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Measurement and Prediction of Fundamental Tensile Failure Limits of Hot Mix Asphalt (HMA)

Permanent Link: http://ufdc.ufl.edu/UFE0021968/00001

Material Information

Title: Measurement and Prediction of Fundamental Tensile Failure Limits of Hot Mix Asphalt (HMA)
Physical Description: 1 online resource (191 p.)
Language: english
Creator: Romeo, Elena
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

Subjects

Subjects / Keywords: asphalt, fracture, imaging, mixture, polymer, superpave
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: The purpose of this research program was to provide insight into key mechanisms and asphalt mixture properties that control fracture in asphalt concrete. A Digital Image Correlation (DIC) (non contact, full-field, surface displacement/strain measurement technique) was developed to more accurately capture localized or non-uniform stress distributions in asphalt mixtures and as a tool for detecting first fracture. The experimental analysis of asphalt mixture cracking behavior was based on the Hot Mix Asphalt (HMA) Fracture Mechanics visco-elastic crack growth law. Asphalt mixture cracking mechanism and fundamental tensile failure limits were investigated using multiple laboratory test configurations, namely the Superpave Indirect Tensile (IDT) test, the Semi-Circular Bending (SCB) test and the Three-Point Bending Beam (3PB) test. Both unmodified and polymer modified mixtures were tested. Results show that the DIC method could be used to reliably identify first fracture and to determine asphalt tensile failure limits. It was found that these failure limits are independent of the specimen geometry and of the test configuration. Also, importantly the tensile failure limits were shown to be sensitive to both presence and level of polymer modification. Results also show that first fracture and crack growth in asphalt mixtures can be predicted effectively using a Displacement Discontinuity (DD) boundary element method, for various different boundary condition problems, and not just for the calibrated laboratory test conditions. The numerical simulations and the DIC results showed that significant damage, stress redistribution and other changes after initial fracture make the analysis after peak load difficult to interpret meaningfully. The effect of polymer modification on crack localization was also investigated using horizontal full-field strain maps obtained from the DIC. Polymer modified mixtures showed high strains only up to the location of impending fracture, while unmodified mixtures showed highly distributed damage in both the critical area and around the point of fracture.
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 Elena Romeo.
Thesis: Thesis (Ph.D.)--University of Florida, 2008.
Local: Adviser: Roque, Reynaldo.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2009-02-28

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0021968:00001

Permanent Link: http://ufdc.ufl.edu/UFE0021968/00001

Material Information

Title: Measurement and Prediction of Fundamental Tensile Failure Limits of Hot Mix Asphalt (HMA)
Physical Description: 1 online resource (191 p.)
Language: english
Creator: Romeo, Elena
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

Subjects

Subjects / Keywords: asphalt, fracture, imaging, mixture, polymer, superpave
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: The purpose of this research program was to provide insight into key mechanisms and asphalt mixture properties that control fracture in asphalt concrete. A Digital Image Correlation (DIC) (non contact, full-field, surface displacement/strain measurement technique) was developed to more accurately capture localized or non-uniform stress distributions in asphalt mixtures and as a tool for detecting first fracture. The experimental analysis of asphalt mixture cracking behavior was based on the Hot Mix Asphalt (HMA) Fracture Mechanics visco-elastic crack growth law. Asphalt mixture cracking mechanism and fundamental tensile failure limits were investigated using multiple laboratory test configurations, namely the Superpave Indirect Tensile (IDT) test, the Semi-Circular Bending (SCB) test and the Three-Point Bending Beam (3PB) test. Both unmodified and polymer modified mixtures were tested. Results show that the DIC method could be used to reliably identify first fracture and to determine asphalt tensile failure limits. It was found that these failure limits are independent of the specimen geometry and of the test configuration. Also, importantly the tensile failure limits were shown to be sensitive to both presence and level of polymer modification. Results also show that first fracture and crack growth in asphalt mixtures can be predicted effectively using a Displacement Discontinuity (DD) boundary element method, for various different boundary condition problems, and not just for the calibrated laboratory test conditions. The numerical simulations and the DIC results showed that significant damage, stress redistribution and other changes after initial fracture make the analysis after peak load difficult to interpret meaningfully. The effect of polymer modification on crack localization was also investigated using horizontal full-field strain maps obtained from the DIC. Polymer modified mixtures showed high strains only up to the location of impending fracture, while unmodified mixtures showed highly distributed damage in both the critical area and around the point of fracture.
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 Elena Romeo.
Thesis: Thesis (Ph.D.)--University of Florida, 2008.
Local: Adviser: Roque, Reynaldo.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2009-02-28

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0021968:00001


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1 MEASUREMENT AND PREDICTION OF FUND AMENTAL TENSILE FAILURE LIMITS OF HOT MIX ASPHALT (HMA) By ELENA ROMEO A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2008

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2 2008 Elena Romeo

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3 To my father

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4 ACKNOWLEDGMENTS With great pleasure I thank and acknowledge those individuals who were involved in the advancement of this research, he lping me with their support, suggestions and comments, or just by listening to my ideas. First, my sincere th anks and deep appreciation go to Professor Reynaldo Roque, the chair of my supervisory co mmittee, for his unfailing support and guidance during my doctoral program and for the generous contribution of his discussion and thinking to this work; his insightful comments and constructi ve criticisms led my research to a successful achievement. I am deeply thankful to Prof essor Antonio Montepara for offering me the wonderful opportunity to be schooled at such a pr estigious university. I owe enormous gratitude to Professor Bjorn Birgisson, who has been a continuous source of knowledge, encouragement and guidance in both academic and non-academic lif e and who taught me how to think critically, develop research skills and write scientific papers. I am grateful to Dr. Gabriele Tebaldi who spent much of his time supporting and helping me solve the many problems I faced from time to time. My sincerest thanks go to Professor Gianfranco Forlani and Dr. Riccardo Roncella for their assistance and valuable contributions in developing the DIC system and fo r their true friendship. Many th anks and much appreciation go to Mr. George Lopp for his time, expertise and pa tience in teaching me a ll the laboratory testing procedures. Special thanks go to Dr. John A. L. Napier, who let me use his boundary element code.I would like to take this opportunity to acknowledge the Associatio n of Asphalt Pavement Technologists (AAPT) for the scholarship they aw arded me, which supported part of my travel expenses for going back and fort h from Parma to Gainesville. A very special acknowledgment is sent to a ll the “GNV’s Italian Buddies,” and everyone in the materials group at the University of Florida whose friendship and help made my experience there something I will always remember. Last, but not least, my eternal thanks go to

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5 my parents, my brother and Riccardo for thei r love, encouragement and constant advice throughout my academic life, especi ally while away from home.

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6 TABLE OF CONTENTS page ACKNOWLEDGMENTS ............................................................................................................... 4 LIST OF TABLES ................................................................................................................ ...........9 LIST OF FIGURES ............................................................................................................... ........10 ABSTRACT ...................................................................................................................... .............17 CHAPTER 1 INTRODUCTION ................................................................................................................ ..19 Background .................................................................................................................... .........19 Hypothesis .................................................................................................................... ..........20 Objective ..................................................................................................................... ............20 Scope ......................................................................................................................... ..............20 Key Results ................................................................................................................... ..........21 2 LITERATURE REVIEW .......................................................................................................22 Crack Initiation and Propagation ............................................................................................22 Conventional Fracture Mechanics ..........................................................................................23 Linear Elastic Fracture Mechanics (LEFM) ....................................................................24 Non Linear Fracture Mechanics (NLFM) .......................................................................26 Application of Conventiona l Fracture Mechanics ...........................................................28 Cohesive Crack Model ....................................................................................................29 Continuum Damage Approach ...............................................................................................31 Development of HMA Fracture Mechanics ...........................................................................34 Tensile Failure Limits of HMA Mixes ...................................................................................37 Tensile Strength .............................................................................................................. .37 Fracture Energy ............................................................................................................... 41 Polymer Modified Mixtures ...................................................................................................44 3 MATERIALS AND METHODS ...........................................................................................47 Materials ..................................................................................................................... ............47 Aggregates .................................................................................................................... ...47 Asphalt Binders ............................................................................................................... 48 Specimen Preparation .......................................................................................................... ...49 Test Methods .................................................................................................................. ........51 Indirect Tension Fracture Test .........................................................................................51 Semi-Circular Bending Test ............................................................................................53 Three-Point Bending Beam Test .....................................................................................56

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7 4 DIGITAL IMAGE CORRELATION (DIC) SYSTEM .........................................................58 Background .................................................................................................................... .........58 Image System Characteristics .................................................................................................6 0 Experimental Setup .........................................................................................................60 Specimen Preparation ......................................................................................................60 Theoretical Principles ........................................................................................................ .....62 Cross-Correlation ............................................................................................................6 3 Least Squares Matching (LSM) .......................................................................................64 Optimization with LSM ...................................................................................................66 Data Extraction ............................................................................................................... .67 Verification of Method Accuracy ...........................................................................................69 Accuracy in Displacement Measurements ......................................................................69 Accuracy in Strain Measurements ...................................................................................71 Potential Measurement Errors .........................................................................................72 Tests on Asphalt Mixture Specimens .....................................................................................76 Accuracy Achievable in HMA Strength Tests ................................................................76 Description of Software Tools ................................................................................................7 8 Potential Measurement Errors in HMA Tests .................................................................80 5 PREDICTION OF HMA CRACK INITIATION AND PROPAGATION ............................82 Background .................................................................................................................... .........82 Displacement Discontinuity (DD) Boundary Element Method with Tessellation .................84 Theoretical Background ..................................................................................................86 Numerical Implementation ..............................................................................................88 Crack Growth Algorithm .................................................................................................90 Fracture Test Models .......................................................................................................... ....92 Indirect Tension Model ...................................................................................................93 Semi-Circular Bending Model ........................................................................................94 Three-Point Bending Model ............................................................................................95 Parameters Calibration ........................................................................................................ ....96 Evaluation of Fracture Energy Density with DD .................................................................100 6 FINDING AND ANALYSIS ...............................................................................................105 Fracture Tests Results ........................................................................................................ ...105 Displacement Discontinuity Predictions ...............................................................................126 Measured and Simulated Crack Patterns ..............................................................................135 Effect of SBS Modifiers on HMA Cracking Resistance ......................................................155 Resilient Modulus ..........................................................................................................156 Creep Compliance .........................................................................................................156 Indirect Tensile Strength a nd Energy-Based Parameters ..............................................157 Energy Ratio .................................................................................................................. 159 Crack Localization and Crack Growth ..........................................................................160 7 SUMMARY AND CONCLUSIONS ...................................................................................162

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8 Summary of Findings ........................................................................................................... 163 Conclusions ................................................................................................................... ........164 APPENDIX A STANDARD SUPERPAVE IDT .........................................................................................165 Resilient Modulus ............................................................................................................. ....165 Creep Test .................................................................................................................... .........166 Strength Test ................................................................................................................. ........168 B DISPLACEMENT DISCONTINUITY PRE/POST PROCESSOR .....................................170 Coordinate Systems ............................................................................................................ ..171 Text Files Associated with PRE/POST Processor ................................................................172 Pre Processor Files for the Three Specimen Models ............................................................173 Input File (*.IN) ............................................................................................................. 173 Segment File (*.VSG) ...................................................................................................175 Data File (*.DAT) .........................................................................................................176 Output File (*.OUT) ......................................................................................................177 LIST OF REFERENCES ............................................................................................................ .180 BIOGRAPHICAL SKETCH .......................................................................................................191

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9 LIST OF TABLES Table page 3-1 Aggregate gradation ....................................................................................................... ....47 3-2 Asphalt binder properties ................................................................................................. ..49 3-3 Volumetric properties for the six mixtures ........................................................................50 3-4 HBM-Y series strain gauge specifications .........................................................................54 4-1 Theoretical image system accuracy ...................................................................................71 4-2 Displacement and strain errors for a common camera set up ............................................75 5-1 Calibrated material parameters for th e parametric study of the six mixtures ....................96 5-2 Correction factors accoun ting for bulging effects ...........................................................100 6-1 Comparison between experimental and im age correlation (as mean values) tensile strength and fracture energy values .................................................................................115 6-2 Comparison between experimental and pi npoint tensile failure limits of the six mixtures....................................................................................................................... .....125 6-3 Comparison between predicted and meas ured tensile failure limits of the six mixtures....................................................................................................................... .....136 6-4 Superpave IDT test results of the five mixtures...............................................................155 6-5 Energy-based mixture specification criteria ....................................................................160

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10 LIST OF FIGURES Figure page 2-1 Fracture process zone in asphalt mixtures .........................................................................23 2-2 Typical fatigue crack growth behavior ..............................................................................25 2-3 Cohesive crack model ...................................................................................................... ..30 2-4 Crack propagation in asphalt mixtures according to “HMA Fracture Mechanics” ...........35 2-5 Crack initiation or crack growth development in asphalt mixtures ...................................36 2-6 Determination of the lower and uppe r thresholds for asphalt mixtures .............................37 2-7 Load-deflection plot from RILEM test ..............................................................................42 3-1 Aggregate curve of the six mixtures ..................................................................................48 3-2 Indirect Tensile Test setup ............................................................................................... ..52 3-3 Semi-Circular Bending Test setup .....................................................................................53 3-4 Semi-Circular Bending Test strain maps of mix N2 at crack opening ..............................55 3-5 Three-Point Bending Beam Test setup ..............................................................................57 4-1 Digital Image Correlation (DIC ) system experimental setup ............................................61 4-2 Specimen surface treatment ...............................................................................................6 1 4-3 Area Based Matching (ABM) principles ...........................................................................62 4-4 Cross-correlation approach ................................................................................................ 64 4-5 Region of interest (ROI) meshing ......................................................................................68 4-6 Accuracies achievable accord ing to the template size .......................................................70 4-7 Comparison between image correlation a nd strain gauge measurements in uniaxial tensile test................................................................................................................... ........72 4-8 Potential elements leading to measurement errors .............................................................73 4-9 Comparison between image correlati on and strain gauge measurements .........................77 4-10 Visual graphic inte rface of DIC system .............................................................................78

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11 4-11 Mixture N1 during IDT test. .............................................................................................. 79 4-12 Evaluation of strain field. .............................................................................................. .....79 4-13 Other information used to obtain correct strain values. .....................................................80 4-14 Example of a potential meas urement error in HMA tests ..................................................81 5-1 Displacement discontinuity elemen t in local coordinates (y-z). ........................................86 5-2 Voronoi tessellations with internal fractur e paths representing the aggregate structure ...91 5-3 Failure criterion for dete rmining crack mobilization .........................................................91 5-4 Indirect Tensile specimen model .......................................................................................94 5-5 Semi-Circular Bending specimen model ...........................................................................95 5-6 Three-Point Bending Beam model .....................................................................................95 5-7 Mixture N1: Experimental and DD stress-strain response ................................................97 5-8 Mixture N2: Experimental and DD stress-strain response ................................................97 5-9 Mixture RM3.5: Experimental and DD stress-strain response ..........................................98 5-10 Mixture RM5.0: Experimental and DD stress-strain response ..........................................98 5-11 Mixture LM3.5: Experimental and DD stress-strain response ..........................................99 5-12 Mixture LM6.5: Experimental and DD stress-strain response ..........................................99 5-13 Simulated deformation di fferential for Mixture N1. ........................................................102 5-14 Simulated deformation di fferential for Mixture N2. ........................................................102 5-15 Simulated deformation di fferential for Mixture RM3.5. .................................................103 5-16 Simulated deformation di fferential for Mixture RM5.0. .................................................103 5-17 Simulated deformation di fferential for Mixture LM3.5. .................................................104 5-18 Simulated deformation di fferential for Mixture LM6.5. .................................................104 6-1 Experimental and mean image correlati on horizontal stressstrain response for mixture N1 during IDT. ...................................................................................................106 6-2 Experimental and mean image correlati on horizontal stressstrain response for mixture N2 during IDT. ...................................................................................................106

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12 6-3 Experimental and mean image correlati on horizontal stressstrain response for mixture RM3.5 during IDT. .............................................................................................107 6-4 Experimental and mean image correlati on horizontal stressstrain response for mixture RM5.0 during IDT. .............................................................................................107 6-5 Experimental and mean image correlati on horizontal stressstrain response for mixture LM3.5 during IDT. .............................................................................................108 6-6 Experimental and mean image correlati on horizontal stressstrain response for mixture LM6.5 during IDT. .............................................................................................108 6-7 Experimental and mean image correlati on horizontal stressstrain response for mixture N1 during SCB. ..................................................................................................109 6-8 Experimental and mean image correlati on horizontal stressstrain response for mixture N2 during SCB. ..................................................................................................109 6-9 Experimental and mean image correlati on horizontal stressstrain response for mixture RM3.5 during SCB. ............................................................................................110 6-10 Experimental and mean image correlati on horizontal stressstrain response for mixture RM5.0 during SCB. ............................................................................................110 6-11 Experimental and mean image correlati on horizontal stressstrain response for mixture LM3.5 during SCB. ............................................................................................111 6-12 Experimental and mean image correlati on horizontal stressstrain response for mixture LM6.5 during SCB. ............................................................................................111 6-13 Experimental and mean image correlati on horizontal stressstrain response for mixture N1 during 3PB. ...................................................................................................112 6-14 Experimental and mean image correlati on horizontal stressstrain response for mixture N2 during 3PB. ...................................................................................................112 6-15 Experimental and mean image correlati on horizontal stressstrain response for mixture RM3.5 during 3PB..............................................................................................113 6-16 Experimental and mean image correlati on horizontal stressstrain response for mixture RM5.0 during 3PB..............................................................................................113 6-17 Experimental and mean image correlati on horizontal stressstrain response for mixture LM3.5 during SCB .............................................................................................114 6-18 Experimental and mean image correlati on horizontal stressstrain response for mixture LM6.5 during 3PB ..............................................................................................114

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13 6-19 Experimental and pinpoint DIC horizontal stress-strain response for mixture N1 during IDT. ................................................................................................................... ...116 6-20 Experimental and pinpoint DIC horizontal stress-strain response for mixture N2 during IDT. ................................................................................................................... ...116 6-21 Experimental and pinpoint DIC horizontal stress-strain response for mixture RM3.5 during IDT .................................................................................................................... ...117 6-22 Experimental and pinpoint DIC horizontal stress-strain response formixture RM5.0 during IDT. ................................................................................................................... ...117 6-23 Experimental and pinpoint DIC stre ss-strain response formixture LM3.5 during IDT .................................................................................................................... ...118 6-24 Experimental and pinpoint DIC horizontal stress-strain response for mixture LM6.5 during IDT .................................................................................................................... ...118 6-25 Experimental and pinpoint DIC horizontal stress-strain response for mixture N1 during SCB..................................................................................................................... ..119 6-26 Experimental and pinpoint DIC horizontal stress-strain response formixture N2 during SCB..................................................................................................................... ..119 6-27 Experimental and pinpoint DIC horizontal stress-strain response for mixture RM3.5 during SCB..................................................................................................................... ..120 6-28 Experimental and pinpoint DIC horizontal stress-strain response formixture RM5.0 during SCB..................................................................................................................... ..120 6-29 Experimental and pinpoint DIC horizontal stress-strain response for mixture LM3.5 during SCB..................................................................................................................... ..121 6-30 Experimental and pinpoint DIC horizontal stress-strain response for mixture LM6.5 during SCB..................................................................................................................... ..121 6-31 Experimental and pinpoint DIC horizontal stress-strain response for mixture N1 during 3PB. ................................................................................................................... ...122 6-32 Experimental and pinpoint DIC horizontal stress-strain response for mixture N2 (virgin; PG 58-22) during 3PB. .......................................................................................122 6-33 Experimental and pinpoint DIC horizontal stress-strain response for mixture RM3.5 (cross-linked polymer modifi ed PG 64-22) during 3PB. .................................................123 6-34 Experimental and pinpoint DIC horizontal stress-strain response for mixture RM5.0 (cross-kinked polymer modifi ed PG 70-22) during 3PB. ................................................123

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14 6-35 Experimental and pinpoint DIC horizontal stress-strain response for mixture LM3.5 (linear polymer modified PG 70-22) during 3PB. ...........................................................124 6-36 Experimental and pinpoint DIC correla tion horizontal stress-strain response for mixture LM6.5 (linear polymer modi fied PG 76-22) during 3PB. ..................................124 6-37 Mixture N1 (IDT) horizontal stress-strain response ........................................................126 6-38 Mixture N2 (IDT) horizontal stress-strain response ........................................................127 6-39 Mixture RM3.5 (IDT) horizont al stress-strain response ..................................................127 6-40 Mixture RM5.0 (IDT) horizont al stress-strain response ..................................................128 6-41 Mixture LM3.5 (IDT) horizont al stress-strain response ..................................................128 6-42 Mixture LM6.5 (IDT) horizont al stress-strain response ..................................................129 6-43 Mixture N1 (SCB) horizontal stress-strain response .......................................................129 6-44 Mixture N2 (SCB) horizontal stress-strain response .......................................................130 6-45 Mixture RM3.5 (SCB) horizon tal stress-strain response .................................................130 6-46 Mixture RM5.0 (SCB) horizon tal stress-strain response .................................................131 6-47 Mixture LM3.5 (SCB) horizon tal stress-strain response .................................................131 6-48 Mixture LM6.5 (SCB) horizon tal stress-strain response .................................................132 6-49 Mixture N1 (3PB) horizontal stress-strain response ........................................................132 6-50 Mixture N2 (3PB) horizontal stress-strain response ........................................................133 6-51 Mixture RM3.5 (3PB) horizon tal stress-strain response..................................................133 6-52 Mixture RM5.0 (3PB) horizon tal stress-strain response..................................................134 6-53 Mixt LM3.5 (3PB) horizontal stress-strain response .......................................................134 6-54 Mixture LM6.5 (3PB) horizon tal stress-strain response ..................................................135 6-55 Mixture N1 (IDT) crack pattern s and full field strain maps ............................................137 6-56 Mixture N2 (IDT) crack pattern s and full field strain maps ............................................138 6-57 Mixture RM3.5 (IDT) crack patter ns and full field strain maps ......................................139 6-58 Mixture RM5.0 (IDT) crack patter ns and full field strain maps ......................................140

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15 6-59 Mixture LM3.5 (IDT) crack patter ns and full field strain maps ......................................141 6-60 Mixture LM6.5 (IDT) crack patter ns and full field strain maps ......................................142 6-61 Mixture N1 (SCB) crack patterns and full field strain maps ...........................................143 6-62 Mixture N2 (SCB) crack patterns and full field strain maps ...........................................144 6-63 Mixture RM3.5 (SCB) crack patter ns and full field strain maps .....................................145 6-64 Mixture RM5.0 (SCB) crack patter ns and full field strain maps .....................................146 6-65 Mixture LM3.5 (SCB) crack patter ns and full field strain maps .....................................147 6-66 Mixture LM6.5 (SCB) crack patter ns and full field strain maps .....................................148 6-67 Mixture N1 (3PB) crack pattern s and full field strain maps ............................................149 6-68 Mixture N2 (3PB) crack pattern s and full field strain maps ............................................150 6-69 Mixture RM3.5 (3PB) crack patter ns and full field strain maps......................................151 6-70 Mixture RM5.0 (3PB) crack patter ns and full field strain maps......................................152 6-71 Mixture LM3.5 (3PB) crack patter ns and full field strain maps ......................................153 6-72 Mixture LM6.5 (3PB) crack patter ns and full field strain maps ......................................154 6-73 Creep compliance curves for the five mixtures ...............................................................157 6-74 Tensile strengths obtaine d for the five mixtures ..............................................................158 6-75 Fracture energy densities and dissipated creep strain energies for the five mixtures ......158 6-76 Failure strains for the five mixtures .................................................................................159 6-77 Energy ratio values obtained for the five mixtures ..........................................................160 A-1 Power model of the creep compliance .............................................................................167 A-2 Determination of fracture energy and di ssipated creep strain energy to failure ..............169 B-1 Global (Y-Z) and local (y-z) coordinate systems used by DD ........................................171 B-2 IDT.IN pre processor file ................................................................................................. 173 B-3 SCB.IN pre processor file ................................................................................................1 74 B-4 3PB.IN pre processor file ................................................................................................. 174

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16 B-5 IDT.VSG pre processor file .............................................................................................175 B-6 Boundary conditions. A) IDT model. B) SCB model. C) 3PB model .............................178 B-7 .DAT file used for simulating the IDT test ......................................................................179

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17 Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy MEASUREMENT AND PREDICTION OF FUND AMENTAL TENSILE FAILURE LIMITS OF HOT MIX ASPHALT (HMA) By Elena Romeo August 2008 Chair: Reynaldo Roque Major: Civil Engineering The purpose of this research program was to provide insight into key mechanisms and asphalt mixture properties that control fracture in asphalt concrete. A Digital Image Correlation (DIC) (non contact, full-fiel d, surface displacement/strain measurement technique) was developed to more accurately capture localized or non-uniform stress distributions in asphalt mixtures and as a tool for detecting first fracture. The experimental analysis of asphalt mixtur e cracking behavior was based on the Hot Mix Asphalt (HMA) Fracture Mechanics visco-elastic crack growth law. Asphalt mixture cracking mechanism and fundamental tensile failure limits were investigated using multiple laboratory test configurations, namely the Superpave Indire ct Tensile (IDT) test, the Semi-Circular Bending (SCB) test and the Three-Point Bending B eam (3PB) test. Both unmodified and polymer modified mixtures were tested. Results show that the DIC method could be us ed to reliably identify first fracture and to determine asphalt tensile failure limits. It was f ound that these failure limits are independent of the specimen geometry and of the test configur ation. Also, importantly th e tensile failure limits were shown to be sensitive to both pres ence and level of polymer modification.

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18 Results also show that first fracture and crack growth in asphalt mixtures can be predicted effectively using a Displacement Discontinu ity (DD) boundary element method, for various different boundary condition problems, and not just for the calibrated laboratory test conditions. The numerical simulations and the DIC resu lts showed that significant damage, stress redistribution and other changes afte r initial fracture make the analysis after peak load difficult to interpret meaningfully. The eff ect of polymer modification on crack localization was also investigated using horizontal full-field strain maps obtained from the DIC. Polymer modified mixtures showed high strains only up to the location of impending fracture, while unmodified mixtures showed highly distribut ed damage in both the critical area and around the point of fracture.

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19 CHAPTER 1 INTRODUCTION Background The need for improved models and design appr oaches for asphalt pavements has driven efforts to better understand and model the physi cal phenomena of fracture in asphalt mixtures. The benefits of an improved understanding of the mechanism of cracking in asphalt include improved analysis and design formulations a nd an improved framework for optimizing the fracture resistance of asphalt mi xtures during the material de sign stage. Generally, cracking models describe how a crack nuc leates, initiates and propagate s using fundamental material properties. Asphalt mixtures fall within a category of materials that are defined quasi-brittle, for which the fracture mechanism is generally cons idered as a complex phenomenon that occurs within a zone ahead of the crack tip. This zone is often entitled the frac ture process zone (FPZ) (e.g., Bazant, 1986; Hu & Wittmann, 1992; Little et al., 1997; Carpinteri et al., 2003; Wagoner & Buttlar, 2007, Li & Marasteanu, 2007). Recent work conducted at the University of Florida by Roque et al., 2001 and Zhang et al., 2002, has shown that the fracture properties of asphalt mixtures can be described within a viscoelastic fracture mechanics-based law, enti tled HMA Fracture Mechanics. This framework introduced a new definition for a fundamental crack growth energy threshol d as a key parameter in describing the cracking mechanism of asphalt mixture. The threshold was identified as the Fracture Energy (FE) density at fi rst fracture and corresponds to th at energy required to fracture the mixture with a single load application. However, this work was based solely on Superpave IDT test results. It is essential to verify the energy parameter independence of the geometry of the specimen and test configuration to a ssume it is an objective material property.

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20 Hypothesis € Using rigorous interpretation of test conditi on and appropriate anal ysis techniques for identification of first fracture, it is possible to accurately determine tensile failure limits from multiple test configurations for both unmodified and polymer modified mixtures. € Tensile failure limits measured at firs t fracture are fundamental HMA properties, independent of specimen geometry. € First fracture can be predicted using fundame ntal mixture properties obtained with the Superpave Indirect Tension test as input in the Displacement Discontinuity (DD) boundary element method, regardless of test configuration. Objective The purpose of this research program is to provide insight into key mechanisms and asphalt mixture properties that c ontrol fracture in asphalt materi als. The main objective is to investigate the independence of asphalt mixture tensile failure limits, identified as tensile strength and fracture energy de nsity, from specimen geometries and test configurations. Scope This study focuses on the measurement and pred iction of fundamental tensile failure limits of asphalt mixtures from multiple laboratory test configurations, namely the Superpave Indirect Tensile Test (IDT), the Semi-Circular Bending Test (SCB) and the Three Point Bending Beam Test (3PB). Six 12.5 nominal maxi mum size fine graded Marshall mixtures, two unmodified and four SBS cross-linked and SBS linear polymer modified, were examined. A Digital Image Correlation (DIC) (non contact, full-field, surface displacement/s train measurement technique) was developed to more accurately capture localiz ed or non-uniform stress distributions in asphalt mixtures and as a tool for detecting first fr acture. The method, which is based on a wellestablished technique (area-base d matching), was implemented and customized according to the specific asphalt testing requirements.

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21 Key Results The results presented herein illustrate that the DIC method could be used to reliably determine asphalt tensile failure limits at first fr acture. It was found that these failure limits are independent of the specimen geometry and of the test configuration. Also, importantly the tensile failure limits were shown to be se nsitive to both presence and leve l of polymer modification. It is also shown that first fracture and crack growth in asphalt mixtures can be predicted effectively using a Displacement Discontinuity (DD) boundary element method. Obtaining calibrated input parameters from the Superpave IDT test results, it is possible to successf ully predict the stressstrain evolution for the Superpave IDT, SCB and 3PB tests. The effect of polymer modification on crack localization was investigated through th e use of horizontal full-field strain maps obtained from the DIC. It was found that polyme r modified mixtures e xhibit high strains only up to the location of impending fracture, while unm odified mixtures exhib it highly distributed damage in both the critical area and around the point of fracture.

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22 CHAPTER 2 LITERATURE REVIEW The primary purpose of this section is to summarize theoretical background and experimental confirmations that have supplie d the motivations for this research. Current understanding of cracking mechanis m and damage criteria in the area of design and evaluation of flexible pavement were examined. Crack Initiation and Propagation Observation of crack initiation and propagation in asphalt mixture i ndicates that cracks may start as microcracks that later propagate, de nsify and coalesce to from macrocracks as the mixture is subjected to tensile stresses, shear stresses or a combina tion of both. An improved understanding of the mechanism of cracking would lead to improved mixture tests, materials and pavement models that predict field performan ce of asphalt mixtures more reliably. Recognizing that both crack initiation and propa gation processes are directly rela ted to stress-strain fields in asphalt layers, researchers recently have focused on developing constitutive relationships that can describe the cracking res ponse of asphalt mixtures under realistic traffic conditions composed of multiple load levels and random rest periods. The cracking mechanism of asphalt pavements have been studied since the early 1970s when several researchers began to apply fracture mechanics to analyze the fatigue behavior in asphalt materials (Majidzadeh et al. 1971; Schaper y, 1973). Unfortunately, the complexity of crack propagation in HMA mixtures has been an obstacle to the incor poration of fracture mechanics-based approaches in the bituminous pavement area. In recent years, it was found that asphalt mixture’s cracking mechanism can be simulated using nonlinear models with an appropriate c onstitutive law for the damaged material in the fracture process zone (FPZ), identified as a strongly nonlinear region ahead of the crack tip

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23 where intense damage and microcrack coales cence occur (see Figure 2-1, Wagoner and Buttlar, 2007). Specifically, the FPZ ahead of the cr ack tip involves comp lex phenomena where aggregates can slide along the crack face, bridge the crack face, and the asphalt binder can yield under high strain (Wagoner & Buttlar, 2007). Th is approach, named Cohesive Crack Model (CCM), introduced the concept of a nonlinear fracture model a ppropriate for quasi-brittle materials (concrete, asphalt concrete, ceramics, etc.). MACRO-CRACK FRACTURE PROCESS ZONE Figure 2-1. Fracture process z one in asphalt mixtures A further pavement cracking model enti tled HMA Fracture Mechanics was recently developed at the University of Florida by Zha ng et al. (2001) and Roque et al. (2002) observing that crack in HMA grows in a stepwise rather than a continuous ma nner. Central to this framework is the concept of the existence of a fundamental crac k growth threshold as the key element defining the cracking mechanism and fracture resistance of asphalt mixtures. Conventional Fracture Mechanics The science of fracture mechanics was firstly introduced in the 1920s by Griffith to describe the propagation of cr acks through materials. Griff ith invoked the first law of

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24 thermodynamics to formulate a fracture theory ba sed on a simple energy balance: the crack will increase in size if the induced potential energy is greater than the surface energy of the material. Fracture mechanics concepts have been subs equently adopted by several researchers to quantify fracture resistance of asphalt mixtures resulting in the development of fracture mechanics-based models to predict cr ack growth in asphalt concrete. Linear Elastic Fracture Mechanics (LEFM) Linear Elastic Fracture Mechanics (LEFM) pr esumes that there are intrinsic flaws in a material from which a crack propagates any tim e a load is applied. The most common parameter used in LEFM is the stress intensity factor K, wh ich characterizes the stre ss distribution in the vicinity of a macro-crack. In LEFM, crack growth rate is generally de scribed using Paris la w (Paris and Erdogan, 1963), in which: (2-1) where a is the crack length, N is the number of repeated loads, K is the range in stress intensity factor, and A and n are material parameters dete rmined from fitting crack growth test data. As shown in Figure 2-2, Kth represents a material related th reshold, below which no fatigue is assumed to occur. Fracture toughness Kc represents the resistance of the material to failure from fracture and is considered an intrinsic materi al constant. The sigmoidal curve (Figure 2-2) contains three distinct regions: in region I, da/dN approaches zero at the threshold Kth; in region II, the crack growth rate increases linearly with increasing K but deviates from the linear trend at high and low K levels; in region III, the crac k growth rate accelerates as K approaches Kcrit, the fracture toughness of th e material (Anderson, 1995).

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25 Figure 2-2. Typical fatigue crack growth behavior Several researchers have developed equations that modeled all or part of the sigmoidal da/dNK relationship (Foreman, 1967; Weertma n, 1966; Klesnil and Lukas, 1972; McEvily, 1988). As Paris law became widely used for predicti on of fatigue crack growth, it was realized that this simple expression was not universally applicable. Theref ore, further research work led to insight into crack performan ce. For example, in 1970, Elber pr oposed a modified Paris law: (2-2) where Keff is the effective stress in tensity range, defined as Kmax-Kop, where Kop is the stress intensity factor at which the crack opens. Recently, Roque et al. (1999) investigated the possibility of developing a fracture method to indirectly measure crack grow th rates (A and n) in the laboratory. Using the linear elastic finite element method to simulate specimens under Indirect Tensile test (IDT) condition at different crack lengths, they found a relationship between the theoretical length and the elastic

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26 deformation between two gauge points located acro ss the crack line. The theoretical crack length allowed them to monitor the crack growth co rresponding to the incremen t of cycling loading. This method was further investigated by Zhang et al. (2001) by comparing crack growth rates measured in the lab from 4 Superpave mixtur es with field performa nce. They found that laboratory crack growth rates di d not correlate with the observe d field cracking performance and did not agree with expected trends for the Supe rpave mixtures. They concluded that Paris law does not incorporate all aspects involved in the mechanism of cracking of asphalt mixtures subjected to generalized loading conditions, such as those encount ered in the field. Non Linear Fracture Mechanics (NLFM) The Non-Linear Fracture Mechanics (NLFM) theory extends fracture mechanics methodology beyond the validity limits of LEFM. The most common parameter for characterizing non-linear material s is the J integral, first in troduced by Rice (1968). The J integral has physical meaning for both non-linear elastic and elastic-p lastic behaviors, and can be used as an energy parameter as well as a stress intensity parameter (Anderson, 1995): (2-3) where W is the strain energy density, is any boundary around the crack and ds is a length increment along the boundary. Several studies based on J-integral theory have been conducted to characterize fracture resistance, low temperatur e properties and fatigue properties of asphalt mixtures (Abdulshafi & Majidzadeh 1985; Little et al., 1987; Button et al., 1987; Sulaiman & Stock, 1995; Mull et al., 2002). A more mechanics-based model was devel oped by Ramsamooj (1980). He used the nonlinear differential equation governing subcritical growth of a crack em bedded in an elastic-

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27 plastic matrix up to the point of gross instabil ity derived by Wnuk (1971), to formulate a fatigue crack growth model for a beam on elastic foundation: (2-4) where t = yield stress in flexural tension, KI = stress intensity at service load, K0 = value of stress intensity at endurance limit. Ramsamooj (1991) then again used the same nonlinear differential equation with an estimated value of plastic zone for asphalt concrete ( = 0.125(KI/ t)2) to formulate a general expression for fatigue behavior of asphalt conc rete under any configur ation of loading and boundary conditions. A further approach is the viscoelatic fract ure mechanics theory developed by Schapery (1973). This approach evaluates fatigue crack growth in homogeneous linear viscoelastic materials by estimating the parameters A and n (Equation 2-1) from mechanical, chemical and thermodynamics characteristics such as creep co mpliance, tensile strength and adhesive and cohesive surface energy density. According to Sc hapery’s theory, the parameters A and n are given as follows: (2-5) for force controlled tests for displacement controlled tests where m = tensile strength, I1 = result of the integration of stress near the crack tip over a sma ll region ahead of the crack tip known as the failure zone,

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28 = Poisson’s ratio, D2 = compliance at t = 1s, m = slope of the creep compliance curve (log-log scale), = energy needed to produce a unit surface of fracture, w(t) = wave shape of st ress intensity factor, t = the period of loading to co mplete one cycle of loading. Application of Conventional Fracture Mechanics Since the fracture mechanics approach has b een well accepted for analyzing crack growth in materials, many researchers have adopted th e concepts and applied them to the field of pavements. Jacobs (1995 and 1996) used fracture mechanics princi ples to characterize fracture toughness and construct master curves. He conducted uniaxial static testing on double edge notched specimen (50x50x150mm) to obt ain maximum tensile strength ( m) and fracture energy ( ). He also conducted fatigue te sts of the double edge notched sp ecimen to determine material parameters A and n. According to this research, he c oncluded that theoretical derivations for A and n for viscoelastic materials by Schape ry (1973, 1975, 1978) appeared to be valid. Ramsamooj (1993) modified an analytical so lution for a thin plat e resting on elastic foundation by including 3 cracking conditions: crack in transverse direction, crack in longitudinal direction and semi elliptical crack at the bottom of the plate. The equations can be used to evaluate stress intensity factor ahead of the crack tip for those th ree types of cracking in pavement. Collop and Cebon (1995) investigated the cause s of cracking on the top and bottom layer of an asphalt concrete pavement. According to their findings, the surface cracking was caused by transverse shear stress of a radial tire and pe rhaps combined with the presence of stiffness gradients due to aging and thermal effects. They formulated an analytical solution for determining stress intensity factor for a surface crack in a semi-infinite plate subjected to a general remote stress. They also derived a form ula based on parametric studies to quantify the

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29 stress intensity factor due to traffic and ther mal loading for various pavement structures at progressive crack growth in pavement. Myers (2000) and Myers et al. (2001) also i nvestigated the mechanis m of surface initiated cracking along the wheel path but they used m easured tire contact st resses instead of the traditionally assumed circular load. Accordi ng to their findings, surface cracking could be explained by transverse shear stre ss of a radial tire and perhaps combined with thermal stress due to rapid cooling. They used a fracture mechanic s approach with the finite element software ABAQUS to study propagation of top-down cr acking. By assuming cracks propagate perpendicular to the major prin cipal (tensile) stress, they found the cr acks grew vertically downward in the pavement, then turned 30 degrees toward the wheel load. The predicted crack path was found similar to what has been observed in the field. They also performed parametric studies to quantify the stress inte nsity factor ahead of the crac k tip for various load positions, stiffness ratios and thickness ratios for progre ssive crack growth in a flexible pavement. Cohesive Crack Model The Cohesive Crack Model (CCM) is a simple m odel used to describe a nonlinear fracture process at the front of a preexisting crack. This model was fi rst introduced by Dugdale (1960) and Barenblatt (1962) to account for a relatively la rge plastic yield zone ahead of a crack tip. Hillerborg et al. (1976) extended this model to conc rete fracture and described a fairly large FPZ. According to this model, the material can be characterized by a couple of constitutive laws: a stress–strain relationship, valid for the unda maged material, and a stress–crack opening displacement relationship, the so-c alled cohesive law (Figure 2-3) This law describes how the stress decreases from its maximum value to zero as the distance between the crack lips increases from zero to the critical displacement wc. The area below the stress–crack opening displacement

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30 curve represents the energy spent to create the unit crack surfa ce (Fracture Energy GF). If the two portions into which the specimen is separated un dergo elastic unloading, the work done to split the specimen can be considered to be exactly equal to the product of GF times the cracked area. The fracture energy GF can be obtained from: (2-6) According to Hillerborg’s work, the cohesive cr ack model is able to explain different size effects encountered in concrete st ructures. More specifically, the model is able to simulate tests where high stress gradients are present, i.e., test s on pre-notched specimens. In these cases, the cohesive crack model captures the ductile–brittle transition occurring by increasing the size of the structure. On the other hand, relevant scale effects are encountered al so in uniaxial tension tests on dog-bone shaped specimens, where much sm aller stress gradients are present. In this case, size effects should be inherent to the ma terial behavior rather than to the stress intensification. Figure 2-3. Cohesive crack model. A) Stress-str ain curve. B) Cohesive stress-crack opening displacement law. A B stressstrain uu stresscrack opening uwcGF

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31 Work conducted by Carpinteri & Ferro (1994, 1998) and Mier & Vliet (1999) proved that the physical parameters characterizing the cohesi ve law are scale dependent, thus showing the limits of Hillerborg's model. In fact, by increasi ng the size of the specimen, the ultimate stress decreases while the fracture energy increases. The CCM has been applied extensively to Po rtland cement concrete and has only recently been investigated for asphalt mixture. Jenq et al. (1991) used both indi rect tensile tests and notched beams to assess the tensile strength a nd fracture energy of asphalt mixes. Seo et al. (2004) determined the cohesive model paramete rs using constant crosshead rate monotonic tension tests using double-edge no tched specimens. They calculated the fracture energy using the crack opening displacement within the FPZ iden tified as a 5 mm high band between notches. Following are the basic hypotheses of the CCM: € A crack is assumed to form at a point when the maximum principal stress at that point reaches the tensile strength. The crack form s perpendicular to the maximum principal stress direction (i.e., crack init iation and propagation criteria). € The properties of the material outside the process zone are governed by the undamaged state. € The stress transferred between the faces of the crack is de scribed by a post-peak function (i.e., softening function). Continuum Damage Approach The Continuum Damage approach analyzes mi crocracks in asphalt mi xtures under realistic loading conditions and healing effect. Research conducted by Kim et al. (1990) has shown that continuous cycles of loading at a constant strain or stress amplitude, which are generally applied in laboratory test, do not repr esent the realistic fi eld loading conditions. The major difference between is attributed to the rest period between loading applications, which in the field occurs with random length. It was observed (Kim et al., 1990) that in a partially cracked asphalt pavement, two different mechanisms occur during re st periods: the relaxa tion of stresses in the

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32 system due to the viscoelastic nature of aspha lt concrete and the chemical healing across microcrack and macro-crack faces. A mechanics approach to fatigue characteriza tion of asphalt mixture using viscoelasticity and continuum damage theory was introduced by Kim Y.R. et al. (1997). They modeled damage accumulation (assumed to grow continuously und er uniaxial tensile cyclic loading), and microdamage healing during rest periods usi ng the visco-elastic co rrespondence principle developed by Schapery (1984). Schapery stat ed that constitutive equations for certain viscoelastic media are identical to those for th e elastic cases, but stre sses and strains are not necessarily physical quantities in the viscoelastic body; instead they are pseudo variables (e.g., pseudo-stress, pseudo-strain). According to Schape ry’s theory, the pseudo-strain is defined as: (2-7) where R = pseudo-strain, = time-dependent strain, ER = reference modulus (arbitrary constant), E(t) = relaxation modulus at time t. If there is no damage cont ributed in the loading respons e, the stress-pseudo strain relationship can be represente d by an elasticlike equation: (2-8) When the material experiences significant dama ge due to higher tensile loading the stresspseudo strain relationship is represented by a nonlin ear response with a hysteresis loop. Damage accumulation can be demonstrated by observing ch anges in the loop area and loop secant slope during fatigue tests. Based on the relationship be tween the pseudo strain and physical stress, Kim

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33 et al. (1994, 1995) introduced th e pseudo stiffness parameter (SR) to characterize the change in slope of each R cycle and give a quantitati ve measure of microdamage: (2-9) where R mis peak pseudo strain in each stress-pseudo strain cycle, and m is the stress corresponding to R m. The pseudo stiffness decreases as repe ated loading continues. The material is considered to fail when the stiffness is redu ced to 50% its original value (Kim Y.R. et at., 1997). Based on experimental data of asphalt conc rete subjected to co ntinuous and uniaxial loading in tension, Lee and Kim (1998a) proposed a constitutive model that describes the mechanical behavior of the material under these conditions: (2-10) where I = initial pseudo stiffness, = effective pseudo strain, F = damage function, G = hysteresis function. The effective pseudo strain accounts for th e accumulating pseudo strain in a controlled stress mode. A mode factor is also applied to the damage function, F, to allow a single expression for both modes of loading. The parame ter I is used to account for the specimen’s variability. The damage function F re presents the change in slope of the stress-pseudo strain loop as damage accumulates in the specimen. The hyste resis function G describes the difference in the loading and unloading paths.

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34 Lee and Kim (1998b) also proposed a model to describe the fatigue life for controlledstrain testing mode, finding that in these conditions, the hysteresis function G is not to be taken into account: (2-11) where C = coefficient of secant pseudo stiffness reduction, S = internal state variable. The disadvantage of the continuum damage method is the requirement of numerous functions such as relaxation modul us to determine pseudo strain, as well as the F and G functions to describe the damage process. In addition, given the fact that only a continuum can be modeled, continuum damage mechan ics is incapable of properly addressing the mechanics of crack propagation (i.e., once a cr ack develops, the system is no longer a continuum). Finally, damage mechanics does not provide a realistic physical interpretation of damage, since failure is generally assumed to coincide with a 50-percen t reduction in pseudo-sti ffness, which is not applicable to the field, as a failure criterion. Development of HMA Fracture Mechanics Previous work by Zhang et al. (2001) and Roque et al. (2002) has show n that the fracture properties of mixtures can be described with in a viscoelastic fracture mechanics-based framework they called HMA Fracture Mechanics, which was recently developed at the University of Florida. They observed that a crack in HMA grows in a stepwise rather than in a continuous manner, as shown in Figure 2-4. The imp lication with this work is that it may not be sufficient to monitor changes in a single paramete r such as strength or s tiffness to evaluate the effects of microand macro-damage in mixtures Rather, changes in stiffness and strength are

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35 typically accommodated by changes in the viscoelast ic properties of mixtures as well as strength and stiffness. Crack Propagation (Paris Law) Crack Length, aNumber of Load Applications, N Threshold Micro-crack Threshold Macro-crack Micro-crack Figure 2-4. Crack propagation in asphalt mixt ures according to “HMA Fracture Mechanics” The topic of the framework presented by Zhang et al. (2001) is the concept of the existence of a fundamental crack growth threshold. The concept is based on the observation that microdamage (i.e., damage not associated with crack initiation or crack growth) appears to be fully healable, while macro-damage (i.e., damage associ ated with crack initia tion or growth) does not appear to be healable. This indicates that a dama ge threshold exists below which damage is fully healable. Therefore, the thres hold defines the development of macro-cracks, at any time during either crack initiation or propa gation, at any point in the mi xture. If load ing and healing conditions are such that the induced energy doe s not exceed the mixture threshold, then the mixture may never crack, regardless of the number of loads applied. As discussed by Roque et al. ( 2002), fracture (crack initiation or crack growth) can develop in asphalt mixtures in two distin ct ways, defined by two distinct thresholds (Figure 2-5). The lower threshold is associated with continuous repeated lo ading. When cyclic stresses significantly below the tensile stre ngth occur, cracking will even tually occur if the rate of

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36 damage accumulation exceeds the rate of healin g during the loading period. In contrast, the upper energy threshold corresponds to that thres hold required to fractur e the mixture with a StraiEnergy No Failure by a critical load Failure No Failure Number of Load Replications (N) FailureRepeated Load Cyclic Fatigue Failure at Critical LoadLower Threshold Upper Threshold Figure 2-5. Crack initiation or crack gr owth development in asphalt mixtures single load application. In this case, fracture would occur if an y single load applied during the loading cycle exceeds the threshold required to fracture the mixture with a single load application. Essentially, fracture would not occur during a single load applica tion unless the upper threshold is exceeded, even when the lower threshold is exceeded. It has been determined that the dissipated cr eep strain energy (DCSE) limit and the fracture energy (FE) limit of asphalt mixtures suitably defi ne the lower and the upper threshold values. These parameters can be easily determined from th e stress-strain response of an Indirect Tensile (IDT) Strength Test, as shown in Figure 2-6 an d discussed by Roque et al. (2002). The fracture energy limit is determined as the area under the stress-strain curve at first fracture, while the dissipated creep strain energy limit is the fract ure energy minus the elas tic energy. First fracture in the IDT specimen is determined as the poi nt when the difference between vertical and horizontal deformation (V-H) reaches a maximum.

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37 MR Stress, Strain, Dissipated Creep Strain Energy(DCSE) xStf (fracture)FIRST FRACTURE Elastic Energy(EE) Figure 2-6. Determination of the lower a nd upper thresholds for asphalt mixtures Tensile Failure Limits of HMA Mixes The critical location for load-i nduced cracking is gene rally considered to be at the bottom of the asphalt mixture layer. Cracks are assumed to initiate at the bottom of this layer and later propagate due to the repeated tensile stresses caused by bendi ng beneath the wheel loads. HMA failure limits are needed to determine whether the induced pavement response is critical enough to result in failure under one or more load appli cations. Several testing modes can generally be used to obtain these properties, but if the property is not fundamental, then different testing modes may yield different results. Funda mental properties of asphalt mixture can be obtained from multiple testing configurations wh en appropriate test procedures, measurement systems and analytical methods are used. Tensile Strength Tensile strength is an importa nt property because it probabl y has a strong influence in cracking performance. Several laboratory test methods have been proposed and used to determine mixture tensile strengt h, which is usually calculated from the overall response of a

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38 specimen subjected to a specific monotonic load. It must be pointed out that the response of the material is controlled by the specimen geometry and material factors, thus the simpler the stress field applied to the specimen, the easier the in terpretation. One of the most popular test methods for HM A tensile strength estimation at low and intermediate pavement temperature is the Supe rpave Indirect Tension test (IDT), developed by Roque & Buttlar (1992) and Bu ttlar & Roque (1994) under the St rategic Highway Research Program (SHRP). A compressive lo ad is applied along the diametral axis of a 150 mm diameter specimen in an indirect tensile test device at a co ntrolled vertical deformation rate until failure. The mechanics of the test are such that a nearly uniform state of tensile stress is achieved across the vertical diametral plane. Both the vertical and horiz ontal stress distributi on are fairly uniform near the center of the face of the indirect tensile specimen as discussed by Roque & Buttlar (1992). Vertical and horiz ontal deformations are measured by two strain gauges with a length of 38.1 mm placed at the center of the circular sp ecimen. According to the Superpave Indirect Tension test procedure, the horiz ontal stress at the center of the specimen is computed using the following IDT plane stress equation: (2-12) where h = maximum tensile stress (MPa), P = load of the specimen (N), D = diameter of the specimen (mm), t = thickness of the specimen(mm), C h = stress correction factor. The Semi-Circular Bending (SCB) test on semi-c ircular specimens as been proposed in the recent past as an alternative to the Indirect Te nsion test to determine the fracture properties of

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39 HMA mixes. The SCB test was first introduced by Lim et al. (1994) to conduct mode I and mix mode fracture toughness experiments on rock material s. Afterwards, Krans et al. (1996) and Van de Ven et al. (1997) investigated the possibilities of the SCB test as a practical crack growth test for asphalt mixtures. They developed a load-stre ss relationship using a 2-D linear-elastic finite element analysis for maximum horizontal tensile stress: (2-13) where x = maximum horizontal tensile stress (MPa), P = load per unit thickness of the specimen (N/mm), D = diameter of the specimen (mm). However, this relationship appeared to be in adequate for describing the stress state of a semi-circular bending specimen since the resulting tensile strength was structurally higher than the tensile strength determined with the IDT. Mole naar et al. (2002) invest igated the stress field development in a SCB specimen by means of a finite element program, assuming that the material behaves linear elasti c. They proposed the following e quation for SCB horizontal stress computation: (2-14) where t = maximum tensile stress at the bottom of the specimen (MPa), F = load per unit width of th e specimen at failure (N/mm), D = diameter of the specimen (mm). It was pointed out that in SCB specimens te nsion might be the dominant failure mode but that damage due to compression develops with in the specimen during loading. Equation 2-14 has proved to be inadequate for SCB tensile strength analysis since large di fferences were observed between tensile strength values obtained from the SCB and the IDT (2.1 times higher than the real tensile strength). It has al so been shown that the tensile st rength as calculated by means of

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40 Equation 2-14 is not the true te nsile strength but only an indi cation of the tensile strength characteristics of the material Li and Marasteanu (2004) used the SCB to evaluate the lowtemperature fracture resistance of asphalt mixtur es. They performed a finite element stress analysis to identify the correct specimen thic kness for assuming plane stress conditions, resulting in a 25 mm thick specimen. A further test which can be widely found in literature as a candidate for HMA fracture properties determination is the Single Edge No tched Beam (SENB) test. The SENB is a threepoint bending test which uses beam specimens obtained from slabs. Various beam sizes, test temperatures and testing procedures have been employed (Majidzadeh et al., 1971; Mobasher et al., 1997; Kim & El Hussein, 1997; Marasteanu et al., 2002; Wend ling et al., 2004; Wagoner et al., 2005a). The test procedures are usually developed with guidance from the ASTM E399 (2002) and ASTM 1820 (2002) standards for fracture testing of metallic specimens. The loading configuration allows simple stress states and ease of test control with closed-loop servohydraulic equipment, as indicate d by Wagoner et al. (2005a). Th e SENB test is not commonly performed to estimate the tensile strength of the material, but rath er to estimate the fracture energy parameter (load-deformation response), meant as the energy required to initiate and fully break a unit surface of crack. However, it is pos sible to determine the maximum tensile strength at the bottom edge of the beam using the te nsion bending beam equati on (Kaloush et al., 2003): (2-15) where t = maximum tensile stress (MPa), P = applied load (N), b = average specimen width (mm), h = average specimen height (mm).

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41 Fracture Energy Fracture energy is one of the most important parameters for describing and modeling the fracture behavior of cohesive mate rials. It is defined as the amount of energy required to create a unit area of a crack. The objective definition of fr acture energy and optimal testing procedure for its determination is a hot topic, recently stud ied by committees of the American Society for Testing and Materials (ASTM) and thor oughly discussed by many researchers. According to LEFM theory, energy dissipation takes place only at the crack tip; thus fracture energy is directly relate d to the separation energy requir ed to create a new surface by a clean cut in the material. However, the assumpti ons of LEFM lead to a singularity at the crack tip and to unbounded stress field. In real materials, stresses cannot become arbitrarily large, and the crack tip is always surrounded by a process zone in which the mate rial response is not elastic. In 1985, the RILEM Technical Committee 50-FMC (Fracture Mechanics of Concrete Test Methods), proposed a draft recommendation to dete rmine the material fracture energy using a three-point beam bending test. In the RILEM test, the experimental beams are notched and subjected to a three-point loadi ng while a clip gage measures the load point displacement. The typical load-deflection plot obtained from a RILEM test is shown in Figure 2-7. During formation of a crack, a certain amount of ener gy is dissipated in th e process zone, and the fracture energy (GF) is considered as the total energy dissipation (W0) per unit area of the ligament (Alig) that represents the idealized (smooth) crack trajectory: (2-16) where Alig is defined as the projection of the fracture process zone on a plane parallel to the main crack direction.

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42 a0 l PP W0RILEM three-point bending test set-up Figure 2-7. Load-deflection plot from RILEM test The problem with this definition is that it doe s not specify an objectiv e material property that would be independent of the size and shape of the tested specimen. Indeed, measured values of GF obtained using the RILEM pro cedure, in general, increase with increasing size specimen (Hillerborg, 1985; Wittmann, 1986; Mi hashi et al., 1989; Swartz et al., 1987; Xu & Zhao, 1991). Even if one considers only pure Mode-I fracture (only normal crack openi ng, no relative sliding of the crack faces), measurements on different sp ecimens lead to different results for the same material. Also for a fixed specimen geometry and type of loading, fracture energy defined in this way depends on the specimen size (Abdalla & Kariha loo, 2003; Carpinteri et al., 1994; Elices et al., 1992; Wittmann et al., 1990) and therefore it shoul d be considered only a “nominal fracture energy.” Even though the RILEM procedure was develo ped specifically for mo rtar and concrete specimens, in the recent past it has also been us ed for asphalt concrete fr acture analysis. In 1999, Hossain et al. conducted an e xperimental study for investigat ing the fracture and tensile properties of asphalt-rubber concrete mixtures using the RILEM three-point bending test.

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43 Wagoner et al. (2005a) used the Cohesive Zone Model (CZM) to describe the fracture characteristics of asphalt concrete for which th e critical tip opening and the fracture energy (as previously defined) are two of the three required material properties. Afterwards, they developed a Disk-Shaped Compact Tension (DCT) specimen geometry that maximizes the ligament length to easier determine the fracture energy parame ter (Wagoner et al. 2005b). Li & Marasteanu (2004) investigated the use of a Semi Circul ar Bend (SCB) test as a candidate for a lowtemperature asphalt mixture cracking specifications calculating the fracture energy on the base of the RILEM procedure. Seo et al. (2004) adopted a cohesive crack mode l-based approach to ca lculate the fracture energy on a single asphalt mixture using monoton ic and cyclic tension tests performed on prismatic, double-edge notched specimens. Th e fracture energy was represented by the area below the stress-elongation curve (Equation 2-6), as previously discussed. The crack opening displacement (w) was measured from a 5 mm th ick band between the notches of the specimen. Then, fracture energy was obtai ned by subtracting the area th at is surrounded by stresselongation outside the cracked section fr om the area under the stress-crack opening displacement. The limitations developing when applying the RILEM model to asphalt mixtures can be summarized as follows: € The area of ligament in asphalt mixtures is very hard to measure due to its high variability from a cut plane, which is due to the random effects of aggregate arrangements and their influence on crack path. € The properties of the material outside th e FPZ are assumed to be governed by the undamaged state, which is inconsistent fo r asphalt mixtures in which cracks occur randomly at the same time at different locations. € A notch is required to address crack initiati on and FPZ preventing th e identification of a real fracture initiation.

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44 The discussion presented above indicates th at HMA Fracture Mechanics is a promising model for determining HMA failure limits, sin ce it provides a more fundamental approach. HMA Fracture Mechanics accounts for both crack initiation and propagation which are governed by the same mixture parameters, considers genera lized loading conditions and models HMA as a viscoelastic material in which cracks are assumed to grow discontinuously. Polymer Modified Mixtures Cracking is widely recognized as an asphalt binder-related distress, thus the fracture resistance of asphalt mixtures s hould be generally corre lated to its properties. Polymer modifiers are introduced in an attempt to in crease the mixture’s high temperat ure stiffness to resist rutting and low temperature flexibility to resist fati gue and thermal cracking. Previous research has indicated that polymer-modified asphalt binder has the ability to improve asphalt pavement’s resistance to permanent deformation (Freeman et al., 1997; Bahia et al., 2001; Sargand & Kim, 2001). However, polymer modified asphalt mixt ures may either degrade or enhance asphalt mixture fatigue life (Aglan, 1997; Deacon et al., 1997; Khattak & Baladi, 1998; Newman, 2000; Romero et al. 2000; Bahia et al., 2001, Lundstrm & Isacsso n, 2004). Studies by Harvey and Monismith (1995, 1997) and Bahia et al. (2001) ha ve shown that the addition of the same modifier to different asphalt binde rs may lead to contrasting results in terms of fatigue resistance. These studies indicate that modi fiers had different effects on mi x stiffness, fatigue life and cumulative dissipated energy. The addition of poly mers to asphalt binders may also increase the resistance to low-temperature cracking of asphalt pavements (K ing et al., 1993; Lu & Isacsson, 1997; Pucci et al., 2004; Khattak et al., 2007). However, studies conducted on low temperature properties of polymer-modified mixtures have sh own that polymer modification does not show benefits as compared to the correspo nding base asphalt binder (Lu et al., 2003).

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45 Currently, the most commonly used polymer for binder modification is the elastomer Styrene Butadiene Styrene (SBS) (Airey, 2004). It be longs to the class of copolymers, defined as polymers made up of two or more different repea ting units in the molecular chain. The structure of an SBS copolymer consists of styrene butadie ne styrene tri-block chains, having a two-phase morphology of spherical polystyrene block domains within a matrix of polybutabiene (Isacsson & Lu, 1995). SBS copolymers derive their strength and elasticity from physical cross-linking of the molecules into a three-dimensional network. The polystyrene end-blocks impart the strength to the polymer, while the polybutad iene rubbery matrix mid-blocks give the material elasticity. When SBS is blended with asphalt, the elastome tric phase of the SBS copolymer absorbs the maltenes (oil fractions) from the asphalt and swe lls up to nine times its initial volume. At suitable SBS concentrations, a continuous polym er network (phase) is formed throughout the polymer modified binder, significantly m odifying its properties (Airey, 2004). Recent research conducted by Kim et al. (2003) showed that the SBS modified mixtures generally have a lower creep rate than unmodifi ed ones resulting in a reduced rate of microdamage accumulation without a reduction in fractur e energy limit or healing rates. Kim et al. (2003) also found that the asphalt mixture fracture limits as measured by the fracture energy density and the dissipated creep strain energy di d not change with the 3 percent SBS polymer modification as percent of the binder used. They claimed that the reduction in tensile creep rate observed could either be explained as a benef it associated with SBS modification or possibly with age-hardening or further combined effects. In summary, it appears that polymers may improve the cracking resistance of asphalt mixtures through the reduction of tensile creep ra te. However, the effect of higher percent of

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46 polymer modification on the fracture resistance a nd tensile creep rate of asphalt mixtures has not been thoroughly investigated.

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47 CHAPTER 3 MATERIALS AND METHODS Tensile failure limits were evaluated from thr ee different test confi gurations: the Indirect Tensile test (IDT), the Semi-Circular Bending test (SCB) and the Three-Point Bending Beam test (3PB). Six different 12.5-mm nominal maximum size fine-graded Marshall mixtures with the same aggregate type and gradation but differe nt asphalt binders were investigated. All the mixtures were prepared in la boratory, while the asphalt binders were provided by Valli Zabban Asphalt Refining Company. Materials Aggregates The gradation selected is a fine-graded mix which had been successfully used to produce acceptable mix designs in the past. The batch is composed by limestone and marly limestone, calcarenite and fine and coarse sand, mined from Parma, North Italy by Spotti Srl. The aggregate gradation and curve of the six mixtures are gi ven in Table 3-1 and Fi gure 3-1, respectively. Table 3-1. Aggregate gradation Sieve size (mm) % Passing 19.0 100 12.5 93 9.5 82 4.75 51 2.36 39 1.18 27 0.6 19 0.3 14 0.15 11 0.075 8

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48 0 10 20 30 40 50 60 70 80 90 100 00110% passingsieve size (log) lower limit upper limit mix design gradation Figure 3-1. Aggregate curve of the six mixtures Asphalt Binders Six different asphalt binders were used in this research, named as N1, N2, RM3.5, RM5.0, LM3.5 and LM6.5. N1 and N2 are two unmodifi ed binders, graded as PG64-22 and PG58-22, respectively. RM3.5 and LM3.5 are two polymer modified binders obtai ned blending the N2 unmodified one with a 3.5% of SBS cross-linked and SBS lin ear polymers, respectively. RM5.0 and LM6.5 are two heavily polymer modified binde rs prepared blending the N2 virgin binder with the maximum percentage of polymer modifier to maintain asphalt stable, resulting in 5% for the cross-linked polymer and 6.5% for the linear polymer. The SBS were blended with the base asphalt by the manufacturer using high shear milling. Details on the asphalt binder composition and PG grading test results are listed in Table 3-2.

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49 Table 3-2. Asphalt binder properties Asphalt Binder N1 N2 RM3.5 RM5.0 LM3.5 LM6.5 Performance grade PG 64-22 PG 58-22 PG 64-22 PG 70-22 PG 70-22 PG 76-22 Blend Unmodified Unmodified N2+3.5% SBS cross-linked N2+5.0% SBS cross-linked N2+3.5% SBS linear N2+6.5% SBS linear Un-Aged Asphalt Dynamic shear (10rad/sec) G*/sin kPa 2.52@64 C 2.58@58 C 2.46@64 C 1.55@70 C 1.40@70 C 2.12@76 C RTFO Aged Residue Dynamic shear (10rad/sec) G*/sin kPa 4.71@64 C 4.77@58 C 4.64@64 C 4.64@70 C 2.35@70 C 3.05@76 C PAV Aged Residue @ 100 C Creep stiffness and m-value, 60 sec. 154 and 0.329 @-22 C 179 and 0.353 @-22 C 130 and 0.335 @-22 C 147 and 0.323 @-22 C 173 and 0.311 @-22 C 150 and 0.324 @-22 C Specimen Preparation The two unmodified asphalt mixtures (N1 a nd N2) were designed according to the Marshall mix design procedure, resulting in 5.4 % and 5.2% design asphalt content, respectively (medium traffic level). All the modified mixtures were prepared with the same effective asphalt content as the N2 unmodified one to assure that the SBS modifi er was the only fa ctor affecting the test results. For each mixture, five 4500 g and one 15000 g aggregate batches were prepared to produce a total of 30-150 mm diameter cylindrical specimens and six 300x300x75 mm slabs. The aggregates, the asphalt binders and mixing equipment were heated for three hours at 150 C for unmodified mixes and at 175C for the modified ones to achieve appropriate uniform mixing

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50 temperature. The batches were then mixed with the design asphalt content percentage and heated for another two hours at 135C for short-term aging. The cylindrical specimens were obtained by co mpacting the mixes to 6 ( 0.5) percent air voids into 150 mm diameter specimens using the Superpave Gyratory Compactor. The slabs were compacted to produce 300 mm long by 300 mm wide by 75 mm tall specimens. This equipment is made up of a cylindrical horiz ontally pivoted steel cup upon which a 3 ton maximum load hydraulic press is placed. Below the press, a 300x300 mm mobile basement is placed with the formwork containing the mate rial. This formwork moves while the pivoted element applies a given pressure to compact the material to the desired air void percentage, in this case 6 ( 0.5) percent. After compaction an d cooling of the specimens, volumetric analyses of the mixtures were performed, results of which are shown in Table 3-3. Table 3-3. Volumetric prope rties for the six mixtures Asphalt Mixture N1 N2 RM3.5 RM5.0 LM3.5 LM6.5 Asphalt content, AC% 5.4 5.2 5.2 5.2 5.2 5.2 Theoretical maximum specific gravity, Gmm 2.4562.5852.557 2.546 2.581 2.595 Bulk specific gravity of compacted mix ,Gmb 2.3052.4292.399 2.391 2.416 2.432 Bulk specific gravity of aggregate, Gsb 2.6322.6322.632 2.632 2.632 2.632 Effective specific gravity of aggregate, Gse 2.6502.6502.650 2.650 2.650 2.650 Percent VMA in compacted mix ,VMA 17.1512.45 13.62 13.88 12.99 12.41 Percent air voids in compacted mix, Av 6.1 6.0 6.2 6.1 6.4 6.3 Percent VFA in compacted mix, VFA 64.4351.95 54.48 56.07 50.73 49.25 Each compacted cylindrical specimen was sawn to obtain two test specimens, each 30 mm thick discarding the top and the bottom plates for reducing density gradient effects. For each mixture, three circular shaped specimens we re used to perform resilient modulus, creep compliance, and strength test at 10 C accordi ng to the Superpave IDT procedure developed by Roque and Buttlar (1992) and Buttlar and Roque (1994). Three other specimens were used to perform IDT fracture tests usi ng the Digital Image Correlation system. Three circular test

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51 specimens were sawn in half to obtain 75 mm height Semi-Circular specimens for performing SCB fracture tests. The slabs were cut to produce 3 beam specimens for each mixture to the final dimension of 300 mm long by 75 mm tall by 100 mm wide. In summary, the following specimens were prepared: € Three 150 mm diameter (30 mm thick) circul ar shaped specimens for each mixture to perform resilient modulus, creep compliance and strength tests; € Three 150 mm diameter (30 mm thick) circul ar shaped specimens for each mixture to perform IDT fracture analysis by Digital Image Correlation; € Three 150 mm diameter and 76 mm height (30 mm thick) Se mi-Circular specimens for each mixture to perform SCB fracture tests using both traditional strain measurement devices (strain gauges) and Digital Image Correlation; € Three 300 mm long, 100 mm thick, 75 mm height beam specimens for each mixture to perform Three-Point Bending fracture tests us ing both traditional strain measurement devices (strain gauges) and Digital Image Correlation. Test Methods Three different test methods, the Indirect Te nsile test (IDT), the Semi-Circular Bending test (SCB) and the Three-Point Bending Beam test (3PB) were performed on three replicates at 10C, using an MTS closed-loop servo-hydrau lic loading system. The specimens were conditioned inside an MTS Environmental Cham ber enabling the testin g of materials and components within a range of high and low temp erature environments. A temperature controller associated with the Environmental Chamber mo nitors the temperature to a desired point. Temperature stability inside the chamber is within 0.2C. Indirect Tension Fracture Test The IDT fracture test loads monotonically a 150 mm diameter cylindrical specimen to failure applying a constant stroke of 0.084mm/sec. The top and the bottom loading plates are 19 mm wide and 50.8 mm long. Two strain gauges with a length of 38.1 mm are placed at the center of the specimen to measure ve rtical and horizontal deforma tions during loading. The IDT

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52 experimental setup is shown in Figure 3-2. To take into account 3D effects, the procedure described by Roque and Buttlar (2002) and But tlar and Roque (1994) was applied. According to this procedure, bulging correction factors are n eeded to correct the measured horizontal and vertical deformation to fit the deformation in a fl at plane. These are then divided with the gauge length GL to obtain the average strai n. Finally, center correction factors are used to correct the strain values at the center of specimen. Figure 3-2. Indirect Tensile Test setup According to the Superpave Indirect Tensi on test procedure (Roque and Buttlar, 2002; Buttlar and Roque, 1994) the horizonta l stress at the center of the specimen was computed using a 2D plane stress equation, corrected with the stress correction factor C h to convert 2D plane stress to the stresses on the surface of a 3D specimen: (3-1) where h = tensile stress at the cen ter of the specimens (MPa), P = load of the specimen (N), D = diameter of the specimen (mm),

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53 t = thickness of the specimen (mm). Semi-Circular Bending Test The Semi-Circular Bending test was performed by applying a static load on a semi-circular specimen with a length of 150 mm and a hei ght of 75 mm placed under a loading ring. The diameter of the top and bottom rings (which function as supports) is 30 mm. The load transmission occurs with a displacement control system, where the top loading ring drops with a 0.084mm/sec speed. One HBM-Y series strain gauge arranged in a quarter Wheatstone bridge with a length of 20 mm, is m ounted on the central bottom edge of the specimen to measure horizontal deformations during fr acture testing. The Semi-Circula r Bending test experimental setup is shown in Figure 3-3. Strain gauge specifications are listed in Table 3-4. Strain gauge signals are ac quired by a National Instrument SCXI Chassis which scans input channels at rates up to 333kS/s. A co mmercial software de veloped in a LabView environment was used to calculate stain gauge pa rameters and acquire ou tput signals. Strain measurements were acquired at a frequency of 10Hz. Figure 3-3. Semi-Circular Bending Test setup

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54 Table 3-4. HBM-Y series st rain gauge specifications Item Specification Maximum elongation ( m/m) 50,000 (5%) Fatigue life > 107 Operating temperature range (C) -70…+200 Mechanical hysteresis ( m/m) 1 The stress field in a SCB specimen was previous ly studied by Van de Ven et al. (1997) and Molenaar et al. (2002). In these studies both tensile and compressi ve stresses were computed by means of a finite element analysis. It was point ed out that in SCB specimens, tension might be the dominant failure mode but that damage due to compression develops within the specimen during loading. The development of a compression ar ch was considered in this research work observing the full field strain maps obtained by Digital Image Correlation analyses. However, the damage due to compression appeared to be much less predominant than the tension damage in the area of interest, as shown in Figure 3-4 (w here x and y axes are the lengths of the Region of Interest in mm). The length covered by the strain gauge in Figure 3-4 is from 20 mm to 40 mm (x axis). Initially, the SCB horizontal stress was computed using the equation proposed by Molenaar et al. (2002): (3-2) where h = tensile stress at the central bottom area of the specimens (MPa), P = load of the specimen (N), D = diameter of the specimen (mm), t = thickness of the specimen (mm). Equation 3-2 has proved to be inadequate fo r SCB tensile strength analysis since large differences were observed between tensile stre ngth values obtained from the SCB (2.1 times higher than the real tensile strength ) and the IDT (Molen aar et al., 2002).

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55 Figure 3-4. SCB strain maps of mix N2 at crack opening. A) Horiz ontal. B) Vertical. A Strain Exx component at time: 84.139 10 20 30 40 50 60 5 10 15 20 25 30 35 40 45 B Strain Eyy component at time: 84.139 10 20 30 40 50 60 5 10 15 20 25 30 35 40 45

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56 It has also been shown that th e tensile strength as calculate d by means of Equation 3-2 is not the true tensile strength but only an indication of the tensile strength characteristics of the material. For these reasons the SCB tensile st ress at the bottom edge of the specimen was evaluated by means of a Displacement Discontin uity (DD) boundary element method adopting a nonlinear failure law for the crackin g criterion. From the results, the following equation has been proposed: (3-3) where h = tensile stress at the central bottom area of the specimens (MPa), P = load of the specimen (N), D = diameter of the specimen (mm), t = thickness of the specimen (mm). Equation 3-3 was estimated modeling all the six mi xtures used in this research work. Input parameters for the SCB test simulations we re obtained from Superpave IDT testing and simulation, followed by the interpretation approa ch developed by Birgi sson et al. (2003) for obtaining a suitable set of material parame ters for the micromechanical displacement discontinuity modeling of mixtures. Furthe r discussion is provided in Chapter 5. Three-Point Bending Beam Test The Three-Point Bending fracture test proced ure was developed with guidance from the SCB test. The same test equipment consisting of loading and supporting rings, type of strain gauge and data acquisition system was used. Th e beam dimension was selected based on the capability of the beam compactor resulting in 300 mm long by 75 mm ta ll by 100 mm wide beam specimens. The span length of the specimen is s upported at 0.8 of the beam length (240 mm). A static load is applied in the middle section of the beam by the upper load ing ring which applies a constant stroke of 0.084mm/sec. One HBM-Y series strain gauge (see Table 3-4 for

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57 specifications) with a length of 50 mm is placed on the surface of the specimen in the central bottom area to measure horizontal deforma tions. The Three-Point Bending Beam test experimental setup is shown in Figure 3-5. Figure 3-5. Three-Point Bending Beam Test setup The tensile stress at the bottom edge of the beam is calculated us ing the tension bending beam equation: (3-4) where h = tensile stress at the central bottom area of the specimens (MPa), P = load of the specimen (N), L = span of the specimen (mm), t = thickness of the specimen (mm), h = height of the specimen (mm).

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58 CHAPTER 4 DIGITAL IMAGE CORRELATION (DIC) SYSTEM Background The evaluation of HMA material properties (such as tensile strength and fracture energy density) rests on the accuracy of displacement and strain measurements. The most common fracture tests performed on aspha lt mixture specimens employ on-specimen mechanical strain measurement techniques (e.g., strain gauges and LVDTs). These devi ces are simple to use, but their drawback is not being capable of accurate ly capturing localized or non-uniform strain distributions, thus not al lowing for true point-wise analyses of a strain field. This prevents the exact determination of the important locati on of crack initiation, not easily allowing the determination of the strain values at the in stance and location at wh ich a crack initiates. Traditional on-specimen strain measurement tec hniques also do not provide flexibility, because the measurement location must be decided prior to the test. This precludes the possibility of a “back analysis” of the resulting strain field over an area of finite extent, and, above all, does not capture full field displacement/strain measur ements in the specimen. In comparison, the detection of crack initiation in HMA specime ns is simplified by field measurements of deformation over an area of finite extent, si nce typically cracks a ppear in somewhat non predictable locations. During the last decade, severa l types of full-field deform ation measurement techniques have been proposed for composite material ch aracterization, as desc ribed by Grdiac (2004). Since the advent of target lo cation in digital or digitized images (Van den Heuvel & Kroon, 1992), alternatives based on analogue photogrammetr y and vision metrology have also become viable (Crippa et al., 1993). Digital image correlation was proposed in the 1980’s as an automated approach for the computation of su rface strains and displacem ents (Sutton et al.,

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59 1983; Chu et al., 1985; Sutton et al., 1986; Ranson et al., 1987; Bruck et al., 1989). It was later advanced to study 2-D solid mechanics problems, be ing successfully applied to determine strains in specimens of resin films (Muszynski et al., 2002), fiber reinforced polymer composites (Melrose et al., 2004), and c oncrete (Choi & Shah, 1997). Kim & Wen (2002) first proposed the us e of a DIC technique as a possible displacement/strain measurement method for aspha lt mixtures. They applied the DIC technique to determine the proper gauge length for a 100-mm diameter IDT specimen. They also demonstrated that the DIC technique is a good alternative to LVDTs for HMA noncontact deformation/strain measurements. Seo et al. (2 004) and Chehab et al (2007) utilized a DIC technique to investigate the size and shape of the fracture process zone for asphalt mixtures performing uniaxial monotonic and cyclic tension tests on prismatic specimens with symmetric double notches and on cylindrical specimens cored from Superpave gyratory compacted specimens. However, all these studies were conduc ted adopting a commercial package for twodimensional digital image correlations, which has the drawback of not providing flexibility. Conversely, an in-house developed DIC system gives important advantages brought by the ability to customize the system for specific appli cations. In particular, the current Digital Image Correlation (DIC)-based method was developed specifically for imaging asphalt specimens. This means that the software was designed to fac ilitate the quantification of large strains in the mastic in between the aggregates in a typical asphalt mixture. The Least Squares Matching technique (For stner, 1982; Ackermann, 1984; Gruen, 1985) was employed for the purpose of providing matche s with sub-pixel accuracy. Finally, an efficient optimization of the algorithm was developed to achieve accurate image correlations.

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60 The DIC technique involves specimen surface treatment, appropriate illumination, and a suitable equipment placement. A sequence of imag es is then acquired with a digital camera during the tensile fracture testing of the HMA specimen; a dense set of features, artificially generated on the specimen surface, is accura tely tracked by the algorithm along the image sequence. From the image coordinates, displacem ents and deformations can be evaluated in image space and, with an appropriate transformation, in object space. Image System Characteristics The system is composed of three elements: th e hardware (i.e., the digital camera and the illumination devices), the specimen set up, and the so ftware (image acquisition and processing). Experimental Setup A digital camera Basler AF 101 (resoluti on 1300x1030, focal length 8mm, pixel size 6.7 micrometers, 12 fps@max resolution) is curr ently employed. The optics adopted at maximum magnification allow 30 m per pixel resolution. The camera whic h is directly connected with a personal computer, is located on a support inside the climatic chamber, focusing up to 3.5 cm from the area of most interest of the specimen (i.e., the most stressed area). A lighting system, created for the purpose of providing adequate illumination of the specimen inside the climatic chamber, is compos ed of 4 white lights, which can be oriented according to the specimen shape and/or dimensions: two horizontal guide rails allow horizontal movements while two 20 cm eyelets in which th e lights are embedded, allow vertical settings. The experimental setup is shown in Figure 4-1. Specimen Preparation The specimen requires a preliminary surface tr eatment to ensure a successful imaging acquisition and the subsequent application of the DIC method. The technique involves measurements of the grayscale level at each pixel location of the image, thus very well-contrasted images

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61 HMA specimen white lights Basler AF101 MTS climatic chamber PC: image acquisition Figure 4-1. Digital Image Correlation (DIC) system experimental setup are fundamental for achieving high measurement accuracy. The surface treatment adopted for asphalt mixtures consists of the application of a thin film of white pa int overlain by a speckle pattern of black, resultin g in a homogeneous randomly oriented texture (Figure 4-2). Care must be taken to ensure thin enough la yer thickness to avoid tracking the deformation of the paint film rather than the specimen deformation. The pain t adopted was a water-based paint, which is lightly absorbed by the asphalt mixture so as not to affect the estimation of the real cracking behavior of the specimen. Figure 4-2. Specimen surface treatment

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62 Theoretical Principles The feature tracking is achieved using Ar ea Based Matching (ABM), a long established technique for the extraction of im age correspondences based on similarities between grey values (g.v.). In ABM, each image point to be matched is the centre of a small window of pixels (template) in an undeformed reference image (m aster image), which usua lly corresponds to the first image in the sequence of frames. The grey va lues of the template ar e statistically compared with those of an equally sized window of pixels (patch) in a deformed search image (slave image), which corresponds to another image in the sequence of frames (Figure 4-3). UNDEFORMED DEFORMED TEMPLATEPATCHImage 1 11 Image 2 initialposition finalposition Figure 4-3. Area Based Ma tching (ABM) principles Two different approaches can be adopted for the evaluation of the similarities between patch and template’s grey values : cross-correlation a nd least squares matching. The former uses a proper correlation function to de termine a coefficient which establishes whether a point in the template corresponds to another in the patch, wh ile the latter is based on an iterative leastsquares resolution algorithm.

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63 The maximum correspondence between the grey values of the two windows is established if patch and template are exactly the same. Howe ver, grey value correspondences always differ since the patch is affected by both radiomet ric and geometric differences. Radiometric differences are due to sensor response, illumination changes, and object reflective changes. Geometric differences arise from object move ments (translations and rotations), object deformation, and perspective effects (camera location and object shape). The DIC system developed for HMA full field displacement/strain estimation was developed using the least squares matching appr oach; however, a brief description of the two techniques is provided. Cross-Correlation The cross-correlation function tracks the point of interest by shifti ng pixel by pixel the template window within a specific range in th e patch window using a simple translation, as shown in Figure 4-4. The nearest location at the pi xel level is selected ba sed on the occurrence of the best-matched pattern, which has the minimum value of the mutual cross-correlation coefficient Essentially, the cross-correlation function is estimated over the search area: its maximum provides the best ma tch position. The coefficient is computed as a discrete function of patch displacement ( x, y): (4-1) where and are the mean values of the grey leve ls of the template and patch windows, respectively. Sub-pixel accuracy can be obtained by inte rpolating the cross-correlation coefficient using a smooth continuous function, thus allowing for the analytical check ing of its maximum.

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64 TEMPLATEPATCH Reference Image ithImage Figure 4-4. Cross-correlation approach Cross-correlation is a method of choice in comput er science, since it is faster to implement and results in a more efficient computational pe rformance. However cross-correlation tracks the point of interest only by shifting the template along the hor izontal and /or vertical axes, not accounting for rotations. Thus, it works well only if geometric and radiometric distortions of the patches are kept to a minimum. During Hot Mix Asphalt fracture tests, rotations and/or scale changes between two images always occur, thus the cross-correlation approach may not be adequate for these types of tests. In contrast, the Least Squares Matching techniqu e uses a more complete functional model, providing matches with sub pixel accuracy while accounting for bot h translation and rotations. Least Squares Matching (LSM) The LSM method is based on the minimization of the squared differences of the grey values between patch and template. Given two image points, LSM considers the two conjugate image regions as discrete two-dime nsional functions: the template f(x1,y1) and the patch g(x2,y2). The matching process establishes a correspondence if: (4-2)

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65 However, Equation 4-2 is not consistent due to radiometric and geometric differences, as previously discussed. Th erefore, the patch g(x2,y2) is transformed by applying both radiometric and geometric corrections to obtai n a new, more reliable, patch g’(x2,y2): (4-3) where e(x1,y1) is the residual for the point (x1,y1) in the master image reference system. Radiometric changes during testing are easily modeled by accounting for brightness and contrast changes of grey va lues in the patch function: (4-4) where r0 and r1 are two parameters accoun ting, respectively, for brightne ss and contrast changes in the slave image. Geometric corrections are achieved by mini mizing a goal function, which measures the distances between the gray levels in the templa te and in the patch. The goal function to be minimized is the L2-norm of the residuals of least squares esti mation. The new location g’(x2,y2) is generally described by shift paramete rs which are estimated with respect to the initial position of g(x2,y2) by means of an affine transformation: (4-5) 2 2 (4-6) where (a1, a2 b1, b2 ) are model shape differences, while (a3, b3) are the shift parameters. Radiometric and geometric correction para meters are then estimated solving, for ||e(x1,y1)||= min, the following least squares system, obtained by s ubstituting the transformed functions in Equation 4-3: (4-7)

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66 The function is linearized and the system is solved with GaussMarkov least squares estimation model. Optimization With LSM When proper illumination is provided, the two radiometric parameters r0 and r1 tend to be zero, while showing high correlation coefficients. In this case, the use of both parameters may lead to numerical instability of the estimation pro cess, resulting in high computational efforts. To overcome these drawbacks, a parameter rejecti on algorithm was developed to check whether one or more function parameters are highly correlat ed with each other and must be fixed during the estimation. To account for geometric corrections, different shape functions were tested (Sutton et al., 1988; Bruck et al., 1989; Lu & Ca ry, 2000). It was found that th e use of a simplified shape function leads to lower computational effort but provides inaccuraci es when significant deformations occur. In contrast, higher shape function polynomial orders lead to numerical instability from the over-parameterization of the system of equations, even when the parameter rejection algorithm is employed. In this case, good accuracies can be achieved only using a bigger template window to maintain high redundancy in the system of equations. However, the larger the templates, the lowe r the correspondence betw een the shape function and the real local deformation of the specimen, which means that accuracies do not improve. The affine transformation seemed to provide the best performance even when high local deformation gradients occur. Indeed, the affine shaping function is cap able of describing a transformation corresponding to a shear defo rmation plus a compressive and a tensile deformation along two mutual orthogonal direc tions; thus providing a correct geometric description of the specimen defo rmation in a localized area.

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67 At the end of the estimation, the initial assumption (e(x1,y1) = random error vector) must be verified to account for poten tial discrepancies between the nu merical image correlation model and the real image acquisition (i.e., specimen flat surface, C0 continuity of the displacement field, ideal sensor without noise, etc.). An ite rative statistical procedure, named data snooping (Schwarz & Kok, 1993), was employed for this purpose. Data snoopi ng discards all the observations which show a normalized residual a pos terior higher than a threshold. The solution is then re-evaluated until no furthe r gross errors are identified. Data Extraction The image correlation technique tracks a dens e set of features along the acquired image sequence using an approximate value of the patch position estimated at the previous frame. The displacement is computed as the difference of the feature location betw een each image frame in the sequence and the reference one (which is fixe d). Displacement estimation depends mostly on two concurrent factors: the partial or tota l rigid displacement of the specimen and the displacements occurring in the imag e system, e.g., camera vibrations. These effects must be minimized to recover only strain field info rmation. Thus, in each sequence, a point is selected as the origin of a reference system attached to the specimen (Figure 4-5). The origin is selected as a distinct point f eature, with high and consis tent correlation values between epochs and located on a specimen area not significantly stressed. The region of interest (ROI) is then meshed re gularly in both (x,y) directions. Th e displacements are computed at the nodes of the regular grid by linea r interpolation of the displace ment values estimated by LSM over the template bordering the same nodes.

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68ReferencePoint Measurement window Mesh Nodes Figure 4-5. Region of in terest (ROI) meshing Finally, strains are estimated by using a finite difference scheme from measurements at opposite sides of the template window. If u and v are the displacement components in x and y directions, the strain tens or can be computed as: (4-8) Strain values outside the mesh nodes are estimated by bilinear or bicubic interpolation. The accuracy achievable in the strain tensor components depends on the Least Square Matching accuracy. Let assume that displacement measuremen ts are independent. This is true when the mesh step is larger than the templa te size and the accuracy is uniform ( u = v) such as in the case of assumed isotropic specimen texture. Assu ming no uncertainty in th e determination of the mesh step x, and according to the error propagation law:

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69 (4-9) The mesh step directly affects the uncertainty in the strain estimation: a small one provides a point strain description but with less accuracy; a larger one gives an average value of the strain with better accuracy. Thus, considering that both u and v depend on the accuracy in the image space, the pixel size in the object space directly define s the achievable accuracy. Verification of Method Accuracy The performance of the method was investigated by means of several tests, aimed to assess its accuracy for both displacem ent and strain measurements. Comparisons were also made between the image method strain measurem ents and strain gauge measurements. Accuracy in Displacement Measurements The accuracy in the displacement measurements is affected by both LSM performance and template dimension. Using a small template, th e assumption of strain isotropy and affine deformations becomes more realistic but the measurement redundancy drastically decreases (in terms of number of pixels considered, number of equations involved, and the likelihood of finding well-contrasted pixels). On the other hand, the use of large templates improves the redundancy but adversely affects in itial assumptions of affine deformations. Indeed, the use of larger templates makes the approximation of local displacements by affine transformations harder. The displacement measurements accuracy was assessed performing two different kinds of tests. The first set of tests was performed on synt hetic images, re-sampling the original one with

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70 different transformations (translation, rotation, n on-isotropic scaling and shear). The second set of tests was performed using a micrometric 10 m slide. This kind of test was selected to account only for translations, thus eliminating the po ssible development of local deformations. An enlarged picture of the specimen surface was glued on the micrometer slide and imaged at each 100 m shift. An appropriate distance between the camera and the target texture was chosen to achieve an object space accuracy of th e slide of 1/1000 pixel in image space. Figure 4-6 shows the accuracies estimated according to the template size using the 10 m micrometric slide test. The theoretical xx accuracy for locally homogeneous strain fields according to the ROI dimension and the mesh step size are listed in Table 4-1 assuming a sensor with 1300x1000 pixels and u = 1/100 pixel. For instance, fo r a 4 cm wide ROI and a 1300 pixel resolution in x direction, the pi xel size in object space is 30 m. Least Square Matching accuracy between 1/100 pixel and 1/150 pixel was ach ieved corresponding to value between 0.30 m 0 20 40 60 80 100 120 0204060801001/RMS (pixel)TemplateSize X Y Figure 4-6. Accuracies achievable according to the template size

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71 Table 4-1. Theoretical image system accuracy Region of interest (ROI) 1 cm 3 cm 5 cm 10 cm Displ Accuracy ( m) 0.08 0.23 0.38 0.77 grid 1 mm 0.011% 0.033% 0.054% 0.109% grid 2 mm 0.005% 0.016% 0.027% 0.054% grid 5 mm – 0.007% 0.011% 0.022% and 0.20 m in image space. Assuming x = y = 1 mm (1200 measurement nodes), the1 accuracy of the tensor components is: (4-10) Accuracy in Strain Measurements The accuracy achievable in the strain meas urements rests on the distribution of the measurement points on the specimen surface. If the nodes are too close to each other, even a small inaccuracy in the displacement measurements ma y lead to large errors in the strain values as can be observed in Equation 4-9. On the other hand, if the reciprocal n odes are too distant, the local effects can be lost due to the interpolation process. The accuracy in the strain measurements was assessed performing a test in which results obtained from the image method was compared to results obtained with on-specimen strain gauge measurements. A strain gauge, arranged in a quarter Wheatstone bridge, was mounted on an aluminum bar, machined to a dog-bone shape fo r an uniaxial tensile test. The strain gauge was painted to obtain a dotted pattern and imaged during the testing. Strain gauge and digital image measurements were recorded. The strain values obtained with the digital image correlation method were averaged over the strain gauge ar ea; their differences we re computed during the linear elastic portion of the stressstrain response as well as duri ng the initial yielding stage. The ROI was about 1 cm wide and the displacement measurement grid was 0.5 mm spaced. The root mean square of the differences between the stra in gauge measurement and the DIC mean strain

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72 value over the strain gauge length was about 0.00 3%. as shown in Figure 4-7. The result agree with the variance propagation law: (4-11) where mean is the error in the mean value and n is the number of measurement points. Indeed, 100 measurement points uniformly distributed over the strain gauge area (with expected local accuracy = 0.020.03%) were used to obtain the m ean strain value at each epoch. 0 0.5 1 1.5 2 2.5 3 3.5 020406080100120140160180Strain (x 1000)Time (sec) STRAIN GAUGE DIC Figure 4-7. Comparison between image correlati on and strain gauge measurements in uniaxial tensile test Potential Measurement Errors The DIC method can be affected by measuremen t inaccuracy due to both test errors and image peculiarities. The first sour ce of errors develops when the specimen and the load direction are not parallel to the camera sensor (Figure 4-8A ). In this case, persp ective transformation of the object plane in the image space precludes a scale reproduction picture of the specimen surface.

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73A B C D E Figure 4-8. Potential elements leading to meas urement errors. A) Specimen and load direction out of plane. B) Reference target to control unparallelism. C) Specimen out of plane movement. D) Specimen unflatness. E) Local roughness. Perspective projections are described by a mathematical framework, namely the collinearity equations which ar e commonly satisfied by a tran sformation. Assuming a planar specimen surface, the most generic transforma tion is the homography. Collinearity equations are described as follows: P2 P1 DL DZ Homography plane

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74 (4-12) where (x,y) represent image space coor dinates of the specimen surface, ( ) represent the corresponding coordinates in a planar re ference system in object space and a1..3, b1…3, c1…2,are the eight parameters of the homography itself. Drawing reference targets on th e boundaries of the selected area by means of a calibrated mould to standardize both target dimensions and their mutual dist ances (Figure 4-8B), allows for the estimation of the homography (ai, bi and ci parameters in Equation 4-12) and then for the correction of specimen point coordinates (and thus their correct displacements) in object space. Nonetheless, providing a good orie ntation of the specimen with respect to the camera sensor ensures that all the specimen regions are im aged with the same resolution, leading to approximately the same level of accuracy at all points. A more serious issue develops when the spec imen is affected by out of plane movements during test conditioning (along the image seque nce) as shown in Figure 4-8C. When the specimen or part of it moves forward or backward a perspective deformation is registered by the camera (its picture suddenly becomes wider or smaller) leading to unr eliable displacement estimation. This drawback cannot be solved w ith a monoscopic approach. However, using two (or more) synchronized cameras (stereoscopic ap proach), the 3D object displacements can be computed and relative motion between the sp ecimen and the camera can be determined. Specimen roughness, shown in Figure 4-8E, is th e last issue of concern related to test setup. It occurs in the case of non-smooth speci men surfaces and it appears troublesome since it invalidates both the assumption that an affi ne transformation can approximately model the mapping between the patch and the template pictur e, and the hypothesis th at the specimen can be

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75 approximated with a planar surface. The former issue usually becomes significant only for very rough surfaces. The template size represents just a small part of the specimen area: if the roughness is not too high, its lo cal roughness might be well described by the affine transformation. The latter issue still remains a main concer n for correct global strain field evaluation. Since homographic mapping between object and image space is strictly corrected fo r planar transfers, errors arise during specimen displacement estim ation. The out-of-plane mapping error can be observed as a miscalculated image scale factor va rying linearly on the specimen surface with the out-of-plane entity itself and the point distance from the principal point (projection of the projective centre on the image frame) in image sp ace. In other words, the displacements in some areas of the image become larger or smaller than they really are, due to perspective effects not properly corrected by the homograp hic transformation. Even in th is case the only practical way to solve the issue is a stereosc opic or multi-image approach. In Table 4-2, errors in terms of displacement are presented with respect to local roughness (di fference between the points set nearer and farther from the camera) in speci men regions with only tw o points using a common camera and test set-ups and assuming a 10 pixel overall displacement (Fi gure 4-8E). It can be observed that even with a small out-of-plane in accuracy (0.1 mm) with a region of interest smaller than 40x30 mm the final st rain error is not negligible. Table 4-2. Displacement and strain errors fo r a common camera set up (focal length 8mm, 1300x1000 resolution) due to out of plane spec imen roughness. DZ is the error due to local roughness; DL is the spac ing between the points in the mesh. ROI (mm) Out of plane displacement DZ (mm) (for a point on the frame border) 0.1 0.2 0.5 1.0 Displ (pix) Strain ‰ Displ (pix) Strain ‰ Displ (pix) Strain ‰ Displ (pix) Strain ‰ 20x15 ( x = 0.5 mm) 0.054 1.0 0.109 2.1 0.272 5.2 0.544 10.3 40x30 ( x = 1 mm) 0.027 0.3 0.054 0.5 0.136 1.3 0.272 2.6 60x45 ( x = 1.5 mm) 0.018 0.1 0.036 0.2 0.091 0.6 0.181 1.1 100x75 ( x = 2.5 mm) 0.011 0.0 0.022 0.1 0.054 0.2 0.109 0.4

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76 Tests on Asphalt Mixture Specimens For verifying the accuracy obtainable from DIC measurements during HMA strength test, a single mixture (unmodified N1) was tested using all three configurations: IDT, SCB, 3PB. The camera, placed inside the climatic chamber on an adequate support, was set at 5 frames per second (fps) and focused at the shortest dist ance, providing a 5x4cm ROI located in the more stressed area of the opposite face of the speci men. The measurement grid spacing was set equal to 1mm; the pattern size was in the range of 3040 pixels, dot size was about 3 pixels. The origin point of the reference system attached to the specimen was selected according to the highest values of correlation between epochs and in an ar ea not significantly stressed during all test long. Accuracy Achievable in HMA Strength Tests The results obtained from the th ree HMA strength tests are pr esented in this section. For each test setup one strain gauge was mounted on one face of the specimen. The same face was then treated to obtain the required texture for di gital image analysis. The test was imaged and processed; then the mean strain value of the le ngth covered by the strain gauge was estimated by the digital image system by interpolating all the st rain values of the grid points located along the length of the strain gauge. Strain s registered by the strain gauge were then compared with those estimated with the DIC System. Computing the Root Mean Square (RMS) of the differences between measured and estimated strain values, accuracies of 0.015% for the IDT test, 0.034% for the SCB test, and 0.017% for the 3PB were obtaine d, as shown in Figure 4-9. These results agree well with the mean error previously estimated (~0.03%). The DIC System accuracy matches that obtained with strain gauges, while allowing a dense description of the field of interest where the cracking is developing. A big adva ntage resulting from the method is the opportunity of locating the specific point(s) at which cr acks initiate and propagate, without constraining the analysis of HMA cracking behavior in a larger area of interest.

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77 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0510152025Strain (x1000)Time (sec)INDIRECT TENSILE TEST STRAIN GAUGE DIGITAL IMAGE CORRELATION 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 02468101214161820Strain (x1000)Time (sec)SEMI-CIRCULAR BENDING TEST STRAIN GAUGE DIGITAL IMAGE CORRELATION 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 051015202530Strain (x1000)Time (sec)3 POINT BENDING BEAM TEST STRAIN GAUGE DIGITAL IMAGE CORRELATION Figure 4-9. Comparison between image correlation and strain gauge measurements. A) Indirect Tensile (IDT) test. B) Semi-Circular Bending (SCB) test. C) 3-Point Bending Beam (3PB) test. A B C

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78 Description of Software Tools The visual graphic interface of the image co rrelation software was conceived with the purpose of selecting the point of interest, and for choosing which information is requested (horizontal/vertical/shear strains, horizontal/vertical displacements). The strain values are then exported to plot stress-strain re sponses at the specific chosen point, as shown in Figure 4-10. This tool is very convenient for fracture mechan ics analysis since it allows for strain response estimation at the accurate point in which a crack initiates. Figure 4-10. Visual graphic interface of DIC system Figure 4-11 shows an example of a comparis on between horizontal strain map for the mixture during IDT test at major crack ope ning and the corresponding specimen image. The figure emphasizes the capability of the DIC met hod to capture strain values and to visualize crack patterns at crack in itiation and propagation.

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79 Figure 4-11. Mixture N1 during IDT test. A) Full-field tensile strain map. B) Corresponding specimen image. Full field strain estimations allow for a comp rehensive analysis of HMA cracking behavior since strains vary within the overall ROI. Traditionally, for wi de area analysis, users mount multiple sensors with different lengths and posit ions; while in the image correlation system a single camera functions as a single sensor from wh ich information from the entire selected area is achievable. Moreover, since th e strain field is evaluated fra me by frame, it is possible to analyze at each load step the current mechani cal behavior of the speci men, selecting the option of making denser the measurement grid where a fracture opening can be spotted by looking for large gradients of the strain field (see Figure 4-12). Figure 4-12. Evaluation of strain field. A) Colormap of gradient value of tensile strain. B) Thresholding of the gradient field to obtain growing fracture zones. A B A B

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80 Finally, other information not achievable by dire ct strain measurements can be collected. The DIC system allows for taking into account the mechanical behavior of the mastic and aggregates. Using reference marks and an image ac quired before the specimen is painted, it is possible to automatically or manually generate the aggregate map, whic h can be used during strain field estimation to obtain lo cal strain values (Figure 4-13). Figure 4-13. Other information used to obtain corr ect strain values. A) Image acquired before the specimen is painted. B) Generated aggregate map. Potential Measurement Errors in HMA Tests As previously described, the following elemen ts can affect DIC measurement accuracy: € Unparallelism between specimen/lo ad direction and camera sensor; € Specimen’s out of plane movements during loading; € Specimen roughness. Two of these sources of error have shown to occur in typical asphalt mixture testing configurations. The first may be checked when the specimen is affected by out of plane movements. These out-of-plane movements may occur when the specimen is not cut perpendicular to its axis, or when th e specimen supports are not fully aligned. Figure 4-14 shows the horizontal displacements of a semi-circular HMA specimen: during test loading the right side shif ted forward so that artificially large displacements have been registered by the DIC system. The second source of error is due to excessive specimen surface A B

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81 roughness. It is therefore recommended that the specimen be thoroughly cleaned and possibly etched prior to painting. Figure 4-14. Example of a potential measurement error in HMA tests

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82 CHAPTER 5 PREDICTION OF HMA CRACK INITIATION AND PROPAGATION Background One of the main obstacles to improved understanding of fracture mechanics-based approaches involves the complexity of modeling crack propagation. Various models for cracks in granular materials have received considerab le attention among researchers. Bazant (1986) provided a good review of existing cracking models that have been used to analyze brittle materials such as rock and concrete. The analysis of cracks is commonly carried out by either a fracture mechanics approach or a smeared crack approach. The former assumes that a crack can be represented as a series of connected single line segments, which initiate from one or more pre-existing flaws and which propagates through the material according to certa in crack growth criteria, such as maximum energy release rate. Alternatively, the smeared crack approach assumes that cracks are distributed over a finite region such that an average tensile st rain adequately represents the physical presence of the cracks. With appropriate material models for compression and tension, the smeared crack approach can reasonably pr edict the cracking beha vior of materials. Nevertheless, both methods cannot fully capture the nature of cracks in gra nular materials, where cracks randomly initiate along weak planes, coales ce to form a major crack band and propagate through the material. Explicit fracture modeling using random assemblies of displacement discontinuity boundary elements provides a more realistic appro ach in the simulation of discrete cracks in granular materials, as discussed by Steen et al. (2001). The method employs known stress and displacement field influence functions due to defi ned displacement discon tinuity elements that are distributed through the region of interest. The change in geomet ry due to crack propagation is

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83 easily handled by allowing cracks to grow only al ong the predefined crack paths, which can be assumed to be along aggregate boundaries or to fo llow internally defined fracture paths within the aggregates. The complexity of modeling the mechanics of crack initiation and crack growth with traditional numerical methods, such as the finite element method (FEM) has been an obstacle to the incorporation of fracture m echanics-based approaches in the bituminous pavement area, as discussed in Birgisson et al (2002). The FEM requires hi ghly refined meshes around the cracking area in order to simulate the stresses in the vicinity of the cr ack tip. Improper mesh generation will result in a failure to capture the very important stre ss singularity at the crack tip. The simulation of crack growth with the FEM also requires elaborate re-meshing to simulate the geometry of a growing crack. The computational intensity required puts these types of problems out of the realm of reasonablen ess for the typical capabilities of personal computers, which means that only select research organizations a nd major universities have the capabilities to perform these types of calculations. The Displacement Discontinuity (DD) B oundary Element Method (BEM) provides an attractive alternative to finite element-based methods for modeling crack initiation and crack growth. The DD method requires meshes only on the boundaries of an object or pavement, including cracks. This means that the number of elements required is reduced significantly. Also, the stress singularity at the crack tip is naturally included in the DD by usi ng a representative displacement distribution around the crack tip. Crack growth is addressed simply by adding more DD elements in regions of crack growth. Birgisson et al. (2002; 2003) first used the DD to assess the mechanic s of fracture in the Superpave Indirect Tension test (IDT). The same method was applied and improved in this

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84 research work to model the microstructure of asphalt mixtures and pred ict crack initiation and propagation in the IDT, the SCB and the 3PB tests for all the six mixtures. Displacement Discontinuity (DD) Boundary Element Method with Tessellation The Displacement Discontinuity method is an indirect boundary element method developed by Crawford & Curran (1982) and Crouch & Starfield (1983) which has been extensively used in the fields of rock mechanics and geological engineering. The method has the potential to be an analytical tool for assessi ng cracking in granular materials such as asphalt concrete. The numerical model consists of two types of elements: exterior boundary elements and potential crack elements. The exterior boundary elements are placed along the boundary of a problem to simulate the edge of specimen, wh ile potential crack elements are randomly placed inside the specimen to simulate predefined crack paths, which normally are assumed to be along the grain boundary or perhaps through the grain as well. The displacement discontinuity boundary el ement method can be coupled with various tessellation schemes. The use of tessellations to represent granular structure in simulation of fracture process zone is very well accepted. It improves the realism of predicted failure mechanisms at the particle level. Two basi c tessellation schemes Delanuay and Voronoi have been used in various fields. Both tessellations can be used to si mulate polycrystalline or ductile material (Van der Burg & Giessen, 1993; Helms et al., 1999). The tessellation schemes are also applicable to simulate granular structure of br ittle rocks, as discusse d by Napier & Peirce (1995), Napier & Malan (1997), Napier et al. (1997) and St een et al. (2001). The suitable choice of tessellations to represent granular structure depends on the realisti c looks of failure pattern and observed responses.

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85 In 1995, Napier and Peirce developed a new boundary element solution technique, termed the “multipole method” for solving multiple inte racting crack problem that involve several thousand boundary elements. They applied the new technique to study the different failure mechanisms of a rectangular rock sample unde r displacement control using two tessellations schemes (Delaunay and Voronoi) fo r three levels of grain densiti es. It appeared that Voronoi assemblies are less prone to shed load than th e Delanuay triangulations With increasing the density of Voronoi polygons, it seemed to not change this conclusion. Steen et al. (2001) introduced a new type of tessellation pattern, the Voronoi tessellations with internal fracture path to simulate a confin ed compression test of a rock sample. From this study they found that the use of Vo ronoi tessellations w ith internal fracture paths best simulate the formation of shear band in the specimen. Al so, both Rankine and Coul omb failure criteria were analyzed to identify the appropriate failure law that allowed the fo rmation of shear bands. The results of the simulation reve aled that only Coulomb failure criterion enabled localization of shear band. Birgisson et al. (2002; 2003) us ed exterior boundary elements to create a 2D plain stress IDT specimen and randomly laid down potential crack elements forming Voronoi tessellation inside the specimen. With an appropr iate set of material parameters for local failure at potential crack elements, the numerical prediction was f ound to be suitable for capturing stress strain responses and crack patterns. They found that the method was capable of evaluating mixture properties with acceptable accuracy. Also, they proved that the DD is suitable for modeling aggregate and mastic separately such that the deta il of aggregate structure and strength of mastic can be investigated.

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86 Theoretical Background The DD method assumes displacements in a bod y are continuous everywhere except at a line of discontinuity (Figure 5-1). When the di splacement crosses the line of discontinuity, its value jumps by the amount of the displacement discontinuity Di, in which its component in local axis coordinates y-z are: (5-1) where z = 0+ is the positive side and z = 0is the negative side of th e discontinuity element. z y c1c2Q(yq,0) p(yp,zp) -bb r Figure 5-1. Displacement discontinuity element in local coordinates (y-z) A linear discontinuity element has the total length of 2b with tw o collocation points (c1 and c2) at The distance r is measured from the field point p(yp,zp) in the domain to the source point Q(yq,0) at boundary. Napier and Pierce (1995) have s how that in two-dimensional pl ane strain problems, if the line of discontinuity has a length of 2b, centered on the yaxis of a local coor dinate system y-z, and has normal vector components ny and nz along the surfaces, the contribution of a given element to the total displacem ent components at point p is:

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87 (5-2) where uy, uz are the local components of the displacement vector, is Poisson ratio and the symbols in matrix are given by: (5-3) The biharmonic function for plain strain problem is given by: and (5-4) As discussed by Napier and Pe irce (1995), the contribution of the element to the total stress tensor components at point p is given by: (5-5) For numerical implementation, the displacement discontinuity Di is approximated by a polynomial function: (5-6) More accurate results can be obtained by using several terms in the approximation, but increasing computing time. For mo st practical applications it is better to approximate the displacement discontinuity with a linear function as done for the Discontinuity Interaction and Growth Simulation (DIGS) (Napier, 1990; Napi er & Hildyard, 1992; Napier & Peirce, 1995; Malan & Napier, 1995; Kuijpers & Napier, 1996; Napier et al., 1997, Napier & Malan, 1997).

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88 The linear variation of discont inuity can be written as: ai and bi are constants (5-7) By substituting Equation 4-7 into Equation 4-6, and carrying out the mathematical manipulation, the analytical solution for normal stress on the y-axis of the local coordinates system (y-z) is given by: (5-8) It is obvious from Equation 5-8 that the analytical normal stress zz approaches infinity as y approaches the tip of the element y = b. Howe ver, in boundary element formulations, stress in Equation 5-8 is evaluated at suitable colloca tion points y = c, namely the Gauss-Chebyshev points, as described by Crawford and Curran (1982): i = 1, 2, ..., n (5-9) The stresses at collocation point s will have finite values and are solvable using a numerical algorithm. Numerical Implementation The DD method employs the fundamental solutions of a discontinuity surface (or crack) to formulate a system of governing equations. For a problem with one crack in an infinite elastic body without far field stresses, the general syst em of governing equations can be written as: iijjijj sssssnn j iijjijj nnssnnn j =AD+AD =AD+AD (5-10)

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89 where i s and i n are the shear and normal stress of the element i, respectively; Aij ss, Aij sn, Aij ns and Aij nn are the influence coefficients due to element j on element i, and Dj s and Dj n and are the displacement discontinuity components of the element j which are the unknow ns of the system. In simulations of crack interaction problems, a displacement discontinuity element can either slide if the driving shear stress exceeds the shear strength or open up if the applied tensile stress exceeds the tensile strength. Although the DDM was initially developed for an open crack, it can be easily extended to include contacting crack surfaces and sliding cracks in softening mode. When two crack surfaces are in contact at collocation point I, the shear and normal stress components i s and i n depend on the stiffness (Ks and Kn) and the displacement discontinuity components (Dj s and Dj n). The relationships can be written in matrix forms as follows: (5-11) By substituting Equation 5-11 into Equation 510 and rearranging the terms so that the unknowns are on the right hand side, the system of governing equations then becomes: (5-12) When an element is mobilized, the crack su rface will deform according to the softening models, which will be described shortly in the next session. The residual strength of the element i, namely i s and i n can be assumed to decrease as a function of the discontinuities Dj s and Dj n, which are expressed as follows: (5-13)

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90 Substituting Equation 5-13 in Equation 5-10 and rearranging the unknowns to the right hand side, the system of equations becomes: (5-14) Finally, a set of algebraic equations that consists of known driving forces, influence coefficients and the unknown displacement discon tinuities can be written in matrix form: (5-15) Since the mobilization of cracks is associated wi th a softening model in which stresses depend on the unknown discontinuities, an interactive technique needs to be employed in solving the equations. Once displacement discontinuities at all boundary elements have been determined, displacements and stresses at any designated po ints can be computed by using known solutions of discontinuity surfac es as discussed by Napi er and Peirce (1995). Crack Growth Algorithm The numerical model consists of two types of elements: exterior boundary elements and potential crack elements (Figure 5-2). These represent, respective ly, the boundary surface of the specimen and internal sites where potential crack elements are selected for mobilization (slip or tensile opening modes). The Voronoi tessellation approach is adopt ed to account for the presence of aggregates in which displacement disconti nuity elements are randomly placed inside the specimen forming Voronoi pa tterns of predefined paths. At each load step, stresses are computed at collocation points inside the potential crack elements; these stresses are then checked against a failure limit to determine whether or not a crack has been activated. A nonlinear Mohr-Coulomb type of failure law, shown in Figure 53, is adopted for the cracking criterion.

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91 Exteriorboundaryelements Potential crack elements (for mastic) Potential crack elements (for aggregates) Potential crack elements (for mastic at cracked state) Figure 5-2. Voronoi tessellations with internal fracture path s representing the aggregate structure = S –tan( ) n RCoCR ToShear stress Failure envelope Residual failure envelope S = Co–Csof t |Ds| t= To–Tsof t |Dn| = 0 if Dn> DNCR Figure 5-3. Failure criterion for determining crack mobilization The failure law comprises a linear portion in the compression region that changes over to a power law curve in the tension re gion, with a continuous slope at n = 0. The linear portion has the following form: when (5-16)

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92 where S is the cohesion, is the friction angle and n is the normal stress across the discontinuity that is assumed to be negative when compressive. The power law curve is defined by: when (5-17) where t is the tensile strength and the constants a a nd b are the parameters that fit the power law curve to the tension cutoff T0 at shear stress s = 0 and the linear portion at normal stress n = 0. For every load step, a crack search algorithm is performed to detect cracks that may occur in the specimen. At the end of each search step, the detected cracks are a dded to the system and resolved for determining new cracks in the ne xt search step, until no more cracks are found. When a potential crack element is mobilized, the cohesion S is assumed to weaken as a linear function of the slip Ds: (5-18) where C0 is the original cohesion intercept and Csoft is the rate of cohesi on softening. Similarly, the tensile strength t is also assumed to weaken as a li near function of the opening displacement Dn: (5-19) where T0 is the tension cutoff and Tsoft is the rate of tension soften ing. When crack slip occurs, the tensile strength is implicitly de graded as the cohesion softens, congruently with the extent of cohesion softening. Fracture Test Models The IDT, SCB and 3PB specimen geometries we re modeled using an appropriate number of discontinuity elements defining the relevant load or displacement conditions on the boundary. The regions inside the specimen models are covered by a random me sh of Voronoi polygons, providing a specific number of potential crack elements accordi ng to the aggregate nominal

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93 maximum size; additional crack paths are obtaine d in the Voronoi tessellation by connecting the geometric center of the Voronoi polygons with the vertices of the polygons to simulate potential fracturing of aggregates. A pre liminary study to evaluate the op timal average Voronoi particle sizes for the mixtures was performed. The IDT tessellation has 503 particles filling the circular area of 17662.5 mm2, the SCB tessellation has 251 particles filling the semi-circular area of 8831.2 mm2 and the 3PB tessellation has 618 particles filling the rectangular area of 22500 mm2. Thus, it was found that for realis tic simulations, Voronoi particle s with an average size of 6.8 mm diameter or D50 (aggregate size at 50% passing of th e gradation) represented the aggregate structure of the mixes reasonably well. Indirect Tension Model The IDT specimen model is shown in Figure 54. The perimeter of the modeled specimen is defined using 152 appropriately located displa cement discontinuity elements; of those, 8 elements are placed at the top and forced to move downward to simulate displacement control; another 8 elements are fixed at the top to provi de a static condition. The remaining 136 elements along the circumference are specifie d with zero traction to simulate traction free surface. Inside the specimen model, the random mesh of Voronoi polygons provides 1826 potential crack elements (for mastic) and 3549 additional potentia l aggregate fracture paths. The elements under the top platen were subsequently displaced in 16 equal steps to simulate the total measured vertical displacement. For each load step, horizon tal and vertical stresses are evaluated at the center of the specimen using 2D plane stress formulas: (5-20)

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94 where, v is the vertical stress at th e center of the specimen, P is a total applied load, D is the diameter of the specimen, t is the thickness of the specimen, v is an average vertical strain over a vertical strain gauge, V is a vertical deformation measured at a vertical strain gauge, Lgauge is a gauge length (38.1 mm). The stress component h is the theoretical uniform tensile stress across the depth of the IDT specimen, h is an average horizontal strain over a horizontal strain gauge, H is a horizontal deformation measur ed at a horizontal strain gauge. Figure 5-4. Indirect Tensile specimen model Semi-Circular Bending Model The SCB model is shown in Figure 5-5. The pe rimeter of the modeled SCB specimen is defined using 128 appropriately lo cated displacement discontinuity elements. The region inside the specimen model is covered by 665 (for mastic) po tential crack elements and 1268 additional potential aggregate fracture paths. The edges below the SCB top ring consist of 8 elements, while the edges above each of the two SCB support rings consist of 4 elements. The remaining 112 elements along the semi circumference are speci fied with zero traction to simulate a traction free surface. The elements under the top ring were s ubsequently displaced in 16 equal load steps.

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95 For each load step, the horizontal stress was co mputed using Equation 3-3, while the simulated horizontal deformation h was computed as for the IDT but assuming a gauge length of 20mm. Figure 5-5. Semi-Circular Bending specimen model Three-Point Bending model The 3PB specimen model is shown in Figure 56. The modeled beam specimen consists of 252 DD boundary elements, 1718 potential crack elements (for mastic) and 3562 additional potential aggregate fracture paths. As in the S CB, the edges below the top ring consist of 8 elements, while the edges above each support ring consists of 4 elements. The remaining 236 elements along the perimeter are specified with ze ro traction to simulate a traction free surface. Elements under the top ring were subsequently disp laced in 16 equal load steps. For each load step, horizontal stress was computed using Equa tion 3-4, while the simulated horizontal deformation h was computed as for the IDT and the SCB but assuming a gauge length of 50 mm. Figure 5-6. Three-Poin t Bending Beam model

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96 Parameter Calibration The global material parameters (Young modulus and Poisson ratio) for the numerical models of the six mixtures were obtained from Superpave IDT tests. Fo r a given stress-strain curve, the secant modulus at any po int on the curve is calculated by: (5-21) The secant modulus at half the ul timate load seems to result in reasonable simulations of the stress-strain curves. Local material parameters for the mastic and internal fracture paths for the three numerical models of the six mixtures were determined by numerical calibration fr om a parametric study based on Superpave IDT results. In this parametric study, local material properties were varied in a systematic fashion until a reas onable fit to the experi mental data (vertica l and horizontal stressstrain response) was achieved. On ce the input parameters were obtained for the Superpave IDT test results, these same parameters were used to predict the stress-stain response in the SCB and the 3PB tests. The resulting calibrated paramete rs for each mixture are listed in Table 5-1. The same local material parameters for the internal fracture paths were used for the six mixtures numerical models since all the six mixtur es have the same aggregate gradation. Table 5-1. Calibrated material parameters fo r the parametric study of the six mixtures Parameters Internal fracture paths Mastic N1 Mastic N2 Mastic RM3.5 Mastic RM5.0 Mastic LM3.5 Mastic LM6.5 T0 (MPa) 6.40 3.60 2.20 3.40 3.50 3.50 3.60 DNCR (mm) 0.09 0.12 0.12 0.14 0.13 0.16 0.12 Tsoft (MPa/mm) 10.0 10.0 10.0 10.0 10.0 10.0 10.0 C0 (MPa) 6.40 3.60 2.20 3.20 3.20 3.20 3.20 CR (MPa) 0.12 0.18 0.11 0.10 0.11 0.09 0.11 Csoft (MPa/mm) 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0 (degree) 40 38 44 38 40 38 40 R (degree) 36 32 38 36 38 36 34 Young Modulus (MPa) 10500 6200 6100 4600 5800 3800 Poisson’s ratio 0.36 0.35 0.26 0.26 0.29 0.29

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97 The plots obtained from the numerical calibra tion for the six mixtures are shown from Figure 5-7 to Figure 5-12. Once the stress-strain response has been determined, the tensile strength at fracture and fracture energy density were evaluated. 0.00 2.00 4.00 6.00 8.00 10.00 12.00 0.001.002.003.004.005.006.007.008.0 0 stress (Mpa)strain (x1000)CALIBRATION -MIX N1 Vertical (Experimental) Vertical (DD) Horizontal (Experimental) Horizontal (DD) Figure 5-7. Mixture N1experimental and DD stress-strain response 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 0.001.002.003.004.005.006.007.008.009.00stress (Mpa)strain (x1000)CALIBRATION -MIXN2 Vertical (Experimental) Vertical (DD) Horizontal (Experimental) Horizontal (DD) Figure 5-8. Mixture N2 experiment al and DD stress-strain response

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98 0.0 2.0 4.0 6.0 8.0 10.0 12.0 0.02.04.06.08.010.0stress (Mpa)strain (x1000)CALIBRATION -MIX LM3.5 Vertical (Experimental) Vertical (DD) Horizontal (Experimental) Horizontal (DD) Figure 5-9. Mixture RM3.5 experiment al and DD stress -strain response 0.00 2.00 4.00 6.00 8.00 10.00 12.00 0.002.004.006.008.0010.0012.0014.00stress (Mpa)strain (x1000)CALIBRATION -MIX RM5.0 Vertical (Experimental) Vertical (DD) Horizontal (Experimental) Horizontal (DD) Figure 5-10. Mixture RM5.0 experiment al and DD stress -strain response

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99 0.00 2.00 4.00 6.00 8.00 10.00 12.00 0.002.004.006.008.0010.00stress (Mpa)strain (x1000)CALIBRATION -MIX LM3.5 Vertical (Experimental) Vertical (DD) Horizontal (Experimental) Horizontal (DD) Figure 5-11. Mixture LM3.5 experiment al and DD stress-strain response 0.00 2.00 4.00 6.00 8.00 10.00 12.00 0.002.004.006.008.0010.0012.0014.00stress (Mpa)strain (x1000)CALIBRATION -MIX LM6.5 Vertical (Experimental) Vertical (DD) Horizontal (Experimental) Horizontal (DD) Figure 5-12. Mixture LM6.5 experiment al and DD stress-strain response

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100 Evaluation of Fracture Energy Density with DD In the IDT simulation, “simulated strain” gauge deformation are evaluated across the center portion of the specimen at offsets of 19 mm horizontally away from the line of symmetry. In the SCB simulation, “simulated stra in” gauge deformation values are picked over the central portion of the bottom edge of the semi -circular specimen at a vertical distance of 10.0 mm above the bottom edge of the specimen and at offsets of 10 mm horizontally away from the line of symmetry. Similarly, in the 3PB simulation the “simulated strain” gauge deformation value is obtained over the central portion of the bottom edge of the beam specimen a vertical distance of 10.0 mm above the bottom edge of the specimen and at offsets of 25 mm horizontally away from the lin e of symmetry. 3D effects are accounted for applying bulging correction factors Cbh and Cbv, shown in Table 5-2, to correc t the measured horizontal and vertical deformation to fit the deformation in a flat plane, as described by Roque and Buttlar (1992) and Birgisson, et al. (2003): (5-22) Table 5-2. Correction factor s accounting for bulging effects Poisson’s ratio Diameter/length-to-thickness ratio (t/D) 0.167 0.333 0.500 0.625 0.750 Cbh 0.20 0.35 0.45 0.9816 0.9751 0.9722 0.9638 0.9518 0.9466 0.9461 0.9299 0.9234 0.9358 0.9179 0.9111 0.9294 0.9108 0.9040 Cbv 0.20 0.35 0.45 0.9886 0.9808 0.9759 0.9748 0.9588 0.9492 0.9677 0.9479 0.9361 0.9674 0.9473 0.9358 0.9688 0.9493 0.9380 The corrected horizontal and vertical deformatio n is then divided with the gauge length GL to obtain the average strain. Fina lly, center correction factors Ceh = 1.072 and Cev = 0.977 are used to correct the strain values:

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101 (5-23) Likewise, horizontal and vertical stresses are evaluated (at the center of the specimen for IDT test and at central portion of the bottom e dge for SCB and 3PB tests), using 2D plane stress formulas and then are corrected with the stress correction factors C h and C v to convert 2D plane stress to the stresses on the surface of a 3D specimen: for IDT (5-24) for SCB (5-25) for 3PB (5-26) The fracture point in the specimens was determ ined by plotting the deformation differential (Vcorrected Hcorrected) during the numerical simulation, and vi sually observing the point at which the deformation differential starts to deviate from a smooth curve. Figures from 5-13 to 5-19 show the predicte d deformation differential for each mixture determined for each test simulation. Based on the fracture point, the predicted horizontal deformations were used to eval uate the fracture energy density.

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102 0 2 4 6 8 10 12 14 16 18 024681012V-H (microns)Load stepPREDICTED V -H MIX N1 V-H IDT V-H SCB V-H BEAM FRACTURE POINTS Figure 5-13. Simulated deformati on differential for mixture N1 0 5 10 15 20 25 30 02468101214V-H ( m i crons ) Load stepPREDICTED V-H MIX N2 V-H IDT V-H SCB V-H BEAM FRACTURE POINTS Figure 5-14. Simulated deformati on differential for mixture N2

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103 0 5 10 15 20 25 02468101214V-H (microns)Load stepPREDICTED V-H MIX RM3.5 V-H IDT V-H SCB V-H BEAM FRACTURE POINTS Figure 5-15. Simulated deformati on differential for mixture RM3.5 0 2 4 6 8 10 12 14 16 18 20 0246810121416V-H (microns)Load stepPREDICTED V-H MIX RM5.0 V-H IDT V-H SCB V-H BEAM FRACTURE POINTS Figure 5-16. Simulated deformati on differential for mixture RM5.0

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104 0 5 10 15 20 25 02468101214V-H (microns)Load stepPREDICTED V-H MIX LM3.5 V-H IDT V-H SCB V-H BEAM FRACTURE POINTS Figure 5-17. Simulated deformati on differential for mixture LM3.5 0 5 10 15 20 25 30 35 0246810121416Microns (V-H)Load StepPREDICTED V-H MIX LM6.5 V-H IDT V-H SCB V-H BEAM FRACTURE POINTS Figure 5-18. Simulated deformati on differential for mixture LM6.5

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105 CHAPTER 6 FINDING AND ANALYSIS Results from laboratory investigation and num erical predictions are shown and discussed in this chapter. Fracture Tests Results A total of 54 specimens, 9 for each mixture (3 IDT, 3 SCB, 3 3PB) were tested at 10 C. For each testing setup, three replicates were perf ormed monitoring strains with both strain gauge and digital image correlation analyses. The tests we re imaged and processed; two different strain curves were estimated with the DIC System: a “pinpoint” one obtained estimating the strain value at the specific point in which a crack de velops and an “averag e” one obtained estimating the mean strain value of the length covered by the strain gauge. The mean strain value was estimated by interpolating all the strain values co mputed over the strain gauge length. It must be highlighted that the strain gauge was mounted on the same face of the imaged one. In the tests performed, fracture points were identified as the point in the instant in which a crack was found to have visibly initiated, then fracture energy densities were com puted as the resulting area under the stress-strain curve up to the fracture point Figures from 6-1 to 6-18 compare the horizonta l stress-strain responses of the three tests, evaluated by strain gauge and image correlation as mean values. Fracture points obtained by the DIC System match very well with the strain ga uge results. This means that fracture energy corresponds to that specific st rain energy value at the poin t of impending macro-cracking. As shown in Table 6-1, the image correlation and experimental fracture energy densities are well correlated with the fracture energy values obtained from the three tests. All of these results indicate that the fracture energy limit defi nes the onset of macro-cracks in the mixture,

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106 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 0.001.002.003.004.005.006.007.008.009.00stress (Mpa)strain (x1000)IDT -MIX N1 Horizontal stress -strain Strain gauge Digital Image Correlation Fracture point Figure 6-1. Experimental and mean image correla tion of horizontal stress -strain response for mixture N1 (virgin; PG 64-22) during IDT 0.00 0.50 1.00 1.50 2.00 2.50 3.00 0.001.002.003.004.005.006.007.008.009.00Stress (Mpa)Strain (x1000)IDT -MIX N2 Horizontal stress -strain Strain gauge Digital image correlation Fracture point Figure 6-2. Experimental and mean image correla tion of horizontal stress -strain response for mixture N2 (virgin; PG 58-22) during IDT

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107 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 0.001.002.003.004.005.006.007.008.009.00 S tress ( Mpa ) Strain (x1000)IDT -MIX RM3.5 Horizontal stress -strain Strain gauge Digital image correlation Fracture point Figure 6-3. Experimental and mean image corre lation horizontal stre ss-strain response for mixture RM3.5 (cross-linked polymer modified PG 64-22) during IDT 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.01.02.03.04.05.06.07.08.09.0stress (Mpa)strain (x1000)IDT -MIX RM5.0 Horizontal stress -strain Strain gauge Digital image correlation Fracture point Figure 6-4. Experimental and mean image corre lation horizontal stre ss-strain response for mixture RM5.0 (cross-kinked polymer modified PG 70-22) during IDT

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108 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.01.02.03.04.05.06.07.08.09.0stress (Mpa)strain (x1000)IDT -MIX LM3.5 Horizontal stress -strain Strain gauge Digital image correlation Fracture point Figure 6-5. Experimental and mean image corre lation horizontal stre ss-strain response for mixture LM3.5 (linear polymer mo dified PG 70-22) during IDT 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 0.001.002.003.004.005.006.007.008.009.00stress (MPa)strain (x1000)IDT -LM6.5 Horizontal stress -strain Strain gauge Digital image correlation Fracture point Figure 6-6. Experimental and mean image corre lation horizontal stre ss-strain response for mixture LM6.5 (linear polymer mo dified PG 76-22) during IDT

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109 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.01.02.03.04.05.06.07.08.09.0stress (MPa)strain (x1000)SCB -MIX N1 Horizontal stress -strain strain gauge Digital image correlation Fracture Point Figure 6-7. Experimental and mean image corre lation horizontal stre ss-strain response for mixture N1 (virgin; PG 64-22) during SCB 0 0.5 1 1.5 2 2.5 3 3.5 0.01.02.03.04.05.06.07.08.09.0stress (MPa)strain (x1000)SCB -Mix N2 Horizontal stress -strain Strain gauge Digital image correlation Fracture point Figure 6-8. Experimental and mean image corre lation horizontal stre ss-strain response for mixture N2 (virgin; PG 58-22) during SCB

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110 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.01.02.03.04.05.06.07.08.09.0stress (MPa)strain (x1000)SCB -Mix RM3.5 Horizontal stress -strain Strain gauge Digital image correlation Fracture point Figure 6-9. Experimental and mean image corre lation horizontal stre ss-strain response for mixture RM3.5 (cross-linked polymer modified PG 64-22) during SCB 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.01.02.03.04.05.06.07.08.09.0stress (MPa)strain (x1000)SCB -Mix RM5.0 Horizontal stress -strain Strain gauge Digital image correlation Fracture point Figure 6-10. Experimental and mean image corre lation horizontal stre ss-strain response for mixture RM5.0 (cross-kinked polymer modified PG 70-22) during SCB

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111 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.01.02.03.04.05.06.07.08.09.0stress (MPa)strain ( x1000 ) SCB -Mix LM3.5 Horizontal stress -strain Strain gauge Digital image correlation Fracture point Figure 6-11. Experimental and mean image corre lation horizontal stre ss-strain response for mixture LM3.5 (linear polymer modified PG 70-22) during SCB 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.01.02.03.04.05.06.07.08.09.0stress (MPa)strain (x1000)SCB -MIX LM6.5 Horizontal stress -strain Strain gauge Digital image correlation Fracture point Figure 6-12. Experimental and mean image corre lation horizontal stre ss-strain response for mixture LM6.5 (linear polymer modified PG 76-22) during SCB

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112 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.01.02.03.04.05.06.07.08.09.0stress (Mpa)strain (x1000)BEAM -MIX N1 Horizontal stress -strain Strain gauge Digital image correlation Fracture point Figure 6-13. Experimental and mean image corre lation horizontal stre ss-strain response for mixture N1 (virgin; PG 64-22) during 3PB 0 0.5 1 1.5 2 2.5 3 3.5 0.01.02.03.04.05.06.07.08.09.0stress (MPa)strain (x1000)BEAM -MIX N2 Horizontal stress -strain Strain gauge Digital image correlation Fracture point Figure 6-14. Experimental and mean image corre lation horizontal stre ss-strain response for mixture N2 (virgin; PG 58-22) during 3PB

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113 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.01.02.03.04.05.06.07.08.09.0stress (MPa)strain (x1000)BEAM -MIX RM3.5 Horizontal stress -strain Strain gauge Digital image correlation Fracture point Figure 6-15. Experimental and mean image corre lation horizontal stre ss-strain response for mixture RM3.5 (cross-linked polymer modified PG 64-22) during 3PB 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 0.01.02.03.04.05.06.07.08.09.0stress (MPa)strain (x1000)BEAM -MIX RM5.0 Horizontal stress -strain Strain gauge Digital image correlation Fracture point Figure 6-16. Experimental and mean image corre lation horizontal stre ss-strain response for mixture RM5.0 (cross-kinked polymer modified PG 70-22) during 3PB

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114 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.01.02.03.04.05.06.07.08.09.0stress (MPa)strain (x1000)BEAM -MIX LM3.5 Horizontal stress -strain Strain gauge Digital image correlation Fracture point Figure 6-17. Experimental and mean image corre lation horizontal stre ss-strain response for mixture LM3.5 (linear polymer modified PG 70-22) during SCB 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.01.02.03.04.05.06.07.08.09.0stress (MPa)strain (x1000)BEAM -MIX LM6.5 Horizontal stress -strain Strain gauge Digital image correlation Fracture point Figure 6-18. Experimental and mean image co rrelation horizontal stress-strain response for mixture LM6.5 (linear polymer mo dified PG 76-22) during 3PB

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115 independently of mode of loading and test sp ecimen geometry, and independently of polymer modification. Table 6-1. Comparison between experimental a nd image correlation (as mean values) tensile strength and fracture energy values Tensile strength from Fr acture energy density from Strain gauge acquisition of first fracture (MPa) Image correlation acquisition of first fracture (MPa) Strain gauge acquisition of first fracture (kJ/m3 ) Image correlation acquisition of first fracture (kJ/m3 ) Mix N1: IDT SCB 3PB 2.84 2.83 2.86 2.84 2.81 2.86 1.99 2.00 2.04 1.93 1.96 2.03 Mix N2: IDT SCB 3PB 2.49 2.54 2.46 2.41 2.54 2.47 3.80 3.67 3.72 3.80 3.72 3.78 Mix RM3.5: IDT SCB 3PB 2.93 2.90 2.95 2.94 2.90 2.92 5.20 5.21 5.26 5.25 5.25 5.32 Mix RM5.0: IDT SCB 3PB 2.90 2.95 2.95 2.90 2.96 2.98 6.30 6.31 6.34 6.35 6.35 6.48 Mix LM3.5: IDT SCB 3PB 3.08 3.08 3.14 3.08 3.02 3.14 5.70 5.76 5.71 5.80 5.70 5.73 Mix LM6.5: IDT SCB 3PB 3.03 3.03 3.04 3.02 3.04 3.03 7.30 7.29 7.31 7.34 7.26 7.30 Comparisons between “pinpoint” and average te nsile stress-strain responses obtained from the three tests for all the mixtures are shown in Figures from 6-19 to 6-36. Respective tensile strengths and fracture energy dens ities are listed in Table 6-2.

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116 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.01.02.03.04.05.06.07.08.09.0stress (Mpa)strain (x1000)IDT -MIX N1 Horizontal stress -strain Strain gauge DIC pointwise analysis Strain gauge Fracture Point DIC Fracture Point Figure 6-19. Experimental and pinpoint DIC horiz ontal stress-strain response for mixture N1 (virgin; PG 64-22) during IDT 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.01.02.03.04.05.06.07.08.09.0stress (Mpa)strain (x1000)IDT -MIX N2 Horizontal stress-strain Strain gauge DIC pointwise analysis Strain gauge fracture point DIC Fracture Point Figure 6-20. Experimental and pinpoint DIC horiz ontal stress-strain response for mixture N2 (virgin; PG 58-22) during IDT

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117 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.01.02.03.04.05.06.07.08.09.0stress (Mpa)strain (x1000)IDT -MIX RM3.5 Horizontal stress -strain Strain gauge DIC pointwise analysis Strain gauge Fracture Point DIC Fracture Point Figure 6-21. Experimental and pinpoint DIC hor izontal stress-strain response for mixture RM3.5 (cross-linked polymer modified PG 64-22) during IDT 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.01.02.03.04.05.06.07.08.09.0stress (M pa ) strain (x1000)IDT -MIX RM5.0 Horizontal stress -strain Strain gauge DIC pointwise analysis Strain Gauge Fracture Point DIC Fracture Point Figure 6-22. Experimental and pinpoint DIC hor izontal stress-strain response for mixture RM5.0 (cross-kinked polymer m odified PG 70-22) during IDT

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118 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.01.02.03.04.05.06.07.08.09.0stress (Mpa)strain (x1000)IDT -MIX LM3.5 Horizontal stress -strain Strain gauge DIC pointwise analysis Strain gauge Fracture Point DIC Fracture Point Figure 6-23. Experimental and pinpoint DIC st ress-strain response for mixture LM3.5 (linear polymer modified PG 70-22) during IDT 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.01.02.03.04.05.06.07.08.09.0stress (MPa)strain (x1000)IDT -MIX LM6.5 Horizontal stress-strain Strain gauge DIC pointwise analysis Strain gauge Fracture Point DIC Fracture Point Figure 6-24. Experimental and pinpoint DIC hor izontal stress-strain response for mixture LM6.5 (linear polymer modified PG 76-22) during IDT

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119 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.01.02.03.04.05.06.0stress (MPa)strain (x1000)SCB -MIX N1 Horizontal stress -strain Strain gauge DIC pointwise analysis Strain gauge fracture point DIC fracture point Figure 6-25. Experimental and pinpoint DIC horiz ontal stress-strain response for mixture N1 (virgin; PG 64-22) during SCB 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.01.02.03.04.05.06.07.08.09.0stress (MPa)strain (x1000)SCB -MIX N2 Horizontal stress -strain Strain gauge DIC pointwise analysis Strain gauge fracture point DIC fracture point Figure 6-26. Experimental and pinpoint DIC horiz ontal stress-strain response for mixture N2 (virgin; PG 58-22) during SCB

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120 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.01.02.03.04.05.06.07.08.09.0stress (MPa)strain (x1000)SCB -MIX RM3.5 Horizontal stress -strain Strain gauge DIC pointwise analysis Strain gauge fracture point DIC fracture point Figure 6-27. Experimental and pinpoint DIC hor izontal stress-strain response for mixture RM3.5 (cross-linked polymer modified PG 64-22) during SCB 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.01.02.03.04.05.06.07.08.0stress (MPa)strain (x1000)SCB -MIX RM5.0 Horizontal stress -strain Strain gauge DIC pointwise analysis Strain gauge fracture point DIC Fracture Point Figure 6-28. Experimental and pinpoint DIC hor izontal stress-strain response for mixture RM5.0 (cross-kinked polymer m odified PG 70-22) during SCB

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121 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.01.02.03.04.05.06.07.08.09.0stress (MPa)strain (x1000)SCB -MIX LM3.5 Horizontal stress -strain Strain gauge DIC pointwise analysis Strain gauge fracture point DIC fracture point Figure 6-29. Experimental and pinpoint DIC hor izontal stress-strain response for mixture LM3.5 (linear polymer modified PG 70-22) during SCB 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.01.02.03.04.05.06.07.08.09.0stress (MPa)strain (x1000) SC B -M i x LM6.5 Horizontal stress-strain Strain gauge DIC pointwise analysis Strain gauge fracture point DIC fracture point Figure 6-30. Experimental and pinpoint DIC hor izontal stress-strain response for mixture LM6.5 (linear polymer modified PG 76-22) during SCB

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122 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.01.02.03.04.05.06.07.08.09.0stress (MPa)strain (x 1000)BEAM -MIX N1 Horizontal stress -strain Strain gauge DIC pointwise analysis Strain gauge fracture point DIC fracture point Figure 6-31. Experimental and pinpoint DIC horiz ontal stress-strain response for mixture N1 (virgin; PG 64-22) during 3PB 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.01.02.03.04.05.06.07.08.09.0stress (MPa)strain (x1000)BE A M -MIX N 2 Horizontal stress-strain Strain gauge DIC pointwise analysis Strain gauge fracture point DIC fracture point Figure 6-32. Experimental and pinpoint DIC horiz ontal stress-strain response for mixture N2 (virgin; PG 58-22) during 3PB

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123 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.01.02.03.04.05.06.07.08.09.0stress (MPa)strain (x1000)Beam -MIX RM3.5 Horizontal stress-strain Strain gauge DIC pointwise analysis Strain gauge fracture point DIC fracture point Figure 6-33. Experimental and pinpoint DIC hor izontal stress-strain response for mixture RM3.5 (cross-linked polymer modified PG 64-22) during 3PB 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.01.02.03.04.05.06.07.08.09.0stress (MPa)strain (x1000)Beam -MIX RM5.0 Horizontal stress-strain Strain gauge DIC pointwise analysis Strain gauge fracture point DIC fracture point Figure 6-34. Experimental and pinpoint DIC hor izontal stress-strain response for mixture RM5.0 (cross-kinked polymer modified PG 70-22) during 3PB

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124 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.01.02.03.04.05.06.07.08.09.0stress (MPa)strain (x1000)BEAM -MIX LM3.5 Horizontal stress -strain Strain gauge DIC pointwise analysis Strain gauge Fracture point DIC Fracture point Figure 6-35. Experimental and pinpoint DIC hor izontal stress-strain response for mixture LM3.5 (linear polymer modified PG 70-22) during 3PB 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.01.02.03.04.05.06.07.08.09.0stress (MPa)strain (x1000)BEAM -MIX LM6.5 Horizontal stress-strain Strain gauge DIC pointwise analysis Strain gauge fracture point DIC fracture point Figure 6-36. Experimental and pinpoint DIC co rrelation horizontal stress-strain response for mixture LM6.5 (linear polymer mo dified PG 76-22) during 3PB

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125 Table 6-2. Comparison between experimental a nd pinpoint tensile failure limits of the six mixtures Tensile strength from Fr acture energy density from Strain gauge (mean value) (MPa) DIC (pinpoint value) (MPa) Strain gauge (mean value) (kJ/m3 ) DIC (pinpoint value) (kJ/m3 ) Mix N1: IDT SCB 3PB 2.84 2.83 2.86 2.84 2.81 2.86 1.99 2.00 2.04 2.41 2.42 2.37 Mix N2: IDT SCB 3PB 2.49 2.54 2.46 2.41 2.54 2.47 3.80 3.67 3.72 4.61 4.70 4.77 Mix RM3.5: IDT SCB 3PB 2.93 2.90 2.95 2.94 2.90 2.92 5.20 5.21 5.26 6.04 6.11 6.08 Mix RM5.0: IDT SCB 3PB 2.90 2.95 2.95 2.90 2.96 2.98 6.30 6.31 6.34 7.66 7.72 7.67 Mix LM3.5: IDT SCB 3PB 3.08 3.08 3.14 3.08 3.02 3.14 5.70 5.76 5.71 6.87 6.81 6.81 Mix LM6.5: IDT SCB 3PB 3.03 3.03 3.04 3.02 3.04 3.03 7.30 7.29 7.31 8.76 8.86 8.83 “Pinpoint” tensile strengths do not differ significantly from those obtained with experimental analysis; conversely, fracture energy densities obtained at the specific point in which a crack has initiated are always about 20% higher than those eval uated along the strain gauge area. This means that tensile strains valu es obtained as average va lues along a finite area might be not totally representativ e of localized strains at impe ding fracture. Rather, it may be

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126 more appropriate to perform a point-wise analysis of localized strains at the point of impending fracture. Unfortunately, the eff ect of stress concentration due to the impending fracture would require the introduction of a dama ge or fracture model, thus fu rther complicating the analysis. Displacement Discontinuity Predictions Comparisons between predicted and measured horizontal stress-strain curves of the six mixtures for IDT, SCB, 3PB are shown in Figur es from 6-37 to 6-54. The resulting numerical simulations match the horizontal tensile stress-stra in curves up to the ultimate load. The results clearly show that there is signi ficant damage prior reaching the p eak of the stress-strain curves for all the tests. The results also show that firs t fracture does occur well prior to peak load. In contrast, the post peak/post-first fracture interpretation is clearly very problematic. This leads to the statement that a fracture and/or damage model for the post peak cracking behavior is required if post fracture data is to be properly interpreted. Comparison between the predicted tensile strengths and fracture energy densities at the fractu re points to the average measured ones for the mixtures are listed in Table 6-3. 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.01.02.03.04.05.06.07.08.09.0stress (MPa)strain (x1000)IDT -MIX N1 Horizontal stress -strain Experimental DDM Fracture Point Figure 6-37. Mixture N1 (IDT) horiz ontal stress-strain response

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127 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.01.02.03.04.05.06.07.08.09.0stress (MPa)strain (x1000)IDT -MIX N2 Horizontal stress -strain Experimental DDM Fracture point Figure 6-38. Mixture N2 (IDT) hor izontal stress-strain response 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.01.02.03.04.05.06.07.08.09.010.0stress (MPa)strain (x1000)IDT -MIX RM3.5 Horizontal stress -strain Experimental DDM Fracture point Figure 6-39. Mixture RM3.5 (IDT) hori zontal stress-strain response

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128 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.01.02.03.04.05.06.07.08.09.010.0stress (MPa)strain (x1000)IDT -MIX RM5.0 Horizontal stress -strain Experimental DDM Fracture point Figure 6-40. Mixture RM5.0 (IDT) ho rizontal stress-strain response 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.01.02.03.04.05.06.07.08.09.0stress (MPa)strain (x1000)IDT -MIX LM3.5 Horizontal stress -strain Experimental DDM Fracture point Figure 6-41. Mixture LM3.5 (IDT) ho rizontal stress-strain response

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129 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.01.02.03.04.05.06.07.08.09.0stress (MPa)strain (x1000)IDT-Mix LM6.5 Horizontal stress -strain Experimental DDM Fracture point Figure 6-42. Mixture LM6.5 (IDT) ho rizontal stress-strain response 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.01.02.03.04.05.06.07.08.09.0stress (MPa)strain (x1000)SCB -MIX N1 Horizontal stress-strain Experimental DDM Fracture Point Figure 6-43. Mixture N1 (SCB) hor izontal stress-strain response

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130 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.01.02.03.04.05.06.07.08.09.0stress(MPa)strain (x1000)SCB -MIX N2 Horizontal stress -strain Experimental DDM Fracture point Figure 6-44. Mixture N2 (SCB) hor izontal stress-strain response 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.01.02.03.04.05.06.07.08.09.0stress ( MPa ) strain (x1000)SCB -MIX RM3.5 Horizontal stress -strain Experimental DDM Fracture point Figure 6-45. Mixture RM3.5 (SCB) horizontal stress-strain response

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131 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.01.02.03.04.05.06.07.08.09.0stress (MPa)strain (x1000)SCB -MIX RM5.0 Horizontal stress -strain Experimental DDM Fracture point Figure 6-46. Mixture RM5.0 (SCB) hor izontal stress-strain response 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.01.02.03.04.05.06.07.08.09.0stress (MPa)strain (x1000)SCB -MIX LM3.5 Horizontal stress -strain Experimental DDM Fracture point Figure 6-47. Mixture LM3.5 (SCB) hor izontal stress-strain response

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132 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.01.02.03.04.05.06.07.08.09.0stress (MPa)strain (x1000)SCB -Mix LM6.5 Horizontal stress -strain Experimental DDM Fracture point Figure 6-48. Mixture LM6.5 (SCB) hor izontal stress-strain response 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.01.02.03.04.05.06.07.08.09.0stress (MPa)strain (x1000)BEAM -MIX N1 Horizontal stress -strain Experimental DDM Fracture Point Figure 6-49. Mixture N1 (3PB) hor izontal stress-strain response

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133 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.01.02.03.04.05.06.07.08.09.0stress (MPa)strain (x1000)BEAM -MIX N2 Horizontal stress -strain Experimental DDM Fracture point Figure 6-50. Mixture N2 (3PB) hor izontal stress-strain response 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.01.02.03.04.05.06.07.08.09.0stress (MPa)strain (x1000)BEAM -MIX RM3.5 Horizontal stress -strain Experimental DDM Fracture point Figure 6-51. Mixture RM3.5 (3PB) horizontal stress-strain response

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134 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.50.01.02.03.04.05.06.07.08.09.0stress (MPa)strain (x1000)BEAM -MIX RM5.0 Horizontal stress -strain Experimental DDM Fracture point Figure 6-52. Mixture RM5.0 (3PB) hor izontal stress-strain response 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00.01.02.03.04.05.06.07.08.09.0stress (MPa)strain (x1000)BEAM -MIX LM3.5 Horizontal stress -strain Experimental DDM Fracture point Figure 6-53. Mixture LM3.5 (3PB) hor izontal stress-strain response

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135 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.01.02.03.04.05.06.07.08.09.0stress (MPa)strain (x1000)BEAM -MIX LM6.5 Horizontal stress -strain Experimental DDM Fracture point Figure 6-54. Mixture LM6.5 (3PB) hor izontal stress-strain response The differences between predicted and measur ed tensile strengths and fracture energy densities at fracture for each mixture in each test are always less than 13.0%. This implies that the method is able to predict the fracture behavi or of asphalt mixtures regardless of the test configuration. Indeed the fact that it is possible to obtain calibr ated input parameters from the Superpave IDT test results and su ccessfully predict the stress-stra in evolution for the Superpave IDT, SCB and 3PB tests, implies that the process represented in the models is capturing a real fracture process. Measured and Simulated Crack Patterns Figures from 6-55 to 6-72 show both simula ted crack patterns and measured full field strain maps for the six mixtures during IDT, S CB and 3PB tests at representative load steps ranging from crack initiation to major crack ope ning. In the IDT test simulation, a huge number of small cracks are clearly visible within the center area of the specimen where high tensile stress is concentrated. As load steps continue, these sm all cracks coalesce into larger and more visible cracks until failure.

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136 Table 6-3. Comparison between predicted and measured tensile failure limits of the six mixtures Tensile strength Fr acture energy density Measured from strain gauge (MPa) Predicted from DD (MPa) Measured from strain gauge (kJ/m3 ) Predicted from DD (kJ/m3 ) Mix N1: IDT SCB 3PB 2.84 2.83 2.86 2.86 2.79 2.75 1.99 2.00 2.04 2.05 1.91 1.92 Mix N2: IDT SCB 3PB 2.49 2.54 2.46 2.33 2.55 2.46 3.80 3.67 3.72 3.68 3.74 3.81 Mix RM3.5: IDT SCB 3PB 2.93 2.90 2.95 2.97 2.86 2.88 5.20 5.21 5.26 5.24 5.14 5.21 Mix RM5.0: IDT SCB 3PB 2.90 2.95 2.95 2.85 3.00 2.98 6.30 6.31 6.34 6.38 6.32 6.43 Mix LM3.5: IDT SCB 3PB 3.08 3.08 3.14 3.06 3.14 3.05 5.70 5.76 5.71 5.65 5.83 5.72 Mix LM6.5: IDT SCB 3PB 3.03 3.03 3.04 3.01 3.05 3.00 7.30 7.29 7.31 7.29 7.12 7.29 In both SCB and 3PB test simulations small cr acks are visible with in the center-bottom area of the specimen, which is the area of hi ghest bending moment. Small cracks can also be noted above the specimen supports. These small cr acks stabilize early not growing into larger, visible cracks. As load steps continue, the cen tral crack growth regi on for both SCB and 3PB region extends along the bottom e dge of the specimen, coalescing into a single larger macro-

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137 IDTMIX N1 (PG58-22) Crack patterns at microcrack initiation Crack patterns at fracture point Crack patterns at peak load Crack pattern at final load step Strains at microcrack initiation Strains at fracture point Strains at peak load Visible experimental cracks Figure 6-55. Mixture N1 (IDT) crack patterns and full field strain maps

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138 IDT – MIX N2 (PG58-22) Crack patterns at microcrack initiation Crack patterns at fracture point Crack patterns at peak load Crack pattern at final load step Strains at microcrack initiation Strains at fracture point Strains at peak load Visible experimental cracks Figure 6-56. Mixture N2 (IDT) crack patterns and full field strain maps

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139 IDT – MIX RM3.5 (PG64-22) Crack patterns at microcrack initiation Crack patterns at fracture point Crack patterns at peak load Crack pattern at final load step Strains at microcrack initiation Strains at fracture point Strains at peak load Visible experimental cracks Figure 6-57. Mixture RM3.5 (IDT) crack pa tterns and full field strain maps

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140 IDT – MIX RM5.0 (PG70-22) Crack patterns at microcrack initiation Crack patterns at fracture point Crack patterns at peak load Crack pattern at final load step Strains at microcrack initiation Strains at fracture point Strains at peak load Visible experimental cracks Figure 6-58. Mixture RM5.0 (IDT) crack pa tterns and full field strain maps

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141 IDT – MIX LM3.5 (PG70-22) Crack patterns at microcrack initiation Crack patterns at fracture point Crack patterns at peak load Crack pattern at final load step Strains at microcrack initiation Strains at fracture point Strains at peak load Visible experimental cracks Figure 6-59. Mixture LM3.5 (IDT) crack pa tterns and full field strain maps

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142 IDT – MIX LM6.5 (PG76-22) Crack patterns at microcrack initiation Crack patterns at fracture point Crack patterns at peak load Crack pattern at final load step Strains at microcrack initiation Strains at fracture point Strains at peak load Visible experimental cracks Figure 6-60. Mixture LM6.5 (IDT) crack pa tterns and full field strain maps

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143 SCB – MIX N1 (PG64-22) Crack patterns at microcrack initiation Crack patterns at fracture point Crack patterns at peak load Crack pattern at final load step Strains at microcrack initiation Strains at fracture point Strains at peak load Visible experimental cracks Figure 6-61. Mixture N1 (SCB) crack pa tterns and full field strain maps

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144 SCB – MIX N2 (PG58-22) Crack patterns at microcrack initiation Crack patterns at fracture point Crack patterns at peak load Crack pattern at final load step Strains at microcrack initiation Strains at fracture point Strains at peak load Visible experimental cracks Figure 6-62. Mixture N2 (SCB) crack patterns and full field strain maps

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145 SCB MIX RM3.5 (PG64-22) Crack patterns at microcrack initiation Crack patterns at fracture point Crack patterns at peak load Crack pattern at final load step Strains at microcrack initiation Strains at fracture point Strains at peak load Visible experimental cracks Figure 6-63. Mixture RM3.5 (SCB) crack pa tterns and full field strain maps

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146 SCB MIX RM5.0 (PG70-22) Crack patterns at microcrack initiation Crack patterns at fracture point Crack patterns at peak load Crack pattern at final load step Strains at microcrack initiation Strains at fracture point Strains at peak load Visible experimental cracks Figure 6-64. Mixture RM5.0 (SCB) crack patterns and full field strain maps

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147 SCB – MIX LM3.5 (PG70-22) Crack patterns at microcrack initiation Crack patterns at fracture point Crack patterns at peak load Crack pattern at final load step Strains at microcrack initiation Strains at fracture point Strains at peak load Visible experimental cracks Figure 6-65. Mixture LM3.5 (SCB) crack pa tterns and full field strain maps

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148 SCB – MIX LM6.5 (PG76-22) Crack patterns at microcrack initiation Crack patterns at fracture point Crack patterns at peak load Crack pattern at final load step Strains at microcrack initiation Strains at fracture point Strains at peak load Visible experimental cracks Figure 6-66. Mixture LM6.5 (SCB) crack pa tterns and full field strain maps

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149 3PB – MIX N1 (PG64-22) Crack patterns at microcrack initiation Crack patterns at fracture point Crack patterns at peak load Crack pattern at final load step Strains at microcrack initiation Strains at fracture point Strains at peak load Visible experimental cracks Figure 6-67. Mixture N1 (3PB) crack patterns and full field strain maps

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150 3PB – MIX N2 (PG58-22) Crack patterns at microcrack initiation Crack patterns at fracture point Crack patterns at peak load Crack pattern at final load step Strains at microcrack initiation Strains at fracture point Strains at peak load Visible experimental cracks Figure 6-68. Mixture N2 (3PB) crack patterns and full field strain maps

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151 3PB – MIX RM3.5 (PG64-22) Crack patterns at microcrack initiation Crack patterns at fracture point Crack patterns at peak load Crack pattern at final load step Strains at microcrack initiation Strains at fracture point Strains at peak load Visible experimental cracks Figure 6-69. Mixture RM3.5 (3PB) crack patterns and full field strain maps

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152 3PB – MIX RM5.0 (PG70-22) Crack patterns at microcrack initiation Crack patterns at fracture point Crack patterns at peak load Crack pattern at final load step Strains at microcrack initiation Strains at fracture point Strains at peak load Visible experimental cracks Figure 6-70. Mixture RM5.0 (3PB) crack pa tterns and full field strain maps

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153 3PB – MIX LM3.5 (PG70-22) Crack patterns at microcrack initiation Crack patterns at fracture point Crack patterns at peak load Crack pattern at final load step Strains at microcrack initiation Strains at fracture point Strains at peak load Visible experimental cracks Figure 6-71. Mixture LM3.5 (3PB) crack pa tterns and full field strain maps

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154 3PB – MIX LM6.5 (PG76-22) Crack patterns at microcrack initiation Crack patterns at fracture point Crack patterns at peak load Crack pattern at final load step Strains at microcrack initiation Strains at fracture point Strains at peak load Visible experimental cracks Figure 6-72. Mixture LM6.5 (3PB) crack patterns and full field strain maps crack along the vertical plane. Me asured strain maps agree well w ith the numerical results; high strain values develop within the whole center area of the IDT specimen, while in both SCB and 3PB specimens, the highest strain results only in a restricted zone located at the bottom edge of the specimens. From full field strain maps it can be observed how tens ile strains are greatly localized in the area in which a crack initiates. The full field strain maps also allows for the observation of tensile strain development around aggregates, while no strains are registered where a coarse aggregate exists.

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155 Effect of SBS Modifiers on HMA Cracking Resistance The effect of SBS modifiers on HMA cracki ng resistance was evaluated using the five polymer modified mixtures composed by the same ba se binder N2 to assure that the presence of the SBS modifier was the only f actor affecting the results. Ac cording to the “HMA Fracture Mechanics,” mixture’s cracking performance can be estimated using the following tensile asphalt mixture properties: € Resilient Modulus (MR) € Creep compliance power law parameters (D1 and m-value) € Tensile Strength (St) € Dissipated creep strain energy to failure (DCSEf) € Fracture energy (FE) € Energy Ratio (ER) These properties were easily determined from the Superpave IDT test as discussed by Roque et al. (2002). A summary of Superpave IDT test results and a detailed analysis of each mixture property is presented. The relationship between mixture propertie s and mixture cracking performance is also described. All the results ob tained from the Superpave IDT test are listed in Table 6-4. Table 6-4. Superpave IDT test results of the five mixtures Asphalt Mixture N2 RM3.5 RM5.0 LM3.5 LM6.5 Resilient modulus (Gpa) 13.35 13.11 12.54 13.34 12.43 Creep compliance @1000 seconds (1/Gpa) 4.23 2.07 1.85 2.13 1.59 m-value 0.55 0.46 0.45 0.51 0.39 D1 6.309E-07 5.687E-07 5.584E-07 4.203E-07 7.205E-07 Tensile strength (Mpa) 2.49 2.93 2.90 3.08 3.03 Failure strain (10-6) 2061.3 2336.1 2804.4 2450.1 3176.2 DCSEf (kJ/m3) 3.57 4.87 5.96 5.34 6.93 DCSEmin (kJ/m3) 2.33 1.32 1.77 1.32 1.02 Fracture energy (kJ/m3) 3.80 5.20 6.30 5.70 7.30 Energy ratio 1.53 3.69 5.07 4.03 6.76

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156 Resilient Modulus The resilient modulus is defined as the ratio of the applied stress to the recoverable strain when repeated loads are applied, resulting in a measure of the material ’s elastic stiffness. Looking at the results listed in Ta ble 6-4, it’s clearly evident that either cross-linked and linear SBS polymer modifiers have very little effect on resilient modulus. It can be observed that the higher the percent of polymer modification, the lo wer is the resilient modulus value. However, this difference has shown to be insignificant with respect to the unmodified mixture. The results indicate that, at small strain a nd/or short loading times, the amount and the type of SBS modifier do not affect the mixture’s elastic response. Creep Compliance Creep compliance is a function of time-depende nt strain over stress; it is related to the ability of a mixture to relax stresses. The creep compliance curve represents the time-dependent behavior of asphalt mixture. Work by Kim et al (2003) has shown that viscous or creep response can be used to evaluate the rate of damage accumulation of asphalt mixtures. Three mixture parameters can be obtained from creep compliance tests: D0, D1, and m-value. D0 and D1 are more descriptive of the initial portion of the creep compliance curve, while m-value describes the longer-term portion of th e same curve. The m-value has proved to be related to the rate of damage accumulation and the fracture resistance of asphalt mixtures (Kim et al., 2003). An asphalt mixture with a low m-value generally exhibits a low rate of damage accumulation. According to the HMA Fracture Mechanics fr amework, the slope of the creep compliance curve at 1000 seconds is essentially a measure of the rate of permanent deformation: the higher the slope, the higher the rate of permanent deformation (Zhang et al., 2001). The crack growth process is exhibited by higher rates of permanent de formation, thus mixtures with high m-values or high creep rates exhibit high er crack growth rates. Creep compliance curves are shown in

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157 Figure 6-73. The curve trend is clearly affected by the type and the amount of SBS modifier. The results show that both cross-linked and linea r SBS polymers strongly decrease the rate of permanent deformation leading to lower rate of micro-damage accumulation. Also, the higher is the amount of polymer in the asphalt binder, the lower is the mixture creep compliance. However, it should be noted that the cross-linke d SBS asphalt modifier exhibits a lower creep rate than the linear one within the soft modified mixtures. In contrast, at higher percentages of modifiers, linear polymer seems to incr ease mixture’s creep-related performance. 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 020040060080010001200Compliance, D(t) (1/Gpa)Time (sec) MIX N2 (unmodified) MIX RM3.5 (3.5% cross-linked polymer) MIX LM3.5 (3.5% linear polymer) MIX RM5.0 (5% cross-linked polymer) MIX LM6.5 (6.5% linear polymer) Figure 6-73. Creep compliance cu rves for the five mixtures Indirect Tensile Strength and Energy-Based Parameters As shown in Figure 6-74, the te nsile strength is slightly improved by SBS polymer modification while not affected by the am ount of polymer in the binder. This improvement is a modest 17% for cross-linked polymer modification a nd 24% for linear polymer modification. Conversely, the dissipated creep strain energy to failure and fracture energy are strongly enhanced by polymer modifications (Figure 6-75), as well as failu re strain (Figure 6-76). This

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158 means that both cross-linked and linear SBS polym ers have the ability of increasing both the upper and the lower energy thresholds required to crack the mixture. Besides, linear polymers provide greater benefits in cracking resistance than the cross-linked ones. N2 2.49 RM3.5 2.93 LM3.5 3.08 RM5.0 2.90 LM6.5 3.030.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5Tensile StrengthMPa Figure 6-74. Tensile strengths obt ained for the five mixtures N2 3.57 N2 3.80 RM3.5 4.87 RM3.5 5.20 LM3.5 5.34 LM3.5 5.70 RM5.0 5.96 RM5.0 6.30 LM6.5 6.93 LM6.5 7.300 1 2 3 4 5 6 7 8DCSEf Fracture EnergykJ/m3 Figure 6-75. Fracture energy densitie s and dissipated creep strain en ergies for the five mixtures

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159 N2 2061.30 RM3.5 2336.10 LM3.5 2450.12 RM5.0 2804.36 LM6.5 3176.160 500 1000 1500 2000 2500 3000 3500Failure Strainmicro strain Figure 6-76. Failure strains for the five mixtures Energy Ratio The Energy Ratio (ER) is a dimensionless pa rameter which defines a single criterion for top-down cracking performance of mixtures in pavement structures. The Energy Ratio is defined as follows: (6-1) where DCSEf is the dissipated creep strain ener gy threshold of the mixture and DCSEmin is the minimum dissipated creep strain energy require d (function of the creep compliance power low parameters). Further details ar e discussed by Roque et al. (2004). According to the performance-based mixtur e specification developed by Roque et al. (2004), for a mixture to be acceptable, the ER sh ould be greater than a certain value depending on the traffic volume, as detailed in Table 6-5. Figure 6-77 shows the Energy Ratio values obtained for the five mixtures. The results highl ight that the addition of SBS polymer strongly improves asphalt mixture’s resistance to top-dow n cracking. Even in this case, the SBS linear

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160 polymer modifier provides more benefits than the SBS cross-linked one especially for hard modified mixtures. Table 6-5. Energy-based mixt ure specification criteria Traffic ESALS/year 1000 Minimum Energy Ratio < 250 1 < 500 1.3 < 1000 1.95 N 1.53 RM3.5 3.69 LM3.5 4.03 RM5.0 5.07 LM6.5 6.760 1 2 3 4 5 6 7 8Energy Ratio Figure 6-77. Energy ratio values obtained for the five mixtures Crack Localization and Crack Growth The previously shown figures (from 6-55 to 6-72), showing measur ed full field tensile strain maps for the five mixes, emphasize how te nsile strains are greatly localized in the area in which a crack initiates. SBS polymer modified mixtures exhibit high strains only up to the location of impending fracture, while unmodified mi xtures exhibit highly distributed damage in both the critical area and around the point of fracture. This is possibly attri butable to the polymer network established within the m odified binders. Indeed, it is po ssible that a continuous polymer

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161 network may form throughout the asphalt binder ac ting to distribute loads to some degree throughout the matrix, thus minimizing local areas of excessive damage. However, eventually a polymer modified mixture will reac h its fracture limit, at which localized damage may lead to a macro-crack with any further loading.

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162 CHAPTER 7 SUMMARY AND CONCLUSIONS The purpose of this research program was to provide an insight into key mechanisms and asphalt mixture properties that c ontrol fracture in asphalt materials. A Digital Image Correlation (DIC) System was developed for the purpose of accurately capturing localized or non-uniform stress distributions in aspha lt mixtures and as a tool fo r detecting first fracture. The DIC system was tested and shown to overcome the shortcomings of traditional onspecimen strain measurement devices, such as st rain gauges. The major advantages of the new DIC method may be summarized as follows: € It achieves satisfactory accuracy compared to strain gauges which is important for the investigation of fracture in HMA. € It provides full field displacement analysis a nd full field compressive/tensile/shear strain analysis, thus not requiring the user to attempt to determine the location of crack initiation prior to the test or to mount multip le sensors on the specimen surface. € It provides point-wise analys is, allowing for the exact dete rmination of the location of crack initiation, and also for the calculation of strain valu es at the instant of crack initiation. € It is a non contact measurement tool, thus fu rther minimizing potential errors associated with on-specimen measurements. The experimental analysis of asphalt mixtur e cracking behavior was based on the “HMA Fracture Mechanics” visco-elastic crack growth law recently developed at the University of Florida (Zhang et al. 2001; Roque et al.; 2002). Investigation of the asphalt cracking mechanism and identification of fundamental tensile fail ure limits were achieved by performing multiple laboratory test configurations, namely the Supe rpave Indirect Tensile test (IDT), the SemiCircular Bending test (SCB) and the Three-Point Bending Beam test (3PB). First fracture and crack growth in asphalt mixtures were predic ted using a Displacement Discontinuity (DD) boundary element method. Finally, the effect of polymer modification on crack localization,

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163 cracking patterns and damage di stribution were investigated th rough the use of horizontal fullfield strain maps obtained from the DIC. Summary of Findings The major findings of this study may be summarized as follows : € Using rigorous interpretation of test conditions and appropriate DIC analysis techniques for identification of first fracture, the same fracture energy density a nd tensile strength at fracture were obtained from the Superpave Indi rect test (IDT), the Semi-Circular Bending test (SCB), and the Three-Point Bending Beam test (3PB) for both unmodified and polymer modified mixtures. € Fracture energy densities resulting from the stress-strain response evaluated around the point of impeding fracture were 20% higher than those evaluated as a mean value along the strain gauge area. Conversely, the corres ponding tensile strengths were found to not significantly differ. This means that tensile st rains values obtained as average values along a finite area might not be totally representativ e of localized strains at impeding fracture. € First fracture was shown to occur prior to p eak load for each test configuration, meaning that post-first fracture behavior is at the present not easily interpretable, due to the highly localizing effects of crac ks in the specimen. € Using a Displacement Discontinuity (DD) boundary element method it was possible to successfully predict the stress-strain evoluti on for the Superpave IDT, SCB and 3PB tests, obtaining calibrated input parameters fr om the Superpave IDT test results. € Polymer modification at intermediate temperatur es does not have a significant effect on the resilient modulus, but during te nsile creep testing, the rate of creep was significantly less implying less micro-damage accumulation. Po lymer modification has also proven to improve tensile failure limits of mixtures slightly increasing tensile strength and enhancing both dissipated creep energy to failu re and fracture energy density. It was also found that SBS polymer modified mixtures exhibit a higher energy ratio than the unmodified one, implying a better top-down cracking performance. € Polymer modified mixtures exhibited high strains only up to the point of impending fracture, while unmodified mixtur es exhibit highly distributed damage in both the critical area and around the point of fracture.

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164 Conclusions Based on the above findings, the fo llowing conclusions were achieved : € HMA tensile failure limits at first fracture ar e independent of the specimen geometry and test configuration. These limits are also sens itive to both presence and level of polymer modification. € Significant damage, stress redist ribution and other changes fo llowing initial fracture make the analysis at peak load difficult to inte rpret meaningfully. The effect of stress concentration due to impending fracture woul d require the introduction of a post-first fracture damage model. € The Displacement Discontinuity (DD) method can be used to predict fracture process of mixtures for various different boundary conditio n problems, and not just for the calibrated laboratory test conditions. € SBS polymer modifiers improve the cracking resistance of asphalt mixtures by reducing the tensile creep rate and in creasing the fracture energy and dissipated creep strain energy thresholds of the modified mixtur es over the unmodified mixture. € It is possible that a conti nuous polymer network may form throughout the asphalt binder acting to distribute loads to some degree throughout the matrix, thus minimizing local areas of excessive damage. However, eventually a polymer modified mi xture will reach its fracture limit, at which localized damage ma y lead to a macro-crack with any further loading.

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165 APPENDIX A STANDARD SUPERPAVE IDT From the evaluation of the SHRP Indirect Tens ile testing system developed by Roque et al. (1997), it was shown that SHRP IDT can provi de reasonable and accurate asphalt mixture properties at in-service temper ature where cracking is generally presumed to occur. These mixture properties (which include resilient modul us, creep compliance, m-value, failure strain, tensile strength and fracture energy), are directly and/or indirectly re lated to their cracking response. The procedures for specimen prepara tion before testing are as follows: € The specimens compacted are cut parallel to th e top and bottom faces using a water-cooled masonry saw to produce 25/50 mm thick speci mens having smooth and parallel faces. € Four brass gage points are affixed with epoxy to each trimme d smooth face of the specimen. € Test samples are stored in a humidity chamber at a constant relative humidity of 60 percent for at least 2 days. Specimens are then cooled at the test temperature for at least 3hours before testing. € Extensometers are mounted and centered on th e specimen to the gage points for the measurement of the horizontal a nd vertical deformations. Resilient Modulus The Resilient Modulus is defined as the ratio of the applied stress to the recoverable strain when repeated loads are applied. The Resilient M odulus test is performed in load control mode by applying a repeated haversine waveform load to the specimen for a 0.1 second followed by a rest period of 0.9 seconds. The load is selected to keep the horizontal strain in the linear viscoelastic range, in which horiz ontal strain is typical ly 150 to 350 micro-strain. A constant preloading of approximately 45 N is applied to the te st specimen to ensure proper contact with the loading heads before test loads are applied. If the horizontal strains ar e higher than 350 micronstrains, the load is immediately removed from the specimen, and specimen is allowed to recover

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166 for a minimum 3 minutes before re loading at different loading level. When the applied load is determined, data acquisition program begins reco rding data. Data are acq uired at a rate of 150 points per seconds. The Resilent Modulus and Poisson’s Ratio are calculated by the following equations, which were developed based on three dimensiona l finite element analysis conducted by Roque and Buttlar (1992). The equations ar e involved in the Superpave I ndirect Tensile test at low temperatures (ITLT) program, which wa s developed by Roque et al. (1997): (A-1) (A-2) where MR = Resilient Modulus, P = maximum load, GL = gauge length, H = horizontal deformation, t, D = thickness, diameter, Ccmpl = 0.6354 x (X/Y)-1-0.323, = Poisson’s Ratio, (X/Y) = ratio of horizontal to vertical deformation. Creep Test Creep compliance is a function of time-depende nt strain over stress. The creep compliance curve was originally developed to predict thermally induced stress in asphalt pavement. However, since it represents the time-dependent behavior of asphalt mixture, it can be used to evaluate the rate of damage accumulation of asph alt mixture. From creep compliance test, three different parameters, shown in Figure A-1, can be calculated: D0, D1, and m-value.

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167 Time(t) D0D(t) D0+D1D(t)=D0+D1tm1 Log (time) Log D0Log D(t) Log (D0+D1) Log D(t) = Log D1+m*Log(t) 0 m Figure A-1. Power model of the creep compliance Although D1 and m-value are related to each other, D1 is more related to the initial portion of the creep compliance curve, while m-value is more related to the longer-term portion of the creep compliance curve. The m-value has been kn own to be related to the rate of damage accumulation and the fracture resistance of aspha lt mixtures. In other words, the lower the mvalue, the lower the lower the rate of damage accumulation. However, mixtures with higher mvalue typically have higher DCSE limits. The creep compliance is a time dependant strain (t) divided by the applied stress (t). According to the analysis conducted by Roque et al. (1997), MR is higher than creep compliance stiffness at 1 second. The test is conducted in a load control mode by applying a static load selected to keep the horizontal strain in the linear viscoelastic ra nge, which is below an horizontal strain of 500 micro-strain. The load is then held for 1000 seconds. If the horiz ontal strains are not between 150 and 200 micro-strain at 30 seconds, the load is immediately removed from the specimen, and specimen is allowed to recover for a minimum 3 mi nutes before reloading at a different level. When the applied load is determined, the da ta acquisition program records the loads and deflections at a rate of 10 Hz for the first 10 s econds, 1 Hz for the next 290 seconds, and 0.2 Hz for the remaining 700 seconds of the creep test. Creep compliance is computed by the following equation:

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168 (A-3) where D(t) = creep compliance at time t, P = maximum load, GL = gauge length, H = horizontal deformation, t, D = thickness, diameter, Ccmpl = 0.6354 x (X/Y)-1-0.323, = Poisson’s Ratio, (X/Y) = ratio of horizontal to vertical deformation. Strength Test The strength test is conducted in a displacem ent control mode by applying a constant rate of displacement of 50mm/min until the specimen fails. The horizontal and vertical deformation, and the applied load are recorded at the rate of 20Hz during the test. The maximum tensile strength is calculated as the following equation: (A-4) where St = maximum indirect tensile strength, P = failure load at first fracture, Csx = 0.984-0.01114 x (t/d) – 0.2693 x + 1.436 x (t/D) x t, D = thickness, diameter, = Poisson’s Ratio. From the strength test and the resilient modul us test, fracture ener gy and dissipated creep strain energy can be determine. Fracture energy is a total energy applied to the specimen until the specimen fractures. Dissipated creep strain energy (DCSE) is the absorbed energy that damages the specimen, and dissipated creep strain energy to failure (DCSEf) is the absorbed energy to fracture. The fracture point in the IDT specime n is determined by plotting the deformation differential (Vcorrected Hcorrected) during the numerical simulation, and visually observing the point at which the deformation differential st arts to deviate from a smooth curve.

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169 As shown in Figure A-2, fracture energy and DCSEf can be determined as follows: (A-5) (A-6) (A-7) (A-8) where St = tensile strength, f = failure strain. MR Stress, Strain Dissipated Creep Strain Energy(DCSE) xStf (fracture)FIRST FRACTURE Elastic Energy(EE)0 Figure A-2. Determination of fracture energy an d dissipated creep strain energy to failure

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170 APPENDIX B DISPLACEMENT DISCONTINUITY PRE/POST PROCESSOR The DD method is a graphic user interface wh ich operates under window environment. It can read and write codes to the files associated with DIGS (Discontinuity Interaction and Growth Simulation) and DVT (Delaunay Vo ronoi Tessellation Generator). Three file types (*.IN,* ._SG and *.DAT) are involved with PRE processor and other three file types (*.OUT, *.REQ and *.RPT) are involved with POST processor. DIGS is a two-dimensional (plane strain) stress analysis computer code that can be used to solve crack, fault and tabular stope interaction an d intersection problems. The code is based on the displacement discontinuity boundary element method and employs linear-variation shape functions in the element. DVT is a mesh gene rator for Delaunay and Voronoi tessellation. The result of meshing can be used to simulate granular structure of the desired material. Input file (*.IN) contains information of meshing parameters and boundary definition of the regions to be meshed. The IN file is used with the DVT to generate two segment files (*._SG): Delaunay (*.DSG) and Voronoi with inte rnal fracture path (*.VSG). Segment file contains definitions of ‘Line’ segments that desc ribe geometry of the problem to be solved. User can use PRE processor to open thes e two segment files, edit segm ent definitions and save them to other segment file names (*._SG) for later use. Data file (*.DAT) contains essential in formation (background material properties, primitive stress fields, boundary conditions, load step, segment file name and request output report) to run boundary elemen t analysis with DIGS. Output file (*.OUT) contains the results fr om boundary element analysis. POST processor can open this file to view the result graphicall y. Users can also request specific output variables

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171 at desired load steps by writing co mmand codes in the request file (*.REQ) and reporting them to the report file (*.RPT). Coordinate Systems The DDM assumes that all discontinuity positio ns are defined with respect to a global Y-Z coordinate system as depicted in Figure B-1. The X-axis is assumed to point into the plane of the diagram and all displacements in the X-direction ar e assumed to be zero (i.e., plane strain with respect to the Y-Z plane). Z Y y z c1 c2 + x x Figure B-1. Global (Y-Z) and local (y-z) coordinate systems used by DD Each defined element is flat and has a local y-z coordinate system as shown in Figure B-1. The ends of the element are marked “o” and discontinuity values are computed at two collocation points (c1 and c2) within the element, marked “x”. The local element axis system implies an orientation of the element with the po sitive (+) side in the positive z direction and the negative (-) side in the opposite direction. No con tinuity conditions on the discontinuity slip or opening values are enforced betwee n adjoining elements. It is impor tant that elements should not be defined to intersect one another but may be defined to be connected at their end points.

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172 Text Files Associated with PRE/POST Processor There are total 6 files (*.IN, *._SG, *.DAT *.OUT, *.REQ and *.RPT) associated with PRE/POST Processor. The IN file is an input text file containi ng computer codes for the program DVT to generate two tessellations: Delaunay a nd Voronoi with internal fracture path. The computer codes are written in fixed field format. That mean users have to write the codes within a specific range of columns. The structure of IN f ile consists of 3 coding blocks as following: € Random point generation € Seed triangle for creating tessellation € Boundary definitions The segment file is a text file containing defini tion of segments that describe geometry of the problem. The DVT uses the IN file to generate two segment files named Dealuanay tessellation file (*.DSG) and Vor onoi with internal fracture path tessellation file (*.VSG). The computer codes of these two file s are written in fixed field format. The structure of the segment file consists of several lines of segment definitions. The DAT file is a text file that contains command codes describing background material, primitive stress fields, boundary conditions, material constitutive models, load steps and output reports. The codes are written in fixed field format. The structure of the DAT f ile consists of 4 coding blocks: € General parameters for background material and primitive stress fields € Boundary conditions € Material constitutive models for potential crack segments € Processing steps (or load step): € Processing step element report requests € Processing step field point report requests The OUT file contains the results obtained from DD. The OUT file first echoes the information in the DAT file and subsequently repo rts the requested output variables at elements and field points for each load step. The output vari able names will be explained in three subsets: € Output variables at element (requested with command code ‘RX’ or ‘RA’)

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173 € Output variable at field point in cartesian coord. (requested with command code ‘RC’) € Output variables at field poi nt in principal coord. (request ed with command code ‘RG’) The REQ file is a text file containing request command code s to report output variables at each load step to the report f ile (*.RPT). The request command codes are written in free field format; separate each field with comma “,”. The structure of REQ file co nsists of any of these coding blocks (not in particular order): € Request output variables at elements € Request output variables at field po ints (Cartesian coordinate ‘RC’) € Request output variables at field po ints (Principal coordinate ‘RG’) The RPT file is a result of using the request file (*.REQ) to request the output variables stored in the POST processor. The requested out put variables are written in fixed field format, convenient to be opened with Spr eadsheet program such as Excel. Pre Processor Files for the Three Specimen Models Input File (*.IN) Figures B-2, B-3 and B-4 show the input f ile for obtaining IDT, SCB and 3PB specimen models, respectively. IDT.IN RMG 1000 1 4.00 -76.00 -76.00 76.00 76.00 10.00 S 30.00 0.00 32.0 0.00 31.00 2.0 R/ BCB 76 7.00 0.00 0.00 76.0 0.00 B/ *** use DVT.exe to generate tessellation *** None = 0, Delaunay = 1, Voronoi = 2 Figure B-2. IDT.IN pre processor file

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174 SCB.IN RMG 7000 1 4 -76 -76 76 0 10 S 30 0 40 0 35 10 R/ BLB 26 5 -76 0 76 0 BCB 76 6 0 0 0 76 B/ *** use DVT.exe to generate tessellation *** None = 0, Delaunay = 1, Voronoi = 2 Figure B-3. SCB.IN pre processor file 3PB.IN RMG 7000 1 5 -150 -39 150 39 10 S 30 0 40 0 35 10 R/ BLB 50 5 -150 -39 150 -39 BLB 50 5 -150 39 150 39 BLB 13 5 -150 -39 -150 39 BLB 13 5 150 -39 150 39 B/ *** use DVT.exe to generate tessellation *** None = 0, Delaunay = 1, Voronoi = 2 Figure B-4. 3PB.IN pre processor file Random Point Generation is defined in the fi rst line “RMG” where the nominal number of points to be generated, the minimum point spac ing constraint, the st arting and ending (x,y) coordinates for random points to be generated ar e listed. Second line define s the seed triangle for construction of tessellation. The tr iangle will be used as a starte r to form Delaunay tessellation and construct its dual mesh Voronoi. The codes “BLB” and “BCB” defines the boundary conditions. BLB is used to create a line, while BCB is used to crea te a circle. This line defines

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175 the number of elements along the boundary line, the minimum distance a point is allowed from the boundary, starting and ending coor dinates of the lines or of cen ter of the circumference. Segment File (*.VSG) The segment file is a text file containing defini tion of segments that describe geometry of the problem. The structure of the segment file c onsists of several lines of segment which define the segment type code (S for ordinary boundary segment, ? for potential crack element), the segment number, the number of elements per segment and the starting and ending coordinates for a line segment. A letter code refers to boundary condition code for ordinary boundary segment or material constitutive code for potential crack segment (i.e: 1,2,3,4,5,6,7,8, B, M, V). Figure B-5 shows the result of using DVT with IDT.IN to generate Vo ronoi with internal fracture path tessellations and the code written in the segment file. The segment file can then be attached to the .DAT file to run the boundary element analysis. S1 1 1 -12.542 -75.161 -9.417 -75.550 0.0 0.0 W T T S2 2 1 -9.417 -75.550 -6.293 -75.940 0.0 0.0 W T T S3 3 1 -6.293 -75.940 -3.146 -76.070 0.0 0.0 W T T SB 9 1 12.542 75.161 9.417 75.550 0.0 0.0 W T T SB 10 1 9.417 75.550 6.293 75.940 0.0 0.0 W T T SB 11 1 6.293 75.940 3.146 76.070 0.0 0.0 W T T SA 18 1 15.624 -74.515 18.706 -73.868 0.0 0.0 W T T SA 19 1 18.706 -73.868 21.724 -72.970 0.0 0.0 W T T SA 20 1 21.724 -72.970 24.742 -72.071 0.0 0.0 W T T ?M 153 1 -20.550 1.500 -20.550 -1.500 0.0 0.0 W T T ?M 154 1 -17.550 1.500 -17.550 -1.500 0.0 0.0 W T T ?M 155 1 -20.550 1.500 -17.550 1.500 0.0 0.0 W T T ?V1979 1 0.000 -22.050 1.500 -20.550 0.0 0.0 W T T ?V1980 1 1.500 -20.550 3.000 -19.050 0.0 0.0 W T T ?V1981 1 3.000 -19.050 1.500 -17.550 0.0 0.0 W T T Figure B-5. IDT.VSG pre processor file

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176 Data File (*.DAT) The structure of the DAT file consists of 4 c oding blocks. The first block contains general parameters for background material (Young M odulus, Poisson’s Ratio) and primitive stress fields (constant yy, yz, zz component of the prim itive stress field). The second block defines the boundary conditions (shear “S” and normal “N”) where “T” is a local normal traction component specification, “D” is a local nominal discontinuity component specification, “+” is a local z displacement component spec ification on the “+” side of the element, “-“ is a local z displacement component specification on the ““ side of the element. Following are the numerical value of selected normal boundary condition at collocation points 1 and 2. The third block contains the material consti tutive model for potential crack segments: € C0 = Initial intact cohesion (MPa); € o = Initial fiction angle (Degree) € o = Initial sliding dilation angle, (Degree) € CR = Residual cohesion, (MPa) € R = Residual friction angle, (Degree) € R = Reverse dilation angle relative to initial sliding direction, (Degree) € To = Tension cut off, (MPa) € DNCR = Opening crack limit over which tensile st rength is lost, (This defines implicitly the tension softening slope, Tsoft = To/DNCR, with respect to the opening crack limit. € Csoft = Cohesion softening slope, (MPa / mm) € Tsoft = Tension softening slope, (MPa / mm). € Parameter LAMDA: it is an exponent in tensi on weakening law controlling residual tensile strength as a function of crack opening. LAMDA = 1 for linear tension weakening (default) € Viscoelastic parameter 1, VP1 (mm/(s.MPa) ). It is proportionality constant in relaxation creep law or may be ignored if creep not being simulated. € Viscoelastic parameter 2, VP2. It is an e xponent in creep law or ignored if creep not simulated. The last block defines the processing steps or load steps. The first line contains the step identification name, the maximum number of crack growth search increments per time step interval, the stress tolerance for solution iterati on, the maximum number of iterations allowed in each solution cycle. Following is the processing step element report request (defining which

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177 elements are to be reported) and the processing st ep field point report request which indicates the type of system used to report stress components (Cartesian coordi nates or principal directions), the number of filed points in both Y and Z directions the origin field point coordinates, the angle of a line of field points, the incremental distance between field points in both Y and Z directions. Figures B-6 shows the boundary conditions for IDT, SCB and 3PB, respectively, while Figure B-7 shows one of the .DAT file used for simulating the IDT test. Output File (*.OUT) The OUT file contains the anal ysis result obtained from DIGS The OUT file first echoes the information in the DAT file and subsequen tly reports the requested output variables at elements and field points for each load step. € Output variables at element: angle measured fr om Y-axis to Z-axis; local tangential stress yy components on both positive and negative si des; local shear stress yz and zz components; local normal stress zz com ponent; cohesion strength; sliding crack displacement; opening crack displacement; local displacement in both y and z directions. € Output variables at field poi nt (req.1): major and minor pr incipal stresses; major angle measured from Y-axis to Z-axis; global disp lacements in both Y and Z directions; distance to a Mohr-Coulomb envelope ; strain energy density. € Output variables at field poi nt (req.2): normal stress YY comp onent in global Cartesian coordinates; shear stress YZ component in global Cartesian coordinates; normal stress ZZ component in global Cartesian coordinates; di splacements in both Y and Z directions in global Cartesian coordinates.

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178 A B C Figure B-6. Boundary conditions. A) IDT model. B) SCB model. C) 3PB model.

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179 **...GENERAL PARAMETERS ** YM PR GY GZ CYY CYZ CZZ CPP PPGR PR 6200 0.350 0.0 0.000 0.0 0.0 0.0 0.0 0.0 ** CBCS+ 0.0 0.0N+ 0.0 0.0 CACST 0.0 0.0NT 0.0 0.0 V1CS+-0.0006240-0.0006240N+ 0.0049609 0.0049609 V2CS+-0.0006258-0.0006258N+ 0.0049607 0.0049607 V3CS+-0.0002066-0.0002066N+ 0.0049957 0.0049957 V4CS+-0.0002067-0.0002067N+ 0.0049957 0.0049957 V5CS+ 0.0002067 0.0002067N+ 0.0049957 0.0049957 V6CS+ 0.0002066 0.0002066N+ 0.0049957 0.0049957 V7CS+ 0.0006258 0.0006258N+ 0.0049607 0.0049607 V8CS+ 0.0006240 0.0006240N+ 0.0049609 0.0049609 ** ** WID COH FRN DIL FCOH FFRN RDIL TCUT DNCR CSOFT TSOFT# LAMDA VP1 VP2 CM 0.0 2.20 44.0 0.0 0.11 38.0 0.0 2.20 0.12 1.00 10.00 1.0 0.00000 1.0 CV 0.0 6.40 40.0 0.0 0.12 36.0 0.0 6.40 0.09 1.00 10.00 1.0 0.00000 1.0 0.00000 1.0 ** **STEP MSKIP MXINC MXSTP TSTEP TTOL DTOL MAXIT SOR C S !PLD00 10 300 1 6.00 0.005 0.0 250 0.4 B # SAMPLE. I PIDT.FSG RX RS RG 1 51 0.00 -75.00 0.0 0.0 3.00 RG 51 1 -75.00 0.00 0.0 3.0 0.00 RG 1 2 0.00 -19.05 0.0 0.0 38.10 RG 2 1 -19.05 0.00 0.0 38.10 0.00 ** !PL010 10 300 1 6.00 0.005 0.0 250 0.4 B # SAMPLE. AM RA RG 1 51 0.00 -75.00 0.0 0.0 3.00 RG 51 1 -75.00 0.00 0.0 3.0 0.00 RG 1 2 0.00 -19.05 0.0 0.0 38.10 RG 2 1 -19.05 0.00 0.0 38.10 0.00 Figure B-7. .DAT file used for simulating the IDT test

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180 LIST OF REFERENCES Abdalla H.M. & B.L. Karihaloo. “Determination of size-independent specific fracture energy of concrete from three-point be nd and wedge splitting tests.” Magazine of Concrete Research Vol.55, pp. 133-141, 2003. Abdulshafi A.A. & K. Majidzadeh. “J-Integral and Cyclic Plastici ty Approach to Fatigue and Fracture of Asphaltic Mixtures.” Transportation Research Record. 1034, pp. 112-123, 1985. Ackermann F. “Digital image correlation: pe rformance and potential application in photogrammetry.” Photogrammetric record. Vol. 11(64), pp. 429-439, 1984. Aglan A. Hesmat. “Polymer Modifiers for Im proved Performance of Asphaltic Mixtures.” Asphalt Science and Technology Arthur Usmani, 1997. Airey G.D. “Styrene Butadiene Styrene Po lymer Modification of Road Bitumens.” Journal of Materials Science. Vol. 39, pp. 951-959, 2004. Anderson T.L. “Fracture Mechanics – Fundamental and Applications – 2nd ed.” CRC Press 688 pp, 1995. ASTM E399-90. “Standard Test Method for Pl ane-Strain Fracture Toughness of Metallic Materials.” Annual Book of ASTM Standards. Vol. 03.01, pp. 443-473, 2002. ASTM E1820-01. “Standard Test Method for Measurement of Fracture Toughness.” Annual Book of ASTM Standards. Vol. 03.01, pp. 1031-1076, 2002. Bahia H.U., D.I. Hanson, M. Zeng, H. Zhia, M.A. Khatri and R.M. Ande rson. “Characterization of Modified Asphalt Binders in Superpave Mix Design.” NCHRP Report 459 2001. Bazant Z. P. Mechanics of Distributed Cracking. Applied Mechanics Review Vol. 39, No. 5, pp. 675-705, 1986. Barenblatt G.I. “The Mathematical Theory of Equilibrium Cracks in Brittle Fracture.” Advances in Applied Mechanics. Vol. VII, pp. 55-129, 1962. Birgisson B, C. Soranakom, J.A.L. Napier and R. Roque. “Microstru cture and Fracture in Asphalt Mixtures Using a Bounda ry Element Approach.” ASCE Journal of Civil Engineering Materials New York, 2002. Birgisson B., C. Soranakom, J.A. L. Napier and R. Roque. “Simul ation of Fracture Initiation in Hot Mix Asphalt Mixtures.” Transportation Research Record 1849, TRB, National Research Council. Washington, DC, pp.183-190 2003. Bruck H.A., S.R. McNeill, M.A. Sutton and W.H. I. Peters. “Digital Image Correlation Using Newton-Raphson Method for a Part ial Differential Correction.” Experimental Mechanics. Vol. 28(3), pp. 261-267, 1989.

PAGE 181

181 Buttlar W.G. & R. Roque, “Development and Ev aluation of the Strategic Highway Research Program Measurement and Analysis System for Indirect Tensile Test at Low Temperatures.” Transportation Research Record 1454, TRB, National Research Council. Washington, DC, pp.163-171, 1994. Carpinteri A. & G. Ferro. “Size effects on tensil e fracture properties: a unified explanation based on disorder and fractality of concrete microstructure.” Materials and Structures. Vol. 28, pp. 563–571, 1994. Carpinteri A. & G. Ferro. “Scaling behavior a nd dual renormalization of experimental tensile softening responses.” Materials and Structures. Vol. 31, pp. 303–309, 1998. Carpinteri A., B. Chiaia, S. I nvernizzi. “Numerical Analysis of Identation Fracture in QuasiBrittle Materials.” Engineering Fracture Mechanics. Vol. 71(4-6), pp. 567-577, 2003. Chehab G.R., Y. Seo, Y.R. Kim. “Viscoelast oplastic Damage Characterization of AsphaltAggregate Mixtures using Digital Image Correlation.” International Journal of Geomechanics Vol. 7, No. 2, pp. 111-118 2007. Choi S. and S.P. Shah. “Measurement of Deformations on Concrete Subjected to Compression using Image Correlation.” Experimental Mechanics. Vol. 37(3), pp.307-313, 1997. Chu T.C., W.F. Ranson, W.H. Peters and M. A. Sutton. “Applications of Digital-ImageCorrelation Techniques to E xperimental Mechanics.” Experimental Mechanics. Vol. 25(3), pp. 232-245, 1985. Collop A. & D. Cebon. “A Theoretical Analysis of Fatigue Cracking in Flexible Pavements.” Proceedings of the Instituti on of Mechanical Engineers. Vol. 209, pp. 345-361, 1995. Crawford A.M. & J.H. Curran. “Higher-Order F unctional Variation Displacement Discontinuity Elements.” International Journal of Ro ck Mechanics and Mining Sciences Vol.19, pp.143-148, 1982. Crippa B, G. Forlani and A. de Haan. “Aut omatic deformation measurement from digital images.” Optical 3-D Measurement Techniques II Gruen/Kahmen (Ed's), Wichman Verlag, Karlsruhe, pp.557-563, 1993. Crouch S.L. and A.M. Starfield. Boundary Element Methods in Solid Mechanics George Allen & Unwin, London, U.K, 1983. Deacon J.A., A. Tayebali, Harvey J.T. and C. M. Monismith. “Influence of Binder Loss Modulus on the Fatigue Performance of Asphalt Concrete Pavements.” Journal of the Association of Asphalt Paving Technologists. Vol. 66, pp. 633, 1997. Dugdale D.S. “Yielding of Steel Sheets Containing Slits.” Journal of the Mechanics and Physics of Solids. Vol. 8, pp. 100-108, 1960.

PAGE 182

182 Elber W. “Fatigue Crack Closure Under Cyclic Tension.” Engineering Frac ture Mechanics. Vol. 2, pp. 37-45, 1970. Elices M., G.V. Guinea, J. Planas “Measuremen t of the fracture energy using the three point bend test: Part 3 – Influence of cutting the Ptail.” Materials and Structures. Vol. 25, pp. 327-334, 1992. Ewalds H.L. & R.J. Wanhill. “Fracture Mechanics-Delft.” Delftse U.M., London, 1986. Foreman R.G., V.E. Keary & R.M. Engle. “Numeri cal Analysis of Crack Propagation in CyclicLoaded Structures.” Journal of Basic Engineering. Vol. 9, pp. 459-464, 1967. Forstner W. “On the geometric precision of digital image correlation.” IAPRS Vol. 24 (3), pp. 176-189, 1982. Freeman R.B., J.K. Newman and R.A. Ahlrich. “Effect of Polymer Modifiers on Dense-Graded, Heavy-Duty Mixtures.” Eighth International Confer ence on Asphalt Pavements Seattle, Washington, 1997. Grdiac M. “The use of full-field measurement me thods in composite mate rial characterization: interest and limitations. Composites, Part A.” Applied Science and Manufacturing. Vol. 35, pp. 751-761, 2004. Griffith A.A. “The Phenomena of Rupture and Flow in Solids.” Philosophical Transaction, Series A. Vol. 221, pp.163-198, 1920. Gruen A.W. “Adaptive Least Squares Correlati on: a Powerful Image Matching Technique.” South African Journal of Photogrammetr y, Remote Sensing and Cartography. Vol. 14, No. 3, pp. 175-187, 1985. Harvey J.T., J.A. Deacon, B. Tsai and C.L. Monismith. “A Fatigue Performance of Asphalt Concrete Mixes and its Relationship to As phalt Concrete Pavement Performance in California.” California Department of Transportation. Report No. RTA-65W485-2, 1995. Harvey J.T., J.A. Deacon, A.A. Tayebali, R.B. Leahy and C.L. Monismith. “A Reliability-Based Mix Design and Analysis System for Mitigating Fatigue Distress.” Eighth International Conference on Asphalt Pavements Seattle, Washington, 1997. Helms K.L.E., D.H. Allen and L.D. Hurtado. “A Model for Predicting Grain Boundary Cracking in Polycrystalline Viscoplastic Material Including Scale Effects.” International Journal of Fracture, Vol. 95, pp. 175-194, 1999. Hillerborg A., M. Modeer & P.E. Petersson. “Ana lysis of crack formation and crack growth in concrete by means of fracture m echanics and finite elements.” Cement Concrete. Res 6, pp. 773–782, 1976.

PAGE 183

183 Hillerborg A., “Results of Three Comparative Te st Series for Determining the Fracture Energy GF of Concrete.” Materials and Structures. Vol.18, No. 107, pp. 407-413, 1985. Hossain M., S. Swartz, E. Hoque. “Fracture a nd Tensile Characteristics of Asphalt-Rubber Concrete.” Journal of Materials in Civil Engineering. Vol. 11, issue 4, pp. 287-294, 1999. Hu X.Z. and F.H. Wittmann. “Fracture Energy and Fracture Process Zone.” Materials and Structres Vol. 25, pp. 319-326, 1992. Isacsson U., & X. Lu. “Testing a nd appraisal of polymer modified road bitumens—state of the art.” Materials & Structures. Nol. 28, No. 3, pp.139-159, 1995. Jacobs M.M.J. “Crack Growth in Asphaltic Mixes.” Ph.D. Dissertation. Delft Universiy of Technology, Road and Railroad Research Laboratory, 1995. Jacobs M.M.J. “P.C. Hopman & A.A.A. Mole naar. “Application of Fracture Mechanics Principles to Analyze Crack ing in Asphalt Concrete.” Journal of the Association of Asphalt Paving Technologists. Vol.65, pp. 1-39, 1996. Jenq Y.S. & J.D. Perng. “Analysis of Crack Prop agation in Asphalt Concrete Using a Cohesive Crack Model.” Transportation Research Record. No. 1317, pp. 90-99, 1991. Kaloush K.E., W.M. Witczak, G.B Way. “Perfo rmance Evaluation of Arizona Asphalt Rubber Mixtures using Advanced Dynamic Material Characterization Tests.” Final Report Submitted to Alberta Transportation. Edmonton, Alberta, June 2003. Khattak M.J. & G.Y. Baladi. “Engineering Prope rties of Polymer Modified Asphalt Mixture.” Transportation Research Record. TRB No. 1638, pp.12-22, 1998. Khattak M.J., G.Y. Baladi and L.T. Drzal “L ow Temperature Binder-A ggregate Adhesion and Mechanistic Characteristics of Po lymer Modified Asphalt Mixtures.” Journal of Materials in Civil Engineering. Vol. 19, issue 5, pp. 411-422, 2007. Kim Y.R., D.L. Little and F. Benson. “Chemi cal and Mechanical Evaluation on Healing Mechanism of Asphalt Concrete.” Journal of the Association of Asphalt Paving Technologists. Vol.59, pp. 240-276, 1990. Kim Y.R., S.L. Whitmoyer and D.N. Little “Healing in Asphalt Conc rete Pavements: is it real?” Transportation Research Record. 1454, pp. 89-96, 1994. Kim Y.R., Y.C. Lee and H.J. Lee “Corresponde nce Principle for Characterization of Asphalt Concrete.” Journal of Materials in Civil Engineering. Vol. 7, issue 1, pp. 59-68, 1995. Kim K.W. & El Hussein. “Var iation of Fracture Toughness of Asphalt Concrete under Low Temperature.” Construction & Building Materials. Vol.11, pp. 403-411, 1997.

PAGE 184

184 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, pp. 520-569, 1997. Kim Y.R. and Wen H. “Fracture Ener gy from Indirect Tension Test.” Journal of the Association of Asphalt Paving Technologists. Vol.71, pp. 779-793, 2002. Kim B., Roque R., Birgisson B. “Effect of St yrene Butadiene Styrene Modifier on Cracking Resistance of Asphalt Mixture.” Transpor tation Research Record. No. 1829, pp. 8-15, 2003. King G.N, H.W. King, O. Harders, W. Arand and P. Planche. “Influence of Asphalt Grade and Polymer Concentration on the Low-Temperat ure Performance of Polymer Modified Asphalt.” Journal of the Asso ciation of Asphalt Pa ving Technologists. Vol.62, pp. 1-22, 1993. Klesnil M. & P. Lukas. “Influence of Strength and Stress History on Growth and Stabilization of Fatigue Cracks.” Engineering Frac ture Mechanics. Vol. 4, pp. 77-92, 1972. Krans R.L., F. Tolman, M.F.C. Van de Ven. “S emi-Circular Bending Test: a Practical Crack Growth Test using Asphalt Concrete Cores.” 3rd International RILEM Conference on Reflective Cracking in Pavements. Maastricht, October 1996. Kuijpers J.S. & J.A.L. Napier. “Effective Growth Rules for Macrofracture Simulation in Brittle Rock under Compression.” Eurorock ’96 (edited by G. Barla), Balkema, Rotterdam, pp. 469-479, 1996. Lee H.J. & Y.R. Kim. “Viscoelastic Constitu tive Model for Asphalt Concrete under Cyclic Loading.” Journal of Engineering Mechanics Vol. 124, No 1, pp. 32-40, 1998a. Lee H.J., & Y.R. Kim. “Viscoelastic Conti nuum Damage Model of Asphalt Concrete with Healing.” Journal of Engineering Mechanics. Vol. 124, No. 11, pp. 1224-1232, 1998b. Li X. & M. Marateanu. “Evaluation of the Low Temperature Fractur e Resistance of Asphalt Mixtures using the Semi Circular Bend Test.” Journal of the Association of Asphalt Paving Technologists. Vol.73, pp. 401-426, 2004. Li X. and M. Marasteanu. “Study of Temper ature Cracking in Asphalt Mixtures using Mechanical Testing and Acoustic Emission Methods.” Journal of the Association of Asphalt Paving Technologists. Vol.76, pp. 427-454, 2007. Lim I.L., I.W. Johnston, S.K. Choi, J.N. Boland. “Fracture Testing of a Soft Rock with SemiCircular Specimens under Three Point Bending” Part I and II. International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts. Vol.31, No 3, pp.185, 1994. Little D.N., J.W. Button, R.M. White, E.K. En sley, Y. Kim, S.J. Ahmed. “Investigation of Asphalt Additives.” Texas Transportati on Institute, Report no FHWA/RD-87/001, 1987.

PAGE 185

185 Little D.L., R. Lytton, D. Williams, Y.R. Kim. “Propagation and Healing of Microcracks in Asphalt Concrete and Their C ontributions to Fatigue.” Asphalt Science and Technology, Usmani. pp. 149, 1997. Lu H. and P.D. Cary. “Deformation measuremen ts by digital image correlation: implementation of a second-order displacement gradient.” Experimental Mechanics Vol. 40, pp. 393-400, 2000. Lu X. & U. Isacsson. “Rheological Characteriza tion of Styrene-Butadiene-Styrene Copolymer Modified Bitumens.” Construction and Building Materials. Vol.11, issue 1, pp. 23-32, 1997. Lu X., U. Isacsson, J. Ekblad. “Influence of Polymer Modification on Low Temperature Behaviour of Bituminous Binders and Mixtures.” Materials and Structures Vol. 36, pp.652-656, 2003. Lundstrm, R. & U. Isacsson. “Linear Viscoela stic and Fatigue Characteristics of StyreneButadiene-Styrene Modified Asphalt Mixtures.” Journal of Materials in Civil Engineering. Vol.16, issue 6, pp. 629-638, 2004. Majidzadeh K. E.M. Kaufmann, and D.V. Ramsam ooj. “Application of Fr acture Mechanics in the Analysis of Pavement Fatigue.” Journal of the Associatio n of Asphalt Technologists Vol.40, pp.227-246, 1971. Malan D.F. & J.A.L. Napier. “Computer Modeli ng of Granular Materi al Microfracturing.” Tectonophysics. Vol. 248, pp. 21-37, 1995. Marasteanu M.O., J.F. Labuz, S. Dai and X. Li. “Determining the Low-Temperature Fracture Toughness of Asphalt Mixtures.” Transportation research Record. No. 1789, pp. 191199, 2002. McEvily A.J. “On Closure in Fatigue Crack Growth.” ASTM STP 982, American Society for Testing and Materials. Philadelphia, pp. 35-43, 1988. Melrose P, R. Lopez-Anido, L. Muszynski. “Ela stic Properties of Sandwich Composite Panels using 3-D Digital Image Correlation w ith the Hydromat Test System.” SEM XII International Congress a nd Exposition on Experimental Mechanics and Applied Mechanics, Costa Mesa, CA, 2004. Mier J.G.M & M.R.A. van Vliet. “Effect of strain gradients on the size effect of concrete in uniaxial tension.” International Jour nal of Fracture. Vol.94, pp. 195–219, 1999. Mihashi H., H. Takhashi and F.H. Wittmann. “Tension-Softening Curve Measurements for Fracture Toughness Determination in Granite.” Proceedings of the International Workshop on Fracture Toughness and Fracture Energy-Test Methods for Concrete and Rock. Balkema, Rotterdam, pp.47-55, 1989.

PAGE 186

186 Mobasher B.M., M.S. Mamlouk and H.M. Lin. “Eva luation of Crack Propagation Properties of Asphalt Mixtures.” ASCE Journal of Transportation Engineering. Vol. 123, No. 5, pp. 405-413, 1997. Molenaar A.A.A., A. Scarpas, X. Liu and G. Er kens. “Semi-Circular bending Test; Simple but Useful?” Journal of the Associati on of Asphalt Technologists Vol.71, pp.794-815, 2002. Mull M.A., K. Stuart, A. Yehia. “Fracture Resi stance Characterization of Chemically Modified Crumb Rubber Asphalt Pavement.” Journal of Material Science. Vol. 37, pp. 557-566, 2002. Muszynski L, R. Lopez-Anido and S.M. Shal er. “Image Correlation Analysis Applied to Measurement of Shear Strains in Laminated Composites.” SEM XI International Congress on Experimental Mechanics Orlando, FL, 2000. Muszynski L., F. Wang and S.M. Shaler. “Shor t Term Creep Tests on Phenol Resorcinol Formaldehyde (PRF) Resin Undergoing Moisture Cement.” Wood and Fiber Science. Vol. 34 (4), pp. 612-624, 2002. Myers L. “Development and Propagation of Surface -Initiated Longitudinal Wh eel Path Cracks in Flexible Highway Pavements.” Ph.D. Dissertation. University of Florida, 2000. Myers L., R. Roque & B. Birgisson. “ Propagation Mechanisms for Surface-Initiated Longitudinal Wheel Path Cracks.” Transportation Research Record. No. 1778, pp. 113121, 2001. Napier J.A.L. “Modelling of Fracturing near Deep Level Gold Mine Excavations Using a Displacement Discontinuity Approach.” Proceedings of the Second International Conference on Mechanics of Jointed and Faulted Rock (Edited by H. P: Rossmanith), Balkema, Rotterdam, pp. 709-715, 1990. Napier J.A.L and M.W. Hildyard. “Simulation of Fracture Growth Openings in Highly Stressed Brittle Rock.” Journal of the South African Inst itute of Mining and Metallurgy Vol. 92, pp. 159-168, 1992. Napier J.A.L. & A.P. Peirce. “Simulation of Ex tensive Fracture Formation and Interaction in Brittle Materials.” Mechanics of Jointe d and Faulted Rock; (edited by H. P. Rossmanith), Balkema, Rotterdam pp. 63-74, 1995. Napier J.A.L & D.F. Malan. “A Viscoplastic Di scontinuum Model of Time-Dependent Fracture and Seismicity Effect in Brittle Rock.” International Journal of Rock Mechanics and Miming Sciences Vol. 34, pp. 1075-1089, 1997. Napier J.A.L., A. Daehnke, T. Dede, M. W. Hildya rd, J. S. Kuijpers, D. F. Malan, E. J. Sellers, and P. A. Turner. “Quantification of Stope Fr acture Zone Behaviour in Deep Level Gold Mines.” Journal of the South African In stitute of Mining and Metallurgy Vol. 97, pp. 119-134, 1997.

PAGE 187

187 Newman J.K. “Polymer Modification of Aspha lt Mixtures Designed for Military Airfield Pavements; Fatigue Properties according to AASHTO TP-8.” Transportation System 2000 Workshop. San Antonio, Texas, February 28-March 3, 2000. Paris P.C. & F. Erdogan. “A Critical Analysis of Crack Propagation Laws.” Transactions of the ASME, Journal of Basic Engineering. Vol. 85, pp. 528-534, 1963. Pucci T., A.G. Dumont, H. Di Benedetto. “Thermomechanical and Mechanical Behavior of Asphalt Mixtures at Cold Temperature. Road and Laboratory Investigations.” Road Materials and Pavement Design. Vol. 5, issue 1, pp. 45-72, 2004. Ramsamooj D.V. “Fatigue Cracking of Asphalt Pavements.” Journal of Transportation Research Record. No. 756, pp.43-48, 1980. Ramssamooj D.V. “Prediction of Fatigue Life of Asphalt Concrete Beams from Fracture Test.” Journal of Testing and Evaluation. Vol.19, No. 3, pp. 231-239, May 1991. Ramssamooj D.V. “Fracture of Highway and Airport Pavements.” Journal of Engineering Fracture Mechanics. Vol. 44, No. 4, pp. 609-626, 1993. Ranson W.F., M.A. Sutton and W.H.I. Peters. “Holographic and Spackle Interferometry” SEM Handbook of Experimental Mechanics New Jersey: Prentice-Hall, Inc, pp. 388-429, 1987. Rice J.R. “A Path Independent Integral and th e Approximate Analysis of Strain Contration by Notches and Cracks.” Journal of Applied Mechanics. June, pp. 379-386, 1968. RILEM Technical Committee 50. “ Determination of Fracture Energy of Mortar and Concrete by means of three-point bend tests on notched beams.” Materials and Structures. Vol. 18, pp. 287-290, 1985. Romero P., K.D. Stuart and W. Mogawer. “Fat igue Response of Asphalt Mixtures tested by the Federal Highway Administration’s Accelerated Load Facility.” Journal of the Association of Asphalt Technologists Vol. 69, pp.212, 2000. Roque R. & W.G. Buttlar. “The Development of a Measurement and Analysis System to Accurately Determine Asphalt Concrete Prope rties Using The Indire ct Tensile Mode.” Journal of the Associati on of asphalt Technologists Vol. 61, pp. 304-332, 1992. Roque R., Z. Zhang and B. Sankar. “Determinati on of Crack Growth Rate Parameters of Asphalt Mixtures using the Superpave Indirect Tension Test (IDT).” Journal of the Association of Asphalt Paving Technologists. Vol. 68, pp. 404-433, 1999. Roque R., B. Birgisson, S. Sangptegnam, Z. Zh ang. “Asphalt Fracture Mechanis: A Fundamental Crack Growth Law for Asphalt Mixtures.” Journal of the Associ ation of Asphalt Paving Technologists. Vol. 71, pp. 816-827, 2002.

PAGE 188

188 Roque R., B. Birgisson, C. Drakos, B. Dietri ch. “Development and Fiel d Evaluation of EnergyBased Criteria for Top-down Cracking Performance of Hot Mix Asphalt.” Journal of the Association of Asphalt Paving Technologists. Vol. 73, pp. 229-260, 2004. Sargand S.M. & S.S. Kim. “Performance Evaluation of Polymer Modified and Unmodified Superpave mixes.” Second International Symposium on Maintenance and Rehabilitation of Pavements and Technological Control. Auburn, AL, 2001. Schapery R.A. “A Theory of Crack Growth in Visco-Elastic Media.” Report MM 2764-73-1, Mechanics and Materials Research Center. Texas A&M University, College Station, TX, 1973. Schapery R.A. “A Theory of Crack Initiation and Growth in Visco-Elastic Media, I: Theoretical Development, II: Approximate Methods of Analysis, III: Analysis of Continuous Growth.” International Journal of Fracture Vol. 11, No. 1, pp. 141-159. Vol. 11, No. 3, pp 369-388 and Vol. 11, No. 4, pp. 549-563, 1975. Schapery R.A. “A Method for predicting Crac k Growth in Non-Hom ogeneous Visco-Elastic Media.” International Journal of Fracture Vol. 14, No. 3, pp. 293-309, 1978. 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, pp. 195-223, 1984. Schwarz C.R. & J.J. Kok. Blunder Detection and Data Snooping in LS and Robust Adjustments. Journal of Surveying Engineering Vol. 119, issue 4, pp. 127-136, 1993. Seo Y., Y.R. Kim, R. Schapery, M. Witczac, R. Bonaquist. “A Study of Crack-Tip Deformation and Crack Growth in Asphalt Conc rete using Fracture Mechanics.” Journal of the Association of Asphalt Paving Technologists. Vol. 73, pp. 697-730, 2004. Steen B.V.D., A. Vervoort and J.A.L. Napier. “N umerical Modeling of Fr acture Initiation and Propagation in Biaxial Tests on Rock Samples.” International Journal of Fracture Vol. 108, pp. 165-191, 2001. Sulaiman S.J, A.F. Stock. “The Use of Fractur e Mechanics for the Evaluation of Asphalt Mixes.” Journal of the Association of Asphalt Paving Technologists. Vol. 64, pp. 500-533, 1995. Sutton M.A., W.J. Wolters, W.H. Peters, W.F. Ranson, and S. R. McNeil. “Determination of Displacements Using an Improved Digital Correlation Method.” Image and Vision Computing Vol. 1, issue 3, pp. 133-139, 1983. Sutton M.A., M.Q. Cheng, W.H. Peters, Y.J. Chao and S.R. McNeill. “Application of an Optimized Digital Correlation Method to Planar Deformation Analysis.” Image and Vision Computing Vol. 4, issue 3, pp. 143-151, 1986.

PAGE 189

189 Sutton M.A., S.R. McNeill, J. Jang and M. Baba i. “Effects of Subpixe l Image Restoration on Digital Correlation Error.” Journal of Optical Engineering. Vol. 27, issue 10, pp. 870877, 1988. Swartz S.E. & T.M.E. Refai. “Influence of Si ze Effects on Opening Mode Fracture Parameters for Precracked Concrete Beams in Bending.” Proceedings of the SEM/RILEM International Conference on Fracture of Concrete and Rock. Huston, 1987. Van de Ven M.F.C., A. Smit, R. L. Krans. “Pos sibilities of a Semi-C ircular Bending Test.” 8th International Conference on Asphalt Pavements. Seattle, August, 1997. Van den Heuvel F, Kroon R. “Digital Close-Rang e Photogrammetry using Artificial Targets.” IAPRS 29(5), pp. 222-229, 1992. Van der Burg M.W.D. and E. Van der Giessen; Delanuay-Network Modelling of Creep Failure in Regular Polycrystalline Aggre gates by Grain Boundary Cavitations. Delft University of Technology, LMT Report No. 1004, 1993. Wagoner M.P., W.G. Buttlar and G.H. Paulino. “Development of a Single-Edge Notched Beam Test for the Study of Asphalt Concrete Fracture.” ASTM Journal of Testing and Evaluations. Vol. 33, No. 6, 2005a. Wagoner M.P., W.G. Buttlar and G.H. Paulino. “D isk-shaped Compact Tension Test for Asphalt Concrete Fracture.” Experimental Mechanics. Vol. 45, No. 3, pp. 270-277, 2005b. Wagoner M.P. and W.G. Buttlar. “Influence of Specimen Size on Fracture Energy of Asphalt Concrete.” Journal of the Asso ciation of Asphalt Pa ving Technologists. Vol. 76, pp. 391426, 2007. Wendling L., E. Xolin, D. Gimenez, P. Reynaud, C. De La Roche, J. Chevalier & G. Fantozzi. “Characterization of Crack Propa gation in Bituminous Mixtures.” 5th International RILEM Conference on Cracking Pavements. Limoges, France, RILEM Publications, pp. 639-646, 2004. Weertman J. “Rate of Growth of Fatigue Cracks Calculated from the Theory of Infinitesimal Dislocations Distributed on a Plane.” International Journal of Fracture Mechanics. Vol. 2, pp. 460-467, 1966. Winnie D.H. & B.M. Wundt. “Application of the Giffith-Irwin Theory of Crack Propagation to the Bursting Behavior of Disc, Includi ng Analytical and Experimental Studies.” Transaction ASME. Vol. 80, pp. 1643-1655, 1958. Wittmann F.H. “Fracture Toughness a nd Fracture Energy of Concrete.” Proceedings of the International Conference on Frac ture Mechanics of Concrete. Lausanne, Switzerland, 1986.

PAGE 190

190 Wittmann F.H., H. Mihashi, N. Nomura. “Siz e effect on fracture energy of concrete.” Engineering Fracture Mechanics. Vol. 35, pp. 107-115, 1990. Wnuk M.P. “Subcritical Growth of Fracture.” International Journal of Fracture Mechanic. Vol. 7, pp. 383-486, 1971. Xu S. & G. Zhao. “Fracture Energy of Concrete and its Variational Trend in Size Effect studied by using Three Point Bending Beams.” Journal of Dalian Univ ersity of Technology. Vol. 31, No. 1, pp. 79-86, 1991. Zhang Z., R. Roque, B. Birgisson & B. Sangpet gnam. “Identification and Verification of a Suitable Crack Growth Law.” Journal of the Association of Asphalt Paving Technologists. Vol. 70, pp. 206-241, 2001.

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191 BIOGRAPHICAL SKETCH Elena Romeo was born in Parma, Italy, in1975. Sh e received both Bachel or of Science and Master of Science degrees in civil engineering from University of Parma in December 2003. In spring 2006 she joined the Ph.D. pr ogram of the materials group at the University of Florida and worked as a graduate research assistant firstl y with Dr. Bjorn Birgi sson and after with Dr. Reynaldo Roque. She is currently completing the Doctor of Philosophy Degree in civil engineering at the University of Florida. U pon completion of her doctoral program, Elena would like to pursue a career in research and academia.