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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 ataA 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 31 Coarse gradations for fine aggregate effects.......................................................20 32 Fine gradations for fine aggregate effects........................................... ................ 21 33 Physical properties of fine aggregates.....................................................21 34 Gradations for White Rock coarse graded mixtures ...........................................23 35 Gradations for White Rock fine graded mixtures ...............................................23 36 Granite based m ixture gradations.................. .................................................. 25 37 G radiation of fi eld projects......................................... ....................... ................ 26 38 Superpave gyratory com action effort................................................ ................ 29 39 Volumetric properties of coarse graded mixtures ...............................................30 310 Volumetric Properties of Fine Graded Mixtures.................................................30 311 Volumetric properties of coarse graded mixtures ...............................................31 312 Volumetric properties of fine graded Whiterock mixtures .................................31 313 Volum etric properties of Granite m ixtures ......................................... ................ 32 314 V olum etric properties of field projects ............................................... ................ 32 41 Sam ple preparation data .......................................... ......................... ................ 35 42 Average dynam ic m odulus testing results........................................... ................ 39 43 A average phase angle testing results .........................................................................41 44 Brookfield rotational viscometer results on unaged and RTFO aged binder...........55 45 Dynamic shear rheometer results on unaged and RTFO aged binder...................56 46 Viscositytemperature regression coefficients for unaged and R T F O aged P G 6722 asphalt ..................................................................................57 47 Typical viscositytemperature regression coefficients for AC30 at different hardening states ...................................... ....................... ................ 57 48 Calculated viscosity at four complex modulus test temperatures ......................... 57 49 Predicted dynamic moduli for Georgia granite mixtures using the M ix/L aydow n condition ......................................... ......................... ................ 59 410 Predicted dynamic moduli for Whiterock mixtures using the Mix/Laydown c o n d itio n ............................................................................................................... ... 5 9 411 Predicted dynamic moduli for FAA Mixtures using the Mix/Laydown c o n d itio n .............................................................................................................. ... 6 0 412 Predicted dynamic moduli for Superpave project mixtures using the M ix/L aydow n condition .......................................... ......................... ................ 60 413 Predicted dynamic moduli for Georgia granite mixtures using RTFO aged binder results from the Brookfield rotational viscometer test...............................60 414 Predicted dynamic modulus for Whiterock mixtures Using RTFO aged binder results from the Brookfield rotational viscometer test........................................61 415 Predicted dynamic moduli for FAA mixtures using RTFO aged binder results from the Brookfield rotational viscometer test ................................... ................ 61 416 Predicted dynamic moduli for Superpave mixtures using RTFO aged binder results from the Brookfield rotational viscometer test........................................62 417 Predicted dynamic moduli for Georgia granite mixtures using RTFO aged binder results from the dynamic shear rheometer Test. .....................................62 418 Predicted dynamic moduli for Whiterock mixtures using RTFO aged binder results from the dynamic shear rheom eter test.................................... ................ 63 419 Predicted dynamic moduli for FAA mixtures using RTFO aged binder results from the dynam ic shear rheom eter test ............................................... ................ 63 420 Predicted dynamic moduli for Superpave mixtures using RTFO aged binder results from the dynamic shear rheometer test.................................... ................ 64 52 Results of correlation study between power law parameters and dynamic m odulus at 400C and 1 H z frequency.................................................. ................ 74 53 Partial correlation analysis for nca and E40* when controlling for nfa...................75 54 Mean and standard deviation of E40* for the four different categories ...............76 55 OneW ay analysis of variance of E40* ........................................................ 76 56 PostHoc analysis for homogeneous subsets of hypothesized categories .............76 57 M ixtures in coursegraded category .................................................... ................ 77 58 M ixtures in finegraded category ........................................................ ................ 77 59 ZeroOrder correlation analysis for nca, nfa, and E40o* for course graded m ix tu re s ................................................................................................................. ... 7 8 510 ZeroOrder correlation analysis for nca, nfa, and E40o* for fine graded ..................78 61 Dynamic modulus E*, phase angle and asphalt pavement analyzer rut depth measurements from mixture testing at 40 C. ..........................................82 62 Average static creep testing results for test temperature of 40C .........................84 I1 Dynamic creep parameter summary...........................................167 J1 Static creep param eter summary ....... ....... ........ ...................... 170 Ki Short term creep parameter summary ........................................173 LIST OF FIGURES Figure page 11 The testing components of the complex modulus................................................7... 22 Proportionality of Viscoelastic M aterials............................................ ............... 12 23 Superposition of V iscoelastic M aterials.............................................. ............... 13 31 G radiation curves for C l and F l .......................................................... ................ 20 32 Coarse gradations for gradation effects studies...................................................24 33 Fine gradations for gradation effects studies....................................... ................ 24 34 Coarse graded Granite aggregate gradations.......................................................25 35 Fine graded Granite aggregate gradations........................................... ................ 26 36 Gradations for Superpave project mixtures number 2, 3, and 7...............................27 37 Gradations for field projects 1 and 5 ...................................................27 38 Servopac superpave gyratory compactor ............... ....................................29 41 Typical plot of force and LVDT displacement versus time at low temperature for m mixture W R C ................................................................. ........................ 37 42 Typical plot of force and LVDT displacement versus time at high temperature for m mixture W R C 1 .............. ......................... ...................... .................... .... 37 43 Typical plot of vertical stress versus strain at low temperature for m ix tu re W R C 1 ........................................................................................................ 3 8 44 Typical plot of vertical stress versus strain at high temperature for m ix tu re W R C 1 ........................................................................................................ 3 8 45 Dynamic modulus E* of GAF1 at 100C............... ...................................44 46 Phase angle of G A F1 m ixture at 100C ................................................ ................ 44 47 Dynam ic m odulus E* of GAF1 at 25C ............................................ ................ 45 48 Phase angle of G AF1 m ixture at 250C ................................................ ................ 45 49 Dynam ic m odulus E*I of GAF1 at 40C ............................................ ................ 45 410 Phase angle of G AF1 m ixture at 400C ................................................ ................ 46 411 Dynam ic m odulus E* of GA Ci at 100C ........................................... ................ 46 412 Phase angle of G A CI m ixture at 10C ................................................ ................ 46 413 Dynam ic m odulus E*I of GACI at 250C ........................................... ................ 47 414 Phase angle of G A CI m ixture at 25C ................................................ ................ 47 415 Dynam ic m odulus E*I of GACI at 400C ........................................... ................ 47 416 Phase angle of G A CI m ixture at 40C ................................................ ................ 48 417 Parameters used in sigmoidal fitting function..................................... ................ 50 418 Shift function for coarsegraded GAC3 mixture.................................................51 419 M aster curve for coarsegraded GAC3 mixture .................................. ................ 52 420 Shift function for finegraded GAF1 mixture. .................................... ................ 52 421 M aster curve for finegraded GAF1 mixture. ..................................... ................ 52 422 Shift function for finegraded GAF1 mixture. .................................... ................ 53 423 M aster curve for coarsegraded GAC1 mixture .................................. ................ 53 424 Measured values versus predicted values of IE* on a loglog scale..................... 66 425 Measured values versus predicted values of IE* on a loglog scale..................... 66 426 Measured values versus predicted values of IE* on a loglog scale..................... 66 427 Measured vs. predicted dynamic modulus values for Whiterock limestone m ixtures: at testing frequency of 4 H z ................................................ ................ 67 428 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 61 Qualitative diagram of the stress and total deformation during the creep test........ 83 62 Dynamic modulus at testing frequencies of 1 Hz and 4 Hz versus APA rut depth m easurem ents. ............................... .. ....................... .......................... 86 63 Dynamic modulus at testing frequencies of 1 Hz and 4 Hz versus APA rut depth measurements for coarse and finegraded mixtures.................................86 64 Dynamic modulus, E* versus test track rutting for the 2000 NCAT test track se c tio n s ................................................................................................................ .... 8 7 65 Phase angle at a testing frequency of 1 Hz versus APA rut depth m easu rem en ts ........................................................................................................... 8 8 66 Plot of E*/Sin4) at 40C and 1 Hz. versus the APA rut depths for all mixtures .......88 67 E*/sin6 versus Test Track Rutting for the 2000 NCAT test track sections............89 68 Plot of E*sin6 at 40C and 1 Hz versus APA rut depth.....................................90 69 Relationship between dynamic modulus at 1 Hz frequency and static creep com pliance after 1000 seconds ........................................................... ................ 91 610 Relationship between dynamic modulus at 1 Hz frequency and the power law creep com pliance param eter D 1 .................................................... ................ 91 611 Relationship between dynamic modulus at 1 Hz frequency and power law mvalue parameter ....................... .......... .......................... 92 612 Relationship between phase angle at 1 Hz frequency and static creep compliance after 1000 seconds ................... .... ........... .........................92 613 Relationship between phase angle at 1 Hz frequency and the power law creep com pliance param eter D 1 ......................................... ........................ ................ 93 614 Relationship between phase angle at 1 Hz frequency and power law mvalue p a ra m ete r.............................................................................................................. .. 9 3 A1 E* vs. co for coarse Whiterock gradations at 10, 30 and 400 C ..............................97 A2 4 vs. o for coarse Whiterock gradations at 10, 30 and 400 C. ................................98 A3 E*I vs. o for fine Whiterock gradations at 10, 30 and 400 C ................................99 A4 4 vs. o for fine Whiterock gradations at 10, 30 and 40 C. .............................101 Bi Measured test results versus predicted dynamic modulus values for fine gradation W hiterock mixtures at 1 Hertz ....... .......... ..................................... 104 B2 Measured test results versus predicted dynamic modulus values for fine gradation W hiterock mixtures at 4 Hertz ....... .......... ..................................... 105 B3 Measured test results versus predicted dynamic modulus values for fine gradation W hiterock mixtures at 10 Hertz ....... ... .................. .................. 106 B4 Measured test results versus predicted dynamic modulus values for fine gradation W hiterock mixtures at 16 Hertz ....... ... .................. .................. 107 C1 Measured test results versus predicted dynamic modulus values for fine gradation W hiterock m ixtures ....... ......... ......... ..................... 109 C2 Measured test results versus predicted dynamic modulus values for Coarse gradation W hiterock m ixtures ............................................................................. 111 C3 Measured test results versus predicted dynamic modulus values for coarse gradation G granite m ixtures.......................................................... ............... 113 C4 Measured test results versus predicted dynamic modulus values for fine gradation G granite m ixtures.......................................................... ............... 115 C5 Measured test results versus predicted dynamic modulus values for fine gradation FA A m ixtures...................................... ........................ ............... 117 C6 Measured test results versus predicted dynamic modulus values for fine gradation FA A m ixtures...................................... ........................ ............... 119 D1 Measured test results versus predicted dynamic modulus values for fine gradation W hiterock m ixtures ....... ......... ......... ..................... 122 D2 Measured test results versus predicted dynamic modulus values for coarse gradation W hiterock m ixtures ....... ......... ......... ..................... 124 D3 Measured test results versus predicted dynamic modulus values for coarse gradation G granite m ixtures.......................................................... ............... 126 D4 Measured test results versus predicted dynamic modulus values for fine gradation G granite m ixtures.......................................................... ............... 128 D5 Measured test results versus predicted dynamic modulus values for fine gradation "FAA" m fixtures ........................................................ 130 D6 Measured test results versus predicted dynamic modulus values for coarse gradation "FAA" m fixtures ........................................................ 131 E1 Comparison of measured dynamic modulus test results vs. Witzack's2002 predicted results at 100C degrees ....... ......... ........ ..................... 133 E2 Comparison of measured dynamic modulus test results vs. Witzack's2002 predicted results at 400C degrees ....... ......... ........ ..................... 134 E3 Comparison of measured dynamic modulus test results vs. Witzack's2002 predicted results at 100C degrees, on log scale....... .................. ................... 135 Fi Dynamic modulus values for fine graded Whiterock mixtures........................... 138 F2 Do values for fine graded Whiterock mixtures.......................... ...................140 F3 D1 values for fine graded Whiterock mixtures........................... ...................142 F4 Dynamic modulus values for fine graded Project mixtures............................. 144 F5 Do values for fine graded Project mixtures ....... ... ...................................... 146 F6 Do values for fine graded Whiterock mixtures........................... ...................148 F7 Do values for fine graded "FAA" mixtures.......... ..................................... 150 G1 Gradation line and power regression lines of fine gradation Whiterock sa m p le s ............................................................................................................... ... 1 5 3 G2 Gradation line and power regression lines of coarse gradation Whiterock sa m p le s ............................................................................................................... ... 1 5 5 G5 Gradation line and power regression lines of fine gradation Project samples ....... 157 H1 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 highvolume 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 highvolume highways that require superior load resistance. The guide is based on mechanistic principle and requires a modulus to compute stresses and strains in hotmix 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 "nonstatic" load conditions. The packing of particles into a confined volume has been studied for over 300 years. Sir Isaac Newtonamong the first to study this phenomenonwas 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 shortterm dynamic modulus measurements compare to staticcreep testing results. To achieve these objectives, complexmodulus testing and staticcreep 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 tensioncompression 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 tensioncompression 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. StroupGardiner (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 mid1990s as part of the NCHRP Project 919 (Superpave Support and Performance Models Management) and NCHRP Project 929 (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 30799. 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 21 (Yoder & Witczak, 1975). E* = o (Eq. 21) 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 11. 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 21. Equation 22 describes the relationship between the various components and E*: S = tan E (Eq. 22a) E' E"= E *E sin(S) (Eq. 22b) E'= E *cos(3) (Eq. 22c) 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 23. S= tlg f. (3600) (Eq. 23) 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 24 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 25. 3 = tan \G'1 (Eq. 25a) \G'j G"= G sin(3) (Eq. 25b) G'= G *cos(3) (Eq. 25c) 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 26. G* = 2(1 (Eq. 26) 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 26 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 timetemperature 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 thermorheologically simple material, and that the timetemperature 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. 27) 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 WilliamsLandelFerry (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 28. log(E *) = 3 + (Eq. 28) 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 28 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 919, 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 100mm diameter cored specimens from a 150mm diameter gyratory compacted specimen, with a final saw cut height of 150mm. 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 nonuniform air void distribution both along their diameter and along height. SGCcompacted 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 29. (C a(t)) = C (at)) (29) 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 210 describes this concept. (oa, (t) +,2 (t t))=)) = s(02 (t 1)) (Eq. 210) 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 22 and 23 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 22. 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 23. 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 mechanisticempirical design procedure (NCHRP 137A 2002 Design Guide Draft, 2002). Level 1 Analysis requires actual dynamic modulus test data to develop master curves and shift factor based on Equations (27) and (28). 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 137A 2002 Design Guide Draft, 2002) is used with typical temperatureviscosity 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 211). loE* = 1.249937+ 0.029232x (p200) 0.001767x (p200)2 0.002841x (p4) 0.802208ViJ) (Eq. 211) 0.058097x (V) 0 (Eq. 211) 3.871977 0.0021(p4) + 0.00395p3/8) 0.00017p3/8)2 + 0.00547(p3/4) 1 + e(0 6033130313351log(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 19mm sieve, by total aggregate weight; P3/8 = percent weight retained on 9.5mm sieve, by total aggregate weight; P4 = percent weight retained on 4.75mm sieve, by total aggregate weight; P200 = percent weight passing 0.75mm sieve, by total aggregate weight; The above dynamic modulus predictive equation has the capability to predict the dynamic modulus of densegraded 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 919 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. 212) 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 41 F=+ + e 354h15 408) (Eq. 213) A volumetric adjustment factor, Ki,, corrects the number of repetitions to failure by taking into account the binder and mix properties. In the equation 214, 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. 214) Equation (212) 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. 215) Finally, it is expected that each state agency will have to develop local calibration factors for Equation 215. 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, AC30 (PG6722), 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 (1/2in). These Superpave mixtures were selected because they are commonly used FDOT gradations and they are known to perform well in the field. Figure 31 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 C1 17 and a washed sieve analyses were performed according to ASTM C136. 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 FC3 (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 31. Gradation curves for Cl and Fl The aggregates are designated in this project as follows: * CaleraCAL * WhiterockWR * Cabbage GroveCG * RubyRB * Chattahoochee FC3 CH Table 31. 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 32. 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 33 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 finegraded aggregates used. Bulk Specific Gravity ranged from 227 for relatively porous limestone to 268 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 17 to 46, while average particle shape values ranged from 24 to 43. Table 33. 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 FC3 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: 3040; 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 C128. 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 C1252 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 31. G Wr = G .WL (Eq. 31) 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 34 and 35 show the gradations for the coarse and fine blends respectively. These are also displayed in Figures 32 and 33. Table 34. 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 35. 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 36 to 38 show the gradations, which are also displayed in Figures 34 to 37. 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 32. 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 33. Fine gradations for gradation effects studies Table 36. 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 34. 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 35 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 rNCo C . O CC 0 Co0) CO (""" Sieve Size (raised to 0.45 power) mm Figure 35. Fine graded Granite aggregate gradations Table 37. 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 36. 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 LD LD LID Sieve Size (raised to 0.45 power) mm Sieve Size (raised to 0.45 power) mm Figure 37. 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 coarsegraded (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 38 shows a picture of the Servopac gyratory compactor. Table 38 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 1030 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, 600kPa 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 39 to 314 show the volumetric properties of all the mixtures used in this research. Figure 38. Servopac superpave gyratory compactor Table 38. 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 39. 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 310. 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 311. 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 312. 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 313. 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 314. 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 Proj1 Proj2 Proj3 Proj7 Proj8 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 51mm. 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 61. All specimens were compacted directly to 6.65in to 7.04in (170.0mm to 180mm) height in a 4inch (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 41. 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 41. 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 41. 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 HVS6722 1 6.9 150.2 2 7.1 150.8 3 6.8 151.1 HVS7622 1 7.3 150.4 2 6.8 150.7 3 7.0 150.3 Figures 41 and 42 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 44 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 4Hz1 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 41. Typical plot of force and LVDT displacement versus time at low temperature (100C and 4 Hz) for mixture WRC1. 0 1000 S2000 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 42. 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 4Hz100C 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 43. 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 4Hz400C 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 44. Typical plot of vertical stress versus strain at high temperature (400C and 4 Hz) for mixture WRC 1. DataAnalysis 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 42 and 43 list the average values for the three specimens for each asphalt mixture. Table 42. 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 42. 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 42. 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 HVS6722 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 HVS7622 30 1226.468 1855.661 2401.104 2639.515 40 646.3819 967.5163 1260.443 1439.98 Table 43. 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 43. 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 HVS6722 10 40 10 HVS7622 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 45 through 410 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 411 through 416 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 coarsegraded mixtures. The degree of variability shown in the dynamic modulus and phase angle results for mixtures GAF1 and GAC1 in Figures 45 through 416 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 46 and 48 shows that the phase angle also increases with higher testing temperatures. Also interestingly, a comparison of Figures 46 and 48 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 48 and 410. 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.  F101 UF102 F103 * Sum 10 Frequency (Hz) 15 20 Figure 45. Dynamic modulus E* of GAF1 at 10C 10000 8000 6000 4000 2000 n 0 5 10 15 20 Frequency (Hz) Figure 46. Phase angle of GAF1 mixture at 10C *F101 1 F102  F103 A Avg IMF I I I 5000 4000 3000 2000 1000 n 0 5 10 15 20 Frequency (Hz) Figure 47. Dynamic modulus E* of GAF at 25C 0 5 10 15 20 Frequency (Hz) Figure 48. Phase angle of GAF mixture at 25C 2000 1600 u 800 400 0 0 5 10 15 20 Frequency (Hz) Figure 49. Dynamic modulus E* of GAF1 at 40C  F101  F102 * F103 A Avg *F101  F102 *F103 A Avg *F101  F102  F103 *Avg  i nn!!!!!! !! !I jiiiiii 60 50 0)40 CQ  30 w 20 1 10 0 5 10 15 20 Frequency (Hz) Figure 410. Phase angle of GAF1 mixture at 40C 10000 8000 6000 4000 2000 0 * F101  F102 * F103 Avg 0 5 10 15 20 Frequency (Hz) Figure 411. Dynamic modulus iE*I of GACi at 10C 50 4 40 (D S30  20 1 a 10 0  Cl01 * C 1 0 1 *Cl03 * Sum 0 5 10 15 20 Frequency (Hz) Figure 412. Phase angle of GAC1 mixture at 10C AvC1 *Avg 5000 4000 3000 Lu 2000 1000 0  C101 C102 0C103  Avg 0 4 8 12 16 20 Frequency (Hz) Figure 413. Dynamic modulus IE* of GACI at 25C 50 40 3 C101 C C102 20 0  C103 10  Sum 0 5 10 Frequency (Hz) 15 20 Figure 414. Phase angle of GAC mixture at 250C 2000 1600 1200 800 400 0 * C101  C102 *OC103 i Avg 0 5 10 15 20 Frequency (Hz) Figure 415. Dynamic modulus IE* of GACI at 40C ~jI 75 0) gff  > WC102 t 15  Avg 0 5 10 15 20 Frequency (Hz) Figure 416. 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 137A, 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. 41) 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 nonlinear 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 (42). log(E*) = +og (Eq. 42) 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. 43) 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 (617). Sigmoidal Function 7 (increase) 6+a P j3 (neg) o/ P3 (pos) Log Reduced Frequency Figure 417. 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 GAC3 and GAF1 are presented in Figures 418 through Figure 421 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 Sshape. Rather, the mastercurve showed a slight concavedown curvature. Figures 422 and 423 show the shift function and predicted mastercurve for mixture GAC1, respectively. The predicted mastercurve for GAC 1 does not show an Sshape. It shows a slight concavedown 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 418. Shift function for coarsegraded GAC3 mixture. Master Curue C3 6 4 2 0 2 4 Reduced Frequency Figure 419. Master curve for coarsegraded 4 2 0 2 4 Figure 4: GAC3 mixture. 0 20 40 60 80 100 120 Temperature(F) 20. Shift function for finegraded GAF1 mixture. Master Curve F1 6 4 2 0 2 4 6 Reduced Frequency Figure 421. Master curve for finegraded GAF1 mixture. y = 0.061x 4.9197 R2 = 0.9867  2 4 Figure 42 1 y = 0.0722x + R2 R 1 5.5655 5.5655 0 20 40 60 80 100 120 Temperature (OF) 12. Shift function for finegraded GAF1 mixture. s Predicted 10Odc 2 A 30dc S40dc J 1 6 4 2 0 2 4 6 Log reduced frequency Figure 423. Master curve for coarsegraded 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 (43). lodE* = 1.249937+ 0.029232x (p00) 0.001767x (p00)2 0.00284 lx( (4) 0.80220Ve) (. 43 0.058097x (V,) 0.80220Vbff (Eq. 43) b +Va Vbeff +a 3.871977 0.002(p4)+0.00395p3,8) 0.00017(p'38)2 +0.00547q(p34) 1+e (0 6033130 313351 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 19mm sieve, by total aggregate weight; P3/8 = percent weight retained on 9.5mm sieve, by total aggregate weight; P4 = percent weight retained on 4.75mm sieve, by total aggregate weight; P200 = percent weight passing 0.75mm sieve, by total aggregate weight; The above dynamic modulus predictive equation has the capability to predict the dynamic modulus of densegraded 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 61 lists the air voids for each specimen tested. For each mixture listed in Table 61, 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 shortterm RTFO aged specimens. * Dynamic Shear Rheometer results on shortterm 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 PG6722 (AC30). The HVS mixture with SBS modified binder graded as PG7622 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 64 shows the results of the Brookfield Rotational Viscometer testing, performed at three testing temperatures (60.5 C, 70.7 C, Table 44. 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 45 shows the results of viscosity test results obtained from the Dynamic Shear Rheometer. The viscosity is reported in centiPoise (cP). Table 45. 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 44 and 45, the viscosity for each complex modulus test temperature was obtained using the equation (44). Log(log(r) = A + VTSlog(T) (Eq. 44) 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 46 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 47 lists typical A and VTS values for PG 6722 (AC 30), recommended by Witzcak and Fonseca (1996), for two conditions: (a) original, and (b) shortterm (mix/laydown). A comparison of Tables 46 and 47 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 46 and 47, the viscosity (in Poise) was finally calculated for the complex modulus testing temperatures used. The viscosities of Table 46. Viscositytemperature regression coefficients for unaged and RTFO aged PG 6722 (AC30) 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 47. Typical viscositytemperature regression coefficients for AC30 (PG 6722) at different hardening states (Witzcak and Fonseca, Transportation Research Record 1540, 1996, pp. 1523) 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 AC30 asphalt, (b) Dynamic Shear Rheometer testing of RTFO aged PG 6722 (AC30) asphalt, and (c) Mix/Laydown conditions from Witzcak and Fonseca (1996). Table 48 summarizes the results of the calculated viscosities for condition and test temperature. Table 48. 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 7622 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 49 through 420 list the predicted dynamic modulus values for all test temperatures and testing frequencies (Proposed by Witzcak and Fonseca1996). Similarly, Figures 424 through 426 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 423 through 426. 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 49. 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 410. 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 411. 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 412. 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 413. 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 414. 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 415. 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 413. 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 416. 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 417. 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 415. 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 418 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 419. 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 417. Table 419. 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 420. 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 MixLaydown 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 DSRbased 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 427 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 428 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 (GAC1, GAC2, GA C3, GAF1, GAF2, GAF3), 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 (WRC1, WRC2, WRC3, WRF 1, WRF2, WRF3) 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 424. Measured values versus predicted values of E* on a loglog scale (MixLaydown binder) 1000 10000 Predicted IE*I (MPa) Figure 425. Measured values versus predicted values of E* on a loglog scale (RTFObinder) 1000 10000 Predicted IE* (MPa) Figure 426. Measured values versus predicted values of E* on a loglog scale (DSRRTFO 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 WRF1 WRF2 WRF4 WRF5 WRF6 WRC1 WRC2 WRC3 Whiterock Mixtures 300 C (4 Hz) 6000 , S6000 EActual Values 5000 Predicted Values S4000 MB 4 (3000 0 2000 o B 12 000 WRF1 WRF2 WRF4 WRF5 WRF6 WRC1 WRC2 WRC3 Whiterock Mixtures 400 C (4 Hz) 3000 U Actual Values Figure 427. Measured vs. pPredicted Values 2500 C C) 40 r 2000 'S 1500 *. 1000 500 C WRF1 WRF2 WRF4 WRF5 WRF6 WRC1 WRC2 WRC3 Whiterock Mixtures Figure 427. 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 428. 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 DSRbased 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 (WRC1, WRC2, WRC3, WRF 1, WRF2, and WRF3) 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 loglog 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 experiencebased 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 4.75mm or 2.36mm sieves that were used to characterize ten different coarse and finegraded 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. 51) and PFA aF d)a A (Eq. 52) 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. 53) 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 12.5mm nominal maximum size mix, the primary control sieve is 2.36 mm (NMPS x 0.22 = 2.750), whereas for a 19.0mm nominal maximum size mix, the primary control sieve is 4.75 (NMPS x 0.22 = 4.180). Table 51 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 "FineGraded" mixtures, and * nca > nof for "CoarseGraded" mixtures. Table 51. 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 51 and dynamic modulus, a zeroorder correlation study was performed using the power law coefficients listed in Table 51 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 "zeroorder" means that no controls are imposed on the correlation study. Table 52 shows the results of the zeroorder 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 52. 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 53 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 53. 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 54 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 oneway 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 55, 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 posthoc 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 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 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 54. 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 55. OneWay 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 56. PostHoc 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 51 were divided into two subsets, depending on whether the mixtures were coarsegraded or finegraded, according to the Superpave mixture design system. A mixture is considered to be coarsegraded if the gradation band passes below the restricted zone. Conversely, a gradation band for a finegraded mixture passes above the restricted zone. Hence, the two different graded subsets to be tested are as follows: * CoarseGraded Mixtures, * FineGraded Mixtures. Tables 57 and 58 list the coarse and finegraded mixtures and their categories, respectively. Table 57. Mixtures in coursegraded 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 58. Mixtures in finegraded 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 59 shows the correlation analysis results for the Course Graded mixtures. A zeroorder bivariate correlation study found no statistically significant relationship between nca, nfa, and E40*. However, considering the small sample size (N = 7), Table 59 shows that a strong negative correlation exists between nfa and E40o* Table 59. ZeroOrder 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 510 shows the results from the correlation analysis for the Fine Graded mixtures. The zeroorder bivariate correlation study found a statistically significant relationship between nfa, and E40*. In addition, considering the small sample size (N= 6), Table 510 also shows that a strong negative relationship appears between nfa and nca. Table 510. ZeroOrder 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 coarseand 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 finegraded 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 coarsegraded mixtures in Table 57 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 coarsegraded 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 coarsegraded 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 finegraded mixtures in Table 58 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 finegraded mixtures on the fine and coarse sides tends to be lower than for the coarsegraded 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. Gapgrading 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 150mm diameter by 75mm 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 predetermined to produce an optimum Hot Mix Asphalt (HMA) using Superpave Volumetric Mix Design procedures. * The mixture is then subjected to two hours of shortterm 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 75mm 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 61 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 61. 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 HVS6722 29.01 32.96 620.85 925.02 7.5 HVS7622 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 timedependent vertical deformation is measured. Figure 71 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 61. 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 microinches 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 (61). D(t) = Do + D1 tm (Eq. 61) 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 62 lists the static creep test results, along with the power law parameters D1 and m. Table 62. Average static creep testing results for test temperature of 400C. Mixture Creep Power Law Parameters Compliance D (1000 DI mvalue seconds) (1/Mpa) (1/MPa) _(xl000) Georgia Granite Mixtures GAC1 19.63 8.93E03 0.114 GAC2 17.02 5.01E03 0.177 GAC3 15.97 6.83E03 0.123 GAF1 17.79 5.31E03 0.175 GAF2 9.52 3.45E03 0.147 GAF3 11.64 3.50E03 0.174 Whiterock Mixtures (Oolitic Limestone) WRC1 1.57 4.14E04 0.193 WRC2 1.23 3.78E04 0.171 WRC3 1.96 6.27E03 0.164 WRF1 26.03 8.50E03 0.162 Table 62. Continued Mixture Creep Power Law Parameters Compliance WRF2 3.95 1.29E03 0.162 WRF4 4.86 1.23E03 0.199 WRF5 6.45 1.61E03 0.201 WRF6 4.52 1.56E03 0.154 Mixtures From Fine Aggregate Angularity Study RBC 16.49 6.40E03 0.137 RBF 10.39 3.30E03 0.166 CALC 3.83 5.50E04 0.281 CALF 1.91 3.50E03 0.128 CGF 10.76 5.00E03 0.111 CHC 1.74 3.30E04 0.330 CHF 15.97 4.90E03 0.171 Superpave Project Mixtures P1 1.73 5.85E04 0.157 P2 5.75 1.57E03 0.188 P3 25.43 3.05E03 0.307 P5 13.25 5.35E03 0.155 P7 1.73 5.55E03 0.126 Heavy Vehicle Simulator Mixtures HVS6722 24.17 9.00E03 0.143 HVS7622 15.57 6.00E03 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, * 0.020.2 Hz to simulate parking, * 0.22.0 Hz to simulate street and intersection speed, * 2.020 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 