<%BANNER%>

Determining Gradation and Creep Effects in Mixtures Using the Complex Modulus Test


PAGE 1

DETERMINING GRADATION AND CREEP E FFECTS IN MIXTURES USING THE COMPLEX MODULUS TEST By ERKAN RUHI EKINGEN A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ENGINEERING UNIVERSITY OF FLORIDA 2004

PAGE 2

This thesis is dedicated to my father.

PAGE 3

iii ACKNOWLEDGMENTS It was a privilege to work with my advi sor, Dr. Bjorn Birgisson. I would like to thank him for his supervision and guidance. I also thank the other members of my committee. I thank Dr. Reynaldo Roque for his help and knowledge which kept me on track. I also thank to Dr. Frank Townse nd and Dr. M. C. McVay for their support throughout my graduate study. My sincere appreciation goes to Jaese ung Kim, George Loop, Linh Viet Pham and Daniel Darku. Their expertise in the field he lped my work go much faster and easier. I also want to thank the entire Geotech group for their friendship and support while I was at the University of Florida.

PAGE 4

iv TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................................................................................. iii LIST OF TABLES........................................................................................................... vii LIST OF FIGURES ........................................................................................................... x ABSTRACT..................................................................................................................... xv CHAPTER 1 INTRODUCTION........................................................................................................1 A Brief Introduction to D ynamic Modulus (|E*|).........................................................1 Objectives..................................................................................................................... 2 2 LITERATURE REVIEW.............................................................................................3 Background and History of Co mplex Modulus Testing...............................................3 Superpave Shear Tester................................................................................................4 Modulus Measurement in Visc oelastic Asphalt Mixtures............................................5 Master Curves and Shift Factors...................................................................................9 Sample Preparation.....................................................................................................10 Load Level..................................................................................................................11 Complex Modulus as a Design Parameter..................................................................14 Witczak Predictive Modulus Equation.......................................................................14 Complex Modulus as a Simple Performance Test......................................................15 Fatigue Cracking.........................................................................................................16 Rutting........................................................................................................................ 17 3 MATERIALS USED IN AXIAL COMPLEX MODULUS TESTING.....................18 Introduction.................................................................................................................18 Overview of Mixtures Used........................................................................................18 Asphalt Binders Used.................................................................................................18 Aggregates..................................................................................................................19 Fine Aggregate Angular ity (FAA) Mixtures..............................................................19 Determination of Fine A ggregate Batch Weights......................................................22 Limestone Gradation Study Mixture Gradations........................................................22 Granite Mixtures Used................................................................................................23 Superpave Field Monitori ng Mixture Gradations.......................................................25

PAGE 5

v Mixture Design...........................................................................................................28 4 AXIAL COMPRESSION DYNAMIC MODULUS: RESULTS AND DISCUSSION.............................................................................................................33 Introduction.................................................................................................................33 Data Variables............................................................................................................33 Raw Data Plots...........................................................................................................34 Data-Analysis Method................................................................................................38 Analysis of Test Data Results.....................................................................................39 Master Curve Construction.........................................................................................48 Typical Predicted Master Cu rves for Florida Mixtures..............................................50 Dynamic Modulus Calculated from Predictive Regression Equations.......................53 Binder Testing Results................................................................................................55 Comparison of Predicted and Measured Dynamic Modulus......................................57 Conclusions.................................................................................................................65 5 EVALUATION OF GRDATION EFFECTS.............................................................70 Introduction.................................................................................................................70 The Evaluation of the Effects of Aggr egate Gradations on Dynamic Modulus.........71 Correlation Study between Power Law Gradation Factors and Dynamic Modulus.................................................................................................................73 Category Analysis of Power Law Parameters............................................................75 Category Analysis of Power Law Parame ters for Coarse and Fine Graded Mixtures.................................................................................................................76 Summary and Conclusions.........................................................................................78 6 EVALUATION OF POTENTIAL CORELATION BETWEEN COMPLEX MODULUS PARAMETERS AND RUTTI NG RESISTANCE OF MIXTURES....80 Background.................................................................................................................80 Asphalt Pavement Analyzer Test Procedure and Test Results...................................80 Static Creep Test Results............................................................................................82 Evaluation of Dynamic Test results for HMA Rutting Resistance.............................85 Evaluation of Static Creep Parameters.......................................................................89 Effects of Binder Type on Relationshi p between Dynamic Modulus and Rutting Potential of Mixtures..............................................................................................93 Summary and Conclusions.........................................................................................94 APPENDIX A ELASTICITY MODULUS AND PHASE ANGLE SUMMARY FOR SAMPLE GRADATIONS..........................................................................................................96 B PREDICTED DYNAMIC MODULUS VALUES VS.MEASURED DYNAMIC VALUES...................................................................................................................103

PAGE 6

vi C MEASURED DYNAMIC MODULUS V.S. PREDICTED VALUES FOR DIFFERENT FREQUENCIES.................................................................................108 D MEASURED DYNAMIC MODULUS VALUES V.S. PREDICTED VALUES AT DIFFERENT TEMPERATURES......................................................................121 E COMPARISON OF MEASURED DYNAMIC MODULUS TEST RESULTS VS. PREDICTED RESULTS.................................................................132 F DYNAMIC CREEP COMPLIANCE TEST RESULTS..........................................137 G GRADATION EFFECT ON COMPLEX MODULUS PREDICTION...................152 H VISCOSITY EFFECTS ON COMPLEX MODULUS PREDICTION...................161 I DYNAMIC CREEP TEST PARAMETERS............................................................166 J STATIC CREEP TEST PARAMETERS.................................................................169 K SHORT TERM CREEP TEST PARAMETERS......................................................172 LIST OF REFERENCES.................................................................................................175 BIOGRAPHICAL SKETCH...........................................................................................177

PAGE 7

vii LIST OF TABLES Table page 3-1 Coarse gradations for fine aggregate effects............................................................20 3-2 Fine gradations for fine aggregate effects................................................................21 3-3 Physical properties of fine aggregates......................................................................21 3-4 Gradations for White Rock coarse graded mixtures................................................23 3-5 Gradations for White Ro ck fine graded mixtures....................................................23 3-6 Granite based mixture gradations.............................................................................25 3-7 Gradation of field projects........................................................................................26 3-8 Superpave gyratory compaction effort.....................................................................29 3-9 Volumetric properties of coarse graded mixtures....................................................30 3-10 Volumetric Properties of Fine Graded Mixtures......................................................30 3-11 Volumetric properties of coarse graded mixtures....................................................31 3-12 Volumetric properties of fi ne graded Whiterock mixtures......................................31 3-13 Volumetric propertie s of Granite mixtures..............................................................32 3-14 Volumetric propertie s of field projects....................................................................32 4-1 Sample preparation data...........................................................................................35 4-2 Average dynamic modulus testing results................................................................39 4-3 Average phase angle testing results.........................................................................41 4-4 Brookfield rotational viscometer re sults on unaged and RTFO aged binder...........55 4-5 Dynamic shear rheometer results on unaged and RTFO aged binder......................56

PAGE 8

viii 4-6 Viscosity-temperature regressi on coefficients for unaged and RTFO aged PG 67-22 asphalt..................................................................................57 4-7 Typical viscosity-temperature re gression coefficients for AC-30 at different hardening states.....................................................................................57 4-8 Calculated viscosity at four complex modulus test temperatures............................57 4-9 Predicted dynamic moduli for Ge orgia granite mixtures using the Mix/Laydown condition...........................................................................................59 4-10 Predicted dynamic moduli for Whitero ck mixtures using the Mix/Laydown condition...................................................................................................................59 4-11 Predicted dynamic moduli for FAA Mixtures using the Mix/Laydown condition...................................................................................................................60 4-12 Predicted dynamic moduli for Supe rpave project mixtures using the Mix/Laydown condition...........................................................................................60 4-13 Predicted dynamic moduli for Georgia granite mixtures using RTFO aged binder results from the Brookfield rotational viscometer test..................................60 4-14 Predicted dynamic modulus for Whitero ck mixtures Using RTFO aged binder results from the Brookfield rotational viscometer test.............................................61 4-15 Predicted dynamic moduli for FAA mixtur es using RTFO aged binder results from the Brookfield rotational viscometer test........................................................61 4-16 Predicted dynamic moduli for Superpave mixtures using RTFO aged binder results from the Brookfield rotational viscometer test.............................................62 4-17 Predicted dynamic moduli for Georgia granite mixtures using RTFO aged binder results from the dynamic shear rheometer Test............................................62 4-18 Predicted dynamic moduli for Whiterock mixtures using RTFO aged binder results from the dynamic shear rheometer test.........................................................63 4-19 Predicted dynamic moduli for FAA mixt ures using RTFO aged binder results from the dynamic shear rheometer test....................................................................63 4-20 Predicted dynamic moduli for Superpave mixtures using RTFO aged binder results from the dynamic shear rheometer test.........................................................64 5-2 Results of correlation study between power law parameters and dynamic modulus at 40C and 1 Hz frequency.......................................................................74 5-3 Partial correlation analysis for nca and |E40*| when controlling for nfa.....................75

PAGE 9

i x 5-4 Mean and standard deviation of |E40*| for the four di fferent categories..................76 5-5 One-Way analysis of variance of |E40*|....................................................................76 5-6 Post-Hoc analysis for homogeneous subsets of hypothesized categories................76 5-7 Mixtures in cour se-graded category.........................................................................77 5-8 Mixtures in fine-graded category.............................................................................77 5-9 Zero-Order correlation analysis for nca, nfa, and |E40*| for course graded mixtures....................................................................................................................78 5-10 Zero-Order correlation analysis for nca, nfa, and |E40*| for fine graded .....................78 6-1 Dynamic modulus |E*|, phase angle and asphalt pavement analyzer rut depth measurements from mi xture testing at 40 C.................................................82 6-2 Average static creep testing resu lts for test temperature of 40C............................84 I-1 Dynamic creep parameter summary.......................................................................167 J-1 Static creep pa rameter summary............................................................................170 K-1 Short term creep parameter summary ....................................................................173

PAGE 10

x LIST OF FIGURES Figure page 1-1 The testing components of the complex modulus......................................................7 2-2 Proportionality of Viscoelastic Materials.................................................................12 2-3 Superposition of Viscoelastic Materials...................................................................13 3-1 Gradation curves for C1 and F1...............................................................................20 3-2 Coarse gradations for gradation effects studies........................................................24 3-3 Fine gradations for gradation effects studies............................................................24 3-4 Coarse graded Granite aggregate gradations............................................................25 3-5 Fine graded Granite aggregate gradations................................................................26 3-6 Gradations for Superpave proj ect mixtures number 2, 3, and 7...............................27 3-7 Gradations for field projects 1 and 5........................................................................27 3-8 Servopac superpave gyratory compactor.................................................................29 4-1 Typical plot of force and LVDT disp lacement versus time at low temperature for mixture WRC1....................................................................................................37 4-2 Typical plot of force and LVDT disp lacement versus time at high temperature for mixture WRC1....................................................................................................37 4-3 Typical plot of vertical stress ve rsus strain at low temperature for mixture WRC1.........................................................................................................38 4-4 Typical plot of vertical stress ve rsus strain at high temperature for mixture WRC1.........................................................................................................38 4-5 Dynamic modulus |E *| of GAF1 at 10 C.................................................................44 4-6 Phase angle of GAF1 mixture at 10 C.....................................................................44 4-7 Dynamic modulus |E *| of GAF1 at 25 C.................................................................45

PAGE 11

xi 4-8 Phase angle of GAF1 mixture at 25 C.....................................................................45 4-9 Dynamic modulus |E *| of GAF1 at 40 C.................................................................45 4-10 Phase angle of GAF1 mixture at 40 C.....................................................................46 4-11 Dynamic modulus |E *| of GAC1 at 10 C................................................................46 4-12 Phase angle of GAC1 mixture at 10 C.....................................................................46 4-13 Dynamic modulus |E *| of GAC1 at 25 C................................................................47 4-14 Phase angle of GAC1 mixture at 25 C.....................................................................47 4-15 Dynamic modulus |E *| of GAC1 at 40 C................................................................47 4-16 Phase angle of GAC1 mixture at 40 C.....................................................................48 4-17 Parameters used in si gmoidal fitting function..........................................................50 4-18 Shift function for coarse-graded GAC3 mixture......................................................51 4-19 Master curve for coarse-graded GAC3 mixture.......................................................52 4-20 Shift function for fine-graded GAF1 mixture..........................................................52 4-21 Master curve for fi ne-graded GAF1 mixture...........................................................52 4-22 Shift function for fine-graded GAF1 mixture..........................................................53 4-23 Master curve for coarse-graded GAC1 mixture.......................................................53 4-24 Measured values versus predicted values of |E*| on a log-log scale........................66 4-25 Measured values versus predicted values of |E*| on a log-log scale........................66 4-26 Measured values versus predicted values of |E*| on a log-log scale........................66 4-27 Measured vs. predicted dynamic modu lus values for Whiterock limestone mixtures: at testing frequency of 4 Hz.....................................................................67 4-28 Measured vs. predicted dynamic mo dulus for fine aggregate angularity mixtures Superpave project mixtures Granite mixtures and Whitrock mixtures at a Test Temperature of 40 C and a testing frequency of 4 Hz..............68 6-1 Qualitative diagram of th e stress and total deformation during the creep test........83 6-2 Dynamic modulus at testing frequencie s of 1 Hz and 4 Hz versus APA rut depth measurements.................................................................................................86

PAGE 12

xii 6-3 Dynamic modulus at testing frequencie s of 1 Hz and 4 Hz versus APA rut depth measurements for coarse and fine-graded mixtures......................................86 6-4 Dynamic modulus, |E*| versus test tr ack rutting for the 2000 NCAT test track sections.....................................................................................................................87 6-5 Phase angle at a testing frequenc y of 1 Hz versus APA rut depth measurements...........................................................................................................88 6-6 Plot of E*/Sin at 40oC and 1 Hz. versus the APA rut depths for all mixtures.......88 6-7 |E*|/sin versus Test Track Rutting for the 2000 NCAT test track sections............89 6-8 Plot of |E*|sin at 40oC and 1 Hz versus APA rut depth..........................................90 6-9 Relationship between dynamic modulus at 1 Hz frequency and static creep compliance after 1000 seconds................................................................................91 6-10 Relationship between dynamic modulu s at 1 Hz frequency and the power law creep compliance parameter D1.........................................................................91 6-11 Relationship between dynamic modulu s at 1 Hz frequency and power law m-value pa rameter....................................................................................................92 6-12 Relationship between phase angle at 1 Hz frequency and static creep compliance after 1000 seconds....................................................................................................92 6-13 Relationship between phase angle at 1 Hz frequency and the power law creep compliance parameter D1.........................................................................................93 6-14 Relationship between phase angle at 1 Hz frequency and power law m-value parameter..................................................................................................................93 A-1 |E*| vs. for coarse Whiterock gr adations at 10, 30 and 40 C..............................97 A-2 vs. for coarse Whiterock gradations at 10, 30 and 40 C..................................98 A-3 |E*| vs. for fine Whiterock gradations at 10, 30 and 40 C..................................99 A-4 vs. for fine Whiterock gradations at 10, 30 and 40 C....................................101 B-1 Measured test results versus pred icted dynamic modulus values for fine gradation Whiterock mixtures at 1 Hertz...............................................................104 B-2 Measured test results versus pred icted dynamic modulus values for fine gradation Whiterock mixtures at 4 Hertz...............................................................105

PAGE 13

xiii B-3 Measured test results versus pred icted dynamic modulus values for fine gradation Whiterock mixtures at 10 Hertz.............................................................106 B-4 Measured test results versus pred icted dynamic modulus values for fine gradation Whiterock mixtures at 16 Hertz.............................................................107 C-1 Measured test results versus pred icted dynamic modulus values for fine gradation Whiterock mixtures................................................................................109 C-2 Measured test results versus pred icted dynamic modulus values for Coarse gradation Whiterock mixtures................................................................................111 C-3 Measured test results versus pred icted dynamic modulus values for coarse gradation Granite mixtures.....................................................................................113 C-4 Measured test results versus pred icted dynamic modulus values for fine gradation Granite mixtures.....................................................................................115 C-5 Measured test results versus pred icted dynamic modulus values for fine gradation FAA mixtures.........................................................................................117 C-6 Measured test results versus pred icted dynamic modulus values for fine gradation FAA mixtures.........................................................................................119 D-1 Measured test results versus pred icted dynamic modulus values for fine gradation Whiterock mixtures................................................................................122 D-2 Measured test results versus pred icted dynamic modulus values for coarse gradation Whiterock mixtures................................................................................124 D-3 Measured test results versus pred icted dynamic modulus values for coarse gradation Granite mixtures.....................................................................................126 D-4 Measured test results versus pred icted dynamic modulus values for fine gradation Granite mixtures.....................................................................................128 D-5 Measured test results versus pred icted dynamic modulus values for fine gradation FAA mixtures.....................................................................................130 D-6 Measured test results versus pred icted dynamic modulus values for coarse gradation FAA mixtures.....................................................................................131 E-1 Comparison of measured dynamic m odulus test results vs. Witzacks-2002 predicted results at 10 C degrees...........................................................................133 E-2 Comparison of measured dynamic m odulus test results vs. Witzacks-2002 predicted results at 40 C degrees...........................................................................134

PAGE 14

xiv E-3 Comparison of measured dynamic m odulus test results vs. Witzacks-2002 predicted results at 10 C degrees, on log scale......................................................135 F-1 Dynamic modulus values for fine graded Whiterock mixtures..............................138 F-2 D0 values for fine graded Whiterock mixtures.......................................................140 F-3 D1 values for fine graded Whiterock mixtures.......................................................142 F-4 Dynamic modulus values for fine graded Project mixtures...................................144 F-5 D0 values for fine graded Project mixtures............................................................146 F-6 D0 values for fine graded Whiterock mixtures.......................................................148 F-7 D0 values for fine graded FAA mixtures............................................................150 G-1 Gradation line and power regression lines of fine gradation Whiterock samples...................................................................................................................153 G-2 Gradation line and power regression lines of coarse gradation Whiterock samples...................................................................................................................155 G-5 Gradation line and power regression lin es of fine gradati on Project samples.......157 H-1 Complex modulus values predicte d by using Witczaks 2002 Predictive equation by using different viscosity conditions....................................................162

PAGE 15

xv Abstract of Thesis Presen ted to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Engineering DETERMINING GRADATION AND CREEP E FFECTS IN MIXTURES USING THE COMPLEX MODULUS TEST By Erkan Ruhi Ekingen August 2004 Chair: Bjorn Birgisson Cochair: Reynaldo Roque Major Department: Civil and Coastal Engineering The 2002 revision of the AASHTO Guide to the Design of Pavement Structures uses the dynamic modulus test (|E*|) to ch aracterize mixes used on interstate highways and most other high-volume highways that require superior load resistance. An understanding of its mechanics and procedur es is fundamental for understanding how the test can be used. The purpose of this study was to establish a correlation between Complex Modulus and a number of issues such as the Vi scosity, Gradation, and Rutting Resistance

PAGE 16

1 CHAPTER 1 INTRODUCTION A Brief Introduction to Dynamic Modulus (|E*|) Dynamic Modulus1 (|E*|) has been known to some researchers since the 1960s. But the use of |E*| by departments of transpor tation has not been widespread. However, current efforts in pavement research (r evising the AASHTO Guide to the Design of Pavement Structures and modeling for SuperPaveTM) rely on the use of |E*|. The 2002 revision of the AASHTO Guide to the Design of Pavement Structures uses the dynamic modulus test (|E*|) to characterize mixes used on interstate highways and most other high-volume highways that requ ire superior load resistan ce. The guide is based on mechanistic principle and requires a modulus to compute stresses and strains in hot-mix asphalt (HMA) pavements. Briefly, |E*| is the absolute value of the modulus of a viscoelastic material. The dynamic (complex) modulus of a viscoelas tic test is a response developed under sinusoidal loading conditions. It is a true complex number as it contains both a real and an imaginary component of the modulus and is normally identifie d by |E*| (or G*).A Brief Introduction to Gradation and Packing 1 In viscoelastic theory, the absolute value of the complex modulus |E*|, by definition, is the Dynamic Modulus. In the general litera ture, however, the term, “Dynamic Modulus” is often used to denote any t ype of modulus that has been determined under “non-static” load conditions.

PAGE 17

2 The packing of particles into a confin ed volume has been studied for over 300 years. Sir Isaac Newton—among the first to study this phenomenon—was not able to prove the existence of a maxi mum density. In more modern times, Nijboer, Goode and Lufsey (AAPT 1961), and Huber and Shuler (ASTM 1991) have added to our knowledge regarding the effect of gradation on the packing of aggregate particles. In hot mix asphalt design, aggregate type and gradation are considered routinely. Mix designers learn by experience the combin ation of aggregates that will provide adequate voids in the mineral aggregate. Adequa te rules or laws that govern the effect of gradation on aggregate packing ar e not available to mix designers. Objectives The objectives of th is study include: Evaluating the Predictive equation by Witczak et al. (2002) for use in Florida materials used in HMA designs Evaluating the effects of gradation a nd aggregate type on dynamic modulus Evaluating how well creep properties obtai ned from short-term dynamic modulus measurements compare to static-creep testing results. To achieve these objectives, complex-modulus testing and static-creep testing were performed on 25 mixtures of varying gradation and aggregate types.

PAGE 18

3 CHAPTER 2 LITERATURE REVIEW Background and History of Complex Modulus Testing Complex modulus testing for asphalt mixtures is not a new concept. Papazian (1962) was one of the first to delineate visc oelastic characterizati on of asphalt mixtures using the triaxial cyclic complex modulus test He concluded that viscoelastic concepts could be applied to asphalt pavement design and performance. Forty years after these experiments, the concept of complex modulus testing is still being used to develop mix design criteria, and to ev aluate performance of material in pavement. Work continued in the next decade that considered compression, tension, and tension-compression loading. A number of studies indicated differences in dynamic modulus testing obtained from different load ing conditions. The differences especially affect the phase angle, and tend to become more significant at higher temperatures. Witczak and Root (1974) indicate that the tension-compression test may be more representative of field loading conditions. Khanal and Mamlouk (1995) affirmed this assertion. They performed complex modulus tests under five different modes of loading and obtained different results, es pecially at high temperatures Bonneaure et al. (1977) determined the complex modulus from a bending test. Deformation was measured, and the complex modulus was calculated from the results. In the 1980s and early 1990s, the Internat ional Union of Testing and Research Laboratories for Materials and Structures (RILEM) Technical Committee on Bitumen and Asphalt Testing organized an internati onal testing program ( 1996). The goal of the

PAGE 19

4 program was to promote and develop mi x design methodologies (and associated significant measuring methods) for asphalt pa vements. Complex modulus tests were performed by 15 participating laboratories, in countries throughout Europe. Results showed that bending tests and indirect tens ion tests were in reasonable agreement under certain conditions. The laboratories were ab le to reproduce the pha se angle much better with complex modulus than dynamic modulus. Stroup-Gardiner (1997), Drescher, Newcomb, and Zhang (1997), and Zhang, Drescher and Newcomb (1997) performed comple x modulus tests on both tall cylindrical specimens and indirect tensile specimens. Results were mixed, showing that tests on the same material with the two different setups sometimes yielded different results for the dynamic modulus and phase angle. The phase an gle was especially vari able in both test setups. The most comprehensive research effort started in the mid-1990s as part of the NCHRP Project 9-19 (Superpave Support and Performance Models Management) and NCHRP Project 9-29 (Simple Performance Te ster for Superpave Mix Design). Their research proposed new guidelines for the pr oper specimen geometry and size, specimen preparation, testing procedure, loading pattern, and empirical modeling. Some of their key findings were reported by Witczak (2000) Kaloush (2002), and Pellinen (2002). Superpave Shear Tester As part of the SHRP program, the comple x shear modulus (G*) was introduced for asphalt binder specifications (AASHTO TP 5, 1998), allowing bette r characterization of the rheological behavior of asphalt binders at different temperatures. Similar efforts were undertaken on mixtures as a part of SHRP, where testing methods for the complex modulus of mixtures were evaluated by usi ng a torsional hollow cylinder test. Their

PAGE 20

5 researches lead to the development of the SHRP Constant Height Simple Shear Test (CHSST). The complex shear modulus (G*) was the main parameter obtained from the CHSST test. However, a number of issues remain regarding the applicability of the CHSST test. In particular, the adherence to constant height requirements remains controversial at best, resulting in highly variable stress stat es during testing. Results from the CHSST test have been shown to relate to rutting performance. However, the data from the CHSST tests are highly variable. Seve ral attempts have been made to lower the variation, including reducing th e generally accepted specimen air void range of 0.5 percent to a tighter tolerance, increasing th e number of specimens, and using additional LVDTs. In the following, an overview of the various stiffness measurements used in flexible pavement characterization will be provided, followed by a summary of the state of art complex modulus testing of mixtures. Modulus Measurement in Viscoelastic Asphalt Mixtures The resilient modulus (Mr) has long been considered th e defining characteristic for HMA layers. It has been used since 1993 in the AASHTO Desi gn Guide (AASHTO, 1993). The laboratory procedure for the Mr test is described in AASHTO T 307-99. The test is well defined as a repeated 0.1 second haversine lo ad followed by a 0.9 second rest period, repeated at 1 Hz intervals. Due to the long history of using Mr in pavement design, many empirical relationships have been devel oped throughout the years relating Mr to other tests like the California Bearing Ratio (CBR) and the Ma rshall stability test (AASHTO, 1993). However, the ability of the Mr to account for vehicle speed effects has lead to a push to

PAGE 21

6 develop methods that account fully for the va riation of stiffness in HMA pavements with vehicle speeds. The concept behind the complex modulus test is to account not only for the instantaneous elastic response, without delaye d elastic effects, but also the accumulation of cyclic creep and delayed elastic effects with the number of cycles. Hence, the fundamental difference between the complex mo dulus test and the resilient modulus test is that the complex modulus test does not allow time for any delayed elastic rebound during the test. The dynamic modulus (|E*|) relates the cyclic strain to cyclic stress in a sinusoidal load test. The dynamic modulus test procedure outlined in ASTM D 3497 uses a standard triaxial cell to apply stress or strain amplitudes to a material at 16 Hz, 4 Hz, and 1 Hz. It also recommends that the test be repeated at 5C, 25C, and 40C (ASTM D 3497). The dynamic modulus is calculated using Equation 2-1 (Yoder & Witczak, 1975). 0 0* E (Eq. 2-1) Where 0 is the stress amplitude, 0 is the strain amplitude. This parameter includes the rate dependent stiffness e ffects in the mixture. However, it does not provide insight into the vi scous components of the strain response. The dynamic modulus test can be expanded on to find the complex modulus (E*). The complex modulus is composed of a storag e modulus (E’) that describes the elastic component and a loss modulus (E’’) that desc ribes the viscous component. The storage and the loss moduli can be dete rmined by the measurement of the lag in the response

PAGE 22

7 TimeStress/Strain 00 1-1. The testing components of the complex modulus between the applied stress and the measured st rains. This lag, referred to as the phase angle ( ), shown in Figure 2-1. Equation 2-2 describes the relationship between the various components and E*: tan1E E (Eq. 2-2a) ) sin( E E (Eq. 2-2b) ) cos( E E (Eq. 2-2c) The phase angle is typically determined by measuring the time difference between the peak stress and the peak strain This time can be converted to using Equation 2-3. 360 f tlag (Eq. 2-3) Where f is the frequency of the dynamic load (in Hz), tlag is the time difference betw een the signals (in seconds). A phase angle of zero indicates a purely elastic material and a of 90 indicates a purely viscous material.

PAGE 23

8 For linear elastic materials, only two propert ies are required to describe the stressstrain behavior under any loading condition. The Young’s modulus is typically used to describe changes due to the normal stresse s and the shear modulus (G) describes the change in the material due to shear stresses. Similarly, the inclusion of Poisson effects is captured by the Poisson’s ratio ( ). In viscoelastic material s, G* and E* are the most commonly used parameters. The magnitude of G* is calculated using the shear stress amplitude ( 0) and the shear strain amplitude ( 0) in Equation 2-4 by Witczak et al. (1999). 0 0* G (Eq. 2.4) Similar to the complex modulus, G* has an elastic component (G’) and a viscous component (G’’) by Witczak et al. (1999). These components are related through the phase angle ( ) as seen in Equation 2-5. tan1G G (Eq. 2-5a) ) sin( G G (Eq. 2-5b) ) cos( G G (Eq. 2-5c) To calculate both the E* and the G* coeffici ents, it must be possible to measure not only the axial compressive stresses and strains, but also the shear stresses and strains. Harvey et al. (2001) concluded that G* can be related to E* using Equation 2-6. 1 2 *E G (Eq. 2-6) By directly measuring changes in the he ight and radius of the asphalt sample, Poisson’s ratio can be calculated This is done by calculating as the ratio of lateral

PAGE 24

9 expansion to the axial compre ssion. Equation 2-6 assumes th at the Poisson’s ratio is constant and some testing has shown that the Poisson’s ratio for HMA is frequency dependent. Master Curves and Shift Factors The master curve of an asphalt mixtur e allows comparisons to be made over extended ranges of frequencies and temperatures. Master cu rves are generated using the time-temperature superposition principle. This principle allows for test data collected at different temperatures and frequencies to be shifted horiz ontally relative to a reference temperature or frequency, th ereby aligning the various curv es to form a single master curve. The procedure assumes that the aspha lt mixture is a thermo-rheologically simple material, and that the time-temperature s uperposition principle is applicable. The shift factor, a(T), defines the shif t at a given temperature. The actual frequency is divided by this shift f actor to obtain a reduced frequency, fr, for the master curve, ) (T a f fr or log(fr) = log(f) log[a(T)] (Eq. 2-7) The master curve for a material can be c onstructed using an ar bitrarily selected reference temperature, TR, to which all data are shifted. At the reference temperature, the shift factor a(T) = 1. Several different mode ls have been used to obtain shift factors for viscoelastic materials. The most comm on model for obtaining shift factors is the Williams-Landel-Ferry (WLF) equation (Williams, Landel, Ferry, 1955). When experimental data are available, a master curve can be constructed for the mixture. The maser curve can be represen ted by a nonlinear sigmoidal function of the Equation 2-8.

PAGE 25

10 ) log(1 ) log(rfe E (Eq. 2-8) Where log(|E*|) = log of dynamic modulus, = minimum modulus value, fr = reduced frequency, = span of modulus value, = shape parameters. Note that in this equation is not related to th e phase angle – it is just the notation chosen by Pellinen and Witzcak (2002) for th e minimum modulus value. The sigmoidal function of the dynamic modulus master curv e can be justified by physical observations of the mixture behavior. The upper part of the function approaches asymptotically the mixture’s maximum stiffness, which depends on the binder stiffness at cold temperatures. At high temperatures, the compressive loading causes aggregate interlock stiffness to be an indicator of mixture stiffness. The si gmoidal function shown in Equation 2-8 captures the physical behavior of as phalt mixtures observed in complex modulus testing throughout the entire temperature range (Pellinen and Witzcak, 2002). Sample Preparation Currently, there is much discussion about th e shape and size of specimen to be used in complex modulus testing. In NCHRP Project 9-19, Witzcak and his colleagues investigated the proper size a nd geometry of test specimens (Witzcak et al. 2000). Based on numerous complex modulus test results they recommended using 100-mm diameter cored specimens from a 150-mm diameter gyr atory compacted specimen, with a final saw cut height of 150-mm. This recomm endation came from a study (Chehab et al., 2000) that considered the vari ation in air voids within sp ecimens compacted using the Superpave Gyratory Compactor (SGC). The studies showed that specimens compacted

PAGE 26

11 using the SGC tend to have non-uniform air void distribution both along their diameter and along height. SGC-compacted specimens ha ve higher air void cont ent at the top and bottom edges, and in sections adjacent to the mold walls, as compared to the interior portion of the specimens. Finally, fully lubric ated end plates were found to minimize end restraint on the specimen. Increasing the num ber of gages used to measure axial strain decreases the number of test specimens necessary. Load Level Since the interpretation of the complex modulus is based on the assumption of linear viscoelasticity of the mixture, it is ne cessary to maintain a fairly low strain level during testing to avoid any nonlinear effects. Maintaining a stress level that results in a strain response that is close to linear is cr itical to achieve a test that is reproducible. The concept of material linearity is base d upon two principles. The first principle, proportionality, is described with Equation 2-9. t C t C (2-9) It implies that if a stress is increased by any factor then the strain will also increase by the same factor. This allows the shape of the stress/strain relationship to be more easily mapped out across the linear range. The principle of superposition is the othe r condition that describes linearity. Equation 2-10 describes this concept. 1 2 1 1 2 1t t t t t t (Eq. 2-10) This implies that if it is known how the material will behave under a single loading condition that it will be known how it would behave under multiple loads. Figure 2-2 and 2-3 show graphically the concept pr oportionality and superposition. The

PAGE 27

12 combination of these principles allows the ma terial behavior to be predicted with fewer parameters. Figure 2-2. Proportionality of Viscoelastic Materials HMA has been found to behave linearly, but only for specific temperature and strain regions. Mehta and Christense n (1999) describe HMA as linear for low temperatures (–20C to –10C) and shear stra ins under 200 microstrain. For intermediate temperatures (4C to 20C), shear strains s hould be less then 50 microstrain, to stay within the viscoelastic limits. However, it should be noted that the determination of

PAGE 28

13 linearity might also be affected by the lo ading mechanism (i.e., compression, tension, torsion). Figure 2-3. Superposition of Viscoelastic Materials For dynamic modulus measurements usi ng uniaxial compression testing, the ASTM D 3497 recommends using an axial stre ss amplitude of 241.3 kPa (35 psi) at all temperatures as long as the total deformati on is less then 2500. Daniel and Kim (1998) showed successful triaxial compression testing results with stress levels under 96.5 kPa for 15 C testing. Strain amplitudes of 75 to 200 mi crostrains have also been suggested to maintain material linearity during triaxial compression testing (Witczak et al. 1999).

PAGE 29

14Complex Modulus as a Design Parameter The 2002 AASHTO Guide for the Design of Pavement Structures recommends the complex modulus as a design input parame ter for the mechanistic-empirical design procedure (NCHRP 1-37A 2002 Design Guide Dr aft, 2002). Level 1 Analysis requires actual dynamic modulus test data to develop master curves and sh ift factor based on Equations (2-7) and (2-8). This testing is performed on replicate samples at five temperatures and four rates of loading per temp erature. Binder testing must be performed at this level to shift the data into smooth master curves. Level 2 Analysis constructs a master curve using actual asphalt binder te st data based on the relationship between binder viscosity and temperature. Level 3 An alysis requires no laboratory test data. Instead, the Witczak modulus equation (N CHRP 1-37A – 2002 Design Guide Draft, 2002) is used with typical temperature-viscos ity relationships estab lished for all binder grades. Witczak Predictive Modulus Equation The complex modulus test is relatively difficult and expensive to perform. Therefore, numerous attempts have been made to develop regression equations to calculate the dynamic modulus from conventio nal volumetric mixture properties. For example, a predictive regression equation is proposed as a part of the 2002 Design Guide (Witczak et al., 2002) to calculate the dyna mic modulus, |E*|, based on the volumetric properties of any given mixture. The pred ictive equation developed by Witczak et al. (2002) is one of the most comprehensive mixture dynamic modulus models available today (Equation 2-11).

PAGE 30

15 )). log( 39353 0 ) log( 313351 0 603313 0 ( 4 / 3 2 8 / 3 8 / 3 4 4 2 200 2001 ) ( 005470 0 ) ( 00017 0 ) ( 003958 0 ) ( 0021 0 871977 3 ) ( 802208 0 ) ( 058097 0 ) ( 002841 0 ) ( 001767 0 ) ( 029232 0 249937 1 log f a beff beff ae p p p p V V V V p p p E(Eq. 2-11) Where |E*| = dynamic modulus, in 105 psi; bitumen viscosity, in 06 Poise; f = loading frequency, in Hz; Va = percent air void content, by volume; Vbeff = effective bitumen content, percent by volume; P3/4 = percent weight retained on 19-mm sieve, by total aggregate weight; P3/8 = percent weight retained on 9.5-mm sieve, by total aggregate weight; P4 = percent weight retained on 4.75-mm sieve, by total aggregate weight; P200 = percent weight passing 0.75-mm si eve, by total aggregate weight; The above dynamic modulus predictive equa tion has the capability to predict the dynamic modulus of dense-graded HMA mixtures over a range of temperatures, rates of loading, and aging conditions from inform ation that is readily available from conventional binder tests and the volumetric properties of the HMA mixture. This predictive equation is based on more than 2,800 different HM A mixtures tested in the laboratories of the Asphalt Institute, th e University of Maryland, and FHWA. Complex Modulus as a Simple Performance Test The goal of NCHRP Project 9-19 was to de velop a Simple Performance Test (SPT) for asphalt mixtures. Various te sting configurations were ev aluated from several of the most promising test methods. The potential SPT methods can be categorized as stiffnessrelated tests, deformability tests, and fracture tests. The stiffness parameters were obtained from compressive complex modulus, SHRP Simple Shear Tester (SST), and ultrasonic wave propagation. Of these thre e candidates, the complex modulus appeared to be the most promising for relating material properties to rutti ng and fatigue cracking observed in the field (Pellinen and Witzcak, 2002).

PAGE 31

16Fatigue Cracking Witczak et al. (2002) performed numerous complex modulus tests to perfect the recommendations for fatigue and cracking in asphalt mixtures. The results led to the development of a fatigue distress model in wh ich the number of repetitions to failure, Nf, is a function of the hor izontal tensile strain, t, which represents the largest of the transverse and longitudinal horizontal strain, and dynamic modulus of the mix, |E*|: 4 1 5 11 1 E FK Nt f (Eq. 2-12) The adjustment factor, F, that indicates the stress or strain controlled fatigue behavior in the pavement st ructure, is a function of the dynamic modulus and pavement thickness, hac: 408 5 354 1 4 0 *1 1 13909 1 ache E F (Eq. 2-13) A volumetric adjustment factor, K1 corrects the number of repetitions to failure by taking into account the binder and mix properties. In the equation 2-14, PI is the binder penetration index and Vb is the volume of binder in the mix: 5 10167 0 00673 0 00126 0 0252 0 b bV V PI PI K (Eq. 2-14) Equation (2-12) can be re duced to the following equation, where the constants n and kn can be assigned to nationally ca librated fatigue model constants: 3 3 2 2* 1 11 1k k t f ff fE k N (Eq. 2-15)

PAGE 32

17 Finally, it is expected that each state agency will have to deve lop local calibration factors for Equation 2-15. Rutting The complex modulus test also showed good correlation to permanent deformation of asphalt mixtures. Witczak et al. (2002) pe rformed research on asphalt mixtures similar to the SPT for fatigue cracking. Cylindrical specimens were tested at five temperatures and six frequencies, as well as different level of confini ng pressure. They come to preliminary findings that warranted a closer look at the dynamic m odulus test for rutting susceptibility. Pellinen and Witczak (2002) recommended using dynamic modulus obtained in unconfined compression at 54.4 C and a frequency of 5 Hz. The stress levels must remain small to keep the sample in the linear viscoelastic region.

PAGE 33

18 CHAPTER 3 MATERIALS USED IN AXIAL COMPLEX MODULUS TESTING Introduction This chapter provides information on the materials used in the testing of the axial complex modulus. The physical properties of ma terials used are discussed, such as their aggregate gradation, aggregate physical pr operties, mixture design procedure, and material preparation. Overview of Mixtures Used. Four distinctive group of mixture were used for the purpose of this research. Eight mixtures of varying gradations with oolitic limestone (Whiterock) from South Florida, entitled “Limestone Grad ation Study Mixtures” (C and F). Six mixtures of varying gradations with Georgia granite (GA185), entitled “Granite Gradation Study Mixtures” (GAC and GAF) Five field mixtures of varying gradati ons and aggregate types from Superpave monitoring test sites in Florida, entitled “Superpave Field Monitoring Mixtures” (P). Eight mixtures (entitled “Fine Aggregate A ngularity (FAA) Mixtures ”) with different fine aggregates (defined as material passi ng the no. 4 Sieve) and the coarse portion of the aggregates consisting of oolitic limest one (Whiterock) from South Florida, Asphalt Binders Used The grade of the asphalt cement used in mixt ures is one factor that can have an effect on the amount of rutting that occurs in the mix. All other things being equal, the stiffer the asphalt cement, the less the rutting that is expected in the mix under a given weight and volume of truck. In this rese arch, only one type of unmodified asphalt cement, AC-30 (PG67-22), which is commonly us ed in Florida was used for all mixtures

PAGE 34

19 tested, except for the modified HVS mixtur e, in which an SBS modified binder (PG 7622) was used. Aggregates This section describes the type of aggregates, aggregate gradations and combination of various aggr egates in this research. Fine Aggregate Angularity (FAA) Mixtures The first part of the research was perform ed using gradations of coarse and fine Whiterock limestone mixtures (C1 and F1) provided by FDOT for use as the reference mixtures. The nominal maximum aggregate size for these mixtures is 12.5 mm (1/2-in). These Superpave mixtures were selected because they are commonly used FDOT gradations and they are know n to perform well in the field. Figure 3-1 shows the gradation curves for the C1 and F1 mixtures. The fine aggregate portions of these mixt ures were volumetrically replaced by four other fine aggregate types (passing the No. 4 Si eve) to obtain five fine graded and five coarse graded mixtures. All materials were washed in accordance with ASTM C-117 and a washed sieve analyses were performed accord ing to ASTM C-136. The fine aggregates used were selected to be of varying angular ity, texture, toughness, and historical rutting performance. The designations for the fine aggregates used are as follows. Limestone Whiterock (baseline aggregate) Cabbage Grove (FL) Calera (AL) Granite Ruby (GA) Gravel Chattahoochee FC-3 (TN)

PAGE 35

20 Nominal Size 12.5 mm0 10 20 30 40 50 60 70 80 90 100 Sieve Size (raised to 0.45 power) mmPercentage passing F1 C1 lowercontrol upper control Max Dent.Line Restricted Zone0.075 0.300 0.600 1.18 2.36 4.75 9.5 19.0 0.150 12.5 Figure 3-1. Gradation curves for C1 and F1 The aggregates are designated in this project as follows: Calera-CAL Whiterock-WR Cabbage Grove-CG Ruby-RB Chattahoochee FC-3 – CH Table 3-1. Coarse gradations for fine aggregate effects Sieve Size (mm) WRC CGC RBC CHC CALC 25 100.0 100.0 100.0 100.0 100.0 19 100.0 100.0 100.0 100.0 100.0 12.5 97.4 97.4 97.5 97.5 97.5 9.5 90.0 88.8 89.5 89.4 89.3 4.75 60.2 54.8 57.6 56.9 56.5 2.36 33.1 30.4 31.6 31.3 31.2 1.18 20.3 20.5 21.1 20.9 20.9 0.600 14.7 14.8 15.1 15.0 15.0 0.300 10.8 11.0 11.0 11.0 11.0 0.150 7.6 7.2 7.0 7.1 7.1 0.075 4.8 5.5 5.2 5.2 5.3

PAGE 36

21 Table 3-2. Fine gradations for fine aggregate effects Sieve Size (mm) WRF CGF RBF CALF CHF 25 100.0 100.0 100.0 100.0 100.0 19 100.0 100.0 100.0 100.0 100.0 12.5 95.5 97.4 95.1 94.9 95.0 9.5 85.1 83.8 85.0 84.6 84.7 4.75 69.3 66.0 68.5 67.6 67.9 2.36 52.7 49.4 51.2 50.6 50.8 1.18 34.0 33.3 34.2 33.9 34.0 0.600 22.9 21.9 22.4 22.2 22.2 0.300 15.3 13.9 14.0 14.0 14.0 0.150 9.6 7.0 6.9 6.9 6.9 0.075 4.8 4.5 4.3 4.3 4.3 Table 3-3 shows the Bulk specific gravity, toughness, and the surface texture, particle shape, direct shear strength (DST) from a Geotechni cal direct shear box test, and Fine Aggregate Angularity (FAA) values of th e five fine-graded aggregates used. Bulk Specific Gravity ranged from 2-27 for relativ ely porous limestone to 2-68 for very nonporous granite. Toughness of the parent rock varied from 18.0 % as the lowest value to 42.0 % as the highest value of the L.A. Ab rasion test. Average surface texture values ranged from 1-7 to 4-6, while average partic le shape values ranged from 2-4 to 4-3. Table 3-3. Physical proper ties of fine aggregates Material Bulk Specific Gravity Los Angeles Abrasiona Toughnessb Surface Texturec Particle Shaped FAA DST (psi) White Rock 2.48 34% Medium 3.3 3.0 43.4 134.4 Calera 2.56 25% High 1.7 3.5 42.7 140.8 Cabbage Grove 2.56 41% Low 4.6 2.4 53.1 106.7 Ruby 2.68 20% High 2.7 4.3 46.3 120.5 Chattahoochee FC-3 2.60 42% Low 2.3 3.5 44.0 106.9 a) Los Angeles Abrasion Test performed on the parent rock. Values provided by the Florida DOT Materials Office. b) Definition of toughness based on L.A. Abrasi on. High: <30; Medium: 30-40; Low: >40 c) Average of 8 evaluations, where 1 = smooth and 5 = rough. d) Average of 8 evaluations, where 1 = rounded and 5 = angular. Bulk Specific Gravities for each material were determined in accordance with ASTM C-128. The Florida Department of Transportation (FDOT) provided LA Abrasion values. The FAA values were calculated us ing the Uncompacted Void Content of Fine Aggregate Test (ASTM C-1252 and AASHTO TP 33), and the Direct Shear Test (DST,

PAGE 37

22 ASTM Standard Method D 3080) was used to determine the shear strength of each fine aggregate. Both FAA and DST values we re provided by previous research done by Casanova (2000). Determination of Fine Aggregate Batch Weights To volumetrically replace the fine aggregat es in the FDOT Whiterock limestone C1 and F1 mixtures with the ot her aggregate types, the weight of Whiterock aggregate retained on each sieve (from #8 Sieve to # 200 Sieve) was replaced with an equivalent volume of fine aggregate of the replacemen t material during the batching process using the following equation 3-1. L mbL mbr rW G G W (Eq. 3-1) WL : Weight of Whiterock limestone retained on a specified sieve Wr : Weight of replacement fine aggregat e retained on the specified sieve size GmbL : Bulk specific gravity of Whiterock Limestone Gmbr : Bulk specific gravity of replacement aggregate Limestone Gradation Study Mixture Gradations The second part of the research was done with an oolitic limestone aggregate, entitled “Whiterock” aggregate, which is common ly used in mixtures in Florida. This aggregate was made up of three components: co arse aggregates (S1A), fine aggregates (S1B) and screenings. These were blended together in di fferent proportions to produce ten (10) HMA mixtures consisti ng of five coarse and five fi ne gradations, two of which are the same gradations as in the Fine A ggregate study, namely WR C and WRF. Georgia granite (GA 185) mineral filler was used in a ll the above gradations. These gradations were produced and extensively studied in a previous research at UF (Nukunya, 2000).

PAGE 38

23 Tables 3-4 and 3-5 show the gr adations for the coarse and fine blends respectively. These are also displayed in Figures 3-2 and 3-3. Table 3-4. Gradations for White Rock coarse graded mixtures Sieve Size (mm) C1 C2 C3 25 100.0 100.0 100.0 19 100.0 100.0 100.0 12.5 97.4 91.1 97.6 9.5 90 73.5 89.3 4.75 60.2 47.1 57.4 2.36 33.1 29.6 36.4 1.18 20.3 20.2 24 0.600 14.7 14.4 17.7 0.300 10.8 10.4 12.9 0.150 7.6 6.7 9.0 0.075 4.8 4.8 6.3 Table 3-5. Gradations for White Rock fine graded mixtures Sieve Size (mm) F1 F2 F4 F5 F6 25 100.0 100.0 100.0 100.0 100.0 19 100.0 100.0 100.0 100.0 100.0 12.5 95.5 90.8 95.5 95.5 95.5 9.5 85.1 78 85.1 85.1 85.1 4.75 69.3 61.3 69.3 61.3 69.3 2.36 52.7 44.1 52.7 52.7 44.1 1.18 34.0 34.7 40.0 34.0 34.7 0.600 22.9 23.6 29.0 22.9 23.6 0.300 15.3 15.7 20.0 15.3 15.7 0.150 9.8 8.9 12.0 9.6 9.1 0.075 4.8 6.3 6.3 4.8 6.3 Granite Mixtures Used Three mixtures were prepared by volumetrica lly replacing the aggregate particles in the GAC1, GAC2, GAC3, GAF1, GAF2 and GAF3 limestone mixtures with the appropriate sizes of Georgia granite (GA185) aggregates from pit #185 (code #7 for 12.5 and 9.5 mm sieves, code #89 for 4.75mm (#4) si eve and code #W10 for sieves less than #4). Table 3-6 to 3-8 show the gradations, whic h are also displayed in Figures 3-4 to 3-7.

PAGE 39

24 Nominal Size 12.5 mm0 10 20 30 40 50 60 70 80 90 100 Sieve Size (raised to 0.45 power) mmPercentage passing C1 C2 C3 lowercontrol upper control Max Dent.Line Restricted Zone0.075 0.300 0.600 1.18 2.36 4.75 9. 19.0 0.150 12.5 Figure 3-2. Coarse gradations for gradation effects studies Nominal Size 12.5 mm0 10 20 30 40 50 60 70 80 90 100 Sieve Size (raised to 0.45 power) mmPercentage passing F1 F2 F4 F5 F6 lowercontro l upper control Max Dent.Line Restricted Zone0.075 0.300 0.600 1.18 2.36 4.75 9.5 19.0 0.150 12.5 Figure 3-3. Fine gradations for gradation effects studies

PAGE 40

25 Table 3-6. Granite based mixture gradations Sieve Size (mm) GAC1 GAC2 GAC3 GAF1 GAF2 GAF3 25 100.0 100.0 100.0 100.0 100.0 100.0 19 100.0 100.0 100.0 100.0 100.0 100.0 12.5 97.39 90.9 97.3 94.7 90.5 94.6 9.5 88.99 72.9 89.5 84.0 77.4 85.1 4.75 55.46 45.9 55.4 66.4 60.3 65.1 2.36 29.64 28.1 33.9 49.2 43.2 34.8 1.18 19.24 18.9 23.0 32.7 34.0 26.0 0.600 13.33 13.2 16.0 21.0 23.0 18.1 0.300 9.30 9.2 11.2 12.9 15.3 12.5 0.150 5.36 5.6 6.8 5.9 8.7 7.7 0.075 3.52 3.9 4.7 3.3 5.4 5.8 Nominal Size 12.5 mm0 10 20 30 40 50 60 70 80 90 100 Sieve Size ( raised to 0.45 power ) mmPercentage passing GC1 GC2 GC3 lowercontro l upper control Max Dent.Line Restricted Zone0.075 0.300 0.600 1.18 2.36 4.75 9.5 19.0 0.150 12.5 Figure 3-4. Coarse graded Gr anite aggregate gradations Superpave Field Monitoring Mixture Gradations Five Superpave mixtures from Florida, and tested for performance at the University of Florida (Asiamah 2001) were also ev aluated. Figures 3-5 and 3.7 display the gradations of these mixtures.

PAGE 41

26 Nominal Size 12.5 mm0 10 20 30 40 50 60 70 80 90 100 Sieve Size (raised to 0.45 power) mmPercentage passing GF1 GF2 GF3 lowercontro l upper control Max Dent.Line Restricted Zone0.075 0.300 0.600 1.18 2.36 4.75 9.5 19.0 0.150 12.5 Figure 3-5. Fine graded Gran ite aggregate gradations Table 3-7. Gradation of field projects Sieve Size (mm) P1 P2 P3 P5 P7 25 100.0 100.0 100.0 100.0 100.0 19 100.0 100.0 100.0 100.0 100.0 12.5 100.0 98.0 94.0 100.0 95.0 9.5 99.0 89.0 90.0 94.0 88.0 4.75 64.0 45.0 67.0 64.0 70.0 2.36 40.0 28.0 34.0 34.0 57.0 1.18 29.0 22.0 25.0 24.0 41.0 0.600 21.0 17.0 18.0 19.0 30.0 0.300 14.0 12.0 13.0 13.0 19.0 0.150 8.0 7.0 7.0 8.0 9.0 0.075 5.1 4.9 4.4 3.9 4.2

PAGE 42

27 Figure 3-6. Gradations for Superpave pr oject mixtures number 2, 3, and 7. Figure 3-7. Gradations fo r field projects 1 and 5

PAGE 43

28 Project 1 (P1) and Project 5 (P5) are 9.5 mm nominal gradations while all the other projects are of 12.5 mm nominal size. All the field mixt ures are coarse-graded (i.e., the gradations pass below the Superpave Restricted Zone). Mixture Design Before the production of test specimens, the mixture design process was verified for the mixture volumetric properties. The or iginal Superpave design procedure was used for all the mixtures. The Servopac Superpave gyratory compactor was used in this process. Figure 3-8 shows a picture of the Servopac gyratory compactor. Table 3-8 displays the Superpave compacti on requirements for specified traffic levels as a guide for the design of asphalt paving mixtures. The mi xture volumetric proper ties are calculated based on the design number of gyrations (Ndes). At this number of gyrations, a specified air voids level of 4% provides the optimum design asphalt content. All mixtures were designed for a traffic level of 10-30 million ESALS that is an Ndes of 109 and Nmax of 174. The project mixes except proj ect 7, were designed at an Ndes of 96 and Nmax of 152. Project 7 has an Ndes of 84. The Servopac compaction parameters used for the design are 1.25o gyratory angle, 600-kPa ram pressu re and 30 revolutions per minute. For each mixture, two pills were produ ced at the specified asphalt content. Compaction of the mixtures was made to 109 gyrations with the Servopac gyratory compactor, after which the bulk densities were measured. To verify the volumetric properties of the mixtures, the maximum theo retical specific gravity was measured using the Rice maximum theoretical specific gravity method specified in AASHTO T 209/ASTM D 2041 standards. In this case, th e mixtures were allowed to cool down in the loose state. Tables 3-9 to 3-14 show the volumetric properties of all the mixtures used in this research.

PAGE 44

29 Figure 3-8. Servopac superpave gyratory compactor Table 3-8. Superpave gyratory compaction effort (After asphalt institute Superpave series no. 2) Design Average Design High Air Temperature ESALS <30 C (Millions) Nini Ndes Nmax <0.3 7 68 104 03. to 1 7 76 117 1 to 3 7 86 134 3 to 10 8 96 152 10 to 30 8 109 174 30 to 100 9 126 204 >100 9 143 233

PAGE 45

30 Table 3-9. Volumetric properties of coarse graded mixtures Table 3-10. Volumetric Propertie s of Fine Graded Mixtures Mixture Property Symbol WRF CGF RBF CALF CHF Maximum Theoretical Density Gmm 2.338 2.381 2.416 2.480 2.407 Specific Gravity of Asphalt Gb 1.035 1.035 1.035 1.035 1.035 Bulk Specific Gravity of Compacted mix Gmb 2.244 2.288 2.327 2.386 2.315 Asphalt Content Pb 6.3 6.7 5.9 5.3 5.5 Bulk Specific Gravity of Aggregate Gsb 2.488 2.403 2.599 2.524 2.549 Effective Specific Gravity of Aggregate Gse 2.554 2.63 2.637 2.691 2.608 Asphalt Absorption Pba 1.1 1.2 1.2 1.2 1.0 Effective Asphalt Content in the Mixture Pbe 5.3 3.2 5.7 3.4 4.8 Percent VMA in Compacted Mix VMA 15.6 11.2 16.0 10.5 14.1 Percent Air Voids in Compacted Mix Va 4.0 3.9 3.7 3.8 3.7 Percent VFA in Compacted Mi x VFA 74.2 65.2 76.8 63.8 73.7 Dust/Asphalt ratio D/A 0.8 1.4 0.7 1.3 0.9 Surface Area (m2/kg) SA 5.4 4.8 4.7 4.7 4.7 Theoretical Film Thickness FT 9.0 6.3 10.2 5.2 8.7 Effective VMA in Compacted Mix VMAe 25.7 21.3 27.3 18.8 24.7 Effective Film Thickness Fte 19.3 14.6 22.8 11.7 19.7 Mixture Property Symbol WRC CGC RBC CALC CHC Maximum Theoretical Density Gmm 2.328 2.386 2.393 2.454 2.394 Specific Gravity of Asphalt Gb 1.035 1.035 1.035 1.035 1.035 Bulk Specific Gravity of Compacted mix Gmb 2.235 2.295 2.300 2.353 2.289 Asphalt Content Pb 6.5 6.5 6.25 5.8 5.7 Bulk Specific Gravity of Aggregate Gsb 2.469 2.418 2.576 2.540 2.535 Effective Specific Gravity of Aggregate Gse 2.549 2.625 2.622 2.680 2.601 Asphalt Absorption Pba 1.1 3.0 0.6 1.7 0.7 Effective Asphalt Content in the Mixture Pbe 5.3 3.3 5.6 3.7 4.7 Percent VMA in Compacted Mi x VMA 15.4 11.2 16.1 12.6 14.8 Percent Air Voids in Compacted Mix Va 4.0 3.8 3.9 4.1 4.4 Percent VFA in Compacted Mi x VFA 74.0 66.5 77.3 67.4 70.6 Dust/Asphalt ratio D/A 1.0 1.7 0.9 1.4 1.1 Surface Area (m2/kg) SA 4.2 4.4 4.3 4.3 4.3 Theoretical Film Thickness FT 11.2 6.7 11.7 9.8 7.7 Effective VMA in Compacted Mix VMA 35.4 28.6 38.4 31.7 35.6 Effective Film Thickness Fte 39.2 25.1 42.5 27.4 36.0

PAGE 46

31 Table 3-11. Volumetric properties of coarse graded mixtures Mixture Property Symbol C1 C2 C3 Maximum Theoretical Density Gmm 2.328 2.347 2.349 Specific Gravity of Asphalt Gb 1.035 1.035 1.035 Bulk Specific Gravity of Compacted mix Gmb 2.235 2.255 2.254 Asphalt Content Pb 6.5 5.8 5.3 Bulk Specific Gravity of Aggregate Gsb 2.469 2.465 2.474 Effective Specific Gravity of Aggregate Gse 2.549 2.545 2.528 Asphalt Absorption Pba 1.3 1.3 0.9 Effective Asphalt Content in the Mixture Pbe 5.3 4.6 4.5 Percent VMA in Compacted Mix VMA 15.4 13.8 13.6 Percent Air Voids in Compacted Mix Va 4.0 3.9 4.0 Percent VFA in Compacted Mix VFA 74.1 71.6 70.2 Dust/Asphalt ratio D/A 0.7 0.8 1.2 Surface Area (m2/kg) SA 4.9 4.6 5.7 Theoretical Film Thic kness FT 11.2 10.1 8.0 Effective VMA in Compacted Mix VMAe 35.4 35.3 30.4 Effective Film Thic kness Fte 39.2 39.3 24.1 Table 3-12. Volumetric properties of fine graded Whiterock mixtures Mixture Property Symbol F1 F2 F4 F5 F6 Maximum Theoretical Density Gmm 2.338 2.375 2.368 2.326 2.341 Specific Gravity of Asphalt Gb 1.035 1.035 1.035 1.035 1.035 Bulk Specific Gravity of Compacted mix Gmb 2.244 2.281 2.272 2.233 2.244 Asphalt Content Pb 6.3 5.4 5.7 6.7 6.1 Bulk Specific Gravity of Aggregate Gsb 2.488 2.489 2.491 2.485 2.489 Effective Specific Gravity of Aggregate Gse 2.554 2.565 2.568 2.555 2.550 Asphalt Absorption Pba 1.1 1.2 1.2 1.2 1.0 Effective Asphalt Content in the Mixture Pbe 5.3 4.2 4.5 5.6 5.2 Percent VMA in Compacted Mi x VMA 15.6 13.2 14.0 16.2 15.4 Percent Air Voids in Compacted Mix Va 4.0 3.9 4.0 4.0 4.2 Percent VFA in Compacted Mi x VFA 74.2 70.1 71.2 75.0 72.8 Dust/Asphalt ratio D/A 0.8 1.4 1.3 0.8 1.1 Surface Area (m2/kg) SA 5.4 5.7 6.0 6.5 4.1 Theoretical Film Thickness FT 9.0 6.9 9.7 8.2 10.8 Effective VMA in Compacted Mix VMAe 25.7 25.8 23.5 26.8 28.9 Effective Film Thickness Fte 19.3 17.1 13.2 20.7 20.9

PAGE 47

32 Table 3-13. Volumetric prope rties of Granite mixtures Table 3-14. Volumetric pr operties of field projects Mixture Property Symbol GAC1 GAC2 GAC3 Gaf1 GAF2 GAF3 Maximum Theoretical Density Gmm 2.442 2.500 2.492 2.473 2.532 2.505 Specific Gravity of Asphalt Gb 1.035 1.035 1.035 1.035 1.035 1.035 Bulk Specific Gravity of Compacted mix Gmb 2.442 2.399 2.391 2.473 2.433 2.404 Asphalt Content Pb 6.63 5.26 5.25 5.68 4.56 5.14 Bulk Specific Gravity of Aggregate Gsb 2.687 2.687 2.686 2.686 2.687 2.687 Effective Specific Gravity of Aggregate Gse 2.710 2.719 2.709 2.706 2.725 2.720 Asphalt Absorption Pba 0.37 0.43 0.31 0.28 0.53 0.46 Effective Asphalt Content in the Mixture Pbe 6.32 4.85 4.96 5.42 4.06 4.70 Percent VMA in Compacted Mix VMA 18.5 15.4 15.7 16.6 13.6 15.1 Percent Air Voids in Compacted Mix Va 4.0 4.0 4.1 4.0 3.9 4.0 Percent VFA in Compacted Mix VFA 78.5 73.8 74.2 75.9 71.2 73.3 Dust/Asphalt ratio D/A 0. 6 0.8 0.9 0.6 1.2 1.2 Surface Area (m2/kg) SA 3.3 3.5 4.2 4.1 5.3 4.9 Theoretical Film Thickness FT 19.9 14.3 12.1 13.4 7.7 9.9 Effective VMA in Compacted Mix VMAe 42.9 39.0 35.1 28.4 26.6 33.5 Effective Film Thickness Ft e 67.3 50.8 35.7 27.3 17.8 28.4 Mixture Property Symbol Proj-1 Proj -2 Proj-3 Proj-7 Proj-8 Maximum Theoretical Density Gmm 2.509 2.523 2.216 2.334 2.382 Specific Gravity of Asphalt Gb 1.035 1.035 1.035 1.035 1.035 Bulk Specific Gravity of Compacted mix Gmb 2.407 2.445 2.122 2.229 2.284 Asphalt Content Pb 5.5 5.0 8.3 6.1 6.0 Bulk Specific Gravity of Aggregate Gsb 2.691 2.694 2.325 2.47 2.503 Effective Specific Gravity of Aggregate Gse 2.736 2.725 2.475 2.573 2.598 Asphalt Absorption Pba 0.6 0.4 2.7 1.7 1.4 Effective Asphalt Content in the Mixture Pbe 4.9 4.5 5.7 5.2 4.5 Percent VMA in Compacted Mi x VMA 15.5 14.8 16.4 16.0 14.0 Percent Air Voids in Compacted Mix Va 4.1 4.4 4.2 4.5 3.9 Percent VFA in Compacted Mi x VFA 73.7 70.6 74.1 71.9 72.4 Dust/Asphalt ratio D/A 1.2 0.6 0.6 0.6 1.0 Surface Area (m2/kg) SA 5.2 3.0 3.7 4.6 4.3 Theoretical Film Thickness FT 9.2 8.7 11.3 7.7 8.9 Effective VMA in Compacted Mix VMAe 31.1 38.1 35.4 22.1 34.3 Effective Film Thickness Fte 24.4 52.3 48.3 18.6 35.3

PAGE 48

33 CHAPTER 4 AXIAL COMPRESSION DYNAMIC MODULU S: RESULTS AND DISCUSSION Introduction In this Chapter, the results of the axial complex modulus testing will be described. The triaxial compression dynamic modulus test s produced large amounts of test data. There were two to three test temperat ures based on the mixtures tested: 10C and 40C, for early tests on the FAA mixtures, described in Chapter 3. 10C, 25C, and 40C, for intermediate ti me tests on Georgia granite mixtures and Superpave Project mixtures, described in Chapter 3. 10C, 30C, and 40C for all Whiterock aggregate mixtures and HVS mixtures, described in Chapter 3. For all temperatures tested, the followi ng frequencies were used: 1 Hz, 4 Hz, 10 Hz, and 16 Hz. The tests were performed fr om the lowest temperature to the highest temperature and from the highest freq uency to the lowest frequency. Data Variables The test variables obtained from the data acquisition system include the time, axial force, axial displacement, and the displacemen t from the LVDT’s. The variable time is the period from the test start to the data reco rding time. The axial force is the vertical load on the specimen, and the axial displacemen t is the vertical displacement of the load piston. Four LVDT’s were used for each test, and the average displacements from the four LVDT’s were calculated. The LVDT’s had an axial gage length of 51-mm. Three specimens were tested for each mixture. Befo re the tests were performed, the height for each specimen was measured. The diameter was fixed at 102.0 mm (4 in). To arrive at

PAGE 49

34 the actual stress under certain test cond itions, the axial force was divided by the calculated area of the specimen. Similarly, the LVDT displacements were divided by the axial gage length to arrive at the axial stra in for the test under the same test conditions. For any given test temperature, four da ta files were acquired for each specimen, namely for 16 Hz, 10 Hz, 4 Hz, and 1 Hz. At 16 Hz and 10 Hz, the test data were obtained from the 190th to the 200th cycle. For 4 Hz, the test data was obtained from the 90th to the 100th cycle. For the 1 Hz data, the data was obtained from the 10th to the 20th cycle. A rest period of at least 2 minutes and less than 10 minutes was observed between each frequency. If at the end of any test period, the cumulative unrecovered deformation was found to be greater than 1500 micro units of strain the test data was kept up to this last testing period and the sp ecimen was discarded. A new specimen was used for the rest of the testing periods. For each frequency, there are about 50 sample points per cycle. In this project, triaxial compression co mplex modulus tests were performed on 57 specimens, namely three specimens per mixture listed in Table 1. All specimens were prepared at 7 percent air voids plus or minus 0.5 percent, as listed in Table 6-1. All specimens were compacted directly to 6.65in to 7.04-in (170.0-mm to 180-mm) height in a 4-inch (102 mm) diameter mold, using the Servopac gyratory compactor. Then, the ends of each specimen were trimmed with a saw, so that the target height of each specimen would be 6 inches (150 mm). Th e final heights are listed in Table 4-1. Raw Data Plots For asphalt mixtures, the complex dynamic modulus and phase angle change with the temperature and frequency of loading. At low temperature, the modulus for asphalt mixtures is large, so it is easy to control the applied axial force to obtain small

PAGE 50

35 displacements. At high temperatures, such as 40C, the modulus is lower, making it more difficult to control the axial force to get small displacements. Table 4-1. Sample preparation data Mixture Sample Number Air Voids Height, mm Georgia Granite Mixtures GAC1 1 2 3 7.1 6.8 6.9 150.3 150.2 150.3 GAC2 1 2 3 6.9 6.7 7.0 150.1 150.1 150.0 GAC3 1 2 3 6.8 6.7 7.2 150.1 150.0 150.2 GAF1 1 2 3 7.2 7.3 6.9 150.1 150.3 150.1 GAF2 1 2 3 6.7 6.9 6.7 150.1 150.0 150.2 GAF3 1 2 3 7.1 6.7 6.8 151.0 150.6 150.8 Whiterock Mixtures (Oolitic Limestone) WRC1 1 2 3 6.8 6.6 7.1 150.5 150.2 150.8 WRC2 1 2 3 7.4 6.7 6.9 151.2 150.7 150.8 WRC3 1 2 3 6.9 7.4 7.3 15.2 150.8 150.2 WRF1 1 2 3 7.1 7.0 6.6 150.4 150.2 150.9 WRF2 1 2 3 6.9 6.8 6.9 150.5 151.1 150.4 WRF4 1 2 3 7.1 7.4 6.9 150.9 150.2 151.3 WRF5 1 2 3 7.1 7.3 6.9 150.3 150.7 150.2 WRF6 1 2 3 7.2 7.0 7.1 150.2 150.6 150.3 Mixtures From Fine Aggregate Angularity Study RBC 1 2 3 7.0 7.3 6.8 151.2 150.2 150.7

PAGE 51

36 Table 4-1. Continued Mixture Sample Number Air Voids Height, mm RBF 1 2 3 7.2 7.4 6.7 151.2 150.3 151.3 CALC 1 2 3 7.1 7.2 6.9 150.5 150.6 151.3 CALF 1 2 3 7.1 6.8 6.9 150.5 151.4 150.5 CGC 1 2 3 6.9 7.3 6.7 150.3 150.6 151.3 CGF 1 2 3 6.7 7.3 6.8 150.6 150.4 150.9 CHC 1 2 3 6.8 6.9 6.9 150.5 150.2 150.3 CHF 1 2 3 7.2 7.3 7.1 150.8 150.5 151.3 Superpave Project Mixtures P1 1 2 3 6.8 7.1 7.2 151.2 151.1 151.3 P2 1 2 3 7.2 7.3 6.8 150.2 150.5 151.7 P3 1 2 3 6.7 6.7 7.4 151.4 150.5 151.8 P5 1 2 3 6.7 7.2 6.9 150.5 150.4 151.0 P7 1 2 3 6.5 6.7 6.6 151.4 151.2 150.9 Heavy Vehicle Simulator Mixtures HVS67-22 1 2 3 6.9 7.1 6.8 150.2 150.8 151.1 HVS76-22 1 2 3 7.3 6.8 7.0 150.4 150.7 150.3 Figures 4-1 and 4-2 show typical force a nd single LVDT displacement versus time plots at 10C and 40C for the frequency of 4 Hz. The displacement results have very little noise in the data, even at the higher te sting temperature of 40 C. Finally, Figures 43 and 4-4 show the calculated stress and strain versus time plots after averaging the

PAGE 52

37 displacements from the four LVDTs, which we re used to calculat e the dynamic modulus and the phase angle. The final stress and st rain time histories were found to be sinusoidal for all frequencies tested. Figure 4-1. Typical plot of force and LVDT displacement versus time at low temperature (10C and 4 Hz) for mixture WRC1. Figure 4-2. Typical plot of force and LVDT displacement versus time at high temperature (40C and 4 Hz) for mixture WRC1

PAGE 53

38 Figure 4-3. Typical plot of vertical stress versus strain at low temperature (10C and 4 Hz) for mixture WRC1. Figure 4-4. Typical plot of vertical stress versus strain at high temperature (40C and 4 Hz) for mixture WRC1. Data-Analysis Method The data obtained for the complex modulus test is quite extensive; for one temperature, there are thousands of lines of data for one specimen. To analyze the

PAGE 54

39 complex modulus data, this project used th e linear regression approach, presented in Chapter 5. For each sample at a given te st temperature and frequency, 10 cycles consisting of 1000 points were analyzed to obt ain the dynamic modulus and phase angle. For interpretation purposes, within these 10 cycles, the axial strain history was assumed to consist of a linear trend with a sinusoidal oscillation around the tr end. All calculations were performed using the SI system. Analysis of Test Data Results Test Data. One analysis file was obtained for each load frequency and testing temperature. In this analys is file, the dynamic modulus in GPa and the phase angle in degrees were obtained for the given test temperature and fr equency. There were three replicate specimens tested for each asphalt mi xture. After all the dynamic modulus and phase angle values were calculated for each specimen under the same test conditions, the average value for both of these parameters wa s calculated. Tables 4-2 and 4-3 list the average values for the three specimens for each asphalt mixture. Table 4-2. Average dynamic modul us (|E*|) testing results Frequency Mixture Temperature C 1 Hz 4 Hz 10 Hz 16 Hz Georgia Granite Mixtures 10 3457.54 4696.16 5577.41 6222.62 25 931.93 1440.62 1788.84 1962.27 GAC1 40 317.12 475.14 656.60 742.96 10 5289.30 7142.33 7983.76 8913.45 25 1559.11 2308.10 2776.70 3318.24 GAC2 40 535.77 787.74 1126.96 1313.66 10 5096.07 6797.11 7250.03 7660.00 25 1606.35 2523.14 3079.15 3496.77 GAC3 40 530.76 757.09 1109.68 1250.70 10 4594.94 6228.22 7302.91 7636.35 25 1409.17 2107.13 2672.85 2950.80 GAF1 40 401.02 635.50 867.07 1035.55 10 7142.75 9597.93 11966.62 12883.30 25 2277.25 3201.00 4068.22 4630.38 GAF2 40 535.97 905.80 1309.77 1574.02

PAGE 55

40 Table 4-2. Continued Frequency Mixture Temperature C 1 Hz 4 Hz 10 Hz 16 Hz 10 5184.00 6523.47 7956.86 8798.66 25 1586.94 2400.60 3041.56 3437.54 GAF3 40 377.70 14.91 886.58 1044.15 Whiterock Mixtures (Oolitic Limestone) 10 3540.81 4757.85 5512.43 5953.88 30 1026.46 1896.38 2552.73 2951.30 WRC1 40 526.05 898.81 1222.07 1464.86 10 3499.12 5327.66 6449.00 7073.89 30 1379.32 2256.92 3051.51 3466.68 WRC2 40 759.48 1368.38 1835.72 2073.94 10 5405.49 6995.86 7967.39 8463.57 30 1653.59 2852.46 3718.31 4441.98 WRC3 40 801.08 1470.36 1996.97 2375.12 10 5122.06 6630.20 7917.74 8456.48 30 1769.34 2662.57 3518.02 4005.78 WRF1 40 849.60 1273.70 1663.57 1960.74 Whiterock Mixtures (Oolitic Limestone) 10 6301.77 7744.18 8990.34 9662.49 30 2030.73 2931.80 3764.94 4442.58 WRF2 40 1076.16 1610.34 2169.11 2512.69 10 7037.92 9142.90 10511.22 11141.74 30 2211.26 3357.67 4339.52 5024.28 WRF4 40 1044.19 1584.81 2076.40 2431.11 10 5285.91 6581.71 7583.78 8229.52 30 1515.52 2442.77 3188.31 3688.46 WRF5 40 726.94 1146.45 1556.87 1912.52 10 4391.76 5725.85 6722.84 7152.49 30 1753.47 2479.71 3195.30 3643.92 WRF6 40 879.93 1374.06 1850.43 2136.52 Mixtures From Fine Aggregate Angularity Study 10 5521.86 6877.95 7694.13 8327.94 RBC 40 770.75 1175.36 1492.91 1962.94 10 6242.28 7994.98 9592.44 9862.88 RBF 40 954.17 1415.66 1799.59 2027.84 10 5434.98 7143.53 8025.87 8248.25 CALC 40 1182.66 1792.49 2357.34 2730.40 10 6651.62 8106.39 9194.52 10285.22 CALF 40 1184.06 1779.33 2413.68 2682.04 10 4320.02 5210.02 6136.57 6307.82 CGC 40 923.08 1363.60 1772.90 2003.03 10 6693.18 7387.65 9630.43 9827.05 CGF 40 1217.77 1777.24 2219.22 2500.47 10 4624.45 6216.22 7417.98 7848.56 CHC 40 744.73 1166.04 1559.65 2500.47 10 8812.68 14397.88 16405.10 18827.05 CHF 40 756.82 1073.82 1554.89 2500.47 Superpave Project Mixtures 10 5517.08 7454.96 8422.86 P1 40 523.74 807.66 1161.49 1447.81

PAGE 56

41 Table 4-2. Continued Frequency Mixture Temperature C 1 Hz 4 Hz 10 Hz 16 Hz 10 4459.33 5616.50 6668.22 6728.17 P2 40 606.97 953.37 1349.82 1578.43 10 2869.59 3797.12 4583.94 4754.91 P3 40 458.87 655.21 892.31 978.19 10 5147.749 6263.335 7132.291 7648.227 P5 40 638.095 918.3859 1180.378 1354.904 10 3479.68 4640.86 5562.11 6055.44 P7 40 549.95 796.88 1048.63 1193.51 Heavy Vehicle Simulator Mixtures 10 5559.568 6676.453 7747.892 8016.232 30 1309.809 1900.426 2349.412 2638.219 HVS67-22 40 620.8512 925.0246 1179.977 1323.562 10 5021.711 6411.433 7161.738 7702.334 30 1226.468 1855.661 2401.104 2639.515 HVS76-22 40 646.3819 967.5163 1260.443 1439.98 Table 4-3. Average phase angle ( ) testing results Frequency Mixture Temperature C 1 Hz 4 Hz 10 Hz 16 Hz Georgia Granite Mixtures 10 26.59 26.18 27.84 29.96 25 30.61 33.25 35.01 36.92 GAC1 40 27.11 32.77 40.96 46.10 10 25.20 23.37 24.94 26.96 25 30.17 31.79 34.67 36.72 GAC2 40 26.67 32.14 37.23 41.91 10 25.79 26.05 26.58 31.13 25 29.87 31.44 33.30 35.24 GAC3 40 37.05 42.79 48.87 51.98 10 26.84 25.68 27.65 29.81 25 32.47 33.68 36.02 38.65 GAF1 40 27.25 32.35 38.16 45.09 10 21.62 20.66 22.25 24.82 25 28.84 30.89 32.67 35.46 GAF2 40 31.63 38.32 43.39 48.28 10 22.38 21.47 23.64 25.13 25 30.32 31.86 33.78 36.42 GAF3 40 32.91 38.87 44.30 49.53 Whiterock Mixtures (Oolitic Limestone) 10 22.85 22.03 22.39 23.89 30 33.13 29.81 31.75 33.18 WRC1 40 29.02 30.42 35.05 37.62 10 21.73 20.03 20.63 22.43 30 33.29 29.93 31.08 32.74 WRC2 40 32.19 32.15 35.12 37.04 10 19.08 18.02 18.81 20.72 30 32.79 29.05 29.81 30.49 WRC3 40 32.84 32.25 34.98 37.07

PAGE 57

42 Table 4-3. Continued Frequency Mixture Temperature C 1 Hz 4 Hz 10 Hz 16 Hz 10 19.59 18.00 19.01 21.42 30 32.00 31.07 32.14 33.91 WRF1 40 29.38 32.11 34.78 38.42 10 18.37 17.62 18.81 20.82 30 31.76 29.54 30.53 32.76 WRF2 40 31.21 33.67 35.68 37.73 10 19.83 19.11 20.57 22.76 30 33.64 30.43 31.56 33.14 WRF4 40 31.70 34.00 35.85 37.65 10 22.20 20.17 20.94 22.24 30 32.65 31.28 31.67 33.20 WRF5 40 30.05 33.13 36.10 38.59 10 22.27 20.76 22.02 23.52 30 31.63 30.28 30.88 32.14 WRF6 40 31.92 33.59 36.09 37.62 Mixtures From Fine Aggregate Angularity Study 10 22.75 20.91 23.20 26.69 RBC 40 27.38 31.09 35.68 39.56 10 14.08 15.34 15.82 17.91 RBF 40 25.90 28.66 31.85 36.08 10 17.58 17.23 19.56 20.82 CALC 40 30.53 34.24 38.89 43.18 10 18.31 18.27 20.55 22.61 CALF 40 26.97 33.92 39.90 44.36 10 23.02 22.81 24.74 26.58 CGC 40 31.40 31.10 34.84 38.26 10 16.22 18.64 20.70 23.58 CGF 40 25.70 30.95 34.18 38.65 10 21.91 20.96 22.35 25.52 CHC 40 30.45 33.33 36.00 39.82 10 29.84 29.65 33.06 32.94 CHF 40 35.50 35.40 41.68 49.31 Superpave Project Mixtures 10 23.62 22.99 24.18 P1 40 27.71 33.57 38.46 43.02 10 23.80 23.67 26.44 28.96 P2 40 28.33 32.46 38.35 46.19 10 31.93 29.13 30.46 29.29 P3 40 30.63 34.67 45.24 49.35 10 19.67 19.12 21.15 23.34 P5 40 23.83 28.44 33.38 38.13 10 24.60 23.99 24.62 26.15 P7 40 26.99 32.15 38.96 43.28 Heavy Vehicle Simulator Mixtures 10 21.98 21.11 22.93 24.82 HVS67-22 40 29.01 32.96 37.97 43.17 10 19.47 18.51 20.04 23.31 HVS76-22 40 29.24 31.81 37.52 41.59

PAGE 58

43 Figures 4-5 through 4-10 show dynamic modulus and phase angle results for mixture GAF1 for 10C, 25C, and 40C, which exhibited a typical response for the finegraded mixtures. Similarly, Figures 4-11 through 4-16 display typical dynamic modulus and phase angle results at th e 3 different testing temperat ures for mixture GAC1, which also exhibited a typical response fo r the coarse-graded mixtures. The degree of variability shown in the dyna mic modulus and phase angle results for mixtures GAF1 and GAC1 in Figures 4-5 thro ugh 4-16 are typical fo r the other mixtures tested. The results also clearly show th e expected rate dependence of the dynamic modulus for asphalt mixtures, as the dynamic modulus increases with higher frequencies (e.g., Sousa, 1987). As expected, a comparis on of Figures 4-6 and 4-8 shows that the phase angle also increases with higher tes ting temperatures. Also interestingly, a comparison of Figures 4-6 and 4-8 shows how the phase angle decreased slightly between 1 Hz and 4Hz, but increases w ith frequency up to 16 Hz. At higher temperatures, the phase angle tends to increa se with increased frequency, as shown for example in Figures 4-8 and 4-10. The resu lts for each specimen for the other mixtures tested are provided in the Complex Modulus Microsoft Access Database, described in Appendix B. In summary, the dynamic modulus and pha se angle results s how the following trends, Under a constant loading frequency, the dynamic modulus decreases with an increase in test temperature for the same mixture. The phase angle increases with the increase of test temperature. Under a constant test temper ature, the dynamic modulus incr eases with increased test frequencies.

PAGE 59

44 Both the dynamic modulus and phase angl e data shows relatively smooth trends, irrespective of test temperature. The above trends are consistent with the research results reported by others. 0 10 20 30 40 50 0 5 10 15 20 Frequency (Hz)Phase Angle (Degrees) F1-01 F1-02 F1-03 Sum Figure 4-5. Dynamic modulus |E*| of GAF1 at 10 C 0 2000 4000 6000 8000 10000 0 5 10 15 20 Frequency (Hz)|E*|(MPa) F1-01 F1-02 F1-03 A vg Figure 4-6. Phase angle of GAF1 mixture at 10 C

PAGE 60

45 0 1000 2000 3000 4000 5000 0 5 10 15 20 Frequency (Hz)|E*| (MPa) F1-01 F1-02 F1-03 Avg Figure 4-7. Dynamic modulus |E*| of GAF1 at 25 C 0 10 20 30 40 50 0 5 10 15 20 Frequency (Hz)Phase Angle (Degrees) F1-01 F1-02 F1-03 Avg Figure 4-8. Phase angle of GAF1 mixture at 25 C 0 400 800 1200 1600 2000 0 5 10 15 20 Frequency (Hz)|E*|(MPa) F1-01 F1-02 F1-03 A vg Figure 4-9. Dynamic modulus |E*| of GAF1 at 40 C

PAGE 61

46 0 10 20 30 40 50 60 0 5 10 15 20 Frequency (Hz)Phase Angle (Degrees) F1-01 F1-02 F1-03 A vg Figure 4-10. Phase angle of GAF1 mixture at 40 C 0 2000 4000 6000 8000 10000 0 5 10 15 20 Frequency (Hz)|E*|(MPa) C1C1C1A vg Figure 4-11. Dynamic modulus |E*| of GAC1 at 10 C Figure 4-12. Phase angle of GAC1 mixture at 10 C

PAGE 62

47 0 1000 2000 3000 4000 5000 0 4 8 12 16 20 Frequency (Hz)|E*|(MPa) C1-01 C1-02 C1-03 Avg Figure 4-13. Dynamic modulus |E*| of GAC1 at 25 C Figure 4-14. Phase angle of GAC1 mixture at 25 C Figure 4-15. Dynamic modulus |E*| of GAC1 at 40 C 0 10 20 30 40 50 0 5 10 15 20 Frequency (Hz)Phase Angle (Degrees) C1-01 C1-02 C1-03 Sum 0 400 800 1200 1600 2000 0 5 10 15 20 Frequency (Hz)|E*|(MPa) C1-01 C1-02 C1-03 Avg

PAGE 63

48 Figure 4-16. Phase angle of GAC1 mixture at 40 C Master Curve Construction The dynamic modulus and phase angle of mixtures can be shifted along the frequency axis to form single characterist ic master curves at a desired reference temperature or frequency. In the propos ed “2002 Guide for the Design of Pavement Systems” currently under development in th e NCHRP Project 1-37A, the modulus of the asphalt mixture, at all analysis levels of temperature and time rate of load, is determined from a master curve constructed at a referen ce temperature. The procedure assumes that the asphalt mixture is a thermorheological ly simple material, and that the timetemperature superposition pr inciple is applicable. Typically, the shift factors a(T) are obtained from the WLF equation (Williams et al., 1955). r rT T C T T C T a 2 1) ( log (Eq. 4-1) Where C1 and C2 are constants, Tr is the reference temperature, and T is the temperature of each individual test. 0 15 30 45 60 75 0 5 10 15 20 Frequency (Hz)Phase Angle (Degrees) C1-01 C1-02 C1-03 Avg

PAGE 64

49 A new method of developing the master cu rve for asphalt mixtures was developed by Pellinen and Witczak (2002), in which the ma ster curves were constructed fitting a sigmoidal function to the measured comple x modulus test data using non-linear least squares regression techniques. The shift can be achieved by solv ing the shift factors simultaneously with the coefficien ts of the sigmoidal function. The sigmoidal fitting function for master curve construction used by Pellinen and Witczak (2002) is defined equation (4-2). ) log(1 ) log(rfe E (Eq. 4-2) Where log(|E*|) = log of dynamic modulus, = minimum modulus value, fr = reduced frequency, = span of modulus value, = shape parameters. The reduced frequency, fr, is defined as, ) ( T a f fr (Eq. 4-3) or alternatively, log(fr) = log(f) + log[a(T)] in which f = testing frequency, and a(T) is the shift factor that define s the required shift at a given temperature to ge t the reduced frequency fr. At the reference temperature, the shift factor a(Tr) = 1. Finally, the parameter influences the steepness of the function (rate of change between minimum and maximum) and influences the horizontal position of the turning point, shown in Figure (6-17).

PAGE 65

50 Log Reduced Frequency Sigmoidal Function (pos) (increase)log/E*/(neg) Figure 4-17. Parameters used in sigmoidal fitting function The justification of using a sigmoidal function for fitting the compressive dynamic modulus data is based on the physical observa tions of the mix behavior. The upper part of the sigmoidal function approaches asympt otically the maximum stiffness of the mix, which is dependent on limiting binder stiffn ess at cold temperatures. At high temperatures, the compressive loading causes aggregate influence to be more dominant than the viscous binder influence. The modul us starts to approach a limiting equilibrium value, which is dependent of the aggregat e gradation. Thus, the sigmoidal function captures the physical behavior of the asphalt mixture observed in the mechanical testing using compressive cyclic load ing through the entire range of temperatures that are typically of interest. Typical Predicted Master Curves for Florida Mixtures In the following, the procedure developed by Pellinen and Witczak (2002) for obtaining predicted master curves for GAC3 and GAF1 is used, and the resulting master curves are presented. Master curves for all ot her mixtures that were tested at three testing temperatures are presented in Appendix C. In all cases, the reference temperature was taken as 25C (77F). As stated previ ously, the shifting was accomplished by obtaining

PAGE 66

51 the shift factors simultaneously with the coe fficients of the sigm oidal function through nonlinear regression, without assuming any functi onal form of a(T) versus temperature. The nonlinear regression was performed using the Solver Function in a Microsoft Excel spreadsheet. The resulting shift functions and mast er curves for GA-C3 and GA-F1 are presented in Figures 4-18 thr ough Figure 4-21 below. The tails on the predicted master curves are extrapolated. In a few cases, depe nding on the mixture prop erties, the tails of the predicted mastercurve did not follow an Sshape. Rather, the mastercurve showed a slight concave-down curvature. Figures 4-22 and 4-23 show the shift function and predicted mastercurve for mixture GA-C1, resp ectively. The predicted mastercurve for GAC1 does not show an S-shape. It shows a slight concave-down curvature, indicating that for this particular mixtur e, higher and lower temperature results are needed to define the tails of the mastercurve adequately. Future testing at higher and lower temperatures would help in defining the tails better. Figure 4-18. Shift function for coarse-graded GAC3 mixture. y = -0.0614x + 4.9497 R2 = 0.9872 -4 -2 0 2 4 0 20 40 60 80 100 120 Temperature(0F)Log a(T)

PAGE 67

52 Figure 4-19. Master curve for coarse-graded GAC3 mixture. Figure 4-20. Shift function fo r fine-graded GAF1 mixture. Figure 4-21. Master curve fo r fine-graded GAF1 mixture. y = -0.061x + 4.9197 R2 = 0.9867 -4 -2 0 2 4 0 20 40 60 80 100 120 Temperature(0F)Log a(T)

PAGE 68

53 Figure 4-22. Shift function fo r fine-graded GAF1 mixture. Figure 4-23. Master curve for coarse-graded GAC1 mixture. Dynamic Modulus Calculated from Predictive Regression Equations The complex modulus test is relatively difficult and expensive to perform. Therefore, numerous attempts have been made to develop regression equations to y = -0.0722x + 5.5655 R 2 = 1 -4 -2 0 2 4 0 20 40 60 80 100 120Temperature (0F)Log a(T)

PAGE 69

54 calculate the dynamic modulus from conventio nal volumetric mixture properties. For example, a predictive regression equation is proposed as a part of the 2002 Design Guide (Witczak et al., 2002) to calculate |E*| base d on the volumetric properties of any given mixture. The predictive equation developed by Witczak et al. (2002) is one of the most comprehensive mixture dynamic modulus models available today (Witczak 2002). The equation is presented in equation (4-3). )). log( 39353 0 ) log( 313351 0 603313 0 ( 4 / 3 2 8 / 3 8 / 3 4 4 2 200 2001 ) ( 005470 0 ) ( 00017 0 ) ( 003958 0 ) ( 0021 0 871977 3 ) ( 802208 0 ) ( 058097 0 ) ( 002841 0 ) ( 001767 0 ) ( 029232 0 249937 1 log f a beff beff ae p p p p V V V V p p p E( Eq. 4-3) Where |E*| = dynamic modulus, in 105 psi; bitumen viscosity, in 06 Poise; f = loading frequency, in Hz; Va = percent air void content, by volume; Vbeff = effective bitumen content, percent by volume; P3/4 = percent weight retained on 19-mm sieve, by total aggregate weight; P3/8 = percent weight retained on 9.5-mm sieve, by total aggregate weight; P4 = percent weight retained on 4.75-mm sieve, by total aggregate weight; P200 = percent weight passing 0.75-mm si eve, by total aggregate weight; The above dynamic modulus predictive equa tion has the capability to predict the dynamic modulus of dense-graded HMA mixtures over a range of temperatures, rates of loading, and aging conditions from inform ation that is readily available from conventional binder tests and the volumetric properties of the HMA mixture. This predictive equation is based on more than 2,800 different HM A mixtures tested in the laboratories of the Asphalt Institute, th e University of Maryland, and FHWA. In this research, the dynamic modulus wa s calculated using the predictive equation developed by Witczak et al (2002). Gradati ons data for each mixture, binder content and

PAGE 70

55 volumetric properties, were obtained from th e design mixture properties, discussed in Chapter 3. The air voids were measur ed using test method AASHTO T 166 on the prepared test specimens. Table 6-1 lists th e air voids for each specimen tested. For each mixture listed in Table 6-1, the average air vo ids from the three pills tested were used. The binder viscosity was obtained at each testing temperature using, Brookfield rotational viscometer results on short-term RTFO aged specimens. Dynamic Shear Rheometer results on short-term RTFO aged specimens. Recommended viscosity values by Witczak and Fonseca (1996) for “Mixture Laydown” conditions. In the next section, the binder test re sults will be presented, followed by a presentation of the predicted dynamic modul us results calculated from the predictive equation by Witczak et al. (2002). Binder Testing Results The asphalt binder used for all mixtures but one of the mixtures te sted is graded as PG67-22 (AC-30). The HVS mixture with SB S modified binder graded as PG76-22 was not tested, due to lack of availability. The “as produced” mix was used for the complex modulus testing of the HVS mixtures, making it hard to ensure that exactly the same binder be used for the rheological testing. Table 6-4 shows the resu lts of the Brookfield Rotational Viscometer testing, performed at th ree testing temperatures (60.5 C, 70.7 C, Table 4-4. Brookfield rotational viscomet er results on unaged and RTFO aged binder Testing Temperature (C) Unaged Binder Viscosity (cP) RTFO Aged Binder Viscosity (cP) 60.5 328260.5 1041945.2 70.7 95682.1 236166.7 80.7 33681.6 81193.0

PAGE 71

56 and 80.7 C). Similarly, table 4-5 shows the re sults of viscosity test results obtained from the Dynamic Shear Rheometer. The visc osity is reported in centiPoise (cP). Table 4-5. Dynamic shear rheometer results on unaged and RTFO aged binder Testing Temperature (C) Unaged Binder Viscosity (cP) RTFO Aged Binder Viscosity (cP) 30 2.46E+06 5.08E+06 40 1.99E+05 1.20E+06 Based on the results shown in Tables 4-4 and 4-5, the viscosity for each complex modulus test temperature was obt ained using the equation (4-4). Log(log( ) = A + VTSlog(T) (Eq. 4-4) in which is bitumen viscosity in centipoises, T is test temperature in Rankine, and A and VTS are regression constant s reflecting the specific type of asphalt cement and aging conditions of the material. Table 4-6 summa rizes the calculated A and VTS values for the unaged binder, and the RTFO aged binde r results from the Brookfield Rotational Viscometer test and the Dynamic Shear Rheomete r test. Similarly, Table 4-7 lists typical A and VTS values for PG 67-22 (AC30), recommended by Witzcak and Fonseca (1996), for two conditions: (a) original, and (b) short-term (mix/laydown). A comparison of Tables 4-6 and 4-7 shows th at the parameters obtained fr om the Brookfield Rotational Viscometer test for RTFO aged asphalt are close in values to the A and VTS values recommended by Witzcak and Fonseca (1996) for Mix/Laydown conditions. The A and VTS values obtained from the Dynamic Shear Rheometer are slightly lower. Based on the results presented in Tables 46 and 4-7, the viscosity (in Poise) was finally calculated for the complex modulus tes ting temperatures used. The viscosities of

PAGE 72

57 Table 4-6. Viscosity-temperature re gression coefficients for unaged and RTFO aged PG 67-22 (AC-30) asphalt Results Based on Viscosities Obtained From Brookfield Rotational Viscometer Test Results Based on Viscosities Obtained From Dynamic Shear Rheometer Test Regression Constants Unaged Binder RTFO Aged Binder Unaged Binder RTFO Aged Binder A -5.6362 -3.4655 -5.7817 -3.0165 VTS 16.207 10.407 16.63 9.0824 Table 4-7. Typical viscosity-t emperature regression coeffici ents for AC-30 (PG 67-22) at different hardening states (Witzcak and Fonseca, Transportation Research Record 1540, 1996, pp.15-23) Regression Constants Original Conditions (Unaged Binder) Mix/Laydown Conditions A -3.6666 -3.56455 VTS 10.928 10.6768 interest are obtained from: (a ) Brookfield Rotational Viscomet er testing of RTFO aged AC-30 asphalt, (b) Dynamic Shear Rheometer testing of RTFO aged PG 67-22 (AC-30) asphalt, and (c) Mix/Laydown conditions from Witzcak and Fonseca (1996). Table 4-8 summarizes the results of the cal culated viscosities for conditi on and test temperature. Table 4-8. Calculated vi scosity at four complex modulus test temperatures Test and Aging Condition Calculated Viscosity (in Poise) Complex Modulus Test Temperature 10 C 25 C 30 C 40 C Brookfield test RTFO 3.89E+08 7.17E+06 2.29E+06 2.95E+05 DSR test RTFO 1.73E+06 1.12E+05 5.08E+04 1.20E+04 From Witzcak and Fonseca (1996) Mix/lay down condition 4.57E+08 7.39E+06 2.28E+06 2.79E+05 Comparison of Predicted and Measured Dynamic Modulus The predictive regression equation by W itczak et al. (2002) is used to obtain predicted dynamic modulus values for all test temperature and frequencies for all mixtures tested, except the Superpave P5 mi x for which a total volumetric description

PAGE 73

58 was not available, and the HVS PG 76-22 mix, for which binder vi scosity measurements were not available. The three conditions considered are: Mix/Laydown Condition from Witzcak and Fonseca (1996), RTFO aged binder results from Brookfie ld Rotational Viscometer Test, and RTFO aged binder results from the DSR test. Tables 4-9 through 4-20 list the predicte d dynamic modulus values for all test temperatures and testing frequencies (Proposed by Witzcak and Fonseca-1996). Similarly, Figures 4-24 through 4-26 show the resulting comparisons between predicted and measured dynamic moduli for the three conditi ons studied. In order to evaluate the relative quality of the predictions, linear regr essions with zero inte rcept were performed for the three cases. The results of the re gression analysis are shown on Figures 4-23 through 4-26. The coefficient describing the sl ope of the regression line is a measure of the quality of fit, the closer the slope coeffici ent is to unity, the less of a bias is built into the prediction. A slope that is less than one indicates an unconser vative prediction, in which the predicted dynamic modulus is hi gher than the measured dynamic modulus. Similarly, a slope that is greater than unity indicates a conservative prediction, in which the predicted dynamic modulus is lower than the measured dynamic modulus. Similarly, the R2 value is a measure of the goodness of fit of the regression line. A high R2 value indicates a good fit, whereas a low R2 indicates an inadequate fit. The results from the regression analysis show that the RTFO ag ed binder results from Brookfield Rotational Viscometer test provide a sl ope that is closest to unity (0.6857), and the highest R2 value (0.845). The Mix/Laydown binder viscos ity conditions proposed by Witzcak and Fonseca (1996) provide very similar results. However, the RTFO aged binder results from the DSR test have a slope, which is higher

PAGE 74

59 Table 4-9. Predicted dynamic moduli fo r Georgia granite mixtures using the Mix/Laydown condition. Frequency Mixture Temperature C 1 Hz 4 Hz 10 Hz 16 Hz Georgia Granite Mixtures 10 6348.09 7833.00 8867.60 9409.14 25 2233.40 3076.22 3740.45 4114.03 GAC1 40 743.46 1099.89 1409.71 1594.90 10 7228.04 8935.16 10126.30 10750.27 25 2519.90 3480.55 4239.32 4666.60 GAC2 40 830.82 1233.33 1584.17 1794.22 10 7312.96 9022.68 10213.82 10837.27 25 2519.90 3545.00 4310.05 4740.31 GAC3 40 857.33 1268.11 1625.12 1838.52 10 7843.40 9699.73 10995.38 11674.21 25 2729.02 3771.68 4595.62 5059.72 GAF1 40 897.89 1333.89 1714.14 1941.87 10 8766.05 10836.87 13038.76 13038.76 25 3055.47 4220.57 5140.85 5659.10 GAF2 40 1007.18 1495.26 1920.69 2175.41 10 9224.27 11413.04 13742.22 13742.22 25 3201.60 4428.16 5397.98 5944.44 GAF3 40 1050.65 1562.27 2008.80 2276.34 Table 4-10. Predicted dynamic moduli for Whiterock mixtures using the Mix/Laydown condition Frequency Mixture Temperature C 1 Hz 4 Hz 10 Hz 16 Hz Whiterock Mixtures (Oolitic Limestone) 10 6281.57 7755.35 8782.67 9320.53 30 1518.78 2156.30 2677.98 2978.17 WRC1 40 731.38 1083.18 1389.22 1572.26 10 7203.20 8917.48 10114.99 10742.70 30 1709.95 2438.73 3037.24 3382.33 WRC2 40 815.70 1214.19 1562.28 1770.95 10 7869.28 9728.22 11025.33 11704.82 30 1886.08 2683.56 3337.27 3713.79 WRC3 40 904.17 1342.32 1724.24 1952.90 10 7377.84 9133.15 10359.26 11001.94 30 1752.11 2498.61 3111.62 3465.07 WRF1 40 835.98 1244.25 1600.84 1814.59 10 9442.18 11682.78 13247.26 14067.13 30 2249.92 3205.85 3990.33 4442.46 WRF2 40 1075.37 1599.05 2056.11 2329.97 10 9534.34 11792.37 13368.55 14194.41 30 2277.65 3243.34 4035.42 4491.81 WRF4 40 1090.05 1619.74 2081.78 2358.54 10 7756.29 9584.35 10859.48 11527.34 30 1864.47 2650.89 3295.16 3666.12 WRF5 40 895.17 1327.87 1704.80 1930.39 10 10642.12 13162.50 14921.81 15843.63 30 2542.29 3620.17 4504.29 5013.71 WRF6 40 1216.70 1807.93 2323.66 2632.57

PAGE 75

60 Table 4-11. Predicted dynamic modu li for FAA mixtures using the Mix/Laydown condition Frequency Mixture Temperature C 1 Hz 4 Hz 10 Hz 16 Hz Mixtures From Fine Aggregate Angularity Study 10 8739.16 10785.05 12210.69 12956.96 RBC 40 745.75 1103.59 1414.71 1600.71 10 9850.64 12182.68 13810.43 14663.28 RBF 40 868.59 1290.50 1658.48 1878.88 10 12281.01 13903.68 14753.05 CALC 40 844.89 1250.10 1602.35 1812.93 10 11670.26 14432.67 16360.78 17370.99 CALF 40 1029.34 1529.24 1965.23 2226.36 10 9581.79 10852.29 11517.53 CGC 40 1335.85 1713.68 1939.69 10 12080.89 14939.98 16935.52 17981.05 CGF 40 1053.09 1564.43 2010.37 2277.46 10 6783.37 8377.25 9488.52 10070.40 CHC 40 787.55 1166.97 1497.19 1694.73 10 8464.11 10483.62 11894.88 12634.78 CHF 40 953.71 1420.92 1829.33 2074.26 Table 4-12. Predicted dynamic moduli for Superpave project mixtures using the Mix/Laydown condition Frequency Mixture Temperature C 1 Hz 4 Hz 10 Hz 16 Hz Superpave Project Mixtures 10 7987.27 9213.04 10423.32 P1 40 708.26 959.39 1228.08 1388.54 10 7531.50 8304.65 9394.88 9965.25 P2 40 654.75 876.40 1121.68 1268.14 10 6738.42 9866.87 11177.65 11864.09 P3 40 593.73 1050.05 1347.64 1525.71 10 7474.52 9283.27 10502.78 11140.81 P7 40 649.79 966.71 1237.44 1399.13 Table 4-13. Predicted dynamic moduli for Georgia granite mixtures using RTFO aged binder results from the Brookf ield rotational viscometer test. Frequency Mixture Temperature C 1 Hz 4 Hz 10 Hz 16 Hz Georgia Granite Mixtures 10 6141.71 7609.33 8636.32 9175.20 25 2212.78 3050.25 3710.90 4082.68 GAC1 40 759.06 1121.94 1436.89 1624.97 10 6991.03 8677.83 9859.92 10480.69 25 2496.43 3450.91 4205.54 4630.73 GAC2 40 848.40 1258.28 1614.99 1828.34 10 7075.32 8765.16 9947.56 10567.95 25 2496.43 3515.08 4276.02 4704.20 GAC3 40 875.31 1293.53 1656.45 1873.16

PAGE 76

61 Table 4-13. Continued Frequency Mixture Temperature C 1 Hz 4 Hz 10 Hz 16 Hz 10 7585.74 9419.86 10705.60 11380.92 25 2703.55 3739.50 4558.93 5020.76 GAF1 40 916.93 1360.92 1747.55 1978.87 10 8478.56 10524.71 12711.72 12711.72 25 3027.01 4184.62 5099.88 5615.60 GAF2 40 1028.50 1525.51 1958.07 2216.79 10 8920.55 11082.99 13396.18 13396.18 25 3171.66 4390.29 5354.78 5898.56 GAF3 40 1072.99 1594.01 2048.04 2319.82 Table 4-14. Predicted dynamic modulus for Whiterock mixtures Using RTFO aged binder results from the Brookf ield rotational viscometer test Frequency Mixture Temperature C 1 Hz 4 Hz 10 Hz 16 Hz Whiterock Mixtures (Oolitic Limestone) 10 6076.80 7533.31 8553.00 9088.18 30 1520.14 2158.09 2680.08 2980.43 WRC1 40 746.77 1104.95 1416.09 1601.98 10 6965.40 8658.91 9847.10 10471.47 30 1711.50 2440.78 3039.65 3384.93 WRC2 40 833.08 1238.93 1592.88 1804.86 10 7611.20 9448.00 10735.25 11411.25 30 1887.78 2685.81 3339.90 3716.62 WRC3 40 923.31 1369.48 1757.79 1990.05 10 7134.35 8868.40 10084.98 10724.24 30 1753.69 2500.71 3114.09 3467.73 WRF1 40 853.79 1269.59 1632.19 1849.33 10 9131.27 11344.91 12897.32 13712.88 30 2251.95 3208.54 3993.49 4445.87 WRF2 40 1098.22 1631.53 2096.28 2374.47 10 9220.94 11451.92 13016.02 13837.59 30 2279.71 3246.05 4038.61 4495.25 WRF4 40 1113.17 1652.59 2122.38 2403.51 10 7502.42 9308.83 10574.35 11238.80 30 1866.14 2653.10 3297.75 3668.91 WRF5 40 914.08 1354.68 1737.90 1967.03 10 10292.30 12782.49 14528.33 15445.35 30 2544.58 3623.20 4507.85 5017.55 WRF6 40 1242.51 1844.60 2368.98 2682.77 Table 4-15. Predicted dynamic moduli fo r FAA mixtures using RTFO aged binder results from the Brookfield rotational viscometer test Frequency Mixture Temperature C 1 Hz 4 Hz 10 Hz 16 Hz Mixtures From Fine Aggregate Angularity Study 10 8454.83 10476.87 11891.99 12634.58 RBC 40 761.40 1125.73 1442.01 1630.91 10 9526.95 11831.08 13446.37 14294.80 RBF 40 887.02 1316.66 1690.81 1914.69

PAGE 77

62 Table 4-15. Continued Frequency Mixture Temperature C 1 Hz 4 Hz 10 Hz 16 Hz 10 11930.23 13540.94 14386.14 CALC 40 862.62 1275.17 1633.26 1847.12 10 11286.83 14016.19 15929.55 16934.52 CALF 40 1051.17 1560.24 2003.54 2268.79 10 9307.21 10568.24 11230.14 CGC 40 1362.73 1746.85 1976.39 10 11684.03 14508.93 16489.22 17529.32 CGF 40 1075.42 1596.13 2049.56 2320.85 10 6561.95 8137.08 9240.06 9819.02 CHC 40 804.14 1190.46 1526.18 1726.80 10 8184.06 10178.95 11579.14 12315.06 CHF 40 974.08 1449.93 1865.25 2114.08 Table 4-16. Predicted dynamic moduli for Superpave mixtures using RTFO aged binder results from the Brookfield rotational viscometer test Frequency Mixture Temperature C 1 Hz 4 Hz 10 Hz 16 Hz Superpave Project Mixtures 10 7232.74 8951.29 10152.84 P1 40 663.35 978.53 1251.64 1414.59 10 6520.58 8068.85 9151.24 9718.88 P2 40 606.11 893.88 1143.18 1291.91 10 7726.21 9583.62 10884.56 11567.53 P3 40 723.20 1071.22 1373.77 1554.63 10 7287.87 9019.52 10230.24 10865.22 P7 40 668.41 985.99 1261.18 1425.37 Table 4-17. Predicted dynamic moduli for Ge orgia granite mixtures using RTFO aged binder results from the dynamic shear rheometer Test. Frequency Mixture Temperature C 1 Hz 4 Hz 10 Hz 16 Hz Georgia Granite Mixtures 10 1170.78 1673.53 2088.55 2328.65 25 441.77 662.60 859.21 978.60 GAC1 40 190.72 289.03 380.32 437.41 10 1346.09 1936.46 2426.29 2710.49 25 499.15 754.10 982.42 1121.53 GAC2 40 212.28 324.10 428.56 494.12 10 1249.63 1786.03 2228.79 2484.93 25 499.15 707.35 917.17 1044.56 GAC3 40 203.68 308.64 406.08 467.01 10 1464.90 2104.70 2634.99 2942.50 25 545.09 822.33 1070.31 1221.30 GAF1 40 232.51 354.47 468.26 539.63 10 1410.28 2025.09 2829.73 2829.73 25 525.57 792.37 1030.90 1176.10 GAF2 40 224.48 342.00 451.60 520.31

PAGE 78

63 Table 4-17. Continued Frequency Mixture Temperature C 1 Hz 4 Hz 10 Hz 16 Hz 10 1567.56 2258.91 3166.82 3166.82 25 578.57 875.78 1142.36 1304.93 GAF3 40 245.06 374.91 496.40 572.72 Table 4-18 Predicted dynamic moduli fo r Whiterock mixtures using RTFO aged binder results from the dynamic shear rheometer test. Frequency Mixture Temperature C 1 Hz 4 Hz 10 Hz 16 Hz Whiterock Mixtures (Oolitic Limestone) 10 1331.74 1905.40 2379.31 2653.59 30 371.92 562.39 735.10 841.28 WRC1 40 215.91 327.57 431.33 496.26 10 1487.22 2144.65 2691.16 3008.59 30 403.87 616.28 810.29 930.08 WRC2 40 231.68 354.72 469.91 542.31 10 1459.92 2097.11 2625.16 2931.34 30 401.99 610.65 800.56 917.57 WRC3 40 231.96 353.55 466.97 538.10 10 1567.89 2256.36 2827.73 3159.30 30 428.90 652.91 857.15 983.11 WRF1 40 246.80 376.97 498.61 574.97 10 1593.26 2295.72 2879.29 3218.13 30 433.91 661.49 869.22 997.42 WRF2 40 249.21 381.21 504.69 582.27 10 1626.84 2337.06 2925.67 3266.97 30 447.83 680.35 891.98 1022.38 WRF4 40 258.38 393.86 520.24 599.49 10 1392.47 1997.11 2497.57 2787.54 30 385.55 584.63 765.55 876.93 WRF5 40 223.00 339.28 447.58 515.44 10 1813.53 2605.27 3261.44 3641.91 30 499.22 758.41 994.34 1139.70 WRF6 40 288.03 439.05 579.93 668.28 Table 4-19. Predicted dynamic moduli for FAA mixtures using RTFO aged binder results from the dynamic shear rheometer test. Frequency Mixture Temperature C 1 Hz 4 Hz 10 Hz 16 Hz Mixtures From Fine Aggregate Angularity Study 10 1441.83 2062.97 2576.12 2873.12 RBC 40 233.72 354.60 466.94 537.23 10 1777.05 2556.73 3203.69 3579.08 RBF 40 280.06 427.66 565.55 652.10 10 2371.26 2960.94 3302.23 CALC 40 268.78 407.75 536.90 617.70 10 2098.32 3019.18 3783.32 4226.72 CALF 40 330.58 504.84 667.65 769.85

PAGE 79

64 Table 4-19. Continued Frequency Mixture Temperature C 1 Hz 4 Hz 10 Hz 16 Hz 10 2479.73 3096.16 3452.91 CGC 40 426.65 561.73 646.24 10 2151.50 3096.06 3879.95 4334.83 CGF 40 338.75 517.39 684.31 789.10 10 1511.78 2162.93 2700.85 3012.18 CHC 40 245.13 371.89 489.68 563.39 10 1873.27 2695.30 3377.41 3773.21 CHF 40 295.16 450.74 596.09 687.32 Table 4-20. Predicted dynamic moduli fo r Superpave mixtures using RTFO aged binder results from the dynamic shear rheometer test. Frequency Mixture Temperature C 1 Hz 4 Hz 10 Hz 16 Hz Superpave Project Mixtures 10 881.97 1548.08 1548.08 P1 40 151.15 295.65 295.65 338.70 10 1308.41 1884.07 2362.05 2639.49 P2 40 205.33 205.33 415.30 479.02 10 1547.87 1547.87 2785.58 3110.94 P3 40 245.30 245.30 494.31 569.72 10 1646.80 1646.80 7703.09 3331.44 P7 40 256.53 256.53 520.32 600.49 than unity (2.7402), and a lower R2 value (0.7257), which is like ly the result of the higher bias in the prediction. Hence, even though the predictions based on the viscosity obtained from the Brookfield Rotational Viscometer test a nd the Mix-Laydown conditions proposed by Witzcak and Fonseca (19 96) are statistically better than the results based on the viscosity obtained from the DSR test, the latter is the only conservative estimate of the three evaluated. This bias in the DSRbased predictions of dynamic modulus values follow similar publis hed results (e.g., Clyne et al. 2003). Hence, consistent with the recommendations by Witzcak et al. (2002), in order to obtain conservative predictions, it is recommended that viscosity input values for the predictive equation be obtained from the DSR test. Interestingly, it is of interest to note th at the predictions at higher temperatures (i.e., lower modulus values) gene rally are closer to the line of equity for all three cases

PAGE 80

65 than the predictions at lower temperatures. Figures 4-27 presents a comparison of predicted and measured dynamic modulus valu es for the Whiterock oolitic limestone mixtures tested (F1, F2, F4, F5, F6, C1, C2, C3). As the temperature increases from 10 C to 40 C, the predicted dynamic modulus approaches the measured dynamic modulus values. This is likely the result of the much of the database used to develop the predictive equation being biased toward mixtures tested at higher temperatures. Finally, Figure 4-28 shows measured vs predicted dynamic modulus for Fine Aggregate Angularity Mixtures (“FAA”), Superpave Projec t Mixtures (“Project”), Granite Mixtures (“Granite”), and Whitrock Mi xtures (“WR”) at a Test Temperature of 40 C and a Testing Frequency of 4 Hz. Mo st of the mixture groups scatter around the line of unity, with the exception of the Georgia Granite mixtures (GA-C1, GA-C2, GAC3, GA-F1, GA-F2, GA-F3), which land below the line of unity. Since the testing protocol for all mixtures was the same, the asphalt used was the same, and these mixtures were designed to be volumetrically similar to the Whiterock oolitic limestone mixtures (WR-C1, WR-C2, WR-C3, WR-F1, WR-F2, WR-F 3) it is likely that this difference has to do with the aggregate type. This warrant s further study through mo re detailed testing of mixtures of different mineral origin. Conclusions This Chapter presented dynamic modulus testing results for 29 mixtures of different gradations and aggreg ate types. Mixtures were te sted at two or more of the following test temperatures: 10 C, 25 C 30 C, and 40 C. At each testing temperature, testing was conducted at four di stinct frequencies, namely 16 Hz, 10 Hz, 4 Hz, and 1 Hz. The

PAGE 81

66 Figure 4-24. Measured values versus predic ted values of |E*| on a log-log scale (Mix-Laydown binder) Figure 4-25. Measured values versus predic ted values of |E*| on a log-log scale (RTFO-binder) Figure 4-26. Measured values versus pred icted values of |E*| on a log-log scale (DSR-RTFO binder)

PAGE 82

67 10 C (4 Hz)0 2000 4000 6000 8000 10000 12000 14000 WR-F1WR-F2WR-F4WR-F5WR-F6WR-C1WR-C2WR-C3 Whiterock MixturesDynamic Modulus, |E*| (MPa) Actual Values Predicted Values 30 C (4 Hz) 0 1000 2000 3000 4000 5000 6000 WR-F1WR-F2WR-F4WR-F5WR-F6WR-C1WR-C2WR-C3 Whiterock MixturesDynamic Modulus, |E*| (MPa) Actual Values Predicted Values 40 C (4 Hz)0 500 1000 1500 2000 2500 3000 WR-F1WR-F2WR-F4WR-F5WR-F6WR-C1WR-C2WR-C3 Whiterock MixturesDynamic Modulus, |E*| (MPa) Actual Values Predicted Values Figure 4-27. Measured vs. predicted dynamic modulus values for Whiterock limestone mixtures: at testing frequency of 4 Hz. A) Testing temperature is 10 C, B) 30 C C) 40 C C B A

PAGE 83

68 0 1000 2000 3000 4000 5000 6000 0100020003000400050006000 Predicted Dynamic Modulus, |E*| (MPa)Measuredl Dynamic Modulus, |E*| (MPa) FAA Project Granite WR Figure 4-28. Measured vs. predicted dynami c modulus for fine aggregate angularity mixtures (FAA), Superpave project mixt ures (Project), Granite mixtures (Granite), and Whiterock mixtures (WR) at a test temperature of 40 C and a testing frequency of 4 Hz. The procedure developed by Pellinen and Witczak (2002) for obtaining predicted master curves was used for all mixtures tested at more than two temperatures. The results showed that further testing at higher and lower temperatures would help in better defining the tails of the predicted master curves. Finally, the predictive regression equation developed by Witzcak et al. (2002) was used to predict dynamic modulus values for mo st of the mixtures tested. The results showed that dynamic modulus predictions using DSR-based viscosity measurements result in conservative predictions of the dyna mic modulus. Therefore, it is recommended that viscosity input values fo r the predictive equation be obtained from the DSR test, in

PAGE 84

69 lieu of the Brookfield Rotational Viscometer Test, or published Mix/Laydown viscosities by Witzcak and Fonseca (1996). The resu lts also showed that dynamic modulus predictions at higher temperatur es generally are closer to th e line of equity for all three cases than the predictions at lower temperatures This is likely the result of the much of the database used to develop the predictive equation being biased toward mixtures tested at higher temperatures. Finally, a comparison was performed betw een measured vs. predicted dynamic modulus at 40 C for the fo llowing mixture categories: Fine Aggregate Angularit y Mixtures (“FAA”), Superpave Project Mixtures (“Project”), Granite Mixtures (“Granite”), and Whiterock Mixtures (“WR”). Most of the mixture groups scatter around the line of unity, w ith the exception of the Georgia Granite mixtures, which land be low the line of unity. Since the testing protocol for all mixtures was the same, the asphalt used was the same, and these mixtures were designed to be volumetrically similar to the Whiterock oolitic limestone mixtures (WR-C1, WR-C2, WR-C3, WR-F1, WR-F2, and WR-F3) it is likely that this difference has to do with the aggregate type. This warrants further study through more detailed testing of mixtures of different mineral origin.

PAGE 85

70 CHAPTER 5 EVALUATION OF GRDATION EFFECTS Introduction The packing of particulate matter into a c onfined volume has long been of interest to mix designers. In the 1930’s, Nijboer (1948) investigated the effect s of particle size distribution using aggregate pa rticles. He found that a gradation plotted on a log-log graph as a straight line with a slope of 0.45 produced the densest packing. He showed it to be the case for both crushed and uncrushe d aggregates. In 1962, Goode and Lufsey (1962) published the results of studies they pe rformed at the Bureau of Public Works. They performed an experiment to confirm Nijboer’s findings and then investigated further to determine the packing of simulated gradations that might be actually used in road construction. As a result of their st udies, they developed a specialized graph in which the vertical axis is th e percent passing a sieve size a nd the horizontal axis is the sieve opening raised to the 0.45 power. To reduce confusion, the horizontal axis does not contain the actual calculated numbers, but inst ead has marks that indicate different size sieves. This specializ ed graph became known as the 0.45 power chart. In 1992, Huber and Shuler (1992) investigated the size distribution of par ticles that gives the densest packing. They determined that a gradation drawn on a 0.45 power char t as a straight line from the origin to the aggregate nominal maximum size produced the densest packing. In 2001, Vavrik et al. (2001) presented the Bail ey method of gradation analysis. Bailey method takes into consideration the packing and aggregate interlock characteristics of

PAGE 86

71 individual aggregates and pr ovides criteria that can be used to adjust the packing characteristics of a blend of materials. Finally, in 2002 Ruth et al. (2002) pr ovided an experience-based methodology for the assessment of potential problems associ ated with aggregate gradation in the performance of asphalt pavements. Th e method presented introduced aggregate gradation factors based on power law regression slopes combined with either the percent passing the 4.75-mm or 2.36-mm si eves that were used to characterize ten different coarseand fine-graded aggregate gradations These gradation factors were used to develop relationships with surface area, tens ile strength, fracture energy, and failure strain. In the following, the gradation factors proposed by Ruth et al. (2002) will be obtained for 13 mixtures. These mixtures include the VMA mixtures described in Chapter 3 (F1, F2, F4, F5, F6, C1, C2, C3), and the Superpave Monitoring Project mixtures listed in Chapter 3 (P1, P2, P3, P5 P7). A relationship between the power law gradation factors and the dynami c modulus will be explored through a correlation study. Based on the findings from the correlation study, tentative gradation factor values for optimizing mixtures for high dynamic modul us values will be presented. The Evaluation of the Effects of Agg regate Gradations on Dynamic Modulus Description of power law relationship Following the procedure developed by Ruth Roque, and Nukunya (2002), the first step in the evaluation of gradation effects wa s to fit a power law model to the gradation curve for each mixture. Power law constants (aca, afa) and exponents (nca, nfa) for the coarse and fine aggregate por tions of these mixtures we re established by regression analyses. The format of the power law e quations used in this investigation was,

PAGE 87

72CAn CA CAd a P (Eq. 5-1) and FAn FA FAd a P (Eq. 5-2) Where PCA or PFA = percent of material by weight passing a given sieve having opening of width d, aca = constant (intercept) for the coarse aggregate, aFA = constant (intercept) for the fine aggregate, d = sieve opening width, mm, nCA = slope (exponent) for the coarse aggregate, nFA = slope (exponent) for the fine aggregate. The method used for determining the “break” be tween coarse and fine aggregate is based on the Bailey method (Vavrik et al., 2001). Th e primary control sieve defining the break between fine and coarse aggregate in the mix is determined as follows to find the closest sieve size: PCS = NMPS x 0.22 (Eq. 5-3) Where PCS = Primary control sieve for the overall blend (i.e., division between coarse and fine aggregate), NMPS = Nominal maximum particle size for the overall ble nd as defined in Superpave, which is one sieve larger than the first sieve that retains more than 10%. The 0.22 value used in the equation was dete rmined empirically, as discussed by Vavrik et al. (2002). For example, for a 12.5mm nominal maximum size mix, the primary control sieve is 2.36 mm (NMPS x 0.22 = 2.750), whereas for a 19.0-mm nominal maximum size mix, the primary control sieve is 4.75 (NMPS x 0.22 = 4.180). Table 5-1 presents the power law coefficien ts for the fine and the coarse aggregate portions of the mixtures studied. Generally, the R2 values obtained indicate a fairly good

PAGE 88

73 power law fit to the existing gradation curves (R2 greater than 0.88 for all cases). A preliminary observation of the re sults in Table 5.1 shows that nfa > nca for “Fine–Graded” mixtures, and nca > nfa for “Coarse–Graded” mixtures. Table 5-1. Power regression constants and dynamic modulus for all mixtures Coarse Aggregate Portion Fine Aggregate Portion Mixture Dynamic Modulus, |E*| at 1 Hz and 40C aca nca R2 afa nfa R2 F1 850 39.445 0.348 0.996 31.196 0.667 0.988 F2 1076 31.469 0.410 0.993 29.525 0.588 0.989 F4 1044 39.445 0.348 0.996 35.612 0.530 0.986 F5 727 37.017 0.366 0.972 28.719 0.612 0.978 F6 880 31.519 0.448 0.996 29.564 0.586 0.989 C1 526 17.948 0.734 0.887 19.852 0.534 0.988 C2 759 16.644 0.667 0.965 18.763 0.527 0.998 C3 801 20.964 0.644 0.883 22.984 0.498 0.998 P1 524 25.295 0.593 0.999 24.489 0.624 0.997 P2 607 13.074 0.834 0.989 19.921 0.509 0.975 P3 459 24.33 0.571 0.972 22.523 0.698 0.989 P5 638 23.739 0.625 0.992 26.238 0.591 0.963 P7 550 40.857 0.339 0.999 36.146 0.899 0.985 Correlation Study between Power Law Gr adation Factors and Dynamic Modulus In order to identify a potential relatio nship between the power law gradation parameters in Table 5-1 and dynamic m odulus, a zero-order correlation study was performed using the power law coefficients li sted in Table 5-1 and the dynamic modulus at 40C and 1 Hz frequency. The dynamic modu lus at 40C was selected in lieu of lower testing temperature results to better capture any potential relationshi p with the gradation characteristics of the mixtures tested. The term “zero-order” means that no controls are imposed on the correlation study.

PAGE 89

74 Table 5-2 shows the results of the zero-ord er correlation study. Strong correlations exist between aca and nca (R = -0.98) and afa and nfa (R = 0.543), respectively. Based on the strong correlation observed between the para meters studied, it was decided to focus the study on only two out of the four power law parameters, namely nca and nfa. The results show a weak nega tive correlati on between nca, nfa, and |E40*|. Further testing for statistical significance revealed no statisti cally significant correlations between nca, nfa, and |E40*|. Table 5-2. Results of correlation study between power law parameters and dynamic modulus at 40C and 1 Hz frequency Power Law Regression Coefficients |E40*|1 aca nca afa nfa |E40*|1 1.000 0.414 -0.498 0.464 -0.348 aca 0.414 1. 000 -0.980 0.948 0.578 nca -0.498 -0.98 1.000 -0.908 -0.536 afa 0.464 0.948 -0.908 1.000 0.543 nfa -0.348 0.578 -0.536 0.543 1.000 1Denotes the dynamic modulus at 1 Hz frequency and 40C. In order to further evaluate the relationship between nca, nfa and |E40*|, a bivariate partial correlation study was perf ormed. In here, a bivariat e partial corre lation denotes the correlation obtained between two variables, while controlling for a third variable. For example, r12.3 denotes the correlation of variables 1 and 2, while controlling for variable 3. In most cases, a partial correlation of the general form r12.3 will turn out to be smaller than the original correlation r12. In the rare cases where it tu rns out to be larger, the third variable, 3, is considered to be a suppressor variable, based on the assumption that it is suppressing the larger correlati on that would appear between 1 and 2 if the effects of variable 3 were held constant. Table 5-3 presents the results of the biva riate partial correlation study, in which p denotes the level of significance of a potential correlation. Hence, p < 0.01 means that

PAGE 90

75 the probability of not having a significant re lationship in the popul ation is less than 1 percent. The results revealed a statistically significant negative correlation (r = -0.8654, p =0 .0008) between nca and |E40*|, when controlling for nfa, implying that a high nca results in a low |E40*|. Table 5-3. Partial correlation analysis for nca and |E40*| when controlling for nfa nca N r (Correlation Coefficient) |E40*| 13 -0.8654** p <0.05, ** p <0.01 Category Analysis of Power Law Parameters In order to further evaluate the rela tionship between power law parameters (nca and nfa) and the dynamic modulus, four simplified cat egories of power law parameters were hypothesized. The four hypothesized categor ies to be tested are as follows: Category 1 – [Low nca (smaller than 0.50) and Low nfa (smaller than 0.59)]. Category 2 – [Low nca (smaller than 0.50) and High nfa (greater than 0.59)]. Category 3 – [High nca (greater than 0.50) and Low nfa (smaller than 0.59)]. Category 4 – [High nca (greater than 0.50) and High nfa (greater than 0.59)]. Table 5-4 shows the Mean a nd Standard Deviation of |E40*| for the four different categories studied. Since the unde rlying power law parameters nfa and nca are slightly correlated, a discriminate category analysis is not appropriate. Rather, a one-way analysis of variance (ANOVA) is used to uncove r the effects of the categorical variables (i.e., four different categories) on the interval dependent variable (i.e., |E40*|). According to Table 5-5, the results ar e statistically significant at an alpha level of 0.01 ( F (3,9) = 7.64, p = 0.008). Since the results showed a si gnificant omnibus F, a post-hoc analysis

PAGE 91

76 using a Tukey test was performed to evaluate whether differences between any two pairs of category means were significant. Tabl e 5.6 displays the means for groups in homogeneous subsets. According to Table 56, only the dynamic modulus values for the first category (combination of Low nca and Low nfa) are significantly different from the other category groups at an alpha le vel = .05. This means that if nca is less than 0.5 and nfa is less than 0.59, a “high” dynamic m odulus will likely be obtained for a given aggregate type and asphalt grade. Table 5-4. Mean and standard deviation of |E40*| for the four di fferent categories Category Groups N Mean Std. Deviation Low nca + Low nfa 3 1000.00 105.14 Low nca + High nfa 3 709.00 150.80 High nca + Low nfa 4 673.25 128.76 High nca + High nfa 3 540.33 90.61 Total 13 726.23 198.83 Table 5-5. One-Way analysis of variance (ANOVA) of |E40*| (total N=13) Sum of Squares df Mean Square F Sig. Between Groups 340640.89 3 113546.96 7.64 0.008 Within Groups 133763.41 9 14862.60 Total 474404.30 12 Table 5-6. Post-Hoc analysis for hom ogeneous subsets of hypothesized categories Subset for alpha = 0.05 Group N Statistically Significant Not statistically Significant Low nca + Low nfa 3 1000.00 Low nca + High nfa 3 709.00 High nca + Low nfa 4 673.25 High nca + High nfa 3 540.33 Category Analysis of Power Law Parameters for Coarse and Fine Graded Mixtures The mixtures in Table 5-1 were divided into two subsets, depending on whether the mixtures were coarse-graded or fine-graded, according to the S uperpave mixture design

PAGE 92

77 system. A mixture is considered to be co arse-graded if the grad ation band passes below the restricted zone. Conversely, a gradati on band for a fine-graded mixture passes above the restricted zone. Hence, the two different graded subsets to be tested are as follows: Coarse-Graded Mixtures, Fine-Graded Mixtures. Tables 5-7 and 5-8 list the coarseand fine-graded mixt ures and their categories, respectively. Table 5-7. Mixtures in course-graded category Coarse Aggregate Portion Fine Aggregate Portion Mixture Dynamic Modulus, |E*| at 1 Hz and 40C Classification Category nca nfa C1 526 Category 3 0.734 0.534 C2 759 Category 3 0.667 0.527 C3 801 Category 3 0.644 0.498 P1 524 Category 4 0.593 0.624 P2 607 Category 3 0.834 0.509 P3 459 Category 4 0.571 0.698 P5 638 Category 4 0.625 0.591 Table 5-8. Mixtures in fine-graded category Coarse Aggregate Portion Fine Aggregate Portion Mixture Dynamic Modulus, |E*| at 1 Hz and 40C Classification Category nca nfa F1 850 Category 2 0.348 0.667 F2 1076 Category 1 0.410 0.588 F4 1044 Category 1 0.348 0.530 F5 727 Category 2 0.366 0.612 F6 880 Category 1 0.448 0.586 P7 550 Category 2 0.339 0.899 Table 5-9 shows the correlation analysis re sults for the Course Graded mixtures. A zero-order bivariate correlat ion study found no statistical ly significant relationship between nca, nfa, and |E40*|. However, considering the sma ll sample size (N = 7), Table 5-9 shows that a strong negative correlation exists between nfa and |E40*|.

PAGE 93

78 Table 5-9. Zero-Order correlation analysis for nca, nfa, and |E40*| for course graded mixtures (N = 7) nca nfa E40 nca 1 -0.7120 -0.1350 nfa 1 -0.7280 E40 1 p <0.05, ** p <0.01 Table 5-10 shows the results from the co rrelation analysis for the Fine Graded mixtures. The zero-order bivariate corre lation study found a stat istically significant relationship between nfa, and |E40*|. In addition, consideri ng the small sample size (N = 6), Table 5-10 also shows that a strong negative relationship appears between nfa and nca. Table 5-10. Zero-Order correlation analysis for nca, nfa, and |E40*| for fine graded (N=6) nca nfa |E40*| nca 1 -0.4472 -0.3928 nfa 1 -0.8447* |E40*| 1 p <0.05, ** p <0.01 Summary and Conclusions The results of the combined analysis of coarse-and fine graded mixtures together showed a low nfa combined with a low nca results in a “high” dynamic modulus value. Importantly, the nfa variable was identified as a suppressor variable on nca, meaning that a low nca by itself was not sufficient in guarant eeing a high dynamic modulus value. The results of the separate analyses on coarseand fine-grade d mixtures showed that a negative correlation was observed between nfa and the dynamic modulus at 40C. Again, this means that the lower the nfa value, the higher the dynamic modulus. Since nfa is a measure of the rate of change in the gr adation band on the fine side of the gradation,

PAGE 94

79 the results indicate that a gradual or a slow rate of change of th e gradation band on the fine side results in a high er dynamic modulus value. Observation of the coarse-graded mixtures in Table 5-7 shows that all the coarsegraded mixtures are either in category 3 (high nca and low nfa) or in category 4 (high nca and high nfa). The overall high nca values are likely due to the nature of coarse-graded Superpave mixtures, where the gradation ba nd starts above the maximum density line, but has to cross the maximum density line in order to pass below the restricted zone. Hence, for coarse-graded mixtures the rate of change in the slope of the gradation band on the coarse side is fairly high, translating into a relatively high nca value. Similarly, all of the fine-graded mixtures in Table 5-8 are in category 1 (low nca and low nfa) or category 2 (low nca and high nfa). Hence, since thei r gradation bands do not typically cross the maximum density line, the ra te of change in the slope of the gradation bands for fine-graded mixtures on the fine and coarse sides tends to be lower than for the coarse-graded mixtures. In summary, a relationship between a low nfa and a high dynamic modulus (at 40C) has been identified. This means that a slow rate of change in the gradation band on the fine side of the gradation is related to a high dynamic modulus value. Gap-grading the mixture on the fine side wi ll generally increase the rate of change in the gradation band, and thus nfa, and will lead to a lower dynamic modulus.

PAGE 95

80 CHAPTER 6 EVALUATION OF POTENTIAL CORELATION BETWEEN COMPLEX MODULUS PARAMETERS AND RUTTING RESISTANCE OF MIXTURES Background In this chapter, potential relationships are evaluated between complex modulus parameters and other common measures of the rutting potential of mixtures. In particular, the complex modulus parameters are compared against asphalt pavement analyzer (APA) rut depth results and creep test results from static unconfined compressive creep testing. First, the APA test procedures and test results are discussed, followed by a description of the static creep te st procedure used and presentation of creep test results. Then, comparisons are made between dynamic modulus and phase angle results presented in Chapter 6 to APA rut depth measurements and static creep testing results. Asphalt Pavement Analyzer Test Procedure and Test Results Asphalt Pavement Analyzer (APA) equipm ent is designed to test the rutting susceptibility or rutting resist ance of hot mix asphalt. With APA, rut performance testing is performed by means of a constant load a pplied repeatedly through pressurized hoses to a compacted test specimen. The test specime n for this research is a 150-mm diameter by 75-mm thick cylindrical specimen. The procedure for sample preparation and testing is as follows: 4500 g samples of the aggregate are batched in accordance with the required job mix formula. The aggregate and asphalt binder are preheated separately to 300 F for about three hours, after which they are mixed until the aggregates are thoroughly coated with the bi nder; amount of binder used is pre-determined to

PAGE 96

81 produce an optimum Hot Mix Asphalt (HMA ) using Superpave Volumetric Mix Design procedures. The mixture is then subjected to two hours of short-term oven aging at 275 F in accordance with AASHTO PP2. The sample is compacted, at the above temperature, to contain 7.00.5% air voids in the Servopac Superpave gyratory compact or. The compaction is done by first determining the compaction height needed to obtain the requi red air void content from the compaction results obtained for the mixture design. The mix is then compacted o he determined height. The specimen was allowed to cool at room temperature (approximately 25 C) for a minimum of 24 hours. After the cooling pr ocess, the Bulk Specific Gravity of the specimen is determined in accordance with AASHTO T 166 or ASTM D 2726. The maximum specific gravity of the mixture was determined in accordance with ASTM D2041 (AASHTO T 209). Then, the air void content of the specimen was determined in accordance with ASTM D 3203 (AASHTO T 269) to check if the target air void content is achieved. The specimen is trimmed to a height of 75-mm and allowed to air dry for about 48 hours. The specimen was preheated in the APA ch amber to a temperature of 60 C (140 F) for a minimum of 6 hours but not more th an 24 hours before the test is run. The hose pressure gage read ing was set to 1005psi. The load cylindrical pressure reading fo r each wheel was set to obtain a load of 1005lbs. Secure the preheated, molded specimen in the APA, close the chamber doors and allow 10 minutes for the temperature to stabilize before starting the test. 25 wheel strokes were applied to seat th e specimen before initial measurements were taken. The mold and the specimen are securely positioned in the APA, the chamber doors are closed and 10 minutes are allowed for the temperature to stabilize. Restart the APA and continue ru t testing, now for 8000 cycles. Table 6-1 lists the resulti ng APA rut depth measurements, along with the dynamic modulus values obtained at 40 C at te sting frequencies of 1 Hz and 4 Hz.

PAGE 97

82 Table 6-1. Dynamic modul us (|E*|), phase angle ( ), and asphalt pavement analyzer rut depth measurements from mi xture testing at 40 C. Phase Angle ( ) Results (Degrees) Dynamic Modulus (|E*|) Results (MPa) Frequency Mixture 1 Hz 4 Hz 1 Hz 4 Hz Asphalt Pavement Analyzer Rut Depth (mm) Georgia Granite Mixtures GAC1 27.11 32.77 317.12 475.14 7.1 GAC2 26.67 32.14 535.77 787.74 7.1 GAC3 37.05 42.79 530.76 757.09 5.9 GAF1 27.25 32.35 401.02 635.50 5.1 GAF2 31.63 38.32 535.97 905.80 5.1 GAF3 32.91 38.87 377.70 614.91 4.4 Whiterock Mixtures (Oolitic Limestone) WRC1 29.02 30.42 526.05 898.81 5.4 WRC2 32.19 32.15 759.48 1368.38 4.6 WRC3 32.84 32.25 801.08 1470.36 4.6 WRF1 29.38 32.11 849.60 1273.70 5.1 WRF2 31.21 33.67 1076.161610.34 5.2 WRF4 31.70 34.00 1044.191584.81 4.3 WRF5 30.05 33.13 726.94 1146.45 7.1 WRF6 31.92 33.59 879.93 1374.06 4.8 Mixtures From Fine Ag gregate Angularity Study RBC 27.38 31.09 770.75 1175.36 7.3 RBF 25.90 28.66 954.17 1415.66 8.5 CALC 30.53 34.24 1182.661792.49 6.9 CALF 26.97 33.92 1184.061779.33 6.2 CGC 31.40 31.10 923.08 1363.60 4.3 CGF 25.70 30.95 1217.771777.24 4.6 CHC 30.45 33.33 744.73 1166.04 11.9 CHF 35.50 35.40 756.82 1073.82 13.9 Superpave Project Mixtures P1 23.62 22.99 523.74 807.66 7.1 P2 28.33 32.46 606.97 953.37 6.6 P3 30.63 34.67 458.87 655.21 3.2 P7 26.99 32.15 549.95 796.88 4.3 Heavy Vehicle Simulator Mixtures HVS67-22 29.01 32.96 620.85 925.02 7.5 HVS76-22 29.24 31.81 646.38 967.52 6.5 Static Creep Test Results Once the complex modulus test was complete d, a static creep test was performed on the same samples tested in the complex modulus test. In the static creep test, a

PAGE 98

83 constant vertical load is applied to an unconfined (no lateral c onfinement pressures) HMA specimen, and the resulting time-depende nt vertical deformation is measured. Figure 7-1 shows a qualitative diagram of the vertical stress and total vertical deformation during a creep test. The same LVDT’s that were used for the complex modulus test were used in the static creep test to measure vertic al deformation. The creep compliance from creep test at a higher temperature may be an indicator of the rutting potential of the mix. The compliance is calculated from this test by dividing the strain by the applied stress at a specified time in seconds. Figure 6-1. Qualitative diagram of the stress and total deformation during the creep test. The following equation is used to calculate the creep compliance, D(t) = t D(t) = Creep compliance at the test te mperature T and time of loading, t. t= Strain at time t (inch/inch), and applied stress, psi.

PAGE 99

84 The static creep test was run for a tota l 1000 seconds. The test load was chosen such that it produced a horizontal deform ation of 150 – 200 micro-inches after 30 seconds of loading. The test te mperature was taken to be 40 C. Finally, the measured creep compliance D( t) can be represen ted using the power function equation (6-1). D(t) = D0 + D1 tm (Eq. 6-1) Where D0, D1, and m are parameters obtained from creep tests. In accordance with the findings from the evaluation of creep para meters from the Superpave Indirect Tensile Test (Chapter 9) the value of D0 is taken as 1/|E*|. The dynamic modulus |E*| is obtained from the 10 Hz frequency test, to minimize vari ability of the results. Table 6-2 lists the static creep test results, along with the power law parameters D1 and m. Table 6-2. Average static creep testi ng results for test temperature of 40C. Creep Compliance Power Law Parameters Mixture D (1000 seconds) (1/MPa) (x1000) D1 (1/Mpa) m-value Georgia Granite Mixtures GAC1 19.63 8.93E-03 0.114 GAC2 17.02 5.01E-03 0.177 GAC3 15.97 6.83E-03 0.123 GAF1 17.79 5.31E-03 0.175 GAF2 9.52 3.45E-03 0.147 GAF3 11.64 3.50E-03 0.174 Whiterock Mixtures (Oolitic Limestone) WRC1 1.57 4.14E-04 0.193 WRC2 1.23 3.78E-04 0.171 WRC3 1.96 6.27E-03 0.164 D (1000 seconds) (1/Mpa) (x1000) D1 (1/Mpa) m-value WRF1 26.03 8.50E-03 0.162

PAGE 100

85 Table 6-2. Continued Mixture Creep Compliance Power Law Parameters WRF2 3.95 1.29E-03 0.162 WRF4 4.86 1.23E-03 0.199 WRF5 6.45 1.61E-03 0.201 WRF6 4.52 1.56E-03 0.154 Mixtures From Fine Ag gregate Angularity Study RBC 16.49 6.40E-03 0.137 RBF 10.39 3.30E-03 0.166 CALC 3.83 5.50E-04 0.281 CALF 1.91 3.50E-03 0.128 CGF 10.76 5.00E-03 0.111 CHC 1.74 3.30E-04 0.330 CHF 15.97 4.90E-03 0.171 Superpave Project Mixtures P1 1.73 5.85E-04 0.157 P2 5.75 1.57E-03 0.188 P3 25.43 3.05E-03 0.307 P5 13.25 5.35E-03 0.155 P7 1.73 5.55E-03 0.126 Heavy Vehicle Simulator Mixtures HVS67-22 24.17 9.00E-03 0.143 HVS76-22 15.57 6.00E-03 0.138 Evaluation of Dynamic Test res ults for HMA Rutting Resistance In this section, the dynami c modulus measurements are compared to the rutting performance of the various mixtures as measured by the APA rut depths. Rutting resistance is evaluated at the high temperature of 40oC at the frequencies of 1 Hz, and 4 Hz. Berthelot et al. (1996), proposed the following ranges of testing frequencies for simulating various highway speeds, 0.02–0.2 Hz to simulate parking, 0.2–2.0 Hz to simulate street and intersection speed, 2.0–20 Hz to simulate highway speed. However, Shenoy and Romero (2002) and Witczak et al. (2002), used a testing frequency of 5.0 Hz as representative of tra ffic speed that will trigger pavement rutting in the evaluation of the SuperpaveTM simple performance tests. Test results were therefore

PAGE 101

86 plotted for the lower frequencies of 1.0 Hz a nd 4 Hz. Figure 6-2 depi cts the results. No discernable correlation appears to exist betw een the dynamic modulus and APA rut depth Figure 6-2. Dynamic modulus at testing frequencies of 1 Hz and 4 Hz versus APA rut depth measurements (Test temperature for dynamic modulus test and APA test is 40 C). Figure 6-3. Dynamic modulus at testing frequencies of 1 Hz and 4 Hz versus APA rut depth measurements for coarseand fi ne-graded mixtures (Test temperature for dynamic modulus test and APA test is 40 C). measurements. To check if the scatter in Figur e 6-2 might be due to gradation effects, the coarseand fine-graded mixtures were separa ted into two different categories and plotted 0 2 4 6 8 10 12 14 16 0 200 400 600 800 1000 1200 140 0 1600 1800 2000 Dynamic Modulus at 1 Hz |E*| (MPa)APA Rut Depth (mm) 1 Hz 4 Hz

PAGE 102

87 in Figures 6-3 for a testing frequency of 1 Hz Again, the results in Figure 6-3 show no relationship between the dynamic modulus a nd the rut resistance for both fineand coarse-graded mixtures at the high temperature of 40oC and low frequency of 1 Hz at which pavement rutting is most likely to occur. These results are similar to those presented by Brown et al. (2004), in an eval uation of the rutting performance on the 2000 NCAT test track sections. Figure 6.4 shows the results obtained by Brown et al. (2004), in which the relationship between the dynamic m odulus at 10 Hz and te st track rutting (in mm) is evaluated. No discernable relati onship between dynamic modulus and test track rutting is detectable. Figure 6-5 presents a plot of the phase angle at 1 Hz testing frequency and APA rut depth. The results again show no correlation. Figure 6-4. Dynamic modulus, |E*| versus test track rut ting (in mm) for the 2000 NCAT test track sections. The viscous stiffness based on the Maxw ell model (Ullidtz (1987)), |E*|/sin at 40oC and 1 Hz frequency was plotted agains t the APA rut depth to observe any

PAGE 103

88 Figure 6-5. Phase angle at a testing frequency of 1 Hz versus APA rut depth measurements (Test temperature for dyna mic modulus test and APA test is 40 C). relationship of this parameter with the rutti ng resistance of the mixtures tested. Figure 6-6 shows the results. Again, no relationship between |E*|/sin and APA rut depth measurements can be detected. Figure 6. 7 shows the corresponding results obtained by Brown et al. (2004), in which the relationship between the |E*|/sin at 10 Hz and test Figure 6-6. Plot of E*/Sin at 40oC and 1 Hz. versus the APA rut depths for all mixtures 0 2 4 6 8 10 12 14 16 20.00 22.00 24.00 26.00 28.00 30.00 32.00 34.00 36.00 38.00 40.00 Phase Angle ( ) at 1 Hz (Degrees)APA Rut Depth (mm) 0 2 4 6 8 10 12 14 16 0.00 500.00 1000.00 1500.00 2000.00 2500.00 3000.00 |E*|/sin( ) (MPa)APA Rut Depth (mm)

PAGE 104

89 track rutting (in mm) is evaluated. Agai n, no discernable relationship between dynamic modulus and test track rutting is detectable. Figure 6-7. |E*|/sin versus Test Track Rutting (in mm) for the 2000 NCAT test track sections. Finally, Figure 6.8shows a plot of the loss modulus, |E*|sin at 40oC and 1 Hz frequency versus the APA rut depth. Agai n, there was no correlation between this parameter and the rutting resistance of th e mixtures as measured with the APA. In summary, no relationship was found between the dynamic complex modulus parameters and the APA rut depth measurements. Furthermore, research from the NCAT test track sections shows no relations hip between the dynamic complex modulus parameters and track rut depths. Evaluation of Static Creep Parameters Figure 6-9 shows a weak relationship be tween the dynamic modulus at a 1 Hz testing frequency and the static creep complia nce at 1000 seconds. Similarly, Figures 610 and 6-11 show a weak trend between th e dynamic modulus and the creep compliance

PAGE 105

90 parameters D1 and m. As expected, the higher th e dynamic modulus, the lower the creep compliance. Interestingly, the power law parameter D1 exhibits the same trend with Figure 6-8. Pl ot of |E*|sin at 40oC and 1 Hz versus APA rut depth. higher modulus as the creep compliance, wher eas the m-value increases very slightly with increasing modulus values. Unfortuna tely, the relationship between the dynamic modulus and static creep properties is too weak for use in any predictive type of a relationship. Figure 6-12 shows that there is no discerna ble relationship between the phase angle and the creep compliance at 1000 seconds. However, Figures 6-13 and 6-14 show a weak relationship between the phase a ngle and the power law parameters D1 and m. The power law parameter D1 shows a slight decrease with in creasing phase angle, whereas the m-value shows a slight increase. Again, unfor tunately the observed trends are too weak to infer anything about the physical behavior of the mixtures. In summary, the dynamic modulus exhib its a weak relationship with creep compliance. Unfortunately, the observed relatio nship is too weak for use in a predictive 0 2 4 6 8 10 12 14 16 0.00 100.00 200.00 300.00 400.00 500.00 600.00 700.00 |E*|sin( ) (MPa)APA Rut Depth (mm)

PAGE 106

91 relationship. Similarly, no predictive relationship could be obtained from the phase angle. Figure 6-9. Relationship between dynamic m odulus at 1 Hz frequency and static creep compliance after 1000 seconds. Figure 6-10. Relationship between dynamic modulus at 1 Hz frequency and the power law creep compliance parameter D1.

PAGE 107

92 Figure 6-11. Relationship between dynamic modulus at 1 Hz frequency and power law m-value parameter. Figure 6-12. Relationship between phase a ngle at 1 Hz frequency and static creep compliance after 1000 seconds.

PAGE 108

93 Figure 6-13. Relationship between phase a ngle at 1 Hz frequency and the power law creep compliance parameter D1. Figure 6-14. Relationship between phase a ngle at 1 Hz frequency and power law m-value parameter. Effects of Binder Type on Relationship between Dynamic Modulus and Rutting Potential of Mixtures Witczak et al. (2002) presented a comp rehensive evaluation of any potential relationships between the dynamic modulus a nd the rutting performance of mixtures. The findings showed that for a given aggreg ate structure, but di fferent grades of unmodified binders, the dynamic modulus a ppears to relate reasonably well to the y = 0.0026x + 0.0998 R 2 = 0.0218 0.0 0.1 0.2 0.3 0.4 0.5 20.00 22.00 24.00 26.00 28.00 30.00 32.00 34.00 36.00 38.00 Phase Angle ( ) at 1 Hz, |E*| (MPa)Power Law m-Value

PAGE 109

94 observed rutting performance of mixtures. This means that the dynamic modulus is sensitive to the binder viscosity of mixtures. Unfortunately, the work presented in this report and the results from the NCAT test track sections (Bro wn et al., 2004) show that when the aggregate structure in varied, no relationship can be found between the dynamic modulus and the rutting potential of mixtures. Summary and Conclusions In this chapter, the dynamic modulus a nd phase angle are compared against asphalt pavement analyzer (APA) rut depth results a nd static creep test results from unconfined axial compressive creep testing. The result s showed that no predic tive relationship could be identified between the dynamic modulus and phase angle on one hand and the APA rut depth on the other hand. Similarly as expected, a weak relationship was observed between the dynamic modulus and the creep co mpliance. Unfortunately, the quality of the regression relationship was marginal at best, precluding the development of a predictive relationship betw een the dynamic modulus and creep compliance. Importantly, the mixtures used were of varyi ng aggregate structure a nd aggregate types. Previous work by Witczak et al. (2002) has shown that for a given aggregate structure, but different grades of unmodifi ed binders, the dynamic modulus appears to relate reasonably well to the observed rutting performance of mixtures. This means that the dynamic modulus is sensitive to the binder viscosity of mixtures. Unfortunately, the work presented in this report and the results from the NCAT test track sections (Brown, et al., 2004) show that when the aggregate structure in varied, no relationship can be found between the dynamic modulus and the rutting potential of mixtures. The AASHTO 2002 Flexible Design Proce dure uses the dynamic modulus as an input into the rutting predicti on relationship used for thickness design. The relationship

PAGE 110

95 between dynamic modulus and the rutting resist ance of the flexible pavement layer is based on traditional mechanistic-empirical pavement design considerations. The permanent deformation with the number of applied wheel loads is assumed to be inversely related to the dynamic modulus. For a given number of wheel loads, as the dynamic modulus increases, the predicted perman ent strains in the pavement decrease. Importantly, the mechanistic-empirical pavement rutting performance relationship used in the AASHTO 2002 design procedure does not account for the potential for instability rutting. Rather, the dynamic modulus in the AASHTO 2002 framework is simply used as a measurement of stiffness. The research presented in this study shows that the dynamic modulus does not relate to the mixture properties th at might be control instability rutting, as experienced in the AP A and the NCAT test track for the mixtures with observed rutting (Brown, 2004). In summary, there appears to be no other off the shelf material property available right now to replace the use of the dynamic modulus as a m easure of stiffness in the AASHTO 2002 Flexible Pavement Design Procedure. Based on the results from this research project and other similar effort s by NCAT (Brown, 2004), the dynamic modulus should be used with caution to predict the rutting performance of mixtures.

PAGE 111

APPENDIX A ELASTICITY MODULUS AND PHASE ANGLE SUMMARY FOR SAMPLE GRADATIONS

PAGE 112

97 Figure A-1. |E*| vs. for coarse Whiterock gradations at 10, 30 and 40 C, A) C1 gradation, B) C2 gradation, C) C3 gradation C B A Average Values for C10 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 1 10 100 E* 10 30 40 Average Values for C20 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 1 10 100 E* 10 30 40 Average Values for C30 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 1 10 100 E* 10 30 40

PAGE 113

98 Figure A-2. vs. for coarse Whiterock gradations at 10, 30 and 40 C. A) C1 gradation B) C2 gradation C) C3 gradation C B A Average Values for C10 5 10 15 20 25 30 35 40 1 10 100 10 30 40 Average Values for C20 5 10 15 20 25 30 35 40 1 10 100 10 30 40 Average Values for C30 5 10 15 20 25 30 35 40 1 10 100 10 30 40

PAGE 114

99 Figure A-3. |E*| vs. for fine Whiterock gradations at 10, 30 and 40 C, A) F1 gradation, B) F2 gradation, C) F4 gradation, D) F5 gradation, E) F6 gradation C B A Average Values for F10 1000 2000 3000 4000 5000 6000 7000 8000 9000 1 10 100 E* 10 30 40 Average Values for F20 2000 4000 6000 8000 10000 12000 14000 1 10 100 E* 10 30 40 Average Values for F40 2000 4000 6000 8000 10000 12000 1 10 100 E* 10 30 40

PAGE 115

100 Figure A-3. Continued F D Average Values for F50 1000 2000 3000 4000 5000 6000 7000 8000 9000 1 10 100 E* 10 30 40 Average Values for F60 1000 2000 3000 4000 5000 6000 7000 8000 1 10 100 E* 10 30 40

PAGE 116

101 Figure A-4. vs. for fine Whiterock gradations at 10, 30 and 40 C. A) F1 gradation B) F2 gradation, C) F4 gradation, D) F5 gradation, E) F6 gradation. Averaeg Values for F10 5 10 15 20 25 30 35 40 45 1 10 100 10 30 40 Average Values for F20 5 10 15 20 25 30 35 40 45 1 10 100 10 30 40 Average Values for F40 5 10 15 20 25 30 35 40 1 10 100 10 30 40 A B C

PAGE 117

102 Figure A-4. Continued Average Values for F50 5 10 15 20 25 30 35 40 45 1 10 100 10 30 40 Average Values for F60 5 10 15 20 25 30 35 40 1 10 100 10 30 40 D E

PAGE 118

APPENDIX B PREDICTED DYNAMIC MODULUS VALUES VS.MEASURED DYNAMIC VALUES

PAGE 119

104 10 C (1 H er t z ) 0 2000 4000 6000 8000 10000 12000 F1F2F4F5F6C1C2C3White Rock Mixtures|E*| (MPa) Actual Values Predicted Values 0 1000 2000 3000 4000 5000 6000 F1F2F4F5F6C1C2C3 White Rock Mixtures|E*| (MPa) Actual Values Predicted Values 0 500 1000 1500 2000 2500 3000 F1F2F4F5F6C1C2C3 White Rock Mixtures|E*| (MPa) Actual Values Predicted Values Figure B-1. Measured test results versus predicted dynami c modulus values for fine gradation Whiterock mixtures at 1 Hertz, A) Comparison at 10 Degrees, B) Comparison at 30 Degrees, C) Comparison at 40 Degrees A B C

PAGE 120

105 10 C (4 Hertz)0 2000 4000 6000 8000 10000 12000 F1F2F4F5F6C1C2C3 White Rock Mixtures|E*| (MPa) Actual Values Predicted Values 30 C (4 Hertz) 0 1000 2000 3000 4000 5000 6000 F1F2F4F5F6C1C2C3 White Rock Mixtures|E*| (MPa) Actual Values Predicted ValuesB 0 500 1000 1500 2000 2500 3000 F1F2F4F5F6C1C2C3 White Rock Mixtures|E*| (MPa) Actual Values Predicted Values Figure B-2. Measured test results versus predicted dynami c modulus values for fine gradation Whiterock mixtures at 4 Hertz, A) Comparison at 10 Degrees, B) Comparison at 30 Degrees, C) Comparison at 40 Degrees A B C

PAGE 121

106 10 C (10 Hertz) 0 2000 4000 6000 8000 10000 12000 F1F2F4F5F6C1C2C3 White Rock Mixtures|E*| (MPa) Actual Values Predicted Values Figure B-3. Measured test results versus predicted dynami c modulus values for fine gradation Whiterock mixtures at 10 Hertz, A) Comparison at 10 Degrees, B) Comparison at 30 Degrees, C) Comparison at 40 Degrees C B A

PAGE 122

107 10 C (16 Hertz) 0 2000 4000 6000 8000 10000 12000 F1F2F4F5F6C1C2C3 White Rock Mixtures|E*| (MPa) Actual Values Predicted Values 30 C (16 Hertz)0 1000 2000 3000 4000 5000 6000F1F2F4F5F6C1C2C3White Rock Mixtures|E*| (MPa) Actual Values Predicted Values 40 C (16 Hertz) 0 500 1000 1500 2000 2500 3000 F1F2F4F5F6C1C2C3White Rock Mixtures|E*| (MPa) Actual Values Predicted Values Figure B-4. Measured test results versus predicted dynami c modulus values for fine gradation Whiterock mixtures at 16 Hertz, A) Comparison at 10 Degrees, B) Comparison at 30 Degrees, C) Comparison at 40 Degrees A B C

PAGE 123

APPENDIX C MEASURED DYNAMIC MODULUS V.S. PREDICTED VALUES FOR DIFFERENT FREQUENCIES

PAGE 124

109 1 HERTZ (Fine Gradation)0 2000 4000 6000 8000 10000 12000 020004000600080001000012000Predicted E* (Mpa)Actual E* (Mpa) 4 HERTZ (Fine Gradation)0 2000 4000 6000 8000 10000 12000 020004000600080001000012000Predicted E* (Mpa)Actual E* (Mpa) Figure C-1. Measured test results versus predicted dynami c modulus values for fine gradation Whiterock mixtures, A) at1 Hert z, B) at 4 Hertz, C) at10 Hertz, D) at16 Hertz A B

PAGE 125

110 10 HERTZ (Fine Gradation)0 2000 4000 6000 8000 10000 12000 020004000600080001000012000Predicted E* (Mpa)Actual E* (Mpa) 16 HERTZ (Fine Gradation)0 2000 4000 6000 8000 10000 12000 020004000600080001000012000Predicted E* (Mpa)Actual E* (Mpa) Figure C-1. Continued C D

PAGE 126

111 1 HERTZ (Coarse Gradation)0 2000 4000 6000 8000 10000 12000 020004000600080001000012000Predicted E* (Mpa)Actual E* (Mpa) 4 HERTZ (Coarse Gradation)0 2000 4000 6000 8000 10000 12000 020004000600080001000012000Predicted E* (Mpa)Actual E* (Mpa) Figure C-2. Measured test results versus predicted dynamic modulus values for Coarse gradation Whiterock mixtures, A) at1 Hert z, B) at 4 Hertz, C) at10 Hertz, D) at16 Hertz A B

PAGE 127

112 10 HERTZ (Coarse Gradation)0 2000 4000 6000 8000 10000 12000 020004000600080001000012000Predicted E* (Mpa)Actual E* (Mpa) 16 HERTZ (Coarse Gradation)0 2000 4000 6000 8000 10000 12000 020004000600080001000012000Predicted E* (Mpa)Actual E* (Mpa) Figure C-2. Continued C D

PAGE 128

113 4 HERTZ (Coarse Gradation)0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 0200040006000800010000 Predicted |E*| (Mpa)Actual |E*| (Mpa) 10 HERTZ (Coarse Gradation)0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 0200040006000800010000 Predicted |E*| (Mpa)Actual |E*| (Mpa) Figure C-3. Measured test results versus predicted dynami c modulus values for coarse gradation Granite mixtures, A) at 4 He rtz, B) at10 Hertz, C) at16 Hertz A B

PAGE 129

114 16 HERTZ (Coarse Gradation)0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 0200040006000800010000 Predicted |E*| (Mpa)Actual |E*| (Mpa) Figure C-3. Continued C

PAGE 130

115 1 HERTZ (Fine Gradation)0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 0200040006000800010000Predicted |E*| (Mpa)Actual |E*| (Mpa) 4 HERTZ (Fine Gradation)0 2000 4000 6000 8000 10000 12000 14000 02000400060008000100001200014000Predicted |E*| (Mpa)Actual |E*| (Mpa) Figure C-4. Measured test re sults versus predicted dynami c modulus values for fine gradation Granite mixtures, A) at1 Hertz, B) at 4 Hertz, C) at10 Hertz, D) at16 Hertz A B

PAGE 131

116 10 HERTZ (Fine Gradation)0 2000 4000 6000 8000 10000 12000 14000 02000400060008000100001200014000Predicted |E*| (Mpa)Actual |E*| (Mpa) 16 HERTZ (Fine Gradation)0 2000 4000 6000 8000 10000 12000 14000 02000400060008000100001200014000Predicted |E*| (Mpa)Actual |E*| (Mpa) Figure C-4. Continued D C

PAGE 132

117 1 HERTZ (Fine Gradation)0 2000 4000 6000 8000 10000 0200040006000800010000Predicted |E*| (Mpa) Actual |E*| (Mpa) 4 HERTZ (Fine Gradation)0 2000 4000 6000 8000 10000 0200040006000800010000Predicted |E*| (Mpa) Actual |E*| (Mpa) Figure C-5. Measured test re sults versus predicted dynami c modulus values for fine gradation FAA mixtures, A) at1 Hertz, B) at 4 Hertz, C) at10 Hertz, D) at16 Hertz B A

PAGE 133

118 10 HERTZ (Fine Gradation)0 2000 4000 6000 8000 10000 12000 020004000600080001000012000Predicted |E*| (Mpa) Actual |E*| (Mpa) 16 HERTZ (Fine Gradation)0 2000 4000 6000 8000 10000 12000 020004000600080001000012000Predicted |E*| (Mpa) Actual |E*| (Mpa) Figure C-5. Continued D C

PAGE 134

119 1 HERTZ (Coarse Gradation)0 2000 4000 6000 8000 02000400060008000Predicted |E*| (Mpa) Actual |E*| (Mpa) 4 HERTZ (Coarse Gradation)0 2000 4000 6000 8000 02000400060008000Predicted |E*| (Mpa) Actual |E*| (Mpa) Figure C-6. Measured test re sults versus predicted dynami c modulus values for fine gradation FAA mixtures, A) at1 Hertz, B) at 4 Hertz, C) at10 Hertz, D) at16 Hertz B A

PAGE 135

120 10 HERTZ (Coarse Gradation)0 2000 4000 6000 8000 10000 0200040006000800010000Predicted |E*| (Mpa) Actual |E*| (Mpa) 16 HERTZ (Coarse Gradation)0 2000 4000 6000 8000 10000 0200040006000800010000Predicted |E*| (Mpa) Actual |E*| (Mpa) Figure C-6. Continued C D

PAGE 136

APPENDIX D MEASURED DYNAMIC MODULUS VALUES V.S. PREDICTED VALUES AT DIFFERENT TEMPERATURES

PAGE 137

122 10 C DEGREE (Fine Gradation)0 3000 6000 9000 12000 030006000900012000Predicted |E*| (Mpa)Actual |E*| (Mpa ) 30 C DEGREE (Fine Gradation)0 1000 2000 3000 4000 5000 6000 0100020003000400050006000Predicted |E*| (Mpa)Actual |E*| (Mpa ) Figure D-1. Measured test re sults versus predicted dynami c modulus values for fine gradation Whiterock mixtures, A) at 10 C Degrees, B) at 30 C Degrees, C) at 40 C degrees A B

PAGE 138

123 40 C DEGREE (Fine Gradation)0 1000 2000 3000 0100020003000Predicted |E*| (Mpa)Actual |E*| (Mpa ) Figure D-1. Continued C

PAGE 139

124 10 C DEGREE (Coarse Gradation)0 3000 6000 9000 12000 030006000900012000Predicted |E*| (Mpa)Actual |E*| (Mpa ) 30 C DEGREE (Coarse Gradation)0 1000 2000 3000 4000 5000 010002000300040005000Predicted |E*| (Mpa)Actual |E*| (Mpa ) Figure D-2. Measured test re sults versus predicted dynamic modulus values for coarse gradation Whiterock mixtures, A) at 10 C Degrees, B) at 30 C Degrees, C) at 40 C degrees B A

PAGE 140

125 40 C DEGREE (Coarse Gradation)0 1000 2000 3000 0100020003000Predicted |E*| (Mpa)Actual |E*| (Mpa ) Figure D-2. Continued C

PAGE 141

126 10 C Degrees (Coarse Gradation)0 2000 4000 6000 8000 10000 12000 14000 02000400060008000100001200014000Predicted |E*| (Mpa)Actual |E*| (Mpa)y 25 C Degrees (Coarse Gradation)0 1000 2000 3000 4000 5000 010002000300040005000Predicted |E*| (Mpa)Actual |E*| (Mpa) Figure D-3. Measured test re sults versus predicted dynamic modulus values for coarse gradation Granite mixtures, A) at 10 C Degrees, B) at 25 C Degrees, C) at 40 C degrees A B

PAGE 142

127 40 C Degrees (Coarse Gradation)0 500 1000 1500 2000 0500100015002000Predicted |E*| (Mpa)Actual |E*| (Mpa) Figure D-3. Continued C

PAGE 143

128 10 C Degrees (Fine Gradation)0 2000 4000 6000 8000 10000 12000 14000 02000400060008000100001200014000Predicted |E*| (Mpa)Actual |E*| (Mpa) 25 C Degrees (Fine Gradation)0 1000 2000 3000 4000 5000 010002000300040005000Predicted |E*| (Mpa)Actual |E*| (Mpa) Figure D-4. Measured test re sults versus predicted dynami c modulus values for fine gradation Granite mixtures, A) at 10 C Degrees, B) at 25 C Degrees, C) at 40 C degrees B A

PAGE 144

129 40 C Degrees (Fine Gradation)0 500 1000 1500 2000 0500100015002000Predicted |E*| (Mpa)Actual |E*| (Mpa) Figure D-4. Continued C

PAGE 145

130 10 C Degrees (Fine Gradation)0 2000 4000 6000 8000 10000 12000 14000 02000400060008000100001200014000Predicted |E*| (Mpa)Actual |E*| (Mpa) 40 C Degrees (Fine Gradation)0 500 1000 1500 2000 2500 3000 3500 4000 05001000150020002500300035004000Predicted |E*| (Mpa)Actual |E*| (Mpa) Figure D-5. Measured test re sults versus predicted dynami c modulus values for fine gradation “FAA” mixtures, A) at 10 C degrees, B) at 40 C degrees A B

PAGE 146

131 10 C Degrees (Coarse Gradation)0 2000 4000 6000 8000 10000 12000 14000 02000400060008000100001200014000Predicted |E*| (Mpa)Actual |E*| (Mpa) 40 C Degrees (Coarse Gradation)0 500 1000 1500 2000 2500 3000 3500 4000 05001000150020002500300035004000Predicted |E*| (Mpa)Actual |E*| (Mpa) Figure D-6. Measured test re sults versus predicted dynamic modulus values for coarse gradation “FAA” mixtures, A) at 10 C degrees, B) at 40 C degrees B A

PAGE 147

APPENDIX E COMPARISON OF MEASURED DYNAMIC MODULUS TEST RESULTS VS. PREDICTED RESULTS

PAGE 148

133 Comparison Of Dynamic Modulus Values for Fine Aggregate Gradation (10C)0 2000 4000 6000 8000 10000 12000 14000 0200040006000800010000120001400 Predicted |E*| (MPa) Witzack-2002Actual |E*| (MPa) Comparison Of Dynamic Modulus Values for Coarse Aggregate Gardation (10C)0 2000 4000 6000 8000 10000 12000 14000 0200040006000800010000120001400 0 Predicted |E*| (MPa) Witzack-2002Actual |E*| (MPa) Figure E-1. Comparison of meas ured dynamic modulus test resu lts vs. predicted results at 10 C degrees, A) For fine graded mixt ures, B) For coarse graded mixtures B A

PAGE 149

134 Comparison Of Dynamic Modulus Values for Fine Aggregate Gradation (40C)0 500 1000 1500 2000 2500 3000 0500100015002000250030 0 Predicted |E*| (MPa) Witzack-2002Actual |E*| (MPa) Comparison Of Dynamic Modulus Values for Coarse Aggregate Gradation (40C)0 500 1000 1500 2000 2500 3000 0500100015002000250030 0 Predicted |E*| (MPa) Witzack-2002Actual |E*| (MPa) Figure E-2. Comparison of meas ured dynamic modulus test resu lts vs. predicted results at 40 C degrees, A) For fine graded mixtur es, B) For coarse graded mixtures B A

PAGE 150

135 Comparison Of Dynamic Modulus Values for Fine Aggregate Gradation (10C)100 1000 10000 100000 100100010000100000 Log Predicted |E*| (MPa) Witzack-2002Log Actual |E*| (MPa) Comparison Of Dynamic Modulus Values for Coarse Aggregate Gradation (10C)100 1000 10000 100000 100100010000100000 Log Predicted |E*| (MPa) Witzack-2002Log Actual |E*| (MPa) Figure E-3. Comparison of meas ured dynamic modulus test resu lts vs. predicted results at 10 C degrees, on log scale A) For fine gr aded mixtures, B) For coarse graded mixtures B A

PAGE 151

136 Comparison Of Dynamic Modulus Values for Fine Aggregate Gradation (40C)100 1000 10000 100 1000 10000 Log Predicted |E*| (MPa) Witzack-2002Log Actual |E*| (MPa) Comparison Of Dynamic Modulus Values for Coarse Aggregate Gradation (40C)100 1000 10000 100 1000 10000 Log Predicted |E*| (MPa) Witzack-2002Log Actual |E*| (MPa)

PAGE 152

APPENDIX F DYNAMIC CREEP COMPLIANCE TEST RESULTS

PAGE 153

138 m@1 Hz0.000 0.100 0.200 0.300 0.400 0.500 0.600 01020304050 Temperature (C)m F1 F2 F4 F5 F6 m@4 Hz0.000 0.100 0.200 0.300 0.400 0.500 0.600 01020304050 Temperature (C)m F1 F2 F4 F5 F6 Figure F-1. Dynamic modulus valu es for fine graded Whiterock mixtures A) at 1 Hertz, B) at 4 Hertz, C) at 10 Hertz, D) at 16 Hertz, B A

PAGE 154

139 m@10 Hz0.000 0.100 0.200 0.300 0.400 0.500 0.600 01020304050 Temperature (C)m F1 F2 F4 F5 F6 m@16 Hz0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 01020304050 Temperature (C)m F1 F2 F4 F5 F6 Figure F-1. Continued C D

PAGE 155

140 D0@1 Hz-1.2E-04 -1.0E-04 -8.0E-05 -6.0E-05 -4.0E-05 -2.0E-05 0.0E+00 01020304050 Temperature (c)Do (1/MPa) F1 F2 F4 F5 F6 D0@4 hz-1.2E-04 -1.0E-04 -8.0E-05 -6.0E-05 -4.0E-05 -2.0E-05 0.0E+00 01020304050 Temperature (C)Do (1/MPa) F1 F2 F4 F5 F6 D0@10 Hz-1.2E-04 -1.0E-04 -8.0E-05 -6.0E-05 -4.0E-05 -2.0E-05 0.0E+00 01020304050 Temperature (c)Do (1/MPa) F1 F2 F4 F5 F6 Figure F-2. D0 values for fine graded Whiterock mixtur es A) at 1 Hertz, B) at 4 Hertz, C) at 10 Hertz, D) at 16 Hertz, A B C

PAGE 156

141 D0@16 Hz-1.2E-04 -1.0E-04 -8.0E-05 -6.0E-05 -4.0E-05 -2.0E-05 0.0E+00 01020304050 Temperature (C)Do (1/MPa) F1 F2 F4 F5 F6 Figure F-2. Continued D

PAGE 157

142 D1@1 Hz0.0E+00 5.0E-05 1.0E-04 1.5E-04 2.0E-0401020304050 Temperature (C)D1 (1/MPa) F1 F2 F4 F5 F6 D1@ 4 Hz0.0E+00 5.0E-05 1.0E-04 1.5E-04 2.0E-04 01020304050Temperature (C)D1 (1/MPa) F1 F2 F4 F5 F6 Figure F-3. D1 values for fine graded Whiterock mixt ures A) at 1 Hertz, B) at 4 Hertz, C) at 10 Hertz, D) at 16 Hertz A B

PAGE 158

143 D1@10 Hz0.0E+00 5.0E-05 1.0E-04 1.5E-04 2.0E-04 01020304050Temperature (C)D1 (1/MPa) F1 F2 F4 F5 F6 D1@16 Hz0.0E+00 5.0E-05 1.0E-04 1.5E-04 2.0E-04 01020304050Temperature (C)D1 (1/MPa) F1 F2 F4 F5 F6 Figure F-3. Continued C D

PAGE 159

144 m@1 Hz0.000 0.100 0.200 0.300 0.400 0.500 0.600 01020304050 Tempeature (C)m p1 p3 p5 p7 m@4 Hz0.000 0.100 0.200 0.300 0.400 0.500 0.600 01020304050 Tempeature (C)m p1 p3 p5 p7 Figure F-4. Dynamic modulus values for fine graded Project mixt ures A) at 1 Hertz, B) at 4 Hertz, C) at 10 Hertz, D) at 16 Hertz, A B

PAGE 160

145 m@10 Hz0.000 0.100 0.200 0.300 0.400 0.500 0.600 01020304050 Tempeature (C)m p1 p3 p5 p7 m@16 Hz0.000 0.100 0.200 0.300 0.400 0.500 0.600 01020304050 Tempeature (C)m p1 p3 p5 p7 Figure F-4. Continued C D

PAGE 161

146 D0@1 Hz-3.0E-05 -2.0E-05 -1.0E-05 0.0E+00 1.0E-05 2.0E-05 3.0E-05 01020304050 Temperature (C)D0(1/MPa) p1 p3 p5 p7 D0@4 Hz-3.0E-05 -2.5E-05 -2.0E-05 -1.5E-05 -1.0E-05 -5.0E-06 0.0E+00 5.0E-06 01020304050 Temperature (C)D0(1/MPa) P1 P3 P5 P7 Figure F-5. D0 values for fine graded Project mixtures A) at 1 Hertz, B) at 4 Hertz, C) at 10 Hertz, D) at 16 Hertz A B

PAGE 162

147 D0@10 Hz-3.0E-05 -2.5E-05 -2.0E-05 -1.5E-05 -1.0E-05 -5.0E-06 0.0E+00 5.0E-06 01020304050 Temperature (C)D0(1/MPa) P1 P3 P5 P7 D0@16 Hz-3.0E-05 -2.5E-05 -2.0E-05 -1.5E-05 -1.0E-05 -5.0E-06 0.0E+00 5.0E-06 01020304050 Temperature (C)D0(1/MPa) P1 P3 P5 P7 Figure F-5. Continued C D

PAGE 163

148 D1@1 Hz0.000E+00 5.000E-05 1.000E-04 1.500E-04 01020304050Temperature (C)D1(1/MPa) p1 p3 p5 p7 D1@4 Hz0.000E+00 5.000E-05 1.000E-04 1.500E-04 01020304050 Temperature (C)D1(1/MPa) p1 p3 p5 p7 D1@10 Hz0.000E+00 5.000E-05 1.000E-04 1.500E-04 01020304050 Temperature (C)D1(1/MPa) p1 p3 p5 p7 Figure F-6. D0 values for fine graded Whiterock mixt ures A) at 1 Hertz, B) at 4 Hertz, C) at 10 Hertz, D) at 16 Hertz A B C

PAGE 164

149 D1@16 Hz0.000E+00 5.000E-05 1.000E-04 1.500E-04 01020304050 Temperature (C)D1(1/MPa) p1 p3 p5 p7 Figure F-6. Continued D

PAGE 165

150 CALC-Do-6.0E-06 -5.0E-06 -4.0E-06 -3.0E-06 -2.0E-06 -1.0E-06 0.0E+00 1.0E-06 2.0E-06 3.0E-06 01020304050Temperature (C)D0 (1/MPa) CALC-1Hz CALC-4Hz CALC-10Hz CALC-16Hz CHF-Do-6.0E-06 -5.0E-06 -4.0E-06 -3.0E-06 -2.0E-06 -1.0E-06 0.0E+00 1.0E-06 2.0E-06 3.0E-06 01020304050Temperature (C)D0 (1/MPa) CALC-1Hz CALC-4Hz CALC-10Hz CALC-16Hz CHC-Do-6.0E-06 -5.0E-06 -4.0E-06 -3.0E-06 -2.0E-06 -1.0E-06 0.0E+00 1.0E-06 2.0E-06 3.0E-06 01020304050Temperature (C)D0 (1/MPa) CALC-1Hz CALC-4Hz CALC-10Hz CALC-16Hz Figure F-7. D0 values for fine graded “FAA” mixtures A) at 1 Hertz, B) at 4 Hertz, C) at 10 Hertz, D) at 16 Hertz A B C

PAGE 166

151 RBC-Do-6.0E-06 -5.0E-06 -4.0E-06 -3.0E-06 -2.0E-06 -1.0E-06 0.0E+00 1.0E-06 2.0E-06 3.0E-06 01020304050Temperature (C)D0 (1/MPa) CALC-1Hz CALC-4Hz CALC-10Hz CALC-16Hz RBF-Do-6.0E-06 -5.0E-06 -4.0E-06 -3.0E-06 -2.0E-06 -1.0E-06 0.0E+00 1.0E-06 2.0E-06 3.0E-06 01020304050Temperature (C)D0 (1/MPa) CALC-1Hz CALC-4Hz CALC-10Hz CALC-16Hz CGC-Do-0.00001 -0.00001 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 01020304050Temperature (C)D0 (1/MPa) CALC-1Hz CALC-4Hz CALC-10Hz CALC-16Hz Figure F-7. Continued D E F

PAGE 167

APPENDIX G GRADATION EFFECT ON COMPLEX MODULUS PREDICTION

PAGE 168

153 A B Figure G-1. Gradation line and power regression lines of fine gradation Whiterock samples, A) F1 B) F2 C) F4 D) F5 E) F6

PAGE 169

154 C D E Figure G-1 Continued

PAGE 170

155 A B Figure G-2. Gradation line a nd power regression lines of coarse gradation Whiterock samples, A) C1 B) C2 C) C3

PAGE 171

156 C Figure G-2. Continued

PAGE 172

157 A B C Figure G-5. Gradation line and power regression lines of fine gradation Project samples, A) P1 B) P2 C) P3 D) P5 E) P7

PAGE 173

158 D Figure G-5. Continued E Figure G-5. Continued

PAGE 174

159 E* Value Comparison 1 Hz-10Cy = 0.790x + 1004.806 R2 = 0.7900 1 2 3 4 5 6 7 8 9 0123456789ThousandsThousands Measured (1/MPa)Predicted (1/MPa) E* Value Comparison 1 Hz-40Cy = 0.910x + 65.168 R2 = 0.9100 2 4 6 8 10 12 024681012HundredsHundreds Measured (1/MPa)Predicted (1/MPa) Figure G-6. Predicted values vs. measur ed by using multi regression at 1 Hz (10 and 40C). E* Value Comparison 4 Hz-40Cy = 0.921x + 90.749 R2 = 0.9210 2 4 6 8 10 12 14 16 0246810121416HundredsHundreds Measured (1/MPa)Predicted (1/MPa) E* Value Comparison 4 Hz-10Cy = 0.794x + 1278.814 R2 = 0.7940 1 2 3 4 5 6 7 8 9 10 012345678910ThousandsThousands Measured (1/MPa)Predicted (1/MPa) Figure G-7. Predicted values vs. measured by using multi regression at 4 Hz (10 and 40C).

PAGE 175

160 E* Value Comparison 10 Hz-10Cy = 0.802x + 1430.216 R2 = 0.802 0 2 4 6 8 10 12 024681012ThousandsThousands Measured (1/MPa)Predicted (1/MPa) E* Value Comparison 10 Hz-40Cy = 0.919x + 124.078 R2 = 0.9190 4 8 12 16 20 24 04812162024HundredsHundreds Measured (1/MPa)Predicted (1/MPa) Figure G-8. Predicted values vs. measured by using multi regression at 10 Hz (10 and 40C). E* Value Comparison 10 Hz-40Cy = 0.919x + 124.078 R2 = 0.9190 4 8 12 16 20 24 04812162024HundredsHundreds Measured (1/MPa)Predicted (1/MPa) E* Value Comparison 10 Hz-40Cy = 0.919x + 124.078 R2 = 0.9190 4 8 12 16 20 24 04812162024HundredsHundreds Measured (1/MPa)Predicted (1/MPa) Figure G-9. Predicted values vs. measured by using multi regression at16 Hz (10 and 40C).

PAGE 176

APPENDIX H VISCOSITY EFFECTS ON COMPLEX MODULUS PREDICTION

PAGE 177

162 40 C (Original) 0 500 1000 1500 2000 2500 3000 3500 4000 05001000150020002500300035004000Predicted |E*| (1/MPa)Measuredl |E*| (1/MPa) FAA Project White Rock GraniteA 40 C (Mix-Laydown) 0 500 1000 1500 2000 2500 3000 3500 4000 05001000150020002500300035004000Predicted |E*| (1/MPa)Measuredl |E*| (1/MPa) FAA Project White Rock GraniteB Figure H-1. Complex modulus values predicted by using predictive equation by using different viscosity conditions A) Original averaged viscosity values B) MixLaydown viscosity values C) Long term oven aged viscosity values D) Original viscosity values from DSR test s, E) Short term oven aged viscosity values F) Extracted binder viscosity values from DSR tests, G) Viscosity values from Brookfield tests

PAGE 178

163 40 C (Aged) 0 500 1000 1500 2000 2500 3000 3500 4000 05001000150020002500300035004000Predicted |E*| (1/MPa)Measuredl |E*| (1/MPa) FAA Project White Rock GraniteC 40 C (Original-DSR)0 500 1000 1500 2000 2500 3000 3500 4000 05001000150020002500300035004000 Predicted |E*| (1/MPa)Measuredl |E*| (1/MPa) FAA Project White Rock GraniteD Figure H-1 Continued

PAGE 179

164 40 C (STOA-DSR)0 500 1000 1500 2000 2500 3000 3500 4000 05001000150020002500300035004000 Predicted |E*| (1/MPa)Measuredl |E*| (1/MPa) FAA Project White Rock Granite`E 40 C (Extracted Binder-DSR)0 500 1000 1500 2000 2500 3000 3500 4000 05001000150020002500300035004000Predicted |E*| (1/MPa)Measuredl |E*| (1/MPa) FAA Project White Rock GraniteF Figure H-1 Continued

PAGE 180

165 40 C (Original-Lab-BROOKFIELD)0 500 1000 1500 2000 2500 3000 3500 4000 05001000150020002500300035004000 Predicted |E*| (1/MPa)Measuredl |E*| (1/MPa) FAA Project White Rock Granite`G Figure H-1. Continued

PAGE 181

APPENDIX I DYNAMIC CREEP TEST PARAMETERS

PAGE 182

167 Table I-1. Dynamic creep parameter summary Power Law Parameters Mixture Temperature C D0 (1/MPa) D1 (1/MPa) m-value 10 2.599E-095.21E-060.388 30 -6.007E-059.92E-050.144 WRC1 40 -1.155E-042.20E-040.091 10 -1.448E-073.05E-060.399 30 -5.107E-058.34E-050.147 WRC2 40 -8.209E-051.43E-040.102 10 1.888E-071.99E-060.344 30 -2.164E-053.70E-050.188 WRC3 40 -9.371E-051.53E-040.111 10 2.248E-072.06E-060.319 30 -1.700E-053.13E-050.220 WRF1 40 -8.330E-051.38E-040.131 10 -3.018E-072.04E-060.268 30 -1.798E-053.03E-050.225 WRF2 40 -6.897E-051.10E-040.132 10 2.535E-071.31E-060.331 30 -1.533E-052.61E-050.222 WRF4 40 -7.715E-051.24E-040.126 10 1.519E-072.16E-060.343 30 -3.346E-055.38E-050.181 WRF5 40 -1.094E-041.85E-040.113 10 -2.068E-065.68E-060.248 30 -1.982E-053.40E-050.207 WRF6 40 -7.550E-051.27E-040.125 10 4.739E-071.18E-060.371 RBC 40 -1.351E-054.01E-050.179 10 8.366E-071.04E-060.423 RBF 40 -8.946E-063.37E-050.206 10 6.190E-074.87E-070.486 CALC 40 2.204E-061.46E-050.300 10 4.626E-076.38E-070.370 CALF 40 -7.023E-062.10E-050.131

PAGE 183

168 Table I-1 Continued 10 -5.551E-073.03E-060.262 CGC 40 -8.660E-062.67E-050.133 10 2.943E-072.16E-060.397 CHC 40 -8.367E-064.12E-050.226 10 1.214E-071.47E-060.370 CHF 40 1.363E-051.70E-050.398 10 8.189E-079.96E-070.441 P1 40 7.774E-061.81E-050.452 10 8.516E-073.69E-060.454 P3 40 2.338E-051.58E-050.552 10 1.287E-061.95E-060.387 P5 40 3.620E-062.51E-050.256 10 5.498E-072.93E-060.426 P7 40 -1.721E-055.43E-050.142 10 8.707E-071.04E-060.402 HVS67-22 40 -3.460E-058.40E-050.211 10 1.148E-051.87E-050.349 HVS76-22 40 -1.787E-042.94E-040.096

PAGE 184

APPENDIX J STATIC CREEP TEST PARAMETERS

PAGE 185

170 Table J-1. Static creep parameter summary Power Law Parameters Mixture Temperature C D0 (1/MPa) D1 (1/MPa) m-value 10 -4.18E-052.45E-050.289 30 WRC1 40 -1.80E-033.85E-030.070 10 -7.78E-053.96E-050.320 30 --WRC2 40 -1.90E-033.18E-030.060 10 -1.19E-049.67E-050.280 30 --WRC3 40 -1.91E-031.97E-030.080 10 -1.11E-051.11E-050.409 30 -1.42E-042.42E-040.210 WRF1 40 -1.95E-048.11E-040.142 10 -8.78E-068.59E-060.397 30 -1.63E-042.32E-040.232 WRF2 40 -1.99E-047.02E-040.155 10 -8.27E-068.60E-060.346 30 -1.00E-041.64E-040.227 WRF4 40 -2.03E-045.98E-040.168 10 -7.87E-068.63E-060.426 30 -1.01E-041.70E-040.233 WRF5 40 -1.64E-047.30E-040.178 10 -7.69E-069.75E-060.410 30 -7.61E-051.80E-040.187 WRF6 40 -1.39E-046.89E-040.130 10 -7.69E-067.78E-060.383 RBC 40 -6.69E-053.52E-040.148 10 -1.21E-058.77E-060.476 RBF 40 -4.33E-051.74E-040.192 10 -1.39E-057.54E-060.458 CALF 40 -3.33E-051.34E-040.155 10 -1.55E-051.14E-050.427 CGC 40 -4.72E-051.99E-040.176 10 -2.21E-052.05E-050.384 CHC 40 -5.07E-051.75E-040.206

PAGE 186

171 Table J-1 Continued 10 -1.75E-051.56E-050.419 CHF 40 -9.09E-053.00E-040.189 10 -1.11E-058.83E-060.464 P1 40 -1.14E-044.43E-040.166 10 -1.42E-052.08E-050.434 P3 40 -8.92E-052.66E-040.293 10 -1.33E-051.15E-050.448 P5 40 -5.77E-052.22E-040.172 10 -2.82E-052.71E-050.376 P7 40 -5.06E-052.47E-040.156 10 -9.92E-068.26E-060.457 HVS67-22 40 -9.79E-057.30E-040.134 10 -9.53E-061.08E-050.401 HVS76-22 40 -1.27E-046.10E-040.146

PAGE 187

APPENDIX K SHORT TERM CREEP TEST PARAMETERS

PAGE 188

173 Table K-1 Short term creep parameter summary Power Law Parameters Mixture Temperature C D0 (1/MPa) D1 (1/MPa) m-value 10 5.15E-064.95E-040.241 25 1.39E-042.05E-030.453 GAC1 40 -4.05E-038.93E-030.114 10 1.31E-062.49E-040.189 25 -2.35E-051.25E-030.302 GAC2 40 -1.95E-034.69E-030.122 10 8.71E-052.80E-040.462 25 -3.69E-051.32E-030.294 GAC3 40 -3.31E-035.80E-030.083 10 6.11E-053.23E-040.339 25 -1.57E-041.33E-030.225 GAF1 40 -1.56E-034.24E-030.133 10 5.43E-052.20E-040.379 25 -1.33E-048.06E-040.190 GAF2 40 -2.14E-044.00E-030.345 10 25 3.07E-051.22E-030.331 GAF3 40 -7.06E-046.11E-030.286 10 -4.18E-052.45E-050.289 30 WRC1 40 -1.80E-033.85E-0310 -7.78E-053.96E-050.320 30 --WRC2 40 -1.90E-033.18E-0310 -1.19E-049.67E-050.280 30 WRC3 40 10 6.320E-052.76E-040.321 30 -2.259E-041.11E-030.177 WRF1 40 -4.078E-042.42E-030.211 10 5.329E-052.16E-040.230 30 -2.914E-059.47E-040.251 WRF2 40 -2.191E-041.83E-030.233 10 3.857E-051.95E-040.277 30 -6.715E-057.14E-040.223 WRF4 40 -3.369E-042.21E-030.211

PAGE 189

174 Table K-1 Continued 10 2.064E-052.91E-040.217 30 3.810E-051.06E-030.363 WRF5 40 -3.369E-042.26E-030.260 10 4.430E-053.25E-040.255 30 2.767E-051.27E-030.348 WRF6 40 -2.412E-042.29E-030.239 10 5.26E-051.87E-040.356 RBC 40 -1.15E-033.25E-030.140 10 3.33E-052.24E-040.255 RBF 40 -9.93E-052.03E-030.266 10 CALC 40 -2.55E-041.75E-030.227 10 CALF 40 -1.88E-041.85E-030.265 10 CGF 40 -2.97E-041.66E-030.200 10 2.35E-053.24E-040.243 CHC 40 -8.52E-052.90E-030.326 10 4.04E-055.62E-040.730 CHF 40 10 P1 40 -1.61E-034.92E-030.160 10 2.62E-053.00E-040.205 P2 40 -1.25E-034.12E-030.169 10 7.64E-054.41E-040.272 P3 40 10 P5 40 -8.88E-043.50E-030.164 10 -1.69E-064.38E-040.202 P7 40 -1.27E-034.27E-030.156

PAGE 190

175 LIST OF REFERENCES AASHTO “Guide for Design of Pave ment Structures”, AASHTO, 1993. AASHTO “Guide for Design of Pave ment Structures”, AASHTO, 2002. Bonnaure, F., Gest, G., Gravois, A., and Uge P., “A New Method of Predicting the Stiffness of Asphalt Paving Mixtures”, Pr oceedings, Association of Asphalt Paving Technologists, Vol. 46, 1977, pp.64-100. Darku D.D., “Evaluation of the Superpave Gy ratory Compactor for Assessing the Rutting Resistance of Asphalt Mixtures”, Doctor of Philosophy Dissertation, University of Florida, Gainesville, 2003. Drescher, A., Newcomb, D. E., and W. Zhang, “Interpretation of I ndirect Tension Test Based on Viscoelasticity”. Transportation Research Record 1590, 1997, pp. 45-52. Goode J.F., Lufsey L.A., “A new Graphical Chart for Evaluating Aggregate Gradations”, Proceedings, AAPT, Vol. 31, 1962. Huber G.A., Shule T.S., “Providing Su fficient Void Space for Asphalt Cement: Relationship of Mineral Aggregate Void and Aggregate Gradation. Effects of Aggregates and Mineral Fillers on Aspha lt Mixture Performance”, ASTM, 1992. Khanal, P. P., and M. S. Mamlouk, “Tens ile Versus Compressive Moduli of Asphalt Concrete”, Transportation Resear ch Record 1492, 1995, pp. 144-150. Lambe W., Soil Mechanics. John Wiley & Son Publishing, New York, 1968. Nijboer L.W., “Plasticity as a Factor in th e Design of Dense Bituminous Road Carpets”, Elsevier Publishing Company Inc., New York, NY, 1948. NCHRP Project 9-19, Draft Test Protocol A1, “Dynamic Modulus of Asphalt Concrete Mixtures and Master Curves”. Papazian, H. S., “The Response of Linear Viscoelastic Material s in the Frequency Domain with Emphasis on Asphaltic Concrete”, (1st) International Conference on the Structural Design of Asphalt Pavements, 1962, pp.454-463. Pellinen T.K, Witczak M.W., “Linear and N on-Linear (Stress dependent) Master Curve Construction for Dynamic (Complex) Modul us”, Journal of th e Association of Asphalt Paving Technologists, Vo lume 71, Preprint (2002).

PAGE 191

176 Pellinen, T. K., and Witczak M. W., “Use of Stiffness of Hot-Mix Asphalt as a Simple Performance Test”, Transportation Res earch Board (TRB), 2002 Annual Meeting, Washington, D.C. Pellinen, T.K., and Witczak M.W., “Stress Dependent Master Curve Construction for Dynamic (Complex) Modulus”, Annual Me eting Association of Asphalt Paving Technologists, Colorado Springs, Colorado, USA, March 2002. Ruth B.E., Roque R., Nukunya B., “Aggregat e Gradation Characte rization Factors and Their Relationships to Fracture Energy a nd Failure Strain of Asphalt Mixtures”, Journal of Association of Asphalt Paving Technologists, Tallahassee, March 18-20, 2002. Stroup-Gardiner, M., and Newcomb D. E., “Inve stigation of Hot Mix Asphalt Mixtures at Mn ROAD”, Minnesota Department of Transportation Final Report 97-06, 1997. Swan D.J., “Evaluation of the Testing Pro cedure and Data Analysis for the Uniaxial Complex Modulus Test on Hot Mix Aspha lt”, Master of Engineering Thesis, University of Florida, Gainesville, 2002. Vavrik W.R., Pine W.J., Huber G., Carpen ter S.H., “The Bailey Method of Gradation Evaluation: The Influence of Aggregate Gradation and Packing Characteristics on Voids in the Mineral Aggregate”, Vol.70-01, pp.132, 2001. Williams, M. L., Landel, R. F., and Ferry, J. D., “The Temperature Dependence of Relaxation Mechanism in Amorphous Polyme rs and Other Glass-Liquids”, Journal of American Chem. Soc., Vol. 77, 1955, pp.370. Witczack M.W., Fonesca O.A., “Revised M odel for Dynamic (Complex) Modulus of Asphalt Mixtures”, Transportation Research Record 1540, 1996, pp.15-23. Witczack M.W, Kaloush K, Pellinen T., El-Basyouny M., Quintus H.V., “Simple Performance Test for Superpave Mix Design”, NCHRP Report 465, 2002, pp.6. Witczak, M. W., and R. E. Root, “Summa ry of Complex Modulus Laboratory Test Procedures and Results”, STP 561, Ameri can Society for Testing and Materials, 1974, pp.67-94. Zhang, W., Drescher, A., and D. E. Newc omb, “Viscoelastic Behavior of Asphalt Concrete in Diametral Compression”, J ournal of Transportation Engineering, November/December 1997, pp. 495-502. 2002 Design Guide Draft – 2.4 “Modulus of El asticity for Major Material Groups”, NCHRP Project 1-37A.

PAGE 192

177 BIOGRAPHICAL SKETCH Erkan Ekingen was born in Opelika, Alabam a. He completed his college education in Turkey. He earned his Civil Engineering degree from Istanbul Technical University, Civil Engineering Faculty in 1992. Upon his grad uation, he worked in the same faculty as a research assistant at the Department of Engineering Mechanics. In 1994, by a scholarship from World Bank he studie d in Sheffield Hallam University in Sheffield/U.K. He worked as a lecturer in University of Mersin, Icel/Turkey until 2002 when he started his graduate study in University of Florida, Civil and Coastal Engineering Department.


Permanent Link: http://ufdc.ufl.edu/UFE0005367/00001

Material Information

Title: Determining Gradation and Creep Effects in Mixtures Using the Complex Modulus Test
Physical Description: Mixed Material
Copyright Date: 2008

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0005367:00001

Permanent Link: http://ufdc.ufl.edu/UFE0005367/00001

Material Information

Title: Determining Gradation and Creep Effects in Mixtures Using the Complex Modulus Test
Physical Description: Mixed Material
Copyright Date: 2008

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0005367:00001


This item has the following downloads:


Full Text












DETERMINING GRADATION AND CREEP EFFECTS IN MIXTURES USING THE
COMPLEX MODULUS TEST














By

ERKAN RUHI EKINGEN


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

UNIVERSITY OF FLORIDA


2004

































This thesis is dedicated to my father.















ACKNOWLEDGMENTS

It was a privilege to work with my advisor, Dr. Bjorn Birgisson. I would like to

thank him for his supervision and guidance. I also thank the other members of my

committee. I thank Dr. Reynaldo Roque for his help and knowledge which kept me on

track. I also thank to Dr. Frank Townsend and Dr. M. C. McVay for their support

throughout my graduate study.

My sincere appreciation goes to Jaeseung Kim, George Loop, Linh Viet Pham and

Daniel Darku. Their expertise in the field helped my work go much faster and easier.

I also want to thank the entire Geotech group for their friendship and support while

I was at the University of Florida.















TABLE OF CONTENTS


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

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

LIST OF FIGURES ........................................ .............. x

A B S T R A C T ..................................................................................................................... x v

CHAPTER

1 IN TR O D U C T IO N ........ .. ......................................... ..........................................1.

A Brief Introduction to Dynamic M odulus (|E*|)...................................................1...
O bjectiv e s ........................................................................ ................................. . .2

2 LITER A TU R E R EV IEW .................................................................... ...............3...

Background and History of Complex Modulus Testing.........................................3...
Superpave Shear Tester ........................................................ .... .... ............ ........ .... .. 4
Modulus Measurement in Viscoelastic Asphalt Mixtures......................................5...
M aster C urves and Shift F actors.............................................................. ...............9...
Sample Preparation ....................... ........... ............................... 10
Load Level ................................................................ .. ..................... 11
Com plex M odulus as a D esign Param eter............................................. ................ 14
W itczak Predictive M odulus Equation .............. .................................... ............... 14
Complex Modulus as a Simple Performance Test ................................................15
F atig u e C rack in g ......................................................................................................... 16
R u ttin g ...................................................................................................... ....... .. 17

3 MATERIALS USED IN AXIAL COMPLEX MODULUS TESTING ..................... 18

In tro d u c tio n ................................................................................................................. 1 8
O verview of M ixtures U sed........................................ ........................ ............... 18
A sphalt B inders U sed .............. ................ ............................................... 18
A g g re g ate s .............. ................................................................................................ .. 1 9
Fine Aggregate Angularity (FAA) M ixtures......................................... ............... 19
Determination of Fine Aggregate Batch Weights .................................................22
Limestone Gradation Study Mixture Gradations...................................................22
G ranite M ixtures U sed ........................................................................... ................ 23
Superpave Field Monitoring Mixture Gradations..................................................25









M ix tu re D esig n ........................................................................................................... 2 8

4 AXIAL COMPRESSION DYNAMIC MODULUS: RESULTS AND
D ISCU SSION ............................................................................ ....... ........ ............... 33

In tro d u ctio n ................................................................................................................ 3 3
D ata V ariab le s ............................................................................................................ 3 3
R aw D ata P lots .............. ...................................... ............. ................. .. 34
D ata-A analysis M ethod ... ................................................................... ............... 38
A analysis of T est D ata R esults....................................... ...................... ................ 39
M aster C urve C construction .................................................................... ................ 48
Typical Predicted Master Curves for Florida Mixtures.........................................50
Dynamic Modulus Calculated from Predictive Regression Equations....................53
Binder Testing R results .............................................. .................. ....... ........ ......................... 55
Comparison of Predicted and Measured Dynamic Modulus................................57
C o n c lu sio n s............................................................................................................... .. 6 5

5 EVALUATION OF GRDATION EFFECTS ................ ....................................70

In tro d u ctio n ............... .......... .. ... .. ......... ......... .. ............................................. 7 0
The Evaluation of the Effects of Aggregate Gradations on Dynamic Modulus.........71
Correlation Study between Power Law Gradation Factors and Dynamic
M o d u lu s .................... ..... ..... ..................................................................... .. 7 3
Category Analysis of Power Law Parameters ................................. ...................... 75
Category Analysis of Power Law Parameters for Coarse and Fine Graded
M ix tu re s ............................................................................................................. .. 7 6
Sum m ary and C conclusions ......................................... ........................ ................ 78

6 EVALUATION OF POTENTIAL CORRELATION BETWEEN COMPLEX
MODULUS PARAMETERS AND RUTTING RESISTANCE OF MIXTURES ....80

B a ck g ro u n d .................... ....... ... ................................... ... .. .................................. .. 8 0
Asphalt Pavement Analyzer Test Procedure and Test Results ................................... 80
Static C reep T est R esu lts ............................................. ............................................ 82
Evaluation of Dynamic Test results for HMA Rutting Resistance .............................85
Evaluation of Static Creep Param eters .................... ............................................. 89
Effects of Binder Type on Relationship between Dynamic Modulus and Rutting
Potential of M ixtures ......................................................... ............. 93
Sum m ary and C conclusions ......................................... ........................ ................ 94

APPENDIX

A ELASTICITY MODULUS AND PHASE ANGLE SUMMARY FOR SAMPLE
G R A D A T IO N S ............... ............................... ...............................................9 6

B PREDICTED DYNAMIC MODULUS VALUES VS.MEASURED DYNAMIC
V A L U E S ................................................................................................................... 1 0 3









C MEASURED DYNAMIC MODULUS V.S. PREDICTED VALUES FOR
D IFFEREN T FRE Q U EN C IE S .................................................................................108

D MEASURED DYNAMIC MODULUS VALUES V.S. PREDICTED VALUES
AT DIFFERENT TEMPERATURES ....... ... .......................... 121

E COMPARISON OF MEASURED DYNAMIC MODULUS TEST
RESULTS VS. PREDICTED RESULTS........................................ 132

F DYNAMIC CREEP COMPLIANCE TEST RESULTS .................................... 137

G GRADATION EFFECT ON COMPLEX MODULUS PREDICTION................ 152

H VISCOSITY EFFECTS ON COMPLEX MODULUS PREDICTION................ 161

I DYNAM IC CREEP TEST PARAM ETERS ............... .............. ..................... 166

J STATIC CREEP TEST PARAMETERS........... ........................169

K SHORT TERM CREEP TEST PARAMETERS.................................... ............... 172

L IST O F R E F E R E N C E S ................................................................................................. 175

BIOGRAPH ICAL SKETCH .................. .............................................................. 177















LIST OF TABLES


Table page

3-1 Coarse gradations for fine aggregate effects.......................................................20

3-2 Fine gradations for fine aggregate effects........................................... ................ 21

3-3 Physical properties of fine aggregates.....................................................21

3-4 Gradations for White Rock coarse graded mixtures ...........................................23

3-5 Gradations for White Rock fine graded mixtures ...............................................23

3-6 Granite based m ixture gradations.................. .................................................. 25

3-7 G radiation of fi eld projects......................................... ....................... ................ 26

3-8 Superpave gyratory com action effort................................................ ................ 29

3-9 Volumetric properties of coarse graded mixtures ...............................................30

3-10 Volumetric Properties of Fine Graded Mixtures.................................................30

3-11 Volumetric properties of coarse graded mixtures ...............................................31

3-12 Volumetric properties of fine graded Whiterock mixtures .................................31

3-13 Volum etric properties of Granite m ixtures ......................................... ................ 32

3-14 V olum etric properties of field projects ............................................... ................ 32

4-1 Sam ple preparation data .......................................... ......................... ................ 35

4-2 Average dynam ic m odulus testing results........................................... ................ 39

4-3 A average phase angle testing results .........................................................................41

4-4 Brookfield rotational viscometer results on unaged and RTFO aged binder...........55

4-5 Dynamic shear rheometer results on unaged and RTFO aged binder...................56









4-6 Viscosity-temperature regression coefficients for unaged and
R T F O aged P G 67-22 asphalt ..................................................................................57

4-7 Typical viscosity-temperature regression coefficients for AC-30
at different hardening states ...................................... ....................... ................ 57

4-8 Calculated viscosity at four complex modulus test temperatures ......................... 57

4-9 Predicted dynamic moduli for Georgia granite mixtures using the
M ix/L aydow n condition ......................................... ......................... ................ 59

4-10 Predicted dynamic moduli for Whiterock mixtures using the Mix/Laydown
c o n d itio n ............................................................................................................... ... 5 9

4-11 Predicted dynamic moduli for FAA Mixtures using the Mix/Laydown
c o n d itio n .............................................................................................................. ... 6 0

4-12 Predicted dynamic moduli for Superpave project mixtures using the
M ix/L aydow n condition .......................................... ......................... ................ 60

4-13 Predicted dynamic moduli for Georgia granite mixtures using RTFO aged
binder results from the Brookfield rotational viscometer test...............................60

4-14 Predicted dynamic modulus for Whiterock mixtures Using RTFO aged binder
results from the Brookfield rotational viscometer test........................................61

4-15 Predicted dynamic moduli for FAA mixtures using RTFO aged binder results
from the Brookfield rotational viscometer test ................................... ................ 61

4-16 Predicted dynamic moduli for Superpave mixtures using RTFO aged binder
results from the Brookfield rotational viscometer test........................................62

4-17 Predicted dynamic moduli for Georgia granite mixtures using RTFO aged
binder results from the dynamic shear rheometer Test. .....................................62

4-18 Predicted dynamic moduli for Whiterock mixtures using RTFO aged binder
results from the dynamic shear rheom eter test.................................... ................ 63

4-19 Predicted dynamic moduli for FAA mixtures using RTFO aged binder results
from the dynam ic shear rheom eter test ............................................... ................ 63

4-20 Predicted dynamic moduli for Superpave mixtures using RTFO aged binder
results from the dynamic shear rheometer test.................................... ................ 64

5-2 Results of correlation study between power law parameters and dynamic
m odulus at 400C and 1 H z frequency.................................................. ................ 74

5-3 Partial correlation analysis for nca and |E40*| when controlling for nfa...................75









5-4 Mean and standard deviation of |E40* for the four different categories ...............76

5-5 One-W ay analysis of variance of E40* ........................................................ 76

5-6 Post-Hoc analysis for homogeneous subsets of hypothesized categories .............76

5-7 M ixtures in course-graded category .................................................... ................ 77

5-8 M ixtures in fine-graded category ........................................................ ................ 77

5-9 Zero-Order correlation analysis for nca, nfa, and |E40o* for course graded
m ix tu re s ................................................................................................................. ... 7 8

5-10 Zero-Order correlation analysis for nca, nfa, and |E40o* for fine graded ..................78

6-1 Dynamic modulus |E*|, phase angle and asphalt pavement analyzer rut
depth measurements from mixture testing at 40 C. ..........................................82

6-2 Average static creep testing results for test temperature of 40C .........................84

I-1 Dynamic creep parameter summary...........................................167

J-1 Static creep param eter summary ....... ....... ........ ...................... 170

K-i Short term creep parameter summary ........................................173
















LIST OF FIGURES


Figure page

1-1 The testing components of the complex modulus................................................7...

2-2 Proportionality of Viscoelastic M aterials............................................ ............... 12

2-3 Superposition of V iscoelastic M aterials.............................................. ............... 13

3-1 G radiation curves for C l and F l .......................................................... ................ 20

3-2 Coarse gradations for gradation effects studies...................................................24

3-3 Fine gradations for gradation effects studies....................................... ................ 24

3-4 Coarse graded Granite aggregate gradations.......................................................25

3-5 Fine graded Granite aggregate gradations........................................... ................ 26

3-6 Gradations for Superpave project mixtures number 2, 3, and 7...............................27

3-7 Gradations for field projects 1 and 5 ...................................................27

3-8 Servopac superpave gyratory compactor ............... ....................................29

4-1 Typical plot of force and LVDT displacement versus time at low temperature
for m mixture W R C ................................................................. ........................ 37

4-2 Typical plot of force and LVDT displacement versus time at high temperature
for m mixture W R C 1 .............. ......................... ...................... .................... .... 37

4-3 Typical plot of vertical stress versus strain at low temperature for
m ix tu re W R C 1 ........................................................................................................ 3 8

4-4 Typical plot of vertical stress versus strain at high temperature for
m ix tu re W R C 1 ........................................................................................................ 3 8

4-5 Dynamic modulus |E*| of GAF1 at 100C............... ...................................44

4-6 Phase angle of G A F1 m ixture at 100C ................................................ ................ 44

4-7 Dynam ic m odulus |E*| of GAF1 at 25C ............................................ ................ 45









4-8 Phase angle of G AF1 m ixture at 250C ................................................ ................ 45

4-9 Dynam ic m odulus |E*I of GAF1 at 40C ............................................ ................ 45

4-10 Phase angle of G AF1 m ixture at 400C ................................................ ................ 46

4-11 Dynam ic m odulus |E*| of GA Ci at 100C ........................................... ................ 46

4-12 Phase angle of G A CI m ixture at 10C ................................................ ................ 46

4-13 Dynam ic m odulus |E*I of GACI at 250C ........................................... ................ 47

4-14 Phase angle of G A CI m ixture at 25C ................................................ ................ 47

4-15 Dynam ic m odulus |E*I of GACI at 400C ........................................... ................ 47

4-16 Phase angle of G A CI m ixture at 40C ................................................ ................ 48

4-17 Parameters used in sigmoidal fitting function..................................... ................ 50

4-18 Shift function for coarse-graded GAC3 mixture.................................................51

4-19 M aster curve for coarse-graded GAC3 mixture .................................. ................ 52

4-20 Shift function for fine-graded GAF1 mixture. .................................... ................ 52

4-21 M aster curve for fine-graded GAF1 mixture. ..................................... ................ 52

4-22 Shift function for fine-graded GAF1 mixture. .................................... ................ 53

4-23 M aster curve for coarse-graded GAC1 mixture .................................. ................ 53

4-24 Measured values versus predicted values of IE*| on a log-log scale..................... 66

4-25 Measured values versus predicted values of IE*| on a log-log scale..................... 66

4-26 Measured values versus predicted values of IE*| on a log-log scale..................... 66

4-27 Measured vs. predicted dynamic modulus values for Whiterock limestone
m ixtures: at testing frequency of 4 H z ................................................ ................ 67

4-28 Measured vs. predicted dynamic modulus for fine aggregate angularity
mixtures Superpave project mixtures Granite mixtures and Whitrock
mixtures at a Test Temperature of 400 C and a testing frequency of 4 Hz ............68

6-1 Qualitative diagram of the stress and total deformation during the creep test........ 83

6-2 Dynamic modulus at testing frequencies of 1 Hz and 4 Hz versus APA rut
depth m easurem ents. ............................... .. ....................... .......................... 86









6-3 Dynamic modulus at testing frequencies of 1 Hz and 4 Hz versus APA rut
depth measurements for coarse- and fine-graded mixtures.................................86

6-4 Dynamic modulus, |E*| versus test track rutting for the 2000 NCAT test track
se c tio n s ................................................................................................................ .... 8 7

6-5 Phase angle at a testing frequency of 1 Hz versus APA rut depth
m easu rem en ts ........................................................................................................... 8 8

6-6 Plot of E*/Sin4) at 40C and 1 Hz. versus the APA rut depths for all mixtures .......88

6-7 |E*|/sin6 versus Test Track Rutting for the 2000 NCAT test track sections............89

6-8 Plot of |E*|sin6 at 40C and 1 Hz versus APA rut depth.....................................90

6-9 Relationship between dynamic modulus at 1 Hz frequency and static creep
com pliance after 1000 seconds ........................................................... ................ 91

6-10 Relationship between dynamic modulus at 1 Hz frequency and the power
law creep com pliance param eter D 1 .................................................... ................ 91

6-11 Relationship between dynamic modulus at 1 Hz frequency and power law
m-value parameter ....................... .......... .......................... 92

6-12 Relationship between phase angle at 1 Hz frequency and static creep compliance
after 1000 seconds ................... .... ........... .........................92

6-13 Relationship between phase angle at 1 Hz frequency and the power law creep
com pliance param eter D 1 ......................................... ........................ ................ 93

6-14 Relationship between phase angle at 1 Hz frequency and power law m-value
p a ra m ete r.............................................................................................................. .. 9 3

A-1 E*| vs. co for coarse Whiterock gradations at 10, 30 and 400 C ..............................97

A-2 4 vs. o for coarse Whiterock gradations at 10, 30 and 400 C. ................................98

A-3 |E*I vs. o for fine Whiterock gradations at 10, 30 and 400 C ................................99

A-4 4 vs. o for fine Whiterock gradations at 10, 30 and 40 C. .............................101

B-i Measured test results versus predicted dynamic modulus values for fine
gradation W hiterock mixtures at 1 Hertz ....... .......... ..................................... 104

B-2 Measured test results versus predicted dynamic modulus values for fine
gradation W hiterock mixtures at 4 Hertz ....... .......... ..................................... 105









B-3 Measured test results versus predicted dynamic modulus values for fine
gradation W hiterock mixtures at 10 Hertz ....... ... .................. .................. 106

B-4 Measured test results versus predicted dynamic modulus values for fine
gradation W hiterock mixtures at 16 Hertz ....... ... .................. .................. 107

C-1 Measured test results versus predicted dynamic modulus values for fine
gradation W hiterock m ixtures ....... ......... ......... ..................... 109

C-2 Measured test results versus predicted dynamic modulus values for Coarse
gradation W hiterock m ixtures ............................................................................. 111

C-3 Measured test results versus predicted dynamic modulus values for coarse
gradation G granite m ixtures.......................................................... ............... 113

C-4 Measured test results versus predicted dynamic modulus values for fine
gradation G granite m ixtures.......................................................... ............... 115

C-5 Measured test results versus predicted dynamic modulus values for fine
gradation FA A m ixtures...................................... ........................ ............... 117

C-6 Measured test results versus predicted dynamic modulus values for fine
gradation FA A m ixtures...................................... ........................ ............... 119

D-1 Measured test results versus predicted dynamic modulus values for fine
gradation W hiterock m ixtures ....... ......... ......... ..................... 122

D-2 Measured test results versus predicted dynamic modulus values for coarse
gradation W hiterock m ixtures ....... ......... ......... ..................... 124

D-3 Measured test results versus predicted dynamic modulus values for coarse
gradation G granite m ixtures.......................................................... ............... 126

D-4 Measured test results versus predicted dynamic modulus values for fine
gradation G granite m ixtures.......................................................... ............... 128

D-5 Measured test results versus predicted dynamic modulus values for fine
gradation "FAA" m fixtures ........................................................ 130

D-6 Measured test results versus predicted dynamic modulus values for coarse
gradation "FAA" m fixtures ........................................................ 131

E-1 Comparison of measured dynamic modulus test results vs. Witzack's-2002
predicted results at 100C degrees ....... ......... ........ ..................... 133

E-2 Comparison of measured dynamic modulus test results vs. Witzack's-2002
predicted results at 400C degrees ....... ......... ........ ..................... 134









E-3 Comparison of measured dynamic modulus test results vs. Witzack's-2002
predicted results at 100C degrees, on log scale....... .................. ................... 135

F-i Dynamic modulus values for fine graded Whiterock mixtures........................... 138

F-2 Do values for fine graded Whiterock mixtures.......................... ...................140

F-3 D1 values for fine graded Whiterock mixtures........................... ...................142

F-4 Dynamic modulus values for fine graded Project mixtures............................. 144

F-5 Do values for fine graded Project mixtures ....... ... ...................................... 146

F-6 Do values for fine graded Whiterock mixtures........................... ...................148

F-7 Do values for fine graded "FAA" mixtures.......... ..................................... 150

G-1 Gradation line and power regression lines of fine gradation Whiterock
sa m p le s ............................................................................................................... ... 1 5 3

G-2 Gradation line and power regression lines of coarse gradation Whiterock
sa m p le s ............................................................................................................... ... 1 5 5

G-5 Gradation line and power regression lines of fine gradation Project samples ....... 157

H-1 Complex modulus values predicted by using Witczak's 2002 Predictive
equation by using different viscosity conditions......................... ................... 162















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

DETERMINING GRADATION AND CREEP EFFECTS IN MIXTURES USING THE
COMPLEX MODULUS TEST

By

Erkan Ruhi Ekingen

August 2004

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

The 2002 revision of the AASHTO Guide to the Design of Pavement Structures

uses the dynamic modulus test (|E*|) to characterize mixes used on interstate highways

and most other high-volume highways that require superior load resistance. An

understanding of its mechanics and procedures is fundamental for understanding how the

test can be used.

The purpose of this study was to establish a correlation between Complex Modulus

and a number of issues such as the Viscosity, Gradation, and Rutting Resistance














CHAPTER 1
INTRODUCTION

A Brief Introduction to Dynamic Modulus (IE*|)

Dynamic Modulus1 (IE*|) has been known to some researchers since the 1960s. But

the use of |E*| by departments of transportation has not been widespread. However,

current efforts in pavement research (revising the AASHTO Guide to the Design of

Pavement Structures and modeling for SuperPaveTM) rely on the use of |E*|. The 2002

revision of the AASHTO Guide to the Design of Pavement Structures uses the dynamic

modulus test (IE*|) to characterize mixes used on interstate highways and most other

high-volume highways that require superior load resistance. The guide is based on

mechanistic principle and requires a modulus to compute stresses and strains in hot-mix

asphalt (HMA) pavements.

Briefly, |E*| is the absolute value of the modulus of a viscoelastic material. The

dynamic (complex) modulus of a viscoelastic test is a response developed under

sinusoidal loading conditions. It is a true complex number as it contains both a real and

an imaginary component of the modulus and is normally identified by |E*| (or G*).A

Brief Introduction to Gradation and Packing




1 In viscoelastic theory, the absolute value of the complex modulus |E*|, by definition, is
the Dynamic Modulus. In the general literature, however, the term, "Dynamic Modulus"
is often used to denote any type of modulus that has been determined under "non-static"
load conditions.









The packing of particles into a confined volume has been studied for over 300

years. Sir Isaac Newton-among the first to study this phenomenon-was not able to

prove the existence of a maximum density. In more modern times, Nijboer, Goode and

Lufsey (AAPT 1961), and Huber and Shuler (ASTM 1991) have added to our knowledge

regarding the effect of gradation on the packing of aggregate particles.

In hot mix asphalt design, aggregate type and gradation are considered routinely.

Mix designers learn by experience the combination of aggregates that will provide

adequate voids in the mineral aggregate. Adequate rules or laws that govern the effect of

gradation on aggregate packing are not available to mix designers.

Objectives

The objectives of this study include:
* Evaluating the Predictive equation by Witczak et al. (2002) for use in Florida
materials used in HMA designs

* Evaluating the effects of gradation and aggregate type on dynamic modulus

* Evaluating how well creep properties obtained from short-term dynamic modulus
measurements compare to static-creep testing results.

To achieve these objectives, complex-modulus testing and static-creep testing were

performed on 25 mixtures of varying gradation and aggregate types.













CHAPTER 2
LITERATURE REVIEW

Background and History of Complex Modulus Testing

Complex modulus testing for asphalt mixtures is not a new concept. Papazian

(1962) was one of the first to delineate viscoelastic characterization of asphalt mixtures

using the triaxial cyclic complex modulus test. He concluded that viscoelastic concepts

could be applied to asphalt pavement design and performance. Forty years after these

experiments, the concept of complex modulus testing is still being used to develop mix

design criteria, and to evaluate performance of material in pavement.

Work continued in the next decade that considered compression, tension, and

tension-compression loading. A number of studies indicated differences in dynamic

modulus testing obtained from different loading conditions. The differences especially

affect the phase angle, and tend to become more significant at higher temperatures.

Witczak and Root (1974) indicate that the tension-compression test may be more

representative of field loading conditions. Khanal and Mamlouk (1995) affirmed this

assertion. They performed complex modulus tests under five different modes of loading

and obtained different results, especially at high temperatures. Bonneaure et al. (1977)

determined the complex modulus from a bending test. Deformation was measured, and

the complex modulus was calculated from the results.

In the 1980s and early 1990s, the International Union of Testing and Research

Laboratories for Materials and Structures (RILEM) Technical Committee on Bitumen

and Asphalt Testing organized an international testing program (1996). The goal of the









program was to promote and develop mix design methodologies (and associated

significant measuring methods) for asphalt pavements. Complex modulus tests were

performed by 15 participating laboratories, in countries throughout Europe. Results

showed that bending tests and indirect tension tests were in reasonable agreement under

certain conditions. The laboratories were able to reproduce the phase angle much better

with complex modulus than dynamic modulus.

Stroup-Gardiner (1997), Drescher, Newcomb, and Zhang (1997), and Zhang,

Drescher and Newcomb (1997) performed complex modulus tests on both tall cylindrical

specimens and indirect tensile specimens. Results were mixed, showing that tests on the

same material with the two different setups sometimes yielded different results for the

dynamic modulus and phase angle. The phase angle was especially variable in both test

setups.

The most comprehensive research effort started in the mid-1990s as part of the

NCHRP Project 9-19 (Superpave Support and Performance Models Management) and

NCHRP Project 9-29 (Simple Performance Tester for Superpave Mix Design). Their

research proposed new guidelines for the proper specimen geometry and size, specimen

preparation, testing procedure, loading pattern, and empirical modeling. Some of their

key findings were reported by Witczak (2000), Kaloush (2002), and Pellinen (2002).

Superpave Shear Tester

As part of the SHRP program, the complex shear modulus (G*) was introduced for

asphalt binder specifications (AASHTO TP 5, 1998), allowing better characterization of

the rheological behavior of asphalt binders at different temperatures. Similar efforts were

undertaken on mixtures as a part of SHRP, where testing methods for the complex

modulus of mixtures were evaluated by using a torsional hollow cylinder test. Their









researches lead to the development of the SHRP Constant Height Simple Shear Test

(CHSST). The complex shear modulus (G*) was the main parameter obtained from the

CHSST test. However, a number of issues remain regarding the applicability of the

CHSST test. In particular, the adherence to constant height requirements remains

controversial at best, resulting in highly variable stress states during testing. Results from

the CHSST test have been shown to relate to rutting performance. However, the data

from the CHSST tests are highly variable. Several attempts have been made to lower the

variation, including reducing the generally accepted specimen air void range of + 0.5

percent to a tighter tolerance, increasing the number of specimens, and using additional

LVDTs.

In the following, an overview of the various stiffness measurements used in flexible

pavement characterization will be provided, followed by a summary of the state of art

complex modulus testing of mixtures.

Modulus Measurement in Viscoelastic Asphalt Mixtures

The resilient modulus (Mr) has long been considered the defining characteristic for

HMA layers. It has been used since 1993 in the AASHTO Design Guide (AASHTO,

1993). The laboratory procedure for the Mr test is described in AASHTO T 307-99. The

test is well defined as a repeated 0.1 second haversine load followed by a 0.9 second rest

period, repeated at 1 Hz intervals.

Due to the long history of using Mr in pavement design, 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 (AASHTO, 1993).

However, the ability of the Mr to account for vehicle speed effects has lead to a push to









develop methods that account fully for the variation of stiffness in HMA pavements with

vehicle speeds.

The concept behind the complex modulus test is to account 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. Hence, the

fundamental difference between the complex modulus test and the resilient modulus test

is that the complex modulus test does not allow time for any delayed elastic rebound

during the test.

The dynamic modulus (IE*|) relates the cyclic strain to cyclic stress in a sinusoidal

load test. The dynamic modulus test procedure outlined in ASTM D 3497 uses a

standard triaxial cell to apply stress or strain amplitudes to a material at 16 Hz, 4 Hz, and

1 Hz. It also recommends that the test be repeated at 50C, 250C, and 400C (ASTM D

3497). The dynamic modulus is calculated using Equation 2-1 (Yoder & Witczak, 1975).


E*| = o (Eq. 2-1)
go

Where

co is the stress amplitude,
So is the strain amplitude.

This parameter includes the rate dependent stiffness effects in the mixture.

However, it does not provide insight into the viscous components of the strain response.

The dynamic modulus test can be expanded on to find the complex modulus (E*). The

complex modulus is composed of a storage modulus (E') that describes the elastic

component and a loss modulus (E") that describes the viscous component. The storage

and the loss moduli can be determined by the measurement of the lag in the response




















CO \






Time

1-1. The testing components of the complex modulus

between the applied stress and the measured strains. This lag, referred to as the phase

angle (6), shown in Figure 2-1. Equation 2-2 describes the relationship between the

various components and E*:


S = tan E (Eq. 2-2a)
E'

E"= E *E sin(S) (Eq. 2-2b)
E'= E *cos(3) (Eq. 2-2c)

The phase angle is typically determined by measuring the time difference between

the peak stress and the peak strain. This time can be converted to 6 using Equation 2-3.

S= tlg f. (3600) (Eq. 2-3)

Where
f is the frequency of the dynamic load (in Hz),
tlag is the time difference between the signals (in seconds).
A phase angle of zero indicates a purely elastic material and a 6 of 900 indicates a

purely viscous material.









For linear elastic materials, only two properties are required to describe the stress-

strain behavior under any loading condition. The Young's modulus is typically used to

describe changes due to the normal stresses and the shear modulus (G) describes the

change in the material due to shear stresses. Similarly, the inclusion of Poisson effects is

captured by the Poisson's ratio (u). In viscoelastic materials, G* and E* are the most

commonly used parameters. The magnitude of G* is calculated using the shear stress

amplitude (To) and the shear strain amplitude (Yo) in Equation 2-4 by Witczak et al.

(1999).


G = 0 (Eq. 2.4)
70

Similar to the complex modulus, G* has an elastic component (G') and a viscous

component (G") by Witczak et al. (1999). These components are related through the

phase angle (6) as seen in Equation 2-5.


3 = tan \G'1 (Eq. 2-5a)
\G'j

G"= G sin(3) (Eq. 2-5b)

G'= G *cos(3) (Eq. 2-5c)

To calculate both the E* and the G* coefficients, it must be possible to measure not

only the axial compressive stresses and strains, but also the shear stresses and strains.

Harvey et al. (2001) concluded that G* can be related to E* using Equation 2-6.


G* = 2(1 (Eq. 2-6)


By directly measuring changes in the height and radius of the asphalt sample,

Poisson's ratio can be calculated. This is done by calculating v as the ratio of lateral









expansion to the axial compression. Equation 2-6 assumes that the Poisson's ratio is

constant and some testing has shown that the Poisson's ratio for HMA is frequency

dependent.

Master Curves and Shift Factors

The master curve of an asphalt mixture allows comparisons to be made over

extended ranges of frequencies and temperatures. Master curves are generated using the

time-temperature superposition principle. This principle allows for test data collected at

different temperatures and frequencies to be shifted horizontally relative to a reference

temperature or frequency, thereby aligning the various curves to form a single master

curve. The procedure assumes that the asphalt mixture is a thermo-rheologically simple

material, and that the time-temperature superposition principle is applicable.

The shift factor, a(T), defines the shift at a given temperature. The actual

frequency is divided by this shift factor to obtain a reduced frequency,f, for the master

curve,

f=- f or log(fr) = log(f) log[a(T)] (Eq. 2-7)
a(T)

The master curve for a material can be constructed using an arbitrarily selected

reference temperature, TR, to which all data are shifted. At the reference temperature, the

shift factor a(T) = 1. Several different models have been used to obtain shift factors for

viscoelastic materials. The most common model for obtaining shift factors is the

Williams-Landel-Ferry (WLF) equation (Williams, Landel, Ferry, 1955).

When experimental data are available, a master curve can be constructed for the

mixture. The maser curve can be represented by a nonlinear sigmoidal function of the

Equation 2-8.










log(E *) = 3 + (Eq. 2-8)


Where

log(|E*|) = log of dynamic modulus,
6 = minimum modulus value,
fr = reduced frequency,
U. = span of modulus value,
P, y = shape parameters.

Note that 6 in this equation is not related to the phase angle it is just the notation

chosen by Pellinen and Witzcak (2002) for the minimum modulus value. The sigmoidal

function of the dynamic modulus master curve can be justified by physical observations

of the mixture behavior. The upper part of the function approaches asymptotically the

mixture's maximum stiffness, which depends on the binder stiffness at cold temperatures.

At high temperatures, the compressive loading causes aggregate interlock stiffness to be

an indicator of mixture stiffness. The sigmoidal function shown in Equation 2-8 captures

the physical behavior of asphalt mixtures observed in complex modulus testing

throughout the entire temperature range (Pellinen and Witzcak, 2002).

Sample Preparation

Currently, there is much discussion about the shape and size of specimen to be used

in complex modulus testing. In NCHRP Project 9-19, Witzcak and his colleagues

investigated the proper size and geometry of test specimens (Witzcak et al. 2000). Based

on numerous complex modulus test results, they recommended using 100-mm diameter

cored specimens from a 150-mm diameter gyratory compacted specimen, with a final

saw cut height of 150-mm. This recommendation came from a study (Chehab et al.,

2000) that considered the variation in air voids within specimens compacted using the

Superpave Gyratory Compactor (SGC). The studies showed that specimens compacted









using the SGC tend to have non-uniform air void distribution both along their diameter

and along height. SGC-compacted specimens have higher air void content at the top and

bottom edges, and in sections adjacent to the mold walls, as compared to the interior

portion of the specimens. Finally, fully lubricated end plates were found to minimize end

restraint on the specimen. Increasing the number of gages used to measure axial strain

decreases the number of test specimens necessary.

Load Level

Since the interpretation of the complex modulus is based on the assumption of

linear viscoelasticity of the mixture, it is necessary to maintain a fairly low strain level

during testing to avoid any nonlinear effects. Maintaining a stress level that results in a

strain response that is close to linear is critical to achieve a test that is reproducible.

The concept of material linearity is based upon two principles. The first principle,

proportionality, is described with Equation 2-9.

(C a(t)) = C (at)) (2-9)

It implies that if a stress is increased by any factor then the strain will also increase

by the same factor. This allows the shape of the stress/strain relationship to be more

easily mapped out across the linear range.

The principle of superposition is the other condition that describes linearity.

Equation 2-10 describes this concept.

(oa, (t) +,2 (t -t))=)) = s(0-2 (t- 1)) (Eq. 2-10)

This implies that if it is known how the material will behave under a single loading

condition that it will be known how it would behave under multiple loads. Figure 2-2

and 2-3 show graphically the concept proportionality and superposition. The






12


combination of these principles allows the material behavior to be predicted with fewer

parameters.


Time


Time


Figure 2-2. Proportionality of Viscoelastic Materials

HMA has been found to behave linearly, but only for specific temperature and

strain regions. Mehta and Christensen (1999) describe HMA as linear for low

temperatures (-200C to -100C) and shear strains under 200 microstrain. For intermediate

temperatures (40C to 200C), shear strains should be less then 50 microstrain, to stay

within the viscoelastic limits. However, it should be noted that the determination of


S






13


linearity might also be affected by the loading mechanism (i.e., compression, tension,

torsion).


Time


Time

Figure 2-3. Superposition of Viscoelastic Materials

For dynamic modulus measurements using uniaxial compression testing, the

ASTM D 3497 recommends using an axial stress amplitude of 241.3 kPa (35 psi) at all

temperatures as long as the total deformation is less then 2500. Daniel and Kim (1998)

showed successful triaxial compression testing results with stress levels under 96.5 kPa

for 150C testing. Strain amplitudes of 75 to 200 microstrains have also been suggested to

maintain material linearity during triaxial compression testing (Witczak et al. 1999).









Complex Modulus as a Design Parameter

The 2002 AASHTO Guide for the Design of Pavement Structures recommends the

complex modulus as a design input parameter for the mechanistic-empirical design

procedure (NCHRP 1-37A 2002 Design Guide Draft, 2002). Level 1 Analysis requires

actual dynamic modulus test data to develop master curves and shift factor based on

Equations (2-7) and (2-8). This testing is performed on replicate samples at five

temperatures and four rates of loading per temperature. Binder testing must be performed

at this level to shift the data into smooth master curves. Level 2 Analysis constructs a

master curve using actual asphalt binder test data based on the relationship between

binder viscosity and temperature. Level 3 Analysis requires no laboratory test data.

Instead, the Witczak modulus equation (NCHRP 1-37A 2002 Design Guide Draft,

2002) is used with typical temperature-viscosity relationships established for all binder

grades.

Witczak Predictive Modulus Equation

The complex modulus test is relatively difficult and expensive to perform.

Therefore, numerous attempts have been made to develop regression equations to

calculate the dynamic modulus from conventional volumetric mixture properties. For

example, a predictive regression equation is proposed as a part of the 2002 Design Guide

(Witczak et al., 2002) to calculate the dynamic modulus, E*|, based on the volumetric

properties of any given mixture. The predictive equation developed by Witczak et al.

(2002) is one of the most comprehensive mixture dynamic modulus models available

today (Equation 2-11).









loE* = -1.249937+ 0.029232x (p200) -0.001767x (p200)2 -0.002841x (p4)
0.802208ViJ) (Eq. 2-11)
-0.058097x (V) -0 (Eq. 2-11)

3.871977- 0.0021(p4) + 0.00395p3/8) -0.00017p3/8)2 + 0.00547(p3/4)
1 + e(-0 603313-0313351log(f)-039353dlog(,r))

Where
|E*| = dynamic modulus, in 105 psi;
r| = bitumen viscosity, in 06 Poise;
f = loading frequency, in Hz;
Va = percent air void content, by volume;
Vbeff = effective bitumen content, percent by volume;
P3/4 = percent weight retained on 19-mm sieve, by total aggregate weight;
P3/8 = percent weight retained on 9.5-mm sieve, by total aggregate weight;
P4 = percent weight retained on 4.75-mm sieve, by total aggregate weight;
P200 = percent weight passing 0.75-mm sieve, by total aggregate weight;

The above dynamic modulus predictive equation has the capability to predict the

dynamic modulus of dense-graded HMA mixtures over a range of temperatures, rates of

loading, and aging conditions from information that is readily available from

conventional binder tests and the volumetric properties of the HMA mixture. This

predictive equation is based on more than 2,800 different HMA mixtures tested in the

laboratories of the Asphalt Institute, the University of Maryland, and FHWA.

Complex Modulus as a Simple Performance Test

The goal of NCHRP Project 9-19 was to develop a Simple Performance Test (SPT)

for asphalt mixtures. Various testing configurations were evaluated from several of the

most promising test methods. The potential SPT methods can be categorized as stiffness-

related tests, deformability tests, and fracture tests. The stiffness parameters were

obtained from compressive complex modulus, SHRP Simple Shear Tester (SST), and

ultrasonic wave propagation. Of these three candidates, the complex modulus appeared

to be the most promising for relating material properties to rutting and fatigue cracking

observed in the field (Pellinen and Witzcak, 2002).









Fatigue Cracking

Witczak et al. (2002) performed numerous complex modulus tests to perfect the

recommendations for fatigue and cracking in asphalt mixtures. The results led to the

development of a fatigue distress model in which the number of repetitions to failure, Nf,

is a function of the horizontal tensile strain, St, which represents the largest of the

transverse and longitudinal horizontal strain, and dynamic modulus of the mix, E*|:

5 14
Nf = FK- (Eq. 2-12)


The adjustment factor, F, that indicates the stress or strain controlled fatigue

behavior in the pavement structure, is a function of the dynamic modulus and pavement

thickness,

hac:

13909E -4-1
F=+ + e 354h1-5 408) (Eq. 2-13)


A volumetric adjustment factor, Ki,, corrects the number of repetitions to failure

by taking into account the binder and mix properties. In the equation 2-14, PI is the

binder penetration index and Vb is the volume of binder in the mix:

K1, = [0.0252PI 0.00126PI(Vb)+ 0.00673Vb -0.0167]5 (Eq. 2-14)

Equation (2-12) can be reduced to the following equation, where the constants o3n

and kn can be assigned to nationally calibrated fatigue model constants:


N, = Pf k I (Eq. 2-15)









Finally, it is expected that each state agency will have to develop local calibration

factors for Equation 2-15.

Rutting

The complex modulus test also showed good correlation to permanent deformation

of asphalt mixtures. Witczak et al. (2002) performed research on asphalt mixtures similar

to the SPT for fatigue cracking. Cylindrical specimens were tested at five temperatures

and six frequencies, as well as different level of confining pressure. They come to

preliminary findings that warranted a closer look at the dynamic modulus test for rutting

susceptibility. Pellinen and Witczak (2002) recommended using dynamic modulus

obtained in unconfined compression at 54.4 C and a frequency of 5 Hz. The stress

levels must remain small to keep the sample in the linear viscoelastic region.














CHAPTER 3
MATERIALS USED IN AXIAL COMPLEX MODULUS TESTING

Introduction

This chapter provides information on the materials used in the testing of the axial

complex modulus. The physical properties of materials used are discussed, such as their

aggregate gradation, aggregate physical properties, mixture design procedure, and

material preparation.

Overview of Mixtures Used.

Four distinctive group of mixture were used for the purpose of this research.

* Eight mixtures of varying gradations with oolitic limestone (Whiterock) from South
Florida, entitled "Limestone Gradation Study Mixtures" (C and F).

* Six mixtures of varying gradations with Georgia granite (GA185), entitled "Granite
Gradation Study Mixtures" (GAC and GAF)

* Five field mixtures of varying gradations and aggregate types from Superpave
monitoring test sites in Florida, entitled "Superpave Field Monitoring Mixtures" (P).

* Eight mixtures (entitled "Fine Aggregate Angularity (FAA) Mixtures") with different
fine aggregates (defined as material passing the no. 4 Sieve) and the coarse portion of
the aggregates consisting of oolitic limestone (Whiterock) from South Florida,

Asphalt Binders Used

The grade of the asphalt cement used in mixtures is one factor that can have an

effect on the amount of rutting that occurs in the mix. All other things being equal, the

stiffer the asphalt cement, the less the rutting that is expected in the mix under a given

weight and volume of truck. In this research, only one type of unmodified asphalt

cement, AC-30 (PG67-22), which is commonly used in Florida was used for all mixtures









tested, except for the modified HVS mixture, in which an SBS modified binder (PG 76-

22) was used.

Aggregates

This section describes the type of aggregates, aggregate gradations and

combination of various aggregates in this research.

Fine Aggregate Angularity (FAA) Mixtures

The first part of the research was performed using gradations of coarse and fine

Whiterock limestone mixtures (Cl and F 1) provided by FDOT for use as the reference

mixtures. The nominal maximum aggregate size for these mixtures is 12.5 mm (1/2-in).

These Superpave mixtures were selected because they are commonly used FDOT

gradations and they are known to perform well in the field. Figure 3-1 shows the

gradation curves for the Cl and F 1 mixtures.

The fine aggregate portions of these mixtures were volumetrically replaced by four

other fine aggregate types (passing the No. 4 Sieve) to obtain five fine graded and five

coarse graded mixtures. All materials were washed in accordance with ASTM C-1 17 and

a washed sieve analyses were performed according to ASTM C-136. The fine aggregates

used were selected to be of varying angularity, texture, toughness, and historical rutting

performance. The designations for the fine aggregates used are as follows.

* Limestone
* Whiterock (baseline aggregate)
* Cabbage Grove (FL)
* Calera (AL)
* Granite
* Ruby (GA)
* Gravel
* Chattahoochee FC-3 (TN)











Nominal Size 12.5 mm


n o Co


F 1


lowercontrol
upper control
.--- -. M ax Dent Line
-- Restricted Zone

LO LO C


Sieve Size (raised to 0.45 power) mm


Figure 3-1. Gradation curves for Cl and Fl

The aggregates are designated in this project as follows:


* Calera-CAL
* Whiterock-WR
* Cabbage Grove-CG
* Ruby-RB
* Chattahoochee FC-3 CH


Table 3-1. Coarse gradations for fine aggregate effects
Sieve Size (mm) WRC CGC RBC CHC CALC
25 100.0 100.0 100.0 100.0 100.0
19 100.0 100.0 100.0 100.0 100.0
12.5 97.4 97.4 97.5 97.5 97.5
9.5 90.0 88.8 89.5 89.4 89.3
4.75 60.2 54.8 57.6 56.9 56.5
2.36 33.1 30.4 31.6 31.3 31.2
1.18 20.3 20.5 21.1 20.9 20.9
0.600 14.7 14.8 15.1 15.0 15.0
0.300 10.8 11.0 11.0 11.0 11.0
0.150 7.6 7.2 7.0 7.1 7.1
0.075 4.8 5.5 5.2 5.2 5.3










Table 3-2. Fine gradations for fine aggregate effects
Sieve Size (mm) WRF CGF RBF CALF CHF
25 100.0 100.0 100.0 100.0 100.0
19 100.0 100.0 100.0 100.0 100.0
12.5 95.5 97.4 95.1 94.9 95.0
9.5 85.1 83.8 85.0 84.6 84.7
4.75 69.3 66.0 68.5 67.6 67.9
2.36 52.7 49.4 51.2 50.6 50.8
1.18 34.0 33.3 34.2 33.9 34.0
0.600 22.9 21.9 22.4 22.2 22.2
0.300 15.3 13.9 14.0 14.0 14.0
0.150 9.6 7.0 6.9 6.9 6.9
0.075 4.8 4.5 4.3 4.3 4.3

Table 3-3 shows the Bulk specific gravity, toughness, and the surface texture,

particle shape, direct shear strength (DST) from a Geotechnical direct shear box test, and

Fine Aggregate Angularity (FAA) values of the five fine-graded aggregates used. Bulk

Specific Gravity ranged from 2-27 for relatively porous limestone to 2-68 for very non-

porous granite. Toughness of the parent rock varied from 18.0 % as the lowest value to

42.0 % as the highest value of the L.A. Abrasion test. Average surface texture values

ranged from 1-7 to 4-6, while average particle shape values ranged from 2-4 to 4-3.

Table 3-3. Physical properties of fine aggregates
Bulk DAA
r S Los Angeles b Surface Particle DST
Material Specific A a Toughnessb Texture Shaped FAA (psi)
Gravity Abrasiona Texture Shape
White Rock 2.48 34% Medium 3.3 3.0 43.4 134.4
Calera 2.56 25% High 1.7 3.5 42.7 140.8
Cabbage Grove 2.56 41% Low 4.6 2.4 53.1 106.7
Ruby 2.68 20% High 2.7 4.3 46.3 120.5
Chattahoochee 2.60 42% Low 2.3 3.5 44.0 106.9
FC-3
a) Los Angeles Abrasion Test performed on the parent rock. Values provided by the Florida DOT Materials Office.
b) Definition of toughness based on L.A. Abrasion. High: <30; Medium: 30-40; Low: >40
c) Average of 8 evaluations, where 1 = smooth and 5 = rough.
d) Average of 8 evaluations, where 1 = rounded and 5 = angular.

Bulk Specific Gravities for each material were determined in accordance with

ASTM C-128. The Florida Department of Transportation (FDOT) provided LA Abrasion

values. The FAA values were calculated using the Uncompacted Void Content of Fine

Aggregate Test (ASTM C-1252 and AASHTO TP33), and the Direct Shear Test (DST,









ASTM Standard Method D 3080) was used to determine the shear strength of each fine

aggregate. Both FAA and DST values were provided by previous research done by

Casanova (2000).

Determination of Fine Aggregate Batch Weights

To volumetrically replace the fine aggregates in the FDOT Whiterock limestone Cl

and F 1 mixtures with the other aggregate types, the weight of Whiterock aggregate

retained on each sieve (from #8 Sieve to # 200 Sieve) was replaced with an equivalent

volume of fine aggregate of the replacement material during the watching process using

the following equation 3-1.

G
Wr = G .WL (Eq. 3-1)
GmbL

WL : Weight of Whiterock limestone retained on a specified sieve

Wr : Weight of replacement fine aggregate retained on the specified sieve size

GmbL: Bulk specific gravity of Whiterock Limestone

Gmbr : Bulk specific gravity of replacement aggregate

Limestone Gradation Study Mixture Gradations

The second part of the research was done with an oolitic limestone aggregate,

entitled "Whiterock" aggregate, which is commonly used in mixtures in Florida. This

aggregate was made up of three components: coarse aggregates (S1A), fine aggregates

(S1B) and screenings. These were blended together in different proportions to produce

ten (10) HMA mixtures consisting of five coarse and five fine gradations, two of which

are the same gradations as in the Fine Aggregate study, namely WRC and WRF. Georgia

granite (GA 185) mineral filler was used in all the above gradations. These gradations

were produced and extensively studied in a previous research at UF (Nukunya, 2000).










Tables 3-4 and 3-5 show the gradations for the coarse and fine blends respectively. These

are also displayed in Figures 3-2 and 3-3.

Table 3-4. Gradations for White Rock coarse graded mixtures
Sieve Size (mm) C1 C2 C3
25 100.0 100.0 100.0
19 100.0 100.0 100.0
12.5 97.4 91.1 97.6
9.5 90 73.5 89.3
4.75 60.2 47.1 57.4
2.36 33.1 29.6 36.4
1.18 20.3 20.2 24
0.600 14.7 14.4 17.7
0.300 10.8 10.4 12.9
0.150 7.6 6.7 9.0
0.075 4.8 4.8 6.3

Table 3-5. Gradations for White Rock fine graded mixtures
Sieve Size (mm) F1 F2 F4 F5 F6
25 100.0 100.0 100.0 100.0 100.0
19 100.0 100.0 100.0 100.0 100.0
12.5 95.5 90.8 95.5 95.5 95.5
9.5 85.1 78 85.1 85.1 85.1
4.75 69.3 61.3 69.3 61.3 69.3
2.36 52.7 44.1 52.7 52.7 44.1
1.18 34.0 34.7 40.0 34.0 34.7
0.600 22.9 23.6 29.0 22.9 23.6
0.300 15.3 15.7 20.0 15.3 15.7
0.150 9.8 8.9 12.0 9.6 9.1
0.075 4.8 6.3 6.3 4.8 6.3

Granite Mixtures Used

Three mixtures were prepared by volumetrically replacing the aggregate particles in

the GAC1, GAC2, GAC3, GAF1, GAF2 and GAF3 limestone mixtures with the

appropriate sizes of Georgia granite (GA185) aggregates from pit #185 (code #7 for 12.5

and 9.5 mm sieves, code #89 for 4.75mm (#4) sieve and code #W10 for sieves less than

#4). Table 3-6 to 3-8 show the gradations, which are also displayed in Figures 3-4 to 3-7.











Nominal Size 12.5 mm


U0 0 0 0 C(D LO C6 0

Sieve Size (raised to 0.45 power) mm
Sieve Size (raised to 0.45 power) mm


Figure 3-2. Coarse gradations for gradation effects studies

Nominal Size 12.5 mm


o0 0 0 O CD U) U U 0
-0 UO 0 )zCO ( t o i 06m
P C? l (q

Sieve Size (raised to 0.45 power) mm


Figure 3-3. Fine gradations for gradation effects studies











Table 3-6. Granite based mixture gradations


GAC2 GAC3


100.0
100.0
90.9
72.9
45.9
28.1
18.9
13.2
9.2
5.6
3.9


100.0
100.0
97.3
89.5
55.4
33.9
23.0
16.0
11.2
6.8
4.7


GAF1

100.0
100.0
94.7
84.0
66.4
49.2
32.7
21.0
12.9
5.9
3.3


GAF2

100.0
100.0
90.5
77.4
60.3
43.2
34.0
23.0
15.3
8.7
5.4


Nominal Size 12.5 mm


LO 0 C0
0- LO 0
0 CO (0
CC C- C C)


Sieve Size (raised to 0.45 power) mm

Figure 3-4. Coarse graded Granite aggregate gradations

Superpave Field Monitoring Mixture Gradations

Five Superpave mixtures from Florida, and tested for performance at the University

of Florida (Asiamah 2001) were also evaluated. Figures 3-5 and 3.7 display the


gradations of these mixtures.


Sieve Size
(mm)
25
19
12.5
9.5
4.75
2.36
1.18
0.600
0.300
0.150
0.075


GAC1

100.0
100.0
97.39
88.99
55.46
29.64
19.24
13.33
9.30
5.36
3.52


GAF3

100.0
100.0
94.6
85.1
65.1
34.8
26.0
18.1
12.5
7.7
5.8


LO LO
SNi












Nominal Size 12.5 mm


LO o O OO (O LO LO LO O
rN-Co C .- O CC 0
Co0) CO ("""

Sieve Size (raised to 0.45 power) mm

Figure 3-5. Fine graded Granite aggregate gradations

Table 3-7. Gradation of field projects


Sieve Size
(mm)


19
12.5
9.5
4.75
2.36
1.18
0.600
0.300
0.150
0.075


100.0

100.0
100.0
99.0
64.0
40.0
29.0
21.0
14.0
8.0
5.1


100.0

100.0
98.0
89.0
45.0
28.0
22.0
17.0
12.0
7.0
4.9


100.0

100.0
94.0
90.0
67.0
34.0
25.0
18.0
13.0
7.0
4.4


100.0

100.0
100.0
94.0
64.0
34.0
24.0
19.0
13.0
8.0
3.9


P7

100.0

100.0
95.0
88.0
70.0
57.0
41.0
30.0
19.0
9.0
4.2











Nominal Size 12.5 mm


D) C0 C C 0 c CO l Lko Lfl C0


Sieve Size (raised to 0.45 power) mm

Figure 3-6. Gradations for Superpave project mixtures number 2, 3, and 7.


Nominal Size 9.5 mm


C
W' 60
,m

50


CL
( 40
n


LD OG O CO UO L-D LD LID

Sieve Size (raised to 0.45 power) mm
Sieve Size (raised to 0.45 power) mm


Figure 3-7. Gradations for field projects 1 and 5









Project 1 (P1) and Project 5 (P5) are 9.5 mm nominal gradations while all the other

projects are of 12.5 mm nominal size. All the field mixtures are coarse-graded (i.e., the

gradations pass below the Superpave Restricted Zone).

Mixture Design

Before the production of test specimens, the mixture design process was verified

for the mixture volumetric properties. The original Superpave design procedure was used

for all the mixtures. The Servopac Superpave gyratory compactor was used in this

process. Figure 3-8 shows a picture of the Servopac gyratory compactor. Table 3-8

displays the Superpave compaction requirements for specified traffic levels as a guide for

the design of asphalt paving mixtures. The mixture volumetric properties are calculated

based on the design number of gyrations (Ndes). At this number of gyrations, a specified

air voids level of 4% provides the optimum design asphalt content. All mixtures were

designed for a traffic level of 10-30 million ESALS that is an Ndes of 109 and Nmax of

174. The project mixes except project 7, were designed at an Ndes of 96 and Nmax of 152.

Project 7 has an Ndes of 84. The Servopac compaction parameters used for the design are

1.250 gyratory angle, 600-kPa ram pressure and 30 revolutions per minute.

For each mixture, two pills were produced at the specified asphalt content.

Compaction of the mixtures was made to 109 gyrations with the Servopac gyratory

compactor, after which the bulk densities were measured. To verify the volumetric

properties of the mixtures, the maximum theoretical specific gravity was measured using

the 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. Tables 3-9 to 3-14 show the volumetric properties of all the mixtures

used in this research.
















































Figure 3-8. Servopac superpave gyratory compactor

Table 3-8. Superpave gyratory compaction effort (After asphalt institute Superpave series
no. 2)
Design Average Design High Air Temperature
ESALS <300C
(Millions) Nim Ndes Nmax
<0.3 7 68 104
03. to 1 7 76 117
1 to 3 7 86 134
3 to 10 8 96 152
10 to 30 8 109 174
30 to 100 9 126 204
>100 9 143 233











Table 3-9. Volumetric properties of coarse graded mixtures

Mixture
Property Symbol WRC CGC RBC CALC CHC
Maximum Theoretical Density Gmm 2.328 2.386 2.393 2.454 2.394
Specific Gravity of Asphalt Gb 1.035 1.035 1.035 1.035 1.035
Bulk Specific Gravity of Compacted mix Gmb 2.235 2.295 2.300 2.353 2.289
Asphalt Content Pb 6.5 6.5 6.25 5.8 5.7
Bulk Specific Gravity of Aggregate Gsb 2.469 2.418 2.576 2.540 2.535
Effective Specific Gravity of Aggregate G.e 2.549 2.625 2.622 2.680 2.601
Asphalt Absorption Pba 1.1 3.0 0.6 1.7 0.7
Effective Asphalt Content in the Mixture Pbe 5.3 3.3 5.6 3.7 4.7
Percent VMA in Compacted Mix VMA 15.4 11.2 16.1 12.6 14.8
Percent Air Voids in Compacted Mix Va 4.0 3.8 3.9 4.1 4.4
Percent VFA in Compacted Mix VFA 74.0 66.5 77.3 67.4 70.6
Dust/Asphalt ratio D/A 1.0 1.7 0.9 1.4 1.1
Surface Area (m2/kg) SA 4.2 4.4 4.3 4.3 4.3
Theoretical Film Thickness FT 11.2 6.7 11.7 9.8 7.7
Effective VMA in Compacted Mix VMA 35.4 28.6 38.4 31.7 35.6
Effective Film Thickness Fte 39.2 25.1 42.5 27.4 36.0


Table 3-10. Volumetric Properties of Fine Graded Mixtures
Mixture
Property Symbol WRF CGF RBF CALF CHF
Maximum Theoretical Density G. 2.338 2.381 2.416 2.480 2.407
Specific Gravity of Asphalt Gb 1.035 1.035 1.035 1.035 1.035
Bulk Specific Gravity of Compacted Gmb 2.244 2.288 2.327 2.386 2.315
mix
Asphalt Content Pb 6.3 6.7 5.9 5.3 5.5
Bulk Specific Gravity of Aggregate Gsb 2.488 2.403 2.599 2.524 2.549
Effective Specific Gravity of Aggregate Gse 2.554 2.63 2.637 2.691 2.608
Asphalt Absorption Pba 1.1 1.2 1.2 1.2 1.0
Effective Asphalt Content in the Pbe 5.3 3.2 5.7 3.4 4.8
Mixture
Percent VMA in Compacted Mix VMA 15.6 11.2 16.0 10.5 14.1

Percent Air Voids in Compacted Mix Va 4.0 3.9 3.7 3.8 3.7
Percent VFA in Compacted Mix VFA 74.2 65.2 76.8 63.8 73.7
Dust/Asphalt ratio D/A 0.8 1.4 0.7 1.3 0.9
Surface Area (m2/kg) SA 5.4 4.8 4.7 4.7 4.7
Theoretical Film Thickness FT 9.0 6.3 10.2 5.2 8.7
Effective VMA in Compacted Mix VMAe 25.7 21.3 27.3 18.8 24.7
Effective Film Thickness Fte 19.3 14.6 22.8 11.7 19.7











Table 3-11. Volumetric properties of coarse graded mixtures


Property
Maximum Theoretical Density
Specific Gravity of Asphalt
Bulk Specific Gravity of Compacted mix
Asphalt Content
Bulk Specific Gravity of Aggregate
Effective Specific Gravity of Aggregate
Asphalt Absorption
Effective Asphalt Content in the Mixture
Percent VMA in Compacted Mix
Percent Air Voids in Compacted Mix
Percent VFA in Compacted Mix
Dust/Asphalt ratio
Surface Area (m2/kg)
Theoretical Film Thickness
Effective VMA in Compacted Mix
Effective Film Thickness


Symbol

Gmm
Gb
Gmb
Pb
Gsb
Gae
Pba
Pbe
VMA
Va
VFA
D/A
SA
FT
VMA,
Fte


Cl
2.328
1.035
2.235
6.5
2.469
2.549
1.3
5.3
15.4
4.0
74.1
0.7
4.9
11.2
35.4
39.2


Mixture
C2
2.347
1.035
2.255
5.8
2.465
2.545
1.3
4.6
13.8
3.9
71.6
0.8
4.6
10.1
35.3
39.3


Table 3-12. Volumetric properties of fine graded Whiterock mixtures
Mixture


Property
Maximum Theoretical Density
Specific Gravity of Asphalt
Bulk Specific Gravity of Compacted
mix
Asphalt Content
Bulk Specific Gravity of Aggregate
Effective Specific Gravity of Aggregate
Asphalt Absorption
Effective Asphalt Content in the
Mixture
Percent VMA in Compacted Mix
Percent Air Voids in Compacted Mix
Percent VFA in Compacted Mix
Dust/Asphalt ratio
Surface Area (m2 /kg)
Theoretical Film Thickness
Effective VMA in Compacted Mix
Effective Film Thickness


Symbol
Gmm
Gb

Gmb

Pb
Gsb
Gse
Pba

Pbe
VMA
Va
VFA
D/A
SA
FT
VMAe
Fte


Fl F2 F4 F5 F6
2.338 2.375 2.368 2.326 2.341
1.035 1.035 1.035 1.035 1.035

2.244 2.281 2.272 2.233 2.244


6.3
2.488
2.554
1.1


5.4
2.489
2.565
1.2


5.7
2.491
2.568
1.2


6.7
2.485
2.555
1.2


6.1
2.489
2.550
1.0


5.3 4.2 4.5 5.6 5.2


C3
2.349
1.035
2.254
5.3
2.474
2.528
0.9
4.5
13.6
4.0
70.2
1.2
5.7
8.0
30.4
24.1











Table 3-13. Volumetric properties of Granite mixtures


Property


Sym


bol


Maximum Theoretical Density G.
Specific Gravity of Asphalt Gb
Bulk Specific Gravity of Gmb
Compacted mix
Asphalt Content Pb
Bulk Specific Gravity of Aggregate Gsb
Effective Specific Gravity of


Aggregate se
Asphalt Absorption Pba
Effective Asphalt Content in the p
Mixture
Percent VMA in Compacted Mix VMA
Percent Air Voids in Compacted Va
Mix
Percent VFA in Compacted Mix VFA
Dust/Asphalt ratio D/A
Surface Area (m2/kg) SA
Theoretical Film Thickness FT
Effective VMA in Compacted Mix VMAe
Effective Film Thickness Fte


Mixture
GAC1 GAC2 GAC3 Gafl GAF2 GAF3
2.442 2.500 2.492 2.473 2.532 2.505
1.035 1.035 1.035 1.035 1.035 1.035

2.442 2.399 2.391 2.473 2.433 2.404

6.63 5.26 5.25 5.68 4.56 5.14
2.687 2.687 2.686 2.686 2.687 2.687

2.710 2.719 2.709 2.706 2.725 2.720

0.37 0.43 0.31 0.28 0.53 0.46

6.32 4.85 4.96 5.42 4.06 4.70

18.5 15.4 15.7 16.6 13.6 15.1

4.0 4.0 4.1 4.0 3.9 4.0

78.5 73.8 74.2 75.9 71.2 73.3
0.6 0.8 0.9 0.6 1.2 1.2
3.3 3.5 4.2 4.1 5.3 4.9
19.9 14.3 12.1 13.4 7.7 9.9
42.9 39.0 35.1 28.4 26.6 33.5
67.3 50.8 35.7 27.3 17.8 28.4


Table 3-14. Volumetric properties of field projects


Property


Symbol


Maximum Theoretical Density Gmm
Specific Gravity of Asphalt Gb
Bulk Specific Gravity of Compacted mix Gmb
Asphalt Content Pb
Bulk Specific Gravity of Aggregate Gsb
Effective Specific Gravity of Aggregate G.e
Asphalt Absorption Pba
Effective Asphalt Content in the Mixture Pbe
Percent VMA in Compacted Mix VMA
Percent Air Voids in Compacted Mix V.
Percent VFA in Compacted Mix VFA
Dust/Asphalt ratio D/A
Surface Area (m2/kg) SA
Theoretical Film Thickness FT
Effective VMA in Compacted Mix VMAe
Effective Film Thickness Fte


Mixture
Proj-1 Proj-2 Proj-3 Proj-7 Proj-8
2.509 2.523 2.216 2.334 2.382
1.035 1.035 1.035 1.035 1.035
2.407 2.445 2.122 2.229 2.284
5.5 5.0 8.3 6.1 6.0
2.691 2.694 2.325 2.47 2.503
2.736 2.725 2.475 2.573 2.598
0.6 0.4 2.7 1.7 1.4
4.9 4.5 5.7 5.2 4.5
15.5 14.8 16.4 16.0 14.0
4.1 4.4 4.2 4.5 3.9
73.7 70.6 74.1 71.9 72.4
1.2 0.6 0.6 0.6 1.0
5.2 3.0 3.7 4.6 4.3
9.2 8.7 11.3 7.7 8.9
31.1 38.1 35.4 22.1 34.3
24.4 52.3 48.3 18.6 35.3














CHAPTER 4
AXIAL COMPRESSION DYNAMIC MODULUS: RESULTS AND DISCUSSION

Introduction

In this Chapter, the results of the axial complex modulus testing will be described.

The triaxial compression dynamic modulus tests produced large amounts of test data.

There were two to three test temperatures based on the mixtures tested:

* 100C and 400C, for early tests on the FAA mixtures, described in Chapter 3.

* 100C, 250C, and 400C, for intermediate time tests on Georgia granite mixtures and
Superpave Project mixtures, described in Chapter 3.

* 100C, 300C, and 400C for all Whiterock aggregate mixtures and HVS mixtures,
described in Chapter 3.

For all temperatures tested, the following frequencies were used: 1 Hz, 4 Hz, 10

Hz, and 16 Hz. The tests were performed from the lowest temperature to the highest

temperature and from the highest frequency to the lowest frequency.

Data Variables

The test variables obtained from the data acquisition system include the time, axial

force, axial displacement, and the displacement from the LVDT's. The variable time is

the period from the test start to the data recording time. The axial force is the vertical

load on the specimen, and the axial displacement is the vertical displacement of the load

piston. Four LVDT's were used for each test, and the average displacements from the

four LVDT's were calculated. The LVDT's had an axial gage length of 51-mm. Three

specimens were tested for each mixture. Before the tests were performed, the height for

each specimen was measured. The diameter was fixed at 102.0 mm (4 in). To arrive at









the actual stress under certain test conditions, the axial force was divided by the

calculated area of the specimen. Similarly, the LVDT displacements were divided by the

axial gage length to arrive at the axial strain for the test under the same test conditions.

For any given test temperature, four data files were acquired for each specimen,

namely for 16 Hz, 10 Hz, 4 Hz, and 1 Hz. At 16 Hz and 10 Hz, the test data were

obtained from the 190th to the 200th cycle. For 4 Hz, the test data was obtained from the

90th to the 100th cycle. For the 1 Hz data, the data was obtained from the 10th to the 20th

cycle. A rest period of at least 2 minutes and less than 10 minutes was observed between

each frequency. If at the end of any test period, the cumulative unrecovered deformation

was found to be greater than 1500 micro units of strain, the test data was kept up to this

last testing period and the specimen was discarded. A new specimen was used for the

rest of the testing periods. For each frequency, there are about 50 sample points per

cycle.

In this project, triaxial compression complex modulus tests were performed on 57

specimens, namely three specimens per mixture listed in Table 1. All specimens were

prepared at 7 percent air voids plus or minus 0.5 percent, as listed in Table 6-1. All

specimens were compacted directly to 6.65-in to 7.04-in (170.0-mm to 180-mm) height

in a 4-inch (102 mm) diameter mold, using the Servopac gyratory compactor. Then, the

ends of each specimen were trimmed with a saw, so that the target height of each

specimen would be 6 inches (150 mm). The final heights are listed in Table 4-1.

Raw Data Plots

For asphalt mixtures, the complex dynamic modulus and phase angle change with

the temperature and frequency of loading. At low temperature, the modulus for asphalt

mixtures is large, so it is easy to control the applied axial force to obtain small











displacements. At high temperatures, such as 400C, the modulus is lower, making it

more difficult to control the axial force to get small displacements.

Table 4-1. Sample preparation data
Mixture Sample Number Air Voids Height, mm
Georgia Granite Mixtures
GAC1 1 7.1 150.3
2 6.8 150.2
3 6.9 150.3
GAC2 1 6.9 150.1
2 6.7 150.1
3 7.0 150.0
GAC3 1 6.8 150.1
2 6.7 150.0
3 7.2 150.2
GAF1 1 7.2 150.1
2 7.3 150.3
3 6.9 150.1
GAF2 1 6.7 150.1
2 6.9 150.0
3 6.7 150.2
GAF3 1 7.1 151.0
2 6.7 150.6
3 6.8 150.8
Whiterock Mixtures (Oolitic Limestone)
WRC1 1 6.8 150.5
2 6.6 150.2
3 7.1 150.8
WRC2 1 7.4 151.2
2 6.7 150.7
3 6.9 150.8
WRC3 1 6.9 15.2
2 7.4 150.8
3 7.3 150.2
WRF1 1 7.1 150.4
2 7.0 150.2
3 6.6 150.9
WRF2 1 6.9 150.5
2 6.8 151.1
3 6.9 150.4
WRF4 1 7.1 150.9
2 7.4 150.2
3 6.9 151.3
WRF5 1 7.1 150.3
2 7.3 150.7
3 6.9 150.2
WRF6 1 7.2 150.2
2 7.0 150.6
3 7.1 150.3
Mixtures From Fine Aggregate Angularity Study
RBC 1 7.0 151.2
2 7.3 150.2
3 6.8 150.7





Table 4-1. Continued
Mixture Sample Number
RBF 1
2
3
CALC 1
2
3
CALF 1
2
3
CGC 1
2
3
CGF 1
2
3
CHC 1
2
3
CHF 1
2
3
Superpave Project Mixtures
P1 1
2
3
P2 1
2
3
P3 1
2
3
P5 1
2
3
P7 1
2
3
Heavy Vehicle Simulator Mixtures
HVS67-22 1


6.9 150.2


2 7.1 150.8
3 6.8 151.1
HVS76-22 1 7.3 150.4
2 6.8 150.7
3 7.0 150.3

Figures 4-1 and 4-2 show typical force and single LVDT displacement versus time

plots at 100C and 400C for the frequency of 4 Hz. The displacement results have very

little noise in the data, even at the higher testing temperature of 400C. Finally, Figures 4-

3 and 4-4 show the calculated stress and strain versus time plots after averaging the


Air Voids
7.2
7.4
6.7
7.1
7.2
6.9
7.1
6.8
6.9
6.9
7.3
6.7
6.7
7.3
6.8
6.8
6.9
6.9
7.2
7.3
7.1


Height, mm
151.2
150.3
151.3
150.5
150.6
151.3
150.5
151.4
150.5
150.3
150.6
151.3
150.6
150.4
150.9
150.5
150.2
150.3
150.8
150.5
151.3


151.2
151.1
151.3
150.2
150.5
151.7
151.4
150.5
151.8
150.5
150.4
151.0
151.4
151.2
150.9










displacements from the four LVDTs, which were used to calculate the dynamic modulus

and the phase angle. The final stress and strain time histories were found to be sinusoidal

for all frequencies tested.

Typical Force and Disp. vs. Time
at 4Hz-1 u0(


20i00

0

-20100

-4000

-6000

-80100


1.5

1.486
E



1.44

1.42
1,4
1.4


1 1.5 2 2.5 3 3.5 4
Time (s)

Figure 4-1. Typical plot of force and LVDT displacement versus time at low temperature
(100C and 4 Hz) for mixture WRC1.


0


-1000


S-2000
0
-3000
-3000


- A0nN


1 .24


1.22 E
E
a)
1.2 E
CD
U
_o3
1
1.16 0


1 1.5 2 2.5 3 3.5 4
Time (s)

Figure 4-2. Typical plot of force and LVDT displacement versus time at high temperature
(400C and 4 Hz) for mixture WRC1


--Force
.......... Displacem ent









Typical Stress and Strain vs. Time
at 4Hz-100C


1

0.8
CL
S0.6

2 0.4

0.2

n


0.0005

0.0004

0.0003 ,

0.0002 O

0.0001

n


1 1.5 2 2.5 3 3.5 4
Time (s)

Figure 4-3. Typical plot of vertical stress versus strain at low temperature (100C and 4
Hz) for mixture WRC 1.

Typical Stress and Strain vs. Time
at 4Hz-400C


U.'

0.4
CFUS
CL
S0.3

S0.2

0.1

0


Stress
.......... S tra in

A7


______'I _______


U. UU2

0.0018

0.0016 -
CO
0.0014

0.0012

0.001


1 1.5 2 2.5 3 3.5 4
Time (s)
Figure 4-4. Typical plot of vertical stress versus strain at high temperature (400C and 4
Hz) for mixture WRC 1.

Data-Analysis Method

The data obtained for the complex modulus test is quite extensive; for one

temperature, there are thousands of lines of data for one specimen. To analyze the


--Stress
Strain __

s I

fffiSBBB'.fI'










complex modulus data, this project used the linear regression approach, presented in

Chapter 5. For each sample at a given test temperature and frequency, 10 cycles

consisting of 1000 points were analyzed to obtain the dynamic modulus and phase angle.

For interpretation purposes, within these 10 cycles, the axial strain history was assumed

to consist of a linear trend with a sinusoidal oscillation around the trend. All calculations

were performed using the SI system.

Analysis of Test Data Results

Test Data. One analysis file was obtained for each load frequency and testing

temperature. In this analysis file, the dynamic modulus in GPa and the phase angle in

degrees were obtained for the given test temperature and frequency. There were three

replicate specimens tested for each asphalt mixture. After all the dynamic modulus and

phase angle values were calculated for each specimen under the same test conditions, the

average value for both of these parameters was calculated. Tables 4-2 and 4-3 list the

average values for the three specimens for each asphalt mixture.

Table 4-2. Average dynamic modulus (IE*|) testing results
Mixture Temperature Frequency
0 C 1 Hz 4 Hz 10 Hz 16 Hz
Georgia Granite Mixtures
10 3457.54 4696.16 5577.41 6222.62
GAC1 25 931.93 1440.62 1788.84 1962.27
40 317.12 475.14 656.60 742.96
10 5289.30 7142.33 7983.76 8913.45
GAC2 25 1559.11 2308.10 2776.70 3318.24
40 535.77 787.74 1126.96 1313.66
10 5096.07 6797.11 7250.03 7660.00
GAC3 25 1606.35 2523.14 3079.15 3496.77
40 530.76 757.09 1109.68 1250.70
10 4594.94 6228.22 7302.91 7636.35
GAF1 25 1409.17 2107.13 2672.85 2950.80
40 401.02 635.50 867.07 1035.55
10 7142.75 9597.93 11966.62 12883.30
GAF2 25 2277.25 3201.00 4068.22 4630.38
40 535.97 905.80 1309.77 1574.02












Table 4-2. Continued
Mixture Temperature
C


GAF3


Whiterock Mixtures (Oolitic Limestone)


WRC1


WRC2


WRC3 30
40
10
WRF1 30
40
Whiterock Mixtures (Oolitic Limestone)


1Hz
5184.00
1586.94
377.70

3540.81
1026.46
526.05
3499.12
1379.32
759.48
5405.49
1653.59
801.08
5122.06
1769.34
849.60


Frequency
4 Hz
6523.47
2400.60
14.91


4757.85
1896.38
898.81
5327.66
2256.92
1368.38
6995.86
2852.46
1470.36
6630.20
2662.57
1273.70


10 Hz
7956.86
3041.56
886.58


5512.43
2552.73
1222.07
6449.00
3051.51
1835.72
7967.39
3718.31
1996.97
7917.74
3518.02
1663.57


16 Hz
8798.66
3437.54
1044.15

5953.88
2951.30
1464.86
7073.89
3466.68
2073.94
8463.57
4441.98
2375.12
8456.48
4005.78
1960.74


10 6301.77 7744.18 8990.34 9662.49
WRF2 30 2030.73 2931.80 3764.94 4442.58
40 1076.16 1610.34 2169.11 2512.69
10 7037.92 9142.90 10511.22 11141.74
WRF4 30 2211.26 3357.67 4339.52 5024.28
40 1044.19 1584.81 2076.40 2431.11
10 5285.91 6581.71 7583.78 8229.52
WRF5 30 1515.52 2442.77 3188.31 3688.46
40 726.94 1146.45 1556.87 1912.52
10 4391.76 5725.85 6722.84 7152.49
WRF6 30 1753.47 2479.71 3195.30 3643.92
40 879.93 1374.06 1850.43 2136.52
Mixtures From Fine Aggregate Angularity Study
10 5521.86 6877.95 7694.13 8327.94
40 770.75 1175.36 1492.91 1962.94
10 6242.28 7994.98 9592.44 9862.88
40 954.17 1415.66 1799.59 2027.84
10 5434.98 7143.53 8025.87 8248.25
40 1182.66 1792.49 2357.34 2730.40
10 6651.62 8106.39 9194.52 10285.22
40 1184.06 1779.33 2413.68 2682.04
10 4320.02 5210.02 6136.57 6307.82
40 923.08 1363.60 1772.90 2003.03
10 6693.18 7387.65 9630.43 9827.05
40 1217.77 1777.24 2219.22 2500.47
10 4624.45 6216.22 7417.98 7848.56
40 744.73 1166.04 1559.65 2500.47
10 8812.68 14397.88 16405.10 18827.05
40 756.82 1073.82 1554.89 2500.47
Superpave Project Mixtures
10 5517.08 7454.96 8422.86


523.74


807.66


1161.49


1447.81











Table 4-2. Continued
Mixture Temperature


Frequency


o C 1 Hz 4 Hz 10 Hz 16 Hz
10 4459.33 5616.50 6668.22 6728.17
40 606.97 953.37 1349.82 1578.43
10 2869.59 3797.12 4583.94 4754.91
40 458.87 655.21 892.31 978.19
10 5147.749 6263.335 7132.291 7648.227
40 638.095 918.3859 1180.378 1354.904
10 3479.68 4640.86 5562.11 6055.44
40 549.95 796.88 1048.63 1193.51
Heavy Vehicle Simulator Mixtures
10 5559.568 6676.453 7747.892 8016.232
HVS67-22 30 1309.809 1900.426 2349.412 2638.219
40 620.8512 925.0246 1179.977 1323.562
10 5021.711 6411.433 7161.738 7702.334
HVS76-22 30 1226.468 1855.661 2401.104 2639.515
40 646.3819 967.5163 1260.443 1439.98

Table 4-3. Average phase angle (6) testing results
Mixture Temperature Frequency
C 1 Hz 4 Hz 10 Hz 16 Hz
Georgia Granite Mixtures
10 26.59 26.18 27.84 29.96
GAC1 25 30.61 33.25 35.01 36.92
40 27.11 32.77 40.96 46.10
10 25.20 23.37 24.94 26.96
GAC2 25 30.17 31.79 34.67 36.72
40 26.67 32.14 37.23 41.91
10 25.79 26.05 26.58 31.13
GAC3 25 29.87 31.44 33.30 35.24
40 37.05 42.79 48.87 51.98
10 26.84 25.68 27.65 29.81
GAF1 25 32.47 33.68 36.02 38.65
40 27.25 32.35 38.16 45.09
10 21.62 20.66 22.25 24.82
GAF2 25 28.84 30.89 32.67 35.46
40 31.63 38.32 43.39 48.28
10 22.38 21.47 23.64 25.13
GAF3 25 30.32 31.86 33.78 36.42
40 32.91 38.87 44.30 49.53
Whiterock Mixtures (Oolitic Limestone)
10 22.85 22.03 22.39 23.89


WRC1


WRC2


WRC3


33.13
29.02
21.73
33.29
32.19
19.08
32.79
32.84


29.81
30.42
20.03
29.93
32.15
18.02
29.05
32.25


31.75
35.05
20.63
31.08
35.12
18.81
29.81
34.98


33.18
37.62
22.43
32.74
37.04
20.72
30.49
37.07











Table 4-3. Continued
Mixture Temperature
0C 1 Hz
10 19.59
WRF1 30 32.00
40 29.38
10 18.37
WRF2 30 31.76
40 31.21
10 19.83
WRF4 30 33.64
40 31.70
10 22.20
WRF5 30 32.65
40 30.05
10 22.27
WRF6 30 31.63
40 31.92
Mixtures From Fine Aggregate Angularity Study
10 22.75
40 27.38
10 14.08
40 25.90
10 17.58
40 30.53
10 18.31
40 26.97
10 23.02
40 31.40
10 16.22
40 25.70
10 21.91
40 30.45
CHF 10 29.84
40 35.50
SuDeroave Proiect Mixtures


40
10
P240

P3 10
40
10
40
10
40
Heavy Vehicle Simulator Mixtures
10
HVS67-22 10
40
10
HVS76-22


23.62
27.71
23.80
28.33
31.93
30.63
19.67
23.83
24.60
26.99

21.98
29.01
19.47
29.24


Frequency
4 Hz
18.00
31.07
32.11
17.62
29.54
33.67
19.11
30.43
34.00
20.17
31.28
33.13
20.76
30.28
33.59


20.91
31.09
15.34
28.66
17.23
34.24
18.27
33.92
22.81
31.10
18.64
30.95
20.96
33.33
29.65
35.40


22.99
33.57
23.67
32.46
29.13
34.67
19.12
28.44
23.99
32.15

21.11
32.96
18.51
31.81


24.18
38.46
26.44
38.35
30.46
45.24
21.15
33.38
24.62
38.96

22.93
37.97
20.04
37.52


10 Hz
19.01
32.14
34.78
18.81
30.53
35.68
20.57
31.56
35.85
20.94
31.67
36.10
22.02
30.88
36.09

23.20
35.68
15.82
31.85
19.56
38.89
20.55
39.90
24.74
34.84
20.70
34.18
22.35
36.00
33.06
41.68


16 Hz
21.42
33.91
38.42
20.82
32.76
37.73
22.76
33.14
37.65
22.24
33.20
38.59
23.52
32.14
37.62

26.69
39.56
17.91
36.08
20.82
43.18
22.61
44.36
26.58
38.26
23.58
38.65
25.52
39.82
32.94
49.31


43.02
28.96
46.19
29.29
49.35
23.34
38.13
26.15
43.28

24.82
43.17
23.31
41.59









Figures 4-5 through 4-10 show dynamic modulus and phase angle results for

mixture GAF1 for 100C, 250C, and 400C, which exhibited a typical response for the fine-

graded mixtures. Similarly, Figures 4-11 through 4-16 display typical dynamic modulus

and phase angle results at the 3 different testing temperatures for mixture GAC 1, which

also exhibited a typical response for the coarse-graded mixtures.

The degree of variability shown in the dynamic modulus and phase angle results for

mixtures GAF1 and GAC1 in Figures 4-5 through 4-16 are typical for the other mixtures

tested. The results also clearly show the expected rate dependence of the dynamic

modulus for asphalt mixtures, as the dynamic modulus increases with higher frequencies

(e.g., Sousa, 1987). As expected, a comparison of Figures 4-6 and 4-8 shows that the

phase angle also increases with higher testing temperatures. Also interestingly, a

comparison of Figures 4-6 and 4-8 shows how the phase angle decreased slightly

between 1 Hz and 4Hz, but increases with frequency up to 16 Hz. At higher

temperatures, the phase angle tends to increase with increased frequency, as shown for

example in Figures 4-8 and 4-10. The results for each specimen for the other mixtures

tested are provided in the Complex Modulus Microsoft Access Database, described in

Appendix B.

In summary, the dynamic modulus and phase angle results show the following

trends,

* Under a constant loading frequency, the dynamic modulus decreases with an increase
in test temperature for the same mixture.

* The phase angle increases with the increase of test temperature.

* Under a constant test temperature, the dynamic modulus increases with increased test
frequencies.







44


Both the dynamic modulus and phase angle data shows relatively smooth trends,
irrespective of test temperature.

The above trends are consistent with the research results reported by others.


-- F1-01

-U--F1-02

--F1-03

-*- Sum


10
Frequency (Hz)


15 20


Figure 4-5. Dynamic modulus |E*| of GAF1 at 10C


10000

8000

6000

4000

2000

n


0 5 10 15 20
Frequency (Hz)

Figure 4-6. Phase angle of GAF1 mixture at 10C


-*-F1-01

-1- F1-02

-- F1-03

-A- Avg


IMF-


I I I











5000

4000

3000

2000

1000

n


0 5 10 15 20
Frequency (Hz)


Figure 4-7. Dynamic modulus |E*| of GAF at 25C


0 5 10 15 20
Frequency (Hz)

Figure 4-8. Phase angle of GAF mixture at 25C

2000

1600




u 800

400

0
0 5 10 15 20
Frequency (Hz)

Figure 4-9. Dynamic modulus |E*| of GAF1 at 40C


-- F1-01

--- F1-02

-*- F1-03

-A- Avg


-*--F1-01

-- F1-02

-*--F1-03

-A- Avg


-*-F1-01

--- F1-02

-- F1-03

*Avg


- i nn!!!!!! !! !I jiiiiii











60

50

0)40
CQ
| 30

w 20
1-
10


0 5 10 15 20
Frequency (Hz)

Figure 4-10. Phase angle of GAF1 mixture at 40C


10000

8000

6000

4000

2000

0


-*- F1-01

-- F1-02

-*- F1-03

--Avg


0 5 10 15 20
Frequency (Hz)

Figure 4-11. Dynamic modulus iE*I of GACi at 10C


50


4 40
(D

S30

- 20

1-
a 10

0


---- Cl-01
-*- C 1 -0 1


-*-Cl-03

-*- Sum


0 5 10 15 20
Frequency (Hz)


Figure 4-12. Phase angle of GAC1 mixture at 10C


--AvC1




*-Avg











5000

4000

3000

Lu 2000

1000

0


-- C1-01

---C1-02

-0-C1-03

-- Avg


0 4 8 12 16 20
Frequency (Hz)

Figure 4-13. Dynamic modulus IE*| of GACI at 25C


50

40
3- C1-01

C C1-02
20
0 --- C1-03

10 ---- Sum


0 5 10
Frequency (Hz)


15 20


Figure 4-14. Phase angle of GAC mixture at 250C


2000

1600

1200

800

400

0


-*- C1-01

---- C1-02

-*-OC1-03

-i- Avg


0 5 10 15 20
Frequency (Hz)

Figure 4-15. Dynamic modulus IE*| of GACI at 40C


-~jI









7-5
0)
gff --------------------------
> -W--C1-02


t-
15 ---- Avg


0 5 10 15 20
Frequency (Hz)

Figure 4-16. Phase angle of GAC1 mixture at 40C

Master Curve Construction

The dynamic modulus and phase angle of mixtures can be shifted along the

frequency axis to form single characteristic master curves at a desired reference

temperature or frequency. In the proposed "2002 Guide for the Design of Pavement

Systems" currently under development in the NCHRP Project 1-37A, the modulus of the

asphalt mixture, at all analysis levels of temperature and time rate of load, is determined

from a master curve constructed at a reference temperature. The procedure assumes that

the asphalt mixture is a thermorheologically simple material, and that the time-

temperature superposition principle is applicable.

Typically, the shift factors a(T) are obtained from the WLF equation (Williams et

al., 1955).

c (r T )
loga(T) = C2 V-_- (Eq. 4-1)
C2T TF

Where Ci and C2 are constants, Tr is the reference temperature, and T is the temperature

of each individual test.









A new method of developing the master curve for asphalt mixtures was developed

by Pellinen and Witczak (2002), in which the master curves were constructed fitting a

sigmoidal function to the measured complex modulus test data using non-linear least

squares regression techniques. The shift can be achieved by solving the shift factors

simultaneously with the coefficients of the sigmoidal function. The sigmoidal fitting

function for master curve construction used by Pellinen and Witczak (2002) is defined

equation (4-2).


log(E*) = +og (Eq. 4-2)


Where

log(IE*|) = log of dynamic modulus,
6 = minimum modulus value,
fr = reduced frequency,
Uc = span of modulus value,
P, y = shape parameters.

The reduced frequency, fr, is defined as,

f= (Eq. 4-3)
a(T)

or alternatively,

log(fr) = log(f) + log[a(T)]

in which f = testing frequency, and a(T) is the shift factor that defines the required shift at

a given temperature to get the reduced frequency fr. At the reference temperature, the

shift factor a(Tr) = 1. Finally, the parameter y influences the steepness of the function

(rate of change between minimum and maximum) and P3 influences the horizontal

position of the turning point, shown in Figure (6-17).










Sigmoidal Function

7 (increase) 6+a


P j3 (neg)
o/ P3 (pos)





Log Reduced Frequency
Figure 4-17. Parameters used in sigmoidal fitting function

The justification of using a sigmoidal function for fitting the compressive dynamic

modulus data is based on the physical observations of the mix behavior. The upper part

of the sigmoidal function approaches asymptotically the maximum stiffness of the mix,

which is dependent on limiting binder stiffness at cold temperatures. At high

temperatures, the compressive loading causes aggregate influence to be more dominant

than the viscous binder influence. The modulus starts to approach a limiting equilibrium

value, which is dependent of the aggregate gradation. Thus, the sigmoidal function

captures 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.

Typical Predicted Master Curves for Florida Mixtures

In the following, the procedure developed by Pellinen and Witczak (2002) for

obtaining predicted master curves for GAC3 and GAF1 is used, and the resulting master

curves are presented. Master curves for all other mixtures that were tested at three testing

temperatures are presented in Appendix C. In all cases, the reference temperature was

taken as 250C (77F). As stated previously, the shifting was accomplished by obtaining







51


the shift factors simultaneously with the coefficients of the sigmoidal function through

nonlinear regression, without assuming any functional form of a(T) versus temperature.

The nonlinear regression was performed using the Solver Function in a Microsoft Excel

spreadsheet.

The resulting shift functions and master curves for GA-C3 and GA-F1 are

presented in Figures 4-18 through Figure 4-21 below. The tails on the predicted master

curves are extrapolated. In a few cases, depending on the mixture properties, the tails of

the predicted mastercurve did not follow an S-shape. Rather, the mastercurve showed a

slight concave-down curvature. Figures 4-22 and 4-23 show the shift function and

predicted mastercurve for mixture GA-C1, respectively. The predicted mastercurve for

GAC 1 does not show an S-shape. It shows a slight concave-down curvature, indicating

that for this particular mixture, higher and lower temperature results are needed to define

the tails of the mastercurve adequately. Future testing at higher and lower temperatures

would help in defining the tails better.


4
y = -P.0614x + 4.9497
R2= 0.9872
2





-2


-4
0 20 40 60 80 100 120
TemperatureeF)

Figure 4-18. Shift function for coarse-graded GAC3 mixture.











Master Curue
C3


-6 -4 -2 0 2 4
Reduced Frequency


Figure 4-19. Master curve for coarse-graded


4


2


0



-2


-4





Figure 4-:


GAC3 mixture.


0 20 40 60 80 100 120
Temperature(F)


20. Shift function for fine-graded GAF1 mixture.


Master Curve
F1


-6 -4 -2 0 2 4 6
Reduced Frequency


Figure 4-21. Master curve for fine-graded GAF1 mixture.


y = -0.061x 4.9197
R2 = 0.9867





-






















-2



-4




Figure 4-2


1-


y = -0.0722x +
R2
R 1


5.5655



5.5655


0 20 40 60 80 100 120
Temperature (OF)

12. Shift function for fine-graded GAF1 mixture.


s Predicted
10Odc
2 A 30dc
S40dc
-J
1


-6 -4 -2 0 2 4 6
Log reduced frequency

Figure 4-23. Master curve for coarse-graded GAC 1 mixture.

Dynamic Modulus Calculated from Predictive Regression Equations

The complex modulus test is relatively difficult and expensive to perform.

Therefore, numerous attempts have been made to develop regression equations to









calculate the dynamic modulus from conventional volumetric mixture properties. For

example, a predictive regression equation is proposed as a part of the 2002 Design Guide

(Witczak et al., 2002) to calculate |E*| based on the volumetric properties of any given

mixture. The predictive equation developed by Witczak et al. (2002) is one of the most

comprehensive mixture dynamic modulus models available today (Witczak 2002). The

equation is presented in equation (4-3).


lodE* = -1.249937+ 0.029232x (p00) -0.001767x (p00)2 -0.00284 lx( (4)
0.80220Ve) (. 4-3
-0.058097x (V,) 0.80220Vbff (Eq. 4-3)
b +Va
Vbeff +a
3.871977- 0.002(p4)+0.00395p3,8) -0.00017(p'38)2 +0.00547q(p34)
1+e (-0 603313-0 313351 Where
|E*| = dynamic modulus, in 105 psi;
q1 = bitumen viscosity, in 06 Poise;
f = loading frequency, in Hz;
Va = percent air void content, by volume;
Vbeff = effective bitumen content, percent by volume;
P3/4 = percent weight retained on 19-mm sieve, by total aggregate weight;
P3/8 = percent weight retained on 9.5-mm sieve, by total aggregate weight;
P4 = percent weight retained on 4.75-mm sieve, by total aggregate weight;
P200 = percent weight passing 0.75-mm sieve, by total aggregate weight;

The above dynamic modulus predictive equation has the capability to predict the

dynamic modulus of dense-graded HMA mixtures over a range of temperatures, rates of

loading, and aging conditions from information that is readily available from

conventional binder tests and the volumetric properties of the HMA mixture. This

predictive equation is based on more than 2,800 different HMA mixtures tested in the

laboratories of the Asphalt Institute, the University of Maryland, and FHWA.

In this research, the dynamic modulus was calculated using the predictive equation

developed by Witczak et al (2002). Gradations data for each mixture, binder content and









volumetric properties, were obtained from the design mixture properties, discussed in

Chapter 3. The air voids were measured using test method AASHTO T 166 on the

prepared test specimens. Table 6-1 lists the air voids for each specimen tested. For each

mixture listed in Table 6-1, the average air voids from the three pills tested were used.

The binder viscosity was obtained at each testing temperature using,

* Brookfield rotational viscometer results on short-term RTFO aged specimens.

* Dynamic Shear Rheometer results on short-term RTFO aged specimens.

* Recommended viscosity values by Witczak and Fonseca (1996) for "Mixture
Laydown" conditions.

In the next section, the binder test results will be presented, followed by a

presentation of the predicted dynamic modulus results calculated from the predictive

equation by Witczak et al. (2002).

Binder Testing Results

The asphalt binder used for all mixtures but one of the mixtures tested is graded as

PG67-22 (AC-30). The HVS mixture with SBS modified binder graded as PG76-22 was

not tested, due to lack of availability. The "as produced" mix was used for the complex

modulus testing of the HVS mixtures, making it hard to ensure that exactly the same

binder be used for the rheological testing. Table 6-4 shows the results of the Brookfield

Rotational Viscometer testing, performed at three testing temperatures (60.5 C, 70.7 C,

Table 4-4. Brookfield rotational viscometer results on unaged and RTFO aged binder
Testing TemperatureUnaged Binder ViscosityRTFO Aged Binder Viscosity (cP)
(C) (cP)
60.5 328260.5 1041945.2
70.7 95682.1 236166.7
80.7 33681.6 81193.0









and 80.7 C). Similarly, table 4-5 shows the results of viscosity test results obtained from

the Dynamic Shear Rheometer. The viscosity is reported in centiPoise (cP).

Table 4-5. Dynamic shear rheometer results on unaged and RTFO aged binder
Testing Temperature Unaged Binder Viscosity RTFO Aged Binder Viscosity
(0C) (cP) (cP)
30 2.46E+06 5.08E+06
40 1.99E+05 1.20E+06

Based on the results shown in Tables 4-4 and 4-5, the viscosity for each complex

modulus test temperature was obtained using the equation (4-4).

Log(log(r) = A + VTSlog(T) (Eq. 4-4)

in which qr is bitumen viscosity in centipoises, T is test temperature in Rankine, and A

and VTS are regression constants reflecting the specific type of asphalt cement and aging

conditions of the material. Table 4-6 summarizes the calculated A and VTS values for

the unaged binder, and the RTFO aged binder results from the Brookfield Rotational

Viscometer test and the Dynamic Shear Rheometer test. Similarly, Table 4-7 lists typical

A and VTS values for PG 67-22 (AC- 30), recommended by Witzcak and Fonseca

(1996), for two conditions: (a) original, and (b) short-term (mix/laydown). A comparison

of Tables 4-6 and 4-7 shows that the parameters obtained from the Brookfield Rotational

Viscometer test for RTFO aged asphalt are close in values to the A and VTS values

recommended by Witzcak and Fonseca (1996) for Mix/Laydown conditions. The A and

VTS values obtained from the Dynamic Shear Rheometer are slightly lower.

Based on the results presented in Tables 4-6 and 4-7, the viscosity (in Poise) was

finally calculated for the complex modulus testing temperatures used. The viscosities of









Table 4-6. Viscosity-temperature regression coefficients for unaged and
RTFO aged PG 67-22 (AC-30) asphalt
Results Based on Viscosities Obtained Results Based on Viscosities
Regression From Brookfield Rotational Viscometer Obtained From Dynamic Shear
Constants Test Rheometer Test
Unaged Binder RTFO Aged Binder Unaged Binder RTFO Aged
B___inder
A -5.6362 -3.4655 -5.7817 -3.0165
VTS 16.207 10.407 16.63 9.0824


Table 4-7. Typical viscosity-temperature regression coefficients for AC-30 (PG 67-22) at
different hardening states (Witzcak and Fonseca, Transportation Research
Record 1540, 1996, pp. 15-23)
Regression Constants Original Conditions Mix/Laydown
(Unaged Binder) Conditions
A -3.6666 -3.56455
VTS 10.928 10.6768


interest are obtained from: (a) Brookfield Rotational Viscometer testing of RTFO aged

AC-30 asphalt, (b) Dynamic Shear Rheometer testing of RTFO aged PG 67-22 (AC-30)

asphalt, and (c) Mix/Laydown conditions from Witzcak and Fonseca (1996). Table 4-8

summarizes the results of the calculated viscosities for condition and test temperature.

Table 4-8. Calculated viscosity at four complex modulus test temperatures
Test and Aging Condition Calculated Viscosity (in Poise) Complex Modulus
Test and Aging Condition T Tepeat r
Test Temperature
10 C 25 C 30 C 40 C
Brookfield test 3.89E+08 7.17E+06 2.29E+06 2.95E+05
RTFO
DSR test 1.73E+06 1.12E+05 5.08E+04 1.20E+04
RTFO
From Witzcak and Fonseca (1996) 4.57E+08 7.39E+06 2.28E+06 2.79E+05
Mix/lay down condition

Comparison of Predicted and Measured Dynamic Modulus

The predictive regression equation by Witczak et al. (2002) is used to obtain

predicted dynamic modulus values for all test temperature and frequencies for all

mixtures tested, except the Superpave P5 mix for which a total volumetric description









was not available, and the HVS PG 76-22 mix, for which binder viscosity measurements

were not available. The three conditions considered are:

* Mix/Laydown Condition from Witzcak and Fonseca (1996),

* RTFO aged binder results from Brookfield Rotational Viscometer Test, and

* RTFO aged binder results from the DSR test.

Tables 4-9 through 4-20 list the predicted dynamic modulus values for all test

temperatures and testing frequencies (Proposed by Witzcak and Fonseca-1996).

Similarly, Figures 4-24 through 4-26 show the resulting comparisons between predicted

and measured dynamic moduli for the three conditions studied. In order to evaluate the

relative quality of the predictions, linear regressions with zero intercept were performed

for the three cases. The results of the regression analysis are shown on Figures 4-23

through 4-26. The coefficient describing the slope of the regression line is a measure of

the quality of fit, the closer the slope coefficient is to unity, the less of a bias is built into

the prediction. A slope that is less than one indicates an unconservative prediction, in

which the predicted dynamic modulus is higher than the measured dynamic modulus.

Similarly, a slope that is greater than unity indicates a conservative prediction, in which

the predicted dynamic modulus is lower than the measured dynamic modulus. Similarly,

the R2 value is a measure of the goodness of fit of the regression line. A high R2 value

indicates a good fit, whereas a low R2 indicates an inadequate fit. The results from the

regression analysis show that the RTFO aged binder results from Brookfield Rotational

Viscometer test provide a slope that is closest to unity (0.6857), and the highest R2 value

(0.845). The Mix/Laydown binder viscosity conditions proposed by Witzcak and

Fonseca (1996) provide very similar results. However, the RTFO aged binder results

from the DSR test have a slope, which is higher











Table 4-9. Predicted dynamic moduli for Georgia granite mixtures using the
Mix/Laydown condition.
Mixture Temperature Frequency
C 1 Hz| 4Hz 10 Hz 16 Hz
Georgia Granite Mixtures
10 6348.09 7833.00 8867.60 9409.14
GAC1 25 2233.40 3076.22 3740.45 4114.03
40 743.46 1099.89 1409.71 1594.90
10 7228.04 8935.16 10126.30 10750.27
GAC2 25 2519.90 3480.55 4239.32 4666.60
40 830.82 1233.33 1584.17 1794.22
10 7312.96 9022.68 10213.82 10837.27
GAC3 25 2519.90 3545.00 4310.05 4740.31
40 857.33 1268.11 1625.12 1838.52
10 7843.40 9699.73 10995.38 11674.21
GAF1 25 2729.02 3771.68 4595.62 5059.72
40 897.89 1333.89 1714.14 1941.87
10 8766.05 10836.87 13038.76 13038.76
GAF2 25 3055.47 4220.57 5140.85 5659.10
40 1007.18 1495.26 1920.69 2175.41
10 9224.27 11413.04 13742.22 13742.22
GAF3 25 3201.60 4428.16 5397.98 5944.44
40 1050.65 1562.27 2008.80 2276.34

Table 4-10. Predicted dynamic moduli for Whiterock mixtures using the
Mix/Laydown condition
Mixture Temperature Frequency
C 1 Hz| 4Hz 10 Hz 16Hz
Whiterock Mixtures (Oolitic Limestone)


10 6281.57
WRC1 30 1518.78
40 731.38
10 7203.20
WRC2 30 1709.95
40 815.70
10 7869.28
WRC3 30 1886.08
40 904.17
10 7377.84
WRF1 30 1752.11
40 835.98
10 9442.18
WRF2 30 2249.92
40 1075.37
10 9534.34
WRF4 30 2277.65
40 1090.05
10 7756.29
WRF5 30 1864.47
40 895.17
10 10642.12
WRF6 30 2542.29
40 1216.70


7755.35
2156.30
1083.18
8917.48
2438.73
1214.19
9728.22
2683.56
1342.32
9133.15
2498.61
1244.25
11682.78
3205.85
1599.05
11792.37
3243.34
1619.74
9584.35
2650.89
1327.87
13162.50
3620.17
1807.93


8782.67
2677.98
1389.22
10114.99
3037.24
1562.28
11025.33
3337.27
1724.24
10359.26
3111.62
1600.84
13247.26
3990.33
2056.11
13368.55
4035.42
2081.78
10859.48
3295.16
1704.80
14921.81
4504.29
2323.66


9320.53
2978.17
1572.26
10742.70
3382.33
1770.95
11704.82
3713.79
1952.90
11001.94
3465.07
1814.59
14067.13
4442.46
2329.97
14194.41
4491.81
2358.54
11527.34
3666.12
1930.39
15843.63
5013.71
2632.57












Table 4-11. Predicted dynamic moduli for FAA mixtures using the
Mix/Laydown condition
Mixture Temperature Frequency
C 1 Hz 4 Hz 10 Hz 16 Hz
Mixtures From Fine Aggregate Angularity Study
10 8739.16 10785.05 12210.69 12956.96
40 745.75 1103.59 1414.71 1600.71
10 9850.64 12182.68 13810.43 14663.28
40 868.59 1290.50 1658.48 1878.88
10 12281.01 13903.68 14753.05
40 844.89 1250.10 1602.35 1812.93
10 11670.26 14432.67 16360.78 17370.99
40 1029.34 1529.24 1965.23 2226.36
10 9581.79 10852.29 11517.53
40 1335.85 1713.68 1939.69
10 12080.89 14939.98 16935.52 17981.05
40 1053.09 1564.43 2010.37 2277.46
10 6783.37 8377.25 9488.52 10070.40
40 787.55 1166.97 1497.19 1694.73
10 8464.11 10483.62 11894.88 12634.78
40 953.71 1420.92 1829.33 2074.26

Table 4-12. Predicted dynamic moduli for Superpave project mixtures using the
Mix/Laydown condition
Mixture Temperature Frequency
C 1 Hz| 4 Hz 10 Hz 16Hz
Superpave Project Mixtures
10 7987.27 9213.04 10423.32
40 708.26 959.39 1228.08 1388.54
10 7531.50 8304.65 9394.88 9965.25
40 654.75 876.40 1121.68 1268.14
10 6738.42 9866.87 11177.65 11864.09
40 593.73 1050.05 1347.64 1525.71
10 7474.52 9283.27 10502.78 11140.81
40 649.79 966.71 1237.44 1399.13

Table 4-13. Predicted dynamic moduli for Georgia granite mixtures using RTFO
aged binder results from the Brookfield rotational viscometer test.
Mixture Temperature Frequency
C 1 Hz| 4Hz 10 Hz 16 Hz
Georgia Granite Mixtures
10 6141.71 7609.33 8636.32 9175.20


GAC1


GAC2


GAC3


2212.78
759.06
6991.03
2496.43
848.40
7075.32
2496.43
875.31


3050.25 3710.90 4082.68


1121.94
8677.83
3450.91
1258.28
8765.16
3515.08
1293.53


1436.89
9859.92
4205.54
1614.99
9947.56
4276.02
1656.45


1624.97
10480.69
4630.73
1828.34
10567.95
4704.20
1873.16












Mixture Temperature Frequency
C 1 Hz 4Hz 10 Hz 16 Hz


GAF1


GAF2


GAF3


10
25
40
10
25
40
10
25
40


7585.74
2703.55
916.93
8478.56
3027.01
1028.50
8920.55
3171.66
1072.99


9419.86
3739.50
1360.92
10524.71
4184.62
1525.51
11082.99
4390.29
1594.01


10705.60
4558.93
1747.55
12711.72
5099.88
1958.07
13396.18
5354.78
2048.04


11380.92
5020.76
1978.87
12711.72
5615.60
2216.79
13396.18
5898.56
2319.82


Table 4-14. Predicted dynamic modulus for Whiterock mixtures Using RTFO
aged binder results from the Brookfield rotational viscometer test
Mixture Temperature Frequency
C 1 Hz 4Hz 10 Hz 16 Hz


Whiterock Mixtures (Oolitic Limestone)
10 6076.80
WRC1 30 1520.14
40 746.77
10 6965.40
WRC2 30 1711.50
40 833.08
10 7611.20
WRC3 30 1887.78
40 923.31
10 7134.35
WRF1 30 1753.69
40 853.79
10 9131.27
WRF2 30 2251.95
40 1098.22
10 9220.94
WRF4 30 2279.71
40 1113.17
10 7502.42
WRF5 30 1866.14
40 914.08
10 10292.30
WRF6 30 2544.58
40 1242.51


7533.31
2158.09
1104.95
8658.91
2440.78
1238.93
9448.00
2685.81
1369.48
8868.40
2500.71
1269.59
11344.91
3208.54
1631.53
11451.92
3246.05
1652.59
9308.83
2653.10
1354.68
12782.49
3623.20
1844.60


8553.00
2680.08
1416.09
9847.10
3039.65
1592.88
10735.25
3339.90
1757.79
10084.98
3114.09
1632.19
12897.32
3993.49
2096.28
13016.02
4038.61
2122.38
10574.35
3297.75
1737.90
14528.33
4507.85
2368.98


9088.18
2980.43
1601.98
10471.47
3384.93
1804.86
11411.25
3716.62
1990.05
10724.24
3467.73
1849.33
13712.88
4445.87
2374.47
13837.59
4495.25
2403.51
11238.80
3668.91
1967.03
15445.35
5017.55
2682.77


Table 4-15. Predicted dynamic moduli for FAA mixtures using RTFO aged
binder results from the Brookfield rotational viscometer test
Mixture Temperature Frequency
C 1 Hz 4 Hz 10 Hz 16 Hz
Mixtures From Fine Aggregate Angularity Study
10 8454.83 10476.87 11891.99 12634.58


40 761.40
10 9526.95
40 887.02


L


1125.73
11831.08
1316.66


1442.01
13446.37
1690.81


1630.91
14294.80
1914.69


Table 4-13.


Continued












Mixture Temperature Frequency
C 1IHz 4 Hz 10 Hz 16 Hz
10 11930.23 13540.94 14386.14
40 862.62 1275.17 1633.26 1847.12
10 11286.83 14016.19 15929.55 16934.52
40 1051.17 1560.24 2003.54 2268.79
10 9307.21 10568.24 11230.14
40 1362.73 1746.85 1976.39
10 11684.03 14508.93 16489.22 17529.32
40 1075.42 1596.13 2049.56 2320.85
10 6561.95 8137.08 9240.06 9819.02
40 804.14 1190.46 1526.18 1726.80
10 8184.06 10178.95 11579.14 12315.06
40 974.08 1449.93 1865.25 2114.08

Table 4-16. Predicted dynamic moduli for Superpave mixtures using RTFO aged
binder results from the Brookfield rotational viscometer test
Mixture Temperature Frequency
C 1Hz 4Hz 10 Hz 16 Hz
Superpave Project Mixtures


7232.74
663.35
6520.58
606.11
7726.21
723.20
7287.87
668.41


8951.29
978.53
8068.85
893.88
9583.62
1071.22
9019.52
985.99


10152.84
1251.64
9151.24
1143.18
10884.56
1373.77
10230.24
1261.18


1414.59
9718.88
1291.91
11567.53
1554.63
10865.22
1425.37


Table 4-17. Predicted dynamic moduli for Georgia granite mixtures using RTFO aged
binder results from the dynamic shear rheometer Test.
Mixture Temperature Frequency
C 1 Hz| 4Hz| 10 Hz 16 Hz
Georgia Granite Mixtures


1673.53 2088.55 2328.65


662.60 859.21


978.60


289.03 380.32 437.41


1936.46
754.10
324.10
1786.03
707.35
308.64
2104.70
822.33
354.47
2025.09
792.37
342.00


2426.29
982.42
428.56
2228.79
917.17
406.08
2634.99
1070.31
468.26
2829.73
1030.90
451.60


2710.49
1121.53
494.12
2484.93
1044.56
467.01
2942.50
1221.30
539.63
2829.73
1176.10
520.31


GAC1



GAC2


GAC3


GAF1


GAF2


1170.78
441.77
190.72
1346.09
499.15
212.28
1249.63
499.15
203.68
1464.90
545.09
232.51
1410.28
525.57
224.48


Table 4-15.


Continued












Mixture Temperature Frequency
C 1 Hz 4Hz 10 Hz 16 Hz


GAF3


1567.56
578.57
245.06


2258.91
875.78
374.91


3166.82
1142.36
496.40


3166.82
1304.93
572.72


Table 4-18 Predicted dynamic moduli for Whiterock mixtures using RTFO
aged binder results from the dynamic shear rheometer test.


Mixture Temperature
0 C 1 Hz
Whiterock Mixtures (Oolitic Limestone)
10 1331.74
WRC1 30 371.92
40 215.91
10 1487.22
WRC2 30 403.87
40 231.68
10 1459.92
WRC3 30 401.99
40 231.96
10 1567.89
WRF1 30 428.90
40 246.80
10 1593.26
WRF2 30 433.91
40 249.21
10 1626.84
WRF4 30 447.83
40 258.38
10 1392.47
WRF5 30 385.55
40 223.00
10 1813.53
WRF6 30 499.22
40 288.03


Frequency
S 4Hz 10 Hz 16 Hz


1905.40
562.39
327.57
2144.65
616.28
354.72
2097.11
610.65
353.55
2256.36
652.91
376.97
2295.72
661.49
381.21
2337.06
680.35
393.86
1997.11
584.63
339.28
2605.27
758.41
439.05


2379.31
735.10
431.33
2691.16
810.29
469.91
2625.16
800.56
466.97
2827.73
857.15
498.61
2879.29
869.22
504.69
2925.67
891.98
520.24
2497.57
765.55
447.58
3261.44
994.34
579.93


2653.59
841.28
496.26
3008.59
930.08
542.31
2931.34
917.57
538.10
3159.30
983.11
574.97
3218.13
997.42
582.27
3266.97
1022.38
599.49
2787.54
876.93
515.44
3641.91
1139.70
668.28


Table 4-19. Predicted dynamic moduli for FAA mixtures using RTFO aged binder results
from the dynamic shear rheometer test.
Mixture Temperature Frequency
C 1 Hz 4Hz| 10 Hz| 16 Hz
Mixtures From Fine Aggregate Angularity Study
10 1441.83 2062.97 2576.12 2873.12


BD kl

RBF

CALC

CALF


233.72
1777.05
280.06

268.78
2098.32
330.58


354.60
2556.73
427.66
2371.26
407.75
3019.18
504.84


466.94
3203.69
565.55
2960.94
536.90
3783.32
667.65


537.23
3579.08
652.10
3302.23
617.70
4226.72
769.85


Continued


Table 4-17.










Table 4-19. Continued
Mixture Temperature Frequency
C 1 Hz 4 Hz 10 Hz 16 Hz
10 2479.73 3096.16 3452.91
40 426.65 561.73 646.24
10 2151.50 3096.06 3879.95 4334.83
40 338.75 517.39 684.31 789.10
10 1511.78 2162.93 2700.85 3012.18
40 245.13 371.89 489.68 563.39
10 1873.27 2695.30 3377.41 3773.21
40 295.16 450.74 596.09 687.32

Table 4-20. Predicted dynamic moduli for Superpave mixtures using RTFO
aged binder results from the dynamic shear rheometer test.
Mixture Temperature Frequency
C 1 Hz 4 Hz 10 Hz 16 Hz
Superpave Project Mixtures
10 881.97 1548.08 1548.08
40 151.15 295.65 295.65 338.70
10 1308.41 1884.07 2362.05 2639.49
40 205.33 205.33 415.30 479.02
10 1547.87 1547.87 2785.58 3110.94
40 245.30 245.30 494.31 569.72
10 1646.80 1646.80 7703.09 3331.44
40 256.53 256.53 520.32 600.49

than unity (2.7402), and a lower R2 value (0.7257), which is likely the result of the higher

bias in the prediction. Hence, even though the predictions based on the viscosity

obtained from the Brookfield Rotational Viscometer test and the Mix-Laydown

conditions proposed by Witzcak and Fonseca (1996) are statistically better than the

results based on the viscosity obtained from the DSR test, the latter is the only

conservative estimate of the three evaluated. This bias in the DSR-based predictions of

dynamic modulus values follow similar published results (e.g., Clyne et al. 2003).

Hence, consistent with the recommendations by Witzcak et al. (2002), in order to obtain

conservative predictions, it is recommended that viscosity input values for the predictive

equation be obtained from the DSR test.

Interestingly, it is of interest to note that the predictions at higher temperatures

(i.e., lower modulus values) generally are closer to the line of equity for all three cases









than the predictions at lower temperatures. Figures 4-27 presents a comparison of

predicted and measured dynamic modulus values for the Whiterock oolitic limestone

mixtures tested (Fl, F2, F4, F5, F6, Cl, C2, C3). As the temperature increases from 10

C to 40 C, the predicted dynamic modulus approaches the measured dynamic modulus

values. This is likely the result of the much of the database used to develop the predictive

equation being biased toward mixtures tested at higher temperatures.

Finally, Figure 4-28 shows measured vs. predicted dynamic modulus for Fine

Aggregate Angularity Mixtures ("FAA"), Superpave Project Mixtures ("Project"),

Granite Mixtures ("Granite"), and Whitrock Mixtures ("WR") at a Test Temperature of

400 C and a Testing Frequency of 4 Hz. Most of the mixture groups scatter around the

line of unity, with the exception of the Georgia Granite mixtures (GA-C1, GA-C2, GA-

C3, GA-F1, GA-F2, GA-F3), which land below the line of unity. Since the testing

protocol for all mixtures was the same, the asphalt used was the same, and these mixtures

were designed to be volumetrically similar to the Whiterock oolitic limestone mixtures

(WR-C1, WR-C2, WR-C3, WR-F 1, WR-F2, WR-F3) it is likely that this difference has

to do with the aggregate type. This warrants further study through more detailed testing

of mixtures of different mineral origin.

Conclusions

This Chapter presented dynamic modulus testing results for 29 mixtures of

different gradations and aggregate types. Mixtures were tested at two or more of the

following test temperatures: 10 C, 25 C, 30 C, and 40 C. At each testing

temperature, testing was conducted at four distinct frequencies, namely 16 Hz, 10 Hz, 4

Hz, and 1 Hz. The






























1000 10000
Predicted IE*I| OPa)


Figure 4-24. Measured values versus predicted values of |E*| on a log-log scale
(Mix-Laydown binder)


1000 10000
Predicted IE*I (MPa)


Figure 4-25. Measured values versus predicted values of |E*| on a log-log scale
(RTFO-binder)


1000 10000
Predicted IE*| (MPa)


Figure 4-26. Measured values versus predicted values of |E*| on a log-log scale
(DSR-RTFO binder)


100000




0. 10000

LU


i 1000
~1 000


100 L-
100


1 00000




L 10000




S1000


100 -
100


100000


100000



C_ 10000

LU

1000

w


100 L
100


100000












100 C (4 Hz)


14000
*Actual Values
12000 Predicted Values

10000

8000

Z 6000

4000

2000
A
WR-F1 WR-F2 WR-F4 WR-F5 WR-F6 WR-C1 WR-C2 WR-C3
Whiterock Mixtures


300 C (4 Hz)














6000 -----------------,
S6000 EActual Values

5000 Predicted Values

S4000


MB
4 (3000
0
2000



o B





12- 000------------------------
WR-F1 WR-F2 WR-F4 WR-F5 WR-F6 WR-C1 WR-C2 WR-C3
Whiterock Mixtures


400 C (4 Hz)


3000
U Actual Values
Figure 4-27. Measured vs. pPredicted Values
2500 C C) 40
r 2000


'S 1500

*. 1000

500
C

WR-F1 WR-F2 WR-F4 WR-F5 WR-F6 WR-C1 WR-C2 WR-C3
Whiterock Mixtures

Figure 4-27. Measured vs. predicted dynamic modulus values for Whiterock limestone
mixtures: at testing frequency of 4 Hz. A) Testing temperature is 10 0C, B) 30
C C) 40 C















6000


a. 5000


u 4000


3000
E .0 DFAA
O 2000 O Project
Q 2000
SO0 A Granite
OWR
g 1000



0 1000 2000 3000 4000 5000 6000
Predicted Dynamic Modulus, IE*I (MPa)


Figure 4-28. Measured vs. predicted dynamic modulus for fine aggregate angularity
mixtures (FAA), Superpave project mixtures (Project), Granite mixtures
(Granite), and Whiterock mixtures (WR) at a test temperature of 400 C and a
testing frequency of 4 Hz.




The procedure developed by Pellinen and Witczak (2002) for obtaining predicted

master curves was used for all mixtures tested at more than two temperatures. The results

showed that further testing at higher and lower temperatures would help in better defining

the tails of the predicted master curves.

Finally, the predictive regression equation developed by Witzcak et al. (2002) was

used to predict dynamic modulus values for most of the mixtures tested. The results

showed that dynamic modulus predictions using DSR-based viscosity measurements

result in conservative predictions of the dynamic modulus. Therefore, it is recommended

that viscosity input values for the predictive equation be obtained from the DSR test, in









lieu of the Brookfield Rotational Viscometer Test, or published Mix/Laydown viscosities

by Witzcak and Fonseca (1996). The results also showed that dynamic modulus

predictions at higher temperatures generally are closer to the line of equity for all three

cases than the predictions at lower temperatures. This is likely the result of the much of

the database used to develop the predictive equation being biased toward mixtures tested

at higher temperatures.

Finally, a comparison was performed between measured vs. predicted dynamic

modulus at 40 C for the following mixture categories:

* Fine Aggregate Angularity Mixtures ("FAA"),
* Superpave Project Mixtures ("Project"),
* Granite Mixtures ("Granite"), and
* Whiterock Mixtures ("WR").
Most of the mixture groups scatter around the line of unity, with the exception of

the Georgia Granite mixtures, which land below the line of unity. Since the testing

protocol for all mixtures was the same, the asphalt used was the same, and these mixtures

were designed to be volumetrically similar to the Whiterock oolitic limestone mixtures

(WR-C1, WR-C2, WR-C3, WR-F 1, WR-F2, and WR-F3) it is likely that this difference

has to do with the aggregate type. This warrants further study through more detailed

testing of mixtures of different mineral origin.














CHAPTER 5
EVALUATION OF GRDATION EFFECTS

Introduction

The packing of particulate matter into a confined volume has long been of interest

to mix designers. In the 1930's, Nijboer (1948) investigated the effects of particle size

distribution using aggregate particles. He found that a gradation plotted on a log-log

graph as a straight line with a slope of 0.45 produced the densest packing. He showed it

to be the case for both crushed and uncrushed aggregates. In 1962, Goode and Lufsey

(1962) published the results of studies they performed at the Bureau of Public Works.

They performed an experiment to confirm Nijboer's findings and then investigated

further to determine the packing of simulated gradations that might be actually used in

road construction. As a result of their studies, they developed a specialized graph in

which the vertical axis is the percent passing a sieve size and the horizontal axis is the

sieve opening raised to the 0.45 power. To reduce confusion, the horizontal axis does not

contain the actual calculated numbers, but instead has marks that indicate different size

sieves. This specialized graph became known as the 0.45 power chart. In 1992, Huber

and Shuler (1992) investigated the size distribution of particles that gives the densest

packing. They determined that a gradation drawn on a 0.45 power chart as a straight line

from the origin to the aggregate nominal maximum size produced the densest packing. In

2001, Vavrik et al. (2001) presented the Bailey method of gradation analysis. Bailey

method takes into consideration the packing and aggregate interlock characteristics of









individual aggregates and provides criteria that can be used to adjust the packing

characteristics of a blend of materials.

Finally, in 2002 Ruth et al. (2002) provided an experience-based methodology for

the assessment of potential problems associated with aggregate gradation in the

performance of asphalt pavements. The method presented introduced aggregate

gradation factors based on power law regression slopes combined with either the percent

passing the 4.75-mm or 2.36-mm sieves that were used to characterize ten different

coarse- and fine-graded aggregate gradations. These gradation factors were used to

develop relationships with surface area, tensile strength, fracture energy, and failure

strain.

In the following, the gradation factors proposed by Ruth et al. (2002) will be

obtained for 13 mixtures. These mixtures include the VMA mixtures described in

Chapter 3 (Fl, F2, F4, F5, F6, Cl, C2, C3), and the Superpave Monitoring Project

mixtures listed in Chapter 3 (PI, P2, P3, P5, P7). A relationship between the power law

gradation factors and the dynamic modulus will be explored through a correlation study.

Based on the findings from the correlation study, tentative gradation factor values for

optimizing mixtures for high dynamic modulus values will be presented.

The Evaluation of the Effects of Aggregate Gradations on Dynamic Modulus

Description of power law relationship
Following the procedure developed by Ruth, Roque, and Nukunya (2002), the first

step in the evaluation of gradation effects was to fit a power law model to the gradation

curve for each mixture. Power law constants (aca, afa) and exponents (nca, nfa) for the

coarse and fine aggregate portions of these mixtures were established by regression

analyses. The format of the power law equations used in this investigation was,










PC = aC, (d)"n (Eq. 5-1)

and

PFA aF- d)a A (Eq. 5-2)

Where

PeA or PFA = percent of material by weight passing a given sieve having
opening of width d,
aca = constant (intercept) for the coarse aggregate,
aFA = constant (intercept) for the fine aggregate,
d = sieve opening width, mm,
nCA = slope (exponent) for the coarse aggregate,
nFA = slope (exponent) for the fine aggregate.

The method used for determining the "break" between coarse and fine aggregate is based

on the Bailey method (Vavrik et al., 2001). The primary control sieve defining the break

between fine and coarse aggregate in the mix is determined as follows to find the closest

sieve size:

PCS = NMPS x 0.22 (Eq. 5-3)

Where
PCS = Primary control sieve for the overall blend (i.e., division between coarse and
fine aggregate),
NMPS = Nominal maximum particle size for the overall blend as defined in
Superpave, which is one sieve larger than the first sieve that retains more than 10%.

The 0.22 value used in the equation was determined empirically, as discussed by Vavrik

et al. (2002). For example, for a 12.5-mm nominal maximum size mix, the primary

control sieve is 2.36 mm (NMPS x 0.22 = 2.750), whereas for a 19.0-mm nominal

maximum size mix, the primary control sieve is 4.75 (NMPS x 0.22 = 4.180).

Table 5-1 presents the power law coefficients for the fine and the coarse aggregate

portions of the mixtures studied. Generally, the R2 values obtained indicate a fairly good










power law fit to the existing gradation curves (R2 greater than 0.88 for all cases). A

preliminary observation of the results in Table 5.1 shows that

* nfa > nca for "Fine-Graded" mixtures, and

* nca > nof for "Coarse-Graded" mixtures.

Table 5-1. Power regression constants and dynamic modulus for all mixtures
Mixture Dynamic
Modulus, Coarse Aggregate Portion Fine Aggregate Portion
E*| at 1
Hz and aca na R2 af nf R2
400C
F1 850 39.445 0.348 0.996 31.196 0.667 0.988
F2 1076 31.469 0.410 0.993 29.525 0.588 0.989
F4 1044 39.445 0.348 0.996 35.612 0.530 0.986
F5 727 37.017 0.366 0.972 28.719 0.612 0.978
F6 880 31.519 0.448 0.996 29.564 0.586 0.989
C1 526 17.948 0.734 0.887 19.852 0.534 0.988
C2 759 16.644 0.667 0.965 18.763 0.527 0.998
C3 801 20.964 0.644 0.883 22.984 0.498 0.998
P1 524 25.295 0.593 0.999 24.489 0.624 0.997
P2 607 13.074 0.834 0.989 19.921 0.509 0.975
P3 459 24.33 0.571 0.972 22.523 0.698 0.989
P5 638 23.739 0.625 0.992 26.238 0.591 0.963
P7 550 40.857 0.339 0.999 36.146 0.899 0.985


Correlation Study between Power Law Gradation Factors and Dynamic Modulus

In order to identify a potential relationship between the power law gradation

parameters in Table 5-1 and dynamic modulus, a zero-order correlation study was

performed using the power law coefficients listed in Table 5-1 and the dynamic modulus

at 400C and 1 Hz frequency. The dynamic modulus at 400C was selected in lieu of lower

testing temperature results to better capture any potential relationship with the gradation

characteristics of the mixtures tested. The term "zero-order" means that no controls are

imposed on the correlation study.









Table 5-2 shows the results of the zero-order correlation study. Strong correlations

exist between aca and nca (R = -0.98) and afa and nfa (R = 0.543), respectively. Based on

the strong correlation observed between the parameters studied, it was decided to focus

the study on only two out of the four power law parameters, namely nca and nfa. The

results show a weak negative correlation between nca, nfa, and |E40*|. Further testing for

statistical significance revealed no statistically significant correlations between nca, nfa,

and E40* .

Table 5-2. Results of correlation study between power law parameters and dynamic
modulus at 400C and 1 Hz frequency
Power Law Regression Coefficients
E,,,*1 aca nca afa nfa
E ,,*11 1.000 0.414 -0.498 0.464 -0.348
aca 0.414 1.000 -0.980 0.948 0.578
nca -0.498 -0.98 1.000 -0.908 -0.536
afa 0.464 0.948 -0.908 1.000 0.543
nfa -0.348 0.578 -0.536 0.543 1.000
'Denotes the dynamic modulus at 1 Hz frequency and 400C.

In order to further evaluate the relationship between nca, nfa and |E40*|, a bivariate

partial correlation study was performed. In here, a bivariate partial correlation denotes

the correlation obtained between two variables, while controlling for a third variable. For

example, r12.3 denotes the correlation of variables 1 and 2, while controlling for variable

3. In most cases, a partial correlation of the general form r12.3 will turn out to be smaller

than the original correlation r12. In the rare cases where it turns out to be larger, the third

variable, 3, is considered to be a suppressor variable, based on the assumption that it is

suppressing the larger correlation that would appear between 1 and 2 if the effects of

variable 3 were held constant.

Table 5-3 presents the results of the bivariate partial correlation study, in which p

denotes the level of significance of a potential correlation. Hence, p < 0.01 means that









the probability of not having a significant relationship in the population is less than 1

percent. The results revealed a statistically significant negative correlation (r = -0.8654,

p =0 .0008) between nca and |E40*|, when controlling for nfa, implying that a high nca

results in a low E40o*.

Table 5-3. Partial correlation analysis for nca and |E40*| when controlling for nfa
nca
N r (Correlation Coefficient)
|E40*| 13 -0.8654**

p<0.05, ** p<0.01


Category Analysis of Power Law Parameters

In order to further evaluate the relationship between power law parameters (nca and

nfa) and the dynamic modulus, four simplified categories of power law parameters were

hypothesized. The four hypothesized categories to be tested are as follows:

Category 1 [Low nca (smaller than 0.50) and Low nfa (smaller than 0.59)].

Category 2 [Low nca (smaller than 0.50) and High nfa (greater than 0.59)].

Category 3 [High nca (greater than 0.50) and Low nfa (smaller than 0.59)].

Category 4 [High nca (greater than 0.50) and High nfa (greater than 0.59)].

Table 5-4 shows the Mean and Standard Deviation of E40*l for the four different

categories studied. Since the underlying power law parameters nfa and nca are slightly

correlated, a discriminate category analysis is not appropriate. Rather, a one-way

analysis of variance (ANOVA) is used to uncover the effects of the categorical variables

(i.e., four different categories) on the interval dependent variable (i.e., |E40*|). According

to Table 5-5, the results are statistically significant at an alpha level of 0.01 (F(3,9) =

7.64, p = 0.008). Since the results showed a significant omnibus F, a post-hoc analysis









using a Tukey test was performed to evaluate whether differences between any two pairs

of category means were significant. Table 5.6 displays the means for groups in

homogeneous subsets. According to Table 5-6, only the dynamic modulus values for the

first category (combination of Low nca and Low nfa) are significantly different from the

other category groups at an alpha level = .05. This means that if nca is less than 0.5 and

nfa is less than 0.59, a "high" dynamic modulus will likely be obtained for a given

aggregate type and asphalt grade.

Table 5-4. Mean and standard deviation of |E40*| for the four different categories

Category Groups N Mean Std. Deviation

Low nca + Low nfa 3 1000.00 105.14
Low nca + High nfa 3 709.00 150.80
High nca + Low nfa 4 673.25 128.76
High nca + High nfa 3 540.33 90.61
Total 13 726.23 198.83

Table 5-5. One-Way analysis of variance (ANOVA) of |E40*| (total N=13)
Sum of Squares df Mean Square F Sig.
Between Groups 340640.89 3 113546.96 7.64 0.008
Within Groups 133763.41 9 14862.60
Total 474404.30 12

Table 5-6. Post-Hoc analysis for homogeneous subsets of hypothesized categories
Subset for alpha = 0.05
Group N Statistically Not statistically
Significant Significant
Low nca + Low nfa 3 1000.00
Low nca + High nfa 3 709.00
High nca + Low nfa 4 673.25
High nca + High nfa 3 540.33

Category Analysis of Power Law Parameters for Coarse and Fine Graded Mixtures

The mixtures in Table 5-1 were divided into two subsets, depending on whether the

mixtures were coarse-graded or fine-graded, according to the Superpave mixture design









system. A mixture is considered to be coarse-graded if the gradation band passes below

the restricted zone. Conversely, a gradation band for a fine-graded mixture passes above

the restricted zone. Hence, the two different graded subsets to be tested are as follows:

* Coarse-Graded Mixtures,

* Fine-Graded Mixtures.

Tables 5-7 and 5-8 list the coarse- and fine-graded mixtures and their categories,

respectively.

Table 5-7. Mixtures in course-graded category
Mixture Dynamic Coarse Aggregate Fine Aggregate
Modulus, |E*| at Classification Portion Portion
1 Hz and 400C Category noa nfa
Cl 526 Category 3 0.734 0.534
C2 759 Category 3 0.667 0.527
C3 801 Category 3 0.644 0.498
P1 524 Category 4 0.593 0.624
P2 607 Category 3 0.834 0.509
P3 459 Category 4 0.571 0.698
P5 638 Category 4 0.625 0.591

Table 5-8. Mixtures in fine-graded category
Mixture Dynamic Coarse Aggregate Fine Aggregate
Modulus, |E*| at Classification Portion Portion
1 Hz and 400C Category
unca nfa
Fl 850 Category 2 0.348 0.667
F2 1076 Category 1 0.410 0.588
F4 1044 Category 1 0.348 0.530
F5 727 Category 2 0.366 0.612
F6 880 Category 1 0.448 0.586
P7 550 Category 2 0.339 0.899

Table 5-9 shows the correlation analysis results for the Course Graded mixtures. A

zero-order bivariate correlation study found no statistically significant relationship

between nca, nfa, and |E40*|. However, considering the small sample size (N = 7), Table

5-9 shows that a strong negative correlation exists between nfa and |E40o*









Table 5-9. Zero-Order correlation analysis for nca, nfa, and |E40* for course graded
mixtures (N = 7)
nca nfa E40

nca 1 -0.7120 -0.1350
nfa 1 -0.7280
E40 1
p<0.05, ** p<0.01

Table 5-10 shows the results from the correlation analysis for the Fine Graded

mixtures. The zero-order bivariate correlation study found a statistically significant

relationship between nfa, and E40*|. In addition, considering the small sample size (N=

6), Table 5-10 also shows that a strong negative relationship appears between nfa and nca.

Table 5-10. Zero-Order correlation analysis for nca, nfa, and |E40* for fine graded (N=6)
nca nfa |E40*

nca 1 -0.4472 -0.3928

nfa 1 -0.8447*

|E40* 1
p<0.05, ** p<0.01

Summary and Conclusions

The results of the combined analysis of coarse-and fine graded mixtures together

showed a low nfa combined with a low nca results in a "high" dynamic modulus value.

Importantly, the nfa variable was identified as a suppressor variable on nca, meaning that a

low nca by itself was not sufficient in guaranteeing a high dynamic modulus value.

The results of the separate analyses on coarse- and fine-graded mixtures showed

that a negative correlation was observed between nfa and the dynamic modulus at 400C.

Again, this means that the lower the nfa value, the higher the dynamic modulus. Since nfa

is a measure of the rate of change in the gradation band on the fine side of the gradation,









the results indicate that a gradual or a slow rate of change of the gradation band on the

fine side results in a higher dynamic modulus value.

Observation of the coarse-graded mixtures in Table 5-7 shows that all the coarse-

graded mixtures are either in category 3 (high nca and low nfa) or in category 4 (high nca

and high nfa). The overall high nca values are likely due to the nature of coarse-graded

Superpave mixtures, where the gradation band starts above the maximum density line,

but has to cross the maximum density line in order to pass below the restricted zone.

Hence, for coarse-graded mixtures the rate of change in the slope of the gradation band

on the coarse side is fairly high, translating into a relatively high nca value.

Similarly, all of the fine-graded mixtures in Table 5-8 are in category 1 (low nca and

low nfa) or category 2 (low nca and high nfa). Hence, since their gradation bands do not

typically cross the maximum density line, the rate of change in the slope of the gradation

bands for fine-graded mixtures on the fine and coarse sides tends to be lower than for the

coarse-graded mixtures.

In summary, a relationship between a low nfa and a high dynamic modulus (at

40C) has been identified. This means that a slow rate of change in the gradation band

on the fine side of the gradation is related to a high dynamic modulus value. Gap-grading

the mixture on the fine side will generally increase the rate of change in the gradation

band, and thus nfa, and will lead to a lower dynamic modulus.














CHAPTER 6
EVALUATION OF POTENTIAL CORRELATION BETWEEN COMPLEX MODULUS
PARAMETERS AND RUTTING RESISTANCE OF MIXTURES

Background

In this chapter, potential relationships are evaluated between complex modulus

parameters and other common measures of the rutting potential of mixtures. In

particular, the complex modulus parameters are compared against asphalt pavement

analyzer (APA) rut depth results and creep test results from static unconfined

compressive creep testing. First, the APA test procedures and test results are discussed,

followed by a description of the static creep test procedure used and presentation of creep

test results. Then, comparisons are made between dynamic modulus and phase angle

results presented in Chapter 6 to APA rut depth measurements and static creep testing

results.

Asphalt Pavement Analyzer Test Procedure and Test Results

Asphalt Pavement Analyzer (APA) equipment is designed to test the rutting

susceptibility or rutting resistance of hot mix asphalt. With APA, rut performance testing

is performed by means of a constant load applied repeatedly through pressurized hoses to

a compacted test specimen. The test specimen for this research is a 150-mm diameter by

75-mm thick cylindrical specimen.

The procedure for sample preparation and testing is as follows:

* 4500 g samples of the aggregate are batched in accordance with the required job
mix formula. The aggregate and asphalt binder are preheated separately to 300 F
for about three hours, after which they are mixed until the aggregates are
thoroughly coated with the binder; amount of binder used is pre-determined to









produce an optimum Hot Mix Asphalt (HMA) using Superpave Volumetric Mix
Design procedures.

* The mixture is then subjected to two hours of short-term oven aging at 275 F in
accordance with AASHTO PP2.

* The sample is compacted, at the above temperature, to contain 7.00.5% air voids
in the Servopac Superpave gyratory compactor. The compaction is done by first
determining the compaction height needed to obtain the required air void content
from the compaction results obtained for the mixture design. The mix is then
compacted o he determined height.

* The specimen was allowed to cool at room temperature (approximately 25 C) for a
minimum of 24 hours. After the cooling process, the Bulk Specific Gravity of the
specimen is determined in accordance with AASHTO T 166 or ASTM D 2726.
The maximum specific gravity of the mixture was determined in accordance with
ASTM D2041 (AASHTO T 209). Then, the air void content of the specimen was
determined in accordance with ASTM D 3203 (AASHTO T 269) to check if the
target air void content is achieved.

* The specimen is trimmed to a height of 75-mm and allowed to air dry for about 48
hours.

* The specimen was preheated in the APA chamber to a temperature of 60 C (140
F) for a minimum of 6 hours but not more than 24 hours before the test is run.

* The hose pressure gage reading was set to 100+5psi.

* The load cylindrical pressure reading for each wheel was set to obtain a load of
10051bs.

* Secure the preheated, molded specimen in the APA, close the chamber doors and
allow 10 minutes for the temperature to stabilize before starting the test.

* 25 wheel strokes were applied to seat the specimen before initial measurements
were taken.

* The mold and the specimen are securely positioned in the APA, the chamber doors
are closed and 10 minutes are allowed for the temperature to stabilize.

* Restart the APA and continue rut testing, now for 8000 cycles.

Table 6-1 lists the resulting APA rut depth measurements, along with the dynamic

modulus values obtained at 40 C at testing frequencies of 1 Hz and 4 Hz.









Table 6-1.


Dynamic modulus (|E*|), phase angle (6), and asphalt pavement analyzer rut
depth measurements from mixture testi C


Mixture Phase Angle (6) Dynamic Modulus Asphalt Pavement
Results (Degrees) (IE*|) Results Analyzer Rut Depth
(MPa) (mm)
Frequency
1 Hz 4 Hz 1 Hz 4 Hz
Georgia Granite Mixtures
GAC1 27.11 32.77 317.12 475.14 7.1
GAC2 26.67 32.14 535.77 787.74 7.1
GAC3 37.05 42.79 530.76 757.09 5.9
GAF1 27.25 32.35 401.02 635.50 5.1
GAF2 31.63 38.32 535.97 905.80 5.1
GAF3 32.91 38.87 377.70 614.91 4.4
Whiterock Mixtures (Oolitic Limestone)
WRC1 29.02 30.42 526.05 898.81 5.4
WRC2 32.19 32.15 759.48 1368.38 4.6
WRC3 32.84 32.25 801.08 1470.36 4.6
WRF1 29.38 32.11 849.60 1273.70 5.1
WRF2 31.21 33.67 1076.16 1610.34 5.2
WRF4 31.70 34.00 1044.19 1584.81 4.3
WRF5 30.05 33.13 726.94 1146.45 7.1
WRF6 31.92 33.59 879.93 1374.06 4.8
Mixtures From Fine Aggregate Angularity Study
RBC 27.38 31.09 770.75 1175.36 7.3
RBF 25.90 28.66 954.17 1415.66 8.5
CALC 30.53 34.24 1182.66 1792.49 6.9
CALF 26.97 33.92 1184.06 1779.33 6.2
CGC 31.40 31.10 923.08 1363.60 4.3
CGF 25.70 30.95 1217.77 1777.24 4.6
CHC 30.45 33.33 744.73 1166.04 11.9
CHF 35.50 35.40 756.82 1073.82 13.9
Superpave Project Mixtures
PI 23.62 22.99 523.74 807.66 7.1
P2 28.33 32.46 606.97 953.37 6.6
P3 30.63 34.67 458.87 655.21 3.2
P7 26.99 32.15 549.95 796.88 4.3
Heavy Vehicle Simulator Mixtures
HVS67-22 29.01 32.96 620.85 925.02 7.5
HVS76-22 29.24 31.81 646.38 967.52 6.5


Static Creep Test Results

Once the complex modulus test was completed, a static creep test was performed

on the same samples tested in the complex modulus test. In the static creep test, a










constant vertical load is applied to an unconfined (no lateral confinement pressures)

HMA specimen, and the resulting time-dependent vertical deformation is measured.

Figure 7-1 shows a qualitative diagram of the vertical stress and total vertical

deformation during a creep test. The same LVDT's that were used for the complex

modulus test were used in the static creep test to measure vertical deformation.

The creep compliance from creep test at a higher temperature may be an indicator

of the rutting potential of the mix. The compliance is calculated from this test by

dividing the strain by the applied stress at a specified time in seconds.




wI
Ln






creep test.ti
Co
0






Figure 6-1. Qualitative diagram of the stress and total deformation during the
creep test.

The following equation is used to calculate the creep compliance,

D(t) =st



D(t) = Creep compliance at the test temperature T and time of loading, t.

st Strain at time t (inch/inch), and

a = applied stress, psi.









The static creep test was run for a total 1000 seconds. The test load was chosen

such that it produced a horizontal deformation of 150 200 micro-inches after 30

seconds of loading. The test temperature was taken to be 40 oC.

Finally, the measured creep compliance D(t) can be represented using the power

function equation (6-1).

D(t) = Do + D1 tm (Eq. 6-1)

Where Do, Di, and m are parameters obtained from creep tests. In accordance with

the findings from the evaluation of creep parameters from the Superpave Indirect Tensile

Test (Chapter 9) the value of Do is taken as 1/|E*|. The dynamic modulus |E*| is obtained

from the 10 Hz frequency test, to minimize variability of the results. Table 6-2 lists the

static creep test results, along with the power law parameters D1 and m.

Table 6-2. Average static creep testing results for test temperature of 400C.
Mixture Creep Power Law Parameters
Compliance
D (1000 DI m-value
seconds) (1/Mpa)
(1/MPa)
_(xl000)
Georgia Granite Mixtures
GAC1 19.63 8.93E-03 0.114
GAC2 17.02 5.01E-03 0.177
GAC3 15.97 6.83E-03 0.123
GAF1 17.79 5.31E-03 0.175
GAF2 9.52 3.45E-03 0.147
GAF3 11.64 3.50E-03 0.174
Whiterock Mixtures (Oolitic Limestone)
WRC1 1.57 4.14E-04 0.193
WRC2 1.23 3.78E-04 0.171
WRC3 1.96 6.27E-03 0.164


WRF1 26.03


8.50E-03 0.162









Table 6-2. Continued
Mixture Creep Power Law Parameters
Compliance
WRF2 3.95 1.29E-03 0.162
WRF4 4.86 1.23E-03 0.199
WRF5 6.45 1.61E-03 0.201
WRF6 4.52 1.56E-03 0.154
Mixtures From Fine Aggregate Angularity Study
RBC 16.49 6.40E-03 0.137
RBF 10.39 3.30E-03 0.166
CALC 3.83 5.50E-04 0.281
CALF 1.91 3.50E-03 0.128
CGF 10.76 5.00E-03 0.111
CHC 1.74 3.30E-04 0.330
CHF 15.97 4.90E-03 0.171
Superpave Project Mixtures
P1 1.73 5.85E-04 0.157
P2 5.75 1.57E-03 0.188
P3 25.43 3.05E-03 0.307
P5 13.25 5.35E-03 0.155
P7 1.73 5.55E-03 0.126
Heavy Vehicle Simulator Mixtures
HVS67-22 24.17 9.00E-03 0.143
HVS76-22 15.57 6.00E-03 0.138

Evaluation of Dynamic Test results for HMA Rutting Resistance

In this section, the dynamic modulus measurements are compared to the rutting

performance of the various mixtures as measured by the APA rut depths. Rutting

resistance is evaluated at the high temperature of 40C at the frequencies of 1 Hz, and 4

Hz. Berthelot et al. (1996), proposed the following ranges of testing frequencies for

simulating various highway speeds,

* 0.02-0.2 Hz to simulate parking,
* 0.2-2.0 Hz to simulate street and intersection speed,
* 2.0-20 Hz to simulate highway speed.

However, Shenoy and Romero (2002) and Witczak et al. (2002), used a testing

frequency of 5.0 Hz as representative of traffic speed that will trigger pavement rutting in

the evaluation of the SuperpaveTM simple performance tests. Test results were therefore