Verification Analyses 43
3.3 Modification of Two-Dimensional Finite Element Model to Capture
Bending Response of Asphalt Pavement System 61
3.3.1 Finite Element Model Types 63
iii

3.3.2 Finite Element Modeling of Pavement System Using ABAQUS 65
3.3.3 Evaluation of Predicted Stresses 68
3.3.3-1 Definition of Bending Stress Ratio 71
3.3.3-2 Relations Between Bending Stress Ratio and Structural
Parameters 72
3.3.4 Application of Bending Stress Ratio 79
3.3.5 Additional Observations 81
3.3.6 Summary 82
3.4 Description of Pavement Model 83
3.4.1 Structural Parameters of Model 84
3.4.2 Crack Length 85
3.4.3 Modeling System 88
3.5 Selection of Fracture Mechanics Theory For Analysis 93
3.5.1 Description of Fracture Parameters 94
3.5.2 Application of Fracture Mechanics 95
3.6 Summary 98
4 PARAMETRIC STUDY - PAVEMENT STRUCTURE 99
4.1 Overview 99
4.2 Factors Investigated for Structural Analysis 100
4.3 Effects of Pavement Structure on Crack Propagation 104
4.3.1 Asphalt Concrete Thickness 104
4.3.2 Asphalt Concrete-to-Base Layer Stiffness Ratio 105
4.3.3 Results 114
4.4 Effects of Loading on Crack Propagation 114
4.4.1 Determination of Appropriate Load Positions 116
4.4.2 Load Position With Respect to Crack 119
4.4.3 Direction of Crack Growth 130
4.5 Summary 134
5 PARAMETRIC STUDY - TEMPERATURE AND
ENVIRONMENTAL CONDITIONS 135
5.1 Overview 135
5.2 Analysis Procedure For Evaluating Induced Stiffness Gradient 137
5.3 Analysis of Cracked Pavement With Induced Stiffness Gradient 147
5.3.1 Effect of Pavement Structure on Cracked Pavement With Stiffness
Gradients 153
5.3.2 Effect of Stiffness Gradient on Direction of Crack Growth 161
5.4 Summary 162
6 POTENTIAL IMPLICATIONS FOR PAVEMENT DESIGN AND
PERFORMANCE 165
6.1 Overview 165
6.2 Implications of Load Spectra 166
IV

6.3 Implications of Rate of Cracking 175
6.4 Summary 182
7 FINDINGS AND CONCLUSIONS 183
7.1 Findings 183
7.2 Conclusions 186
8 RECOMMENDATIONS 188
APPENDICES
A SAMPLE CALCULATION OF STRESS INTENSITY FACTORS 191
B STRESS INTENSITY FACTOR DATA 195
REFERENCES 204
BIOGRAPHICAL SKETCH 208
v

LIST OF TABLES
Table Page
3.1 Pavement Structures Used for Analysis 43
3.2 Parameters Used in Development of Pavement Finite Element Models 66
3.3 Parameters Evaluated For Identification of Factors Critical to Development of
Surface Cracking Mechanism 85
3.4 Boundary Conditions Applied to Model of Entire Pavement System 89
3.5 Boundary Conditions Applied to Refined Model of Surface Layer 91
4.1 Transverse Stress Distribution Along Surface of Pavement For Each Pavement
Modeled, As Predicted in BISAR Elastic Layer Analysis Program 118
4.2 Example Calculation of Direction of Crack Growth For Thick Pavement (hi= 8 in)
With Low Base Stiffness (Ei:E2 = 800:20 ksi) 131
6.1 Rate of Crack Growth For Given K-value From Fracture Tests Performed on
Laboratory Specimens 174
B.l Stress Intensity Factors Predicted in ABAQUS For Uniform Stiffness 4-inch
Pavement Layer With Low Stiffness Base (E2=20 ksi) 196
B.2 Stress Intensity Factors Predicted in ABAQUS For Uniform Stiffness 4-inch
Pavement Layer With High Stiffness Base (E2=44 ksi) 197
B.3 Stress Intensity Factors Predicted in ABAQUS For 4-inch Pavement Layer With
Stiffness Gradients and Low Stiffness Base (E2=20 ksi) 198
B.4 Stress Intensity Factors Predicted in ABAQUS For 4-inch Pavement Layer With
Stiffness Gradients and High Stiffness Base (E2=44 ksi) 199
B.5 Stress Intensity Factors Predicted in ABAQUS For Uniform Stiffness 8-inch
Pavement Layer With Low Stiffness Base (E2=20 ksi) 200
B.6 Stress Intensity Factors Predicted in ABAQUS For Uniform Stiffness 8-inch
Pavement Layer With High Stiffness Base (E2=44ksi) 201
vi

B.7 Stress Intensity Factors Predicted in ABAQUS For 8-inch Pavement Layer With
Stiffness Gradients and Low Stiffness Base (E2=20 ksi) 202
B.8 Stress Intensity Factors Predicted in ABAQUS For 8-inch Pavement Layer With
Stiffness Gradients and High Stiffness Base (E2=44 ksi) 203
Vll

LIST OF FIGURES
Figure Page
1.1 Overall Research Approach Flowchart 9
2.1 Stress Intensity Factor Plotted As a Function of Crack Length for a Surface Crack
Due to Vehicular Loading For Three Different Pavement Structures With Different
Modulus Ratios (after Collop and Cebón 1995) 17
2.2 Structural Characteristics of Bias Ply and Radial Truck Tires and Their Effects on
the Pavement Surface (after Roque et al. 1998) 20
2.3 Schematic of System Used to Measure Tire Contact Stresses (after Roque et al.
1998) 21
2.4 Experimental Setup of Vehicle-Road Surface Pressure Transducer Array (VRSPTA)
System Used to Measure Tire Contact Stresses (after de Beer et al. 1997) 22
2.5 Three-dimensional Vertical and Lateral Contact Stress Distributions Under Radial
(R22.5) Truck Tire at Rated Load (after de Beer et al. 1997) 23
2.6 Effect of Pavement Bending Due to a Bias Ply and Radial Truck
Tire on Surface Stress Distribution (after Myers et al. 1999) 25
2.7 Transverse Contact Shear Stresses Measured For a Bias Ply, Radial, and Wide Base
Radial Tire At the Appropriate Rated Load and Inflation Pressure (after Myers et al.
1999) 26
2.8Vertical Contact Stresses Measured For a Bias Ply, Radial, and Wide Base Radial
Tire At the Appropriate Rated Load and Inflation Pressure
(after Myers et al. 1999) 27
2.9Predicted Transverse Stress Distribution Induced By Radial Truck Tire Near
Pavement Surface (after Myers et al. 1998 30
3.1 Cross-Section of a Typical Radial Truck Tire 37
3.2 Finite Element Representation of Tire Tread Structure 37
3.3 Measured and Predicted Vertical Stress Distribution at Surface of Steel Bed 40
viii

3.4 Measured and Predicted Transverse Stress Distribution at Surface of Steel Bed 41
3.5 Vertical Stresses Predicted at Surface of 4-in Pavement System: Stiffness Ratio of
4.6(E, = 200 ksi, E2 = 44 ksi) 44
3.6 Transverse Stresses Predicted at Surface of 4-in Pavement System: Stiffness Ratio
of 4.6 (E, = 200 ksi, E2 = 44 ksi) 45
3.7 Vertical Stresses Predicted at Surface of 4-in Pavement System:. Stiffness Ratio of
39.4 (E, = 800 ksi, E2 = 20 ksi) 46
3.8 Transverse Stresses Predicted at Surface of 4-in Pavement System: Stiffness Ratio
of 39.4 (Ei = 800 ksi, E2 = 20 ksi) 47
3.9 Vertical Stresses Predicted at Surface of 4-in Pavement System: Stiffness Ratio of
10.0 (Ei = 200 ksi, E2 = 20 ksi) 48
3.10 Transverse Stresses Predicted at Surface of 4-in Pavement System: Stiffness Ratio
of 10.0 (E, = 200 ksi, E2 = 20 ksi) 49
3.11 Vertical Stresses Predicted at Surface of 4-in Pavement System: Stiffness Ratio of
18.0 (E, = 800 ksi, E2 = 44 ksi) 50
3.12 Transverse Stresses Predicted at Surface of 4-in Pavement System: Stiffness Ratio
of 18.0 (E, = 800 ksi, E2 = 44 ksi) 51
3.13 Vertical Stresses Predicted at Surface of 2-in Pavement System: Stiffness Ratio of
4.6 (Ei = 200 ksi, E2 = 44 ksi) 53
3.14 Transverse Stresses Predicted at Surface of 2-in Pavement System: Stiffness Ratio
of 4.6 (E, = 200 ksi, E2 = 44 ksi) 54
3.15 Vertical Stresses Predicted at Surface of 2-in Pavement System: Stiffness Ratio of
39.4 (Ei = 800 ksi, E2 = 20 ksi) 55
3.16 Transverse Stresses Predicted at Surface of 2-in Pavement System: Stiffness Ratio
of 39.4 (Ei = 800 ksi, E2 = 20 ksi) 56
3.17 Vertical Stresses Predicted at Surface of 2-in Pavement System: Stiffness Ratio of
10.0 (Ei = 200 ksi, E2 = 20 ksi) 57
3.18 Transverse Stresses Predicted at Surface of 2-in Pavement System: Stiffness Ratio
of 10.0 (Ei = 200 ksi, E2 = 20 ksi) 58
IX

3.19 Vertical Stresses Predicted at Surface of 2-in Pavement System: Stiffness Ratio of
18.0 (E, = 800 ksi, E2 = 44 ksi) 59
3.20 Transverse Stresses Predicted at Surface of 2-in Pavement System: Stiffness Ratio
of 18.0 (Ei - 800 ksi, E2 = 44 ksi) 60
3.21 Schematic of Axisymmetric and 2-D Finite Element Pavement Models 64
3.22 Schematic and Detailed View of Pavement System Modeled Using the Finite
Element Program, ABAQUS 67
3.23 Transverse Stress Distribution Along Bottom of 4-in Asphalt Concrete Layer for
Stiffness Ratio of 4.6 (Ei = 203 ksi: E2 = 44 ksi) 69
3.24 Transverse Stress Distribution Along Bottom of 8-in Asphalt Concrete Layer for
Stiffness Ratio of 59 (Ei = 1200 ksi: E2= 20 ksi) 70
3.25 Effect of Asphalt Concrete Thickness on Bending Stress Ratio 75
3.26 Effect of Stiffness Ratio (Ei / E2) on Bending Stress Ratio 76
3.27 Effect of Asphalt Concrete and Base Layer Stiffness on Bending Stress Ratio 77
3.28 Effect of Subgrade Stiffness on Bending Stress Ratio at Various Stiffness Ratios
(E,/E2) 78
3.29 Application of Approach - Parametric Study of a Cracked Pavement 80
3.30 Typical Finite Element Model of Pavement Used In Parametric Study For
Determining Factors Critical to Development of Crack Propagation 86
3.31 Detailed View of Crack in Finite Element Model of Pavement 87
3.32 System Used For Two-Step Approach to Finite Element Modeling of Pavement. ...90
3.33 Example of Spring Constant Computation Used For Application of Boundary
Conditions to 4-inch Finite Element Pavement Model From EXCEL Computer
Program 92
3.34 Detailed View of Finite Element Mesh Surrounding Crack Tip 96
4.1 Determination of Ki For Two Different 4-inch Pavement Sections With a 0.5 inch
Surface Crack, and Load Centered 25 inches From Crack 102
4.2 Determination of Kn For Two Different 4-inch Pavement Sections With a 0.5 inch
Surface Crack, and Load Centered 25 inches From Crack 103
x

4.3 Effects of Asphalt Concrete Thickness: Distribution of Ki Versus Crack Length For
Loading Position Centered 25 inches From Crack 106
4.4 Effects of Asphalt Concrete Thickness and Base Layer Stiffness: Distribution of Ki
Versus Crack Length For Loading Position Centered 7 inches From Crack 107
4.5 Effects of Asphalt Concrete Thickness and Base Layer Stiffness: Distribution of Ki
Versus Crack Length For Loading Position With Wide Rib Centered on Top of
Crack 108
4.6 Effects of Asphalt Concrete Thickness and Base Layer Stiffness: Distribution of Kn
Versus Crack Length For Loading Position Centered 25 inches From Crack 109
4.7 Effects of Asphalt Concrete Thickness and Base Layer Stiffness: Distribution of Kn
Versus Crack Length For Loading Position Centered 7 inches From Crack 110
4.8 Effects of Asphalt Concrete Thickness and Base Layer Stiffness: Distribution of Kn
Versus Crack Length For Loading Position With Wide Rib Centered on Top of
Crack Ill
4.9 Comparison of Stress Intensity Magnitudes For Ki and Kn At The Crack Tip For:
8-inch AC, 1 inch Crack, Load Centered 25 inches From Crack 112
4.10 Effects of Asphalt Concrete and Base Layer Stiffness: Distributions of Ki and Kn
Versus Crack Length For Loading Centered 25 inches From Crack 113
4.11 Visual Example of Vertical and Lateral Load Application to Finite
Element Model 115
4.12 Visual Example of Transverse Stress Distribution in Response to Loading:
Undeformed Pavement, Deformed Loaded Pavement, and Transverse Stress
Distribution Along the Pavement’s Surface 117
4.13 Effects of Individual Layer Stiffness Values on Transverse Stress Distribution Along
Surface of Pavement From Center of Load For Layer Stiffness Ratio of 40 120
4.14 Effect of Load Positioning on Opening At the Crack Tip For a 4-inch Surface Layer
and Low Stiffness (E1/E2 = 800:20 ksi) Ratio 122
4.15 Effect of Load Positioning on Shearing At the Crack Tip For a 4-inch Surface Layer
and Low Stiffness (E1/E2 = 800:20 ksi) Ratio 123
4.16 Effect of Load Positioning on Opening At the Crack Tip For a 4-inch Surface Layer
and High Stiffness (E1/E2 = 800:44.5 ksi) Ratio 124
xi

4.17 Effect of Load Positioning on Shearing At the Crack Tip For a 4-inch Surface Layer
and High Stiffness (E1/E2 = 800:44.5 ksi) Ratio 125
4.18 Effect of Load Positioning on Opening At the Crack Tip For an 8-inch Surface
Layer and Lower Stiffness (E1/E2 = 800:20 ksi) Ratio 126
4.19 Effect of Load Positioning on Shearing At the Crack Tip For an 8-inch Surface
Layer and Lower Stiffness (E1/E2 = 800:20 ksi) Ratio 127
4.20 Effect of Load Positioning on Opening At the Crack Tip For an 8-inch Surface
Layer and High Stiffness (E1/E2 = 800:44.5 ksi) Ratio 128
4.21 Effect of Load Positioning on Shearing At the Crack Tip For an 8-inch Surface
Layer and High Stiffness (E1/E2 = 800:44.5 ksi) Ratio 129
4.22 Example Field Section and Core Exhibiting Short Crack: Pure Tensile Failure
Mechanism 132
4.23 Example Field Section and Core Exhibiting Intermediate or Deep Crack: Tensile
Failure Mechanism and Directional Change in Crack Growth 133
5.1 Temperature Gradient Cases Used to Determine Stiffness Gradients in the Asphalt
Concrete Layer to be Evaluated in ABAQUS 138
5.2 Dynamic Modulus versus Temperature Plot For Unaged AC-30 Asphalt Cement
Mixture Used to Convert Temperature Gradients Into Stiffness Gradients 141
5.3 Asphalt Concrete Sublayer Configuration Used For Analyzing Case 1 Uniform
Layer Stiffness Temperature Gradient 142
5.4 Asphalt Concrete Sublayer Configuration Used For Analyzing Case 2 Temperature
Gradient 143
5.5 Asphalt Concrete Sublayer Configuration Used For Analyzing Case 3 Temperature
Gradient 144
5.6 Asphalt Concrete Sublayer Configuration Used For Analyzing Case 4 Temperature
Gradient 145
5.7 Effect of Temperature-Induced Stiffness Gradients on Stress Intensity Ki Predicted
At the Crack Tip For 8-inch Asphalt Concrete (Load Centered 30 in From Crack). 147
5.8 Effect of Temperature-Induced Stiffness Gradients on Stress Intensity Kn Predicted
At the Crack Tip For 8-inch Asphalt Concrete (Load Centered 30 in From Crack). 148
xii

5.9 Effect of Temperature-Induced Stiffness Gradients on Transverse Stress Distribution
Within 8-inch Asphalt Concrete with a 1.0 inch Crack (Load Centered 30 in From
Crack) 149
5.10 Effect of Load Wander on Stress Intensity Within 8-inch Asphalt Concrete
(Stiffness Gradient Case 3) 150
5.11 Illustration of Effects of Stiffness Gradients on Crack Propagation in 4-inch Asphalt
Pavement (Load Centered 25 in From Crack) 151
5.12 Illustration of Effects of Stiffness Gradients on Crack Propagation in 8-inch Asphalt
Pavement (Load Centered 30 in From Crack) 153
5.13 Effects of Stiffness Gradients and Base Layer Stiffness on Crack Propagation in
8-inch Asphalt Pavement (Load Centered 30 in From Crack) 154
5.14 Effects of Stiffness Gradients and Asphalt Concrete Layer Thickness on Crack
Propagation (Load Centered 25 in and 30 in From Crack) 155
5.15 Effects of Stiffness Gradients and Asphalt Concrete Layer Thickness on Crack
Propagation (Load Centered 20 in and 25 in From Crack) 156
5.16 Effects of Stiffness Gradients and Asphalt Concrete Layer Thickness on Crack
Propagation (Load Centered 15 in and 20 in From Crack) 157
5.17 Effects of Stiffness Gradients and Asphalt Concrete Layer Thickness on Crack
Propagation (Load Centered 7in From Crack) 158
5.18 Effects of Stiffness Gradients and Asphalt Concrete Layer Thickness on Crack
Propagation (Wide Rib Load Centered on Top of Crack) 159
5.19 Effects of Stiffness Gradient Case 2 on Direction of Crack Growth in 4-inch
Pavement (Angle Relative to Vertical) : 161
5.20 Effects of Various Stiffness Gradients on Direction of Crack Growth in 8-inch
Pavement (Angle Relative to Vertical) 163
5.21 Effects of Various Stiffness Gradients on Direction of Crack Growth: Photo of
Cracked Trench Extracted From Florida Highway 301 164
6.1 View of Lane Exhibiting Visible Surface-Initiated Longitudinal Cracks in the Wheel
Paths 167
6.2 Transverse Distribution of Load Within Wheel Path and Critical Load Positions For
Pavements For a 4-inch Asphalt Concrete Layer of Uniform Stiffness 170
xiii

6.3 Transverse Distribution of Load Within Wheel Path and Critical Load Positions For
Pavements For an 8-inch Asphalt Concrete Layer of Uniform Stiffness 171
6.4 Effect of Temperature-Induced Stiffness Gradients on Transverse Distribution of
Load Within Wheel Path and Critical Load Positions For 4-inch Pavement 172
6.5 Effect of Temperature-Induced Stiffness Gradients on Transverse Distribution of
Load Within Wheel Path and Critical Load Positions For 8-inch Pavement 173
6.6 Example Field Section and Core Exhibiting Short Crack: Pure Tensile Failure
Mechanism 176
6.7 Example Field Section and Core Exhibiting Intermediate or Deep Crack: Tensile
Failure Mechanism and Directional Change in Crack Growth 177
6.8 Field Core Showing Longitudinal Wheel Path Crack Opened At Surface From
Florida Interstate I-10 178
6.9 Potential For Crack Growth and Time Available For Identification and
Rehabilitation For 8-inch Pavement and Given Load Spectrum 180
6.10 Potential For Crack Growth and Time Available For Identification and
Rehabilitation For 4-inch Pavement and Given Load Spectrum 181
A.l Distribution of Transverse Stresses Computed At Increasing Vertical Distance From
0.5-in Crack: 8-in Asphalt Concrete, Stiffness Gradient Case 2, Load Positioned At
0, 7, and 20 inches From Crack 192
A.2 Distribution of Shear Stresses Computed At Increasing Vertical Distance From 0.5-
in Crack: 8-in Asphalt Concrete, Stiffness Gradient Case 2, Load Positioned At 0, 7,
and 20 inches From Crack 192
A.3 Distribution of Transverse Stresses Computed At Increasing Vertical Distance From
0.5-in Crack: 8-in Asphalt Concrete, Stiffness Gradient Case 2, Load Positioned At
25 inches From Crack 193
A.4 Distribution of Shear Stresses Computed At Increasing Vertical Distance From 0.5-
in Crack: 8-in Asphalt Concrete, Stiffness Gradient Case 2, Load Positioned At 25
inches From Crack 193
A.5 Distribution of Transverse Stresses Computed At Increasing Vertical Distance From
0.5-in Crack: 8-in Asphalt Concrete, Stiffness Gradient Case 2, Load Positioned At
30 inches From Crack 194
xiv

A.6 Distribution of Shear Stresses Computed At Increasing Vertical Distance From 0.5-
in Crack: 8-in Asphalt Concrete, Stiffness Gradient Case 2, Load Positioned At 30
inches From Crack 194
xv

Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
DEVELOPMENT AND PROPAGATION OF SURFACE-INITIATED
LONGITUDINAL WHEEL PATH CRACKS IN FLEXIBLE HIGHWAY PAVEMENTS
By
Leslie Ann Myers
December 2000
Chairman: Dr. Reynaldo Roque
Major Department: Civil Engineering
The primary distress mode of over 90% of high-type bituminous pavements
scheduled for rehabilitation in Florida is longitudinal wheel path cracking. This situation
creates an immediate need for a clear definition of the growth mechanisms of this costly
mode of failure. These cracks initiate at the surface of thick and thin asphalt concrete
layers and propagate downwards in an opening mode, as evidenced by observations of
trench sections and cores taken from field sites. Literature review has shown that several
researchers have presented observations and/or hypotheses that attempt to explain the
surface cracking phenomenon, but a complete identification for the crack propagation
mechanism that considers factors found in the field does not exist.
Parametric study analyses performed were focused on predicting near-surface
crack tip stresses and determining which factors result in tensile crack growth downwards
from the surface of the pavement. The finite element analysis program ABAQUS was
xvi

used along with other analytical models to compute stress intensity factors at the crack tip
and to determine the propensity of effects such as pavement structure, crack length, load
spectra (load magnitude and wander in wheel path), tire-pavement interface stresses, and
temperature- or aged-induced stiffness gradients. Stress analyses were performed using
actual measured radial truck tire-pavement interface stresses obtained from a tire research
company in Ohio. Thermal analyses were conducted using temperatures measured by
National Oceanic and Atmospheric Agency (NOAA) daily for several years in various
north-central Florida locations. Furthermore, a sensitivity analysis of finite element
model types indicated that modified 2D pavement models are suitable for representing 3D
pavement bending.
The physical presence of a crack or discontinuity must be considered in pavement
design in order to properly account for surface crack growth in asphalt concrete
pavements. The load spectra, such as tire-pavement interface stresses produced under
radial truck tires and load wander in the wheel path, in combination with stiffness
gradients caused by seasonal temperatures and aging, will apparently result in tensile
failure that is the primary mechanism of surface-initiated longitudinal crack propagation
in the wheel paths.
XVII

CHAPTER 1
INTRODUCTION
1.1 Background
Longitudinal wheel path cracking that initiates at the surface of asphalt pavements
is a relatively recent phenomenon that has major cost implications to highway
departments. In Florida alone, over 90% of flexible pavements are scheduled for
rehabilitation of surface cracking, making it the predominant mode of failure. Cores and
trench sections taken from pavement sections that are found to have substandard crack
ratings clearly show that cracks initiated at the surface and worked their way down. The
surface cracking phenomenon has been reported in other areas of the United States and
documented in Europe, which indicates the immediate importance of the scope of this
study to be expanded to include environmental and geographical conditions other than
those found in Florida. However, the development and mechanism for this mode of
failure, as well as the conditions that make the pavement susceptible to crack growth,
have not been clearly defined.
The aspects which define the traditional approach to pavement evaluation have
been cited in numerous publications (e.g., Huang 1993; Yoder and Witczak 1975). The
existing approach to performance prediction classifies pavement failure types that have
been observed, studied and documented many times. However, until recently
1

2
longitudinal surface cracking was not associated with damage propagating from the
surface of the pavement. Therefore, the loading as defined in the existing performance
analyses is not representative of field observations for longitudinal pavement surface
cracking. As described in Huang’s book, performance prediction is based on a collection
of general data that is geared more specifically for traditional load-associated cracks that
initiate at the bottom of flexible pavements. The loading included for these response
predictions is a uniformly distributed vertical surface load with an average tire pressure.
This loading is applied at only one position, in the location found to be critical for
traditional cracking. No effort is made to distinguish between tire types nor to capture the
possible effects of changing load positioning due to wander in the wheel paths.
The pavement structures analyzed using typical performance relationships are also
not representative of those currently found in the field. For example, in order to capture
the effects of temperature, a seasonally-averaged definition of the pavement structure is
often made using a relationship developed by the Asphalt Institute (Huang 1993). This
procedure has been used to find a uniform asphalt concrete stiffness, as based on the
temperature computed at one-third of the depth of the asphalt concrete layer. Another key
factor that is missing from pavement structures analyzed using the traditional approach is
the presence of discontinuities or flaws. There is no allowance for the introduction or
growth of cracks when analyzing a traditional pavement structure. Therefore, using the
traditional approach to analysis is not only inconsistent with field observations, but also
will not address the various conditions that lead to surface cracking.
Work done recently with measured contact stresses under radial truck tires (Roque
et al. 1998; de Beer et al. 1997; Woodside et al. 1992; Bonaquist 1992) appears to define

3
conditions under which cracking initiates (Myers et al. 1999). However, because surface-
initiated longitudinal wheel path cracking is a relatively recent phenomenon, as reported
by some researchers (Myers et al. 1998; Jacobs 1995; Matsuno et al. 1992), failure
theories that may apply towards addressing its development are not definitive at the
present time. In fact, most failure theories do not address the possibility of a critical
condition existing near the pavement’s surface. The distortion energy approach has been
used by some researchers (Center for Research and Contract Standardization in Civil and
Traffic Engineering 1990) to analyze development of surface cracking; however, this
approach will always compute the highest distortion energy at the bottom rather than at
the top of the asphalt layer. Another approach currently in development incorporates
continuum damage mechanics (Kim et al. 1997). Continuum damage mechanics may be
used to create a reduced stiffness area within a continuum that approximates the presence
of a discontinuity or flaw; however, the physical characteristics of a crack and crack tip
stresses are not addressed in this method.
Several researchers have addressed the propagation of cracks in asphalt concrete
by using the fracture mechanics approach. Unfortunately, the analyses presented in the
studies were often limited to traditional pavement structures and loading conditions. The
parameters used in the studies were often limited to either traditional bottom-up cracks
(Ramsamooj 1993) or uniform and/or pneumatic truck tire loading (Collop and Cebón
1995; Merrill et al. 1998). Jacobs et al. (1996) applied an approach to characterize both
surface and bottom cracking by calculating the stress intensity factors at the tip of cracks
in the asphalt layer; however, the loading used in the approach was based on contact
stresses measured from a bias ply truck tire. In a primarily laboratory study of cracking in

4
the asphalt layer, Jacobs et al. (1996) described the continuously changing stress
distribution during the crack growth process by applying linear elastic fracture mechanics
principles such as Paris’s Law and Schapery’s theory. Because fracture mechanics can be
used to describe the conditions ahead of the crack tip, it appears to be a suitable approach
to describing surface crack development.
This study is part of a general investigation on the characteristics and generation
of longitudinal wheel path cracking undertaken by University of Florida and supported by
the Florida Department of Transportation (FDOT) and Federal Highway Administration
(FHWA). Results from this study can be used to relate fracture behavior from the field to
laboratory testing of asphalt concrete. Substantiating the cracking predictions would
require additional field data on the characteristics of wander in the wheel paths and the
frequency of critical temperatures (or gradients) in the pavement.
1.2 Research Hypothesis
The purpose of this investigation is to determine whether propagation will only
occur under critical conditions by identifying the mechanisms, and the most critical
factors, that lead to the development and propagation of surface-initiated longitudinal
wheel path cracks. The effects of factors such as realistic tire contact stresses and load
position, thermal gradients in asphalt layer, presence of discontinuities, and other certain
critical conditions on cracking performance will be investigated. The implication would
be that traditional approaches to pavement analysis, which typically include average

5
conditions that do not capture these key factors, cannot properly describe this failure
mode.
1.3 Objectives
The primary objectives of this research study were as follows:
• To identify the most likely mechanisms for the development and propagation of
longitudinal wheel path cracks that initiate at the surface of bituminous
pavements.
• To investigate and identify critical conditions that result in surface crack
propagation, in order to capture the key factors that lead to this type of failure.
• To evaluate the use of fracture mechanics for the analysis of surface-initiated
longitudinal crack growth.
• To examine the critical conditions leading to failure, in order to assist in the
development of analysis and design tools for asphalt mixtures and pavements.
1.4 Scope
The research conducted in this study focused on identifying the critical conditions
that contribute to the propagation mechanism of surface-initiated longitudinal wheel path
cracking. A detailed literature review revealed that nontraditional approaches, including
critical loading and pavement structural conditions, to evaluating longitudinal surface
cracking have not been extensively investigated. Defining the conditions which
propagate surface-initiated cracks may lead to ideas on how to best address the problem
through remediation and/or prevention, ft should be noted that the specific mixture

6
characteristics (mixture type, gradation, etc.) that can help to alleviate this problem were
beyond the scope of this study.
The study primarily focused on analyses which predict the effects of near-surface
and crack tip stresses. The analyses necessary for developing the hypothesis on surface-
initiated crack growth were not comparable to those of typical pavement response
models. Some characteristics and/or limitations of the analyses included in the study are
as follows:
• Two-dimensional (2D) finite element analysis was conducted for pavements with a
surface crack and complex surface loading conditions using the finite element
computer program ABAQUS. The primary focus was on using 2D modeling to
evaluate the effects of different factors on crack propagation. As a first step, the
method of approximating three-dimensional (3D) pavement responses using modified
2D models was determined to be adequate for predicting the various effects.
• The evaluations and approach presented herein were designed to be suitable for near¬
surface stress states and. most specifically, the development and propagation of
surface-initiated longitudinal wheel path cracks.
• Application of a single radial truck tire load was used on the pavement models. The
analyses were performed at one static load magnitude, as measured and provided by
Dr. Marion Pottinger at Smithers Scientific Services, Inc. in Ohio. This magnitude
was deemed representative of a typical value for a radial tire found on a high-volume
highway.
• Conventional pavement structures were considered in the study (i.e., asphalt surface
on aggregate base and subgrade).
• Linear elastic fracture mechanics was utilized to predict stress intensity factors (Kj,
Kn) and fracture energy release rate (J). These parameters were descriptive of crack
tip stress states and conditions.
Some of the assumptions on which the analyses were based include:
• A study was conducted that indicated use of two-dimensional (2D) finite element
analysis was reasonable for approximating three-dimensional (3D) finite element
analysis, if certain modifications were applied to match pavement response.

7
• Plane strain conditions were assumed for 2D analyses and the stress-strain response of
the asphalt concrete layer was considered in the evaluation. The accuracy of the stress
distributions within the base and subgrade layers was not considered.
• Linear elastic materials were used in the models, which allowed for the evaluation of
effects on pavement response, while reducing modeling time and computational
effort. It also allowed for the evaluation of pavement models using linear elastic
fracture mechanics. However, it should be noted that using linear elastic
isoparametric elements in a model does not allow for the exact estimation of stress
concentrations under the edge of a concentrated loading. Likewise, linear elastic
materials are assumed to have infinite strength, which does not reflect the physical
reality of the pavement.
A range of factors was defined to represent critical structural or loading conditions
for the pavement model. The values assumed to represent specific load and pavement
structure include load positioning (wander) with respect to crack, realistic (vertical and
lateral contact stresses) tire load application, crack depth, asphalt pavement thickness,
surface and base layer stiffness, and stiffness gradients induced in asphalt concrete layer
due to daily environmental and temperature fluctuations.
1.5 Research Approach
The research was mainly an analytical study supplemented by the acquisition of
measured tire-pavement interface stresses and other specific truck tire data. The overall
research approach for the development of an explanation for the propagation mechanism
of surface cracking is presented in Figure 1.1. The main purpose of the analyses was to
identify different factors that determine the critical conditions that lead to the
development and propagation of surface-initiated cracking. Studies conducted as part of
the research are described in the following areas:

8
• Literature Review: existing ideas and theories published on the subject of surface-
initiated cracking in asphalt concrete pavements and traditional continuum mechanics
versus fracture or damage mechanics are examined. The findings in the literature
yielded different methods available for explaining crack growth such that selection of
the most plausible theory could be made.
• Tire Contact Stress Verification: finite element modeling was used to verify
measured tire contact stress use in pavement systems and to determine the effects of
tire type, loading, and inflation pressure.
• Pavement Analysis: pavement analyses were conducted and used in the development
of an approach to modify two-dimensional analyses to approximate three-dimensional
pavement response.
• Parametric Studies of Pavement System: analytical studies were conducted to discern
structural and temperature-related effects on pavement response. Evaluations were
conducted by predicting stress states in the process zone ahead of crack tip, as well as
by evaluating different stages of crack length and various positions of loading relative
to crack location. Characterization of crack tip conditions was accomplished by
predicting stress intensity factors and the fracture energy release rate parameter.
• Identification of Critical Conditions For Surface Crack Propagation: analytical
studies were conducted to determine the factors that induce critical conditions near
cracked pavement surface. The purpose was to distinguish which factors produced
conditions most likely to result in the propagation of surface-initiated longitudinal
cracks observed in the field.
• Final recommendations were made for the development of an analysis and design tool
for asphalt mixtures and pavements.

Figure 1.1: Overall Research Approach Flowchart.

CHAPTER 2
LITERATURE REVIEW
2.1 Overview
A comprehensive literature search was conducted to identify existing publications
dealing with the evaluation of surface-initiated cracking. Previous work had
demonstrated that surface cracking was most likely initiated by near-surface lateral
stresses induced by radial truck tires. The following subjects were examined:
• Classical fatigue approach
• Continuum damage approach
• Fracture mechanics approach
• Measurement of tire contact stresses
• Analysis of surface cracking
With the exception of the literature on tire contact stresses, until recently researchers had
not focused on the possibility of critical stresses occurring at the surface of the pavement.
The primary focus had traditionally been on the critical stress induced by pavement
bending at the bottom of the asphalt concrete layer.
10

11
2.2 Classical Fatigue Approach
Longitudinal wheel path cracking has been observed in the field and cited in
publications as initiating at the pavement surface (Myers et al. 1998; Roque et al. 1998).
This type of damage occurs in a situation not considered by classical fatigue approaches
to pavement cracking. The aspects which define the traditional approach to pavement
evaluation have been cited in numerous publications (Huang 1993; Yoder and Witzcak
1975). The existing approach to performance prediction is broad and classifies pavement
failure types that have been studied and documented extensively; therefore in this way, it
fails to account for recent damage found in the field (i.e., longitudinal surface cracking).
For example, loading as defined in existing performance analyses is far removed from
field observations. As described by Huang (1993), performance prediction is based on a
collection of general data that is geared more specifically for traditional load-associated
cracks that initiate at the bottom of flexible pavements. The loading included for these
response predictions is a uniformly distributed vertical surface load with an average tire
pressure. This loading is applied at only one position, in the location found to be critical
for traditional cracking. No effort is made to distinguish between tire types nor to capture
the possible effects of changing load positioning due to wander in the wheel paths.
The pavement structures analyzed using typical performance relationships are also
not representative of those currently found in the field. For example, in order to capture
the effects of temperature, a seasonally-averaged definition of the pavement structure is
made using a relationship developed by the Asphalt Institute (Huang 1993). This
procedure has been used to find a uniform asphalt concrete stiffness, as based on the

12
temperature computed at one-third of the depth of the asphalt concrete layer. Another key
factor that is missing from pavement structures analyzed using the traditional approach is
the presence of discontinuities or flaws. There is no allowance for the introduction or
growth of cracks when analyzing a traditional pavement structure. Therefore, using the
traditional approach to analysis is not only inconsistent with field observations, but also
will not address the various conditions that may lead to surface cracking.
Studies and pavement performance modeling conducted in the United States have
usually concentrated on classical fatigue approaches that consider failure to start at the
bottom of the asphalt surface layer (e.g., Asphalt Institute mechanistic-empirical design
procedure (Huang 1993); and the performance models developed for Superpave in the
SHRP program, (Lytton et al. 1990)). The Asphalt Institute method for pavement design
is based on this approach. The number of cycles to failure (Nf) can be calculated as a
function of the dynamic modulus and tensile strain at the bottom of the asphalt layer for
the prediction of fatigue cracking for a standard mix with an asphalt volume of 11% and
air void volume of 5%, although an adjustment for different mixture volumetries is
available (Huang 1993). The following fatigue equation was used as the failure criterion
for cracking in the Asphalt Institute’s design procedure:
Nf = 0.0796 (et)'3 291|E*| ’0 854
where Nf = allowable number of load repetitions to control fatigue cracking,
|E*| = dynamic modulus of the asphalt mixture (psi),
8t = tensile strain at the bottom of the asphalt layer, computed by elastic
layer theory (in/in).

13
Such predictions for failure are based on laboratory tests which are calibrated to
the field and offer limited correlation to field occurrence in accounting for traffic load
relaxation times and the subsequent crack propagation rates. Therefore, this elastic layer
analysis approach will neither predict nor provide design input for the type of surface
cracking found on Florida’s interstate roads.
2.3 Continuum Damage Approach
An approach currently in development to explain damage growth incorporates
continuum damage mechanics (Kim et al. 1997). Continuum damage mechanics may be
used to create a reduced stiffness area within a continuum that approximates the presence
of a discontinuity or flaw. The method utilizes the work potential theory to model
damage growth during both controlled-strain and controlled-stress loading cycles and
healing during rest periods. The research has primarily been applied to evaluation of
classical fatigue cracking, which does not develop in the same manner as longitudinal
surface cracking. Another limitation of the continuum damage approach is the inability
to replicate the physical characteristics of a crack and the prediction of crack tip stresses
and behavior.
Boundary element methods have been described in detail by Crouch and Starfield
(1990). Boundary element methods have been widely used in the geomechanics field and
offer a different computational technique for predicting damage in asphalt concrete
pavements.

14
Another theory which was a possibility for explaining the mechanism of surface
cracking was the distortion energy approach. The distortion energy model was used by
some researchers (CROW 1990) in an attempt to explain the development of surface
cracking. This approach is based on the existence of a relationship between distortion
energy and fatigue life. That is, fatigue of a viscoelastic material develops with the
accumulation of distortion energy induced by load repetitions (Stulen and Cunnings
1954). It assumes that failure occurs by exceeding the energy tolerance of a material and
the pavement has no crack present initially. The basic idea behind the distortion energy
model is that repeated applications of a moving wheel results in an accumulation of
distortion energy in a viscoelastic material that will eventually exceed the tolerance of the
asphalt mixture.
But as the study pointed out, this approach will always compute the highest
distortion energy at the bottom rather than at the top of the asphalt layer, which may limit
its usefulness in explaining crack development at the pavement surface. However, the
study mentioned that the combination of tensile stresses at the surface (induced by
horizontal contact shear forces) and high values of dissipated distortion energy could
cause cracking in the wearing course. It should be noted that linear elastic multi-layer
analysis programs cannot be used to compute dissipated energy values due to passing
loads, although approximations are available in the literature.

15
2.4 Fracture Mechanics Approach
The concept of crack propagation that proceeds downwards from the surface of
the asphalt has not been fully analyzed using traditional pavement analysis tools. In fact,
most failure theories do not address the possibility of a critical condition existing near the
pavement’s surface. Several researchers have addressed the general propagation of
cracks in asphalt concrete by using the fracture mechanics approach. Unfortunately, the
analyses presented in the studies were often limited to traditional pavement structures and
uniform loading conditions. Nevertheless, existing solutions for uncracked pavements
(uniform stress distribution) are not appropriate for use in evaluating pavements with a
crack. Ramsamooj (1993) adopted existing solutions by employing the fundamentals of
fracture mechanics to predict crack growth under dynamic loading. The stress intensity
factors (SIF) at the crack tip were calculated at incremental stages of crack growth, from
the initial crack at the surface, to a short through-crack and finally into a long through-
crack. Three different crack types were evaluated: transverse (across wheel path),
longitudinal (parallel to wheel path), and semi-elliptical. Fracture was defined as
occurring when the stress intensity factor computed at the crack tip under fatigue loading
exceeds the fracture toughness of the material. The effects of temperature on fracture
susceptibility were also considered. Closed-form solutions were manipulated to predict
stress intensity factors for various crack types at different stages of crack growth;
however, a uniform vertical loading was used for the analyses which does not reflect a
realistic loading case.

16
Collop and Cebón (1995) also conducted a study on the use of fracture mechanics
for analyzing surface crack growth in pavement systems. The authors sought to
theoretically define the mechanisms of fatigue cracking in flexible pavements under
different traffic and cyclic thermal loading conditions by using linear elastic fracture
mechanics. An axisymmetric finite element model (FEM) was developed using the
ABAQUS computer program (HKS 1997) to investigate stresses ahead of the longitudinal
cracks in the surface layer. Loading data taken from work done by Jacobs (1995) for a
bias ply truck tire were used in the analysis. A parametric study was conducted to
evaluate the effects of pavement thickness and elastic modulus ratio and found that
increasing the modulus ratio and reducing the asphalt thickness will tend to reduce the
transverse tensile stress at the pavement’s surface. The Mode I stress intensity factor
(Broek 1982) was predicted ahead of the crack tip and it was shown that the crack
propagates vertically downward to about 10 to 20 mm and then stops. Also, increasing
the asphalt thickness and decreasing the elastic modulus ratio will increase the magnitude
of the stress intensity factor and the depth to which the crack propagates, as illustrated in
Figure 2.1
Increasing temperature fluctuation also increased the stress intensity factor at the
surface crack tip, which helped to explain longitudinal cracking that occurs in warmer
climates where thermal cooling gradients are found to be high. The effects of other
modes of fracture were not included in the study.

17
A THEORETICAL ANALYSIS OF FATIGUE CRACKING IN FLEXIBLE PAVEMENTS
Figure 2.1: Stress Intensity Factor Plotted As a Function of Crack Length for a
Surface Crack Due to Vehicular Loading For Three Different Pavement Structures
With Different Modulus Ratios, (after Collop and Cebón 1995)
Using fracture mechanics principles, Jacobs et al. (1996) analyzed the crack
growth process. Specimens measuring 50-mm by 50-mm by 150-mm were subjected to
tension-compression tests under repeated loading conditions. Analysis of crack opening
displacement (COD) measurements yielded crack growth parameters n and A. Results of
the study showed that Schapery’s theoretical derivations for n and A for viscoelastic
materials were valid and that the exponent in the Paris Law can be estimated by the slope
of the compliance curve. They also concluded that the constant A from the Paris Law
may be estimated from a combination of the fracture energy, mixture stiffness, and
maximum tensile strength.

18
2.5 Measurement of Tire Contact Stresses
Tire engineers have tried for many years to model the three-dimensional contact
patch between a tire and the pavement. It should be noted that stresses predicted by
automotive models were those of the pavement on the tire and were thus opposite the
orientation of the pavement engineers. Also, because measuring pressure was so difficult
and expensive, studies conducted were limited to tires run on steel plates rather than on
actual asphalt or other viscoelastic materials.
It is important to understand how tire-pavement interface stresses are measured
and where they come from. Work has been done in this area by various tire researchers.
M.G. Pottinger (1992) has done considerable work in the area of contact patch stress
fields for both truck and car tires. He explained that the effect of free rolling radial truck
tires on a pavement is very different than that of bias ply truck tires. Two types of effects
exist under truck tires. These are generally referred to as the pneumatic effect and
Poisson’s effect (Roque et al. 1998). Figure 2.2 illustrates the basic difference in contact
effects. Although both fields exist under both types of tires, one effect will be more
dominant for a given type of tire.
The overriding effect induced under radial truck tires is the Poisson effect. In
other words, the pneumatic effect is less, such that Poisson effect is dominant. This is a
-direct result of tire construction. Radial tires are constructed to have stiffer treads and
less stiff sidewalls, so that the tread does not deform as much as the tire rolls. Thus, the
lateral stresses induced on the road by the radial truck tire will tend to push out from
center of the tire ribs, as shown in Figure 2.2. On the other hand, the pneumatic effect is

19
dominant under bias ply truck tires, such that lateral stresses pull the pavement surface
toward the center of the tire.
By using triaxial load pin transducers inserted onto a flat steel test track, Pottinger
was able to measure tire-pavement interface stresses and displacements for vertical,
longitudinal and transverse axes. He also determined the rolling tire footprint shape.
Figure 2.3 shows the test track configuration that was utilized.
Other researchers have developed measurement systems to capture the contact
patch between the tire and the underlying structure. In South Africa, de Beer et al. (1997)
conducted a laboratory and field experiment on the development of the Vehicle-Road
Pressure Transducer Array (VRSPTA) System that measures three-dimensional stresses
induced under bias ply, radial and wide based radial truck tires at different loads and
inflation pressures. The experimental setup consisted of 13 triaxial strain gauge steel pins
(spaced 17mm transversely) mounted on a steel plate and fixed flush with the road
surface. The setup is illustrated in Figure 2.4. The contact stress distributions measured
by de Beer, although a less refined patch was captured, were comparable in both stress
magnitude and pattern to those measured on Pottinger’s steel bed device. As seen in
Figure 2.5, both the nonuniform vertical load and transverse stress reversals were
captured by the VRSPTA system.
Woodside et al. (1992) also developed a similar steel bed-transducer array device
to measure the contact stress patch between the tire and underlying material in the
laboratory. Normal and tangential contact stresses were measured under both static and
dynamic radial car and truck tires. The steel plate system was fitted with 12 transducers
and repeatedly measured a strip transversely every 5 mm over the entire contact patch. A

20
Pneumatic
Effect
Poisson
Effect
Composite
Effect
Figure 2.2: Structural Characteristics of Bias Ply and Radial Truck Tires and Their
Effects on the Pavement Surface, (after Roque et al. 1998)

21
Coaxial Load and Displacement
Transducer Detail
Figure 2.3: Schematic of System Used to Measure Tire Contact Stresses, (after
Roque et al. 1998)

22
TYRE ON HVS
(or Vehicle)
¡
Figure 2.4: Experimental Setup of Vehicle-Road Surface Pressure Transducer
Array (VRSPTA) System Used to Measure Tire Contact Stresses.
(after de Beer et al. 1997)

Vertical Contad Stress (MPa)
315/80 R22.5: TYPE IV, Table 1
Inflation Pressure = 800 kPa ; Load = 40 kN
23
15 "
Longitudinal rear Lateral
Vertical Contact Stress Distribution
Lateral Contact Stress Distribution
Figure 2.5: Three-dimensional Vertical and Lateral Contact Stress Distributions
Under Radial (R22.5) Truck Tire at Rated Load, (after de Beer et al. 1997)

24
total of 90 contad stresses were obtained for each test. The contact stresses were then
used in the evaluation of durability of surface chippings on asphalt overlays. Results
concluded that implementation of surface chippings of 1 mm macro-texture may improve
skid resistance on pavements.
A tire-pavement study was conducted by Bonaquist (1992) at the FHWA
Accelerated Loading Facility to determine the flexible pavement response to wide based
single tires. The focus of the experiment was to capture the tensile strain at the bottom of
the surface layer and the vertical strains in the asphalt concrete, base and subgrade layers.
He reported that a wide base single tire results in higher vertical compressive strains in all
of the pavement layers, generates increased tensile strains at the bottom of the asphalt
concrete layer, and induces more rutting damage in less time than the traditional dual tire
configuration. Responses near the surface of the pavement were not evaluated.
Work done recently by researchers in Florida focused on the effects of tire type,
loading, and inflation pressure on measured contact stresses under various truck tires
(Myers et al. 1999). The study showed that the contact stress distributions measured
under radial truck tires appear to contribute to the prevalence in recent years of surface-
initiated wheel path cracking and near-surface rutting. It was explained that tire structure
has a significant influence on contact stresses; in fact, stress states induced by radial and
wide base radial tires were determined to be potentially more detrimental to the
pavement’s surface than stress states induced by bias ply tires. The primary difference
was found in lateral contact stresses, rather than in vertical stresses, that develop under
each type of tire. The effect of tire structure is shown in Figure 2.6.

25
Radial Truck Tire
I
»—i i i r—i i—i
Near-Surface Stresses
Tension
A AAA A
Compression
Truck Tire
Tread Effect
( + )
(-) *•••
Pavement
• • Bending Effect
( + ) -
XX
(-)
-^Vi-
Overall Effect
Bias Ply Truck Tire
| +
__l a CO CO CO
Near-Surface Stresses
Tension
Compression
( + )
(-)
• •
* MM
• •
Truck Tire
Tread Effect
Pavement
Bending Effect
a
XX
( +
(-
• Ml*
**
• ■
Overall Effect
Figure 2.6: Effect of Pavement Bending Due to a Bias Ply and Radial Truck
Tire on Surface Stress Distribution, (after Myers et al. 1999)

26
The research stated that vertical and lateral tire contact stresses must be considered in the
design and evaluation of asphalt pavements. Lateral stresses under radial tires appear to
result in stress states that are more conducive to surface cracking in asphalt pavements
(Figure 2.7). The vertical stresses for various tire types are different, as shown in Figure
2.8, but do not influence surface failure to the extent that the lateral
Transverse Location, X (mm)
Figure 2.7: Transverse Contact Shear Stresses Measured For a Bias Ply, Radial,
and Wide Base Radial Tire At the Appropriate Rated Load and Inflation Pressure,
(after Myers et al. 1999)

Vertical Contact Stress (kPa)
27
Transverse Location, X (mm)
Figure 2.8: Vertical Contact Stresses Measured For a Bias Ply, Radial, and Wide
Base Radial Tire At the Appropriate Rated Load and Inflation Pressure.
(after Myers et al. 1999)

28
stresses do. It appears that lateral stresses induce tension at the pavement’s surface and
consequently may initiate cracking and/or reduce the mixture’s confinement and
resistance to shear and permanent deformation.
Wide base radial (Super-single) tires were observed to induce vertical contact
stresses as high as 2.5 times the inflation pressure, as shown in Figure 2.8. The authors
explained that this case represents a severe loading condition that, when combined with
lateral stresses under the tire that reduce mixture confinement, greatly increases the
potential for near-surface damage.
2.6 Analysis of Surface Cracking
Because surface-initiated longitudinal wheel path cracking has been cited as
critical pavement damage in recent years, failure theories that may apply towards
addressing its development are not yet definitive. In Europe, the effects of lateral stresses
at the tire-pavement interface have been studied and published. The belief is that these
lateral stresses initiate cracking at the pavement surface which somehow propagates
downwards. It is recognized that these cracks are neither of the traditional fatigue nor
reflective nature. Traditional fatigue is generally identified by the appearance of alligator
cracking in the wheel paths and is typically assumed to be caused by large tensile stresses
and strains at the bottom of the asphalt concrete surface layer.
Hugo and Kennedy (1985) presented observations that allude to the phenomenon of
surface-initiated cracks. They reported the initiation of cracks at the pavement’s surface
directly underneath the rubber pressure pads of the heavy vehicle simulator after the

29
pavement was subjected to repeated stationary cyclic loads. They attributed the cracks to
the presence of horizontal shear stresses induced by the rubber pads on the pavement.
Analytical work in the Netherlands illustrated how inward radial (horizontal) stresses
could lead to tension at the edges of a circular load (CROW 1990). This work prompted
M.M Jacobs of Delft Institute of Technology (the Netherlands) to describe the occurrence
of maximum tensile stresses at the surface of the pavement through analytical evaluation
(Jacobs 1995). This study predicted tensile stresses at the edge of a truck tire on the
pavement’s surface which were sufficient to cause fracture. These tensile stresses were
found to dissipate rapidly with increasing depth; that is, they typically existed in the top
10 millimeters of the asphalt layer. These tensile stresses were cited as the most probable
cause for the initiation of longitudinal cracking found in flexible pavements. However,
tensile stresses were generated at the edge of the tire load because measurements were
obtained from a bias ply truck tire, since Jacobs did not use recently measured tire-
pavement interface stresses. The predictions provided by Jacobs supported the theory
that lateral stresses in the surface may initiate cracking. However, the study was limited
by the following factors:
• Lateral stresses were inferred from values published in the literature, not measured.
• Exclusion of dimensional (layer thickness) effects.
• Sources of tire-pavement interface stress data are considered outdated in comparison
to current tire characteristics.
• There did not appear to be access to measured tire-interface stresses for radial truck
tires.
Recent work (Myers 1997; Myers et al. 1998) has shown that longitudinal surface
cracking appears to be initiated by significant lateral contact stresses that are induced

30
under radial truck tires. Measured contact stresses were obtained for a typical radial tire
from Pottinger’s steel bed device and were analyzed in the BISAR program. Analyses
showed that a high magnitude of tension was induced under certain ribs of the tire tread
that are in contact with the pavement’s surface, as presented in Figure 2.9.
Figure 2.9: Predicted Transverse Stress Distribution Induced By Radial Truck Tire
Near Pavement Surface, (after Myers et al. 1998)

31
Tensile stresses were found to be more significant in thicker and stiffer asphalt concrete
pavements. The study gave a viable explanation for longitudinal crack initiation;
however, use of linear elastic layer analysis did not allow for analysis of crack growth or
discontinuities in the pavement.
Researchers in Japan (Matsuna and Nishizawa 1992) indicated that longitudinal
surface cracks have been reported as a major problem in asphalt pavements. Results from
a visual condition survey indicated that the cracks are due to large tensile strains that
develop close to the tire shoulders at high temperatures. By using an axisymmetric finite
element model, they explained that tensile strains are concentrated at the tip of a small
crack that has been induced at the pavement’s surface. The analysis work included a
traditional uniform circular vertical loading, which is not representative of a realistic tire
loading.
Finite element modeling was used by Merrill et al. (1998) to analyze a flexible
pavement system modeled with a nonuniform tire load. An axisymmetric model was
developed using the ABAQUS finite element analysis computer program (HKS 1997)
and was loaded with lateral and vertical stress measurements taken from the South
African VRSPTA (de Beer et al. 1997) device. Significant transverse tensile strains were
predicted at the pavement surface under the tire’s edges and were found to be more
pronounced in thicker pavements. The authors stated that conventional pavement
response models are inadequate for the prediction of surface crack initiation. The effects
of temperature on the predicted strains near the pavement surface were not considered
and discontinuities (i.e. cracks) were not introduced into the pavement system in the
study. However, it was significant to find that other researchers found the concept of

32
critical condition (versus those included in traditional pavement analysis) essential to the
initiation of surface cracks and recommend a move to utilizing more complex pavement
analysis tools.
2.7 Summary
The discussion and review presented above indicate that there is an immediate
need to more completely define the behavior of surface-initiated longitudinal wheel path
cracking. Identification of the critical conditions that induce the cracking mechanism, as
well as obtaining a clearer understanding of the effects of different factors involved, is
essential for this problem to be addressed fully.

CHAPTER 3
ANALYTICAL APPROACH
3.1 Introduction
An analytical approach was formulated to identify critical factors on surface
crack development. The purpose of the approach was multifaceted, ranging from detailed
verification of tire load measurements to the development of a systematic pavement
analysis method. The basic objective for analyzing a series of pavement systems was to
establish the circumstances in which a critical condition that induces crack growth will
occur. The study was restricted to the analysis of the asphalt concrete layer, particularly
with respect to the portion immediately surrounding the initiated surface crack. For this
reason, the approach that was developed concentrated on the validation, evaluation, and
methodology applicable to near-surface response of the asphalt pavement. The validation
segment of the research involved verifying the use of measured tire contact stresses in
pavement analysis and calibrating the pavement model to approximate the bending
response of a real pavement system. The evaluation section included the actual approach
to modeling a cracked pavement system and analyzing the stress states that occur once a
crack was induced and complex loading was applied. The selection of a method for
33

34
analysis incorporated fracture mechanics as an analysis tool for describing the
characteristics of crack tip conditions and growth. Expanding these segments of the
approach gave a comprehensive basis for analysis.
3.2 Validation of Measured Tire Contact Stresses
As discussed in Chapter 2, tire measurements were obtained from Smithers
Scientific Services, Inc. for three different truck tire types at three load and inflation
pressure levels. The tire contact stresses were measured on a steel bed device and were
then presented in database form for use in analysis. However, there was a need to
determine whether tire contact stresses measured on a rigid foundation are significantly
different than contact stresses under the same tire on an actual pavement. Therefore,
finite element modeling was used to verify measured tire contact stress use in pavement
systems and to define the effects of pavement structure on contact stress distribution. A
two-dimensional (2D) finite element tire model was designed and analyzed in the
ABAQUS computer program (HKS 1997) to verify that tire contact stresses measured on
sensors embedded in a steel foundation can be used appropriately for pavement analysis.
The basic idea was to compare tire contact stresses measured on a steel bed with tire
contact stresses for the same tire on typical asphalt pavement structures. A comparison
between near-surface stresses in the asphalt concrete layer between the following two
cases was made:
• Tire contact stresses measured on a steel bed, then applied to the pavement structure.
• The same tire applied directly to the pavement structure.

35
Since measured contact stresses were typically applied to the surface of a modeled
pavement structure to evaluate pavement response and performance, the most important
question to be answered was whether there is a significant difference between pavement
stresses predicted by the application of these measured stresses and pavement stresses
predicted when a tire structure of equivalent load is applied directly to the surface.
Therefore, the following steps were involved in the research:
1. Development and validation of a tire tread model that adequately represented the
behavior of a real tire. The measured tire contact responses to inflation were used
to verify the reasonableness of the tire tread model.
2. Use of the tire model to predict tire contact stress distributions on a steel bed.
These predicted stresses then served as the “measured” contact stresses on the
steel bed.
3. Application of the “measured” contact stresses obtained in step 2 to a range of
pavement structures, and determination of the resulting pavement contact stresses.
4. Application of the tire model to the same range of pavement structures and
determination of the resulting pavement contact stresses.
5. Evaluation of the vertical and transverse pavement contact stresses predicted in
steps 4 and 5 to determine whether the use of contact stresses measured on a steel
bed were reasonable for the evaluation of pavement response and performance.
3.2.1 Development of Tire Model
A secondary objective of this study was to develop a reasonable tire model that
represents the structural behavior and response of a typical radial truck tire tread. This
was a critical step in this investigation. A tire model had to be used to make fair
comparisons of contact stress distributions, since actual measurements of contact stresses
under tires could not be made on real pavements.

36
The development of a comprehensive structural model of a truck tire was a major
challenge. Furthermore, radial tires and bias-ply tires are totally different from a structural
point of view (Myers et al. 1999) and the actual structural make-up of these tires is
proprietary information not available to the general public. However, some basic
response data regarding the behavior of typical radial truck tires and their structural make¬
up was provided by Smithers Scientific Services, Inc. and was used along with a basic
knowledge of the structural behavior of radial truck tires to develop a two-dimensional
model of a radial truck tire tread.
As discussed previously, the structural behavior of radial truck tires is governed
by a wall structure of very low stiffness and a very stiff tread structure resulting from the
steel strands used to reinforce the tread. A cross-section of a typical radial tire is
illustrated in Figure 3.1 and shows a tread area that is 8.12 inches wide and 1.4 inches
high. The steel reinforcement was concentrated in an area that is 0.33 inches high,
approximately 0.96 inches above the outer surface of the tire.
Data provided by Dr. Pottinger indicated that the radius of curvature of the tread
structure shown in Figure 3.1 was 20.32 inches at an inflation pressure of 110 psi. This
radius of curvature corresponded to a deflection of 0.4 inches at the center of the tread
structure relative to the uninflated position of the tread. This measured structural
response was used to develop a tire tread structural model by determining the structural
characteristics (essentially, the amount of steel) required to match the measured response.

37
Figure 3.1: Cross-Section of a Typical Radial Truck Tire.
1 1
l I
1.4in 28 @0.05in
Material Properties: Tire Part
Material
Elastic Modulus. E
Poisson’s Ratio, v
Reinforcing Beads
Steel
29.0E6 psi
0.15
Tire Tread
Rubber
1160 psi
0.48
Tire Grooves
Air
9.8E-6 psi
0.4955
Inflation Pressure 110 psi
Figure 3.2: Finite Element Representation of Tire Tread Structure.

38
The ABAQUS finite element program was used to model the tire tread as shown in
Figure 3.2, which is a reasonable representation of the actual tire tread shown in Figure
3.1. The steel strands were modeled as a solid strip of steel, and the connection between
the steel strands and the rim were modeled as a pin connection at either end of the steel
strip used to represent the strands. Typical modulus values were used for tire rubber and
steel, as presented in Figure 3.2. An inflation pressure of 110 psi was used.
The height of the steel strip was determined by varying the height of the steel until
the predicted deformation response of the tire matched the measured deformation
response of the real tire. Thus, the overall stiffness of the tire tread was matched for the
generation of a tire model. It was determined that a 0.1 inch steel strip embedded in the
tire tread resulted in the same structural response as the 0.34 inch high area of steel strand
reinforcement in the actual tire.
In order to further assess the potential of the tire model developed, a comparison
was made between contact stresses predicted by the tire model applied to a steel bed, and
contact stresses measured under the actual tire on a steel bed. The ABAQUS finite
element computer program was used to apply the tire model (Figure 3.2) to a steel bed
and determine the resulting vertical and transverse contact stresses. Predicted stresses
were captured under the tire model at the nodal points of a finely-graded finite element
mesh. As stated previously, measured contact stresses for the tire modeled were provided
by Sqfithers Scientific Services, Inc. for comparison purposes.
Figures 3.3 and 3.4 clearly indicate that the tire modeled on a steel bed predicted
both vertical and transverse contact stresses similar to those actually measured under the
real tire. Although some variation in magnitude was observed, the tire model captured

39
the patterns of both the vertical and transverse contact stress distributions, as well as
predicted the maximum stress values, reported to exist under typical radial truck tires
(Myers et al. 1999; de Beer et al. 1997). The model’s ability to capture the transverse
contact stress reversals under the individual tire ribs was particularly important (Figure
3.4).
3.2.2 Selection of Pavement Structures For Analysis
The key question to be answered was whether there is a significant difference
between pavement stresses predicted by the application of contact stresses measured on a
rigid foundation, and pavement stresses predicted when a tire structure of equivalent load
is applied directly to the pavement surface. The primary source of variation between the
two cases was related to the degree of interaction that occurs between the tire structure
and the pavement structure. Therefore, for a given tire structure, the answer to this
question varied with the structural characteristics of the pavement system. However, a
basic understanding of stress distributions within layered systems (Huang 1993; Yoder
1975) indicated that the greatest differences would occur in pavements with thinner
asphalt concrete surface layers and in pavements with higher surface-to-base layer
modulus ratios (E1/E2).
Boussinesq’s theory (e.g., see Huang 1993) clearly indicated that stress
distributions caused by surface loads applied to a semi-infinite mass (i.e., one-layer

Vertical Stress, (psi)
40
Transverse Distance, x (in)
Figure 3.3: Measured and Predicted Vertical Stress Distribution at Surface
of Steel Bed.

41
Figure 3.4: Measured and Predicted Transverse Stress Distribution at
Surface of Steel Bed.

42
theory) are independent of stiffness. Thus the stress distribution induced by a uniformly
distributed load applied to a steel foundation was identical to the stress distribution
induced by a uniformly distributed load applied to a rubber foundation. On the other
hand, multi-layer theory (e.g., see Huang 1993) clearly indicated that near-surface stress
distributions are primarily governed by relative stiffness between the surface and the base
layer. Consequently, near-surface stress distributions deviate most from one-layer theory
as the surface-to-base layer modulus ratio (E1/E2) increases and as the surface-to-base
layer thickness ratio (hl/h2) decreases. Furthermore, base thickness and subgrade
stiffness have almost no influence on the near-surface stress distribution of pavements,
which made these factors of no consequence to this study (Huang 1993; Yoder and
Witczak 1975).
Therefore, relatively thin asphalt surface layers having a range of E1/E2 ratios
were targeted for this study. Analyses were first conducted using a 4-in surface layer with
E1/E2 ratios ranging from about 4 to 40. As indicated below in the discussion of results,
no difference in pavement surface stresses was observed, indicating there was no need to
evaluate thicker surface layers. Therefore, analyses were then conducted using a 2-in
surface layer with E1/E2 ratios ranging from about 4 to 40 to determine if an effect would
develop. A summary of the eight pavement structures analyzed is presented in Table 3.1.

43
Table 3.1: Pavement Structures Used for Analysis.
Parameter
Pavement Structure
1
2
3
4
5
6
7
8
Surface Layer Thickness (in)
2
4
2
4
2
4
2
4
Base Layer Thickness (in)
12
12
12
12
12
12
12
12
Subgrade Thickness (in)
92
92
92
92
92
92
92
92
Surface Layer Modulus (ksi)
200
200
200
200
800
800
800
800
Base Layer Modulus (ksi)
44
44
20
20
44
44
20
20
Subgrade Modulus (ksi)
15
15
15
15
15
15
15
15
Surface-to-Base Layer Stiffness
Ratio (E1/E2)
4.7
4.7
10
10
18.3
18.3
39.3
39.3
3.2.3 Results of Verification Analyses
The vertical and transverse stresses at the surface of the pavement system were
predicted for the following two cases:
1. The tire model developed in this study was applied directly to the pavement structure.
2. Contact stresses predicted by applying the tire model to a steel bed were converted to
nodal point forces that were applied to the surface of the pavement structure. This
corresponds to the case of using contact stresses measured on a steel bed to predict
pavement response.
Figures 3.5 through 3.8 show that there was little difference between either the
vertical or the transverse surface stresses predicted by these two cases for the 4-in surface
layer over the range of stiffness ratios evaluated. Figures 3.5 and 3.6 show results for a
stiffness ratio of 4.6, while Figures 3.7 and 3.8 show results for a stiffness ratio of 39.4.
The analyses clearly indicated that use of contact stresses measured on a steel bed
predicted pavement stresses adequately, in terms of both the pattern of the stress

Vertical Stress, aD (psi)
44
Transverse Distance, X (in)
Figure 3.5: Vertical Stresses Predicted at Surface of 4-in Pavement System:
Stiffness Ratio of 4.6 (Ei = 200 ksi, E2 = 44 ksi).

Transverse Contact Stress (psi)
45
Figure 3.6: Transverse Stresses Predicted at Surface of 4-in Pavement
System: Stiffness Ratio of 4.6 (Ei = 200 ksi, E2 = 44 ksi).

Vertical Stress, na (psi)
46
Transverse Distance, X (in)
Figure 3.7: Vertical Stresses Predicted at Surface of 4-in Pavement System:
Stiffness Ratio of 39.4 (Ei = 800 ksi, E2 = 20 ksi).

Transverse Contact Stress (psi)
47
Figure 3.8: Transverse Stresses Predicted at Surface of 4-in Pavement
System: Stiffness Ratio of 39.4 (Ej = 800 ksi, E2 = 20 ksi).

48
Transverse Distance, X (in)
Figure 3.9: Vertical Stresses Predicted at Surface of 4-in Pav ement System:
Stiffness Ratio of 10.0 (Ej = 200 ksi, E2 = 20 ksi).

Transverse Contact Stress (psi)
49
Figure 3.10: Transverse Stresses Predicted at Surface of 4-in Pavement
System: Stiffness Ratio of 10.0 (Ej = 200 ksi, E2 = 20 ksi).

Vertical Stress, (psi)
50
Transverse Distance, X (in)
Figure 3.11: Vertical Stresses Predicted at Surface of 4-in Pavement System:
Stiffness Ratio of 18.0 (Ej = 800 ksi, E2 = 44 ksi).

Transverse Contact Stress (psi)
51
Transverse Distance, X (in)
Figure 3.12: Transverse Stresses Predicted at Surface of 4-in Pavement
System: Stiffness Ratio of 18.0 (Ei = 800 ksi, E2 = 44 ksi).

52
distributions and the magnitude of stresses. As expected, similar comparisons for the 4-in
pavement structures at the intermediate stiffness ratios of 10.0 and 18.0 yielded similar
results (Figures 3.9 through 3.12). Also, as explained earlier, pavements with surface
layer thickness greater than 4-in would exhibit less difference between the two surface
loading conditions and therefore do not require evaluation.
Figures 3.13 through 3.16 show similar comparisons for the 2-in surface layer
with stiffness ratios of 4.6 (Figures 3.13 and 3.14) and 39.4 (Figures 3.15 and 3.16). As
seen in Figures 3.13 and 3.15, the vertical stresses agreed almost exactly for the two
loading cases, whereas Figures 3.14 and 3.16 show that there was slightly greater
variation between the transverse stresses than there was for the 4-in pavement. However,
the correspondence was still very good. As was the case of the 4-in pavement, in which
intermediate stiffness ratios exhibited similar results, the same effect was observed for the
2-in pavement as indicated in Figures 3.17 through 3.20.
The findings from this study were summarized as follows:
• The radial tire model developed in this study did a very reasonable job of
predicting both the vertical and transverse contact stresses measured under the real
tire. The ability of the model to capture transverse contact stress reversals under
individual tire ribs was of great importance.
• Finite element analyses of a range of pavement structures indicated that the use of
contact stresses measured on a steel bed predicted vertical and transverse
pavement stresses very well, as compared to stresses predicted when the tire was
applied directly to the pavement system. Both the pattern of the stress
distributions and the magnitude of stresses were predicted well.

Vertical Stress, atl (psi)
53
Transverse Distance, X (in)
Figure 3.13: Vertical Stresses Predicted at Surface of 2-in Pavement System:
Stiffness Ratio of 4.6 (Ej = 200 ksi, E2 = 44 ksi).

Transverse Contact Stress (psi)
54
Figure 3.14: Transverse Stresses Predicted at Surface of 2-in Pavement
System: Stiffness Ratio of 4.6 (Ei = 200 ksi, E2 = 44 ksi).

Vertical Stress, 55
Transverse Distance, X (in)
Figure 3.15: Vertical Stresses Predicted at Surface of 2-in Pavement System:
Stiffness Ratio of 39.4 (Ej = 800 ksi, E2 = 20 ksi).

Transverse Contact Stress (psi)
56
Figure 3.16: Transverse Stresses Predicted at Surface of 2-in Pavement
System: Stiffness Ratio of 39.4 (Ej = 800 ksi, E2 = 20 ksi).

Vertical Stress, na (psi)
57
Figure 3.17: Vertical Stresses Predicted at Surface of 2-in Pavement System:
Stiffness Ratio of 10.0 (Ei = 200 ksi, E2 = 20 ksi).

Transverse Contact Stress (psi)
58
Transverse Distance, X (in)
Figure 3.18: Transverse Stresses Predicted at Surface of 2-in Pavement
System: Stiffness Ratio of 10.0 (Ei = 200 ksi, E2 = 20 ksi).

Vertical Stress, a„ (psi)
59
Figure 3.19: Vertical Stresses Predicted at Surface of 2-in Pavement System:
Stiffness Ratio of 18.0 (Ei = 800 ksi, E2 = 44 ksi).

Transverse Contact Stress (psi)
60
Transverse Distance, X (in)
Figure 3.20: Transverse Stresses Predicted at Surface of 2-in Pavement
System: Stiffness Ratio of 18.0 (Ej = 800 ksi, = 44 ksi).

61
• Some minor differences were observed for thin (2-in surface) pavements on weak
bases, but the correspondence in terms of both distribution and magnitude was
still very good.
Based on these findings, it was concluded that contact stresses measured using devices
with rigid foundations are suitable for the prediction of response and performance of
highway pavements.
3.3 Modification of Two-Dimensional Finite Element Model to Capture Bending
Response of Asphalt Pavement System
Although three-dimensional FEM provides the most accurate representation of a
pavement structure, it remains a relatively challenging and costly technique, particularly
for pavement performance predictions that involve a continuously changing structure and
thousands of load applications of varying magnitudes and positions. Axisymmetric and
two-dimensional analyses provide simpler, more cost-effective solutions at the expense of
accuracy. A study was undertaken to evaluate the discrepancies between two- and three-
dimensional analysis of pavement structures, and to determine whether a modified two-
dimensional analysis could be used as a reasonable approximation of the three-
dimensional bending response of asphalt pavements. Therefore, the primary objectives of
this study were as follows:
• To develop a procedure for using two-dimensional analysis to predict pavement
response at critical locations with respect to fracture propagation for several
structural and loading cases.
• To evaluate and illustrate the differences between two- and three-dimensional
bending response of asphalt pavement structures.

62
• To identify/develop an approach to calibrate two-dimensional analyses such that
reasonable approximations of the three-dimensional response of asphalt pavements.
• To illustrate how the modified approach may be used in practice for the analysis and
evaluation of pavement systems.
The evaluation conducted in this investigation was then restricted to the following
constrictions:
• Only the stress-strain response of the asphalt concrete layer was considered in the
evaluation. The accuracy of stress distributions within base and subgrade were not
considered, such that the evaluation and approach were primarily suitable for load-
associated cracking within the asphalt surface layer.
• A broad range of conventional pavement structures (i.e., asphalt surface on aggregate
base and subgrade) were considered. However, overlays on rigid pavements were not
addressed.
• Well-established principles of pavement response (i.e., layered systems) indicated that
near-surface stresses within the asphalt concrete surface layer are almost exclusively
governed by surface thickness, surface stiffness, and base course stiffness. Therefore,
these were the three primary variables investigated and used to define the range of
pavement structures investigated. Limited analyses of the effects of subgrade
stiffness and base layer thickness on near-surface response were conducted.
• All two- and three-dimensional analyses were conducted using the ABAQUS finite
element computer program (HKS 1997). Plane strain conditions were assumed for
nonsymmetrical simulations and all analyses were conducted taking advantage of
symmetry.
The primary objectives of the research were met by comparing stresses from the three-
dimensional finite element analyses to stresses obtained from two-dimensional plane
strain analyses using the same contact stress and width of load on a broad range of
pavement structures. The observed differences were evaluated to identify characteristic
patterns in the differences, and to determine whether specific relationships could be
established between these solutions. Specifically, relationships were sought that would

63
allow reasonable estimates of the three-dimensional solutions based on the two-
dimensional analyses.
3.3.1 Finite Element Model Types
Axisymmetric and two-dimensional analyses provide simpler and more cost-
effective solutions, but often at the expense of accuracy. Axisymmetric solutions have
long been used to analyze pavement structures; for example, it forms the core of the FEM
program ILLIPAVE (1990). These solutions are generally limited to the application of a
single symmetrical tire load, although recent work has been done that allows
axisymmetric solutions to handle multiple loads and nonlinear analysis. In any case,
discontinuities in the form of damage zones and/or cracks cannot be properly modeled
using axisymmetric solutions. As shown in Figure 3.21, in an axisymmetric model, a
crack would essentially be modeled a discontinuous ring around the symmetrical load,
which would result in inaccurate stress distributions and/or stress concentrations at the
crack tip.
Also shown in Figure 3.21 is a two-dimensional model that resulted in
considerably better representation of a continuous longitudinal crack in a pavement
system. Multiple loads and cracks, as well as non-symmetrical tire contact stresses, can
be represented in the two-dimensional model. Unfortunately, the analysis would be
conducted by assuming either plane stress or plane strain conditions, and the load(s)
would be considered essentially as strip loads, which then result in different bending
patterns than a true wheel load applied in three-dimensional analysis. Therefore, before
attempting to use two-dimensional analysis for the evaluation of pavement response and

64
performance, a thorough understanding of the differences in stress distributions between
two- and three-dimensional analyses was developed. Furthermore, an approach was
developed to determine stress distributions for pavement analysis using a two-
dimensional model that reasonably estimated the stresses predicted by a true three-
dimensional model. This modified approach was used for parametric studies to show the
relative effects of different factors on pavement response and performance, as will be
discussed in Chapter 4.
Crack
\
Crack
Axisymmetric Model 2 -D Model
Figure 3.21: Schematic of Axisymmetric and 2-D Finite Element Pavement Models.

65
3.3.2 Finite Element Modeling of Pavement System Using ABAQUS
The range of pavement structures that were evaluated is summarized in Table 3.2.
Asphalt concrete layer thickness was varied from 2 to 8 inches, which encompassed the
range of surface layer thickness typically used on conventional pavements with aggregate
base. Preliminary analyses indicated that the difference between two- and three-
dimensional analysis was found not to change for asphalt concrete thicknesses greater
than 8 inches. Base course and subgrade thickness were held constant at 12 inches and
336 inches, respectively. As cited by Huang (1993) and others, it is common knowledge
that base course thickness has a negligible effect on near-surface stress distributions.
Three levels of asphalt concrete modulus (200, 800, and 1200 ksi) and two levels
of base course modulus (20 and 44 ksi) were used. These resulted in surface to base layer
stiffness ratios (E1/E2) ranging from 4.6 to 59.0. The asphalt modulus values were
selected to capture the asphalt concrete stiffness within the in-service temperature range.
The base course values were selected to represent a poor and a good granular base course.
Two subgrade layer modulus values were used (7.0 and 14.5 ksi) to verity that subgrade
modulus has a negligible effect on near-surface stress distributions.
An applied contact stress of 115 ksi, which corresponded to a standard inflation
pressure for a typical radial truck tire was used to conduct all analyses. Also, a contact
width (two-dimensional) or diameter (three-dimensional) of 8 inches was used for all
analyses, which corresponds to the width of a typical radial truck tire.
A general schematic of a typical finite element mesh used to model the pavement
structures in ABAQUS is shown in Figure 3.22, which also shows a more detailed view

66
Table 3.2: Parameters Used in Development of Pavement Finite Element Models.
AC La>er Stiffness Modulus (ksi)
(in)Asphalt Concrete Layer Base Layer Subgrade Layer
2
200
800
1200
20
44
-
14.5
3
200
800
1200
20
44
7.0
14.5
4
200
800
1200
20
44
7.0
14.5
6
200
800
1200
20
44
7.0
14.5
8
200
800
1200
20
44
7.0
14.5
Note: Applied contact stress on models = 115 psi
Base Thickness = 12 in Subgrade Thickness = 336 in
of the typical mesh structure used near the loading area. Since only one load was used to
meet the necessary objectives of the study, an axisymmetric model was used to represent
the three-dimensional loading case for comparison to the two-dimensional analyses.
Therefore, the same mesh structure was used for both two-dimensional and three-
dimensional (axisymmetric) analyses.
The accuracy of the mesh structures used in the analyses was evaluated by
comparing the ABAQUS solutions to solutions obtained with the BISAR elastic layer
computer program. Detailed results showed that excellent correspondence was obtained
for stress distributions predicted by both of the programs. Thus, it was confirmed that the
ABAQUS code was working well.

\ /
67
y
Nonuniform
Vertical
Load
Tac
,, hpE^ariable
Base
h2,E2variable
Subgrade
h3 constant
Ejvariable
â–¼
ABAQUS Finite Element
2-D and Axisymmetric Model
Detailed View of Model Near
Loading Area
Figure 3.22: Schematic and Detailed View of Pavement System Modeled
Using the Finite Element Program, ABAQUS.

68
3.3.3 Evaluation of Predicted Stresses
Figures 3.23 and 3.24 show that differences between two- and three-dimensional
solutions were highly dependent upon the characteristics of the pavement structure.
These figures show the transverse (horizontal) stress distributions beneath the loaded area
at the bottom of the asphalt concrete surface layer, as predicted by two- and three-
dimensional representation of the pavement structure. This stress was selected because
the tensile response immediately underneath the load traditionally has been considered as
the critical response related to fatigue cracking in pavements (critical tensile stress).
Figure 3.23 shows that for a pavement structure with a low stiffness ratio, the two- and
three-dimensional solutions predicted almost exactly the same critical tensile stress. On
the other hand, Figure 3.24 shows that the two-dimensional solution grossly over¬
predicted the tensile stress for a pavement with high stiffness ratio (E1/E2 = 59.0).
Tensile stress at the bottom of the asphalt concrete layer was nearly a factor of four
greater for the two-dimensional analysis than for the three-dimensional analysis (334 psi
versus 87 psi). Figures 3.23 and 3.24 also indicate that significant differences were
observed between the two- and three-dimensional stress distributions at distances further
from the center of the loaded area. However, the accurate prediction of stresses in this
region was less critical for two reasons: firstly, the stresses were compressive for
pavements with low stiffness ratios (Figure 3.23); and secondly, even when the stresses
were tensile (Figure 3.24), they were significantly lower than under the center of the
loaded area.

Transverse Stress, a» (psi)
69
Figure 3.23: Transverse Stress Distribution Along Bottom of 4-in Asphalt
Concrete Layer for Stiffness Ratio of 4.6 (Ei = 203 ksi: E2 = 44 ksi).

Transverse Stress, 70
Figure 3.24: Transverse Stress Distribution Along Bottom of 8-in Asphalt
Concrete Layer for Stiffness Ratio of 59 (Ej = 1200 ksi: E2 = 20 ksi).

71
An evaluation of similar comparisons for the range of pavement structures under
investigation indicated that the difference between tensile stresses predicted by two- and
three-dimensional analyses was related to the relative stiffness between the surface and
base layers. That is, the relative difference between the two solutions appeared to be
governed primarily by the stiffness ratio (E1/E2) and the thickness of the surface layer.
Based on these observations, analyses were conducted to determine whether a
structurally-dependent correction factor could be identified to estimate three-dimensional
tensile stresses using results obtained from the two-dimensional analysis. The idea
involved the determination of a factor that could be used to modify surface loads applied
to the two-dimensional analysis, such that the predicted bending stress (specifically, the
critical tensile stress) would closely approximate the bending stress predicted by three-
dimensional analysis.
3.3.3-1 Definition of Bending Stress Ratio
A ratio between the critical tensile stress predicted by three-dimensional analysis
and the critical tensile stress predicted using two-dimensional analysis was defined to
normalize the difference between the two stresses via calibration. The ratio was related to
pavement structural characteristics to act as a modifying factor for two-dimensional loads
(strip load), in order to obtain accurate three-dimensional stress predictions using two-
dimensional analysis.
The bending stress ratio was defined as follows:
bsr = CTxx<3~d>
a
XX(2-D)
(3.1)

72
where, BSR = bending stress ratio
<^xx(3-D) = critical tensile stress based on three-dimensional analysis
Cxx(2-D) = critical tensile stress based on two-dimensional analysis
A BSR was calculated for each of the pavement structures analyzed. For the
pavement structure used to obtain the results presented in Figure 3.23, the BSR computed
from Equation 3.1 was approximately 1.0. A BSR of 3.8 was determined for the
pavement structure used to obtain the results presented in Figure 3.24. Figures 3.23 and
3.24 also show modified stress distributions obtained by multiplying the two-dimensional
results by the corresponding BSR. As shown in Figure 3.23, the modified two-
dimensional results for a low stiffness ratio case agreed well with the three-dimensional
stress distribution immediately underneath the load, but the correspondence between the
compressive stresses further from the load were not improved. Figure 3.24 shows that for
the high stiffness ratio case, the correspondence was excellent immediately underneath
the load, and was also improved significantly further from the load. As previously
mentioned, the area of tensile stress immediately under the load is generally considered
the critical area for evaluating load-associated fatigue cracking of asphalt pavements.
Therefore, it was logical to define the bending stress ratio such that response was matched
most accurately in this zone.
3.3.3-2 Relations Between Bending Stress Ratio and Structural Parameters
As mentioned earlier, the relative difference in critical tensile stresses between the
two- and three-dimensional solutions appeared to be primarily governed by the stiffness

73
ratio (E1/E2) and the thickness of the surface layer (h). Therefore, the bending stress ratio
(BSR) should be related to E1/E2 and h. Figures 3.25 and 3.26 show the relationships
between BSR and h, and BSR and E1/E2. The two figures show essentially the same data
presented in two ways. The following general observations were made on the basis of the
results presented in Figures 3.25 and 3.26:
• BSR increased as stiffness ratio or surface layer thickness decreased.
• BSR decreased at a decreasing rate as surface layer thickness increased or as stiffness
ratio increased.
• For a given stiffness ratio, the BSR approached a constant value as the surface layer
thickness was increased. That is, beyond a certain surface layer thickness
(approximately 8 inches), the relative difference between the two- and three-
dimensional solutions did not change.
• For a given surface layer thickness, the BSR approached a constant value as stiffness
ratio was increased. In other words, beyond a certain stiffness ratio (approximately
40), the relative difference between the two- and three-dimensional solutions did not
change.
• For the majority of pavement structures, BSR was less than 1.0, indicating that two-
dimensional analysis over-estimated the critical tensile stress for most pavement
structures.
• BSR exceeded 1.0 (i.e., two-dimensional analysis under-estimated critical tensile
stress) for cases with thin surface layers and low stiffness ratios. Flowever, a sharp
reversal occurred, and even negative BSR’s were observed, in cases of very thin (2-
inch) surface layers with low stiffness ratios. These results were explained by the fact
that the bottom of a very thin surface layer may be in compression rather than tension,
particularly in cases where the stiffness ratio is low.
It should be noted that highway pavements, particularly those in relatively high-traffic
areas, are rarely found to have a surface layer thickness less than 3 inches. Therefore, the
observed reversal in the BSR relationship was of little or no practical significance.

74
Based on the observations from Figures 3.25 and 3.26 discussed above, the
following non-linear relationship was developed for BSR as a function of stiffness ratio
(E1/E2) and thickness ratio (h]/h2), where hi was the thickness of the surface layer and h2
was the thickness of the base layer:
log(BSR) = -0.29655^ /E2)0 29531(h1 /h2)095659
R2 = 0.97
The following range of parameters was used to develop Equation (3.2):
• Surface layer thickness from 3 inches to 8 inches, which corresponded to surface to
base layer thickness ratios (h]/h2) from 0.25 to 0.67.
• Stiffness ratios (E1/E2) from 4.6 to 59.0.
In other words, pavement structures that resulted in reversals in the BSR trends were not
included in the development of the equation.
It must be noted that the relationships presented in Figures 3.25 and 3.26 assumed
that BSR was only a function of the stiffness ratio (E1/E2), and not of the magnitude of
the stiffness of the individual layers (Ei or E2) used to determine the stiffness ratio. It
was also assumed that BSR was independent of subgrade stiffness. Therefore, additional
analyses were conducted to evaluate the validity of these assumptions. Figure 3.27
clearly shows that the magnitude of E] and E2 had no effect on the relationship between
BSR and surface layer thickness. As shown in the figure, stiffness ratios of 10 and 40
were achieved by using two different levels of surface and base layer stiffness. Results of
the analyses indicated that identical BSR’s were determined regardless of how the
(3.2)
stiffness ratio was achieved.

Bending Stress Ratio (3D:2D), 75
Figure 3.25: Effect of Asphalt Concrete Thickness on Bending Stress Ratio.

Bending Stress Ratio (3D:2D),cj3d 'â–  CT20
76
Figure 3.26: Effect of Stiffness Ratio (Ei / E2) on Bending Stress Ratio.

Bending Stress Ratio (3D:2D), cyjD : ct2d
77
Figure 3.27: Effect of Asphalt Concrete and Base Layer Stiffness on Bending
Stress Ratio.

Bending Stress Ratio (3D:2D),ct3D : ct2d
78
Similarly, Figure 3.28 shows that subgrade stiffness had a negligible effect on the
relationship between BSR and surface layer thickness for stiffness ratios ranging from 10
to 28. As shown in the figure, BSR’s that were essentially identical were determined at a
given surface layer thickness and stiffness ratio for different values of subgrade modulus.
Figure 3.28: Effect of Subgrade Stiffness on Bending Stress Ratio at Various
Stiffness Ratios (Ei / E?).

79
3.3.4 Application of Bending Stress Ratio
The bending stress ratio (BSR) described in the previous section provided a useful
tool for predicting the three-dimensional bending stresses in asphalt pavement systems
using two-dimensional finite element analysis. The benefits were particularly important
for evaluating highly complex contact stress conditions, or for cases where a large
number of computer runs are required to predict pavement performance. For example,
the prediction of crack propagation using fracture mechanics, not only requires a large
number of runs for a pavement structure and wheel loads that are continually changing,
but also requires continually changing the finite element mesh as crack growth
progresses. Using a two-dimensional model would be considerably beneficial, in terms
of reduced complexity and computer run times. An example of the generalized two-
dimensional model that could be used to represent the longitudinal wheel path cracking
situation is presented in Figure 3.29, showing a pavement surface with multiple cracks
loaded using a realistic tire contact stress distribution involving non-uniform vertical and
transverse stresses. An axisymmetric model was an unsuitable choice for this problem
because it did not properly model the tire contact stresses or the discontinuities caused by
the cracks. On the other hand, modeling this problem in three dimensions for a broad
range of pavement structural characteristics, load positions, and crack lengths posed a
formidable and time-consuming problem. The modified two-dimensional approach
provided reasonable solutions comparable to those obtained using a three-dimensional
model, but with considerably less complexity and cost.

80
Crack
Variable|V
Variable
Vertical Load
Magnitude
Variable
Distance
JSL
Variable
Crack
Variable
h, E,
Variable
h2 E2
Figure 3.29: Application of Approach - Parametric Study of a Cracked Pavement.

81
The following procedure was used, including the BSR relationships presented
earlier (Figures 3.25 and 3.26 or Equation 3.2), to obtain a modified two-dimensional
solution that approximated the true three-dimensional bending response of typical
pavement structures:
1. Calculate the surface-to-base layer stiffness ratio (E1/E2) and the surface-to-base layer
thickness ratio (hj/h2) for the pavement structure being analyzed.
2. Use these ratios to determine the BSR using either Figure 3.25, Figure 3.26, or
Equation 3.2. Only use Equation 3.2 if the pavement structural parameters are within
the range used to generate the equation.
3. Multiply only the vertical contact stresses by the BSR. The calculated stresses are
then considered the modified vertical contact stresses. The transverse tire contact
stresses were not modified for two-dimensional analysis.
4. Apply the modified vertical contact stresses and the transverse contact stresses to the
two-dimensional finite element representation of the pavement structure. The width
of the wheel load(s) used in the two-dimensional analysis was equal to the width or
diameter of the actual tire.
Based on the analyses conducted in this investigation, the resulting tensile stresses within
the asphalt concrete surface layer in the vicinity of the tire reasonably approximated the
tensile stresses for the true three-dimensional loading condition. Furthermore, for cases
similar to the one shown in Figure 3.29, the modified two-dimensional analysis could be
used to determine realistic stress intensity factors and crack growth rates for variable
loading conditions.
3.3.5 Additional Observations
The correspondence between two- and three-dimensional analysis was obtained
for the case of linear elastic layered systems. Although the development of a similar

82
approach for a layered system composed of materials exhibiting non-linear behavior
would need to be investigated, it was clearly shown that the assumption of a
homogeneous, linear elastic layered material could be used to obtain reasonable
predictions of measured field loading responses on typical Interstate flexible pavement
systems (Chaboum et al. 1997). At first glance, it appeared that the number of structural
and material parameters influencing the bending stress ratio between two- and three-
dimensional analysis was overwhelming, such that the development of a simplified
approach would not be possible. However, earlier research work suggested that a
modified version of the approach developed may be suitable for the case of predicting
bending stresses within the asphalt concrete layer. Roque et al. (1992) showed that for a
broad range of pavement structures and non-linear material properties, linear elastic
analysis could be used to accurately determine the stress-strain response within the
surface layer if suitable effective layer modulus values were included in the analysis. A
procedure was presented for determining suitable effective layer modulus values of non¬
linear layers that involved prediction of the non-linear deflection response of the
pavement system, then back-calculation of effective layer moduli using the linear elastic
layer model. Their work suggested that a stiffness ratio calculated using the effective
layer modulus values determined in this manner could be used along with the surface-to-
base layer thickness ratio to apply the bending stress ratio (BSR) concept. It is
recommended that this approach be investigated further prior to full implementation.
3.3.6 Summary
Discrepancies between two- and three-dimensional analysis of pavement

83
structures were evaluated, and the question of whether a modified two-dimensional
analysis could be used as a reasonable approximation of the three-dimensional response
of asphalt pavements was addressed. Two- and three-dimensional analysis of a range of
pavement structures typically encountered in highway pavements indicated that
discrepancies between two- and three-dimensional analyses were highly dependent upon
the structural characteristics of the pavement. A bending stress ratio (BSR) was defined
as the ratio between the critical tensile stress from three-dimensional analysis and the
critical tensile stress from two-dimensional analysis. It was determined that the BSR was
primarily a function of surface-to-base layer stiffness ratio (E1/E2) and surface-to-base
layer thickness ratio (hj/h2) and specific relationships were developed between BSR and
these parameters. An approach was developed to use the pavement structural
characteristics and BSR to modify two-dimensional loads such that two-dimensional
analyses reasonably estimated the true three-dimensional pavement stresses.
Based on the comparisons presented, it was concluded that the modified two-
dimensional analysis developed reasonably approximated three-dimensional tensile
stresses within the asphalt concrete surface layer for the typical range of conventional
pavement structures encountered in highway pavements.
3.4 Description of Pavement Model
Longitudinal wheel path cracks have been observed in the field and the resulting
core and trench sections have shown that they initiate at the surface and propagate
downwards in the surface layer. Therefore, analysis of the problem involved replication

84
of the surface cracking mechanism, in terms of both crack geometry and structural
properties, in a pavement model.
Several factors were considered in the development of a standard finite element
model that best represented the actual pavement, while at the same time was relatively
user-friendly and inexpensive. Because one of the main purposes of the research was to
determine the localized effects of various factors on the cracked surface, the decision was
taken to use a linear elastic model with isotropic material properties. Although certain
restrictions were associated with using a linear elastic analysis, as discussed previously in
Section 3.3, there were not strong implications on the results of a localized effects study.
3.4.1 Structural Parameters of Model
Table 3.3 shows the variables considered in the parametric study of the pavement
structure. The values were chosen to reflect the typical structural and material properties
of flexible pavements found on interstate highways. As seen in Table 3.3, several factors
were varied such as the thickness of the asphalt surface layer, stiffness of both the asphalt
and base layers, crack depth, and load positioning with respect to crack location. Some
factors were kept constant such as the subgrade stiffness, and base and subgrade
thickness. A visual example of the general pavement model is presented in Figure 3.30.
This is the typical pavement actually modeled in finite element analysis and printed from
ABAQUS.

85
3.4.2 Crack Length
Because the study was focused on the development and propagation of
longitudinal wheel path cracks, an initial crack length was assumed in order to evaluate
Table 3.3: Parameters Evaluated For Identification of Factors Critical to
Development of Surface Cracking Mechanism.
Variable
Parameter Values
Pavement
Thickness, h ^
4 in
8 in
Crack Length, a
0.25 in 0.5 in 0.75 in
1.0 in
1.5 in
Center of Load
Position Relative
to Crack
Tire’s widest
rib over crack
7 in
to right
15 in
to right
20 in
to right
25 in
to right
Asphalt Layer Stiffness
E 800 ksi
1200 ksi
Variable Stiffness due to
T em perature-lnduced
Gradient
Base Layer Stiffness
E2(ksi)
20.3ksi
44.5 ksi
Subgrade Layer Stiffness
E - constant-14.5 ksi
3
Base Thickness, hj
Constant - 12 in
Subgrade Thickness, h^
Constant - 90 in
the effects of the changing variables. An initial crack length of 0.25 inch (5 mm) was
assumed and was increased by increments of 0.25 inch, and at the final step by 0.5 inch.
The value of the initial crack length was based on laboratory experiments conducted by
Roque (1999). Figure 3.31 shows a detailed view of the cracked surface, loaded by a

86
steel-reinforced radial truck tire tread, in a finite element model printed from ABAQUS.
The crack surface was modeled by allowing nodes on the finite element mesh to remain
Figure 3.30: Typical Finite Element Model of Pavement Used In Parametric
Study For Determining Factors Critical to Development of Crack
Propagation.

87
Figure 3.31: Detailed View of Crack in Finite Element Model of Pavement.
disjointed or uncollapsed. A crack in a finite element model is analogous to a vertical
notch cut into a chicken wire fence. When the fence is loaded, the area into which the
notch was cut will displace, and the stresses generated to hold that notch in-place can be

88
calculated. The values of the additional crack lengths were chosen to reflect those
typically observed in field sections.
3.4.3 Modeling System
Some finite element models can be both simple and cost-effective while others
can be complex and time-consuming. The complexity of the model depended on the size
and refinement of the structure, realistic loading, and the purpose for the analysis. The
purpose of this study was to model a detailed pavement system, loaded with measured tire
contact stresses, in order to predict the effects of various structural and temperature-
related factors on surface crack advancement. These criteria called for a pavement
system model that included several thousand elements and was considerably time-
consuming, all at the expense of refinement. For these reasons, an alternative approach to
modeling the pavement system was developed. The two-step approach started with the
generation of the entire pavement system and finished with modeling of only the cracked
surface layer.
In the first step, the entire pavement system consisting of asphalt concrete surface
layer, granular base, and subgrade was loaded with measured vertical and transverse tire
contact stresses. As explained in Section 3.3, a modified two-dimensional model was
used, meaning that it was calibrated to three-dimensional bending response. The
boundary conditions that were applied to the edges of the model are shown in Table 3.4:

89
Table 3.4: Boundary Conditions Applied to Model of Entire Pavement System.
Location on Model
Type of Constraint
Definition of Constraint
Sides
Rollers
u=0, v*0, w=0
ru=0, rv=0, rw=0
Bottom Edge
Rollers ^
u*0, v=0, w=0
ru=0, rv=0, rw=0
Bottom Corners
Pins
u=0, v=0, w=0
ru=0, rv=0, rw=0
The entire pavement model is shown in Figure 3.32. Because of the size of the
model, several thousand elements were generated when the finite element mesh was
applied; however, the number of elements decreased dramatically when the surface crack
and the refined isomesh around the crack tip were omitted. Therefore, for the first step in
modeling the pavement system, no crack was present.
The purpose of the second step in the approach was to introduce a crack into the
model and significantly increase the refinement of the finite element mesh. The size of
the pavement system was reduced by modeling only the asphalt concrete surface layer
with applied reaction forces obtained by modeling the entire pavement system in the first
step. In this manner, a smaller amount of elements was used and refinement was heavily
concentrated around the crack tip. Both vertical and transverse tire contact stresses were
applied as surface loading and corresponding vertical and transverse reaction forces were
applied along the bottom of the asphalt concrete to account for the omitted base and
subgrade support. Reaction forces were predicted along the bottom of the surface layer in
the first step of the approach. These forces were then applied as concentrated loads along

90
Mesh Size in AC = 0.5 x 0.5 in
i>i
Vertical and Transverse
Tire Contact Load
Boundary Condition
Applied to Sides: £>
Rollers . t A
í>‘
'• '-'""TV ■..3 ■ ■ -Ixl*
w
I I I
ft I I I I Jj' I I
Predict Vertical and Horizontal
Reaction Forces
Base Layer
Subgrade
Layer
Rollers Applied to Bottom Side
Pins Applied to
Bottom Corners
Predicted Vertical and Horizontal Reaction
Forces Applied Along Bottom Nodes
Spring
Constant
“k” Applied
Mesh Size in AC = 0.0125 x 0.0125 in2
Boundary Condition
Applied on Sides:
Rollers
Vertical and Transverse
Tire Contact Load
Figure 3.32: System Used For Two-Step Approach to Finite Element Modeling of
Pavement.

91
the bottom of the surface layer in the second step of the approach. The procedure is
shown visually in Figure 3.32.
In order to account for pavement bending, the boundary conditions were changed
for the reduced model. Grounded springs were applied to the bottom comers of the
surface layer. Spring constants were computed by dividing the vertical reaction force by
vertical deflection, predicted at each of the bottom comers of the asphalt concrete in the
original pavement system model. An example of the procedure performed on a
spreadsheet for a 4-inch pavement model is presented in Figure 3.33. The boundary
conditions applied to the newly refined pavement model are shown in Table 3.5.
Table 3.5: Boundary Conditions Applied to Refined Model of Surface Layer.
Location on Model
Type of Constraint
Definition of Constraint
Sides
Rollers ^
u=0, v*0, w=0
ru=0, rv=0, rw=0
Bottom Edge
Reaction Forces
Fx > Fy
Bottom Corners
Grounded ;
Springs —
kx=0, ky *0, kz=0
The refined model was then loaded and analyzed to predict the effects of several factors
on crack propagation. The two-step approach was followed for each model, generated
anew for each increased crack length, surface layer thickness, and thermal stiffness
regime.

92
Spring Constants
4" Pavement
Left Node ID Number 4009
at various load positions
All Crac
k Lengths
Right Node ID Number 86
Load on top of crak
Load P,,
Deflectiony
Sorina Constant, k
File name:
Left
Boundary:
0.15
1.12E-04
1338.1
orig4 00L
Right
Boundary:
0.22
1.84E-04
1195.7
Load center 7" from crak
Load P,,
Deflection,,
Sprina Constant, k
File name:
Left
Boundary:
6.10E-02
2.32E-05
2633.2
orig4 07L
Right
Boundary:
0.3412
3.03E-04
1126.5
Load center 15" from crak
Load Pv
Deflection,,
Sprinq Constant, k
File name:
Left
Boundary:
-5.60E-04
-3.29E-05
17.0
orig4 15L
Right
Boundary:
0.3107
2.26E-04
1375.6
Load center 20" from crak
Load P,,
Deflection,,
Sprina Constant, k
File name:
Left
Boundary:
-1.19E-02
-3.84E-05
309.3
orig4 20L
Right
Boundary:
-0.1238
-2.89E-04
428.9
Load center 25" from crak
Load P,,
Deflection,,
Sprinq Constant, k
File name:
Left
Boundary:
-1.31E-02
-3.36E-05
391.1
orig4 25L
Right
Boundary:
-1.24
-1.52E-03
816.9
E1/E2 = 800/20 ksi
Figure 3.33: Example of Spring Constant Computation Used For Application of
Boundary Conditions to 4-inch Finite Element Pavement Model From EXCEL
Computer Program.

93
3.5 Selection of Fracture Mechanics Theory For Analysis
Several theories were considered for use in the analysis of surface crack
propagation. Although approaches involving continuum damage mechanics or boundary
element methods have been applied to analyze pavement damage, fracture mechanics was
selected for the evaluation of surface crack growth. The continuum damage mechanics
approach was described in Chapter 2. Because physical modeling of the crack itself was
not possible, the continuum damage mechanics approach was not selected for this study.
The theory of fracture mechanics and some applications of the approach in the
pavement area were outlined in Chapter 2. Physical representation of flaws or cracks
introduced in the asphalt concrete pavement was made possible through the use of finite
element modeling. Once a finite element model was compiled, an analysis of the loaded
pavement model was conducted using the finite element analysis program, ABAQUS.
There are also other finite element analysis programs that would have been suitable for
this purpose as well. Fracture parameters were predicted by ABAQUS that described the
conditions near the crack tip, as an indicator of the conditions that may be found in
pavement field sections. The primary reason for using fracture mechanics is that it
accurately considers the effects of the change in geometry induced by the crack on the
stress distribution within the pavement. This was considered to be a critical aspect of the
mechanism, which cannot be accurately described by continuum damage mechanics (i.e.
without fracture mechanics).

94
3.5.1 Description of Fracture Parameters
Evaluations of a cracked pavement were conducted by predicting stress states in
the process zone ahead of crack tip. Different stages of crack depth and various positions
of loading relative to crack location were evaluated. Characterization of crack tip
conditions was accomplished by predicting both the stress intensity factors and the
fracture energy release rate parameter. Some variables analyzed as critical factors were
shown in Table 3.3 and the effects of these factors on the stress state ahead of the crack
tip were monitored by changing one variable at a time and keeping all others constant.
The fracture parameters predicted for these purposes were the stress intensity factors Ki
and Kn and the fracture energy contour interval J, as described by Anderson (1995) and
Broek (1982). The following relationships were used:
Fracture Energy
for plane strain analysis (3.3)
Stress Intensity Factor
Opening Mode I
(3.4)
Stress Intensity Factor
Shearing Mode II
(3.5)

95
3.5.2 Application of Fracture Mechanics
The stress states and orientation of the major principal stress in the process zone
ahead of the crack tip were reported. Stresses were predicted in ABAQUS and were
plotted individually as a function of vertical distance from crack tip, in order to predict
the stress intensity factors (Figure 3.34). Computation of Ki and Kn provided a local
description of the crack tip region that could be used in the determination of the effects of
various factors. Each time a change was applied to the pavement structural parameters, a
comparison of the effect on the stress intensity factors and crack tip stress states was
made.
Various methods for performing fracture mechanics studies are provided by
ABAQUS, namely quasi-static crack growth using contour integrals (HKS 1997).
Contour integrals (J-integral) are calculated in ABAQUS for cracks that will propagate
along a predefined path in two-dimensional cases. Focused meshes like the one shown in
Figure 3.34 are required by the analysis code in order to compute J-integral as an estimate
of the energy release associated with crack growth. If the material response is linear, the
J-integral can be related to stress intensity factors as was done in this research study.
Contours are defined as a ring of elements that completely surround the crack tip
or crack front from one crack face to the opposite crack face (see Figure 3.34). ABAQUS
automatically identifies the elements forming each ring and each contour gives an
evaluation of the contour integral. The number of evaluations is equal to the number of
rings of elements or contours. The domain integral method was employed to evaluate
contour integrals, which can be estimated even with coarse meshes.

96
Tire Loading
Figure 3.34: Detailed View of Finite Element Mesh Surrounding Crack Tip

97
Coarse meshes could be used since the integral is taken over a domain of elements
surrounding the crack front, and errors in local solution parameters will then have less
influence on energy-like determinations such as J. Numerical studies suggested that the
estimate from the first contour nearest to the crack tip does not give a high accuracy
result; therefore, the ABAQUS manual recommended using at least two contours.
The J-integral is used to characterize the energy release rate associated with crack
advance was given by:
j= [ A (j)n-H-qflM (3.3)
JA
where dA = surface element along vanishing tubular surface enclosing crack tip,
n = outward normal to dA,
q = local direction of virtual crack propagation, and
H is given by
H=(Wl-a~ ) O-4)
dx
where W= elastic strain energy (for elastic material behavior).
The ABAQUS manual also suggests that smaller the element size, the more accurate the
results will be. Since crack tips cause stress concentrations, stress and strain gradients are
often larger as the distance from the crack tip is reduced. Although accurate J-integral
results can often be attained with a coarser mesh, it was suggested that the finite element
mesh be refined in the vicinity of the crack to obtain more accurate stresses and strains
(HKS 1997).

98
3.6 Summary
The analytical research approach selected for the evaluation of surface-initiated
longitudinal wheel path crack propagation was described. The sequence of components
in the development of the approach included the validation of measured tire contact
stresses and calibration of two-dimensional finite element models, followed by the
description of the pavement models and analysis method used. Finite element modeling
was chosen for creating a cracked pavement system and fracture mechanics was used to
evaluate the effects critical for inducing crack growth.

CHAPTER 4
PARAMETRIC STUDY - PAVEMENT STRUCTURE
4.1 Overview
A comprehensive parametric study was conducted to identify the mechanism
for surface crack development and propagation. Several factors were evaluated for their
individual and combined effects on the stress condition at the crack tip. Results indicated
that there are key factors that induce more critical stress states ahead of the crack tip. Of
all the analyses conducted in the parametric study, load positioning with respect to crack
location was found to be the overriding contributor to propagation of surface cracks.
Other findings in the analytical evaluation of pavement structure are listed as follows:
• Load spectra (load magnitude and position) were critical in the determination of
crack propagation mechanism.
• Combination of a high stiffness asphalt layer and decreased base stiffness resulted
in increased tensile crack tip stresses. This observation may be explained by the
increased pavement bending and subsequent increase in tension, as load wander
distance increased.
• In most cases, as the load was moved further away from the crack, tension
induced near the crack tip increased.
99

100
• At smaller crack lengths, the primary mode of failure appeared to be purely tensile
(Ki); however, the results depended greatly on the load positioning in the lane.
• Results indicated that surface-initiated crack propagation was primarily a tensile
failure mechanism. The presence of shear may contribute to stress conditions at
the crack tip, but doesn’t appear to control crack growth. Tension predicted at the
crack tip offered an explanation for cracking observed in the field.
• Analyzing crack growth with realistic load spectra (magnitude and position) is
critical to predicting surface-initiated cracking. Load wander must be considered
for predicting failure and is critical in determining future design conditions.
• Structural characteristics such as crack length and layer stiffness had significant
effects on the tensile response of surface cracks; however, load positioning was
found to be the overriding contributor to surface-crack propagation
4,2 Factors Investigated for Structural Analysis
Several characteristics of a pavement structure were investigated via repetitive
analysis of a cracked pavement surface. The two pavement thickness values that were
chosen encompassed the range typically found on high-volume interstate roadways.
Elastic layer moduli were selected to represent an aged asphalt concrete pavement. Base
layer stiffness moduli included a range of values found in field sections to capture the
effects of pavement bending. Crack lengths were identified that reflected cracking to
variable depths, as measured in cored or trenched pavement sections from the field. The
initial crack length (0.25 inch) assumed was equivalent to that determined from indirect
tension tests in the laboratory (Roque 1999). Loading positions were varied until a wide
range of wheel path wander was covered for the analyses. All specific parametric values
were presented in Table 3.3, and as seen in the table, the load was varied from directly on
top of the crack up to 25 inches away from the crack. In most cases, conditions more

101
intense than the average were considered since it appeared that critical conditions, rather
than average pavement conditions, were required for crack propagation.
As previously described, finite element analysis was conducted for each pavement
section modeled and both the transverse (axx) and shear stresses (txy) were reported. The
stress distributions were plotted as a function of vertical distance from the crack tip, r.
Fracture mechanics theory states that the Mode I stress intensity factor, Ki, is defined as
the limit of ctxx*(2tix) as r approaches zero. Therefore, Ki can be linearly extrapolated
from the plotted distribution of axx*(2nr) versus r. The same procedure is applicable
for finding the value of Mode II stress intensity factor, Kn by substituting xxy for axx
(Anderson 1995). Based on experience, the tangent to the distribution of axx*(27xr)1/2
versus r should be extrapolated from data located beyond ten percent of the crack length
(0.1a). For example, the transverse distribution for a 4-inch asphalt concrete with a load
center positioned 25 inches from a 0.5 inch crack is shown in Figure 4.1. As seen in the
figure, the line used to approximate Ki was extrapolated from the data points located after
0.05 inch (or 10% of a = 0.5 inch). The value for Kn was determined similarly as
presented in Figure 4.2. Further understanding of the method can be obtained by
observing additional distributions used in the determination of Ki and Kn, included in
Appendix A. By reporting the stress intensity factors, a description of the effects of each
structural parameter on the conditions near the crack tip can be identified.

102
100
90
80
70
60
50
30
c
t20
â– a io
u>
o_^ 0
Tension
Linear Extrapolate to Y-Intercept for K
aaaaaaaa-aa-a ¿—a~
“I 1 1-
“1 1 1 1 1 1 1 1 1 1 1 1 1 1
£ _W 0.03 Q05 Q08 0.1 Q13 Q15 Q18 Q2 0.23 Q25 0.28 Q3 Q33 Q35 Q38 0.4 Q43 0.45 0.48 0.5 0.53 Q
CNI
*
-10
< -20
>
-30
^0
-50
-60
-70
-80
-90
-100
£
-A- 0.5in Gack -4in Pavement with E1:E2 = 80Q20 ksi
- 0.5n Oack - 4in Ffefverrent with E1:E2 = 80044 ksi
Compression
Vertical Dstance From Crack Tip, r (in)
Figure 4.1: Determination of Ki For Two Different 4-inch Pavement Sections With
a 0.5 inch Surface Crack, and Load Centered 25 inches From Crack.

103
Figure 4.2: Determination of Kn For Two Different 4-inch Pavement Sections With
a 0.5 inch Surface Crack, and Load Centered 25 inches From Crack.

104
4.3 Effects of Pavement Structure on Crack Propagation
Finite element analyses were conducted to identify the effects of pavement
structural characteristics on crack growth. Propensity for crack growth was evaluated
using the fracture parameters J, Ki and Kn, described earlier. Transverse and shear
stresses were reported in the vicinity of the crack tip and throughout the depth of the
asphalt concrete layer. Reporting these responses helped to assess the combined and, as
much as possible, individual effects of each structural parameter on crack propagation.
That is, predictions were used to indicate whether the pavement response was significant
enough to induce further crack growth. The orientation of the major principal plane was
also computed at the crack tip for each structural combination and crack length, and will
be discussed in more detail later.
4,3.1 Asphalt Concrete Thickness
Asphalt concrete thickness was evaluated analytically for its effect on surface
crack growth. The crack tip stress states were plotted for each crack length at each load
position and likewise, the stress intensity factors were extracted. The distributions of
Mode I stress intensity factor Ki with crack length, for three different load positions
relative to the crack, are presented in Figures 4.3 through 4.5. All five loading positions
were evaluated; however in the interest of space, results of only the most critical locations
are presented herein: wide rib loaded over crack, load center 7 inches from crack, and
load center 25 inches from crack. Other data are presented in the tables included in
Appendix B. The corresponding shear distributions of Mode II stress intensity factor Kn

105
with crack length are presented in Figures 4.6 through 4.8. The distributions clearly
showed that more significant tensile stresses at the crack tip resulted in the thicker (8-
inch) asphalt concrete lift. In other words, surface tension (K[) was most critical in
thicker pavements. Results showed that shear (Km) was greater in the thin (4-inch)
pavement section; however, a comparison of the relative magnitudes of both stress
intensity factors indicated that K¡ was dominant in each case. Figure 4.9 shows that
tension was the primary mode of failure for surface crack propagation, regardless of
pavement structural characteristics.
4.3.2 Asphalt Concrete-to-Base Laver Stiffness Ratio
A sensitivity analysis was conducted to determine the effects of variable pavement
layer stiffness on crack tip response. The asphalt concrete pavement stiffness was
initially fixed at 800 ksi and 1200 ksi before the sensitivity analysis of temperature effects
was performed. The base layer stiffness was varied between 20 ksi and 44.5 ksi for every
analysis. Observation of Figures 4.3 through 4.8 indicates that the effect of lower base
stiffness depended greatly on the load positioning and pavement thickness. In Figure
4.10, when the load was centered 25 inches from the crack, it appeared that a higher
stiffness ratio (Ea<;:Ebase = 1200:20 ksi) resulted in more critical stresses at the crack tip.
High asphalt concrete stiffness and/or lower base layer stiffness resulted in greater
potential for tensile crack growth. Shear stresses were increased near the crack tip in the
pavement section with the lower stiffness base, independently of load positioning and
surface layer thickness. However, the magnitude of the shear stresses was not significant

106
Figure 4.3: Effects of Asphalt Concrete Thickness: Distribution of K¡ Versus
Crack Length For Loading Position Centered 25 inches From Crack.

107
Crack Length, a (in)
Figure 4.4: Effects of Asphalt Concrete Thickness and Base Layer Stiffness:
Distribution of Ki Versus Crack Length For Loading Position Centered 7 inches
Front Crack.

108
250
225
200
175
C
X
’
Q.
*
0)
k.
3
-*-1
O
re
150
125
Tension
-a—4in Pavement - Stiffness Ratio E1:E2 = 800:20ksi
-♦—4in Pavement - Stiffness Ratio E1:E2 = 800:44ksi
• - -A • • 8in Pavement - Stiffness Ratio E1E2 = 800:20ksi
■ • -X - • 8in Pavement - Stiffness Ratio E1:E2 = 800:44ksi
::: "X
100
75
50
25
a>
TJ
O
5
•. X
0.25
0.5
0.75 1 1.25
Crack Length, a (in)
1.5
1.75
Figure 4.5: Effects of Asphalt Concrete Thickness and Base Layer Stiffness:
Distribution of Versus Crack Length For Loading Position With Wide Rib
Centered on Top of Crack.

109
Crack Length, a (in)
Figure 4.6: Effects of Asphalt Concrete Thickness and Base Layer Stiffness:
Distribution of Kn Versus Crack Length For Loading Position Centered 25 inches
From Crack.

110
I
Figure 4.7: Effects of Asphalt Concrete Thickness and Base Layer Stiffness:
Distribution of Kn Versus Crack Length For Loading Position Centered 7 inches
From Crack.

Ill
Figure 4.8: Effects of Asphalt Concrete Thickness and Base Layer Stiffness:
Distribution of Kn Versus Crack Length For Loading Position With Wide Rib
Centered on Top of Crack.

112
250
225
E 200
in
a
175
150
125
100
75
• • -a - - K1 - 8in Pavement - Stiffness Ratio E1:E2 = 800:20ksi
• -X- • K1 - 8in Pavement - Stiffness Ratio E1:E2 = 800:44ksi
—b— K2 - 8in Pavement - Stiffness Ratio E1 :E2 = 800:20ksi
—♦— K2 - 8in Pavement - Stiffness Ratio E1:E2 = 800:44ksi
-o
c
ra
in
in
ai
£ 50
•A--''
w
25
A
-X-
■-X—• ■
X-
•X
0.25 0.5 0.75 1 1.25
Crack Length, a (in)
1.5
1.75
Figure 4.9: Comparison of Stress Intensity Magnitudes For Kr and Kn At The
Crack Tip For: 8-inch AC, 1 inch Crack, Load Centered 25 inches From Crack.

113
Figure 4.10: Effects of Asphalt Concrete and Base Layer Stiffness: Distributions of
Ki and Kn Versus Crack Length For Loading Centered 25 inches From Crack.

114
enough to control crack growth, regardless of load position, as shown in Figure 4.10.
4.3.3 Results
It was clearly shown that for most loading cases a thicker asphalt concrete layer
combined with a low base stiffness induced the most critical conditions for crack growth;
however, base stiffness caused the more pronounced effect. That is, the magnitude of
tension appeared to vary more with base stiffness, rather than layer thickness. Asphalt
concrete pavements of high stiffness were also more vulnerable to tension. Examination
of both pavement thickness and base stiffness effects indicated that tension at the crack
tip was the primary mechanism for crack propagation, since the magnitude of tension
overwhelmed that of shear at the crack tip in the asphalt concrete. It is apparent that
asphalt-to-base layer stiffness had the most pronounced effect by increasing the
magnitude of tensile response.
4.4 Effects of Loading on Crack Propagation
The position of the load relative to the crack location was studied in order to
capture the effects of wander in the wheel path on crack tip stresses. The application of
vertical and horizontal loads was crucial for the determination of the proper stress
distribution at the surface of the pavement. An example of the surface loading on the
finite element model is shown in Figure 4.11, which illustrates how the loads were
applied to each node along the surface of the finite element mesh. The nodes that were
loaded represent the ribs along the truck tire tread. The horizontal loads were also

115
Rib 1 - 2.5” Rib 2 - 1.0”
Vertical
Contact
Loads
^ ^ ^ ^ ^ ^ ^ ^ ^
Element-
Node'
—
i 1
t <
9 «
i
1
9 1
9
9
—
Hor
â– izon
tal C(
Dntac
t Loc
ids
4
1
>
Finite Element Mesh
Figure 4.11: Visual Example of Vertical and Lateral Load Application to
Finite Element Model.

116
applied at the nodes under each rib, but were varied to simulate the tearing action under
the ribs. The loading that was utilized in the models was designed to be as close to reality
as possible.
4,4.1 Determination of Appropriate Load Positions
A smaller analytical study was done to determine which load positions were
within the range that suitably captured the maximum tensile zone induced at the
pavement surface. The elastic layer analysis computer program BISAR was used to
determine the location of maximum tensile stresses along the pavement’s surface, for
each pavement thickness and layer stiffness ratio combination used in the parametric
study. The transverse stress distribution along the pavement’s surface was plotted for
each case to identify the load positions that induced critical tensile stresses. An example
transverse stress distribution is shown in Figure 4.12, along with views of the unloaded
cracked pavement that deformed with loading, and subsequently shows the crack located
in a zone of high tension at the surface of the pavement. The transverse stress
distribution data for each pavement section is given in Table 4.1. The maximum tensile
surface stresses were observed between 20 and 30 inches from the load center in the 8-
inch pavement sections, while maximum tension was found between 15 and 25 inches
from the load center in the 4-inch pavement sections. Thus, in order to capture the tensile
zone all pavement models were analyzed with the load center at 15, 20, and 25 inches
from the crack for the 4-inch pavement and 20, 25, and 30 inches from the crack for the
8-inch pavement. The models were also analyzed with the load center at 7 inches from
the crack to identify the potential effects of vertical shear stresses on the crack. Finally,

117
since it had been reported by Myers et al. (1997) that high tensile stresses are induced at
the pavement’s surface under the widest rib of a radial truck tire, the case of the wide rib
centered over the crack was also examined.
LOAD
Figure 4.12: Visual Example of Transverse Stress Distribution in Response to
Loading: Undeformed Pavement, Deformed Loaded Pavement, and Transverse
Stress Distribution Along the Pavement’s Surface.

118
Table 4.1: Transverse Stress Distribution Along Surface of Pavement For
Each Pavement Modeled, As Predicted in BISAR Elastic Layer Analysis
Program.
4.1
Asphalt Concrete 8" Asphalt Concrete 4" Asphalt Concrete 4" Asphalt Concrete
:E2
=800:44 E,:E2=
800:20 E,:E
2=800:44 E,:E
¡=800:20
* =
18 SR = 40 SR =
18 SR =
40
DISTANCE, x (in)
x (in)
„ at surface o».
at surface
at surface c
„ at surface from center of load
(from edae of
-10.7
-15.1
6.4
3.7
10.0
5.5
-8.5
-12.4
9.5
9.2
11.0
6.5
-6.6
-9.8
11.5
13.2
12.0
7.5
-4.9
-7.6
12.6
16.0
13.0
8.5
-3.4
-5.5
13.2
, 17.9
,_14.0
9.5
-2.1
-3.8
13.3
19.1
< 15.0
10.5
-1.0
-2.2
13.2
19.7
i 16.0
11.5
-0.1
-0.9
12.8
19.9
! 17.0
12.5
0.6
0.3
12.3
19.8
! 18.0
13.5
1.3
1.3
11.7
19.3
! 19.0
14.5
C 1.8
2.2
11.0
18.8
Load
! 20.0
15.5
2.3
C 2.9
L 10.4
18.1
Position
¡ 21.0
16.5
ss
2.7
3.7
10.0
L 17.7
Range
¡ 22.0
17.5
4.1
5.4
12.0
21.6
¡ 23.0
18.5
ge
3.3
4.8
5.5
10.3
i 24.0
19.5
3.6
5.4
3.7
6.7
1 30.0
25.5
3.0
4.7
2.2
3.5
'-36.0
31.5
2.1
3.5
1.2
1.5
42.0
37.5
1.3
2.4
0.5
0.3
48.0
43.5
0.7
1.5
0.1
-0.2
54.0
49.5
0.8
1.4
0.2
-0.1
60.0
55.5
5.4
MAXIMUM VALUES
13.3
OF Sxx FOR EACH
21.6

119
Although in this particular part of the study only two asphalt concrete-to-base
stiffness combinations were analyzed, other layer stiffness ratios were also of interest. In
order to avoid running a number of extra analysis compilations, a range of asphalt
concrete and base stiffnesses, that yielded the equivalent stiffness ratios already analyzed,
were tested in BISAR. It was found that for the same stiffness ratio (E1/E2) and asphalt
concrete depth (hi), the location of maximum tensile stress along the pavement’s surface
was the same. That is, the magnitude and location of the maximum tension at the surface
was dependent mostly on the stiffness ratio (E1/E2), and not dependent on the individual
layer stiffnesses (Ei, E2). For example, the transverse stress distribution along the
pavement’s surface was plotted with distance from the load center for a pavement with a
layer stiffness ratio of 40 (E]/E2= 40). The distributions for both pavement thicknesses
were determined and are illustrated in Figure 4.13. As presented in the figure, two
different asphalt concrete and base layer stiffnesses were used to compile the same
stiffness ratio of 40. In one case, the asphalt concrete-to-base configuration was 500 ksi-
to-12.5 ksi, while the other configuration was 800 ksi-to-20 ksi. It was illustrated that the
stress distribution was independent of individual layer stiffnesses, especially at distances
far from the load center, where the crack would eventually be located in the model when
the effects of load wander would be analyzed. Obviously, this observation was valid for
linear elastic, two-dimensional models with the same load magnitude applied.
4.4,2 Load Position With Respect to Crack
A comprehensive parametric study was conducted to determine the effects of load
spectra and pavement structure on crack propagation. The results indicated that the key

120
Figure 4.13: Effects of Individual Layer Stiffness Values on Transverse Stress
Distribution Along Surface of Pavement From Center of Load For Layer Stiffness
Ratio of 40.

121
factor that induced critical stress states ahead of the crack tip was load magnitude and
position. In order to analyze the importance of load spectra (load magnitude and
positioning), each model was analyzed at five different loading positions, relative to crack
location. The stress conditions at the crack tip were then reported
as stress intensity factors, K| and Kn. The distributions of Ki and Kn with crack length
were plotted as a function of load positioning for each pavement thickness and layer
stiffness ratio.
Figure 4.14 illustrates the effect of load positioning on opening at the crack tip for
a 4-inch surface layer and lower stiffness ratio case, while Figure 4.15 indicates the same
for shearing at the crack tip. The same distributions for Ki and Kn were plotted for a 4-
inch surface layer and the higher stiffness ratio case in Figures 4.16 and 4.17. Figures
4.18 through 4.21 show stress intensity distributions for an 8-inch surface layer at both
stiffness ratio cases.
The trends plotted in Figures 4.14 through 4.21 indicate that load positioning
clearly has a significant effect on the magnitude of the stress intensity predicted at the
crack tip. The figures show that wander in the wheel path will have an effect on the
magnitude of tension ahead of the crack tip. As the load wander varies from the crack,
the surface of the pavement is in tension and increases stresses at the crack tip, leading to
possible propagation. This data indicated that a critical condition may exist when the
load wander increases in distance from the actual crack. It was also shown in Figures
4.18 and 4.20 that for shorter crack lengths, tension was predicted under the stress
reversals that exist under the widest tire rib. Initially, opening at the crack tip increased

122
Figure 4.14: Effect of Load Positioning on Opening At the Crack Tip For a 4-inch
Surface Layer and Low Stiffness (E1/E2 = 800:20 ksi) Ratio.

123
Figure 4.15: Effect of Load Positioning on Shearing At the Crack Tip For a 4-inch
Surface Layer and Low Stiffness (E1/E2 = 800:20 ksi) Ratio.

124
Figure 4.16: Effect of Load Positioning on Opening At the Crack Tip For a 4-inch
Surface Layer and High Stiffness (E1/E2 = 800:44.5 ksi) Ratio.

125
Crack Length (in)
Figure 4.17: Effect of Load Positioning on Shearing At the Crack Tip For a 4-inch
Surface Layer and High Stiffness (E1/E2 = 800:44.5 ksi) Ratio.

126
Figure 4.18: Effect of Load Positioning on Opening At the Crack Tip For an 8-inch
Surface Layer and Lower Stiffness (E1/E2 = 800:20 ksi) Ratio.

Mode II Fracture, K2 (psi-(in)
127
250
- • ± ■ - Crack Located 7" Away From Center of Load
150
—♦— Crack Located 20" Away From Center of Load
—a— Crack Located 25" Away From Center of Load
- - • - - Crack Located 30" Away From Center of Load
25 -
0 8— ^ ' j y
0
1 0.25 0.5 0.75 1 1.25 1.5 1.75
E.,:E2 = 800:20
-17=;
-250 â– 
Crack Length (in)
Figure 4.19: Effect of Load Positioning on Shearing At the Crack Tip For an 8-inch
Surface Layer and Lower Stiffness (E1/E2 = 800:20 ksi) Ratio.

128
Figure 4.20: Effect of Load Positioning on Opening At the Crack Tip For an 8-inch
Surface Layer and High Stiffness (E1/E2 = 800:44.5 ksi) Ratio.

Mode II Fracture, K2 (psi-(in)
129
Figure 4.21: Effect of Load Positioning on Shearing At the Crack Tip For an 8-inch
Surface Layer and High Stiffness (Ei/E2 = 800:44.5 ksi) Ratio.

130
as the crack length increased, and then decreased after a certain crack length; however, all
observations were dependent on the load position.
Not only were the stress intensity factors considered important for determining the
effects of pavement structure on crack growth, but the distribution of transverse stresses
generated throughout the depth of the surface layer was also considered. Obviously, the
location of the neutral axis within the asphalt concrete moved with respect to load
position. The crack length also affected the position of the neutral axis since stress
redistribution occurred incrementally with increasing crack length. The stress distribution
within the asphalt concrete layer will be discussed in more detail in Chapter 5.
4.4.3 Direction of Crack Growth
The direction of crack propagation was also investigated by computing the
orientation of the major principal stress plane. It was found that as the crack propagated
further into the depth of the pavement, it began to grow in toward the center of tire
loading at a computed angle of 30 degrees relative to the vertical. An example of the
calculation procedure is outlined in Table 4.2 for a thick pavement with a high stiffness
layer ratio. The orientation of the maximum shear stress plane was also computed for
each structural case, but is not shown.
The computations of direction of crack growth can be used to explain
observations made in the field sections. An example of the directional change in crack
growth as crack length increases is shown in Figures 4.22 and 4.23. At shorter crack
lengths, propagation is driven purely by tension and the crack grows straight down into
the pavement. However, at intermediate depths, the crack changes direction since the

131
stress states within the asphalt layer change with depth. It appears that computed crack
direction had confirmed field observations, like those shown in Figure 5.21 in the next
chapter.
Table 4.2: Example Calculation of Direction of Crack Growth For Thick Pavement
(hi= 8-in) With Low Base Stiffness (Ei:E2 = 800:20 ksi).
Thick Pavement 8"AC with Stiffness Ratio E,:E2=800:20
Transverse
Vertical
Shear
Angle
Angle of Major Principal Plane (Relative to Vertical)
CTx
Oi
Txv
20
0
Case 1 (ctx>ctv)
Case 2 (crx 8" AC
Rib Load
209.8
204
-37.145
-85.5
-42.8
42.8
E,:E2=800:20
7" load
n/a
n/a
n/a
n/a
n/a
n/a
Crack, a=0.25"
20" load
9.608
7.056
-4.03
-72.4
-36.2
-36.2
25" load
82.395
61.255
-15.07
-55.0
-27.5
-27.5
30" load
107.915
80.315
-18.7
-53.6
-26.8
-26.8
8" AC
Rib Load
212.3
219.65
-31.9
83.4
41.7
41.7
E,:E2=800:20
7" load
n/a
n/a
n/a
n/a
n/a
n/a
Crack, a=0.5"
20" load
120.55
89.745
-21.81
-54.8
-27.4
-27.4
25" load
86.53
66.435
-15.35
-56.8
-28.4
-28.4
30" load
140.6
107.97
-25.79
-57.7
-28.8
-28.8
8" AC
Rib Load
n/a
n/a
n/a
n/a
n/a
n/a
E,:E2=800:20
7" load
n/a
n/a
n/a
n/a
n/a
n/a
Crack, a=0.7S"
20" load
58.59
46.77
-14.065
-67.2
-33.6
-33.6
25" load
77.01
61.49
-15.155
-62.9
-31.4
-31.4
30" load
116.9
93.34
-23.465
-63.3
-31.7
-31.7
8” AC
Rib Load
n/a
n/a
n/a
n/a
n/a
n/a
E,:E2=800:20
7" load
n/a
n/a
n/a
n/a
n/a
n/a
Crack, a=1.0"
20" load
n/a
n/a
n/a
n/a
n/a
n/a
25" load
64.495
51.455
-19.15
-71.2
-35.6
-35.6
30" load
134.05
108.69
-28.5
-66.0
-33.0
-33.0
8" AC
Rib Load
n/a
n/a
n/a
n/a
n/a
n/a
E,:E2=800:20
7"load
n/a
n/a
n/a
n/a
n/a
n/a
Crack, a=1.5"
20" load
52.845
43.135
-20.725
-76.8
-38.4
-38.4
25" load
125.65
105.18
-28.095
-70.0
-35.0
-35.0
30" load
116.25
96.785
-30.475
-72.3
-36.1
-36.1

132
Load
-I>
Pure
Mode I
Extracted
Core
id • d
1
1 Short
Crack
Figure 4.22: Example Field Section and Core Exhibiting Short Crack: Pure Tensile
Failure Mechanism.

133
Load
h
Principal Plane
Changes with Crack Growth
y0 - 30°
Extracted
Core
Intermediate
or Deep Crack
Figure 4.23: Example Field Section and Core Exhibiting Intermediate or Deep
Crack: Tensile Failure Mechanism and Directional Change in Crack Growth.

134
4.5 Summary
A detailed parametric study indicated that pavement structural characteristics have
a significant effect on the nature of longitudinal wheel path crack growth. Results from
the parametric study showed that most crack growth occurred under the critical loading
conditions. The position of the loading, with respect to crack location, had the greatest
effect on crack propagation downwards in the surface layer. The surface-to-base layer
stiffness also affected the magnitude and direction of crack tip stresses, as dependent on
crack length. Based on these findings, it may be concluded that analyzing the physical
presence of a crack, as well as variable load and pavement structure, had a significant
effect on asphalt pavement response by capturing stress redistributions local to the crack
tip. An explanation for the mechanism of surface crack propagation was defined. The
study was then extended to include effects of temperature conditions on the response of
surface cracks in highway pavements, as will be described in the next chapter.

CHAPTER 5
PARAMETRIC STUDY - TEMPERATURE AND ENVIRONMENTAL CONDITIONS
5.1 Overview
Another parametric study was conducted to identify the effects of temperature and
environmental conditions and determine their part in the mechanism for surface crack
development and propagation. Stiffness gradients within the bituminous surface layer,
induced by temperature differentials, age-hardening, or sudden rains which result in rapid
cooling of the pavement surface were analyzed. Results indicated that introduction of a
temperature-induced stiffness gradient significantly increased the tensile opening at the
crack. Once again, load positioning in the wheel path was found to have major influence
on the propagation of surface cracks. Other findings in the analytical evaluation of
temperature effects on surface cracking include the following:
• Asphalt pavements analyzed with stiffness gradients produced significantly higher
stress intensities at all crack lengths, depending on load wander distance.
• Stresses generated at the crack tip were generally more critical as the pavement
thickness increased and base layer stiffness decreased.
• The direction of crack growth varied according to different stiffness gradients and
load position.
• Given the magnitude of stress intensities predicted, the primary mode of failure
appeared to be tensile (Ki) for all crack lengths.
135

136
5.2 Analysis Procedure For Evaluating Induced Stiffness Gradient
The asphalt concrete layer of a pavement system is ordinarily modeled as having a
uniform stiffness throughout its cross-section for pavement analysis purposes. However,
the stiffness of the asphalt concrete layer is almost never uniform because of induced
temperature gradients and variations in age-hardening and pavement cooling rates. The
effect of stiffness gradients on stresses induced at the crack tip was investigated as part of
the research study.
Because the effects of temperature-induced stiffness gradients were predicted for a
continuum pavement by Myers (1997), it was determined that for best comparison
purposes the same approach used by Myers was followed for analysis of a cracked
pavement. However, a broader range of load positions was evaluated, as the effects of
wander are considered crucial to the analysis of surface crack propagation. Temperature
gradients were analytically determined for a pavement system by using the FHWA
Environmental Effects Model (Lytton et al. 1990) with air temperature data for north-
central Florida from NOAA. The asphalt concrete modulus-temperature relationship
developed by Ruth et al. (1981) was utilized to generate a stiffness gradient that
corresponded to the temperature gradients determined. The approach developed by the
Asphalt Institute for fatigue analysis was employed to find a uniform stiffness, as based
on the temperature computed at one-third of the depth of the asphalt concrete layer
(Huang 1993). A detailed description of the FHWA Environmental Effects Model
(EEM) and its use was provided in a study conducted by Myers (1997).

Predicting the effect of a stiffness gradient on pavement responses can be
considered important for the climatic and solar conditions found in Florida. In order to
evaluate the effects of a stiffness gradient on the pavement responses, a procedure for
simulating induced temperature gradients was formulated.
The following four cases, which are illustrated in Figure 5.1, were selected to
evaluate the effects of stiffness gradients on stresses at the pavement’s surface:
• Case 1: Uniform temperature distribution (i.e., no stiffness gradient) was selected as
the control case. The mean pavement temperature was computed at one-
third of the depth at an hour when temperature conditions are warm.
• Case 2: Sharpest temperature gradient near surface. Temperatures at 7 PM were
selected to represent this condition.
• Case 3: Highest temperature differential between the surface and the bottom of the
asphalt concrete layer. Temperatures at 5 AM were selected to represent this
condition.
• Case 4: Rapid cooling near the surface was selected to represent the case of sudden
rains.
These conditions were identified by reviewing the pavement temperature file
created by the FHWA environmental effects model for 1985 in Melrose, Florida for a 24-
hour period. This 24-hour temperature profile was then plotted as a function of depth to
view the distribution of temperatures and isolate the conditions of interest, as seen in
Figure 5.1. A temperature gradient of 5°F per inch (1.1°C per centimeter) of depth was
determined to be typical of that present during winter months.

Depth (in)
Case 1 - No Gradient (11 AM) Case 3 - Greatest Differential (5 AM)
Case 2 - Sharpest Gradient (7PM) Case 4 - Rapid Cooling (daytime)
Figure 5.1: Temperature Gradient Cases Used to Determine Stiffness Gradients
the Asphalt Concrete Layer to be Evaluated in ABAQUS.

139
The following asphalt concrete modulus-binder viscosity relationships developed
by Ruth et al. (1981) was utilized to compute a stiffness gradient that corresponded to the
temperature gradient chosen:
For r| loo < 9.19 E8 Pa-s,
log E = 7.18659 + 0.30677 log r|100
For r\ loo > 9.19 E8 Pa-s,
log E = 9.51354 + 0.04716 log r)100
where: E = asphalt concrete modulus,
tli oo = previously determined binder viscosity of the asphalt concrete.
The constant power viscosity can be found by evaluating the following equation:
logr|ioo=Bo+Bi * log (T)
where T) !0o = binder viscosity of the asphalt at constant power of 100 watts/m3,
B0 = 178.28, from data measured for an unaged Coastal AC-30 (Lee 1996),
Bi = -69.70, from data measured for an unaged Coastal AC-30 (Lee 1996),
T = temperature in °K.
The asphalt concrete modulus was plotted as a function of temperature using
constant power viscosity data for an unaged Coastal AC-30 asphalt cement (see Figure
5.2). The unaged AC-30 asphalt cement curve was used for the analyses conducted in
this study. Figure 5.2 was used to determine the stiffness at different depths
corresponding to pavement temperatures at the same depths.

140
ABAQUS was used to predict pavement response for the different structural
characteristics for cracked pavements and the temperature cases illustrated in Figure 5.1.
The different cases evaluated were represented by dividing the asphalt concrete layer into
sublayers of variable thicknesses and stiffnesses, corresponding to the pavement
temperatures at different depths as predicted by the environmental effects model. Again,
these stiffnesses at different depths were determined by using the dynamic modulus
versus temperature relationship presented above (Ruth et al. 1981).
The stiffness configurations used in ABAQUS are shown in Figures 5.3 through
5.6 for a thick (8-in) pavement structure. Case 1 (no temperature gradient) was
determined by using the Asphalt Institute approach for fatigue analysis of a uniform
stiffness asphalt concrete layer (Huang 1993). The uniform stiffness is based on the
temperature calculated at one-third of the depth of the asphalt concrete layer. The
relationships used are listed sequentially below:
Mp = Ma (1 + l/(z+4)) - 34/(z+4) + 6
where Mp = Mean Pavement Temperature
Ma = Mean Monthly Air Temperature
z = Depth Below Surface (in)

Dynamic Modulus (psi)
141
Temperature (degrees F)
Figure 5.2: Dynamic Modulus versus Temperature Plot For Unaged AC-30 Asphalt
Cement Mixture Used to Convert Temperature Gradients Into Stiffness Gradients.
For a temperature regime with a mean annual air temperature (MAAT) of 75°F (24°C),
the Asphalt Institute proposed a mean monthly air temperature of 55°F (12.8°C). Thus,
the equation above was used to determine the mean pavement temperature of 64°F at one-
third of the depth in the asphalt concrete layer. This mean pavement temperature was
used to compute the stiffness that represents the entire layer, as shown in Figure 5.3. A
situation like Case 1 was found around 11 AM when no gradient will occur since
temperature conditions are intermediate to warm.

Figure 5.3: Asphalt Concrete Sublayer Configuration Used For Analyzing Case 1
Uniform Layer Stiffness Temperature Gradient.
The modulus profile for Case 2 (sharpest temperature gradient) was defined by
dividing the asphalt concrete layer into a series of variable thickness asphalt concrete
sublayers. A Case 2 distribution was found around 7 PM when the sun first goes down
and then pavement is coldest at the surface and still remains very warm in the underlying
depths. Based on the predicted pavement temperatures, the sharpest temperature gradient
was determined to be 5°F. The resulting profile is shown in Figure 5.4.

143
E = 1200 ksi r
0.5 in
i
E = 1099 ksi
0.5 in
E = 950 ksi
1 in
E = 780 ksi
1 in
E = 640 ksi
1 in
8 in
E = 480 ksi
2 in
E = 320 ksi
2 in
r
Figure 5.4: Asphalt Concrete Sublayer Configuration Used For Analyzing Case 2
Temperature Gradient.
The modulus profile for Case 3 (highest temperature differential) was defined by
dividing the asphalt concrete layer into a series of equivalent asphalt concrete sublayers,
shown in Figure 5.5. A Case 3 distribution was found around 5 AM when the greatest
temperature differential exists in the pavement since the surface temperature is at its
lowest and the bottom temperature is still relatively warm. For example, the temperature
at the surface may be 23 °F and the temperature at the bottom remains at 68°F.

144
Figure 5.5: Asphalt Concrete Sublayer Configuration Used For Analyzing Case 3
Temperature Gradient.
The modulus profile for Case 4 (i.e., rapid cooling induced by sudden rains) was
defined by dividing the asphalt concrete layer into a very thin sublayer of very high
stiffness on top of a relatively thick sublayer of moderate stiffness, seen in Figure 5.6.
This case can be represented for any time during the daylight hours when a sudden
rainstorm (which is common in Florida) causes rapid cooling of the pavement surface,
while the entire depth is still at an extremely warm temperature.

145
8 in
i
Figure 5.6: Asphalt Concrete Sublayer Configuration Used For Analyzing Case 4
Temperature Gradient.
Preliminary analyses indicated that the number of sublayers used to make up the
surface layer had some influence on the stress predictions. However, the system shown in
Figure 5.4 depicting the steepest stiffness gradient, which was used for the “with
temperature gradient” case, resulted in adequate predictions (i.e., further division of
layers did not significantly alter the stress distributions predicted by the program).

146
5.3 Analysis of Cracked Pavement With Induced Stiffness Gradient
The procedure for finite element analysis of a cracked pavement was outlined in
Chapters 3 and 4. All pavements were modeled with each of the four stiffness gradient
cases. Fracture parameters and stress distributions were predicted and the direction of
crack growth was also computed. The results of the stiffness gradient analysis showed a
significant increase in the tension produced at the crack tip. Figure 5.7 illustrates the
effect of the stiffness gradient on the distribution of opening fracture with increasing
crack length, at one load position for the 8-inch pavement. It clearly shows that when a
stiffness gradient is induced in the pavement, tension at the crack tip is greatly increased
relative to the case of uniform stiffness (Case 1). Both conditions in Cases 2 and 3
resulted in significantly higher stress intensities at all crack lengths. The sudden rain case
(Case 4) was similar to Case 1 except at crack lengths of 0.25-inch and 0.75-inch where
an increase in stress intensity occurred. Figure 5.8 again shows the insignificance of
shear stresses on crack tip behavior.
Figure 5.9 presents another view of the significant increase in stress in the
pavements with temperature-induced gradients. A comparison of the transverse stress
distribution within the asphalt concrete depth, with a one inch crack, for different
stiffness gradient cases is illustrated. It appears that the magnitude of transverse stress is
twice as high in some cases. As was previously reported by Myers (1997), the neutral
axis of pavements with stiffness gradients moves up, as much as two inches in some
cases, when the load is positioned directly over the crack. However, the distribution

Mode I Fracture K , (psi-(in)
147
presented in Figure 5.9 was captured at the load position found to be most critical for
inducing significant tension.
Load Centered 30 in From Crack
Figure 5.7: Effect of Temperature-Induced Stiffness Gradients on Stress Intensity
Ki Predicted At the Crack Tip For 8-inch Asphalt Concrete (Load Centered 30 in
From Crack).

Mode II Fracture, K 2 (psi-(in)
148
Load Centered at 30 in From Crack
Crack Length, a (in)
Figure 5.8: Effect of Temperature-Induced Stiffness Gradients on Stress Intensity
Kn Predicted At the Crack Tip For 8-inch Asphalt Concrete (Load Centered 30 in
From Crack).

Depth in Asphalt Concrete, z (in)
149
Transverse Stress, axx (psi)
Figure 5.9: Effect of Temperature-Induced Stiffness Gradients on Transverse
Stress Distribution Within 8-inch Asphalt Concrete with a 1.0 inch Crack (Load
Centered 30 in From Crack).

150
As was found in previous analyses described in Chapter 4, the position of the load
in the wheel path appeared to be most critical to the development of surface cracking.
Figure 5.10 clearly shows the influence of load position on stress intensity induced at
each crack length in an 8-inch pavement. The stiffness gradient (Case 3) analyzed in
Figure 5.10 appears to be the most critical to propagation and induced the greatest stress
intensity.
Opening Failure - Stiffness Gradient Case 3
Figure 5.10: Effect of Load Wander on Stress Intensity Within 8-inch Asphalt
Concrete (Stiffness Gradient Case 3).
Another view of the predicted stress intensity distributions may help to further
clarify the significant influence of stiffness gradients on crack propagation. Figure 5.11
illustrates the relationship between stress intensity Ki and crack length for a 4-inch

151
Case 1
Case 2
Case 3
Case 4
0.25”-
0.5-
0.75” -
Crack 10”-
Length
(in)
1.5’L
2.0”--
67*
>82
*>100
♦115
80
-*â– 100
*>90
> 95
—*-185
89
*â– 118
-♦120
>104
220
50
70
58
â–º65
-♦150
•4- 45
4.0”-
' Numbers Indicate Stress
Intensity K, in psi(in)1/2
4” Asphalt Concrete Pavement
Base Stiffness = 20 ksi
Figure 5.11: Illustration of Effects of Stiffness Gradients on Crack Propagation in
4-inch Asphalt Pavement (Load Centered 25 in From Crack).

152
pavement with an attempt to define it in a visual sense. It is clearly shown that stiffness
gradients significantly affect the way a crack will develop in the pavement. A similar
illustration for an 8-inch pavement is presented in Figure 5.12.
5.3.1 Effect of Pavement Structure on Cracked Pavement With Stiffness Gradients
In addition to the presence of temperature-induced stiffness gradients in the
asphalt concrete layer, the effects of pavement structure were explored. The effect of
base layer stiffness on stress intensities resulting at the crack tip was investigated. As
expected, asphalt concrete laid on lower stiffness base layers resulted in increased tension
near the surface of the pavement and consequently, greater stress intensities at the crack
tip for all crack lengths. The influence of base layer stiffness is demonstrated in Figure
5.13 and the increase in tensile magnitude is apparent. In some cases, it appears that the
tensile stress intensity produced in a cracked pavement over a lower stiffness base (E2=20
ksi) is double that predicted in a higher stiffness structure (E2=44.5 ksi). The results for
the stiffness gradient cases analyzed correspond to the same findings reported in Chapter
4 on the influence of base layer stiffness.
The influence of asphalt concrete thickness on perpetuating crack propagation was
also predicted. The distributions for stress intensity with crack length at each loading
position are presented in Figures 5.14 through 5.18. The plots shown were analyzed on a
base layer of lower stiffness (E2=20 ksi). Figures 5.14 through 5.16 clearly show that the
thicker pavement is more greatly influenced by the presence of a temperature-induced
stiffness gradient and as a result, the stress intensity was generally more critical in the
thicker (8-in) pavement than in the thin pavement (4-in). Examination of each of the five

153
Case 1 Case 2 Case 3 Case 4
Figure 5.12: Illustration of Effects of Stiffness Gradients on Crack Propagation in
8-inch Asphalt Pavement (Load Centered 25 in From Crack).

154
8" Asphalt Concrete - Load Centered 30 in From Crack
Figure 5.13: Effects of Stiffness Gradients and Base Layer Stiffness on Crack
Propagation in 8-inch Asphalt Pavement (Load Centered 30 in From Crack).

155
Load Centered 25 in (4"AC) and 30 in (8"AC) From Crack
Crack Length, a (in)
Figure 5.14: Effects of Stiffness Gradients and Asphalt Concrete Layer Thickness
on Crack Propagation (Load Centered 25 in and 30 in From Crack).

156
Load Centered 20 in (4"AC) and 25 in (8"AC) From Crack
Figure 5.15: Effects of Stiffness Gradients and Asphalt Concrete Layer Thickness
on Crack Propagation (Load Centered 20 in and 25 in From Crack).

157
Load Centered 15 in (4"AC) and 20 in (8"AC) From Crack
Figure 5.16: Effects of Stiffness Gradients and Asphalt Concrete Layer Thickness
on Crack Propagation (Load Centered 15 in and 20 in From Crack).

158
Load Centered 7 in From Crack
Figure 5.17: Effects of Stiffness Gradients and Asphalt Concrete Layer Thickness
on Crack Propagation (Load Centered 7in From Crack).

159
Wide Rib Load Centered on Top of Crack
Figure 5.18: Effects of Stiffness Gradients and Asphalt Concrete Layer Thickness
on Crack Propagation (Wide Rib Load Centered on Top of Crack).

160
figures indicates that propagation may exist in both types of asphalt lifts; however, thicker
pavement appear to exhibit an increased potential for developing crack propagation
because more load positions result in tensile stresses that drive the crack. The increase in
crack tip tension at more load positions in the thick pavement is clearly shown in the
sequence of Figures 5.14 through 5.16. It appears that the prediction of high tensile stress
intensities may validate the significant amount of surface cracking observed in thick
highway sections extracted from the field.
5.3.2 Effect of Stiffness Gradient on Direction of Crack Growth
The direction of crack growth was computed using the procedure described in
Chapter 4 in order to identify the effects of an induced stiffness gradient in the pavement.
Surface cracks were computed to grow approximately 30 degrees relative to vertical
toward the direction of the applied loading for an asphalt pavement of uniform stiffness.
However, the changes in direction of crack growth were also determined after
introduction of stiffness gradients into the asphalt pavement was performed.
It appears that different stiffness gradients vary the direction of crack growth,
which changes with increasing crack length. Figure 5.19 shows the orientation of major
principal stress plane with increasing crack length in a 4-inch pavement. The distribution
presented is one calculated from stiffness gradient Case 2. It is shown that the orientation
of the major principal stress plane varies significantly with loading position and crack
lengths, and may even start to grow outward away from the loading at some crack
lengths.

161
Crack Length a (in)
Figure 5.19: Effects of Stiffness Gradient Case 2 on Direction of Crack Growth in
4-inch Pavement (Angle Relative to Vertical).

162
The effect of an induced stiffness gradient on crack direction is also demonstrated
in Figure 5.20. The angles of the crack plane are shown to vary significantly at every load
position, although only a load positioning of 25 inches was plotted herein. Cracks grew
mostly within -20° to -40° off the vertical plane (growing in toward the load), although at
some locations the cracks actually grew in a direction nearly +40° off the vertical plane
(growing away from load). In any case, the range of angles predicted seem to correspond
with the direction of cracks observed from field trench and core sections, as demonstrated
in the photograph of an extracted trench section in Figure 5.21.
5.4 Summary
A detailed parametric study indicated that temperature-induced characteristics in an
asphalt pavement have a significant effect on the mechanism for longitudinal wheel path
crack growth. Results showed that the introduction of a temperature-induced stiffness
gradient magnified tension at the crack tip, sometimes as high as double the tension
produced in a pavement analyzed with uniform stiffness. However, it is well-documented
that asphalt concrete is not a medium of uniform stiffness and is affected by temperature
in the field. For this reason, temperature-induced stiffness gradients should be considered
when analyzing the propagation of surface cracking in asphalt pavements.

163
8" AC Pavement - Load Centered 25in From Crack
Figure 5.20: Effects of Various Stiffness Gradients on Direction of Crack Growth in
8-inch Pavement (Angle Relative to Vertical).

164
Figure 5.21: Effects of Various Stiffness Gradients on Direction of Crack Growth:
Photo of Cracked Trench Extracted From Florida Highway 301.

CHAPTER 6
POTENTIAL IMPLICATIONS FOR PAVEMENT DESIGN AND PERFORMANCE
6.1 Overview
As seen from the previous chapters, the mechanism for development of surface-
initiated longitudinal wheel path cracks doesn’t appear to be straightforward. There is not
one single cause for crack propagation or one single factor that dominates the rate of
cracking since the mechanism depends on so many factors: load spectra, presence and
type of stiffness gradient, asphalt concrete thickness, base stiffness, and so on. However,
it may to be possible to isolate the most critical factor, or a more critical combination of
factors, that will induce conditions favorable to crack growth. The data and results
provided by the analyses presented herein can assist in developing alternative or new
approaches to pavement design and evaluation of pavement performance in areas where
longitudinal surface cracks persist as a major problem. In addition, presenting some of
the potential implications of the work must reveal a direction for how the information can
be useful.
165

166
6.2 Implications of Load Spectra
It was determined from analyses that the effects of load spectra (load magnitude
and wander) were most instrumental in the development of surface cracks. Some load
positions were significantly more influential than others, depending on both crack length
and pavement structure. Figure 6.1 confirms that cracks are concentrated in the wheel
path but the most critical load position, meaning the position that induces the greatest
tensile stress intensities, was not always directly in the wheel path on top of the crack. In
general, the critical positions can be identified for both thinner and thicker asphalt
concrete pavements, but the results may vary slightly depending on the type of stiffness
gradient induced in the asphalt concrete as well. However, the concept of identifying
different crack length stages could help to better describe crack growth.
The stages of crack growth were described as follows:
• Short crack lengths may be described as the range including 0.25 and 0.5 inch.
• Intermediate crack lengths may be defined between 0.75 and 1.5 inches.
The range for short cracks was limited to 0.5 inch because once cracks grew past 0.5 inch,
critical load positions shifted and the mechanism for propagation changed. More
specifically, it was found that after a crack length of 0.5 inch, the wide rib loaded over top
of the crack no longer induced tension.
The distributions of load positions with respect to crack location can be illustrated
for different crack growth stages. As mentioned previously, only a single radial tire was
evaluated in this study. However, single and dual loads must be evaluated separately to
determine the implications on pavement design.

167
Figure 6.1: View of Lane Exhibiting Visible Surface-Initiated Longitudinal Cracks
in the Wheel Paths.

168
The transverse distribution of load position within the wheel path is represented by the
normal distribution function shown in Figure 6.2 (b) and (c) for both short and
intermediate crack lengths in a 4-inch pavement of uniform stiffness. It should be noted
that the crack is assumed to initiate under the center of the outer wide rib of the tire since
this was the location where critical tensile stress occurs at the pavement’s surface (Myers
1997). The cross-hatched area in the figure represents the load position relative to the
crack that resulted in tension at the crack tip. Magnitude of tension (Ki) predicted at each
of these designated load positions is indicated on the figure. Area under the normal
distribution accounts for the total number of loads for a given traffic level. The question
that must be answered is: how many loads induce significant tension or increased Ki at
the crack tip? The answer lies in observation of the normal distribution function. That is,
the more area covered under the load function, the higher number of loads found to
induce tension.
Figure 6.2 shows that for a given level of traffic, a greater number of loads induce
tension for a short crack case than for a pavement with an intermediate length crack.
Data plotted for an 8-inch pavement (Figure 6.3) reflects the same observation: as cracks
grow to an intermediate length, a fewer number of loads are identified as inducing critical
tensile stresses, even though the load spectrum is the same. The figures indicate that
loads closer to the crack do not induce tension, specifically in the case of intermediate
cracks, implying that crack growth initially slows down as the crack grows beyond the
short crack length stage. However, an exception is found in the 8-inch pavement where
tension is predicted when the load is centered in the wheel path. The reason is when the
load is positioned in the center of the wheel path, with the tire’s outer wide rib centered

169
over the crack, tension is still induced near the surface of the pavement by lateral stresses
under the rib and results in increased tension at the crack tip for short crack lengths
(shown in Figure 6.3b).
Temperature-induced stiffness gradients in the asphalt concrete also affect the
distribution of load wander critical to crack growth. Figures 6.4 and 6.5 illustrate the
effect of the type of stiffness gradient on the number of loads that induce tension for short
and intermediate cracks in both a 4- and 8-inch asphalt concrete layer. In a thin
pavement, the induced stiffness gradients do not appear to alter the critical positions
significantly although a smaller number of loads result in tension. In the thicker
pavement, an increase in the number of loads that induced tension was found at certain
stiffness gradients. Observation of Figure 6.5 showed that the magnitude of Ki at these
numerous load positions was significantly greater (sometimes more than double) than
those found in the uniform stiffness case in Figure 6.3.
It is important to note the magnitude of the stress intensity (IQ) factors reported in
the figures. In order to gauge the physical meaning of the magnitude of stress intensity
(Ki) values predicted in ABAQUS, results of fracture tests performed in the laboratory by
Zhang (2000) were consulted. The rate of crack growth was used to compare the physical
significance of IQ computed analytically.
Fracture tests performed in the laboratory determined the crack growth rate
(da/dN) for any given stress intensity factor (IQ) for Superpave fine and coarse mixtures,
at a given temperature of 10°C (Zhang 2000). The magnitude of IQ predicted using finite
element analysis ranged approximately from 29 to 288 psi(in)l/2 [1 to 10 MPa(mm)1/2].

170
T ire
Position
n g n n
Center) of
Wheel ' Path
â–º x
(a) Normal Position of Tire in Wheel Path
(b) Critical Load Distribution For Short Cracks
(c) Critical Load Distribution For Intermediate Cracks
Figure 6.2: Transverse Distribution of Load Within Wheel Path and Critical Load
Positions For Pavements For a 4-inch Asphalt Concrete Layer of Uniform Stiffness.

171
T ire
P os it i o n
n rj n n
Center
Wheel
of
Path
(a) Normal Position of Tire in Wheel Path
(b) Critical Load Distribution For Short Cracks
(c) Critical Load Distribution For Intermediate Cracks
Figure 6.3: Transverse Distribution of Load Within Wheel Path and Critical Load
Positions For Pavements For an 8-inch Asphalt Concrete Layer of Uniform
Stiffness.

172
Tire
Position
ZA
â–¡ â–¡â–¡ n
=*x-
Center of
Wheel Path
Case 2 Sharp Surface Gradient * , Kl2
Case 3 Highest Temperature O , Kl3
Differential Throughout Depth
Case 4 Sudden Rain Hardening O , Kl.
(a) Normal Position of Tire in Wheel Path and Stiffness Gradient Cases
(b) Critical Load Distribution For Short Cracks
(c) Critical Load Distribution For Intermediate Cracks
Figure 6.4: Effect of Temperature-Induced Stiffness Gradients on Transverse
Distribution of Load Within Wheel Path and Critical Load Positions For
4-inch Pavement.

Tire
Position
â–¡.nan
173
x
Center of
Wheel Path 3®
Case 2 Sharp Surface Gradient * ,
Case 3 Highest Temperature I I â– 
Differential Throughout Depth
Case 4 Sudden Rain Hardening O , Kl4
(a) Normal Position of Tire in Wheel Path and Stiffness Gradient Cases
I
I
(c) Critical Load Distribution For Intermediate Cracks
Figure 6.5: Effect of Temperature-Induced Stiffness Gradients on Transverse
Distribution of Load Within Wheel Path and Critical Load Positions For
8-inch Pavement.

174
The da/dN for both Superpave fine and coarse mixtures were extracted from Zhang’s
(2000) data for Ki values of 172, 201, 230, and 259 psi(in)1/2 [6, 7, 8, and 9 MPa(mm)’/2].
Table 6.1 presents the rate of crack growth (in inches per 10,000 cycles) for higher-level
stress intensities required for propagating surface cracks.
Table 6.1: Rate of Crack Growth For Given K-value From Fracture Tests
Performed on Laboratory Specimens.
Superpave
Mixture
Stress Intensity Factor K, (psi (in)1/2)
K, = 172
o
(N
II
£
Ki =230
=259
Fine
0.354 in
per 10,000 eye
0.63 in
per 10,000 eye
1.1 in
per 10,000 eye
1.57 in
per 10,000 eye
Coarse
1.57 in
per 10,000 eye
3.15 in
per 10,000 eye
7.87 in
per 10,000 eye
15.75 in
per 10,000 eye
The data clearly indicates that as the magnitude of Ki increases, da/dN increases. Further
observation of the table indicates that the rate of crack growth is faster for a coarse
Superpave mixture than for a fine Superpave mixture. For example, at a K¡ of 201
(metric, Ki = 7), the cracking rate is 3.15 inches for 10,000 cycles in the coarse Superpave
mix and 0.63 inch for the same number of cycles in the fine Superpave mix. The rate of
crack growth was also found to be faster in an 8-inch asphalt concrete pavement than in a
thinner 4-inch pavement. Observation of the table indicates that crack growth rates are
significant for the Mode I stress intensity factors (Ki) computed analytically in ABAQUS.
Computations of direction of crack growth can be used to explain what is being
observed in the field sections. The direction of crack growth may be visualized as a

175
function of load spectra and various crack lengths. Figure 6.6 illustrates an example of
the directional change in crack growth as crack length increases for shorter crack lengths.
At shorter crack lengths, propagation is driven purely by tension and the crack grows
straight down into the pavement. However Figure 6.7 shows that at intermediate depths,
the crack changes direction since the stress states within the asphalt layer change with
depth. Observation of Figure 5.21 indicates that computed crack direction confirm field
observations.
The potential for crack growth as defined by Mode I stress intensity factors will
vary, even if the traffic is the same, because of crack length and the number of loads
resulting from wander in the wheel path.
6.3 Implications of Time on Cracking
Finite element analyses were conducted to identify the effects of pavement
structural and temperature characteristics on crack growth. Computed fracture stress
intensities varied significantly with crack length. This observation appears to validate the
field cores that exhibit cracking down to a certain depth and then ceases, as shown in
Figure 6.8, although some cores exhibited cracking throughout the entire asphalt concrete
depth. For purposes of predicting crack growth in the field, it appears to be of interest to
seek an alternative way to view distributions of stress intensity with crack length. This
may be accomplished by translating Ki versus crack length into time. That way, for a

Pure
Mode I
Extracted
Core
id • d
1
f Short
Crack
Figure 6.6: Example Field Section and Core Exhibiting Short Crack: Pure Tensile
Failure Mechanism.

177
Load
-
Principal Plane Changes with Crack
\ * Length and Stiffness Gradient
\e - 20°- 40°
Extracted
Core
Intermediate
Crack
Figure 6.7: Example Field Section and Core Exhibiting Intermediate or Deep
Crack: Tensile Failure Mechanism and Directional Change in Crack Growth.

178
Figure 6.8: Field Core Showing Longitudinal Wheel Path Crack Opened At Surface
From Florida Interstate 1-10.

179
given load spectra, a conceptual plot of crack growth with increasing crack length may be
formulated.
For a given load spectra, the potential of cracking will vary with crack length.
The preceding section introduced the implications of load wander, and how often those
loads may occur within the wheel path. Based on that information, cracking may be
expected to slow at intermediate crack lengths since a fewer number of loads will result
in tensile stresses significant enough to drive the crack (see Figures 6.5 and 6.7).
Consequently, a conceptual “time of low crack growth activity” could be defined for each
individual pavement depending heavily on recorded load wander, pavement structure, and
seasonal temperatures. Further definition of this concept then leads to development of an
approach to pavement management that can help to determine when to perform
rehabilitation.
The rate of crack growth, as defined by the Mode I stress intensity factor Ki, is
shown as a function of increased crack length in Figure 6.9 for an 8-inch pavement with
the load centered 30 inches from the crack. The figure clearly shows a slowing of the rate
of crack growth between crack lengths of 0.25 and 0.75 inch. Figure 6.10 presents the
rate of crack growth with crack length for a 4-inch pavement with the load centered 25
inches from the crack. Conceptual translation of the distributions to time illustrates the
portion of slow crack growth, indicating potential time available for identification of
severity of surface cracks and possible rehabilitation (e.g., mill and replace methods).
Use of an approach similar to this may allow for cracks to develop to a certain
intermediate length, specific to the defined “time of low crack growth activity” and other

180
characteristics; however, before the crack exceeds this intermediate length and the rate of
cracking begins to increase, pavement rehabilitation may be employed. More detailed
Figure 6.9: Potential For Crack Growth and Time Available For Identification and
Rehabilitation For 8-inch Pavement and Given Load Spectrum.

181
Figure 6.10: Potential For Crack Growth and Time Available For Identification
and Rehabilitation For 4-inch Pavement and Given Load Spectrum.

182
calculations are needed, but may imply that it is critical to rehabilitate the pavement early
in the cracking process depending on the time available before the crack rate speeds up
again.
6.4 Summary
An enormous amount of data resulted from the analyses performed for this
project, and it was demonstrated how the information could be potentially used in
practice. The mechanism for longitudinal wheel path cracking will develop only under
critical conditions. Therefore, understanding the potential implications of the critical
factors and their relationship to field performance is the key to designing less crack-
susceptible pavements.

CHAPTER 7
FINDINGS AND CONCLUSIONS
7.1 Findings
Surface-initiated longitudinal wheel path cracking has become the prevailing
mode of failure among the world’s flexible pavements and as of yet, has remained
relatively unexplored and unexplained. It may be concluded that designing and analyzing
pavements using the current approach that employs averaged pavement conditions and
ESALs will neither predict nor address longitudinal wheel path cracks that initiate and
grow down from the surface. The results of this research confirmed that existing design
and evaluation methods based upon averaged conditions are inadequate for predicting this
type of surface cracking. It was proven that the propagation of surface-initiated
longitudinal cracks advances only under critical conditions. The mechanism for crack
development is highly dependent on load spectra (magnitude and position) and
differential pavement temperature gradients. Neither factor is addressed in the
conventional approach to pavement analysis; therefore, an alternative approach to
designing and rehabilitating pavements should be formulated, or the existing approach
adjusted, to include surface-initiated longitudinal wheel path cracks.
183

184
Finite element analysis of a cracked pavement was conducted to define the critical
design conditions at which crack growth will occur and several pavement structural
factors were varied to determine the effects crucial to crack propagation. Factors
conducive to inducing crack growth were identified and must include measured tire
contact stresses and load wander, presence of a crack, introduction of temperature-
induced stiffness gradients in the asphalt concrete layer, and variable pavement structure.
Without including all of these factors, and neglecting the critical conditions by using
averaged conditions described in traditional approaches, the propagation of surface
cracking cannot be predicted or explained.
The use of fracture mechanics was employed and evaluated for the analysis of
surface-initiated longitudinal crack growth. Stress intensities descriptive of crack tip
conditions were predicted and helped to define the local effects of various factors on
crack growth. When evaluating a physical crack in the pavement, fracture mechanics is a
suitable method for prediction of cracking mechanism. It is recommended that creation
of a database of fracture data from the analytical pavement evaluation study be combined
with crack growth rate data from laboratory studies (Zhang 2000) to form the basis of a
comprehensive pavement performance model.
The primary cause of the initiation of longitudinal wheel path surface cracking
appeared to be the generation of high tensile stresses underneath the treads of radial and
wide-base (Supersingle) radial truck tires. Thermal stresses contributed to the initiation
mechanism as a secondary factor. The tension predicted near the surface of a continuum
pavement was reportedly unaffected by pavement structure (Myers 1997). However once
a crack is initiated, the failure mechanism changes and other factors become crucial. The

185
main mechanisms for crack propagation depend on load spectra (magnitude and position),
stiffness gradients in the asphalt concrete, and pavement structure. Thus, when
addressing the development and propagation of surface cracking, it is important to obtain
sufficient information on the pavement structure and seasonal temperatures, as well as
consider material alteration by using more fracture-resistant asphalt mixtures.
Often times, the method for repairing pavements exhibiting surface-initiated
longitudinal wheel path cracks involves overlaying the asphalt concrete structural layer.
As seen in the analyses, the cracking potential for surface-initiated longitudinal wheel
paths was found to be exacerbated in thicker asphalt concrete pavements, indicating that
perhaps this method may not be the most effective or helpful technique. Since the
potential for crack growth was lessened in thinner pavements underlain with a stiff base
course, it may be concluded that altering the existing method for rehabilitation by
implementing milling and replacing techniques will keep the layer thinner and hinder
crack growth. Additional research may be required to determine the minimum asphalt
concrete layer thickness required to adequately protect the base course.
Tire structure was found to have a significant influence on contact stresses; in
fact, stress states induced by radial and wide base radial tires were determined to be more
instrumental in inducing damage to the pavement’s surface than stress states induced by
bias ply tires. The primary difference lies in lateral contact stresses, rather than in vertical
stresses, that develop under each type of tire. Measured tire-pavement interface stresses,
including lateral stresses, are a crucial factor that must be considered for an appropriate
evaluation of pavement cracking performance. The use of vertical stress distributions
alone, even when combined with nonuniform vertical stress distributions, will not capture

186
this critical mode of failure. For this reason, analyses performed to define the
propagation mechanism must include measured tire contact stresses as the load.
The effects of stiffness gradients (induced by temperature gradients or aging)
contribute significantly in intensifying the mechanism. Inducing a temperature gradient
produces higher tensile stress intensities in the asphalt concrete for all stages of crack
growth, as compared to a case of a cracked pavement with uniform stiffness throughout
the layer. Recent research tied thermal cooling to the inducing of tension at the pavement
surface and was recommended for further exploration in the future (Merrill 2000).
7.2 Conclusions
Conclusions from this study may be summarized as follows:
• It is necessary to utilize methods that consider discontinuities by modeling the
physical characteristics of cracks to identify critical conditions, predict stress
redistributions, and compute direction of crack growth that lead to surface-initiated
crack propagation.
• Surface-initiated longitudinal wheel path crack propagation was primarily a Mode I
tensile failure mechanism. Shear stresses may contribute slightly to conditions at the
crack tip, but clearly doesn’t appear to control crack growth. Tension predicted at the
crack tip offered an explanation for cracking observed in the field.
• Analyzing crack growth with realistic load spectra (magnitude and position) is critical
to predicting pavement performance, as load positioning was found to be the
overriding contributor to crack propagation. Load wander must be considered for
predicting failure and is critical in determining future design conditions.
• Factors such as crack length and temperature-induced stiffness gradients in the asphalt
concrete layer had significant effects on the tensile response of surface cracks, and
therefore must be included in the approach to pavement design.

187
• Development of a sensitivity analysis for the rate of crack growth relative to time can
be adopted as a strategy for pavement management. From a pavement management
standpoint, a period of time can be defined, at intermediate crack lengths, in which
the crack rate slows down. However further work and additional field and mixture
information would be needed to define the length of time when cracking slows down,
in order to establish guidelines for pavement management.

CHAPTER 8
RECOMMENDATIONS
Based on the findings, it may be concluded that analyzing the physical presence of
a crack, as well as variable load and pavement structure, had a significant effect on
asphalt pavement response by capturing stress redistributions local to the crack tip. An
explanation for the mechanism of surface crack propagation was defined; however, the
study should be extended to include effects of thermal stresses, deeper cracks, and other
loading conditions, such as loading on a graded surface or superelevated road, on the
response of surface cracks in highway pavements.
The mechanism for crack growth was determined, and it is further recommended
that a pavement performance model be developed using the results provided from this
study. A performance model would assist pavement engineers in designing proper
asphalt mixtures that resist this type of fracture development. Pavement responses can be
predicted by defining the mixture characteristics and material properties, along with
pavement structural characteristics and load spectra, beforehand and then entering them
into a performance model that would possibly simulate the development and propagation
of surface-initiated longitudinal wheel path cracks.
188

189
The rehabilitation of pavement sections plagued with surface-initiated
longitudinal wheel path cracks is costly and failure is often premature for the designed
pavement life. Some preventive procedures may be employed to avoid full-scale
rehabilitation. For pavements without surface treatments, or existing pavements with
cracks, development and use of nondestructive testing techniques may be employed to
monitor crack growth and define crack length. Cores extracted from the wheel paths can
be used to identify mixture properties and help to define the remaining pavement life.
Knowing the pavement structural characteristics and temperatures relating to the time of
season, and using a procedure similar to the rate of crack growth suggested in Chapter 6,
the time available for identification and expected rehabilitation can be assessed.
However, the procedure would depend on the traffic wander and type of traffic vehicles
(i.e., mostly automobiles or heavily trucked).
Because the cracking mechanism for propagation depends so much on load
spectra, data on the lateral range of load wander and frequency of loads in that range
should be investigated and provided. Data of load wander in and out of the wheel paths
found in a field study may help to statistically calculate which positions the load hits most
often. This data may then assist in gauging the appropriate time when to take
rehabilitative measures.
Once cracking in the pavements is investigated and appears to be initiated at the
surface, field personnel from the Florida Department of Transportation may commence
observation of damaged pavement sections. Using the information provided on identified
critical conditions, monitoring of cracked sections would indicate when the pavement
should be cored or trenched before full-scale rehabilitation is required.

190
Another option for preventing growth of surface cracks would be implementation
of a surface layer or overlay. Again, the type of surfacing layer would depend on the
pavement structure and critical conditions expected for the section under evaluation. It is
recommended that the surface layer be at least 0.5 inch thick (up to 1.0 inch thick,
depending on the pavement section) and designed to have a high resistance to tension. A
modified mixture may be used, ensuring stress relief within the friction coarse. An
example of a highly-resistive additive may include Novachip.
Another potential idea for preventing propagation of surface cracks includes
laying a polymer-modified interlayer approximately 0.75 to 1.5 inches thick (again,
depending on the characteristics of the pavement structure) between the asphalt structural
layer and a normal overlain friction course. The reasoning behind the idea is that the
surface of the friction coarse will eventually crack and begin to ravel anyway, but use of a
highly-modified interlayer may prolong the structural layer’s performance life. This
procedure may then help to avoid full-depth replacement of the pavement and abate the
propagation of surface cracks into the structural layer.

APPENDIX A
SAMPLE CALCULATION OF STRESS INTENSITY FACTORS (Ki and K„)

K, for Loads Positioned 0, 7, 20" away from 0.5" crack
8 in pavement - Stiffness Gradient Case 2
Distance from crack tip, r (in)
Figure A.l: Distribution of Transverse Stresses Computed At Increasing Vertical
Distance From 0.5-in Crack: 8-in Asphalt Concrete, Stiffness Gradient Case 2,
Load Positioned At 0, 7, and 20 inches From Crack.
K2 for Loads Positioned 0, 7, 20" away from 0.5" crack
8 in pavement - Stiffness Gradient Case 2
Figure A.2: Distribution of Shear Stresses Computed At Increasing Vertical
Distance From 0.5-in Crack: 8-in Asphalt Concrete, Stiffness Gradient Case 2,
Load Positioned At 0, 7, and 20 inches From Crack.
192

K, for Loads Positioned 25" away from 0.5" crack
8 in pavement - Stiffness Gradient Case 2
Distance from crack tip, r (in)
Figure A.3: Distribution of Transverse Stresses Computed At Increasing Vertical
Distance From 0.5-in Crack: 8-in Asphalt Concrete, Stiffness Gradient Case 2,
Load Positioned At 25 inches From Crack.
K2 for Loads Positioned 25" away from 0.5" crack
8 in pavement - Stiffness Gradient Case 2
Figure A.4: Distribution of Shear Stresses Computed At Increasing Vertical
Distance From 0.5-in Crack: 8-in Asphalt Concrete, Stiffness Gradient Case 2,
Load Positioned At 25 inches From Crack.
193

K, for Loads Positioned 30" away from 0.5" crack
8 in pavement • Stiffness Gradient Case 2
Distance from crack tip, r (in)
Figure A.5: Distribution of Transverse Stresses Computed At Increasing Vertical
Distance From 0.5-in Crack: 8-in Asphalt Concrete, Stiffness Gradient Case 2,
Load Positioned At 30 inches From Crack.
K2 for Loads Positioned 30" away from 0.5" crack
8 in pavement - Stiffness Gradient Case 2
Figure A.6: Distribution of Shear Stresses Computed At Increasing Vertical
Distance From 0.5-in Crack: 8-in Asphalt Concrete, Stiffness Gradient Case 2,
Load Positioned At 30 inches From Crack.
194

APPENDIX B
STRESS INTENSITY FACTOR (K, and K„) DATA

Table B.l: Stress Intensity Factors Predicted in ABAQUS For Uniform Stiffness 4-
inch Pavement Layer With Low Stiffness Base (E2=20 ksi).
Wide Rib Centered over Crack
E1=800ksi
Crack length
K1
K2
(in)
psi (in) 0 5
psi (in)0 5
0.25
0
-9
0.5
0
-8
0.75
0
-20
1
0
-30
1.5
0
-45
Load 7" away
E1=800ks
Crack length
K1
K2
(in)
psi (in) 0 5
psi (in)0 5
0.25
20
-4.5
0.5
0
-3
0.75
15
-10
1
0
-21
1.5
0
-30
Load 15" awaj
/
E1=800ksi
Crack length
K1
K2
(in)
psi (in)0 5
psi (in)0 5
0.25
25
-0.3
0.5
22
-0.8
0.75
16
-1.5
1
0
-2
1.5
39
-5
Load 20" away
!
E1=800ks
Crack length
K1
K2
(in)
psi (in) 0 5
psi (in) 0 5
0.25
19
-2
0.5
18
-1
0.75
0
-0.3
1
8
0
1.5
0
-1
Load 25" away
E1=800ksi
Crack length
K1
K2
(in)
psi (in) 0 5
psi (in)0 5
0.25
67
-5
0.5
82
-8
0.75
100
-9.5
1
115
-11
1.5
80
-10.5
196

Table B.2: Stress Intensity Factors Predicted in ABAQUS For Uniform Stiffness 4-
inch Pavement Layer With High Stiffness Base (E2=44 ksi).
Wide Rib Centered over Crack
E1=800ksi
Crack length
K1
K2
(in)
psi (in) 0 5
psi (in)0 5
0.25
0
-11
0.5
0
-6.5
0.75
0
-21
1
0
-20
1.5
0
-50
Load 7" away
E1=800ks
Crack length
K1
K2
(in)
psi (in) 0 5
psi (in)05
0.25
45
-4
0.5
18
-1.5
0.75
35
-10
1
0
-18
1.5
0
-25
Load 15" awa]
t
E1=800ksi
Crack length
K1
K2
(in)
psi (in) 0 5
psi (in)0 5
0.25
10
-1
0.5
9.5
-0.3
0.75
0
-0.5
1
0
-5
1.5
16
-2
Load 20" away
f
E1=800ks
Crack length
K1
K2
(in)
psi (in)0 5
psi (in)0 5
0.25
0
0.5
0.5
0
-1.8
0.75
0
-0.1
1
0
-2
1.5
0
-0.25
Load 25" away
E1=800ksi
Crack length
K1
K2
(in)
psi (in) 0 5
psi (in) 0 5
0.25
20
-3.8
0.5
32
-5.2
0.75
42
-8.3
1
60
-10
1.5
0
-14
197

Table B.3: Stress Intensity Factors Predicted in ABAQUS For 4-inch Pavement
Layer With Stiffness Gradients and Low Stiffness Base (E2=20 ksi).
Wide Rib Centered over Crack
Stiffness
Wide Rib Centered over Crack
Stiffness
Wide Rib Centered over Crack
Stiffness
Crack length
K1
K2
Gradient
Crack length
K1
K2
Gradient
Crack length
K1
K2
Gradient
(in)
psi (in)01
psi (in)05
Case 2
(in)
psi (in)01
psi (in)05
Case 3
(in)
psi (in)01
psi (in)01
Case 4
0.25
0
-12
0.25
0
-10.5
025
0
-13.5
0.5
0
-15
0.5
0
-17
0.5
0
-14.5
0.75
0
-23
0.75
0
-29
0.75
0
-21
1
0
-27
1
0
-35
1
0
-28
1.5
0
-37
1.5
0
-57
1.5
0
-40
Load 7" away
Case 2
Load 7" away
Case 3
Load 7" away
Case 4
Crack length
K1
K2
Crack length
K1
K2
Crack length
K1
K2
(in)
psi (in)01
psi (in)01
(in)
psi (in)01
psi (in)01
(in)
psi (in)01
psi (in)01
0.25
0
-3
0.25
48
-4
0.25
20
-12
0.5
0
-7
0.5
0
-7
0.5
0
-6
0.75
0
-15
0.75
0
-15
0.75
0
-10.5
1
0
-20
1
0
-16
1
0
-15
1.5
0
-25
1.5
0
-28
1.5
0
-16
Load 15" awa
Case 2
Load 15" awa
Case 3
Load 15" awa)
Case 4
Crack length
K1
K2
Crack length
Ki
K2
Crack length
KI
K2
(in)
psi (in)05
psi (in)01
(in)
psi (in)0 5
psi (in)01
(in)
psi (in)01
psi (in)01
0.25
38
-2.5
0.25
55
-1.5
0.25
28
-3.5
0.5
35
-3
0.5
58
-4
0.5
23
-3
0.75
24
-5
0.75
25
-5
0.75
14
-2
1
0
1
1
0
12
1
0
2.5
1.5
41
-9
1.5
37
-5
1.5
30
-5.5
Load 20" awa
Case 2
Load 20" away
Case 3
Load 20" away
Case 4
Crack length
K1
K2
Crack length
K1
K2
Crack length
K1
K2
(in)
psi (in)01
psi (in)0 5
(in)
psi (in)01
psi (in)01
(in)
psi (in)01
psi (in)01
0.25
65
-2.7
0.25
65
-2
0.25
38
-1
0.5
55
-3.4
0.5
66
-3
0.5
30
-1.5
0.75
15
-2.5
0.75
0
1
0.75
0
0
1
55
-3.5
1
24.5
-3
1
8.5
-0.4
1.5
13
â– A
1.5
0
-0.5
1.5
0
-0.2
Load 25" awa)
Case 2
Load 25" awa
t
Case 3
Load 25" away
Case 4
Crack length
K1
K2
Crack length
K1
K2
Crack length
K1
K2
(in)
psi fin)01
psi (in)01
(in)
psi (in)01
psi (in)01
(in)
psi fin)01
psi (in)01
0.25
100
-5
0.25
118
-5.5
0.25
70
-2
0.5
90
-5.7
0.5
120
-6.5
0.5
58
-3
0.75
95
-3
0.75
104
-4.8
0.75
65
-2.5
1
185
-7
1
220
-10
1
150
-4
1.5
89
-2.5
1.5
50
-2
1.5
45
-1.8
198

Table B.4: Stress Intensity Factors Predicted in ABAQUS For 4-inch Pavement
Layer With Stiffness Gradients and High Stiffness Base (E2=44 ksi).
Wide Rib Centered over Crack ¡ Stiffness
Wide Rib Centered over Crack
Stiffness
¡Wide Rib Centered over Crack
Stiffness
Crack length
K1
K2
Gradient
Crack length
K1
K2
Gradient
! Crack length
K1
K2
Gradient
(in)
psi (in)"
psi (in)"
Case 2
(in)
psi (in)06
psi (in)0 5
Case 3
(in)
psi (in)"
psi (in)"
Case 4
0.25
0
-7
0.25
0
-9
0.25
0
-10
0.5
0
-12
0.5
0
-15
0.5
0
-12.8
0.75
0
-20
0.75
0
-25
0.75
0
-20
1
0
-29
1
0
-36
1
0
-27
1.5
0
-40
1.5
0
-61
1.5
0
-41
Load T away
Case 2
Load 7" away
Case 3
Load T away
Case 4
Crack length
K1
K2
Crack length
K1
K2
Crack length
K1
K2
(in)
psi (in)"
psi (in)"
(in)
psi (in)0 6
psi (in)"
(in)
psi (in)"
psi (in)"
0.25
25
-3
0.25
95
-5
025
48
-6
0.5
0
-5
0.5
47
-5
0.5
20
-7
0.75
12
-10
0.75
65
-12
0.75
32
-9
1
0
-15
1
0
-24
1
0
-11
1.5
0
-20
1.5
0
-23
1.5
0
-15
Load 15" awa
Case 2
Load 15" awa
y
Case 3
Load 15" awav
Case 4
Crack length
K1
K2
Crack length
K1
K2
Crack length
K1
K2
M
PSÍ (in)"
psi (in)"
(in)
psi (in)"
psi (in)0 5
(in)
psi (in)"
psi (in)"
0.25
29
-2
0.25
37
-1
025
15
-2
0.5
27
-2
0.5
35
-2
05
13
-2.3
0.75
16
-2.5
0.75
13
-3.5
0.75
4
-1
1
0
5
1
0
10
1
0
3
1.5
35
-8
15
24
-4
1.5
18
-2
Load 20" awa
Case 2
Load 20" awa
Case 3
Load 20" awav
Case 4
Crack length
K1
K2
Crack length
K1
K2
Crack length
K1
K2
(in)
PSI (in)"
psi (in)"
(in)
psi (in)01
psi (in)06
(in)
psi (in)"
psi (in)"
0.25
38
2
0.25
39
-2
0.25
24
-0.8
0.5
36
-2
0.5
37
-5
0.5
17
-2
0.75
0
-0.4
0.75
0
1
0.75
0
-0.4
1
24
-2.5
1
0
-0.8
1
0
-1
1.5
0
-1.5
1.5
0
0
1.5
0
-0.8
Load 25" away
Case 2
Load 25" awa
Case 3
Load 25" away
Case 4
Crack length
K1
K2
Crack length
K1
K2
Crack lenqth
K1
K2
(in)
psi (in)06
psi (in)"
(in)
psi (in)"
psi (in)"
(in)
psi (in)"
psi (in)"
0.25
78
-4
0.25
95
-5
0.25
62
-2.5
0.5
75
-4.5
0.5
105
-6
0.5
50
-1.8
0.75
93
-4 8
0.75
99
-5
0.75
59
-3
1
160
-75
1
200
-12
1
133
-5
1.5
86
-6
1.5
48
-3
1.5
39
-5
—
199

Table B.5: Stress Intensity Factors Predicted in ABAQUS For Uniform Stiffness 8-
inch Pavement Layer With Low Stiffness Base (E2=20 ksi).
Wide Rib Centered over Crack
E1=800ksi
Crack length
K1
K2
(in)
psi (in)0 5
psi (in)0 5
0.25
69
9
0.5
71
9
0.75
0
8
1
0
24
1.5
0
15
Load 7" away
E1=800ksi
Crack length
K1
K2
(in)
psi (in)0 5
psi (in)0 5
0.25
0
3
0.5
0
3
0.75
0
6
1
0
0
1.5
0
25
Load 20" awaj
/
E1=800ksi
Crack length
K1
K2
(in)
psi (in)05
psi (in)0 5
0.25
3.2
1
0.5
50
6
0.75
28
3
1
0
0
1.5
25
9
Load 25" awaj
\
E1=800ksi
Crack length
K1
K2
(in)
psi (in) 05
psi (in)0 5
0.25
26.5
1
0.5
41
3
0.75
36
3
1
30
6
1.5
62
6
Load 30" away
E1=800ksi
Crack length
K1
K2
(in)
psi (in) 0 5
psi (in) 0 5
0.25
35
2
0.5
68
5
0.75
56
5
1
63
5
1.5
57
8
200

Table B.6: Stress Intensity Factors Predicted in ABAQUS For Uniform Stiffness 8-
inch Pavement Layer With High Stiffness Base (E2=44 ksi).
Wide Rib Centered over Crack
E1=800ksi
Crack length
K1
K2
(in)
psi (in)05
psi (in)05
0.25
72
8
0.5
77
4
0.75
19
2
1
0
23
1.5
0
22
Load 7" away
E1=800ks
Crack length
K1
K2
(in)
psi (in) 0 5
psi (in)05
0.25
0
1
0.5
0
0.5
0.75
12
4
1
0
0
1.5
0
10
Load 20" awa\
/
E1=800ksi
Crack length
K1
K2
(in)
psi (in) 05
psi (in)0 5
0.25
6.8
1
0.5
24
2
0.75
11
3
1
0
0
1.5
0
7.5
Load 25" away
t
E1=800ksi
Crack length
K1
K2
(in)
psi (in) 05
psi (in)05
0.25
23
2.75
0.5
31
2
0.75
28
3
1
30
4
1.5
44
8
Load 30" away
E1=800ksi
Crack length
K1
K2
(in)
psi (in)05
psi (in)0 5
0.25
25
3
0.5
34
3
0.75
39
3
1
45
4
1.5
39
5
201

Table B.7: Stress Intensity Factors Predicted in ABAQUS For 8-inch Pavement
Layer With Stiffness Gradients and Low Stiffness Base (E2=20 ksi).
Wide Rib Centered over Crack
Stiffness
¡Wide Rib Centered over Crack
Stiffness
Wide Rib Centered over Crack
Stiffness
Crack length
K1
K2
Gradient
Crack length
K1
K2
Gradient
Crack length
K1
K2
Gradient
(in)
psi (in)05
psi (in)05
Case 2
(in)
psi (in)05
psi (in)05
Case 3
(in)
psi (in)05
psi (in)05
Case 4
0.25
122
-0.7
0.25
625
-3.5
0.25
164
-7
0.5
66
-5.2
0.5
25
-4
0.5
70
-7.3
0.75
0
-2
0.75
0
-2.5
0.75
0
-13
1
0
5
1
0
3
1
0
5
1.5
0
-31
1.5
0
-45
1.5
0
-34
Load 7" away
Case 2
Load 7" away
Case 3
Load 7" away
Case 4
Crack length
K1
K2
Crack length
K1
K2
Crack length
K1
K2
M
psi (in)05
psi (in)05
(in)
psi (in)05
psi (in)05
(in)
psi (in)05
psi (in)05
0.25
5
-1
0.25
0
-2
0.25
26
-5
0.5
10
-4
0.5
0
-4.5
0.5
16
-5.2
0.75
0
-11
0.75
0
-12.5
0.75
0
-14
1
15
-10.8
1
0
-15
1
26
-9
1.5
0
-27
1.5
0
-45
1.5
0
-31
Load 20" awa
Case 2
Load 20" awa
y
Case 3
Load 20" awa}
Case 4
Crack length
K1
K2
Crack length
K1
K2
Crack length
K1
K2
Sol
psi (in)05
psi (in)05
(in)
psi (in)05
psi (in)05
(in)
psi (in)05
psi (in)05
025
120
-5
0.25
136
-7
025
157
-12
0.5
89
-7
0.5
110
-8
0.5
68
-5.5
0.75
180
-12
0.75
210
-17
0.75
112.5
-9
1
104
-10
1
152
-14
1
81.5
-11
1.5
162.5
-23
1.5
113
-34
1.5
110
-21
Load 25" awa}
Case 2
Load 25" awa
y
Case 3
Load 25" awa}
Case 4
Crack length
K1
K2
Crack length
K1
K2
Crack length
K1
K2
(in)
Psi(in)°5
psi (in)05
(in)
psi (in)05
psi (in)05
(in)
psi (in)05
psi (in)05
0.25
136
-5
0.25
170
-7
0.25
165
-12.5
0.5
100
-5.8
0.5
140
-8
0.5
69
-3.6
0.75
205
-12
0.75
270
-17
0.75
112
-6.5
1
119
-7.5
1
198
-13.5
1
82
-7
1.5
188
-18.5
1.5
187.5
-24
1.5
118
-16
Load 30" awa}
Case 2
Load 30*’ awa
i
Case 3
Load 30" away
Case 4
Crack length
K1
K2
Crack length
K1
K2
Crack length
K1
K2
(in)
psi (in)05
psi (in)05
(in)
psi (in)05
psi (in)05
(in)
psi (in)05
psi (in)05
0.25
108
-3.8
0.25
161
-6
0 25
97
-6.5
0.5
62
-3.3
0.5
108
-7
0.5
35
-2 5
0.75
175
-9
0.75
268
-148
0.75
87.5
-5.5
1
90
-5
1
187
-10
1
57
-4
1.5
159
-11
1.5
160
-17.5
1.5
76.5
-8
202

Table B.8: Stress Intensity Factors Predicted in ABAQUS For 8-inch Pavement
Layer With Stiffness Gradients and High Stiffness Base (E2=44 ksi).
Wide Rib Centered over Crack
Stiffness
Wide Rib Centered over Crack
Stiffness
Wide Rib Centered over Crack
Stiffness
Crack length
K1
K2
Gradient
Crack length
K1
K2
Gradient
Crack length
K1
K2
Gradient
(in)
psi (in)05
psi (in)05
Case 2
(in)
psi (in)05
psi (in)05
Case 3
(in)
psi (in)05
psi (in)05
Case 4
0.25
95
-2.5
0.25
24
-2.5
0.25
139
-8
0.5
50
-5
• 0.5
0
-3.8
0.5
61
-6
0.75
0
-5
0.75
0
-7
0.75
43
-10
1
0
4
1
0
4
1
0
2
1.5
0
-34
1.5
0
-44
1.5
18
-35
Load T' away
Case 2
Load 7” away
Case 3
Load 7" away
Case 4
Crack length
K1
K2
Crack length
K1
K2
Crack length
K1
K2
(in)
psi (in)05
psi (in)05
(in)
psi (in)0 5
psi (in)05
(in)
psi (in)05
psi (in)05
0.25
0
-0.5
0.25
0
0
0.25
0
0
0.5
0
-2
0.5
0
-2
0.5
0
-4
0.75
0
-10.3
0.75
31
-12
0.75
19.8
-10
1
0
-11
1
0
-15
1
0
-9
1.5
0
-26
1.5
0
-35.5
1.5
19.5
-26
Load 20" awa
Case 2
Load 20" away
Case 3
Load 20" awa^
Case 4
Crack length
K1
K2
Crack length
K1
K2
Crack length
K1
K2
(in)
psi (in)05
psi (in)05
(in)
psi (in)05
psi (in)0 5
(in)
psi (in)05
psi (in)05
0.25
103
-4.6
0.25
126
-6
0.25
137
-9
0.5
78
-6
0.5
102
-7
0.5
58
-3
0.75
160
-10
0.75
200
-12.5
0.75
98
-5
1
92
-5.5
1
147
-16
1
69
-6
1.5
147
-16
1.5
111
-25
1.5
95
-14
Load 25" awa
Case 2
Load 25" awa
i
Case 3
Load 25" awa)
Case 4
Crack length
K1
K2
Crack length
K1
K2
Crack length
K1
K2
(in)
psi (in)05
PS (in)05
(in)
psi (in)05
psi (in)05
(in)
psi (in)05
psi (in)05
0.25
113
-3.7
0.25
146
-5
0.25
144
-10
0.5
82
-4.3
0.5
118
-4.7
0.5
56
-2
0.75
170
-8
0.75
225
-13
0.75
89
-4.5
1
96
-5.3
1
172
-10
1
68
-5
1.5
160
-12.8
1.5
150
-17.5
1.5
95
-10.5
Load 30" awa)
Case 2
Load 30" awa
Case 3
Load 30" away
Case 4
Crack length
K1
K2
Crack length
K1
K2
Crack length
K1
K2
(in)
psi (in)05
psi (in)05
(in)
psi (in)05
psi (in)05
(in)
psi (in)05
psi (in)05
0.25
68
-3
0.25
107
-3.8
0.25
75
-5
0.5
36
-2
0.5
65
-3
0.5
15
-2
0.75
120
-6.5
0.75
180
-9
0.75
56.5
-3
1
56.3
-3.2
1
120
-7
1
28
-2.5
1.5
91
-7.5
1.5
100
-11
1.5
39
-6
203

LIST OF REFERENCES
Anderson, T. L., Fracture Mechanics, Fundamentals and Applications, Second Edition,
CRC Press, Inc., Ann Arbor, 1995.
Bonaquist, R., “An Assessment of the Increased Damage Potential of Wide Based Single
Tires,” Proceedings of the Seventh International Conference on Asphalt Pavements,
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August 2000.

BIOGRAPHICAL SKETCH
Leslie Ann Myers was bom in Riverside, New Jersey, on April 23, 1974, to Dr.
Robert W. and Bonnie (Harper) Myers. She graduated from Rancocas Valley Regional
High School in Mt. Holly, New Jersey, in 1992.
Leslie attended Pennsylvania State University and received a Bachelor of Science
degree in civil engineering in 1996. During her undergraduate studies, Leslie worked for
Barba-Arkhon International and Citadel Engineering and Construction Consultants, both
engineering and construction claims firms in southern New Jersey. Leslie also worked as
an undergraduate research assistant at the Pennsylvania Transportation Institute in State
College, Pennsylvania.
Leslie continued on to complete her Master of Engineering degree from the
University of Florida. The focus of her research was analytical studies of asphalt concrete
materials and pavement systems. Leslie is currently completing a Ph.D. in civil
engineering at the University of Florida with a specialization in pavement materials and
design.
208

I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and quality,
as a thesis for the degree of Doctor of Philosophy.
lZ¿c Uytfdc
Reynaldo Roque, Chairman
Professor of Civil Engineering
I certify that 1 have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and quality,
as a thesis for the degree of Doctor of Philosophy.
^ - &ürfZ
Byron fe. Ruth. Cochairman
Professor Emeritus of Civil Engineering
I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and quality,
as a thesis for the degree of Doctor of Philosophy.
3joitfi Birgisson J
Bjo
Assistant Professor of Civil Engineering
1 certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and quality,
as a thesis for the degree of Doctor of Philosophy.
Mang Tia
Professor of
Engineering
I certify' that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and quality,
as a thesis for the deuree of Doctor of Philosophy.
Bhavani Sankar
Professor of Aerospace Engineering,
Mechanics, and Engineering Science

This thesis was submitted to the Graduate Faculty of the College of Engineering
and to the Graduate School and was accepted as partial fulfillment of the requirements for
the degree of Doctor of Philosophy.
December 2000
M. J. Ohanian
Dean. College of Engineering
Winfred M. Phillips
Dean, Graduate School

UNIVERSITY OF FLORIDA
3 1262 08555 3799




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