UFDC Home  myUFDC Home  Help 



Full Text  
DYNAMIC TORSIONAL SHEAR TEST FOR HOT MIX ASPHALT By LINH V. PHAM A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ENGINEERING UNIVERSITY OF FLORIDA 2003 Copyright 2003 by Linh V. Pham This document is dedicated to the graduate students of the University of Florida. ACKNOWLEDGMENTS I would like to thank my advisor, Dr. Bjorn Birgisson, for his supervision and guidance throughout the project. Without his expertise, I would not have been able to finish this task. I would like to thank the other members of my committee, Dr. Reynaldo Roque and Dr. David Bloomquist, for their time and knowledge that kept me on the right track. I would like to thank D.J Swan, George Loop 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 throughout my stay in Gainesville. Finally, I would like to spend a special thank to my parent, my brother and friend in Vietnam. I am always blessed by their love, encouragement and support. TABLE OF CONTENTS Page A C K N O W L E D G M E N T S ................................................................................................. iv LIST OF TABLES ........................................................................ .............. viii LIST OF FIGURES ......... ......................... ...... ........ ............ ix A B S T R A C T .......................................... ..................................................x iii CHAPTER 1 IN TR OD U CTION ............................................... .. ......................... .. 1.1 B background ......... ...... ................................................................... ........... 1 1.2 Problem Statem ent....... ............................ .. .............. ................ .2 1.3 O bjectiv es .................................................................... 2 1.4 Scope..................................................... . 3 2 LITER A TU R E REV IEW ............................................................. ....................... 4 2.1 A xial C om plex M odulus............................................................................. 4 2.2 Torsional Com plex M odulus ............................ .. .................................... 8 2.3 Solid Specimen versus Hollow Specimen ........................ .................. 10 2.3.1 D distribution of Shear ............................................................................... 10 2.3.2 Comparison of Solid and Hollow Specimens..............................11 3 MATERIALS PREPARATION AND TESTING PROGRAM.............................13 3.1 G granite M fixtures ....................................................... .... ........ .... 13 3.2 Sam ple P reparations ........................................... ........................... .......... 16 3.3 Testing Program .................. .................. .................. ......... ............. 16 4 IMPROVEMENT OF COMPLEX MODULUS TESTING PROGRAM ..................17 4.1 N ew M T S C controlling System .................................................. ..................... 17 4.2 T em perature C ontrol.................................................. ............................... 19 4 .3 Som e T est Issues............ ... ........................................ .............. ........... ...... 20 v 4.3.1 Calibration ............................................................................ 20 4 .3 .2 C control Issu e............. ...................................... ................ .. .... ...... 20 4.3.3 Seating Load .................. .......................... .... .... ................. 22 4.3.4 End plate and G lue .............................................................................. 23 4.4 Com plex M odulus Testing Setup ........................................ ...... ............... 23 4.4 Torsional Shear M odulus Testing Setup................................... ............... 27 5 SIGNAL AND DATA ANALYSIS ........................................ ....................... 30 5 .1 T est Sign al .........................................................................30 5.2 D ata A naly sis .............................................. .............................34 5.2.1 Iterative Curve Fit M ethod .................................... .................................. 34 5.2 .2 R egression M ethod ......................................................................... .. .... 36 5.2.3 FFT M ethod...................................................... .. ........ .. ...... .. 37 5.2.4 Evaluation of Data Interpretation Method...............................................40 5.2.5 Com puter Program .................................. .....................................41 6 AXIAL COMPLEX MODULUS TEST RESULTS...............................................48 6.1 Result of Complex Modulus Test................................. ...............48 6.1.1 D ynam ic M odulus R results ........................................ ...... ............... 48 6.1.2 Phase A ngle R results ........................... ....... .................................. 51 6.1.3 D discussion of Testing R results ........................................ .....................53 6.2 Master Curve Construction.............. ................................. 57 6.2.1 Timetemperature Superposition Principle................... ...............57 6.2.2 Constructing Master Curve using Sigmoidal Fitting Function...................58 6 .3 P redictiv e E qu action .................................................................... ....................6 1 7 TORSIONAL SHEAR TEST RESULTS....................... ...... ..............64 7.1 R esult of Torsional Shear Test ........................................ ......... ............... 64 7.1.1 Stress versus Strain Study ....................................... ....................... 64 7.1.2 Dynamic Torsional Shear Modulus Results ......... ..............................66 7.1.3 Phase A ngle R results ............................................................................68 7 .2 P oisson R atio ................................................................72 7.3 Summary ............. ................................................... ......... 74 8 CONCLUSION AND RECOMMENDATION ............................... ...............76 8.1 C conclusion .......... ................ .............. ................ ..................... 76 8.1.1 Testing Procedures and Setup ........................................ .....................76 8.1.2 Signal and Data Analysis ............................. .... .... ............... 77 8.1.3 Axial Com plex M odulus Test ....................................... ............... 77 8.1.4 T orsional Shear T est........................................................ ............... 78 8.2 R ecom m endation ............................................................................. 79 APPENDIX A M IX D E S IG N ..................................................................................... .................. 8 0 B DATA FROM TESTING ........................................................................... 87 L IST O F R E FE R E N C E S ......................................................................... ................... 115 BIOGRAPH ICAL SKETCH ........................................................................117 LIST OF TABLES Table pge 4.1 Suggested value for P gain for GCTS system .............................................. 22 5.1 Evaluation of data interpretation method.............. ............................ ............... 40 7 .1 P o isso n ratio ...................................................................... 7 4 LIST OF FIGURES Figure p 2.1 Stress and strain signal of axial complex modulus test..............................................5 2.2 Relation among E*, E' and E" ..................................................................... 6 2.3 Torsional shear test for HM A Colum n ........................................ ...... ............... 8 2.4 Description of the nonuniformity of shear stresses across a specimen for different ratios of inner to outer radii ........................................................................ 11 2.5 Difference in torque between hollow and solid specimens to achieve the same av erag e strain ................................................... ................ 12 3.1 G radiation Plot for Coarse M ixture ........................................ ........................ 15 3.2 G radiation Plot for Fine M ixture ........................................ ........................... 15 4.1 Temperature control by circulating water ............... .......................................19 4.2 LVD T calibration device. ................................................ ............................... 20 4.3 E effect of using P gain ............... ........................ .................... .. ...... 22 4.4 Texture end plate for torsional shear test............................................ ...............23 4.5 Complex modulus testing setup in the triaxial cell....................................................24 4.6 Picture of sample set up in triaxial cell for complex modulus test ...........................26 4.7 Torsional shear testing set up........................................................................ 27 4.8 Picture of torsional shear testing set up. ............................................ ............... 29 5.1 Typical test signal. ...................................................................... 30 5.2 Dynamic sinusoid component of the signal .......... ................................................31 5.3 Signal in higher scale ............... ................ ......................... .........31 5.4 N oise signal ...................................................... ................. 32 5.5 Signal after filtering .............. ......................... .................... .. ...... 33 5.6 N oise filter function in Lab View ........................................ ......................... 33 5.7 T est signal in tim e dom ain ................................................................................38 5.8 T est signal in frequency dom ain .............................................................................. 38 5.9 Strain w ith m missing peak data ............................................. ............................ 39 5.10 Flow chart of data analysis program ............................................................ ....... 43 5.11 C om plex M odulus Program ........................................................................... ...... 44 5.12 Torsional Shear M odulus Program. ............................................... ............... 44 5.13 Output page of Torsional Shear Modulus Program. ............................................45 5.15 Linear regression versus quadratic regression analysis ........................................47 6.1 Dynamic Modulus E* of GAF at 250C ........................... ...............49 6.2 Dynamic Modulus E* of GAF1 at 100C .................... .. ........................ 49 6.3 Dynamic Modulus E* of GAF1 at 400C ........................................................49 6.4 Dynamic Modulus E* of GAC1 at 250C .......... ...............................................50 6.5 Dynamic Modulus E* of GAC1 at 10C ........ ............................ 50 6.6 Dynamic Modulus E* of GAC1 at 400C .......................................... ...............50 6.7 Phase angle of GAF1 m ixture at 250C ..................... ............................... .. ....... 51 6.8 Phase angle of GAF1 mixture at 10 C ............................ .. .... ..................... 51 6.9 Phase angle of GAF1 m mixture at 400C ..................... ............................... .. ....... 52 6.10 Phase angle of GAC1 mixture at 250C ....................................... ............... 52 6.11 Phase angle of GAC1 mixture at 100C ......................................................... 52 6.12 Phase angle of GAC1 mixture at 400C ....................................... ................53 6.13 Average Complex Modulus result at 10 Hz 250C.................... .......................... 53 6.14 Average Complex Modulus result at 10Hz at 10C ............... .... ............... 54 6.15 Average Complex Modulus result at 10Hz at 400C ............................. ...............54 x 6.16 A average of phase angle at 250C ............................................................................ 55 6.17 A average of phase angle at 10 C ........................................................................... ... 56 6.18 A average of phase angle at 400C ............................................................................ 56 6.19 Average of phase angle at 4Hz at 250C ................ .. ......... .................56 6.20 Average of phase angle at 4Hz at 100C ........... ... .........................57 6.21 Average of phase angle at 4Hz at 400C .................. ........................................57 6 .22 Sigm oidal F unction ......................................................................... ....................59 6.23 Log complex modulus master curve for coarse mix ...........................................60 6.24 Log complex modulus master curve for fine mix...............................................60 6.24 Actual values versus Predicted value of E* at 250C for 16Hz test...........................62 6.25 Actual values versus Predicted value of E* at 100C for 16Hz test...........................63 6.26 Actual values versus Predicted value of E* at 400C for 16Hz test...........................63 7.1 Torsional shear stress versus shear strain. ...................................... ............... 65 7.2 Phase angle versus shear strain level. .............................................. ............... 65 7.3 Dynamic Torsional Shear Modulus IG*I of GAF1 at 250C ....................................66 7.4 Dynamic Torsional Shear Modulus IG*I of GAF1 at 100C ................. ..............66 7.5 Dynamic Torsional Shear Modulus IG*I of GAF at 400C ....................................67 7.6 Dynamic Torsional Shear Modulus IG* of Cl at 250C...........................................67 7.7 Dynamic Torsional Shear Modulus IG*I of Cl at 100C.......................... ...........67 7.8 Dynamic Torsional Shear Modulus IG* of Cl at 400C...........................................68 7.9 Phase angle of GAF1 mixture at 250............ ..................................... .................69 7.10 Phase angle of GAF1 mixture at 100.................................... .. ..... ...............69 7.11 Phase angle of GAF1 mixture at 400.................. ................ ...............70 7.12 Phase angle of GAC1 mixture at 250 ......... ................... ...............70 7.13 Phase angle of GAC1 mixture at 100 ......... ............................... 70 7.14 Phase angle of GAC1 mixture at 400 ........... ........ .................................. 71 7.15 Average of torsional shear modulus at 10 Hz at 250C ................. ...................71 7.16 Average of torsional shear modulus at 10 Hz at 100C.............. ...... .............. 72 7.17 Average of torsional shear modulus at 10 Hz at 400C.................... ...............72 7.18 Poisson ratio of coarse m ixture C2 ................................................ ............... 73 7.19 Poisson ratio of fine mixture F2............. .......................................... .................73 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 DYNAMIC TORSIONAL SHEAR TEST ON HOT MIX ASPHALT By Linh V. Pham August 2003 Chair: Bjorn Birgisson Major Department: Civil and Coastal Engineering The development of torsional shear test provides a new approach to studying shear deformation of hot mix asphalt. Study on simple shear test (SST) suggested that a laboratory which measures primarily shear deformation appears to be the most effective way to define the propensity of a mix for rutting. An understanding of its mechanics and procedures is fundamental for understanding how the test can be used. With complex modulus E* now formally integrated into the 2002 AASHTO Pavement Design Guide, the complex shear modulus obtained from torsional shear test measurements has the potential for being a simple alternative to the more involved triaxial type of test needed to obtain the confined axial complex modulus. The purpose of this study was to establish the testing and interpretation methodology needed to obtain the torsional complex shear modulus. A number of issues such as the length of testing time, loading level, and temperature control related to the test were studied. Because a good understanding of the axial complex modulus test is needed in the first place, further examination on testing set up, testing procedure and data analysis of previous studies on axial complex modulus was also carried out. CHAPTER 1 INTRODUCTION 1.1 Background The complex modulus (/E*/) has been proposed as a Superpave simple performance test (Wictzak et al., 2002). The complex modulus is also the proposed stiffness measure of asphalt concrete in the new Superpave design (2001). The dynamic complex modulus test, as currently being advocated, is performed without any confining stress. The lack of confinement means the complex modulus is unable to simulate field conditions where a pavement material is surrounded by adjacent materials providing confinement during loading. This lack of confinement makes the mobilization of the shear characteristics under confinement of the mixture impossible to measure and describe. The torsional shear test, which is a direct test to measure the shear characteristics of a mixture may therefore be more appropriate. The torsional shear modulus may be a useful parameter in characterizing the shear behavior of HMA mixtures. A study of simple shear test (SST) conducted by Harvey et al., (2001) suggests that a laboratory test which measures primarily shear deformation would be the most effective way to define the propensity of rutting for a mixture. In the linear viscoelastic range (75 to 200 strainsns, the dynamic modulus of asphalt mixtures can be investigated by either an axial or torsional complex modulus test. These two tests can be performed on the same sample, so that sample variability is reduced. The axial complex modulus test can provide E* and phase angle. The torsional complex modulus test can provide the dynamic shear modulus G* and the phase angle 6 of a mixture. The complex shear modulus G* can then be used in combination with E* to obtain the complex Poisson's ratio, v*. Harvey et al.(2001) concluded that G* can be related to E* using Equation 1.1: E* G* = (1.1) 2(1 +v) in which the Poisson's ratio can be taken as a constant. However, previous work by Monismith et al. (2000) has shown that the Poisson's ratio is actually dependent upon frequency. 1.2 Problem Statement With complex modulus E* now formally integrated into 2002 AASHTO Pavement Design Guide, there is a growing need for simple measurement of the complex modulus of a mixture. The complex shear modulus obtained from torsional shear test has the potential to be a simple alternative to the more involved confined axial complex modulus test. 1.3 Objectives The objectives of this research are as follows: * The testing and interpretation methodology needed to obtain the complex shear modulus from a torsional shear test. * A comparison of the torsional shear test to the hollow cylinder torsional shear test to obtain an estimate of the error associated with the testing of solid cylinders. * A comparison of the torsional shear complex modulus to the axial complex modulus from a triaxial test to obtain the complex Poisson's ratio. * A comparison to predicted complex modulus results using the predictive equation by Witzhak et al., (2002). * A focus on the systematic identification of the issues related to the measurement and interpretation of the complex modulus. S The completion of a testing set up, testing procedure and an analysis of previous studies on axial complex modulus. 1.4 Scope A brief review of theory of axial complex modulus and torsional complex modulus is presented in Chapter 2. Chapter 3 will describe the material and the mixtures used in the study. It also presents the testing program. Chapter 4 will outline the previous study, the improvement on controlling issue and data acquisition system. Axial complex modulus and torsional shear modulus testing set up and procedures will also be presented. Chapter 5 will outline the data analysis method, testing signal analysis and the problems related to data analysis. Chapter 6 will present the test result and analysis for axial complex modulus test. Chapter 7 will present the test result and analysis for torsional shear test. Conclusions and Recommendations will be presented in Chapter 8. CHAPTER 2 LITERATURE REVIEW 2.1 Axial Complex Modulus A mechanistic empirical design approach is in the new AASHTO 2002 pavement design procedure. This means that the mechanistic design model is coupled with the empirical performance characteristics of hot mix asphalt for pavement design. The mechanistic behavior of asphalt mixtures is characterized by temperature dependent stiffness, strength, and viscosity. The prediction of pavement life based on mechanistic empirical performance criteria requires the ability to address temperature effects and to track changes and damage in the material over the projected life span of a pavement. The complexity of Superpave models and the AASHTO 2002 performance criteria guidelines can be greatly reduced by the introduction of parameters that can be used to characterize the temperature dependency of through its projected life span. The axial complex modulus is potentially one such parameter. Research by numerous groups has shown that the complex modulus can be used to characterize the temperature dependency of a mixture's stiffness and viscosity over time. Papazian (1962) first proposed the dynamic modulus test on hot mix asphalt. He applied a sinusoidal load to a cylindrical sample to measure the ratio of stress and strain amplitudes. Thus, the axial complex modulus test measures the amplitude ratio and the time delay in the responding signal, as shown in Figure 2.1. 0 so Cos Time Figure 2.1 Stress and strain signal of axial complex modulus test The dynamic modulus is defined as E = (2.1) where oo is the stress amplitude, So is the strain amplitude. The complex modulus is composed of a storage modulus (E') that represents the elastic component and loss modulus (E") that represents the viscous component. The storage and the loss modulus can be obtained by measuring the lag in the response between the applied stress and the measured strain. This lag or phase angle (6) is described previously in Figure 2.1. The relationship between E*, E' and E" are described in Figure 2.2 S= tan' (2.2) E"= E*.sin(3) (2.3) E'= E*.cos(3) (2.4) E" = E*sin(6) E'=E*cos(6) Figure 2.2 Relation among E*, E' and E" The phase angle can be determined in the laboratory by measuring the time difference between the peak stress and the peak strain. This time can be converted to 6 using the following relationship: S= t, g f. (360) (2.5) where f is the frequency of dynamic load (in Hz), tlag is the time difference between the signals (in seconds). In the calculation of phase angle, the stress signal has the form A sin(o t + 8,), the strain signal has the form B sin(o t + 85 ), with the phase angle equaling 5, 82 .A 6 of zero indicates a purely elastic response and a 6 of 900 indicates a purely viscous response. The procedure for the axial dynamic modulus test is based on ASTM D 3947. It suggests the use of a standard triaxial cell to apply stress or strain amplitude to a material at 16Hz, 4Hz and 1Hz. It also recommends that the test be carried out at temperatures of 50C, 250C, and 400C. The main reason for using a sinusoidal stress loading is simplicity. One problem with triaxial testing is that other stresses can be induced on a sample, such as end effects due to loading. However, end effects are usually minimized by maintaining the ratio between the diameter and the height of specimen and by reducing the friction around the ends of the specimen. According to Witczak et al. (2000), a ratio of 1.5 is adequate for complex modulus testing. A minimum diameter of 100 mm is also recommended as a part of the complex modulus testing procedure. These minimums were recommended for mixtures with nominal aggregate size of 12.5 mm, 19 mm, 25 mm and 37.5 mm (Witczak et al., 2000). To minimize the end effects, lubrication between the end platens and the sample is recommended to reduce friction and prevent localized stress conditions (Harvey et al., 2001). A rubber membrane is often used between the end platen and the sample. In cases where a more compliant membrane is used to reduce friction, it is important to measure the deformation of the sample by means of an onspecimen gauge system. This prevents measuring any deflection of the membrane or frame compliance (Perraton et al., 2001). 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 result in a strain response that is close to linear is critical to achieve a test that is reproducible and allow for proper analysis. 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 than 2500. Daniel and Kim (1998) showed successful triaxial compression testing results with stress levels under 96.5 kPa for 150C testing. Witczak et al. (2000) suggested the strain amplitudes of 75 to 200 microstrain in order to maintain linearity during triaxial compression testing. This range of strain amplitude, 75 to 200 microstrain, is used in the study. 2.2 Torsional Complex Modulus The principle of torsional complex modulus test is to apply a cyclic torsional force to the top of specimen, and measure the displacement on the outside diameter (Figure 2.3). Knowing the torsional stress and strain, the shear modulus is then calculated based on the theory of elasticity. The torsional force is generated by a piston that can move laterally. The specimen is glued to the platens at the top and bottom ends. The bottom is rigidly fixed and the top is connected to a torsional load actuator. The frequencies used in the test are the same as those used in the axial complex modulus test. STcrcq atpeak Rctatimn (117 HVR Y.P Lpiu 1 aBemingSrah Rigidly Tixs1 utE~tiin Figure 2.3 Torsional shear test for HMA Column The dynamic shear modulus is calculated from the following relationship: G* = Y (2.6) assuming that pure torque, T, is applied to the top of a HMA column, the shearing stress varies linearly across the radius of the specimen. The average torsional shear stress, on a cross section of a specimen Tavg is defined as Tavg = S/A (2.7) where A is the net area of the cross section of the specimen, i.e A = r(ro2ri2), ro and ri are the outside and inside radius of a hollow specimen, respectively. (For a solid specimen, ri = 0), and S is the total magnitude of shearing stress. S can be calculated as S = (2,r)dr (2.8) where Tr is the shear stress at the distance r from the axis of the specimen, i.eCr = Cmr/ro, where cm is the maximum shearing stress at r = 0. On the other hand, the torque, T, can be calculated from ro T= J[(2r)rdr = 'J (2.9) r r, where J is the area polar of inertia, J = 7r(ro4 ri4)/2. From Equation 2.9, ,cm can be expressed as Cm = Tro/J (2.10) From Equation (2.7) (2.8) and (2.10), one can write the equation for Cavg as 3 3 2 ro r, T ag = r, (2.11a) 3 ro r2 J T rvg = req (2. lb) where req is defined as the equivalent radius. It can be seen in Equation (2.9a) that req = 2/3ro for a solid specimen. req = 2/3 (ro3 ri3)/(r2 ri2) for hollow specimen. In practice, req is defined as the average of the inside and outside radii. Shear strain is calculated in the Equation 2.12: r 6 =eq (2.12) where 1 is the length of specimen, and 0 is the angle of twist. The angle of twist, 0, can be measured either using an LVDT or a proximitor, In order to maintain the linear relationship between shear stress and shear strain, shear strain should be below a certain range. From the study on axial complex modulus testing, shear strains smaller than 200 microstrain were found reasonable. 2.3 Solid Specimen versus Hollow Specimen 2.3.1 Distribution of Shear The level of shear stress nonuniformity across a specimen is typically quantified with the following nonuniformity coefficients (1): R= max min avg =3 xAv r A g dr ro r avg r, A plot of these two coefficients is given below. 11 16 045 14 04 0 35 12 S03 0 25 02 06 06 015 04 01 02 005 0 0 0 01 02 03 04 05 06 07 rro Figure 2.4. Description of the nonuniformity of shear stresses across a specimen for different ratios of inner to outer radii. 2.3.2 Comparison of Solid and Hollow Specimens The use of hollow specimens over solid specimens or torsional complex modulus testing provides no advantage. This is because testing occurs solely in the linear range across the specimen, regardless if the specimen is hollow or solid. The equations presented above ensure this is true as long as testing is at low strain levels across the specimen. If testing were to result in large strains (nonlinear range), large creep strains, or failure were to occur, the equations would no longer be valid, and solid and hollow specimen testing could not be equated. The fact that there is more stress uniformity in a hollow specimen only means that the same material tested as a hollow specimen needs less torque to achieve the same average strain and shear stress across it. The following 12 figure depicts the decrease in torque needed to maintain the same strain level between a hollow and solid specimen. 30 25 20 15 5 0 I o . 0 01 02 03 04 05 ri/ro Figure 2.5. Difference in torque between hollow and solid specimens to achieve the same average strain. CHAPTER 3 MATERIALS PREPARATION AND TESTING PROGRAM 3.1 Granite Mixtures Six granite mixtures were used to prepare testing specimens. All of these mixtures were developed according to Superpave mix design method.. Mixture design methodology is very well documented over the years. A detailed description of Superpave mix design method can be found in FHWA report number FHWASA95003, 1995 Superpave mix design method uses volumetric properties of the mix to decide on the optimum asphalt content. Mixtures are compacted to provide a laboratory density equal to the estimated field density after various levels of traffic. In this project all the mixtures were designed corresponding to traffic level 5 (<30 million ESALs). The number of gyrations can be varied to simulate anticipated traffic. The percent air voids at Ni (Ninitial), Nd (Ndesign), and Nm (Nmaximum) are measured to evaluate the mixture quality. The mixture should have at least 11 percent air voids at N i, 4 percent air voids at N d, and at least 2 percent air voids at N m. Asphalt content for all of the mixtures were determined according to Superpave mix design criteria, such that each mix had 4% air voids at NDesign = 109 revolutions. AC30 asphalt was used for all of granite mixture in this study. Job Mix Formulas for the mixtures used in this project were developed based on Bensa's (Nukunya 2001) oolitic limestone mixtures by substituting the volume occupied by limestone in the HMA with Georgia Granite stone. For these mixtures No. 7 stone was used as coarse material, No. 89 stone as intermediate material, W10 screens as screen material and Granite filler as filler material. One coarsegraded (GAC1) and one finegraded (GAF1) were used as the basis mixtures. From those, two more coarse gradation and two more fine gradations were then produced by changing the coarse or fine portions of the basic gradations to produce more gradation of substandard void structure and permeability. The purpose of this was to test the effect of void structure and gradation on the rutting performance of mixtures. In all, six granite mixtures were used: GAC1, GAC2, GAC3 for the coarse gradations and GAF1, GAF2, GAF3 for fine gradations. In fact, GAF3 mixture was derived from the fine mixture (GAF 1) but was adjusted to fall below the restricted zone to achieve a higher VMA and permeability, thus it can be considered a coarse mix as well. The detail gradations are shown in Table 3.1 and Figure 3.1 and 3.2 For more information on mixture properties and aggregate gradation, see Appendix B Table 3.1 Gradation of granite mixtures. Percent Passing (%) Sieve size (mm) GAC1 GAC2 GAC3 GAF1 GAF2 GAF3 19 100 100 100 100 100 100 12.5 97.39 90.9 97.3 94.7 90.5 94.6 9.5 88.99 72.9 89.5 84.0 77.4 85.1 4.75 55.46 45.9 55.4 66.4 60.3 65.1 2.36 29.64 28.1 33.9 49.2 43.2 34.8 1.18 19.24 18.9 23.0 32.7 34.0 26.0 0.6 13.33 13.2 16.0 21.0 23.0 18.1 0.3 9.30 9.2 11.2 12.9 15.3 12.5 0.15 5.36 5.6 6.8 5.9 8.7 7.7 0.075 3.52 3.9 4.7 3.3 5.4 5.8 100 90 80 S70 S60 S50 a. 4 40 . 30 20 10 0 Gradation Chart C1, C2 & C3 0.075 0.3 0.6 1.18 2.36 4.75 9.5 12.5 19 0.15 Sieve size (mm)A0.45 Figure 3.1 Gradation Plot for Coarse Mixture Gradation Chari F1, F2 & F3 100 90 80 70 60 50 40 S30 20 10  0 0.075 0.3 0.6 1.18 2.36 4.75 0.15 Qinu fin in mm\In C c 45 . . I. Figure 3.2. Gradation Plot for Fine Mixture  C1  C2 . C3  F1 F2  F3 t 3.2 Sample Preparations Cylindrical samples with a diameter of 100 mm and a height of 150 mm were prepared with the optimum asphalt content. First, the aggregates and asphalt binder were heated to 1500C ( 3000E) for 3 hours prior to mixing. Once the mixing is completed, the mixture is reheated to 1350C (2750 F) in 2 hours before compaction. The sample were then compacted to 7% + 0.5% air voids on Superpave Gyratory compactor. There was no cooling period and long term over aging period in this process. After the samples were compacted and cooled, the bulk density of the sample were determined according to AASHTO 166 to see if the required air voids were met. Finally, the ends of the sample were cut using a wet saw to make parallel ends that are perpendicular to sample sides. 3.3 Testing Program Three samples, which satisfy the air voids condition in each of six mixtures, are prepared. The axial complex modulus test is carried out first in room temperature (250 C), then in 100 C and 400 C. In each temperature, four testing frequencies of 16Hz, 10Hz, 4Hz and 1Hz are applied. Then samples are moved to torsional complex modulus test. The same testing sequence, temperature and frequency will be carried out. Finally, three more samples will be prepared for hollow cylinder testing. Unfortunately because sample has to be broken up after torsional complex modulus test, more sample need to be prepared if something goes wrong during the test. The detail sample information used in the tests is presented in Appendix B CHAPTER 4 IMPROVEMENT OF COMPLEX MODULUS TESTING PROGRAM The complex modulus test was conducted on MTS 810 load frame. This is a hydraulic loading system that has the maximum capacity of 100 kN (22 Kip) of applying load. A load cell connected on the top actuator will measure and control the amount of force applied to the sample. The system will stop automatically when the applied stress exceeds the maximum or minimum force that assigned to the load cell. The system can be controlled by force mode and displacement mode. The torsional shear test was conducted on GCTS system. This hydraulic system has the capacity of applying both vertical and torsional load. Axial force can be applied in 5 kips range. The torsional movement is created due to a hydraulic actuator positioned horizontally. The horizontal actuator is also controlled by a load cell and a LVDT. The maximum horizontal movement is 2 inches and the maximum torsional force that can be applied is 500 inlbf. 4.1 New MTS Controlling System The MTS and GCTS are controlled by Testar IIm controller program provided by MTS. This is an upgrade from Testar IIs controller system. The old controller system is only capable of control one station. It means that only MTS or GCTS system can be used. More over, it doesn't have the data acquisition build in on board, therefore the output signal (i.e. displacement) has to be recorded using a separated software. This may cause the problem of phase lag between the input applied load signal and output displacement signal. This is important because the phase lag is important in the dynamic test. More over, the output signal is subjected to a lot of noise. Also it needs to write a program to monitor the output signal and save the digital signal to a spreadsheet file. All of those problems have happened before and they brought a lot of difficulties in order to receive a good dynamic test result. The new controller system has much higher capability and performance quality than the old one. It is capable of control four stations, which is very crucial in order to operate the torsional shear test on GCTS load frame. However, the greater advantage of the system is that the date acquisition capacity is improved greatly. The new Testar IIm controller program has the capacity of recording up to 12 output signals. Therefore, a very complicated test, which may include thermocouple, pressure transducer, LVDT can be carried out. The output signal and input signal can be viewed during the test with the meter option in the controller program. It helps to watch for a limit of the measurement device. The new controller system also provides the chart option, which shows the ongoing input signal and output signal of test result. Normally, LVDT signals are looked during the complex modulus test. Torsional force command and actual applied torsional force are looked during torsional shear test. Therefore, possible error of testing set up or of measurement device can be noticed, thus the reliability of the test can be assured. Testing sequences are programmed due to multi purpose test ware model 793.10 tool. This program is capable of creating complex test procedures that include command, data acquisition, event detection and external control instructions. It permits to generate a test control program based on profile created with a text editor application, a spreadsheet application, or the Model 793.11 profile editor application. Real time trend or fatigue data can be acquired and monitored. 4.2 Temperature Control One significant improvement in the testing program was the introduction of temperature controlling unit. In the previous research, the tests were carried out in the room temperature only. It needs the heating unit and cooling unit separately because of cost effective reason. It will be very expensive if one unit can do both heating and chilling water. The temperature cooling and heating unit work based on the principle of circulating water through the triaxial cell. For cooling unit, it needs to create a water pressure of at least 10 psi in order to circulate the water, then water has to be filled up to the top of the cell before circulating. For heating unit, it needs to fill up water above the top of the sample only. It takes 1 hour and 30 minutes for sample from room temperature to 100C or 400C. The working principle of the two unit are plotted in the figure below: Water in EILrI T Heating unit SWater out Cooling unit Figure 4.1 Temperature control by circulating water. 4.3 Some Test Issues 4.3.1 Calibration Before carrying out the testing and program, the machine and LVDT need to be checked. Because after testing in dynamic mode for a while, all the bold, nuts and the connectors may loose, cause the system unstable and cause shacking and noise signal during the test. Therefore, it's important to tight up the machine before testing. For LVDT, after using for some time in variable environment and temperature, the excitation voltage will reduce gradually cause the reducing in the range of LVDT. And because the measurement needs to be very accuracy, it needs to set up the schedule to calibrate the LVDT and readjust the excitation voltage. The LVDT can be calibrated using this accurate calibration device Figure 4.2 LVDT calibration device. 4.3.2 Control Issue The control program controls the system by sending command signal to the hydraulic servo valve. Then the program will receive the feed back signal pointing how the command is realized. In theory, the feed back signal is supposed to coincident with control command. For low frequency, i.e 4Hz, 1Hz or lower, this can be achieved easily. But for higher frequencies, i.e. 10Hz, 16Hz, feed back signal may be exceed or below the command signal, which means the actual applied load is higher or below or even have the noisy shape compare to the designed load. It can easily be seen in the signal window provided in the program. It is noted that the stiffness of the system is affected by the stiffness of the specimen. Furthermore, the stiffness of the specimen is temperature dependent, high or low according to high and low testing temperature. Thus, the stiffness of the system is changed during the test. Because of that, when running the test in a high frequency, one may encounter the shacking of the system. That may cause the noisy shape in the feed back load signal and LVDT deformation signal. This can be corrected by modifying the gains in the control program. It is worthwhile to know that there is four gain options provided to compensate a signal to the command. They are P, I, D and F gains: * Proportional gain (P Gain) increases system response. * Integral gain (I Gain) increases system accuracy during static or lowfrequency operation and maintains the mean level at high frequency operation. * Derivative gain (D Gain) improves the dynamic stability when high proportional gain is applied. * Feed forward gain (F gain) increases system accuracy during highfrequency operation. P gain is used most of the time. It introduces a control factor that is proportional to the error signal. Proportional gain increases the system response by boosting the effect of error signal on the servo valve. As proportional gain increases, the error decreases and the feedback signal tracks the command signal more closely. Higher gain setting increase the speed of the system response, but too much proportional gain can cause the system to become unstable. Too little proportional gain can cause the system to become sluggish. Gain setting for different control modes may vary greatly. For example, the gain for force may be as low as 1 while the gain for strain may be as high as 10000. The rule of thumb is adjust gain as high as it will go without going unstable. Gain Too Low OQplimum Gain Gain Too High Figure 4.3 Effect of using P gain. For MTS system, because of its heavy weight and high capacity, the stiffness of the specimen doesn't have much effect on the stability of the system. P gain of 16 is used. However, for GCTS system, using appropriate P gains in each frequency and temperature is more important. Firstly, its lighter weight makes it easier to vibrate during the test. Secondly, because the specimen is glued to bottom and top end plate, which are fixed to the triaxial chamber and torsional head consecutively, this set up makes the stability of the system more dependent on the stiffness of the specimen. Throughout experiment, for the particular GCTS system in the Material Lab, the value of P gain is suggested as below. The variation depends on the stiffness of the mix. Higher gain is for stiffer mix. Table 41. Suggested value for P gain for GCTS system Frequency 100 C 250C 400 C 1Hz 0.6 0.5 0.3 0.5 4Hz 0.6 0.5 0.3 0.5 10Hz 0.45 0. 55 0.4 0.20.3 16 Hz 0.65 0.75 0.5 0.2 0.5 4.3.3 Seating Load Using adequate seating load will help the stabilization of the specimen and the system during testing. High seating load proves to give better deformation signal than low seating load. However, too high seating load may cause permanent deformation of specimen. Seating load of 200N (25 kPa), 600N(75 kPa) and 800N (100 kPa) are used for 400 C, 250C and 100 C respectively. 4.3.4 End plate and Glue It needs textures end plate for torsional shear test. Texture surface helps to increase the contact surface and of the glue to the end plates. Plus, it creates the interlock in the glue, therefore, the glue will not deform in torsional mode. Otherwise, the glue may deform and increase the phase angle during the test. Figure 4.4 Texture end plate for torsional shear test. The glue used in the test was epoxy. It needs about 8 hours for epoxy to develop its full strength. It is observed that changing in the type of glue doesn't cause the change in the shear modulus. In order to remove the specimen and epoxy after the test, the specimen need to be heated up to 3200 F in 1 hour. 4.4 Complex Modulus Testing Setup The sample was set up inside the triaxial cell. Because the sample will work in water environment during heating and chilling process, a thin membrane is used to cover the sample. The thickness of membrane is 0.012". Using the membrane too thick will influence the measurement of phase angle later. Axial rod Top platenAxial r   O ring Axial LVDT\ O  Membrane Rigid clamp STriaxial chamber Sample Base platen Figure 4.5 Complex modulus testing setup in the triaxial cell The axial LVDT is mounted in the middle of the sample using a rigid clamp. In order to get the constant space (50 mm) between two clamp, two spacer are used to maintain the shape of the clamp. When the clamp is tightened to the sample, these spacers will be taken out. Each half of the clamp is attached at 4 points along 900 intervals. In order to reduce eccentricity, a ball joint on the tip of the actuator is used. A high viscosity vacuum grease and rubber membrane was used as a lubricant between the end platens and the sample. This will allow the sample to expand radially without unnecessary friction. Two high resolutions, hermetically sealed LVDT were used to measure vertical deformation. The range of the LVDT is 4.0 mm. These sensors have a maximum resolution of 0.076tlm (16bit). For a better result, two more LVDT can be added. The procedure of the test is described in a chronicle order as below: * Apply the seating load. For a particular temperature, seating load remains the same, but it will increase when the temperature decrease. * Start the test. Start recording the signal. The rate of recording the signal is determined to be 50 points per cycle, therefore it will vary with testing frequency, For example, for 1Hz test, the recording rate is one point every 0.02 second, and for 16 Hz test, the recording rate is one point for every 0.00125 second. Start applying the cyclic load. The response of the sample will be steady after few cycle, therefore it isn't necessary for the test to be long. It is determined that the test will take place 50 cycle for each frequency. The test was carried out from higher frequency to lower frequency. The load level was designed to reach the strain amplitudes between 75 and 200 microstrain to maintain linearity. These strain levels were recognized within the linear range based on prior testing (Wictzak et al, 2000; Pellinen et al, 2002). However, it was observed that for complex modulus test, the linear range goes beyond this range, up to more than 300 microstrain. It is suggested that for the first trial, the load level for 100C, 250 C and 400C would be 4000 N, 2000N and 1200N consecutively. The test was carried out from higher frequency to lower frequency. The testing frequencies (16 Hz, 4Hz and 1 Hz) were recommended in ASTM D 3497. The testing temperature of 100C and 400C were recommended in ASH TO 2002. Room temperature is used in order to provide more data. * When the cyclic load is terminated, stop recording the signal and remove the load. Normally, one trial test was performed first in order to verify the set up and ensure excessive eccentricity does not occur (by looking at the signal chart) Figure 4.6 Picture of sample set up in triaxial cell for complex modulus test. I 4.4 Torsional Shear Modulus Testing Setup After complex modulus testing, sample was removed and used for torsional shear test. The sample was glued to a fixed base platen and a top stainless steel platen in the triaxial cell. There was a small plate connecting the top platen and the vertical rod. The displacement on top of the sample was measured by the movement of a small arm connected at the top platen and two LVDT attached to the support strut of the cell. The outer of sample was also protected from water by a membrane. The configuration of the set up was described in the drawing below: 'Axial rod Top platen Rigid arm LVDT collar O rinmg LVDT Triaxial chamber Figure 4.7 Torsional shear testing set up Basically, this test was performed as same as complex modulus test in term of frequency and temperature control. The torsional force was introduced at 16 Hz, 10 Hz, 4Hz and 1 Hz. The test was carried out at room temperature (250C), then 100C and 400C. The procedure of the test is described in chronicle order as below: * Apply the seating load. The seating load was the same as complex modulus test. They were 200 N at 400C, 600N at 250C and 800N at 100C. * Apply the seating torque. The reason for applying seating torque is that it prevents the torque force from going below zero in high frequency because of control problem mentioned above. * Start recording the signal. The rate of recording is 50 points per cycle. Two LVDT are used, thus the result would be the average of those two. * Start applying the cyclic torsional force. The magnitude of the force was selected in order to get the strain in range of 75 to 200 microstrain. The torsional force may vary depend on the stiffness of the mixture. The torsional force remained the same for a particular temperature and increases when the temperature decreases. Also, the torsional force may vary depend on the stiffness of the mixture. It is suggested that the first trial would be 12000Nmm, 20000Nmm and 30000Nmm for 400C, 250C and 100C successively. Because the GCTS system is lighter than MTS system, therefore it is less stable, and then it needs longer time for the signal to stabilize. It 's suggested that the duration of 16 Hz test is 150 cycles, 100 cycles for 10 Hz and 50 cycles for 4 and 1 Hz test. Also it needs to change the P gain according to control section above. * After the applying cyclic torsional force is terminated, stop recording the signal, remove the seating load, and remove the seating torque to before test level. Normally, one trial test is performed at first to verify the load level and the feedback signal before the whole test sequence is carried out. The picture of a sample set up in the triaxial chamber is presented in the next page. Figure 4.8 Picture of torsional shear testing set up. CHAPTER 5 SIGNAL AND DATA ANALYSIS 5.1 Test Signal The response of a sample under cyclic load is composed of two parts: creep response and elastic response. Complex modulus analysis requires the removal of the permanent creep component from the cyclic strain response. Figure 5.1 presents a typical deformation signal recorded after the test. The dynamic deformationtime response is shown in Figure 5.2, once the creep component has been eliminated after regression analysis. Creep component So 0 10 20 30 Time (s) Figure 5.1 Typical test signal. 40 50 60 & () 'I U 20 30 40 50 ED Time (s) Figure 5.2. Dynamic sinusoid component of the signal. The first part of the signal is still curved because the regression equation is based on the last 10 cycles, but is applied for the whole signal. Although recording very small deformation, one hundredth of a millimeter, it can be observed that the deformation signal is smooth and clean. Also, the response achieves a stable state in a sort period of time. This is important because the duration of the test can be reduced significantly. Figure 5.3 will show the signal in Figure 5.2 on a larger scale. Time (s) Figure 5.3 Signal in higher scale Some factors that may affect the quality of signal are shortly discussed below. It was observed that sometimes the strain signal is affected by noise of the testing system and environment. Figure 5.4 displays a strain signal with noise. Noise is a high frequency electrical vibration, caused by several factors such as the vibration of the system during the test, the quality of measurement device, or the instability of data acquisition card. Time (s) Figure 5.4 Noise signal. Noise will cause error in the calculation of modulus and phase angle. Low levels of noise will cause higher amplitude in strain signal when using curvefitting method for data interpretation. High levels of noise may damage the signal totally. One solution to reduce the level of noise is to increase the excitation voltage of the LVDT. The curve fitting technique, the regression method, works pretty well with noise data. However, in order to eliminate noise signal completely, it is better to have the noise filter option in data acquisition card. A Fast Fourier Transform Analysis (FFT) can be performed with the resulting file. There are several available programs, which are strong in signal processing, including Mat lab, Lab View that provides the FFT filter option. A program based on the FFT filtering method was created using Lab View. The FFT requires 2m data points and it was an error at the first part and last past of data. Thus, it needs to start the test after 6,7 seconds after recording the data and wait 6,7 second after finishing the test to stop recording data. Figure 5.5 is a plot of a signal after filtering. Figure 5.6 is a plot of an example of filtering function in Lab View. When using the filtering option in such program, it should be noticed that phase angle would be changed. Therefore, a regression analysis should be performed first in order to get phase angle. Time Figure 5.5 Signal after filtering 1 I + ,tlat th Sine Wave figure 3.o lNoise tilter function in Lao view. Another problem that may happen is the misshaping of the sinusoid of stress signal or skewing of the stress signal. The signal can be wider at the bottom half than the top half or the trend of signal is stiffer in removing load part of the sinusoid than the loading part. These are testing issues and can be eliminated by properly applied seating load and tuning the system. 5.2 Data Analysis 5.2.1 Iterative Curve Fit Method Zhang et al. (1996) (University of Minnesota) proposed that the stress and strain functions were of the form seen in Equation 5.1. F(t) = A + Bt + Ccos(ot6) (5.1) The parameter C is half of the amplitude of the wave and 6 is a phase shift. The angular frequency (co ), in rad/s, is found based on the test frequency (f), in Hz, as presented in Equation 5.2 co = 2.7.f (5.2) The phase lag can be calculated in Equation 5.3 by determining the bestfit curves for both the stress and the strain. 6 = 6e 6 (5.3) In order to match the predicted equation to the data, a nonlinear least squared error regression technique is used. Since the phase lag is unknown and inside the trigonometric operator, a standard linear regression cannot be used to calculate all of the variables. So to find the optimal signal, the 6 was guessed at many points through out the possible range until the error was minimized. Zhang et al. (1996) employed a bracketed search technique where he would guess 6 at regular intervals. He would then find out which range the lowest error was in and search the system again in that reduced range. For every guess of 6 the set of matrices seen in Equation 2.12 were used to solve Equation 2.9. n t, cost 5) A .cos@F(tf) lt It, 2 lt.COS(Y xF(t,) cos@ )t,.cos@) cod(C) j cos(tS)xF(t,) After the least squared error values for A, B, and C were found, the least squared error was compared to the other guesses of 6. A minimum number of 4 guesses must be used per iteration to reduce the scope of the search. The search algorithm used is: Stepi: Set 6start=0, 6end=180, A6 =(6start 6end)/M (M is an integer, M>1) Step 2: Calculate 6j=s6tart + j*A6 (j=l, 2, 3, ..., M) Step 3: Solve for A, B, and C using Equation 2.12 (j=l, 2, 3, ..., M) Step 4: Calculate the squared error for all values ofj (j=l, 2, 3, ..., M) Step 5: Select the value d that provided that least squared error (6k) Step 6: Check Convergence: If A6 > Tolerance, then update the range of A and repeat (6start=k A6 , 6end=6k + A6, A6 = (,start 6end)/M If A6 < Tolerance, then stop By repeating this system several times, Zhang et al. (1996) showed that the 6 could be roughly predicted. There is a problem associated with this method. It is only designed to read the signal of a sinusoid on a straight line. Since this is an iterative method, it can be very time consuming. The level of acceptable error is also very important to balance with the time restraints. 5.2.2 Regression Method Using a regression method with trigonometric function, the stress and strain signal can be described with: F(t) = Ao + Ai.t +A2.t2 + ... + Am.tm1 + B. cos(wt) + C.sin(wt) (5.4) This equation has a polynomial degree of m 1. In order to find all the coefficients, a least square error regression approach can be used. The unknown coefficients satisfy following matrix equation: Ax= B where: A is an m+2 by m+2 symmetric matrix with the following configuration: a = t for i = 1 to m and j = 1 to m a, = _t Cos(a t) for i = 1 to m andj = m+1 al, = t Sin(ao t) for i = 1 to m andj = m+2 al t = _t Cos(a t) fori =m+l andj=l tom a V = t ) Sin(ca t) for i = m+2 andj = 1 to m a1,m, = am+2,m = 1 Sin(c.t) Cos(o t) am+,m+l Cos2 (o t) am+2, = Sin2(o). t) x is an m+2 matrix with: x = [A0 A, ...Am B C]T and B is an m+2 column matrix with: b, = t"" .F for i= I to m bm = ZCos(c t) F b, = ZSin(c.t) F The algorithm to solve this matrix equation has been written by Swan (2001). Normally, the degree of polynomial of 2 (m=3) is used in the analysis. The amplitude of the sinusoid can be calculated using Equation 5.5 and the phase angle then can be calculated using Equation 5.6: Amplitude = B2 +C2 (5.5) Phase Angle = tan' () (5.6) 5.2.3 FFT Method In case of complex signal containing noise, the signal can be transformed from time domain into frequency domain using concept of Fourier transform. Then the amplitude of the signal of testing frequency can be picked up. Normally, with digital data, which is recorded at a specified interval, Discrete Fourier Transform (DFT) is used. This is a computer algorithm that is deigned to change a complex signal into a serious of sinusoids at discrete frequency intervals. An example of the transformation of a typical 4 Hz axial strain signal can be seen in Figure 5.7 and Figure 5.8. For a perfectly clean sinusoid signal, there should be a spike at the given frequency and all other values should be zero. 0.0008 0.00075 0.0007 0.00065 0.000 0.00055 0.0005 0.00045 0.0004 0 1 2 3 Sime s) Figure 5.7 Test signal in time domain 4 5 6 U.n 3 0.01 0005, 0 2 4 6 8 10 12 14 18 18 20 Frequency (Hz) Figure 5.8 Test signal in frequency domain The DFT is performed using Equation 5.7 Sn 2.x.k.p 2.f.k.p y, = xk.(cos( )+i..sin( ) k=O n n (5.7) The value of yp is the complex output in frequency space where p is a counter integer representing frequency as seen in Equation 5.8 Frequency p.(Sampling rate) (5.8) Frequency = (5.8) /7 i 4 i I V V I V V I I T V f Y I T I , The amplitude of the sinusoid represented by p is given in Equation 5.9 where N is the number of samples recorded in the signal. 2yp Ampitude = (5.9) The phase angle of each sinusoid can be calculated by finding the angle that is represented by the complex components of yp. This method may have a leaking problem, which means if the testing frequency did not occur at one of the discrete points in frequency space, therefore the magnitude was reduced and split between the closest frequencies on either side of the true frequency. This provided results that seemed to vary depending on the number of points tested. An example of this effect can be seen in Figure 5.9 0.03  0025  0.02 0 1  .15  ,.,:,......,. __..._ [0B01 0 2 4 6 8 10 12 14 18 18 20 Frequency (Hz) Figure 5.9 Strain with missing peak data The way this was corrected was to find an integer value of p for the testing frequency using equation 5.8. Since the sampling rate was constant and so was the testing frequency, the only variable that was easy to manipulate was the number of samples examined. To manipulate this, the mean value of the signal was added before and after the sample until the signal was the correct length. The value of p for the testing frequency can then be calculated using Equation 5.10, where N' is the modified number of samples in the signal. f.N' PTestng fequncy fN (5.10) Sampling rate It lets to the conclusion that when using DFT analysis, if only a few cycles were used (i.e. under 20 cycles with 50 data points per cycle) then the magnitude of the signal may not accurately reflect the true value. Therefore higher data recording rate should be used. 5.2.4 Evaluation of Data Interpretation Method. In order to evaluate the methods calculating complex modulus, the idea of generating artificial signals are introduced. Then the modulus and phase angle are known before hand. For example, these signals below are generated. Three methods: Iterative Curve Fit, Regression, FFT are evaluated. Here is the artificial signal. Strain and stress pure signals of 20 Hz, added white noise and creep trend. Phase angle of 720, dynamic modulus of 21.22 MPa, scan rate of 500 points/sec. The summary of the analysis is presented in table 5.1 Table 5.1 Evaluation of data interpretation method Pure signal Signal with noise and Pure signal with noise creep Calculation Phase E* Phase E* Phase method Angle Angle Angle Iterative 72 21.22 73.6 23.03 72.91 22.15 Curve Fit Regression Regression 72 21.22 73.53 23.03 72.88 22.0.4 Analysis FFT 67.97 19 68.04 19.81 73.62 18.57 From above results and results from the test, some conclusion can be made: * For the pure signal, Iterative Curve Fit and Regression methods give an exact result. FFT gives the result a little bit lower than designed value. * For the signal with noise, due to the noise, Iterative Curve Fit method and Regression method give the result slightly higher than designed result. FFT method gives the result lower than designed values. * Most of the time, Iterative Curve Fit method gives the good result but still gives the unexpected result sometimes. Regression method is very stable, therefore is the best method available. 5.2.5 Computer Program In chapter 2, the equations to calculate complex modulus and torsional shear modulus have been mentioned. In this section, more detail about how the data analysis program is written and the modified version of torsional shear modulus from the original axial complex modulus is illustrated. Figure 5.10 describes the flow chart of data analysis program written by Swan (2001). The program was written by Visual Basic for Excel. This has an advantage of analyzing column data in a familiar Excel environment. The modified version for calculating torsional shear modulus based on the same flow chart, only a change in the calculation of torsional shear stress and shear strain has been introduced. For complex modulus program: Force column Axial stress column =Fore (5.11) Surface area Axial strain column LVDTdisplacement column (. Axial strain column = (5.12) Spacer length(50mm) For torsional shear modulus program: Torque x r, i.' alr stress column =Torque r (5.13) J LVDTdisplacement x r, V/.hear strain column =VDTdisplacement x r (5.14) lxL where: ro is the radius of sample, ro = 50mm J is the area polar of inertia, J = t*ro4/2 1 is the length from center of sample to measurement point, 1 = 107.7mm L is the height of sample, L = 150mm The input data file was recorded in a standard order that the program can understand. Any change in that order will need a change in the program. At first, the load and deformation data column are converted to stress and strain data column. The regression analysis will work with a pair column of time and stress or time and strain. The program automatically determines the duration of the test and the number of loop required. The number of loop equal to the total number of test cycles divided by number of test cycles used for calculating dynamic modulus. 10 cycles of complex modulus was chosen. Besides the dynamic modulus and phase angle, the analysis program was also designed to write down the bestfit signal equation and the least square errors. Figure 5.11 and 5.12 will show the data input page of Complex Modulus Program and Torsional Shear program. It is shown that the time, stress and strain data column, start time and stop time of the test as well as degree of polynomial of regression analysis are predetermined. Only input needed is test frequency. Convert Data to Stress and Strain Read Time. Stress & Strain Column Data for 10 Cycles Call Regression Analysis Number of loop = Total of test cycle/lO Call Write Regression Equation Call Write R2 Get Modulus & Phase Angle Output Page Figure 5.10 Flow chart of data analysis program. Complex Modulus Data Location Time Column I Axial Stress ] Axial Strain 1 K Axial Strain 2 L First Data Row 6  Time and Repition Start Time 1,825 Stop Time 201.69  Analysis Parameters Frequency Degree of Polynomial Start Calculations Written by: DJ. Swan and Michael Wagoner Figure 5.11 Complex Modulus Program Torsional Complex Modulus Data Location Time and Repition Time Column [I Start Time 0.2603 Torsional Stress Stop Time 49.7285 Strain 1 K Strain 2 L Analysis Parameters First Data Row 6 Frequency Degree of Polynomial Start Calculations Original Code: DJ Swan and Mike Wagner Modified by: Linh Pham Figure 5.12 Torsional Shear Modulus Program. Besides the version of complex modulus program for two axial LVDT, the version of torsional shear modulus for LVDT, there are versions of complex modulus program for four axial LVDT and torsional shear modulus for proximitor. Figure 5.13 will present the output file torsional shear modulus program of a 10Hz Complex Modulusm? I iComplex Modulus Complex Shear Modulus Test Results Saillle: Tesi Freilllelicy IIn Nllllther ol Cycles: I 1: Calcillalioi Dale: ri I, i Shear Stress Amllliijle 111I Shear Slrain Ainillhile 10lOp Dyllaiic Slear M lliilllis 'lli qMPa Phase AliJle Ili iDegjrees Elaslic Slear Modiilus IG'i IMPam Loss Shear ModIulhs qG"I iMPap ' I' I liii I11 Sliilial EiiIallols: . L,I, : = I : I ., I '" I I .' r' ii i l .. I .. I I I 1. I. i = I, I I_ E.T E, 1.1 1 " ll E l' I E ( I ) I ) i ? ( ) i i I P I Dynamic Shear Modulus Chart Tillie isp Figure 5.13 Output page of Torsional Shear Modulus Program. The output page of axial complex modulus program has a similar format. It contains all the information necessary such as shear stress, shear strain amplitude, phase Phase Angle Chart 50 30 S20 10 0 0 5 10 15 Time (s) ~ angle... It noticed that the signal equation is only for last 10 cycles. Also, for the stress signal equation, the creep component has the value approximate to zero. The calculation of modulus as an average of 10 test cycles gave a better result than an average of 5 test cycles. Figure 5.14 shows the dynamic modulus calculated as an average modulus of 10 cycles versus 5 cycles. It was shown that the results is less scattered if we calculate the modulus for average of 10 cycles than that of 5 cycles. It was noted that in previous study, the quality of signal was much less than that of present study. 4000 3500 m 3000 Avg of 5 o 2500 2 Avg of 10 F 2000 o 1500 1000 0 3 6 9 12 15 Time (s) Figure 5.14 Calculation of Modulus, average of 10 cycles versus 5 cycles Figure 5.15 presents linear regression analysis on alO Hz complex modulus test versus quadratic regression analysis. It was observed that there is almost no different between two analyses. As seen in figure 5.1, quadratic trend of creep component of test data developed only in first 10 or 20 cycles, therefore the different between quadratic and linear regression is expected in this zone. However, the regression analysis is calculated for every 10 cycles, there is almost no different between linear and quadratic in that range. After that, the creep component developed almost linearly (Figure 5.1) 3000 2600 2200 4 Linear S1800  Quadratic 1400 1000 0 2 4 6 8 Time(s) Figure 5.15 Linear regression versus quadratic regression analysis With new control system, it was observed that a test gets to its stable state very soon. For example, in figure 5.13 and figure 5.15, the dynamic modulus remains almost constant after second or third points. Therefore, the duration of the test doesn't need to be long. For axial complex modulus test, the duration of 50 cycles was found sufficient. For torsional shear modulus test, the duration of 150 cycles for 16 Hz test, 100 cycles for 10Hz test, 50 cycles for 4Hz and 1 Hz test were found sufficient. CHAPTER 6 AXIAL COMPLEX MODULUS TEST RESULTS 6.1 Result of Complex Modulus Test In Chapter Four, the procedures for complex modulus testing were been presented. In the following, axial complex modulus test results are presented from three coarsegraded granite mixture GAC1, GAC2, GAC3 and three fine granite mixture GAF 1, GAF2, GAF3. Three specimens for each mixture were tested. For temperature effects on the complex modulus three test temperatures of 400C, 250C and 100C were used. The testing frequencies included 16Hz, 10 Hz, 4 Hz and 1Hz. 6.1.1 Dynamic Modulus Results Figure 6.1 through 6.3 plot the result of dynamic modulus E* for the GAF1 mixture, which had a typical response for the finegraded mixtures. Figures 6.4 through 6.6 show the complex modulus results for the GAC1 mixture, which had a typical response for the coarsegraded mixtures. The results for the other mixtures (GAC2, GAC3, GAF2, and GAF3) are provided in Appendix B. The plots show the typical results of IE*I from the test. Although there is some degree of variability in the testing results, a consistent value of E* plus a consistent trend of E* versus frequency were obtained. The results clearly show E* increasing with increasing frequency. That was expected because it is known that asphalt concrete get stiffer with increased loading rate (e.g. Sousa, 1987). 5000 4000  F101 $3 3000  F102 2 000 0 F103 w, 1000 AAve 0 0 5 10 15 20 Frequency (Hz) Figure 6.1 Dynamic Modulus E* of GAF1 at 250C 10000 8000 6000 4000 2000 0 *F101 F102 F103 Ave 0 5 10 15 Frequency (Hz) Figure 6.2 Dynamic Modulus E* of GAF1 at 100C 2000 1600  F101 a 1200 F102 u 800 e F103 400 AAve 0 0 5 10 Frequency (Hz) 15 20 Figure 6.3 Dynamic Modulus E* of GAF1 at 400C 4 5000 4000 3000 2000 1000 0 C101  C102 0 C103 Ave 0 4 8 12 Frequency (Hz) Figure 6.4 Dynamic Modulus E* of GAC1 at 250C 10000 8000 6000 4000 2000 0 0 5 10 Frequency (Hz)  C101  C102 *C103  Ave 15 20 Figure 6.5 Dynamic Modulus E* of GAC1 at 100C 2000 1600 1200 800 400 0 4C101  C102 0C103 Ave 0 5 10 15 20 Frequency (Hz) Figure 6.6 Dynamic Modulus E* of GAC1 at 400C I I I 0 ~f~5~ 6.1.2 Phase Angle Results Figure 6.7 to 6.12 show the phase angle with frequency for the GAF1 and GAC1 mixtures. For 250C and 400C, the results clearly show that the phase angle increases with increasing frequency. For higher temperatures, this trend becomes even more pronounced. Phase angles increase from 300 to 400 at 250C and from 280 to 500 at 400C. For 100C tests, the phase angle decreased slightly at 4Hz test, but increases with frequency up to 16 Hz. 50 (, 4 40 0) S30 (, S20 (, 2 10 0 0_ F101 F102 F103  Avg 5 10 15 Frequency (Hz) Figure 6.7 Phase angle of GAF1 mixture at 250C F101 F102  F103 Avg 0 5 10 15 20 Frequency (Hz) Figure 6.8 Phase angle of GAF1 mixture at 100C 60 50 0) o  0 g 40 "  30 F 0 5 10 Frequency (Hz) F101  F102 F103 4 Avg 15 20 Figure 6.9 Phase angle of GAF1 mixture at 400C 50 40 0) 0) o 30 0) 20 10 0  C101 mC102  C103  Avg 0 5 10 15 20 Frequency (Hz) Figure 6.10 Phase angle of GAC1 mixture at 250C 50 ' 40 0) o 30 < 20 0) U) r_ a 10 0  C101 EC101  C102  C103  Avg 0 5 10 15 20 Frequency (Hz) Figure 6.11 Phase angle of GAC1 mixture at 100C ~se~ 53 75 ? 60  60 0 4 C101 () 15  Avg 0) 0 I I I 0 5 10 15 20 Frequency (Hz) Figure 6.12 Phase angle of GAC1 mixture at 400C 6.1.3 Discussion of Testing Results Figures 6.13 through 6.15 show the dynamic modulus at 10 Hz for each temperature. 5000 a 4000 E C1 SC2 3000 OC3 0 E 2000 OR .U F2 1000 EF3 0 Mixtures Figure 6.13 Average Complex Modulus result at 10 Hz 250C 54 12000 S10000 m Cl 8000 m C2 o C3 o 6000 E Ei [F1 .2 4000 m F2 E 2000 m F3 0 Mixtures Figure 6.14 Average Complex Modulus result at 10Hz at 10C 2000 1600 C1 m C2 1200 003 E 800 0 F1 .2 m F2 400 F3 0 Mixtures Figure 6.15 Average Complex Modulus result at 10Hz at 400C It was observed that the coarse mixtures ranked consistently for different temperatures. The magnitude of the dynamic modulus for the GAC1 mixture has the lowest value of. The GAC2 and GAC3 mixtures have almost the same dynamic modulus. For example atl00C, E* of GAC1 is 2090 (MPa), E* of GAC2 and GAC3 are 3020 and 3172 (MPa) consecutively. For the finegrade mixtures, the GAF2 mixture consistently showed the highest dynamic modulus, with GAF3 is stiffer than GAF1 at 25C and 100C but softer at 400 C. This is maybe because the test for these mixtures contains some degree of variability. From the gradation of these mixtures (Table 3.1), GAF2 has higher percentage of coarse aggregate remaining on 12.5mm and 9.5mm sieve than GAF3 and GAF1, which provides better aggregate interlock. Therefore the stiffness of GAF2 is higher than the other two mixtures. For coarse mixtures, GAC2 also has higher percentage of coarse aggregate than GAC1 and GAC2, and GAC2 is stiffer than GAC1 and GAC3 Figures 6.16 through 6.18 present a summary of phase angles for all the mixture tested. These plots show very consistent average results. Within the same frequency, phase angles are higher at higher temperatures. This is reasonable because the sample will be softer at higher temperature, the viscosity of asphalt binder is lower, and thus it results in a less elastic response of strain versus stress. Except for the 4 Hz test at 100C, the entire test shows the phase angle increases with increasing frequency. Figure 6.19 through 6.21 present the average of phase angle of the mixtures for 4Hz test. 50 40 C1 30 C3 0 Figure 6.16 Average of phase angle at 250C S20 F1 <" F3 0 5 10 15 20 Frequencies (Hz) Figure 6.16 Average of phase angle at 25C 50 40  C1 40 m C2 30 _.a __ C3 20 F1 )K F2 S10 0 * F3 a. 0 0 5 10 15 20 Frequencies (Hz) Figure 6.17 Average of phase angle at 100C 100 80 * C1  C2 20 U 260 0 0 I 2  I 0 5 10 15 20 Frequencies (Hz) Figure 6.18. Average of phase angle at 400C 50 S40 C1 SC2 S30 0C3 SFC3 20 n F1 e F2 .10 F3 0 Mixtures Figure 6.19 Average of phase angle at 4Hz at 250C Mixtures Figure 6.20 Average of phase angle at 4Hz at 100C 50 40 mC1 *C2 30 EO C3 20 F1 A m F2 10 F3 Mixtures Figure 6.21 Average of phase angle at 4Hz at 400C 6.2 Master Curve Construction A master curve of an asphalt mix allows comparison of linear viscoelastic materials when testing has been conducted using different loading times (frequencies) and test temperatures. A master curve can be constructed utilizing the time temperature superposition principle, which describes the viscoelastic behavior of asphalt binders and mixtures. 6.2.1 Timetemperature Superposition Principle Test data collected at different temperatures can be "shifted" relative to the time of loading frequency, so that the various curves can be aligned to form a single master 50  40 mC1 N C2 O 30 DC3 30 20 n F1 ci F2 10 F3 0 curve. The shift factor a(T) defines the required shift at a given temperature, i.e, a constant by which the frequency must be divided to get a reduced frequency fr for the master curve: f, or log(fr) = log(f) + log[a(T)] a(T) Master curves can be constructed using an arbitrarily selected reference temperature Tr to which all data are shifted. At the reference temperature, the shift factor a(Tr) = 1. 6.2.2 Constructing Master Curve using Sigmoidal Fitting Function. For a testing frequency or a given time dependency, the generalized power law is a widely accepted mathematical model for bituminous material response. However, a new method of developing master curves for asphalt mixtures by Pellinen was used in this thesis (Pellinen et al., 2002). In his study, master curves were constructed fitting a sigmoidal function to the measured compressive dynamic (complex) modulus test data using nonlinear least square regression. In the experimental shift approach, the fitting function for master curve construction is a sigmoidal function defined by Equation (6.1): log(E*)= + a (6.1) 1+e f ,log(f,) where log(/E*/) = log of dynamic modulus, 6 = minimum modulus value, fr = reduced frequency, a = span of modulus value, P, y = shape parameter. The parameter y influences the steepness of the function (rate of change between minimum and maximum) and 3 influences the horizontal position of the turning point, shown in Figure (6.16). The shifting was done using an experimental approach by solving shift factors simultaneously with the coefficients of the sigmoidal function, without assuming any functional form of a(T) versus temperature. The master curve of the mix can be constructed using the Solver Function in an Microsoft Excel spreadsheet. The justification of using a sigmoidal function for fitting the compressive dynamic 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 entire temperature range. Sigmoidal Function 7 (increase) 6+ct *j3 (neg) j3 (pos) Log Reduced Frequency Figure 6.22 Sigmoidal Function 60 The results of complex modulus tests for all mixtures tested are presented in the master curves in Figures 6.17 and Figure 6.18 below. All the data were shifted to the reference temperature of 250 C. Master Curve For Coarse Mix 13 20 2  * C1 * C2 A C3 3 1 1 3 5 Log Reduced Frequency Figure 6.23 Log complex modulus master curve for coarse mix Master Curve For Fine Mix * F1 * F2 A F3 3 1 1 3 5 Log Reduced Frequency Figure 6.24 Log complex modulus master curve for fine mix 6.3 Predictive Equation Many predictive techniques for determining the dynamic modulus of asphalt concrete mixes have evolved over the past 30 years. The predictive equation developed by Witzack et al. at the University of Maryland is one of the most comprehensive mixture dynamic modulus models available today (Witzack et al., 2002). That equation is presented below: log E = 1.249937 + 0.029232 x (200) 0.001767 x (200)2 0.002841 x (4) 0.802208(Vb ,) 0.058097 x (Va) ff beff+ Va 3.871977 0.0021(p4) + 0.003958(p38) 0.00017(p38)2 + 0.005470(p34) 1 (0.6033130.313351xlog(f)0.39353xlog(i7)). (6.2) where: /E*/ = dynamic modulus, 105 psi r = bitumen viscosity, 106 Poise, f = loading frequency, Hz, Va = air void content, percent, Vbeff = effective bitumen content, percent by volume, P34 = cumulative percent retained on 19mm sieve, P38 = cumulative percent retained on 9.5mm sieve. P4 = cumulative percent retained on 4.76mm, and P300 = percent passing 0.pp75mm sieve. It is noted that for the mixtures used in the test, p34 = 0, using p12 in the equation (6.2) instead of p34 will give a better result than using p34 = 0. The regression model above has the capability of predicting the dynamic modulus of densegraded HMA mixtures over a range of temperatures, rates of loading, and aging conditions. Figure 6.24 through 6.26 plot the predicted dynamic modulus versus the measured values for six mixtures at 16 Hz. It was observed that the predictive model underestimates the real performance of the mixes. However, the predicted values are proportion to the actual ones. For example, the predictive model predicts GAF2 mix having the highest modulus among fine mixtures and GAC2 mix having the highest modulus among the coarse mixtures, which is consistent with experimental results. Therefore the predictive equation can help to estimate the performance of mixtures during the mix design and pavement thickness design processes although it only provides approximate values. 8000 6000 n. f Actual Values 2 4000 2000 0 I' ll h *Predictived Values C1 C2 C3 F1 F2 F3 Mixtures Figure 6.24 Actual values versus Predicted value of E* at 250C for 16Hz test. 15000 12000 " 9000 iu 6000 3000 0 SActual Values * Predictived Values C1 C2 C3 F1 Mixtures Figure 6.25 Actual values versus Predicted value of E* at 100C for 16Hz test. 3000 2500 2000 0.n Actual Values ^1500 U Predictived Values 1000 500 0 C1 C2 C3 F1 F2 F3 Mixtures Figure 6.26 Actual values versus Predicted value of E* at 400C for 16Hz test. The comparison of the predicted values dynamic modulus actual dynamic modulus at other frequencies will be presented in appendix B. F2 F3 CHAPTER 7 TORSIONAL SHEAR TEST RESULTS 7.1 Result of Torsional Shear Test Chapter 4 described the procedures for the Torsional Shear Test. In order to investigate the relationship between this test and axial complex modulus test, the test was performed under the same temperature and frequency conditions as used for the axial testing in Chapter 6. The same 18 samples from the same six mixtures were tested at 250C first. The temperature then was reduced to 100C. Finally, the samples were heated up and tested at 400C. Full frequency sweep of 16 Hz, 10Hz, 4Hz and 1 Hz were used. It was noted that at 100C, because of controlling problem of the servohydraulic system, the applied force for 16Hz test was much higher than the command force, therefore the result of the test at this frequency doesn't reflect the right answer. Thus, for 100C, the results are only reported for 1Hz, 4Hz and 10Hz tests. 7.1.1 Stress versus Strain Study The primary concern of the test was the relationship of torsional shear stress and torsional shear strain in term of micro strain. By draw the stress versus strain curve, the linearity of the result, the magnitude of applying load, and the variation of the modulus in designed testing strain can be investigated. Figure 7.1 shows the torsional stress versus strain curve at 1 Hz and 10Hz test. The linearity relationship is observed between shear stress and shear strain. 0.3 0.25 0.2 0.15 0.1 0.05 0 0 0.0001 0.0002 0.0003 Torsional Shear Strain 1Hz 10Hz 0.0004 Figure 7.1 Torsional shear stress versus shear strain. Figure 7.2 show the relationship between phase angle and shear strain. It shows that higher shear strain results in smaller phase angle. It is reasonable because higher shear strain will result in higher interlock among particles in the sample, therefore the viscous effect of asphalt binder is reduced, which result in faster deformation response of specimen under loading. 60.0 50.0 0) 0) p 40.0 0, S30.0 S20.0 a 10.0 0.0 Hz 1 OHz 0 0.00005 0.0001 0.00015 0.0002 0.00025 0.0003 Torsional Shear Strain Figure 7.2 Phase angle versus shear strain level. I I I I I 7.1.2 Dynamic Torsional Shear Modulus Results Figures 7.3 through 7.5 present the results of the dynamic torsional shear modulus IG* for the GAF1 mixture, which was found to be representative for finegraded mixtures. Similarly, Figures 7.4 through 7.6 show the results for the dynamic torsional shear modulus IG* for the GAC1 mixture, which was also representative for the coarsegraded mixtures. The results for the other mixtures are shown in Appendix B. 3000 2500  F101 S2000  F102 1500 150  F103 S1000  Avg 500 'g 0 0 5 10 15 20 Frequency (Hz) Figure 7.3 Dynamic Torsional Shear Modulus IG*I of GAF1 at 250C 5000 4000 Fl01 2000 4 F103 1000 ~ Avg 0 0 3 6 9 12 Frequency (Hz) Figure 7.4 Dynamic Torsional Shear Modulus IG*I of GAF1 at 100C 1000 800 600 400 S200 0 0 5 10 15 Frequency (Hz) Figure 7.5 Dynamic Torsional Shear Modulus G* of GAF1 at 400C 2000 1600 1200 800 400 0 0 4 8 12 Frequency (Hz) Figure 7.6 Dynamic Torsional Shear Modulus G* of Cl at 250C 4000 3000 2000 1000 0 0 3 6 9 Frequency (Hz) Figure 7.7 Dynamic Torsional Shear Modulus G* of Cl at 100C  F101  F102 F103 A Avg *C101 W C102 * C103 *Avg 16 20 C101  C102 C103 . Avg  800 600 ciol 4o C102 400 03 Cl03 S200 .Ar Avg 0 0 5 10 15 20 Frequency(Hz) Figure 7.8 Dynamic Torsional Shear Modulus IG*I of Cl at 400C The results show a high degree of consistency for the different conditions and samples tested Similar to the dynamic axial modulus test results in Chapter 6 G* increases with increased frequency, as expected. At 250C, G* increases from about 400 MPa at 1Hz test to 900 MPa at 16Hz test for the GAC1 mixture and from 500 MPa at 1Hz test to 1200 MPa at 16Hz test for the GAF1 mixture. At 100C, G* increases from 1100 MPa (1Hz) to 2100 MPa (16Hz) for the GAClmixture and from 2000 MPa (1Hz) to 3000 MPa (16Hz) for the GAF1 mixture. At 400C, IG* increases from 140 MPa (1hz) to 390 MPa (16Hz) for the GAC1 mixture and from 200 MPa (1Hz) to 480 (16Hz) for the GAF1 mixture. 7.1.3 Phase Angle Results Because the phase angle varies according to strain level, therefore it exists a variability in the test result. Figures 7.9 through 7.14 show the measured phase angles for the GAF1 and GAC1 mixtures. It was observed that phase angle for the torsional shear test is higher than the axial complex modulus test about 120 on average. One possible explanation for this difference is the anisotropic nature of hot mix asphalt samples. 69 there is also a variability associated with the test results at 100 C and 250 C, thus it is not very clear that the phase angle increases or decreases with varying frequencies. However, at test temperatures of 400 C, the phase angle increases with increasing frequency. S60 , 50 0) = 40 S30 < 20 S10 0 ) 10 21 Frequency (Hz)  F101 c F102 F103 Ave Figure 7.9 Phase angle of GAF1 mixture at 250 S60 50 0) S40 30 < 20 l,  10 0 0 F101  F102 *F103 Ave Figure 7.10 Phase angle of GAF1 mixture at 100 0 3 6 9 Frequency (Hz) 0 I I I 100 80 60 40 20 n 0 5 10 15 20 Frequency(Hz) Figure 7.11 Phase angle of GAF1 mixture at 400 . 100 80 C, S60 (D S40 c 20 C 0 0 10 Frequency (Hz) Figure 7.12 Phase angle of GAC1 mixture at 250 100 Cd, c, 80 0),  60 0) 40 S20 n c 0 SC101 SC102  C103 Ave 0 3 6 9 Frequency (Hz) Figure 7.13 Phase angle of GAC1 mixture at 100  F101  F102 F103 Ave C101 SC102 *C103 Ave w 4pA I I I 71 100 Uo 80 0  S 60  ,. i C102 40 SI Ave 20 0 0 10 20 Frequency (Hz) Figure 7.14 Phase angle of GAC1 mixture at 400 Figures 7.15 through 7.17 plot the magnitude of dynamic torsional shear modulus IG*ranked consistently for the different temperatures tested. The Coarsegraded GAC1 mix had the lowest modulus, with the finegrade mixture GAF2 showing the highest dynamic torsional shear modulus, with other mixtures showing similar results. 2000 1600 E C1 o 0 C2 E 1200 ui rC3 .c F1 U 800 I F2 .0 400 m F3 0 I Mixtures Figure 7.15 Average of torsional shear modulus at 10 Hz at 250C 5000 4000 m C1 0o C2 E 3000 "E rC3 [] F1 2000 a I m F2 #A 1000 m F3 0 I 0 Mixtures Figure 7.16 Average of torsional shear modulus at 10 Hz at 100C 1000 800 m C1 0o C2 E 600 400 oF1 S400 Figure 7.17 Average of torsional shear modulus at 10 Hz at 400C 7.2 Poisson Ratio The Torsional shear complex modulus can be related to axial complex modulus by the Poisson ratio. Harvey et al. (2001) concluded that the Poisson's ratio could be taken to be constant, resulting in the following relationship between G* and E*: E* G* (7.1a) 2(1+ v) or E* v = 1 (7.1b) 2G* 73 For each test, the Poisson ratio was calculated using Equation (7.lb). Figures 7.18 and 7.19 show typical results for the Poisson's ratio at different temperatures for the coarsegraded GAC2 mixture and the finegraded GAF2 mixture. It can be observed that Poisson ratio is not constant, but varies according to loading rate. 1.00 S0.80 0.60 25 dc 010 dc S0.40 40 dc S0.20 0.00 0 5 10 15 20 Frequencies (Hz) Figure 7.18 Poisson ratio of coarse mixture C2 1.00 0 0.80 1 0.60 25 dc 0  10dc S0.40 4 dc 0.20 40 0.00 0 5 10 15 20 Frequencies (Hz) Figure 7.19 Poisson ratio of fine mixture F2 Although there is some degree of variability in the Poisson ratio results, it was observed that for 100C, Poisson ratio increases with higher frequency. That means the rate of changing in E* is faster than the rate of change in G*. For 250C and 400C, the Poisson's ratio drop from 1Hz test to 4Hz test for the coarsegraded GAC2 mixture. However, the finegraded GAF2 mixture showed a smaller drop between 1 Hz and 4 Hz than the GAC2 mixture at 250C, and no drop at 400C for the finegraded GAF2 mixture. The reasons for this variability may be that the characteristic of asphalt samples change at some point, where the interlock between the aggregates has more effect or the viscosity of asphalt binder has more effect. Table 7.1 shows the Poisson ratio calculations for all the mixtures. Table 7.1 Poisson ratio GAC1 GAC2 GAC3 GAF1 GAF2 GAF3 40dc 1Hz 0.059 0.562 0.200 0.447 0.025 0.117 4Hz 0.054 0.305 0.062 0.284 0.067 0.133 10Hz 0.113 0.317 0.218 0.335 0.176 0.027 16Hz 0.277 0.478 0.316 0.481 0.290 0.097 25dc 1Hz 0.323 0.149 0.029 0.305 0.188 0.077 4Hz 0.293 0.110 0.015 0.219 0.160 0.042 10Hz 0.268 0.169 0.079 0.267 0.301 0.095 16Hz 0.377 0.299 0.219 0.396 0.418 0.218 1Odc 1Hz 0.250 0.284 0.206 0.123 0.233 0.107 4Hz 0.254 0.359 0.219 0.175 0.355 0.075 10Hz 0.331 0.413 0.184 0.257 0.460 0.217 16Hz N/A 0.523 N/A N/A N/A N/A 7.3 Summary The consistent results for the dynamic torsional shear test presented in this chapter have shown that this test may be a useful tool for studying the deformational characteristics of asphalt concrete during shear. After the axial complex modulus test, instead of wasting the sample, it is of great advantage to use the sample for studying the dynamic shear modulus. With the observation that the phase angles in the torsional shear test is higher than for the axial test, implies that the dynamic torsional shear modulus test may be sensitive to the anisotropy in the sample during testing. 75 Although the torsional shear test is preformed on a solid specimen, and therefore the stress distribution in the sample varies, due to its simplicity, it can be regarded as a promising test to study the shear stress state of mixtures and an important step before studying torsional shear stress in hollow cylinder of asphalt concrete. CHAPTER 8 CONCLUSION AND RECOMMENDATION 8.1 Conclusion 8.1.1 Testing Procedures and Setup Over the past year, a lot of improvements on the testing apparatus, system control and data acquisition in the complex modulus program have been made. The introduction of new controller system Test Start IIm brought much higher capability and performance quality than the old Test Start IIs. The capacity of controlling test frame increased from one to four kips, permitting the operation of the torsional shear test on GCTS load frame. The data acquisition capacity is also improved greatly. The new Testar IIm controller program has the capacity of recording up to 12 output signals. Therefore, a very complicated test, which may include thermocouple, pressure transducer, LVDT can be carried out. The ability to view the output signal and input signal separately or simultaneously helps to examine the set up and quality of signal during the test. Another significant improvement in the testing program was the introduction of temperature controlling unit. It permits to test specimen in various temperature than only room temperature like previously. Finally, a new testing set up and procedure has been introduced for torsional shear modulus test. The new simple test set up provides a tool to study shear capacity of cylindrical specimen after axial complex modulus test. 8.1.2 Signal and Data Analysis With new data acquisition system, the quality of the signal increased greatly. Although recording very small deformation, one over thousand millimeters, the deformation signals recorded are smooth and clean. Also, it gets to stable state in a shorter period of time. Therefore, it is clear that one doesn't need to perform 1000 cycles (D.J Swan 2001) per test. The duration of the test reduced to 50 cycles for complex modulus test. For torsional shear modulus test, the stable state of signal takes longer time. The duration of 150 cycles for 16 Hz test, 100 cycles for 10 Hz test, 50 cycles for 4Hz and 1 Hz test were found suitable. The regression analysis proved to be a dependable technique to analyze sinusoid signal. With a closer look at test result data, the calculation of axial complex modulus and torsional shear modulus as an average of 10 cycles gave a better result than an average of 5 cycles. 8.1.3 Axial Complex Modulus Test The results form axial complex modulus test clearly show that IE* increasing with increasing frequency as expected because it is known that asphalt concrete get stiffer with increased loading rate (Sousa, 1987). The test results also showed phase angle increases with increasing frequency. For a higher temperature such as 250C and 400C, this trend is better to observe. For 100C tests, it was shown that phase angle decreases at 4Hz test and go up again. This may be because of controlling issue. At this temperature and frequency, it was noticed that the MTS system vibrates more than normal. Therefore the result may be affected. The values of phase angle are almost the same through different mixtures. The mixtures performed consistently throughout different temperatures and frequencies. The magnitude of complex modulus of GAC 1 mixture has the lowest value. GAC2 and GAC3 mixtures have almost the same value. For fine mixtures, GAF2 mixture consistently shows the highest magnitude, GAF3 and GAF1 performed likely GAC2 and GAC3. The predictive model underestimates the real performance of the mixes. However, the predicted values are proportion to the actual one. For example, the predictive model predicts GAF2 mix having the highest modulus among fine mixtures and GAC2 mix having the highest modulus among the coarse mixtures. That is also shown in the actual values. Therefore the predictive equation can help to estimate the performance of mixture during the mix design process although it only gives the approximate values. 8.1.4 Torsional Shear Test The consistent result of torsional shear test has shown that this test is a promising tool to study the deformational characteristic of asphalt concrete during shear. After axial complex modulus test, instead of wasting the sample, with a simple set up, it is of great advantage to use the sample for studying dynamic shear modulus. The torsional shear test is a dependable test. The results of the test are consistent throughout different samples. Coarse mix GAC1 has shown the lowest modulus magnitude, fine mixture GAF2 has shown the highest result when the other mixtures have shown the similar results. Like E* because sample gets stiffer with higher frequency, IG* increases with increased frequency. Torsional shear modulus can be related to axial complex modulus by Poisson ratio. Poisson ratio is not constant but it varies according to loading rate. Although it exits some degree of inconsistent among the results of Poisson ratio, it was observed that for 100C, Poisson ratio increase with higher frequency. That means the rate of changing E* is faster than the rate of changing G*. For 250C and 400C, sometime Poisson ratio drop from 1Hz test to 4Hz test and increase back again at 10 Hz test and 16 Hz test. The reason may be on the control issue during the test or characteristic of asphalt sample change at some point, where the interlock between the aggregate has more effect or the viscosity of asphalt binder has more effect. It is observed that the phase angles in torsional shear test is higher than those of axial test, and the trend of Poisson ratio constantly show a turning point poses the question of anisotropy of asphalt concrete during shear. Although torsional shear test is preformed on a solid specimen, therefore the stress distribution in the sample vary, due to its simplicity, it can be regarded as a promising test to study the shear stress state of sample and an important step before studying torsional shear stress in hollow cylinder of asphalt concrete 8.2 Recommendation In order to have a better confirmation of Poisson ratio and phase angle, further research with larger frequency sweeps and temperature ranges should to be carried out. In this study, the torsional shear test program has only a limited purpose of introducing an alternative tool of studying shear stress in asphalt concrete. More research needs to be carried out in order to benefit the simplicity of the test in the asphalt pavement industry. Based on the testing procedure, set up and study of torsional shear test on solid specimen, further study of hollow cylinder will be interesting and necessary. APPENDIX A MIX DESIGN Table A. 1: Mixture Cl Properties Superpave Property Symbol Blend Design Ctperia Criteria 1 2 3 % AC 5.00 5.50 6.00 6.63 Bulk Specific Gravity Gmb 2.308 2.324 2.337 2.345 of Compacted Mix at Ndes Maximum Theoretical ci Gera Gmm 2.505 2.485 2.471 2.442 Specific Gravity Percent Air Voids in PercentAirVoidsin Va 7.84 6.46 5.43 3.98 4.0% Compacted Mix Percent VMA in VMA P t VA in VA 18.37 18.25 18.24 18.50 14% Minimum Compacted Mix (%) Percent VFA in VFA Pe t VA in 57.34 64.58 70.26 78.51 65% to 75% Compacted Mix (%) Effective Specific Gse 2.712 2.711 2.717 2.710 Gravity of Aggregate Asphalt Absorption Pba 0.37 0.35 0.44 0.34 Effective Asphalt Effective Asphalt Pbe 4.65 5.17 5.59 6.32 Content of Mixture Dust Dust to Asphalt ratio p 0.76 0.68 0.63 0.56 0.6% to 1.2% prop.(%) %GmmatNini 83.07 83.62 84.72 86.02 89% Maximum %Gmm atNdes 92.16 93.53 94.57 96.02 %GmmatNmax 93.40 94.84 96.17 97.60 98% Maximum Asphalt Specific Gb 1.035 1.035 1.035 1.035 Gravity Bulk Specific Gravity Gsb of Aggregate Table A.2: Cl Batch Sheet Sieve #7 stone # 89 stone W10 scr Filler Size "3/4 0.0 311.7 1260.9 2734.3 "1/2 73.9 311.7 1260.9 2734.3 "3/8 311.7 311.7 1260.9 2734.3 #4 311.7 1260.9 1260.9 2734.3 #8 311.7 1260.9 1991.9 2734.3 #16 311.7 1260.9 2286.3 2734.3 #30 311.7 1260.9 2453.8 2734.3 #50 311.7 1260.9 2567.8 2734.3 100 311.7 1260.9 2679.3 2734.3 200 311.7 1260.9 2734.3 2734.3 <200 Table A.3: Mixture C2 Properties Property Symbol Blend Design Superpave Criteria 1 2 3 % AC 4.5 5 5.5 5.26 Bulk Specific Gmb Gravity 2.367 2.390 2.411 2.399 c at Ndes of Compacted Mix at Maximum Theoretical Gmm 2.531 2.511 2.492 2.500 Specific Gravity Percent Air Voids in CompactedVa 6.499 4.835 3.270 4.046 4.0% Compacted Mix Percent VMA in VMA PA in VA 15.908 15.542 15.241 15.448 14% Minimum Compacted Mix (%) Percent VFA in VFA t V i V 59.149 68.891 78.542 73.812 65% to75% Compacted Mix (%) Effective Specific Effective Specific Gse 2.721 2.720 2.721 2.719 Gravity of Aggregate Asphalt Absorption Pba 0.466 0.453 0.461 0.434 Effective Asphalt Pbe 4.055 4.570 5.064 4.849 Content of Mixture Dust Dust to Asphalt ratio p 0.972 0.863 0.779 0.813 0.6% to 1.2% prop.(%) %Gmm at Nini 84.180 85.177 86.509 85.868 89% Maximum %Gmm atNdes 93.501 95.165 96.730 95.956 %Gmm at Nmax 95.248 96.326 98.158 97.263 98% Maximum Asphalt Specific Gb 1.035 1.035 1.035 1.035 Gravity Bulk Specific Gravity of Aggregate Table A.4: C2 Batch Sheet Sieve size #7 #89 W10 filler 12.5(1/2) 256.5 767.7 1530.7 2718.8 9.5(3/8) 767.7 767.7 1530.7 2718.8 4.75(#4) 767.7 1530.7 1530.7 2718.8 2.36(#8) 767.7 1530.7 2033.8 2718.8 1.18(#16) 767.7 1530.7 2295.0 2718.8 600(#30) 767.7 1530.7 2457.1 2718.8 300(#50) 767.7 1530.7 2568.6 2718.8 150(#100) 767.7 1530.7 2672.7 2718.8 75(#200) 767.7 1530.7 2718.8 2718.8 <75(#200) 767.7 1530.7 2718.8 2830.4 Table A.5: Mixture C3 Properties Property Symbol Blend Design Superpave Criteria 1 2 3 % AC 4.5 5 5.5 5.25 Bulk Specific Gravity Gmb 2.373 2.387 2.396 2.391 of Compacted Mix at Ndes Maximum Theoretical Gmm 2.519 2.502 2.480 2.492 Specific Gravity Percent AirVoids in Va 5.798 4.592 3.401 4.051 4.0% Compacted Mix Percent VMA in VMA P t VA in VA 15.660 15.602 15.737 15.680 14% Minimum Compacted Mix (%) Percent VFA in VFA erce in A 62.979 70.570 78.391 74.163 65% to 75% Compacted Mix (%) Effective Specific Effective Specific Gse 2.706 2.709 2.706 2.709 Gravity of Aggregate Asphalt Absortion Pba 0.273 0.311 0.262 0.305 Effective Asphalt p Effective Asphalt Pbe 4.240 4.705 5.252 4.961 Content of Mixture Dust Dust to Asphalt ratio Dust 1.103 0.994 0.891 0.943 0.6% to 1.2% prop.(%) %Gmm atNini 85.051 85.565 86.319 86.071 89% Maximum %Gmm at Ndes 94.202 95.408 96.599 95.949 %Gmm atNmax 94.751 96.054 98.266 96.820 98% Maximum Asphalt Specific Gb 1.035 1.035 1.035 1.035 Gravity Bulk Specific Gravity of Aggregate Table A.6: C3 Batch Sheet Sieve size #7 #89 W10 Filler 12.5(1/2) 77.4 295.6 1257.0 2688.4 9.5(3/8) 295.6 295.6 1257.0 2688.4 4.75(#4) 295.6 1257.0 1257.0 2688.4 2.36(#8) 295.6 1257.0 1864.5 2688.4 1.18(#16) 295.6 1257.0 2171.8 2688.4 600(#30) 295.6 1257.0 2368.2 2688.4 300(#50) 295.6 1257.0 2503.6 2688.4 150(#100) 295.6 1257.0 2627.6 2688.4 75(#200) 295.6 1257.0 2688.4 2688.4 <75(#200) 295.6 1257.0 2688.4 2820.3 Table A.7: Mixture Fl Properties Property Symbol Blend Design Superpave Criteria 1 2 3 % AC 5.000 5.500 6.000 5.680 Bulk Specific Gmb Gravity 2.348 2.364 2.402 2.374 of Compacted Mix at Maximum Theoretical Gmm 2.502 2.480 2.461 2.473 Specific Gravity Percent Air Voids in e c idS Va 6.145 4.673 2.386 4.016 4.0% Compacted Mix Percent VMA in VMA A in VA 16.937 16.833 15.941 16.631 14% Minimum Compacted Mix (%) Percent VFA in VFA Percent VFA in VFA 63.718 72.240 85.033 75.852 65% to 75% Compacted Mix (%) Effective Specific Effective Specific Gse 2.709 2.705 2.704 2.706 Gravity of Aggregate Asphalt Absorption Pba 0.329 0.268 0.259 0.276 Effective Asphalt Effective Asphalt Pbe 4.687 5.247 5.756 5.420 Content of Mixture Dust Dust to Asphalt ratio Dust 0.701 0.626 0.571 0.606 0.6% to 1.2% prop.(%) %Gmm atNini 85.798 86.904 89.018 87.725 89% Maximum %Gmm atNdes 93.855 95.327 97.614 95.984 %Gmm atNmax 94.298 96.749 98.112 97.365 98% Maximum Asphalt Specific Gb 1.035 1.035 1.035 1.035 Gravity Bulk Specific Gravity of Aggregate Table A.8: Fl Batch Sheet Sieve size #7 #89 W10 Filler 12.5(1/2) 147 447.53 940.01 2709.6 9.5(3/8) 448 447.53 940.01 2709.6 4.75(#4) 448 940.01 940.01 2709.6 2.36(#8) 448 940.01 1422.1 2709.6 1.18(#16) 448 940.01 1886 2709.6 600(#30) 448 940.01 2212.6 2709.6 300(#50) 448 940.01 2440.3 2709.6 150(#100) 448 940.01 2637 2709.6 75(#200) 448 940.01 2709.6 2709.6 <75(#200) 448 940.01 2709.6 2801.7 Table A.9: Mixture F2 Properties Property Symbol Blend Design Superpave Criteria 1 2 3 %AC 4.500 5.000 5.500 4.560 Bulk Specific Gravity Gmb 2.430 2.448 2.466 2.433 of Compacted Mix at Ndes Maximum Theoretical Gmm 2.536 2.514 2.496 2.532 Specific Gravity Percent Air Voids in Va 4.186 2.637 1.186 3.910 4.0% Compacted Mix Percent VMA in VMA P t VA in VA 13.653 13.455 13.269 13.574 14% Minimum Compacted Mix (%) Percent VFA in VFA SV i V 69.340 80.401 91.064 71.195 65% to 75% Compacted Mix (%) Effective Specific Effective Specific Gse 2.727 2.724 2.725 2.725 Gravity of Aggregate Asphalt Absorption Pba 0.550 0.519 0.532 0.527 Effective Asphalt Effective Asphalt Pbe 3.975 4.507 4.997 4.057 Content of Mixture Dust Dust to Asphalt ratio Dust 1.190 1.071 0.974 1.174 0.6% to 1.2% prop.(%) %Gmm at Nini 88.213 89.384 90.669 88.617 89% Maximum %GmmatNdes 95.814 97.363 98.814 96.105 %Gmm at Nmax 96.847 98.066 99.478 97.166 98% Maximum Asphalt Specific Gb 1.035 1.035 1.035 1.035 Gravity Bulk Specific Gravity of Aggregate Table A. 10: F2 Batch Sheet Sieve size #7 #89 W10 Filler 12.5(1/2) 265.0 631.1 1109.9 2644.8 9.5(3/8) 631.1 631.1 1109.9 2644.8 4.75(#4) 631.1 1109.9 1109.9 2644.8 2.36(#8) 631.1 1109.9 1586.5 2644.8 1.18(#16) 631.1 1109.9 1844.7 2644.8 600(#30) 631.1 1109.9 2150.7 2644.8 300(#50) 631.1 1109.9 2367.9 2644.8 150(#100) 631.1 1109.9 2549.9 2644.8 75(#200) 631.1 1109.9 2644.8 2644.8 <75(#200) 631.1 1109.9 2644.8 2794.4 Table A. 11: Mixture F3 Properties Property Symbol Blend Design Superpave Criteria 1 2 3 % AC 4.500 5.000 5.500 5.140 Bulk Specific Gravity Gmb6 28 2 2.376 2.398 2.419 2.404 of Compacted Mix at Ndes Maximum Theoretical i Grai GGmm 2.531 2.510 2.490 2.505 Specific Gravity Percent AirVoids in c d Va 6.123 4.457 2.859 4.026 4.0% Compacted Mix Percent VMA in VMA Per A in VA 15.556 15.206 14.906 15.103 14% Minimum Compacted Mix (%) Percent VFA in VFA t VA i V 60.638 70.687 80.819 73.344 65%to 75% Compacted Mix (%) Effective Specific Effective Specific Gse 2.720 2.719 2.719 2.720 Gravity of Aggregate Asphalt Absortion Pba 0.471 0.451 0.445 0.465 Effective Asphalt Effective Asphalt Pbe 4.050 4.572 5.079 4.699 Content of Mixture Dust Dust to Asphalt ratio Dust 1.434 1.271 1.144 1.236 0.6% to 1.2% prop.(%) %Gmm at Nini 84.957 85.666 87.010 85.215 89% Maximum %Gmm at Ndes 93.877 95.543 97.141 95.974 %Gmm at Nmax 94.945 96.828 98.219 97.306 98% Maximum Asphalt Specific Gb 1.035 1.035 1.035 1.035 Gravity Bulk Specific Gravity of Aggregate Table A.12: F3 Batch Sheet Sieve size #7 #89 W10 Filler 12.5(1/2) 150.6 418.8 981.5 2647.0 9.5(3/8) 418.8 418.8 981.5 2647.0 4.75(#4) 418.8 981.5 981.5 2647.0 2.36(#8) 418.8 981.5 1831.4 2647.0 1.18(#16) 418.8 981.5 2078.5 2647.0 600(#30) 418.8 981.5 2300.5 2647.0 300(#50) 418.8 981.5 2459.3 2647.0 150(#100) 418.8 981.5 2593.7 2647.0 75(#200) 418.8 981.5 2647.0 2647.0 <75(#200) 418.8 981.5 2647.0 2810.3 