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Suggested Citation:"Front Matter." National Academies of Sciences, Engineering, and Medicine. 2018. A Mechanistic–Empirical Model for Top–Down Cracking of Asphalt Pavements Layers. Washington, DC: The National Academies Press. doi: 10.17226/25304.
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Suggested Citation:"Front Matter." National Academies of Sciences, Engineering, and Medicine. 2018. A Mechanistic–Empirical Model for Top–Down Cracking of Asphalt Pavements Layers. Washington, DC: The National Academies Press. doi: 10.17226/25304.
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Suggested Citation:"Front Matter." National Academies of Sciences, Engineering, and Medicine. 2018. A Mechanistic–Empirical Model for Top–Down Cracking of Asphalt Pavements Layers. Washington, DC: The National Academies Press. doi: 10.17226/25304.
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Suggested Citation:"Front Matter." National Academies of Sciences, Engineering, and Medicine. 2018. A Mechanistic–Empirical Model for Top–Down Cracking of Asphalt Pavements Layers. Washington, DC: The National Academies Press. doi: 10.17226/25304.
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Suggested Citation:"Front Matter." National Academies of Sciences, Engineering, and Medicine. 2018. A Mechanistic–Empirical Model for Top–Down Cracking of Asphalt Pavements Layers. Washington, DC: The National Academies Press. doi: 10.17226/25304.
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Suggested Citation:"Front Matter." National Academies of Sciences, Engineering, and Medicine. 2018. A Mechanistic–Empirical Model for Top–Down Cracking of Asphalt Pavements Layers. Washington, DC: The National Academies Press. doi: 10.17226/25304.
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Suggested Citation:"Front Matter." National Academies of Sciences, Engineering, and Medicine. 2018. A Mechanistic–Empirical Model for Top–Down Cracking of Asphalt Pavements Layers. Washington, DC: The National Academies Press. doi: 10.17226/25304.
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Suggested Citation:"Front Matter." National Academies of Sciences, Engineering, and Medicine. 2018. A Mechanistic–Empirical Model for Top–Down Cracking of Asphalt Pavements Layers. Washington, DC: The National Academies Press. doi: 10.17226/25304.
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Suggested Citation:"Front Matter." National Academies of Sciences, Engineering, and Medicine. 2018. A Mechanistic–Empirical Model for Top–Down Cracking of Asphalt Pavements Layers. Washington, DC: The National Academies Press. doi: 10.17226/25304.
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NCHRP Web-Only Document 257: A Mechanistic–Empirical Model for Top–Down 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 Contractor’s 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.

The National Academy of Sciences was established in 1863 by an Act of Congress, signed by President Lincoln, as a private, non- governmental institution to advise the nation on issues related to science and technology. Members are elected by their peers for outstanding contributions to research. Dr. Marcia McNutt is president. The National Academy of Engineering was established in 1964 under the charter of the National Academy of Sciences to bring the practices of engineering to advising the nation. Members are elected by their peers for extraordinary contributions to engineering. Dr. C. D. Mote, Jr., is president. The National Academy of Medicine (formerly the Institute of Medicine) was established in 1970 under the charter of the National Academy of Sciences to advise the nation on medical and health issues. Members are elected by their peers for distinguished contributions to medicine and health. Dr. Victor J. Dzau is president. The three Academies work together as the National Academies of Sciences, Engineering, and Medicine to provide independent, objective analysis and advice to the nation and conduct other activities to solve complex problems and inform public policy decisions. The National Academies also encourage education and research, recognize outstanding contributions to knowledge, and increase public understanding in matters of science, engineering, and medicine. Learn more about the National Academies of Sciences, Engineering, and Medicine at www.national-academies.org. The Transportation Research Board is one of seven major programs of the National Academies of Sciences, Engineering, and Medicine. The mission of the Transportation Research Board is to increase the benefits that transportation contributes to society by providing leadership in transportation innovation and progress through research and information exchange, conducted within a setting that is objective, interdisciplinary, and multimodal. The Board’s varied committees, task forces, and panels annually engage about 7,000 engineers, scientists, and other transportation researchers and practitioners from the public and private sectors and academia, all of whom contribute their expertise in the public interest. The program is supported by state transportation departments, federal agencies including the component administrations of the U.S. Department of Transportation, and other organizations and individuals interested in the development of transportation. Learn more about the Transportation Research Board at www.TRB.org.

C O O P E R A T I V E  R E S E A R C H  P R O G R A M S  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 ................................................................................................... 1  Introduction ................................................................................................................................. 1  Objective ..................................................................................................................................... 1  Research Scope and Approach ................................................................................................... 1  Organization of the Report ......................................................................................................... 2  CHAPTER 2. SYNTHESIS OF CURRENT KNOWLEDGE ....................................................... 4  Mixture Material Property Models ............................................................................................. 5  Mixture Aging Models ................................................................................................................ 5  Traffic Traction Stress and Strain Models .................................................................................. 6  Traffic Load Spectrum Models ................................................................................................... 6  Thermal Stress Models ............................................................................................................... 7  Pavement Temperature Models .................................................................................................. 7  Crack Initiation Models .............................................................................................................. 7  Crack Propagation Models .......................................................................................................... 8  Finite Element Crack Growth Models ........................................................................................ 8  Artificial Neural Networks (ANN) Models ................................................................................ 8  Cumulative Damage Models ...................................................................................................... 8  Observed Geometry of a Crack as It Propagates Downward ..................................................... 9  CHAPTER 3. RESEARCH PLAN ............................................................................................... 10  Laboratory Testing of Asphalt Field Cores .............................................................................. 11  Kinetics-Based Aging Modeling .............................................................................................. 11  Finite Element Modeling of J-Integral ...................................................................................... 11  Artificial Neural Network Modeling of J-Integral .................................................................... 12  Top-Down Cracking Modeling Due to Thermal Loading ........................................................ 12  Top-Down Crack Initiation and Growth Modeling Due to Traffic Loading ............................ 13  Cumulative Damage Modeling for Top-Down Crack Growth ................................................. 13  Data Collection for Model Development and Calibration ........................................................ 14  CHAPTER 4. FINDINGS ............................................................................................................. 16  Introduction ............................................................................................................................... 16  Determination of Complex Modulus Gradient of Field-Aged Asphalt Mixtures ..................... 16  Time-Temperature-Aging-Depth Shift Functions for Dynamic Modulus Master Curves ....... 20  Construction of Aging Dynamic Modulus Master Curve for LMLC Mixtures .................... 21  Construction of Dynamic Modulus Master Curve of Field Cores ........................................ 27  Kinetics-Based Aging Prediction for Asphalt Pavements in the Field ..................................... 30  Prediction of Field Aging Gradient ....................................................................................... 30  Prediction of Field Aging Using Deflection Data ................................................................. 40  Pseudo J-Integral Based Paris’ Law for Crack Growth Prediction .......................................... 52  Quasi-Elastic Simulation of Viscoelasticity ......................................................................... 53  Modified Paris’ Law with Application of Quasi-Elastic Simulation .................................... 54  Estimation of Fracture Coefficients by Performance-Related Properties ............................. 55  Pseudo J-Integral Based Paris’ Law for Crack Initiation Prediction ........................................ 60  Development of Crack Initiation Model ............................................................................... 61 

vi Characterization of LTPP Data ............................................................................................. 64  Statistical Analysis for Top-Down Initiation Time .............................................................. 68  Numerical Modeling and Artificial Neural Network (ANN) for Predicting J-Integral ............ 73  Three-Dimensional Finite Element Modeling ...................................................................... 73  Artificial Neural Network Modeling of J-Integral ................................................................ 82  Prediction of Crack Growth under Thermal Loading ............................................................... 87  Theoretical Models for Top-Down Cracking under Thermal Loading................................. 87  Assembly of Thermal Top-Down Computer Program ......................................................... 91  Computation of Top-Down Cracking Calibration Coefficients ............................................... 98  CHAPTER 5. INTERPRETATIONS, APPRAISAL, AND APPLICATIONS ......................... 101  Introduction ............................................................................................................................. 101  The Model Development Process ....................................................................................... 101  Mechanistic Prediction of Top-Down Cracking ................................................................. 101  Asphalt Pavement Layer Material Properties ..................................................................... 102  Weather Data and Temperature Prediction ......................................................................... 102  Consistent Description of Top-Down Cracking.................................................................. 102  Calibrated Results Compared with Observed Field Data ....................................................... 103  Determination of Number of Days for Critical Crack Depth ............................................. 103  Calibration Coefficients by Regression Analysis ............................................................... 103  Prediction of Top-Down Cracking Distress Curve ................................................................. 105  CHAPTER 6. SUMMARY ......................................................................................................... 109  Summary ................................................................................................................................. 109  Laboratory Testing of Asphalt Field Cores ........................................................................ 109  Kinetics-Based Modeling of Long-Term Field Aging ........................................................ 110  Finite Element Computation and ANN Modeling of J-Integral ......................................... 111  Prediction of Crack Propagation by Pseudo J-Integral Based Paris’ Law .......................... 111  Prediction of Crack Initiation by Pseudo J-Integral Based Paris’ Law............................... 111  Prediction of Crack Growth under Thermal Loading ......................................................... 112 Prediction of Calibration Coefficients and Distress Curve ................................................. 112 REFERENCES ........................................................................................................................... 114  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 Paris’ 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 A’ and n’ ............................................. 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 ................................................................ 63 

ix Figure 4.30. Example of Axle Load Distribution ......................................................................... 65  Figure 4.31. Determination of Top-Down Crack Initiation Time ................................................ 67  Figure 4.32. Comparison of Predicted and Calculated Energy Coefficient 0 02 a A ......................... 71  Figure 4.33. Comparison of Predicted and Calculated Top-Down Crack Initiation Time ........... 72  Figure 4.34. Validation LTPP Pavement Sections for Top-Down Crack Initiation Time ............ 72  Figure 4.35. Modulus Gradient Curves in Asphalt Layers ........................................................... 74  Figure 4.36. Simplified Patterns of 3D Vertical, Longitudinal and Transverse Contact Stresses .............................................................................................................................. 75  Figure 4.37. Example of Load and Tire Length Relationship ..................................................... 76  Figure 4.38. Three Components of Tire-Pavement Contact Stress in ABAQUS ......................... 77  Figure 4.39. 3D FEM Model and Mesh Details for Top-Down Cracking and Loading ............... 79  Figure 4.40. J-Integral in Pavement Depth with Various Values of n, k and Asphalt Layer Thickness .......................................................................................................................... 81  Figure 4.41. Structure of Artificial Neural Network ..................................................................... 84  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 .................................. 84  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 ................................ 85  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 ................................ 85  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 ............................. 86  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 ........................... 86  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 ........................... 87  Figure 4.48 Results of ANN Modeling for Measuring and Predicting J-Integral for Training and Validation. ................................................................................................... 90  Figure 4.49 Flow Chart of the Process of the Thermal Crack Growth Computations .................. 92  Figure 4.50. Pavement Temperature versus Time ........................................................................ 94  Figure 4.51. Longitudinal Thermal Stress versus Time ................................................................ 95  Figure 4.52. Aged Modulus versus Time...................................................................................... 97  Figure 4.53 Crack Depth versus Time .......................................................................................... 97  Figure 5.1. Prediction of Calibration Coefficients ...................................................................... 105  Figure 5.2 Pavement Distress Curves for Pavement Sections in Different Climatic Zones ....... 108 

x LIST OF TABLES Table 2.1. Crack Width and the Corresponding Severity of the Distress ....................................... 9  Table 4.1. Calculated CAM Model Parameters ............................................................................ 22  Table 4.2 Laboratory Testing Results and Calculation Results for Field Condition .................... 32  Table 4.3 Results of Aging Activation Energies and Pre-Exponential Factors of Field Cores ................................................................................................................................. 40  Table 4.4 Results of Aging Activation Energies and Pre-Exponential Factors of Field Core Binder (125) ............................................................................................................. 40  Table 4.5 Information of LTPP Pavement Sections ..................................................................... 43  Table 4.6 Examples of Modulus and Mixture Property Data Collected from the LTPP Database ............................................................................................................................ 44  Table 4.7. Examples of Calculated Modulus and Field Aging Temperature in Each Aging Segment............................................................................................................................. 49  Table 4.8. Examples of Values of Fracture Coefficients and Performance-Related Material Properties Segment ............................................................................................. 58  Table 4.9. Summary Output of Multiple Regression Analysis of n’ Using Performance- Related Material Properties ............................................................................................... 60  Table 4.10. Characteristics of LTPP Axle Type ........................................................................... 65  Table 4.11 Distribution of Vehicle Classes (123) ......................................................................... 66  Table 4.12 Average Number of Axle for Each Vehicle Class (123) ............................................ 66  Table 4.13. Regression Analysis of Tire–Pavement Contact Stress ............................................. 75  Table 4.14. Materials and Structures Inputs in the FEM .............................................................. 78  Table 4.15 Pavement Structure and Inputs in the FEM ................................................................ 89  Table 4.16 Section Information and Material Properties. ............................................................. 95  Table 4.17 Fracture Parameters .................................................................................................... 96  Table 4.18 Summary of Calibration Coefficients for Four Climatic Zones ................................. 99  Table 5.1 Typical Pavement Sections in Different Climatic Zones ............................................ 106

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TRB's National Cooperative Highway Research Program (NCHRP) Web-Only Document 257: A Mechanistic–Empirical Model for Top–Down Cracking of Asphalt Pavements Layers develops a calibrated mechanistic-empirical (ME) model for predicting the load-related top-down cracking in the asphalt layer of flexible pavements. Recent studies have determined that some load-related fatigue cracks in asphalt pavement layers can be initiated at the pavement surface and propagate downward through the asphalt layer. However, this form of distress cannot entirely be explained by fatigue mechanisms used to explain cracking that initiates at the bottom of the pavement. This research explores top-down cracking to develop a calibrated, validated mechanistic-empirical model for incorporation into pavement design procedures.

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