Florida State University Librariesdiginole.lib.fsu.edu/islandora/object/fsu:168556/... · florida...

Florida State University Libraries

Electronic Theses, Treatises and Dissertations The Graduate School

2009

Evaluation of Engineering Properties of HotMix Asphalt Concrete for the Mechanistic-Empirical Pavement DesignYuan Xiao

Follow this and additional works at the FSU Digital Library. For more information, please contact [email protected]

http://fsu.digital.flvc.org/

mailto:[email protected]

FLORIDA STATE UNIVERSITY

COLLEGE OF ENGINEERING

EVALUATION OF ENGINEERING PROPERTIES OF HOT MIX

ASPHALT CONCRETE FOR THE MECHANISTIC-EMPIRICAL

PAVEMENT DESIGN

By

YUAN XIAO

A Dissertation submitted to the Department of Civil & Environmental Engineering

in partial fulfillment of the requirements for the degree of

Doctor of Philosophy

Degree Awarded: Spring Semester, 2009

ii

The members of the Committee approve the Dissertation of Yuan Xiao defended on January 30, 2009.

__________________________ Wei-Chou V. Ping Professor Directing Dissertation __________________________ Xufeng Niu Outside Committee Member __________________________ Tarek Abichou Committee Member __________________________ John Sobanjo Committee Member

Approved: _____________________________________________________________ Kamal Tawfiq, Chair, Department of Civil & Environmental Engineering

_____________________________________________________________ Ching-Jen Chen, Dean, College of Engineering

The Graduate School has verified and approved the above named committee members.

iii

ACKNOWLEDGEMENTS

I would like to express my sincere gratitude to my advisor, Dr. W. Virgil Ping, for his

guidance, support and patience during the whole study of my Ph.D. program. My

special thanks go to Ms. Ginger Ling for her generous help in every stage of my work. I

also wish to thank all other members of my committee: Dr. Xufeng Niu, Dr. Tarek

Abichou, and Dr. John Sobanjo for their friendly encouragement and valuable advice.

I extend many thanks to my colleague, Mr. Ed Mallory, who provided unconditional

support during the whole experimental program for this research. I would also like to

thank the engineers and staff from Florida Department of Transportation and other

contracting companies who offered financial and contractual support.

iv

TABLE OF CONTENTS

LIST OF TABLES................................................................................................................ vii

LIST OF FIGURES ............................................................................................................... ix

ABSTRACT ...................................................................................................................... xv

CHAPTER 1 INTRODUCTION............................................................................................ 1

1.1 Background................................................................................................................. 1

1.2 Objectives ................................................................................................................... 3

1.3 Dissertation Outline.................................................................................................... 4

CHAPTER 2 LITERATURE REVIEW................................................................................. 6

2.1 Introduction ................................................................................................................ 6

2.2 Asphalt Cement Properties ......................................................................................... 6

2.3 Hot Mix Asphalt (HMA) Mixture Design................................................................ 21

2.4 Mechanical Tests for Characterization of Asphalt Mixtures.................................... 35

2.5 HMA Fracture Mechanics Concepts ........................................................................ 47

CHAPTER 3 MATERIALS AND EXPERIMENTAL PROGRAM ................................... 54

3.1 General...................................................................................................................... 54

3.2 Mix Designs and Materials....................................................................................... 55

3.3 SBS Polymer-modified Asphalt Binder.................................................................... 56

3.4 Aggregates Gradation Modification ......................................................................... 60

3.5 Specimen Preparation and Volumetric Properties.................................................... 60

3.6 Test Procedures......................................................................................................... 64

3.7 Testing Program ....................................................................................................... 70

CHAPTER 4 FRACTURE MECHANICS PROPERTIES FROM IDT .............................. 73

4.1 Resilient Modulus Testing Procedures and Results ................................................. 73

v

4.2 Creep Compliance Testing Procedures and Results ................................................. 76

4.3 Tensile Strength Testing Procedures and Results..................................................... 77

CHAPTER 5 EVALUATION OF FRACTURE MECHANICS PROPERTIES ................. 81

5.1 Evaluation of Gradation Effects ............................................................................... 81

5.2 Evaluation of SBS Polymer-modified Binder Effects .............................................. 92

5.3 Effect of Aggregate Type........................................................................................ 108

5.4 Summary of Analysis and Findings from Fracture Mechanics Tests ..................... 113

CHAPTER 6 COMPLEX MODULUS AND RESILIENT MODULUS TEST RESULTS.................................................................................................................... 116

6.1 Test Procedures....................................................................................................... 116

6.2 Presentation of DMT and IDT Testing Results ...................................................... 118

CHAPTER 7 CORRELATION OF INDIRECT TENSION RESILIENT MODULUS AND COMPLEX MODULUS TEST RESULTS................................................ 121

7.1 General.................................................................................................................... 121

7.2 HMA Master Curve Development ......................................................................... 121

7.3 Master Curve Construction..................................................................................... 123

7.4 Verification of Dynamic Complex Modulus Experimental Results....................... 126

7.5 Comparison between Resilient Modulus and Dynamic Modulus .......................... 128

CHAPTER 8 SUMMARY AND CONCLUSIONS........................................................... 134

8.1 Summary................................................................................................................. 134

8.2 Findings and Conclusions....................................................................................... 135

8.3 Recommendations .................................................................................................. 138

APPENDIX A MATERIALS AND MIX DESIGNS......................................................... 139

APPENDIX B CREEP COMPLIANCE TEST RESULTS................................................ 155

APPENDIX C TEST RESULTS FOR IDT AND DMT .................................................... 163

vi

REFERENCES................................................................................................................... 174

BIOGRAPHICAL SKETCH .............................................................................................. 183

vii

LIST OF TABLES

Table 2-1: Generic classification of asphalt additives and modifiers (Roberts et al. 1996) ........... 9

Table 2-2: Chosen unit weight ranges by mix type....................................................................... 30

Table 2-3: Recommended aggregate ratios................................................................................... 31

Table 3-1: Number of specimens prepared for fracture mechanics tests ...................................... 62

Table 3-2: Specimens tested for fracture mechanics properties.................................................... 62

Table 3-3: Specific gravities and air voids of the mixtures .......................................................... 63

Table 4-1: Resilient modulus test results at -10˚C........................................................................ 75

Table 4-2: Resilient modulus test results at 5˚C ........................................................................... 75

Table 4-3: Resilient modulus test results at 25˚C ......................................................................... 76

Table 4-4: Resilient modulus test results at 40˚C ......................................................................... 76

Table 4-5: Tensile strength test results for F2 series mixtures ..................................................... 79

Table 4-6: Tensile strength test results for F4 series mixtures ..................................................... 80

Table 5-1: Power law regression coefficients for modified gradation mixes ............................... 83

Table 5-2: Power model regression coefficients for modified gradation tests.............................. 86

Table 5-3: Power model regression coefficients for PMA mixture tests ...................................... 95

Table 6-1: Cycles for DTM test sequence................................................................................... 118

Table A-1: Superpave mix designs sorted by test series............................................................. 139

Table A-2: Performance grade binder grading report ................................................................. 140

Table A-3: Summary of mix designs and aggregates ................................................................. 141

Table A-4: Aggregate gradations for series 1 - 5 ........................................................................ 142

Table A-5: Aggregate gradations for series 6 - 10 ...................................................................... 142

Table A-6: Aggregate gradations for series 11 - 15 .................................................................... 143

Table A-7: Aggregate gradations for series 16 - 20 .................................................................... 143

Table A-8: Lab analysis report for 0.0% polymer base asphalt (Graded as PG67-22) ............... 148

viii

Table A-9: Lab analysis report for 3.0% polymer asphalt (Graded as PG76-22) ....................... 149

Table A-10: Lab analysis report for 4.5% polymer asphalt (Graded as PG82-22) ..................... 150

Table A-11: Lab analysis report for 6.0% polymer asphalt (Graded as PG82-28) ..................... 151

Table A-12: Gradations for F2C and its adjustments ................................................................. 152

Table A-13: Gradations for F4C and its adjustments ................................................................. 152

Table A-14: Volumetric properties of mixture design series 1 - 5 ............................................. 153

Table A-15: Volumetric properties of mixture design series 6 - 10 ........................................... 153

Table A-16: Volumetric properties of mixture design series 11 - 15 ......................................... 154

Table A-17: Volumetric properties of mixture design series 16 - 20 ......................................... 154

Table B-1: Creep compliance test results at -10˚C (1/GPa)........................................................ 155

Table B-2: Creep compliance test results at 5˚C (1/GPa)........................................................... 156

Table B-3: Creep compliance test results at 25˚C (1/GPa)......................................................... 156

Table B-4: Creep compliance test results at 40˚C (1/GPa)......................................................... 157

Table C-1: Summary of resilient modulus and Poisson’s Ratio test results ............................... 163

Table C-2: Summary of dynamic modulus testing results .......................................................... 170

Table C-3: Summary of phase angle testing results.................................................................... 172

ix

LIST OF FIGURES

Figure 2-1: Polymer classifications based on link structure ......................................................... 11

Figure 2-2: SBS polymer modifier structure................................................................................. 11

Figure 2-3: Complex modulus of SBS-modified asphalt at 60°C (Chen et al. 2002)................... 13

Figure 2-4: Relationship between the observed critical cracking temperature (Tcr) and SBS polymer concentration (Collins et al. 1991).................................................................................. 15

Figure 2-5: Comparison of the rut depths measured on sections with PMA and the companion sections without PMA mixtures (Quintus et al. 2007).................................................................. 17

Figure 2-6: Components of complex modulus G* ........................................................................ 18

Figure 2-7: Viscous and elastic behavior of asphalt binders......................................................... 18

Figure 2-8: Dynamic shear rheometer........................................................................................... 19

Figure 2-9: Stress-strain response of viscoelastic material ........................................................... 19

Figure 2-10: Typical aggregate gradations.................................................................................... 24

Figure 2-11: The four principles of Bailey method for coarse-graded mix .................................. 29

Figure 2-12: Combined blend evaluation for coarse-graded mixes. ............................................. 30

Figure 2-13: Combined blend evaluation for fine-graded mixes. ................................................. 30

Figure 2-14: Illustration of gradation requirements for 12.5 mm (1/2 in.) nominal size .............. 34

Figure 2-15: Conceptual schematic of dynamic complex modulus test ....................................... 40

Figure 2-16: Typical test set-up for dynamic complex modulus .................................................. 41

Figure 2-17: The schematic components of dynamic complex modulus test ............................... 41

Figure 2-18: Kelvin model under sinusoidal loading.................................................................... 42

Figure 2-19: Indirect diametral test during loading and at failure ................................................ 43

Figure 2-20: Theoretical stress distribution on horizontal diametral plane for indirect tensile test (After Yoder et al. 1975)............................................................................................................... 45

Figure 2-21: Theoretical stress distribution on vertical diametral plane for indirect tensile test (After Yoder et al. 1975)............................................................................................................... 45

Figure 2-22: Illustration of potential loading condition (Roque et al. 2002) ................................ 50

x

Figure 2-23: Determination of fracture energy and dissipated creep strain energy ...................... 50

Figure 3-1: Gradation curves for F2 and its trial adjustments ...................................................... 58

Figure 3-2: Gradation curves for F4 and its trial adjustments ...................................................... 58

Figure 3-3: Change of percent retained on top 3 sieves for F2 series........................................... 59

Figure 3-4: Change of percent retained on top 3 sieves for F4 series........................................... 59

Figure 3-5: Cutting of raw specimen ............................................................................................ 59

Figure 3-6: Coring of the Superpave specimen............................................................................. 63

Figure 3-7: Cutting of the dynamic modulus specimen ................................................................ 63

Figure 3-8: Indirect Diametral Resilient Modulus Test Setup...................................................... 65

Figure 3-9: Load & deformations in a typical resilient modulus test............................................ 66

Figure 3-10: Load and deformation curves of creep compliance test ........................................... 67

Figure 3-11: Specimen fails after tensile strength test .................................................................. 68

Figure 3-12: Dynamic complex modulus test setup...................................................................... 69

Figure 3-13: Flowchart of the experimental program for measuring fracture mechanics properties of HMA mixtures.......................................................................................................................... 71

Figure 3-14: Flowchart of the testing program for MR vs. E* ....................................................... 72

Figure 4-1: Instantaneous and total resilient deformations ........................................................... 74

Figure 4-2: Determination of fracture energy and dissipated creep strain energy ........................ 78

Figure 5-1: Power law regression for F2 gradation series ............................................................ 82

Figure 5-2: Power law regression for F4 gradation series ............................................................ 83

Figure 5-3: Resilient modulus for mixtures with modified gradations......................................... 84

Figure 5-4: Comparison of resilient modulus between control and modified gradations............. 85

Figure 5-5: Power model parameter D1 for modified gradations.................................................. 86

Figure 5-6: Power model parameter m for modified gradations................................................... 86

Figure 5-7: Comparison of creep compliance for granite gradation series ................................... 87

Figure 5-8: Comparison of creep compliance for limestone gradation series............................... 87

xi

Figure 5-9: Tensile strength for control and modified gradation mixes ....................................... 89

Figure 5-10: Comparison of TS between control and modified gradation mixes......................... 89

Figure 5-11: Fracture Energy for modified gradation mixes ........................................................ 90

Figure 5-12: DCSE for modified gradation mixes........................................................................ 90

Figure 5-13: Comparison of Fracture Energy for modified gradation mixtures ........................... 91

Figure 5-14: Comparison of DCSE for modified gradation mixtures .......................................... 91

Figure 5-15: Comparison of resilient modulus for F2 SBS PMA mixes ...................................... 93

Figure 5-16: Comparison of resilient modulus for F4 SBS PMA mixes ...................................... 93

Figure 5-17: Comparison of MR between control and PMA mixtures ......................................... 94

Figure 5-18: Power model parameter D1 for mixes with SBS PMA ............................................ 96

Figure 5-19: Power model parameter m for mixes with SBS PMA ............................................. 96

Figure 5-20: Creep compliance master curves for granite PMA mixtures ................................... 97

Figure 5-21: Creep compliance master curves for limestone PMA mixtures............................... 97

Figure 5-22: Comparison of creep compliance at -10˚C for F2 series.......................................... 98

Figure 5-23: Comparison of creep compliance at 5˚C for F2 series ............................................. 98

Figure 5-24: Comparison of creep compliance at 25˚C for F2 series ........................................... 99


Figure 5-26: Comparison of creep compliance at -10˚C for F4 series........................................ 100


Figure 5-28: Comparison of creep compliance at 25˚C for F4 series ......................................... 101

Figure 5-29: Comparison of creep compliance at 40˚C for F4 series ......................................... 101

Figure 5-30: Tensile strength for granite PMA mixes ................................................................ 103

Figure 5-31: Tensile strength for limestone PMA mixes............................................................ 103

Figure 5-32: Comparison of tensile strength between control and PMA mixes......................... 104

Figure 5-33: Fracture Energy for granite PMA mixes ................................................................ 104

xii

Figure 5-34: Fracture Energy for limestone PMA mixes............................................................ 105

Figure 5-35: DCSE for granite PMA mixes................................................................................ 105

Figure 5-36: DCSE for limestone PMA mixes ........................................................................... 106

Figure 5-37: Comparison of Fracture Energy between control and PMA mixes........................ 106

Figure 5-38: Comparison of Fracture Energy between control and PMA mixes........................ 107

Figure 5-39: Relationship between the observed Failure Strain and SBS polymer content ....... 107

Figure 5-40: Gradation curves for control mixes and modified gradation mixes ....................... 109

Figure 5-41: Comparison of resilient modulus for granite and limestone mixtures ................... 110

Figure 5-42: Comparison of CP between granite and limestone mixes at -10˚C ....................... 110

Figure 5-43: Comparison of CP between granite and limestone mixes at 5˚C........................... 111

Figure 5-44: Comparison of CP between granite and limestone mixes at 25˚C......................... 111

Figure 5-45: Comparison of CP between granite and limestone mixes at 40˚C......................... 112

Figure 5-46: Comparison of Tensile Strength between granite and limestone mixes ................ 112

Figure 5-47: Comparison of Fracture Energy between granite and limestone mixes ................. 113

Figure 6-1: Specimen and LVDTs setup for DMT test............................................................... 117

Figure 6-2: Resilient modulus at different testing temperatures................................................. 119

Figure 6-3: Poisson’s Ratio from IDT test for all mixture series................................................ 119

Figure 6-4: Average phase angles for different type of materials ............................................... 120

Figure 7-1: Parameters used in sigmoidal fitting function of master curve................................ 123

Figure 7-2: Master curves for granite materials .......................................................................... 124

Figure 7-3: Master curves for limestone materials ..................................................................... 125

Figure 7-4: Master curves for all mixtures.................................................................................. 125

Figure 7-5: Measured vs. predicted dynamic modulus values for all mixtures .......................... 128

Figure 7-6: Comparison of average air void content between IDT and DMT specimens .......... 130

Figure 7-7: Resilient modulus versus dynamic complex modulus at 10 Hz............................... 131

xiii

Figure 7-8: Resilient modulus versus dynamic complex modulus at 5 Hz................................. 132

Figure 7-9: Resilient modulus versus dynamic complex modulus at 1 Hz................................. 132

Figure 7-10: Resilient modulus versus dynamic modulus at various loading frequencies ......... 133

Figure 7-11: Relationship of linear multiplication factors with DMT loading frequency.......... 133

Figure A-1: Gradation chart for S1 to S3.................................................................................... 144

Figure A-2: Gradation chart for S4 and S5 ................................................................................. 144

Figure A-3: Gradation chart for S7 to S9.................................................................................... 145

Figure A-4: Gradation chart for S10 to S12................................................................................ 145

Figure A-5: Gradation chart for S14, S15, and S18.................................................................... 146

Figure A-6: Gradation chart for S16 and S17 ............................................................................. 146

Figure A-7: Gradation chart for S6 and S13 ............................................................................... 147

Figure A-8: Gradation chart for S19 and S20 ............................................................................. 147

Figure B-1: Creep compliance of F2 control and all polymer-modified levels at -10˚C. ........... 157

Figure B-2: Creep compliance of F4 control and all polymer-modified levels at -10˚C. ........... 158

Figure B-3: Creep compliance of F2 control and all polymer-modified levels at 5˚C. .............. 158

Figure B-4: Creep compliance of F4 control and all polymer-modified levels at 5˚C. .............. 158

Figure B-5: Creep compliance of F2 control and all polymer-modified levels at 25˚C. ............ 159




Figure B-9: Creep compliance of F2 control and modified gradation levels at -10˚C................ 160

Figure B-10: Creep compliance of F4 control and modified gradation levels at -10˚C.............. 160

Figure B-11: Creep compliance of F2 control and modified gradation levels at 5˚C................. 161

Figure B-12: Creep compliance of F4 control and modified gradation levels at 5˚C................. 161

Figure B-13: Creep compliance of F2 control and modified gradation levels at 25˚C............... 161

xiv




xv

ABSTRACT

Hot Mix Asphalt (HMA) is a viscoelastic material and has been broadly used in pavement

structures. It is important to understand the mechanism of complex behaviors of HMA mixtures

in field for improving pavement mechanical performance. Aggregate gradation and asphalt

binder are two key factors that influence the engineering properties of HMA. The asphalt binder

plays a significant role in elastic properties of HMA and it is the essential component that

determines HMA’s viscous behavior. Many research works suggest that the Styrene-Butadiene-

Styrene (SBS) polymer is a promising modifier to improve the asphalt binder, and hence benefit

the HMA viscoelastic properties. The specific beneficial characteristics and appropriate polymer

concentration need to be identified. In addition, aggregate gradation requirements have been well

defined in Superpave mix design criteria. However, a potentially sound coarse mixture with the

gradation curve passing below the coarse size limit may be disqualified from being used. There is

a need to evaluate the Superpave coarse aggregate gradation limits by studying mixtures

purposely designed exceeding the control limits. Moreover, the mechanical parameters adopted

by AASHTO to characterize HMA properties are shifting from indirect diametral tensile (IDT)

test to dynamic modulus test (DMT), because the DMT has the ability to simulate real traffic

conditions and to record more viscoelastic information of HMA. Thus, the DMT and the IDT test

for implementing the AASHTO Mechanistic-Empirical Design Guide (M-E PDG) are needed to

be discussed.

The primary objective of this research study was to evaluate the fracture mechanics

properties of HMA concrete and to study the correlation between the DMT and the IDT test for

Superpave mixtures. An experimental program was performed to evaluate the engineering

properties of the asphalt mixtures with various types of materials. The laboratory testing program

was developed by applying a viscoelastic fracture mechanics-based framework that appeared to

be capable of describing the comprehensive mechanical properties of HMA mixtures according

to past research studies. The goals for these experiments are to evaluate the effect of aggregate

type, the effect of coarse aggregate gradation adjustment to mix designs, and the effect of SBS

polymer modifier on fracture mechanics properties of HMA concrete.

To achieve the objectives and goals, a complete dynamic testing system was acquired to

perform the temperature controlled dynamic tests to determine the engineering properties for all

xvi

selected asphalt concrete mixtures. The laboratory experimental program for fracture mechanics

properties involved two standard asphalt mix designs as control levels: one granite mixture and

one limestone mixture. Each control mix design was modified to two different gradation levels

with the control asphalt binder (PG 67-22) and three SBS polymer content levels (3.0%, 4.5%,

and 6.0%) with the original aggregate gradation. The experimental program for dynamic complex

modulus test involved 20 Superpave asphalt concrete mixtures commonly used in Florida with a

range of aggregates and mix designs including the following types of aggregates: 14 Georgia

granite materials, one Nova Scotia granite, one North Florida limestone, two Central Florida

limestone materials, one South Florida oolite, and one Alabama limestone. One type of base

asphalt binder, PG 67-22, was used for all mixtures tested for dynamic modulus. The volumetric

properties of all the mixtures were verified to ensure that the specimens’ air voids are as close to

the optimum (4.0%) as possible. The DMT specimens were cored from the 150 mm diameter

Superpave samples. The 20 Superpave asphalt concrete mixtures were tested for both dynamic

complex modulus and indirect tensile resilient modulus.

The SHRP IDT test procedure was generally followed to perform the indirect diametral

tensile test. The measurement and analysis system developed for SHRP IDT was also applied.

Three types of IDT test, the resilient modulus test, the creep compliance test, and the tensile

strength test were performed to determine the fracture mechanics properties of asphalt concrete at

four temperature levels: -10, 5, 25, and 40°C (14, 41, 77, and 104°F). Data evaluation of the test

results indicated the following characteristics: 1) the increase of nominal maximum size

aggregate amount to the standard mix designs in this study had negligible or adverse effect on

HMA fracture mechanics properties. 2) The SBS polymer-modified asphalt binder improved the

fracture mechanics behavior of asphalt mixtures comprehensively. The resilient modulus values

of polymer-modified asphalt (PMA) mixtures decreases with an increase of SBS polymer content

throughout the concentration range tested at low temperatures. At the high testing temperature of

40˚C, an optimum SBS content appeared to exist around 4.5% which would make the HMA

stiffest, which suggested that limiting the concentration within an optimal range is especially

important at high service temperatures. The SBS polymer also helps the HMA obtain an

upgraded creep performance. The mixtures with SBS polymer modifiers are more compliant at

the low temperature level (-10˚C) and become less compliant at the high testing temperature

(40˚C), which should lead to improved resistance to rutting and thermal cracking of HMA

xvii

mixtures. At a specific temperature level, a higher SBS polymer concentration generally results

in higher creep compliance values. Furthermore, the SBS polymer modifier improves the asphalt

mixture fracture properties by increasing the fracture energy (FE) limit or dissipated creep strain

energy (DCSE) limit which were indicators of mixtures’ resistance to fatigue cracking. The

failure strain of PMA mixtures tends to increase with an increase of SBS polymer content at low

temperatures (-10˚C and 5˚C). 3) It was found that the limestone mixtures were more compliant

than granite mixtures at low temperatures and turned to be less compliant than granite at high

temperature (40˚C). Therefore limestone materials hold advantages over granite materials in

improving the performance of thermal cracking at low service temperature and the rutting

resistance at high service temperatures.

The dynamic complex modulus tests were conducted at three temperature levels: 5, 25, and

40°C (41, 77, and 104°F). For all temperatures tested, the following frequencies were used: 25,

10, 5, 1, and 0.5 Hz. The master curves for all 20 mixtures were developed and constructed using

the time-temperature superposition principle. The Witczak prediction model was adopted to

verify the relationship between predicted and measured dynamic modulus for all mixture series.

The comparison indicated that the Witczak prediction model worked well for the asphalt

concrete mixtures tested in this study. A comparative study was also made between the dynamic

modulus and resilient modulus test results. The linear regression analysis indicated that the total

resilient modulus increased with an increase in dynamic modulus at a specific loading frequency.

The resilient modulus values were comparable with the dynamic modulus values at the loading

frequency of 4 Hz.

1

CHAPTER 1

INTRODUCTION

1.1 Background

The Superpave asphalt mix design method has been increasingly accepted, and the

system has been implemented in Florida. The current Superpave mix design approach is

based on meeting certain asphalt binder, aggregate and volumetric properties such as the

asphalt binder performance grading (PG) specification, aggregate gradation control limits,

gradation restricted zone, asphalt mix air voids, voids in mineral aggregate (VMA), voids

filled with asphalt (VFA), etc. The Superpave mix design system has continuously been

under evaluation to search for further improvements.

Gradation is perhaps the most important property of an aggregate. It affects almost all

the important properties of hot mix asphalt (HMA) mixtures including stiffness, stability,

durability, permeability, workability, fatigue resistance, frictional resistance, and

resistance to moisture damage. Therefore, gradation is a primary consideration in asphalt

mix design, and the Superpave specifications place limits on the aggregate gradations that

can be used in HMA mixtures. The gradation of the aggregate is important to ensure that

1) the maximum aggregate size is not too large or too small, 2) VMA requirements are

met, and 3) a satisfactory aggregate skeleton is obtained. According to the Superpave, the

aggregate gradation must be within the control limits to meet the Superpave requirements.

For example, if a 19-mm (3/4-inch) maximum aggregate size is specified, then 100

percent of the aggregate must pass the 25-mm (1-inch) sieve size. At least 90-100 percent

of the aggregate must be finer than the nominal maximum size (19 mm). Less than 90%

of the aggregate must pass the 12.5-mm sieve. In order to meet the Superpave

requirements, a coarse graded aggregate will have to be “gap-graded” to be within the

nominal size control limits. However, a “smoother” coarse gradation passing below the

lower control limit of the nominal maximum sieve size may exist to provide as similar

results to the “gap-graded” curve. Research is needed to evaluate the nominal size control

limits for Superpave mix design and to study its effect on mechanical properties of HMA

mixes.

2

In addition, modified binders have been used in Superpave mixtures of many state

agencies in an effort to improve the mixtures. SBS (styrene-butadiene-styrene) polymer

has been used to modify the asphalt binders. Some laboratory and full-scale field tests

have been performed to evaluate the beneficial effects of adding the SBS polymer to

asphalt binders and modified asphalt mixtures. SBS polymer modifiers appear to provide

greater benefit to open graded mixtures than to dense graded mixtures. It has been

recommended that asphalt binder modified with 3% SBS polymer is an effective way of

treating the Superpave mixtures. However, modifiers with higher percentage of SBS

polymer have been successfully used in Europe. It appears that research is needed to

evaluate the beneficial effect of using higher dosages of SBS polymer. The fracture

mechanics concept/approach has been studied extensively and proposed by Roque et al.

(2002). The fracture energy-based approach was developed and verified by an analysis of

22 field test sections throughout the state of Florida and appeared to be capable of

describing the HMA structural characteristics related to pavement cracking performance

(Roque et al. 2004). The proposed experimental framework may be adopted to evaluate

the fracture mechanics properties of the HMA mixtures.

Recently, the new AASHTO Mechanistic-Empirical (M-E) Design Guide research

team advocated the use of the dynamic complex modulus (E*) as the primary test protocol

to characterize the modulus response of HMA mixtures. The research team supported the

role, selection, and utilization of the dynamic complex modulus test for asphalt concrete

mixtures over the indirect tensile resilient modulus (MR) in the National Cooperative

Highway Research Program (NCHRP) 1-37A Project concerning the AASHTO M-E

Design Guide for Pavement Structures, which is currently aiming to introduce more

rigorous measures of performance into HMA mixtures and pavement design procedures.

The use of the indirect tensile test was also encouraged as a means of determining the

relative moduli response of field cores taken for rehabilitation designs. However, the use

of the test to characterize modulus at high temperatures was not recommended.

The difference between a resilient modulus test and a dynamic complex modulus test

for HMA mixtures is that the former uses loading of any waveform with a given rest

period, while the latter applies a sinusoidal or haversine loading with no rest period. The

dynamic complex modulus is one of the many methods for describing the stress-strain

3

relationship of viscoelastic materials. The modulus is a complex quantity, of which the

real part represents the elastic stiffness and the imaginary part characterize the internal

damping of the materials. The absolute value of the complex modulus is commonly

referred to as the dynamic modulus. A detailed comparison of key differences between

the dynamic complex modulus test and the indirect diametral resilient modulus test for

asphalt concrete mixtures was summarized in a position paper by the NCHRP 1-37A

2002 Project research team (Witczak 1999). The transition from the resilient modulus test

to the use of the dynamic complex modulus test for design of flexible pavement structures

has hardly been smooth. The potential impact of adopting the dynamic complex modulus

for implementation of the new AASHTO M-E Design Guide is tremendous for state

transportation agencies, such as the Florida Department of Transportation (FDOT). The

IDT has traditionally been used to characterize the HMA mixtures for flexible pavement

design in Florida, and the test method has been shown to be both an expedient and a

reliable way of obtaining mixture properties from field cores. In response to the need, an

effort is desired to characterize the empirical relationship between dynamic complex

modulus and indirect resilient modulus of HMA mixtures.

1.2 Objectives

The primary objectives of this study were to evaluate the effects of coarse aggregate

gradation limits, aggregate type, and SBS polymer-modified asphalt binder on the

engineering properties of HMA mixtures. Specifically, the research goals were to evaluate

the gradation limits on nominal maximum sieve size specified in the Superpave mix

design guide, to evaluate the benefits of using SBS polymer modifier in HMA concrete

pavements, and to evaluate the effect of aggregate type on fracture mechanics properties

of asphalt mixtures.

Since the mechanical parameters adopted by AASHTO to characterize HMA

properties are shifting to dynamic complex modulus, the relationship between the

dynamic complex modulus test (DMT) and the indirect diametral tensile test (IDT) for

implementing the AASHTO Mechanistic-Empirical Design Guide for Pavement

Structures is also needed to be discussed.

4

To achieve these objectives, a series hot mix asphalt mix designs were selected for

testing. An experimental program was developed to measure the fracture mechanics

properties of all HMA specimens fabricated in the laboratory. The dynamic modulus test

was also performed on corresponding mixture specimens in order to develop a rational

comparison with the resilient modulus.

1.3 Dissertation Outline

This dissertation summarizes the study to evaluate the HMA gradation effect, to

study the SBS polymer-modified binder effect, and to develop a rational relationship

between dynamic complex modulus test (DMT) and indirect diametral test (IDT) for

implementing the AASHTO Mechanistic-Empirical Design Guide for Flexible Pavement

Structures. The dissertation is organized as the following structures:

Chapter 1 introduces the background, objective, and scope of the study.

Chapter 2 gives a comprehensive literature review of the aggregate gradation effect

and SBS polymer modifier effect on HMA. The fracture mechanics model developed by

Roque et al. (2004) is introduced to evaluate the engineering properties of asphalt

concrete. The complex modulus and resilient modulus for characterizing the hot mix

asphalt concrete mixtures are also summarized.

Chapter 3 introduces the materials and develops a whole experimental program.

Detailed testing methods and procedures are specified.

Chapter 4 presents the results from IDT sweep set of tests for the two control mixes,

four modified gradation mixes, and six mixes with SBS polymer-modified asphalt at

different concentrations (3%, 4.5%, and 6%).

Chapter 5 analyzes the IDT test results in detail to account for the gradation effect

and SBS polymer modifier effect on HMA mixtures.

Chapter 6 shows the results of dynamic modulus from DMT and resilient modulus

from IDT for 20 selected standard mix designs.

Chapter 7 discusses a comparison between DMT and IDT. The dynamic modulus

master curves for the selected mixes are constructed. The correlation between dynamic

modulus and resilient modulus results is developed.

5

Chapter 8 summarizes the whole dissertation. Concluding remarks are presented.

6

CHAPTER 2

LITERATURE REVIEW

2.1 Introduction

The purpose of this study is to evaluate the engineering properties of asphalt concrete

mixtures obtained from laboratory tests. Asphalt concrete pavement performance is

influenced by a great number of factors. HMA mixtures are essentially made up of

various kinds of aggregates in appropriate size combinations and different types of

asphalt binders. Our research work is focused on the material effects of aggregate

gradation and Styrene-butadiene-styrene (SBS) polymer-modified asphalt binders. There

are many lab test methods developed for measuring the mechanical properties of asphalt

concrete over the past twenty years. The most common ones are the indirect diametral

tensile (IDT) test and the dynamic modulus test (DMT). They were introduced in the

AASHTO flexible pavement design guide in 1993 and 2004 respectively. In this chapter

the following are to be discussed:

• To conduct a comprehensive literature review on publications related to aggregate

gradation effect and SBS polymer-modified asphalt binder effect on flexible

asphalt mixture characteristics.

• To introduce test methods and procedures, corresponding comparisons of testing

methodologies, and prediction models that have been used to evaluate mechanical

responses of asphalt concrete mixtures.

• To review the fracture mechanics and energy models that were developed and

used to evaluate cracking performance of HMA mixtures.

The following sections provide an explanation of the basic material mechanisms and

approaches used to evaluate the performance of asphalt pavement.

2.2 Asphalt Cement Properties

Asphalt cement is bituminous material that is either naturally occurring or produced

by distillation process from crude petroleum using different refining techniques. It is

7

widely used throughout the world in roadway paving applications. Asphalt cement is a

black, sticky and highly viscous material at ambient temperatures. It is also resistant to

the action of most acids, alkalis and salts. The largest use of asphalt cement is in the

production of Hot Mix Asphalt for construction of flexible pavements. By applying heat

to the asphalt cement, it can be liquefied for mixing with mineral aggregates; it adheres to

aggregate particles and binds them to form HMA. After cooling to ambient temperature,

with asphalt cement’s excellent adhesive and waterproofing characteristics, HMA

become a very strong and durable paving material which can sustain heavy traffic loads.

Three methods, based on penetration, viscosity and performance are used to classify

asphalt cements into different standard grades. The penetration grading of asphalt cement

is specified in ASTM D946 and is primarily controlled by the penetration test. The

viscosity grading is specified in ASTM D3381. It is based on either the viscosity of the

original asphalt cement or on the viscosity of the asphalt cement after aging in the rolling

thin film oven (RTFO) test. The performance-based method of classifying asphalt binders

was developed in the Strategic Highway Research Program (SHRP).

2.2.1 Chemical Properties of Additives and Polymer Modifiers

Asphalt modifiers have been used over 60 years. They are more commonly used in

Europe compared to the United States in the 20th century. A greatly increased effort has

been dedicated to the research and application of asphalt modifiers over the past 20 years

in the United States. The Superpave asphalt binder specifications based on SHRP require

the asphalt binders to meet stiffness criteria at both high and low pavement service

temperatures. However, most regular asphalt binders are not qualified for the

requirements in areas with extreme climate conditions. In the meantime, traffic volume

and loads have increased significantly in recent years. This has caused lots of premature

rutting and cracking of HMA pavement constructed with neat asphalt binders.

Modifications of asphalt binders become of considerable interest in the improvement of

pavement performance and service life. Although low initial cost discourages the use of

modifiers, some state highway agencies started to specify modified asphalt binders and to

be willing to pay a higher initial cost for pavements with a longer service life and reduced

8

risk of premature distress, and therefore, lower life cycle costs. Additionally, the disposal

of waste materials and industrial byproducts, such as tires, glass, sulfur, etc., used as

additives in HMA is economical and benefits the environment.

Some specific technical reasons for using additives and modifiers in HMA are listed

as follows (Roberts et al. 1996):

1. Obtaining stiffer mixtures at high service temperatures to minimize rutting.

2. Obtain softer mixtures at low service temperatures to minimize thermal cracking.

3. Improve fatigue resistance of HMA mixtures.

4. Improve asphalt-aggregate bonding to reduce stripping or moisture susceptibility.

5. Improve resistance to aging or oxidation; rejuvenate aged asphalt binders.

6. Permit thicker asphalt films on aggregate for increased mix durability.

7. Improve abrasion resistance of mixture to reduce raveling.

8. Reduce flushing or bleeding; reduce structural thickness of pavement layers.

9. Reduce life cycle costs and improve overall performance of HMA pavements.

Additives and modifiers can be classified in different ways. A generic classification

system was first suggested by Terrel and Walter (1986). A modified version of the system

(Table 2-1) and a discussion of each additive or modifier were given by Roberts et al.

(1996).

It can be seen in Table 2-1 that polymers are comprised of rubber, plastic and their

combination materials. Elastomers (rubber) and plastomers (plastic) are the two basic

categories. Elastomers resist deformation from applied stress with their high extensibility

and contractibility and rapidly recover upon removal of the load. The initial modulus is

usually low but they stiffen when stretched. Plastomers resist deformation by their tough

and rigid three-dimensional network. Earlier research showed that elastomers (rubbers)

increase asphalt binders’ tensile strength with elongations whereas little additional

strength is obtained from the rubbers by asphalt binders until they are stretched. On the

other hand, plastomers exhibit quick early strength on loading but may fracture under

strain (Hines 1993). Therefore, when elastomers are used for modifying asphalt cements,

HMA pavements generally get more flexible and resilient. In contrast, asphalt binders

modified with plastomers usually improve the stiffness moduli of HMA pavement.

9

Table 2-1: Generic classification of asphalt additives and modifiers (Roberts et al. 1996)

Type Generic Examples

1. Filler

� Mineral Filler: crusher fines lime Portland cement fly ash

� Carbon black

2.Extender � Sulfur � Lignin

Rubber: a. Natural latex b. Synthetic latex c. Block copolymer d. Reclaimed rubber

� Natural rubber � Styrene-butadiene or SBR � Polychloroprene latex � Styrene-butadiene-styrene (SBS),

Styrene-isoprene-styrene (SIS) � Crumb rubber modifier

Plastic

� Polyethylene/Polypropylene � Ethylene acrylate copolymer � Ethyl-vinyl-acetate (EVA) � Polyvinyl chloride (PVC) � Ethylene propylene or EPDM � Polyolefins

3. Polymers

Combination Blends of polymers above

4. Fiber

� Natural: asbestos rock wool

� Man-made: polypropylene polyester fiberglass mineral cellulose

5. Oxidant Manganese salts

6.Antioxidant � Lead compounds � Carbon � Calcium salts

7. Hydrocarbon � Recycling and rejuvenating oils � Hard and natural asphalts

8. Anti-stripping Agent

� Amines � Lime

9. Waste Materials � Roofing shingles � Recycled tires � Glass

10. Miscellaneous � Silicones � Deicing calcium chloride granules

A polymer molecule is produced by the reaction of many monomers, which are

smaller molecules, with one another in long chains or clusters. The term “poly” means

10

many as opposed to “mono”. Homopolymers are made up of only one kind of repeating

monomer in the polymer molecular chain. Copolymers are composed of the combination

of two or more different monomers in a random or block arrangement. The types of

polymers are listed below.

• Homopolymer: only one monomer is used along the chain.

• Random Copolymer: the repeating units are in random sequence.

• Alternating Copolymer: the two units repeat in an ordered manner.

• Block Copolymer: the chain consists of long sequence (blocks) of repeating units.

• Grafted Copolymer: branched copolymer in which the side chains are structurally

distinct from the main chain.

• Periodic copolymers: with A and B units arranged in a repeating sequence, e.g.

(− ABABBAAAABBB−)n

The physical properties of polymers vary remarkably depending on the sequence,

structure, and chemical process for the composing monomers (Usmani 1997). Polymers

can also be categorized into linear polymers, branched polymers, and cross-linked

polymers as shown in Figure 2-1 according to their structures.

Polymers may also be classified as thermosets and thermoplastics. Thermosets are

usually rigid and tightly cross-linked. When mixed with asphalt at high temperatures, the

thermoset’s particles may swell to more than twice the original volume as a result of

chemical interaction which leads to a remarkable increase in mixture viscosity.

Thermoplastic elastomers are commonly applied in the modification of asphalt binders.

They are usually linear or branched in types of block copolymer (SB)nX, where ‘S’

11

denotes the styrene block, ‘B’ denotes the butadiene block, and ‘X’ denotes the coupling

agent, as shown in Figure 2-2. It was found that a separation takes place between

butadiene (soft block) and the styrene (hard block) because they are mutually

incompatible; as a result, the styrene remains dispersed in a continuous elastomeric

matrix (Diani et al. 1997).

Linear

Branched

Cross - Linked

Figure 2-1: Polymer classifications based on link structure

Figure 2-2: SBS polymer modifier structure

As listed in Table 2-1, Elastomers or rubbers used as asphalt modifiers include

natural rubber, styrene-butadiene latexes (SBR), polychloroprene latex, styrene-

butadiene-styrene block polymers (SBS), styrene-isoprene-styrene block polymers (SIS),

and crumb rubber modifiers (ground tires). SBS block copolymers are usually in the solid

forms of pellets, crumbs, or ground material in bags or bulk. The common concentration

level is about 3 to 5 percent by weight of asphalt cement in the HMA industry. High shear

12

mixing equipment is used for blending the SBS modifier with hot asphalt cement

maintained at 350-380˚F (177-193˚C). Since the asphalt binder must be within specified

viscosity ranges for workability purposes during mixing and compaction, it is probably

necessary to increase the mixing and compaction temperatures while conducting

laboratory work and testing.

Polymer modifiers have complex characteristics and their effects on asphalt binders

depend on quite a few factors such as polymer concentration, molecular weight, chemical

composition, and molecular structure. Other important things include the source of

original asphalt binder, production process, binder grade, reaction between binder and

modifier, etc. Special properties can be obtained through various combinations of

elastomers and plastomers to meet desired requirements. However, it should be noted that

it is very difficult to predict whether a particular combination will be able to provide

improvements in the desired property. Sometimes polymer properties may get diluted or

even changed when blended with asphalt binders. The structures of the pure polymer-

modified binder generally are different from those of the PMB in the asphalt mixture.

Therefore, it is necessary to test the polymer-modified asphalt binder; or in more practical

situations, it would be more advisable to evaluate the performance of actual HMA

produced with modified asphalt binder (Wegon and Brule 1999). It is hoped that polymer

modifiers can be used in Superpave mix design and evaluation procedures to obtain a

stiffer HMA at high service temperatures to minimize rutting, a more elastic HMA to

resist fatigue cracking at intermediate temperatures, and a softer HMA at low service

temperatures to resist thermal cracking.

Chen et al. (2002, 2003) investigated the morphology of the SBS modified binders

described by the concentration and the presence of the microstructure of the copolymer.

As the polymer content increases, the dispersed polymer particles gradually swell to form

local SBS networks which highly enhance the mechanical properties of the asphalt binder

(viscosity, softening point, toughness and complex modulus, etc). A continuous polymer

structure was observed to begin at an SBS content between about 5% and 6%, yet the

minimum percentage depends more on the base asphalt and the polymer itself. The

optimum SBS content is based on the formation of the critical network between asphalt

and polymer, which appeared to be slightly higher than the phase inversion content that

13

occurs when the SBS entered the continuous matrix phase. However, once the critical

networks begin to form, increases in polymer content have less significant effect on PMA

property improvement (Figure 2-3), or may even lead to the separation of polymer and

bitumen. Recent work by Chen and Huang (2007) showed that the SBS-asphalt blended

with sulfur resulted in improved rheological characteristics.

Brule et al. (1988) studied the relationship between the composition, structure, and

properties of asphalt binders incorporated with SBS block copolymers. It was found that

increasing the agitation time made the microstructure finer, which led to a greater

deformability. They also found that the amount of polymer required for matrix inversion

and for obtaining highly modified practical properties depended significantly on the

asphalt itself. However, the value of this inversion threshold was not predictable. The

extent of swelling in asphalt-SBS blends was not highly dependent on content for high

polymer concentrations, but increased substantially as the amount of polymer decreased;

it also appeared to be independent of temperature in the high-level range (80-160˚C). In

addition, the SBS polymer was no longer swollen in the binder but dissolved beyond a

colloidal instability index value.

Frequency (Hz) Figure 2-3: Complex modulus of SBS-modified asphalt at 60°C (Chen et al. 2002)

Lu et al. (1998) reported that SBS polymer modification improves the low-

temperature properties of bitumens. The polymer modification reduces the creep stiffness

14

and limiting stiffness temperature of bitumens. The changes generally increase with SBS

content and are influenced slightly by SBS structure.

Many studies (Huffman 1980; Lalwani et al. 1982; Scofield 1989) have reported that

the polymer-modified asphalt can lower temperature susceptibility, which is the primary

drawback of regular asphalt, reduce binder penetration, increase the viscosity and

softening point, and improve resistance to aging and oxidation. These effects should lead

to increased resistance to deformation (rutting) and thermal cracking in practice. King et

al. (1986) documented a correlation between styrene-butadiene elastomer-modified

asphalt and pavement durability. The addition of polymer improves stiffness, rutting

resistance, fatigue life, adhesion and stripping resistance to the bituminous mix.

Carpenter et al. (1987) conducted a series of lab tests on asphalt mixtures including

the diametral resilient modulus test, indirect tensile test at temperatures ranging from

72˚F to -20˚F (22.2˚C to -28.9˚C), and permanent deformation testing at 72˚F (22.2˚C)

and 100˚F (37.8˚C). The testing indicated that the polymer additives reduced stiffness at

low temperatures yet maintained adequate stiffness at elevated temperatures. The low-

temperature performance was greatly improved over that of untreated asphalt cements of

all grades, whereas the permanent deformation characteristics were greatly improved at

elevated temperatures. Carpenter et al. (2006) conducted further tests and showed that the

healing/recovery rate of the polymer-modified binders is significantly greater than the

neat binder. Button (1992) drew a summary of asphalt additive performance which

indicated positive influences by polymer addition in bitumens.

Collins et al. (1991) studied the performance of paving asphalt modified by SB

polymers. The modification resulted in a substantial improvement of fatigue life by

reducing flexural fatigue cracking and a dramatic increase of strength and resistance to

creep at high temperatures. They also found that the actual critical cracking temperature

was significantly lower than that of the base asphalt and decreased with increasing

polymer content (Figure 2-4). The poly-butadiene chains in polymer contribute to the

flexibility of the binder and the elastomeric lattice between asphalt molecules and SBS

polymer improves the elastic characteristics of the binder without increasing the stiffness

binders at low service temperatures. Similar findings were reported by many other

researchers. Verhaeghe et al. (1994) conducted studies on asphalt binder modified with

15

Ethylene Vinyl Acetate (EVA) which improves the compressive strength and rutting

resistance of asphalt mixes. Pradhan (1993) reported that the addition of commercial SBR

modifiers improves the physical properties related to rutting problems on Montana

asphalt pavements. Testing programs conducted by Kennedy et al. (1992) showed that

SBS and SBR polymers generally increase the mixture’s tensile strength at high

temperatures and tensile strain at failure at low temperatures. The permanent deformation

resistance was also improved, indicated by indirect creep testing.

King et al. (1993) studied a type of standard mixture containing four control

bitumens with styrene-butadiene polymer of three different contents (x%, 1.5x% and

2x%). They found that the softer the base asphalt, the lower the cracking temperature; and

that increasing the polymer content generally lowered the cracking temperature. Shih

(1996) conducted testing studies to compare the effects of different additives on typical

Florida asphalt mixtures. Test results showed that the addition of modifiers generally

benefits the rutting resistance of pavement and the SBR-modified asphalt mixtures have

lower resilient moduli at low temperatures; thus, the addition of modifiers would be

beneficial to the resistance of thermal cracking.

Figure 2-4: Relationship between the observed critical cracking temperature (Tcr) and SBS polymer concentration (Collins et al. 1991)

16

Aglan (1997) analyzed the fatigue tests and electron microscopic scans on polymer

modification for asphalt mixtures. The binder-rich areas were observed to contain ridges

produced by the micro-stretching of the SBS modified binder on the fracture surface, and

the mixture test results showed a superior resistance to fracture.

Jones et al. (1998) performed Superpave IDT creep and strength tests on five

different modified mixtures. Higher tensile strength was observed at intermediate

temperatures, yet it appeared that there was no noticeable difference at low temperatures

(around and below 0˚C). Khattak and Baladi (1998, 2001) evaluated the effects of SBS

polymer-modified binder on mechanical properties of mixtures. The measurement results

showed increased fatigue life and tensile strength at intermediate temperature whereas

low temperature elastic properties were almost the same. They also found that the fatigue

life and permanent deformation were strongly related to the rheological properties of

polymer-modified binders. Kim et al. (2003) investigated the use of SBS modifier in

asphalt pavement mixtures through lab testing for cracking resistance and healing

characteristics. Although the SBS does not show an influence on healing of the asphalt

mixture, it appears to reduce the rate of micro-damage accumulation which justified the

benefits of SBS modification on creep and failure properties of the mixtures. More

recently, Quintus et al. (2007) conducted an investigation of a large amount of real-world

pavement sections to quantify the benefits of using PMA mixtures. It was found that the

PMA significantly enhanced the rutting performance of asphalt pavement (Figure 2-5)

and its fatigue and fracture performance.

2.2.2 Mechanical Properties of Asphalt Cement

The Strategic Highway Research Program (SHRP) was launched in 1987. The

program made a research effort to develop performance-based tests and specifications for

asphalt binders and HMA mixtures. The Superpave (Superior Performing Asphalt

Pavements) binder tests and specifications have a few prominent features (McGennis et

al. 1994; Warren et al. 1994; Asphalt Institute 1994) compared with the old physical

testing system for asphalt cement.

17

Figure 2-5: Comparison of the rut depths measured on sections with PMA and the companion sections without PMA mixtures (Quintus et al. 2007)

The rolling thin film oven (RTFO) test is specified in AASHTO T240 and ASTM

D2872. The RTFO simulates the asphalt binder aging during the manufacture and

construction of HMA pavements. It continually exposes fresh binder to heat and air flow

during rolling. This test mode does not allow any asphalt surface skin to be formed, this

inhibits aging. And modifiers, if used in asphalt cement, usually remain dispersed due to

rolling action, which makes the modified binder age more sufficiently. The RTFO test

determines the mass of volatiles lost from the binder, which indicates the amount of aging

that occurs during HMA production and construction. However, some asphalt binders

gain weight during the RTFO aging due to the oxidative products formed during the test.

The Dynamic Shear Rheometer (DSR) Test is used to characterize the viscous and elastic

behavior of asphalt binders at high and intermediate service temperatures. The DSR

measures the complex shear modulus G* and phase angle � of asphalt binders at the

desired temperature and loading frequency. Complex modulus G* can be considered as

the total resistance of the binder to deformation at repeated shear load. Complex modulus

G* consists of two components as shown in Figure 2-6: (a) elastic modulus G’, also

known as the storage or recoverable part; (b) loss modulus G”, also known as the viscous

or non-recoverable part (McGennis et al. 1994).

The values of G* and � for asphalt binders are affected by both service temperature

and loading frequency. Most asphalt binders are viscoelastic at usual pavement service

18

temperatures. They behave like elastic solids as well as viscous fluids simultaneously.

The magnitude G* and phase angle � define a complete picture of the behavior of asphalt

binders in certain conditions, as shown in Figure 2-7. The elastic component or storage

modulus is related to the amount of energy stored in the sample during each testing cycle.

The viscous component or loss modulus is related to the energy lost during each testing

cycle through permanent flow or deformation (ASTM 1994).

��

��

�

Figure 2-6: Components of complex modulus G

*

Vis

co

us B

eh

avio

r

Elastic Behavior

1δ2δ

*

1G

*

2G

Figure 2-7: Viscous and elastic behavior of asphalt binders

The DSR test procedure is given in AASHTO TP5. The asphalt cement sample is

sandwiched between a fixed plate and an oscillating plate or spindle as shown in Figure

2-8. Two types of oscillatory shear rheometer are usually used: constant stress and

constant strain. Constant stress rheometers use a fixed torque to oscillate the top spindle

and the strain will vary. Constant strain rheometers move the spindle with a fixed

distance (e.g., from point A to B) and measure the torque resulting from this movement.

All Superpave DSR tests are conducted in constant stress mode which uses a fixed torque

to oscillate the top plate at a frequency of 10 radians per second (about 1.59 Hz). When

torque is applied to the oscillating plate, it starts at point A and moves to point B, and

then the spindle moves back and goes to point C passing point A. From point C it returns

back to point A. This movement comprises one cycle of oscillation. When the spindle is

oscillated back and forth with constant stress, the resulting strain is monitored.

19

Oscillating Plate

Asphalt

Fixed Plate

Applied Stress or Strain

B CA

Figure 2-8: Dynamic shear rheometer

δmaxγ

maxτ

Time

Time

Applied

Shear

Stress

Resulting

Shear

Strain

LagTime

G

=

=

δ

γ

τ

max

max*

Figure 2-9: Stress-strain response of viscoelastic material

The relationship between the applied stress and the resulting strain is used to

compute complex modulus G* and phase angle �, which is the time lag between the

applied stress and resulting strain. Theoretically, the phase angle � is zero for a perfect

elastic material because the strain response is instant. For an ideal viscous fluid, the time

lag is 90 degrees. In reality, asphalt binders behave like viscoelastic materials with a

20

stress-strain response between the two extreme conditions at certain service temperatures

as shown in Figure 2-9, in which the resulting phase angle is between 0 and 90 degrees.

G* is the ratio of maximum shear stress (�max) to maximum shear strain (�max), which

are calculated by the following formulas:

max

max*

γ

τ=G (2-1)

3max

2

r

T

πτ = (2-2)

h

r⋅=

θγ max (2-3)

Where,

T = maximum applied torque,

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

� = deflection (rotation) angle,

h = specimen height (either 1 or 2 mm).

The SHRP researchers considered rutting to be a stress-controlled, cyclic loading

phenomenon. Work is being done to deform the HMA pavement surface with each traffic

loading cycle. A part of this work is recoverable in elastic rebound mode while some is

dissipated in the form of permanent deformation and heat energy. The amount of

dissipated work must be minimized in order to minimize rutting. The work dissipated per

loading cycle at a constant stress can be expressed as follows (Bahia and Anderson 1995):

��

��

�×=

δσπ

sin/

1*

2

0G

Wc (2-4)

Where,

Wc = work dissipated per load cycle,

�0 = stress applied during the load cycle,

G* = complex modulus,

� = phase angle.

The work dissipated per loading cycle is inversely proportional to G*/�, as indicated

from the equation. A high complex modulus G* value and low phase angle � are both

desirable for rutting resistance. This relationship appears logical because the asphalt

21

binder will be stiffer with higher G* value; the lower the � value, the more elastic the

asphalt binder will be, and thus the more resistant to rutting and permanent deformation.

Therefore, the G*/� parameter was chosen as a Superpave asphalt binder specification.

Fatigue cracking is typically considered a strain-controlled phenomenon in thin HMA

pavement layers and a stress-controlled phenomenon in thick ones. The SHRP

researchers assumed that fatigue cracking should be considered mainly a strain-controlled

phenomenon since it is known to be more prevalent in thin pavement layers (Bahia and

Anderson 1995). The work dissipated per loading cycle at a constant strain can be

expressed as follows:

[ ]δεπ sin*2

0 ××= GWc (2-5)

Where �0 is the strain and other variables are as described previously. The equation

indicates that the dissipated work will increase as G* and/or � are increased. As G*

decreases, the asphalt binder becomes less stiff and thus able to deform without building

up large stresses which might cause cracking. In addition, low � values indicate more

elastic asphalt binders which can regain their original condition without dissipating work.

Therefore, G*�� was chosen in Superpave specifications to limit the total amount of

energy dissipated for minimizing fatigue cracking.

The Superpave asphalt binder specification is given in AASHTO MP1-93. It is meant

to be performance-based and thus addresses three primary performance parameters of

HMA pavements: permanent deformation (rutting), fatigue cracking, and low temperature

(thermal) cracking. Other common specification criteria include safety, pumping and

handling, excessive aging, etc.

2.3 Hot Mix Asphalt (HMA) Mixture Design

2.3.1 Physical Properties of Aggregates

Aggregates for HMA are usually classified by size as coarse aggregates, fine

aggregates, and mineral fillers. ASTM defines coarse aggregate as particles retained on a

No. 4 (4.75 mm) sieve, fine aggregate as that passing a No. 4 sieve (4.75 mm), and

mineral filler as material with at least 70 percent passing the No. 200 (75 µm) sieve.

22

Some agencies use another sieve size as the dividing line between coarse and fine

aggregates. For example, the Asphalt Institute uses the No. 8 (2.36 mm) sieve as the

dividing line.

Specifications for coarse aggregates, fine aggregates, and mineral fillers are given in

ASTM D692, D1073 and D242, respectively. Aggregates for HMA are generally required

to be strong, sound, and properly graded; to have a clean surface without deleterious

materials; to consist of angular particles with low porosity and appropriate absorption for

asphalt cement.

The specific gravity of an aggregate is a basic parameter for HMA mix design. It is

used to make weight-volume conversions and to calculate the void content in a

compacted HMA. The specific gravity is defined as the ratio of the weight of a unit of

volume of the material to the weight of an equal volume of water at approximately 23˚C

(73.4˚F). Two different aggregate specific gravities are often used for HMA based on the

method used to define the volume of the aggregate particles: (a) bulk specific gravity; and

(b) effective specific gravity.

When the sample aggregates consist of separate aggregate fractions of coarse

aggregate, fine aggregate and mineral filler, the bulk specific gravity of total aggregate

can be calculated from the following equation:

n

n

n

sb

G

P

G

P

G

P

PPPG

+++

+++=

�

�

2

2

1

1

21 (2-6)

Where,

Gsb = bulk specific gravity for the total aggregates,

Pi = individual percentages by mass of aggregate, i = 1, 2, …, n;

Gi = individual bulk specific gravity of aggregate, i = 1, 2, …, n.

The effective specific gravity of aggregate, Gse includes all void spaces in the aggregate

particles excluding voids permeable to asphalt. It is determined by the following

equation:

b

b

mm

mm

bmm

se

G

P

G

P

PPG

−

−= (2-7)

23

Where,

Gse = effective specific gravity of the aggregate,

Gmm = maximum specific gravity of the mixture,

Pmm = percent by mass of total loose mixture = 100,

Pb = asphalt content,

Gb = specific gravity of asphalt cement.

2.3.2 Aggregate Gradation

Aggregate gradation is the distribution of particle sizes expressed as a percent of the

total weight. It is one of the most important properties of an aggregate. The gradation of

an aggregate is normally expressed as total percent passing various sieve sizes. It affects

the HMA performance in many respects including stiffness, durability, stability,

permeability, workability, resistance to rutting and fatigue cracking, and frictional

resistance. Therefore, gradation is a critical consideration in asphalt mix design.

Aggregate gradations are described as dense (well-graded), open (uniformly-graded), and

gap-graded, as shown in Figure 2-10. Most states place limits on the aggregate gradations

for HMA. Fuller and Thompson (1907) proposed one of the best known gradations for

maximum density. The equation for Fuller’s maximum density curve is:

nDdP )/(100 ⋅= (2-8)

Where d is the diameter of the sieve size in question, P is the total percent passing or finer

than the sieve, and D is the maximum size of the aggregate. Studies by Fuller and

Thompson showed that a maximum density can be obtained for an aggregate when n=0.5.

In the early 1960s, the Federal Highway Administration introduced an aggregate grading

chart which is based on the Fuller gradation but uses a 0.45 exponent in the equation. The

maximum density lines can be conveniently obtained by drawing a straight line from the

origin at the lower left corner of the chart to the actual percentage point of the nominal

maximum size, which was defined in the specification as the largest sieve size retaining

any material. The maximum aggregate size is normally limited to about one-half of the

lift thickness in construction. The use of large stone mixes has been increased in recent

years in order to minimize rutting. However, large maximum aggregate size (e.g. greater

24

than 1 inch, or 25.4 mm) usually results in segregation during placement of HMA.

Special attention is required when these large stone mixes are used.

#

20

0

#1

00

#

50

#

30

#

16

#

8

#

4

3

/8"

1

/2"

3

/4"

1

"

0

10

20

30

40

50

60

70

80

90

100

Sieve Sieze (No.)

Tota

l P

erc

ent

Passin

g Gap -graded

Well-graded or

Dense-graded

Uniformly or

Open-graded

Figure 2-10: Typical aggregate gradations.

Some guidance for developing gradation limits and potential problem areas were

proposed by Hveem in 1940. Theoretically, the gradation that gives the densest packing

provides enhanced stability and reduces void space in the mineral aggregate through

increased interlocking between mixture particles. However, gradations of maximum

density may not provide enough voids in the aggregate. There must be sufficient air void

space in HMA to permit enough asphalt cement to be incorporated to provide adequate

film thickness for maximum durability. In addition, appropriate HMA air voids content

must be ensured in the mixture to avoid bleeding or rutting. Therefore, deviations from

the maximum density curves are necessary in order to increase the total voids in the

mineral aggregate (VMA). VMA is an important parameter and minimum values of VMA

are required and suggested by most pavement agencies depending on the maximum

25

nominal aggregate size of the mixture design. It is preferred that the gradation curve be

approximately parallel to the maximum density line with a few percentage points offset,

either above or below the line. Most specifications for HMA define aggregate gradation

band and tolerance for each nominal maximum size mixture according to accumulated

field experiences. In particular, the Superpave mix design developed by the Strategic

Highway Research Program (SHRP) requires a selected number of control points on the

gradation chart. The Superpave mix design system uses the following aggregate size

definitions:

• Maximum size: one sieve size larger than the nominal maximum size.

• Nominal maximum size: one sieve size larger than the first sieve to retain more

than 10 percent.

The maximum density line is obtained in Superpave by connecting the origin at the

lower left of the 0.45 power gradation chart to the maximum aggregate size at the upper

right of the chart (FHWA 1995).

Birgisson and Ruth (2001) developed a power law model to evaluate and classify

gradation curves according to mixture performance. Ruth et al. (2002) expanded the

parametric study and provided an experience-based methodology which introduced

aggregate gradation factors based on regression analysis of power law constants (aca and

afa) and exponents (nca and nfa). These gradation factors were used to evaluate

relationships with tensile strength, fracture energy, and failure strain of the mixtures. The

findings appeared to imply that the gradation characterization factors relate well to

mixture properties. Birgisson et al. (2004) and Ekingen (2004) established a correlation

between dynamic modulus and aggregate gradation factors at high temperature (40˚C)

based on the power law model. The relationship between a low nfa and a high dynamic

modulus at 40˚C has been identified, which indicates that power law parameters can be

used to optimize mixture gradations for the dynamic modulus and the rate of change in

the gradation on the fine side affects the stiffness and rutting resistance of the mixture. In

addition, it was also found that a high nca results in a low dynamic modulus when

controlling for nfa. More recently, Roque et al. (2006) developed a conceptual and

theoretical approach to evaluate the relationship between coarse aggregate structure based

on gradation and the pavement rutting performance. They found that the relative

26

proportion of particles from two contiguous size ranges can be no greater than 70/30 and

the porosity must be no more than 50% in order to form an interactive network.

2.3.3 HMA Mix Design

Most HMA produced before 1990s in the United States was designed using the

Marshall or Hveem method. The Superpave mix design procedures were developed by

the Strategic Highway Research Program (SHRP) and were adopted by a few states for

some pavement projects starting in 1995. The key points for all three design methods are

the same: to determine an appropriate asphalt content with which to begin field

construction.

The concept of the aggregate maximum density line for the densest packing of HMA

was first validated by Nijboer (1948). Goode and Lufsey (1962) then proposed that

aggregates should be graded using a mathematical concept of packing the void space

between aggregates of large diameter with aggregates of smaller diameter. They noted

that if the gradation corresponding to the exponent of 0.5 is used as proposed by Fuller in

1907, then the VMA may be too low to ensure both sufficient air void content and enough

asphalt cement for durability and stability. Therefore, the FHWA included the suggested

use of the 0.45 power curve as well as the maximum density line to evaluate and adjust

aggregate gradations. Huber and Shuler (1992) presented the relationship of VMA to

aggregate gradation and particle characteristics for a controlled experiment. They

investigated different methods of drawing maximum density lines that produces the

densest packing.

Hveem first noticed that there was a relationship between the gradation of the

mineral aggregate and the amount of oil required to maintain a consistent color and

appearance of the mixture. Then he realized that having the proper oil content did not

guarantee good performance relative to rutting. This led to the development of Hveem

stabilometer test to evaluate the ability of HMA mixtures to resist the shear forces applied

by traffic loads. The basis for selecting the optimum asphalt content in the Hveem method

is to use a well-graded aggregate with high friction and appropriate amount of fines and

add as much asphalt cement as the mixture will tolerate without losing stability. A

27

detailed account of the evolution of the Hveem mixture design method was given by

Vallerga and Lovering (1985). Details of specimen preparation and testing by Hveem

apparatus are given in ASTM D1561 and D1560, respectively.

A detailed introduction of the Marshall mix design method is given by a few

researchers (Foster 1982; White 1985). The acceptance tests on the aggregates and

asphalt cement are conducted at the beginning. If the materials pass these tests, the test

procedure for the Marshall method can be performed (The Asphalt Institute 1993). The

test protocol calls for fabricating 18 test specimens for the volumetric analysis. Three

loose mixture specimens are made near the optimum asphalt content to measure Rice

specific gravity or theoretical maximum density (TMD). Three compacted specimens

each are prepared at five different asphalt contents with 0.5 percent increments with at

least two above the estimated optimum asphalt content and two below the estimated

optimum. The approximate optimum asphalt content can be based on experience or

specific guide.

The amount of compaction is selected based on traffic level. The test specimens are

compacted using a Marshall hammer with 35, 50 or 75 blows per side for light, medium

or heavy traffic, respectively. The bulk specific gravity is then measured for each

specimen after proper handling. The Rice Specific Gravity (Gmm) is calculated for each of

the asphalt content mixes using the equation (relationship between Gmm, Gse and Pb).

Other volumetric parameters, including air voids (VTM), VMA, and VFA, are also

calculated using the related equations presented earlier. The compaction procedure will

produce specimens with decreasing air voids as a function of increasing asphalt binder

content. The compacted specimens are usually 4 inches (100 mm) in diameter and 2.5

inches (63.5 mm) in height.

These specimens are then used for conducting the Marshall stability and flow test.

The test is performed at 140˚F (60˚C), which is considered a critical temperature for

permanent deformation. A load at 2 inches/minute (50.8 mm/min) is applied to the

specimen until the maximum load is reached. The stability is the maximum load in

pounds (Newtons) and the flow is the deformation in 0.01 inch (0.25 mm). The stability

generally increases with increasing asphalt content, reaches a peak, and then decreases.

The asphalt content at the peak stability value is a good indicator of optimum binder

28

content based on the idea that constant compaction effort across varying asphalt content

produces a maximum stability value near the optimum asphalt content. In addition, the

percent VMA will decrease with increasing asphalt content, reach a minimum, and then

increase. Since the mixture strength increases as the VMA decreases, the mix with

minimum VMA should have the maximum strength or stability at the optimum asphalt

content. Finally the optimum asphalt content is determined by averaging the three asphalt

contents at maximum stability, maximum density and midpoint of the specified air voids

range (typically 4 percent). All parameters are checked at this optimum binder content for

acceptability according to the Marshall mix design criteria.

2.3.3.1 Bailey Method

The Marshall mix design method was broadly used in the United States before the

1980s. It provides some guidance on the use of coarse and fine mixes. However,

numerous trial and error process still have to be conducted to obtain a proper aggregate

blend. The Bailey method gives a good starting point for mix design when adjustments

are required to improve the volumetric properties of the mix (Vavrik et al. 2001; Asphalt

Institute and the Heritage Group 2005). The detailed methodology is summarized herein.

The Bailey mix design method was originally developed by Robert. D. Bailey in the

early 1980s. The primary purpose of this methodology is to control the mix properties

during construction including volumetric properties, segregation, workability, and

compatibility by focusing on aggregate packing. There are four key principles in the

Bailey method:

1. Determine the coarse and fine aggregate. The coarse fraction creates voids and the

fine fraction fills in the voids.

2. Analysis of coarse fraction which influences the packing of fine fraction.

3. Analysis of coarse part of the fine fraction, which relates to the packing of the

overall fine fraction in the blend.

4. Analysis of fine part of the fine fraction, which relates to the packing of the fine

portion of the gradation in the blend.

29

Figure 2-11 shows the four principles on a typical gradation curve for a coarse

gradation mix. The Bailey method defines the break between coarse and fine fractions as

the Primary Control Sieve (PCS). The PCS is the closest sieve to the result of

0.22×NMPS, where the NMPS denotes the Nominal Maximum Particle Size, which is

equivalent to the Nominal Maximum Aggregate Size (NMAS) used in the Superpave

system. The Bailey method uses AASHTO T19 to determine the Loose Unit Weight

(LUW) and the Rodded Unit Weight (RUW) of each individual aggregate used in the

mix. The suggested Chosen Unit Weight ranges for each mix type are shown in Table 2-

2. It should be noted that Stone Mastic Asphalt (SMA) references the RUW condition of

coarse aggregate, while coarse-graded and fine-graded mixtures reference the LUW

condition. The combined blend evaluation for coarse-graded and fine-graded mixes is

shown in Figure 2-12 and Figure 2-13, respectively. SCS and TCS denote Secondary

Control Sieve and Tertiary Control Sieve, respectively.

100

90

80

70

60

50

40

30

20

10

0

Sieve Size (mm) Raised to 0.45 Power

% P

assin

g

Fine Fraction Coarse Fraction

K J I H G F E D C B A

Coarse-Graded

4

3

1

2

Figure 2-11: The four principles of Bailey method for coarse-graded mix

30

Table 2-2: Chosen unit weight ranges by mix type

Fine-Graded Coarse-Graded SMA

90% or less LUW 95% − 105%

LUW 110% − 125%

RUW

Figure 2-12: Combined blend evaluation for coarse-graded mixes.

��

��

��

��

��

��

��

��

��

��

� �� !"#

$ �� %��

& �� %��

' �� %��

(�)��

(�)��

(�)��

��

��

Figure 2-13: Combined blend evaluation for fine-graded mixes.

The Coarse Aggregate ratio (CA), Coarse part of Fine Aggregate ratio (FAc), and

Fine part of Fine Aggregate ratio (FAf) can be calculated by the following equations:

31

sievehalfpassing

PCSpassingsievehalfpassingRatioCA

%100

%%

−

−= (2-9)

PCSpassing

SCSpassingRatioFAc

%

%= (2-10)

SCSpassing

TCSpassingRatioFA f

%

%= (2-11)

Table 2-3 shows the recommended values of the different ratios for coarse and fine

mixes. The Bailey mix design method provides a useful and practical approach for

evaluating volumetric properties and compactability and thus helps in better

understanding the aggregate structure in asphalt mixtures as well as quality control at the

plant or in the field.

Table 2-3: Recommended aggregate ratios

NMPS (mm) 37.5 25.0 19.0 12.5 9.5 4.75

Coarse 0.80−0.95 0.70−0.85 0.60−0.75 0.50−0.65 0.40−0.55 0.30−0.45 CA Ratio

Fine 0.6 − 1.0

Coarse 0.35 − 0.50 FAc Ratio

Fine 0.35 − 0.50

Coarse 0.35 − 0.50 FAf Ratio

Fine 0.35 − 0.50

2.3.3.2 Superpave Mix Design

Since the early 1980s, traffic volume and axle loads have been increasing remarkably

in the United States. There emerged a need to develop an improved mix design method

that could be used in various traffic conditions and environments. With this as a primary

goal, the Strategic Highway Research Program (SHRP) was initiated in 1988 and

completed in 1993 resulting in the Superior Performing Asphalt Pavement (Superpave)

System. The Superpave system consists of the following components: new grading

system for asphalt binder (performance graded (PG) grading system), consensus

32

properties of aggregate, new mix design procedure, and mixture analysis procedures

(FHWA 1995; Asphalt Institute 1995; TRB 1994).

The aggregate properties that are specified by the SHRP are the coarse and fine

aggregate angularity, flat and elongated particles, and sand equivalent results. The

angularity of aggregate is related to the shear strength of the HMA mix and thus

influences the rutting performance of HMA pavement. The coarse aggregate angularity is

determined by measuring the percentage of coarse aggregate particles with fractured

faces, whereas the angularity for fine aggregate is measured by determining the amount of

voids by the National Aggregate Association (NAA) flow test in accordance with

AASHTO TP33 Method A. Flat or elongated particles tend to lie flat or even break down

during compaction, which may affect the workability of the mixtures. In addition, flat or

broken aggregates will make the mixture VMA lower than designed or expected. The test

procedure for flat or elongated particles is specified in ASTM D4791, “Flat or Elongated

Particles in Coarse Aggregate”. The clay content is related to the stripping problem of the

mixture. Excessive amounts of clay may result in a poor bond between the asphalt binder

and aggregate. The clay content is measured by the sand equivalent test conducted in

accordance with AASHTO T176 or ASTM D2419.

Aggregate blend is one of the most important factors to consider in HMA mix design

to ensure that a satisfactory gradation skeleton is obtained and volumetric requirements

are met. According to the definition given by Superpave, at least 90 − 100 percent of the

aggregate must be finer than the nominal maximum aggregate size. Control points are

also set on the 2.36 mm (No. 8) and the 0.075 mm (No.200) sieve sizes. Superpave

requires the aggregate gradation curve to be within the control limits. Another part of the

Superpave specification for gradation curve is the restricted zone. The restricted zone

provides a guide to help avoid too much natural rounded sand being used in the mixture

and to help ensure minimum VMA requirements are met. However, Kandhal et al. (2001)

showed that potential good mixes may get rejected because their gradations pass through

the restricted zone. Chowdhury et al. (2001) found that there is no relationship between

the restricted zone and permanent deformation when crushed aggregates are used in the

mixture design. In practice, there are aggregate blends that pass through the restricted

zone while not using an excessive amount of rounded aggregates that meet the minimum

33

VMA requirements. A typical gradation curve along with the corresponding gradation

limits is shown in Figure 2-14.

The Superpave Gyratory Compactor (SGC) is a key component of the Superpave mix

design. The compaction equipment is designed to compact HMA samples to conditions

similar to those obtained in the field under traffic loads. The compaction effort is

controlled by three parameters: vertical pressure, angle of gyration, and number of

gyrations. In the Superpave mix design procedure the vertical pressure is set at 600 kPa

(87 psi), the angle of gyration is set at 1.25˚, the rate of gyration is 30 revolutions per

minute, and the number of applied gyrations depends on the design traffic level and

average high air temperature. Ni, Nd, and Nm are three numbers of gyrations specified for

the Superpave Gyratory Compactor. Ni is N-initial which measures the mixture

compactibility to ensure that the mix will not compact too quickly. Nd is N-design and

represents the number of gyrations required to produce a density in the mixture similar to

that ultimately obtained in the field when subjected to traffic. Nm is the N-maximum and

is the number of gyrations that provides a compacted density which should not be

exceeded in the field, for a too-densified mix will result in low VMA which may cause a

rutting problem. Generally Nd is determined based on lab and field test data through

comparison of in-place density and laboratory density at various numbers of gyrations. Ni

and Nm are then given by the following equations:

45.0)( di NN = (2-12)

10.1)( dm NN = (2-13)

Superpave defines the optimum asphalt content as the one that produces 4 percent air

voids at Nd. An estimate of the optimum asphalt content is selected from aggregate blend

trials. Three samples each are prepared at 0.5% below estimated optimum, at estimated

optimum, at 0.5% above, and at 1.0% above estimated optimum. All samples are put into

an oven to be aged at 135˚C (275˚F) allowing absorption of the asphalt cement into

aggregate pores before compaction. Each sample is compacted up to Nm. The estimated

bulk specific gravity at each number of gyrations is calculated by using the specimen

weight, diameter (6 inches, or 150 mm) and height which is measured and recorded

during the compaction process. This estimated density is slightly lower than the actual

34

density because usually the raw compacted specimens have many surface voids on the

top, bottom and cylindrical sides. The actual bulk specific density at Nm is measured by

weighing the samples in air and water. The correction factor is calculated at Nm by the

following equation:

)(

)(

estimatedG

actualGCF

mb

mb= (2-14)

The actual bulk specific gravity at Ni and Nd can be back-calculated using the

correction factor and the estimated density at the corresponding number of gyrations. The

theoretical maximum density (TMD) is measured from the rice test on loose mixtures.

The air voids can then be determined by knowing the Gmm and the actual Gmb at various

compaction levels. The air voids of three samples at each asphalt content are averaged

and plotted on a graph. The actual optimum asphalt content that provides 4 percent air

voids at Nd can be determined by interpolation. It is required that the air voids be greater

than 11% at Ni and greater than 2% at Nm. Other requirements that must be satisfied

include VMA and VFA according to Superpave specifications.

#

20

0

#1

00

#

50

#

30

#

16

#

8

#

4

3

/8"

1

/2"

3

/4"

1

"

0

10

20

30

40

50

60

70

80

90

100

Pe

rce

nt P

assin

g

Restricted Zone

upper control

lower control

Gradation Curve

Maximum Density Line

Figure 2-14: Illustration of gradation requirements for 12.5 mm (1/2 in.) nominal size

35

2.4 Mechanical Tests for Characterization of Asphalt Mixtures

2.4.1 Introduction

Flexible pavements constructed with asphalt mixtures are subjected to a wide range

of traffic loads and environmental conditions. Characterization of HMA mixtures is the

measurement and analysis of their response to these conditions. The performance of any

HMA mixture is dependent upon the entire pavement structure, and the structural

capacity of the pavement layers is dependent on the quality of materials and their

compositions in the mixture. An understanding of fundamental engineering properties of

HMA mixtures is required for satisfactory performance of pavement structures in service.

There have been many testing protocols developed in the laboratory for measuring

mixture properties related to thermal cracking, fatigue cracking, and permanent

deformation over the past few decades. These test procedures are used to evaluate the

distress of HMA mixtures under various types of load at different loading rates and

temperature levels similar to those encountered in the field.

The test methods can be categorized into in-place and laboratory tests. The testing

program developed for this study is conducted on lab-prepared HMA specimens with a

complete set of equipment. Laboratory mechanical tests can be further grouped based on

the test mode, such as direct tension, indirect tension, compression, flexural, shear, and

torsion. Pavement design using elastic layer theory needs two elastic parameters for each

material layer used: Young’s modulus (stiffness) and Poisson’s ratio. In the NCHRP 9-19

report (2001), many tests had been proposed as a Simple Performance Test, including the

dynamic modulus test, the indirect tensile creep compliance test, resilient modulus test,

tensile strength test and other test methods. Details of the test methods utilized in this

study are discussed in the following sections.

2.4.2 Dynamic Complex Modulus Test (DMT)

Papazian (1962) was one of the first to present the concepts and definitions

concerning the dynamic complex modulus (E*) for characterizing the viscoelastic

behaviors of HMA mixtures. In the early 1970s, the Asphalt Institute selected the

36

dynamic complex modulus as one of the choices for the modulus test. The dynamic

modulus test was then specified in ASTM D3497-79 “Standard Test Method for the

Dynamic Modulus of Asphalt Mixtures”. The complex modulus test accounts not only for

the instantaneous elastic response without delayed elastic effects, but also the

accumulation of cyclic creep and delayed elastic effects with the number of cycles. The

test is usually conducted on cylindrical specimens subjected to a compressive sinusoidal

vertical load at a given temperature and loading frequency. After the specimens are well

prepared, they are placed in a controlled temperature cabinet and brought to the specified

test temperature. The conditioned specimen is then placed into the loading apparatus and

the strain gauge wires are connected to the measurement system. A hardened steel disk is

put on both top and bottom of the specimen and centered under the loading apparatus.

The electronic measuring system is adjusted and balanced as necessary. The sinusoidal

loading is applied to the specimen without impact and with loads varying between 0 and

35 psi (0 to 241.5 kPa) for each load application for a minimum of 30 seconds and a

maximum of 45 seconds at temperatures of 41, 77, and 104°F (5, 25, and 40°C) and at

loading frequencies of 1, 4, and 16 Hz for each temperature. Both the loading stress and

axial strain are monitored during the test. One piece of test equipment that is required is a

loading device capable of transmitting haversine waveforms at a frequency range of 0.1 to

20 Hz and a maximum stress of about 100 psi (690 kPa). Because of the importance of

testing asphalt mixes at various temperatures, some form of temperature control system is

required. This device can be either external or internal to the loading device depending

upon how the test is conducted. Strains are usually obtained by use of bonded wire strain

gages or calculated from vertical deformations measured with Linear Variable

Displacement Transducers (LVDTs). Test specimens usually have a minimum 4-inch

diameter and a height-to-diameter ratio of two. A minimum of three specimens is

required for testing. A conceptual schematic of the dynamic complex modulus test is

shown in Figure 2-15. A typical illustration of set-up for dynamic modulus is shown in

Figure 2-16.

It is critical to maintain an appropriate stress level during the dynamic modulus test

to obtain a proper strain response, since the concept of dynamic complex modulus is

based on the assumption of linear viscoelasticity of HMA mixtures. The concept of

37

material linearity is based on the following two conditions of superposition and

homogeneity according to Schapery (1972):

)()()( 2121 σεσεσσε +=+ (2-15)

)()( σβεβσε = (2-16)

Where,

�, �1, �2 = stress histories,

� = strain histories,

� = constant

The original ASTM 3497 protocol for the dynamic modulus test only defines the

haversine load level (0 to 35 psi or 241 kPa) as long as the deformation is not excessive

(2500 micro-strains). Since the 1990s, the dynamic modulus (|E*|) has been one of the

most widely-used structural parameters for asphalt cement mixtures used in Mechanistic-

Empirical (M-E) structural pavement design procedures. It becomes a primary material

input to compute stress, strain, rutting and cracking damage in flexible pavement systems.

Witczak et al. (1996) reviewed the approach for conducting the dynamic modulus test and

suggested strain amplitudes of 75 to 200 micro-strains to maintain the HMA material in

linear viscoelastic range. The dynamic modulus test protocol was then modified and

developed in the National Cooperative Highway Research Program (NCHRP) Project 9-

19 and 1-37A and has been standardized in the new Mechanistic-Empirical Pavement

Design Guide (PDG) as AASHTO Provisional Standard TP62-03: “Standard Method of

Test for Determining Dynamic Modulus of Hot-Mix Asphalt Concrete Mixtures.” This

test protocol calls for a minimum of two replicate specimens to be tested at temperatures

of 14, 40, 70, 100, and 130˚F (-10, 4.4, 21.1, 37.8, and 54.4˚C) and loading frequencies of

25, 10, 5, 1.0, 0.5, and 0.1 Hz. The dynamic modulus tests carried out in NCHRP 9-19

project (Witczak et al. 2002) selected the stress levels for a given test temperature to

produce resilient strains of less than 100 micro-strains

As introduced earlier, |E*| is a fundamental property defining the response of HMA

mixtures and strongly influences the performance of asphalt pavement. Huang (1993)

illustrated the theory of complex modulus by the use of the Kelvin model, shown in

38

Figure 2-18, subject to a sinusoidal loading, which can be represented by a complex

number:

tietit ωσωσωσσ 000 )sin()cos( =+= (2-17)

in which �0 is the stress amplitude and is angular velocity, which is related to the

frequency by

fπω 2= (2-18)

The governing differential equation can be written as

tieE

t

ωσεε

λ 011 =+∂

∂ (2-19)

The solution of Equation (2-19) can be expressed as

)(

0

ϕωεε −= tie (2-20)

in which � is the strain amplitude and is the phase angle by which the strain lags behind

the stress, as shown in Figure 2-17. Substituting Equation (2-20) to Equation (2-19) gives

tititi eeEei ωϕωϕω σεωελ 0

)(

01

)(

01 =+ −− (2-21)

After canceling eit on both sides of Equation (2-21), and equating the real term to �0 and

imaginary terms to zero, the following two equations are obtained to solve �0 and

00101 cossin σϕεϕωελ =+ E (2-22)

0sincos 0101 =− ϕεϕωελ E (2-23)

The solutions of Equation 2-22 and Equation 2-23 are

2

1

2

1

00

)( ωλ

σε

+=

E (2-24)

1

1tanE

ωλϕ = (5b) (2-25)

39

It can be seen from Equation (2-25) that for elastic materials �1 = 0, so = 0; while for

viscous materials E1 = 0, so = �/2. The complex modulus E* is defined as

)(

0

0*

ϕω

ω

ε

σ

ε

σ−

==ti

ti

e

eE (2-26)

Or ϕε

σϕ

ε

σ

ε

σsincos

0

0

0

0* iE +== (2-27)

The dynamic modulus is the absolute value of the complex modulus. Experimentally, the

dynamic modulus is determined as the ratio of the applied stress amplitude to the strain

response amplitude under the sinusoidal loading (Figure 2-17), as calculated by the

following equation (Yoder and Witczak 1975):

0

02

0

02

0

0* )sin()cos(||ε

σϕ

ε

σϕ

ε

σ=+=E (2-28)

The phase lag is simply the angle at which the �0 lags �0:

)360()360( �� ⋅⋅=⋅= ftt

tlag

p

lagϕ (2-29)

Where

tlag = time lag between a cycle of sinusoidal stress and a cycle of strain

tp = time period of a stress cycle (seconds)

f = frequency of the dynamic load (in Hz)

By definition, the complex modulus E* can be expressed as the following:

EiEE ′′+′=∗ (2-30)

Where E’ refers to the real part of the complex modulus; it is the storage modulus that

describes the elastic component of the complex modulus:

40

)cos()cos(||0

0* δε

σδ ⋅=⋅=′ EE (2-31)

and E” refers to the imaginary part of the complex modulus; it is the loss modulus which

describes the viscous component of the complex modulus:

)sin()sin(||0

0* δε

σδ ⋅=⋅=′′ EE (2-32)

The storage and loss moduli can be determined by measuring the lag in the response

between the applied stress and the measured strains. This lag, referred to as the phase

angle , shown in Figure 2-17, can also be determined by Equation 2-33:

)(tan 1

E

E

′

′′= −ϕ (2-33)

The complex modulus can also be written as:

ϕ⋅⋅= ieEE || ** (2-34)

Results

Deformation

Sin. Load

1,4,16 Hz

Temperature

5,25,40°C

Schematic of Dynamic Complex Modulus

Test (ASTM D3497-79)

Figure 2-15: Conceptual schematic of dynamic complex modulus test

41

Loading Head

Load Cell

LVDT

Specimen

Environment

Chamber

Figure 2-16: Typical test set-up for dynamic complex modulus

tωσ sin0

)sin(0 ϕωε −t

Figure 2-17: The schematic components of dynamic complex modulus test

42

��

tie

⋅ωσ 0

Figure 2-18: Kelvin model under sinusoidal loading.

2.4.3 Indirect Diametral Tests in Tension

The indirect diametral test is used extensively by state highway and other agencies

for routine tests. The 1986 AASHTO Pavement Design Guide, which recommended the

use of resilient modulus to characterize pavement materials, has led to accelerated use of

this type of test. This test is usually conducted on cylindrical specimens subjected to a

compressive load along two opposite generators resulting in a relatively uniform tensile

stress acting perpendicular to and along the diametral plane of the applied load. A

splitting failure generally occurs as a result along the diametral plane (Figure 2-19). If a

repetitive pulsating load is applied diametrically to the sample, the dynamic load results

in dynamic deformations across the horizontal diametral plane. The transducers mounted

on each side of the horizontal specimen axis record these deformations. The resilient

modulus (MR) of HMA mixtures can be determined by the dynamic load and

deformation. The indirect diametral test is originally specified by ASTM D4123-82

Standard Test Method for Indirect Tension Test for Resilient Modulus of Bituminous

Mixtures, which was withdrawn in 2003. The resilient modulus (MR) has been used in the

AASHTO Design Guide (AASHTO 1993) since 1993. The resilient modulus laboratory

test procedure is described in AASHTO TP 31. The test is defined as a repetitive 0.1

second haversine load followed by a 0.9 second rest period, continued at 1 Hz intervals.

Many empirical relationships have been developed throughout the years relating MR to

other tests like the California Bearing Ratio (CBR) and the Marshall stability test

43

(AASHTO 1993), since it has long been considered the defining characteristic for HMA

layers.

Figure 2-19: Indirect diametral test during loading and at failure

After the specimens were well prepared, they were placed in a controlled temperature

cabinet and brought to the specified test temperature. The specimen was placed into the

loading apparatus and the loading strips were positioned to be parallel and centered on the

vertical diametral plane. The specimen was preconditioned by applying a repeated

haversine or other suitable waveform load without impact for a minimum period

sufficient to obtain uniform deformation readout. Depending upon the loading frequency

and temperatures, a minimum of 50 to 200 load repetitions is typical; however, the

minimum for a given situation must be determined so that the resilient deformations are

stable. Resilient modulus evaluation will usually include tests at three temperatures, for

example, 41, 77, and 104°F (5, 25, and 40°C), at one or more loading frequencies. The

horizontal and vertical deformations were continuously monitored during the test.

The required test equipment is a loading device capable of applying a load pulse over

a range of frequencies, load durations and load levels. Some form of temperature control

system is required. The temperature-control system should be capable of control over a

temperature range from 41 to 104°F (5 to 40°C). The measurement and recording system

44

should include sensors for measuring and recording horizontal and vertical deformations.

The values of vertical and horizontal deformation can be measured by linear variable

differential transducers (LVDTs) or other suitable devices. LVDTs should be at mid-

height opposite each other on the specimen’s horizontal diameter. A metal loading strip

with a concave surface having a radius of curvature equal to the normal radius of the test

specimen is required to apply load to the specimen. The specimens should have a height

of at least two inches and a minimum diameter of four inches for aggregate up to one inch

maximum size, and a height of at least three inches and a minimum diameter of six inches

for aggregate up to 1.5 inches maximum size.

Hondros (1959) derived the stress equations to model the actual test conditions as

well as to determine Young’s modulus and Poisson’s ratio of the material. The theoretical

distribution of stresses for a concentrated load is shown in Figure 2-20 and Figure 2-21.

Roque and Buttlar (1992) developed a measurement and analysis system to

determine asphalt concrete properties, primarily thermal cracking, using the indirect

tensile testing mode, which was incorporated in AASHTO TP9-96, Standard Test Method

for Determining the Creep Compliance and Strength of Hot Mix Asphalt (HMA) Using

the Indirect Tensile Test Device. They proposed the Gauge-Point-Mounted device to

measure horizontal and vertical deformations across a gauge length of 25.4mm (1 inch).

Poisson’s ratio was also obtained from the horizontal and vertical deformations instead of

using assumed values. Correction factors from 3-D finite element analysis were used to

account for: (1) the effect of specimen bulging on deformation measurement, and (2)

approximation of 2-D plane stress assumption. Roque et al. (1997) made further

modifications and improvements on the SHRP IDT system for characterizing relevant

asphalt mixture properties. The test procedures and data reduction methodologies were

also summarized in Long-Term Pavement Performance (LTPP) Protocol P07 (2001): Test

Method for Determining the Creep Compliance, Resilient Modulus and Strength of

Asphalt Materials Using the Indirect Tensile Test Device.

45

� ��

��

2

22

22

4

42��

��

�

+

−

⋅⋅ xd

xd

dt

P

π

��

��

�−

+⋅⋅

−1

4

4222

2

xd

d

dt

P

π

Figure 2-20: Theoretical stress distribution on horizontal diametral plane for indirect tensile test (After Yoder et al. 1975)

dt

P

⋅⋅π

2

��

��

�−

++

−⋅

−

dydydt

P 1

2

2

2

22

π

Figure 2-21: Theoretical stress distribution on vertical diametral plane for indirect tensile test (After Yoder et al. 1975)

46

2.4.4 Relationship between Resilient and Dynamic Moduli

The resilient modulus (MR) of the mixture is calculated by using the measured

horizontal and vertical deformations (Hondros 1959; Kennedy 1977), and is defined as

the ratio between applied stress and recoverable strain. Several different test protocols

and data reduction methods were developed for determining the indirect diametral

resilient modulus of asphalt concrete mixtures (ASTM 4123-82 1982; Barksdale et al.

1997; AASHTO TP-31 1996; Roque and Buttlar 1992; Buttlar and Roque 1994; SHRP-

LTPP P07 2001; Witczak 2004). The dynamic complex modulus is a viscoelastic

response of an asphalt concrete mixture under sinusoidal loading conditions at different

test temperatures and loading frequencies, which accounts for both elastic and viscous

effects of the material. Several different test protocols and methods were also developed

for determining the dynamic complex modulus of asphalt concrete mixtures (ASTM

D3497-79 1979; Witczak et al. 2000; Witczak et al. 2002; Pellinen and Witczak 2002). In

addition, the dynamic complex modulus measurements were also conducted in Europe in

recent research studies to evaluate the mechanical properties of bituminous materials (Di

Benedetto et al. 2001, 2004).

A detailed comparison of key differences between the dynamic complex modulus test

and the indirect diametral resilient modulus test for asphalt concrete mixtures was

summarized in a position paper by the NCHRP 1-37A 2002 Project research team

(Witczak 1999). Basically, the primary difference between the resilient modulus test and

dynamic complex modulus test for asphalt concrete mixtures is that the former uses

loading of any waveform with a given rest period, while the latter applies a sinusoidal or

haversine loading with no rest period; hence, no delayed elastic rebound would occur

during the test. The transition from the resilient modulus test to the use of the dynamic

complex modulus test for design of flexible pavement structures has hardly been smooth.

The potential impact of adopting the dynamic complex modulus for implementing the

new AASHTO M-E Design Guide is tremendous for state transportation agencies such as

the Florida Department of Transportation (FDOT). The IDT has traditionally been used to

characterize the HMA mixtures for flexible pavement design in Florida, and the test

method has been shown to be both an expedient and a reliable way of obtaining mixture

47

properties from field cores. In response to the need, a major effort was undertaken by the

FDOT to characterize Florida HMA mixtures using the dynamic complex modulus

(Birgisson et al. 2004). Despite the fundamental differences between the resilient

modulus and dynamic complex modulus (Witczak 1999; Drescher et al. 1997; Zhang et

al. 1997; Kim et al. 2004), a number of research studies were attempted in order to

establish a direct correlation between the resilient modulus and dynamic complex

modulus of asphalt concrete mixtures (Kim et al. 2004; Birgisson et al. 2004; Loulizi et

al. 2006). Birgisson et al. (2004) developed testing and analysis procedures to accurately

determine the tensile dynamic complex modulus from the SHRP IDT tests. The dynamic

complex modulus was found to be correlated with resilient modulus and testing frequency

for the range of testing temperatures and frequencies. Loulizi et al. (2006) conducted a

comparison study on the dynamic complex modulus and resilient modulus tests, and they

found a strong relationship between the dynamic complex modulus performed at 5 Hz

and the resilient modulus performed at a loading time of 0.03 seconds.

Other alternative approaches have also been attempted in order to determine the

dynamic complex modulus from the IDT test with modified loading conditions using the

theory of viscoelasticity (Drescher et al. 1997; Zhang et al. 1997; Kim et al. 2004).

Recently, an analytical method of calculating resilient modulus from the dynamic

complex modulus was also proposed (Lacroix et al. 2007). The proposed theoretical

prediction involved the application of multiaxial linear viscoelastic theory to linear elastic

solutions for the IDT test. The proposed approach could provide reasonable estimates of

the resilient modulus from the dynamic complex modulus of the asphalt concrete

mixtures. The accuracy of the prediction was not affected by assuming a constant

Poisson’s ratio.

2.5 HMA Fracture Mechanics Concepts

2.5.1 Background

It is commonly considered necessary to study real cracking growth mechanisms in

order to essentially understand the crack damage in HMA. Research conducted by Roque

et al. (2002) on top-down cracking of asphalt pavement indicated that the tearing-apart

48

effect from vehicle tires can cause a certain level of tensile stress leading to cracking of

the pavement surface and crack propagation. The conventional linear elastic fracture

mechanics presume that there are intrinsic flaws in a material. A crack initiates from the

flaws and is propagated continuously under a critical loading condition. The crack growth

rate of linear elastic materials is assumed to follow Paris’s law:

nKA

dN

da)(∆= (2-35)

where a is crack length, N is number of load repetitions, K is stress intensity factor, and A

and n are constants.

However, Jacobs (1996) investigated the fracture mechanics for HMA mixtures and

pointed out that the non-homogeneity of asphalt concrete could cause the discontinuity of

crack propagation in the mixture. It was shown that a crack in asphalt concrete grows

discontinuously. Zhang (2000) and Zhang et al. (2001) found that the continuous crack

growth assumption can not characterize the cracking performance of asphalt concrete

mixtures observed in the field, which occurs in a stepwise manner rather than a

continuous one. They indicated that there is a specific threshold below which the damage

is considered to be on a micro scale and healable with a rest period or temperature

increase, whereas the damage would be permanent on a macro scale when the threshold is

reached or exceeded.

Shen et al. (2005) introduced the Plateau Value (PV) concept using the Ratio of

Dissipated Energy Change (RDEC) to show its relationship with damage and failure at

normal or low strain levels (70 – 500 micro-strains). Carpenter et al. (2006) applied this

RDEC approach to analyze healing and HMA fatigue behavior at normal and low strain

levels using the standard four-point bending beam fatigue test procedure specified in

AASHTO standards (21): constant strain at 500 micro-strains, 20±0.5˚C temperature,

10Hz frequency with haversine load waveform, etc. Healing was observed at low strain

conditions or long rest period, and hence may increase the fatigue life of HMA material.

2.5.2 HMA Fracture Mechanics Model from IDT

49

An HMA fracture model for predicting pavement cracking was developed by Zhang

et al. (2001) and Roque et al. (2002, 2004). Crack growth laws were identified for asphalt

mixtures using IDT. The linear elastic finite element method was used to simulate the

IDT specimens at different cracking lengths. They established a relationship between the

theoretical crack length and the deformation measured between the vertical gage points.

Besides the three types of regular IDT tests (resilient modulus, creep compliance, and

tensile strength), another type of fracture test was performed. The specimens for the

fracture test have 150 mm diameter and 25 mm thickness with an 8 mm hole in the

center. The fracture test was conducted under the same load mode as MR test but at higher

deformation levels in order to determine the crack growth characteristics of the specimen.

The test was performed at 10˚C. The repeated load was applied until the specimen failed.

The crack growth rate parameters for Paris law ( nKAdNda )(/ = were determined by the

following steps:

• Establish the relationships of cracking length (a) versus horizontal deformation

(�H) and stress intensity factor (K) using theoretical finite element analysis.

• Establish a relationship between horizontal deformation (�H) and loading

repetitions (N) from fracture test.

• Incorporate the theoretical calculation into the test results to develop a

relationship between cracking length growth rate (da/dN) and stress intensity

factor (K).

• Obtain the fracture parameters, A and n, by regression analysis.

The regression models were used to evaluate the mixture cracking resistance.

Discrepancies between laboratory tests and field performance were observed. Regression

analyses were conducted to determine the relationship between the mixture properties

(tensile strength, m-value, fracture energy and resilient modulus) and measured crack

growth rates. It was determined that dissipated creep strain energy to failure is not

dependent on mode of loading and could be used as a threshold to explain the

inconsistency of lab and field observations, as shown in Figure 2-22 (Roque et al. 2002).

There are two possible reasons for fracture to occur: 1) a number of continuous repeated

loads can cause damage accumulation due to creep strain energy, and fracture can develop

if the DCSE threshold is reached, even when the loading stress is below the tensile

50

strength. It also should be noted that the mixture may never crack if the healing effect

makes the induced dissipated energy below the threshold regardless of the load

repetitions; 2) fracture may occur if any large single load exceeds the fracture energy (FE)

threshold. Case 3 in Figure 2-22 shows that cracking would not occur during a single load

application unless the upper FE threshold is exceeded, even when the dissipated energy

(DE) is exceeded.

Figure 2-22: Illustration of potential loading condition (Roque et al. 2002)

e0 ef Strain

St

MR

EE

Dissipated Creep Strain Energy

(DCSE)

MR

Str

ess

Figure 2-23: Determination of fracture energy and dissipated creep strain energy

51

The concepts of fracture energy (FE) and dissipate creep strain energy (DCSE) were

introduced in the model to account for the pavement structure crack performance. The

two energy values are determined using the tensile strength test along with the resilient

modulus test. The schematics used to calculate these limits are shown in Figure 2-23. The

values are calculated by the following equations:

� ⋅=tS

dFE0

εσ (2-36)

R

t

fEEM

S=−= 0εεε (2-37)

R

t

tEEM

SSEE

⋅=⋅⋅=

2

)(

2

12

ε (2-38)

EEFEDCSE −= (2-39)

Where

FE = Fracture Energy, total energy applied to the specimen till fracture

EE = Elastic Energy, recoverable energy

DCSE = Dissipated Creep Strain Energy absorbed by the specimen prior to fracture

St = tensile strength of the mixture

�f = failure strain

MR = resilient modulus of the mixture

It was shown that the dissipated creep strain energy at failure (DCSEf) is the

threshold that controls crack propagation, which can be described as a step function

consisting of crack initiation (DCSE below the threshold) and crack propagation (DCSE

over the threshold). It was also found that micro-damage in HMA can be healed while

macro-damage cannot be healed at rest period or temperature increase conditions. DCSE

per cycle and number of load repetitions can be further estimated using the following

equations:

))100((20

1/ 1

1

−= m

AVEAVEnCreepStrai mDcycleDE σσ (2-40)

)//( cycleDCSEDCSEN ff = (2-41)

52

where �ave is the average stress near the crack tip, m and D1 are power law parameters

obtained from the creep compliance test, and Nf is the number of cycles to failure.

Villiers (2004) used the HMA Cracking Model along with the IDT sweep of tests to

evaluate the sensitivity of Superpave mixtures with regards to cracking performance. The

mixtures were tested at 10˚C to determine the cracking performance when subjected to

the Acceptable Variances. A statistical evaluation was conducted to examine the variation

in the IDT testing parameters. Significant variation was observed for all the IDT

parameters which were consistent with research conducted by Roque et al. (2004). It was

found that the average values used from the IDT test parameter could be used to

distinguish between pavements that exhibited top-down cracking and those that did not.

Roque et al. (2004) showed that cracking performance of HMA is complex and

controlled by multiple mixture properties. The Energy Ratio concept was derived as a

fundamental material property using the HMA Fracture Mechanics Model. It is defined as

the ratio of dissipated creep strain energy threshold of the mixture to the minimum

dissipated creep strain energy required, which can be determined from Superpave IDT

including resilient modulus, creep compliance, and tensile strength tests. Nf of 6000 was

set as the critical value that distinguish mixture performance. The equations to calculate

the Energy Ratio are presented below:

1

98.2 Dm

DCSEaER

f

⋅

×= (2-42)

81.3 1046.2)36.6(0299.0 −− ×+−⋅⋅= tSa σ (2-43)

Where

� = Tensile stress of the asphalt layer in psi (pavement structure)

St = Tensile strength in MPa (IDT tensile strength test)

The other parameters are the same as those defined earlier. The HMA fracture mechanics

were implemented to examine all test sections, based on which performance criteria of

ER greater than 1 and DCSE greater than 0.75 were defined to evaluate cracking

performance. They showed that no single property can be an accurate performance

indicator since fracture properties are interrelated as a system. The Energy Ratio appeared

53

to be a suitable parameter for evaluating top-down cracking situations of sections within a

pavement system at low in-service temperatures.

Kim (2005) developed an HMA thermal fracture model based on the same principle

and failure criteria used in the HMA fracture model introduced above. The Superpave

IDT tests were designed at three temperatures (0, 10, and 20˚C) which are typical low in-

service temperatures in Florida. The performance evaluation of the model showed

potential to reliably evaluate the performance of asphalt mixtures subjected to thermally

induced damage.

54

CHAPTER 3

MATERIALS AND EXPERIMENTAL PROGRAM

3.1 General

The two methods of measuring dynamic properties of HMA in this research study

were the triaxial dynamic modulus test (DMT) and indirect diametral tension test (IDT).

Both of these tests were reviewed in more detail in Chapter 2. Originally, the dynamic

modulus test was specified by ASTM D3497-79 Standard Test Method for Dynamic

Modulus of Asphalt Mixtures, while the IDT resilient modulus test was specified by

AASHTO TP31-94 and ASTM D4123-82. This study adopts the SHRP IDT Testing and

Analysis System (Roque et al. 1997) to measure the resilient modulus, creep compliance,

and tensile strength, and the NCHRP 9-29 Equipment Specifications for the Simple

Performance Test System to measure the complex dynamic modulus for all asphalt

concrete specimens. A complete dynamic testing system was acquired to perform the

temperature-controlled dynamic tests to determine the engineering properties of Florida

HMA mixtures. In this study, a Servopac Gyratory Compactor and an Interlaken Asphalt

Test System were used to compact the asphalt mixture and measure the dynamic response

of asphalt concrete, respectively. The laboratory experimental program consists of two

parts.

The first part of the experimental program involved two standard mix designs as

control mixes: Two modified gradations were designed for each control mixture while

using the same base asphalt binder (PG 67-22). In addition, each of the standard

Superpave mixture was modified using three levels of SBS polymer asphalt binder

instead of the original asphalt to evaluate SBS polymer effects on fracture mechanics

properties of asphalt concrete mixes. Therefore, the overall experimental program in this

part of the study involved twelve HMA concrete mixtures. The second part of the

experimental program was developed to study the relationship between the dynamic

complex modulus test and the indirect resilient modulus test. Twenty (20) standard

Florida HMA Superpave mixtures approved by FDOT were selected for determination of

55

the resilient modulus and the dynamic modulus of the HMA mixtures. All specimens

were prepared at targeted optimum air voids of 4%.

The physical properties of the materials used, including their aggregate properties,

aggregate gradation, asphalt binder characteristics, and mixture design series, will be

presented in detail according to the purpose of the studies.

3.2 Mix Designs and Materials

One Georgia granite mix (SP 04-3034A, TL-D, Ga553), referred to as “F2C”, and

one South Florida Limestone mix (LD 02-2529A, TL-D, SFL), called F4C, were selected

as the control mixes for the fracture mechanics tests. The two Superpave mix designs are

commonly used in Florida and approved by Florida Department of Transportation

(FDOT). They are both coarse mixes with the gradation curves passing below the

Superpave restricted zone, which were selected with the intention of making adjustments

to their coarse aggregate proportions to study the effect of gradation on mixtures’ fracture

mechanics properties.

The 20 mix designs for the dynamic modulus test and the resilient modulus test are

summarized in Appendix Table A-1 for information. These mix designs were contributed

by companies involved in the production and use of HMA in Florida. The summary table

consists of 20 mix designs in the format of 19 columns each. The data presented in the

table were sorted by mix design series number. Below is a description of each column:

1. The test series number related to the whole project

2. The mix design number used by the FLDOT for reference

3. The nominal maximum aggregate sizes, which are 19.0, 12.5, or 9.5 millimeters.

4. The type of the design mix, coarse or fine, determined by which side of the

forbidden zone the mix passes when plotted on the 0.45 Power chart.

5. The load level the design represents; Superpave has 5 levels, A-E.

6. The design applied either to a structural or friction course; different qualities are

desired for the two types of courses.

7 – 18. Columns 7-18 list the materials used in the design. The numbers are FDOT’s

reference numbers for sources.

56

19. The type of asphalt used in the design.

The grade of asphalt cement used in mixtures, as introduced in preceding chapters, is

one important factor that can affect the strength of asphalt concrete and amount of rutting

which occurs in the mix. In this part of the study, only one type of unmodified asphalt

cement, PG67-22 (AC-30), which is commonly used in Florida, was used for all mixtures

tested. The asphalt binder PG67-22 grading report is summarized in Table A-2. The

nominal maximum aggregate sizes for the mixtures tested are 19.0 mm, 12.5 mm, and 9.5

mm, respectively. The Superpave mixture designs were selected as they are commonly

used FDOT gradations and are known to perform well in the field. The types of

aggregates used are as follows:

• Granite Georgia-553 Georgia-206 Nova Scotia Granite (NS)

• Reclaimed Asphalt Pavement (RAP)

• Limestone North Florida Limestone (NFL) Mid Florida Limestone (MFL) South Florida Oolite/Limestone (SFL) Alabama Limestone (AL)

A summary of the 20 mix designs and the aggregate types is presented in Appendix

Table A-3. The 20 mixtures were tested for both complex modulus and indirect tensile

resilient modulus. The gradations of all mix designs, sorted by the mix design series

number and used in this study, are summarized in Table A-4 through Table A-7. The

corresponding gradation charts for all mix design series (sieve size raised to 0.45 power

mm) are presented in Figure A-1 through Figure A-8 for illustration.

3.3 SBS Polymer-modified Asphalt Binder

57

The grade of asphalt cement used in mixtures is one important factor that can affect

the strength of asphalt concrete and amount of rutting which occurs in the mix. The

unmodified asphalt PG 67-22 (AC-30), which is commonly used in Florida, was selected

as the base asphalt for both fracture mechanics tests and the dynamic modulus test. The

asphalt binder PG67-22 grading report is summarized in Appendix Table A-8. Three

levels of SBS polymer-modified asphalt are produced and used in the SBS effects study.

The SBS modified asphalt binder grading reports are summarized in Table A-9 through

Table A-11. The base asphalt and the other three levels of polymer-modified asphalt

(PMA) are listed as follows:

1. Control level

Base asphalt A (PG 67-22) + Aggregates = Control Mix

Mixtures are referred to as F2C and F4C.

The twenty Superpave mixes for DMT also used this base asphalt.

2. Mix plus 3% SBS polymer A

[Base asphalt A + 3% SBS polymer A] = PMA PG 76-22

PMA PG 76-22 + Aggregates = Mix with 3% PMA

Mixtures are referred to as F2P1 and F4P1.

3. Mix plus 4.5% SBS polymer A

[Base asphalt A + 4.5% SBS polymer A] = PMA PG 82-22

PMA PG 82-22 + Aggregates = Mix with 4.5% PMA


4. Mix plus 6% SBS polymer A

[Base asphalt B (softer) + 6% SBS polymer A] = PMA PG 82-22

PMA PG 82-22 + Aggregates = Mix with 6% PMA


58

0.45 Power Gradation Chart

#2

00

#

10

0

#5

0

#3

0

#1

6

#8

#4

3/8

"

1/2

"

3/4

"

1"

0

10

20

30

40

50

60

70

80

90

100

Pe

rce

nt P

assin

g

Restricted Zone

upper control

lower control

F2 Control

F2G1

F2G2

Figure 3-1: Gradation curves for F2 and its trial adjustments


#

20

0

#1

00

#

50

#

30

#

16

#

8

#

4

3

/8"

1

/2"

3

/4"

1

"

0

10

20

30

40

50

60

70

80

90

100

Pe

rce

nt P

assin

g

Restricted Zone

upper control

lower control

F4 Control

F4G1

F4G2

Figure 3-2: Gradation curves for F4 and its trial adjustments

59

0

5

10

15

20

25

30

35

1/2 3/8 4

Sieve Size

Perc

ent

Reta

ined

F2 Control

F2G1

F2G2

Figure 3-3: Change of percent retained on top 3 sieves for F2 series

0

5

10

15

20

25

30

35

1/2 3/8 4

Sieve Size

Perc

ent

Reta

ined

F4 Control

F4G1

F4G2

Figure 3-4: Change of percent retained on top 3 sieves for F4 series

Figure 3-5: Cutting of raw specimen

60

3.4 Aggregates Gradation Modification

As mentioned in section 3.1, the two mix designs used as control mixtures are F2C

Georgia Granite (Ga553) and F4C South Florida Limestone. The nominal maximum

aggregate size for both F2C and F4C is 12.5 mm. They are commonly used FDOT

gradations and are known to perform well in the field. Both gradation curves of the two

control level mixtures go below the restricted zone and then zig upward across the

maximum density line at No. 4 sieve size, and continue a certain amount higher than the

maximum density line through the coarse sizes. The main purpose of this shape is to

assure sufficient air voids content of the asphalt mixture. In order to facilitate study of the

coarse aggregate effect on asphalt concrete mixtures, the coarse part (No. 4 sieve size and

larger) of each mix design was modified to two different compositions with the fine parts

of the mixes kept unchanged. The Job Mix Formulas of the original standard mix designs

and associated gradation modifications are summarized in Table A-12 and Table A-13.

The corresponding gradation charts for all mix design series (sieve size raised to 0.45

power mm) are presented in Figure 3-1 and Figure 3-2 for illustration. As shown in the

charts, the first set of modified gradations, named F2G1 and F4G1, have gradation curves

slightly lower than the original mix design in the coarse part, but still above the maximum

density line. The second set, denoted as F2G2 and F4G2, have gradation curves further

lower than the first modified one, and go below the maximum density line in the coarse

part. Figure 3-3 and Figure 3-4 show comparisons of percent retained on top three sieves

between control level and modified gradations. The asphalt content levels for mixtures

with modified gradation were kept the same as for the original control mixes.

3.5 Specimen Preparation and Volumetric Properties

Raw specimens with dimensions of 150 mm (5.9 in.) in diameter by 165 mm (6.5 in.)

in height were first prepared on the required air void content (4%) using a Servopac

Gyratory Compactor for the selected HMA mixtures. The sample preparation for the IDT

test was based on the findings from the NCHRP Project 1-28A, “Harmonized Test

Methods for Laboratory Determination of Resilient Modulus for Flexible Pavement

61

Design”. At least 6 mm was sawed off both sides of each test specimen to provide

smooth, parallel surfaces for mounting the measurement gauges. The testing specimen

was then sawed to the required thickness (two specimens out of each compacted pill,

Figure 3-5, referred to as A and B). This sample preparation procedure was done to make

four pills, which were then sawed to make eight samples for each HMA mixture. The Gmb

values were measured for the prepared test specimens to assure that the air voids were

within targeted range. Resilient modulus test, creep compliance test, and tensile strength

test were performed on these 150 mm (6 in.) in diameter by 63 mm (2.5 in.) thick test

specimens. Table 3-1 through Table 3-3 show a summary of the specimens prepared for

each mix and the corresponding volumetric properties measured in the lab.

In the second part of the experimental program, the mixture design process was

verified for the mixture volumetric properties before the production of test specimens.

The original Superpave design procedure was used for all twenty mixture designs. The

Servopac Superpave gyratory compactor was used in the process. The Servopac

compaction parameters used for the design were a 150 mm diameter mold, a 1.25°

gyratory angle, a 600-kPa ram pressure, and 30 gyrations per minute. To verify the

volumetric properties of the mixtures, the maximum theoretical specific gravity was

measured using Rice maximum theoretical specific gravity method specified in AASHTO

T 209/ASTM D 2041 standards. In this case, the mixtures were allowed to cool down in

the loose state. Table A-14 to Table A-17 show the volumetric properties of all the

mixtures used in this part of the research project.

The sample preparation for dynamic modulus test was based on the conclusions of an

extensive study on sample geometry and aggregate size conducted during NCHRP Project

9-19. Results show that (1) a minimum height-to-diameter ratio of 1.5 was required in

order to ensure that the response of a sample evaluated in either the dynamic modulus or

permanent deformation test and repeated load tests represents a fundamental engineering

property; (2) a minimum sample diameter of 4 in. (100 mm) was satisfactory for all HMA

mixtures up to a maximum aggregate size of 1.5 in. (37.5 mm); and (3) smooth, parallel

specimen ends were needed to eliminate end friction and violation of the theoretical

boundary effects of the specimen during the test. Similar to the IDT specimen

preparation, raw specimens with dimensions of 150 mm (6 in.) in diameter by 165 mm

62

(6.5 in.) in height were first prepared on the required air void content (4%) using a

Servopac Gyratory Compactor for targeted Florida HMA mixtures. The nominal 100 mm

(4in.) diameter test specimens were cored from the center of the gyratory specimens

(Figure 3-6) and were subsequently cut to 150 mm (6 in.) in height (Figure 3-7). Dynamic

modulus testing was performed on the test specimens measuring 100 mm (4 in.) in

diameter by 150 mm (6 in.) in height.

Table 3-1: Number of specimens prepared for fracture mechanics tests

Mixes F2 Control (F2C) F4 Control (F4C)

# of Specimens 8 8

Gradation Modifications F2G1 F2G2 -- F4G1 F4G2 --

# of Specimens 8 8 -- 8 8 --

SBS Polymer Modification F2P1 F2P2 F2P3 F4P1 F4P2 F4P3

# of Specimens 8 8 8 8 8 8

Table 3-2: Specimens tested for fracture mechanics properties

Gradation Study

Mix F2C F2G1 F2G2 F4C F4G1 F4G2

Specimen Number

1A, 1B 2A, 2B 3A, 3B 4A, 4B

1A, 1B 2A, 2B 3A, 3B 4A, 4B

1A, 1B 2A, 2B 3A, 3B 4A, 4B

1A, 1B 2A, 2B 3A, 3B 4A, 4B

1A, 1B 2A, 2B 3A, 3B 4A, 4B

1A, 1B 2A, 2B 3A, 3B 4A, 4B

SBS Modifier Study

Mix F2P1 F2P2 F2P3 F4P1 F4P2 F4P3

Specimen Number

1A, 1B 2A, 2B 3A, 3B 4A, 4B

1A, 1B 2A, 2B 3A, 3B 4A, 4B

1A, 1B 2A, 2B 3A, 3B 4A, 4B

1A, 1B 2A, 2B 3A, 3B 4A, 4B

1A, 1B 2A, 2B 3A, 3B 4A, 4B

1A, 1B 2A, 2B 3A, 3B 4A, 4B

63

Table 3-3: Specific gravities and air voids of the mixtures

Gradation Study

Mix F2C F2G1 F2G2 F4C F4G1 F4G2

Gmm 2.589 2.585 2.585 2.253 2.260 2.260

Gmb 2.479 2.487 2.490 2.173 2.179 2.179

VTM (Va) 4.3 3.8 3.7 3.5 3.6 3.6

SBS Modifier Study

Mix F2P1 F2P2 F2P3 F4P1 F4P2 F4P3

Gmm 2.573 2.573 2.573 2.253 2.253 2.253

Gmb 2.472 2.463 2.479 2.179 2.130 2.187

VTM (Va) 3.9 4.3 3.7 3.3 5.4 3.0

Figure 3-6: Coring of the Superpave specimen

Figure 3-7: Cutting of the dynamic modulus specimen

64

3.6 Test Procedures

3.6.1 Resilient Modulus Test

After the specimens were well-prepared, they were placed in a controlled-

temperature cabinet and brought to the specified test temperature. The specimens were

placed into the loading apparatus; and the loading strips were positioned in a parallel

format and centered on the vertical diametral plane (Figure 3-8). Tests were performed at

temperatures of -10, 5, 25, and 40ºC at 1.0 Hz frequency. Testing began with the lowest

temperature and proceeded to the highest temperature. Typical load and deformation

outputs that form a resilient modulus test are shown in Figure 3-9.

On the night before testing, extensometers were placed on the test specimen using

glue. The specimen was then placed in a controlled temperature cabinet overnight at

-10ºC to ensure temperature equilibrium. On the morning of testing, the specimen was

placed in the environmental chamber at -10ºC and allowed to equilibrate for two hours.

To begin testing, the extensometers were zeroed, and a minimal contact load was

applied to the specimen. Each stress cycle was made up of a 0.1 second haversine pulse

followed by a 0.9 second hold cycle to simulate moving wheel loads. The data acquisition

system was set up to record the last six cycles at each frequency with about 400 points per

cycle. The raw force and displacement data were manipulated to obtain the resilient

modulus for each specimen. After the entire cycle of testing was complete at -10ºC, the

environmental chamber was set to the next temperature. After two hours of conditioning,

the above steps were repeated until the entire sequence of temperatures was completed.

The test was conducted based on the SHRP IDT testing procedures. The resilient

modulus is the ratio of the applied stress to the recoverable strain as shown in Equation

3.1. During the test, the load was carefully measured so that the horizontal strain was

within 100 and 300 micro-strains. These limits were established based on research

conducted by Roque et al. (1997) to accurately evaluate the resilient modulus and

Poisson’s Ratio of bituminous materials. The upper limit was set to make sure that the

horizontal strains were within the linear viscoelastic range and the lower limit was set to

obtain sufficient amplitude of strain against system noises.

65

rrRM εσ /= (3-1)

The Resilient Modulus and the Poisson’s Ratio were calculated using the equations

developed by Roque et al. (1997) based on a three-dimensional finite element analysis

(Equation 3-2 through Equation 3-4).

CMPL

RCDtH

GLPM

×××∆

×= (3-2)

332.0)(6354.0 1 −×= −

YXCCMPL (3-3)

222 )()(778.0)(480.11.0

YX

Dt

YX ××−×+−=ν (3-4)

Where

MR = Resilient Modulus P = Maximum Load GL = Gage Length

�H = Horizontal Deformation t = Thickness D = Diameter

CCMPL = Non-dimensional Factor � = Poisson’s Ratio

(X/Y) = Ratio of Horizontal to Vertical Deformation

Figure 3-8: Indirect Diametral Resilient Modulus Test Setup

66

Figure 3-9: Load & deformations in a typical resilient modulus test

3.6.2 Creep Compliance Test

Creep Compliance is a function of time-dependent strain (�t) divided by constraint

stress (�) (Equation 3-5). Once the Resilient Modulus Test was completed, the Creep Test

was conducted by applying a static load on the specimen for 100 seconds. Similar to the

MR Test, the horizontal strain was limited from 150 to 300 micro-strains at 100 seconds

to avoid excessive permanent deformation of the specimen. The equation used to

calculate the Creep Compliance is presented in Equation 3-6.

σ

ε )()(

ttD = (3-5)

GLP

CDtHtD CMPL

×

×××∆=)( (3-6)

where D(t) is the creep compliance at time t with a unit of 1/GPa, other parameters are the

same as defined in resilient modulus equations. The specimen set-up and transducers

attachment are the same as for the resilient modulus test. Figure 3-10 displays typical load

and deformation curves of the creep compliance test.

67

Load

De

form

atio

n

Time (sec.)

0

Loa

d

0

Vertical Deformation

Horizontal Deformation

Figure 3-10: Load and deformation curves of creep compliance test

3.6.3 Tensile Strength Test

The strength test is a destructive test. The strength test, along with the MR test, was

used to determine asphalt mixture fracture mechanics properties which included the

Tensile Strength (St), Fracture Energy (FE), Dissipate Creep Strain Energy (DCSE), and

Failure Strain. The procedures used to calculate these limits are presented in the

following equations (Roque et al. 1997):

Dt

DtDtP

Dt

CPS SX

t⋅⋅

⋅⋅+⋅−⋅−⋅=

⋅⋅=

π

νν

π

))/(436.12693.0)/(01114.0948.0(2)(2 (3-7)

� ⋅=tS

dFE0

εσ (2-36)

R

t

tEEM

SSEE

⋅=⋅⋅=

2

)(

2

12

ε (2-38)

EEFEDCSE −= (2-39)

68

Where CSX is the stress correction factor, t is specimen thickness, D is specimen diameter,

� is Poisson’s ratio, and other variables are the same as defined in section 2.5.

The specimen set-up and transducers attachment are the same as for the resilient

modulus test. However, the tensile strength test was conducted in a displacement control

mode by applying a constant rate of displacement of 12.5 mm/min at -10˚C, 25 mm/min

at 5˚C, and 50 mm/min at 25 and 40˚C. Figure 3-11 displays a specimen broken along the

diametral direction after the strength test.

Figure 3-11: Specimen fails after tensile strength test

3.6.4 DMT Test Procedures

The dynamic moduli and phase angle were measured by applying compressive

sinusoidal (haversine) loading. The deformations were measured through three LVDTs

(Linear Variable Differential Transducers). These LVDTs were placed vertically on

diametrically symmetric specimen sides (Figure 3-12). On the night before testing,

parallel studs were glued 100 mm (4”) apart, located approximately 25 mm (1”) from the

top and bottom of the specimen. They were used to secure the LVDTs in place. The

69

diameter of the specimens was 100 mm (4”) and the height was 150 mm (6”). They were

cut and cored from the raw gyratory compacted pills with diameters of 150 mm (6”) and

heights of 165 mm. The specimens were then placed in a controlled temperature cabinet

overnight at 5ºC to ensure temperature equilibrium. On the morning of testing, the

specimen was placed in the environmental chamber at 5ºC and allowed to equilibrate for

two hours. All testing was conducted using this temperature-controlled chamber capable

of accommodating temperatures from -16 to 60°C (3.2 to 140°F). Tests were performed

at temperatures of 5, 25, and 40 ºC and frequencies of 25, 10, 5, 1, and 0.5Hz. Testing

began with the lowest temperature and proceeded to the highest temperature. At a given

temperature level, the testing began with the highest frequency of loading and proceeded

to the lowest frequency. This temperature-frequency sequence was carried out to cause

minimum damage to the specimens before the next sequential test (Pellinen 2001).

Figure 3-12: Dynamic complex modulus test setup


applied to the specimens. A sinusoidal axial compressive load was applied to the

70

specimens without impact in a cyclical manner. The load was adjusted in each case to

attempt to keep the axial strains between 50 and 150 micro-strains. The first step was to

apply a preconditioning load to the specimens with 200 cycles at 25 Hz. Testing

continued with different numbers of cycles for each frequency. The data acquisition


cycle. The raw force and displacement data were manipulated to obtain the dynamic

modulus and phase angle for each specimen. After the entire cycle of testing was

complete at 5ºC, the environmental chamber was set to the next temperature. After two

hours of conditioning, the above steps were repeated until the entire sequence of

temperatures and frequencies was completed.

3.7 Testing Program

One coarse mix of Georgia granite and one coarse mix of limestone were selected

from Florida HMA Superpave mixtures as control mixes to study aggregate gradation and

SBS polymer-modified binder effects using the SHRP IDT testing and data processing

method. Each mix was modified to two gradation levels and three SBS polymer content

levels. In addition, a total of 20 standard mix designs were selected for a study of

correlations between resilient modulus and dynamic modulus. These mix designs were

contributed by companies involved in the production and use of HMA in Florida. The

nominal maximum aggregate sizes for the mixtures tested are 19.0 mm, 12.5 mm, and 9.5

mm, respectively. The Superpave mixture designs were selected because they are

commonly used FDOT gradations and are known to perform well in the field.

The HMA mixtures were compacted in the laboratory and the specimens were

prepared for the IDT and DMT. A flowchart is shown in Figure 3-13 to illustrate the

experimental program for measuring fracture mechanics properties of HMA mixtures.

The standard granite (Ga553, 04-3034A) and South Florida Limestone (SFL, 02-2529A)

mixtures at control level are named F2C and F4C, respectively. The testing program for

the study of the relationship between resilient modulus and complex dynamic modulus is

shown in Figure 3-14.

71

�� !"#$$%��&'(%&%')*

+

�' �!,�-��&�(�$�.)*

"�#/#��,�0/�

��1�/�2��/�"�#/#��

2��3#�4�1�

��"5��"�6��'"5��'"�

71)�322��,�0/�

%�,8,�7�9��

%:&;��':$;��#�/�<;

2��3#�4�1�

��75��7��7%6��'75��'7��'7%

"��#�� #��

,�� 0��=

>��9��1�/090��?��

(5&��$��$��'&@

&:5��A�#/

&:.��>��

�� 9�#��?��

(5&��$��$��'&@

,�#��A�#/

5&&��/�

?��9��,��=�4�?��

(5&��$��$��'&@

��#��B��9#��

��99��#��0��

B#�#�>�/0��

,�#��#9�)�#9��

Figure 3-13: Flowchart of the experimental program for measuring fracture mechanics properties of HMA mixtures

72

Figure 3-14: Flowchart of the testing program for MR vs. E*

TWENTY (20) FDOT HMA MIXTURES

SUPERPAVE GYRATORY

COMPACTION

SPECIMEN CORING & CUTTING

SUPERPAVE LEVEL I

MIX DESIGN

DYNAMIC COMPLEX MODULUS TESTING

(NCHRP 9-29)

INDIRECT RESILIENT MODULUS TESTING

(SHRP IDT Tester)

Temperature

40ºC 25ºC 5ºC

Frequency 25Hz 10Hz 5Hz 1Hz

0.5Hz

Temperature

40ºC 25ºC 5ºC

Frequency

0.1s Load 0.9s Rest

DYNAMIC MODULUS, E* &

PHASE ANGLE, φ

RESILIENT MODULUS, MR &

POISSON’S RATIO, C

DATA ANALYSIS

73

CHAPTER 4

FRACTURE MECHANICS PROPERTIES FROM IDT

The laboratory testing program conducted in this study included resilient modulus

testing, creep compliance testing, and tensile strength testing. All types of testing were

conducted in unconfined conditions. The Interlaken dynamic test system was used for all

of the sliced specimens to get the fracture mechanics properties including resilient

modulus (MR), creep (Dt), Fracture Energy (FE), and Dissipate Creep Strain Energy

(DCSE). The data reductions were conducted according to the procedures presented by

Roque et al. (1997).

4.1 Resilient Modulus Testing Procedures and Results

4.1.1 Test Procedures

After the specimens were well prepared, they were placed in a controlled temperature

cabinet and brought to the specified test temperature. The specimens were placed into the

loading apparatus; the loading strips were positioned in a parallel format and centered on

the vertical diametral plane. Tests were performed at temperatures of -10, 5, 25, and 40ºC

and at 1.0 Hz frequency. Testing began with the lowest temperature and proceeded to the

highest. On the night before testing, extensometers were placed on the test specimen

using glue. The specimen was then placed in a controlled temperature cabinet overnight

at -10ºC to ensure temperature equilibrium. On the morning of testing, the specimen was

placed in the environmental chamber at -10ºC and allowed to equilibrate for two hours.


applied to the specimen. Each stress cycle was made up of a 0.1-second haversine pulse

followed by a 0.9-second hold cycle to simulate moving wheel loads. The data acquisition


cycle. The raw force and displacement data were manipulated to obtain the resilient

modulus for each specimen as described in section 3.2. The load was selected to keep the

horizontal strain in the linear viscoelastic range which is typically 150 to 350 micro-

74

strains. After the entire cycle of testing was complete at -10ºC, the environmental

chamber was set to the next temperature. After two hours of conditioning, the above steps

were repeated until completion of the entire sequence of temperatures. Upon completion

of the resilient modulus tests, all samples were placed in the environmental chamber for

overnight conditioning before creep compliance testing and tensile strength testing.

4.1.2 Resilient Modulus Data Analysis and Results

For the measurement and analysis system used, two vertical and horizontal

measurements were obtained for each specimen. Data from five load cycles were

recorded after 100 cycles of equilibrium. The maximum load and the maximum

deformation were determined for each cycle from the load and deformation curves. Linear

regression was performed on the unloading and recovery portion of each deformation

wave to determine the instantaneous and total recoverable deformations (Figure 4-1). The

trimmed mean deformations and the average load were obtained from the replicate

specimens tested. The average total resilient modulus for each mixture was calculated

using Equation 3-2 through Equation 3-4. Table 4-1 through Table 4-4 show the resilient

modulus test results for all mixtures.

Figure 4-1: Instantaneous and total resilient deformations

75

Table 4-1: Resilient modulus test results at -10˚C

Mixtures with Modified Gradations

Control G1 G2

F2 F4 F2 F4 F2 F4

PrI 0.35 0.35 0.25 0.32 0.29 0.31

PrT 0.35 0.35 0.25 0.32 0.28 0.31

MrI (GPa) 28.91 20.98 30.08 21.79 29.19 20.55

MrT (GPa) 28.15 20.61 29.62 21.41 28.50 20.26

Mixtures with SBS Polymer-modified Binder

P1 (3.0%) P2 (4.5%) P3 (6.0%)

F2 F4 F2 F4 F2 F4

PrI 0.33 0.28 0.35 0.26 0.31 0.33

PrT 0.33 0.27 0.35 0.26 0.31 0.33

MrI (GPa) 27.10 19.24 24.93 16.42 23.06 14.49

MrT (GPa) 26.61 18.91 24.49 16.14 22.45 14.01

Note: PrI: Poisson’s Ratio, instantaneous; PrT: Poisson’s Ratio, total; MrI: Resilient Modulus, instantaneous; MrT: Resilient Modulus, total. 1 GPa = 145 ksi

Table 4-2: Resilient modulus test results at 5˚C


Control G1 G2

F2 F4 F2 F4 F2 F4

PrI 0.36 0.31 0.32 0.33 0.36 0.32

PrT 0.36 0.32 0.32 0.33 0.36 0.33

MrI (GPa) 19.22 13.40 18.57 13.31 19.50 11.90

MrT (GPa) 18.25 12.90 17.59 12.81 18.52 11.36


P1 (3.0%) P2 (4.5%) P3 (6.0%)

F2 F4 F2 F4 F2 F4

PrI 0.35 0.36 0.35 0.27 0.29 0.39

PrT 0.34 0.36 0.35 0.27 0.29 0.39

MrI (GPa) 19.71 12.49 17.24 10.97 14.80 7.93

MrT (GPa) 18.86 11.98 16.39 10.57 13.57 7.26

76



Control G1 G2

F2 F4 F2 F4 F2 F4

PrI 0.43 0.43 0.28 0.34 0.32 0.46

PrT 0.44 0.45 0.31 0.33 0.34 0.44

MrI (GPa) 6.21 4.80 5.58 4.96 5.29 4.90

MrT (GPa) 5.53 4.22 4.92 4.51 4.56 4.36


P1 (3.0%) P2 (4.5%) P3 (6.0%)

F2 F4 F2 F4 F2 F4

PrI 0.37 0.37 0.30 0.39 0.28 0.29

PrT 0.37 0.35 0.31 0.39 0.29 0.30

MrI (GPa) 6.15 4.32 4.90 4.53 3.54 2.21

MrT (GPa) 5.24 3.78 4.29 4.04 3.06 1.99



Control G1 G2

F2 F4 F2 F4 F2 F4

PrI 0.35 0.39 0.32 0.32 0.38 0.36

PrT 0.38 0.36 0.32 0.31 0.33 0.39

MrI (GPa) 1.39 1.48 1.40 1.66 1.65 1.42

MrT (GPa) 1.19 1.03 1.23 1.47 1.45 1.28


P1 (3.0%) P2 (4.5%) P3 (6.0%)

F2 F4 F2 F4 F2 F4

PrI 0.41 0.41 0.45 0.36 0.44 0.47

PrT 0.40 0.43 0.46 0.38 0.47 0.41

MrI (GPa) 1.96 1.28 2.09 1.40 1.22 1.25

MrT (GPa) 1.67 1.13 1.93 1.25 1.08 1.10

4.2 Creep Compliance Testing Procedures and Results


The mounting of LVDTs and the preloading for the creep compliance test were the

same as those for the resilient modulus test. A static load was applied on specimen for

100 seconds. The horizontal strains at the 30th second were controlled to be between 100

and 200 micro-strains to ensure the specimen was tested in viscoelastic range. If the range

77

limit was exceeded, the load was immediately removed from the specimen and a

minimum of three minutes rest period was allowed for the specimen to recover before

reloading at another appropriate level. The data acquisition program records the loads and

specimen deformations at a rate of 10 Hz. Matlab scripts were generated to analyze the

load and deformation data and to calculate the creep compliance values at points of

specified time. All specimens were placed in the environmental chamber for at least one

overnight recovery prior to the tensile strength test.

4.2.1 Creep Compliance Data Analysis and Results

For each creep compliance data file collected, the creep test start point and the initial

extensometer reading were determined first. Then the deformations for each creep time

point were calculated by determining the corresponding extensometer readings. The

deformations and axial load were averaged for the replicate specimens tested. The creep

compliance for each time point was calculated using Equation 3-6. The creep compliance

test results are summarized in Appendix B.

4.3 Tensile Strength Testing Procedures and Results


The tensile strength test was conducted in a displacement control mode by applying a

constant rate of displacement until the specimen failed. It was observed that the

specimens crashed too quickly to obtain sufficient data points if the rate of displacement

was relatively high at a certain level of temperature. In order to make data records and

reduction more accurate, the displacement rate was set as 12.5 mm/min (0.5 in/min) at

-10ºC, 25 mm/min (1.0 in/min) at 5ºC, 50 mm/min (2.0 in/min) at 25ºC and 40ºC. The

horizontal and vertical deformation and the applied load were recorded at a rate of 20 Hz

during the test. The dissipated creep strain energy (DCSE) and fracture energy (FE) can

be determined from the tensile strength and resilient modulus of the specimen. The

schematics used to calculate these limits are described in section 2.5 and are displayed in

Figure 4-2 for reference.

78

4.3.2 Tensile Strength Data Analysis and Results

Similar to the data reduction procedures for resilient modulus and creep compliance,

the load and deformations at each time point were determined first for each tensile

strength data file. Specifically, the instant of failure is identified as the point in time at

which the difference between the vertical and horizontal deformations reaches a peak ((Y-

X) peak). The tensile strength was then calculated using Equation 3-7. The strength of the

mixture was obtained by taking the average value of the replicated specimens tested.

Stress and strain at each time point were calculated from the start of the load cycle to the

instant of specimen failure using the following equations (Roque et al. 1997):

))/(436.12693.0)/(01114.0948.0(2

)( ννπ

σ ⋅⋅+⋅−⋅−⋅⋅⋅

⋅= DtDt

Dt

Loadt (4-1)

))/(089.0081.0)/(189.003.1()(

072.1)( 2DtDt

GL

tnDeformatiot ⋅+⋅−⋅−⋅⋅= νε (4-2)

Where �(t) is stress and � is strain. Other variables are the same as defined in section 3.6.

The fracture energy is obtained by integrating the area under the stress-strain curve until

failure as shown in Figure 4-2 for convenience. All fracture mechanics parameters

obtained from the tensile strength test were calculated using Equations 2-36 through 2-39

and are presented in Table 4-5 and Table 4-6.

e0 ef Strain

St

MR

EE

Dissipated Creep Strain Energy

(DCSE)

MR

Str

ess

Figure 4-2: Determination of fracture energy and dissipated creep strain energy

79

Table 4-5: Tensile strength test results for F2 series mixtures

F2 Control Temperature (˚C) -10 5 25 40

EE (KPa) 0.45 0.27 0.07 0.04

DCSE (KPa) 2.37 5.16 3.37 1.84

FE (KPa) 2.82 5.43 3.44 1.88

TS (MPa) 5.04 3.11 0.90 0.32

FS (103 micro) 0.86 4.35 5.56 10.78

F2G1 Temperature (˚C) -10 5 25 40

EE (KPa) 0.28 0.30 0.10 0.05

DCSE (KPa) 1.07 4.82 2.79 1.26

FE (KPa) 1.35 5.12 2.89 1.31

TS (MPa) 4.07 3.23 1.00 0.35

FS (103 micro) 0.54 2.04 3.75 5.13


EE (KPa) 0.39 0.28 0.15 0.06

DCSE (KPa) 2.34 4.69 2.46 2.41

FE (KPa) 2.73 4.97 2.61 2.47

TS (MPa) 4.72 3.22 1.15 0.43

FS (103 micro) 0.87 2.00 2.95 7.63

F2P1 (3.0%) Temperature (˚C) -10 5 25 40

EE (KPa) 0.30 0.50 0.15 0.06

DCSE (KPa) 1.99 6.93 3.14 1.06

FE (KPa) 2.29 7.43 3.29 1.12

TS (MPa) 3.88 4.33 1.23 0.43

FS (103 micro) 0.77 2.28 3.73 3.55

F2P2 (4.5%) Temperature (˚C) -10 5 25 40

EE (KPa) 0.41 0.20 0.46 0.03

DCSE (KPa) 2.58 5.06 4.73 2.37

FE (KPa) 3.00 5.25 5.19 2.40

TS (MPa) 4.44 2.52 1.99 0.34

FS (103 micro) 3.04 2.64 3.30 9.00

F2P3 (6.0%) Temperature (˚C) -10 5 25 40

EE (KPa) 0.42 0.19 0.15 0.08

DCSE (KPa) 3.12 7.27 3.76 2.65

FE (KPa) 3.53 7.46 3.91 2.72

TS (MPa) 4.33 2.25 0.96 0.41

FS (103 micro) 1.66 5.90 5.29 9.19

Note EE: elastic energy DCSE: dissipated creep strain energy FE: total fracture energy TS: tensile strength FS: failure strain 1 MPa = 145 psi 1 KPa = 0.145 psi 1 micro-strain = 10

-6 mm/mm (in./in.)

80

Table 4-6: Tensile strength test results for F4 series mixtures

F4 Control Temperature (˚C) -10 5 25 40

EE (KPa) 0.41 0.49 0.11 0.07

DCSE (KPa) 1.69 4.57 3.86 1.91

FE (KPa) 2.11 5.06 3.98 1.98

TS (MPa) 4.10 3.57 0.98 0.37

FS (103 micro) 0.86 1.95 9.85 6.36


EE (KPa) 0.25 0.40 0.09 0.04

DCSE (KPa) 2.25 4.21 2.01 1.52

FE (KPa) 2.51 4.61 2.10 1.56

TS (MPa) 3.30 3.21 0.88 0.36

FS (103 micro) 1.12 1.84 3.13 5.56


EE (KPa) 0.36 0.45 0.07 0.04

DCSE (KPa) 1.92 4.72 2.80 1.90

FE (KPa) 2.28 5.18 2.87 1.94

TS (MPa) 3.81 3.21 0.77 0.30

FS (103 micro) 0.93 2.16 4.66 8.52

F4P1 (3.0%) Temperature (˚C) -10 5 25 40

EE (KPa) 0.52 0.48 0.10 0.10

DCSE (KPa) 2.44 5.76 4.18 3.68

FE (KPa) 2.96 6.24 4.31 3.79

TS (MPa) 4.42 3.38 0.85 0.48

FS (103 micro) 1.09 2.50 6.25 10.24

F4P2 (4.5%) Temperature (˚C) -10 5 25 40

EE (KPa) 0.67 0.47 0.15 0.06

DCSE (KPa) 1.85 5.83 3.20 3.00

FE (KPa) 2.52 6.29 3.35 3.06

TS (MPa) 4.62 3.14 1.09 0.38

FS (103 micro) 0.89 2.62 4.08 11.00

F4P3 (6.0%) Temperature (˚C) -10 5 25 40

EE (KPa) 0.68 0.31 0.13 0.13

DCSE (KPa) 8.09 6.38 4.80 5.62

FE (KPa) 8.77 6.69 4.92 5.75

TS (MPa) 4.36 2.12 0.71 0.54

FS (103 micro) 3.10 4.24 11.10 13.70

81

CHAPTER 5

EVALUATION OF FRACTURE MECHANICS PROPERTIES

In this chapter, two effects – the effect of coarse aggregate gradation modification

and the effect of SBS polymer-modified asphalt binder – will be further evaluated with

respect to the fracture mechanics properties presented in Chapter 4. The evaluation of

each impact will be focused on the following parameters obtained from the sweep of IDT

tests: resilient modulus, creep compliance, tensile strength, fracture energy, and dissipated

creep strain energy. A brief summary of discussion will be given at the end of this

chapter.

5.1 Evaluation of Gradation Effects

5.1.1 Evaluation of Gradation Curves for Modified Gradation Mixtures

The power law model developed by Ruth et al. (2002) was used to fit the gradation

curve for each mixture. As described in section 4.3, coarse portions of the control

mixtures (percent passing 1/2 in. and 3/8 in. sieves) were modified, and the fine portions

were maintained. Therefore, the power law constant and exponent (aca, nca) for only

coarse aggregate were calculated by regression for the mixtures. The format of the power

law equation is

can

caca daP )(⋅= (5-1)

where Pca is the percent of material by weight passing a given sieve having an opening of

width d. The break sieve size to distinguish coarse and fine aggregate is defined by the

primary control sieve (PCS) based on the Bailey method:

22.0×= NMPSPCS (5-2)

where PCS is the primary control sieve for the overall blend which defines the break

between coarse and fine aggregate, and NMPS is the nominal maximum particle size for

the overall blend as defined in Superpave mix design, which is one sieve larger than the

82

first sieve that retains more than 10%. The NMPS for F2 control and F4 control are both

12.5 mm in this study. The “break” sieve size should be 12.5 × 0.22 = 2.75 mm, which

corresponds to the No. 8 sieve. However, since the percent passing No. 4 and smaller

sieves are all the same for control and modified gradations, the parameters used for the

power law regression are No. 4 and higher sieve sizes. The regression coefficients are

also shown in Figure 5-1 and Figure 5-2. For each series, whether granite or limestone,

the regression parameters (aca and nca) decreased by a small amount as the coarse size

aggregate increased. As expected, the fitted curves are in the same order as their real

gradation curves. Table 5-1 summarizes the regression coefficients for the control mixes

and those with modified gradations. According to Birgisson et al. (2004), a high nca

implies a low dynamic modulus at a high temperature of 40˚C when controlling for nfa.

The fine portions of the control gradations were maintained in this study, and the

mixtures with modified gradations obtained a lower nca. This implies that the modified

gradations would have higher dynamic moduli than control mixes at high temperature

levels which are favorable characteristics for HMA performance.

Power Law Regression F2 Series

y = 25.693x0.491

R2 = 0.9178

y = 25.228x0.4851

R2 = 0.9708

y = 24.917x0.4676

R2 = 0.9979

40

60

80

100

120

5 10 15 20 25

Sieve Size (mm)

Perc

ent

Passin

g (

%) F2

F2G1

F2G2

Pow er (F2)

Pow er (F2G1)

Pow er (F2G2)

Figure 5-1: Power law regression for F2 gradation series

83

Power Law Regression F4 Series

y = 30.548x0.4295

R2 = 0.8941

y = 29.605x0.4256

R2 = 0.9792

y = 28.95x0.4095

R2 = 0.9818

40

60

80

100

120

5 10 15 20 25

Sieve Size (mm)

Perc

ent

Passin

g (

%) F4

F4G1

F4G2

Pow er (F4)

Pow er (F4G1)

Pow er (F4G2)

Figure 5-2: Power law regression for F4 gradation series

Table 5-1: Power law regression coefficients for modified gradation mixes

Mixture F2 F2G1 F2G2 F4 F4G1 F4G2

aca 25.693 25.228 24.917 30.548 29.605 28.95

nca 0.491 0.4851 0.4676 0.4295 0.4256 0.4095

R2 0.9178 0.9708 0.9979 0.8941 0.9792 0.9818

5.1.2 Evaluation of Resilient Modulus for Modified Gradation Mixtures

Figure 5-3 shows the resilient modulus comparisons at various temperature levels.

Using the resilient modulus values at control level in abscissa and the values at modified

gradation in ordinate, a trend line can be plotted to present the relationship of resilient

modulus between control and modified gradation mixes, as shown in Figure 5-4. The

linear regression coefficient ranges from 0.96 to 1.03. The correlation coefficients (R2)

are all higher than 0.99, which indicates the linear relationship is very strong. From these

results, it can be concluded that no significant difference in resilient modulus was present

between the control mix design and the mixes with modified gradations. Increasing the

84

amount of 1/2 in. coarse aggregate within the range of 5% to 15% appeared to have

minimal influence on mixtures’ resilient modulus.

0

10

20

30

-10 5 25 40

Temperature (˚C)

Resili

ent

Modulu

s (

GP

a)

F2 Control

F2G1

F2G2

F4 Control

F4G1

F4G2

Figure 5-3: Resilient modulus for mixtures with modified gradations (1 GPa = 145 ksi)

y = 1.0224x

R2 = 0.9952

0

10

20

30

40

0 20 40

MR for F2 Control (GPa)

MR f

or

F2G

1 (

Gpa)

(a)

y = 1.0087x

R2 = 0.9976

0

10

20

30

40

0 20 40


MR f

or

F2G

2 (

Gpa)

(b)

85

y = 1.028x

R2 = 0.9982

0

10

20

30

0 10 20 30


MR f

or

F4G

1 (

Gpa)

(c)

y = 0.957x

R2 = 0.9932

0

10

20

30

0 10 20 30


MR f

or

F4G

2 (

Gpa)

(d)

Figure 5-4: Comparison of resilient modulus between control and modified gradations

5.1.3 Evaluation of Creep Compliance for Modified Gradation Mixtures

The creep compliance test results were analyzed using the power law relationship

presented by Roque et al. (1997):

m

tDDtD 10)( += (5-3)

It was showed that the parameters obtained from this model are fairly accurate

indicators for the viscous response and rutting performance of HMA mixtures. Kim et al.

(2005) recommended a fixed D0 value (0.0483 1/GPa, or 3.33×10-7 psi) to obtain more

consistent D1 and m values for the tests conducted at 0, 10 and 20˚C. Master curve

construction for creep compliance curves in this study included D0 in the parametric

analysis since the lowest testing temperature of -10˚C was used as the reference

temperature. Table 5-2, Figure 5-5 and Figure 5-6 show the regression coefficients D1 and

m for all mixes at control level and modified gradations. The comparisons of creep

compliance master curves for F2 and F4 gradation series are shown in Figure 5-7 and

Figure 5-8, respectively. The creep compliance curves within each aggregate type are very

similar to each other, with the exception of the control level granite mixture (F2 Control),

which is a little less compliant at high temperature (40˚C) than the other two mixes that

were blended with higher portions of coarse aggregate. This implies that the increase of

86

5% to 15% of 1/2" aggregate did not make a significant difference in the creep

compliance properties for the HMA tested.

Table 5-2: Power model regression coefficients for modified gradation tests

F2C F2G1 F2G2 F4C F4G1 F4G2

D1 (1/GPa) 0.012 0.007 0.009 0.013 0.007 0.010

m 0.360 0.410 0.398 0.369 0.404 0.370

0.0E+00

3.0E-03

6.0E-03

9.0E-03

1.2E-02

1.5E-02

F2 Mixes F4 Mixes

D1 (

1/G

pa)

Control

G1

G2

Figure 5-5: Power model parameter D1 for modified gradations (1/GPa = 6.89×10-6/psi)

0.0

0.1

0.2

0.3

0.4

0.5

F2 Mixes F4 Mixes

m

Control

G1

G2

Figure 5-6: Power model parameter m for modified gradations

87

-2

-1

0

1

2

3

0 2 4 6 8 10

Log (T) (Sec.)

Log (

D)

(1/G

pa)

F2 Control

F2G1

F2G2

Figure 5-7: Comparison of creep compliance for granite gradation series (1/GPa = 6.89×10-6/psi)

-2

-1

0

1

2

3

0 2 4 6 8 10

Log (T) (Sec.)

Log (

D)

(1/G

pa)

F4 Control

F4G1

F4G2

Figure 5-8: Comparison of creep compliance for limestone gradation series (1/GPa = 6.89×10-6/psi)

88

5.1.4 Evaluation of Tensile Strength and Fracture Energy for Modified Gradation

Mixtures

The indirect tensile strength (TS) of control mixtures and the modified gradation

mixtures is presented in Figure 5-9. The tensile strength clearly shows the expected trends

that the strength value decreases as the temperature increases. A comparison of strength

values between control and modified gradation mixtures is shown in Figure 5-10. At mid

to high service temperatures (25 and 40˚C), the tensile strength values for all mixtures are

similar and the differences appear to be negligible. However, at low service temperatures

(-10 and 5˚C), the tensile strength of mixtures with modified gradations are clearly lower

than that of control level mixtures. This tends to indicate that increasing the coarse

aggregate in the standard control mixture has an adverse effect on the tensile strength

property of the HMA at low temperatures.

Figure 5-11 and Figure 5-12 show the test results of Fracture Energy (FE) and

Dissipated Creep Strain Energy (DCSE), respectively, for all mixtures of modified

gradation. It is observed that fracture energy values are lower at both low (-10˚C) and

high (40˚C) temperatures than at mid-range temperatures (5 and 25˚C). The reason for

this trend is that the fracture energy is calculated as the area under the stress-strain curve

of the tensile strength test. At low testing temperatures, the tensile strength of HMA is

large but the failure strain is very small. At high temperatures, in contrast, the tensile

strength of HMA is the lowest but the failure strain is the highest due to the ductile effect

of asphalt binder. At some mid-range temperatures, the integration of the stress and strain

curve attains a peak value. The trend of dissipated energy (DCSE) is essentially the same

as for the fracture energy. Comparisons of fracture energy and DCSE between control

mixtures and modified gradations are presented in Figure 5-13 and Figure 5-14,

respectively. The distributions of the points in the two figures are very similar. A majority

of the point falls close to or under the equality line which means that the fracture energy

values (or DCSE values) of modified gradations are less than those of the control mixes.

89

0

2

4

6

-10 5 25 40

Temperature (˚C)

Tensile

Str

ength

(M

Pa)

F2 Control

F2G1

F2G2

F4 Control

F4G1

F4G2

Figure 5-9: Tensile strength for control and modified gradation mixes (1 MPa = 145 psi)

0

2

4

6

0 2 4 6

Tensile Strength of Control Level (MPa)

Tensile

Str

ength

of

Modifie

d G

radations (

MP

a)

F2G1 vs F2C

F2G2 vs F2C

Equality Line

F4G1 vs F4C

F4G2 vs F4C

Low Service

Temperatures:

-10 and 5˚C

Figure 5-10: Comparison of TS between control and modified gradation mixes

90

0

2

4

6

-10 5 25 40

Temperature (˚C)

Fra

ctu

re E

nerg

y (

KP

a)

F2 Control

F2G1

F2G2

F4 Control

F4G1

F4G2

Figure 5-11: Fracture Energy for modified gradation mixes (1 KPa = 0.145 psi)

0

2

4

6

-10 5 25 40

Temperature (˚C)

DC

SE

(K

Pa)

F2 Control

F2G1

F2G2

F4 Control

F4G1

F4G2

Figure 5-12: DCSE for modified gradation mixes (1 KPa = 0.145 psi)

91

0

2

4

6

0 2 4 6

Fracture Energy

of Control Mixes (KPa)

Fra

ctu

re E

nerg

y o

f

Modifie

d G

radations (

KP

a)

F2G1 vs F2C

F2G2 vs F2C

Equality Line

F4G1 vs F4C

F4G2 vs F4C

Figure 5-13: Comparison of Fracture Energy for modified gradation mixtures

0

2

4

6

0 2 4 6

DCSE of Control Mixes (KPa)

DC

SE

of

Modifie

d G

radations (

KP

a)

F2G1 vs F2C

F2G2 vs F2C

Equality Line

F4G1 vs F4C

F4G2 vs F4C

Figure 5-14: Comparison of DCSE for modified gradation mixtures

92

5.2 Evaluation of SBS Polymer-modified Binder Effects

5.2.1 Evaluation of Resilient Modulus for SBS Polymer-modified Mixtures

Similar to the comparison of resilient modulus between control level and modified

gradation mixtures presented in the last section, Figure 5-15 and Figure 5-16 show

comparisons of resilient modulus values at various temperature levels for the SBS

polymer-modified asphalt mixes of F2 and F4 series, respectively. It can be clearly seen

that at low to mid-range temperature levels (-10, 5, and 25˚C), the resilient modulus

values of PMA mixtures are less than those of control mixtures, and that an increment of

SBS polymer content lowers the resilient modulus magnitude. The only exception is that

the MR of F2P1 at 5˚C is a little higher than that of the F2 control. At a high testing

temperature (40˚C), however, the resilient moduli of PMA mixtures are higher than those

of the control mixtures and increase with the increase of SBS polymer content, except

that the MR values of 6.0% PMA mixtures drop back down. This phenomenon indicates

that the effect of SBS concentration for PMA mixtures appears to be consistent with the

findings presented by Chen et al. (2002, 2003) for SBS modified asphalt binders. It

implies that an optimum SBS content exists within the 3% to 6% range which would

make the PMA mixture stiffness the highest at the high service temperature, but increases

in polymer content after the optimum had an adverse effect on PMA resilient modulus

property, which was probably due to the mixing and distribution problems of SBS

polymer, base bitumen, and aggregate.

Trend lines are developed in Figure 5-17 for each PMA mixture versus the control

mixture. As shown in the figures, the linear regression coefficient decreases as the content

of SBS polymer modifier increases, and all correlation coefficient (R2) values are greater

than 0.97. The linear regression indicates an obvious trend that increasing SBS polymer

content makes the resilient modulus of HMA lower at low and mid-range temperatures.

Based on the above investigations, the MR results show that SBS modifiers make HMA

softer at mid-range to low service temperatures and stiffer at the highest testing

temperature (40˚C), which are both favorable attributes for the improvement of the HMA

performance issues of low temperature thermal cracking and high temperature rutting.

93

0

10

20

30

-10 5 25 40

Temperature (˚C)

Resili

ent

Modulu

s (

GP

a)

F2 Control

F2P1

F2P2

F2P3

Figure 5-15: Comparison of resilient modulus for F2 SBS PMA mixes (1 GPa = 145 psi)

0

5

10

15

20

25

-10 5 25 40

Temperature (˚C)

Resili

ent

Modulu

s (

GP

a)

F4 Control

F4P1

F4P2

F4P3

Figure 5-16: Comparison of resilient modulus for F4 SBS PMA mixes (1 GPa = 145 psi)

94

y = 0.9715x

R2 = 0.9949

0

10

20

30

0 10 20 30


MR f

or

F2P

1 (

Gpa)

(a)

y = 0.9204x

R2 = 0.9997

0

5

10

15

20

25

0 5 10 15 20 25


MR f

or

F4P

1 (

Gpa)

(b)

y = 0.8767x

R2 = 0.9961

0

10

20

30

0 10 20 30


MR f

or

F2P

2 (

Gpa)

(c)

y = 0.7987x

R2 = 0.994

0

5

10

15

20

25

0 5 10 15 20 25


MR f

or

F4P

2 (

Gpa)

(d)

y = 0.7756x

R2 = 0.9923

0

10

20

30

0 10 20 30


MR f

or

F2P

3 (

Gpa)

(e)

y = 0.6425x

R2 = 0.9777

0

5

10

15

20

25

0 5 10 15 20 25


MR f

or

F4P

3 (

Gpa)

(f)

Figure 5-17: Comparison of MR between control and PMA mixtures

95

5.2.2 Evaluation of Creep Compliance for SBS Polymer-modified Mixtures

Table 5-3, Figure 5-18 and Figure 5-19 show the regression coefficients D1 and m

from creep compliance test results for all mixes with SBS polymer-modified binders. The

creep compliance master curves are developed and shown in Figure 5-20 and Figure 5-21

for the F2 and F4 series, respectively. As demonstrated in the figures, at low reduced time

of about 0 to 104.4 seconds, the PMA mixtures are all more compliant than the control

mixes. This means the polymer modifier makes the HMA more ductile at low

temperatures which would be beneficial to the reduction of thermal cracking. At higher

reduced time, the master curves come across each other and the PMA mixture master

curves tend to go under the control ones, indicating that the PMA mixes are stiffer and

more resistant to rutting at high temperatures. The temperature effect for creep

compliance of PMA mixtures can be also observed clearly from the direct testing results

plotted in Figure 5-22 through Figure 5-29. At -10˚C, all the CP values of PMA mixtures

are higher than those of control mixes. On the other hand, at 40˚C, the points all drop

below the equality line except that F4P2 is a little higher than the F4 control. These

observations further verify the SBS polymer effect discussed in the resilient modulus

results. At mid-range temperatures (5˚C and 25˚C), the creep compliance of specimens

did not differ significantly. In addition, the linear regression indicates that at a specific

temperature level for each mix series, an increment of SBS polymer content usually

results in higher creep compliance values. The two exceptions are that the creep

compliance of F2P1 is a little higher than that of F2P2 at 5˚C, and the creep compliance

of F4P2 is higher than that of F4P3 at 40˚C.

Table 5-3: Power model regression coefficients for PMA mixture tests

F2P1 F2P2 F2P3 F4P1 F4P2 F4P3

D1 (1/GPa) 0.011 0.014 0.034 0.016 0.015 0.017

m 0.413 0.365 0.279 0.353 0.365 0.318

96

0.0E+00

1.0E-02

2.0E-02

3.0E-02

4.0E-02

F2 Mixes F4 Mixes

D1 (

1/G

pa) Control

P1

P2

P3

Figure 5-18: Power model parameter D1 for mixes with SBS PMA (1/GPa = 6.89×10-6/psi)

0.0

0.1

0.2

0.3

0.4

0.5

F2 Mixes F4 Mixes

m

Control

P1

P2

P3

Figure 5-19: Power model parameter m for mixes with SBS PMA

97

-2

-1

0

1

2

3

0 2 4 6 8 10

Log (T) (Sec.)

Log (

D)

(1/G

pa)

F2 Control

F2P1

F2P2

F2P3

Low Reduced

Time

High Reduced

Time

Figure 5-20: Creep compliance master curves for granite PMA mixtures (1/GPa = 6.89×10-6/psi)

-2

-1

0

1

2

3

0 2 4 6 8 10

Log (T) (Sec.)

Log (

D)

(1/G

pa)

F4 Control

F4P1

F4P2

F4P3

Low Reduced

Time

High Reduced

Time

Figure 5-21: Creep compliance master curves for limestone PMA mixtures (1/GPa = 6.89×10-6/psi)

98

0.03

0.06

0.09

0.12

0.15

0.03 0.06 0.09 0.12 0.15

D(t) of Control Mixtures (1/GPa)

D(t

) of

PM

A M

ixtu

res (

1/G

Pa)

F2P1 vs F2C

F2P2 vs F2C

F2P3 vs F2C

Equality Line

F2P1 Fit, y=1.096x

F2P2 Fit, y=1.122x

F2P3 Fit, y=1.424x

Figure 5-22: Comparison of creep compliance at -10˚C for F2 series

0.0

0.2

0.4

0.6

0.8

0.0 0.2 0.4 0.6 0.8


D(t

) of

PM

A M

ixtu

res (

1/G

Pa) F2P1 vs F2C

F2P2 vs F2C

F2P3 vs F2C

Equality Line

F2P1 Fit, y=0.782x

F2P2 Fit, y=0.693x

F2P3 Fit, y=0.966x

Figure 5-23: Comparison of creep compliance at 5˚C for F2 series

99

0

2

4

6

0 2 4 6


D(t

) of

PM

A M

ixtu

res (

1/G

Pa) F2P1 vs F2C

F2P2 vs F2C

F2P3 vs F2C

Equality Line

F2P1 Fit, y=0.760x

F2P2 Fit, y=1.031x

F2P3 Fit, y=1.126x


0

3

6

9

12

15

0 3 6 9 12 15


D(t

) of

PM

A M

ixtu

res (

1/G

Pa) F2P1 vs F2C

F2P2 vs F2C

F2P3 vs F2C

Equality Line

F2P1 Fit, y=0.519x

F2P2 Fit, y=0.540x

F2P3 Fit, y=0.742x


100

0.03

0.06

0.09

0.12

0.15

0.03 0.06 0.09 0.12 0.15


D(t

) of

PM

A M

ixtu

res (

1/G

Pa)

Equality Line

F4P1 vs F4C

F4P2 vs F4C

F4P3 vs F4C

F4P1 Fit, y=1.145x

F4P2 Fit, y=1.269x

F4P1 Fit, y=1.418x

Figure 5-26: Comparison of creep compliance at -10˚C for F4 series

0.0

0.2

0.4

0.6

0.8

0.0 0.2 0.4 0.6 0.8


D(t

) of

PM

A M

ixtu

res (

1/G

Pa) Equality Line

F4P1 vs F4C

F4P2 vs F4C

F4P3 vs F4C

F4P1 Fit, y=0.831x

F4P2 Fit, y=0.924x

F4P3 Fit, y=1.208x


101

0

2

4

6

0 2 4 6


D(t

) of

PM

A M

ixtu

res (

1/G

Pa) Equality Line

F4P1 vs F4C

F4P2 vs F4C

F4P3 vs F4C

F4P1 Fit, y=0.872x

F4P2 Fit, y=1.063x

F4P3 Fit, y=1.084x


0

3

6

9

12

15

0 3 6 9 12 15


D(t

) of

PM

A M

ixtu

res (

1/G

Pa)

Equality Line

F4P1 vs F4C

F4P2 vs F4C

F4P3 vs F4C

F4P1 Fit, y=0.578x

F4P2 Fit, y=1.055x

F4P3 Fit, y=0.692x


102

5.2.3 Evaluation of Tensile Strength and Fracture Energy for SBS Polymer-

modified Mixtures

Figure 5-30 and Figure 5-31 show the test results of Tensile Strength (TS) for control

mixtures and polymer-modified asphalt mixtures. The comparison of tensile strength

between control and PMA mixtures is presented in Figure 5-32. The SBS polymer did not

seem to critically affect the HMA tensile strength.

Figure 5-33 through Figure 5-36 show the test results of fracture energy (FE) and

Dissipated Creep Strain Energy (DCSE) for control mixtures and PMA mixtures. As

discussed in modified gradation mixes, the trend of dissipated energy (DCSE) is the same

as for the fracture energy, since the elastic energy part of HMA mixture is essentially

determined by tensile strength and resilient modulus, which did not differ noticeably; for

a specific HMA specimen, the magnitude of the elastic energy observed (0-0.7 KPa) is

usually much lower than the magnitude of the total fracture energy (1-9 KPa).

Comparisons of fracture energy and DCSE values are displayed in Figure 5-37 and Figure

5-38. Most of the points fall above the equality line indicating that SBS polymer tends to

increase the fracture energy or DCSE and hence improve the fatigue cracking

performance of HMA mixtures. However, no specific relationship was observed between

the fracture energy parameters and the SBS polymer content.

At mid-range to high temperatures (25˚C and 40˚C), the PMA mixtures exhibit

complicated behavior on failure strains which did not show any clear trend, probably due

to the enhanced viscous effect of the polymer-modified binder, which makes the mixture

properties more dependent on the overall particle distributions of the SBS polymer, the

asphalt, and the aggregate. At low testing temperatures (-10˚C and 5˚C), it is found that

the failure strain of PMA mixtures tends to increase with an increase of SBS polymer

content, as shown in Figure 5-39. This phenomenon is in agreement with the findings

reported by Kennedy et al. (1992).

103

0

2

4

6

-10 5 25 40

Temperature (˚C)

Tensile

Str

ength

(M

Pa)

F2 Control

F2P1

F2P2

F2P3

Figure 5-30: Tensile strength for granite PMA mixes (1 MPa = 145 psi)

0

2

4

6

-10 5 25 40

Temperature (˚C)

Tensile

Str

ength

(M

Pa)

F4 Control

F4P1

F4P2

F4P3

Figure 5-31: Tensile strength for limestone PMA mixes (1 MPa = 145 psi)

104

0

2

4

6

0 2 4 6

Tensile Strength of Control Level (MPa)

Tensile

Str

ength

of

PM

A M

ixes (

MP

a)

F2P1 vs F2C

F2P2 vs F2C

F2P3 vs F2C

Equality Line

F4P1 vs F4C

F4P2 vs F4C

F4P3 vs F4C

Figure 5-32: Comparison of tensile strength between control and PMA mixes

0

2

4

6

8

10

-10 5 25 40

Temperature (˚C)

Fra

ctu

re E

nerg

y (

KP

a)

F2 Control

F2P1

F2P2

F2P3

Figure 5-33: Fracture Energy for granite PMA mixes (1 KPa = 0.145 psi)

105

0

2

4

6

8

10

-10 5 25 40

Temperature (˚C)

Fra

ctu

re E

nerg

y (

KP

a)

F4 Control

F4P1

F4P2

F4P3

Figure 5-34: Fracture Energy for limestone PMA mixes (1 KPa = 0.145 psi)

0

2

4

6

8

10

-10 5 25 40

Temperature (˚C)

DC

SE

(K

Pa)

F2 Control

F2P1

F2P2

F2P3

Figure 5-35: DCSE for granite PMA mixes (1 KPa = 0.145 psi)

106

0

2

4

6

8

10

-10 5 25 40

Temperature (˚C)

DC

SE

(K

Pa)

F4 Control

F4P1

F4P2

F4P3

Figure 5-36: DCSE for limestone PMA mixes (1 KPa = 0.145 psi)

0

2

4

6

8

10

0 2 4 6 8 10

Fracture Energy of Control Mixes (KPa)

Fra

ctu

re E

nerg

y o

f P

MA

Mix

ture

s (

KP

a)

F2P1 vs F2C

F2P2 vs F2C

F2P3 vs F2C

Equality Line

F4P1 vs F4C

F4P2 vs F4C

F4P3 vs F4C

Figure 5-37: Comparison of Fracture Energy between control and PMA mixes

107

0

2

4

6

8

10

0 2 4 6 8 10

DCSE of Control Mixes (KPa)

DC

SE

of

PM

A M

ixtu

res (

KP

a)

F2P1 vs F2C

F2P2 vs F2C

F2P3 vs F2C

Equality Line

F4P1 vs F4C

F4P2 vs F4C

F4P3 vs F4C

Figure 5-38: Comparison of Fracture Energy between control and PMA mixes

0.0E+00

1.0E+03

2.0E+03

3.0E+03

4.0E+03

5.0E+03

0.0 2.0 4.0 6.0 8.0

SBS Polymer Content, % weight

Failu

re S

train

(m

icro

-str

ain

)

F2 Series -10˚C

F2 Series 5˚C

F4 Series -10˚C

F4 Series 5˚C

Figure 5-39: Relationship between the observed Failure Strain and SBS polymer content

108

5.3 Effect of Aggregate Type

Another important factor that influences HMA engineering properties is aggregate

type. As introduced in the preceding chapter, two major aggregate types, granite and

limestone, were used in this HMA fracture mechanics study. For control mixes (F2C and

F4C), the mix designs with two different types of aggregate have the same nominal

maximum aggregate size (1/2 in. or 12.5 mm), the same control limit points, the same

restricted zone, and hence very similar gradation curves (Figure 5-40). For the modified

gradation mixes, the adjustment of aggregate amount for each gradation level (G1 or G2)

at each sieve size is also close, and this makes the adjusted shapes of gradation curves for

the two different types of aggregate appear to be alike. For the mixtures with SBS

polymer-modified asphalt binder, the polymer content is identical at each level (3.0%,

4.5%, and 6.0%). All these analogues provide a basis to evaluate the differences of

fracture mechanics properties between the two types of aggregate. It is commonly known

that limestone aggregate is usually softer than granite aggregate. Figure 5-41 shows a

comparison of resilient modulus between granite and limestone mixtures. All points fall

below the line of equality, which confirms that the granite mixtures are stiffer than

limestone mixtures. In particular, the difference of resilient modulus values between the

two types of aggregate at mid-range to low temperature levels (-10˚C and 5˚C) is much

more remarkable than that at elevated testing temperatures (25˚C and 40˚C). From this

point of view, the limestone mixtures would appear more ductile under low service

temperature conditions, and as a result would be capable of improving the performance of

thermal cracking of pavement structures.

The comparisons of creep compliance between granite and limestone mixtures at

each testing temperature are shown in Figure 5-42 through Figure 5-45. The result is not

as simple as the limestone always being more compliant than granite. At low

temperatures (-10˚C and 5˚C), the creep compliance values of limestone mixtures are all

higher than those of granite mixtures. At 25˚C, the data points are distributed closely

along the line of equality. When the temperature goes up to 40˚C, most of the data points

go under the line of equality, which means that the limestone specimens become less

compliant than the granite specimens. These characteristics exhibited by limestone

109

mixtures are advantageous to pavement structures in improving performance of thermal

cracking at low service temperatures and increasing rutting resistance at high service

temperatures. This effect, in creep aspect of view, is analogous to that of SBS polymer-

modified asphalt binders.

It was expected that the granite mixtures would have higher tensile strength values

than limestone mixtures because generally granite material exhibits a higher hardness

nature than limestone material. Figure 5-46 shows the comparison of tensile strength

between granite and limestone mixtures. The strength values of the two aggregate types

are generally in the same magnitude. The zero interception linear trendline indicates that

the limestone mixtures have less tensile strength than the granite mixtures by a small

margin. The comparison of fracture energy between granite and limestone mixtures is

displayed in Figure 5-47. The plot shows a poor correlation of fracture energy between

granite and limestone mixtures. The reason for this is that the fracture energy result

depends on a few other basic variables including tensile strength, failure strain, and the

dynamic stress-strain behavior of each specific specimen.


#

20

0

#1

00

#

50

#

30

#

16

#

8

#

4

3

/8"

1

/2"

3

/4"

1

"

0

10

20

30

40

50

60

70

80

90

100

Pe

rce

nt P

assin

g

Restricted Zone

upper control

lower control

F2 Control

F2G1

F2G2

F4 Control

F4G1

F4G2

Figure 5-40: Gradation curves for control mixes and modified gradation mixes

110

y = 0.8293x

R2 = 0.921

y = 0.6856x

R2 = 0.9376

0

10

20

30

40

0 10 20 30 40

Resilient Modulus of Granite Mixtures (GPa)

Resili

ent

Modulu

s o

f Lim

esto

ne M

ixtu

res (

GP

a)

Testing Temperature of

25˚C and 40˚C

Testing Temperature of

-10˚C and 5˚C

Figure 5-41: Comparison of resilient modulus for granite and limestone mixtures

y = 1.2519x

R2 = 0.7599

0.03

0.06

0.09

0.12

0.15

0.03 0.06 0.09 0.12 0.15

D(t) of Granite Mixtures (1/GPa )

D(t

) of

Lim

esto

ne M

ixtu

res (

1/G

Pa)

Figure 5-42: Comparison of CP between granite and limestone mixes at -10˚C

111

y = 1.1903x

R2 = 0.8368

0.0

0.2

0.4

0.6

0.8

0.0 0.2 0.4 0.6 0.8

D(t) of Granite Mixtures (1/GPa)

D(t

) of

Lim

esto

ne M

ixtu

res (

1/G

Pa)

Figure 5-43: Comparison of CP between granite and limestone mixes at 5˚C

y = 1.0069x

R2 = 0.9195

0

2

4

6

0 2 4 6

D(t) of GraniteMixtures (1/GPa)

D(t

) of

Lim

esto

ne M

ixtu

res (

1/G

Pa)


112

y = 0.7773x

R2 = 0.6655

0

3

6

9

12

15

0 3 6 9 12 15

D(t) of Granite Mixtures (1/GPa)

D(t

) of

Lim

esto

ne M

ixtu

res (

1/G

Pa)


y = 0.9279x

R2 = 0.9252

0

2

4

6

0 2 4 6

Tensile Strength of Granite Mixtures (MPa)

Tensile

Str

ength

of

Lim

esto

ne M

ixtu

res (

MP

a)

Figure 5-46: Comparison of Tensile Strength between granite and limestone mixes

113

0

2

4

6

8

10

0 2 4 6 8 10

Fracture Energy of Granite Mixtures (KPa)

Fra

ctu

re E

nerg

y o

f

Lim

esto

ne M

ixtu

res (

KP

a)

Figure 5-47: Comparison of Fracture Energy between granite and limestone mixes

5.4 Summary of Analysis and Findings from Fracture Mechanics Tests

In gradation modifications, the amount of aggregate retained in nominal maximum

sieve was increased. However, the power law regression curves for the mix design series

turned out to be close to each other. The effect of adjusting coarse aggregate gradation by

increasing the 12.5 mm (1/2 in.) sieve aggregate with a range of 5% to 15% appeared to

be negligible on mixtures’ resilient modulus. Similarly, the proposed coarse gradation

modifications did not make a significant difference in the creep compliance properties for

the HMA tested in this study. The tensile strength test results indicated that the increase

of nominal maximum size aggregate downgraded the HMA tensile strength property at

low temperature levels. The reason for this is probably that at low temperatures, the

condition of particle composition is critical to the strength of HMA. The addition of

coarse aggregate decreased the bonding condition between aggregate and asphalt binder.

On the other hand, at high testing temperatures, the asphalt binder becomes softer and

plays a more important role in the mixture. Since both the control mixes and the mixtures

with modified gradations used the same type of asphalt binder (PG 67-22), all mixes

114

showed similar strength properties at elevated temperatures. It is found that most of the

fracture energy values of modified gradations were lower than those of control mixtures,

which means that the mixtures with modified coarse gradations would probably have less

resistance to fatigue cracking than the control mixtures according to the fracture

mechanics model proposed by Roque et al. (2004). Overall, increasing the amount of

nominal maximum size aggregate in this study had negligible or adverse effect on HMA

fracture mechanics properties.

The SBS polymer-modified asphalt binder was found to be beneficial to HMA

fracture mechanics properties in a few ways. Firstly, the SBS polymer improves the

stiffness behavior of asphalt mixtures. The SBS polymer-modified binder makes the

PMA mixtures less stiff than control mixes with unmodified asphalt at low to mid-range

temperature levels (-10˚C and 5˚C). The resilient modulus values of PMA mixtures

decrease with an increase of SBS polymer content throughout the concentration range

tested except at high temperatures. At the testing temperature of 40˚C, the stiffness of

PMA mixtures appeared to be maintained or even increased. The increment of SBS

polymer dosage results in an enhanced resilient modulus superior to that of the control

mixtures. Moreover, it is interesting to note that when the SBS polymer concentration

increases from 4.5% to 6.0%, the resilient modulus values of PMA mixtures drop back

slightly. This implies that an optimum SBS content exists around 4.5% which would

make the HMA stiffest at the high testing temperature. This finding is analogous with the

results reported by many other research studies (Collins et al. 1991; Shih 1996; Chen et

al. 2002, 2003) on polymer-modified binders and PMA mixtures. The analysis performed

on resilient modulus results based on this study indicates that when SBS polymer is used

in the HMA, although increasing the SBS polymer content will always improve low

temperature performance of pavement, limiting the concentration within an optimal range

is especially important at high service temperatures. Secondly, the SBS polymer helps the

HMA obtain an upgraded creep performance. The PMA mixtures are more compliant

than the control mixes with unmodified asphalt binders at the low temperature level (-

10˚C). On the other hand, the PMA mixtures become less compliant than the control

mixes at the high testing temperature (40˚C). At a specific temperature level, a higher

SBS polymer concentration generally results in higher creep compliance values. At some

115

mid-range temperature levels, the PMA mixtures show similar creep property to the

control mixes. These effects should lead to improved resistance to rutting and thermal

cracking of HMA mixtures, and provide a good verification to conclusions drawn by

previous research studies (Lalwani et al. 1982; Carpenter et al. 1987; Pradhan 1993).

Thirdly, the SBS polymer modifier improves the asphalt mixture fracture properties. The

indirect tensile strength test showed that the SBS polymer did not significantly affect

HMA tensile strength as Jones et al. (1998) observed at low temperature levels (around

0˚C). However, the SBS polymer generally increases the fracture energy or creep strain

energy which were indicators of mixtures’ resistance to fatigue cracking. At low

temperatures (-10˚C and 5˚C), the failure strain of PMA mixtures tends to increase with

an increase of SBS polymer content. These performances further justify the benefits of

polymer-modified binder documented by a few other researchers (Kennedy et al. 1992;

King et al. 1993).

Comparison between the two different types of aggregate showed that the limestone

mixtures are less stiff than the granite mixtures for all specimens tested in this study. The

difference in resilient modulus values between the two types of aggregate is more

remarkable at low temperature levels (-10˚C and 5˚C). In addition, the limestone mixtures

are more compliant than granite mixtures at low temperatures. As the temperature

increases, the limestone mixtures shows a creep property similar to that of the granite

mixtures at 25˚C, and then the limestone mixtures become less compliant than granite at

the high temperature (40˚C). These characteristics exhibited by limestone mixtures are

advantageous to pavement structures in improving performance of thermal cracking at

low service temperatures and increasing rutting resistance at high service temperatures.

116

CHAPTER 6

COMPLEX MODULUS AND RESILIENT MODULUS

TEST RESULTS

6.1 Test Procedures

The laboratory testing program conducted in this project included dynamic modulus

testing and indirect tension testing. Both types of testing were conducted in unconfined

conditions. The Interlaken dynamic test system was used to load the specimens. The IDT

resilient modulus test procedures are the same as described in Chapter 4, while in this part

of the study, the specimens were tested at only three temperatures: 5, 25, and 40˚C. The

dynamic modulus tests were conducted at the same three temperature levels and the

procedures are as follows:

The dynamic moduli and phase angle were measured by applying compressive

sinusoidal (haversine) loading. The deformations were measured through three LVDTs

(Linear Variable Differential Transducers). These LVDTs were placed vertically on

diametrically symmetric specimen sides (Figure 6-1).

On the night before testing, parallel studs, used to secure the LVDTs in place, were

glued 100 mm (4 in.) apart and located approximately 25 mm (1 in.) from the top and

bottom of the specimen. The diameter of the specimens was 100 mm (4 in.) and the

height was 150 mm (6 in.), cut and cored from the raw gyratory compacted pills with a

diameter of 150 mm (6 in.) and a height of 165 mm. The specimens were then placed in a

controlled temperature cabinet overnight at 5ºC to ensure temperature equilibrium. On the

morning of testing, the specimens were placed in the environmental chamber at 5ºC and

allowed to equilibrate for two hours. All testing was conducted using this temperature

controlled chamber capable of holding temperatures from -16 to 60°C (3.2 to 140°F).

Tests were performed at temperatures of 5, 25, and 40 ºC and frequencies of 25, 10, 5, 1,

and 0.5Hz. Testing began with the lowest temperature and proceeded to the highest

temperature. At a given temperature level, the testing began with the highest frequency of

loading and proceeded to the lowest. This temperature-frequency sequence was carried

117

out to cause minimum damage to the specimens before the next sequential test (Pellinen

2001).


applied to the specimens. A sinusoidal axial compressive load was applied to the

specimens without impact in a cyclic manner. The load was adjusted in each case to

attempt to keep the axial strains between 50 and 150 micro-strains. The first step was to

apply a preconditioning load to the specimens with 200 cycles at 25 Hz. Testing

continued with different numbers of cycles for each frequency as shown in Table 6-1. The

data acquisition system was set up to record the last six cycles at each frequency with

about 200 points per cycle. The raw force and displacement data were manipulated to

obtain the dynamic modulus and phase angle for each specimen. After the entire cycle of

testing was complete at 5ºC, the environmental chamber was set to the next temperature.

After two hours of conditioning, the above steps were repeated until completion of the

entire sequence of temperatures and frequencies.

Figure 6-1: Specimen and LVDTs setup for DMT test

118

Table 6-1: Cycles for DTM test sequence

Frequency, Hz Number of Cycles

Preconditioning (25) 200

25 50

10 50

5 50

1 25

0.5 6

6.2 Presentation of DMT and IDT Testing Results

The measurement and analysis system developed for the SHRP indirect tensile test

(IDT) (Roque et al. 1992, 1997) was applied as described in Chapter 4. The SHRP IDT

could obtain an accurate determination of tensile properties of asphalt mixtures at low

temperatures, with an accurate measuring of Poisson’s ratio. The deformation

measurement mounting system was modified in the SHRP IDT in order to account for

specimen bulging. The resilient modulus and Poisson’s ratio test results are summarized

in Table C-1 for the 20 Superpave HMA mixtures. The average values of resilient

modulus and Poisson’s ratio for each mixture are also shown in Figure 6-2 and Figure 6-3

for the 20 HMA mixes.

Similarly, the dynamic complex moduli for all 20 mixtures were tested at the selected

temperature levels: 5, 25, and 40°C (41, 77, and 104˚F). For all temperatures tested, the

frequencies listed in Table 6-1 were used: 25, 10, 5, 1, and 0.5 Hz. The tests were

conducted from the lowest temperature to the highest temperature and from the highest

frequency to the lowest frequency, as explained earlier. The data processing procedures

described in the National Cooperative Highway Research Program (NCHRP) Project 9-

29, “Simple Performance Tester for Superpave Mix Design”, are used in this study to

process the raw data and compute the dynamic moduli and phase angles. All of the

dynamic modulus and phase angle test results are summarized in Table C-2 and Table C-

3 respectively. The phase angles were grouped together and are shown in Figure 6-4 for

granite, limestone and RAP materials at each testing temperature.

119

0

5

10

15

20

25

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Mix Design Series Number

Resili

ent

Modulu

s (

GP

a)

40 degree C 25 degree C 5 degree C

Figure 6-2: Resilient modulus at different testing temperatures (1GPa = 145 psi)

0.1

0.2

0.3

0.4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Mix Design Series Number

Pois

son's

Ratio

40 degree C 25 degree C 5 degree C

Figure 6-3: Poisson’s Ratio from IDT test for all mixture series

120

0

10

20

30

40

0 5 10 15 20 25 30

Frequency (Hz)

Phase A

ngle

Granite RAP Limestone

40°

25°

5°C

Figure 6-4: Average phase angles for different type of materials

As displayed in the tables and plots, the results clearly show the expected trends of

the dynamic modulus and phase angle for asphalt mixtures. In summary, the two

variables showed the following trends:

1. The dynamic modulus increased as the test frequency increased under a certain

testing temperature.

2. The dynamic modulus increased with a decrease in test temperature under a

certain loading frequency.

3. The phase angle increased as the test temperature increased.

4. The phase angle has a decreasing trend with increasing load frequency under a

certain temperature. A more complex behavior of the phase angle as a function of

the loading frequency was observed at elevated temperatures.

These trends are in agreement with the research results reported by others.

121

CHAPTER 7

CORRELATION OF INDIRECT TENSION RESILIENT MODULUS

AND COMPLEX MODULUS TEST RESULTS

7.1 General

A comparative study between the indirect tension resilient modulus and dynamic

complex modulus experimental results is performed in this chapter. A detailed

comparison of key differences between the dynamic complex modulus test and the

indirect diametral resilient modulus test for asphalt concrete mixtures was summarized in

a position paper by the NCHRP 1-37A 2002 Project research team (Witczak 1999).

Basically, the primary difference between the resilient modulus test and dynamic complex

modulus test for asphalt concrete mixtures is that the former uses loading of any

waveform with a given rest period, while the latter applies a sinusoidal or haversine

loading with no rest period; hence, no delayed elastic rebound would occur during the

test. The transition from the resilient modulus test to the use of the dynamic complex

modulus test for design of flexible pavement structures has hardly been smooth. The

potential impact of adopting the dynamic complex modulus for implementing the new

AASHTO M-E Design Guide is tremendous for state transportation agencies such as the

Florida Department of Transportation (FDOT). The IDT has traditionally been used to

characterize the HMA mixtures for flexible pavement design in Florida, and the test

method has been shown to be both an expedient and a reliable way of obtaining mixture

properties from field cores. In response to the need, a major effort was undertaken by the

FDOT to characterize the Florida HMA mixtures using the dynamic complex modulus

(Birgisson et al. 2004). The Witczak prediction model was adopted to verify the dynamic

modulus results obtained in the laboratory for all mixture series.

7.2 HMA Master Curve Development

In the new AASHTO Mechanistic-Empirical (M-E) Pavement Design Guide, the

dynamic modulus of HMA, at all levels of temperature and loading frequency, was

122

determined from a master curve constructed at a reference temperature. The dynamic

modulus and phase angle of HMA were shifted with respect to the frequency axis until

the curves merged to form a single smooth characteristic curve, which is referred to as the

time-temperature superposition principle. The master curve of the HMA stiffness

described the time dependency of the material. The shift factor, a(T), as a function of

temperature, defined the required shift at a given temperature to obtain the reduced

frequency. It is shown in the following form:

)log()log()](log[)( r

r

ffTaorf

fTa −== (7-1)

where:

f = testing frequency at desired temperature

fr = reduced frequency

T = temperature of interest

Obviously, a(T) = 1 at the reference temperature.

Pellinen and Witczak (2002) developed a mathematical model by a sigmoidal fitting

function for master curve construction. The shift can be calculated by solving the shift

factors simultaneously with the coefficients of the sigmoidal function:

rfeE

log1|)log(|

γβ

αδ

+

∗

++= (7-2)

where

log(|E*|) = log of dynamic modulus

fr = reduced frequency

� = minimum modulus value

D = span of modulus value

�, � = shape parameters

As indicated in the sigmoidal function, the upper limit of the log of dynamic modulus

was D+�, and the minimum value is �. � and � are shape factors that determine the shape

of the master curve. The parameters used in sigmoidal fitting function are demonstrated

123

in Figure 7-1. The characteristics of the sigmoidal function are described as follows. At

the reference temperature, the shift factor a(T) = 1 . The parameter � influenced the

steepness of the function (rate of change between minimum and maximum) and �

influenced the horizontal position of the turning point. The upper part of the sigmoidal

function asymptotically approached the maximum stiffness of the mix, which was

dependent on limiting binder stiffness at cold temperatures. At high temperatures, the

compressive loading caused aggregate influence to be more dominant than the viscous

binder influence. The modulus started to approach a limiting equilibrium value, which is

dependent on the aggregate gradation. Thus, the sigmoidal function captured the physical

behavior of the asphalt mixture observed in the mechanical testing using compressive

cyclic loading through the entire range of temperatures that are typically of interest.

Figure 7-1: Parameters used in sigmoidal fitting function of master curve

7.3 Master Curve Construction

The procedure developed by Pellinen and Witczak (2002) was used for obtaining

predicted master curves for all mixtures in this study. In all master curve constructions,

124

the reference temperature was taken as 25°C (77°F). The shifting factors were obtained

simultaneously with the coefficients of the sigmoidal function through nonlinear

regression, without assuming any functional form of a(T) with respect to temperature.

The nonlinear regression was performed by using the Solver Function of a Microsoft

Excel spreadsheet. For instance, a set of testing values of dynamic modulus for a specific

specimen was obtained, at test temperatures of 5, 25 and 40°C and loading frequencies of

25, 10, 5, 1 and 0.5 Hz. Then the parameters of the sigmoidal function D, �, �, and � were

assumed as well as the shift factor a(T) at each corresponding temperature. Equation 7-1

was used to calculate the sigmoidal fitting values of log(|E*|). Nonlinear regression was

then performed to achieve an optimum fitting between the testing values and the

sigmoidal model calculation, which resulted in obtaining the optimized parameters of the

sigmoidal function and the shift factors.

100

1000

10000

100000

-4 -3 -2 -1 0 1 2 3 4 5 6

Reduced Frequency Log(fr) (Hz)

|E*| (

MP

a)

Figure 7-2: Master curves for granite materials

125

100

1000

10000

100000

-4 -3 -2 -1 0 1 2 3 4 5 6


|E*| (

MP

a)

Figure 7-3: Master curves for limestone materials

100

1000

10000

100000

-4 -3 -2 -1 0 1 2 3 4 5 6


|E*

| (M

Pa)

)log(5680.05069.0

*

1

3543.20214.2|)log(|

rfe

E⋅−−+

+=

Figure 7-4: Master curves for all mixtures

126

The master curves for granite and limestone materials are grouped together and

shown in Figure 7-2 and Figure 7-3, respectively. The master curves were all similar in

shape and close to each other for the same type of materials. This could be due to the fact

that one type of asphalt binder (PG 67-22) was used for all the dynamic modulus test of

HMA mixtures. All of the master curves were then grouped together and are shown in

Figure 7-4. One regression equation was derived for all the mixtures, presented as

follows:

)log(5680.05069.0

*

1

3543.20214.2|)log(|

rfeE

⋅−−++= (7-3)

7.4 Verification of Dynamic Complex Modulus Experimental Results

Efforts were made by asphalt pavement researchers to develop regression equations

to estimate the dynamic complex modulus for a specific HMA mixture. One of the most

comprehensive mixture dynamic complex modulus models is the Witczak prediction

model (Witczak and Fonseca 1996; Fonseca and Witczak 1996). This prediction model

was based on the volumetric properties of a given mixture and was adopted in the

AASHTO M-E design guide. Past studies (Birgisson et al. 2004; Schwartz 2005; King et

al. 2005; Loulizi et al. 2006) showed that the Witczak predictive model provided

sufficiently accurate and reasonably robust estimates of dynamic complex modulus for

use in the M-E performance prediction and design, although it had more limited ability to

make fine distinctions between the performance of different mixtures at the same

temperature and other design conditions. In this study, the predicted dynamic complex

modulus values from the Witczak prediction equation were compared with the measured

dynamic complex modulus values to verify the test results. The Witczak prediction

equation is presented as follows:

127

[ ])log393532.0log313351.0603313.0(

34

2

38384

4

2

200200

*

1

00547.0)(000017.0003958.00021.0871977.3

)(802208.0058097.0002841.0

)(001767.0029232.0249937.1log

η−−−+

+−+−+

+−−−

−+−=

f

abeff

beff

a

e

PPPP

VV

VVP

PPE

(7-4)

where

|| *E = dynamic (complex) modulus, in 105 psi

η = bituminous viscosity, in 106 poise (at any temperature, degree of aging)

f = load frequency, in Hz

aV = percent air voids content, by volume

beffV = percent effective bitumen content, by volume

34P = percent retained on 19-mm sieve, by total aggregate weight (cumulative)

38P = percent retained on 9.5-mm sieve, by total aggregate weight (cumulative)

4P = percent retained on 4.75-mm sieve, by total aggregate weight (cumulative)

200P = percent passing 0.75-mm sieve, by total aggregate weight (cumulative)

In this model, the parameter E (bitumen viscosity) for each dynamic complex

modulus test temperature is determined by:

TVTSA log)log(log ⋅+=η (7-5)

where A is the regression intercept, T is Rankine temperature and VTS is the slope of log-

log viscosity versus temperature relationship. The A and VTS parameters are functions of

binder type and material characteristics, and they are determined by regression using

experimental data of binder viscosity versus temperature T. For this study, the input

binder viscosity was obtained from Brookfield rotational viscometer results on short-term

Rotational Thin Film Oven (RTFO) aged PG 67-22 specimens (Birgisson et al. 2004).

The binder viscosity values thus obtained are: A = 10.407 and VTS = -3.4655.

The comparison between the measured and predicted dynamic complex moduli for

all mixture series is presented in Figure 7-5. A linear regression with zero intercept was

performed for the comparative analysis. The R2 indicated the goodness of fit, whereas the

linear coefficient (slope) was a measure of the quality of fit between the prediction and

128

test measurement. Since the comparison was made by using measured dynamic complex

modulus as the horizontal x-values, the points below the line of equality indicated a

prediction that is conservative, in which the predicted dynamic complex modulus was

lower than the measured one. However, the regression analysis shown in the figure

indicated a reasonable estimate of the predicted dynamic complex modulus for the

mixtures tested in this study. Since the Witczak prediction model was shown to provide

sufficiently accurate and reasonably robust estimates of dynamic complex modulus for

use in the M-E pavement performance prediction and design, the reasonable correlation

between the measured and predicted dynamic complex moduli for all the mixtures in this

study could be interpreted as the measured dynamic complex modulus values also being

reasonably accurate.

y = 0.927x

R2 = 0.88

100

1000

10000

100000

100 1000 10000 100000

Measured |E*| (MPa)

Pre

dic

ted

|E*|

(M

Pa)

Figure 7-5: Measured vs. predicted dynamic modulus values for all mixtures

7.5 Comparison between Resilient Modulus and Dynamic Modulus

Despite the fundamental differences between the resilient modulus and dynamic

complex modulus (Witczak 1999; Drescher et al. 1997; Zhang et al. 1997; Kim et al.

2004), a number of research studies had been attempted in order to establish direct

129

correlation between the resilient modulus and dynamic complex modulus of asphalt

concrete mixtures (Kim et al. 2004; Birgisson et al. 2004; Loulizi et al. 2006). Birgisson

et al. (2004) developed testing and analysis procedures to accurately determine the tensile

dynamic complex modulus from the SHRP IDT tests. The dynamic complex modulus

was found to be correlated with resilient modulus and testing frequency for the range of

testing temperatures and frequencies. Loulizi et al. (2006) conducted a comparison study

on the dynamic complex modulus and resilient modulus tests, and they found a strong

relationship between the dynamic complex modulus performed at 5 Hz and the resilient

modulus performed at loading time of 0.03 seconds.

Other alternative approaches had also been attempted in order to determine the

dynamic complex modulus from the IDT test with modified loading conditions using the

theory of viscoelasticity (Drescher et al. 1997; Zhang et al. 1997; Kim et al. 2004).

Recently, an analytical method of calculating resilient modulus from the dynamic

complex modulus was also proposed (Lacroix et al. 2007). The proposed theoretical

prediction involved the application of multiaxial linear viscoelastic theory to linear elastic

solutions for the IDT test. The proposed approach could provide reasonable estimates of

the resilient modulus from the dynamic complex modulus of the asphalt concrete

mixtures. The accuracy of the prediction was not affected by assuming a constant

Poisson’s ratio.

In this study, a strong effort was devoted to preparing the cored dynamic complex

modulus specimens with a targeted air void content (approximately 4.0 percent) as close

as possible to the design air void content (4.0 percent) of the resilient modulus specimens.

As shown in Figure 7-6, the air void content between the dynamic complex modulus and

resilient modulus test specimens are reasonably comparable. Thus, the influence of air

void content on the modulus properties of HMA mixtures could be neutralized.

Therefore, temporarily setting aside the fundamental differences in loading mode

(compression versus tension), loading condition (no rest period versus with rest period),

and basic property (elastic versus viscoelastic) between the two test methods, the resilient

modulus and dynamic complex modulus test results for this study may be compared

empirically on the basis of loading frequency.

130

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0

Va from IDT Specimens (%)

Va

fro

m D

MT

Sp

ecim

ens

(%)

Figure 7-6: Comparison of average air void content between IDT and DMT specimens

The dynamic complex modulus varies with the loading frequency. A proper

frequency that most closely simulates the actual traffic loading should be selected for the

test, so the dynamic complex modulus thus determined would be equivalent to the

resilient modulus for pavement design purposes. The comparisons between the (total)

resilient modulus and dynamic complex modulus test results are shown in Figure 7-7

through Figure 7-9, for the loading frequencies of 10 Hz, 5 Hz, and 1 Hz, respectively.

The linear regression analysis clearly showed a trend of the dynamic complex modulus

increasing with an increase in total resilient modulus at a specific loading frequency. In

particular, the resilient modulus values were very close to the dynamic complex modulus

values at the loading frequency of 5 Hz (Figure 7-8). The comparisons for the loading

frequencies of 25 Hz, 10 Hz, 5 Hz, 1 Hz, and 0.5 Hz are presented in Figure 7-10, and the

linear regression equations at each frequency are also shown in the figure for illustration.

The closest interpreted loading frequency for obtaining an equal value of the resilient

modulus and dynamic complex modulus would be approximately 4 Hz (Figure 7-11).

Hence, based on this empirical correlation, the dynamic complex modulus values

measured at a loading frequency of 4 Hz may be comparable with the resilient modulus

values obtained from the indirect diametral test at the same temperature level (Ping et al.

2008).

131

As mentioned in the introduction, the transition from the use of resilient modulus to

the use of dynamic complex modulus in implementing the AASHTO M-E Pavement

Design Guide was hardly smooth. A significant amount of resilient modulus data

collected in the past are currently in state highway agencies’ inventory; these data are on

the verge of becoming obsolete. The rational comparative approach presented in this

experimental study could be utilized to establish an empirical correlation between

resilient modulus and dynamic complex modulus test results so that the developed

regression correlation could be used to predict the dynamic complex modulus from

measured resilient modulus values of the HMA mixtures already in the inventory or in the

system.

y = 1.1233x

R2 = 0.8919

0

5000

10000

15000

20000

25000

0 5000 10000 15000 20000 25000

Resilient Modulus (MR), MPa

Dy

nam

ic M

od

ulu

s (|

E*

|),

MP

a

Figure 7-7: Resilient modulus versus dynamic complex modulus at 10 Hz

132

y = 1.0265x

R2 = 0.9065

0

5000

10000

15000

20000

25000

0 5000 10000 15000 20000 25000


Dy

nam

ic M

od

ulu

s (|

E*

|),

MP

a


y = 0.8087x

R2 = 0.9043

0

5000

10000

15000

20000

25000

0 5000 10000 15000 20000 25000


Dy

nam

ic M

od

ulu

s (|

E*

|),

MP

a


133

0

5000

10000

15000

20000

25000

0 5000 10000 15000 20000 25000


Dy

nam

ic M

od

ulu

s (|

E*

|),

MP

a

line of equality

0.5 Hz, y=0.7162x

1 Hz, y=0.8087x

5 Hz, y=1.0265x

10 Hz, y=1.1233x

25 Hz, y=1.2416x

Figure 7-10: Resilient modulus versus dynamic modulus at various loading frequencies

y = 0.1349Ln(x) + 0.8096

R2 = 0.9999

0.6

0.8

1

1.2

1.4

0.1 1 10 100

Frequency

Lin

ear

Mu

ltip

lica

tio

n F

acto

rs

Figure 7-11: Relationship of linear multiplication factors with DMT loading frequency

134

CHAPTER 8

SUMMARY AND CONCLUSIONS

8.1 Summary

The primary objective of this study was to evaluate the engineering properties of Hot

Mix Asphalt concrete for implementing the AASHTO Mechanistic-Empirical Design

Guide for Pavement Structures. The specific goals of the study were to evaluate the

coarse aggregate gradation limits by adjusting the coarse aggregate amount of the mix

designs and to evaluate the styrene-butadiene-styrene (SBS) polymer-modified asphalt

binder effect utilizing the fracture mechanics tests in Indirect Diametral Tension testing

mode. Another goal of the study was to develop a rational comparison between the

dynamic complex modulus and indirect resilient modulus obtained in laboratory. To

achieve the objectives and goals, a complete dynamic testing system was established to

perform the temperature controlled dynamic tests. A laboratory experimental program

was developed to evaluate two standard control mixes, four mixes with modified coarse

gradation, six mixes with SBS polymer modifier, and twenty selected Superpave asphalt

concrete mixes with a range of aggregates and mix designs.

The two control mix designs included one granite material (F2C) and one limestone

material (F4C). Their coarse part gradations were adjusted to evaluate the effect of

gradation limits specified in the AASHTO mix design guide. The two control mixtures

were further modified by using SBS polymer-modified binder at different concentrations

instead of the base asphalt to study the polymer binder effect on fracture mechanics

properties of the mixtures. The 20 mixtures tested for dynamic complex modulus

included the following types of aggregates: 14 Georgia granite materials, one Nova Scotia

granite, one North Florida limestone, two Central Florida limestone materials, one South

Florida oolite, and one Alabama limestone. Only one base asphalt binder, PG 67-22 (AC-

30), was used for the dynamic modulus test.

The sweep of IDT tests included the resilient modulus test, the creep compliance test,

and the tensile strength test to characterize the fracture mechanics properties of the

asphalt mixtures. The tests were conducted at four temperature levels (-10, 5, 25, and

135

40°C) covering a typical range of asphalt concrete pavement service temperatures. The

creep compliance master curves and the fracture mechanics parameters were analyzed

using the fracture energy model developed by Roque et al. (2004). The analysis indicated

that the modification of coarse part gradation of the mix designs did not influence the

fracture properties noticeably. However, the use of SBS polymer modifier improved the

creep parameters as well as the stiffness characteristics at both low and high

temperatures.

The dynamic complex modulus tests were conducted at three temperature levels: 5,

25, and 40°C. For all temperatures, the following frequencies were used for the dynamic

modulus test: 25, 10, 5, 1, and 0.5 Hz. The dynamic modulus master curves for all 20

mixtures were constructed using the time-temperature superposition principle. The

Witczak prediction model was adopted to verify the laboratory test results. A comparative

study was then made between the dynamic modulus and resilient modulus test results.

The linear regression analysis indicated that the total resilient modulus increased with an

increase in dynamic modulus at a specific loading frequency. The resilient modulus

values were comparable to the dynamic modulus values at the loading frequency of 4 Hz.

8.2 Findings and Conclusions

8.2.1 Coarse Aggregate Gradation Effect

Based on the test results and analyses of this study, the findings may be drawn as

follows for the specific mix designs with 1/2" nominal maximum size:

1. The increase in 1/2" aggregate from 5% to 15% has minimum influence on

mixtures’ resilient modulus and does not make a significant difference in the

creep compliance properties for the coarse mixes tested.

2. At low testing temperatures (-10˚C and 5˚C), the tensile strength values of

mixtures with modified coarse aggregate gradations are less than those of control

level mixtures, which indicated that increasing the amounts of nominal

maximum size aggregate in the standard control mixtures has an adverse effect

on the tensile strength property of the HMA at low temperatures. At mid to high

testing temperatures, the differences are negligible.

136

3. The fracture energy and dissipated creep strain energy values of modified

gradations are slightly less than those of the control mixes, which means that the

mixtures with modified gradations would probably have less resistance to

fatigue cracking than the control mixtures.

Based on the above findings, the aggregate percentage of maximum nominal size

should not exceed 10% to 20% range, because mixtures with modified gradations in this

study show similar or even downgraded fracture mechanics characteristics.

8.2.2 SBS Polymer Modifier Effect

The SBS polymer modifier improved the HMA properties in the following aspects:

1. SBS polymer modifiers make HMA softer at mid to low service temperatures

and stiffer at high temperatures, which are both favorable attributes for the

improvement of HMA performance in terms of low temperature thermal

cracking and high temperature rutting.

2. The polymer modifier makes the HMA more ductile at low temperatures which

would be beneficial for the reduction of thermal cracking. At high temperatures,

the PMA mixes are less compliant and thus more resistant to rutting.

3. The SBS polymer did not critically affect the HMA tensile strength. However, it

tends to increase the fracture energy limit, and hence, improve the fatigue

cracking performance of HMA mixtures.

4. The failure strain of PMA mixtures tends to increase with an increase of SBS

polymer content at low testing temperatures (-10˚C and 5˚C), which is a desired

attribute to improve the low temperature cracking of HMA pavement.

These findings are in agreement with the theoretical suppositions and with other

practical studies. Furthermore, the effect of SBS concentration for PMA mixtures appears

to be consistent with the findings for SBS modified asphalt binders documented by other

researchers. An optimum SBS content exists around 4.5% which would make the PMA

mixture stiffness the highest at high service temperatures. Excessive increase of polymer

content above the optimum level may improve the stiffness, creep, and failure strain

behavior at low temperatures, however, it had an adverse effect on the PMA resilient

modulus property at high temperatures, which was probably due to a combined

137

performance of mixing and distribution of SBS polymer modifier, base bitumen, and

aggregate.

8.2.3 Effect of Aggregate Type

The limestone mixtures are less stiff than granite mixtures. This difference appeared

to be more significant at low temperatures. In addition, limestone materials show

favorable behaviors in creep performance compared with granite materials at all testing

temperatures. These properties implies that limestone materials are much more ductile

than granite under low service temperature conditions and hence presents an advantage

for the thermal cracking performance of HMA, and at high temperatures, limestone

materials have the potential to increase rutting resistance while maintaining the stiffness

of pavement structures. It should be noted that these findings were observed in the

laboratory for the two specific types of aggregate commonly used in Florida.

8.2.4 Correlation between Dynamic Modulus and Resilient Modulus

The dynamic complex modulus test results were comparable with those from other

research studies. The linear regression analysis between the resilient modulus and

dynamic complex modulus test results clearly showed a trend of the dynamic complex

modulus increasing with an increase in resilient modulus at a specific loading frequency.

The resilient modulus values were very close to the dynamic complex modulus values at

the loading frequency of 5 Hz. Based on the empirical correlation, the dynamic complex

modulus values measured at the loading frequency of 4 Hz may be comparable with the

resilient modulus values obtained from the indirect tension diametral test at the same

temperature level. The empirical correlation was established based on the experimental

results of Florida asphalt concrete mixtures. This empirical correlation may not be

applicable to those HMA mixtures with different types of asphalt binders. However, the

rational comparative approach presented could be adopted to establish an empirical

correlation between resilient modulus and dynamic complex modulus test results for

different types of HMA mixtures so that the developed regression correlation could be

138

used to predict the dynamic complex modulus from measured resilient modulus values of

the HMA mixtures.

8.3 Recommendations

Based on the conclusions and limitations of this research study, the primary

recommendations are as follows:

The effect of coarse aggregate gradation should be further evaluated by investigating

more Superpave mixture designs commonly used in field. The dynamic complex modulus

may also be adopted as an indicator. The gradation adjustment for fine aggregate could be

taken into consideration with a desire to reduce the mix design cost while maintaining the

HMA mechanical quality. A broad range of mixtures should be tested to evaluate the

effect of SBS polymer modifier and to obtain a more confident range of optimum

concentration. Similarly, more research work should be conducted to statistically verify

the effect of aggregate type on fracture mechanics properties of HMA. The HMA fracture

energy approach should be further verified for evaluating HMA pavement structures at

some high service temperatures by incorporating the practical fracture and rutting data in

field. The relationship between fracture energy and temperature should be evaluated by

studying the parameters at more temperature levels.

139

APPENDIX A MATERIALS AND MIX DESIGNS

Table A-1: Superpave mix designs sorted by test series

Series Mix Design Size Type Load Application Rap # 7 # 67 S-1-A S-1-B # 78 #89 5/16" W-10 M-10 Stone Sand Asphalt

Level Stone Stone Stone Stone Stone Stone Stone Screenings Screenings Screenings

S-1 SP 03-2460A 12.5 C Structural A0704 43 51 20 CWR AC-30

A0704-3 GA-553 GA-553 GA-553 Quincy

S-2 LD 00-2502A 12.5 Fine D Structural 41 51 20 Starvation Hill PG 67-22

S-3 LD 02-2529A 12.5 Coarse D Structural 41 51 20 PG 67-22

S-4 SP 02-2180A 9.5 Fine B Structural 51 20 21 A/C PG 67-22

GA-553 GA-553 GA-553 Mayo

S-5 SP 03-2921A 9.5 Coarse D Structural 51 20 21 PG 67-22

GA-553 GA-553 GA-553

S-6 SP 03-2922A 19.0 Coarse D Structural 42 43 51 21 PG 67-22

GA-553 GA-553 GA-553 GA-553

S-7 SP 04-3034A 12.5 Coarse D Structural 42 43 51 20 21 PG 67-22

GA-553 GA-553 GA-553 GA-553 GA-553

S-8 SP 03-2610A 12.5 Fine C Structural 52 51 20 PG 67-22

AL-149 AL-149 AL-149

S-9 SP 03-2627A 12.5 Fine C Structural 42 51 20 PG 67-22

87-145 87-145 87-145

S-10 SP 04-3225A 12.5 Fine C Structural 43 51 21 TM-35 PG 67-22

GA-553 GA-553 GA-206 Hill


NS-315 NS-315 NS-315


GA-383 GA-383 GA-383

S-13 SP 03-2941A 19.0 Fine C Structural 42 43 51 20 JCH PG 67-22

GA-553 GA-553 GA-553 GA-553 Ruben

S-14 SP 03-2351A 12.5 Fine B Structural 43 51 20 A/C PG 67-22

GA-553 GA-553 GA-553 Sunny Hills

S-15 SP 05-4015A 12.5 Fine C Structural 43 51 20 A/C PG 67-22

GA-553 GA-553 GA-553 Grandin

S-16 SPM 05-4044A 9.5 Fine B Structural 51 20 21 A/C PG 67-22

GA-553 GA-553 GA-554 Compass Lake

S-17 SPM 05-4051A 9.5 Fine C Structural 51 20 A/C PG 67-22

GA-553 GA-553 Compass Lake

S-18 SP 05-4061A 12.5 Fine C Structural A0638 41 53 20 A/C PG 67-22

38-286 38-268 GA-553 Quincy

S-19 SP 05-4100A 12.5 Fine C Structural 43 51 20 A/C PG 67-22

GA-553 GA-553 GA-553 Quincy

S-20 SP 02-2052A 12.5 FC C Friction 43 51 20 A/C PG 67-22

GA-553 GA-553 GA-553 Quincy

Table A-2: Performance grade binder grading report

Project FSU Dynamic Modulus Testing Date Received 02-17-05

Submitted By Dr. Ping (from C. W. Roberts) Date Tested 02-22 thru 02-24-05

Tested By Hill & Stickles Date Reported 02-24-05

Test Test Temp.

Test Result

P / F

Florida Specification

Spot Test n/a Negative P Negative

Solubility, % n/a 99.71 P Minimum 99.0%

Smoke Point COC, °C n/a 174 P Minimum 125°C

Flash Point COC, °C n/a 316 P Minimum 230°C

Absolute Viscosity, poises 60°C 3329 P 2400 – 3600 poises

Rotational Viscosity, Pa•s 135°C 0.58 P Maximum 3.0 Pa•s

67°C 1.32 P Original Dynamic Shear, G*/sin�, kPa

70°C 0.87 F

Minimum 1.0 kPa

The initial High Temperature Grade is PG 67

RTF Mass Loss, % 163°C 0.293 P Maximum 0.500%

67°C 2.82 P RTF Dynamic Shear, G*/sin�, kPa

70°C 1.88 F

Minimum 2.20 kPa

The final High Temperature Grade is PG 67

25°C 3260 P PAV Dynamic Shear, G*sin�, kPa

22°C 5361 F

Maximum 5000 kPa

The initial Low Temperature Grade is -22

Creep Stiffness S, MPa -12 154 P

Creep Stiffness, M-value -12 0.346 P

Creep Stiffness S, MPa -18 369 F

Creep Stiffness, M-value -18 0.275 F

S Maximum 300 MPa M-value Minimum 0.300

This sample graded out to a final grade of PG 67-22

Note: When heated and stirred there was a granular texture to the asphalt. The Solubility test revealed what appears to be very fine ground tire rubber but the percentage is within acceptable parameters specified by the State of Florida Department of Transportation.

141

Table A-3: Summary of mix designs and aggregates

Test SP RAP Ga-553 Ga-206 Nova Sco. North Fl Central Fl South Fl Alabama

Series Spec # Granite Granite Granite Limestone Limestone Oolite Limestone

S-1 2460

S-2 2502

S-3 2529

S-4 2180

S-5 2921

S-6 2922

S-7 3034

S-8 2610

S-9 2627

S-10 3225

S-11 2194

S-12 2452

S-13 2941

S-14 2351

S-15 4015

S-16 4044

S-17 4051

S-18 4061

S-19 4100

S-20 2052

142

Table A-4: Aggregate gradations for series 1 - 5

Sieve Size (mm) S-1 S-2 S-3 S-4 S-5

19 100 100 100 100 100

12.5 100 93 94 100 100

9.5 89 89 89 100 100

4.75 67 71 56 74 71

2.36 50 53 30 48 42

1.18 37 42 20 39 28

0.6 27 35 15 28 18

0.3 14 22 10 16 13

0.15 8 9 6 7 9

0.075 5.6 4.5 4.3 4.5 6.9



19 100 100 100 100 100

12.5 90 95 96 96 98

9.5 77 84 90 88 90

4.75 51 52 72 69 57

2.36 32 32 52 54 40

1.18 22 21 34 38 34

0.6 16 15 24 27 28

0.3 12 9 11 19 16

0.15 9 6 6 12 4

0.075 6.4 5.2 4.5 4.5 4.5

143



19 100 100 100 100 100

12.5 98 99 90 100 99

9.5 89 75 79 90 90

4.75 58 44 61 55 61

2.36 38 29 44 40 42

1.18 24 19 35 34 33

0.6 16 13 26 28 26

0.3 10 9 18 16 18

0.15 5 6 8 4 7

0.075 4.5 4.5 4.4 2.9 2.8



19 100 100 100 100 100

12.5 100 100 91 100 98

9.5 100 100 83 90 90

4.75 74 75 68 60 59

2.36 50 48 51 43 40

1.18 39 40 39 34 34

0.6 31 30 30 27 26

0.3 23 16 16 19 11

0.15 9 6 8 7 4

0.075 5.6 3.0 4.8 3.0 3.5

144


#

20

0

#

10

0

#5

0

#

30

#

16

#

8

#

4

3

/8"

1

/2"

3

/4"

1

"

0

10

20

30

40

50

60

70

80

90

100

Pe

rce

nt P

assin

g Restricted Zone

upper control

lower control

S1

S2

S3

Figure A-1: Gradation chart for S1 to S3


#

20

0

#1

00

#

50

#

30

#

16

#

8

#

4

3

/8"

1

/2"

3

/4"

1

"

0

10

20

30

40

50

60

70

80

90

100

Pe

rce

nt P

assin

g

Restricted Zone

upper control

lower control

S4

S5

Figure A-2: Gradation chart for S4 and S5

145


#2

00

#

10

0

#5

0

#3

0

#1

6

#8

#4

3/8

"

1/2

"

3/4

"

1"

0

10

20

30

40

50

60

70

80

90

100

Pe

rce

nt P

assin

g Restricted Zone

upper control

lower control

S7

S8

S9



#

20

0

#

10

0

#5

0

#

30

#

16

#

8

#

4

3

/8"

1

/2"

3

/4"

1

"

0

10

20

30

40

50

60

70

80

90

100

Pe

rce

nt P

assin

g Restricted Zone

upper control

lower control

S10

S11

S12


146


#

20

0

#

10

0

#5

0

#

30

#

16

#

8

#

4

3

/8"

1

/2"

3

/4"

1

"

0

10

20

30

40

50

60

70

80

90

100

Pe

rce

nt P

assin

g Restricted Zone

upper control

lower control

S14

S15

S18

Figure A-5: Gradation chart for S14, S15, and S18


#2

00

#

10

0

#5

0

#3

0

#1

6

#8

#4

3/8

"

1/2

"

3/4

"

1"

0

10

20

30

40

50

60

70

80

90

100

Pe

rce

nt P

assin

g

Restricted Zone

upper control

lower control

S16

S17


147


#

20

0

#

50

#

30

#

16

#

8

#

4

3

/8"

1

/2"

3

/4"

1

"

0

10

20

30

40

50

60

70

80

90

100

Pe

rce

nt P

assin

g

Restricted Zone

upper control

lower control

S6

S13

#1

00



#2

00

#

10

0

#5

0

#3

0

#1

6

#8

#4

3/8

"

1/2

"

3/4

"

1"

0

10

20

30

40

50

60

70

80

90

100

Pe

rce

nt P

assin

g

Restricted Zone

upper control

lower control

S19

S20


148

Table A-8: Lab analysis report for 0.0% polymer base asphalt (Graded as PG67-22)

Report Date: 10/1/08 Bituminous Tech. Lab No:

374208

Terminal: Mariani Asphalt Co.

Address: 500 North 19th St.

Tampa, FL 33605

Sample: 0.0% Polymer Date Tested: 9/10/08 – 9/11/08

Test Test Method Specification Test Results Original Binder

Absolute Viscosity, Poise

T202 3290 Poise

Solubility, % soluble T44 99.0% minimum 99.98%

Spot Test Negative Negative

Flash Point, ˚C T48 230˚C minimum 316˚C+

Smoke Point, ˚C 260˚C

Softening Point, ˚F 125˚F

Rotational Viscosity, Pa.s, @135˚C

T316 3.0 maximum 0.5 Pa.s

Dynamic Shear, kPa (G*/sin�, 10 rad/sec)

T315 1.0 minimum at 64˚C 1.0 minimum at 67˚C 1.0 minimum at 76˚C

1.97 kPa 1.32 kPa

0.9617 kPa

RTFOT Residue Mass Change, % T240 1.0 maximum +0.028%



3.42 kPa 2.64 kPa 1.659 kPa

R28, PAV @100˚C Residue Dynamic Shear, kPa (G*/sin�, 10 rad/sec)

T315 5000 maximum at 25˚C 5000 maximum at 22˚C

4070 kPa 5840 kPa

Creep Stiffness, S, @60 sec.

T314 300 maximum at -12˚C 300 maximum at -18˚C

213 479

Creep Stiffness, m-value, @60 sec.

T314 0.3 minimum at -12˚C 0.3 minimum at -18˚C

0.321 0.248

149

Table A-9: Lab analysis report for 3.0% polymer asphalt (Graded as PG76-22)


374108



Tampa, FL 33605




T202 19583 Poise









T315 1.0 minimum at 76˚C 1.0 minimum at 82˚C

1.359 kPa 0.9178 kPa

RTFOT Residue Mass Change, % T240 1.0 maximum -0.026%


T315 2.2 minimum at 76˚C 2.2 minimum at 82˚C

2.37 kPa 1.38 kPa


T315 5000 maximum at 31˚C 5000 maximum at 28˚C 5000 maximum at 25˚C 5000 maximum at 22˚C 5000 maximum at 19˚C

1880 kPa 2330 kPa 3450 kPa 4870 kPa 6100 kPa



176 371



0.329 0.266

150



374008



Tampa, FL 33605




T202 Too viscous





Softening Point, ˚F 197.5˚F




T315 1.0 minimum at 76˚C 1.0 minimum at 82˚C 1.0 minimum at 88˚C 1.0 minimum at 94˚C 1.0 minimum at 100˚C

3.47 kPa 2.40 kPa 1.70 kPa 1.26 kPa

0.3799 kPa




4.45 kPa 2.82 kPa 1.78 kPa


T315 5000 maximum at 31˚C 5000 maximum at 25˚C 5000 maximum at 19˚C 5000 maximum at 16˚C 5000 maximum at 13˚C

969 kPa 1860 kPa 3530 kPa 4780 kPa

NA



87.7 368



0.371 0.262

151



373908



Tampa, FL 33605




T202 Too viscous









T315 1.0 minimum at 76˚C 1.0 minimum at 82˚C 1.0 minimum at 88˚C 1.0 minimum at 94˚C 1.0 minimum at 100˚C

3.32 kPa 2.17 kPa 1.47 kPa 1.05 kPa

0.8748 kPa



T315 2.2 minimum at 76˚C 2.2 minimum at 82˚C 2.2 minimum at 88˚C 2.2 minimum at 94˚C

6.94 kPa 4.52 kPa 2.95 kPa 1.91 kPa


T315 5000 maximum at 31˚C 5000 maximum at 25˚C 5000 maximum at 19˚C 5000 maximum at 16˚C

947 kPa 1960 kPa 3840 kPa 5340 kPa


T314 300 maximum at -12˚C 300 maximum at -18˚C 300 maximum at -24˚C

105 231 380


T314 0.3 minimum at -12˚C 0.3 minimum at -18˚C 0.3 minimum at -24˚C

0.369 0.314 0.250

152

Table A-12: Gradations for F2C and its adjustments

Sieve Size (um) F2C F2G1 Adjustment F2G2 Adjustment

1 25000

3/4 19000 100 100 0 100 0

1/2 12500 95 90 -5 80 -15

3/8 9500 84 78 -6 71 -13

4 4750 52 52 0 52 0

8 2360 32 32 0 32 0

16 1180 21 21 0 21 0

30 600 15 15 0 15 0

50 300 9 9 0 9 0

100 150 6 6 0 6 0

200 75 5.2 5.2 0 5.2 0

Table A-13: Gradations for F4C and its adjustments

Sieve Size (um) F4C F4G1 Adjustment F4G2 Adjustment

1 25000

3/4 19000 100 100 0 100 0

1/2 12500 94 89 -5 79 -15

3/8 9500 89 80 -9 71 -18

4 4750 56 56 0 56 0

8 2360 30 30 0 30 0

16 1180 20 20 0 20 0

30 600 15 15 0 15 0

50 300 10 10 0 10 0

100 150 6 6 0 6 0

200 75 3.6 3.6 0 3.6 0

153

Table A-14: Volumetric properties of mixture design series 1 - 5

Property Symbol S1 S2 S3 S4 S5

Maximum theoretical density Gmm 2.543 2.276 2.253 2.550 2.563

Specific gravity of asphalt Gb 1.035 1.035 1.035 1.035 1.035

Bulk specific gravity of compacted mix Gmb 2.441 2.185 2.162 2.448 2.460

Asphalt content Pb 5.3 8.2 8.2 5.3 5.8

Bulk specific gravity of aggregate Gsb 2.725 2.346 2.311 2.745 2.776

Effective specific gravity of aggregate Gse 2.769 2.549 2.518 2.778 2.819

Asphalt absorption Pba 0.6 3.514 3.676 0.442 0.572

Effective asphalt content in the mixture Pbe 4.7 4.97 4.8 4.9 5.2

Percent VMA in compacted mix VMA 15.2 14.5 14.1 15.5 16.5

Percent air voids in compacted mix Va 4.0 4.0 4.0 4.0 4.0

Percent VFA in compacted mix VFA 74 72 72 74 76

Dust/asphalt ratio D/A 1.2 0.9 0.9 0.9 1.3















154





























155

APPENDIX B CREEP COMPLIANCE TEST RESULTS

Table B-1: Creep compliance test results at -10˚C (1/GPa)

Mixtures for Gradation Effects

Control G1 G2

Time (sec.) F2 F4 F2 F4 F2 F4

1 0.044 0.055 0.040 0.058 0.048 0.058

2 0.048 0.062 0.045 0.062 0.053 0.062

5 0.055 0.069 0.049 0.068 0.059 0.068

10 0.061 0.076 0.055 0.073 0.064 0.073

20 0.067 0.081 0.061 0.078 0.071 0.079

50 0.078 0.099 0.069 0.086 0.085 0.093

100 0.091 0.111 0.079 0.091 0.096 0.098

Pr 0.382 0.347 0.299 0.322 0.296 0.352


P1 (3.0%) P2 (4.5%) P3 (6.0%)


1 0.044 0.069 0.076 0.077 0.054 0.091

2 0.049 0.076 0.087 0.084 0.060 0.101

5 0.057 0.087 0.104 0.093 0.069 0.116

10 0.064 0.098 0.116 0.104 0.078 0.128

20 0.072 0.109 0.123 0.118 0.088 0.145

50 0.091 0.126 0.156 0.134 0.109 0.178

100 0.105 0.149 0.184 0.151 0.130 0.196

Pr 0.387 0.378 0.380 0.377 0.356 0.296

Note: 1/GPa = 6.89×10-6/psi

156

Table B-2: Creep compliance test results at 5˚C (1/GPa)


Control G1 G2


1 0.093 0.120 0.099 0.117 0.125 0.131

2 0.117 0.148 0.127 0.138 0.152 0.163

5 0.158 0.198 0.172 0.183 0.200 0.216

10 0.198 0.246 0.221 0.230 0.249 0.266

20 0.268 0.313 0.297 0.295 0.308 0.322

50 0.377 0.449 0.421 0.402 0.430 0.437

100 0.516 0.598 0.557 0.529 0.555 0.540

Pr 0.317 0.334 0.371 0.343 0.357 0.416


P1 (3.0%) P2 (4.5%) P3 (6.0%)


1 0.092 0.126 0.077 0.140 0.116 0.182

2 0.109 0.145 0.095 0.164 0.140 0.223

5 0.138 0.185 0.121 0.198 0.187 0.288

10 0.171 0.220 0.156 0.246 0.227 0.344

20 0.209 0.268 0.187 0.304 0.297 0.407

50 0.292 0.364 0.269 0.424 0.367 0.535

100 0.388 0.476 0.335 0.512 0.440 0.658

Pr 0.428 0.452 0.489 0.303 0.299 0.433



Control G1 G2


1 0.692 0.699 0.744 0.839 0.794 1.108

2 0.899 0.962 1.045 1.146 1.075 1.547

5 1.420 1.400 1.547 1.662 1.546 2.285

10 1.954 1.819 2.107 2.257 2.192 3.023

20 2.535 2.420 2.854 2.997 2.905 3.885

50 3.626 3.259 4.159 4.359 4.206 5.282

100 4.733 4.028 5.604 5.778 5.509 6.534

Pr 0.338 0.358 0.269 0.265 0.304 0.357


P1 (3.0%) P2 (4.5%) P3 (6.0%)


1 0.488 0.542 0.709 0.824 1.126 0.881

2 0.669 0.734 1.006 1.077 1.460 1.117

5 1.054 1.084 1.540 1.542 1.932 1.589

10 1.463 1.460 2.066 1.968 2.413 2.020

20 1.916 2.056 2.724 2.524 3.043 2.575

50 2.754 2.854 3.780 3.426 4.043 3.532

100 3.625 3.679 4.725 4.278 4.938 4.305

Pr 0.352 0.352 0.374 0.246 0.305 0.372

157



Control G1 G2


1 3.994 2.266 1.734 1.670 1.976 1.616

2 5.019 2.727 2.242 2.196 2.565 2.195

5 6.800 3.588 3.294 3.400 3.597 2.965

10 8.073 4.468 4.178 4.377 4.585 3.696

20 9.383 5.543 5.055 5.374 5.812 4.706

50 11.049 7.884 7.134 7.139 8.153 6.305

100 12.721 9.516 8.817 8.764 10.921 7.950

Pr 0.291 0.325 0.268 0.312 0.298 0.306


P1 (3.0%) P2 (4.5%) P3 (6.0%)


1 1.357 1.562 1.931 2.080 3.628 1.899

2 1.793 1.840 2.476 2.655 4.147 2.268

5 2.671 2.370 3.323 3.495 4.980 2.972

10 3.457 2.783 4.142 4.897 5.742 3.506

20 4.490 3.299 4.910 6.384 6.669 4.034

50 6.033 4.175 6.089 8.189 8.137 5.179

100 8.108 5.423 7.359 9.983 9.533 6.128

Pr 0.373 0.396 0.383 0.272 0.291 0.418

Creep Compliance for F2 Series at -10 Degree C

0.00

0.05

0.10

0.15

0.20

0 50 100

Time (sec.)

Cre

ep (

1/G

Pa)

Control

F2P1

F2P2

F2P3

Figure B-1: Creep compliance of F2 control and all polymer-modified levels at -10˚C.

158


0.00

0.05

0.10

0.15

0.20

0.25

0 50 100

Time (sec.)

Cre

ep (

1/G

Pa)

Control

F4P1

F4P2

F4P3

Figure B-2: Creep compliance of F4 control and all polymer-modified levels at -10˚C.

Creep Compliance for F2 Series at 5 Degree C

0.0

0.2

0.4

0.6

0 50 100

Time (sec.)

Cre

ep (

1/G

Pa)

Control

F2P1

F2P2

F2P3

Figure B-3: Creep compliance of F2 control and all polymer-modified levels at 5˚C.


0.0

0.2

0.4

0.6

0.8

0 50 100

Time (sec.)

Cre

ep

(1

/GP

a)

Control

F4P1

F4P2

F4P3


159


0

2

4

6

0 50 100

Time (sec.)

Cre

ep (

1/G

Pa)

Control

F2P1

F2P2

F2P3



0

2

4

6

0 50 100

Time (sec.)

Cre

ep (

1/G

Pa)

Control

F4P1

F4P2

F4P3



0

5

10

15

0 50 100

Time (sec.)

Cre

ep (

1/G

Pa)

Control

F2P1

F2P2

F2P3


160


0

3

6

9

12

0 50 100

Time (sec.)

Cre

ep (

1/G

Pa)

Control

F4P1

F4P2

F4P3



0.00

0.05

0.10

0.15

0 50 100

Time (sec.)

Cre

ep (

1/G

Pa)

Control

F2G1

F2G2

Figure B-9: Creep compliance of F2 control and modified gradation levels at -10˚C.


0.00

0.05

0.10

0.15

0.20

0 50 100

Time (sec.)

Cre

ep (

1/G

Pa)

Control

F4G1

F4G2

Figure B-10: Creep compliance of F4 control and modified gradation levels at -10˚C.

161


0.0

0.2

0.4

0.6

0 50 100

Time (sec.)

Cre

ep (

1/G

Pa)

Control

F2G1

F2G2

Figure B-11: Creep compliance of F2 control and modified gradation levels at 5˚C.


0.0

0.2

0.4

0.6

0 50 100

Time (sec.)

Cre

ep (

1/G

Pa)

Control

F4G1

F4G2



0

2

4

6

8

0 50 100

Time (sec.)

Cre

ep (

1/G

Pa)

Control

F2G1

F2G2


162


0

2

4

6

8

0 50 100

Time (sec.)

Cre

ep (

1/G

Pa)

Control

F4G1

F4G2



0

5

10

15

0 50 100

Time (sec.)

Cre

ep (

1/G

Pa)

Control

F2G1

F2G2



0

3

6

9

12

0 50 100

Time (sec.)

Cre

ep (

1/G

Pa)

Control

F4G1

F4G2


163

APPENDIX C TEST RESULTS FOR IDT AND DMT

Table C-1: Summary of resilient modulus and Poisson’s Ratio test results

MR (ksi) Poisson’s Ratio

Total Instantaneous Total Instantaneous Mix Temp.

(°C)

Sample

ID Total Avg. Inst. Avg. Total Avg. Inst. Avg.

S-1-2B 1625 1599 0.39 0.36 5

S-1-5B 1419 1522

1474 1537

0.28 0.34

0.32 0.34

S-1-2B 576 570 --- --- 25

S-1-5B 465 521

462 516

0.34 0.34

0.35 0.35

S-1-2B 165 215 --- ---

S-1

40 S-1-5B 183

174 217

216 0.35

0.35 0.32

0.32

S-2-11A 1279 1507 0.33 0.37

S-2-11B 1113 1180 0.25 0.28

S-2-12A 1283 1490 0.37 0.37 5

S-2-12B 1012

1172

1223

1350

0.29

0.31

0.36

0.34

S-2-11A --- --- --- ---

S-2-11B 439 549 0.27 0.30

S-2-12A 406 505 0.37 0.35 25

S-2-12B 438

428

519

524

0.36

0.33

0.32

0.32

S-2-11A 185 210 0.46 0.46

S-2-11B 168 205 0.20 0.27

S-2-12A 184 229 0.28 0.33

S-2

40

S-2-12B ---

179

---

215

---

0.31

---

0.35

S-3-8A 1035 1208 0.22 0.23

S-3-8B 1194 1357 0.26 0.29

S-3-9A 1194 1357 0.26 0.29 5

S-3-9B 1122

1136

1298

1305

0.32

0.27

0.32

0.28

S-3-8A --- --- --- ---

S-3-8B 467 605 0.28 0.35

S-3-9A 410 543 0.24 0.30 25

S-3-9B 475

451

604

584

0.35

0.29

0.38

0.34

S-3-8A 178 214 0.28 0.25

S-3-8B --- --- --- ---

S-3-9A 164 209 0.32 0.34

S-3

40

S-3-9B 218

186

263

229

0.38

0.33

0.33

0.31

164

Table C-1: Summary of Resilient Modulus and Poisson’s Ratio Test Results (Continued)



(˚C)

Sample


S-4-13B --- --- --- ---

S-4-14A 1272 1464 0.28 0.33 5

S-4-14B 1089

1180

1313

1389

0.31

0.30

0.31

0.32

S-4-13B 367 447 0.28 0.25

S-4-14A --- --- --- --- 25

S-4-14B 414

390

524

485

0.23

0.26

0.25

0.25

S-4-13B --- --- --- ---

S-4-14A 94 122 0.22 0.23

S-4

40

S-4-14B ---

94

---

122

---

0.22

---

0.23

S-5-3A 2392 2620 0.33 0.33

S-5-3B 2732 2953 0.33 0.30

S-5-4A 2443 2768 0.31 0.28

S-5-5A 2845 3122 0.33 0.34

5

S-5-5B 2957

2674

3320

2958

0.34

0.32

0.36

0.33

S-5-3A 672 942 0.29 0.26

S-5-3B 833 1004 0.30 0.29

S-5-4A 717 912 0.38 0.32

S-5-5A 855 1079 0.27 0.34

25

S-5-5B 870

789

1261

1040

0.37

0.32

0.40

0.32

S-5-3A 245 329 0.29 0.31

S-5-3B 313 411 0.35 0.39

S-5-4A 253 305 0.40 0.35

S-5-9A 296 181 0.25 0.34

S-5

40

S-5-9B 194

237

339

336

0.33

0.33

0.47

0.37

S-6-5A 3312 3505 0.30 0.27 5

S-6-6B 2955 3134

3170 3337

0.17 0.24

0.16 0.21

S-6-5A 1204 1378 0.38 0.38 25

S-6-6B 1361 1282

1550 1464

0.35 0.37

0.31 0.34

S-6-5A 279 451 0.31 0.30

S-6

40 S-6-6B 387

333 564

508 0.31

0.31 0.32

0.31

165




(˚C)

Sample


S-7-4B 2264 2536 0.20 0.20

S-7-5A 2303 2564 0.25 0.25 5

S-7-5B 1430

1999

1570

2223

0.16

0.20

0.15

0.20

S-7-4B 718 977 0.27 0.26

S-7-5A 681 957 0.29 0.31 25

S-7-5B 486

629

641

858

0.16

0.24

0.13

0.23

S-7-4B 196 298 0.34 0.35

S-7-5A 167 276 0.31 0.33

S-7

40

S-7-5B 122

162

197

257

0.18

0.28

0.24

0.31

S-8-4A 1952 2178 0.17 0.18

S-8-4B 1723 1929 0.22 0.21 5

S-8-5B 1805

1827

2015

2041

0.23

0.21

0.22

0.20

S-8-4A 542 804 0.23 0.27

S-8-4B 590 785 0.41 0.40 25

S-8-5B 407

513

613

734

0.17

0.27

0.19

0.29

S-8-4A 175 280 0.35 0.39

S-8-4B 136 220 0.36 0.40

S-8

40

S-8-5B 145

152

232

244

0.34

0.35

0.42

0.40

S-9-4A 1797 1985 0.22 0.22

S-9-5A 1991 2165 0.22 0.22 5

S-9-5B 1538

1776

1715

1955

0.19

0.21

0.20

0.21

S-9-4A 690 836 0.24 0.22

S-9-5A 523 675 0.21 0.21 25

S-9-5B 483

566

621

711

0.19

0.22

0.20

0.21

S-9-4A 227 375 0.28 0.34

S-9-5A 172 275 0.22 0.24

S-9

40

S-9-5B 161

187

258

303

0.19

0.23

0.21

0.26

166




(˚C)

Sample


S-10-5B 2070 2270 0.26 0.24

S-10-6A 1993 2210 0.19 0.20 5

S-10-6B 2344

2136

2580

2353

0.20

0.22

0.19

0.21

S-10-5B 584 780 0.31 0.30

S-10-6A 612 805 0.26 0.26 25

S-10-6B 651

616

824

803

0.23

0.27

0.18

0.25

S-10-5B 175 445 0.40 0.46

S-10-6A 177 269 0.28 0.37

S-10

40

S-10-6B 170

174

293

336

0.19

0.29

0.25

0.36

S-11-3A 1936 2146 0.24 0.25

S-11-3B 2017 2213 0.19 0.19 5

S-11-4B 2036

1996

2222

2193

0.21

0.22

0.19

0.21

S-11-3A 557 801 0.35 0.35

S-11-3B 486 742 0.23 0.24 25

S-11-4B 553

532

766

770

0.30

0.29

0.27

0.29

S-11-3A 180 301 0.14 0.19

S-11-3B 166 271 0.24 0.27

S-11

40

S-11-4B 167

171

267

280

0.29

0.22

0.30

0.25

S-12-3B 2427 2738 0.24 0.24

S-12-4A 1953 2148 0.19 0.18 5

S-12-4B 2103

2161

2388

2425

0.20

0.21

0.24

0.22

S-12-3B 579 862 0.22 0.23

S-12-4A 510 676 0.25 0.27 25

S-12-4B 532

541

765

768

0.20

0.22

0.23

0.23

S-12-3B 112 171 0.25 0.24

S-12-4A 125 197 0.24 0.26

S-12

40

S-12-4B 142

126

231

200

0.30

0.26

0.34

0.28

167




(˚C)

Sample


S-13-3B 2315 2564 0.21 0.22

S-13-5A 2702 2979 0.15 0.17 5

S-13-5B 2359

2459

2657

2733

0.23

0.20

0.24

0.21

S-13-3B 903 1081 0.29 0.29

S-13-5A 1059 1167 0.22 0.17 25

S-13-5B 831

931

1038

1095

0.18

0.23

0.20

0.22

S-13-3B 238 385 0.25 0.30

S-13-5A 292 487 0.26 0.34

S-13

40

S-13-5B 228

253

376

417

0.29

0.27

0.34

0.33

S-14-3B 1993 2170 0.23 0.21

S-14-4B 2561 2783 0.28 0.29 5

S-14-5A 1974

2176

2198

2384

0.20

0.23

0.20

0.23

S-14-3B 625 997 0.25 0.33

S-14-4B 942 1131 0.34 0.27 25

S-14-5A 600

722

904

1011

0.20

0.26

0.25

0.28

S-14-3B 154 247 0.29 0.38

S-14-4B 327 518 0.35 0.39

S-14

40

S-14-5A 146

209

240

335

0.17

0.27

0.24

0.34

S-15-4B 2937 3222 0.33 0.33

S-15-5A 2311 2550 0.25 0.25 5

S-15-5B 2277

2509

2459

2744

0.18

0.25

0.17

0.25

S-15-4B 889 1088 0.37 0.30

S-15-5A 674 911 0.26 0.25 25

S-15-5B 807

790

1137

1045

0.24

0.29

0.25

0.27

S-15-4B 265 422 0.34 0.33

S-15-5A 206 336 0.33 0.39

S-15

40

S-15-5B 254

242

367

375

0.36

0.34

0.34

0.35

168




(˚C)

Sample


S-16-3A 2153 2344 0.24 0.23

S-16-5A 2016 2257 0.18 0.19 5

S-16-5B 2084

2084

2322

2308

0.18

0.20

0.19

0.20

S-16-3A 746 985 0.31 0.30

S-16-5A 601 815 0.22 0.22 25

S-16-5B 622

656

869

890

0.19

0.24

0.24

0.25

S-16-3A 216 355 0.23 0.28

S-16-5A 198 314 0.21 0.26

S-16

40

S-16-5B 209

208

334

334

0.19

0.21

0.27

0.27

S-17-3A 2147 2403 0.31 0.33

S-17-3B 1928 2089 0.17 0.16 5

S-17-5A 1855

1977

2066

2186

0.18

0.22

0.19

0.23

S-17-3A 886 1029 0.35 0.31

S-17-3B 753 976 0.20 0.20 25

S-17-5A 659

766

789

931

0.22

0.26

0.18

0.23

S-17-3A 285 411 0.31 0.31

S-17-3B 265 396 0.29 0.31

S-17

40

S-17-5A 247

266

401

403

0.28

0.29

0.32

0.31

S-18-4A 2631 2835 0.24 0.25

S-18-4B 2551 2787 0.19 0.21 5

S-18-5A 2696

2626

2923

2848

0.26

0.23

0.28

0.25

S-18-4A 1702 1809 0.48 0.43

S-18-4B 1343 1475 0.19 0.19 25

S-18-5A 1347

1464

1540

1608

0.28

0.31

0.28

0.30

S-18-4A 807 919 0.38 0.35

S-18-4B 783 936 0.25 0.28

S-18

40

S-18-5A 640

743

968

941

0.31

0.31

0.47

0.37

169




(˚C)

Sample


S-19-3A 2102 2324 0.13 0.13

S-19-4A 2040 2243 0.10 0.10 5

S-19-5B 2076

2073

2255

2274

0.12

0.12

0.12

0.12

S-19-3A 907 1025 0.21 0.22

S-19-4A 713 891 0.13 0.14 25

S-19-5B 735

785

880

932

0.27

0.20

0.25

0.20

S-19-3A 224 353 0.27 0.27

S-19-4A 174 274 0.16 0.17

S-19

40

S-19-5B 209

202

324

317

0.30

0.25

0.30

0.25

S-20-3B 1838 2046 0.15 0.15

S-20-4A 2070 2281 0.17 0.17 5

S-20-4B 2077

1995

2283

2203

0.19

0.17

0.19

0.17

S-20-3B 493 736 0.19 0.19

S-20-4A 653 1004 0.20 0.20 25

S-20-4B 588

578

907

882

0.28

0.22

0.29

0.23

S-20-3B 141 224 0.24 0.25

S-20-4A 132 205 0.26 0.28

S-20

40

S-20-4B 122

131

199

210

0.34

0.28

0.35

0.29

Note: 1 ksi = 6.89 MPa

170

Table C-2: Summary of dynamic modulus testing results

Dynamic Modulus (psi) at Frequency (Hz) Mixture

Temperature

(°C) 25 Hz 10 Hz 5 Hz 1 Hz 0.5 Hz

5 2718556 2505315 2334144 1940728 1763329

25 1363593 1177199 1010382 667755 533823 S1

40 514862 448082 347376 189291 146889

5 2195185 2043910 1928686 1643632 1513252

25 837880 684018 598500 413070 368702 S2

40 370582 349512 275622 156980 130454

5 1665338 1523653 1383432 1041750 926707

25 1015881 840265 708900 471784 393277 S3

40 479986 363429 289464 170541 139570

5 1688377 1515004 1375835 1058085 923347

25 758494 618952 519722 328501 274068 S4

40 321230 239316 189747 124783 102381

5 1940695 1813721 1700122 1423737 1298946

25 1046943 899545 784929 548407 459125 S5

40 437124 332714 265866 155747 128673

5 3219817 2887077 2676451 2166454 1936833

25 1402727 1165921 966038 593581 459123 S6

40 475793 369106 277443 144513 126079

5 2657447 2445081 2254771 1791554 1498947

25 1137414 959075 793326 472220 358789 S7

40 424137 301779 227473 133711 104263

5 2106279 1898941 1711824 1276268 1093710

25 797849 655478 520685 298806 246089 S8

40 276775 198701 158492 95001 73974

5 2279604 2125885 1963997 1563898 1391163

25 1131702 936634 795165 505711 397558 S9

40 431144 327847 254922 159677 129964

5 2771753 2490818 2286261 1808405 1601989

25 1116202 908742 747045 442313 338010 S10

40 390597 273649 203734 121979 95205

171

Table C-2: Summary of dynamic modulus testing results (Continued)

Dynamic Modulus (psi) at Frequency (Hz) Mixture

Temperature

(°C) 25 Hz 10 Hz 5 Hz 1 Hz 0.5 Hz

5 2460067 2216427 2012981 1560490 1367085

25 1012301 824140 672212 392622 306538 S11

40 322355 228212 177715 105194 83242

5 2351471 2090847 1889063 1427932 1233845

25 927331 737812 588777 324985 263962 S12

40 278916 184464 152604 84398 67535

5 3011584 2818300 2624445 2136791 1924084

25 1328278 1125221 953667 612433 485643 S13

40 559182 419748 327764 187856 148362

5 2728458 2499581 2320051 1889681 1703802

25 1218686 1040795 882519 571472 456110 S14

40 554386 414528 324182 189306 142947

5 2572339 2395084 2216750 1775124 1584504

25 1023437 842892 697684 456682 350667 S15

40 400128 285613 214864 132733 102079

5 2677688 2489353 2278723 1827880 1634091

25 1115825 944472 787322 485782 378116 S16

40 385569 281676 220259 131109 101240

5 2526217 2251277 2064508 1640875 1461569

25 1056637 906080 770487 500564 401294 S17

40 409877 311574 248031 153194 120265

5 3453820 3194201 3048829 2708039 2554885

25 1916335 1719572 1566964 1229368 1088818 S18

40 1029854 860866 740421 509969 423155

5 2513563 2344507 2175441 1749294 1564667

25 1144054 935766 779194 466181 357925 S19

40 441512 320771 244152 142058 108477

5 2739617 2560305 2366486 1898011 1689792

25 1048483 842779 696163 407042 309066 S20

40 390325 276400 207707 120487 95873

Note: 1 psi = 6.89 KPa

172

Table C-3: Summary of phase angle testing results

Phase Angle (degree) at Frequency (Hz) Mixture

Temperature

(°C) 25 Hz 10 Hz 5 Hz 1 Hz 0.5 Hz

5 6.9 8.2 9.4 11.8 13.2

25 16.9 19.2 21.6 26.9 30.0 S1

40 28.5 30.4 32.8 35.2 37.6

5 6.5 7.5 8.5 10.4 11.7

25 16.5 18.3 20.2 25.0 28.6 S2

40 29.2 29.1 30.9 32.7 34.7

5 16.1 19.0 20.9 25.2 27.8

25 22.9 25.4 27.7 31.0 32.2 S3

40 31.4 32.0 31.3 29.0 28.8

5 9.5 11.3 12.7 16.5 18.5

25 20.2 22.8 25.2 28.9 31.1 S4

40 30.3 31.5 31.5 27.8 28.1

5 7.4 8.3 9.3 11.2 12.1

25 14.4 17.5 19.1 22.1 23.7 S5

40 22.8 27.9 29.5 30.7 31.2

5 7.2 8.8 10.3 13.3 14.9

25 19.5 22.1 24.9 30.0 32.8 S6

40 35.9 35.1 36.7 36.4 36.2

5 9.6 10.2 11.7 14.3 17.4

25 21.8 24.6 27.2 32.3 35.1 S7

40 32.0 34.7 36.1 33.9 34.6

5 11.7 13.2 14.8 18.7 20.8

25 27.0 28.3 31.1 34.7 37.2 S8

40 35.1 35.2 33.7 29.9 29.4

5 9.0 10.5 11.9 15.0 16.8

25 19.0 21.0 23.6 28.5 31.2 S9

40 30.4 31.4 32.7 29.7 30.3

5 9.2 11.0 12.5 15.7 17.6

25 22.2 24.5 27.1 31.8 34.3 S10

40 32.7 35.8 36.7 32.2 31.9

173

Table C-3: Summary of phase angle testing results (Continued)

Phase Angle (degree) at Frequency (Hz) Mixture

Temperature

(°C) 25 Hz 10 Hz 5 Hz 1 Hz 0.5 Hz

5 9.1 11.8 13.3 16.6 18.4

25 22.2 25.5 28.0 32.6 34.8 S11

40 34.7 37.0 35.6 30.9 30.2

5 8.7 12.7 14.5 18.4 20.7

25 23.0 27.6 30.5 35.8 38.6 S12

40 37.2 38.4 35.2 31.0 29.6

5 7.6 9.3 10.5 13.1 14.6

25 18.6 20.6 22.8 27.3 30.0 S13

40 28.7 30.4 32.0 32.7 34.9

5 9.6 9.8 10.9 13.2 14.5

25 15.4 21.2 23.2 27.2 29.5 S14

40 27.1 28.7 30.4 32.4 33.3

5 6.6 10.3 11.5 14.0 15.5

25 22.6 23.2 25.7 30.7 33.3 S15

40 33.6 34.7 36.1 32.2 32.4

5 4.0 9.7 11.4 14.1 15.5

25 17.1 23.0 25.2 30.0 32.4 S16

40 32.6 33.7 34.2 32.7 33.8

5 5.3 10.8 11.9 14.3 15.6

25 17.9 20.8 22.7 26.4 28.6 S17

40 28.4 29.2 30.4 30.3 31.9

5 3.5 5.9 6.3 7.3 7.8

25 11.1 11.9 13.0 15.1 16.3 S18

40 17.4 19.0 20.4 23.1 24.8

5 8.5 9.6 10.9 13.6 15.2

25 21.1 23.5 26.1 31.7 34.6 S19

40 32.7 34.4 36.0 35.4 36.6

5 8.5 10.1 11.3 14.2 15.8

25 21.2 24.3 26.8 32.3 35.6 S20

40 34.8 36.2 37.4 35.0 35.1

174

REFERENCES

1. AASHTO, “Guide for Design of Pavement Structures”, American Association of State Highway and Transportation Officials (AASHTO), Washington, D.C., 1993.

2. AASHTO TP 31, “Standard Test Method for Determining the Resilient Modulus of Bituminous Mixtures by Indirect Tension”, American Association of State Highway and Transportation Officials (AASHTO), Washington, D.C., 1996.

3. Aglan, H.A., “Polymer Modifiers for Improved Performance of Asphalt” In Asphalt Science and Technology, Usmani, Marcel Dekker, 1997, pp. 197-216.

4. American Society for Testing and Materials. 1994 Annual Book of ASTM Standards, Vol. 04.04, Rubber, Natural and Synthetic-General Test Methods, 1994.

5. Pradhan, M. M. and J. D. Armijo, “Assessing Effects of Commercial Modifiers on Montana Asphalts by Conventional Testing Methods” Transportation Research Record, No. 1417, 1993, pp. 84-92.

6. Asphalt Institute and the Heritage Group, “The Bailey Method: Achieving Volumetrics and HMA Compactability” Asphalt Institute Educational Course and Seminar Materials, Lexington, KY, 2005.

7. Asphalt Institute, “Superpave Level I Mix Design” Asphalt Institute, Lexington, KY, Report No. SP-2, 1995.

8. Asphalt Institute, “Superpave Mix Design” Superpave Series No. 2 (SP-02), Asphalt Institute, Lexington, KY, 2001.

9. ASTM D 3497, “Standard Test Method for Dynamic Modulus of Asphalt Mixtures”, ASTM, Philadelphia, PA., 1997.

10. ASTM D 4123, “Standard Test Method for Indirect Tension Test for Resilient Modulus of Bituminous Mixture”, ASTM International, West Conshohocken, PA, 1982.

11. Bahia, H.U. and D.A. Anderson, “Strategic Highway Research Program Binder Rheological Parameters: Background and Comparison with Conventional Properties” Transportation Research Record, No. 1488, 1995, pp. 32-39.

12. Barksdale, R. D., J. Alba, N. P. Khosla, R. Kim, P. C. Lambe, and M. S. Rahman, «Laboratory Determination of Resilient Modulus for Flexible Pavement Design», NCHRP Program 1-28 Project, TRB, Washington, D.C., June 1997.

175

13. Birgisson, B. and B. Ruth, “Development of Tentative Guidelines for the Selection of Aggregate Gradations for Hot-Mix Asphalt” American Society for Testing and Materials, STP 1412, 2001.

14. Birgisson, B., R. Roque and G. Page, “Evaluation of Water Damage Using Hot Mix Asphalt Fracture Mechanics” Journal of the Association of Asphalt Paving Technologists, 2003, Vol. 72, pp. 424-462.

15. Birgisson, B., R. Roque, J. Kim, L.V. Pham, «The Use of Complex Modulus to Characterize the Performance of Asphalt Mixtures and Pavements in Florida», Final Report, BC-354-22, The Florida Department of Transportation, Tallahassee, Florida, 2004.

16. Birgisson, B., R. Roque, G.C. Page, “Performance-Based Fracture Criterion for Evaluation of Moisture Susceptibility in Hot-Mix Asphalt” Transportation Research Record: Journal of the Transportation Research Board, No. 1891, TRB, National Research Council, Washington, D.C., 2004, pp. 55-61.

17. Brule, B., Y. Brion and A. Tanguy, “Paving Asphalt Polymer Blends: Relationships between Composition, Sturcture and Properties” Proceedings, the Association of Asphalt Paving Technologists, Vol. 57, 1988, pp. 41-64.

18. Buttlar, W. G. and R. Roque, “Development and Evaluation of the Strategic Highway Research Program Measurement and Analysis System for Indirect Tensile Testing at Low Temperatures”, Transportation Research Record: Journal of the Transportation Research Board, No. 1454, Washington, D.C., 1994, pp. 163-171.

19. Button, J.W., “Summary of Asphalt Additive Performance at Selected Sites” Transportation Research Record, No. 1342, 1992, pp. 67-75.

20. Carpenter, S.H. and S. Shen, “Dissipated Energy Approach to Study Hot-Mix Asphalt Healing in Fatigue” Transportation Research Record, 2006, pp.178-185.

21. Carpenter, SH. and T. VanDam, “Laboratory Performance Comparisons of Polymer-Modified and Unmodified Asphalt Concrete Mixtures” Transportation Research Record 1115, TRB. Washington, DC: National Research Council, 1987, pp. 62–74.

22. Chen, J. and C. Huang “Fundamental Characterization of SBS-Modified Asphalt Mixed with Sulfur” Journal of Applied Polymer Science, Vol. 103, pp. 2817–2825, 2007.

23. Chen, J., M. Liao and C. Lin, “Determination of Polymer Content in Modified Bitumen” Materials and Structures, Vol. 36, November 2003, pp. 594-598.

176

24. Chen, J., M. Liao and M. Shiah, “Asphalt Modified by Styrene-Butadiene-Styrene Triblock Copolymer: Morphology and Model” Journal of Materials in Civil Engineering, May/June, pp. 224-229, 2002.

25. Chowdhury, A., J. Grau, J. Button and D. Little, “Effect of Aggregate Gradation on Permanent Deformation of Superpave HMA” the 80th Annual Meeting of Transportation Research Board, Washington, D.C., 2001.

26. Collins, J.H., M.G. Bouldin, R. Gellens and A. Berker, “Improved Performance of Paving Asphalts by Polymer Modifications” Proceedings, Association of Asphalt Paving Technologists, Vol. 60, 1991, pp. 43-79.

27. Di Benedetto, H., F. Olard, C. Sauzeat and B. Delaporte B., “Linear Viscoelastic Behavior of Bituminous Materials: From Binders to Mixes”, International Journal of Road Materials and Pavement Design, Vol. 5, Special Issue, 2004, pp. 163-202.

28. Di Benedetto, H., M. N. Partl, L. Francken and De La Roche St Andre, “Stiffness Testing for Bituminous Mixtures”, Journal of Materials and Structures, Vol. 34, 2001, pp. 66-70.

29. Diani, E., M.D. Via, and M.G. Cavaliere, “Chemistry and Technology of SBS Modifier” Asphalt Science and Technology, Marcel Dekker Inc., New York, pp. 279-295, 1997.

30. Drescher, A., D.E. Newcomb, and W. Zhang, “Interpretation of Indirect Tension Test Based on Viscoelasticity”, Transportation Research Record, No. 1590, 1997, pp. 45-52.

31. Ekingen, E. R., “Determining Gradation and Creep Effects in Mixtures Using the Complex Modulus Test” Master’s Thesis, Department of Civil Engineering, University of Florida, 2004.

32. Federal Highway Administration, “Background of Superpave Asphalt Mixture Design and Analysis” FHWA Report Number FHWA-SA-95-003, 1995.

33. Federal Highway Administration, “Superpave Asphalt Mixture Design: Illustrated Level I Lab Methods”, FHWA Report Number FHWA-SA-95-004, 1995.

34. Fonseca, O. A. and M. W. Witczak, “A Prediction Methodology for the Dynamic Modulus of In-Place Aged Asphalt Mixtures”, Journal of the Association of Asphalt Paving Technologists, Vol. 65, 1996, pp. 532-559.

35. Foster, C.R., “Development of Marshall Procedures for Designing Asphalt Paving Mixtures” National Asphalt Pavement Association, NAPA IS84, 1982.

36. Fuller, W.B. and S. Thompson, “The Laws of Proportioning Concrete” Journal of Transportation Division, ASCE, Vol. 59, 1907, pp. 67-143.

177

37. Goode, J.F., and L.A. Lufsey, “A New Graphical Chart for Evaluating Aggregate Gradations” Proceedings, AAPT, Volume 31, 1962, pp. 176-207.

38. Hines, M.L., “Asphalt Cement Performance Improved by Styrelf-Laboratory and Field Data” Koch Materials Company, 1993.

39. Hondoros, G., “Evaluation of Poisson’s Ratio and the Modulus of Materials of a Low Tensile Resistance by the Brazilian (Indirect Tensile) Test with Particular Reference to Concrete”, Australian Journal of Applied Science, Vol. 10, No. 3, 1959, pp. 243-268.

40. Huang, Y., «Pavement Analysis and Design». Appendix A: Theory of Viscoelasticity. Prentice Hall, Englewood Cliffs New Jersey 07632, 1993.

41. Huber G.A. and T. Shuler, “Providing Sufficient Void Space for Asphalt Cement: Relationship of Mineral Aggregate Void and Aggregate Gradation”, Effects of Aggregates and Mineral Fillers on Asphalt Mixtures performance” ASTM SPT 1147, Philadelphia, 1992.

42. Huffman, J.E., “The Use of Ground Vulcanized Rubber in Asphalt, Asphalt Pavement Construction: New Materials and Techniques” American Society for Testing and Materials, Special Technical Publication 724, 1980, pp. 3-12.

43. Hveem, F.N., “Gradation of Mineral Aggregate for Dense-Graded Bituminous Mixtures” Proceedings, AAPT, Vol. 11, 1940, pp. 315-339.

44. Jones, S.D., K. Mahboub, R. Anderson and H. Bahia, “Applicability of Superpave to Modified Asphalts – A Mixture Study” Transportation Research Record 1630, TRB, National Research Council, Washington, D.C., 1998, pp. 42-50.

45. Kandhal, P. and R. Mallick, “Effect of Mix Gradation on Rutting Potential of Dense-Graded Asphalt Mixtures” Transportation Research Record, No. 1767, 2001, pp. 146-151.

46. Kennedy, T. W., “Characterization of Asphalt Pavement Materials Using the Indirect Tensile Test”, Journal of the Association of Asphalt Paving Technologists, Vol. 46, 1977, pp. 132-150.

47. Kennedy, T., H. Torshizi and D. Jones IV, “Mix Design Procedures and Considerations for Polymer-Modified Asphalt Compatibility and Stability” Center for Transportation Research, Research Report 492-1F, Project 3-9-87/1-492, 1992.

48. Khattak, M.J. and G.Y. Baladi, “Engineering Properties of Polymer-Modified Asphalt Mixtures” Transportation Research Record, No. 1638, 1998, pp. 12-22.

178

49. Khattak, M.J. and G.Y. Baladi, “Fatigue and Permanent Deformation Models for Polymer-Modified Asphalt Mixtures” Transportation Research Record, No. 1767, 2001, pp. 135-145.

50. Kim, B., R. Roque, and B. Birgisson, “Laboratory Evaluation of the Effect of SBS Modifier on Cracking Resistance of Asphalt Mixtures,” Journal of the Transportation Research Board, TRR 1829, Washington, D.C., 2003, pp. 8-15.

51. Kim, J., “Accurate Determination of Dissipated Creep Strain Energy and Its Effect on Load - and Temperature - Induced Cracking of Asphalt Pavement” PhD Dissertation, University of Florida, 2005.

52. Kim, Y. R., Y. Seo, M. King, and M. Momen, “Dynamic Modulus Testing of Asphalt Concrete in Indirect Tension Mode”, Transportation Research Record, No. 1891, 2004, pp. 163-173.

53. King, G.N., H. Muncy, and J. Prudhomme, “Polymer Modification: Binder’s Effect on Mix Properties” Proceedings, AAPT, Vol 55, 1986, pp. 519-540.

54. King, G.N., H.W. King, O. Harders, W. Arand and P. Planche, “Influence of Asphalt Grade and Polymer Concentration on the Low Temperature Performance of Polymer Modified Asphalt” Proceedings, AAPT, Vol. 62, 1993, pp. 1-22.

55. King, M., M. Momen, and Y. R. Kim, “Typical Dynamic Moduli Values of Hot Mix Asphalt in North Carolina and Their Prediction”, Transportation Research Board, 2005 84th Annual Meeting Compendium of Papers CD-ROM, Washington, D.C.

56. Lacroix, A., A. M. Khandan, and Y. R. Kim, “Predicting the Resilient Modulus of Asphalt Concrete from the Dynamic Modulus”, Transportation Research Record: Journal of the Transportation Research Board, No. 2001, 2007, pp. 132-140.

57. Lalwani, S., A. Abushihada and A. Halasa, “Reclaimed Rubber-Asphalt Blends Measurement of Rheological Properties to Access Toughness, Resiliency, Consistency and Temperature Sensitivity” Proceedings, AAPT, Vol. 51, 1982, pp. 562-579.

58. Loulizi, A., G. W. Flintsch, I. L. Al-Qadi and D. Mokarem, “Comparing Resilient Modulus and Dynamic Modulus of Hot-Mix Asphalt as Material Properties for Flexible Pavement Design”, Transportation Research Record: Journal of the Transportation Research Board, No. 1970, Washington, D.C., 2006, pp. 161-170.

59. Lu. X, U. Isacsson and J. Ekblad, “Low-temperature properties of styrene–butadiene–styrene polymer modified bitumens” Construction and Building Materials Vol.12, Issue 8, 1998, pp. 405–414.

179

60. McGennis, R.B., S. Shuler, and H.U. Bahia, “Background of Superpave Asphalt Binder Test Methods” FHWA, Report No. FHWA-SA-94-069, July 1994.

61. National Cooperative Highway Research Program, Project 1-37A-2002 Mechanistic-Empirical (M-E) Pavement Design Guide (Draft), NCHRP, Washington, D.C., 2004.

62. National Cooperative Highway Research Program, Project 9-29 Simple Performance Tester for Superpave Mix Design, “First Article Development and Evaluation”, NCHRP Report 513, Washington, D.C., 2003.

63. Nijboer L.W., “Plasticity as a Factor in the Design of Dense Bituminous Road Carpets” Elsevier Publishing Company Inc., New York, NY, 1948.

64. Papazian, H. S., “The Response of Linear Viscoelastic Materials in the Frequency Domain with Emphasis on Asphaltic Concrete”, (1st) International Conference on the Structural Design of Asphalt Pavements, 1962, University of Michigan, pp. 454-463.

65. Pellinen, T. K. and M. W. Witczak, “Stress Dependent Master Curve Construction for Dynamic (Complex) Modulus”, Journal of the Association of Asphalt Paving Technologists, Vol. 71, 2002, pp. 281-309.

66. Pellinen, T. K., “Investigation of the Use of Dynamic Modulus as an Indicator of Hot-Mix Asphalt Performance”, Ph.D. Dissertation, Arizona State University, 2001.

67. Ping, W. V. and Y. Xiao, «Evaluation of the Dynamic Complex Modulus Test and Indirect Diametral Test for Implementing the AASHTO 2002 Design Guide for Pavement Structures in Florida », Final Report, The Florida Department of Transportation, BC-352-12, Tallahassee, FL, 2007.

68. Ping, W.V. and Y. Xiao, “Empirical Correlation of Indirect Tension Resilient Modulus and Complex Modulus Test Results for Asphalt Concrete Mixtures” International Journal of Road Materials and Pavement Design, Volume 9, 2008, pp. 177-200.

69. Quintus, H., J. Mallela and M. Buncher, “Quantification of Effect of Polymer-Modified Asphalt on Flexible Pavement Performance” Transportation Research Record: Journal of the Transportation Research Board, No. 2001, 2007, pp. 141-154.

70. Roberts, R.L., P.S. Kandhal, E.R. Brown, D. Lee, and T.W. Kennedy, «Hot Mix Asphalt Materials, Mixture Design, and Construction» National Center for Asphalt Technology (NCAT), National Asphalt Pavement Association (NAPA), Research and Education Foundation, Lanham, Maryland, 1996.

71. Roque, R. and W. G. Buttlar, “The Development of a Measurement and Analysis System to Accurately Determine Asphalt Concrete Properties Using the Indirect Tensile

180

Mode”, Journal of the Association of Asphalt Paving Technologists, Vol. 61, 1992, pp. 304-332.

72. Roque, R., B. Birgisson and S. Kim, “Development of Mix Design Guidelines for Improved Performance of Asphalt Mixtures” Florida Department of Transportation, Final Report, BD545, RPWO#16, 2006.

73. Roque, R., B. Birgisson, Z. Zhang, B. Sangpetngam, and T. Grant, “Implementation of SHRP Indirect Tension Tester to Mitigate Cracking in Asphalt Pavements and Overlays” Final Report, Florida Department of Transportation, BA-546, 2002.

74. Roque, R., B. Birgisson, C. Drakos, and B. Dietrich “Development and Field Evaluation of Energy-Based Criteria for Top-down Cracking Performance of Hot Mix Asphalt” Journal of the Association of Asphalt Paving Technologists, Vol. 73, 2004, pp. 229-260.

75. Roque, R., B. Birgisson, B. Sangpetgnam, Z. Zhang, “Hot Mix Asphalt Fracture Mechanics: A Fundamental Crack Growth Law for Asphalt Mixtures” Journal of the Association of Asphalt Paving Technologists, Vol. 71, 2002, pp. 816-828.

76. Ruth B.E., R. Roque, and B. Nukunya, “Aggregate Gradation Characterization Factors and Their Relationships to Fracture Energy and Failure Strain of Asphalt Mixtures” Journal of the Association of Asphalt Paving Technologists, Vol. 71, 2002, pp. 310-344.

77. Schapery, R.A., “Viscoelstic Behavior and Analysis of Composite Materials” Report MM 72-3, Mechanics and Materials Research Center, Texas A&M University, College Station, Texas, 1972.

78. Scofield, L.A., “The History, Development, and Performance of Asphalt Rubber at ADOT” Special Report, Report Number AZ-SP-8902, Arizona Department of Transportation, Materials Section, Phoenix, AZ, December 1989.

79. Shen, S. and S.H. Carpenter, “Application of the Dissipated Energy Concept in Fatigue Endurance Limit Testing” Transportation Research Record, 2005, pp. 165-173.

80. Shih, C., “Evaluation of Asphalt Additives for Improved Cracking and Rutting Resistance of Asphalt Paving Mixtures” PhD Dissertation, University of Florida, 1996.

81. SHRP-LTPP Protocol P07, “Test Method for Determining the Creep Compliance, Resilient Modulus, and Strength of Asphalt Materials Using the Indirect Tensile Test Device”, LAW PCS, SHRP, National Research Council, Washington, D.C., August 2001.

82. Terrel, R.L. and J.L. Walter, “Modified Asphalt Pavement Materials - The European Experience” Proceedings, AAPT, 1986, Vol. 55, pp. 482-518.

181

83. The Asphalt Institute, “Mix Design Methods for Asphalt Concrete and Other Hot Mix Types” MS-2, May 1984.

84. The Asphalt Institute, “Mix Design Methods for Asphalt Concrete and Other Hot Mix Types” Manual Series No. 2 (MS-2). (6th ed.), Lexington, KY, 1993.

85. The Asphalt Institute, “Performance Graded Asphalts Binder Specification and Testing” Superpave Series No.1 (SP-1), Lexington, KY, 1994.

86. Transportation Research Board, “Superior Performing Asphalt Pavements (Superpave): The Product of the SHRP Asphalt Research Program”, TRB Report Number SHRP-A-410, 1994.

87. Usmani, A.M., “Polymer Science and Technology” Asphalt Science and Technology, Marcel Dekker Inc., New York, pp. 307-336, 1997.

88. Vallerga, B.A., and W.R. Lovering, “Evolution of the Hveem Stabilometer Method of Designing Asphalt Paving Mixtures” Proceedings, Association of Asphalt Paving Technologists, Vol. 54, 1985, pp. 243 - 265.

89. Vavrik W.R., W.J. Pine, G. Huber, and S.H. Carpenter, “The Bailey Method of Gradation Evaluation: The Influence of Aggregate Gradation and Packing Characteristics on Voids in the Mineral Aggregate” Journal of the Association of Asphalt Paving Technologists, 2001, Vol. 70, pp. 132-175.

90. Verhaeghe, B.M.J.A., F.C. Rust, R.M. Vos and A.T. Visser, “Properties of Polymer- and Fiber-Modified Porous Asphalt Mixes” 6th Conference on Asphalt Pavements for Southern Africa. Proceedings, Vol. 1, Cape Town, South Africa, October 1994, pp. III-262-280.

91. Villiers C., “Sensitivity of Superpave Mixtures for Development of Performance-Related Specifications” PhD Dissertation, University of Florida, 2004.

92. Warren, R.S., R.B. McGennis, And H.U. Bahia, “Superpave Asphalt Binder Test Methods — An Illustrated Overview” FHWA, Report No. FHWA-SA-94-068, July 1994.

93. Wegon, V. and B. Brule, “The Structure of Polymer Modified Binders and Corresponding Asphalt Mixtures” Proceedings, AAPT, Vol. 68, 1999, pp. 64-88.

94. White, T.D., “Marshall Procedures for Design and Quality Control of Asphalt Mixtures” Proceedings, AAPT, Volume 54, 1985, pp. 265-284.

182

95. Witczak, M. W. and O. A. Fonseca, “Revised Prediction Model for Dynamic (Complex) Modulus of Asphalt Mixtures”, Transportation Research Record: Journal of the Transportation Research Board, No. 1540, Washington, D.C., 1996, pp. 15-23.

96. Witczak, M. W., I. Hafez, H. Ayres, & K. Kaloush, “Comparative Study of MSHA Asphalt Mixtures Using Advanced Dynamic Material Characterization Tests” Maryland Department of Transportation, Maryland Port 532 Administration. Department of Civil Engineering, University of Maryland of College Park, MD, 1996.

97. Witczak, M. W., “A comparison of the Dynamic (Complex) Modulus Test (E*) and Indirect Diametral Test (MR) for AC Mixtures”, 1999.

98. Witczak, M. W., R. Bonaquist, H. Von Quintus, and K. Kaloush, “Specimen Geometry and Aggregate Size Effects in Uniaxial Compression and Constant Height Shear Test”, Journal of the Association of Asphalt Paving Technologists, Vol. 69, 2000, pp. 733-782.

99. Witczak, M. W., K. Kaloush, T. Pellinen and M. El-Basyouny, «Simple Performance Test for Superpave Mix Design», NCHRP Report 465, Washington, D.C., 2002.

100. Witczak, M. W., T. K. Pellinen and M. M. El-Basyouny, “Pursuit of the Simple Performance Test for Asphalt Concrete Fracture/Cracking”, Journal of the Association of Asphalt Paving Technologists, Vol. 71, 2002, pp. 767-778.

101. Witczak, M. W., “Laboratory Determination of Resilient Modulus for Flexible Pavement”, NCHRP Research Results Digest, No. 285. TRB, Washington, D.C., January 2004.

102. Yoder, E.J. and M.W. Witczak, “Principles of Pavement Design” Wiley, New York, 1975.

103. Zhang, W., A. Drescher, and D. E. Newcomb, “Viscoelastic Analysis of Diametral Compression on Asphalt Concrete”, Journal of Engineering Mechanics, Vol. 123, ASCE, 1997, pp. 596-603.

104. Zhang, Z., “Identification of Suitable Crack Growth Law for Asphalt Mixtures Using the Superpave Indirect Tensile Test (IDT)” Ph.D. Dissertation, University of Florida, Gainesville, FL, 2000.

105. Zhang, Z., R. Roque, and B. Birgisson, “Identification and Verification of a Suitable Crack Growth Law for Asphalt Mixtures” Journal of the Association of Asphalt Paving Technologists, Vol. 70, 2001, pp. 206-241.

183

BIOGRAPHICAL SKETCH

Yuan Xiao was born and raised in Hubei, China. He began his college education at Shanghai

JiaoTong University in China and received a Bachelor of Science degree in Mechanical

Engineering in 1999. He then became a graduate student at the Institute of Refrigeration and

Cryogenics in Shanghai JiaoTong University and received a Master’s degree in spring, 2002.

After his graduation from SJTU, Yuan Xiao enrolled in the Department of Mechanical

Engineering at Florida State University in fall, 2002. He received a Master of Science degree in

2004 and then joined the transportation materials group at the Department of Civil Engineering

in Florida State University. He worked as a graduate research assistant with his doctoral advisor,

Dr. Wei-Chou Virgil Ping, from January 2005.

Yuan Xiao was involved in research projects related to the experimental testing and

analytical modeling of flexible pavement materials and design. He plans to complete the Doctor

of Philosophy Degree in Civil Engineering at Florida State University in spring 2009.

Florida State University Librariesdiginole.lib.fsu.edu/islandora/object/fsu:168556/... · florida...

Documents

Transcript of Florida State University Librariesdiginole.lib.fsu.edu/islandora/object/fsu:168556/... · florida...