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NCHRP Web-Only Document 257: A MechanisticâEmpirical Model for TopâDown Cracking of Asphalt Pavement Layers Robert L. Lytton Xue Luo Meng Ling Yu Chen Sheng Hu Fan Gu Texas A&M Transportation Institute The Texas A&M University System College Station, TX Contractorâs Final Report for NCHRP Project 01-52 Submitted March 2018 ACKNOWLEDGMENT This work was sponsored by the American Association of State Highway and Transportation Officials (AASHTO), in cooperation with the Federal Highway Administration, and was conducted in the National Cooperative Highway Research Program (NCHRP), which is administered by the Transportation Research Board (TRB) of the National Academies of Sciences, Engineering, and Medicine. COPYRIGHT INFORMATION Authors herein are responsible for the authenticity of their materials and for obtaining written permissions from publishers or persons who own the copyright to any previously published or copyrighted material used herein. Cooperative Research Programs (CRP) grants permission to reproduce material in this publication for classroom and not-for-profit purposes. Permission is given with the understanding that none of the material will be used to imply TRB, AASHTO, FAA, FHWA, FMCSA, FRA, FTA, Office of the Assistant Secretary for Research and Technology, PHMSA, or TDC endorsement of a particular product, method, or practice. It is expected that those reproducing the material in this document for educational and not-for-profit uses will give appropriate acknowledgment of the source of any reprinted or reproduced material. For other uses of the material, request permission from CRP. DISCLAIMER The opinions and conclusions expressed or implied in this report are those of the researchers who performed the research. They are not necessarily those of the Transportation Research Board; the National Academies of Sciences, Engineering, and Medicine; or the program sponsors. The information contained in this document was taken directly from the submission of the author(s). This material has not been edited by TRB.
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CÂ OÂ OÂ PÂ EÂ RÂ AÂ TÂ IÂ VÂ EÂ RÂ EÂ SÂ EÂ AÂ RÂ CÂ HÂ PÂ RÂ OÂ GÂ RÂ AÂ MÂ SÂ CRP STAFF FOR NCHRP Web-Only Document 257 Christopher J. Hedges, Director, Cooperative Research Programs Lori L. Sundstrom, Deputy Director, Cooperative Research Programs Amir N. Hanna, Senior Program Officer Keyara Dorn, Program Coordinator Eileen P. Delaney, Director of Publications Natalie Barnes, Associate Director of Publications Kathleen Mion, Senior Editorial Assistant NCHRP PROJECT 01-52 PANEL Area One: Design-Pavements Linda M. Pierce, Nichols Consulting Engineers, Spokane, WA (Chair) Kent R. Hansen, (formerly with the National Asphalt Pavement Association), Cambrills, MD Richard Y. Ji, Federal Aviation Administration, Atlantic City Intl Airport, NJ Jianhua Li, Washington State DOT, Tumwater, WA Wilfung Martono, California DOT, San Jose, CA Stefan A. Romanoschi, University of Texas - Arlington, Arlington, TX Zhong Wu, Louisiana DOTD, Baton Rouge, LA Wei-Shih Yang, New York State DOT, Albany, NY Katherine A. Petros, FHWA Liaison Stephen F. Maher, TRB Liaison
v CONTENTS CHAPTER 1. INTRODUCTION ................................................................................................... 1Â Introduction ................................................................................................................................. 1Â Objective ..................................................................................................................................... 1Â Research Scope and Approach ................................................................................................... 1Â Organization of the Report ......................................................................................................... 2Â CHAPTER 2. SYNTHESIS OF CURRENT KNOWLEDGE ....................................................... 4Â Mixture Material Property Models ............................................................................................. 5Â Mixture Aging Models ................................................................................................................ 5Â Traffic Traction Stress and Strain Models .................................................................................. 6Â Traffic Load Spectrum Models ................................................................................................... 6Â Thermal Stress Models ............................................................................................................... 7Â Pavement Temperature Models .................................................................................................. 7Â Crack Initiation Models .............................................................................................................. 7Â Crack Propagation Models .......................................................................................................... 8Â Finite Element Crack Growth Models ........................................................................................ 8Â Artificial Neural Networks (ANN) Models ................................................................................ 8Â Cumulative Damage Models ...................................................................................................... 8Â Observed Geometry of a Crack as It Propagates Downward ..................................................... 9Â CHAPTER 3. RESEARCH PLAN ............................................................................................... 10Â Laboratory Testing of Asphalt Field Cores .............................................................................. 11Â Kinetics-Based Aging Modeling .............................................................................................. 11Â Finite Element Modeling of J-Integral ...................................................................................... 11Â Artificial Neural Network Modeling of J-Integral .................................................................... 12Â Top-Down Cracking Modeling Due to Thermal Loading ........................................................ 12Â Top-Down Crack Initiation and Growth Modeling Due to Traffic Loading ............................ 13Â Cumulative Damage Modeling for Top-Down Crack Growth ................................................. 13Â Data Collection for Model Development and Calibration ........................................................ 14Â CHAPTER 4. FINDINGS ............................................................................................................. 16Â Introduction ............................................................................................................................... 16Â Determination of Complex Modulus Gradient of Field-Aged Asphalt Mixtures ..................... 16Â Time-Temperature-Aging-Depth Shift Functions for Dynamic Modulus Master Curves ....... 20Â Construction of Aging Dynamic Modulus Master Curve for LMLC Mixtures .................... 21Â Construction of Dynamic Modulus Master Curve of Field Cores ........................................ 27Â Kinetics-Based Aging Prediction for Asphalt Pavements in the Field ..................................... 30Â Prediction of Field Aging Gradient ....................................................................................... 30Â Prediction of Field Aging Using Deflection Data ................................................................. 40Â Pseudo J-Integral Based Parisâ Law for Crack Growth Prediction .......................................... 52Â Quasi-Elastic Simulation of Viscoelasticity ......................................................................... 53Â Modified Parisâ Law with Application of Quasi-Elastic Simulation .................................... 54Â Estimation of Fracture Coefficients by Performance-Related Properties ............................. 55Â Pseudo J-Integral Based Parisâ Law for Crack Initiation Prediction ........................................ 60Â Development of Crack Initiation Model ............................................................................... 61Â
vi Characterization of LTPP Data ............................................................................................. 64Â Statistical Analysis for Top-Down Initiation Time .............................................................. 68Â Numerical Modeling and Artificial Neural Network (ANN) for Predicting J-Integral ............ 73Â Three-Dimensional Finite Element Modeling ...................................................................... 73Â Artificial Neural Network Modeling of J-Integral ................................................................ 82Â Prediction of Crack Growth under Thermal Loading ............................................................... 87Â Theoretical Models for Top-Down Cracking under Thermal Loading................................. 87Â Assembly of Thermal Top-Down Computer Program ......................................................... 91Â Computation of Top-Down Cracking Calibration Coefficients ............................................... 98Â CHAPTER 5. INTERPRETATIONS, APPRAISAL, AND APPLICATIONS ......................... 101Â Introduction ............................................................................................................................. 101Â The Model Development Process ....................................................................................... 101Â Mechanistic Prediction of Top-Down Cracking ................................................................. 101Â Asphalt Pavement Layer Material Properties ..................................................................... 102Â Weather Data and Temperature Prediction ......................................................................... 102Â Consistent Description of Top-Down Cracking.................................................................. 102Â Calibrated Results Compared with Observed Field Data ....................................................... 103Â Determination of Number of Days for Critical Crack Depth ............................................. 103Â Calibration Coefficients by Regression Analysis ............................................................... 103Â Prediction of Top-Down Cracking Distress Curve ................................................................. 105Â CHAPTER 6. SUMMARY ......................................................................................................... 109Â Summary ................................................................................................................................. 109Â Laboratory Testing of Asphalt Field Cores ........................................................................ 109Â Kinetics-Based Modeling of Long-Term Field Aging ........................................................ 110Â Finite Element Computation and ANN Modeling of J-Integral ......................................... 111Â Prediction of Crack Propagation by Pseudo J-Integral Based Parisâ Law .......................... 111Â Prediction of Crack Initiation by Pseudo J-Integral Based Parisâ Law............................... 111Â Prediction of Crack Growth under Thermal Loading ......................................................... 112 Prediction of Calibration Coefficients and Distress Curve ................................................. 112 REFERENCES ........................................................................................................................... 114Â APPENDICES Appendix A. Measurement of Complex Modulus Gradient Using Direct Tension Test ............ A-1 Appendix B. Inverse Approach to Derive Complex Modulus Gradient of Asphalt Field Cores ..................................................................................................................................... B-1 Appendix C. Derivation and Validation of Quasi-elastic Simulation of Viscoelasticity ........... C-1 Appendix D. Determination of Fracture Coefficients in Pseudo J-Integral Based Parisâ Law .. D-1 Appendix E. Collection of Top-Down Cracking Data for Model Development and Calibration.............................................................................................................................. E-1 Appendix F. Catalog of Fracture Properties of Asphalt Mixtures ............................................... F-1 Appendix G. Catalog of Aging Properties of Asphalt Mixtures ................................................. G-1 Appendix H. Characterization of the Top-Down Cracking Amount and Severity ..................... H-1 Appendix I. Prediction of Top-Down Crack Initiation Time and Determination of Calibration Coefficients for Different Climate Zones ............................................................ I-1
vii Appendix J. Relationship between Crack Depth and Crack Width for a Surface Crack ............. J-1 Appendix K. Sensitivity Analysis of Top-Down Cracking Designing Program ........................ K-1 Appendix L. The Comparison of Predicted Results and Field Data ............................................ L-1 Appendix M. The List of New Input Parameters for the Top-Down Cracking Designing Program ................................................................................................................................ M-1 Appendix N. List of All Variables .............................................................................................. N-1 Appendix O. Manual and Example of Top Down Cracking Software ....................................... O-1
viii LIST OF FIGURES Figure 1.1. Compatibility of Proposed Program with AASHTOWare Pavement ME Design ................................................................................................................................. 2 Figure 2.1. Major Factors Affecting Top-Down Cracking in Asphalt Pavements ......................... 4 Figure 3.1. Proposed Approach to Develop a Complete Mechanistic-Empirical Model for Top-Down Cracking ......................................................................................................... 10 Figure 3.2. Plot of Crack Shape versus Crack Depth of a Top-Down Crack ............................... 14 Figure 4.1. Measured Vertical Strains at Top, Center, and Bottom of Tested Specimen ............. 18 Figure 4.2. Measured Strain at the Bottom of a Field Core Specimen and Associated Pseudo Strains at Different Iterations ............................................................................... 19 Figure 4.3. Modulus Gradients of 8 and 22 Months Aged Field Specimens at Three Temperatures and 0.1 Hz .................................................................................................. 20 Figure 4.4. Dynamic Modulus of Field Cores at Different Conditions ........................................ 21 Figure 4.5. Dynamic Modulus LMLC Master Curves Constructed by CAM Model ................... 23 Figure 4.6. Vertical Shift and Rotation for LMLC Master Curves ............................................... 25 Figure 4.7. Final Aging LMLC Dynamic Modulus Master Curve ............................................... 26 Figure 4.8. Baseline Dynamic Modulus Master Curve for HMA Field Cores ............................. 27 Figure 4.9. Development of Aging Master Curve for Field Mixtures .......................................... 28 Figure 4.10. Application of Depth Shift Function to Top and Center Dynamic Modulus Master Curves ................................................................................................................... 30 Figure 4.11 Laboratory Measured and Field Modulus Gradients in Asphalt Field Cores ............ 31 Figure 4.12. Idealization of Modulus Gradient in Asphalt Pavements ......................................... 33 Figure 4.13. Examples of Arrhenius Plot of Bitumen Viscosity for Field Cores Tested at 10 and 20°C ....................................................................................................................... 35 Figure 4.14. Fast-Rate Period and Constant-Rate Period of Field Core Modulus Gradient ......... 37 Figure 4.15. Examples of Arrhenius Plot of Constant-Rate Reaction Constant for Field Cores Aged at 28 and 16°C ............................................................................................... 38 Figure 4.16. Goodness of Representation by Aging Prediction Model for Field Aging Gradient............................................................................................................................. 39 Figure 4.17. Goodness of Representation by Aging Prediction Model for Field Aging Gradient............................................................................................................................. 39 Figure 4.18. Two-Stage Modulus of Aged FWD Modulus .......................................................... 41 Figure 4.19. Calculated Rheological Activation Energy from FWD Data at Different Ages .................................................................................................................................. 45 Figure 4.20. Predicted Pavement Temperature for the LTPP Section 19-0102 ............................ 47 Figure 4.21. Predicted Pavement Temperature at Different Climate Zones ................................. 48 Figure 4.22. Fitted FWD Backcalculated Modulus Curve ........................................................... 50 Figure 4.23. Example of Fast-Rate Period and Constant-Rate Period of FWD Backcalculated Modulus for the LTPP Section 19-0102 .................................................. 50 Figure 4.24. Calculated Aging Activation Energy from FWD Data and Climate Data in Different Climate Zones ................................................................................................... 51 Figure 4.25. Comparison of Predicted Moduli and Measured FWD Moduli ............................... 52 Figure 4.26. Relationship between Fracture Coefficients Aâ and nâ ............................................. 56 Figure 4.27. Determination of Aggregate Gradation Characteristic Parameters .......................... 57 Figure 4.28. Comparison of Predicted and Measured Fracture Coefficients ................................ 60 Figure 4.29. Air Void Distribution in Pavement Depth ................................................................ 63Â
ix Figure 4.30. Example of Axle Load Distribution ......................................................................... 65Â Figure 4.31. Determination of Top-Down Crack Initiation Time ................................................ 67Â Figure 4.32. Comparison of Predicted and Calculated Energy Coefficient 0 02 a A ......................... 71Â Figure 4.33. Comparison of Predicted and Calculated Top-Down Crack Initiation Time ........... 72Â Figure 4.34. Validation LTPP Pavement Sections for Top-Down Crack Initiation Time ............ 72Â Figure 4.35. Modulus Gradient Curves in Asphalt Layers ........................................................... 74Â Figure 4.36. Simplified Patterns of 3D Vertical, Longitudinal and Transverse Contact Stresses .............................................................................................................................. 75Â Figure 4.37. Example of Load and Tire Length Relationship ..................................................... 76Â Figure 4.38. Three Components of Tire-Pavement Contact Stress in ABAQUS ......................... 77Â Figure 4.39. 3D FEM Model and Mesh Details for Top-Down Cracking and Loading ............... 79Â Figure 4.40. J-Integral in Pavement Depth with Various Values of n, k and Asphalt Layer Thickness .......................................................................................................................... 81Â Figure 4.41. Structure of Artificial Neural Network ..................................................................... 84Â Figure 4.42. Measured and Predicted J-Integral for Training, Validation, and Overall Datasets for Dual Tire Loadings with Dual Tire Length of 19 mm .................................. 84Â Figure 4.43. Measured and Predicted J-Integral for Training, Validation, and Overall Datasets for Dual Tire Loadings with Dual Tire Length of 185 mm ................................ 85Â Figure 4.44. Measured and Predicted J-Integral for Training, Validation, and Overall Datasets for Dual Tire Loadings with Dual Tire Length of 229 mm ................................ 85Â Figure 4.45. Measured and Predicted J-Integral for Training, Validation, and Overall Datasets for Single Tire Loadings with Single Tire Length of 64 mm ............................. 86Â Figure 4.46. Measured and Predicted J-Integral for Training, Validation, and Overall Datasets for Single Tire Loadings with Single Tire Length of 305 mm ........................... 86Â Figure 4.47. Measured and Predicted J-Integral for Training, Validation, and Overall Datasets for Single Tire Loadings with Single Tire Length of 406 mm ........................... 87Â Figure 4.48 Results of ANN Modeling for Measuring and Predicting J-Integral for Training and Validation. ................................................................................................... 90Â Figure 4.49 Flow Chart of the Process of the Thermal Crack Growth Computations .................. 92Â Figure 4.50. Pavement Temperature versus Time ........................................................................ 94Â Figure 4.51. Longitudinal Thermal Stress versus Time ................................................................ 95Â Figure 4.52. Aged Modulus versus Time...................................................................................... 97Â Figure 4.53 Crack Depth versus Time .......................................................................................... 97Â Figure 5.1. Prediction of Calibration Coefficients ...................................................................... 105Â Figure 5.2 Pavement Distress Curves for Pavement Sections in Different Climatic Zones ....... 108Â
x LIST OF TABLES Table 2.1. Crack Width and the Corresponding Severity of the Distress ....................................... 9Â Table 4.1. Calculated CAM Model Parameters ............................................................................ 22Â Table 4.2 Laboratory Testing Results and Calculation Results for Field Condition .................... 32Â Table 4.3 Results of Aging Activation Energies and Pre-Exponential Factors of Field Cores ................................................................................................................................. 40Â Table 4.4 Results of Aging Activation Energies and Pre-Exponential Factors of Field Core Binder (125) ............................................................................................................. 40Â Table 4.5 Information of LTPP Pavement Sections ..................................................................... 43Â Table 4.6 Examples of Modulus and Mixture Property Data Collected from the LTPP Database ............................................................................................................................ 44Â Table 4.7. Examples of Calculated Modulus and Field Aging Temperature in Each Aging Segment............................................................................................................................. 49Â Table 4.8. Examples of Values of Fracture Coefficients and Performance-Related Material Properties Segment ............................................................................................. 58Â Table 4.9. Summary Output of Multiple Regression Analysis of nâ Using Performance- Related Material Properties ............................................................................................... 60Â Table 4.10. Characteristics of LTPP Axle Type ........................................................................... 65Â Table 4.11 Distribution of Vehicle Classes (123) ......................................................................... 66Â Table 4.12 Average Number of Axle for Each Vehicle Class (123) ............................................ 66Â Table 4.13. Regression Analysis of TireâPavement Contact Stress ............................................. 75Â Table 4.14. Materials and Structures Inputs in the FEM .............................................................. 78Â Table 4.15 Pavement Structure and Inputs in the FEM ................................................................ 89Â Table 4.16 Section Information and Material Properties. ............................................................. 95Â Table 4.17 Fracture Parameters .................................................................................................... 96Â Table 4.18 Summary of Calibration Coefficients for Four Climatic Zones ................................. 99Â Table 5.1 Typical Pavement Sections in Different Climatic Zones ............................................ 106