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Use of binder rheology to predict the cracking performance of SBS-modified mixture

University of Florida Institutional Repository

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USE OF BINDER RHEOLOGY TO PRED ICT THE CRACKING PERFORMANCE OF SBS-MODIFIED MIXTURE By ZHANWU CUI A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ENGINEERING UNIVERSITY OF FLORIDA 2003

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ii ACKNOWLEDGMENTS I would like to express my sincere apprecia tion to my supervisor and the chairman of my supervisory committee, Dr. Reynaldo Roque, for his invaluable technical and personal assistance throughout my graduate study. Without his support, guidance and encouragement, this thesis would not be a possible. I would also like to express my appreciation to Dr. Mang Tia and Dr. Bjorn Birgission for participating as members of my supervisory committee. I would also like to acknowledge an d thank the Florida Department of Transportation (FDOT) for providing financia l support for this pr oject. My sincere appreciation and gratitude go to my “r esearch partner,” Mr. Booil Kim for his participation throughout the pr oject. I also thank Mr. Geor ge Lopp for his invaluable assistance in the laboratory. A nd also, I would like to expre ss my sincere appreciation to Jae Seung Kim, Adam, and all the graduate students in the materials group for their assistance and support, and for making my study in the department a pleasure. Finally, I wish to express my sincere a nd heartfelt appreciation to my parents, especially my mother, my brother, for all the years of love, encouragement and support without which I would not have been able to achieve this success.

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iii TABLE OF CONTENTS Page ACKNOWLEDGMENTS..................................................................................................ii LIST OF TABLES.............................................................................................................vi LIST OF FIGURES..........................................................................................................vii ABSTRACT......................................................................................................................x ii CHAPTER 1 INTRODUCTION........................................................................................................1 1.1 Background.............................................................................................................1 1.2 Study Objectives.....................................................................................................2 1.3 Scope of Study........................................................................................................3 2 LITERATURE REVIEW.............................................................................................4 2.1 Introduction.............................................................................................................4 2.2 Binder-to-Mixture Stiffness Relationship...............................................................4 2.2.1 Theoretical Binder-to-Mixtur e Stiffness Relationship.................................4 2.2.1.1 Paul’s equations and the rule of mixtures..........................................5 2.2.1.2 Hashin and Shtrikman’s arb itrary phase geometry model.................5 2.2.1.3 Hashin’s composite spheres model....................................................6 2.2.1.4 Christensen and Lo’s genera lized self-consistent scheme.................8 2.2.2 Empirical Binder-to-Mixtur e Stiffness Relationship....................................9 2.2.2.1 Heukelom and Klomp........................................................................9 2.2.2.2 Bonnaure’s relationship....................................................................12 2.3 Binder Master Curve and Shift Factor..................................................................12 2.4 Power Model.........................................................................................................15 2.4 Modifiers in Asphalt Pavement Materials............................................................16 2.5 HMA Fracture Mechanics Model.........................................................................17 3 RESEARCH PROGRAM AND INSTRUMENTATION..........................................19 3.1 Introduction...........................................................................................................19 3.2 Materials...............................................................................................................19 3.2.1 Binders........................................................................................................19 3.2.2 Mixtures......................................................................................................21

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iv 3.3 Binder Preparation................................................................................................22 3.3.1 Extraction and Recovery of the Binder......................................................22 3.3.2 Rolling Thin Film Oven Test (RTFOT).....................................................22 3.4 Testing of Binders.................................................................................................22 3.4.1 Bending Beam Rheometer Test..................................................................23 3.4.2 Dynamic Shear Rheometer Test.................................................................25 3.5 Testing of Mixtures...............................................................................................28 4 SUMMARY AND ANALYSIS OF LA BORATORY TEST RESULTS..................29 4.1 Introduction...........................................................................................................29 4.2 Summary of Binder Test.......................................................................................29 4.2.1 Bending Beam Rheometer Test..................................................................29 4.2.2 Dynamic Shear Rheometer.........................................................................32 4.2.2.1 Dynamic Shear Rheometer at low frequencies................................32 4.2.2.2 The Dynamic Shear Rheometer Test at high frequencies................33 4.3 Binder Creep Compliance Master Curve..............................................................33 4.3.1 Shift Factors................................................................................................33 4.3.2 The Master Creep Compliance Curve........................................................35 4.3.2.1 Creep compliance from Dynamic Shear Rheometer test results......35 4.3.2.2 Construction of binder creep compliance master curve...................37 4.4 Binder-to-Mixture Stiffness Relationship.............................................................47 4.4.1 Empirical Binder-to-mixtur e Stiffness Relationship..................................48 4.4.2 Volumetrics of the aggregate......................................................................49 4.4.3 Calibration of the binder stiffness..............................................................49 4.5 Use of Binder-to-mixture Stiffness Relationship.................................................51 4.5.1 Prediction of the Mixture Stiffness for the Same Mixture.........................51 4.5.2 Prediction of Mixture Stiffne ss for SBS Modified Mixture.......................72 4.5.3 Use Energy Ratio for Comparison.............................................................75 5 CLOSURE..................................................................................................................88 5.1 Summary of Findings...........................................................................................88 5.2 Conculsion............................................................................................................89 APPENDIX A BENDING BEAM RHEOMETER TEST RESULTS...............................................90 B DYNAMIC SHEAR RHEOMETER TEST RESULTS.............................................97 C BINDER CREEP COMPLIANCE MASTER CURVE DATA...............................104 D MIX DESIGN AND VOLUMETRIC PROPERTIES OF MIXTURES..................112 E BINDER-TO-MIXTURE STIFFNESS RELATIONSHIP DATA..........................120

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v F ENERGY RATIO USING MIXTUR E TEST AT ONE TEMPERAURE...............129 G ENERGY RATIO PREDICTION USING BINDER-TO-MIXTURE STIFFNESS RELATIONSHIP......................................................................................................134 H ENERGY RATIO PREDICTION USING UNMODIFIED BINDER-TO-MIXTURE STIFFNESS RELATIONSHIP FOR MODIFIED MIXTURE................................140 LIST OF REFERENCES.................................................................................................143 BIOGRAPHICAL SKETCH...........................................................................................146

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vi LIST OF TABLES Table page 3.1 Penetration at 25 C (77 F)......................................................................................20 3.2 Dynamic Shear Rheometer at 25 C (77 F).............................................................20 3.3 Dynamic Shear Rheometer at 64 C (147 F)...........................................................21 3.4 Mixture Test Samples..................................................................................................22 4.1 Bending Beam Rheometer Test Result at -10 60 sec..............................................30 4.2 Dynamic Shear Rheometer Test Re sults at Low Frequencies at 10 ........................32 4.3 Power Model Parameters from DSR Test Results at 10 ..........................................36 4.4 Power Model Parameters from DSR Test Results at 20 ..........................................36 4.5 Power Model Parameters for Master Curve.................................................................47 4.6 Data Used to Calibrate Binder Stiffness......................................................................50 4.7Summary of Data Interpretation Methods....................................................................76

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vii LIST OF FIGURES Figure page 2.1 The Composite Spheres Model (3)................................................................................7 2.2 The Generalized Self-Consis tent Scheme Model (3).....................................................8 2.3 Comparison of Mixture Stiffness: Micr omechanical Models Versus IDT Range Established Using Measure Creep Stiffness................................................................10 2.4 Construction of the Master Compliance Curve (13, 14)..............................................13 2.5 Power Model................................................................................................................ 15 3.1 Schematic of Bending Beam Rheometer.....................................................................23 3.2 Bending Beam Rheometer...........................................................................................23 3.3 m-value from the Bending Beam Rheometer..............................................................25 3.4 Schematic of Dynamic Shear Rheometer....................................................................25 3.5 Components of Complex modulus G*.........................................................................26 3.6 a, b DSR equipment.....................................................................................................28 4.1 Comparison of the Measured Stiffness........................................................................31 4.2 Comparison of the m-value..........................................................................................31 4.3 The Log Shear StressLog Frequency Relationship...................................................33 4.4 Master Curve Relationship: PG 67-22, extracted binder @ 6.1% AC.......................38 4.5 Master Curve Relationship: PG 67-22, extracted binder @ 7.2% AC........................38 4.6 Master Curve Relationship: PG 76-22, extracted binder @ 6.1% AC.......................39 4.7 Master Curve Relationship: PG 76-22, extracted binder @ 7.2% AC.......................39 4.8 Master Curve Relationship: PG 67-22, RTFOT aged..................................................40

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viii 4.9 Master Curve Relationship: PG 76-22, RTFOT aged..................................................40 4.10 Master Curve: PG 67-22, extracted binder @ 6.1% AC............................................41 4.11 Master Curve: PG 67-22, extracted binder @ 7.2% AC............................................42 4.12 Master Curve: PG 76-22, extracted binder @ 6.1% AC............................................43 4.13 Master Curve: PG 76-22, extracted binder, 7.2% AC...............................................44 4.14 Master Curve: PG 67-22, RTFOT aged.....................................................................45 4.15 Master Curve; PG 76-22, RTFOT aged.....................................................................46 4.16 Log Sb ’ – Log Sb Relationship: PG 67-22, extracted binder 6.1% AC......................52 4.17 Log Sm – Log Sb Relationship; PG 67-22, extracted binder @ 6.1% AC..................52 4.18 Log Sb ’ – Log Sb Relationship: PG 67-22, extracted binder @ 7.2% AC.................53 4.19 Log Sm – Log Sb Relationship: PG 67-22, extracted binder @ 7.2% AC..................53 4.20 Log Sb ’ – Log Sb Relationship: PG 76-22, extracted binder @ 6.1% AC.................54 4.21 Log Sm – Log Sb Relationship: PG 76-22, extracted binder @ 6.1% AC..................54 4.22 Log Sb ’ – Log Sb Relationship: PG 76-22, extracted binder @ 7.2% AC.................55 4.23 Log Sm – Log Sb Relationship: PG 76-22, extracted binder @ 7.2% AC..................55 4.24 Log Sb ’ – Log Sb Relationship: PG 67-22, RTFOT aged @ 6.1% AC......................56 4.25 Log Sm – Log Sb Relationship: PG 67-22, RTFOT aged @ 6.1% AC......................56 4.26 Log Sb ’ – Log Sb Relationship: PG 67-22, RTFOT aged @ 7.2% AC......................57 4.27 Log Sm – Log Sb Relationship: PG 67-22, RTFOT aged @ 7.2% AC......................57 4.28 Log Sb ’ – Log Sb Relationship: PG 76-22, RTFOT aged @ 6.1% AC......................58 4.29 Log Sm – Log Sb Relationship: PG 76-22, RTFOT aged @ 6.1% AC......................58 4.30 Log Sb ’ – Log Sb Relationship: PG 76-22, RTFOT aged @ 7.2% AC......................59 4.31 Log Sm – Log Sb Relationship: PG 76-22, RTFOT aged @ 7.2% AC......................59 4.32 Stiffness Prediction from PG 67 -22,extracted binder, @ 6.1% AC @ 0 ..............60 4.33 Stiffness Prediction from PG 67 -22,extracted binder, @ 6.1% AC @ 10 ............60

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ix 4.34 Stiffness Prediction from PG 67 -22,extracted binder, @ 6.1% AC @ 20 ............61 4.35 Stiffness Prediction from PG 67 -22, extracted binder, @ 7.2% AC @ 0 .............61 4.36 Stiffness Prediction from PG 67 -22,extracted binder, @ 7.2% AC @ 10 ............62 4.37 Stiffness Prediction from PG 67 -22, extracted binder, @ 7.2% AC @ 20 ...........62 4.38 Stiffness Prediction from PG 76 -22, extracted binder, @ 6.1% AC @ 0 .............63 4.39 Stiffness Prediction from PG 76 -22, extracted binder, @ 6.1% AC @ 10 ...........63 4.40 Stiffness Prediction from PG 76 -22, extracted binder, @ 6.1% AC @ 20 ...........64 4.41 Stiffness Prediction from PG 76 -22, extracted binder, @ 7.2% AC @ 0 .............64 4.42 Stiffness Prediction from PG 76 -22,extracted binder, @ 7.2% AC @ 10 ............65 4.43 Stiffness Prediction from PG 76 -22, extracted binder, @ 7.2% AC @ 20 ...........65 4.44 Stiffness Prediction from PG 67-22, RTFOT aged, @ 6.1% AC @ 0 .................66 4.45 Stiffness Prediction from PG 67-22, RTFOT aged, @ 6.1% AC @ 10 ...............66 4.46 Stiffness Prediction from PG 67-22, RTFOT aged, @ 6.1% AC @ 20 ...............67 4.47 Stiffness Prediction from PG 76-22, RTFOT aged, @ 6.1% AC @ 0 .................67 4.48 Stiffness Prediction from PG 76-22, RTFOT aged, @ 6.1% AC @ 10 ...............68 4.49 Stiffness Prediction from PG 76-22, RTFOT aged, @ 6.1% AC @ 20 ...............68 4.50 Stiffness Prediction from PG 67-22, RTFOT aged, @ 7.2% AC @ 0 .................69 4.51 Stiffness Prediction from PG 67-22, RTFOT aged, @ 7.2% AC @ 10 ...............69 4.52 Stiffness Prediction from PG 67-22, RTFOT aged, @ 7.2% AC @ 20 ...............70 4.53 Stiffness Prediction from PG 76-22, RTFOT aged, @ 7.2% AC @ 0 .................70 4.54 Stiffness Prediction from PG 76-22, RTFOT aged, @ 7.2% AC @ 10 ...............71 4.55 Stiffness Prediction from PG 76-22, RTFOT aged, @ 7.2% AC @ 20 ...............71 4.56 Stiffness Prediction from PG 67-22, extracted binder @ 6.1% AC.........................73 4.57 Stiffness Prediction from PG 67-22, extracted binder @ 7.2% AC..........................73

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x 4.58 Stiffness Prediction from PG 67-22, RTFOT aged, @ 6.1% AC..............................74 4.59 Stiffness Prediction from PG 67-22, RTFOT aged, @ 7.2% AC.............................74 4.60 Energy Ratio Prediction: PG 67-22, 6.1% AC @ 0 ...............................................79 4.61 Energy Ratio Prediction: PG 67-22, 6.1% AC @ 10 .............................................79 4.62 Energy Ratio Prediction: PG 67-22, 6.1% AC @ 20 .............................................79 4.63 Energy Ratio Prediction: PG 67-22, 7.2% AC @ 0 ...............................................80 4.64 Energy Ratio Prediction: PG 67-22, 7.2% AC @ 10 .............................................80 4.65 Energy Ratio Prediction: PG 67-22, 7.2% AC @ 20 .............................................80 4.66 Energy Ratio Prediction: PG 76-22, 6.1% AC @ 0 ...............................................81 4.67 Energy Ratio Prediction: PG 76-22, 6.1% AC @ 10 .............................................81 4.68 Energy Ratio Prediction: PG 76-22, 6.1% AC @ 20 .............................................81 4.69 Energy Ratio Prediction: PG 76-22, 7.2% AC @ 0 ...............................................82 4.70 Energy Ratio Prediction: PG 76-22, 7.2% AC @ 10 .............................................82 4.71 Energy Ratio Prediction: PG 76-22, 7.2% AC @ 20 .............................................82 4.72 Energy Ratio Prediction: PG 67-22, 6.1% asphalt content @ 0 ............................83 4.73 Energy Ratio Prediction: PG 67-22, 6.1% asphalt content @ 10 ..........................83 4.74 Energy Ratio Prediction: PG 67-22, 6.1% asphalt content @ 20 ..........................83 4.75 Energy Ratio Prediction: PG 67-22, 7.2% asphalt content @ 0 ............................84 4.76 Energy Ratio Prediction: PG 67-22, 7.2% asphalt content @ 10 ..........................84 4.77 Energy Ratio Prediction: PG 67-22, 7.2% asphalt content @ 20 ..........................84 4.78 Energy Ratio Prediction: PG 76-22, 6.1% asphalt content @ 0 ............................85 4.79 Energy Ratio Prediction: PG 76-22, 6.1% asphalt content @ 10 ..........................85 4.80 Energy Ratio Prediction: PG 76-22, 6.1% asphalt content @ 20 ..........................85 4.81 Energy Ratio Prediction: PG 76-22, 7.2% asphalt content @ 0 ............................86

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xi 4.82 Energy Ratio Prediction: PG 76-22, 7.2% asphalt content @ 10 ..........................86 4.83 Energy Ratio Prediction: PG 76-22, 7.2% asphalt content @ 20 ..........................86 4.84 Energy Ratio Prediction fr om Unmodified Mixture @ 6.1% asphalt content...........87 4.85 Energy Ratio Prediction fr om Unmodified Mixture @ 7.2% asphalt content...........87

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xii Abstract of Thesis Presen ted to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Engineering USE OF BINDER RHEOLOGY TO PRED ICT THE CRACKING PERFORMANCE OF SBS-MODIFIED MIXTURE By Zhanwu Cui December, 2003 Chair: Reynaldo Roque Cochair: Bjorn Birgisson Major Department: Civil and Coastal Engineering A laboratory investigation was conducted to identify and evaluate the relationships between binder stiffness and mixture stiffness th at could be used to predict the effects of polymer-modified binder on mixture cracking performance once mixture properties are determined with unmodified binder. This wo rk was part of a larger study that was evaluating the effects and cost-benefits of using poly-modified mixtures. The laboratory investigation was conducte d with both unmodified binders and SBS modified binders. Both types of binders in cluded extracted binders from Short Term Oven Aged (STOA) mixtures and the virgin binders after Rolling Thin Film Oven Test (RTFOT). The binders were tested with Bend Beam Rheometer (BBR) and Dynamic Shear Rheometer (DSR) to obtain properties over a range of temperatures. Properties of the binders that were test ed and evaluated include creep at low temperatures and complex modulus and phase angle at intermediate and high temperatures. These properties were used to construct the creep compliance master curve

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xiii of the binders. Mixture creep compliance was measured at multiple temperatures using the Superpave IDT. Test results were used to develop and evaluate the potential use of binder-to-mixture stiffness relationships. Test results indicate that th ere is no single binder-to-mix ture stiffness relationship that is suitable for multiple temperatures. At each temperature in this study, there was one binder-to-mixture stiffness relationship. It appears that microdamage develops in mixtures upon cooling to temperatures below 20 which affects mixture response in a way that is not captured by bi nder test results. For any give n temperature, it appears the modified binder behaves more stiffly in the mix than would be predicted by the unmodified binder-to-mixture stiffness rela tionship. Although this yields conservative estimates of cracking performance, it may not give enough credit to the modification.

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1 CHAPTER 1 INTRODUCTION 1.1 Background The Strategic Highway Research Program (SHRP) was established in 1988 to improve the performance and durability of road s in the United States (1). The Superpave (Superior Performing Asphalt Pavements) mix design method was one of the SHRP research program outcomes. The Superpave mix design method has become very popular in most of the states in America, including Florida. Compared with the traditional Marshall and Hveem mix design methods, Superpave ha s the following advantages: Criteria were introduced to minimize the potential use of substandard or unacceptable aggregates A broader range of in-service temperatures is incorporated in the binder selection specifications, including low temperatures The Gyragtory compactor which simulates more closely the field compaction and traffic conditions was introduced. (2) The creep compliance of the asphalt mixtur e is a function of time and temperature and can be used to predict the stresses a nd cracking in asphalt pa vement. The master creep compliance curve can be determined usi ng a testing and analysis system developed in the SHRP program that incorporates the Superpave Indirect Tens ile Test (IDT). Since it is very costly and time consuming to run mi xture tests, especially over a wide range of temperature and time, identification of the reliable binder-to-mixture stiffness relationships would be extremely useful.

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2 Binder-to-mixture stiffness relationships have been used to study the cracking behavior of asphalt mixtures at low temperature (3). Ho wever, previous study showed that due to the temperature-dependent damage at low temperatures, the binder-to-mixture stiffness relationship at a si ngle temperature can not be used to accurately predict the stiffness at other temperatures. Therefore, the study showed that the use of a singlefunction binder-to-mixture stiffness relations hip will result in the poor estimates of mixture stiffness. (3). The above observation was made at low temperatures (below 0 ). Therefore, it would be important to determine whether a single-function binder-to-mixture stiffness relationship could be used at inte rmediate temperatures (0 to 20 ). It would also be important to determine whether binder-tomixture stiffness relationships apply to modified binders. This would preclude the need to perform physical test on asphalt mixture, specifically modified asphalt mi xture, once the mixture properties are determined with a binde r of known properties. 1.2 Study Objectives The primary objectives of this research are the following: 1. To determine whether creep properties, namely m-value and D1 of the polymermodified mixtures can be determined once the creep properties of the unmodified mixture and the properties of the modified binder are known. If so, there is no need to test polymer modified mixtures. 2. To determine whether mixture properties, particularly D1 and m-value, can be determined for multiple temperatures using the mixture properties at one temperature along with the binder master curve. 3. To determine whether the Energy Ratio (ER) at multiple temperatures can be determined using the binder-to-mixture st iffness relationship at one temperature and whether the Energy Ratio of polymer modified mixtures can be determined using unmodified binder-to-mixture stiffne ss relationship and the modified binder properties.

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3 1.3 Scope of Study This laboratory investigation was co nducted with both unmodified and polymer (SBS) modified binders, PG 67-22 and PG 76-22, respectively and asphalt mixtures produced with these two binders. Both ex tracted binders from corresponding asphalt mixtures and virgin binders after Rolling Thin Film Oven Test (RTFOT) were tested. The Bending Beam Rheoemter (BBR) and Dyna mic Shear Rheometer (DSR) were used. The four mixtures in this study were coarse -graded (gradation below the restricted zone) Superpave mixtures produced by using S outh Florida Limestone. The design asphalt contents were 6.1% and 7.2% wh ich corresponded to two differe nt traffic levels using the Superpave mixture design procedure. The SBS m odified mixtures were prepared to have the same effective asphalt content as the unm odified asphalt mixtures. All the mixtures were Short Term Oven Aged for two hours and then compacted to 7% ( 0.5%) air voids. The creep compliance, m-value, tensile strength, failure strain, fracture energy and dissipated creep strain energy to fail ure were obtained from IDT test.

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4 CHAPTER 2 LITERATURE REVIEW 2.1 Introduction The purpose of this chapter was to revi ew various binder-to-mixture stiffness relationships. The use and effects of the aspha lt modifiers were also reviewed. Available data and information regarding binder creep compliance master cu rve and shift factors were also studied. Some miscellaneous i ssues regarding binder-t o-mixture stiffness relationships were also covered. 2.2 Binder-to-Mixture Stiffness Relationship The practical goal of developing binder-tomixture stiffness relationships is to predict mixture performance with little or no mixture testing. There are two ways to achieve this goal: theoretical and empirical binder-to-mixture stiffness relationships. 2.2.1 Theoretical Binder-to-Mixtu re Stiffness Relationship Theoretical binder-to-mixture stiffness relationships use the micromechanical analysis to develop the relationship. In th is method, the properties of the composite materials can be obtained from the pr operties of the constituents. Several micromechanical models have been proposed. The following were reviewed: 1. Paul’s equation, (4), Rule of Mixtures 2. Hashin and Shtrikman’s arbitrary phase geometry model, (5) 3. Hashin’s composite spheres model (6) 4. Christensen and Lo’s generalized se lf-consistent scheme model (7, 8)

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5 2.2.1.1 Paul’s equations and the rule of mixtures Paul’s equations (equations 2.1 and 2.2) cal culate the effective elastic moduli of two-phase, irregular geometry composite materials. 2 2 1 1 2 2 1 11 c K c K K K c K c (2.1) 2 2 1 1 2 2 1 11 c G c G G G c G c (2.2) where K*, G* = Effective bulk and shear moduli of the composite K1, K2 = Bulk moduli of phase 1 and 2 G1, G2 = Shear moduli of phase 1 and 2 c1, c2 = Volume fractions of phase 1 and 2 The shear and bulk moduli can be related to Young’s modulus (E), and Poisson’s ratio by the following equations: K G E 9 1 3 1 1 (2.3) ) 1 ( 3 E G (2.4) The right-hand side of the equations 2.1 and 2.2 are referred to as the “Law of Mixtures.” 2.2.1.2 Hashin and Shtrikman’s arbitrary phase geometry model Hashin and Shtrikman (5) derived the equations for an n-phase composite of arbitrary phase geometry. The following equa tions are based on a two-phase composite.

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6 1 1 1 1 2 2 1 *4 2 3 1 G K c K K c K KL (2.5) 2 2 2 2 1 1 2 *4 2 3 1 G K c K K c K KU (2.6) where U LK K K* * (2.7) ) 4 3 ( 5 ) 2 ( 6 11 1 1 1 1 1 1 2 2 1 *G K G c G K G G c G GL (2.8) ) 4 3 ( 5 ) 2 ( 6 12 2 2 2 2 2 2 1 1 1 *G K G c G K G G c G GU (2.9) U LG G G* * (2.10) and the following conditions must be met: 1 2K K and 1 2G G (2.11) where K*L = Effective bulk modulus of the composite, lower bound G*L = Effective shear modulus of the composite, lower bound K*U = Effective bulk modulus of the composite, upper bound G*U = Effective bulk modulus of the composite, upper bound 2.2.1.3 Hashin’s composite spheres model The composite spheres model consists of a gradation of infinite ly-packed spherical particles in a continuous matrix phase (3). Th e model assumes that the ratio of particle diameter to the diameter of the surrounding c oncentric matrix (a/b) is constant for all

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7 particles. Under these assumpti ons, the bulk properties of a si ngle composite are identical to the bulk properties of the complete com posite spheres. Figure 2.1 is the classical micromechanics composite sphere model. Figure 2.1 The Composite Spheres Model (3) The equations for the composite spheres model are given as: c K K K G c K G K K K Kp m p m m m m p m) ( 3 3 4 ) 3 4 )( (* (2.12) ) ( 1 *) 1 ( 1y c G Gm L (2.13) ) ) 1 ( 1 () ( 1 *y c G Gm U (2.14) where m pG G (2.15) Km, Gm = Bulk and shear moduli of the matrix Kp, Gp = Bulk modulus of the particles (or inclusions) c = Volume concentration of inclusions = (a/b)3

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8 a, b = Radii of particle and concentric matrix yl( ), yl( ) = Complicated functions of the elastic constants 2.2.1.4 Christensen and Lo’s genera lized self-consistent scheme The generalized self-consistent scheme is illustrated in figure 2.2. Figure 2.2 The Generalized Self-Consistent Scheme Model (3) The shear modulus is given by the following equations: 0 2* 2 C G G B G G Am m (2.16) where A, B, C = Lengthy functions of the elastic constants,. Up to this point, four micromechanical models have been reviewed. Figure 2.3 (9) gives a comparison of mixture stiffne ss calculated from using these four micromechanical models to measured creep stiffness. The figure shows that the bounds of Paul are the widest, followed by the ar bitrary geometry bounds and the composite spheres bounds. Paul’s model and the arbitr ary geometry model cover some measured

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9 values, but they are too wide to provide useful information. Only when the binder stiffness is very high, the micromechanical models tend to converge with the measured values. Predicted values from Christensen and Lo’s scheme are much lower than the measured ones. Figure 2.3 show that the mi cromechanical models give poor estimation on the binder-to-mixture stiffness relationshi ps. Research by Reyna ldo Roque et.al (9) shows that aggregate stiffness, Poison’s ratio of the aggregate, combinations of various constants and the sensitivity to air voids we re not found to explain the large differences observed in figure 2.3. Due to the large discrepancies between the predicted stiffness by the micromechanical models and the IDT measuremen ts, it is believed that the use of these models to predict the mixture stiffness is not warranted. 2.2.2 Empirical Binder-to-Mixtu re Stiffness Relationship The following four empirical binder-to-mixture stiffness models wi ll be discussed: 1. Heukelom and Klomp (10) 2. Bonnaure et al. (11) 2.2.2.1 Heukelom and Klomp The following equations (equations 2.17 thr ough 2.19) were given to calculate the mixture stiffness from the binder stiffne ss and the volumetric parameters of the aggregate: n v v b mC C n S S 1 5 2 1 (2.17)

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10 Figure 2.3 Comparison of Mixture Stiffness: Micromechanical Models Versus IDT Range Established Using Measure Creep Stiffness

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11 bS x n510 4 log 83 0 (2.18) ) ( binder aggregate Volumeof gregate Volumeofag Cv (2.19) where Sm = Stiffness of mixture (GPa or Psi) Sb = Stiffness of binder (GPa or Psi) But these equations are for mixtures with Cv between 0.7 and 0.9 and air voids less than or equal to 3%. If the air voids is greater than 3%, Cv ’ is recommended by Van Draat, Fijn and Sommer (12) H C Cv v 1' (2.20) where H = (Pav/100)-0.03 Pav = Percent air voids in the mixture The equations above are only valid for mi xtures satisfying the following equations ) 1 ( 3 2' v BC C (2.21) where ) ( binder aggregate Volumeof nder Volumeofbi CB (2.22) The use of Hekelom and Klomp’s binderto-mixture stiffness relationship is restricted to the binder stiffness to be above 0.02GPa.

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12 2.2.2.2 Bonnaure’s relationship Bonnaure presented another series of equa tions to predict mixture stiffness from binder stiffness: For 5 x 105 Pa 105 Pa, 2 3 4 3 48 log 2 8 log 2 log b b mS S S (2.23) For 109 Pa 109 Pa, 9 log 0959 2 log4 2 1 4 2 b mS S (2.24) where b g gV V V 100 342 1 82 101 (2.25) 2 20002135 0 00568 0 0 8g gV V (2.26) 1 33 1 1 37 1 log 6 02 3 b bV V (2.27) 2 1 47582 0 (2.28) Sb = Binder Stiffness, Pa Vg = Percent volume of aggregate Vb = Percent volume of binder 2.3 Binder Master Curve and Shift Factor The creep compliance master curve and sh ift factors are very useful tools to characterize the viscoelastic properties of as phalt materials at di fferent temperatures. These are used to extrapolate the creep comp liance of a material over a broader range of temperatures and loading times from a limited set of experiments. The time-temperature

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13 superposition principle is used to construct the creep complia nce master curve. Figure 2.4 (13, 14) illustrates this principle. For linear viscoelastic materials, there is a relationship between the loading time and temperature. To construct a creep compliance master curve, the creep compliance at different temperatur es should be obtained and plotted on a log compliance-log time scale. Then a single te mperature is selected to which the creep compliance at other temperatures is shifte d horizontally to form a continuous smooth curve at this temperature. This smooth curve is called the master creep compliance curve. The selected temperature is ca lled the reference temperature. Figure 2.4 Construction of the Master Compliance Curve (13, 14) The method of reduced time is used to obtain the creep compliance at temperatures other than the reference temperature: Ta t (2.29)

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14 where = Reduced time t = Real time aT = Temperature shift factor The shift factor is another very important parameter obtaine d from constructing the master creep compliance curve. On a log creep compliance – log time scale, log (1/ at) corresponds to the horizo ntal distance of the shifting. Two equations are commonly used to obtain shift factors for asphalt binders: For T Td, the Williams-Landel-Ferry (WLF) (15) equation (2.30) is used: ) ( 92 ( 19)d d T TT T T T a a Logd (2.30) For T Td, the Ahrennius function (2.31) is used: d g a T TT T R E a a Logd1 1 303 2 (2.31) where: aT/aTd = the shift factor relative to the defining temperature T = Temperature at which properties are desired, (K) Td = Defining Temperature, (K) Ea = Activation energy for flow below Td 261,000 J/mol Rg = Ideal gal constant, 8.34 J/mol-K K = C + 273

PAGE 28

15 2.4 Power Model The power model is often used to fit to describe the master curve: mD D D 1 0) ( (2.32) where D() = Creep compliance at reduced time, = Reduced time D0, D1, m = Power model parameters The m-value describes the linear part of the master curve on the log creep compliance-log time scale. Figure 2.5 shows th e power model and the parameters in the master curve.D0 represents the elastic portion of th e creep compliance. Christensen and Anderson (15) found that the maximum stiffness for all asphalts is 3GPa. Therefore, the minimum D0 is: Pa GPa D10 010 33 3 3 / 1 (2.33) Figure 2.5 Power Model

PAGE 29

16 2.4 Modifiers in Asphalt Pavement Materials Asphalt modifiers and additives have been used in asphalt pavement materials for about 100 years (16). With the increase of the traffic volume, higher performance asphalt binder for road construction is required. Modi fied asphalt binders are expected to have higher performance than pure asphalt. Among mo difiers, polymer is one of the most important types used to impr ove the performance of the as phalt binder (17). Research showed that the polymer modifiers can improve the resistance to high temperature rutting and low temperature cracking ( 18). Studies by Booil Kim (19) also showed that the SBS modified mixture generally has a lower m-va lue than unmodified mixture. However, the modifier’s function in the asphalt mixture is still not clearly understood. A general description on the modifiers used in asphalt mixtures is provided below. Polymer is the name given to a kind of materials with high molecular weight, normally 104~106. The word polymer is derive d from the classical Greek Poly meaning “many” and Mers meaning “parts”. So, pol ymer is a substance manufactured by linking many parts of a repeating unit toge ther through chemical reaction. Polymer modifiers are the most advanced asphalt modifiers currently used today (18). There are 3 main kinds of polymer m odifiers: the thermoplastic, crystalline polymers, the thermoplastic rubbers and the thermosetting polymers. Thermoplastics, when reacted with appropr iate ingredients, can usually withstand several heating and cooling cycles without suffering structural breakdown Crystalline polymers, also known as “plastomers” incl udes polyethylene, polypropylene, polyvinyl chloride (PVC), polystyrene, ethylene vinyl acetate (EVA) and ethylene methyl acrylate (EMA). Thermoplastic rubber, also known as “elastomers”, includes natural rubber, styrene-butadiene rubber (SBR), styrene-but adiene-styrene (SBS), styrene-isoprene-

PAGE 30

17 styrene (SIS), polybutadiene (PBD) and polyi soprene. Both the plastomers and the elastomers have an important effect on the temperature susceptibility of the stiffness of the asphalt. Because the polymers are genera lly far less susceptible to changes in temperature due to their chemical structure (18), it will greatly reduce the temperature susceptibility of asphalt binders. A recent st udy showed that a highly entangled fibril network structure has been seen from both unmodified and modifi ed asphalt binders, but the fibrils in the SBS modified asphalt concrete is long and thin, while those found in the unmodified asphalt concrete is thick and short (20). It al so showed that the fibrils exhibited some recovery behavior wh ich may be good for “healing” (20). A thermoset is a polymer that, when heated, undergoes a chemical change to produce a crosslinked solid polymer, but is in capable of undergoing repeated cycles of softening and hardening (21). E poxy falls into this category. It has been showed that the benefit of the epoxy for asphalt mixture is th at it could increase th e stiffness and reduce the rutting characteristics of the asphalt concrete (17). 2.5 HMA Fracture Mechanics Model Research at the University of Florida ha s shown that the dissipated creep strain energy limit can be used to identify th e crack initiation an d propagation (22). Furthermore, this property can be obtained from Superpave IDT. For cyclic loading, the numbers of cycles to failure is defined as: cycle DCSE gthTest tfromStren EnergyLimi CreepSrain Dissipated N / (2.34) 1 1 2100 ) ( 20 1 /m AVEm D cycle DCSE (2.35)

PAGE 31

18 Another parameter to compare th e cracking resistance of different pavement structures is the Energy Ratio (ER) developed by Jajliardo (23). Energy Ratio represents the fracture toughness of the asphalt mixtures The equation for Energy Ratio is given below: 1 98 2D m DCSE a ERf (2.36) where 8 1 310 46 2 ) 36 6 ( 0299 0 tS a = tensile stress of asphalt layer, psi St= tensile strength, MPa DCSEf = Dissipated Creep Strain Energy, KJ/m3 D1= creep parameter, 1/psi m = creep parameter

PAGE 32

19 CHAPTER 3 RESEARCH PROGRAM AND INSTRUMENTATION 3.1 Introduction This chapter provides information on the materials and procedures for the production of binder and mixture specimens in the laboratory, and a summary of the testing procedures and instrumentation. Also presented is the information on the mixtures used in this study. 3.2 Materials This section provides information on th e asphalt binders a nd the corresponding mixtures used in this study. 3.2.1 Binders Two kinds of asphalt binders were used in this study, PG 67-22 and PG 76-22. Both of these binders were produced by CI TGO Asphalt Refining Company. PG 67-22 is unmodified binder and its prope rties are similar to AC-30. PG 76-22 is SBS (Styrene Butadiene Styrene) modified binder. There is approximately 3% SBS in the modified asphalt, and the base asphalt used for modi fication was the unmodified PG 67-22. The SBS was blended with the base asphalt by the manufacturer using high shear milling. PG 67-22 was used as the control binder in this study. Some binder test results provided by the supplier are presented as in tables 3.1, 3.2 and 3.3,.

PAGE 33

20 Table 3.1 Penetration at 25C (77F) Binder Type Replicate Penetration Average Standard Deviation AC-30 1 2 3 61 60 60 60 1 SBS 1 2 3 50 51 50 50 1 Table 3.2 Dynamic Shear Rheometer at 25C (77F) Binder Type Replicate G* (KPa) G* x sin ( Average AC-30 1 2 3 1110 1070 902 66.7 67.4 67.4 1020 985 833 946 SBS 1 2 3 748 737 733 58.7 61.0 60.5 639 644 638 640

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21 Table 3.3 Dynamic Shear Rheometer at 64C (147F) Binder Type Replicate G* (KPa) G* / sin ( Average AC-30 1 2 3 1.93 2.01 2.01 86.2 86.1 86.2 1.93 2.02 2.02 1.99 SBS 1 2 3 6.16 6.24 6.12 63.9 64.5 64.5 6.86 6.91 6.80 6.86 The two binders tested in this study we re the binders extracted from asphalt mixtures after Short Term Oven Aging (STOA) and the virgin binders after Rolling Thin Film Oven Test (RTFOT). The results of these tests are presented later. 3.2.2 Mixtures Four types of asphalt mixture were used in this study. All these mixtures were coarsegraded Superpave mixtures produced with South Florida limestone. The design asphalt contents was 6.1% and 7.2% which corresponded to two traffic levels in the Superpave mixture design procedure. The modified mixtures had the same effective asphalt content as the unmodified mixtures to assure that th e SBS modifier was the only factor affecting the test results. All mixtures were laboratory-prepared samples and were Short Term Oven Aged (STOA) for two hours (AASHT O PP2-94) and then compacted to 7% (0.5%) air voids using the Superpave Gyrato ry Compactor. The mixing temperature for the SBS modified mixture is recommended by the manufacturer. Details about the mixtures are presented in Table 3.4 (19)

PAGE 35

22 Table 3.4 Mixture Test Samples Samples Binder content* Binder type** Aggregate type/gradation Designation 6.1 6.1% Straight Limestone/C1*** Control sample 7.2 7.2% Straight Limestone/C 1 Unmodified higher binder content 6.1SBS 6.1% Modified Limestone/C1 Modified Same binder content 7.2SBS 7.2% Modified Limestone/C 1 Modified higher binder content 6.1% and 7.2 % binder content are corres ponding to traffic le vel 5 and 3 based on Superpave level 1 mix design, respectively. ** Straight binder and modi fied binder are corresponding to PG 67-22 and PG 76-22, respectively. *** C1 is most commonly used in Florida Department of Transportation for coarse gradation with 12.5mm nominal maximum aggregate size Details on gradation and pavement mixture design are in Appendix A. 3.3 Binder Preparation 3.3.1 Extraction and Recovery of the Binder Binder extraction for both the PG 67-22 and PG 76-22 were performed in accordance with FM 5-524 and ASTM 3-D5404. 3.3.2 Rolling Thin Film Oven Test (RTFOT) Both PG 67-22 and PG 76-22 virgin binders were aged using Rolling Thin Film Oven Test (RTFOT) in accordance with D 287297, to simulate the aging process during the conventional hot-mixing which is comparable with the Short Term Oven Aging ( STOA) in mixtures. 3.4 Testing of Binders To develop binder master curve and binderto-mixture stiffness relationships, the binder was tested by performing Bending B eam Rheometer (BBR) and Dynamic Shear Rheometer (DSR) tests.

PAGE 36

23 3.4.1 Bending Beam Rheometer Test The Bending Beam Rheometer (BBR) measures the stiffness of binders at low service temperatures. The device was developed as part of the SHRP bi nder research program. The BBR consists of three parts: the loading system, the temperature control bath and the data acquisition system as illustrated in the following schematic. (1) Figure 3.1 Schematic of Bending Beam Rheometer The Bending Beam Rheometer is as follows (24): Figure 3.2 Bending Beam Rheometer

PAGE 37

24 The BBR applies a transient creep load in bending mode to load the specimen, which is held at a constant temperature. Th e data acquisition system records the load and deflection results and calculate the creep stiffness, S(t), and m-value, which is the slope of the stiffness-time relationship at t = 60s. The creep stiffness of the asphalt binder is a measurement of how the asphalt binder resists creep loading. It is calcu lated using the following equation (1): ) ( 4 ) (3 3t bh PL t S (3.1) where S(t) = creep stiffness at time, t = 60 seconds P = applied constant load, 100g (980mN) L = distance between beam supports, 102mm B = beam width, 12.5mm h = beam thickness, 6.25mm (t) = deflection at time, t = 60 seconds The m-value is defined as the slope of the log creep stiffness versus log time curve at a loading time of 60s. It indicates the rate of change in stiffness with time, S(t). Below is a plot of m-value. (1)

PAGE 38

25 Figure 3.3 m-value from the Bending Beam Rheometer In this study, the BBR test is conducted at -10C. Three specimens of each kind of binder were prepared and tested and the st iffness results were used to develop Power Law parameters and the creep compliance master curve of the binder. 3.4.2 Dynamic Shear Rheometer Test The Dynamic Shear Rheometer (DSR) ch aracterizes the viscous and elastic properties of asphalt binders at intermediate to high temperatures. It measures the complex modulus, G*, and phase angle, of the binder. Below is a schematic of the Dynamic Shear Rheometer (1): Figure 3.4 Schematic of Dynamic Shear Rheometer

PAGE 39

26 The complex modulus, G*, is the total resist ance of the binder to deformation and it has two components: the stor age modulus, G’, which reflec ts the elastic response and the loss modulus, G’’, which reflects the vi scous response. The relationship between G*, G’, and G’’ is shown below (1): Figure 3.5 Components of Complex modulus G* The figure above also shows that the two asphalt binders with the same complex modulus may have different pha se angle and so th e storage modulus and the loss modulus are different. The following equations are used to calculate the complex modulus, G*. max max* G (3.2) 32 r Tmaz (3.3) h r max (3.4) where T = maximum applied torque

PAGE 40

27 r = radius of binder specimen/plate (12.5mm or 4mm) = deflection angle h = specimen height (1mm or 2mm) In Superpave binder testing, the test is conducted at a single frequency of 10 rad /sec. A constant stress is applied as the loading mode. The G* and are reported at the end of the test. But in this study, the Dyna mic Shear Rheometer research software was used to run the DSR test so that the binder ca n be tested at multiple frequencies. G’, G’’, viscosity, stress and strain were al so obtained in addition to G* and From the DSR test at multiple frequencies, the data can then be converted into creep compliance power law parameters. The DSR test was conducted at 10 and 20. Frequencies of 0.5 Hz, 1Hz, 2 Hz, 4 Hz, 8 Hz and 15 Hz were used at each temperature. The constant strain mode is chosen and the 8mm sample w ith 2mm gap was used in this study. The following figures illustrate the DSR equipment (24): Figure 3.6a

PAGE 41

28 Figure 3.6b Figure 3.6 a, b DSR equipment 3.5 Testing of Mixtures Mixture test were obtained using Superpave Indirect Te nsile Test (IDT). Resilient modulus, creep compliance, m-value, tensile st rength, failure strain fracture energy and dissipated creep strain energy to failure were obtained from the tests.

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29 CHAPTER 4 SUMMARY AND ANALYSIS OF LABORATORY TEST RESULTS 4.1 Introduction This chapter presents a discussion of the binder and mixture test results. The test results of the binder include creep stiffness, S(t), m-value, complex modulus, G*, and phase angle, Mixture test result includes creep comp liance, tensile strength, dissipated creep strain energy, m-value. 4.2 Summary of Binder Test 4.2.1 Bending Beam Rheometer Test A summary of the Bending Beam Rheometer results at 60 sec. is presented in Table 4.1. The Bending Beam Rheomete r tests were conducted at -10 for both the extracted binders and the virgin binders after Rolling Thin Film Oven Test. Comparisons of the results at 60 seconds indicate that the stiffness of the SB S modified binders are lower than those of the unmodified binders. Howeve r the m-value at 60 seconds was similar for all binders. The variation in m-value change observed was probably a result of the effects of the extraction process whic h may break the molecular stru cture of the modified binder and affect the results. A summary of the Bending Beam Rheomete r test results for each kind of binders are also presented in Appendix A.

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30 Table 4.1 Bending Beam Rheometer Test Result at -10, 60 sec. Binder Type Replicate Measured Stiffness (MPa) Average m-value Average 1 49 0.484 2 52.8 0.472 PG 67-22 6.1% asphalt content 3 51.4 51.07 0.469 0.475 1 45.9 0.450 2 46.7 0.470 PG 76-22 6.1% asphalt content 3 47.1 46.57 0.461 0.460 1 46.6 0.483 2 46.4 0.479 PG 67-22 7.2% asphalt content 3 47.5 46.83 0.475 0.479 1 39 0.483 2 39.6 0.478 PG 76-22 7.2% asphalt conent 3 40.8 39.80 0.469 0.477 1 48.3 0.485 2 51.7 0.476 PG 67-22 RTFOT aged 3 54.2 51.40 0.476 0.479 1 37.7 0.496 2 37.8 0.491 PG 76-22 RTFOT aged 3 36.7 37.40 0.488 0.492

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31 Ave. Measured Stiffness (MPa) PG 67-22, 6.1% AC PG 76-22, 6.1% AC PG 67-22, 7.2% AC PG 76-22, 7.2% AC PG 67-22, RTFOT PG 76-22, RTFOT 0.00 10.00 20.00 30.00 40.00 50.00 60.00Measured Stiffness (MPa) Figure 4.1 Comparison of the Measured Stiffness Ave. m-value PG 67-22, 6.1% AC PG 76-22, 6.1% AC PG 67-22, 7.2% AC PG 76-22, 7.2% AC PG 67-22, RTFOT PG 76-22, RTFOT 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Measured Stiffness (MPa) Figure 4.2 Comparison of the m-value

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32 4.2.2 Dynamic Shear Rheometer The Dynamic Shear Rheometer test was conducted to obtain G* and at both 10 and 20. This test was conducted at multiple frequencies to convert the dynamic test results to power model creep compliance parameters. 4.2.2.1 Dynamic Shear Rheometer at low frequencies The frequencies used in the low freque ncy test were: 0.001, 0.002, 0.004, 0.008, 0.015, 0.03 Hz. The typical test result is shown in table 4.8. Table 4.2 Dynamic Shear Rheometer Test Results at Low Frequencies at 10 Frequency (Hz) Phase Angle () Viscosity (Pas) Shear Stress (Pa) 0.001 10.72 2.78 x 106 3.68 x 102 0.002 78.80 2.42 x 107 8.60 x 101 0.004 58.93 2.16 x 107 1.02 x 103 0.008 55.97 1.66 x 107 1.67 x 103 0.015 56.48 1.26 x 107 2.38 x 103 0.03 53.86 9.70 x 106 3.77 x 103 The results indicated that, reasonabl e results could not be obtained at very low frequencies. Therefore, the conversion to pow er model parameters was more difficult and unreliable. The figure below showed another problem with very low frequency tests.

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33 Figure 4.3 The Log Sh ear StressLog Frequency Relationship This figure indicated that the binder re sponse was is not in the linear range at low frequencies, consequently. Low frequency tests were not used in this study. 4.2.2.2 The Dynamic Shear Rheometer Test at high frequencies The higher frequency sweeps used in th e study included: 0.5, 1.0, 2.0, 4.0, 8.0, and 15.0 Hz. Test results were presented in Appendix B The test results indicate that there is no big different between the unmodified binder and the SBS modified binder. 4.3 Binder Creep Compliance Master Curve The binder creep compliance master curv e and associated shift factors are two critical elements in developing binder-to-mixture sti ffness relationships. These two topics will be discussed in this section. 4.3.1 Shift Factors The following equations for the shift f actor were presented in Chapter 2:

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34 For T Td, the Williams-Landel-Ferry (WLF) equation (2.30) is used: ) ( 92 ) ( 19d d T TT T T T a a Logd (2.30) For T Td, the Ahrennius function (2.31) is used: d g a T TT T R E a a Logd1 1 303 2 (2.31) where aT/aTd = the shift factor relative to the defining temperature T = Temperature at which properties are desired, (K) Td = Defining Temperature, (K) Ea = Activation energy for flow below Td 261,000 J/mol Rg = Ideal gal constant, 8.34 J/mol-K K = C + 273 To make the computation easy and simple, Td was made to coincide with Tref, So, the equation above resulted in the following equations: For T Tref, the Williams-Landel-Ferry (WLF) equation (2.30) is used: ) ( 92 ) ( 19ref ref Tref TT T T T a a Log (4.1) For T Tref, the Ahrennius function (2.31) is used: ref g a Tref TT T R E a a Log1 1 303 2 (4.2)

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35 A review of literature indicated that the relationship between Log aT and T-Td is linear when T-Td is between -15 and 35 and Td is between -15 and 5(25). In this study, the temperature of interest was between -10 and 20 and T-Td falls between -15 and 35. Linear regression was performed for e quation 4.1 within this temperature range, which resulted in the following equation for the shift factor: ) ( 175 0 logref TT T a (4.3) This equation can be used regardless of whether T>Td or T
Permanent Link: http://ufdc.ufl.edu/UFE0001328/00001

Material Information

Title: Use of binder rheology to predict the cracking performance of SBS-modified mixture
Physical Description: xiii, 143 p. ; ill.
Language: English
Creator: Cui, Zhanwu ( Dissertant )
Roque, Reynaldo ( Thesis advisor )
Tia, Mang ( Reviewer )
Birgission, Bjorn ( Thesis advisor )
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2003
Copyright Date: 2003

Subjects

Subjects / Keywords: Civil and Coastal Engineering thesis, M.E
Dissertations, Academic -- UF -- Civil and Coastal Engineering

Notes

Abstract: A laboratory investigation was conducted to identify and evaluate the relationships between binder stiffness and mixture stiffness that could be used to predict the effects of polymer-modified binder on mixture cracking performance once mixture properties are determined with unmodified binder. This work was part of a larger study that was evaluating the effects and cost-benefits of using poly-modified mixtures. The laboratory investigation was conducted with both unmodified binders and SBS modified binders. Both types of binders included extracted binders from Short Term Oven Aged (STOA) mixtures and the virgin binders after Rolling Thin Film Oven Test (RTFOT). The binders were tested with Bend Beam Rheometer (BBR) and Dynamic Shear Rheometer (DSR) to obtain properties over a range of temperatures. Properties of the binders that were tested and evaluated include creep at low temperatures and complex modulus and phase angle at intermediate and high temperatures. These properties were used to construct the creep compliance master curve of the binders. Mixture creep compliance was measured at multiple temperatures using the Superpave IDT. Test results were used to develop and evaluate the potential use of binder-to-mixture stiffness relationships. Test results indicate that there is no single binder-to-mixture stiffness relationship that is suitable for multiple temperatures. At each temperature in this study, there was one binder-to-mixture stiffness relationship. It appears that microdamage develops in mixtures upon cooling to temperatures below 20℃, which affects mixture response in a way that is not captured by binder test results. For any given temperature, it appears the modified binder behaves more stiffly in the mix than would be predicted by the unmodified binder-to-mixture stiffness relationship. Although this yields conservative estimates of cracking performance, it may not give enough credit to the modification.
General Note: Title from title page of source document.
General Note: Includes vita.
Thesis: Thesis (M.E.)--University of Florida, 2003.
Bibliography: Includes bibliographical references.
Original Version: Text (Electronic thesis) in PDF format.

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0001328:00001

Permanent Link: http://ufdc.ufl.edu/UFE0001328/00001

Material Information

Title: Use of binder rheology to predict the cracking performance of SBS-modified mixture
Physical Description: xiii, 143 p. ; ill.
Language: English
Creator: Cui, Zhanwu ( Dissertant )
Roque, Reynaldo ( Thesis advisor )
Tia, Mang ( Reviewer )
Birgission, Bjorn ( Thesis advisor )
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2003
Copyright Date: 2003

Subjects

Subjects / Keywords: Civil and Coastal Engineering thesis, M.E
Dissertations, Academic -- UF -- Civil and Coastal Engineering

Notes

Abstract: A laboratory investigation was conducted to identify and evaluate the relationships between binder stiffness and mixture stiffness that could be used to predict the effects of polymer-modified binder on mixture cracking performance once mixture properties are determined with unmodified binder. This work was part of a larger study that was evaluating the effects and cost-benefits of using poly-modified mixtures. The laboratory investigation was conducted with both unmodified binders and SBS modified binders. Both types of binders included extracted binders from Short Term Oven Aged (STOA) mixtures and the virgin binders after Rolling Thin Film Oven Test (RTFOT). The binders were tested with Bend Beam Rheometer (BBR) and Dynamic Shear Rheometer (DSR) to obtain properties over a range of temperatures. Properties of the binders that were tested and evaluated include creep at low temperatures and complex modulus and phase angle at intermediate and high temperatures. These properties were used to construct the creep compliance master curve of the binders. Mixture creep compliance was measured at multiple temperatures using the Superpave IDT. Test results were used to develop and evaluate the potential use of binder-to-mixture stiffness relationships. Test results indicate that there is no single binder-to-mixture stiffness relationship that is suitable for multiple temperatures. At each temperature in this study, there was one binder-to-mixture stiffness relationship. It appears that microdamage develops in mixtures upon cooling to temperatures below 20℃, which affects mixture response in a way that is not captured by binder test results. For any given temperature, it appears the modified binder behaves more stiffly in the mix than would be predicted by the unmodified binder-to-mixture stiffness relationship. Although this yields conservative estimates of cracking performance, it may not give enough credit to the modification.
General Note: Title from title page of source document.
General Note: Includes vita.
Thesis: Thesis (M.E.)--University of Florida, 2003.
Bibliography: Includes bibliographical references.
Original Version: Text (Electronic thesis) in PDF format.

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0001328:00001


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USE OF BINDER RHEOLOGY TO PREDICT THE CRACKING PERFORMANCE OF
SBS-MODIFIED MIXTURE















By

ZHANWU CUI


A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF ENGINEERING

UNIVERSITY OF FLORIDA


2003















ACKNOWLEDGMENTS

I would like to express my sincere appreciation to my supervisor and the chairman

of my supervisory committee, Dr. Reynaldo Roque, for his invaluable technical and

personal assistance throughout my graduate study. Without his support, guidance and

encouragement, this thesis would not be a possible. I would also like to express my

appreciation to Dr. Mang Tia and Dr. Bjorn Birgission for participating as members of

my supervisory committee.

I would also like to acknowledge and thank the Florida Department of

Transportation (FDOT) for providing financial support for this project. My sincere

appreciation and gratitude go to my "research partner," Mr. Booil Kim for his

participation throughout the project. I also thank Mr. George Lopp for his invaluable

assistance in the laboratory. And also, I would like to express my sincere appreciation to

Jae Seung Kim, Adam, and all the graduate students in the materials group for their

assistance and support, and for making my study in the department a pleasure.

Finally, I wish to express my sincere and heartfelt appreciation to my parents,

especially my mother, my brother, for all the years of love, encouragement and support

without which I would not have been able to achieve this success.
















TABLE OF CONTENTS
Page

A C K N O W L E D G M E N T S .................................................................................................. ii

LIST OF TABLES ....................................................... ............ ....... ....... vi

L IST O F F IG U R E S .... ...... ................................................ .. .. ..... .............. vii

ABSTRACT .............. ..................... .......... .............. xii

CHAPTER

1 IN TR OD U CTION ............................................... .. ......................... ..

1.1 B background ......... ...... ................................................................... ........... 1
1.2 Study O bjectives............................................. 2
1.3 Scope of Study .......................2....... ......... ..............3...

2 LITER A TU R E REV IEW ............................................................. ....................... 4

2.1 Introduction ................................................ ........ .... ...................... 4
2.2 Binder-to-Mixture Stiffness Relationship..................................4
2.2.1 Theoretical Binder-to-Mixture Stiffness Relationship ..............................4
2.2.1.1 Paul's equations and the rule of mixtures ...................................... 5
2.2.1.2 Hashin and Shtrikman's arbitrary phase geometry model .................5
2.2.1.3 H ashin's com posite spheres m odel ..................................................6
2.2.1.4 Christensen and Lo's generalized self-consistent scheme .................8
2.2.2 Empirical Binder-to-Mixture Stiffness Relationship.............. ......... 9
2.2.2.1 H eukelom and K lom p ............................................. ............... 9
2.2.2.2 Bonnaure's relationship............. ......................... 12
2.3 Binder M aster Curve and Shift Factor............... ........... .............. .............. 12
2.4 Power M odel ................................... ...................... ........... 15
2.4 Modifiers in Asphalt Pavement Materials ....................... ...............16
2.5 HM A Fracture M echanics M odel .................................... .................................. 17

3 RESEARCH PROGRAM AND INSTRUMENTATION ......................................19

3 .1 In tro du ctio n ...................................... ............................ ................ 19
3 .2 M a te ria ls ...............................................................................................................1 9
3.2 .1 B inders ..................................... ......................... ... ... ... ..... 19
3 .2 .2 M ix tu re s............................................................................. ............... 2 1









3.3 Binder Preparation ........................... .. .. .. .... ...... ................22
3.3.1 Extraction and Recovery of the Binder ................................... ...............22
3.3.2 Rolling Thin Film Oven Test (RTFOT) ............................................. 22
3.4 Testing of Binders................................ ............. .................. 22
3.4.1 Bending Beam Rheometer Test.............................................. 23
3.4.2 Dynamic Shear Rheometer Test........................ ...... ...............25
3.5 T testing of M ixtures........... ... ........................................................ .... .... ... ..... 28

4 SUMMARY AND ANALYSIS OF LABORATORY TEST RESULTS..................29

4 .1 In tro d u ctio n ......................... .......................................................................... 2 9
4.2 Sum m ary of B inder Test............................................................ ............... 29
4.2.1 Bending Beam Rheometer Test................................ ............... 29
4.2.2 Dynamic Shear Rheometer ............. ... ........................... ............... 32
4.2.2.1 Dynamic Shear Rheometer at low frequencies .............................32
4.2.2.2 The Dynamic Shear Rheometer Test at high frequencies ...............33
4.3 Binder Creep Compliance M aster Curve................................... ............... 33
4.3.1 Shift Factors.......................... .. .. ................... ....... .... .............. 33
4.3.2 The Master Creep Compliance Curve........................ ...............35
4.3.2.1 Creep compliance from Dynamic Shear Rheometer test results......35
4.3.2.2 Construction of binder creep compliance master curve .................37
4.4 Binder-to-Mixture Stiffness Relationship.............. ..... ............. 47
4.4.1 Empirical Binder-to-mixture Stiffness Relationship..............................48
4.4.2 Volumetrics of the aggregate...................................... ............... 49
4.4.3 Calibration of the binder stiffness ......................... ..................49
4.5 Use of Binder-to-mixture Stiffness Relationship .........................................51
4.5.1 Prediction of the Mixture Stiffness for the Same Mixture ......................51
4.5.2 Prediction of Mixture Stiffness for SBS Modified Mixture....................72
4.5.3 U se Energy Ratio for Comparison .................................. ............... 75

5 CL O SU R E ............. ......................................................................................... 88

5 .1 Su m m ary of F in ding s ........................................ .............................................88
5.2 C onculsion ............. ....................................................................................89

APPENDIX

A BENDING BEAM RHEOMETER TEST RESULTS .............. ............... 90

B DYNAMIC SHEAR RHEOMETER TEST RESULTS .............................................97

C BINDER CREEP COMPLIANCE MASTER CURVE DATA.............................104

D MIX DESIGN AND VOLUMETRIC PROPERTIES OF MIXTURES................12

E BINDER-TO-MIXTURE STIFFNESS RELATIONSHIP DATA..........................120









F ENERGY RATIO USING MIXTURE TEST AT ONE TEMPERATURE ...............129

G ENERGY RATIO PREDICTION USING BINDER-TO-MIXTURE STIFFNESS
RELA TION SH IP .................. ....................................... .. .......... 134

H ENERGY RATIO PREDICTION USING UNMODIFIED BINDER-TO-MIXTURE
STIFFNESS RELATIONSHIP FOR MODIFIED MIXTURE............................140

L IST O F R E FE R E N C E S ...................... .. .. ......... .. ........................... .......................143

BIOGRAPHICAL SKETCH ........................... ............................................... 146
















LIST OF TABLES


Table page

3.1 Penetration at 25 C (77 F) ...................................................... ............... 20

3.2 Dynamic Shear Rheometer at 25 C (77 F).................................. ............... 20

3.3 Dynamic Shear Rheometer at 64 C (147 F)................................ ............... 21

3 .4 M mixture T est Sam ples ......................................................................... ...................22

4.1 Bending Beam Rheometer Test Result at -10C, 60 sec...........................................30

4.2 Dynamic Shear Rheometer Test Results at Low Frequencies at 10C ......................32

4.3 Power Model Parameters from DSR Test Results at 10C .......................................36

4.4 Power Model Parameters from DSR Test Results at 20C .......................................36

4.5 Power M odel Parameters for M aster Curve...................................... ............... 47

4.6 Data Used to Calibrate Binder Stiffness ..................................... ........ ............... 50

4.7Summary of Data Interpretation Methods .............................................................76
















LIST OF FIGURES


Figure page

2.1 The Com posite Spheres M odel (3) ........................................... ......................... 7

2.2 The Generalized Self-Consistent Scheme M odel (3)................... ........... .................. 8

2.3 Comparison of Mixture Stiffness: Micromechanical Models Versus IDT Range
Established U sing M measure Creep Stiffness ..................................... .................10

2.4 Construction of the M aster Compliance Curve (13, 14)........................................... 13

2.5 Power Model ............ .......... .................... 15

3.1 Schem atic of Bending Beam Rheom eter........... ................................. ............... 23

3.2 B ending B eam R heom eter ........... .... ........................................... ................ ....... 23

3.3 m-value from the Bending Beam Rheometer ................................... .................25

3.4 Schematic of Dynamic Shear Rheometer ........ ....... ..................... ..............25

3.5 Components of Complex modulus G*............................................................... 26

3.6 a, b D SR equipm ent ....... .... ...... ............................................................ 28

4.1 Comparison of the Measured Stiffness..................... ........... ...............31

4.2 C om prison of the m -value............................ ........... ................ ............... 31

4.3 The Log Shear Stress- Log Frequency Relationship .........................................33

4.4 Master Curve Relationship: PG 67-22, extracted binder @ 6.1% AC .......................38

4.5 Master Curve Relationship: PG 67-22, extracted binder @ 7.2% AC ......................38

4.6 Master Curve Relationship: PG 76-22, extracted binder @ 6.1% AC .......................39

4.7 Master Curve Relationship: PG 76-22, extracted binder @ 7.2% AC .......................39

4.8 Master Curve Relationship: PG 67-22, RTFOT aged...............................................40









4.9 Master Curve Relationship: PG 76-22, RTFOT aged............... ....... ............... 40

4.10 Master Curve: PG 67-22, extracted binder @ 6.1% AC ..........................................41

4.11 Master Curve: PG 67-22, extracted binder @ 7.2% AC...........................................42

4.12 Master Curve: PG 76-22, extracted binder @ 6.1% AC...........................................43

4.13 Master Curve: PG 76-22, extracted binder, 7.2% AC ............................................44

4.14 Master Curve: PG 67-22, RTFOT aged..................................................................45

4.15 M aster Curve; PG 76-22, RTFOT aged .................................... ......... ............... 46


4.16 Log Sb -

4.17 Log Sm -

4.18 Log Sb -

4.19 Log Sm -

4.20 Log Sb -

4.21 Log Sm -

4.22 Log Sb -

4.23 Log Sm -

4.24 Log Sb -

4.25 Log Sm -

4.26 Log Sb -

4.27 Log Sm -

4.28 Log Sb -

4.29 Log Sm -

4.30 Log Sb -

4.31 Log Sm-

4.32 Stiffness

4.33 Stiffness


Log Sb Relationship: PG 67-22, extracted binder 6.1% AC ....................52

Log Sb Relationship; PG 67-22, extracted binder @ 6.1% AC..................52

Log Sb Relationship: PG 67-22, extracted binder @ 7.2% AC .................53

Log Sb Relationship: PG 67-22, extracted binder @ 7.2% AC..................53

Log Sb Relationship: PG 76-22, extracted binder @ 6.1% AC .................54

Log Sb Relationship: PG 76-22, extracted binder @ 6.1% AC.................. 54

Log Sb Relationship: PG 76-22, extracted binder @ 7.2% AC .................55

Log Sb Relationship: PG 76-22, extracted binder @ 7.2% AC.................55

Log Sb Relationship: PG 67-22, RTFOT aged @ 6.1% AC ....................56

Log Sb Relationship: PG 67-22, RTFOT aged @ 6.1% AC ....................56

Log Sb Relationship: PG 67-22, RTFOT aged @ 7.2% AC ....................57

Log Sb Relationship: PG 67-22, RTFOT aged @ 7.2% AC ....................57

Log Sb Relationship: PG 76-22, RTFOT aged @ 6.1% AC ....................58

Log Sb Relationship: PG 76-22, RTFOT aged @ 6.1% AC ....................58

Log Sb Relationship: PG 76-22, RTFOT aged @ 7.2% AC ....................59

Log Sb Relationship: PG 76-22, RTFOT aged @ 7.2% AC ....................59

Prediction from PG 67-22,extracted binder, @ 6.1% AC @ 0C ..............60

Prediction from PG 67-22,extracted binder, @ 6.1% AC @ 10C ............60









4.34

4.35

4.36

4.37

4.38

4.39

4.40

4.41

4.42

4.43

4.44

4.45

4.46

4.47

4.48

4.49

4.50

4.51

4.52

4.53

4.54


Stiffness

Stiffness

Stiffness

Stiffness

Stiffness

Stiffness

Stiffness

Stiffness

Stiffness

Stiffness

Stiffness

Stiffness

Stiffness

Stiffness

Stiffness

Stiffness

Stiffness

Stiffness

Stiffness

Stiffness

Stiffness


4.55 Stiffness


Prediction from PG 67-22,extracted binder, @ 6.1% AC @ 20C ............61

Prediction from PG 67-22, extracted binder, @ 7.2% AC @ 0C .............61

Prediction from PG 67-22,extracted binder, @ 7.2% AC @ 10C ............62

Prediction from PG 67-22, extracted binder, @ 7.2% AC @ 20C ..........62

Prediction from PG 76-22, extracted binder, @ 6.1% AC @ 0C .............63

Prediction from PG 76-22, extracted binder, @ 6.1% AC @ 10C .........63

Prediction from PG 76-22, extracted binder, @ 6.1% AC @ 20C ...........64

Prediction from PG 76-22, extracted binder, @ 7.2% AC @ 0C .............64

Prediction from PG 76-22,extracted binder, @ 7.2% AC @ 10C ............65

Prediction from PG 76-22, extracted binder, @ 7.2% AC @ 20C ..........65

Prediction from PG 67-22, RTFOT aged, @ 6.1% AC @ 0C .................66

Prediction from PG 67-22, RTFOT aged, @ 6.1% AC @ 10C ...............66

Prediction from PG 67-22, RTFOT aged, @ 6.1% AC @ 20C ...............67

Prediction from PG 76-22, RTFOT aged, @ 6.1% AC @ 0C .................67

Prediction from PG 76-22, RTFOT aged, @ 6.1% AC @ 10C ...............68

Prediction from PG 76-22, RTFOT aged, @ 6.1% AC @ 20"C ...............68

Prediction from PG 67-22, RTFOT aged, @ 7.2% AC @ 0C .................69

Prediction from PG 67-22, RTFOT aged, @ 7.2% AC @ 10C ...............69

Prediction from PG 67-22, RTFOT aged, @ 7.2% AC @ 20C ...............70

Prediction from PG 76-22, RTFOT aged, @ 7.2% AC @ 0C .................70

Prediction from PG 76-22, RTFOT aged, @ 7.2% AC @ 10C ...............71

Prediction from PG 76-22, RTFOT aged, @ 7.2% AC @ 20C ..............71


4.56 Stiffness Prediction from PG 67-22, extracted binder @ 6.1% AC .......................73

4.57 Stiffness Prediction from PG 67-22, extracted binder @ 7.2% AC ........................73









4.58 Stiffness Prediction from PG 67-22, RTFOT aged, @ 6.1% AC............................74

4.59 Stiffness Prediction from PG 67-22, RTFOT aged, @ 7.2% AC ...........................74


4.60 Energy Ratio Prediction: PG 67-22, 6.1% AC @ OC


4.61 Energy Ratio Prediction: PG 67-22, 6.1% AC @

4.62 Energy Ratio Prediction: PG 67-22, 6.1% AC @

4.63 Energy Ratio Prediction: PG 67-22, 7.2% AC @

4.64 Energy Ratio Prediction: PG 67-22, 7.2% AC @

4.65 Energy Ratio Prediction: PG 67-22, 7.2% AC @

4.66 Energy Ratio Prediction: PG 76-22, 6.1% AC @

4.67 Energy Ratio Prediction: PG 76-22, 6.1% AC @

4.68 Energy Ratio Prediction: PG 76-22, 6.1% AC @

4.69 Energy Ratio Prediction: PG 76-22, 7.2% AC @

4.70 Energy Ratio Prediction: PG 76-22, 7.2% AC @


10 o C ..................... ... .......... 79

20 C ..................... ... .......... 79

0 C ....................... ... ........ 80

10 C ....................... ... ............ 8 0

2 0 C .............. ..................... 8 0

C ......................... ............... 8 1

10 C ....................... ... ............ 8 1

2 0 C .............. .................... 8 1

0 C ......................... ............... 82

10 C ....................... ... ............ 8 2


4.71 Energy Ratio Prediction: PG 76-22, 7.2% AC @ 20C ........................................82

4.72 Energy Ratio Prediction: PG 67-22, 6.1% asphalt content @ 0C ............................83

4.73 Energy Ratio Prediction: PG 67-22, 6.1% asphalt content @ 10C ..........................83

4.74 Energy Ratio Prediction: PG 67-22, 6.1% asphalt content @ 20C ..........................83

4.75 Energy Ratio Prediction: PG 67-22, 7.2% asphalt content @ 0C ............................84

4.76 Energy Ratio Prediction: PG 67-22, 7.2% asphalt content @ 10C ..........................84

4.77 Energy Ratio Prediction: PG 67-22, 7.2% asphalt content @ 20C ..........................84

4.78 Energy Ratio Prediction: PG 76-22, 6.1% asphalt content @ 0C ............................85

4.79 Energy Ratio Prediction: PG 76-22, 6.1% asphalt content @ 10C ..........................85

4.80 Energy Ratio Prediction: PG 76-22, 6.1% asphalt content @ 20C ..........................85

4.81 Energy Ratio Prediction: PG 76-22, 7.2% asphalt content @ 0C ............................86









4.82 Energy Ratio Prediction: PG 76-22, 7.2% asphalt content @ 10C ........................86

4.83 Energy Ratio Prediction: PG 76-22, 7.2% asphalt content @ 20OC ........................86

4.84 Energy Ratio Prediction from Unmodified Mixture @ 6.1% asphalt content...........87

4.85 Energy Ratio Prediction from Unmodified Mixture @ 7.2% asphalt content...........87















Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Engineering

USE OF BINDER RHEOLOGY TO PREDICT THE CRACKING PERFORMANCE OF
SBS-MODIFIED MIXTURE

By

Zhanwu Cui

December, 2003

Chair: Reynaldo Roque
Cochair: Bjorn Birgisson
Major Department: Civil and Coastal Engineering

A laboratory investigation was conducted to identify and evaluate the relationships

between binder stiffness and mixture stiffness that could be used to predict the effects of

polymer-modified binder on mixture cracking performance once mixture properties are

determined with unmodified binder. This work was part of a larger study that was

evaluating the effects and cost-benefits of using poly-modified mixtures.

The laboratory investigation was conducted with both unmodified binders and SBS

modified binders. Both types of binders included extracted binders from Short Term

Oven Aged (STOA) mixtures and the virgin binders after Rolling Thin Film Oven Test

(RTFOT). The binders were tested with Bend Beam Rheometer (BBR) and Dynamic

Shear Rheometer (DSR) to obtain properties over a range of temperatures.

Properties of the binders that were tested and evaluated include creep at low

temperatures and complex modulus and phase angle at intermediate and high

temperatures. These properties were used to construct the creep compliance master curve









of the binders. Mixture creep compliance was measured at multiple temperatures using

the Superpave IDT. Test results were used to develop and evaluate the potential use of

binder-to-mixture stiffness relationships.

Test results indicate that there is no single binder-to-mixture stiffness relationship

that is suitable for multiple temperatures. At each temperature in this study, there was one

binder-to-mixture stiffness relationship. It appears that microdamage develops in

mixtures upon cooling to temperatures below 20 C, which affects mixture response in a

way that is not captured by binder test results. For any given temperature, it appears the

modified binder behaves more stiffly in the mix than would be predicted by the

unmodified binder-to-mixture stiffness relationship. Although this yields conservative

estimates of cracking performance, it may not give enough credit to the modification.














CHAPTER 1
INTRODUCTION

1.1 Background

The Strategic Highway Research Program (SHRP) was established in 1988 to

improve the performance and durability of roads in the United States (1). The Superpave

(Superior Performing Asphalt Pavements) mix design method was one of the SHRP

research program outcomes.

The Superpave mix design method has become very popular in most of the states

in America, including Florida. Compared with the traditional Marshall and Hveem mix

design methods, Superpave has the following advantages:

* Criteria were introduced to minimize the potential use of substandard or
unacceptable aggregates

* A broader range of in-service temperatures is incorporated in the binder selection
specifications, including low temperatures

* The Gyragtory compactor which simulates more closely the field compaction and
traffic conditions was introduced. (2)

The creep compliance of the asphalt mixture is a function of time and temperature

and can be used to predict the stresses and cracking in asphalt pavement. The master

creep compliance curve can be determined using a testing and analysis system developed

in the SHRP program that incorporates the Superpave Indirect Tensile Test (IDT). Since

it is very costly and time consuming to run mixture tests, especially over a wide range of

temperature and time, identification of the reliable binder-to-mixture stiffness

relationships would be extremely useful.









Binder-to-mixture stiffness relationships have been used to study the cracking

behavior of asphalt mixtures at low temperature (3). However, previous study showed

that due to the temperature-dependent damage at low temperatures, the binder-to-mixture

stiffness relationship at a single temperature can not be used to accurately predict the

stiffness at other temperatures. Therefore, the study showed that the use of a single-

function binder-to-mixture stiffness relationship will result in the poor estimates of

mixture stiffness. (3).

The above observation was made at low temperatures (below O"C). Therefore, it

would be important to determine whether a single-function binder-to-mixture stiffness

relationship could be used at intermediate temperatures (0 to 20"C). It would also be

important to determine whether binder-to-mixture stiffness relationships apply to

modified binders. This would preclude the need to perform physical test on asphalt

mixture, specifically modified asphalt mixture, once the mixture properties are

determined with a binder of known properties.

1.2 Study Objectives

The primary objectives of this research are the following:

1. To determine whether creep properties, namely m-value and D1 of the polymer-
modified mixtures can be determined once the creep properties of the unmodified
mixture and the properties of the modified binder are known. If so, there is no need
to test polymer modified mixtures.

2. To determine whether mixture properties, particularly D1 and m-value, can be
determined for multiple temperatures using the mixture properties at one
temperature along with the binder master curve.

3. To determine whether the Energy Ratio (ER) at multiple temperatures can be
determined using the binder-to-mixture stiffness relationship at one temperature
and whether the Energy Ratio of polymer modified mixtures can be determined
using unmodified binder-to-mixture stiffness relationship and the modified binder
properties.









1.3 Scope of Study

This laboratory investigation was conducted with both unmodified and polymer

(SBS) modified binders, PG 67-22 and PG 76-22, respectively and asphalt mixtures

produced with these two binders. Both extracted binders from corresponding asphalt

mixtures and virgin binders after Rolling Thin Film Oven Test (RTFOT) were tested.

The Bending Beam Rheoemter (BBR) and Dynamic Shear Rheometer (DSR) were used.

The four mixtures in this study were coarse-graded (gradation below the restricted zone)

Superpave mixtures produced by using South Florida Limestone. The design asphalt

contents were 6.1% and 7.2% which corresponded to two different traffic levels using the

Superpave mixture design procedure. The SBS modified mixtures were prepared to have

the same effective asphalt content as the unmodified asphalt mixtures. All the mixtures

were Short Term Oven Aged for two hours and then compacted to 7% (+0.5%) air

voids. The creep compliance, m-value, tensile strength, failure strain, fracture energy and

dissipated creep strain energy to failure were obtained from IDT test.














CHAPTER 2
LITERATURE REVIEW

2.1 Introduction

The purpose of this chapter was to review various binder-to-mixture stiffness

relationships. The use and effects of the asphalt modifiers were also reviewed. Available

data and information regarding binder creep compliance master curve and shift factors

were also studied. Some miscellaneous issues regarding binder-to-mixture stiffness

relationships were also covered.

2.2 Binder-to-Mixture Stiffness Relationship

The practical goal of developing binder-to-mixture stiffness relationships is to

predict mixture performance with little or no mixture testing. There are two ways to

achieve this goal: theoretical and empirical binder-to-mixture stiffness relationships.

2.2.1 Theoretical Binder-to-Mixture Stiffness Relationship

Theoretical binder-to-mixture stiffness relationships use the micromechanical

analysis to develop the relationship. In this method, the properties of the composite

materials can be obtained from the properties of the constituents. Several

micromechanical models have been proposed. The following were reviewed:

1. Paul's equation, (4), Rule of Mixtures

2. Hashin and Shtrikman's arbitrary phase geometry model, (5)

3. Hashin's composite spheres model (6)

4. Christensen and Lo's generalized self-consistent scheme model (7, 8)










2.2.1.1 Paul's equations and the rule of mixtures

Paul's equations (equations 2.1 and 2.2) calculate the effective elastic moduli of

two-phase, irregular geometry composite materials.


1 K* < Kc, +K2c2 (2.1)
C1 C2
K1 K2


1 < G* < G c,1 + G2C2 (2.2)
C1 C2
G, G2

where

K*, G* = Effective bulk and shear moduli of the composite

K1, K2 = Bulk moduli of phase 1 and 2

G1, G2 = Shear moduli of phase 1 and 2

ci, c2 = Volume fractions of phase 1 and 2

The shear and bulk moduli can be related to Young's modulus (E), and Poisson's

ratio by the following equations:


E = (2.3)
1 1
-+
3G 9K


G = (2.4)
3(1 + v)

The right-hand side of the equations 2.1 and 2.2 are referred to as the "Law of

Mixtures."

2.2.1.2 Hashin and Shtrikman's arbitrary phase geometry model

Hashin and Shtrikman (5) derived the equations for an n-phase composite of

arbitrary phase geometry. The following equations are based on a two-phase composite.










K*L = K1 + 2 (2.5)
1 3c,
K2 -K, 2K + 4G,


K*u = K2 + (2.6)
1 3c2
K, K2 2K2 + 4G2

where

K* < K* < K*u (2.7)


G L = G1 + c2 (2.8)
1 6(K1 + 2G, )c1
+
G2 G, 5G, (3K, + 4G )


Glu = G + c (2.9)
1 6(K2 + 2G2 )c2
G G2 5G2(3K+ 4G2)

G*L < G* < G*u (2.10)

and the following conditions must be met:

K2 > K, and G2 > G, (2.11)

where

K*L = Effective bulk modulus of the composite, lower bound

G*L = Effective shear modulus of the composite, lower bound

K*u = Effective bulk modulus of the composite, upper bound

G*u = Effective bulk modulus of the composite, upper bound

2.2.1.3 Hashin's composite spheres model

The composite spheres model consists of a gradation of infinitely-packed spherical

particles in a continuous matrix phase (3). The model assumes that the ratio of particle

diameter to the diameter of the surrounding concentric matrix (a/b) is constant for all









particles. Under these assumptions, the bulk properties of a single composite are identical

to the bulk properties of the complete composite spheres. Figure 2.1 is the classical

micromechanics composite sphere model.


Figure 2.1 The Composite Spheres Model (3)

The equations for the composite spheres model are given as:

K* +(KP + K)(4G,,, + 3K)c
4G,, +3K, +3(K, K,)c


G*u = GI(1+ c(7 -1)yl-))





Gm

Km, Gm = Bulk and shear moduli of the matrix

Kp, Gp = Bulk modulus of the particles (or inclusions)

c = Volume concentration of inclusions = (a/b)3


where


(2.12)



(2.13)


(2.14)


(2.15)


G;
I + c(I 17)yi ((T









a, b = Radii of particle and concentric matrix

yl), yl(" = Complicated functions of the elastic constants

2.2.1.4 Christensen and Lo's generalized self-consistent scheme

The generalized self-consistent scheme is illustrated in figure 2.2.






b






W SPHERICAL INCLUSION
C MATRIX
EZ3 EFFECTIVE MEDIUM


Figure 2.2 The Generalized Self-Consistent Scheme Model (3)

The shear modulus is given by the following equations:


A:- +2B G + +C= 0 (2.16)


where

A, B, C = Lengthy functions of the elastic constants,.

Up to this point, four micromechanical models have been reviewed. Figure 2.3 (9)

gives a comparison of mixture stiffness calculated from using these four

micromechanical models to measured creep stiffness. The figure shows that the bounds

of Paul are the widest, followed by the arbitrary geometry bounds and the composite

spheres bounds. Paul's model and the arbitrary geometry model cover some measured









values, but they are too wide to provide useful information. Only when the binder

stiffness is very high, the micromechanical models tend to converge with the measured

values. Predicted values from Christensen and Lo's scheme are much lower than the

measured ones. Figure 2.3 show that the micromechanical models give poor estimation

on the binder-to-mixture stiffness relationships. Research by Reynaldo Roque et.al (9)

shows that aggregate stiffness, Poison's ratio of the aggregate, combinations of various

constants and the sensitivity to air voids were not found to explain the large differences

observed in figure 2.3.

Due to the large discrepancies between the predicted stiffness by the

micromechanical models and the IDT measurements, it is believed that the use of these

models to predict the mixture stiffness is not warranted.

2.2.2 Empirical Binder-to-Mixture Stiffness Relationship

The following four empirical binder-to-mixture stiffness models will be discussed:

1. Heukelom and Klomp (10)

2. Bonnaure et al. (11)

2.2.2.1 Heukelom and Klomp

The following equations (equations 2.17 through 2.19) were given to calculate the

mixture stiffness from the binder stiffness and the volumetric parameters of the

aggregate:




S,= Sb [1+^ ,C JC (2.17)
n I1- C































0.01


0.01 -
0.0001


0.001 0.01 0,1 1 1u


Binder Stiffness (GPa)


Figure 2.3 Comparison of Mixture Stiffness: Micromechanical Models Versus IDT Range Established Using Measure Creep Stiffness











4x105
n= 0.831og[ 4xS (2.18)
Sb


C, = (2.19)
Volumeof (aggregate + binder)

where

Sm = Stiffness of mixture (GPa or Psi)

Sb = Stiffness of binder (GPa or Psi)

But these equations are for mixtures with Cv between 0.7 and 0.9 and air voids

less than or equal to 3%. If the air voids is greater than 3%, Cv is recommended by Van

Draat, Fijn and Sommer (12)


C,= C (2.20)
1+H

where

H =(Pav/100)-0.03

Pa = Percent air voids in the mixture

The equations above are only valid for mixtures satisfying the following equations


C, = (1- C,) (2.21)
3

where

Volumeofbinder
C, (2.22)
Volumeof (aggregate + binder)

The use of Hekelom and Klomp's binder-to-mixture stiffness relationship is

restricted to the binder stiffness to be above 0.02GPa.









2.2.2.2 Bonnaure's relationship

Bonnaure presented another series of equations to predict mixture stiffness from

binder stiffness:

For 5 x 105 Pa < Sb < 105 Pa,


log Sm = 4 3(log S -8)+ 4 + AlogSb -8 +/2 (2.23)
2 2

For 109 Pa < Sb < 3 x 109 Pa,

log S =2 +4 + 2.0959(/1 82 -4 Xlog sb 9) (2.24)

where

1.342(100- Vg)
,1 =10.82- (2.25)
Vg b

/2 = 8.0 + 0.00568V + 0.0002135V 2 (2.26)

(1.37V 2 1
/3 = 0.6log 1.3b 1 (2.27)
1.33Vb

/4 = 0.7582(1 -/82) (2.28)

Sb = Binder Stiffness, Pa

Vg = Percent volume of aggregate

Vb = Percent volume of binder

2.3 Binder Master Curve and Shift Factor

The creep compliance master curve and shift factors are very useful tools to

characterize the viscoelastic properties of asphalt materials at different temperatures.

These are used to extrapolate the creep compliance of a material over a broader range of

temperatures and loading times from a limited set of experiments. The time-temperature









superposition principle is used to construct the creep compliance master curve. Figure 2.4

(13, 14) illustrates this principle. For linear viscoelastic materials, there is a relationship

between the loading time and temperature. To construct a creep compliance master curve,

the creep compliance at different temperatures should be obtained and plotted on a log

compliance-log time scale. Then a single temperature is selected to which the creep

compliance at other temperatures is shifted horizontally to form a continuous smooth

curve at this temperature. This smooth curve is called the master creep compliance curve.

The selected temperature is called the reference temperature.




.............................,



LOG -
D(t) a =







Ts T, W T
T 2 ---




AT






Figure 2.4 Construction of the Master Compliance Curve (13, 14)

The method of reduced time is used to obtain the creep compliance at

temperatures other than the reference temperature:

T = t (2.29)









where

S= Reduced time

t = Real time

aT = Temperature shift factor

The shift factor is another very important parameter obtained from constructing the

master creep compliance curve. On a log creep compliance log time scale, log (1/ at)

corresponds to the horizontal distance of the shifting. Two equations are commonly used

to obtain shift factors for asphalt binders:

For T > Td, the Williams-Landel-Ferry (WLF) (15) equation (2.30) is used:


a 19(T- T,,
Log -9(TT (2.30)
a d 92+(T-T,)

For T < Td, the Ahrennius function (2.31) is used:


Log =j 230 (2.31)
aTd 2.303R T Tdj

where:

aT/aTd = the shift factor relative to the defining temperature

T = Temperature at which properties are desired, ( K)

Td = Defining Temperature, ( K)

Ea = Activation energy for flow below Td 261,000 J/mol

Rg = Ideal gal constant, 8.34 J/mol- K

SK= C + 273









2.4 Power Model

The power model is often used to fit to describe the master curve:

D() = Do +Dm (2.32)

where

D( ) = Creep compliance at reduced time, ,

= Reduced time

Do, D1, m = Power model parameters

The m-value describes the linear part of the master curve on the log creep

compliance-log time scale. Figure 2.5 shows the power model and the parameters in the

master curve.Do represents the elastic portion of the creep compliance. Christensen and

Anderson (15) found that the maximum stiffness for all asphalts is 3GPa. Therefore, the

minimum Do is:

DO = 1/3GPa = 3.33 x 10l0Pa (2.33)



LOG T D() = Do + D,"
D(f)


1 LOG 4


Figure 2.5 Power Model









2.4 Modifiers in Asphalt Pavement Materials

Asphalt modifiers and additives have been used in asphalt pavement materials for

about 100 years (16). With the increase of the traffic volume, higher performance asphalt

binder for road construction is required. Modified asphalt binders are expected to have

higher performance than pure asphalt. Among modifiers, polymer is one of the most

important types used to improve the performance of the asphalt binder (17). Research

showed that the polymer modifiers can improve the resistance to high temperature rutting

and low temperature cracking (18). Studies by Booil Kim (19) also showed that the SBS

modified mixture generally has a lower m-value than unmodified mixture. However, the

modifier's function in the asphalt mixture is still not clearly understood. A general

description on the modifiers used in asphalt mixtures is provided below.

Polymer is the name given to a kind of materials with high molecular weight,

normally 104-106. The word polymer is derived from the classical Greek Poly meaning

"many" and Mers meaning "parts". So, polymer is a substance manufactured by linking

many parts of a repeating unit together through chemical reaction.

Polymer modifiers are the most advanced asphalt modifiers currently used today

(18). There are 3 main kinds of polymer modifiers: the thermoplastic, crystalline

polymers, the thermoplastic rubbers and the thermosetting polymers.

Thermoplastics, when reacted with appropriate ingredients, can usually withstand

several heating and cooling cycles without suffering structural breakdown Crystalline

polymers, also known as "plastomers" includes polyethylene, polypropylene, polyvinyl

chloride (PVC), polystyrene, ethylene vinyl acetate (EVA) and ethylene methyl acrylate

(EMA). Thermoplastic rubber, also known as "elastomers", includes natural rubber,

styrene-butadiene rubber (SBR), styrene-butadiene-styrene (SBS), styrene-isoprene-









styrene (SIS), polybutadiene (PBD) and polyisoprene. Both the plastomers and the

elastomers have an important effect on the temperature susceptibility of the stiffness of

the asphalt. Because the polymers are generally far less susceptible to changes in

temperature due to their chemical structure (18), it will greatly reduce the temperature

susceptibility of asphalt binders. A recent study showed that a highly entangled fibril

network structure has been seen from both unmodified and modified asphalt binders, but

the fibrils in the SBS modified asphalt concrete is long and thin, while those found in the

unmodified asphalt concrete is thick and short (20). It also showed that the fibrils

exhibited some recovery behavior which may be good for "healing" (20).

A thermoset is a polymer that, when heated, undergoes a chemical change to

produce a crosslinked solid polymer, but is incapable of undergoing repeated cycles of

softening and hardening (21). Epoxy falls into this category. It has been showed that the

benefit of the epoxy for asphalt mixture is that it could increase the stiffness and reduce

the rutting characteristics of the asphalt concrete (17).

2.5 HMA Fracture Mechanics Model

Research at the University of Florida has shown that the dissipated creep strain

energy limit can be used to identify the crack initiation and propagation (22).

Furthermore, this property can be obtained from Superpave IDT. For cyclic loading, the

numbers of cycles to failure is defined as:

N =DissipatedCreepSrainEnergyLimitfroinii eiigihTest (2.34)
DCSE / cycle


DCSE /cycle = (crA,)2 Dml00m 1 (2.35)
20









Another parameter to compare the cracking resistance of different pavement

structures is the Energy Ratio (ER) developed by Jajliardo (23). Energy Ratio represents

the fracture toughness of the asphalt mixtures. The equation for Energy Ratio is given

below:

ax DCSE,
ER = (2.36)
S298 xD1

where

a = 0.0299r-31(6.36 S,) + 2.46 x 108

o = tensile stress of asphalt layer, psi

St= tensile strength, MPa

DCSEf = Dissipated Creep Strain Energy, KJ/m3

D1= creep parameter, 1/psi

m = creep parameter














CHAPTER 3
RESEARCH PROGRAM AND INSTRUMENTATION

3.1 Introduction

This chapter provides information on the materials and procedures for the

production of binder and mixture specimens in the laboratory, and a summary of the

testing procedures and instrumentation. Also presented is the information on the mixtures

used in this study.

3.2 Materials

This section provides information on the asphalt binders and the corresponding

mixtures used in this study.

3.2.1 Binders

Two kinds of asphalt binders were used in this study, PG 67-22 and PG 76-22.

Both of these binders were produced by CITGO Asphalt Refining Company. PG 67-22 is

unmodified binder and its properties are similar to AC-30. PG 76-22 is SBS (Styrene

Butadiene Styrene) modified binder. There is approximately 3% SBS in the modified

asphalt, and the base asphalt used for modification was the unmodified PG 67-22. The

SBS was blended with the base asphalt by the manufacturer using high shear milling. PG

67-22 was used as the control binder in this study. Some binder test results provided by

the supplier are presented as in tables 3.1, 3.2 and 3.3,.









Table 3.1 Penetration at 25 C (77 F)
Standard
Binder Type Replicate Penetration Average
Deviation

1 61

AC-30 2 60 60 1

3 60

1 50

SBS 2 51 50 1

3 50



Table 3.2 Dynamic Shear Rheometer at 25 C (77 F)
Binder Type Replicate G* (KPa) 6 G* x sin ( ) Average

1 1110 66.7 1020

AC-30 2 1070 67.4 985
946
3 902 67.4 833

1 748 58.7 639

SBS 2 737 61.0 644
640
3 733 60.5 638









Table 3.3 Dynamic Shear Rheometer at 64 C (147 F)
Binder Type Replicate G* (KPa) 6 G* / sin ( 6 ) Average

1 1.93 86.2 1.93

AC-30 2 2.01 86.1 2.02 1.99

3 2.01 86.2 2.02

1 6.16 63.9 6.86

SBS 2 6.24 64.5 6.91 6.86

3 6.12 64.5 6.80



The two binders tested in this study were the binders extracted from asphalt

mixtures after Short Term Oven Aging (STOA) and the virgin binders after Rolling Thin

Film Oven Test (RTFOT). The results of these tests are presented later.

3.2.2 Mixtures

Four types of asphalt mixture were used in this study. All these mixtures were coarse-

graded Superpave mixtures produced with South Florida limestone. The design asphalt

contents was 6.1% and 7.2% which corresponded to two traffic levels in the Superpave

mixture design procedure. The modified mixtures had the same effective asphalt content

as the unmodified mixtures to assure that the SBS modifier was the only factor affecting

the test results. All mixtures were laboratory-prepared samples and were Short Term

Oven Aged (STOA) for two hours (AASHTO PP2-94) and then compacted to 7%

(+0.5%) air voids using the Superpave Gyratory Compactor. The mixing temperature for

the SBS modified mixture is recommended by the manufacturer. Details about the

mixtures are presented in Table 3.4 (19)









Table 3.4 Mixture Test Samples
Samples Binder Binder Aggregate Designation

content* type** type/gradation

6.1 6.1% Straight Limestone/C *** Control sample

7.2 7.2% Straight Limestone/C1 Unmodified higher binder content

6.1SBS 6.1% Modified Limestone/Cl Modified Same binder content

7.2SBS 7.2% Modified Limestone/Cl Modified higher binder content

* 6.1% and 7.2 % binder content are corresponding to traffic level 5 and 3 based on
Superpave level 1 mix design, respectively.
** Straight binder and modified binder are corresponding to PG 67-22 and PG 76-22,
respectively.
*** Cl is most commonly used in Florida Department of Transportation for coarse
gradation with 12.5mm nominal maximum aggregate size

Details on gradation and pavement mixture design are in Appendix A.

3.3 Binder Preparation

3.3.1 Extraction and Recovery of the Binder

Binder extraction for both the PG 67-22 and PG 76-22 were performed in

accordance with FM 5-524 and ASTM 3-D5404.

3.3.2 Rolling Thin Film Oven Test (RTFOT)

Both PG 67-22 and PG 76-22 virgin binders were aged using Rolling Thin Film

Oven Test (RTFOT) in accordance with D 2872-97, to simulate the aging process during

the conventional hot-mixing which is comparable with the Short Term Oven Aging (

STOA) in mixtures.

3.4 Testing of Binders

To develop binder master curve and binder-to-mixture stiffness relationships, the

binder was tested by performing Bending Beam Rheometer (BBR) and Dynamic Shear

Rheometer (DSR) tests.









3.4.1 Bending Beam Rheometer Test

The Bending Beam Rheometer (BBR) measures the stiffness of binders at low service

temperatures. The device was developed as part of the SHRP binder research program.

The BBR consists of three parts: the loading system, the temperature control bath and the

data acquisition system as illustrated in the following schematic. (1)




Deflection
6 Transducer

Control and Air Bearing
Data Acquisition Load Cell
I I /Fluid
Asphalt Beam- I Bath Loading
Frame
Supports






Figure 3.1 Schematic of Bending Beam Rheometer



The Bending Beam Rheometer is as follows (24):


:.'Fluid Bath
Loading


Figure 3.2 Bending Beam Rheometer


~iQ~









The BBR applies a transient creep load in bending mode to load the specimen,

which is held at a constant temperature. The data acquisition system records the load and

deflection results and calculate the creep stiffness, S(t), and m-value, which is the slope

of the stiffness-time relationship at t = 60s.

The creep stiffness of the asphalt binder is a measurement of how the asphalt

binder resists creep loading. It is calculated using the following equation (1):

PL3
S(t) = 3 (3.1)
4bh3g(t)

where

S(t) = creep stiffness at time, t = 60 seconds

P = applied constant load, 100g (980mN)

L = distance between beam supports, 102mm

B = beam width, 12.5mm

h = beam thickness, 6.25mm

6 (t) = deflection at time, t = 60 seconds

The m-value is defined as the slope of the log creep stiffness versus log time

curve at a loading time of 60s. It indicates the rate of change in stiffness with time, S(t).

Below is a plot of m-value. (1)










Log Creep
Stiffness, S

slope = m-value










60
I.og Loading Time, s

Figure 3.3 m-value from the Bending Beam Rheometer

In this study, the BBR test is conducted at -10 C. Three specimens of each kind


of binder were prepared and tested and the stiffness results were used to develop Power

Law parameters and the creep compliance master curve of the binder.

3.4.2 Dynamic Shear Rheometer Test

The Dynamic Shear Rheometer (DSR) characterizes the viscous and elastic

properties of asphalt binders at intermediate to high temperatures. It measures the

complex modulus, G*, and phase angle, 6 of the binder. Below is a schematic of the


Dynamic Shear Rheometer (1):


Applied Stress
or Strain Position of
O( ~ Oscillating Plate

Oscillating CA /
Platec Fixed Plae
A n A
Asphalt A Ame
"x^T--^\r^A Time


C
I cycle
F--


Figure 3.4 Schematic of Dynamic Shear Rheometer









The complex modulus, G*, is the total resistance of the binder to deformation and

it has two components: the storage modulus, G', which reflects the elastic response and

the loss modulus, G", which reflects the viscous response. The relationship between G*,

G', and G" is shown below (1):

Viscous
Part

Viscous
Part

CG G* G*
/G"


GI S G' j
G' G'
s Elastic Part
Elastic Part
Asphalt A Asphalt B

Figure 3.5 Components of Complex modulus G*

The figure above also shows that the two asphalt binders with the same complex

modulus may have different phase angle and so the storage modulus and the loss modulus

are different.

The following equations are used to calculate the complex modulus, G*.


G*= Tmax (3.2)
Ymax

2T
rmz 3 (3.3)


Or
= (3.4)
Ymax h (34)
h

where


T = maximum applied torque









r = radius of binder specimen/plate (12.5mm or 4mm)

o = deflection angle

h = specimen height (1mm or 2mm)

In Superpave binder testing, the test is conducted at a single frequency of 10 rad

/sec. A constant stress is applied as the loading mode. The G* and a are reported at the

end of the test. But in this study, the Dynamic Shear Rheometer research software was

used to run the DSR test so that the binder can be tested at multiple frequencies. G', G",

viscosity, stress and strain were also obtained in addition to G* and a From the DSR

test at multiple frequencies, the data can then be converted into creep compliance power

law parameters. The DSR test was conducted at 10 C and 20C. Frequencies of 0.5 Hz,

1Hz, 2 Hz, 4 Hz, 8 Hz and 15 Hz were used at each temperature. The constant strain

mode is chosen and the 8mm sample with 2mm gap was used in this study.

The following figures illustrate the DSR equipment (24):


DSR Equipment


Figure 3.6a

























Figure 3.6b

Figure 3.6 a, b DSR equipment



3.5 Testing of Mixtures

Mixture test were obtained using Superpave Indirect Tensile Test (IDT). Resilient

modulus, creep compliance, m-value, tensile strength, failure strain, fracture energy and

dissipated creep strain energy to failure were obtained from the tests.














CHAPTER 4
SUMMARY AND ANALYSIS OF LABORATORY TEST RESULTS

4.1 Introduction

This chapter presents a discussion of the binder and mixture test results. The test

results of the binder include creep stiffness, S(t), m-value, complex modulus, G*, and

phase angle, 6 Mixture test result includes creep compliance, tensile strength, dissipated

creep strain energy, m-value.

4.2 Summary of Binder Test

4.2.1 Bending Beam Rheometer Test

A summary of the Bending Beam Rheometer results at 60 sec. is presented in Table

4.1. The Bending Beam Rheometer tests were conducted at -10C for both the extracted

binders and the virgin binders after Rolling Thin Film Oven Test. Comparisons of the

results at 60 seconds indicate that the stiffness of the SBS modified binders are lower

than those of the unmodified binders. However the m-value at 60 seconds was similar for

all binders. The variation in m-value change observed was probably a result of the effects

of the extraction process which may break the molecular structure of the modified binder

and affect the results.

A summary of the Bending Beam Rheometer test results for each kind of binders are

also presented in Appendix A.










Table 4.1 Bending Beam Rheometer Test Result at -10C, 60 sec.
Measured
Binder Type Replicate Stiffness Average m-value Average
(MPa)

1 49 0.484
PG 67-22
6.1% asphalt 2 52.8 51.07 0.472 0.475
content
3 51.4 0.469

1 45.9 0.450
PG 76-22
6.1% asphalt 2 46.7 46.57 0.470 0.460
content
3 47.1 0.461

1 46.6 0.483
PG 67-22
7.2% asphalt 2 46.4 46.83 0.479 0.479
content
3 47.5 0.475

1 39 0.483
PG 76-22
7.2% asphalt 2 39.6 39.80 0.478 0.477
conent
3 40.8 0.469

1 48.3 0.485

PG 67-22
PG67222 51.7 51.40 0.476 0.479
RTFOT aged

3 54.2 0.476

1 37.7 0.496

PG 76-22
PG76222 37.8 37.40 0.491 0.492
RTFOT aged

3 36.7 0.488











Ave. Measured Stiffness (MPa)

60.00

0 50.00

40.00

30.00

20.00

0 10.00

0.00
PG 67-22, PG 76-22, PG 67-22, PG 76-22, PG 67-22, PG 76-22,
6.1%AC 6.1%AC 7.2%AC 7.2%AC RTFOT RTFOT




Figure 4.1 Comparison of the Measured Stiffness


Ave. m-value

0.8

u 0.7
0.6
u,
0 0.5
0.4

S0.3
0.2

S0.1
0
PG 67-22, PG 76-22, PG 67-22, PG 76-22, PG 67-22, PG 76-22,
6.1% AC 6.1% AC 7.2% AC 7.2% AC RTFOT RTFOT


Figure 4.2 Comparison of the m-value









4.2.2 Dynamic Shear Rheometer

The Dynamic Shear Rheometer test was conducted to obtain G* and 6 at both

10"C and 20"C. This test was conducted at multiple frequencies to convert the dynamic

test results to power model creep compliance parameters.

4.2.2.1 Dynamic Shear Rheometer at low frequencies

The frequencies used in the low frequency test were: 0.001, 0.002, 0.004, 0.008,

0.015, 0.03 Hz. The typical test result is shown in table 4.8.

Table 4.2 Dynamic Shear Rheometer Test Results at Low Frequencies at 10C

Frequency (Hz) Phase Angle ( 6 ) Viscosity (Pa s) Shear Stress (Pa)

0.001 10.72 2.78 x 106 3.68 x 102

0.002 78.80 2.42 x 107 8.60 x 101

0.004 58.93 2.16 x 107 1.02 x 103

0.008 55.97 1.66 x 107 1.67 x 103

0.015 56.48 1.26 x 107 2.38 x 103

0.03 53.86 9.70 x 106 3.77 x 103



The results indicated that, reasonable results could not be obtained at very low

frequencies. Therefore, the conversion to power model parameters was more difficult and

unreliable. The figure below showed another problem with very low frequency tests.




























Figure 4.3 The Log Shear Stress- Log Frequency Relationship

This figure indicated that the binder response was is not in the linear range at low

frequencies, consequently. Low frequency tests were not used in this study.

4.2.2.2 The Dynamic Shear Rheometer Test at high frequencies

The higher frequency sweeps used in the study included: 0.5, 1.0, 2.0, 4.0, 8.0, and

15.0 Hz. Test results were presented in Appendix B The test results indicate that there is

no big different between the unmodified binder and the SBS modified binder.

4.3 Binder Creep Compliance Master Curve

The binder creep compliance master curve and associated shift factors are two critical

elements in developing binder-to-mixture stiffness relationships. These two topics will be

discussed in this section.

4.3.1 Shift Factors

The following equations for the shift factor were presented in Chapter 2:


Log Shear Stress- Log Frequency

-*--Log Shear Stress- Log Frequency

4. 00
S3.00
R 2.00
0
S1.00o
0.00 -
-3.50 -3.00 -2.50 -2.00 -1.50 -1.00 -0.50 0.00

Log Frequency









For T > Td, the Williams-Landel-Ferry (WLF) equation (2.30) is used:


-19(T T,)
Log a 19(T T(2.30)
\ay 92 + (T T,)

For T < Td, the Ahrennius function (2.31) is used:


Logr =-- (2.31)
a'd 2.303Rg TdT

where

aT/aTd = the shift factor relative to the defining temperature

T = Temperature at which properties are desired, ( K)

Td = Defining Temperature, ( K)

Ea = Activation energy for flow below Td, 261,000 J/mol

Rg = Ideal gal constant, 8.34 J/mol- K

K = C + 273

To make the computation easy and simple, Td was made to coincide with Tref, So, the

equation above resulted in the following equations:

For T > Tref, the Williams-Landel-Ferry (WLF) equation (2.30) is used:


Log a1 -19(T -T) (4.1)
\arre 92 + (T T )(

For T < Tref, the Ahrennius function (2.31) is used:

Ka E 1 1
Log = 3 (4.2)
Sarref 2.303R9 T ref









A review of literature indicated that the relationship between Log aT and T-Td is

linear when T-Td is between -15 and 35C and Td is between -15 and 5C (25). In this

study, the temperature of interest was between -10 and 20 C, and T-Td falls between -15

and 35C. Linear regression was performed for equation 4.1 within this temperature

range, which resulted in the following equation for the shift factor:

log a, = -0.175(T- Tef) (4.3)

This equation can be used regardless of whether T>Td or T

relationship was obtained when T-Td is between -15 and 35C. It only depends on how to

choose the reference temperature chosen.

4.3.2 The Master Creep Compliance Curve

Using the shift factor developed above, the binder master creep compliance curve can

be generated from Bending Beam Rheometer Test date at -10C, and Dynamic Shear

Rheometer Test at 10C and 20C. However, Dynamic Shear Rheometer test results must

be converted to obtain the creep compliance. A power model was used for this purpose.

4.3.2.1 Creep compliance from Dynamic Shear Rheometer test results

Dynamic Shear Rheomter test results can be converted into a power model of the

following form:

D(t)= Do +Dt' (4.4)

from a computer software developed by Jaesung Kim at the University of Florida. Tables

4.21 and 4.22 show the results after conversion for DSR data at 10 and 20"C,

respectively. The creep compliance can be obtained by inputting t. In this case, the

inverse of the frequencies at which the Dynamic Shear Rheometer tests were conducted









were chosen to determine the creep compliance. On the log creep compliance log t plot,

the number of log cycles covered by log t was the same for the Dynamic Shear

Rheometer test as for the Bending Beam Rheometer test.


Table 4.3 Power Model Parameters from DSR Test Results at 10C

Binder Type Do D1 m

PG 67-22, 6.1% asphalt content 4.834 x10-9 2.101 x10-7 0.476

PG 67-22, 7.2% asphalt content 5.550 x10-9 2.211 x10-7 0.490

PG 76-22, 6.1% asphalt content 5.899 x10-9 1.744 x10-7 0.494

PG 76-22, 7.2% asphalt content 6.575 x10-9 2.275 x10-7 0.498

PG 67-22, RTFOT aged 7.419 x10-9 1.879 x10-7 0.538

PG 76-22, RTFOT aged 5.491 x10-9 2.202 x10-9 0.478





Table 4.4 Power Model Parameters from DSR Test Results at 20C

Binder Type Do D1 m

PG 67-22, 6.1% asphalt content 1.650 xl0- 1.384 xl0-6 0.595

PG 67-22, 7.2% asphalt content 1.854 xl0-8 1.552 x10-6 0.606

PG 76-22, 6.1% asphalt content 1.513 xl0-s 1.134 x10-6 0.581

PG 76-22, 7.2% asphalt content 1.702 xl0-8 1.316 x10-6 0.587

PG 67-22, RTFOT aged 1.532 xl0-8 1.198 x10-6 0.589

PG 76-22, RTFOT aged 1.808 xl0-8 1.469 x10-6 0.595









4.3.2.2 Construction of binder creep compliance master curve

To construct the master curve, the log creep compliance-log t relationship must

first be plotted. Creep compliance from the BBR test was simply taken as the inverse of

the stiffness. The creep compliance from DSR test was obtained by inputting t into the

power model (equation 2.32) and the reduced time, (equation 2.29), was used to

calculate the real time at the appropriate temperature. In this study, 20OC was chosen as

the reference temperature.

Figures 4.4 through Figure 4.9 illustrate the log creep compliance- log relationship

before and after shifting. These results indicate that the creep compliance data at 10OC did

not match well with the master curve at 20C. It appears that it may not be possible to

obtain accurate measurements from the Dynamic Shear Rheometer at 10 C when the

stiffness of the binder is too high relative to the instruments stiffness. Therefore, it was

decided that the data at 10OC can not be used to develop the master curve. The creep

compliance master curve was developed using the BBR test results at -10C and the DSR

test results at 20"C. The resulting master curves are shown in Figure 4.10 through Figure

4.15. The master curve developed by using only the DSR test results at 20C was also

plotted for comparison. The figures clearly show that the characteristics of the master

curve are highly dependent on how it was developed. In this case, there is no big

difference between the two master curves from two methods.

The master curve was fitted using a of the following equation:

D() = Do +D0,m (2.32)















Shifting No.1: PG 67-22,extracted unmodified binder @ 6.1% asphalt content


-6000 -4000 -2000 0000
Log reduced time


2000 4000 6000 8000


Figure 4.4 Master Curve Relationship: PG 67-22, extracted binder @ 6.1% AC



Shifting No 2 PG 67-22,extracted unmodified binder @ 7 2% asphalt content


000


-1 00


-200


-300


-4 00


S-5 00


-600


-700


-8 00


-900
-6 000


-4 000


-2 000


0000


2 000


4 000


6 000


8 000


Log reduced Time


Figure 4.5 Master Curve Relationship: PG 67-22, extracted binder @ 7.2% AC


00


-1 00 I


-400


-500


-*--10C
10C
DSR @10C
-*-DSR 20C
20C
--BBR -10C















i ,
^ ,


t-1OC
-lOC
-*---10C
-- 10C
20C
DSR @ 10C
---DSR @20C
--BBR @-10C







x"

~-" ~JX















Shifting No.3: PG 76-22,extracted SBS modified binder @ 6.1% asphalt content


-1 00


-200


-300


-4 00


-500


-6000 -4000 -2000 0000 2000 4000 6000 8000

Log reduced time




Figure 4.6 Master Curve Relationship: PG 76-22, extracted binder @ 6.1% AC



Shifting No.4: PG76-22,extracted SBS modified binder @ 7.2% asphalt content


000
oo -


-1 00


-200


-300


-4 00
g




-600





-9 700
-800


-900 -
-6000


-4000


-2000


000


2000


4000


6000


8000


Log reduced time


Figure 4.7 Master Curve Relationship: PG 76-22, extracted binder @ 7.2% AC


10C
-.--1oc

20C
DSR @ 10C
-DSR @ 20C
--BBR @i -10C






/"


---10C
-- 10C
20C
DSR @ 10C
--DSR @ 20C
-*-BBR -10C









40




Shifting No.5: PG 67-22,unmodified virgin binder after RTFOT


-400


-500


uu
-6000 -4000 -2000 0000 2000 4000 6000 8000
Log reduced time




Figure 4.8 Master Curve Relationship: PG 67-22, RTFOT aged



Shifting No.6: PG 76-22,SBS modified virgin binder after RTFOT


-4000


-2000 0000 2000
Log reduced time


4000


6000


8000


Figure 4.9 Master Curve Relationship: PG 76-22, RTFOT aged


--10C
--10C
20C
DSR @ 10C
DSR @ 20C
--BBR @ OC












XAA


000


-+--10C
-10C
20C
DSR @ 10C
--DSR @ 20C
--BBR @i -10C


-200


-300


-4 00


-500


-6 00


-700


-8 00


-9 00
-6 00


10













PG 67-22, extracted unmodified binder @ 6.1% asphlat content


* DSR 20C

-10C & 20C

-10C & 20C master curve

- 20C master curve


0.00


-1.00


-2.00


-3.00


-4.00


-5.00


-6.00


-7.00


-8.00


-9.00


-10.00
-10.00


-4.00


-2.00 0.00

Log reduced time


Figure 4.10 Master Curve: PG 67-22, extracted binder @ 6.1% AC


-6.00


-8.00


2.00


4.00












PG 67-22,extracted unmodified binder @ 7.2% asphalt content
0.00


-1.00


-2.00
x DSR @20C
-10C&20C
-3.00 -I- -10C & 20C master curve

20C master curve
-4.00


S-5.00


S-6.00


-7.00


-8.00


-9.00


-10.00
-10.00 -8.00 -6.00 -4.00 -2.00 0.00 2.00 4.00 6.00 8.00
Log reduced Time


Figure 4.11 Master Curve: PG 67-22, extracted binder @ 7.2% AC












PG 76-22,extracted SBS modified binder @ 6.1% asphalt content


x DSR 20C
* -10C & 20C
- -10C & 20C master curve

20C master curve


0.00


-1.00


-2.00


-3.00


-4.00


-5.00


-6.00


-7.00


-8.00


-9.00


-10.00 -
-10.00


-4.00 -2.00 0.00
Log reduced time


Figure 4.12 Master Curve: PG 76-22, extracted binder @ 6.1% AC


-6.00


-8.00












PG 76-22,extracted SBS modified binder @ 7.2% asphalt content


x DSR 20C
* -10C & 20C
- -10C & 20C master curve

20C master curve


-8.000 -6.000 -4.000 -2.000 0.000
Log reduced time


2.000 4.000 6.000 8.000


Figure 4.13 Master Curve: PG 76-22, extracted binder, 7.2% AC


-7.00


-8.00


-9.00


-10.00
-10.000












PG 67-22,unmodified virgin binder after RTFOT


0.00


-1.00


-2.00


-3.00


-4.00


-5.00


-6.00


-7.00


-8.00


-9.00


-10.00 -
-10.00


-6.00


-4.00 -2.00 0.00
Log reduced time


Figure 4.14 Master Curve: PG 67-22, RTFOT aged


x DSR 20C

* -10C & 20C
-- -10C & 20C master curve

20C master curve


-8.00













PG 76-22,SBS modified virgin binder after RTFOT


0.00


-1.00


-2.00


-3.00


-4.00


-5.00


-6.00


-7.00


-8.00


-9.00


-6.00


-2.00 0.00
Log reduced time


Figure 4.15 Master Curve; PG 76-22, RTFOT aged


x DSR 20C
S-10C & 20C
-- -10C & 20C master curve

20C master curve


-10.00 L
-10.1


00


-8.00


6.00


I I I I lI I I I I I I I I lI I I l I I I I I I I I lI I I I I I I l I I









The parameter Do was take as constant, as it has been determined that this leads to greater

consistency in fitting master curve parameters. As mentioned in Chapter 2, Do for all

binders, which is defined as the minimum compliance (or the inverse of the elastic

stiffness) is:

Do = 1/3GPa = 3.33 x10 Pa

The parameters D1 and m were then fit by performing linear regression on binder data

shifted to a reference temperature of 20"C. Table 4.23 gives the resulting power model

parameters for the master curves.

Table 4.5 Power Model Parameters for Master Curve
Binder Type Do D1 m

PG 67-22, 6.1% asphalt content 3.33 xl0-10 1.321 x10-6 0.524

PG 67-22, 7.2% asphalt content 3.33 x10-10 1.474 x10-6 0.527

PG 76-22, 6.1% asphalt content 3.33 xl0-10 1.070 x10-6 0.488

PG 76-22, 7.2% asphalt content 3.33 x10-10 1.238 x10-6 0.487

PG 67-22, RTFOT aged 3.33 xl0-10 1.140 x10-6 0.507

PG 76-22, RTFOT aged 3.33 x10-10 1.380 xl0-6 0.493



The creep compliance at any other temperatures was obtained by using shift factors in

the method of reduced time (equation 2.29).

4.4 Binder-to-Mixture Stiffness Relationship

This section describes how the binder-to-mixture stiffness relationships were

developed and used.









4.4.1 Empirical Binder-to-mixture Stiffness Relationship

In Chapter 2, both micromechanical and empirical binder-to-mixture stiffness

relationships were reviewed. In this study, Heukelom and Klomp's equation (2.17

through 2.19) were used to develop relationships between binder and mixture properties.

These relationships are presented again for the sake of convenience:


Sm = Sb, 2.5 Cv (2.17)



S4x105 (2.18)
n 0.83 log_ S (2.18)
Sb


C V = (2.19)
Volumeof (aggregate + binder)

where:

Sm = Stiffness of mixture (GPa or Psi)

Sb = Stiffness of binder (GPa or Psi)

Research by Mori-Tanaka showed the binder stiffness in the equation 2.17

needs to be calibrated using the following equation (1)

Sb =a(Sb (t,T))b (4.5)

where:

Sb = Calibrated binder stiffness

Sb = Binder stiffness obtained at loading time, t, and temperature, T

a, b = Coefficients determined through regression

In this study, the binder stiffness was calibrated using equation 4.3 to develop the

binder-to-mixture stiffness relationship.









4.4.2 Volumetrics of the aggregate

The binder-to-mixture stiffness relationship is related to the volumetrics as seen in

equation 2.19. The gradation and volumetrics of the mixture in this study are presented in

Appendix C. The following relationships were used to calculate necessary parameters

from the measured values.

Volume of aggregate = Total Volume Voids in Mineral Aggregate

= (1- VMA)x 100%

Volume of (Aggregate + Binder) = Total Volume % Air Voids

= 100 % Air Voids

In this study, all mixtures had the same gradation but two different asphalt content

levels corresponding to two traffic level, 6.1% and 7.2%. Therefore, mixtures with the

same asphalt content had the same volumetrics.

For mixtures with 6.1% asphalt content:


C'
I- C'


8.163


For mixtures with 7.2% asphalt content:


C
= 6.440
1-Cv

4.4.3 Calibration of the binder stiffness

The data used to calibrate binder stiffness is illustrated in table 4.24.









Table 4.6 Data Used to Calibrate Binder Stiffness
Temp.(C) Time (sec.) Sm Sb Sb
1 Smi Sb(l/at) Sbl

0 10 SmlO Sb(10/at) Sbl0

1000 SmO000 Sb(1000/at) Sbl000
1 Smi Sb(l/at) Sbl

10 10 SmIO Sb(10/at) SblO

1000 SmO000 Sb(1000/at) Sbl000
1 Smi Sbl Sbl
210 SmlO Sbl0 SblO
20

1000 SmO000 Sbl000 Sbl000


Mixture stiffness, Sm, for loading times of 1, 2, 5, 10, 20, 50, 100, 200, 500, 1000 sec.

was measured at each test temperatures. Binder creep compliance at 20 C was obtained

from the master curve (power model equation 2.32) by inputting the loading times as in

column 2, table 4.24. At 0C and 10C the reduced time was used to obtain the binder

creep compliance. The binder stiffness, Sb, was taken as the inversion of the creep

compliance. The calibrated binder stiffness, Sb was obtained by iteration such that Sm

from equation 2.17 match the measured Sm. Linear regression was then conducted

between log Sb and log Sb to obtain a and b in equation 4.3. The log Sb log Sb and log

Sb- log Sm relationships were plotted for each mixture and presented in Figure 4.16

through 4.31.

The figures indicated that for each kind of mixture, there is a separate relationship

between Log Sb Log Sb for each of the three temperatures. This implied that one can

not obtain a single (unique) set of a and b for all mixture temperatures. The log Sb- log Sm









indicated that the predicted mixture stiffness using equation 2.17 through 2.19, and

equation 4.3 matched well with the measured mixture stiffness.

4.5 Use of Binder-to-mixture Stiffness Relationship

This section discuss the use of the binder-to-mixture stiffness relationship to predict

the mixture properties.

4.5.1 Prediction of the Mixture Stiffness for the Same Mixture

The above discussion showed that there is a separate binder-to-mixture stiffness

relationship at each of the three temperatures for the same mixture. One of the objectives

of this study is to investigate if the binder and mixture test results at one temperature

could be used to predict the mixture properties at other temperatures. Predictions were

make by taking the binder-to-mixture stiffness relationship at one temperature (equation

4.5 and 2.17) and applying this relationship at other temperatures. The resulting

predictions were plotted in Figure 4.32 through Figure 4.55.

These figures showed that: the stiffness prediction using the binder-to-mixture

stiffness relationship at OC mostly underestimated the mixture stiffness at 10C and

20C, but matched well with the measured stiffness at OC. The stiffness prediction using

the binder-to-mixture stiffness relationship at 10C overestimated the mixture stiffness at

0C and underestimated the mixture stiffness at 20 C, but matched well with the

measured stiffness at 10C. The stiffness prediction using the binder-to-mixture stiffness

relationship at 20C over estimated the mixture stiffness at 0C and 10C, but matched

well with the measured stiffness at 20 C.














Log Sb'- Log Sb PG 67-22 @ 6 1% asphalt content


10C 20C OC -Linear (20C) -Linear (10C) -Linear (OC)




y = 0 8862x- 1 7576
R2 = 0 9941

y =1 3119x+0 1002 y 1 2045x 0 846
R2 = 0 9995 R = 0 9967



.^ i


2. 5
Log Sb (GPa)


Figure 4.16 Log Sb


1.50



1.00



0.50



0.00



0.50


Log Sb Relationship: PG 67-22, extracted binder 6.1% AC


Log Sm Log Sb: PG 67-22 @ 6.1% asphalt content






I


rI


I


* Measured Mixture Stiffness @ 10C
* Sm-Sb(10C)
Sm-Sb(20C)
Measured Mixture Stiffness @ 20C
x Sm-Sb(OC)
* Measured Mixture Stiffness (OC)


5.00 4.50 4.00 3.50 3.00 2.50
Log Sb (GPa)


2.00 -1.50 1.00 0.50 0.00


Figure 4.17 Log Sm Log Sb Relationship; PG 67-22, extracted binder @ 6.1% AC


-0.5 0


2.00














Log Sb' Log Sb: PG 67-22 @ 7.2% asphalt content


-3



-4


-4.5 4 3.5 -3 2.5 2 -1.5 1 0.5
Log Sb (GPa)


Figure 4.18 Log Sb


Log Sb Relationship: PG 67-22, extracted binder @ 7.2% AC


Log Sm-Log Sb: PG 67-22 @ 7.2% asphalt content


1. 50



1.00



0.50



0.00



~ 0. 50


*i
E



-r-

m Measured Stiffness @0 10C
Sm-Sb(lOC)
Sm-Sb(20C)
I Measured Mixture Stiffness @ 20C
x Sm-Sb(OC)
Measured Mixture Stiffness (OC)


1.00



1.50


2.00
5.00 4.50 4.00 3. 50 3.00 2.50
Log Sh (GPa)


2.00 -1.50 1.00 0.50 0.00


Figure 4.19 Log Sm Log Sb Relationship: PG 67-22, extracted binder @ 7.2% AC















Log Sb'-Log Sb: PG 76-22 @ 6.1% asphlat content






10C 20C OC
Linear (OC) Linear (10C) Linear (20C)
2

y = 0.8445x 2.0297


3
R2 = 0.992


y -= 1.0298x- 1.3105
R2 = 0.9966


y-1.146x-0.482 R 2 .996
R2 0.9982
5




-6
-5 -4.5 4 3.5 3 2.5 2 -1.5 1 0.5 0
Log Sb (GPa)







Figure 4.20 Log Sb Log Sb Relationship: PG 76-22, extracted binder @ 6.1% AC


Log Sm-Log Sb: PG 76-22 @ 6.1% asphalt content

1.50



1.00



0.50



0.00



0.50

Sm-Sb(10C)
1.00 Sm-Sb(20C)
Measured Mixture Stiffness -@ 20C
x Sm-Sb(OC)
1.50 Measured Mxiture Stiffness (OC)

0 Measured Mixture Stiffness @ 10C

2.00
5.00 -4.50 4.00 3.50 3.00 2.50 2.00 -1.50 1.00 0.50 0.00
Log Sb (GPa)





Figure 4.21 Log Sm Log Sb Relationship: PG 76-22, extracted binder @ 6.1% AC














Log Sb'-Log Sb: PG 76-22 @ 7.2% asphalt content

0





S10C 20C OC
Linear (OC) Linear (10C) Linear (20C)
2

y = 0.8158x 1.4663 y =1.0202x 0.8361
R2 = 0.9929 R2 = 0.9987


Sy 1.0797x 0.1872
R2 =0.9991




5



6
-5 -4.5 4 3.5 3 2.5 2 -1.5 1 0.5 0
Log Sb (GPa)





Figure 4.22 Log Sb Log Sb Relationship: PG 76-22, extracted binder @ 7.2% AC



Log Sm Log Sb: PG 76-22 @ 7.2% asphalt content

1. 50



1.00



0. 50 ---


S0.00


0 Measured Mixture Stiffness @ 10C
-0. 50 Sm-Sb(10C)

Sm-Sb(20C)
-1.00 Measured Mixture Stiffness @ 20C

x Sm-Sb(OC)

-1. 50 Measrued Mixture Stiffness @2 OC



2. 00
5.00 -4.50 4.00 3.50 -3.00 2.50 -2.00 -1.50 1.00 0.50 0.00
Log Sb (GPa)


Log Sb Relationship: PG 76-22, extracted binder @ 7.2% AC


Figure 4.23 Log Sm














Log Sb' Log Sb: PG 67-22 after RTFOT ( 6.1% asphalt content


.5 4 3.5 3 2.5 2 -1.5 1 -0.5
Log Sb (GPa)


Figure 4.24 Log Sb -Log Sb Relationship: PG 67-22, RTFOT aged @ 6.1% AC



Log Sm -Lgo Sb: PG 67-22 after RTFOT ( 6.1% asphalt content


* Measured Mixture Stiffness @ 10C
* Sm-Sb(10C)
Sm-Sb(20C)
Measured Mixture Stiffness @ 20C
x Sm-Sb(OC)
* Measured Mxiture Stiffness W OC


-5.00 4.50 -4.00 3.50 -3.00 2.50 2.00 -1.50 1.00 0.50 0.00
Log Sb (GPa)




Figure 4.25 Log Sm Log Sb Relationship: PG 67-22, RTFOT aged @ 6.1% AC


2



3


ao
-4



5



-6















Log Sb'- Log Sb: PG 67-22 after RTFOT @ 7.2% asphalt content


.5 4 3. 5 3 2. 5 2 1. 5 1 0.5

Log Sb (GPa)


Figure 4.26 Log Sb -Log Sb Relationship: PG 67-22, RTFOT aged @ 7.2% AC



Log Sm Log Sb: PG 67-22 after RTFOT @ 7.2% asphalt content


1.50



1.00



0. 50



0. 00



-0. 50 Measur
m Measur
Sm-Sb(

1.00 Sm-Sb(
Measur
x Sm-Sb(
1.50 -
Measur


2.00
-5.00 4. 50 4.00 3.50 3.00 2.50 2.00

Log Sb (GPa)


ed Mixture Stiffness @ 10C
10C)
20C)
ed Mixture Stiffness @ 20C
OC)
ed Mxiture Stiffness (a OC


-1.50 1.00 0.50 0.00


Figure 4.27 Log Sm Log Sb Relationship: PG 67-22, RTFOT aged @ 7.2% AC















Log Sb' Log Sb: PG 76-22 after RTFOT @ 6.1% asphalt content


* 10C 20C OC
- Linear (OC) Linear (10C) Linear (20C)


y 0.8349x- 1.9662
R2 -0.992


-5 -4.5 4 3.5 3 2.5 2 -1.5 1 0.5 0
Log Sb (GPa)





Figure 4.28 Log Sb Log Sb Relationship: PG 76-22, RTFOT aged @ 6.1% AC



Log Sm LogSb: PG 76-22 after RTFOT @ 6.1% asphalt content

1.50



1.00



0. 50 o

'
0.00



0. 50 A 0 Measured Mixture Stiffness @ 10C

Sm-Sb(1OC)

1.00 Sm-Sb(20C)
Measured Mixture Stiffness @ 20C

1. 50 x Sm-Sb(OC)
Measured Mixture Stiffness @ OC

2.00
5.00 -4.50 4.00 3.50 3.00 2.50 2.00 -1.50 1.00 0.50 0.00
Log Sb (GPa)


Figure 4.29 Log Sm Log Sb Relationship: PG 76-22, RTFOT aged @ 6.1% AC


2



-3



-4




-5



6















Log Sb'-Log Sb: PG 76-22 after RTFOT @ 7.2% asphalt content


3



-4


-5



-6


.5 4 -3.5 -3 2.5 2 -1.5 1 -0.5

Log Sb (GPa)


Figure 4.30 Log Sb -Log Sb Relationship: PG 76-22, RTFOT aged @ 7.2% AC



Log Sm Log Sb: PG 76-22 after RTFOT @ 7.2% asphalt content
1. 50



1.00



0. 50



0.00




Sm-Sb(10C)

Sm-Sb(20C)
-. 00 -
p Measured Mixture Stiffness 120C
0. 50






x Sm-Sb(OC)
1. 50 Measured Mixture Stiffness 2 OC


o i i i i i i i i i i i i i i i i i


.50 4.00 -3.50 3.00 2.50 2.00

Log Sb (GPa)


-1.50 1.00 0.50 0.00


Figure 4.31 Log Sm Log Sb Relationship: PG 76-22, RTFOT aged @ 7.2% AC









60





Log Sm-Log Sb Prediction from OC: PG 67-22 @ 6.1% asphalt content


3.00
Log Sm-Log Sb @ 10C (predicted)

Log Sm-Log Sb @ 10C (measured)

2.00 Log Sm-Log Sb @ 20C (predicted)

Log Sm-Log Sb @ 20C (measured)

x Log Sm-Log Sb @ OC (predicted)
1.00
Log Sm-Log Sb @ OC (measured)


0.00




1.00


.3
9 U


2.00
5.00 4.50 4.00 3.50 3.00 2.50

Log Sb (GPa)


2.00 -1.50 1.00 0.50 0.00


Figure 4.32 Stiffness Prediction from PG 67-22,extracted binder, @ 6.1% AC @ 0OC



Log Sm-Log Sb Prediction from 10C: PG 67-22 @ 6.1% asphalt content


* Log Sm-L.. I' OC (predicted)

* Log Sm-Log Sb @ OC (measured)

Log Sm-L, I 10C (predicted)

Log Sm-L, I 10C (measured)

x Log Sm-L., I. 20C (predicted)

* Log Sm-L., I. 20C (measured)


. -


m


X
x1




0 x
X
x


.50 4.00 3.50 3.00 2.50
Log Sb (GPa)


2.0 0 1.50 1.00 -0.50 0.00


Figure 4.33 Stiffness Prediction from PG 67-22,extracted binder, @ 6.1% AC @ 10C


1.00


2. 00
-5.00


,


d









61





Log Sm-Log Sb Prediction from 20C: PG 67-22 @ 6.1% asphalt content


4.50 4.00 3.50 3.00 2.50 2.00 -1.50 1.00 0.50 0.00

Log Sb (GPa)


Figure 4.34 Stiffness Prediction from PG 67-22,extracted binder, @ 6.1% AC @ 20C



Log Sm Log Sb Prediction from OC: PG 67-22 ( 7.2% asphalt content


3.00 Log
Log

Log
2.00 Log

x Log

Log
1.00


1. 00


Sm-Log

Sm-Log

Sm-Log

Sm-Log

Sm-Log

Sm-Log


@ 10C (predicted)

@ 10C (measured)

@ 20C (predicted)

@ 20C (measured)

@ OC (predicted)

@ OC (measured)


a
*
U.


* U
U


2. 00
5.00 4.50 4.00 3.50 3.00 2.50
Log Sb (GPa)


2.00 -1.50 1.00 0.50 0.00


Figure 4.35 Stiffness Prediction from PG 67-22, extracted binder, @ 7.2% AC @ OC


I














Log Sm Log Sb Prediction from 10C: PG 67-22 @ 7.2% asphalt content


* Log Sm-Log Sb @ OC (predicted)
* Log Sm-Log Sb @ OC (measured)
Log Sm-Log Sb @ 10C (predicted)
Log Sm-Log Sb @ 10C (measured)
x Log Sm-Log Sb @ 20C (predicted)
* Log Sm-Log Sb @ 20C (measured)





*

r

X*
eX


5.00 -4.50 -4.00 3. 50 3.00 2. 50
Log Sb (GPa)


2.00 -1.50 1.00 0.50 0.00


Figure 4.36 Stiffness Prediction from PG 67-22,extracted binder, @ 7.2% AC @ 10C




Log Sm Log Sb Prediction from 20C: PG 67-22 @ 7.2% asphalt content




3. 00 Log Sm-Log Sb @ OC (predicted)
Log Sm-Log Sb @ OC (measured)
Log Sm-Log Sb @ 10C (predicted) *

S Log Sm-Log Sb @ 10C (measured)
2.00
x Log Sm-Log Sb @ 20C (predicted)
Log Sm-Log Sb @ 20C (measured)


0 1.00




0.00




1.00


5.00 4. 50 -4.00 3. 50 3.00 2. 50
Log Sb (GPa)


2.00 1. 50 1.00 0.50 0.00


Figure 4.37 Stiffness Prediction from PG 67-22, extracted binder, @ 7.2% AC @ 20 C


3.00




2.00




S1.00


I U

I u

*M
_____ __________________________









63




Log Sm -Log Sb Prediction from OC: PG 76-22 @ 6.1% asphalt content


I
V
I


2.00
5.00 4. 50 4.00 3.50 3.00 2. 50
Log Sb (GPa)


2.00 -1.50 1.00 0.50 0.00


Figure 4.38 Stiffness Prediction from PG 76-22, extracted binder, @ 6.1% AC @ OC



Log Sm Log Sb Prediction from 10C: PG 76-22 @ 6.1% asphalt content



3.00 *- Log Sm-Log Sb @ OC (predicted)
Log Sm-Log Sb @ OC (measured)
Log Sm-Log Sb @ 10C (predicted)
2.00 Log Sm-Log Sb @ 10C (measured)
x Log Sm-Log Sb @ 20C (predicted)

Log Sm-Log Sb @ 20C (measured) *
S1.00




0. 00
x*


1 NW X


-2.00 I I
-5.00 4. 50 -4.00 3. 50 -3.00 -2.50
Log Sb (GPa)


2.00 -1.50 1.00 0.50 0.00


Figure 4.39 Stiffness Prediction from PG 76-22, extracted binder, @ 6.1% AC @ 10C


* Log Sb-Sm @ 10C (predicted)
* Log Sb-Sm @ 10C (measured)
Log Sb-Sm @ 20C (predicted)
Log Sb-Sm @ 20C (measured)
x Log Sm-Log Sb @ OC (predicted)
* Log Sm-Log Sb @ OC (measured)


1.00




0.00









64





Log Sm Log Sb Prediction from 20C: PG 76-22 @ 6.1% asphalt content


.50 -4.00 3. 50 3.00 2. 50

Log Sb (GPa)


2.00 -1.50 1.00 -0.50 0.00


Figure 4.40 Stiffness Prediction from PG 76-22, extracted binder, @ 6.1% AC @ 20 C



Log Sm Log Sb Prediction from OC: PG 76-22 @ 7.2% asphalt content


3.00 Log Sm-Log Sb @ 10C (predicted)

Log Sm-Log Sb @ 10C (measured)

Log Sm-Log Sb @ 20C (predicted)
2.00 -
Log Sm-Log Sb @ 20C (measured)

x Log Sm-Log Sb @ OC (predicted)

1. 00 Log Sm-Log Sb @ OC (measured)


5.00 -4.50 4.00 3.50 3.00 2.50
Log Sb (GPa)


2.00 -1.50 1.00 0.50 0.00


Figure 4.41 Stiffness Prediction from PG 76-22, extracted binder, @ 7.2% AC @ 0C


* Log Sm-Log Sb
* Log Sm-Log Sb

Log Sm-Log Sb
Log Sm-Log Sb
x Log Sm-Log Sb

* Log Sm-Log Sb


OC (predicted)
OC (measured)

O1C (predicted)
O1C (measured)
20C (predicted)

20C (measured)


4I U
4
IU
U
U
SI
a
U
9r
















Log Sm Log Sb Prediction from 10C: PG 76-22 @ 7.2% asphalt content


* Log Sm-Log Sb @ OC (predicted)

* Log Sm-Log Sb @ OC (measured)

Log Sm-Log Sb @ 10C (predicted)

Log Sm-Log Sb @ 10C (measured)

x Log Sm-Log Sb @ 20C (predicted)

* Log Sm-Log Sb @ 20C (measured)


3. 00




2. 00




S1.00


o

0.00




-1.00




2.00


.00 3. 50 3.00 2.50

Log Sb (GPa)


2.00 -1.50 1.00 -0.50


Figure 4.42 Stiffness Prediction from PG 76-22,extracted binder, @ 7.2% AC @ 10C




Log Sm Log Sb Prediction from 20C: PG 76-22 @ 7.2% asphalt content


0 Log Sm-Log Sb @ OC (predicted)
3.00
Log Sm-Log Sb @ OC (measured)

Log Sm-Log Sb @ 10C (predicted)

Log Sm-Log Sb @ 10C (measured)
x Log Sm-Log Sb @ 20C (predicted)

Log Sm-Log Sb @ 20C (measured)


5.00 -4.50 4.00 3.50 3.00 2.50
Log Sb (GPa)


2.00 -1.50 1.00 -0.50 0.00


Figure 4.43 Stiffness Prediction from PG 76-22, extracted binder, @ 7.2% AC @ 20 C


a


*

0


4 U
t U


5.00 -4.50


0.00


U

uE
mm U
U Um



Hi
U
a
*
S
S
m















Log Sm Log Sb Prediction from OC: PG 67-22 after RTFOT @ 6.1% asphalt content




* Log Sm-Log Sb @ 10C (predicted)
* Log Sm-Log Sb @ 10C (measured)
Log Sm-Log Sb @ 20C (predicted)
Log Sm-Log Sb @ 20C (measured)
K Log Sm-Log Sb @ OC (predicted)
* Log Sm-Log Sb @ OC (measured)




16
tI

U


1.00


.50 4.00 3. 50 3.00 2.50
Log Sb (GPa)


2.00 1. 50 1.00 0.50 0.00


Figure 4.44 Stiffness Prediction from PG 67-22, RTFOT aged, @ 6.1% AC @ OC



Log Sm Log Sb Prediction from 10C: PG 67-22 after RTFOT ( 6.1% asphalt content


3. 00 Log Sm-Log Sb @ OC (predicted)

Log Sm-Log Sb @ OC (measured)

Log Sm-Log Sb @ 10C (predicted)
2. 00
Log Sm-Log Sb @ 10C (measured)

x Log Sm-Log Sb @ 20C (predicted)

1. 00 Log Sm-Log Sb @ 20C (measured)


000
0. 00


M U
* U


X X






0 Xx
* S


2. 00
5.00 -4.50 4.00 3.50 3.00 2.50
Log Sb (GPa)


2.00 1. 50 1.00 0. 50 0.00


Figure 4.45 Stiffness Prediction from PG 67-22, RTFOT aged, @ 6.1% AC @ 10C


2. 00
-5.00


0









67




Log Sm Log Sb Prediction from 20C: PG 67-22 after RTFOT @ 6.1% asphalt content


3.00 -
Log Sm-Log Sb @ OC (predicted)
Log Sm-Log Sb @ OC (measured)
Log Sm-Log Sb @ 10C (predicted)
2. 00 -
Log Sm-Log Sb @ 10C (measured)
x Log Sm-Log Sb @ 20C (predicted)
Log Sm-Log Sb @ 20C (measured)


U
pr


2. 00
5.00 -4.50 4.00 3. 50 3.00 2.50 2.00 -1.50 1.00 0.50 0.00

Log Sb (GPa)


Figure 4.46 Stiffness Prediction from PG 67-22, RTFOT aged, @ 6.1% AC @ 20OC



Log Sm Log Sb Prediction from OC: PG 76-22 after RTFOT ( 6.1% asphalt content


* Log Sm-Log Sb @ 10C (predicted)
* Log Sm-Log Sb @ 10C (measured)
Log Sm-Log Sb @ 20C (predicted)
Log Sm-Log Sb @ 20C (measured)
x Log Sm-Log Sb @ OC (predicted)
* Log Sm-Log Sb @ OC (measured)


U

U.


a

*
a


2.00
5.00 -4.50 4.00 3.50 3.00 2.50 2.00 -1.50 1.00 0.50 0.00

Log Sb (GPa)


Figure 4.47 Stiffness Prediction from PG 76-22, RTFOT aged, @ 6.1% AC @ 0C


1.00UU



0.00


1.00


&<









68




Log Sm Log Sb Prediction from 10C: PG 76-22 after RTFOT @ 6.1% asphalt content



3. 00 Log Sm-Log Sb @ OC (predicted)

Log Sm-Log Sb @ OC (measured)

Log Sm-Log Sb @ 10C (predicted)
2. 00
Log Sm-Log Sb @ 10C (measured)

x Log Sm-Log Sb @ 20C (predicted)

. 00 Log Sm-Log Sb @ 20C (measured) *
S1. 00



00 X
X x

x
1.00 x




2. 00
5.00 -4.50 4.00 3.50 3.00 2.50 2.00 -1.50 1.00 0.50 0.00
Log Sb (GPa)






Figure 4.48 Stiffness Prediction from PG 76-22, RTFOT aged, @ 6.1% AC @ 10C



Log Sm Log Sb Prediction from 20C: PG 76-22 after RTFOT @ 6.1% asphalt content



3. 00 Log Sm-Log Sb @ OC (predicted)
Log Sm-Log Sb @ OC (measured)

Log Sm-Log Sb @ 10C (predicted)
2. 00 Log Sm-Log Sb @ 10C (measured)

x Log Sm-Log Sb @ 20C (predicted) *

S* Log Sm-Log Sb @ 20C (measured)
S1. 0 0 --- m -- ^------------------
1.00


M
0.00








2. 00
-2. 00 ---------------------------------------------
5.00 -4.50 4.00 3.50 -3.00 2.50 2.00 -1.50 1.00 0.50 0.00
Log Sb (GPa)


Figure 4.49 Stiffness Prediction from PG 76-22, RTFOT aged, @ 6.1% AC @ 20 C









69





Log Sm Log Sb Prediction from OC: PG 67-22 after RTFOT @ 7.2% asphalt content


3. 00 Log Sm-Log Sb @ 10C (predicted)

Log Sm-Log Sb @ 10C (measured)

Log Sm-Log Sb @ 20C (predicted)
2.00 -
Log Sm-Log Sb @ 20C (measured)

x Log Sm-L., I. OC(predicted)

Log Sm-Log Sb @ OC (measured)
1.00


A-


T ; R
U
**


.3
9 U


. 50 -4.00 3. 50 -3.00 2. 50
Log Sb (GPa)


2.00 -1.50 1.00 0.50 0.00


Figure 4.50 Stiffness Prediction from PG 67-22, RTFOT aged, @ 7.2% AC @ 0C




Log Sm Log Sb Prediction from 10C: PG 67-22 after RTFOT @ 7.2% asphalt content


* Log Sm-Log Sb @ OC (predicted)
* Log Sm-Log Sb @ OC (measured)

Log Sm-Log Sb @ 10C (predicted)

Log Sm-Log Sb @ 10C (measured)

x Log Sm-Log Sb @ 20C (predicted)

* Log Sm-Log Sb @ 20C (measured)


U
*
IM

6 3

x

*



* X
a i


-2.00 I I
-5.00 4. 50 -4.00 3. 50 -3.00 2. 50

Log S, (GPa)


2.00 1. 50 1.00 0. 50 0.00


Figure 4.51 Stiffness Prediction from PG 67-22, RTFOT aged, @ 7.2% AC @ 10C


I


2.00
5. 00









70




Log Sm Log Sb Prediction from 20C: PG 67-22 after RTFOT @ 7.2% asphalt content


* Log Sm-Log Sb @ OC (predicted)
* Log Sm-L, I OC (measured)
Log Sm-L,. Il 10C (predicted)
Log Sm-L 1, I 10C (measured)
x Log Sm-L.. I 20C (predicted)
* Log Sm-L,. I 20C (measured)



________________________


5.00 4. 50 -4.00 3.50 3.00 2.50 2.00 -1.50 1.00 0.50 0.00

Log Sb (GPa)


Figure 4.52 Stiffness Prediction from PG 67-22, RTFOT aged, @ 7.2% AC @ 20C



Log Sm -Log Sb Prediction from OC: PG 76-22 after RTFOT ( 7.2% asphalt content


* Log Sm-Log Sb @ 10C (predicted)
* Log Sm-Log Sb @ 10C (measured)

Log Sm-Log Sb @ 20C (predicted)

Log Sm-Log Sb @ 20C (measured)

x Log Sm-Log Sb @ OC (predicted)

* Log Sm-Log Sb @ OC (measured)


I
'3t
*


2.00
5.00 -4.50 4.00 3.50 3.00 2.50 2.00 -1.50 1.00 0.50 0.00

Log Sb (GPa)


Figure 4.53 Stiffness Prediction from PG 76-22, RTFOT aged, @ 7.2% AC @ 0C


1.00


Ii
U
). U
0


1.00














Log Sm Log Sb Prediction from 10C: PG 76-22 after RTFOT @ 7.2% asphalt content



3. 00 Log Sm-Log Sb @ OC (predicted)
Log Sm-Log Sb @ OC (measured)
Log Sm-Log Sb @ 10C (predicted)
2. 00 Log Sm-Log Sb @ 10C (measured)
x Log Sm-Log Sb @ 20C (predicted)
Log Sm-Log Sb @ 20C (measured)
B 1.00

E .m


0.00 i1


a X
1.00 -

X X


2. 00
5.00 -4.50 4.00 3.50 -3.00 2.50 -2.00 -1.50 1.00 0.50 0.00

Log Sb (GPa)






Figure 4.54 Stiffness Prediction from PG 76-22, RTFOT aged, @ 7.2% AC @ 10C



Log Sm Log Sb Prediction from 20C: PG 76-22 after RTFOT @ 7.2% asphalt content



3.00 Log Sm-Log Sb @ OC (predicted)
Log Sm-Log Sb @ OC (measured)
Log Sm-Log Sb @ 10C (predicted)
Log Sm-Log Sb @ 10C (measured)
2.00
x Log Sm-Log Sb @ 20C (predicted)
S*0 Log Sm-Log Sb @ 20C (measured)

SE 1. 00




0.00 N--



-1.00




2.00
-5.00 4. 50 -4.00 3. 50 3.00 2. 50 2.00 -1.50 1.00 0. 50 0.00

Log Sb (GPa)




Figure 4.55 Stiffness Prediction from PG 76-22, RTFOT aged, @ 7.2% AC @ 20C









4.5.2 Prediction of Mixture Stiffness for SBS Modified Mixture

One of the goals of this research is to find if the properties of the SBS modified

mixtures could be predicted by using the binder-to-mixture stiffness relationship of

unmodified mixture and the SBS modified binder properties. The stiffness prediction was

made by taking the unmodified binder-to-mixture stiffness relationships and the SBS

modified binder properties at the same temperature. The resulting prediction were

plotted in Figure 4.5 through Figure 4.59.

Theses figures showed that the stiffness prediction by taking the unmodified binder-

to-mixture stiffness and SBS modified binder properties is not bad for the SBS modified

mixtures, especially at low temperatures, the predicted values are very close to the

measure stiffness.









73





Log Sm Log Sb Prediction from PG 67-22: PG 76-22 @ 6.1% asphalt content


* Log Sm-L.,_

* Log Sm-L..

Log Sm-L ..

Log Sm-L..

* Log Sm-L.,_

* Log Sm-L ..


10C (predicted)

10C (measured)

20C (predicted)

20C (measured)

Oc (predicted)

OC (measured)


t
I.


2.00
5.00 4. 50 4.00 3.50 3.00 2. 50
Log Sb (GPa)


2.00 -1.50 1.00 0.50 0.00


Figure 4.56 Stiffness Prediction from PG 67-22, extracted binder @ 6.1% AC



Log Sm Log Sb Prediction from PG 67-22: PG 76-22 @ 7.2% asphalt content


3. 00 Log Sm-Log Sb @ 10C (predicted)
Log Sm-Log Sb @ 10C (measured)
Log Sm-Log Sb @ 20C (predicted)

2. 00 Log Sm-Log Sb @ 20C (measured)
x Log Sm-Log Sb @ OC (predicted)
Log Sm-Log Sb @ OC (measured)


1. 00


oX
I 'x


**
U
M
M


2. 00
-5.00 -4.50 -4.00 3. 50 -3.00 -2. 50
Log Sb (GPa)


2.00 1. 50 1.00 0.50 0.00


Figure 4.57 Stiffness Prediction from PG 67-22, extracted binder @ 7.2% AC


1.00




0.00









74





Log Sm Log Sb Prediction from PG 67-22: PG 76-22 after RTFOT @ 6.1% asphalt content


* Log Sm-Log Sb @ 10C (predicted)
* Log Sm-Log Sb @ 10C (measured)
Log Sm-Log Sb @ 20C (predicted)
Log Sm-Log Sb @ 20C (measured)
x Log Sm-Log Sb @ OC (predicted)
* Log Sm-Log Sb @ OC (measured)





.
m m
*+


. 50 -4.00 3.50 3.00 2.50
Log Sb (GPa)


2.00 -1.50 1.00 0.50 0.00


Figure 4.58 Stiffness Prediction from PG 67-22, RTFOT aged, @ 6.1% AC



Log Sm Log Sb Prediction from PG 67-22: PG 76-22 after RTFOT @ 7.2% asphalt content





0 Log Sm-Log Sb @ 10C (predicted)

Log Sm-Log Sb @ 10C (measured)

Log Sm-Log Sb @ 20C (predicted)
00 Log Sm-Log Sb @ 20C (measured)

Log Sm-Log Sb @ OC (predicted)

Log Sm-Log Sb @ OC (measured)


U
U
U
U


a
"



iK
EgT

IX


2.00
5.00 4. 50 4.00 3.50 3.00 2.50
Log Sb (GPa)


2.00 -1.50 1.00 0.50 0.00


Figure 4.59 Stiffness Prediction from PG 67-22, RTFOT aged, @ 7.2% AC


1.00




0.00


2.00
5. 00


3.




2.




1.




0.




-1.


00




00




00









4.5.3 Use Energy Ratio for Comparison

As mentioned in Chapter 2, the Energy Ratio was developed at the University of

Florida as a method to compare the cracking performances of different asphalt mixtures.

This method was also used here to compare the difference in predicted performance

observed by using the different way to generate the mixture properties needed for

evaluation. ER was defined as follows: the energy ratio of the dissipated creep strain

energy of the mixture to the minimum DCSE required for the mixture to perform

satisfactorily. The resulting equation for Energy Ratio is:

ax DCSE,
ER = in9 (2.36)
298 xD1

where:

a = 0.0299c-31(6.36 S,) + 2.46 x 108

o = tensile stress of asphalt layer, psi

St= tensile strength, MPa

DCSEf = Dissipated Creep Strain Energy, KJ/m3

D1= creep parameter, 1/psi

m = creep parameter

To facilitate the computation, a tensile stress, a was assumed as 230 psi, St and

DCSEf were the measured for different mixtures using the Superpave IDT. Different data

interpretation methods were used to obtain D1 and m at each temperature. Each method is

described in more detail in Table 4.25.









Table 4.7Summary of Data Interpretation Methods
Method Description
Mixture test data at one temperature combined with the binder shift factor to
predict D1 and m at multiple temperatures.
Mixture test data at one temperature combined with the master curve and shift
2 factor to predict Sm at multiple temperatures assuming m from mix test at one
temperature
Unmodified binder-to-mixture stiffness relationship at one temperature
3 combined with the modified binder properties at the same temperature to
predict the modified mixture properties.


Each method is described in more detail in the following paragraph.

Method 1:

1. Lock-in Do = 0.048 (1/GPa)

2. Determine D1 and m at 20 C from regression

3. Fix m = m at 20OC ( assuming m is a constant at three temperatures for the same

mixture)

4. Calculate D1 at OC and 10C using the following relationship:

1
D(0)= D1(20) (4.4)


1
D(10) = D1(20) x (4.5)
(aTr(o))

5. Repeat Step 1-4 based on D1 and m obtained at 0C and 10C, respectively.

By following the procedures above, the potential use of mixture tests at a single

temperature to predict response and/or performance at multiple temperatures was

evaluated from the measured data.

Method 2

1. Predict the mixture stiffness at 20 C using the binder-to-mixture stiffness at 20 C









2. Lock-in Do = 0.048 (1/GPa)

3. Determine the D1 and m at 20OC from regression

4. Use the binder-to-mixture stiffness relationship at 20OC to predict the mixture

stiffness at OC and 10 C for different times

5. Calculate D1 at OC and 10C using the predicted mixture stiffness from step 4

and assuming:

m m at20C

Do = 0.048 (1/GPa)

6. Repeat Step 1-5 starting 0C and 10"C, respectively.

By the procedure above, the Energy Ratio was obtained from the predicted mixture

data by using the binder-to-mixture stiffness relationship.

Method 3.

1. Develop the binder-to-mixture stiffness relationship for the unmodified mixture at

each of the three temperature

2. Predict the stiffness of modified mixture using the unmodified binder-to-mixture

stiffness relationship at the same temperature

3. Lock-in Do = 0.048 (1/GPa)

4. Determine D1 and m for the modified mixture

Following the three procedures above, the resulting Energy Ratio (ER) was used to

evaluate how well the binder-to-mixture stiffness relationship predicted the mixture

properties. The comparisons were presented in Figure 4.24 Figure 4.29.

The comparison indicates that the using the binder-to-stiffness relationship gave a

good prediction for Energy Ratio at 0C and 10 C in most cases, but the results at 20C






78


and the prediction from unmodified mixtures to SBS modified mixtures are not as good

as at OC and 10OC.











Energy Ratio from Mixture Test @ OC


2.00 1.83 1.83
S1.50
1.00
S0.50
0.00
* Measured 0

* PG 67-22 @ 6.1%
AC


U.6U


20 0.05


20


Temp.(C)


Figure 4.60 Energy Ratio Prediction: PG 67-22, 6.1% AC @ 0C


Energy Ratio from Mixture Test @ 10C


n0 1 n81


Temp.(C)


20 Measured

U PG 67-22 @
6.1%AC


Figure 4.61 Energy Ratio Prediction: PG 67-22, 6.1% AC @ 10C


Energy Ratio from Mixture Test @ 20C


Temp.(C)


0.20 0.20

20 Measured
SPG 67-22 @
6.1% AC


Figure 4.62 Energy Ratio Prediction: PG 67-22, 6.1% AC @ 20C


2.50
S2.00
, 1.50
1.00
S0.50
0.00


10.00
8.00
6.00
4.00
2.00
0.00


Z..3


0.81











Energy Ratio from Mixture Test @ OC


1.20 1.20


0 AA 0.53


Temp.(C)


0.14 0.07


20 Measured
SPG 67-22 @
7.2% AC


Figure 4.63 Energy Ratio Prediction: PG 67-22, 7.2% AC @ OC


Energy Ratio from Mixture Test @ 10C


0.44 0.44
10.14 0.04

i1 ,n Measured


Temp.(C)


* PG 67-22 @
7.2% AC


Figure 4.64 Energy Ratio Prediction: PG 67-22, 7.2% AC @ 10C


Energy Ratio from Mixture Test @ 20C


3.75
0.44 0.14 0.14


Temp.(C)


20 Measured
PG 67-22 @
7.2% AC


Figure 4.65 Energy Ratio Prediction: PG 67-22, 7.2% AC @ 20C


1.50
I-
1.00

8 0.50

0.00


2.00

1.50
1.00
0.50
0.00


28.38


30.00

20.00

10.00

0.00


1.20











Energy Ratio from Mixture Test @ OC


Temp.(C)


0.30 0.11


20 Measured
SPG 76-22 @
6.1% AC


Figure 4.66 Energy Ratio Prediction: PG 76-22, 6.1% AC @ OC


Energy Ratio from Mixture Test @ 10C


2.57


1.Jz/ 1.Jz


Temp.(C)


0.30 0.15 -

20 Measured

PG 76-22 @
6.1% AC


Figure 4.67 Energy Ratio Prediction: PG 76-22, 6.1% AC @ 10C


Energy Ratio from Mixture Test @ 20C


11 "'


3.05
1.32
0.30 0.30

10 20 Measured


*PG 76-22 @
6.1% AC


Temp.(C)


Figure 4.68 Energy Ratio Prediction: PG 76-22, 6.1% AC @ 20OC


3.00

2.00

8 1.00

0.00


5.00
4.00
3.00
2.00
1.00
0.00


15.00

10.00

5.00

0.00


Z,.3 Z,.31











Energy Ratio from Mixture Test @ OC


2.46 2.46


1.05 1.06


0.18 0.10


20 F Measured


Temp.(C)


* PG 76-22 @
7.2% AC


Figure 4.69 Energy Ratio Prediction: PG 76-22, 7.2% AC @ 0C


Energy Ratio from Mixture Test @ 10C


1.05 1.05


0.18 0.08


20 m Measured


Temp.(C)


* PG 76-22 @
7.2% AC


Figure 4.70 Energy Ratio Prediction: PG 76-22, 7.2% AC @ 10C


Energy Ratio from Mixture Test @ 20C


8.00

6.00
4.00

2.00
0.00


2.46


0.18 0.18


20 Measured


Temp.(C)


* PG 76-22 @
7.2% AC


Figure 4.71 Energy Ratio Prediction: PG 76-22, 7.2% AC @ 20C


3.00
*|

S2.00

S1.00

0.00


4.00
3.00

2.00
1.00
0.00











Energy Ratio fromMixture Test @ OC


2.00
1.50
1.00
0.50
0.00


1.83 1 8n 1 8n


Tenp.(C)


20 U Measured
Extracted
O RTFOT


Figure 4.72 Energy Ratio Prediction: PG 67-22, 6.1% asphalt content @ 0C


Energy Ratio fromMixture Test @ 10C


3.00

2.00

1.00

0.00


0.81 0.81 0.81


-7


10

Tenp.(C)


0.20 0.08 0.08


20 U Measured
Extracted
O RTFOT


Figure 4.73 Energy Ratio Prediction: PG 67-22, 6.1% asphalt content @ 10C


Energy Ratio from Mixture Test @ 20C


40.00
30.00
20.00
10.00
0.00


0 10


Tenp.(C)


20 U Measured
Extracted
O RTFOT


Figure 4.74 Energy Ratio Prediction: PG 67-22, 6.1% asphalt content @ 20 C


i.S


I


I


.2 0.2 0.20.











Energy Ratio fromMixture Test @ OC


1.50

1.00

0.50

0.00


0 10


Tenp.(C)


20 U Measured
Extracted
O RTFOT


Figure 4.75 Energy Ratio Prediction: PG 67-22, 7.2% asphalt content @ 0


Energy Ratio fromMixture Test @ 10C


1.61 1.61


r0.44 0.44 0.44
.140.04 0.04


10
Tenp.(C)


20 0 Measured
Extracted
O RTFOT


Figure 4.76 Energy Ratio Prediction: PG 67-22, 7.2% asphalt content @ 10C


Energy Ratio from Mixture Test @ 20C


20.00


0.00

-20.00

-40.00

-60.00


1.20 0.443.853.85 0.140.140.14
--- ____ -I i I ______


-48.28 -48.28


Temp.(C)


* Measured
* Extracted
O RTFOT


Figure 4.77 Energy Ratio Prediction: PG 67-22, 7.2% asphalt content @ 20C


2.00
1.50
1.00
0.50
0.00


-

-











Energy Ratio from Mixture Test @ OC


3.00

2.00

1.00

0.00


0 10

Temp.(C)


20 Measured
U Extracted
O RTFOT


Figure 4.78 Energy Ratio Prediction: PG 76-22, 6.1% asphalt content @ 0C


Energy Ratio from Mixture Test @ 10C


5.00
4.00
3.00
2.00
1.00
0.00


4.66 4.66


Temp.(C)


20 Measured
Extracted
O RTFOT


Figure 4.79 Energy Ratio Prediction: PG 76-22, 6.1% asphalt content @ 10C


Energy Ratio from Mixture Test @ 20C


30.00

20.00

10.00


0.00


0 10


Tenp.(C)


20 Measured
U Extracted
E RTFOT


Figure 4.80 Energy Ratio Prediction: PG 76-22, 6.1% asphalt content @ 20 C


2.5



-I


0.30 0.16 0.161











Energy Ratio from Mixture Test @ OC


2.462.42 2.42


0 10


Temp.(C)


20 U Measured
Extracted
O RTFOT


Figure 4.81 Energy Ratio Prediction: PG 76-22, 7.2% asphalt content @ OC


Energy Ratio from Mixture Test @ 10C


4.00
3.00
2.00
1.00
0.00


0 10


Temp.(C)


20 U Measured
Extracted
O RTFOT


Figure 4.82 Energy Ratio Prediction: PG 76-22, 7.2% asphalt content @ 10C


Energy Ratio from Mixture Test @ 20C


15.00

10.00

5.00


0.00


0 10


Temp.(C)


20 U Measured
Extracted
O RTFOT


Figure 4.83 Energy Ratio Prediction: PG 76-22, 7.2% asphalt content @ 20OC


3.00

2.00

1.00

0.00










Energy Ratio from Unmodified Mixtrue @ 6.1% asphalt
content


3.20
2.57i


2.47
- 1.32
0.98 0.30
0.23 0.13


10

Temp.(C)


20 U Mea.
Extracted
O RTFOT


Figure 4.84 Energy Ratio Prediction from Unmodified Mixture @ 6.1% asphalt content


Energy Ratio from Unmodified Mixtrue @ 7.2% asphalt
content


1.05


0.13
0.18 0.07


Temp.(C)


20 U Mea.
Extracted
O RTFOT


Figure 4.85 Energy Ratio Prediction from Unmodified Mixture @ 7.2% asphalt content


4.00
3.00
2.00
1.00
0.00


Z. .-u


3.00

2.00

1.00

0.00





PAGE 49

36 were chosen to determine the creep complian ce. On the log creep compliance – log t plot, the number of log cycles covered by l og t was the same for the Dynamic Shear Rheometer test as for the Bending Beam Rheometer test. Table 4.3 Power Model Parameters from DSR Test Results at 10 Binder Type D0 D1 m PG 67-22, 6.1% asphalt content 4.834 x10-9 2.101 x10-7 0.476 PG 67-22, 7.2% asphalt content 5.550 x10-9 2.211 x10-7 0.490 PG 76-22, 6.1% asphalt content 5.899 x10-9 1.744 x10-7 0.494 PG 76-22, 7.2% asphalt content 6.575 x10-9 2.275 x10-7 0.498 PG 67-22, RTFOT aged 7.419 x10-9 1.879 x10-7 0.538 PG 76-22, RTFOT aged 5.491 x10-9 2.202 x10-9 0.478 Table 4.4 Power Model Parameters from DSR Test Results at 20 Binder Type D0 D1 m PG 67-22, 6.1% asphalt content 1.650 x10-8 1.384 x10-6 0.595 PG 67-22, 7.2% asphalt content 1.854 x10-8 1.552 x10-6 0.606 PG 76-22, 6.1% asphalt content 1.513 x10-8 1.134 x10-6 0.581 PG 76-22, 7.2% asphalt content 1.702 x10-8 1.316 x10-6 0.587 PG 67-22, RTFOT aged 1.532 x10-8 1.198 x10-6 0.589 PG 76-22, RTFOT aged 1.808 x10-8 1.469 x10-6 0.595

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37 4.3.2.2 Construction of binder creep compliance master curve To construct the master curve, the log creep compliance-log t relationship must first be plotted. Creep compliance from the BB R test was simply taken as the inverse of the stiffness. The creep compliance fr om DSR test was obtained by inputting t into the power model (equation 2.32) and the reduced time, (equation 2.29), was used to calculate the real time at the appropr iate temperature. In this study, 20 was chosen as the reference temperature. Figures 4.4 through Figure 4.9 illustrate the log cr eep compliancelog relationship before and after shifting. Th ese results indicate that the creep compliance data at 10 did not match well with the master curve at 20. It appears that it may not be possible to obtain accurate measurements from the Dynamic Shear Rheometer at 10 when the stiffness of the binder is too high relative to the instruments stiffness. Therefore, it was decided that the data at 10 can not be used to develop the master curve. The creep compliance master curve was develope d using the BBR test results at -10 and the DSR test results at 20. The resulting master curves are shown in Figure 4.10 through Figure 4.15. The master curve developed by us ing only the DSR te st results at 20 was also plotted for comparison. The figures clearly sh ow that the characteristics of the master curve are highly dependent on how it was deve loped. In this case, there is no big difference between the two master curves from two methods. The master curve was fitted using a of the following equation: mD D D 1 0) ( (2.32)

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38 Shifting No.1: PG 67-22,extracted unmodified binder @ 6.1% asphalt content-9.00 -8.00 -7.00 -6.00 -5.00 -4.00 -3.00 -2.00 -1.00 0.00 -6.000-4.000-2.0000.0002.0004.0006.0008.000 Log reduced timeLog D(t) (1/Pa) -10C 10C DSR @10C DSR @ 20C 20C BBR @ -10C Figure 4.4 Master Curve Relationship: PG 67-22, ex tracted binder @ 6.1% AC Shifting No.2: PG 67-22,extracted unmodified binder @ 7.2% asphalt content-9.00 -8.00 -7.00 -6.00 -5.00 -4.00 -3.00 -2.00 -1.00 0.00 -6.000-4.000-2.0000.0002.0004.0006.0008.000 Log reduced TimeLog D(t)(1/Pa) -10C 10C 20C DSR @ 10C DSR @ 20C BBR @ -10C Figure 4.5 Master Curve Re lationship: PG 67-22, extr acted binder @ 7.2% AC

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39 Shifting No.3: PG 76-22,extracted SBS m odified binder @ 6.1% asphalt content-9.00 -8.00 -7.00 -6.00 -5.00 -4.00 -3.00 -2.00 -1.00 0.00 -6.000-4.000-2.0000.0002.0004.0006.0008.000 Log reduced timeLog D(t)(1/Pa) -10C 10C 20C DSR @ 10C DSR @ 20C BBR @ -10C Figure 4.6 Master Curve Relationship: PG 76-22, ex tracted binder @ 6.1% AC Shifting No.4: PG76-22,extracted SBS modified binder @ 7.2% asphalt content-9.00 -8.00 -7.00 -6.00 -5.00 -4.00 -3.00 -2.00 -1.00 0.00 -6.000-4.000-2.0000.0002.0004.0006.0008.000 Log reduced timeLog D(t)(1/Pa) -10C 10C 20C DSR @ 10C DSR @ 20C BBR @ -10C Figure 4.7 Master Curve Relationship: PG 76-22, ex tracted binder @ 7.2% AC

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40 Shifting No.5: PG 67-22,unmodified virgin binder after RTFOT-9.00 -8.00 -7.00 -6.00 -5.00 -4.00 -3.00 -2.00 -1.00 0.00 -6.000-4.000-2.0000.0002.0004.0006.0008.000 Log reduced timeLog D(t)(1/Pa) -10C 10C 20C DSR @ 10C DSR @ 20C BBR @ 0C Figure 4.8 Master Curve Relati onship: PG 67-22, RTFOT aged Shifting No.6: PG 76-22,SBS modi fied virgin binder after RTFOT-9.00 -8.00 -7.00 -6.00 -5.00 -4.00 -3.00 -2.00 -1.00 0.00 -6.000-4.000-2.0000.0002.0004.0006.0008.000 Log reduced timeLog D(t)(1/Pa) -10C 10C 20C DSR @ 10C DSR @ 20C BBR @ -10C Figure 4.9 Master Curve Relati onship: PG 76-22, RTFOT aged

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41 PG 67-22, extracted unmodified binder @ 6.1% asphlat content-10.00 -9.00 -8.00 -7.00 -6.00 -5.00 -4.00 -3.00 -2.00 -1.00 0.00 -10.00-8.00-6.00-4.00-2.000.002.004.006.008.00 Log reduced timeLog D(t) (1/Pa) DSR @ 20C -10C & 20C -10C & 20C master curve 20C master curve Figure 4.10 Master Curve: PG 6722, extracted binder @ 6.1% AC

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42 PG 67-22,extracted unmodified binder @ 7.2% asphalt content-10.00 -9.00 -8.00 -7.00 -6.00 -5.00 -4.00 -3.00 -2.00 -1.00 0.00 -10.00-8.00-6.00-4.00-2.000.002.004.006.008.00 Log reduced TimeLog D(t) (1/Pa) DSR @ 20C -10C & 20C -10C & 20C master curve 20C master curve Figure 4.11 Master Curve: PG 6722, extracted binder @ 7.2% AC

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43 PG 76-22,extracted SBS modified binder @ 6.1% asphalt content-10.00 -9.00 -8.00 -7.00 -6.00 -5.00 -4.00 -3.00 -2.00 -1.00 0.00 -10.00-8.00-6.00-4.00-2.000.002.004.006.008.00 Log reduced timeLog D(t) (1/Pa) DSR @ 20C -10C & 20C -10C & 20C master curve 20C master curve Figure 4.12 Master Curve: PG 7622, extracted binder @ 6.1% AC

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44 PG 76-22,extracted SBS modified binder @ 7.2% asphalt content-10.00 -9.00 -8.00 -7.00 -6.00 -5.00 -4.00 -3.00 -2.00 -1.00 0.00 -10.000-8.000-6.000-4.000-2 .0000.0002.000 4.0006.0008.000 Log reduced timeLog D(t) (1/Pa) DSR @ 20C -10C & 20C -10C & 20C master curve 20C master curve Figure 4.13 Master Curve: PG 7622, extracted binder, 7.2% AC

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45 PG 67-22,unmodified virgin binder after RTFOT-10.00 -9.00 -8.00 -7.00 -6.00 -5.00 -4.00 -3.00 -2.00 -1.00 0.00 -10.00-8.00-6.00-4.00-2. 000.002.004.006.008.00 Log reduced timeLog D(t) (1/Pa) DSR @ 20C -10C & 20C -10C & 20C master curve 20C master curve Figure 4.14 Master Curve: PG 67-22, RTFOT aged

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46 PG 76-22,SBS modified virgin binder after RTFOT-10.00 -9.00 -8.00 -7.00 -6.00 -5.00 -4.00 -3.00 -2.00 -1.00 0.00 -10.00-8.00-6.00-4.00-2.000.002.004.006.008.00 Log reduced timeLog D(t) (1/Pa) DSR @ 20C -10C & 20C -10C & 20C master curve 20C master curve Figure 4.15 Master Curve; PG 76-22, RTFOT aged

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47 The parameter D0 was take as constant, as it has been determined that this leads to greater consistency in fitting master curve para meters. As mentioned in Chapter 2, D0 for all binders, which is defined as the minimum compliance (or the inverse of the elastic stiffness) is: Pa GPa D10 010 33 3 3 / 1 The parameters D1 and m were then fit by performi ng linear regression on binder data shifted to a reference temperature of 20. Table 4.23 gives the resulting power model parameters for the master curves. Table 4.5 Power Model Parameters for Master Curve Binder Type D0 D1 m PG 67-22, 6.1% asphalt content 3.33 x10-10 1.321 x10-6 0.524 PG 67-22, 7.2% asphalt content 3.33 x10-10 1.474 x10-6 0.527 PG 76-22, 6.1% asphalt content 3.33 x10-10 1.070 x10-6 0.488 PG 76-22, 7.2% asphalt content 3.33 x10-10 1.238 x10-6 0.487 PG 67-22, RTFOT aged 3.33 x10-10 1.140 x10-6 0.507 PG 76-22, RTFOT aged 3.33 x10-10 1.380 x10-6 0.493 The creep compliance at any other temperatures was obt ained by using shift factors in the method of reduced time (equation 2.29). 4.4 Binder-to-Mixture Stiffness Relationship This section describes how the bi nder-to-mixture stiffness relationships were developed and used.

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48 4.4.1 Empirical Binder-to-mixtu re Stiffness Relationship In Chapter 2, both micromechanical and empirical binder-to-mixture stiffness relationships were reviewed. In this study, Heukelom and Klomp’s equation (2.17 through 2.19) were used to develop relations hips between binder and mixture properties. These relationships are presented ag ain for the sake of convenience: n v v b mC C n S S 1 5 2 1' (2.17) bS x n510 4 log 83 0 (2.18) ) ( binder aggregate Volumeof gregate Volumeofag Cv (2.19) where: Sm = Stiffness of mixture (GPa or Psi) Sb = Stiffness of binder (GPa or Psi) Research by Mori-Tanaka showed the binder stiffness in the equation 2.17 needs to be calibrated usi ng the following equation (1) b b bT t S a S )) ( (' (4.5) where: Sb ’ = Calibrated binder stiffness Sb = Binder stiffness obtained at loading time, t, and temperature, T a, b = Coefficients determined through regression In this study, the binder stiffness was calibrated using equa tion 4.3 to develop the binder-to-mixture stiffness relationship.

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49 4.4.2 Volumetrics of the aggregate The binder-to-mixture stiffne ss relationship is related to the volumetrics as seen in equation 2.19. The gradation and volumetrics of the mixture in this study are presented in Appendix C. The following relationships were used to calculate necessary parameters from the measured values. Volume of aggregate = Total Volume – Voids in Mineral Aggregate = (1VMA) x 100% Volume of (Aggrega te + Binder) = Total Volume % Air Voids = 100 % Air Voids In this study, all mixtures ha d the same gradation but tw o different asphalt content levels corresponding to two traffic level, 6.1% and 7.2%. Therefore, mixtures with the same asphalt content had the same volumetrics. For mixtures with 6.1% asphalt content: 163 8 1 v vC C For mixtures with 7.2% asphalt content: 440 6 1 v vC C 4.4.3 Calibration of the binder stiffness The data used to calibrate binder st iffness is illustrated in table 4.24.

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50 Table 4.6 Data Used to Calibrate Binder Stiffness Temp.() Time (sec.) Sm Sb Sb ’ 1 Sm1 Sb(1/at) Sb1 ’ 10 Sm10 Sb(10/at) Sb10 ’ ... … … … 0 1000 Sm1000 Sb(1000/at) Sb1000 ’ 1 Sm1 Sb(1/at) Sb1 ’ 10 Sm10 Sb(10/at) Sb10 ’ … … … … 10 1000 Sm1000 Sb(1000/at) Sb1000 ’ 1 Sm1 Sb1 Sb1 ’ 10 Sm10 Sb10 Sb10 ’ … … … … 20 1000 Sm1000 Sb1000 Sb1000 ’ Mixture stiffness, Sm, for loading times of 1, 2, 5, 10, 20, 50, 100, 200, 500, 1000 sec. was measured at each test temper atures. Binder creep compliance at 20 was obtained from the master curv e (power model equation 2.32) by i nputting the loading times as in column 2, table 4.24. At 0 and 10 the reduced time was used to obtain the binder creep compliance. The binder stiffness, Sb, was taken as the i nversion of the creep compliance. The calibrated binder stiffness, Sb ’, was obtained by iteration such that Sm from equation 2.17 match the measured Sm. Linear regression was then conducted between log Sb and log Sb ’ to obtain a and b in equation 4.3. The log Sb log Sb ’ and log Sblog Sm relationships were plotted for each mixture and presented in Figure 4.16 through 4.31. The figures indicated that for each ki nd of mixture, there is a seperate relationship between Log Sb Log Sb ’ for each of the three temperatur es. This implied that one can not obtain a single (uni que) set of a and b for all mixture temperatures. The log Sblog Sm

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51 indicated that the predicte d mixture stiffness using e quation 2.17 through 2.19, and equation 4.3 matched well with th e measured mixture stiffness. 4.5 Use of Binder-to-mixture Stiffness Relationship This section discuss the use of the binder-to-mixture stiffness relationship to predict the mixture properties. 4.5.1 Prediction of the Mixture St iffness for the Same Mixture The above discussion showed that th ere is a separate bind er-to-mixture stiffness relationship at each of the thre e temperatures for the same mixture. One of the objectives of this study is to investigate if the binde r and mixture test resu lts at one temperature could be used to predict the mixture propert ies at other temperatures. Predictions were make by taking the binder-to-mixture stiffne ss relationship at one temperature (equation 4.5 and 2.17) and applying this relations hip at other temperatures. The resulting predictions were plotted in Figure 4.32 through Figure 4.55. These figures showed that: the stiffne ss prediction using th e binder-to-mixture stiffness relationship at 0 mostly underestimated the mixture stiffness at 10and 20, but matched well with the measured stiffness at 0. The stiffness prediction using the binder-to-mixture sti ffness relationship at 10 overestimated the mixture stiffness at 0 and underestimated the mixture stiffness at 20, but matched well with the measured stiffness at 10. The stiffness prediction using the binder-to-mixture stiffness relationship at 20 over estimated the mixture stiffness at 0 and 10, but matched well with the measured stiffness at 20.

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52 Log Sb'Log Sb: PG 67-22 @ 6.1% asphalt content y = 1.3119x + 0.1002 R2 = 0.9995 y = 1.2045x 0.846 R2 = 0.9967 y = 0.8862x 1.7576 R2 = 0.9941 Log Sb (GPa)Log Sb' (GPa) 10C 20C 0C Linear (20C) Linear (10C) Linear (0C) Figure 4.16 Log Sb ’ – Log Sb Relationship: PG 67-22, extracted binder 6.1% AC Log Sm Log Sb: PG 67-22 @ 6.1% asphalt content Log Sb (GPa)Log Sm (GPa) Measured Mixture Stiffness @ 10C Sm-Sb(10C) Sm-Sb(20C) Measured Mixture Stiffness @ 20C Sm-Sb(0C) Measured Mixture Stiffness (0C) Figure 4.17 Log Sm – Log Sb Relationship; PG 67-22, extracted binder @ 6.1% AC

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53 Log Sb' Log Sb: PG 67-22 @ 7.2% asphalt content y = 0.8906x 1.407 R2 = 0.9917 y = 1.2324x 0.3849 R2 = 0.9997 y = 1.655x + 2.0612 R2 = 0.9974 Log Sb (GPa)Log Sb'(GPa) 10C 20C 0C Linear (0C) Linear (10C) Linear (20C) Figure 4.18 Log Sb ’ – Log Sb Relationship: PG 67-22, extracted binder @ 7.2% AC Log Sm-Log Sb: PG 67-22 @ 7.2% asphalt content Log Sb (GPa)Log Sm(GPa) Measured Stiffness @ 10C Sm-Sb(10C) Sm-Sb(20C) Measured Mixture Stiffness @ 20C Sm-Sb(0C) Measured Mixture Stiffness (0C) Figure 4.19 Log Sm – Log Sb Relationship: PG 67-22, extracted binder @ 7.2% AC

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54 Log Sb'-Log Sb: PG 76-22 @ 6.1% asphlat content y = 0.8445x 2.0297 R2 = 0.992 y = 1.0298x 1.3105 R2 = 0.9966 y = 1.146x 0.482 R2 = 0.9982 Log Sb (GPa)Log Sb'(GPa) 10C 20C 0C Linear (0C) Linear (10C) Linear (20C) Figure 4.20 Log Sb ’ – Log Sb Relationship: PG 76-22, extracted binder @ 6.1% AC Log Sm-Log Sb: PG 76-22 @ 6.1% asphalt content Log Sb (GPa)Log Sm (GPa) Sm-Sb(10C) Sm-Sb(20C) Measured Mixture Stiffness @ 20C Sm-Sb(0C) Measured Mxiture Stiffness (0C) Measured Mixture Stiffness @ 10C Figure 4.21 Log Sm – Log Sb Relationship: PG 76-22, extracted binder @ 6.1% AC

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55 Log Sb'-Log Sb: PG 76-22 @ 7.2% asphalt content y = 0.8158x 1.4663 R2 = 0.9929 y = 1.0202x 0.8361 R2 = 0.9987 y = 1.0797x 0.1872 R2 = 0.9991 Log Sb (GPa)Log Sb' (GPa) 10C 20C 0C Linear (0C) Linear (10C) Linear (20C) Figure 4.22 Log Sb ’ – Log Sb Relationship: PG 76-22, extracted binder @ 7.2% AC Log Sm Log Sb: PG 76-22 @ 7.2% asphalt content Log Sb (GPa)Log Sm (GPa) Measured Mixture Stiffness @ 10C Sm-Sb(10C) Sm-Sb(20C) Measured Mixture Stiffness @ 20C Sm-Sb(0C) Measrued Mixture Stiffness @ 0C Figure 4.23 Log Sm – Log Sb Relationship: PG 76-22, extracted binder @ 7.2% AC

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56 Log Sb' Log Sb: PG 67-22 after RTFOT @ 6.1% asphalt content y = 0.9149x 1.7265 R2 = 0.9941 y = 1.2432x 0.8047 R2 = 0.9967 y = 1.3539x + 0.145 R2 = 0.9995 Log Sb (GPa)Log Sb' (GPa) 10C 20C 0C Linear (0C) Linear (10C) Linear (20C) Figure 4.24 Log Sb ’ – Log Sb Relationship: PG 67-22, RTFOT aged @ 6.1% AC Log Sm -Lgo Sb: PG 67-22 after RTFOT @ 6.1% asphalt content Log Sb (GPa)Log Sm (GPa) Measured Mixture Stiffness @ 10C Sm-Sb(10C) Sm-Sb(20C) Measured Mixture Stiffness @ 20C Sm-Sb(0C) Measured Mxiture Stiffness @ 0C Figure 4.25 Log Sm – Log Sb Relationship: PG 67-22, RTFOT aged @ 6.1% AC

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57 Log Sb'Log Sb: PG 67-22 after RTFOT @ 7.2% asphalt content y = 0.9251x 1.401 R2 = 0.9918 y = 1.2794x 0.3783 R2 = 0.9997 y = 1.7181x + 2.0699 R2 = 0.9974 Log Sb (GPa)Log Sb' (GPa) 10C 20C 0C Linear (0C) Linear (10C) Linear (20C) Figure 4.26 Log Sb ’ – Log Sb Relationship: PG 67-22, RTFOT aged @ 7.2% AC Log Sm Log Sb: PG 67-22 after RTFOT @ 7.2% asphalt content Log Sb (GPa)Log Sm (GPa) Measured Mixture Stiffness @ 10C Sm-Sb(10C) Sm-Sb(20C) Measured Mixture Stiffness @ 20C Sm-Sb(0C) Measured Mxiture Stiffness @ 0C Figure 4.27 Log Sm – Log Sb Relationship: PG 67-22, RTFOT aged @ 7.2% AC

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58 Log Sb' Log Sb: PG 76-22 after RTFOT @ 6.1% asphalt content y = 0.8349x 1.9662 R2 = 0.992 y = 1.0188x 1.2311 R2 = 0.9966 y = 1.1339x 0.3935 R2 = 0.9982 Log Sb (GPa)Log Sb' (GPa) 10C 20C 0C Linear (0C) Linear (10C) Linear (20C) Figure 4.28 Log Sb ’ – Log Sb Relationship: PG 76-22, RTFOT aged @ 6.1% AC Log Sm LogSb: PG 76-22 after RTFOT @ 6.1% asphalt content Log Sb (GPa)Log Sm (GPa) Measured Mixture Stiffness @ 10C Sm-Sb(10C) Sm-Sb(20C) Measured Mixture Stiffness @ 20C Sm-Sb(0C) Measured Mixture Stiffness @ 0C Figure 4.29 Log Sm – Log Sb Relationship: PG 76-22, RTFOT aged @ 6.1% AC

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59 Log Sb'-Log Sb: PG 76-22 after RTFOT @ 7.2% asphalt content y = 0.8061x 1.4585 R2 = 0.9929 y = 1.0081x 0.8261 R2 = 0.9987 y = 1.067x 0.1763 R2 = 0.9991 Log Sb (GPa)Log Sb' (GPa) 10C 20C 0C Linear (0C) Linear (10C) Linear (20C) Figure 4.30 Log Sb ’ – Log Sb Relationship: PG 76-22, RTFOT aged @ 7.2% AC Log Sm Log Sb: PG 76-22 after RTFOT @ 7.2% asphalt content Log Sb (GPa)Log Sm (GPa) Measured Mixture Stiffness @ 10C Sm-Sb(10C) Sm-Sb(20C) Measured Mixture Stiffness @ 20C Sm-Sb(0C) Measured Mixture Stiffness @ 0C Figure 4.31 Log Sm – Log Sb Relationship: PG 76-22, RTFOT aged @ 7.2% AC

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60 Log Sm-Log Sb Prediction from 0C: PG 67-22 @ 6.1% asphalt content Log Sb (GPa)Log Sm ( GPa) Log Sm-Log Sb @ 10C (predicted) Log Sm-Log Sb @ 10C (measured) Log Sm-Log Sb @ 20C (predicted) Log Sm-Log Sb @ 20C (measured) Log Sm-Log Sb @ 0C (predicted) Log Sm-Log Sb @ 0C (measured) Figure 4.32 Stiffness Predic tion from PG 67-22,extracted binder, @ 6.1% AC @ 0 Log Sm-Log Sb Prediction from 10C: PG 67-22 @ 6.1% asphalt content Log Sb (GPa)Log Sm ( GPa) Log Sm-Log Sb @ 0C (predicted) Log Sm-Log Sb @ 0C (measured) Log Sm-Log Sb @ 10C (predicted) Log Sm-Log Sb @ 10C (measured) Log Sm-Log Sb @ 20C (predicted) Log Sm-Log Sb @ 20C (measured) Figure 4.33 Stiffness Predic tion from PG 67-22,extracted binder, @ 6.1% AC @ 10

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61 Log Sm-Log Sb Prediction from 20C: PG 67-22 @ 6.1% asphalt content Log Sb (GPa)Log Sm ( GPa) Figure 4.34 Stiffness Predic tion from PG 67-22,extracted binder, @ 6.1% AC @ 20 Log Sm Log Sb Prediction from 0C: PG 67-22 @ 7.2% asphalt content Log Sb (GPa)Log Sm ( GPa) Figure 4.35 Stiffness Predic tion from PG 67-22, extracte d binder, @ 7.2% AC @ 0

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62 Log Sm Log Sb Prediction from 10C: PG 67-22 @ 7.2% asphalt content Log Sb (GPa)Log Sm ( GPa) Log Sm-Log Sb @ 0C (predicted) Log Sm-Log Sb @ 0C (measured) Log Sm-Log Sb @ 10C (predicted) Log Sm-Log Sb @ 10C (measured) Log Sm-Log Sb @ 20C (predicted) Log Sm-Log Sb @ 20C (measured) Figure 4.36 Stiffness Predic tion from PG 67-22,extracted binder, @ 7.2% AC @ 10 Log Sm Log Sb Prediction from 20C: PG 67-22 @ 7.2% asphalt content Log Sb (GPa)Log Sm ( GPa) Log Sm-Log Sb @ 0C (predicted) Log Sm-Log Sb @ 0C (measured) Log Sm-Log Sb @ 10C (predicted) Log Sm-Log Sb @ 10C (measured) Log Sm-Log Sb @ 20C (predicted) Log Sm-Log Sb @ 20C (measured) Figure 4.37 Stiffness Predic tion from PG 67-22, extracte d binder, @ 7.2% AC @ 20

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63 Log Sm -Log Sb Prediction from 0C: PG 76-22 @ 6.1% asphalt content Log Sb (GPa)Log Sm ( GPa) Log Sb-Sm @ 10C (predicted) Log Sb-Sm @ 10C (measured) Log Sb-Sm @ 20C (predicted) Log Sb-Sm @ 20C (measured) Log Sm-Log Sb @ 0C (predicted) Log Sm-Log Sb @ 0C (measured) Figure 4.38 Stiffness Predic tion from PG 76-22, extracte d binder, @ 6.1% AC @ 0 Log Sm Log Sb Prediction from 10C: PG 76-22 @ 6.1% asphalt content Log Sb (GPa)Log Sm ( GPa) Log Sm-Log Sb @ 0C (predicted) Log Sm-Log Sb @ 0C (measured) Log Sm-Log Sb @ 10C (predicted) Log Sm-Log Sb @ 10C (measured) Log Sm-Log Sb @ 20C (predicted) Log Sm-Log Sb @ 20C (measured) Figure 4.39 Stiffness Predic tion from PG 76-22, extracte d binder, @ 6.1% AC @ 10

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64 Log Sm Log Sb Prediction from 20C: PG 76-22 @ 6.1% asphalt content Log Sb (GPa)Log Sm ( GPa) Figure 4.40 Stiffness Predic tion from PG 76-22, extracte d binder, @ 6.1% AC @ 20 Log Sm Log Sb Prediction from 0C: PG 76-22 @ 7.2% asphalt content Log Sb (GPa)Log Sm ( GPa) Log Sm-Log Sb @ 10C (predicted) Log Sm-Log Sb @ 10C (measured) Log Sm-Log Sb @ 20C (predicted) Log Sm-Log Sb @ 20C (measured) Log Sm-Log Sb @ 0C (predicted) Log Sm-Log Sb @ 0C (measured) Figure 4.41 Stiffness Predic tion from PG 76-22, extracte d binder, @ 7.2% AC @ 0

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65 Log Sm Log Sb Prediction from 10C: PG 76-22 @ 7.2% asphalt content Log Sb (GPa)Log Sm ( GPa) Log Sm-Log Sb @ 0C (predicted) Log Sm-Log Sb @ 0C (measured) Log Sm-Log Sb @ 10C (predicted) Log Sm-Log Sb @ 10C (measured) Log Sm-Log Sb @ 20C (predicted) Log Sm-Log Sb @ 20C (measured) Figure 4.42 Stiffness Predic tion from PG 76-22,extracted binder, @ 7.2% AC @ 10 Log Sm Log Sb Prediction from 20C: PG 76-22 @ 7.2% asphalt content Log Sb (GPa)Log Sm ( GPa) Log Sm-Log Sb @ 0C (predicted) Log Sm-Log Sb @ 0C (measured) Log Sm-Log Sb @ 10C (predicted) Log Sm-Log Sb @ 10C (measured) Log Sm-Log Sb @ 20C (predicted) Log Sm-Log Sb @ 20C (measured) Figure 4.43 Stiffness Predic tion from PG 76-22, extracte d binder, @ 7.2% AC @ 20

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66 Log Sm Log Sb Prediction from 0C: PG 67-22 after RTFOT @ 6.1% asphalt content Log Sb (GPa)Log Sm ( GPa) Log Sm-Log Sb @ 10C (predicted) Log Sm-Log Sb @ 10C (measured) Log Sm-Log Sb @ 20C (predicted) Log Sm-Log Sb @ 20C (measured) Log Sm-Log Sb @ 0C (predicted) Log Sm-Log Sb @ 0C (measured) Figure 4.44 Stiffness Pred iction from PG 67-22, RTFO T aged, @ 6.1% AC @ 0 Log Sm Log Sb Prediction from 10C: PG 67-22 after RTFOT @ 6.1% asphalt content Log Sb (GPa)Log Sm ( GPa) Log Sm-Log Sb @ 0C (predicted) Log Sm-Log Sb @ 0C (measured) Log Sm-Log Sb @ 10C (predicted) Log Sm-Log Sb @ 10C (measured) Log Sm-Log Sb @ 20C (predicted) Log Sm-Log Sb @ 20C (measured) Figure 4.45 Stiffness Pred iction from PG 67-22, RTFO T aged, @ 6.1% AC @ 10

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67 Log Sm Log Sb Prediction from 20C: PG 67-22 afte r RTFOT @ 6.1% asphalt content Log Sb (GPa)Log Sm ( GPa) Log Sm-Log Sb @ 0C (predicted) Log Sm-Log Sb @ 0C (measured) Log Sm-Log Sb @ 10C (predicted) Log Sm-Log Sb @ 10C (measured) Log Sm-Log Sb @ 20C (predicted) Log Sm-Log Sb @ 20C (measured) Figure 4.46 Stiffness Pred iction from PG 67-22, RTFO T aged, @ 6.1% AC @ 20 Log Sm Log Sb Prediction from 0C: PG 76-22 after RTFOT @ 6.1% asphalt content Log Sb (GPa)Log Sm ( GPa) Log Sm-Log Sb @ 10C (predicted) Log Sm-Log Sb @ 10C (measured) Log Sm-Log Sb @ 20C (predicted) Log Sm-Log Sb @ 20C (measured) Log Sm-Log Sb @ 0C (predicted) Log Sm-Log Sb @ 0C (measured) Figure 4.47 Stiffness Pred iction from PG 76-22, RTFO T aged, @ 6.1% AC @ 0

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68 Log Sm Log Sb Prediction from 10C: PG 76-22 afte r RTFOT @ 6.1% asphalt content Log Sb (GPa)Log Sm ( GPa) Log Sm-Log Sb @ 0C (predicted) Log Sm-Log Sb @ 0C (measured) Log Sm-Log Sb @ 10C (predicted) Log Sm-Log Sb @ 10C (measured) Log Sm-Log Sb @ 20C (predicted) Log Sm-Log Sb @ 20C ( measured) Figure 4.48 Stiffness Pred iction from PG 76-22, RTFO T aged, @ 6.1% AC @ 10 Log Sm Log Sb Prediction from 20C: PG 76-22 after RTFOT @ 6.1% asphalt content Log Sb (GPa)Log Sm ( GPa) Log Sm-Log Sb @ 0C (predicted) Log Sm-Log Sb @ 0C (measured) Log Sm-Log Sb @ 10C (predicted) Log Sm-Log Sb @ 10C (measured) Log Sm-Log Sb @ 20C (predicted) Log Sm-Log Sb @ 20C ( measured) Figure 4.49 Stiffness Pred iction from PG 76-22, RTFO T aged, @ 6.1% AC @ 20

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69 Log Sm Log Sb Prediction from 0C: PG 67-22 after RTFOT @ 7.2% asphalt content Log Sb (GPa)Log Sm ( GPa) Log Sm-Log Sb @ 10C (predicted) Log Sm-Log Sb @ 10C (measured) Log Sm-Log Sb @ 20C (predicted) Log Sm-Log Sb @ 20C (measured) Log Sm-LogSb @ 0C (predicted) Log Sm-Log Sb @ 0C (measured) Figure 4.50 Stiffness Pred iction from PG 67-22, RTFO T aged, @ 7.2% AC @ 0 Log Sm Log Sb Prediction from 10C: PG 67-22 after RTFOT @ 7.2% asphalt content Log Sb (GPa)Log Sm ( GPa) Log Sm-Log Sb @ 0C (predicted) Log Sm-Log Sb @ 0C (measured) Log Sm-Log Sb @ 10C (predicted) Log Sm-Log Sb @ 10C (measured) Log Sm-Log Sb @ 20C (predicted) Log Sm-Log Sb @ 20C (measured) Figure 4.51 Stiffness Pred iction from PG 67-22, RTFO T aged, @ 7.2% AC @ 10

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70 Log Sm Log Sb Prediction from 20C: PG 67-22 afte r RTFOT @ 7.2% asphalt content Log Sb (GPa)Log Sm ( GPa) Log Sm-Log Sb @ 0C (predicted) Log Sm-Log Sb @ 0C (measured) Log Sm-Log Sb @ 10C (predicted) Log Sm-Log Sb @ 10C (measured) Log Sm-Log Sb @ 20C (predicted) Log Sm-Log Sb @ 20C (measured) Figure 4.52 Stiffness Pred iction from PG 67-22, RTFO T aged, @ 7.2% AC @ 20 Log Sm -Log Sb Prediction from 0C: PG 76-22 after RTFOT @ 7.2% asphalt content Log Sb (GPa)Log Sm ( GPa) Log Sm-Log Sb @ 10C (predicted) Log Sm-Log Sb @ 10C (measured) Log Sm-Log Sb @ 20C (predicted) Log Sm-Log Sb @ 20C (measured) Log Sm-Log Sb @ 0C (predicted) Log Sm-Log Sb @ 0C (measured) Figure 4.53 Stiffness Pred iction from PG 76-22, RTFO T aged, @ 7.2% AC @ 0

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71 Log Sm Log Sb Prediction from 10C: PG 76-22 afte r RTFOT @ 7.2% asphalt content Log Sb (GPa)Log Sm ( GPa) Log Sm-Log Sb @ 0C (predicted) Log Sm-Log Sb @ 0C (measured) Log Sm-Log Sb @ 10C (predicted) Log Sm-Log Sb @ 10C (measured) Log Sm-Log Sb @ 20C (predicted) Log Sm-Log Sb @ 20C (measured) Figure 4.54 Stiffness Pred iction from PG 76-22, RTFO T aged, @ 7.2% AC @ 10 Log Sm Log Sb Prediction from 20C: PG 76-22 after RTFOT @ 7.2% asphalt content Log Sb (GPa)Log Sm ( GPa) Log Sm-Log Sb @ 0C (predicted) Log Sm-Log Sb @ 0C (measured) Log Sm-Log Sb @ 10C (predicted) Log Sm-Log Sb @ 10C (measured) Log Sm-Log Sb @ 20C (predicted) Log Sm-Log Sb @ 20C (measured) Figure 4.55 Stiffness Pred iction from PG 76-22, RTFO T aged, @ 7.2% AC @ 20

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72 4.5.2 Prediction of Mixture Stiffn ess for SBS Modified Mixture One of the goals of this research is to find if the properti es of the SBS modified mixtures could be predicted by using the bi nder-to-mixture stiffness relationship of unmodified mixture and the SB S modified binder properties. The stiffness prediction was made by taking the unmodified binder-to-mixt ure stiffness relationships and the SBS modified binder properties at the same temperature. The resulting prediction were plotted in Figure 4.5 through Figure 4.59. Theses figures showed that the s tiffness prediction by taki ng the unmodified binderto-mixture stiffness and SBS modified binder properties is not bad for the SBS modified mixtures, especially at low temperatures, th e predicted values are very close to the measure stiffness.

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73 Log Sm Log Sb Prediction from PG 67-22: PG 76-22 @ 6.1% asphalt content Log Sb (GPa)Log Sm ( GPa) Log Sm-LogSb @ 10C (predicted) Log Sm-LogSb @ 10C (measured) Log Sm-LogSb @ 20C (predicted) Log Sm-LogSb @ 20C (measured) Log Sm-LogSb @ 0c (predicted) Log Sm-LogSb @ 0C (measured) Figure 4.56 Stiffness Pred iction from PG 67-22, extr acted binder @ 6.1% AC Log Sm Log Sb Prediction from PG 67-22: PG 76-22 @ 7.2% asphalt content Log Sb (GPa)Log Sm ( GPa) Log Sm-Log Sb @ 10C (predicted) Log Sm-Log Sb @ 10C (measured) Log Sm-Log Sb @ 20C (predicted) Log Sm-Log Sb @ 20C (measured) Log Sm-Log Sb @ 0C (predicted) Log Sm-Log Sb @ 0C (measured) Figure 4.57 Stiffness Predic tion from PG 67-22, extrac ted binder @ 7.2% AC

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74 Log Sm Log Sb Prediction from PG 67-22: PG 76-22 after RTFOT @ 6.1% asphalt content Log Sb (GPa)Log Sm ( GPa) Log Sm-Log Sb @ 10C (predicted) Log Sm-Log Sb @ 10C (measured) Log Sm-Log Sb @ 20C (predicted) Log Sm-Log Sb @ 20C (measured) Log Sm-Log Sb @ 0C (predicted) Log Sm-Log Sb @ 0C (measured) Figure 4.58 Stiffness Pred iction from PG 67-22, RTFOT aged, @ 6.1% AC Log Sm Log Sb Prediction from PG 67-22: PG 76-22 after RTFOT @ 7.2% asphalt content Log Sb (GPa)Log Sm ( GPa) Log Sm-Log Sb @ 10C (predicted) Log Sm-Log Sb @ 10C (measured) Log Sm-Log Sb @ 20C (predicted) Log Sm-Log Sb @ 20C (measured) Log Sm-Log Sb @ 0C (predicted) Log Sm-Log Sb @ 0C (measured) Figure 4.59 Stiffness Pr ediction from PG 67-22, RTFOT aged, @ 7.2% AC

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75 4.5.3 Use Energy Ratio for Comparison As mentioned in Chapter 2, the En ergy Ratio was developed at the University of Florida as a method to compar e the cracking performances of different asphalt mixtures. This method was also used here to compar e the difference in predicted performance observed by using the different way to generate the mixt ure properties needed for evaluation. ER was defined as follows: the energy ratio of the dissipated creep strain energy of the mixture to th e minimum DCSE required fo r the mixture to perform satisfactorily. The resulting equation for Energy Ratio is: 1 98 2D m DCSE a ERf (2.36) where: 8 1 310 46 2 ) 36 6 ( 0299 0 tS a = tensile stress of asphalt layer, psi St= tensile strength, MPa DCSEf = Dissipated Creep Strain Energy, KJ/m3 D1= creep parameter, 1/psi m = creep parameter To facilitate the computation, a tensile stress, was assumed as 230 psi, St and DCSEf were the measured for different mixtures using the Superpave IDT. Different data interpretation methods were used to obtain D1 and m at each temperature. Each method is described in more detail in Table 4.25.

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76 Table 4.7Summary of Data Interpretation Methods Method Description 1 Mixture test data at one temperature combined with the binder shift factor to predict D1 and m at multiple temperatures. 2 Mixture test data at one temperature combined with the master curve and shift factor to predict Sm at multiple temperatures assuming m from mix test at one temperature 3 Unmodified binder-to-mixture stiffn ess relationship at one temperature combined with the modified binder properties at the same temperature to predict the modified mixture properties. Each method is described in more detail in the following paragraph. Method 1: 1. Lock-in D0 = 0.048 (1/GPa) 2. Determine D1 and m at 20 from regression 3. Fix m = m at 20 ( assuming m is a constant at three temperatures for the same mixture) 4. Calculate D1 at 0 and 10 using the following relationship: m Ta D D ) ( 1) 0 ( ) 20 ( 1 ) 0 ( 1 (4.4) m Ta D D ) ( 1) 10 ( ) 20 ( 1 ) 10 ( 1 (4.5) 5. Repeat Step 1-4 based on D1 and m obtained at 0 and 10, respectively. By following the procedures above, th e potential use of mixture tests at a single temperature to predict response and/or pe rformance at multiple temperatures was evaluated from the measured data. Method 2 1. Predict the mixture stiffness at 20 using the binder-to-mixture stiffness at 20

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77 2. Lock-in D0 = 0.048 (1/GPa) 3. Determine the D1 and m at 20 from regression 4. Use the binder-to-mixture st iffness relationship at 20 to predict the mixture stiffness at 0 and 10 for different times 5. Calculate D1 at 0 and 10 using the predicted mixture stiffness from step 4 and assuming: m = m at 20 D0 = 0.048 (1/GPa) 6. Repeat Step 15 starting 0 and 10, respectively. By the procedure above, the Energy Ratio was obtained from the predicted mixture data by using the binde r-to-mixture stiffness relationship. Method 3. 1. Develop the binder-to-mixture stiffness re lationship for the unmodified mixture at each of the three temperature 2. Predict the stiffness of m odified mixture using the unm odified binder-to-mixture stiffness relationship at the same temperature 3. Lock-in D0 = 0.048 (1/GPa) 4. Determine D1 and m for the modified mixture Following the three procedures above the resulting Energy Ra tio (ER) was used to evaluate how well the binder-to-mixture s tiffness relationship predicted the mixture properties. The comparisons were presented in Figure 4.24 Figure 4.29. The comparison indicates that the us ing the binder-to-stiffne ss relationship gave a good prediction for Energy Ratio at 0 and 10 in most cases, but the results at 20

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78 and the prediction from unmodi fied mixtures to SBS modifi ed mixtures are not as good as at 0 and 10

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79 Energy Ratio from Mixture Test @ 0C1.83 0.81 0.20 1.83 0.60 0.050.00 0.50 1.00 1.50 2.00 01020 Temp.(C)Energy Rati o Measured PG 67-22 @ 6.1% AC Figure 4.60 Energy Ratio Predictio n: PG 67-22, 6.1% AC @ 0 Energy Ratio from Mixture Test @ 10C1.83 0.81 0.20 2.38 0.81 0.070.00 0.50 1.00 1.50 2.00 2.50 01020 Temp.(C)Energy Rati o Measured PG 67-22 @ 6.1% AC Figure 4.61 Energy Ratio Predictio n: PG 67-22, 6.1% AC @ 10 Energy Ratio from Mixture Test @ 20C1.83 0.81 0.20 2.53 0.20 8.290.00 2.00 4.00 6.00 8.00 10.00 01020 Temp.(C)Energy Rati o Measured PG 67-22 @ 6.1% AC Figure 4.62 Energy Ratio Predictio n: PG 67-22, 6.1% AC @ 20

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80 Energy Ratio from Mixture Test @ 0C1.20 0.44 0.14 1.20 0.53 0.070.00 0.50 1.00 1.50 01020 Temp.(C)Energy Rati o Measured PG 67-22 @ 7.2% AC Figure 4.63 Energy Ratio Predictio n: PG 67-22, 7.2% AC @ 0 Energy Ratio from Mixture Test @ 10C1.20 0.44 0.14 1.56 0.44 0.040.00 0.50 1.00 1.50 2.00 01020 Temp.(C)Energy Rati o Measured PG 67-22 @ 7.2% AC Figure 4.64 Energy Ratio Predictio n: PG 67-22, 7.2% AC @ 10 Energy Ratio from Mixture Test @ 20C1.20 0.44 0.14 28.38 3.75 0.140.00 10.00 20.00 30.00 01020 Temp.(C)Energy Rati o Measured PG 67-22 @ 7.2% AC Figure 4.65 Energy Ratio Predictio n: PG 67-22, 7.2% AC @ 20

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81 Energy Ratio from Mixture Test @ 0C2.57 1.32 0.30 2.57 0.87 0.110.00 1.00 2.00 3.00 01020 Temp.(C)Energy Rati o Measured PG 76-22 @ 6.1% AC Figure 4.66 Energy Ratio Predictio n: PG 76-22, 6.1% AC @ 0 Energy Ratio from Mixture Test @ 10C2.57 1.32 0.30 4.32 1.32 0.150.00 1.00 2.00 3.00 4.00 5.00 01020 Temp.(C)Energy Rati o Measured PG 76-22 @ 6.1% AC Figure 4.67 Energy Ratio Predictio n: PG 76-22, 6.1% AC @ 10 Energy Ratio from Mixture Test @ 20C2.57 1.32 0.30 3.05 0.30 11.330.00 5.00 10.00 15.00 01020 Temp.(C)Energy Rati o Measured PG 76-22 @ 6.1% AC Figure 4.68 Energy Ratio Predictio n: PG 76-22, 6.1% AC @ 20

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82 Energy Ratio from Mixture Test @ 0C2.46 1.05 0.18 2.46 1.06 0.100.00 1.00 2.00 3.00 01020 Temp.(C)Energy Rati o Measured PG 76-22 @ 7.2% AC Figure 4.69 Energy Ratio Predictio n: PG 76-22, 7.2% AC @ 0 Energy Ratio from Mixture Test @ 10C2.46 1.05 0.18 2.92 1.05 0.080.00 1.00 2.00 3.00 4.00 01020 Temp.(C)Energy Rati o Measured PG 76-22 @ 7.2% AC Figure 4.70 Energy Ratio Predictio n: PG 76-22, 7.2% AC @ 10 Energy Ratio from Mixture Test @ 20C2.46 1.05 0.18 7.50 2.54 0.180.00 2.00 4.00 6.00 8.00 01020 Temp.(C)Energy Rati o Measured PG 76-22 @ 7.2% A C Figure 4.71 Energy Ratio Predictio n: PG 76-22, 7.2% AC @ 20

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83 Energy Ratio from Mixture Test @ 0C1.83 0.81 0.20 1.80 1.18 0.20 1.80 1.18 0.200.00 0.50 1.00 1.50 2.00 01020 Temp.(C)Energy Rat i Measured Extracted RTFOT Figure 4.72 Energy Ratio Prediction: PG 67-22, 6.1% asphalt content @ 0 Energy Ratio from Mixture Test @ 10C1.83 0.81 0.20 2.58 0.81 0.08 2.58 0.81 0.080.00 1.00 2.00 3.00 01020 Temp.(C)Energy Rat i Measured Extracted RTFOT Figure 4.73 Energy Ratio Prediction: PG 67-22, 6.1% asphalt content @ 10 Energy Ratio from Mixture Test @ 20C1.83 0.81 0.20 30.57 0.200.20 2.592.59 30.550.00 10.00 20.00 30.00 40.00 01020 Temp.(C)Energy Rat i Measured Extracted RTFOT Figure 4.74 Energy Ratio Prediction: PG 67-22, 6.1% asphalt content @ 20

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84 Energy Ratio from Mixture Test @ 0C1.20 0.44 0.14 1.18 0.64 0.10 1.18 0.64 0.100.00 0.50 1.00 1.50 01020 Temp.(C)Energy Rat i Measured Extracted RTFOT Figure 4.75 Energy Ratio Prediction: PG 67-22, 7.2% asphalt content @ 0 Energy Ratio from Mixture Test @ 10C1.20 0.44 0.14 1.61 0.44 0.04 1.61 0.44 0.040.00 0.50 1.00 1.50 2.00 01020 Temp.(C)Energy Rat i Measured Extracted RTFOT Figure 4.76 Energy Ratio Prediction: PG 67-22, 7.2% asphalt content @ 10 Energy Ratio from Mixture Test @ 20C1.20 0.44 0.14 3.85 0.14 3.85 0.14 -48.28 -48.28-60.00 -40.00 -20.00 0.00 20.00 01020 Temp.(C)Energy Rat i Measured Extracted RTFOT Figure 4.77 Energy Ratio Prediction: PG 67-22, 7.2% asphalt content @ 20

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85 Energy Ratio from Mixture Test @ 0C2.57 1.32 0.30 2.51 1.08 0.18 2.51 1.08 0.180.00 1.00 2.00 3.00 01020 Temp.(C)Energy Rat i Measured Extracted RTFOT Figure 4.78 Energy Ratio Prediction: PG 76-22, 6.1% asphalt content @ 0 Energy Ratio from Mixture Test @ 10C2.57 1.32 0.30 4.66 1.31 0.16 4.66 1.31 0.160.00 1.00 2.00 3.00 4.00 5.00 01020 Temp.(C)Energy Rat i Measured Extracted RTFOT Figure 4.79 Energy Ratio Prediction: PG 76-22, 6.1% asphalt content @ 10 Energy Ratio from Mixture Test @ 20C2.57 1.32 0.30 3.13 0.30 3.13 0.30 25.76 25.770.00 10.00 20.00 30.00 01020 Temp.(C)Energy Rat i Measured Extracted RTFOT Figure 4.80 Energy Ratio Prediction: PG 76-22, 6.1% asphalt content @ 20

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86 Energy Ratio from Mixture Test @ 0C2.46 1.05 0.18 2.42 1.25 0.14 2.42 1.25 0.140.00 1.00 2.00 3.00 01020 Temp.(C)Energy Rat i Measured Extracted RTFOT Figure 4.81 Energy Ratio Prediction: PG 76-22, 7.2% asphalt content @ 0 Energy Ratio from Mixture Test @ 10C2.46 1.05 0.18 3.03 1.05 0.08 1.05 0.09 3.030.00 1.00 2.00 3.00 4.00 01020 Temp.(C)Energy Rat i Measured Extracted RTFOT Figure 4.82 Energy Ratio Prediction: PG 76-22, 7.2% asphalt content @ 10 Energy Ratio from Mixture Test @ 20C2.46 1.05 0.18 10.68 2.58 0.18 2.58 0.18 10.690.00 5.00 10.00 15.00 01020 Temp.(C)Energy Rat i Measured Extracted RTFOT Figure 4.83 Energy Ratio Prediction: PG 76-22, 7.2% asphalt content @ 20

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87 Energy Ratio from Unmodified Mixtrue @ 6.1% asphalt content 2.57 0.98 0.30 1.32 3.20 0.23 0.13 0.63 2.47 0.00 1.00 2.00 3.00 4.00 01020 Temp.(C)Energy Rat i Mea. Extracted RTFOT Figure 4.84 Energy Ratio Predic tion from Unmodifi ed Mixture @ 6.1% asphalt content Energy Ratio from Unmodified Mixtrue @ 7.2% asphalt content 2.46 1.05 0.18 1.77 0.58 1.37 0.07 0.13 0.38 0.00 1.00 2.00 3.00 01020 Temp.(C)Energy Rat i Mea. Extracted RTFOT Figure 4.85 Energy Ratio Predic tion from Unmodifi ed Mixture @ 7.2% asphalt content

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88 CHAPTER 5 CLOSURE 5.1 Summary of Findings Both the unmodified and SBS modi fied binders were obt ained from the binder extraction process of the Short Term Oven Aged (STOA) mixture and from the Rolling Thin Film Oven Test aged virgin binde r. The Bending Beam Rheometer Test and Dynamic Shear Rheometer Test were conducted on both binders at -10, 10, 20 respectively. The binder test results were used to construct the binder creep compliance master curve. The binder-to-mi xture stiffness relationship wa s developed using the binder creep compliance master curve and the mixture IDT test results at 0, 10, 20. The binder-to-mixture stiffness relationship was th en used to predict th e mixture performance in different ways. The findings of this st udy can be generalized as follows: 1. There is one binder-to-mixture stiffness rela tionship at each of the three temperatures. There is no single binde r-to-mixture stiffness relationship for all temperatures in this study. Microdamage appears to develop at 0 and 10 and possibly at 20. 2. The shift factors are different for the binders than for the mixtures. 3. To accurately generate the mixture master cu rve, the shift factors and the mixture data must be obtained from mixture tests at multiple temperatures 4. m-value of the binder is a consta nt independent of temperature 5. The use of the relationship at the lowest temperature does not give a conservative results for the crack prediction us ing the HMA fracture mechanics. 6. The use of the binder-to-mixture stiffness re lationship of unmodifi ed binder to predict the performance of modified mixture does not give a accurate prediction.

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89 7. The development and use of one single bind er-to-mixture stiffne ss relationship for the mixtures with the same asphalt content ignoring the difference between different temperatures gives a good estima tion of the mixture stiffness. 8. The use of the binder-to-mixture stiffness relationship at 0 and 10to predict the mixture performance at 0 and 10 in most cases gives a accurate prediction. 5.2 Conclusion Based on the above findings of this resear ch the following conclusions were made about the development and use of the bi nder-to-mixture stiffness relationship. There is no single binder-to-mi xture stiffness relationship at all temperatures and the shift factors are different for the binders than for the mixtures. Accurate determination of the mixture creep compliance master curve require mixture data at multiple temperatures It seems that the prediction for the mixture performance at 0 and 10 is mostly accurate using the binder-to-mixtur e stiffness relationship at 0 and 10 5.3 Recommendation It seems that the microdamage is possible factor affecti ng the binder-to-mixture stiffness relationship. Thus, fo r further studies it is recommended that the effect of the microdamage need to be characterized in the development of the binder-to-mixture stiffness relationship.

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APPENDIX A BENDING BEAM RHEOMETER TEST RESULTS

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91 Table A1 Bending Beam Rheometer Test Re sults: PG 67-22, 6.1% asphalt content Time (sec.) Replicate Measured Stiffness (MPa) Average m-value Average 1 119 0.395 2 126 0.392 8 3 121 122 0.381 0.389 1 91.7 0.423 2 97.8 0.417 15 3 94.3 94.60 0.409 0.416 1 67.8 0.454 2 72.6 0.445 30 3 70.3 70.23 0.439 0.446 1 49.0 0.484 2 52.8 0.472 60 3 51.4 51.07 0.469 0.475 1 34.7 0.515 2 37.8 0.500 120 3 36.8 36.43 0.500 0.505 1 24.0 0.546 2 26.4 0.528 240 3 25.7 25.37 0.535 0.535

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92 Table A2 Bending Beam Rheometer Test Re sults: PG 76-22, 6.1% asphalt content Time (sec.) Replicate Measured Stiffness (MPa) Average m-value Average 1 106 0.379 2 111 0.388 8 3 111 109.33 0.387 0.385 1 82.7 0.401 2 86.0 0.414 15 3 86.1 84.93 0.410 0.408 1 62.0 0.425 2 63.9 0.442 30 3 64.3 63.40 0.436 0.434 1 45.9 0.450 2 46.7 0.470 60 3 47.1 46.57 0.461 0.460 1 33.3 0.474 2 33.4 0.499 120 3 33.9 33.53 0.487 0.487 1 23.8 0.498 2 23.4 0.527 240 3 24.0 23.73 0.513 0.513

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93 Table A3 Bending Beam Rheometer Test Re sults: PG 67-22, 7.2% asphalt content Time (sec.) Replicate Measured Stiffness (MPa) Average m-value Average 1 114 0.403 2 112 0.398 8 3 114 113.33 0.394 0.398 1 87.4 0.428 2 86.7 0.423 15 3 88.2 87.43 0.419 0.423 1 64.3 0.455 2 64.0 0.451 30 3 65.3 64.57 0.447 0.451 1 46.6 0.483 2 46.4 0.479 60 3 47.5 46.83 0.475 0.479 1 33.1 0.510 2 33.0 0.507 120 3 33.9 33.33 0.503 0.507 1 22.9 0.538 2 23.0 0.535 240 3 23.6 23.17 0.531 0.535

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94 Table A4 Bending Beam Rheometer Test Re sults: PG 76-22, 7.2% asphalt content Time (sec.) Replicate Measured Stiffness (MPa) Average m-value Average 1 94.5 0.396 2 95.5 0.395 8 3 97.4 95.80 0.394 0.395 1 72.9 0.423 2 73.8 0.421 15 3 75.3 74.00 0.418 0.421 1 53.8 0.453 2 54.6 0.449 30 3 55.9 54.77 0.443 0.448 1 39.0 0.483 2 39.6 0.478 60 3 40.8 39.80 0.469 0.477 1 27.6 0.513 2 28.2 0.507 120 3 29.2 28.33 0.495 0.505 1 19.1 0.543 2 19.6 0.536 240 3 20.5 19.73 0.521 0.533

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95 Table A5 Bending Beam Rheometer Test Results: PG 67-22, RTFOT aged Time (sec.) Replicate Measured Stiffness (MPa) Average m-value Average 1 117 0.392 2 124 0.389 8 3 130 123.67 0.391 0.391 1 90.5 0.421 2 95.9 0.416 15 3 100.0 95.47 0.418 0.418 1 66.8 0.453 2 71.2 0.446 30 3 74.7 70.90 0.447 0.449 1 48.3 0.485 2 51.7 0.476 60 3 54.2 51.40 0.476 0.479 1 34.2 0.517 2 36.8 0.506 120 3 38.6 36.53 0.505 0.509 1 23.6 0.548 2 25.6 0.536 240 3 26.9 25.37 0.535 0.540

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96 Table A6 Bending Beam Rheometer Test Results: PG 76-22, RTFOT aged Time (sec.) Replicate Measured Stiffness (MPa) Average m-value Average 1 92.9 0.400 2 93.6 0.409 80 3 89.5 92.0 0.398 0.402 1 71.3 0.430 2 71.8 0.435 15 3 69.0 70.70 0.426 0.430 1 52.4 0.463 2 52.6 0.463 30 3 50.8 51.93 0.457 0.461 1 37.7 0.496 2 37.8 0.491 60 3 36.7 37.40 0.488 0.492 1 26.4 0.528 2 26.6 0.519 120 3 25.9 26.30 0.519 0.522 1 18.1 0.561 2 18.4 0.547 240 3 17.8 18.10 0.550 0.553

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APPENDIX B DYNAMIC SHEAR RHEOMETER TEST RESULTS

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98Table B1 Dynamic Shear Rheometer Test Results at 10: PG 67-22, 6.1% asphalt content G* Result Result Samples Samples Freq.(Hz) Sample 1 Smaple 2 Sample 3 Average Sample 1 Smaple 2 Sample 3 Average 0.5 8.07E+06 8.24E+06 7.86E+06 8.06E+06 47.10 47.63 47.44 47.39 1 1.14E+07 1.17E+07 1.11E+07 1.14E+07 45.09 45.51 45.45 45.35 2 1.60E+07 1.65E+07 1.56E+07 1.60E+07 42.88 42.98 42.76 42.87 4 2.21E+07 2.27E+07 2.15E+07 2.21E+07 40.87 40.73 40.90 40.83 8 2.99E+07 3.10E+07 2.93E+07 3.00E+07 38.61 38.55 38.80 38.65 15 3.90E+07 4.03E+07 3.80E+07 3.91E+07 36.72 36.86 36.89 36.82 Table B2 Dynamic Shear Rheometer Test Results at 10: PG 76-22, 6.1% asphalt content G* Result Result Samples Samples Freq.(Hz) Sample 1 Smaple 2 Sample 3 Average Sample 1 Smaple 2 Sample 3 Average 0.5 1.10E+07 1.01E+07 9.39E+06 1.02E+07 45.73 45.54 45.28 45.52 1 1.55E+07 1.42E+07 1.33E+07 1.44E+07 44.23 43.88 43.50 43.87 2 2.17E+07 1.97E+07 1.84E+07 1.99E+07 41.44 41.45 41.83 41.57 4 2.94E+07 2.68E+07 2.50E+07 2.71E+07 39.23 39.32 39.42 39.32 8 3.94E+07 3.58E+07 3.36E+07 3.63E+07 37.32 37.44 37.34 37.37 15 5.08E+07 4.62E+07 4.33E+07 4.68E+07 35.37 35.35 35.46 35.39

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99Table B3 Dynamic Shear Rheometer Test Results at 10: PG 67-22, 7.2% asphalt content G* Result Result Samples Samples Freq.(Hz) Sample 1 Smaple 2 Sample 3 Average Sample 1 Smaple 2 Sample 3 Average 0.5 8.46E+06 7.67E+06 7.37E+06 7.84E+06 47.59 47.80 47.67 47.69 1 1.18E+07 1.09E+07 1.06E+07 1.11E+07 45.35 46.39 45.83 45.85 2 1.67E+07 1.54E+07 1.49E+07 1.56E+07 43.44 44.07 43.77 43.76 4 2.31E+07 2.14E+07 2.06E+07 2.17E+07 41.21 41.86 41.57 41.55 8 3.12E+07 2.92E+07 2.80E+07 2.95E+07 38.93 39.47 39.29 39.23 15 4.06E+07 3.80E+07 3.66E+07 3.84E+07 36.93 37.52 37.49 37.31 Table B4 Dynamic Shear Rheometer Test Results at 10: PG 76-22, 7.2% asphalt content G* Result Result Samples Samples Freq.(Hz) Sample 1 Smaple 2 Sample 3 Average Sample 1 Smaple 2 Sample 3 Average 0.5 8.00E+06 8.01E+06 7.62E+06 7.88E+06 47.01 46.14 45.93 46.36 1 1.13E+07 1.13E+07 1.08E+07 1.12E+07 44.66 44.72 44.79 44.72 2 1.58E+07 1.59E+07 1.51E+07 1.56E+07 42.92 42.60 42.17 42.56 4 2.18E+07 2.18E+07 2.07E+07 2.14E+07 40.50 40.40 40.53 40.48 8 2.95E+07 2.95E+07 2.81E+07 2.90E+07 38.56 38.49 38.56 38.54 15 3.83E+07 3.83E+07 3.64E+07 3.77E+07 36.71 36.82 36.77 36.77

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100Table B5 Dynamic Shear Rheometer Test Results at 10: PG 67-22, RTFOT aged G* Result Result Samples Samples Freq.(Hz) Sample 1 Smaple 2 Sample 3 Average Sample 1 Smaple 2 Sample 3 Average 0.5 9.69E+06 1.15E+07 9.41E+06 1.02E+07 46.30 46.23 46.65 46.39 1 1.39E+07 1.65E+07 1.36E+07 1.47E+07 44.44 45.88 45.88 45.40 2 1.96E+07 2.26E+07 1.89E+07 2.03E+07 42.64 42.25 42.57 42.49 4 2.70E+07 3.12E+07 2.60E+07 2.80E+07 40.08 40.06 39.75 39.96 8 3.62E+07 4.18E+07 3.51E+07 3.77E+07 37.77 37.61 37.77 37.71 15 4.67E+07 5.40E+07 4.51E+07 4.86E+07 35.90 35.49 35.69 35.69 Table B6 Dynamic Shear Rheometer Test Results at 10: PG 76-22, RTFOT aged G* Result Result Samples Samples Freq.(Hz) Sample 1 Smaple 2 Sample 3 Average Sample 1 Smaple 2 Sample 3 Average 0.5 8.28E+06 7.31E+06 7.75E+06 7.78E+06 46.66 46.24 47.28 46.72 1 1.15E+07 1.04E+07 1.11E+07 1.10E+07 44.91 44.75 44.52 44.73 2 1.62E+07 1.45E+07 1.54E+07 1.53E+07 42.56 42.47 42.25 42.43 4 2.22E+07 2.00E+07 2.12E+07 2.11E+07 40.40 40.60 40.28 40.43 8 3.02E+07 2.69E+07 2.86E+07 2.86E+07 38.26 38.41 38.20 38.29 15 3.90E+07 3.50E+07 3.72E+07 3.70E+07 36.59 36.48 36.42 36.49

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101Table B7 Dynamic Shear Rheometer Test Results at 20: PG 67-22, 6.1% asphalt content G* Result Result Samples Samples Freq.(Hz) Sample 1 Smaple 2 Sample 3 Average Sample 1 Smaple 2 Sample 3 Average 0.5 1.33E+06 1.45E+06 1.41E+06 1.39E+06 57.69 57.24 57.38 57.44 1 2.02E+06 2.24E+06 2.15E+06 2.14E+06 56.22 55.91 56.01 56.05 2 3.09E+06 3.41E+06 3.29E+06 3.26E+06 54.44 54.22 54.33 54.33 4 4.66E+06 5.13E+06 4.92E+06 4.90E+06 52.59 52.51 52.39 52.50 8 6.89E+06 7.59E+06 7.28E+06 7.25E+06 50.61 50.48 50.53 50.54 15 9.75E+06 1.07E+07 1.03E+07 1.02E+07 48.55 48.58 48.43 48.52 Table B8 Dynamic Shear Rheometer Test Results at 20: PG 76-22, 6.1% asphalt content G* Result Result Samples Samples Freq.(Hz) Sample 1 Smaple 2 Sample 3 Average Sample 1 Smaple 2 Sample 3 Average 0.5 1.73E+06 1.76E+06 1.79E+06 1.76E+06 54.16 53.92 54.03 54.03 1 2.57E+06 2.62E+06 2.71E+06 2.63E+06 53.29 53.16 53.18 53.21 2 3.84E+06 3.91E+06 4.06E+06 3.94E+06 51.75 51.63 51.65 51.68 4 5.64E+06 5.75E+06 5.97E+06 5.79E+06 50.14 50.04 50.12 50.10 8 8.24E+06 8.35E+06 8.67E+06 8.42E+06 48.38 48.11 48.30 48.26 15 1.14E+07 1.16E+07 1.20E+07 1.17E+07 46.47 46.22 46.61 46.43

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102Table B9 Dynamic Shear Rheometer Test Results at 20: PG 67-22, 7.2% asphalt content G* Result Result Samples Samples Freq.(Hz) Sample 1 Smaple 2 Sample 3 Average Sample 1 Smaple 2 Sample 3 Average 0.5 1.27E+06 1.27E+06 1.27E+06 1.27E+06 57.64 58.00 57.43 57.69 1 1.98E+06 1.95E+06 1.96E+06 1.96E+06 56.61 56.39 56.58 56.53 2 3.02E+06 2.99E+06 3.00E+06 3.00E+06 54.73 54.90 54.60 54.74 4 4.57E+06 4.49E+06 4.53E+06 4.53E+06 52.76 53.08 52.88 52.91 8 6.79E+06 6.66E+06 6.71E+06 6.72E+06 51.00 51.07 50.97 51.02 15 9.61E+06 9.42E+06 9.48E+06 9.50E+06 48.99 49.12 48.95 49.02 Table B10 Dynamic Shear Rheometer Test Results at 20: PG 76-22, 7.2% asphalt content G* Result Result Samples Samples Freq.(Hz) Sample 1 Smaple 2 Sample 3 Average Sample 1 Smaple 2 Sample 3 Average 0.5 1.55E+06 1.54E+06 1.60E+06 1.57E+06 53.17 53.51 53.55 53.41 1 2.32E+06 2.33E+06 2.41E+06 2.35E+06 52.38 53.04 52.76 52.73 2 3.45E+06 3.49E+06 3.59E+06 3.51E+06 51.00 51.64 51.50 51.38 4 5.06E+06 5.14E+06 5.27E+06 5.16E+06 49.65 50.35 50.25 50.08 8 7.36E+06 7.49E+06 7.67E+06 7.50E+06 48.09 48.75 48.57 48.47 15 1.02E+07 1.04E+07 1.07E+07 1.04E+07 46.33 47.04 46.93 46.77

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103Table B11 Dynamic Shear Rheometer Test Results at 20: PG 67-22, RTFOT aged G* Result Result Samples Samples Freq.(Hz) Sample 1 Smaple 2 Sample 3 Average Sample 1 Smaple 2 Sample 3 Average 0.5 1.56E+06 1.58E+06 1.67E+06 1.60E+06 56.54 56.86 56.68 56.69 1 2.39E+06 2.40E+06 2.54E+06 2.44E+06 55.25 55.60 55.21 55.35 2 3.62E+06 3.65E+06 3.86E+06 3.71E+06 53.52 53.61 53.50 53.54 4 5.42E+06 5.46E+06 5.73E+06 5.54E+06 51.54 51.84 51.65 51.68 8 7.95E+06 8.06E+06 8.45E+06 8.15E+06 49.55 49.58 49.56 49.56 15 1.11E+07 1.13E+07 1.18E+07 1.14E+07 47.48 47.52 47.48 47.49 Table B12 Dynamic Shear Rheometer Test Results at 20: PG 76-22, RTFOT aged G* Result Result Samples Samples Freq.(Hz) Sample 1 Smaple 2 Sample 3 Average Sample 1 Smaple 2 Sample 3 Average 0.5 1.41E+06 1.39E+06 1.45E+06 1.42E+06 54.14 54.06 54.27 54.16 1 2.12E+06 2.12E+06 2.18E+06 2.14E+06 53.47 53.45 53.59 53.51 2 3.18E+06 3.18E+06 3.28E+06 3.22E+06 52.14 51.97 52.10 52.07 4 4.70E+06 4.72E+06 4.86E+06 4.76E+06 50.79 50.76 50.63 50.73 8 6.89E+06 6.91E+06 7.10E+06 6.97E+06 49.18 49.11 49.09 49.13 15 9.65E+06 9.66E+06 9.91E+06 9.74E+06 47.33 47.51 47.29 47.37

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APPENDIX C BINDER CREEP COMPLIANCE MASTER CURVE DATA

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105 The following equations are used to calculate the shift factor, aT, reduced time, ) ( 175 0 logref TT T a (4.3) where: aT = shift factor T = Temperature the data shift from Tref = Temperature the data shift to Tta t (2.29) where: = Reduced time t = Real time aT = Temperature shift factor In this study, the Bending Beam Rheometer Test results at -10 was shifted to 20 and combine with the Dynamic Shear Rheometer Test results to develop the binder creep compliance master curve. The Dynamic Shear Test results at 10 were also presented. The power model parameters, D1 and m were obtained by locking-in D0 and running the regression.

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106 Table C1: Binder Master Curve Data: PG 6722, extracted binder, 6.1% asphalt content t (sec.) Log (t) Log D(t)(1/Pa) Log D(t) 8 0.90 4.499E-05-4.347 8.20E-09 -8.09 15 1.18 8.435E-05-4.074 1.06E-08 -7.97 30 1.48 1.687E-04-3.773 1.42E-08 -7.85 60 1.78 3.374E-04-3.472 1.96E-08 -7.71 120 2.08 6.748E-04-3.171 2.74E-08 -7.56 BBR @ -10C 240 2.38 1.350E-03-2.870 3.94E-08 -7.40 0.067 -1.17 1.191E-03-2.924 6.29E-08 -7.20 0.125 -0.90 2.223E-03-2.653 8.29E-08 -7.08 0.25 -0.60 4.446E-03-2.352 1.13E-07 -6.95 0.5 -0.30 8.891E-03-2.051 1.56E-07 -6.81 1 0.00 1.778E-02-1.750 2.15E-07 -6.67 DSR @ 10 2 0.30 3.557E-02-1.449 2.97E-07 -6.53 0.067 -1.17 6.700E-02-1.174 2.93E-07 -6.53 0.125 -0.90 1.250E-01-0.903 4.17E-07 -6.38 0.25 -0.60 2.500E-01-0.602 6.22E-07 -6.21 0.5 -0.30 5.000E-01-0.301 9.32E-07 -6.03 1 0.00 1.000E+000.000 1.40E-06 -5.85 DSR @ 20 2 0.30 2.000E+000.301 2.11E-06 -5.68 D(t) = 4.834 X 10-9 + t0.476 X 2.101 X 10-7 (10) D(t) = 1.65 X 10-8 + t0.596 X 1.384 X 10-6 (20 Table C2: Power Model Parameter: PG 67-22, extracted binder, 6.1% asphalt content Log D(t) D0' D'() Log D'() -4.347 8.200E-093.33E-10 7.867E-8.104 -4.074 1.060E-083.33E-10 1.027E-7.989 -3.773 1.420E-083.33E-10 1.387E-7.858 -3.472 1.960E-083.33E-10 1.927E-7.715 -3.171 2.740E-083.33E-10 2.707E-7.568 BBR @ -10C -2.870 3.940E-083.33E-10 3.907E-7.408 -1.174 2.929E-073.33E-10 2.925E-6.534 -0.903 4.173E-073.33E-10 4.169E-6.380 -0.602 6.223E-073.33E-10 6.219E-6.206 -0.301 9.321E-073.33E-10 9.318E-6.031 0.000 1.401E-063.33E-10 1.400E-5.854 DSR @ 20 0.301 2.108E-063.33E-10 2.108E-5.676 Log D1=-5.879212 m=0.524 D1=1.321E-06

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107 Table C3: Binder Master Curve Data: PG 6722, extracted binder, 7.2% asphalt content t (sec.) Log (t) Log D(t)(1/Pa) Log D(t) 8 0.904.499E-05-4.3478.82E-09 -8.05 15 1.188.435E-05-4.0741.14E-08 -7.94 30 1.481.687E-04-3.7731.55E-08 -7.81 60 1.783.374E-04-3.4722.14E-08 -7.67 120 2.086.748E-04-3.1713.00E-08 -7.52 BBR @ -10C 240 2.381.350E-03-2.8704.32E-08 -7.36 0.067 -1.171.191E-03-2.9246.43E-08 -7.19 0.125 -0.902.223E-03-2.6538.54E-08 -7.07 0.25 -0.604.446E-03-2.3521.18E-07 -6.93 0.5 -0.308.891E-03-2.0511.63E-07 -6.79 1 0.001.778E-02-1.7502.27E-07 -6.64 DSR @ 10 2 0.303.557E-02-1.4493.16E-07 -6.50 0.067 -1.176.700E-02-1.1743.20E-07 -6.49 0.125 -0.901.250E-01-0.9034.59E-07 -6.34 0.25 -0.602.500E-01-0.6026.88E-07 -6.16 0.5 -0.305.000E-01-0.3011.04E-06 -5.98 1 0.001.000E+000.0001.57E-06 -5.80 DSR @ 20 2 0.302.000E+000.3012.38E-06 -5.62 D(t) = 5.55 X 10-9 + t0.490 X 2.211 X 10-7 (10) D(t) = 1.854 X 10-8 + t0.606 X 1.552 X 10-6 (20) Table C4: Power Model Parameter: PG 67-22, extracted binder, 7.2% asphalt content Log D(t)D0' D' ( ) Lo g D' ( ) -4.347 8.820E-093.33E-108.487E-09 -8.071 -4.074 1.140E-083.33E-101.107E-08 -7.956 -3.773 1.550E-083.33E-101.517E-08 -7.819 -3.472 2.140E-083.33E-102.107E-08 -7.676 -3.171 3.000E-083.33E-102.967E-08 -7.528 BBR @ -10C -2.870 4.320E-083.33E-104.287E-08 -7.368 -1.174 3.202E-073.33E-103.198E-07 -6.495 -0.903 4.587E-073.33E-104.584E-07 -6.339 -0.602 6.885E-073.33E-106.882E-07 -6.162 -0.301 1.038E-063.33E-101.038E-06 -5.984 0.000 1.571E-063.33E-101.570E-06 -5.804 DSR @ 20 0.301 2.381E-063.33E-102.380E-06 -5.623 Log -5.831571m=0.527 D1= 1.474E-06

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108 Table C5: Binder Master Curve Data: PG 7622, extracted binder, 6.1% asphalt content t (sec.) Log (t) Log D(t)(1/Pa) Log D(t) 8 0.90 4.499E-05-4.347 9.17E-09 -8.04 15 1.18 8.435E-05-4.074 1.18E-08 -7.93 30 1.48 1.687E-04-3.773 1.58E-08 -7.80 60 1.78 3.374E-04-3.472 2.15E-08 -7.67 120 2.08 6.748E-04-3.171 2.98E-08 -7.53 BBR @ -10C 240 2.38 1.350E-03-2.870 4.21E-08 -7.38 0.067 -1.17 1.191E-03-2.924 5.18E-08 -7.29 0.125 -0.90 2.223E-03-2.653 6.83E-08 -7.17 0.25 -0.60 4.446E-03-2.352 9.38E-08 -7.03 0.5 -0.30 8.891E-03-2.051 1.30E-07 -6.89 1 0.00 1.778E-02-1.750 1.80E-07 -6.74 DSR @ 10 2 0.30 3.557E-02-1.449 2.52E-07 -6.60 0.067 -1.17 6.700E-02-1.174 2.51E-07 -6.60 0.125 -0.90 1.250E-01-0.903 3.54E-07 -6.45 0.25 -0.60 2.500E-01-0.602 5.22E-07 -6.28 0.5 -0.30 5.000E-01-0.301 7.73E-07 -6.11 1 0.00 1.000E+000.000 1.15E-06 -5.94 DSR @ 20 2 0.30 2.000E+000.301 1.71E-06 -5.77 D(t) = 5.899 X 10-9 + t0.494 X 1.744 X 10-7(10) D(t) = 1.513 X 10-8 + t0.581 X 1.134 X 10-6(20) Table C6: Power Model Parameter: PG 76-22, extracted binder, 6.1% asphalt content Log D(t)D0' D' ( ) Lo g D' ( ) -4.347 9.170E-093.33E-108.837E-09 -8.054 -4.074 1.180E-083.33E-101.147E-08 -7.941 -3.773 1.580E-083.33E-101.547E-08 -7.811 -3.472 2.150E-083.33E-102.117E-08 -7.674 -3.171 2.980E-083.33E-102.947E-08 -7.531 BBR @ -10C -2.870 4.210E-083.33E-104.177E-08 -7.379 -1.174 2.509E-073.33E-102.506E-07 -6.601 -0.903 3.539E-073.33E-103.536E-07 -6.452 -0.602 5.219E-073.33E-105.216E-07 -6.283 -0.301 7.732E-073.33E-107.729E-07 -6.112 0.000 1.149E-063.33E-101.149E-06 -5.940 DSR @ 20 0.301 1.711E-063.33E-101.711E-06 -5.767 Log D1= -5.970712m=0.488 D1= 1.070E-06

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109 Table C7: Binder Master Curve Data: PG 7622, extracted binder, 7.2% asphalt content t (sec.) Log (t) Log D(t)(1/Pa) Log D(t) 8 0.90 4.499E-05-4.347 1.04E-08 -7.98 15 1.18 8.435E-05-4.074 1.35E-08 -7.87 30 1.48 1.687E-04-3.773 1.83E-08 -7.74 60 1.78 3.374E-04-3.472 2.51E-08 -7.60 120 2.08 6.748E-04-3.171 3.53E-08 -7.45 BBR @ -10C 240 2.38 1.350E-03-2.870 5.07E-08 -7.29 0.067 -1.17 1.191E-03-2.924 6.58E-08 -7.18 0.125 -0.90 2.223E-03-2.653 8.73E-08 -7.06 0.25 -0.60 4.446E-03-2.352 1.21E-07 -6.92 0.5 -0.30 8.891E-03-2.051 1.68E-07 -6.78 1 0.00 1.778E-02-1.750 2.34E-07 -6.63 DSR @ 10 2 0.30 3.557E-02-1.449 3.28E-07 -6.48 0.067 -1.17 6.700E-02-1.174 2.86E-07 -6.54 0.125 -0.90 1.250E-01-0.903 4.05E-07 -6.39 0.25 -0.60 2.500E-01-0.602 6.00E-07 -6.22 0.5 -0.30 5.000E-01-0.301 8.93E-07 -6.05 1 0.00 1.000E+000.000 1.33E-06 -5.88 DSR @ 20 2 0.30 2.000E+000.301 1.99E-06 -5.70 D(t) = 6.575 X 10-9 + t0.498 X 2.275 X 10-7(10) D(t) = 1.702 X 10-8 + t0.587 X 1.316 X 10-6(20) Table C8: Power Model Parameter: PG 76-22, extracted binder, 7.2% asphalt content Log D(t)D0' D' ( ) Lo g D' ( ) -4.347 1.040E-083.33E-101.007E-08 -7.997 -4.074 1.350E-083.33E-101.317E-08 -7.881 -3.773 1.830E-083.33E-101.797E-08 -7.746 -3.472 2.510E-083.33E-102.477E-08 -7.606 -3.171 3.530E-083.33E-103.497E-08 -7.456 BBR @ -10C -2.870 5.070E-083.33E-105.037E-08 -7.298 -1.174 2.863E-073.33E-102.859E-07 -6.544 -0.903 4.053E-073.33E-104.050E-07 -6.393 -0.602 6.003E-073.33E-105.999E-07 -6.222 -0.301 8.931E-073.33E-108.928E-07 -6.049 0.000 1.333E-063.33E-101.333E-06 -5.875 DSR @ 20 0.301 1.994E-063.33E-101.993E-06 -5.700 Log D1= -5.907328m=0.487 D1= 1.238E-06

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110 Table C9: Binder Master Curve Data: PG 67-22, RTFOT aged,, t (sec.) Log (t) Log D(t)(1/Pa) Log D(t) 8 0.90 4.499E-05-4.347 8.09E-09 -8.09 15 1.18 8.435E-05-4.074 1.05E-08 -7.98 30 1.48 1.687E-04-3.773 1.41E-08 -7.85 60 1.78 3.374E-04-3.472 1.95E-08 -7.71 120 2.08 6.748E-04-3.171 2.74E-08 -7.56 BBR @ -10C 240 2.38 1.350E-03-2.870 3.94E-08 -7.40 0.067 -1.17 1.191E-03-2.924 5.24E-08 -7.28 0.125 -0.90 2.223E-03-2.653 7.03E-08 -7.15 0.25 -0.60 4.446E-03-2.352 9.87E-08 -7.01 0.5 -0.30 8.891E-03-2.051 1.40E-07 -6.85 1 0.00 1.778E-02-1.750 2.00E-07 -6.70 DSR @ 10 2 0.30 3.557E-02-1.449 2.87E-07 -6.54 0.067 -1.17 6.700E-02-1.174 2.59E-07 -6.59 0.125 -0.90 1.250E-01-0.903 3.67E-07 -6.43 0.25 -0.60 2.500E-01-0.602 5.45E-07 -6.26 0.5 -0.30 5.000E-01-0.301 8.12E-07 -6.09 1 0.00 1.000E+000.000 1.21E-06 -5.92 DSR @ 20 2 0.30 2.000E+000.301 1.82E-06 -5.74 D(t) = 7.419 X 10-9 + t0.538 X 1.879 X 10-7(10) D(t) = 1.532 X 10-8 + t0.589 X 1.198 X 10-6(20) Table C10: Power Model Parame ter: PG 67-22, RTFOT aged, Log D(t)D0' D' ( ) Lo g D' ( ) -4.347 8.090E-093.33E-107.757E--8.110 -4.074 1.050E-083.33E-101.017E--7.993 -3.773 1.410E-083.33E-101.377E--7.861 -3.472 1.950E-083.33E-101.917E--7.717 -3.171 2.740E-083.33E-102.707E--7.568 BBR @ -10C -2.870 3.940E-083.33E-103.907E--7.408 -1.174 2.591E-073.33E-102.588E--6.587 -0.903 3.673E-073.33E-103.670E--6.435 -0.602 5.448E-073.33E-105.445E--6.264 -0.301 8.118E-073.33E-108.114E--6.091 0.000 1.213E-063.33E-101.213E--5.916 DSR @ 20 0.301 1.817E-063.33E-101.817E--5.741 Log D1= -5.943006m=0.507 D1= 1.140E-06

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111 Table C11: Binder Master Curve Data: PG 76-22, RTFOT aged,, t (sec.) Log (t) Log D(t)(1/Pa) Log D(t) 8 0.90 4.499E-05-4.347 1.09E-08 -7.96 15 1.18 8.435E-05-4.074 1.41E-08 -7.85 30 1.48 1.687E-04-3.773 1.93E-08 -7.71 60 1.78 3.374E-04-3.472 2.67E-08 -7.57 120 2.08 6.748E-04-3.171 3.80E-08 -7.42 BBR @ -10C 240 2.38 1.350E-03-2.870 5.52E-08 -7.26 0.067 -1.17 1.191E-03-2.924 6.60E-08 -7.18 0.125 -0.90 2.223E-03-2.653 8.70E-08 -7.06 0.25 -0.60 4.446E-03-2.352 1.19E-07 -6.92 0.5 -0.30 8.891E-03-2.051 1.64E-07 -6.79 1 0.00 1.778E-02-1.750 2.26E-07 -6.65 DSR @ 10 2 0.30 3.557E-02-1.449 3.12E-07 -6.51 0.067 -1.17 6.700E-02-1.174 3.12E-07 -6.51 0.125 -0.90 1.250E-01-0.903 4.44E-07 -6.35 0.25 -0.60 2.500E-01-0.602 6.62E-07 -6.18 0.5 -0.30 5.000E-01-0.301 9.91E-07 -6.00 1 0.00 1.000E+000.000 1.49E-06 -5.83 DSR @ 20 2 0.30 2.000E+000.301 2.24E-06 -5.65 D(t) = 5.491 X 10-9 + t0.478 X 2.202 X 10-7(10) D(t) = 1.808 X 10-8 + t0.595 X 1.469 X 10-6(20) Table C12: Power Model Parame ter: PG 76-22, RTFOT aged, Log D(t)D0' D' ( ) Lo g D' ( ) -4.347 1.090E-083.33E-101.057E--7.976 -4.074 1.410E-083.33E-101.377E--7.861 -3.773 1.930E-083.33E-101.897E--7.722 -3.472 2.670E-083.33E-102.637E--7.579 -3.171 3.800E-083.33E-103.767E--7.424 BBR @ -10C -2.870 5.520E-083.33E-105.487E--7.261 -1.174 3.122E-073.33E-103.119E--6.506 -0.903 4.443E-073.33E-104.440E--6.353 -0.602 6.619E-073.33E-106.616E--6.179 -0.301 9.906E-073.33E-109.903E--6.004 0.000 1.487E-063.33E-101.487E--5.828 DSR @ 20 0.301 2.237E-063.33E-102.237E--5.650 Log D1=-5.860253m=0.493 D1=1.380E-06

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APPENDIX D MIX DESIGN AND VOLUMETRIC PROPERTIES OF MIXTURES

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113 WHITE ROCK COARSE Nominal maximum aggregate size = 12.5mm AGGREGATE S1A S1B SCREEN FILLER Individual % by mass 10.20063.267 25.511 1.022 Individual specific gravity 2.4252.451 2.527 2.690 Gsb 2.4692.469 2.469 2.469 SPECIFIC %AC 6.0 6.5 7.0 GRAVITY Gb 1.0351.035 1.035 Gmm(measured) 2.3472.329 2.311 Gse(calculated) 2.5532.550 2.547 Gmb Ni=7 1.9421.946 1.942 Ni=8 1.9561.959 1.955 Ni=9 1.9681.971 1.968 Gmb Nd=75 2.1982.199 2.203 Nd=100 2.2282.231 2.231 Nd=125 2.2502.253 2.253 Gmb Nmax=115 2.2412.244 2.245 Nmax=160 2.2702.275 2.275 Nmax=205 2.2912.296 2.296 VOLUMETRIC Nd=75 16.32216.721 17.052 PROPERTY Nd=100 15.17615.515 15.983 VMA Nd=125 14.34914.692 15.163 Nd=75 6.3165.540 4.672 Nd=100 5.0344.172 3.444 Va Nd=125 4.1073.238 2.502 Nd=75 61.30266.866 72.598 Nd=100 66.83173.107 78.450 VFA Nd=125 71.37577.958 83.497 % of Gmm 7 82.883.6 84.0 8 83.484.1 84.6 Ni 9 83.984.7 85.2 75 93.794.5 95.3 100 95.095.8 96.6 Ndes 125 95.996.8 97.5 115 95.596.4 97.2 160 96.897.7 98.5 Nmax 205 97.698.6 99.4 MIXTURE Nd 75100125 Requirement PROPERTY %AC 7.26.66.1 AT 4% AIR VOID Va 4.04.04.0 VMA 17.215.614.5 >14 VFA 75.074.073.0 65-78 Ni 84.284.384.1 =< 89 % of Gmm Nmax 97.497.997.8 =< 98

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114 White Rock-Coarse at 4% Va 6.0 6.5 7.0 7.5 5075100125150 # of Gyration% A C White Rock-Coarse at 4% Va 14.0 14.4 14.8 15.2 15.6 16.0 16.4 16.8 17.2 17.6 5075100125150 # of GyrationVMA White Rock-Coarse at 4% Va 65.0 67.0 69.0 71.0 73.0 75.0 77.0 5075100125150 # of GyrationVFA

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115 White Rock-Coarse %AC v.s.Va0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 5.05.56.06.57.07.5 %ACAir Voi d at Nd=75 White Rock-Coarse %AC v.s.VMA16.0 17.0 18.0 19.0 5.05.56.06.57.07.5 %ACVM A at Nd=75 White Rock-Coarse %AC v.s. VFA50.0 60.0 70.0 80.0 5.05.56.06.57.07.5 %ACVF A at Nd=75

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116 White Rock-Coarse % AC v.s. Va 0.0 1.0 2.0 3.0 4.0 5.0 6.0 5.05.56.06.57.07.5 %ACAir Void at Nd=100 White Rock-Coarse %AC v.s. VMA 15.0 16.0 17.0 5.05.56.06.57.07.5 %ACVMA at Nd=100 White Rock-Coarse %AC v.s. VFA 50.0 60.0 70.0 80.0 90.0 5.05.56.06.57.07.5 %ACVFA at Nd=100

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117 White Rock-Coarse %AC v.s. Va 0.0 1.0 2.0 3.0 4.0 5.0 5.05.56.06.57.07.5 %ACAir Void at Nd=125 White Rock-Coarse %AC v.s. VMA 14.0 15.0 16.0 17.0 5.05.56.06.57.07.5 %ACVMA at Nd=125 White Rock-Coarse %AC v.s.VFA 50.0 60.0 70.0 80.0 90.0 5.05.56.06.57.07.5 %ACVFA at Nd=125

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118 White Rock Coarse %AC v.s. Va0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 5.05.56.06.57.07.5 %ACAir Void Nd=75 Nd=100 Nd=125 White Rock Coarse %AC v.s. VMA13.0 14.0 15.0 16.0 17.0 18.0 5.05.56.06.57.07.5 %ACVMA Nd=75 Nd=100 Nd=125 White Rock Coarse %AC v.s. VFA50.0 60.0 70.0 80.0 90.0 5.05.56.06.57.07.5 %ACVFA Nd=75 Nd=100 Nd=125

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119 At Ni 82.5 83.0 83.5 84.0 84.5 85.0 85.5 5.05.56.06.57.07.58.0 % AC% of Gmm Ni=7 Ni=8 Ni=9 At Nmax 95.0 96.0 97.0 98.0 99.0 100.0 5.05.56.06.57.07.58.0 % AC% of Gmm Ni=115 Ni=160 Ni=205 80.0 90.0 100.0 1101001000 # of Gyration% of Gmm AC 6.0% AC 6.5% AC 7.0%

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APPENDIX E BINDER-TO-MIXTURE STIFFN ESS RELATIONSHIP DATA

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121Table E1 a,b regression: PG 67-22, extracted binder, 6.1% asphalt content 0 1020 Log S b Log S b a,bLog S b Log S b 'a,b Log S b Log S b 'a,b -1.295 -2.955 -2.205-3.568-3.121-4.005 -1.450 -3.072 -2.363-3.710-3.279-4.188 -1.657 -3.216 a=-2.571-3.920a= -3.487-4.495a= -1.814 -3.325 1.747E-02-2.728-4.1001.426E-01 -3.645-4.6851.259E+00 -1.971 -3.465 -2.886-4.272-3.802-4.882 -2.178 -3.677 -3.094-4.542-4.011-5.148 -2.336 -3.789 -3.252-4.747 b = -4.168-5.350 b = -2.493 -3.952 0.886-3.409-4.9561.205 -4.326-5.5611.312 -2.702 -4.171 -3.618-5.228-4.534-5.852 -2.859 -4.347 -3.776-5.432-4.692-6.080 Table E2 Predicted Stiffness Using a,b: PG 67-22, extracted binder, 6.1% asphalt content 01020 Log S m Log S b Log S m Log S m 'Log S b Log S m Log S m 'Log S b Log S m 1.261 -1.2951.2220.791-2.2050.7400.400-3.1210.391 1.153 -1.4501.1310.641-2.3630.6270.234-3.2790.245 1.010 -1.6571.0180.441-2.5710.4600.013-3.487-0.004 0.901 -1.8140.9320.288-2.7280.315-0.155-3.645-0.158 0.791 -1.9710.8210.135-2.8860.177-0.324-3.802-0.318 0.645 -2.1780.654-0.068-3.094-0.041-0.548-4.011-0.537 0.534 -2.3360.564-0.223-3.252-0.209-0.718-4.168-0.703 0.422 -2.4930.434-0.378-3.409-0.379-0.889-4.326-0.878 0.274 -2.7020.258-0.584-3.618-0.603-1.117-4.534-1.119 0.162 -2.8590.116-0.741-3.776-0.771-1.289-4.692-1.309

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122Table E3. a,b regression: PG 67-22, ex tracted binder, 7.2% asphalt content 0 1020 Log S b Log S b a,bLog S b Log S b 'a,bLog S b Log S b 'a,b -1.331 -2.668 -2.247-3.160-3.169-3.243 -1.488 -2.748 -2.406-3.364-3.327-3.469 -1.696 -2.896 a=-2.615-3.606a=-3.537-3.683a= -1.853 -3.028 3.92E-02-2.774-3.7874.12E-01 -3.695-4.0251.15E+02 -2.011 -3.153 -2.932-3.998-3.854-4.319 -2.220 -3.347 -3.142-4.254-4.064-4.687 -2.379 -3.489 -3.300-4.443 b =-4.222-4.950 b = -2.537 -3.655 0.89-3.459-4.6361.23-4.381-5.1891.65 -2.747 -3.883 -3.668-4.906-4.590-5.546 -2.905 -4.055 -3.827-5.121-4.749-5.790 Table E4 Predicted Stiffness Using a,b: PG 67-22, extracted binder, 7.2% asphalt content 0 1020 Log S m Log S b Log S m Log S m 'Log S b Log S m Log S m 'Log S b Log S m 0.994 -1.331 0.932 0.536 -2.247 0.527 0.522 -3.169 0.458 0.880 -1.488 0.866 0.375 -2.406 0.359 0.304 -3.327 0.271 0.728 -1.696 0.745 0.160 -2.615 0.156 0.015 -3.537 0.092 0.613 -1.853 0.636 -0.003 -2.774 0.005 -0.205 -3.695 -0.196 0.497 -2.011 0.533 -0.167 -2.932 -0.172 -0.426 -3.854 -0.444 0.342 -2.220 0.373 -0.385 -3.142 -0.389 -0.720 -4.064 -0.757 0.225 -2.379 0.254 -0.550 -3.300 -0.549 -0.944 -4.222 -0.982 0.107 -2.537 0.116 -0.716 -3.459 -0.714 -1.168 -4.381 -1.187 -0.049 -2.747 -0.076 -0.937 -3.668 -0.944 -1.467 -4.590 -1.496 -0.168 -2.905 -0.221 -1.104 -3.827 -1.128 -1.694 -4.749-1.707

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123Table E5. a,b regression: PG 76-22, ex tracted binder, 6.1% asphalt content 0 1020 Log S b Log S b a,bLog S b Log S b 'a,b Log S b Log S b 'a,b -1.329 -3.210 -2.177 -3.611 -3.029 -3.947 -1.474 -3.301 -2.323 -3.701 -3.176 -4.126 -1.666 -3.424 a=-2.517 -3.896 a=-3.370 -4.367 a= -1.812 -3.521 9.34E-03-2.664 -4.017 -3.517 -4.519 3.30E-01 -1.958 -3.644 -2.811 -4.178 -3.664 -4.689 -2.152 -3.807 -3.005 -4.382 -3.858 -4.891 -2.298 -3.953 -3.151 -4.541 -4.005 -5.042 -2.445 -4.086 0.84 -3.298 -4.704 1.03 -4.152 -5.200 1.15 -2.639 -4.277 -3.492 -4.936 -4.346 -5.466 -2.786 -4.436 -3.639 -5.082 -4.493 -5.673 Table E6 Predicted Stiffness Using a,b: PG 76-22, extracted binder, 6.1% asphalt content 0 1020 Log S m Log S b Log S m Log S m 'Log S b Log S m Log S m 'Log S b Log S m 1.073 -1.329 1.022 0.752 -2.177 0.706 0.423 -3.029 0.438 0.977 -1.474 0.951 0.632 -2.323 0.635 0.287 -3.176 0.294 0.850 -1.666 0.854 0.473 -2.517 0.479 0.107 -3.370 0.100 0.753 -1.812 0.777 0.352 -2.664 0.382 -0.029 -3.517 -0.023 0.655 -1.958 0.680 0.231 -2.811 0.253 -0.166 -3.664 -0.161 0.526 -2.152 0.550 0.069-3.005 0.088 -0.349 -3.858 -0.326 0.427 -2.298 0.433 -0.053 -3.151 -0.041 -0.487 -4.005 -0.449 0.329 -2.445 0.326 -0.176 -3.298 -0.173 -0.626 -4.152 -0.580 0.197 -2.639 0.173 -0.339 -3.492 -0.363 -0.810 -4.346 -0.799 0.098 -2.786 0.044 -0.463 -3.639 -0.483 -0.950 -4.493 -0.970

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124Table E7. a,b regression: PG 76-22, ex tracted binder, 7.2% asphalt content 0 1020 Log S b Log S b a,bLog S b Log S b 'a,b Log S b Log S b 'a,b -1.394 -2.664 -2.241-3.149 -3.093-3.506 -1.539 -2.740 -2.387-3.278 -3.239-3.688 -1.731 -2.847 a=-2.581-3.475a= -3.433-3.888a= -1.877 -2.978 3.42E-02-2.728-3.597-3.580-4.0466.50E-01 -2.023 -3.078 -2.874-3.751 -3.726-4.229 -2.216 -3.243 -3.068-3.951 -3.920-4.443 -2.363 -3.374 -3.215-4.099-4.067-4.593 -2.509 -3.512 0.82-3.361-4.2591.02 -4.214-4.7441.08 -2.703 -3.694 -3.555-4.474 -4.407-4.935 -2.849 -3.831 -3.702-4.639 -4.554-5.080 Table E8 Predicted Stiffness Using a,b: PG 76-22, extracted binder, 7.2% asphalt content 0 1020 Log S m Log S b Log S m Log S m 'Log S b Log S m Log S m 'Log S b Log S m 0.980 -1.3940.9360.559-2.2410.536 0.222-3.0930.240 0.883 -1.5390.8730.435-2.3870.429 0.090-3.2390.088 0.754 -1.7310.7850.271-2.5810.266 -0.086-3.433-0.080 0.655 -1.8770.6780.146-2.7280.164 -0.219-3.580-0.213 0.556 -2.0230.5950.021-2.8740.035 -0.353-3.726-0.368 0.425 -2.2160.458-0.145-3.068-0.133 -0.531-3.920-0.549 0.325 -2.3630.350-0.271-3.215-0.258 -0.665-4.067-0.677 0.225 -2.5090.235-0.398-3.361-0.393 -0.800-4.214-0.806 0.092 -2.7030.082-0.566-3.555-0.576 -0.980-4.407-0.969 -0.008 -2.849-0.032-0.693-3.702-0.716 -1.116-4.554-1.094

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125Table E9. a,b regression: PG 67-22, RTFOT aged, 6.1% asphalt content 0 1020Log S b Log S b a,bLog S b Log S b 'a,bLog S b Log S b 'a,b -1.288 -2.955 -2.170 -3.568 -1.439 -3.072 -2.322 -3.710 -1.639 -3.216 a=-2.524 -3.920 a=a= -1.791 -3.325 1.88E-02-2.677 -4.100 1.40E+00 -1.943 -3.465 -2.829 -4.272 -2.144 -3.677 -3.031 -4.542 -2.296 -3.789 -3.184 -4.747 -2.449 -3.952 0.91 -3.337 -4.956 1.24 1.35 -2.651 -4.171 -3.539 -5.228 -2.803 -4.347 -3.691 -5.432 Table E10 Predicted Stiffness Using a,b: PG 67-22, RTFOT aged, 6.1% asphalt content 0 1020 Log S m Log S b Log S m Log S m 'Log S b Log S m Log S m 'Log S b Log S m 1.266 -1.2881.2220.797 -2.170 0.740 0.410 -3.057 0.391 1.159 -1.4391.1310.648 -2.322 0.627 0.244 -3.210 0.245 1.016 -1.6391.0180.448 -2.524 0.460 0.024 -3.412 -0.004 0.908 -1.7910.9320.296 -2.677 0.315 -0.143 -3.565 -0.158 0.798 -1.9430.8210.144 -2.829 0.177 -0.311 -3.717 -0.318 0.653 -2.1440.654-0.059 -3.031 -0.041 -0.535 -3.919 -0.537 0.542 -2.2960.564-0.213 -3.184 -0.209 -0.705 -4.072 -0.703 0.431 -2.4490.434-0.368 -3.337 -0.379 -0.875 -4.225 -0.878 0.284 -2.6510.258-0.573 -3.539 -0.603 -1.102 -4.427 -1.119 0.172 -2.8030.116-0.729 -3.691 -0.771 -1.274 -4.579 -1.309

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126Table E11. a,b regression: PG 76-22, RTFOT aged, 6.1% asphalt content 0 1020 Log S b Log S b a,bLog S b Log S b 'a,bLog S b Log S b 'a,b -1.420 -3.210 -2.278 -3.611 -1.567 -3.301 -2.426 -3.701 -1.762 -3.424 a=-2.622 -3.896 a=a= -1.909 -3.521 1.08E-02-2.770 -4.017 4.04E-01 -2.057 -3.644 -2.919 -4.178 -2.253 -3.807 -3.115 -4.382 -2.401 -3.953 -3.263 -4.541 -2.549 -4.087 0.83 -3.411 -4.704 1.02 1.13 -2.745 -4.277 -3.608 -4.936 -2.893 -4.436 -3.756 -5.082 Table E12 Predicted Stiffness Using a,b: PG 76-22, RTFOT aged, 6.1% asphalt content 0 1020 Log S m Log S b Log S m Log S m 'Log S b Log S m Log S m 'Log S b Log S m 1.073 -1.4201.0220.751 -2.278 0.706 0.442 -3.140 0.438 0.978 -1.5670.9510.631 -2.426 0.635 0.308 -3.288 0.294 0.850 -1.7620.8540.471 -2.622 0.479 0.129 -3.484 0.100 0.753 -1.9090.7770.350 -2.770 0.382 -0.006 -3.633 -0.023 0.656 -2.0570.6800.228 -2.919 0.253 -0.143 -3.781 -0.161 0.527 -2.2530.5500.067 -3.115 0.088 -0.323 -3.977 -0.326 0.428 -2.4010.433-0.056 -3.263 -0.041 -0.461 -4.126 -0.449 0.330 -2.5490.326-0.179 -3.411 -0.173 -0.598 -4.274 -0.580 0.199 -2.7450.173-0.342 -3.608 -0.363 -0.781 -4.470 -0.799 0.099 -2.8930.044-0.466 -3.756 -0.483 -0.920 -4.619 -0.970

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127Table E13. a,b regression: PG 67-22, RTFOT aged, 7.2% asphalt content 0 1020 Log S b Log S b a,bLog S b Log S b 'a,bLog S b Log S b 'a,b -1.288 -2.668 -2.170 -3.160 -1.439 -2.748 -2.322 -3.364 -1.639 -2.896 a=-2.524 -3.606 a=a= -1.791 -3.028 3.97E-02-2.677 -3.787 1.17E+02 -1.943 -3.153 -2.829 -3.998 -2.144 -3.347 -3.031 -4.254 -2.296 -3.489 -3.184 -4.443 -2.449 -3.655 0.93 -3.337 -4.636 1.28 1.72 -2.651 -3.883 -3.539 -4.906 -2.803 -4.055 -3.691 -5.121 Table E14 Predicted Stiffness Using a,b: PG 67-22, RTFOT aged, 7.2% asphalt content 0 1020 Log S m Log S b Log S m Log S m 'Log S b Log S m Log S m 'Log S b Log S m 0.988 -1.2880.9320.531 -2.170 0.527 0.504 -3.057 0.458 0.874 -1.4390.8660.369 -2.322 0.359 0.286 -3.210 0.271 0.721 -1.6390.7450.154 -2.524 0.156 -0.005 -3.4120.092 0.605 -1.7910.636-0.010 -2.677 0.005 -0.226 -3.565 -0.196 0.488 -1.9430.533-0.174 -2.829 -0.172 -0.448 -3.717 -0.444 0.332 -2.1440.373-0.392 -3.031 -0.389 -0.744 -3.919 -0.757 0.214 -2.2960.254-0.558 -3.184 -0.549 -0.968 -4.072 -0.982 0.096 -2.4490.116-0.725 -3.337 -0.714 -1.194 -4.225 -1.187 -0.062 -2.651-0.076-0.946 -3.539 -0.944 -1.494 -4.427 -1.496 -0.181 -2.803-0.221-1.114 -3.691 -1.128 -1.722 -4.579 -1.707

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128Table E15. a,b regression: PG 76-22, RTFOT aged, 7.2% asphalt content 0 1020 Log S b Log S b a,bLog S b Log S b 'a,bLog S b Log S b 'a,b -1.420 -2.664 -2.278 -3.149 -1.567 -2.740 -2.426 -3.278 -1.762 -2.847 a=-2.622 -3.475 a=a= -1.909 -2.978 3.48E-02-2.770 -3.597 6.66E-01 -2.057 -3.078 -2.919 -3.751 -2.253 -3.243 -3.115 -3.951 -2.401 -3.374 -3.263 -4.099 -2.549 -3.512 0.81 -3.411 -4.259 1.01 1.07 -2.745 -3.694 -3.608 -4.474 -2.893 -3.831 -3.756 -4.639 Table E16 Predicted Stiffness Using a,b: PG 76-22, RTFOT aged, 7.2% asphalt content 0 1020 Log S m Log S b Log S m Log S m 'Log S b Log S m Log S m 'Log S b Log S m 0.980 -1.4200.9360.555 -2.278 0.536 0.215 -3.140 0.240 0.883 -1.5670.8730.431 -2.426 0.429 0.082 -3.288 0.088 0.754 -1.7620.7850.266 -2.622 0.266 -0.094 -3.484 -0.080 0.655 -1.9090.6780.141 -2.770 0.164 -0.228 -3.633 -0.213 0.556 -2.0570.5950.016 -2.919 0.035 -0.362 -3.781 -0.368 0.425 -2.2530.458-0.151 -3.115 -0.133 -0.540 -3.977 -0.549 0.325 -2.4010.350-0.277 -3.263 -0.258 -0.675 -4.126 -0.677 0.225 -2.5490.235-0.404 -3.411 -0.393 -0.810 -4.274 -0.806 0.093 -2.7450.082-0.572 -3.608 -0.576 -0.990 -4.470 -0.969 -0.008 -2.893-0.032-0.700 -3.756 -0.716 -1.126 -4.619 -1.094

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APPENDIX F ENERGY RATIO USING MIXTURE TEST AT ONE TEMPERAURE

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130 The following equation was used to calculate the Energy Ratio (ER): 1 98 2D m DCSE a ERf (2.36) where: 8 1 310 46 2 ) 36 6 ( 0299 0 tS a = tensile stress of asphalt layer ,assumed 230 psi St= tensile strength, MPa DCSEf = Dissipated Creep Strain Energy, KJ/m3 D1= creep parameter, 1/psi m = creep parameter St and DCSEf were obtained from IDT test. D1 and m were obtained from the following procedure: 5. Lock-in D0 = 0.048 (1/GPa) 6. Determine D1 and m at 20 from regression 7. Fix m = m at 20 ( assuming m is a constant at three temperatures for the same mixture) 8. Calculate D1 at 0 and 10 using the following relationship: m Ta D D ) ( 1) 0 ( ) 20 ( 1 ) 0 ( 1 (4.4)

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131 m Ta D D ) ( 1) 10 ( ) 20 ( 1 ) 10 ( 1 (4.5) 5. Repeat Step 1-4 for D1 and m at 0 and 10. Table F1. IDT Test Result: PG 67-22, 6.1% asphalt content Temp. Tensile Strength (PMa) DCSE (KJ/m3) m D1(1/Psi) 0 2.67 1.27 0.51 1.93E-07 10 1.87 3.85 0.61 6.04E-07 20 1.02 3.01 0.61 1.61E-06 Table F2. IDT Test Result: PG 67-22, 7.2% asphalt content Temp. Tensile Strength (PMa) DCSE (KJ/m3) m D1(1/Psi) 0 2.54 1.73 0.52 2.99E-07 10 1.69 4.70 0.62 1.21E-06 20 0.73 3.64 0.63 3.68E-06 Table F3. IDT Test Result: PG 76-22, 6.1% asphalt content Temp. Tensile Strength (PMa) DCSE (KJ/m3) m D1(1/Psi) 0 3.00 2.08 0.45 2.63E-07 10 1.95 3.59 0.45 7.69E-07 20 1.19 2.28 0.52 1.55E-06 Table F4. IDT Test Result: PG 76-22, 7.2% asphalt content Temp. Tensile Strength (PMa) DCSE (KJ/m3) m D1(1/Psi) 0 2.89 2.38 0.44 3.48E-07 10 1.93 4.85 0.47 1.33E-06 20 0.94 2.11 0.48 4.10E-06

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132 Table F5. Energy Ratio from Mixture Te st : PG 67-22, 6.1% asphalt content Fix m @ D1 (1/Psi) m Energy Ratio (ER) 0 1.17E-07 1.83 10 1.11E-06 0.60 0 20 1.06E-05 0.560 0.05 0 9.43E-08 2.38 10 8.68E-07 0.81 10 20 7.99E-06 0.551 0.07 0 2.33E-08 8.29 10 2.40E-07 2.53 20 20 2.48E-06 0.579 0.20 Table F6. Energy Ratio from Mixture Te st: PG 67-22, 7.2% asphalt content Fix m @ D1 (1/Psi) m Energy Ratio (ER) 0 4.43E-07 1.20 10 2.81E-06 0.53 0 20 1.79E-05 0.459 0.07 0 1.78E-07 1.56 10 1.77E-06 0.44 10 20 1.76E-05 0.570 0.04 0 4.15E-09 28.38 10 8.87E-08 3.75 20 20 1.90E-06 0.760 0.14 Table F7. Energy Ratio from Mixture Te st: PG 76-22, 6.1% asphalt content Fix m @ D1 (1/Psi) m Energy Ratio (ER) 0 3.22E-07 2.57 10 1.73E-06 0.87 0 20 9.30E-06 0.417 0.11 0 1.61E-07 4.32 10 9.56E-07 1.32 10 20 5.69E-06 0.443 0.15 0 5.01E-08 11.33 10 3.38E-07 3.05 20 20 2.27E-06 0.473 0.30

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133 Table F8. Energy Ratio from Mixture Te st: PG 76-22, 7.2% asphalt content Fix m @ D1 (1/Psi) m Energy Ratio (ER) 0 4.45E-07 2.46 10 2.21E-06 1.06 0 20 1.10E-05 0.398 0.10 0 2.77E-07 2.92 10 1.64E-06 1.05 10 20 9.67E-06 0.441 0.08 0 9.71E-08 7.50 10 6.11E-07 2.54 20 20 3.84E-06 0.456 0.18

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APPENDIX G ENERGY RATIO PREDICTION USING BINDER-TO-MIXTURE STIFFNESS RELATIONSHIP

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135 To calculate D1 and m, the following procedure was followed: 1. Predict the mixture stiffness at 20 using the binder-to-mixture stiffness at 20 2. Lock-in D0 = 0.048 (1/GPa) 3. Determine the D1 and m at 20 from regression 4. Use the binder-to-mixture st iffness relationship at 20 to predict the mixture stiffness at 0 and 10 for different times 5. Calculate D1 at 0 and 10 using the predicted mixtur e stiffness on step 4 and assuming: m = m at 20 D0 = 0.048 (1/GPa) 6. Repeat Step 1-5 for 0 and 10.

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136 Table G1. Energy Ratio from Binder-t o-mixture Stiffne ss Relationship: PG 67-22, extracted binder, 6.1% asphalt content Fix m @ D1 (1/Psi) m Energy Ratio (ER) 0 9.84E-08 1.80 10 4.73E-07 1.18 0 20 2.27E-06 0.596 0.20 0 8.57E-08 2.58 10 8.56E-07 0.81 10 20 7.09E-06 0.554 0.08 0 6.32E-09 30.57 10 2.35E-07 2.59 20 20 2.47E-06 0.579 0.20 Table G2. Energy Ratio from Binder-t o-mixture Stiffne ss Relationship: PG 67-22, extracted binder, 7.2% asphalt content Fix m @ D1 (1/Psi) m Energy Ratio (ER) 0 4.29E-07 1.18 10 2.23E-06 0.64 0 20 1.14E-05 0.466 0.10 0 1.72E-07 1.61 10 1.77E-06 0.44 10 20 1.69E-05 0.570 0.04 0 -2.43E-09 -48.28 10 8.62E-08 3.85 20 20 1.89E-06 0.761 0.14

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137 Table G3. Energy Ratio from Binder-t o-mixture Stiffne ss Relationship: PG 76-22, extracted binder, 6.1% asphalt content Fix m @ D1 (1/Psi) m Energy Ratio (ER) 0 3.10E-07 2.51 10 1.30E-06 1.08 0 20 5.23E-06 0.426 0.18 0 1.47E-07 4.66 10 9.48E-07 1.31 10 20 5.13E-06 0.445 0.16 0 2.20E-08 25.76 10 3.29E-07 3.13 20 20 2.27E-06 0.473 0.30 Table G4. Energy Ratio from Binder-t o-mixture Stiffne ss Relationship: PG 76-22, extracted binder, 7.2% asphalt content Fix m @ D1 (1/Psi) m Energy Ratio (ER) 0 4.34E-07 2.42 10 1.79E-06 1.25 0 20 7.17E-06 0.404 0.14 0 2.66E-07 3.03 10 1.63E-06 1.05 10 20 9.19E-06 0.441 0.08 0 6.82E-08 10.68 10 6.03E-07 2.58 20 20 3.84E-06 0.456 0.18

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138 Table G5. Energy Ratio from Binder-t o-mixture Stiffne ss Relationship: PG 67-22, RTFOT aged, 6.1% asphalt content Fix m @ D1 (1/Psi) m Energy Ratio (ER) 0 9.83E-08 1.80 10 4.73E-07 1.18 0 20 2.27E-06 0.596 0.20 0 8.57E-08 2.58 10 8.56E-07 0.81 10 20 7.09E-06 0.554 0.08 0 6.33E-09 30.55 10 2.35E-07 2.59 20 20 2.47E-06 0.579 0.20 Table G6. Energy Ratio from Binder-t o-mixture Stiffne ss Relationship: PG 76-22, RTFOT aged, 6.1% asphalt content Fix m @ D1 (1/Psi) m Energy Ratio (ER) 0 3.10E-07 2.51 10 5.22E-06 1.08 0 20 1.30E-06 0.426 0.18 0 1.47E-07 4.66 10 9.48E-07 1.31 10 20 5.13E-06 0.445 0.16 0 2.20E-08 25.77 10 3.29E-07 3.13 20 20 2.27E-06 0.473 0.30

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139 Table G7. Energy Ratio from Binder-t o-mixture Stiffne ss Relationship: PG 67-22, RTFOT aged, 7.2% asphalt content Fix m @ D1 (1/Psi) m Energy Ratio (ER) 0 4.29E-07 1.18 10 2.23E-06 0.64 0 20 1.14E-05 0.466 0.10 0 1.72E-07 1.61 10 1.77E-06 0.44 10 20 1.69E-05 0.570 0.04 0 -2.43E-09 -48.28 10 8.62E-08 3.85 20 20 1.89E-06 0.761 0.14 Table G8. Energy Ratio from Binder-t o-mixture Stiffne ss Relationship: PG 76-22, RTFOT aged, 7.2% asphalt content Fix m @ D1 (1/Psi) m Energy Ratio (ER) 0 4.34E-07 2.42 10 1.79E-06 1.25 0 20 7.16E-06 0.404 0.14 0 2.66E-07 3.03 10 1.63E-06 1.05 10 20 9.19E-06 0.441 0.09 0 6.82E-08 10.69 10 6.03E-07 2.58 20 20 3.84E-06 0.456 0.18

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APPENDIX H ENERGY RATIO PREDICTION USING UNMODIFIED BINDER-TO-MIXTURE STIFFNESS RELATIONSHIP FOR MODIFIED MIXTURE

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141 To predict the Energy Ratio fr om unmodified binder-to-mixtu re stiffness relationship to modified mixture, the follo wing procedure was followed: 1. Develop the binder-to-mixture stiffness re lationship for the unmodified mixture at each of the three temperature 2. Predict the stiffness of m odified mixture using the unm odified binder-to-mixture stiffness relationship at the same temperature 3. Lock-in D0 = 0.048 (1/GPa) 4. Determine D1 and m for the modified mixture

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142 Table H1. Energy Ratio from Unmodified Binder-t o-mixture Stiffne ss Relationship: PG 76-22, extracted binder, 6.1% asphalt content D1 (1/Psi) m Energy Ratio (ER) 0 1.19E-07 0.542 3.20 10 7.85E-07 0.521 0.98 20 1.93E-06 0.543 0.23 Table H2. Energy Ratio from Unmodified Binder-t o-mixture Stiffne ss Relationship: PG 76-22, extracted binder, 7.2% asphalt content D1 (1/Psi) m Energy Ratio (ER) 0 5.01E-07 0.427 1.77 10 1.73E-06 0.528 0.58 20 1.44E-06 0.708 0.13 Table H3. Energy Ratio from Unmodified Binder-t o-mixture Stiffne ss Relationship: PG 76-22, RTFOT aged, 6.1% asphalt content D1 (1/Psi) m Energy Ratio (ER) 0 1.94E-07 0.501 2.47 10 1.16E-06 0.530 0.63 20 3.10E-06 0.561 0.13 Table H4. Energy Ratio from Unmodified Binder-t o-mixture Stiffne ss Relationship: PG 76-22, RTFOT aged, 7.2% asphalt content D1 (1/Psi) m Energy Ratio (ER) 0 6.07E-07 0.436 1.37 10 2.37E-06 0.550 0.38 20 2.54E-06 0.736 0.07

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143 LIST OF REFERENCES 1. Freddy L. Roberts, Prithvi S. Kandhal, E. Ray Brown, Dah-Yinn Lee, Thomas W. Kennedy, Hot Mix Asphalt Materials, Mi xture Design, and Construction, Second Edition, 1996, NAPA Ed ucation Foundation 2. Franklin Kwame Twumasi, “Laboratory Ev alution of the Effects of Ground Tire Rubber (GTR) on the Rutting and Cracking Performance of Superpave Mixes,” Master’s Thesis, University of Florida, Gainesville, 2001 3. Buttlar, W. G. “Relationship Between Asphalt Binder and Mixture Stiffness at Low Temperatures for the Control of Therma l Cracking Performance Predictions,” Ph. D. Dissertation, The Pennsylvania Stat e University, University Park, PA, 1996 4. Paul, B. “Prediction of Elastic Constant s of Multiphase Materials,” Journal of Applied Mechanics, Transactions of the ASME, New York, Vol.36, p.218, 1960 5. Hashin, Z., and Shtrikman, S., “ A Variat ional Approach to the Theory of the Elastic Behavior of Multi phase Materials,” Journal of Mechanics and Physics of Solids, Pergamon Press, New York, Vol.11, p.137, 1963 6. Hashin, Z., “Viscoelastic Behavior of He terogeneous Media,” Journal of Applied Mechanics, Transactions of the ASME, New York, No.9, p.630-636, 1965 7. Christensen, R. M. and Lo, K.H.,”Solutions for Effective Shear Properties in Three Phase Sphere and Cylinder Models,” Jour nal of the Mechanics and Physics of Solids, Pergamon Press, New York, Vol. 27, p.315-330, 1979 8. Christensen, R.M. and Lo, K.H., Erratum: ”Solutions for Effective Shear Properties in Three Phase Sphere and Cylinder M odels,” Journal of the Mechanics and Physics of Solids, Pergamon Press, New York, Vol.34, No.6, p.639, 1986 9. Reynaldo Roque, William G. Buttlar, Byron E. Ruth, Mang Tia, Stephen W. Dickison, Brain Reid, “Evaluation of SHRP Indirect Tension Tester to Mitigate Cracking in Asphalt Concrete Pavements a nd Overlays,” Draft Final Report to Florida Department of Transportation, University of Florida, FL, June, 1997 10. Heukelom, W., and Klomp, A.J.G., “ Road Design and Dynamic Loading,” Proceedings, Association of Asphalt Pavi ng Technologists, Ann Arbor, Michigan, Vol.33, 1964

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144 11. Bonnaure, F., G. Gest, A. Gravois, and P. Uge, “ A New Method of Predicting the Stiffness of Asphalt Paving Mixtures,” Pr oceedings, Association of Asphalt Paving Technologists, Vol. 46, p.64-100, 1977 12. Van Draat, W.E. Fijn and P. Somm er, “Ein Great Zur Bestimmung der Dynamichen Elastizitasmoduln von Aspha lt,” Strasse und Autobahn, Vol.6, 1965 13. Roque, R., D. R. Hiltunen, P. Romero, and W. G. Buttlar, “ Canadian SHRP Investigation to Evaluate Asphalt Mixt ure and Binder Criteri a to Predict and Control Thermal Cracking,” Draft Re port to C-SHRP, The Pennsylvania Transportation Institute, Un iversity Park, PA, June, 1994 14. Roque, R., D. R. Hiltunen, W. G. Buttlar, and T. Farwanna, “Development of the SHRP SUPERPAVETM Mixture Specification Test Method to Control Thermal Cracking Performance of Pavements,” Sy mposium on Engineering Properties of Asphalt Mixture and Relation to Performan ce, ASTM STP 1265, G. A. Huber and D. S. Decker, Eds., American Society for Testing and Materials, Philadelphia, PA, 1994 15. Christensen, D. W. and D. A. Anderson, “Interpretation of Dynamic Mechanical Test Data for Paving Grade Asphalt Ceme nts,” Journal of the Association of Asphalt Paving Technologists, Vol. 61, p.67-98, 1992 16. Arthur M Usmani, Asphalt Science and Technology, New York: Marcel Dekker,1997 17. Robert N. Hunter, Asphalts in Road C onstruction, London: Thomas Telford, 2000 18. J.C. Nicholls, Asphalt Surfacings, London ; New York: E & FN Spon, 1998 19. Booil Kim, “Evaluation of the Effects of SBS Polymer Modifier on Cracking Resistance of Superpave Mixture,” Ph.D. dissertation, University of Florida, Gainesville, FL, 2003 20. E. Eugene Shin, Alekh Bhurke, Edward Sc ott, Steve Rozeveld, Lawrence T. Draza, “Microstructure, Mo rphology, and Failure Modes of Polymer-Modified Asphalts,” Transportation Research Record, No. 1535 21. J.D. Ferry, Viscoelastic Properties of Polymers, New York: John Wiley & Sons, 1961, Ch 11 22. Zhiwang Zhang, “Identification and Cr ack Growth Law for Asphalt Mixtures Using the Superpave Indirect Tensile Test (IDT),” Ph.D. Dissertation, University of Florida, 2000 23. Adam P. Jajliardo, “Development of Sp ecification Criteria to Mitigate Top-down Cracking,” Master’s thesis, University of Florida, 2003

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145 24. Tia, Mang, “Lecture Notes: Bituminous Materials.” Department of Civil and Coastal Engineering, University of Florida, Gainesville, Florida, Fall, 2001

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146 BIOGRAPHICAL SKETCH Zhanwu Cui was born in Beijing, China, on Jan. 28, 1973. He attended Yanqing No. 2 Middle School and then went to the No. 2 Middle School at tached to Beijing Normal University where he completed his s econdary education. He gained admission to the Tianjin Institute of Urban Construction, Tianjin, China, in 1992 and graduated with a bachelor’s degree in engineering in polymer materials in July 1996. After graduation, Zhanwu worked as an engineer in the Technology Development Center, Beijing Residence Cons truction Corporation (B.R.C.C.) one of the four biggest construction companies in Beijing, for five y ears. He came to the United States and began his study for the master’s degree in civil engin eering at the University of Florida in Aug., 2001.