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DEVELOPMENT AND PROPAGATION OF SURFACEINITIATED 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 tirepavement 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 TwoDimensional 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 3.3.31 Definition of Bending Stress Ratio ...................................................... 71 3.3.32 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 ConcretetoBase 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 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 RECOMM ENDATIONS ....................................................................... 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 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 Kvalue From Fracture Tests Performed on Laboratory Specimens ........................................................174 B. 1 Stress Intensity Factors Predicted in ABAQUS For Uniform Stiffness 4inch Pavement Layer With Low Stiffness Base (E2=20 ksi)........................ 196 B.2 Stress Intensity Factors Predicted in ABAQUS For Uniform Stiffness 4inch Pavement Layer With High Stiffness Base (E2=44 ksi) ....................... 197 B.3 Stress Intensity Factors Predicted in ABAQUS For 4inch Pavement Layer With Stiffness Gradients and Low Stiffness Base (E2=20 ksi)....................... 198 B.4 Stress Intensity Factors Predicted in ABAQUS For 4inch Pavement Layer With Stiffness Gradients and High Stiffness Base (E2=44 ksi)...................... 199 B.5 Stress Intensity Factors Predicted in ABAQUS For Uniform Stiffness 8inch Pavement Layer With Low Stiffness Base (E2=20 ksi)....... ...... ....... 200 B.6 Stress Intensity Factors Predicted in ABAQUS For Uniform Stiffness 8inch Pavement Layer With High Stiffness Base (E2=44ksi) ......................201 vi B.7 Stress Intensity Factors Predicted in ABAQUS For 8inch Pavement Layer With Stiffness Gradients and Low Stiffness Base (E2=20 ksi) ............................ 202 B.8 Stress Intensity Factors Predicted in ABAQUS For 8inch Pavement Layer With Stiffness Gradients and High Stiffness Base (E2=44 ksi) ............................ 203 vii 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 VehicleRoad Surface Pressure Transducer Array (VRSPTA) System Used to Measure Tire Contact Stresses (after de Beer et al. 1997) .............. 22 2.5 Threedimensional 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 CrossSection 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 4in Pavement System: Stiffness Ratio of 4.6 (E1 = 200 ksi, E2 =44 ksi)............................................................. 44 3.6 Transverse Stresses Predicted at Surface of 4in Pavement System: Stiffness Ratio of 4.6 (B1 = 200 ksi, B2 = 44 ksi).......................................................... 45 3.7 Vertical Stresses Predicted at Surface of 4in Pavement Systemn:. Stiffness Ratio of 39.4 (El1 800 ksi, B2 = 20 ksi) ......................................................... 46 3.8 Transverse Stresses Predicted at Surface of 4in Pavement System: Stiffness Ratio of 39.4 (Bl = 800 ksi, E2 =20 ksi) ........................................................ 47 3.9 Vertical Stresses Predicted at Surface of 4in Pavement System: Stiffness Ratio of 10.0 (B1 = 200 ksi, B2 = 20 ksi)........................................................... 48 3.10 Transverse Stresses Predicted at Surface of 4in Pavement System: Stiffness Ratio of 10.0 (El 200 ksi, E2 = 20 ksi) ........................................................ 49 3.11 Vertical Stresses Predicted at Surface of 4in Pavement System: Stiffness Ratio of 18.0 (Bl = 800 ksi, B2 = 44 ksi) ........................................................... 50 3.12 Transverse Stresses Predicted at Surface of 4in Pavement System: Stiffness Ratio of 18.0 (Bl = 800 ksi, B2 = 44 ksi)........................................................ 51 3.13 Vertical Stresses Predicted at Surface of 2in Pavement System: Stiffness Ratio of 4.6 (El = 200 ksi, E2 =44 ksi) ............................................................ 53 3.14 Transverse Stresses Predicted at Surface of 2in Pavement System: Stiffness Ratio of 4.6 (B1 = 200 ksi, E2 = 44 ksi).......................................................... 54 3.15 Vertical Stresses Predicted at Surface of 2in Pavement System: Stiffness Ratio of 39.4 (El = 800 ksi, B2 = 20 ksi) ......................................................... 55 3.16 Transverse Stresses Predicted at Surface of 2in Pavement System: Stiffness Ratio of 39.4 (E1 = 800 ksi, E2 = 20 ksi) ........................................................ 56 3.17 Vertical Stresses Predicted at Surface of 2in Pavement System: Stiffness Ratio of 10.0 (E1 = 200 ksi, B2 = 20 ksi)........................................................... 57 3.18 Transverse Stresses Predicted at Surface of 2in Pavement System: Stiffness Ratio of 10.0 (E1 = 200 ksi, B2 = 20 ksi) ........................................................ 58 ix 3.19 Vertical Stresses Predicted at Surface of 2in Pavement System: Stiffness Ratio of 18.0 (El = 800 ksi, E2 = 44 ksi) ........................................................... 59 3.20 Transverse Stresses Predicted at Surface of 2in Pavement System: Stiffness Ratio of 18.0 (E1 = 800 ksi, E2 = 44 ksi) ...................................................... 60 3.21 Schematic of Axisymmetric and 2D 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 4in Asphalt Concrete Layer for Stiffness Ratio of 4.6 (Ej = 203 ksi : E2 = 44 ksi) ....................................... 69 3.24 Transverse Stress Distribution Along Bottom of 8in 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 TwoStep Approach to Finite Element Modeling of Pavement. ...90 3.33 Example of Spring Constant Computation Used For Application of Boundary Conditions to 4inch 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 4inch 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 4inch 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: 8inch 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 4inch 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 4inch 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 4inch Surface Layer and High Stifftiess (EI/E2 = 800:44.5 ksi) Ratio ...................................................... 124 xi 4.17 Effect of Load Positioning on Shearing At the Crack Tip For a 4inch 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 8inch 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 8inch 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 8inch 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 8inch 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 AC30 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 TemperatureInduced Stiffness Gradients on Stress Intensity K, Predicted At the Crack Tip For 8inch Asphalt Concrete (Load Centered 30 in From Crack). 147 5.8 Effect of TemperatureInduced Stiffness Gradients on Stress Intensity K11 Predicted At the Crack Tip For 8inch Asphalt Concrete (Load Centered 30 in From Crack). 148 xii 5.9 Effect of TemperatureInduced Stiffness Gradients on Transverse Stress Distribution Within 8inch 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 4inch Asphalt Pavement (Load Centered 25 in From Crack) ........................................................ 151 5.12 Illustration of Effects of Stiffness Gradients on Crack Propagation in 8inch Asphalt Pavement (Load Centered 30 in From Crack) ........................................................ 153 5.13 Effects of Stiffness Gradients and Base Layer Stiffness on Crack Propagation in 8inch 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 4inch Pavement (Angle Relative to Vertical) .................... : ............................................... 161 5.20 Effects of Various Stiffness Gradients on Direction of Crack Growth in 8inch 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 SurfaceInitiated 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 4inch 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 8inch Asphalt Concrete Layer of Uniform Stiffhess ................ 171 6.4 Effect of TemperatureInduced Stiffness Gradients on Transverse Distribution of Load Within Wheel Path and Critical Load Positions For 4inch Pavement ......... 172 6.5 Effect of TemperatureInduced Stiffness Gradients on Transverse Distribution of Load Within Wheel Path and Critical Load Positions For 8inch 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 Intennediate 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 110 .............................................................................................. 178 6.9 Potential For Crack Growth and Time Available For Identification and Rehabilitation For 8inch Pavement and Given Load Spectrum ............................. 180 6. 10 Potential For Crack Growth and Time Available For Identification and Rehabilitation For 4inch Pavement and Given Load Spectrum .............................. 181 A. I Distribution of Transverse Stresses Computed At Increasing Vertical Distance From 0.5in Crack: 8in 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: 8in 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 0.5in Crack: 8in 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: 8in 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 0.5in Crack: 8in 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: 8in 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 SURFACEINITIATED 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 hightype 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 nearsurface 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), tirepavement interface stresses, and temperature or agedinduced stiffness gradients. Stress analyses were performed using actual measured radial truck tirepavement 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 northcentral 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 tirepavement 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 surfaceinitiated 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 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 loadassociated 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 seasonallyaveraged 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 onethird 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 bottomup 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 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 surfaceinitiated 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 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 surfaceinitiated 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 surfaceinitiated 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 surfaceinitiated 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 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 nearsurface 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: " Twodimensional (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 threedimensional (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 surfaceinitiated 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 highvolume 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 twodimensional (2D) finite element analysis was reasonable for approximating threedimensional (3D) finite element analysis, if certain modifications were applied to match pavement response. 7 Plane strain conditions were assumed for 2D analyses and the stressstrain 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 tirepavement 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 surfaceinitiated 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 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 twodimensional analyses to approximate threedimensional pavement response. " Parametric Studies of Pavement System: analytical studies were conducted to discern structural and temperaturerelated 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 surfaceinitiated longitudinal cracks observed in the field. Final recommendations were made for the development of an analysis and design tool for asphalt mixtures and pavements. 9 Continuum Mechanics Theories on SurfaceInitiated 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 surfaceinitiated cracking. Previous work had demonstrated that surface cracking was most likely initiated by nearsurface 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 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 loadassociated 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 seasonallyaveraged 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 onethird 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 tosurface 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 mechanisticempirical 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 ledstrain and controlledstress 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 multilayer 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 throughcrack and finally into a long throughcrack. Three different crack types were evaluated: transverse (across wheel path), longitudinal (parallel to wheel path), and semielliptical. 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. Closedforin 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 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. 17 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, 02 toI 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 50mm by 50mm by 150mm were subjected to tensioncompression 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 threedimensional 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 tirepavement 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 tirepavement 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 VehicleRoad Pressure Transducer Array (VRSPTA) System that measures threedimensional 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 bedtransducer 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 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) 22 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 setup Figure 2.4: Experimental Setup of VehicleRoad 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: Threedimensional 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 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 macrotexture may improve skid resistance on pavements. A tirepavement 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 nearsurface 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 NearSurface Stresses Tension A AA Truck Tire Compression Tread Effect (+) Pavement () "000 Bending Effect (+) ., .' G i 'x. % Overall Effect (0 4010 Bias Ply Truck Tire + NearSurface 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 (Supersingle) 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 nearsurface damage. 2.6 Analysis of Surface Cracking Because surfaceinitiated 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 tirepavement 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 surfaceinitiated 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 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 tirepavement interface stress data are considered outdated in comparison to current tire characteristics. " There did not appear to be access to measured tireinterface 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 surfaceinitiated 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 nearsurface 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 twodimensional (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 nearsurface 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 biasply tires are totally different from a structural point of view (Myers et al. 1999) and the actual structural makeup 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 twodimensional 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 crosssection 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: CrossSection 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 9.8E6 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 finelygraded 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 surfacetobase 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 semiinfinite mass (i.e., onelayer 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 in150A 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 ' IStresses 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, multilayer theory (e.g., see Huang 1993) clearly indicated that nearsurface stress distributions are primarily governed by relative stiffness between the surface and the base layer. Consequently, nearsurface stress distributions deviate most from onelayer theory* as the surfacetobase layer modulus ratio (EI/E2) increases and as the surfacetobase layer thickness ratio (h I /h2) decreases. Furthermore, base thickness and subgrade stiffness have almost no influence on the nearsurface 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 4in 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 2in 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 SurfacetoBase 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 4in 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 4in 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 __It 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 4in 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 4in 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 4in Pavement System: Stiffness Ratio of 39.4 (El = 800 aci, E2 = 20 4i). 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 > 200U1) 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 4in 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 4in 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 4in 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 02 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 4in 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 4in 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 4in 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 2in 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 4in pavement. However, the correspondence was still very good. As was the case of the 4in pavement, in which intermediate stiffness ratios exhibited similar results, the same effect was observed for the 2in 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__________U200 __I*150 RibI Rib 2 Rib 3 Rib 4 Rib 6 UPredicted 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 2in 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 2in 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 2in 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 2in 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 2in 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 2in Pavement System: Stiffness Ratio of 10.0 (El 200 ksi, E2 = 20 ksi). 59 0 2 6 8 10 12 50 100~ U150 __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 2in 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 2in Pavement System: Stiffness Ratio of 18.0 (El = 800 ksi, E2 = 44 ksi). 61 Some minor differences were observed for thin (2in 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 TwoDimensional Finite Element Model to Capture Bending Response of Asphalt Pavement System Although threedimensional 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 twodimensional analyses provide simpler, more costeffective 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 twodimensional 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 threedimensional bending response of asphalt pavement structures. 62 To identify/develop an approach to calibrate twodimensional analyses such that reasonable approximations of the threedimensional 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 stressstrain 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. " Wellestabl i shed principles of pavement response (i.e., layered systems) indicated that nearsurface 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 nearsurface response were conducted. " All two and threedimensional 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 twodimensional 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 threedimensional solutions based on the twodimensional analyses. 3.3.1 Finite Element Model Types Axisymmetric and twodimensional 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 twodimensional model that resulted in considerably better representation of a continuous longitudinal crack in a pavement system. Multiple loads and cracks, as well as nonsymmetrical tire contact stresses, can be represented in the twodimensional 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 threedimensional analysis. Therefore, before attempting to use twodimensional analysis for the evaluation of pavement response and 64 performance, a thorough understanding of the differences in stress distributions between two and threedimensional 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 2D 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 nearsurface 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 inservice 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 nearsurface 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 (twodimensional) or diameter (threedimensional) 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 threedimensional loading case for comparison to the twodimensional analyses. Therefore, the same mesh structure was used for both twodimensional 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 2D 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 threedimensional 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 threedimensional solutions predicted almost exactly the same critical tensile stress. On the other hand, Figure 3.24 shows that the twodimensional 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 twodimensional analysis than for the threedimensional analysis (334 psi versus 87 psi). Figures 3.23 and 3.24 also indicate that significant differences were observed between the two and threedimensional 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 2D Model 250 3D (Axisymmetric) Model 300 ... n 2D 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 4in 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 2D Model 250 . 3D (Axisymmetric) Model 300  2D 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 8in 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 threedimensional 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 structurallydependent correction factor could be identified to estimate threedimensional tensile stresses using results obtained from the twodimensional analysis. The idea involved the determination of a factor that could be used to modify surface loads applied to the twodimensional analysis, such that the predicted bending stress (specifically, the critical tensile stress) would closely approximate the bending stress predicted by threedimensional analysis. 3.3.31 Definition of Bending Stress Ratio A ratio between the critical tensile stress predicted by threedimensional analysis and the critical tensile stress predicted using twodimensional 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 twodimensional loads (strip load), in order to obtain accurate threedimensional stress predictions using twodimensional analysis. The bending stress ratio was defined as follows: BSR = CTXX(3D) (3.1) CFXX(2D) 72 where, BSR = bending stress ratio axx(3D) = critical tensile stress based on threedimensional analysis (Yxx(2D) = critical tensile stress based on twodimensional 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 twodimensional 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 threedimensional 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 loadassociated 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. 3.3.32 Relations Between Bending Stress Ratio and Structural Parameters As mentioned earlier, the relative difference in critical tensile stresses between the two and threedimensional 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 threedimensional solutions did not change. " For the majority of pavement structures, BSR was less than 1.0, indicating that twodimensional analysis overestimated the critical tensile stress for most pavement structures. " BSR exceeded 1.0 (i.e., twodimensional analysis underestimated 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 hightraffic 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 nonlinear 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 E244ksi) 3.5 Stiffness Ratio of 10.0 (El =2O3ksi :E2=2ks).Stiffess Ratio of17.98 (E =80qsi :E244ksi) 3.0 A Stiffness Ratio of 28.0 (El = I20(ksi: E244ksi)  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 0.520 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 : E244ksi) 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: E220ksi) 3.0 Subgrade Stiffness 7.0 ksi (El=800ksi: E220ksi) 3.0  Subgrade Stiffness 14.5 ksi (E1=800Dksi: E220ksi) _2.5 a Subgrade Stiffness 7.0 ksi (E1=1200ksi: E244ksi) 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 threedimensional bending stresses in asphalt pavement systems using twodimensional 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 twodimensional 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 nonuniform 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 timeconsuming problem. The modified twodimensional approach provided reasonable solutions comparable to those obtained using a threedimensional 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 twodimensional solution that approximated the true threedimensional bending response of typical pavement structures: I Calculate the surfacetobase layer stiffness ratio (EI/E2) and the surfacetobase 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 twodimensional analysis. 4. Apply the modified vertical contact stresses and the transverse contact stresses to the twodimensional finite element representation of the pavement structure. The width of the wheel load(s) used in the twodimensional 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 threedimensional loading condition. Furthermore, for cases similar to the one shown in Figure 3.29, the modified twodimensional 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 threedimensional 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 nonlinear 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 nonlinear material properties, linear elastic analysis could be used to accurately determine the stressstrain 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 nonlinear deflection response of the pavement system, then backcalculation 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 surfacetobase 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 threedimensional analysis of pavement 83 structures were evaluated, and the question of whether a modified twodimensional analysis could be used as a reasonable approximation of the threedimensional response of asphalt pavements was addressed. Two and threedimensional analysis of a range of pavement structures typically encountered in highway pavements indicated that discrepancies between two and threedimensional 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 threedimensional analysis and the critical tensile stress from twodimensional analysis. It was determined that the BSR was primarily a function of surfacetobase layer stiffness ratio (EI/E2) and surfacetobase 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 twodimensional loads such that twodimensional analyses reasonably estimated the true threedimensional pavement stresses. Based on the comparisons presented, it was concluded that the modified twodimensional analysis developed reasonably approximated threedimensional 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 