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Development and Evaluation of an HMA Fracture Mechanics Based Model to Predict Top-down Cracking in HMA Layers

Permanent Link: http://ufdc.ufl.edu/UFE0041135/00001

Material Information

Title: Development and Evaluation of an HMA Fracture Mechanics Based Model to Predict Top-down Cracking in HMA Layers
Physical Description: 1 online resource (129 p.)
Language: english
Creator: Zou, Jian
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: aging, cracking, down, fracture, healing, hma, layers, mechanics, top
Civil and Coastal Engineering -- Dissertations, Academic -- UF
Genre: Civil Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: DEVELOPMENT AND EVALUATION OF AN HMA FRACTURE MECHANICS BASED MODEL TO PREDICT TOP-DOWN CRACKING IN HMA LAYERS It is well recognized that load-related top-down cracking commonly occurs in HMA pavements. This phenomenon has been reported to occur in many parts of the United States, as well as in Europe, Japan, and other countries. This mode of failure, however, cannot be explained by traditional fatigue mechanisms used to explain fatigue cracking that initiates at the bottom of the pavement. The primary objective of this research is therefore to identify the causes of top-down cracking and to develop mechanistic-based models for predicting this type of distress in HMA layers. The HMA fracture mechanics (HMA-FM) model developed at the University of Florida (UF) was determined as necessary to form the basis of this study because of its associated threshold concept that is suitable for developing rules for both top-down cracking initiation and propagation, and its ability to model the presence of macro cracks and their effect on response. However, the effect of aging and healing on top-down cracking performance during the entire service life of asphalt concrete pavement had not been considered. Also, the effect of transverse, as opposed to longitudinal, thermal stresses had not been addressed. Therefore, the framework of the existing HMA-FM model was modified by identifying and including appropriate sub-models to address these key factors, based on which the framework of the targeted model was formed. Consequently, the targeted model/system, which was termed the HMA-FM-based model, was completed by development and integration of several key elements into the finalized framework, including material property sub-models that accounts for changes in mixture properties (e.g., fracture energy, creep rate, and healing potential) with aging, and a thermal response model that predicts transverse thermal stresses. The HMA-FM-based model placed emphasis on the bending mechanism. A systematic parametric study showed that the model provided reasonable predictions and expected trends for both crack initiation and propagation. Furthermore, a full calibration of field sections indicated that the predictive system adequately represents and accounts for the most significant factors that influence top-down cracking in the field. The validation efforts using the prediction sum of squares (PRESS) procedure further established the viability of the predictive system. In conclusion, the work performed clearly indicates that the HMA-FM-based model developed and evaluated in this study should form the basis for a top-down cracking model suitable for use in the mechanistic-empirical pavement design guide (MEPDG).
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Jian Zou.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Roque, Reynaldo.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0041135:00001

Permanent Link: http://ufdc.ufl.edu/UFE0041135/00001

Material Information

Title: Development and Evaluation of an HMA Fracture Mechanics Based Model to Predict Top-down Cracking in HMA Layers
Physical Description: 1 online resource (129 p.)
Language: english
Creator: Zou, Jian
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: aging, cracking, down, fracture, healing, hma, layers, mechanics, top
Civil and Coastal Engineering -- Dissertations, Academic -- UF
Genre: Civil Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: DEVELOPMENT AND EVALUATION OF AN HMA FRACTURE MECHANICS BASED MODEL TO PREDICT TOP-DOWN CRACKING IN HMA LAYERS It is well recognized that load-related top-down cracking commonly occurs in HMA pavements. This phenomenon has been reported to occur in many parts of the United States, as well as in Europe, Japan, and other countries. This mode of failure, however, cannot be explained by traditional fatigue mechanisms used to explain fatigue cracking that initiates at the bottom of the pavement. The primary objective of this research is therefore to identify the causes of top-down cracking and to develop mechanistic-based models for predicting this type of distress in HMA layers. The HMA fracture mechanics (HMA-FM) model developed at the University of Florida (UF) was determined as necessary to form the basis of this study because of its associated threshold concept that is suitable for developing rules for both top-down cracking initiation and propagation, and its ability to model the presence of macro cracks and their effect on response. However, the effect of aging and healing on top-down cracking performance during the entire service life of asphalt concrete pavement had not been considered. Also, the effect of transverse, as opposed to longitudinal, thermal stresses had not been addressed. Therefore, the framework of the existing HMA-FM model was modified by identifying and including appropriate sub-models to address these key factors, based on which the framework of the targeted model was formed. Consequently, the targeted model/system, which was termed the HMA-FM-based model, was completed by development and integration of several key elements into the finalized framework, including material property sub-models that accounts for changes in mixture properties (e.g., fracture energy, creep rate, and healing potential) with aging, and a thermal response model that predicts transverse thermal stresses. The HMA-FM-based model placed emphasis on the bending mechanism. A systematic parametric study showed that the model provided reasonable predictions and expected trends for both crack initiation and propagation. Furthermore, a full calibration of field sections indicated that the predictive system adequately represents and accounts for the most significant factors that influence top-down cracking in the field. The validation efforts using the prediction sum of squares (PRESS) procedure further established the viability of the predictive system. In conclusion, the work performed clearly indicates that the HMA-FM-based model developed and evaluated in this study should form the basis for a top-down cracking model suitable for use in the mechanistic-empirical pavement design guide (MEPDG).
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Jian Zou.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Roque, Reynaldo.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0041135:00001


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DEVELOPMENT AND EVALUATION OF AN HMA FRACTURE MECHANICS BASED MODEL TO PREDICT TOP-DOWN CRACKING IN HMA LAYERS By JIAN ZOU 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 2009 1

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2009 Jian Zou 2

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To my wife and parents 3

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ACKNOWLEDGMENTS It is a great pleasure for me to thank and acknowledge the many individuals who assisted and supported me during the course of my doctoral program. First of all, I would like to express my sincere appreciation to my committee chairman, Dr. Reynaldo Roque for his invaluable guidance and support throughout my studies at the University of Florida. I would not have been able to reach this milestone if it was not for his advice and understanding. I would also like to express my gratitude to other committee members, Dr. Dennis R. Hiltunen, Dr. Mang Tia, and Dr. Bhavani V. Sankar, for their support in accomplishing my work. Many thanks should also be given to all former and current colleagues in the material and geotechnical group for their help and friendship during my stay in the Department of Civil and Coastal Engineering at the University of Florida. I would also like to express my appreciation to the Federal Highway Administration and the Florida Department of Transportation for the ongoing financial support to the study of top-down cracking. And lastly, I would like to thank my parents for understanding and supporting my long pursuit of the Ph.D. degree, and special thanks to my wife, Lin Du and her parents for support and enduring love. 4

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TABLE OF CONTENTS page ACKNOWLEDGMENTS ...............................................................................................................4 LIST OF TABLES ...........................................................................................................................8 LIST OF FIGURES .........................................................................................................................9 ABSTRACT ...................................................................................................................................12 CHAPTER 1 INTRODUCTION..................................................................................................................14 Background.............................................................................................................................14 Objectives...............................................................................................................................15 Scope.......................................................................................................................................15 Research Approach.................................................................................................................16 2 LITERATURE REVIEW.......................................................................................................18 Classical Fatigue Approach....................................................................................................18 Continuum Damage Model.....................................................................................................19 HMA Fracture Mechanics Model...........................................................................................21 HMA Fracture Mechanics...............................................................................................21 HMA Fracture Mechanics-based Crack Growth Simulator............................................21 Energy Ratio Approach...................................................................................................22 Modified Energy Ratio Approach...................................................................................22 Material Property Models.......................................................................................................23 Binder Aging Model........................................................................................................23 Dynamic Modulus Model................................................................................................24 Tensile Strength Model...................................................................................................24 Healing Model.................................................................................................................25 3 DEVELOPMENT OF MODEL FRAMEWORK AND COMPONENTS.............................28 Model Framework..................................................................................................................28 Inputs Module and Indirect Tensile Test.........................................................................29 Material Property Model.................................................................................................29 Pavement Response Model..............................................................................................29 Pavement Fracture Model................................................................................................30 Output..............................................................................................................................30 Material Property Model.........................................................................................................30 AC Stiffness (Creep Compliance) Aging Model.............................................................31 AC Tensile Strength Aging Model..................................................................................33 FE Limit (DCSE Limit) Aging Model............................................................................33 5

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Healing Model.................................................................................................................36 A model based on laboratory healing tests...............................................................37 Healing model for use in this research.....................................................................39 Pavement Response Model.....................................................................................................43 Load Response Model.....................................................................................................43 Thermal Response Model................................................................................................44 Pavement Fracture Model.......................................................................................................46 Crack Initiation Model....................................................................................................46 Crack Growth Model.......................................................................................................47 Crack Amount Model......................................................................................................48 4 INTEGRATION OF MODEL COMPONENTS....................................................................50 Critical Condition Concept.....................................................................................................50 Module for Crack Initiation Simulation (CIS)................................................................51 Module for Crack Growth Simulation (CGS).................................................................52 Integration of Healing Model.................................................................................................53 Background of Experiments for Evaluating Healing Effect............................................53 Material and Structural Properties...................................................................................55 Model Predictions without Healing.................................................................................57 Stage one: crack initiation........................................................................................57 Stage two: crack propagation...................................................................................59 Determination of Critical Values for Daily Lowest AC Stiffness...................................60 Model Predictions with Healing......................................................................................62 Stage one: crack initiation........................................................................................62 Stage two: crack propagation...................................................................................64 Integration of Thermal Response Model................................................................................65 Selection of Climatic Environment.................................................................................65 Material and Structural Properties...................................................................................66 Traffic Information..........................................................................................................69 Model Predictions without Thermally Induced Damage.................................................69 Stage one: crack initiation........................................................................................69 Stage two: crack propagation...................................................................................70 Model Predictions with Thermally Induced Damage......................................................71 Stage one: crack initiation........................................................................................71 Stage two: crack propagation...................................................................................72 5 MODEL EVALUATION: PARAMETRIC STUDY.............................................................76 Effects of Material and Structural Properties.........................................................................77 Effect of Initial Fracture Energy......................................................................................78 Effect of Fracture Energy Aging Parameter....................................................................79 Effect of Binder Viscosity...............................................................................................81 Effect of Base Modulus...................................................................................................82 Effect of AC Layer Thickness.........................................................................................83 Effect of Traffic......................................................................................................................87 Effect of Climate.....................................................................................................................88 6

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6 MODEL CALIBRATION AND VALIDATION..................................................................92 Summary of Top-down Cracking Performance Model Data..................................................92 Selection of Pavement Sites............................................................................................92 Data Obtained from SuperPave IDT...............................................................................94 Data for Material Property Model...................................................................................96 Data for Pavement Response Model...............................................................................98 Data for Pavement Fracture Model...............................................................................100 Observed Pavement Performance Data.........................................................................100 Calibration of Model.............................................................................................................102 Calibration Procedure....................................................................................................102 Initial Calibration Results..............................................................................................103 Final Calibration............................................................................................................105 Validation of Model..............................................................................................................107 PRESS Procedure..........................................................................................................107 Validation Process Using PRESS..................................................................................108 Validation Results.........................................................................................................110 Final Model Predictions........................................................................................................111 Predicted vs. Observed Crack Initiation Time..............................................................115 Crack Initiation Time vs. Propagation Time.................................................................115 Crack Amount Development with Time.......................................................................117 7 CONCLUSIONS AND RECOMMENDATIONS...............................................................122 Conclusions...........................................................................................................................122 Recommendations.................................................................................................................123 LIST OF REFERENCES.............................................................................................................124 BIOGRAPHICAL SKETCH.......................................................................................................129 7

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LIST OF TABLES Table page 3-1 Input for a synthetic IDT test.............................................................................................38 4-1 IDT test results (at 10C)...................................................................................................56 4-2 Pavement structure and material properties in the aged section........................................57 4-3 Creep compliance values for aged samples at 0, 10, and 20C.........................................57 4-4 Data for material property aging models...........................................................................67 4-5 Thermal effect on crack initiation......................................................................................74 4-6 Thermal effect on crack propagation.................................................................................74 5-1 Range of parameters selected for sensitivity analysis........................................................77 6-1 Field test sections under Non-Freeze climate of Florida...................................................94 6-2 Field test sections under Hard-Freeze climate of Minnesota.............................................94 6-3 Data from SuperPave IDT resilient modulus and tensile strength tests at 10C...............95 6-4 Data from SuperPave IDT creep compliance tests at 0, 10, and 20C..............................96 6-5 Data used by the material property model.........................................................................97 6-6 Data used by the pavement response model......................................................................99 6-7 Observed top-down cracking performance......................................................................101 6-8 Predicted versus observed cracking performance for different k 1 -values (all test sections in Group I)..........................................................................................................103 6-9 Predicted versus observed cracking performance for different k 1 -values (without test section 5 in Group I)........................................................................................................105 6-10 Predicted cracking performance for various aging parameters using PRESS procedure..........................................................................................................................110 6-11 Crack Depths versus Time Predictions Using Calibrated Aging Parameter (k 1 = 3.0)...113 8

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LIST OF FIGURES Figure page 2-1 Flexural stiffness versus number of cycles to failure with and without rest periods (after Daniel and Kim, 2001).............................................................................................26 2-2 Healing tests at different DCSE for modified mixture: loading with 55 psi & healing at 20 C (after Kim and Roque, 2006)...............................................................................27 3-1 Framework of the Top-down cracking performance model..............................................28 3-2 Daily AC stiffness of one pavement section in Washington D.C. area (Year one)...........32 3-3 Daily AC stiffness of one pavement section in Washington D.C. area (Year five)..........32 3-4 1000 second creep compliance curves at three temperatures............................................33 3-5 Variation of energy limits, tensile strength and stiffness with age....................................35 3-6 FE limit aging curves at different FE i (k 1 = 3)...................................................................36 3-7 FE limit aging curves at different k 1 (FE i = 2 Kpa)...........................................................36 3-8 Predicted damage accumulations with and without healing..............................................38 3-9 Max. healing potential surface aging curves at different FE i ............................................40 3-10 Variation of daily highest temperature..............................................................................41 3-11 Daily lowest AC stiffness (S low ) profile and two critical values (S cr1 & S cr2 )....................42 3-12 Schematic plot for load response at the surface of the AC layer.......................................44 3-13 Schematic plot for thermal response in the AC layer........................................................45 4-1 Flowchart of CCI module..................................................................................................51 4-2 Flowchart of CIS module...................................................................................................52 4-3 Flowchart of CGS module.................................................................................................53 4-4 A typical HVS test section.................................................................................................54 4-5 Cracks observed in the aged section..................................................................................55 4-6 Recovered viscosity at different levels of aging................................................................56 4-7 Prediction of crack initiation w/o healing: damage versus load repetition........................58 9

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4-8 Prediction of crack initiation w/o healing: damage versus time........................................58 4-9 Prediction of crack growth w/o healing: crack depth versus load repetition.....................59 4-10 Prediction of crack growth w/o healing: crack depth versus time.....................................60 4-11 Daily AC stiffness of the aged section...............................................................................61 4-12 Daily AC stiffness of the unaged section...........................................................................62 4-13 Prediction of crack initiation with healing: damage versus load repetition.......................63 4-14 Prediction of crack initiation with healing: damage versus time.......................................63 4-15 Prediction of crack growth with healing: crack depth versus load pass............................64 4-16 Prediction of crack growth with healing: crack depth versus time....................................65 4-17 Geometry and material properties of a 3-layer pavement structure...................................66 4-18 One-year temperature profile at the pavement surface (Washington D.C.)......................68 4-19 Variation of AC stiffness with time...................................................................................68 4-20 Variation of fracture and healing properties with age (and depth)....................................69 4-21 Prediction of crack initiation w/o thermally induced damage...........................................70 4-22 Prediction of crack propagation w/o thermally induced damage.......................................71 4-23 Predicted thermal tresses at four depths of AC layer during Year 10...............................72 4-24 Prediction of crack initiation with thermally induced damage..........................................73 4-25 Prediction of crack propagation with and without thermally induced damage.................73 5-1 Effect of initial fracture energy on cracking performance.................................................79 5-2 Effect of initial fracture energy on average crack growth rate (C t )...................................79 5-3 Effect of fracture energy aging parameter on cracking performance................................80 5-4 Effect of initial fracture energy on average crack growth rate (C t )...................................80 5-5 Effect of binder type on cracking performance.................................................................81 5-6 Effect of binder type on average crack growth rate (C t )....................................................82 5-7 Effect of base modulus on cracking performance..............................................................83 10

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5-8 Effect of base modulus on average crack growth rate (C t )................................................83 5-9 Effect of AC layer thickness on cracking performance.....................................................84 5-10 Effect of AC layer thickness on crack propagation time (t p ).............................................84 5-11 Schematic drawing for one typical traffic lane..................................................................85 5-12 Predictions based on tire-edge cracking mechanism.........................................................86 5-13 Effect of traffic volume on cracking performance.............................................................87 5-14 Effect of traffic volume on average crack growth rate (C t )...............................................88 5-15 Effect of climatic environment on cracking performance.................................................89 5-16 Effect of climatic environment on average crack growth rate (C t )....................................89 5-17 Effect of climatic environment (w/o thermally induced damage) on cracking performance.......................................................................................................................90 5-18 Effect of climatic environment (w/o thermally induced damage) on average crack growth rate (C t )..................................................................................................................91 6-1 Determination of FE limit aging curve (including FE i ) based on measured FE from aged cores for test section I75-1A.....................................................................................98 6-2 Predicted versus observed cracking performance (All 11 sections)................................104 6-3 Predicted versus observed cracking performance (without section 5).............................106 6-4 Predicted versus observed cracking performance (from PRESS)....................................111 6-5 Predicted versus observed crack initiation time for all test sections...............................115 6-6 Predicted crack propagation time versus crack initiation time........................................116 6-7 Predicted crack amount versus time for test sections of level I.......................................118 6-8 Predicted crack amount versus time for test sections of level II......................................119 6-9 Predicted crack amount versus time for test sections of level III....................................120 6-10 Predicted crack amount versus time for test sections of levels IV and V........................121 11

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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 EVALUATION OF AN HMA FRACTURE MECHANICS BASED MODEL TO PREDICT TOP-DOWN CRACKING IN HMA LAYERS By Jian Zou December 2009 Chair: Reynaldo Roque Major: Civil Engineering It is well recognized that load-related top-down cracking commonly occurs in HMA pavements. This phenomenon has been reported to occur in many parts of the United States, as well as in Europe, Japan, and other countries. This mode of failure, however, cannot be explained by traditional fatigue mechanisms used to explain fatigue cracking that initiates at the bottom of the pavement. The primary objective of this research is therefore to identify the causes of top-down cracking and to develop mechanistic-based models for predicting this type of distress in HMA layers. The HMA fracture mechanics (HMA-FM) model developed at the University of Florida (UF) was determined as necessary to form the basis of this study because of its associated threshold concept that is suitable for developing rules for both top-down cracking initiation and propagation, and its ability to model the presence of macro cracks and their effect on response. However, the effect of aging and healing on top-down cracking performance during the entire service life of asphalt concrete pavement had not been considered. Also, the effect of transverse, as opposed to longitudinal, thermal stresses had not been addressed. Therefore, the framework of the existing HMA-FM model was modified by identifying and including appropriate sub-models to address these key factors, based on which the framework of the targeted model was formed. 12

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Consequently, the targeted model/system, which was termed the HMA-FM-based model, was completed by development and integration of several key elements into the finalized framework, including material property sub-models that accounts for changes in mixture properties (e.g., fracture energy, creep rate, and healing potential) with aging, and a thermal response model that predicts transverse thermal stresses. The HMA-FM-based model placed emphasis on the bending mechanism. A systematic parametric study showed that the model provided reasonable predictions and expected trends for both crack initiation and propagation. Furthermore, a full calibration of field sections indicated that the predictive system adequately represents and accounts for the most significant factors that influence top-down cracking in the field. The validation efforts using the prediction sum of squares (PRESS) procedure further established the viability of the predictive system. In conclusion, the work performed clearly indicates that the HMA-FM-based model developed and evaluated in this study should form the basis for a top-down cracking model suitable for use in the mechanistic-empirical pavement design guide (MEPDG). 13

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CHAPTER 1 INTRODUCTION Background It is now well accepted that load-related top-down cracking (i.e., cracking that initiates at or near the surface of the pavement and propagates downward) commonly occurs in hot-mix asphalt (HMA) pavements. The phenomenon has been reported to occur in many parts of the United States (1, 2, 3), as well as in Europe (4, 5), Japan (6), and other countries (7). This mode of failure cannot be explained by traditional fatigue mechanisms used to explain load-associated fatigue cracking that initiated at the bottom of the HMA layer. The lack of an appropriately verified description (i.e., model) of the mechanisms that lead to this type of cracking makes it difficult to effectively mitigate this costly form of distress. Several researchers (8) have developed hypotheses regarding the mechanisms of top-down cracking. Some researchers (9, 10) have also proposed experimental methods that may provide the properties necessary to evaluate the susceptibility of HMA mixtures to this type of distress. In addition, researchers (8, 11, 12) have performed analytical work that has led to the development of preliminary models that offer the potential to predict the initiation and propagation of top-down cracks. However, only limited research has been performed to evaluate and validate these hypotheses, test methods, and models. Research is needed to further evaluate the causes of top-down fatigue cracking and to develop effective laboratory testing systems and models that can assist material and pavement engineers to mitigate this problem. Suitable systems and models would also help to provide guidance for pavement engineers to select HMA mixtures and pavement structures that are the most resistant to top-down fatigue cracking in specified loading and environmental conditions. 14

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Objectives The objectives of this research were: To develop a mechanistic-based model for predicting top-down cracking performance in asphalt concrete pavement. To show that the developed model adequately represents and accounts for the significant factors (e.g., aging, healing, and transverse thermal stresses) that influence top-down cracking. To assess the ability of the developed model to accurately predict top-down cracking in the field. To demonstrate that the model developed and evaluated in this study can form the basis for a top-down cracking model suitable for use in the MEPDG. Scope For years, many researchers have made efforts to identify key factors and fundamental mechanisms that may lead to top-down cracking. Based on these efforts, two major mechanisms for top-down cracking initiation were identified for consideration in this study: The first mechanism is related to the bending-induced surface tension away from the tire (i.e., bending mechanism), which governs crack initiation in HMA layers of thin to medium thickness. The second mechanism is associated with the shear-induced near-surface tension at the tire edge (i.e., near-tire mechanism), which explains crack initiation in thick HMA layers. Of these two mechanisms, emphasis was placed on the bending mechanism because most of the pavement sections evaluated in this study have thickness values within the thin to medium range. However, preliminary investigations were also conducted using the near-tire mechanism. The HMA fracture mechanics (HMA-FM) model developed at the University of Florida (UF) has a threshold concept that is suitable for developing rules for both top-down cracking initiation and propagation, and can model the presence of macro cracks and their effect on response. In fact, these characteristics make the HMA-FM model uniquely suited to address the 15

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mechanisms associated with top-down cracking. Therefore, it was selected as the basis for model development in this study. Field sections from which performance data and field cores for determining mixture properties were obtained for use in calibration and validation were mainly selected from available Florida sections. Only two of the sections were obtained from Minnesota. In addition, one full-scale test was used to estimate two critical stiffness values for use in the healing model. The test was conducted in the Accelerated Pavement Testing (APT) facility at Florida Department of Transportation (FDOT) using the Heavy Vehicle Simulator (HVS). Research Approach The research approach taken for the development of a mechanistic-based model for prediction of top-down cracking is described in the following five phases: Determine key elements that must be part of the top-down cracking predictive system. The HMA-FM model developed at UF was selected to form the basis of the system because of its ability to model the presence of macro cracks which are essentially discontinuities that reduce the effective cross-section of the pavement layer, and their effect on the stress, strain, and energy distribution within the layer. However, the HMA-FM model in its existing form did not account for several key factors (e.g., aging, healing, and thermal stress) critical to properly represent the dominant top-down cracking mechanisms. Therefore, several appropriate sub-models were also identified for incorporation into the predictive system. A finalized framework of the predictive system is presented in Chapter 3 (Section One). Develop sub-models for incorporation into the predictive system. In this phase, several key elements were developed including material property sub-models that accounts for changes in mixture properties (e.g., fracture energy, creep rate, and healing potential) with aging, and a thermal response model that predicts transverse thermal stresses. Integrate model components into the predictive system. First, two core modulus, i.e., the crack initiation simulation (CIS) and crack propagation simulation (CGS) modules were formed on the basis of a critical condition concept. The sub-models developed in the second phase were then integrated into the framework of the predictive system. Consequently, an enhanced model, i.e., an HMA-FM-based model was formed. Evaluate the HMA-FM-based model. A parametric study was conducted using the integrated model to determine whether important factors that affect top-down cracking performance were appropriately captured by the predictive system. 16

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Calibrate and validate the HMA-FM-based model. The integrated system was calibrated and validated using field sections to show that it can reasonably predict top-down cracking performance of HMA pavements using rheological and fracture properties of HMA mixtures. 17

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CHAPTER 2 LITERATURE REVIEW The primary purpose of this chapter was to summarize the current understanding of cracking mechanisms and damage criteria in the area of design and evaluation of asphalt concrete pavement. The following subjects were examined: Classical fatigue approach Continuum damage model HMA fracture mechanics model Material property models Emphasis was placed on the published works on existing HMA facture mechanics model and on material property models, which are crucial to the development of a mechanics-based model to predict top-down cracking in HMA layers. Classical Fatigue Approach Earlier work to predict fatigue cracking of asphalt mixtures was primarily performed using fatigue tests. The allowable number of load repetition determined at failure of a test specimen was considered the life of the asphalt mixture. A more advanced approach, able to account for the effect of pavement structure was developed by calibrating on the basis of tensile strains at the bottom of the asphalt concrete layer. Different types of equations proposed by many researchers have been widely used as fatigue criteria. A typical predictive equation (13) for fatigue cracking is given as 3211fftfEfN (2-1) where E 1 = elastic modulus of asphalt concrete layer t = tensile strain at the bottom of asphalt concrete layer f 1 ,f 2 ,f 3 = constants determined from laboratory fatigue tests N f = allowable number of load repetitions 18

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These constants (i.e., f 1 f 2 and f 3 ), which relate HMA tensile strain or modulus to the allowable number of load repetitions, vary between investigators. However, due to lack of a fundamental mechanism, the approach is somewhat limited, and more mechanistic approaches are being employed. Viscoelastic Continuum Damage Model The evolution of the viscoelastic continuum damage (VECD) model started with the work of Kim and Little (14), in which they successfully applied Schaperys theory (15) for composite materials to sand asphalt concrete under cyclic loading. In their work, a viscoelastic problem was transformed to an elastic case by replacing physical strains by pseudo strains based on the extended elastic-viscoelastic correspondence principle. The above initial work was further developed and applied to asphalt concrete under monotonic loading (16) and cyclic loading (17 20). A fifty percent reduction in initial pseudo stiffness was generally used as a failure criterion for asphalt mixtures. Damage functions developed under a cyclic stress or strain controlled loading test of asphalt mixture were used as input parameters to evaluate cracking performance. Based on experimental data of asphalt concrete subjected to continuous and uniaxial cyclic loading in tension, Kim et al. (18) proposed a constitutive model that describes the mechanical behavior of the material under these conditions: HGFIRe (2-2) where I = initial pseudo stiffness = effective pseudo strain Re F = damage function G = hysteresis function H = microdamage healing function 19

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The effective pseudo strain accounts for the difference in fatigue mechanisms between controlled-strain and controlled-stress modes. The parameter, I is used to account for sample-to-sample stiffness variation in the asphalt specimens. The damage function, F represents the change in slope of the stress-pseudo strain loop as damage accumulates in the specimen. A mode factor is also applied to the damage function, F, to allow a single expression for both modes of loading. The hysteresis function, G describes the difference between the loading and unloading paths. The healing function, H accounts for change in pseudo stiffness due to healing. More details of this model can be found in Kim et al. (17, 18), and Lee et al. (19). To determine the fatigue life for a controlled-strain testing mode, Lee et al. (20) found that the hysteresis function, G need not be considered and that stress and pseudo strain values () at peak loads alone were sufficient. Rm RmmSIC (2-3) where I = initial pseudo stiffness C = coefficient of pseudo stiffness reduction (or, normalized pseudo stiffness) S = internal state variable A framework for including the effect of aging on the pseudo strain calculation was later developed by Daniel, et al. (21) to extend the model for prediction of field performance of mixtures over years. Subsequently, the VECD model was enhanced to incorporate characterization of viscoplastic behavior that might exist at slow loading rates and/or at high temperatures (22, 23, 24). Recently, a simplified fatigue test and analysis procedure (25) was also developed to identify a single characteristic curve that describes the reduction in material integrity as damage grows in the specimen regardless of applied loading conditions. However, the viscoelastic continuum damage based model does not consider a real physical crack in a material; therefore it cannot specifically address the stress redistribution due 20

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to cracking. Also, failure of a material is generally assumed to coincide with a 50 percent reduction in pseudo stiffness, since damage mechanics does not provide a realistic physical interpretation of failure. HMA Fracture Mechanics Model The continuing development of the HMA fracture mechanics (HMA-FM) model, which was determined to be necessary to include effects of aging, healing, and thermal stress on top-down cracking performance, represented a significant proportion of the effort of the researchers at the University of Florida (UF). The enhancements made to this model to make it suitable for use in a MEPDG framework will be reviewed following the sequence of each new development. HMA Fracture Mechanics Recently, researchers at UF (26, 27) developed the HMA fracture mechanics model. In this model, a fundamental crack growth law (named HMA fracture mechanics) was developed that allows for predicting the initiation and propagation of cracking, including top-down cracking, in asphalt mixture. This law is based on the fact that asphalt mixture has been determined to have a dissipated creep strain energy threshold (DCSE f ). Once the damage in asphalt mixture is equal to (or larger than) the threshold, a critical condition is triggered, which results in crack initiation (or propagation). HMA Fracture Mechanics-based Crack Growth Simulator Sangpetngam (28, 29) developed a HMA fracture mechanics-based crack growth simulator, which is based on the displacement discontinuity boundary element method (DDBEM). The resulting simulator is capable of predicting relative cracking performance among asphalt pavements of similar age. 21

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Energy Ratio Approach Roque et al. (30) derived a parameter termed the energy ratio (ER) based on a detailed analysis and evaluation of 22 field test sections in Florida using the HMA fracture mechanics model. The ER, which is defined as DCSE f of the mixture divided by the minimum dissipated creep strain energy (DCSE min ), is determined on the basis of properties that can be obtained from modulus, creep and strength tests performed with the Superpave IDT at a temperature of 10 C. This parameter accounts for effects of both damage and fracture properties on top-down cracking performance. A higher ER implies better cracking performance. Modified Energy Ratio Approach Since ER is limited to the evaluation of load-induced cracking performance, it may not provide a reliable basis to assess pavements located in areas where the thermal effect cannot be neglected. Therefore, Kim et al. (31) derived a system of equations to calculate thermally induced damage and then developed a modified energy ratio (MER) approach by introducing a correction factor into the ER equation accounting for effects of thermally induced damage on top-down cracking. In summary, these research efforts essentially formed the existing HMA fracture mechanics model. However, the effect of aging and healing on top-down cracking performance during the entire service life of asphalt concrete pavements was not considered, which certainly cannot be ignored for more accurate prediction of top-down cracking. Therefore, several mixture property sub-models that were suitable for further development into mixture aging and healing models for incorporation into the HMA-FM model were reviewed in the following subsection. In addition, transverse, instead of longitudinal, thermal stresses needed to be considered for prediction of top-down cracking, since unlike thermal cracking, top-down cracking generally occurs in the longitudinal direction. Furthermore, the thermally induced damage needed to be 22

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directly involved in the computation of damage accumulation, so that damage recovery due to healing can be applied in a more consistent way as compared to the indirect approach used in the MER method. Material Property Models In this part, several existing mixture property sub-models, which were suitable for further development, are reviewed. Binder Aging Model Asphalt aging is sometimes quantified by change in binder viscosity, which is directly related to the prediction of dynamic modulus and the creep properties, as discussed below. The binder viscosity at mix/laydown condition (t = 0) is estimated using the following equation (32): loglog()log()RAVTST (2-4) where is the binder viscosity in centipoises (10 -2 poise), T R is the temperature in Rankine, and A and VTS are regression constants. Typical values of A and VTS for three commonly used asphalt binders are given below (see NCHRP 1-37A design guide): PG 64-22: A = 10.98 VTS = .68 PG 67-22: A = 10.6316 VTS = .548 PG 76-22: A = 9.715 VTS = .208 For aged conditions, the viscosity of the asphalt binder at the pavement surface (depth z = in) can be estimated from the following in-service surface aging model (32): 0log log () loglog()1 tagedAVf f A tFBt (2-5) where t is the time in months, F AV is the air void adjustment factor, and A f and B f are field aging parameters that are functions of the in-service temperature and the mean annual air temperature (MAAT). The expressions for these parameters can be found in the current design guide (33). The viscosity-depth relation is given as: 23

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)0308.0exp(82.23)1(4)41)(()4(0,MaatEandzEzEEttzt (2-6) Dynamic Modulus Model The dynamic modulus |E | of asphalt concrete is used to analyze the response of pavement systems. Numerous attempts have been made to develop regression equations to calculate the dynamic modulus from conventional mixture volumetric properties. The predictive equation developed by Witczak and Fonseca (34) is one of the most comprehensive mixture dynamic modulus models available today. This model is used in the current ME design guide. According to Witczaks model, the dynamic modulus |E | can be represented by a sigmoidal function as follows: *log1 exp( log)rEt (2-7) where |E | is in psi; t r is reduced time in seconds (1/f, f is loading frequency) at a reference temperature; are fitting parameters. Detailed expressions for in terms of the gradation and volumetric properties of the mixture can be found in Witczak and Fonseca (34). Tensile Strength Model In their work on evaluation of mixture low temperature cracking performance, Deme and Young (35) found that the tensile strength of mixture (S t ) is well correlated with the mixture stiffness at a loading time of 1800 second, i.e., S 1800 They had extensive data in the temperature range of -40 to 25 C. Based on these data, the following relation was obtained between the mixture stiffness (in psi) and the tensile strength (in Mpa) through regression: 50lognnfntSaS (2-8) 24

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Where S f is the tensile stiffness that can be obtained from the dynamic modulus |E | by taking t = 1800 s. The constants a n are shown as follows, 012345a284.01,a330.02,a151.02,a34.03,a3.7786,a0.1652 Healing Model The concept of healing to increase mixture fatigue life has been observed and has been more widely accepted by researchers (36 41) in recent years. Button et al. (36) conducted controlled displacement crack growth testing in asphalt concrete mixes modified with various additives. They found an increase in work was required to open cracks after rest periods due to both relaxation in the uncracked body and chemical healing at the micro-crack and macro-crack interface. Zhang (37) conducted fracture tests using the Indirect Tensile Test and showed there is a critical energy level that distinguishes micro-damage from macro-damage; micro-damage is healable and macro-damage is not. Daniel and Kim (38) used a third point bending beam machine to induce flexural damage in beam specimens subjected to cyclic loading. They found the calculated flexural stiffness increased after the specimens were subject to rest periods. Figure 2-1 shows that healing increased the ultimate number of cycles the specimen endured before failure at 20 C. 25

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Figure 2-1. Flexural stiffness versus number of cycles to failure with and without rest periods (after Daniel and Kim, 2001) Recent research by Kim and Roque (39) focused on development of experimental methods to evaluate healing properties of asphalt mixture. First, the DCSE associated with healing during unloading was determined by developing relationships between changes in resilient deformation and DCSE. The healing process was then expressed in terms of DCSE versus time. Figure 2-2 presents healing results at 20 C for different applied DCSEs in the same mixture. Based on these results, they defined a healing rate h r which can be expressed as ttDCSEhhealedrln/ (2-9) where, DCSE healed (t) is the recovered DCSE at time t, which is defined as, tDCSEDCSEtDCSEremaininducedhealed (2-10) where, DCSE induced is the total energy dissipated at the end of the loading period, and DCSE remain (t) is the dissipated energy remaining at time t during the rest period. As a further step, they identified a normalized healing rate h nr which was defined as, inducedrnrDCSEhh/ (2-11) Substituting Eqn (2-9) into Eqn (2-11), leads to the following form, 26

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tDCSEtDCSEhinducedremainnrln/1 (2-12) The normalized healing rate was found to be independent of the amount of damage incurred in the asphalt mixture. It was also found to increase with increasing temperature. Figure 2-2. Healing tests at different DCSE for modified mixture: loading with 55 psi & healing at 20 C (after Kim and Roque, 2006) 27

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CHAPTER 3 DEVELOPMENT OF MODEL FRAMEWORK AND COMPONENTS In this chapter, the finalized model framework was presented, followed by a detailed description of three major components of the HMA-FM-based model (also termed the top-down cracking performance model): material property model, pavement response model, and pavement fracture model. Model Framework As shown in Figure 3-1, the finalized framework of the performance model includes five main parts: 1) inputs module, 2) SuperPave indirect tensile test (IDT), 3) material property model, 4) pavement response model, and 5) pavement fracture model. SUPERPAVE IDTAMOUNT OF CRACKINGPAVEMENT FRACTURE MODELCrack Initiation Model Crack Growth ModelCrack Amount ModelINPUTS MODULEPAVEMENT RESPONSE MODEL MATERIAL PROPERTY MODEL Figure 3-1. Framework of the Top-down cracking performance model 28

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Inputs Module and Indirect Tensile Test The inputs module provides traffic volume (in ESALs), temperatures within HMA layer (as predicted using enhanced integrated climatic model), and pavement material and structural properties. The required input for material and structural properties includes three parts: HMA material property, including basic mixture characteristics (gradation etc.) and damage and fracture properties (Superpave IDT). Modulus of base, subbase, and subgrade Layer thickness The Superpave IDT developed as part of the Strategic Highway Research Program (SHRP) was used to determine damage and fracture properties on field cores as part of the calibration efforts. Three types of tests were performed with the Superpave IDT: resilient modulus, creep compliance (for damage rate), and tensile strength (for fracture energy limit). Material Property Model Based on a brief review of the existing HMA-FM model and material property models relevant to the targeted top-down cracking performance model, four important sub-models were identified and developed, including aging models for asphalt concrete (AC) stiffness, tensile strength, and fracture energy (FE) limit, and a healing model. These sub-models formed the material property model as one key component of targeted predictive system. Details for each new development is presented in Chapter 3 (Section Two). Pavement Response Model The pavement response model is composed of two sub-models: 1) load response model that predicts load-induced surface tensile stresses away from the tire, and 2) thermal response model that accounts for the fact that transverse thermal stresses are limited by the maximum 29

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frictional resistance that can develop between the HMA surface and base layers. A detailed illustration of these two sub-models is given in Chapter 3 (Section Three). Pavement Fracture Model The pavement fracture model consists of three sub-models: 1) crack initiation model, which is a simplified approach (without considering damage zone effects) to predict the onset of crack in HMA layers, 2) crack growth model that predicts increase of crack depth with time, and 3) crack amount model that converts the relationship of crack depth versus time to that of crack amount versus time. Details regarding each of these sub-models are presented in Chapter 3 (Section Four). Output The output for the predictive system is presented in one of the following two forms: 1) crack depth versus time, or 2) crack amount versus time. Material Property Model As can be seen from the literature review, no existing model is available to predict damage and fracture properties, or the changes of these properties with aging. However, development, calibration, and validation of a mixture model to predict damage, healing, and fracture properties is clearly a major research effort in its own right, and well beyond the scope of the current study. Therefore, the goal of this research was to develop rudimentary (place-holder) relationships between basic mixture characteristic and these properties for use when measured properties cannot be obtained. The material property aging models and healing model developed for this purpose will be introduced in the following sub-sections. The plots used to illustrate the implementation of the models were generated using material and structural properties of one pavement section in the Washington D.C. area (see Chapter 4, Section Three for detailed information of that pavement). 30

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AC Stiffness (Creep Compliance) Aging Model An AC stiffness aging model was developed on the basis of binder aging model and dynamic modulus model (at a loading time of 0.1 s). In this model, the aging effect on mixture stiffness was considered using the following empirical equation, **00log||||logttEE (3-1) where |E | t and |E | 0 represent the stiffnesses corresponding to aged and unaged conditions, respectively; t and 0 correspond to the aged and unaged binder viscosity. As an example, Figure 3-2 gives three predicted AC stiffness curves as a function of time (in days), i.e., daily lowest, mean, and highest AC stiffness at surface of the pavement section of Washington D.C. area during Year one (started from July 1st). The AC stiffness curves of the same mixture at Year five (i.e., after being aged for five years), are shown in Figure 3-3. It can be seen from a comparison of these two plots that the effect of aging on AC stiffness is considerable, as expected. With the AC stiffness aging model, creep compliance curves at three different temperatures (e.g., 0, 10, and 20C) can be obtained by simply assuming an inverse relationship between creep compliance and AC stiffness. Figure 3-4 shows the predicted creep compliance curves at multiple temperatures for the same pavement section at Year one. These were used to generate master curve (42) to obtain creep compliance rate, and to predict thermal stresses (43, 44, 45). 31

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0 50 100 150 200 250 300 350 1.5 2 2.5 3 3.5 4 t (day)log-stiffness (ksi)Daily Stiffness of AC at Yr1 SHigh SAve. SLow Figure 3-2. Daily AC stiffness of one pavement section in Washington D.C. area (Year one) 0 50 100 150 200 250 300 350 1.5 2 2.5 3 3.5 4 t (day)log-stiffness (ksi)Daily Stiffness of AC at Yr5 SHigh SAve. SLow Figure 3-3. Daily AC stiffness of one pavement section in Washington D.C. area (Year five) 32

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0 100 200 300 400 500 600 700 800 900 1000 0 0.2 0.4 0.6 0.8 1 1.2 1.4x 10-5 t (sec)D(t) (1/psi)Creep compliances (3-T) Vs. time at Yr1 -10 oC 0 oC 10 oC Figure 3-4. 1000 second creep compliance curves at three temperatures AC Tensile Strength Aging Model The AC tensile strength aging model was developed by directly relating tensile strength to the AC stiffness aging model based on the relationship developed by Deme and Young (35). As an example, Figure 3-5 (c) shows the variation of AC tensile strength with age at the surface of the pavement section. It was obtained based on the AC stiffness aging curve determined at 10C, as shown in Figure 3-5 (d). FE Limit (DCSE Limit) Aging Model The FE limit surface aging model was conceived and expressed in the following form: 1min)()(kniiftSFEFEFEtFE (3-2) where, FE i is the initial fracture energy. FE min is the minimum value of FE limit after a sufficiently long aging period t inf In this research, FE min was determined based on experience (field specimens) to be 0.2 kJ/m3, and t inf was chosen as 50 years. k 1 is an aging parameter to be 33

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determined from calibration. S n (t) is the normalized stiffness at the surface of the AC layer, and is expressed as, 0max0)0,()(SSStStSn (3-3) where, S(t,0) is the stiffness at the surface of the AC layer. S 0 and S max are S(t,0) when t is set as 1 year and 51 years, respectively. Therefore, it can be seen that S n (t) is a variable between zero and one. The following relationship was conceived to describe the FE limit versus depth relation: )0,(/),(),(tSztStFEFEFEztFEfiif (3-4) where S(t,z) is the general expression for AC stiffness. Based on the FE limit aging model, the DCSE limit aging model was developed accordingly. It is expressed as follows, ztSztSztFEztDCSEtff,2/,,,2 (3-5) where, S t (t,z) is the general expression for AC tensile strength. As an example, Figure 3-5 (a) shows the variation of FE limit with age at the surface of the pavement in the Washington D.C. area. Correspondingly, the DCSE limit aging curve is given in Figure 3-5 (b). 34

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0 10 20 30 40 50 0 0.5 1 1.5 2 FEf (kJ/m3) 0 20 40 0 0.5 1 1.5 2 DCSEf (kJ/m3) 0 10 20 30 40 50 0 1 2 3 t (yr)St (Mpa) 0 10 20 30 40 50 0 10 20 30 t (yr)S (Gpa) 0 10 20 30 40 50 0 0.5 1 1.5 2 DCSEf (kJ/m3)(a)(b)(c)(d) Figure 3-5. Variation of energy limits, tensile strength and stiffness with age Clearly, the initial fracture energy FE i and aging parameter k 1 of Equation (3-2) are key parameters that govern the trend of the FE limit aging curve. Figure 3-6 gives FE limit curves at three different values of FE i (for a constant k 1 value of 3). As shown, generally the FE limit value decreases with time. For a larger FE i the entire FE limit curve moves upward (in the plot). But, the initial degradation rate of the curve also becomes larger. Figure 3-7 presents FE limit curves at three different values of k 1 for a constant FE i value of 2. It can be seen that a larger FE limit value is associated with a larger k 1 And, the initial degradation rate of the curve is smaller for a larger k 1 value. 35

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02468100102030405Time (year)Fracture Energy (Kpa) 0 2 5 10FEi (Kpa) :` Figure 3-6. FE limit aging curves at different FE i (k 1 = 3) 00.511.52010203040Time (year)Fracture Energy (Kpa) 50 1 3 5k1 : Figure 3-7. FE limit aging curves at different k 1 (FE i = 2 Kpa) Healing Model The development of a healing model for use in this research was completed in two steps. First, a mixture level healing model was obtained based on the research by Kim and Roque (39). The application of this model was illustrated using a simulated SuperPave IDT repeated load test on an HMA specimen. 36

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As a further step, possible improvements on the basis of this model for application in real pavement sections were investigated, which resulted in the development of a simplified empirically-based healing model for use in this research. A model based on laboratory healing tests As stated in the literature review, the normalized healing rate h nr is a mixture-dependent material property, which can be determined using the laboratory healing test developed at the University of Florida (39). If h nr is known a priori, the remaining dissipated energy after healing time t can be estimated using the following equation, which was derived from Equation (2-12), thDCSEtDCSEnrinducedremainln1 (3-6) where, DCSE induced is the dissipated energy at the end of the loading period. Based on Equation (3-6), a healing model was developed with the following assumptions, Micro-damage can only be healed during rest periods. For cyclic loading condition with more than one rest period, the damage induced during one loading period continuous to be healed during any successive rest period, until it vanishes. A constant temperature condition was assumed for this healing model since shift factors for computing normalized healing rate at different temperatures had not been established because of limited test results. The normalized healing rate is independent of mixture aging. This model was then used in conjunction with the existing HMA-FM model to predict crack initiation for an HMA specimen during a simulated IDT repeated load fracture test. The input information is given in Table 3-1. As shown in the table, a constant healing period of 300 s was introduced between every 300 loading cycles. Each of the loading cycles was composed of 0.1 s of haversine loading and 0.9 s rest period. It was assumed that no healing occurred during loading. 37

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Table 3-1. Input for a synthetic IDT test Parameter Value Loading period (sec) 300 Healing period (sec) 300 Temperature (C) 10 m 0.505 D1 (10 -6 1/Kpa) 0.101 DCSE f (Kpa) 0.978 h nr (1/ln(sec)) 0.1 It includes 300 loading cycles. Each cycle lasts 1-second. Figure 3-8 shows the predicted DCSE versus number of load cycles for the with and without healing conditions. As shown, the damage accumulation when healing was accounted for is much slower than that without considering healing. The healing model based on Equation (3-6) was then incorporated into the existing HMA-FM model to more accurately predict cracking performance. 00.20.40.60.810150030004500600075009000load cycleDCSE (kJ/m3) DCSE Limit without healing with healing Figure 3-8. Predicted damage accumulations with and without healing However, it is emphasized that this model may not be suitable for direct application in field conditions due to the following reasons: Variation of h nr (i.e., healing rate) with age was not taken into account in the model. Similarly, variation of h nr with temperature was not considered in the model. 38

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It is very hard to determine healing period and loading period in the field, which have varying lengths and are randomly distributed. Even if constant healing periods and loading periods are assumed, it is not trivial to track the decrement of damage generated in each loading period with time. In other words, the current model is somewhat computationally inefficient. Healing model for use in this research Since the lab test based healing model is not suitable for application in real pavements, possible improvements were investigated, which resulted in the development of an empirically-based and less computationally involved healing model, which is composed of three components: Maximum healing potential aging model. Daily-based healing criterion. Yearly-based healing criterion. Each of the components is introduced as follows. Maximum healing potential aging model The following relationship describes the maximum healing potential surface aging model: 67.1/1iFEnymtSth (3-7) where, FE i is the initial fracture energy, S n (t) is the normalized stiffness at the surface of the AC layer, and t is time in years. The maximum healing potential versus depth relation is: 0,,11,tSztSthzthymym (3-8) where, S(t,z) is the general expression for AC stiffness, and S(t,0) is the stiffness at surface of AC layer. As shown in Eqn (3-7), the maximum healing potential h ym was controlled by the initial fracture energy. As an example, Figure 3-9 gives maximum healing potential surface aging 39

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curves for three different values of FE i As shown, a higher h ym is generally associated with a larger FE i And, the initial degradation rate of h ym decreases with the increase of FE i value. 00.20.40.60.810102030405Time (year)Maximum Healing Potential 0 2 5 10FEi (Kpa) : Figure 3-9. Max. healing potential surface aging curves at different FE i Daily-based healing criterion A daily-based healing criterion was developed to estimate the recovered damage on any particular day. It was assumed that the damage generated in a day would be healed according to a daily normalized healing parameter h dn which was defined as, induceddremainddnDCSEDCSEh__1 (3-9) where, DCSE d_induced is the dissipated energy induced during the day, and DCSE d_remain is the dissipated energy remaining at the end of the day after healing, which can be obtained from Eqn (3-9) as follows, dninduceddremaindhDCSEDCSE 1__ (3-10) The daily normalized healing parameter is dependent on depth, time, and temperature. In this study, h dn was correlated with the daily lowest stiffness S low of the AC layer. The rationale is 40

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that healing potential is believed to be closely related to the flow capability of the AC material. Since S low is the lowest stiffness of a day, it represents the highest flow capability of the material on that day. Therefore, it was used to estimate the materials healing potential. The daily lowest stiffness can be determined using the daily highest temperature at any depth of the AC layer (refer to AC stiffness aging model). As an example, Figure 3-10 gives the variation of daily highest temperature at the surface of the pavement in the Washington D.C. area. 0 50 100 150 200 250 300 350 -10 0 10 20 30 40 50 time (days)Temperature (oC) Figure 3-10. Variation of daily highest temperature The corresponding daily lowest stiffness S low for five successive years (each year was started from July 1st), after taking the effects of aging into account, are plotted in Figure 3-11. In addition, two critical stiffness values S cr1 and S cr2 are also shown in the figure, which divide the S low profile into three zones, S cr1 is the Lower Bound Value. It was assumed that the daily normalized healing parameter h dn reached the maximum value of a year, i.e., h ym representing the highest healing potential of the mixture for that year, when: S low S cr1 (i.e., when S low falls into Zone A). h ym was determined using the maximum healing potential aging model. 41

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S cr2 is the Upper Bound Value. It was assumed that h dn reached the minimum value of a year, i.e., zero representing the lowest healing potential of the mixture, when: S low S cr2 (i.e., when S low falls into Zone C). For any S low value that is between S cr1 and S cr2 (i.e., when S low is in Zone B), h dn can be determined by linear interpolation between zero and h ym representing intermediate healing potentials. Determination of S cr1 and S cr2 is discussed in Chapter 4 (Section Two). 0 1 2 3 4 5 1 1.5 2 2.5 3 3.5 4 time (year)log-stiffness (ksi) Scr1Scr2 Zone C Zone B Zone A Figure 3-11. Daily lowest AC stiffness (S low ) profile and two critical values (S cr1 & S cr2 ) Yearly-based healing criterion In the daily-based healing criterion, the damage generated in any particular day will be healed only once during that day, after which no healing will be applied to remaining damage. This does not agree well with the observation from laboratory healing tests (39) which indicated that damage can be healed successively during any rest period that follows. Thus, a yearly-based healing criterion was developed to address continuous healing. In this healing criterion, it was assumed that all damage accumulated during a yearly period (started from July 1st) can be at least partially healed according to a yearly normalized healing parameter h yn which was defined as, 42

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inducedyremainyynDCSEDCSEh__1 (3-11) where, DCSE y_induced is the dissipated energy induced during the year, and DCSE y_remain is the dissipated energy remaining at the end of the year after healing, which can be obtained from Eqn (3-11) as follows, yninducedyremainyhDCSEDCSE 1__ (3-12) The yearly normalized healing parameter h yn was determined based on an averaged daily lowest stiffness S lowa over a prolonged period T p (i.e., the last 40 days of the yearly period being analyzed). Pavement Response Model The pavement response model developed as part of this study is composed of two sub-models: load response model and thermal response model. Details of each are explained below. Load Response Model The load response model was primarily aimed to predict bending-induced maximum surface tensile stresses, since the bending mechanism was the main focus of the HMA-FM-based model. A 9-kip circular load was applied repeatedly to the surface of a pavement to simulate the cyclic traffic load. Each cycle included 0.1 s haversine loading period and 0.9 s resting period. The model first estimated the AC modulus (see Chapter 3, Section Two) based on the temperature profiles and aging conditions. The stiffness gradient due to the temperature and aging effects was taken into account by dividing the AC layer into multiple sub-layers with different stiffnesses. The bending-induced tensile stresses at the pavement surface were then predicted using 3-dimensional (3-D) linear elastic analyses (LEA). The model also automatically searched for the maximum tensile stress on the surface of the AC layer. Figure 3-12 shows the bending-induced surface tensile stress away from the tire. 43

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Load response: L AC Figure 3-12. Schematic plot for load response at the surface of the AC layer Thermal Response Model The thermal response model predicts the thermally induced stresses in the transverse direction of asphalt concrete pavement. It was developed based on a thermal stress model for predicting thermal cracking (43). The existing thermal stress model was developed on the basis of the theory of linear viscoelasticity. In this model, the asphalt layer was modeled as a thermorheologically simple material. Based upon Boltzmann superposition principle for linear viscoelastic materials, the time-temperature constitutive equation at time t can be expressed as follows, '')'())'()(()(0dtdttdttEtt (3-13) where ('E ) is the relaxation modulus at reduced time ; and the reduced time is: /Tta where is the temperature shift factor. The strain (t') can be expressed as Ta 0(')(')tTt T where is the linear coefficient of thermal contraction, T(t') and T 0 are pavement temperature at time t' and the reference temperature corresponding to stress-free condition. The following finite difference solution to Equation (3-13) can be obtained by using the Prony series representation for creep compliance, 44

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11)()(Niitt (3-14) where //()()1iiiiiitettEe and are the changes in strain and reduced time, respectively. The existing model was intended to predict thermal stresses in the longitudinal direction. However, top-down cracking is known to occur in the longitudinal direction, so transverse, as opposed to longitudinal, thermal stresses are of particular relevance. The difference in transverse and longitudinal thermal stresses was caused by different boundary conditions to which the AC layer is subjected in these two directions: The AC layer is subjected to a fixed boundary condition in the longitudinal direction, which can induce very high longitudinal thermal stresses, which are the main cause of thermal cracking. However, the AC layer can move in the transverse direction once the maximum friction provided by the base is reached. Therefore, the transverse thermal stress, which contributes to top-down cracking, cannot exceed the friction limit. The limit value was determined to be 10 psi for typical HMA and base materials based on a separate calculation. Figure 3-13 shows the transverse thermal stresses due to change of temperature in an AC layer. Thermal response: TH AC Figure 3-13. Schematic plot for thermal response in the AC layer 45

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Pavement Fracture Model The pavement fracture model consists of three sub-models: (i) crack initiation model, (ii) crack growth model, and (iii) crack amount model. Crack Initiation Model The crack initiation model was developed on the basis of the threshold concept of the existing HMA fracture model. It was used to predict the crack initiation time and location in asphalt pavement sections, in conjunction with the material property model and pavement response model. Details regarding the joint use of all mentioned models were presented in Chapter 4 (Section One). In the crack initiation model, the load-associated damage and thermal-associated damage can be obtained based on the pavement response models as follows, The load-associated damage per cycle (or, DCSE L /cycle) is calculated as: 1.00max10sin10sin/dtttcycleDCSEpAVEL (3-15) where AVE is the average stress within the process zone being analyzed to determine crack initiation, and pmax is the creep strain rate, which is determined from IDT creep tests at 1000 second loading time. The thermal-associated damage over time interval from (t t) to t (or, DCSE T /t) is expressed as: 2//tttttttDCSEcrcrT (3-16) where cr is creep strain at time t. It can be expressed as: tttttttttcrcr21 In the crack initiation model, the rule for determination of crack initiation is given as follows, 46

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0.1tDCSEtDCSEtDCSEfremainnorm (3-17) where, DCSE remain is the accumulated dissipated energy when taking healing into account, DCSE f is the DCSE limit accounting for its degradation with aging, and DCSE norm was named due to the normalized form used for damage accumulation. The threshold for crack initiation is 1.0. The DCSE remain during each time interval t can be further expressed as follows, tDCSEcycleDCSEnhtDCSETLdnremain /1 (3-18) where n is number of load cycles in t. Crack Growth Model The crack growth model was developed on the basis of a two-dimensional (2-D) displacement discontinuity boundary element (DDBE) program (46) and the threshold concept of the existing HMA fracture mechanics model. It was used in conjunction with the material property model and thermal response model to predict increase of crack depth with time in asphalt concrete pavement. Details regarding the joint use of all models were presented in Chapter 4 (Section One). In the crack growth model, load induced tensile stresses ahead of the crack tip were predicted using the DDBE model as follows: The pavement structure was discretized using quadratic displacement discontinuity (DD) boundary elements. An initial crack was assumed to have a length of 6 mm (0.25 inch), which is about one half of the nominal maximum aggregate size of typical asphalt mixtures. It was placed vertically at the location of the maximum surface tensile stress and discretized using DD boundary elements. The load used for the 2-D model was adjusted so that the maximum tensile stress at surface of the pavement predicted by the 2-D model can be matched with the prediction by the 3-D LEA program. A similar strategy was used by Myers et al. (47) to account for 3-D effects on stress distribution by adjusting load applied to a 2-D pavement model. 47

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Meanwhile, the near-tip thermal stresses were estimated by applying the stress intensity factor (SIF) of an edge crack to the thermal stresses predicted using the thermal response model. The load associated damage and thermal associated damage were then calculated in a same manner as introduced in the crack initiation model. The same rule as used for determination of crack initiation was adopted in the crack growth model. Once the rule was satisfied (i.e., the DCSE norm reached 1.0), the crack started to grow. Some key terms used during simulation of step-wise crack growth are explained below: Potential crack growth path: The potential crack growth path was predefined in front of the crack tip at the beginning of crack growth simulation. It was composed of a series of process zones heading toward the bottom of the AC layer. Process zone: The process zone was used as a unit for step-wise increment of crack depth. Each of the process zones was assumed to have a uniform length of 6 mm (0.25 inch). The summation of lengths of all process zones led to the critical crack depth. Critical crack depth (CD c ): The critical crack depth is the final crack depth in the crack growth model, which was preset to be one-half the depth of the AC layer, as field observations showed that top-down cracking generally does not exceed that depth. Crack Amount Model The crack amount model was developed based on the following assumptions: For a 100 feet long pavement section, the maximum crack amount was assumed to be 330 feet. In other words, the pavement was determined to be severely cracked if total crack amount exceeded 330 feet. The crack amount, between zero and the specified maximum value, was assumed to be linearly proportional to the crack depth over AC layer thickness ratio (C/D), which ranges from zero to 0.5 (i.e., when crack depth is equal to CD c ). In accordance with the definition for crack initiation in terms of the crack depth (refer to crack initiation model), the onset of a crack in terms of the crack amount was assumed to be triggered by observing an amount of cracking of at least 12 feet. Based on the above assumptions, the crack amount versus time relationship can be obtained from the crack depth versus time relation predicted by the crack growth model. Using 48

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this model, the predicted amount of cracking at initiation is greater than 12 feet for any pavement that has an HMA layer thickness of no more than 12 inch. 49

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CHAPTER 4 INTEGRATION OF MODEL COMPONENTS Critical Condition Concept The critical condition concept is central to the cracking performance model. The concept, which was developed on the basis of HMA Fracture Mechanics and its associated threshold concept, specifies that crack initiation and growth only develop under specific loading, environmental and healing conditions that are critical enough to exceed the mixtures threshold. The concept is in direct contrast to traditional fatigue theory, which assumes that cracking is a continuous process. The integration of sub-models was completed based on this concept in the following two phases: In phase one, a critical condition identification (CCI) module was developed based on the critical condition concept. Figure 4-1 shows the flowchart of this module. As shown, all model components are involved in this module, including: i) material property model, ii) pavement response model, and iii) pavement fracture model. The module is intended to identify the critical condition by checking normalized dissipated creep strain energy (DCSE norm ) against the threshold, which was determined to be one in this study. On the basis of the CCI module, two follow-up modules i.e., crack initiation simulation (CIS) module and crack growth simulation (CGS) module were formed. These are described in the following two subsections. During phase two, the integration was continued to illustrate effects of healing and thermal stress using two example simulations: 1) healing effects in one pavement section in FDOTs APT facility (see Chapter 4, Section Two), and 2) thermal effects in one pavement section in Washington D.C. area (see Chapter 4, Section Three). 50

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Figure 4-1. Flowchart of CCI module Healing ModelCheck DCSEnorm against ThresholdOption A: Based on Pavement Response & Crack Initiation ModelsOption B: Based on Thermal Response & Crack Growth Models Material Property Aging ModelsDamage (DCSEnorm) Computatio n Module for Crack Initiation Simulation (CIS) The CIS module was developed by directly making use of the CCI module with option A (see Figure 4-1). The AC pavement structure is analyzed using a 3 dimensional (3-D) linear elastic analysis (LEA) program. As shown in Figure 4-2, the CCI module is called to compute the amount of induced damage, as well as damage recovery and accumulation in a step-wise manner until the critical condition is identified. This process usually takes several years. Whenever starting a yearly period, mixture properties are updated with the material property aging models. Upon completion of the simulation, crack initiation time, as well as the location of the initial crack will be reported by this module. 51

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Figure 4-2. Flowchart of CIS module DCSEnorm >= 1.0Call: CCI Module (Option A)End of SimulationPVT Modeling: Create PVT Structure using LEA No Yes Go to next time step Critical Condition Ident ified Module for Crack Growth Simulation (CGS) The CGS module was developed on the basis of CCI module with option B (see Figure 4-1). Figure 4-3 shows the flowchart for this module. Knowing the initiation time and location of initial crack, the CGS module was started by discretizing the pavement structure using 2-D displacement discontinuity boundary elements. The CCI module is then called to compute damage accumulation for each time step. If the critical condition is identified, the crack depth increases by a distance of one process zone (assumed to be 6 mm or 0.25 inch). The updated crack depth is then checked against the critical crack depth (preset to be one-half the depth of the HMA layer as field observations showed that top-down cracking generally does not exceed one-half depth of the layer): If the crack depth is less than the critical crack depth, a new pavement structure with the updated crack depth will be discretized and another simulation is performed using the same steps as mentioned above. For modeling using the displacement discontinuity (DD) boundary element method (BEM), remeshing of the whole pavement structure is not required. The increase in crack depth can be simply addressed by replacing the process zone next to the current crack-tip with a few DD elements. Once the critical crack depth is reached, the simulation is completed. The time and applied loads corresponding to each crack depth increment will be reported at the end of this simulation. 52

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Figure 4-3. Flowchart of CGS module DCSEnorm >= 1.0Update Crack Depth (CD)Call: CCI Module (Option B)End of SimulationCD >= CDcPVT Modeling: Create PVT Structure with Crack using DDBE No Yes No Yes Go to next time step Critical Condition Identified Go to next model Critical Crack Depth (CDC) Reache d Integration of Healing Model The material healing model was integrated into the performance model by determining the two critical values for daily lowest AC stiffness on the basis of a full-scale test conducted in the FDOTs APT facility using the HVS. Background of Experiments for Evaluating Healing Effect Since Accelerated Pavement Testing (APT) offers great potential for evaluation of performance of asphalt mixture and pavement in relatively short periods of time, the Florida Department of Transportation (FDOT) has built an APT facility in Gainesville, Florida. The system includes a fully mobile Heavy Vehicle Simulator (HVS), and eight linear tracks (150 ft long by 12 ft wide). Figure 4-4 shows one typical test section subjected to HVS loading in FDOTs APT facility. 53

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Figure 4-4. A typical HVS test section The University of Florida (UF) has been working on a research project with FDOT to assess cracking potential of asphalt mixture (48). In an effort to simulate aging of in-service pavement, a unit called the Accelerated Pavement Aging System (APAS) was developed and used to induce artificial aging of asphalt pavement test sections in the APT facility. One lane (testing track 1) composed of a dense-graded mixture on limestone base and sand subgrade was divided into three test sections: 1A, 1B, and 1C. Each section was subjected to different levels of aging and HVS loading. Sections 1B and 1C were tested first to assess the capability of the APAS system and to determine whether top-down cracking could be induced within a reasonable period of time. It was found that these two sections, which were subjected to extensive loading with moderate aging, could not be cracked even after many heavy loads were applied. In addition to the excellent properties of the mixture and structure, healing was thought to be playing a major role. Therefore, an experiment was devised to severely age one part of section 1A so as to minimize healing potential. This severely aged part and a companion unaged part were subjected 54

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to the same loading conditions (load and temperature) to more definitively evaluate the effects of healing. The paired portions of section 1A, which were simply called the aged and unaged sections for brevity, were subjected to 18-kip HVS loads to maximize the potential for cracking within a reasonable period of time. Loading on both sections started on February 06, 2007. During February 16 to 19, transverse surface cracks were found in the aged section after around 140,000 passes (see Figure 4-5). Loading was continued until March 27, 2007 with around 488,358 passes, when cracks in the aged section were believed to have approached about half-depth of the AC layer (this was later verified by coring the cracked AC layer). No crack was observed in the unaged section for the entire loading period. Figure 4-5. Cracks observed in the aged section Material and Structural Properties PG 67-22 binder was used in this study. Figure 4-6 shows binder recovery and viscosity measurements performed on cores obtained from the aged section at 0, 1, and 20 heating cycles of artificial aging. The binder viscosity of the unaged section corresponds to zero heating cycle (i.e., only slightly aged). As can be seen, the aging level induced in the top of the aged section 55

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after 20 healing cycles was extremely high, the viscosity at which was much greater than any value determined from field cores in typical Florida pavement. Figure 4-6 also shows that the APAS was able to effectively create a stiffness gradient through the asphalt layer. 0500001000001500002000002500003000003500004000004500000*120Number of heating cycles(48 hr/cycle)Viscosity (Poises) Top Middle Bottom Middle value N/A Figure 4-6. Recovered viscosity at different levels of aging Table 4-1 summarizes the Superpave Indirect Tension Test (IDT) results on cores from the paired sections. The same asphalt mixture with Georgia granite aggregate and 4.6% binder content was used for both sections. Table 4-1. IDT test results (at 10C) APAS m-value D 1 Creep compliance at 1000 sec Creep rate 1/GPa FE DCSEHMA ER Top 0.491 4.90E-07 2.15 7.13E-09 2.7 2.4 1.88 Unaged Bottom 0.537 5.43E-07 3.27 1.19E-08 2.4 2.2 1.22 Top 0.355 1.40E-07 0.29 5.74E-10 1.0 0.8 5.68 Aged Bottom 0.377 4.16E-07 0.88 2.12E-09 1.1 1.0 2.03 The pavement structural and material properties for each layer of the aged section are given in Table 4-2. As shown, the AC layer was further divided into three sub-layers accounting for stiffness gradients due to aging and temperature. Table 4-3 shows creep compliance readings measured at 0, 10, and 20C during 1000 second Superpave IDT creep tests. They were used to generate master curves for use in modeling viscoelastic material behavior. 56

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Table 4-2. Pavement structure and material properties in the aged section E H (psi) (in) AC-Top 2.40E+06 0.35 1.5 AC-Mid 1.20E+06 0.35 1.5 AC-Bot 6.00E+05 0.35 3 Base 4.00E+04 0.35 10.5 Subgrade 3.10E+04 0.4 Inf. Table 4-3. Creep compliance values for aged samples at 0, 10, and 20C TOP BOTTOM TIME (SEC) 0C 10C 20C 0C 10C 20C 1 0.054 0.069 0.129 0.076 0.126 0.248 2 0.059 0.075 0.152 0.076 0.145 0.296 5 0.057 0.084 0.169 0.096 0.171 0.379 10 0.059 0.096 0.196 0.098 0.198 0.443 20 0.065 0.114 0.262 0.111 0.257 0.503 50 0.085 0.126 0.328 0.127 0.296 0.828 100 0.092 0.148 0.425 0.136 0.378 1.154 200 0.095 0.176 0.597 0.146 0.471 1.607 500 0.109 0.238 0.873 0.162 0.669 2.484 1000 0.110 0.282 1.168 0.160 0.884 3.443 Model Predictions without Healing Stage one: crack initiation When healing effect was not considered, the predicted load passes to induce crack initiation for the aged and unaged sections are given in Figure 4-7. As seen in the figure, predicted number of loads to cracking for the unaged section was only about 41,700, which was much less than the 128,300 loads for the aged section. The predictions in Figure 4-8 in terms of DCSE norm versus time showed the same trend: the unaged section required less time for crack initiation than the aged one. 57

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0 20 40 60 80 100 120 140 160 180 200 0 0.2 0.4 0.6 0.8 1 1.2 Load repetition (x103) DCSEnorm Aged Unaged Figure 4-7. Prediction of crack initiation w/o healing: damage versus load repetition 02/06 02/08 02/10 02/12 02/14 02/16 02/18 02/20 02/22 02/24 0 0.2 0.4 0.6 0.8 1 1.2 DCSEnormTime (mm/dd) Aged Unaged Figure 4-8. Prediction of crack initiation w/o healing: damage versus time 58

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Stage two: crack propagation Figure 4-9 shows the step-wise increase of crack depth with load passes for both the aged and unaged sections. In general, the crack propagates at a relatively low rate initially (e.g., for the first process zone). The rate of growth then increases for the next few zones, beyond which the rate slows down again. As also shown in Figure 4-9, the load repetition to the critical crack depth (i.e., 3 inch for these two sections) is about 129,200 for the unaged section. Meanwhile, the load to 3 inch depth of the aged section is about 295,900, which was much more than that for the aged section. Similar trends can be found from Figure 4-10, which shows crack growth as a function of time. Given the time to crack initiation obtained in stage I, an average crack growth rate in the unaged section can be estimated to be 0.34 in/day, which is more than 1.5 times of the value, i.e., 0.20 in/day obtained for the aged section. -0.250.250.751.251.752.252.753.253.75050100150200250300350Load repetition ( x 103 )Crack depth (inch) unaged agedWithout Healing : Figure 4-9. Prediction of crack growth w/o healing: crack depth versus load repetition 59

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-0.250.250.751.251.752.252.753.253.75051015202530Time (day)Crack depth (inch) unaged agedWithout Healing : Figure 4-10. Prediction of crack growth w/o healing: crack depth versus time It is clear that the predicted results in terms of both crack initiation and propagation in the unaged section do not make sense, since as mentioned before, no crack was observed in that section during the entire loading period. Therefore, a mixture healing model must be included in the top-down cracking performance model. However, the two critical values S cr1 and S cr2 of the healing model have to be estimated before it can be used. Determination of Critical Values for Daily Lowest AC Stiffness In order to determine these two critical values S cr1 and S cr2 the daily lowest AC stiffness curves in the aged and unaged sections are plotted in Figures 4-11 and 4-12, respectively. As shown, the stiffnesses of the aged section are much higher than the unaged section. Since the asphalt mixture at surface of the aged section was extensively aged, as indicated by the measured binder viscosity which was much greater than any value determined from field cores in typical Florida pavement, it was believed that no healing would occur in the mixture of this section. According to the definitions of healing zones (refer to Chapter 3, Section Two), the 60

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S low values for this section should be close to S cr2 Therefore, the value for S cr2 was selected to be 2,000 ksi (see Figure 4-11). On the other hand, mixture in the unaged section was only slightly aged, as shown by viscosity test results. The mixture was thus believed to have full healing potential. According to the definitions of healing zones, the S low values for this section should be close to S cr1 As a result, S cr1 was selected to be 320 ksi (see Figure 4-12). 0 5 10 15 20 25 30 35 40 45 50 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 t (day)log-stiffness (ksi) Slow Scr2 Figure 4-11. Daily AC stiffness of the aged section 61

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0 5 10 15 20 25 30 35 40 45 50 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 t (day)log-stiffness (ksi) Slow Scr1 Scr2 Figure 4-12. Daily AC stiffness of the unaged section Model Predictions with Healing Another set of predictions was made using the performance model after incorporating the healing model. Stage one: crack initiation The predicted damage in terms of DCSE norm versus load passes for the paired sections are given in Figure 4-13. The figure clearly shows that no crack occurred in the unaged section, which is consistent with the observation in the full-scale HVS test. On the other hand, the predicted load passes to crack initiation for the aged section remained at 128,300. The similar prediction for the aged section using performance models with and without the healing model is expected, since the aged section had no healing potential due to extensive aging applied in the test. The predicted load passes (128,300) were also found to be close to the actual number of passes (140,000) when the first crack was observed. 62

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The predictions in Figure 4-14 show the same trend: crack occurred in the aged section after about 12 days, and no crack occurred in the unaged section. 0 20 40 60 80 100 120 140 160 180 200 0 0.2 0.4 0.6 0.8 1 1.2 Load repetition (x103) DCSEnorm Aged Unaged Figure 4-13. Prediction of crack initiation with healing: damage versus load repetition 02/06 02/08 02/10 02/12 02/14 02/16 02/18 02/20 02/22 02/24 0 0.2 0.4 0.6 0.8 1 1.2 DCSEnormTime (mm/dd) Aged Unaged Figure 4-14. Prediction of crack initiation with healing: damage versus time 63

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Stage two: crack propagation Performance predictions accounting for healing were continued in the crack propagation stage. As shown in Figure 4-15, the crack in the aged section reached the critical crack depth after 296,600 passes of HVS loading. As expected, the number of load passes was slightly greater than the one predicted by the model without healing, since the healing potential, which increases with depth helped to prolong fatigue life. Figure 4-16 shows predicted crack growth in terms of crack depth versus time in the aged section, which follows a similar pattern as that of Figure 4-15. It took another 14 days for the crack to reach the critical crack depth. -0.250.250.751.251.752.252.753.253.75050100150200250300350Load repetition ( x 103 )Crack depth (inch) unaged agedWith Healing : Figure 4-15. Prediction of crack growth with healing: crack depth versus load pass 64

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-0.250.250.751.251.752.252.753.253.75051015202530Time (day)Crack depth (inch) unaged agedWith Healing : Figure 4-16. Prediction of crack growth with healing: crack depth versus time In summary, the predictions after incorporation of the healing model seemed quite reasonable, as they agreed well with observations from cores, which indicated that the crack had propagated to about half-depth of the AC layer of the aged section. Integration of Thermal Response Model Integration of the thermal response model was completed by simply activating this model in the CCI module. The significance of the thermal response model was illustrated by predicting cracking performance of one pavement section in the Washington D. C. area with and without thermally induced damage accounted for in the performance model. Selection of Climatic Environment Since the thermal response model was fully developed, the key for successful integration of this model was to show that the performance model cannot predict cracking performance accurately without accounting for thermal effects. In other words, it was necessary to demonstrate the need to include the thermal response model. 65

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A limited investigation indicated that thermal damage induced in pavement sections subjected to a non-freeze climate as that of Florida was not high enough to alter the predicted top-down cracking performance of these sections. Therefore, a freeze-thaw climate as that of Washington, D.C., was selected to demonstrate the importance of including the thermal response model. The corresponding temperature data file was used as input for model prediction, containing hourly temperatures at different depths of the AC layer. The temperature data was generated based on the climatic condition and typical pavement material and structural properties using the enhanced integrated climatic model (EICM). Other types of climatic environment such as the hard-freeze climate of North Dakota were evaluated in Chapter 5 (Section Three). Material and Structural Properties The geometry and material properties for the pavement section are illustrated in Figure 4-17. To account for the effects of stiffness gradient due to temperature and aging, the AC layer was divided into 3 sub-layers with thickness h 1 h 2 and h 3 respectively. Since the temperature and aging gradients are greatest near the surface and reduce with depth, the thickness values of the AC sub-layers were taken as h 1 = h 2 = H 1 /4 and h 3 = H 1 /2. AC layer Base Subgrade 240ksiE 312ksiE 212''H 15''H 1h2h3h35.02 4.03 Figure 4-17. Geometry and material properties of a 3-layer pavement structure 66

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The variation of asphalt concrete (AC) modulus with time was estimated using the AC stiffness (creep compliance) aging model. Meanwhile, the degradation of AC fracture properties and healing potential with time were predicted using the FE limit (DCSE limit) aging model and the healing model, respectively. The input information for these material property models is listed in Table 4-4. Table 4-4. Data for material property aging models Parameter Value Aggregate % passing by weight (seive size) 100.0 (3/4 in.), 90.0 (3/8 in.), 60.2 (# 4), 4.8 (# 200) Binder type 67-22 Mean annual air temperature, F 60 Effective binder content, % by volume 12 Air void content, % by volume 7 Initial fracture energy, Kpa 2 Fracture energy aging parameter 3 Figure 4-18 shows the one-year temperature profile at the surface of the AC layer in the Washington D.C. area generated from the EICM. The first day shown in the figure corresponds to July 1st of the year. As an illustration, Figure 4-19 shows the estimated dynamic modulus at year one based on the temperature profile in Figure 4-18. The stiffness was calculated at a load frequency of 10 Hz (i.e., loading time 0.1 s). The variation of FE limit, DCSE limit, tensile strength and maximum healing potential with age (and depth) are given in Figure 4-20. 67

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0 50 100 150 200 250 300 350 -10 0 10 20 30 40 50 time (days)Temperature (oC) Figure 4-18. One-year temperature profile at the pavement surface (Washington D.C.) 0 50 100 150 200 250 300 350 0 200 400 600 800 1000 1200 1400 time (days)Dynamic modulus (ksi) Figure 4-19. Variation of AC stiffness with time 68

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0 20 40 0 0.5 1 1.5 2 FEf (KJ/m3) 0 20 40 0 0.5 1 1.5 2 DCSEf (KJ/m3) 0 20 40 0 1 2 3 t (yr)St (Mpa) 0 20 40 0 0.5 1 t (yr)hmy z=0" z=1" z=2.75" z=0" z=1" z=2.75" z=0" z=1" z=2.75" z=0" z=1" z=2.75" Figure 4-20. Variation of fracture and healing properties with age (and depth) Traffic Information The pavement section was assumed to be subjected to 18 kip single axle wheel load at a rate of 100 cycles per hour, which is equivalent to 17.5 million ESALs per 20 years. Model Predictions without Thermally Induced Damage In this section, predictions for crack initiation and propagation in the pavement section were made without activation of the thermal response model. Stage one: crack initiation Figure 4-21 gives the results of load induced damage accumulation versus time during Year 12. As shown, crack initiation occurred in early October of that Year. The total load passes leading to crack initiation is about 9.9 million ESALs, which were obtained by adding the load passes predicted in Year 12, i.e., 223,700 to the product of the yearly traffic (i.e., 0.876 million ESALs) and 11 (meaning the past 11 years). 69

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Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul 0 0.2 0.4 0.6 0.8 1 1.2 Damage accumulation at Yr12DCSEnorm Time (month) Figure 4-21. Prediction of crack initiation w/o thermally induced damage Stage two: crack propagation The predicted crack propagation without thermally induced damage is shown in Figure 4-22. It started at a slow rate for the first few process zones. Subsequently, it sped up and maintained a faster rate until it reached the critical crack depth (i.e., 2.5 in for this case). The process took about 9.5 years. 70

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00.511.522.530510152025Time (year)Crack depth (inch) without thermalWASH : Figure 4-22. Prediction of crack propagation w/o thermally induced damage Model Predictions with Thermally Induced Damage Another set of predictions were made when both load and thermally induced damage were accounted in the performance model. The thermal effect on predicted cracking performance was then evaluated based on a comparison of these results with those of the prior section. Stage one: crack initiation Figure 4-23 gives the predicted thermal stresses at four depths of the AC layer using the thermal response model. As shown, the thermal stresses at any depth of the AC layer were almost negligible during warmer months (i.e., Jul. to Sep., and Apr. to Jun.), but they were kept at 10 psi during most of the cold times (i.e., the other half of the yearly period), during which significant amount of thermally induced damage can be generated. It can also be seen from the figure that thermal stresses decrease with depth. 71

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0 100 200 300 400 0 2 4 6 8 10 T at Yr10 ( z = 0" )T (psi) 0 100 200 300 400 0 2 4 6 8 10 ( z = 1.25" ) 0 100 200 300 400 0 5 10 ( z = 2.5" )t (day)T (psi) 0 100 200 300 400 0 5 10 ( z = 5" )t (day) Figure 4-23. Predicted thermal tresses at four depths of AC layer during Year 10 The damage accumulation during Year 10 is shown in Figure 4-24. It can be seen that crack initiation occurred in early June of that Year. After accounting for loads applied in prior years, the total loads leading to crack initiation were about 8.7 million. Stage two: crack propagation Figure 4-25 shows the increment of crack depth with time when thermally induced damage was considered (refer to the solid line). Again, the crack propagated at a relatively low growth rate through the first few zones. It then accelerated until it reached the critical crack depth. The process took about 6.4 years. For comparison purpose, the prediction for crack depth versus time without considering thermally induced damage was also presented in the same figure (see the dashed line). 72

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Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul 0 0.2 0.4 0.6 0.8 1 1.2 Damage accumulation at Yr10DCSEnorm Time (mon) Figure 4-24. Prediction of crack initiation with thermally induced damage 00.511.522.530510152025Time (year)Crack depth (inch) with thermal without thermalWASH : Figure 4-25. Prediction of crack propagation with and without thermally induced damage Table 4-5 summarizes the predicted number of years (nyrs) and number of load passes (npas) leading to crack initiation, and location of the initial crack (xs) for two conditions: (a) with and (b) without thermally induced damage. It can be seen that without accounting for thermally induced damage, an additional 1.4 years or 1.2 million loads are needed to see 73

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cracking in this pavement. Clearly, thermal effect cannot be ignored for accurate prediction of crack initiation. Table 4-5. Thermal effect on crack initiation WASH nyrs npas (x 10 6 ) xs (in.) a: with thermal 9.9 8.7 27.5 b: without thermal 11.3 9.9 27.5 Table 4-6 summarizes the predicted number of years (nyrs), number of load passes (npas), and total increment of crack depth (a) for these two conditions during the crack propagation stage. Table 4-6. Thermal effect on crack propagation WASH nyrs npas (x 10 6 ) a (in.) a: with thermal 6.4 5.6 2.25 b: without thermal 9.5 8.3 2.25 Without thermally induced damage, an additional 3.1 years or 2.7 million loads are required to complete the propagation stage. Therefore, the importance of incorporation of thermally induced damage in crack propagation was also emphasized. It is noted that the time for crack initiation will affect the propagation time, since FE limit (DCSE limit) reduces with age. For example, if the FE limit of Year 10 (when crack initiation was identified under condition (a)) was used as the starting FE value for predicting crack propagation under condition (b), additional time or loads are expected. In summary, predicted top-down cracking performance of one pavement section in the Washington D.C. area was compared for two different conditions: with and without thermally induced damage. Based on the comparison for both crack initiation and propagation, it was found that thermal effect is important for an accurate prediction. Therefore, it is necessary to incorporate the thermal response model into the performance model. The results also indicated 74

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that the FE limit (DCSE limit) aging model played an important role in determining the time of crack initiation and the average crack grow rate. 75

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CHAPTER 5 MODEL EVALUATION: PARAMETRIC STUDY The top-down cracking performance model was intended to predict crack initiation (time and location) as well as crack propagation (increase of crack depth or crack amount with time) for calibration and validation using real asphalt concrete pavements. However, in view of the complexity involved in the model, it was necessary to know how various factors affected predicted results and which factors had the strongest influence on performance. More importantly, it was crucial to identify factors that could alter the cracking mechanism used in the model (e.g., bending versus near-tire mechanism). Therefore, a parametric study was conducted using a broad range of input parameters to evaluate these factors. To limit the number of runs, the following conditions were assumed: The pavement structure used in the example for demonstration of the thermal effect was selected (see Chapter 4, Section Three). It consists of three layers: asphalt concrete (with three sub-layers), base and subgrade. The base thickness, and subgrade modulus and thickness were not changed for all analyses conducted. The Poissons ratio for each of the layers was also kept same throughout the study. The variation in AC creep compliance was obtained by varying binder viscosity, i.e., by changing binder type only. Meanwhile, the other material characteristics (e.g., aggregate gradation, air void and effective binder content of asphalt mixture) that also influence creep compliance were not changed. The conditions defined above reduced the input requirements to the following parameters. They are presented below according to three different categories: Material and structural properties including, Initial fracture energy. Fracture energy aging parameter. Binder viscosity. Base modulus. AC layer thickness. 76

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Traffic volume: number of ESALs per year. Climatic information: a mean annual air temperature (MAAT) and its companion hourly temperature data at four different depths of AC layer for a whole year. The values selected for each variable are presented in Table 5-1. For each variable, the value used in the example for demonstration of the thermal effect (Chapter 4, Section Three) is highlighted via a shaded area. The combination of these values (as shown in the shaded area) was used as a standard case. In other words, the example was adopted here as a standard case. Accordingly, the input parameters in Table 4-4 were used in conjunction with those of Table 5-1 to conduct this analysis. Then, each parameter included in the analysis was individually varied relative to the values given in Table 5-1, while the remaining parameters were held constant at the values used for the standard case. In total, the influence of individual parameters was investigated using 16 cases including the standard one. However, interactions and combined effects were beyond the scope of the analysis. Table 5-1. Range of parameters selected for sensitivity analysis Variables Values Initial Fracture Energy FE i (Kpa) 2 5 10 Fracture Energy Aging Parameter k 1 1 3 5 Binder Type 58-28 67-22 76-22 Base Modulus (Ksi) 20 40 60 AC Layer Thickness (in) 2.5 5 7.5 10 Traffic Volume (10 6 ESALs per year) 0.175 0.438 0.876 MAAT (F) 50 60 75 Effects of Material and Structural Properties The material and structural properties under investigation included initial fracture energy, fracture energy aging parameter, binder viscosity, base modulus and AC layer thickness. The influence of each of them is discussed in the following subsections. 77

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Effect of Initial Fracture Energy The initial fracture energy is the starting value (also maximum value) of any fracture energy aging curve (see Figure 3-6). It also controls the degradation rate of any maximum healing potential aging curve (see Figure 3-9). Therefore, it was expected to have a strong influence on pavement cracking performance. To confirm the expected effect, a broad range of initial fracture energies was selected. Plots of crack depth versus time predicted by the model for different values of initial fracture energy are shown in Figure 5-1. As shown, pavement with higher initial fracture energy exhibits better cracking performance, i.e., longer crack initiation time and propagation time. For pavements with the same AC layer thickness, comparison was also made with respect to an average crack growth rate, which was defined as, picttCDCDC (5-1) where, C t is average crack growth rate, CD c is critical crack depth, CD i is initial crack depth of 0.25 inch, and t p is crack propagation time to the critical crack depth. Figure 5-2 shows the predicted average growth rate for different FE i values. It is clear that a higher FE i value leads to a lower crack growth rate (i.e., better cracking performance). 78

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00.511.522.53051015202530354045Time (year)Crack depth (inch) 2 5 10FEi (Kpa) : Figure 5-1. Effect of initial fracture energy on cracking performance 00.10.20.30.40.50.6Ct (inch /year) 2 5 10FEi (Kpa) : Figure 5-2. Effect of initial fracture energy on average crack growth rate (C t ) Effect of Fracture Energy Aging Parameter Fracture energy aging parameter k 1 is an input parameter that governs the shape of the fracture energy aging curve. For a constant initial fracture energy, a larger k 1 value corresponds to a lower rate of degradation in fracture energy with aging (i.e., higher resistance to fracture, see Figure 3-7). 79

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The effect of the fracture energy aging parameter is shown in Figures 5-3 and 5-4. As shown, the increase of k 1 value results in longer time to crack initiation (Figure 5-3) and a lower average crack growth rate (Figure 5-4). 00.511.522.530510152025Time (year)Crack depth (inch) 1 3 5k1 : Figure 5-3. Effect of fracture energy aging parameter on cracking performance 00.10.20.30.40.50.6Ct (inch /year) 1 3 5k1 : Figure 5-4. Effect of initial fracture energy on average crack growth rate (C t ) 80

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Effect of Binder Viscosity A typical range of binder types (from soft to stiff) were selected for the analysis. The predicted cracking performance is presented in Figures 5-5 and 5-6, which shows that crack initiation time is not affected by the change in binder viscosity (Figure 5-5), and a softer binder results in only a slightly higher crack growth rate (Figure 5-6). This appears to be associated with the higher creep rate of the mixture with the softer binder. However, as binder stiffness also affects AC stiffness, a softer binder leads to lower AC stiffness, which can counter-balance the effect of higher creep rate. Therefore, the overall change in the average crack growth rate is small. In other words, pavement cracking performance is not sensitive to the change of binder viscosity. Of course, it must be emphasized that this result does not consider that softer binder may increase mixture fracture energy, which was kept constant in this analysis. 00.511.522.530510152025Time (year)Crack depth (inch) 58-28 67-22 76-22Binder type : Figure 5-5. Effect of binder type on cracking performance 81

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00.10.20.30.40.50.6Cr (inch /year) 58-28 67-22 76-22Binder type : Figure 5-6. Effect of binder type on average crack growth rate (C t ) Effect of Base Modulus The effect of base modulus was investigated using the material properties presented in Table 4-4 and the values of base modulus given in Table 5-1. Pavement cracking performance predicted by the model is given in Figures 5-7 and 5-8, which shows that the pavement with higher base modulus has better performance, i.e., longer crack initiation time (Figure 5-7) and lower crack growth rate (Figure 5-8). This was expected because a stiffer base tends to reduce the load induced tensile stresses at the surface of pavement. For the range of base modulus values studied, the effect of base modulus is fairly strong. 82

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00.511.522.530510152025Time (year)Crack depth (inch) 20 40 60E2 (ksi) : Figure 5-7. Effect of base modulus on cracking performance 00.10.20.30.40.50.6Ct (inch /year) 20 40 60E2 (ksi) : Figure 5-8. Effect of base modulus on average crack growth rate (C t ) Effect of AC Layer Thickness A wide range of AC layer thickness values were selected for this analysis: 2.5 in for a thin AC layer. 5 in for a medium thickness AC layer. 7.5 in for a thick AC layer. 10 in for a very thick AC layer (i.e., a full depth AC pavement). 83

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The predicted pavement cracking performance for the first three AC layer thickness values are shown in Figures 5-9 and 5-10, which shows that the pavement with thicker AC layer had better cracking performance, i.e., longer crack initiation time (Figure 5-9) and longer crack propagation time (Figure 5-10). 00.511.522.533.540510152025Time (year)Crack depth (inch) 2.5 5 7.5H1 (inch) : Figure 5-9. Effect of AC layer thickness on cracking performance 024681012tp (year) 2.5 5 7.5H1 (inch) : Figure 5-10. Effect of AC layer thickness on crack propagation time (t p ) 84

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However, the predicted location of the initial crack for the thick AC layer was found more than 36 inch from the center of one tire. In this circumstance, the initial crack was actually predicted to be either in the compressive zone of the other tire or in the other traffic lane, as indicated by Figure 5-11. In other words, the prediction was not realistic. Therefore, the bending mechanism used for model prediction may not be appropriate for the thick AC layer pavement. 36363636 Wheel Path Wheel Path 12 36363636 Wheel Path Wheel Path 12 Figure 5-11. Schematic drawing for one typical traffic lane The near-tire mechanism, accounting for shear-induced tension at the tire edge, was thus considered for use in thick AC layer. According to this mechanism, the location of initial crack is right next to the tire edge. The major driving force for crack initiation and propagation is the shear-induced principal tensile stress. However, a crack growth simulation tool based on this mechanism was not available at this time. Therefore, the CGS module was used as a surrogate to predict crack growth with time. Due to the localized property of the shear-induced tension at the tire edge, the critical crack depth was redefined to be one fourth of the AC layer depth. Then, a 85

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simplified model with the near-tire mechanism was used to predict cracking performance for the 7.5 inch thick AC layer and a 10 inch full depth AC pavement. The predicted cracking performance is given in Figure 5-12. As shown, both pavements have identical performance, i.e., same crack initiation time and similar crack propagation time. This is expected because the principal tensile stress of 25 psi predicted based on actual tire stresses was the same for both pavements. In fact, this stress was found to be independent of AC thickness and the stiffness ratio of AC to base layer. A comparison of Figure 5-12 and Figure 5-9 appears to indicate that thick pavements may perform even worse than a pavement with a medium thickness AC layer. However, it should be noted that some potential factors affecting the near-tire mechanism are not addressed in the current model, including effects of wander and stress state. Both will result in less damage than currently predicted. Therefore, the comparison may not be accurate without considering these factors. 00.511.522.5302.557.51012.515Time (year)Crack depth (inch) 7.5 10H1 (inch) :Tire-edge Cracking Mechanism Figure 5-12. Predictions based on tire-edge cracking mechanism 86

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Effect of Traffic As shown in Table 5-1, three traffic levels (in million ESALs per year) were selected for this analysis: High traffic: 0.876 Medium traffic: 0.438 Low traffic: 0.175 The high traffic level is equivalent to 100 ESALs in an hour. Accordingly, the medium and low traffic levels correspond to 50 and 20 ESALs per hour. The predicted pavement performance is shown in Figures 5-13 and 5-14. As expected, the pavement subjected to the highest traffic level had the worst performance, i.e., shortest time to crack initiation (Figure 5-13) and highest crack growth rate (Figure 5-14). Overall, the effect of traffic is strong. 00.511.522.530510152025Time (year)Crack depth (inch) 0.876 0.438 0.175Traffic (x106 ESALs/Year) : Figure 5-13. Effect of traffic volume on cracking performance 87

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00.10.20.30.40.50.6Ct (inch /year) 0.876 0.438 0.175Traffic (x106 ESALs/Year) : Figure 5-14. Effect of traffic volume on average crack growth rate (C t ) Effect of Climate Three typical climatic environments were selected for this analysis: Non-freeze (NF) environment, as represented by the climate of Melrose, FL. Freeze-thaw (FT) environment as of Washington, D.C. Hard-freeze (HF) environment as of Fargo, ND. The mean annual air temperature (MAAT) value for each of the climatic environment was given in Table 5-1. Under each climate, the MAAT value and the corresponding temperature data file containing hourly temperature history at four depths of the AC layer for a whole year were used as input for model prediction. The predicted pavement performance is shown in Figures 5-15 and 5-16. As shown, the pavement cracking performance under both the FT and HF environments appears to be identical. Meanwhile, under the NF environment, the pavement exhibits a slightly later crack initiation (Figure 5-15), but a higher crack growth rate (Figure 5-16) as compared to the performance under the other two environments. Overall, the effect of climatic environment (more specifically, temperature) is minimal. 88

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00.511.522.530510152025Time (year)Crack depth (inch) NF FT HFClimate type : Figure 5-15. Effect of climatic environment on cracking performance 00.10.20.30.40.50.6Ct (inch /year) NF FT HFClimate type : Figure 5-16. Effect of climatic environment on average crack growth rate (C t ) This was expected because the influences of climatic environment on damage development in the pavement are two-sided: on one side, colder weather leads to higher thermal stresses and thus higher thermally induced damage. However, it should be noted that transverse, as opposed to longitudinal, thermal stresses were used to compute thermally induced damage in the thermal response model (Chapter 3, Section Three). Therefore, the resulting thermally induced damage is 89

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not as high as that caused by longitudinal thermal stresses. On the other side, colder weather results in lower creep rate and thus lower load induced damage. When both thermally induced damage and load induced damage are combined, the two-sided effects of climatic environment counter-balanced each other. To verify this point, the thermal response sub-model was turned off in the top-down cracking performance predictive system, which was then used to predict cracking performance for the same pavement under these three climatic environments. In other words, the climate was allowed to influence load induced damage only. The results are presented in Figures 5-17 and 5-18. As shown, the climate did not have much influence on crack initiation time (Figure 5-17). However, it did strongly affect the crack growth rate (Figure 5-18). As can be seen, pavement under a warmer climatic environment has a higher crack growth rate. This was expected because the warmer time of a yearly period is longer under warmer climate, which subjects the pavement to a high creep rate for longer time and thus more damage. 00.511.522.530510152025Time (year)Crack depth (inch) NF FT HFClimate type :No Thermal Damage was Accounted Figure 5-17. Effect of climatic environment (w/o thermally induced damage) on cracking performance 90

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00.10.20.30.40.50.6Ct (inch /year) NF FT HFClimate type :No Thermal Damage was Accounted Figure 5-18. Effect of climatic environment (w/o thermally induced damage) on average crack growth rate (C t ) 91

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CHAPTER 6 MODEL CALIBRATION AND VALIDATION The top-down cracking performance model needed to be calibrated and validated to determine whether the model could reasonably predict cracking performance of asphalt concrete pavement using pavement material and structural properties, traffic volume and climatic information. Summary of Top-down Cracking Performance Model Data Calibration of the top-down cracking performance model was conducted by matching as closely as possible top-down cracking predictions with observed cracking performance, more specifically crack initiation time in the field. To complete the calibration, input data were needed to make top-down cracking predictions. In addition, observed field performance of each pavement section was required for comparison to model predictions. This section presents the data used for calibration of the performance model. Selection of Pavement Sites Thirteen pavement sections were evaluated as part of this study. These sections were selected based on quality of data in terms of both laboratory testing and field observation. Only sections for which reliable and high quality material property and pavement performance data were available were used for calibration/validation. According to the climatic condition, these pavement sections fell into two groups. Group I included eleven sections under Non-Freeze climate of Florida. Meanwhile, Group II had two sections under Hard-Freeze climate of Minnesota. The locations of test sections of Groups I and II are presented in Tables 6-1 and 6-2, respectively. As can be seen, Group I was the primary group, containing most of the pavement sections, while Group II was a supplement. The 92

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inclusion of Group II was intended to represent pavement performance under a different climatic condition. However, according to the parametric study presented in Chapter Five, AC layer thickness was found to govern the cracking mechanism. For pavements with thin to medium thickness AC layer as those of Group I (see Table 6-6), the bending mechanism was appropriate. Meanwhile, for full-depth AC pavements as those of Group II (see also Table 6-6), the near-tire mechanism had to be used. To avoid possible inconsistency due to different mechanisms, the pavements in Group II were not used in the model calibration. However, the calibrated performance model was used to predict performance of pavements in Group II to show the potential of the model for including both cracking mechanisms in future developments. 93

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Table 6-1. Field test sections under Non-Freeze climate of Florida Section Section Code County Section Number Name Limits 1 Interstate 75 I75-1A Charlotte MP 161.1 MP 171.3 Section 1 2 Interstate 75 I75-1B Charlotte MP 149.3 MP 161.1 Section 1 3 Interstate 75 I75-3 Lee MP 131.5 MP 149.3 Section 3 4 Interstate 75 I75-2 Lee MP 115.1 MP 131.5 Section 2 5 State Road 80 SR 80-1 Lee From Hickey Creek Bridge Section 1 To East of Joel Blvd. 6 State Road 80 SR 80-2 Lee From East of CR 80A Section 2 To West of Hickey Creek Bridge 7 Interstate 10 I10-8 Suwannee MP 15.144 MP 18.000 Section 8 8 Interstate 10 I10-9 Suwannee MP 18.000 MP 21.474 Section 9 9 State Road 471 SR471 Sumter The northbound lane three miles north of the Withlacoochee River 10 State Road 19 SR19 Lake The southbound lane five miles south of S.R. 40 11 State Road 997 SR997 Dade The northbound lane 7.6 miles south of US-27 Table 6-2. Field test sections under Hard-Freeze climate of Minnesota Section Section Code Location Number Name 12 Interstate 94 I94-4 located near Albertville, Minnesota Cell 4 (40 miles northwest of the Twin Cities) 13 Interstate 94 I94-14 located near Albertville, Minnesota Cell 14 (40 miles northwest of the Twin Cities) Data Obtained from SuperPave IDT The Superpave indirect tensile test (IDT) developed as part of the Strategic Highway Research Program (SHRP) was used to determine tensile properties on field cores obtained from the 13 test sections. The Superpave IDT includes three types of tests: resilient modulus, creep compliance, and tensile strength. 94

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The resilient modulus test was performed in a load-controlled mode by applying a repeated haversine waveform load to the specimen for a period of 0.1 second followed by a rest period of 0.9 seconds. The load was selected to keep the repeated horizontal strain between 100 and 300 micro-strain during the test (49). The resilient moduli of mixtures determined at 10C are presented in Table 6-3. They represent the mixture property at the age when coring was conducted. The creep compliance test was also performed in the load-controlled mode by applying a monotonic static load to the specimen for a period of 1000 seconds. The load is selected to maintain the accumulative horizontal strain below 1000 micro-strain (50). The creep compliance master curve parameters determined based on tests conducted at 0, 10, and 20C are presented in Table 6-4. The strength test was performed in a displacement-controlled mode. A loading rate of 50 mm/min was used. The fracture properties determined at 10C are also shown in Table 6-3. Table 6-3. Data from SuperPave IDT resilient modulus and tensile strength tests at 10C Section M R S t f FE f DCSE f Age Code (Gpa) (Mpa) () (Kpa) (Kpa) (year) I75-1A 11.14 1.65 1028.05 1.1 1.0 15 I75-1B 10.91 2.01 1437.44 2.0 1.8 14 I75-3 11.58 1.68 715.74 0.8 0.7 15 I75-2 10.29 1.89 1066.72 1.3 1.1 14 SR80-1 13.39 1.59 495.27 0.3 0.2 16 SR80-2 13.45 2.39 679.15 1.0 0.8 19 I10-8 9.85 1.56 386.00 0.4 0.3 7 I10-9 10.21 1.27 415.00 0.4 0.3 7 SR471 7.67 1.79 2040.00 2.5 2.3 3 SR19 9.30 1.71 1338.00 1.6 1.4 3 SR997 11.74 2.33 594.00 0.9 0.7 40 I94-4 8.18 1.35 1203.56 1.1 1.0 13 I94-14 9.44 1.78 1760.25 2.4 2.2 13 95

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Table 6-4. Data from SuperPave IDT creep compliance tests at 0, 10, and 20C Section m D 1 AT(3) AT(2) AT(1) Code (1/Gpa) I75-1A 0.441 0.027 251.19 35.48 1 I75-1B 0.471 0.029 177.83 19.95 1 I75-3 0.485 0.022 281.84 14.13 1 I75-2 0.460 0.021 562.34 56.23 1 SR80-1 0.445 0.014 354.81 25.12 1 SR80-2 0.368 0.014 501.19 35.48 1 I10-8 0.441 0.013 112.202 8.913 1 I10-9 0.503 0.006 141.254 14.125 1 SR471 0.783 0.001 223.872 63.096 1 SR19 0.595 0.012 89.125 8.913 1 SR997 0.349 0.019 63.096 3.981 1 I94-4 0.462 0.018 44.668 1 I94-14 0.456 0.019 79.433 1 AT(3) denotes the inverse of shift factor at the highest temperature. Data for Material Property Model The material property model consists of four sub-models: AC stiffness (creep compliance) aging model, strength aging model, fracture energy (dissipated creep strain energy) aging model, and healing model (refer to Chapter 3, Section Two). The AC stiffness aging model estimates the stiffness of the asphalt mixture as a function of temperature and time. The input information for this model is given below: 1) Percent passing 3/4, 3/8, #4, and #200 sieves by weight. 2) Binder type and mean annual air temperature (MAAT). 3) Effective binder content (% by volume) and air void (% by volume). The values used for above parameters are shown in Table 6-5. The AC strength aging model uses the stiffness predicted by the stiffness aging model and the correlation between stiffness and strength to calculate the tensile strength of asphalt mixture. 96

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Table 6-5. Data used by the material property model Section Percent passing by weight V beff V a MAAT Binder Code 3/4 in 3/8 in # 4 # 200 (%) (%) (F) type I75-1A 100.0 91.8 73.6 5.9 10.7 5.4 75 67-22 I75-1B 100.0 93.7 74.6 5.6 10.7 3.2 75 67-22 I75-3 100.0 86.2 65.1 5.5 8.2 7.2 75 67-22 I75-2 100.0 92.5 68.9 5.0 8.4 6.9 75 67-22 SR80-1 100.0 80.4 59.0 5.8 8.6 5.7 75 67-22 SR80-2 100.0 84.8 64.4 6.2 8.9 7.5 75 67-22 I10-8 100.0 90.0 60.2 4.8 10.3 8.7 75 67-22 I10-9 100.0 90.0 60.2 4.8 9.1 9.9 75 67-22 SR471 100.0 90.0 60.2 4.8 13.3 5.7 75 67-22 SR19 100.0 90.0 60.2 4.8 14.2 4.8 75 67-22 SR997 100.0 90.0 60.2 4.8 11.4 7.6 75 67-22 I94-4 100.0 82.1 65.6 5.2 10.3 4.4 50 58-28 I94-14 100.0 83.4 68.3 5.0 11.1 3.7 50 58-28 The fracture energy aging model also uses the stiffness predicted by the stiffness aging model, but in a normalized form. The model has two unknowns: the aging parameter k 1 and the initial fracture energy FE i Of the two unknowns, k 1 was determined from the calibration effort. Meanwhile, FE i can be determined from unaged cores using SuperPave IDT tests. However, since unaged mixture was not available for the field sections used in this study, FE i was back-calculated from tests performed on aged cores. As an example, the FE limit aging curve (including FE i ) determined based on the FE f of 1.1 Kpa measured at an age of 15 years for test section I75-1A (assuming a k 1 value of 3) is shown below, 97

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0 5 10 15 20 25 30 35 40 45 50 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 FEf (kJ/m3) X: 15Y: 1.1t (year) Figure 6-1. Determination of FE limit aging curve (including FE i ) based on measured FE from aged cores for test section I75-1A The healing model has three components: the maximum healing potential aging model, and two criteria for determination of daily-based and yearly-based healing: The maximum healing potential aging model uses the normalized stiffness and initial fracture energy to estimate the loss of maximum healing potential due to aging. The criterion for determination of daily-based healing h dn uses the lowest stiffness S low of any day predicted by the stiffness aging model to determine the healing potential of that day. The daily-based healing h dn is bounded by zero and the maximum value h ym determined by the maximum healing potential aging model. Meanwhile, the S low of any day is bounded by two critical values S cr1 and S cr2 which were determined to be 320 and 2,000 ksi (see Chapter 4, Section Two). The criterion for determination of yearly-based healing h yn is identical to the criterion for daily-based healing except an averaged daily lowest stiffness S lowa for a prolonged period was used instead of S low to obtain the healing potential of any year. Data for Pavement Response Model The pavement response model consists of two sub-models: (i) load response model, and, (ii) thermal response model (refer to Chapter 3, Section Three). 98

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The load response model estimates load-induced stresses due to traffic loads. This model requires the following input parameters: 1) Layer thickness of AC, base, and subbase. 2) Modulus of base, subbase, and subgrade. 3) Poissons ratio of AC, base, subbase, and subgrade. 4) Yearly average traffic volume (in ESALs). 5) Hourly temperatures within the AC layer. 6) The master creep compliance curve, as obtained via the IDT creep compliance tests. The values used for parameters listed in 1), 2), and 4) are shown in Table 6-6. Poissons ratios of 0.3, 0.35, 0.35, and 0.4 were assumed for AC, base, subbase, and subgrade, respectively. The hourly pavement temperatures were estimated by the enhanced integrated climatic model (EICM) using typical pavement material and structural properties and local climatic information. Table 6-6. Data used by the pavement response model Section Layer thickness (in) Layer modulus (ksi) Yearly traffic Code AC Base Sub-base Base Sub-base Sub-grade (10 3 ESAL) I75-1A 6.54 12 12 54.8 50.1 30.1 573 I75-1B 6.24 12 12 63.6 51.4 36.1 558 I75-3 6.48 12 12 59.6 34.8 36.2 674 I75-2 7.42 12 12 107.4 90.3 31.4 576 SR80-1 3.38 12 12 51.3 40.0 39.7 221 SR80-2 6.30 12 12 57.3 45.6 18.8 207 I10-8 7.20 12 12 55.7 54.5 38.9 392 I10-9 7.40 12 12 65.2 41.4 46.6 392 SR471 2.58 12 12 43.0 34.0 33.6 26 SR19 2.40 12 12 50.7 13.0 12.6 51 SR997 2.18 12 12 109.0 53.0 52.7 89 I94-4 9.10 3.2 488 I94-14 10.90 3.2 782 The thermal response model estimates thermally induced stresses caused by changes in pavement temperatures. This model requires the following input parameters: 99

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1) Thickness of AC layer. 2) The master relaxation modulus curve, as obtained via the IDT creep compliance tests. 3) Hourly pavement temperatures within the AC layer. 4) Coefficient of thermal contraction of the asphalt concrete mixture. The values used for parameters listed in 1) to 3) were covered by the input for load response model. The coefficient of thermal contraction was assumed to be 1.2E-5 /C for all test sections of this study. Data for Pavement Fracture Model The pavement fracture model consists of three sub-models: (i) crack initiation model, (ii) crack growth model, and (iii) crack amount model (refer to Chapter 3, Section Four). The crack initiation model uses the load-induced and thermal-induced stresses predicted by the pavement response model, and the rule for determination of crack initiation to predict crack initiation time and location. During the process, the mixture fracture and healing properties determined by the material property model are also required. The crack growth model uses the load-induced stresses on the basis of the 2-D DDBE program, thermally induced stresses predicted by the pavement response model and stress intensity function, and the rule for determination of crack propagation to compute increase of crack depth with time. Similarly, the mixture fracture and healing properties determined by the material property model are required during the process. The crack amount model converts the crack depth versus time relationship predicted by the crack growth model to crack amount versus time relationship. Observed Pavement Performance Data The input data presented in the previous sub-sections was used to make performance predictions for each of the 13 test sections in two phases. During phase one, the predictions for 100

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the eleven sections of Group I were compared with observed performance to calibrate the model. Therefore, the observed field performance for each of the sections was also required, which was obtained via following two resources: A field trip was made to each test section to observe and photograph its performance and take cores in 2003. The cracked sections exhibited a moderate amount of cracking, while the uncracked sections were in an acceptable condition. An inspection of core samples from the cracked sections clearly indicated the presence of top-down cracking. The cracks initiated from the surface and moved downward. The crack rating history for each test section was obtained from the flexible pavement condition survey database, which is maintained by the Florida Department of Transportation (FDOT). The crack initiation time for each test section was determined on the basis of the above information and the best knowledge of the research team. It is shown in Table 6-7. Table 6-7. Observed top-down cracking performance Section Section Observed InitiationNo Code Time (year) 1 I75-1A 10 2 I75-1B 12 3 I75-3 11 4 I75-2 17 5 SR80-1 13 6 SR80-2 22 7 I10-8 8 8 I10-9 8 9 SR471 2 10 SR19 1 11 SR997 38 12 I94-4 4 13 I94-14 6 In phase two, predictions obtained using the calibrated model were presented for all test sections including those of Group II. For comparison purposes, the observed crack initiation time of Group II is also presented in Table 6-7, which was obtained from Minnesota Department of Transportation (MDOT). Based on the observed crack initiation time, pavement cracking performance can be categorized according to one of the following five performance levels: 101

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Level I: 1 to 5 years before crack initiation. Level II: 6 to 10 years before crack initiation. Level III: 11 to 20 years before crack initiation. Level IV: 21 to 30 years before crack initiation. Level V: greater than 30 years before crack initiation. Calibration of Model Model calibration was completed by matching as closely as possible top-down cracking predictions with observed top-down cracking in the field. The 11 pavement sections (Group I) documented in the prior section were used for calibration of the model. Since the aging parameter (k 1 ) was included as an unknown parameter within the fracture energy aging model, R 2 of the predicted initiation times of top-down cracking was determined for each assumed k 1 value using linear regression. A series of linear regressions was conducted with k 1 values ranging from 0.5 to 5. The final model was chosen as the k 1 value resulted in the best fit (highest R 2 ) between observed initiation times of cracking with the predicted ones. Calibration Procedure First, a matrix of runs of the top-down cracking performance model was conducted to obtain crack initiation time predictions for each selected section at 8 values of the aging parameter ranging between 0.5 and 5. This range of k 1 values was determined by a trial-and-error process. It was observed that a value of 0.5 resulted in higher levels of predicted performance i.e., longer time to crack initiation for most of the pavement sections, including those sections known to have poor observed performance. Similarly, a value of 5 resulted in lower levels of predicted performance for most of the sections, including those sections known to have good observed performance. The data obtained from these runs is shown in Table 6-8. 102

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Table 6-8. Predicted versus observed cracking performance for different k 1 -values (all test sections in Group I) Section Observed Predicted t i (year) No. t i k 1 -value (year) 0.5 1 1.5 2 2.5 3 3.5 5 1 10 14.7 14.7 13.8 12.7 11.8 10.9 10.7 9.6 2 12 13.9 13.9 13.9 13.9 13.8 12.9 12.7 11.0 3 11 8.9 8.0 6.9 6.5 5.9 5.5 4.9 4.0 4 17 19.0 19.0 18.8 17.8 16.8 16.0 15.7 14.6 5 13 3.0 2.3 2.2 1.7 1.3 1.2 1.2 1.1 6 22 25.7 25.7 25.7 24.7 23.7 22.8 22.6 20.9 7 8 7.6 6.6 5.9 5.8 5.6 5.6 4.9 4.6 8 8 7.9 6.9 6.7 6.6 5.9 5.8 5.7 4.7 9 2 6.9 5.8 5.5 4.9 4.8 4.8 4.8 4.7 10 1 5.6 4.6 4.3 3.9 3.8 3.8 3.7 3.5 11 38 34.8 34.8 34.8 34.8 34.8 34.8 34.8 34.7 R 2 0.807 0.803 0.802 0.809 0.802 0.801 0.791 0.767 Secondly, for each aging parameter, a linear regression routine was used to determine R 2 by regressing the observed initiation time on the predicted time of crack initiation. The optimum k 1 value was then chosen as the one resulting in the largest R 2 In other words, the value that resulted in the best match (lowest error) between predicted crack initiation time and the time observed in the field was chosen as the optimum k 1 Initial Calibration Results Linear regressions were performed to determine eight different values of R 2 (one for each aging parameter k 1 ), which are also presented in Table 6-8. As shown, eight models were obtained, each with its own k 1 and R 2 The model with the highest R 2 had the following parameters: k 1 = 2.0 R 2 = 0.809 103

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Another way to evaluate the goodness of fit of the model is to directly compare the predicted to the observed levels of cracking performance, as defined in the prior section. The results of this comparison using predicted initiation time determined with the aging parameter presented above are shown in Figure 6-2, which may be summarized as follows: Two of two level I sections were predicted to be level I sections. Two of three level II sections were predicted to be level II sections and only one level II section was predicted to be level III section. Of the four level III sections, two were predicted to be level III sections, one was predicted to be level II, and one was predicted to be level I. The level IV and V sections were predicted to be level IV and V, respectively. Observed Cracking Performance I II III IV V I 2 1 II 2 1 III 1 2 IV 1 Predicted Cracking Performance V 1 Figure 6-2. Predicted versus observed cracking performance (All 11 sections) When viewed in this manner, the correlation between predicted and observed cracking performance appeared fairly strong. As shown in Figure 6-2, only one prediction was off the diagonal by two cells. Of the other 10 predictions, 8 were on the diagonal (representing good 104

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prediction), and 2 were just one cell off the diagonal (implying fairly good prediction). Thus, the correspondence between predicted and observed cracking performance in terms of crack initiation time was good for 10 out of 11 sections. However, the off diagonal by two cells prediction for test section five apparently had a strong influence on R 2 which was not very sensitive to the k 1 value. In other words, the prediction for test section five may have overshadowed the sensitivity of the results. In view of this problem with test section five, it was excluded from the final calibration. However, it was included in the validation process as an independent data point. Final Calibration Because of the problem with test section five, it was not included in the final calibration of the model. Once again linear regressions were performed to determine eight different values of R 2 (one for each aging parameter) and the results are given in Table 6-9: Table 6-9. Predicted versus observed cracking performance for different k 1 -values (without test section 5 in Group I) Section Observed Predicted t i (year) No. t i k 1 -value (year) 0.5 1 1.5 2 2.5 3 3.5 5 1 10 14.7 14.7 13.8 12.7 11.8 10.9 10.7 9.6 2 12 13.9 13.9 13.9 13.9 13.8 12.9 12.7 11.0 3 11 8.9 8.0 6.9 6.5 5.9 5.5 4.9 4.0 4 17 19.0 19.0 18.8 17.8 16.8 16.0 15.7 14.6 6 22 25.7 25.7 25.7 24.7 23.7 22.8 22.6 20.9 7 8 7.6 6.6 5.9 5.8 5.6 5.6 4.9 4.6 8 8 7.9 6.9 6.7 6.6 5.9 5.8 5.7 4.7 9 2 6.9 5.8 5.5 4.9 4.8 4.8 4.8 4.7 10 1 5.6 4.6 4.3 3.9 3.8 3.8 3.7 3.5 11 38 34.8 34.8 34.8 34.8 34.8 34.8 34.8 34.7 R 2 0.902 0.911 0.914 0.930 0.931 0.933 0.924 0.901 It was determined that the model with the highest R 2 had the following parameters: 105

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k 1 = 3.0 R 2 = 0.933 The above aging parameter was used to generate the comparison between predicted and observed performance presented in Figure 6-3. As shown in the figure, no prediction was off the diagonal by more than one cell. 8 out of the 10 predictions were on the diagonal (representing good prediction) and the other 2 were just one cell off the diagonal (implying fairly good prediction). Thus, the correspondence between predicted and observed performance in terms of crack initiation time was good for all 10 test sections. In conclusion, results of the calibration effort clearly indicate that the top-down cracking performance model appears to adequately represent and account for the most significant factors that influence top-down cracking in the field. Observed Cracking Performance I II III IV V I 2 II 2 1 III 1 2 IV 1 Predicted Cracking Performance V 1 Figure 6-3. Predicted versus observed cracking performance (without section 5) 106

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Validation of Model The previous section showed strong correlation between top-down cracking predictions by the performance model and observed crack initiation time in the field, thus establishing the models credibility. The final step in the model-developing process was validation of the selected model. The objective was to assess the ability of the performance model to accurately predict top-down cracking in the field using data not used in developing the model. For validating a regression model, three methods are commonly used including: 1) Collection of new data, 2) Data splitting, and 3) Prediction sum of squares (PRESS). The first method suggests that a new data set should be collected. However, the collection of new data is not possible due to time and resource constraints of this study. The second method is not feasible due to the small sample size of the available data set. The last method is suitable for small data sets where data splitting is impractical. Since it has been successfully used by Lytton and Roque et al. (51) for validation of the thermal cracking model, the PRESS method was selected for use in this study. PRESS Procedure In the PRESS procedure, one data point is removed at a time from the data set (e.g., a data set with n data points) while the unknown parameters in the model are being estimated. In other words, the model is calibrated with (n-1) data points at a time. Then this model is used to predict the value of the removed point. This process is repeated for all the data points in the data set. The predicted values obtained by this method are then compared with the actual values. The R 2 (PRESS) is calculated for the predicted and actual values as follows: iwoiiipYYYYR12 (6-1) 107

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where: Y (i) = observed response for the ith data point = predicted response for the ith data point )(iY )(iwoY = average of the predicted responses of (n-1) data points without the ith data point The R 2 (PRESS) will always be lower than the R 2 obtained from the full model because the PRESS procedure uses (n-1) data points to estimate the unknown parameters as compared to the procedure based on the full model where n data points are used. The degree of closeness of R 2 (PRESS) to R 2 (Full model) serves as a measure of the models predictive ability. Good models will have an R 2 from the PRESS procedure close to the R 2 from the full model. Validation Process Using PRESS For validation purposes, the performance model used to predict crack initiation for any one particular test section was calibrated on the basis of data of the other test sections. For example, the model used to predict crack initiation in test section one was calibrated using the data set without including section one. In this study, the validation process involved two steps. First, as was the case with final calibration of the performance model presented in the prior section, test section five was not included. So, only 10 test sections were included in this step. The calibration procedure (also described in the prior section) was conducted 10 times, once for each test section. The R 2 (PRESS) was then computed using Eqn (6-1). Next, the crack initiation time of test section five was predicted using the model calibrated with the 10 test sections of step one. The error associated with this prediction was also added to the R 2 (PRESS) obtained in the first step. As an example of step one, the top-down cracking performance model used to predict crack initiation for test section one, was calibrated with data from the other 9 test sections, i.e., test sections two through eleven except for test section five. Linear regressions were performed 108

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to determine 8 different values of R 2 (one for each aging parameter) on the basis of the data from the other 9 test sections. The performance model used to predict crack initiation for test section one was selected as the one having the k 1 value that resulted in the highest R 2 This process was repeated 10 times such that a total of 80 linear regressions were performed during step one. A similar process was used in step two, where linear regressions were performed to determine 8 different values of R 2 on the basis of the data from the 10 test sections of step one. The top-down cracking performance model used to predict crack initiation for test section five was selected as the one that resulted in the highest R 2 This process was applied once in step two. The R 2 for each linear regression is presented in Table 6-10. For each pavement section, the model resulting in the largest R 2 is identified via a shaded area, in which the predicted cracking performance level is also presented. The resulting 11 models were used to make an independent prediction of crack initiation time of top-down cracking for each test section in the validation effort. The independent predictions were compared to observed initiation time to evaluate the predictive capability of the model. Results of this evaluation are presented in the following sub-section. 109

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Table 6-10. Predicted cracking performance for various aging parameters using PRESS procedure Predicted Performance Aging Parameter k 1 Section No. Observed Performance 0.5 (R 2 ) 1.0 (R 2 ) 1.5 (R 2 ) 2.0 (R 2 ) 2.5 (R 2 ) 3.0 (R 2 ) 3.5 (R 2 ) 5.0 (R 2 ) 1 II (0.923) (0.932) (0.927) III (0.937) (0.934) (0.933) (0.924) (0.900) 2 III (0.906) (0.915) (0.917) (0.934) III (0.934) (0.934) (0.924) (0.902) 3 III (0.906) (0.920) (0.929) (0.949) (0.956) II (0.962) (0.959) (0.948) 4 III (0.904) (0.913) (0.916) (0.930) (0.930) III (0.933) (0.924) (0.905) 5 III (0.902) (0.911) (0.914) (0.930) (0.931) I (0.933) (0.924) (0.901) 6 IV (0.907) (0.917) (0.920) IV (0.931) (0.928) (0.927) (0.917) (0.893) 7 II (0.900) (0.911) (0.916) (0.934) (0.935) II (0.937) (0.931) (0.910) 8 II (0.900) (0.910) (0.913) (0.931) (0.934) II (0.936) (0.927) (0.909) 9 I (0.914) (0.914) (0.915) (0.930) (0.930) I (0.932) (0.921) (0.895) 10 I (0.909) (0.911) (0.911) (0.928) (0.928) I (0.930) (0.919) (0.891) 11 V (0.736) (0.763) (0.771) (0.821) (0.824) V (0.829) (0.802) (0.734) Predicted and Observed Performance are shown as Levels I to V. Validation Results The R 2 from the PRESS procedure described above was determined to be 0.82. In comparison to the R 2 of 0.93 for the full model (i.e., the model determined from the final calibration), the performance model developed appears to have strong predictive ability. The data were also evaluated by directly comparing the independent performance predictions with the observed levels of performance defined in Section 6.1. The results of the 110

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comparison are presented in Figure 6-4. As shown, only one prediction was off the diagonal by two cells. Of the other 10 predictions, 8 were on the diagonal, and 2 were just one cell off the diagonal. Thus, the correspondence between predicted and observed cracking performance for these independent predictions was good for 10 of 11 test sections. Observed Cracking Performance I II III IV V I 2 1 II 2 1 III 1 2 IV 1 Predicted Cracking Performance V 1 Figure 6-4. Predicted versus observed cracking performance (from PRESS) Based on these results and the R 2 (PRESS) of 0.82, the predictive capability of the model appears to be good. After model calibration and validation, the final predictions using the calibrated model are presented in the next section. Final Model Predictions In this section, final model predictions were conducted using the calibrated model. The complete results are presented in Table 6-11, which will be illustrated in three parts. First, the predicted crack initiation time is compared with the observed initiation time in the field for all 111

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112 thirteen test sections. Second, the predicted propagation time is compared with the predicted initiation time. The purpose is to evaluate th e predicted propagation time by assessing its relationship with the initiation time. Thirdly, the cracking histories of all sections in terms of crack amount versus time are presented, which were obtained using the crack amount model.

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Table 6-11. Crack Depths versus Time Predictions Using Calibrated Aging Parameter (k 1 = 3.0) Section I75-1A I75-1B I75-3 I75-2 SR80-1 SR80-2 Thickness (inch) 6.54 6.23 6.47 7.42 3.38 6.29 Year Opened 1988 1989 1988 1989 1987 1984 Observed Initiation Time (year) 10 12 11 17 13 22 Predictions C.D. C/D + Y.C. @ C/D Y.C. C/D Y.C. C/D Y.C. C/D Y.C. C/D Y.C. 0.25 0.04 10.9 0.04 12.9 0.04 5.5 0.03 16.0 0.07 1.2 0.04 22.8 0.50 0.08 12.7 0.08 14.6 0.08 6.3 0.07 18.4 0.15 1.7 0.08 25.6 0.75 0.11 13.2 0.12 15.1 0.12 6.8 0.10 18.9 0.22 1.9 0.12 26.5 1.00 0.15 13.5 0.16 15.4 0.15 6.9 0.13 19.3 0.30 2.0 0.16 26.9 1.25 0.19 13.7 0.20 15.7 0.19 6.9 0.17 19.6 0.37 2.1 0.20 27.4 1.50 0.23 13.9 0.24 15.9 0.23 7.0 0.20 19.8 0.44 2.1 0.24 27.7 1.75 0.27 14.1 0.28 16.0 0.27 7.0 0.24 20.0 0.52 2.4 0.28 27.9 2.00 0.31 14.2 0.32 16.2 0.31 7.1 0.27 20.1 0.32 28.3 2.25 0.34 14.3 0.36 16.3 0.35 7.1 0.30 20.3 0.36 28.5 2.50 0.38 14.5 0.40 16.4 0.39 7.2 0.34 20.4 0.40 28.6 2.75 0.42 14.7 0.44 16.7 0.43 7.2 0.37 20.6 0.44 28.8 3.00 0.46 14.8 0.48 17.0 0.46 7.3 0.40 20.7 0.48 29.2 3.25 0.50 15.1 0.52 17.2 0.50 7.5 0.44 20.8 0.52 29.4 3.50 0.47 20.9 3.75 0.51 21.1 C.D. stands for Crack Depth (inch); + C/D stands for Crack depth over AC thickness ratio; @ Y.C. stands for time (year) 113

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114 Table 6-11. Continued Section I10-8 I10-9 SR471 SR19 SR997 I94-4 I94-14 Thickness (inch) 7.20 7.40 2.58 2.39 2.17 9.10 10.90 Year Opened 1996 1996 2000 2000 1963 1994 1994 Observed Initiation Time (year) 8 8 2 1 38 4 6 Predictions C.D. C/D + Y.C. @ C/D Y.C. C/D Y.C. C/D Y.C. C/D Y.C. C/D Y.C. C/D Y.C. 0.25 0.03 5.6 0.03 5.8 0.10 4.8 0.10 3.8 0.12 34.8 0.03 4.2 0.02 6.0 0.50 0.07 6.6 0.07 6.9 0.19 5.2 0.21 4.7 0.23 39.6 0.05 5.9 0.05 7.2 0.75 0.10 6.8 0.10 7.3 0.29 5.7 0.31 4.9 0.35 41.4 0.08 6.0 0.07 7.4 1.00 0.14 7.0 0.14 7.5 0.39 6.0 0.42 5.0 0.46 42.8 0.11 6.2 0.09 7.9 1.25 0.17 7.1 0.17 7.6 0.48 6.3 0.52 5.1 0.58 43.2 0.14 6.3 0.11 8.0 1.50 0.21 7.3 0.20 7.7 0.58 7.0 0.16 6.9 0.14 8.3 1.75 0.24 7.4 0.24 7.8 0.19 7.1 0.16 8.8 2.00 0.28 7.5 0.27 7.9 0.22 7.2 0.18 9.0 2.25 0.31 7.5 0.30 8.0 0.25 7.7 0.21 9.2 2.50 0.35 7.6 0.34 8.1 0.23 9.3 2.75 0.38 7.7 0.37 8.2 0.25 9.9 3.00 0.42 7.7 0.41 8.3 3.25 0.45 7.7 0.44 8.4 3.50 0.49 7.8 0.47 8.5 3.75 0.52 7.9 0.51 8.5 C.D. stands for Crack Depth (inch); + C/D stands for Crack depth over AC thickness ratio; @ Y.C. stands for time (year)

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Predicted vs. Observed Crack Initiation Time The predicted crack initiation time versus the observed time in the field for all thirteen test sections are presented in Figure 6-5. As shown, the predictions generally agreed well with the observed time except for SR80-1 (i.e., test section five). 051015202530354045SR19SR471I94-4*I94-14*I10-8I10-9I75-1AI75-3I75-1BSR80-1I75-2SR80-2SR997SectionsTime to Initiation (Year) Observed PredictedWorstBest Performance 1 5 Yr6 10 Yr11 20 Yr21 30 Yr> 30 Yr Figure 6-5. Predicted versus observed crack initiation time for all test sections Crack Initiation Time vs. Propagation Time The initial crack depth of top-down cracking was determined to be 6 mm (0.25 in), and the critical crack depth was defined as the depth equal to one-half of the AC layer thickness (see Chapter 3, Section Four). Therefore, for a vertical crack, the crack propagation time t p can be obtained by computing the difference between the time to initial crack depth (i.e., crack initiation time) and that to critical crack depth. 115

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The crack propagation time was thus determined for each of the test sections using predictions by the calibrated model and plotted against the corresponding crack initiation time in Figure 6-6. As shown, the predicted propagation time appears to increase linearly with the initiation time: 1) For pavement sections that start to crack after in service for 10 to 20 years, the propagation time to failure is about 4 to 5 years, which is consistent with our typical observations in the field. 2) For test sections with an earlier crack initiation, the propagation time tends to be shorter. 3) For pavements that can last for more than 20 years, the predicted time to critical crack depth is also longer. 0.02.55.07.510.00510152025303540Predicted Initiation Time (year)Predicted Propagation Time (year) Group I Group II Linear (Group I) Figure 6-6. Predicted crack propagation time versus crack initiation time Due to difficulties involved in obtaining reliable data on development of a real crack in the field, no further calibration was performed on predicted crack propagation time. However, the comparison in Figure 6-6 can be viewed as an alternative means to assess the reasonableness of the model for propagation time prediction. 116

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117 Crack Amount Development with Time The final model predictions are expressed in terms of crack amount versus time for each of the test sections. They are pres ented according to the performance category (I to V) with respect to observed performance, as shown in Figures 6-7 to 6-10. These predic tions may be summarized as follows: The amount of cracking of a thin pavement at initiation is greater than that of a thicker pavement. This indicates that crack initiati on may be more easily identified in thinner pavements than in thicker ones in the field. For test sections of Group I (governed by th e bending mechanism): 1) Predictions for sections of lower performance levels are ge nerally consistent with field observations (Figures 6-7 and 6-8). The relatively high cr eep rate combined with high surface tensile stresses are believed to be responsible for severe cracking conditions in these sections within a relatively short period. 2) Predictions for sections of higher performance levels also agree reasonably with observations in th e field, except for section five (i.e., SR80-1) (Figures 6-9 and 6-10). The relatively low cr eep rate and high fracture energy of the asphalt mixtures combined with the relatively lo w traffic loads in these sections resulted in longer service life. For test sections of Group II (governed by the near-tire mechanism): Predictions of crack initiation for both sections of this group agr ee well with field observations. However, the trend for crack propagation appear s to be different from those predicted for sections of Group I (Figures 6-7 and 6-8). This is expect ed because a crack growth simulation tool specifically for the near-tire mechanism is not available. The CGS module (focused on the bending mechanism) was used as a surrogate to make these predictions. Therefore, an enhanced crack growth model that also addr esses the near-tire mechanism needs to be developed for more accurate prediction of top-down cracking in thick HMA layers.

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SR1905010015020025030035040002.557.510Time (year)AC (ft/100 ft) SR47105010015020025030035040002.557.510Time (year)AC (ft/100 ft) Initiation Initiation I94-4*025507510012515017520002.557.510Time (year)AC (ft/100ft) Initiation Figure 6-7. Predicted crack amount versus time for test sections of level I ( The maximum amount of cracking was reduced to 165 ft /100 ft for full depth pavement (near-tire mechanism).) 118

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I10-805010015020025030035040002.557.51012.51517.520Time (year)AC (ft/100 ft) I10-905010015020025030035040002.557.51012.51517.520Time (year)AC (ft/100 ft) I75-1A05010015020025030035040002.557.51012.51517.520Time (year)AC (ft/100 ft) Initiation Initiation Initiation I94-14*025507510012515017520002.557.51012.51517.520Time (year)AC (ft/100 ft) Initiation Figure 6-8. Predicted crack amount versus time for test sections of level II ( The maximum amount of cracking was reduced to 165 ft /100 ft for full depth pavement (near-tire mechanism).) 119

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I75-1B0501001502002503003504000510152025Time (year)AC (ft/100 ft) I75-30501001502002503003504000510152025Time (year)AC (ft/100 ft) I75-20501001502002503003504000510152025Time (year)AC (ft/100 ft) SR80-10501001502002503003504000510152025Time (year)AC (ft/100 ft) Initiation Initiation Initiation Initiation Figure 6-9. Predicted crack amount versus time for test sections of level III 120

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121 SR80-2050100150200250300350400051015202530354045Time (year)AC (ft/100 ft) SR997050100150200250300350400051015202530354045Time (year)AC (ft/100 ft) Initiation Initiation Figure 6-10. Predicted crack amount versus time for test sections of levels IV and V

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CHAPTER 7 CONCLUSIONS AND RECOMMENDATIONS Conclusions An HMA-FM-based model was developed to predict top-down cracking performance, with the emphasis placed on the bending mechanism. This model was comprised of several key elements as summarized below: A critical condition concept that can more accurately capture field observations and significantly reduces the computation time required for long-term pavement performance prediction. Material property sub-models that account for changes in near-surface mixture properties with aging, including increase in stiffness (stiffening), reduction in fracture energy (embrittlement), and reduction in healing potential, which make pavements more susceptible to top-down cracking. A thermal response model that predicts transverse thermal stresses that can be an important part of the top-down cracking mechanism. A pavement fracture model that predicts crack growth with time, accounting for the effect of changes in geometry on stress distributions. A systematic parametric study showed that the system provided reasonable predictions and expected trends for both crack initiation and propagation. Furthermore, a full calibration of field sections was completed by matching as closely as possible top-down cracking predictions in terms of crack initiation time with observed top-down cracking in the field. Only one calibration factor (i.e., the aging parameter k 1 ) was included in the calibration process. Results of the calibration effort indicated that the predictive system adequately represents and accounts for the most significant factors that influence top-down cracking in the field. The validation efforts using the prediction sum of squares (PRESS) procedure further established the viability of the predictive system. In conclusion, the work performed clearly indicates that the HMA-FM-based model developed and evaluated in this study can form the basis for a top-down cracking model suitable 122

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for use in the MEPDG. It should also be noted that material property sub-models developed for the model should be considered place-holder relations. Further development and evaluation of the material property place-holder relationships are highly recommended in future work, particularly for models to predict fracture energy (FE), damage rate, healing potential, and their changes with aging. Recommendations The following items are recommended for future research: Damage rate and fracture energy are the most important material properties related to top-down cracking. However, no reliable material model is available for either of them. The place-holder relations introduced in this study to predict damage rate were based on the Witczak model, but should not be considered reliable without further validation. Enhanced relations may need to be developed. Regarding the determination of fracture energy, an initial FE model from mixture characteristics (gradation etc.) and properties of mixture components needs to be developed. A simplified empirical-based healing model was used in this research, but should not be considered reliable without further validation. An enhanced model may need to be developed for more accurate estimation of mixture healing under various conditions. The near-tire mechanism needs to be further investigated for more proper incorporation into the performance model. Considerations are required regarding effects of tire type and cross slope on shear-induced tension at tire edge. Wander effects relative to mechanisms need to be addressed. For example, the significance of the near-tire mechanism is strongly dependent on the extent of wander, because the location for crack initiation is right next to the tire edge. However, the importance of the bending-mechanism is not sensitive to wander. Damage effects on reduction in AC modulus and the change in stress-strain-energy response resulting from the modulus reduction need to be considered and integrated into the performance model. Influence of stress state on damage rate needs to be considered for more accurate determination of critical condition. 123

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LIST OF REFERENCES 1. Roque, R., and B. E. Ruth. Mechanisms and Modeling of Surface Cracking in Asphalt Pavements. Journal of the Association of Asphalt Paving Technologists, Vol. 59, 1990, pp. 397-421. 2. Myers, L., R. Roque, and B. E. Ruth. Mechanisms of Surface Initiated Longitudinal Wheel Path Cracks in High-type Bituminous Pavements. Journal of the Association of Asphalt Paving Technologists, Vol. 67, 1998, pp. 402-432. 3. Uhlmeyer, J. S., K. Willoughby, L. M. Pierce, and J. P. Mahoney. Top-down Cracking in Washington State Asphalt Concrete Wearing Courses. In Transportation Research Record: Journal of the Transportation Research Board, No. 1730, Transportation Research Board of the National Academies, Washington, D.C., 2000, pp. 110-116. 4. Gerritsen, A. H., C. A. P. M. Van Gurp, J. P. J. Van Der Heide, A. A. A. Molenaar, and A. C. Pronk. Prediction and Prevention of Surface Cracking in Asphaltic Pavements. Proc., 6th International Conference on Structural Design of Asphalt Pavements, Ann Arbor, Michigan, 1987, pp. 378-391. 5. De Freitas, E. F., P. Pereira, L. Picado-Santos, and A. T. Papagiannakis. Effect of Construction Quality, Temperature and Rutting on Initiation of Top-downing Cracking. In Transportation Research Record: Journal of the Transportation Research Board, No. 1929, Transportation Research Board of the National Academies, Washington, D.C., 2005, pp. 174-182. 6. Matsuno, S., and T. Nishizawa. Mechanism of Longitudinal Surface Cracking in Asphalt Pavement. Proc., 7th International Conference on Asphalt Pavements. University of Nottingham, UK, Vol. 2, 1992, pp. 277-291. 7. Raju, S., S. S. Kumar, K. S. Reddy, S. Bose, and B. B. Pandey. Analysis of Top-Down Cracking Behavior of Asphalt Pavements. Transportation Research Board, Washington, D.C., 2008. 8. Myers, L. A., and R. Roque. Top-down Crack Propagation in Bituminous Pavements and Implications for Pavement Management. Journal of the Association of Asphalt Paving Technologists, Vol. 71, 2002, pp. 651-670. 9. Zhang, Z., R. Roque, and B. Birgisson. Evaluation of Laboratory-Measured Crack Growth Rate for Asphalt Mixtures. In Transportation Research Record: Journal of the Transportation Research Board, No. 1767, Transportation Research Board of the National Academies, Washington, D.C., 2001, pp. 67-75. 10. Kim, B., R. Roque, and B. Birgisson. Effect of Styrene Butadiene Styrene Modifier on Cracking Resistance of Asphalt Mixture. In Transportation Research Record: Journal of the 124

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Transportation Research Board, No. 1829, Transportation Research Board of the National Academies, Washington, D.C., 2003, pp. 8-15. 11. Roque, R., Z. Zhang, and B. Sankar. Determination of Crack Growth Rate Parameters of Asphalt Mixtures Using the SuperPave Indirect Tensile Test (IDT). Journal of the Association of Asphalt Paving Technologists, Vol. 68, 1999, pp. 404-433. 12. Yoo, P. J., and I. L. Al-Qadi. The Truth and Myth of Fatigue Cracking Potential in Hot-Mix Asphalt: Numerical Analysis and Validation. Journal of the Association of Asphalt Paving Technologists, Vol. 77, 2008, pp. 549-590. 13. Huang, Y. H. Pavement Analysis and Design. New Jersey, Prentice Hall, Inc., 2004, pp. 104. 14. Kim, Y. R., D. N. Little. One-Dimensional Constitutive Modeling of Asphalt Concrete. ASCE Journal of Engineering Mechanics, Vol. 116, No. 4, pp. 751-772, 1990. 15. Schapery, R. A. Correspondence Principles and a Generalized J Integral for Large Deformation and Fracture Analysis of Viscoelastic Media. International Journal of Fracture, Vol. 25, 1984, pp. 195-223. 16. Park, S. W., Y. R. Kim, and R. A. Schapery. A Viscoelastic Continuum Damage Model and Its Application to Uniaxial Behavior of Asphalt Concrete. Mechanics of Materials, Vol. 24, No. 4, pp. 241-255, 1996. 17. Kim, Y. R., Y. C. Lee, and H. J. Lee. Correspondence Principle for Characterization of Asphalt Concrete. ASCE Journal of Materials in Civil Engineering, Vol. 7, No. 1, 1995, pp. 59-68. 18. Kim, Y. R., H. J. Lee, and D. N. Little. Fatigue Characterization of Asphalt Concrete Using Viscoelasticity and Continuum Damage Theory. Journal of the Association of Asphalt Paving Technologists, Vol. 66, 1997, pp. 520-569. 19. Lee, H. J., and Y. R. Kim. Viscoelastic Constitutive Model for Asphalt Concrete under Cyclic Loading. Journal of Engineering Mechanics, Vol. 124, No. 1, 1998, pp. 32-40. 20. Lee, H. J., and Y. R. Kim. A Viscoelastic Continuum Damage Model of Asphalt Concrete with Healing. ASCE Journal of Engineering Mechanics, Vol. 124, No. 11, 1998, pp. 1224-1232. 21. Daniel, J. S., Y. R., Kim, and H. J. Lee. Effects of Aging on Viscoelastic Properties of Asphalt-Aggregate Mixtures. In Transportation Research Record: Journal of the Transportation Research Board, No. 1630, Transportation Research Board of the National Academies, Washington, D.C., 1998, pp. 21-27. 22. Schapery, R. A. Nonlinear Viscoelastic and Viscoplastic Constitutive Equations with Growing Damage. International Journal of Fracture, Vol. 97, 1999, pp. 33-66. 125

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23. Chehab, G. R., Y. R. Kim, R. A. Schapery, M. Witczack, and R. Bonaquist. Time-Temperature Superposition Principle for Asphalt Concrete Mixtures with Growing Damage in Tension State. Journal of the Association of Asphalt Paving Technologists, Vol. 71, 2002, pp. 559-593. 24. Chehab, G. R., Y. R. Kim, R. A. Schapery, M. Witczack, and R. Bonaquist. Characterization of Asphalt Concrete in Uniaxial Tension Using a Viscoelastoplastic Model. Journal of the Association of Asphalt Paving Technologists, Vol. 72, 2003, pp. 315-355. 25. Daniel, J. S., and Y. R. Kim. Development of Simplified Fatigue Test and Analysis Procedure Using a Viscoelastic Continuum Damage Model. Journal of the Association of Asphalt Paving Technologists, Vol. 71, 2002, pp. 619-650. 26. Zhang, Z., R. Roque, B. Birgisson, and B. Sangpetngam. Identification and Verification of a Suitable Crack Growth Law. Journal of the Association of Asphalt Paving Technologists, Vol. 70, 2001, pp. 206-241. 27. Roque, R., B. Birgisson, B. Sangpetngam, and Z. Zhang. Hot Mix Asphalt Fracture Mechanics: A Fundamental Crack Growth Law for Asphalt mixtures. Journal of the Association of Asphalt Paving Technologists, Vol. 71, 2002, pp. 816-827. 28. Sangpetngam, B., B. Birgisson, and R. Roque. Development of Efficient Crack Growth Simulator Based on Hot-mix Asphalt Fracture Mechanics. In Transportation Research Record: Journal of the Transportation Research Board, No. 1832, Transportation Research Board of the National Academies, Washington, D.C., 2003, pp. 105-112. 29. Sangpetngam, B., B. Birgisson, and R. Roque. Multilayer Boundary-element Method for Evaluating Top-down Cracking in Hot-mix Asphalt Pavements. In Transportation Research Record: Journal of the Transportation Research Board, No. 1896, Transportation Research Board of the National Academies, Washington, D.C., 2004, pp. 129-137. 30. Roque, R., B. Birgisson, C. Drakos, and B. Dietrich. Development and Field Evaluation of Energy-Based Criteria for Top-down Cracking Performance of Hot Mix Asphalt. Journal of the Association of Asphalt Paving Technologists, Vol. 73, 2004, pp. 229-260. 31. Kim, J., R. Roque, and B. Birgisson. Integration of Thermal Fracture in the HMA Fracture Model. Journal of the Association of Asphalt Paving Technologists, Vol. 77, 2008, pp. 631-662. 32. Mirza, M. W., and M. W. Witczak. Development of a Global Aging System for Short and Long Term Aging of Asphalt Cements. Journal of the Association of Asphalt Paving Technologists, Vol. 64, 1995, pp. 393-430. 126

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33. ARA, Inc., Guide for Mechanistic-Empirical Design of New and Rehabilitated Pavement Structures. Final Report NCHRP Project 1-37A. National Cooperative Highway Research Program, Transportation Research Board, Washington, D.C., 2004. 34. Witczak, M. W., and O. A. Fonseca. Revised Predictive Model for Dynamic (Complex) Modulus of Asphalt Mixtures. In Transportation Research Record: Journal of the Transportation Research Board, No. 1540, Transportation Research Board of the National Academies, Washington, D.C., 1996, pp. 15-23. 35. Deme, I. J., and F. D., Young. Ste. Anne Test Road Revisited Twenty Years Later. Proceedings, Canadian Technical Asphalt Association, Vol. 32, 1987, pp. 254-283. 36. Button, J. W., D. N. Little, Y. Kim, and J. Ahmed. Mechanistic Evaluation of Selected Asphalt Additives. Journal of the Association of Asphalt Paving Technologists, Vol. 56, 1987, pp. 62-90. 37. Zhang, Z. Identification of Crack Growth Law for Asphalt Mixtures Using the Superpave Indirect Tensile Test (IDT). PhD Dissertation. University of Florida, Gainesville, 2000. 38. Daniel, J. S., and Y. R. Kim. Laboratory Evaluation of Fatigue Damage and Healing of Asphalt Mixtures. ASCE Journal of Materials in Civil Engineering, Vol. 13, No. 6, 2001, pp. 434-440. 39. Kim, B., and R. Roque. Evaluation of Healing Property of Asphalt Mixture. In Transportation Research Record: Journal of the Transportation Research Board, No. 1970, Transportation Research Board of the National Academies, Washington, D.C., 2006, pp. 84-91. 40. Si, Z., D. N. Little, and R. L. Lytton. Characterization of Microdamage and Healing of Asphalt Concrete Mixture. ASCE Journal of Materials in Civil Engineering, Vol. 14, No.6, 2002, pp. 461-470. 41. Kim, Y. R., D. N. Little, and R. L. Lytton. Fatigue and Healing Characterization of Asphalt Mixtures. ASCE Journal of Materials in Civil Engineering, Vol. 15, No.1, 2003, pp. 75-83. 42. Buttlar, W. G., R. Roque, and B. Reid. Automated Procedure for Generation of Creep Compliance Master Curve for Asphalt Mixtures. In Transportation Research Record: Journal of the Transportation Research Board, No. 1630, Transportation Research Board of the National Academies, Washington, D.C., 1998, pp. 28-36. 43. Hiltunen, D. R., and R. Roque. A Mechanics-Based Prediction Model for Thermal Cracking of Asphaltic Concrete Pavements. Journal of the Association of Asphalt Paving Technologists, Vol. 63, 1994, pp. 81-117. 127

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44. Park, S. W., and Y. R. Kim. Interconversion between Relaxation Modulus and Creep Compliance for Viscoelastic Solids. ASCE Journal of Materials in Civil Engineering, Vol. 11, No. 1, 1999, pp. 76-82. 45. Park, S. W., and Y. R. Kim. Fitting Prony-series Viscoelastic Models with Power-law Presmoothing. ASCE Journal of Materials in Civil Engineering, Vol. 13, No. 1, 2001, pp. 26-32. 46. Sangpetngam, B. Development and Evaluation of a Viscoelastic Boundary Element Method to Predict Asphalt Pavement Cracking. PhD Dissertation. University of Florida, Gainesville, 2003. 47. Myers, L. A., R. Roque, and B. Birgisson. Use of Two-dimensional Finite Element Analysis to Represent Bending Response of Asphalt Pavement Structures. International Journal of Pavement Engineering, Vol. 2, 2001, pp. 201-214. 48. Roque, R., A. Guarin, G. Wang, J. Zou, and H. Mork. Develop Methodologies/Protocols to Assess Cracking Potential of Asphalt Mixtures Using Accelerated Pavement Testing. Final Report, FDOT-BD545-49, University of Florida, Gainesville, 2007. 49. Roque, R., and W. G. Buttlar. The Development of a Measurement and Analysis System to Accurately Determine Asphalt Concrete Properties Using the Indirect Tensile Mode. Journal of the Association of Asphalt Paving Technologists, Vol. 61, 1992, pp. 304-332. 50. Buttlar, W. G., and R. Roque. Development and Evaluation of the Strategic Highway Research Program Measurement and Analysis System for Indirect Tensile Testing at Low Temperatures. In Transportation Research Record: Journal of the Transportation Research Board, No. 1454, Transportation Research Board of the National Academies, Washington, D.C., 1994, pp. 163-171. 51. Lytton, R. L., J. Uzan, E. G. Fernando, R. Roque, D. Hiltunen, and S. M. Stoffels. Development and Validation of Performance Prediction Models and Specifications for Asphalt Binders and Paving Mixes. SHRP-A-357, Strategic Highway Research Program, National Research Council, Washington, D.C., 1993. 128

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BIOGRAPHICAL SKETCH Jian Zou was born in Haimen, Jiangsu Province, Peoples Republic of China, on November 12, 1975. He received a Bachelor of Science degree in civil engineering from Hohai University in 1998, and then worked as a research assistant at the same University. In August 2001, Jian started a Master of Engineering program in civil engineering at the National University of Singapore. After finishing his masters degree, he joined the Soil and Foundation Pte. Ltd. of Singapore where he served as a civil engineer for about two years. Jian came to the United States in 2006. He joined the Ph.D. program of the materials group at the University of Florida and worked as a graduate research assistant with his doctoral advisor, Dr. Reynaldo Roque. After completing his Ph.D., he plans to work in academia, government agencies, or private companies in civil engineering. 129