JOURNAL PAPER TYPE Journal of Testing and Evaluation, Sept 2002 Vol XX, No. X Paper ID: Available online at: www.astm.org Published XXXX Lee, K. 1, Kim, H. 2, Kim, N. 3, Kim, Y 4 Dynamic Modulus of Asphalt Mixtures for Development of Korean Pavement Design Guide ABSTRACT: This paper presents the dynamic modulus of asphalt mixtures with granite aggregate, which are highly common in Korea. Dynamic modulus was determined by the simplified master curve using test data covering a large range of temperatures from 10 o C to 55 o C. Four different asphalt mixtures were evaluated in this paper. Four specimens were chosen to evaluate mixtures with two different aggregates (13mm, 19mm) except for two different asphalt binders (PG 58-22, PG 64-16). In addition, the mixture was controlled air void (2, 4, 6%) and asphalt content based on optimum asphalt binder by Superpave gyratory compactor. It adopts sigmoidal function and compressive dynamic modulus test data obtained at matrix combination of different frequencies and test temperatures. The experimental dynamic modulus values were compared against modulus values obtained from the predictive equations proposed by NCHRP 1-37A MEPDG. KEYWORDS: asphalt mixture, dynamic modulus, master curve, phase angle, sigmoidal function 1 Associate Professor, Dept. of Civil Engineering, Kongju National University, Cheonan Si, Chungcheong Nam Do, Korea 330-717 2 RA, Dept. of Civil Engineering, Kyungsung University, Pusan, Korea 608-736 3 Associate Professor, Dept. of Civil Engineering, Seongkyunkwan University, Seoul, Korea Copyright 2002 by ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 14928-2959.
2 Introduction The Korean Pavement Design Guide (KPDG), such as NCHRP 1-37A MEPDG, has been developed for last 3 years as the first stage of whole project. It is important that the Korean Pavement Design method takes a hierarchical structure based on the importance of the pavement in design. That is, depending on the traffic volume, the design method calls for different inputs for different levels of sophistication in the pavement response and/or performance models. For the simplest level, no testing is necessary and the default material properties and performance model coefficients are used based on limited input by the user on the material to be used in the design. For the next level, it is recommended that a set of simple tests (such as the dynamic modulus test, indirect tension strength test, etc.) may be performed with additional inputs from the user on the materials to be used. The highest level will require a sweep of advanced testing on layer materials. The design method needs to be in a modular format so that models of different levels of sophistication can be incorporated for different levels of design. This concept is already being implemented in NCHRP 1-37A MEPDG. In the U.S., there is a tremendous impetus for using the dynamic modulus as the material properties of asphalt concrete for pavement design and mixture design. This change is natural due to several important strengths of this material property summarized as follow : The dynamic modulus is one of the three fundamental properties used in the theory of viscoelasticity. The other two are creep compliance and relaxation modulus. Therefore, if the dynamic modulus is adopted as the material property for the pavement response prediction, the same property can be used in the performance prediction model based on viscoelasticity. 4 Assistant Professor, Dept. of Ocean Engineering, Pukyung National University, Pusan, Korea
3 Different from the resilient modulus, the dynamic modulus is expressed as a function of loading rate, which is one of the most important loading variables in pavement design. The dynamic modulus is based on the PG binder specification. Therefore, adoption of this concept in the pavement design will allow both the binder specification and the mixture testing for pavement design to be on the same theoretical foundation. In the Superpave Models project, it was found that the dynamic modulus is an excellent indicator for rutting performance of asphalt mixtures. This finding is significant because this single material property may be then used for both pavement design and mixture design. The objective of this study was to characterize the dynamic modulus of asphalt mixtures, especially surface course and base course of hot mix asphalt, and to make a predictive equation for developing Korean Pavement Design Guide. This paper shows the limited test results on the first three years of KPDG project. Master Curve and Shift Factor In the proposed 2002 Guide for the Design of Pavement System, currently under development in NCHRP Project 1-37A, the modulus of the asphalt concrete (at all analysis levels of temperature and loading frequency) is determined from a master curve constructed at a reference temperature, generally 21.1 o C. Master curves are constructed using the principle of time-temperature superposition. The data at various temperatures should be shifted with respect to log of time until curves merge into a single smooth function. The resulting master curve of the modulus formed in this manner describes the time dependency of the material. The amount of shift at each temperature required to form the master curve describes the temperature dependency of the material (Pellinen, 2001).
4 The master curve for a material can be constructed using an arbitrarily selected reference temperature, T R, to which all data are shifted. At the reference temperature, the shift factor a(t)=1. Several different models have been used to obtain shift factors of viscoelastic materials, the most common of which is Williams-Landel-Ferry (WLF) equation (Williams et al., 1955). When experimental data is available, a master curve can be constructed for the mixture. The master curve can be represented by a nonlinear sigmoidal function of the following form(aashto, 2002). y = α δ + ( β + γ log( tr )) 1+ exp In this equation, t r is the time of loading at the reference temperature, δ is the minimum value of * E, δ + α is the maximum value of * E, and β and γ are parameters describing the shape of the sigmoidal function. The sigmoidal function of the dynamic modulus master curve can be justified by physical observations of the mixture behavior. The upper part of the function approaches asymptotically the mix s maximum stiffness, which depends on the binder stiffness at cold temperature. At high temperature, the compressive loading causes aggregate interlock stiffness to be an indicator of mixture stiffness. The sigmoidal function captures the physical behavior of asphalt mixtures observed in dynamic modulus testing throughout the entire temperature ranges (Pellinen and Witczak, 2002a & 2002b). Based on dynamic modulus test data, Witczak s research group proposed an empirical model to predict the dynamic modulus of an asphalt mixture(andrei at al., 1999, Fonseca & Witczak, 1996). The model was generated based on 1429 data obtained for 149 different asphalt mixtures. Improvements were made to earlier models, taking into account hardening effects from
short and long-term aging, as well as extreme temperature conditions. The model developed from this statistical study is : 5 log E * 0.802208V V eff = 1.249937 + 0.029232( P + V a eff 200 3.871977 0.0021( P + 1+ e ) 0.001767( P 200 ) 2 4) + 0.003958( P38) 0.000017( P38) ( 0.603313 0.313351log( f ) 0.393532logη) 2 0.00284( P ) 0.086097( V ) 4 a + 0.00547( P 34 ) * E = asphalt mix dynamic modulus, in 10 5 psi; η = bitumen viscosity, in 10 6 psi; f = load frequency, in Hz; V a = percent air voids in the mix, by volume; V eff = percent effective bitumen content, by volume; P 34 = percent retained on 3/4in. sieve, by total aggregate weight; P 38 = percent retained on 3/8in. sieve, by total aggregate weight; P 4 = percent retained on No. 4 sieve, by total aggregate weight; P 200 = percent retained on No. 200 sieve, by total aggregate weight; Research Methodology Materials Four different mixtures for surface course and two different mixtures for base course, which are highly common, were selected. Table 1 showed the gradation of mixtures used. Two different types of asphalt binder, PG 58-22 and PG 64-16, were used. Table 1. Mixture Gradation
6 Sieve Size, mm Number of Percent Passing, % Sieve Size 13 mm 19 mm 25mm 40 100 25 1 100 100 19 3/4 100 97.5 87 12.5 1/2 97.5 82.5 65 4.75 # 4 67.5 55 49 2.36 # 8 51 39.5 37 0.6 # 30 27 23 0.3 # 50 18.5 15.5 14 0.15 # 100 11 10 0.074 # 200 7 5 4 Test Equipments All the tests were carried out on an UTM-25 testing system, which includes an hydraulically-driven load-frame, rated at 25kN, with integrally mounted hydraulic actuator, position transducer, and load cell, in a 20 o C to 200 o C temperature chamber. An intergrated control and data aquisition systems (CDAS) provides accurate force or displacement waveform generation and control and enables automatic sequencing of test procedures. Flat and circular loading plates were used to apply he load to the specimen. Latex sheet was used to reduce friction at the each end plates. The vertical deformation measurements were obtained using two LVDTs. One average strain measurement was obtained from the two LVDTs. Sample Preparation Cylindrical specimens, 100 mm diameter and 150 mm height, were prepared according to NCHRP Project Report 9-29 (AASHTO, 2002). Cylindrical specimens, 150 mm diameter and 170 mm height, were compacted in the laboratory using the Superpave gyratory compactor. They were then cored to a 100 mm diameter and saw to a final height of 150 mm. The air voids were
7 measured on the finished test specimens. Adjustments were made to the number of gyrations during compaction to achieve about 2.0, 4.0, and 6.0 ± 0.5% air void content at the optimum asphalt content(oac). Fig. 1 showed the variation of air void content with number of gyrations to get the target air voids at the optimum asphalt content. Fig. 1 The Determination of Number of Gyration to Get the Target Air Voids (%) Test Procedures The test procedure was based on NCHRP 9-29 proposed standard A1 : Dynamic Modulus of Asphalt Concrete Mixtures and Master Curve. The recommended tests were carried out at several different temperatures (-10 o C, 5 o C, 21 o C, 40 o C, & 55 o C) and loading frequencies (25Hz, 10Hz, 1 Hz, 0.1 Hz, & 0.05 Hz). Each specimen was tested for 25 combinations of temperature and frequency. At very high temperatures and low frequencies, the sample begins to show non-
8 linear effects. Testing began with the lowest temperature and proceeded to the highest. At a given temperature, the testing began with the highest frequency of loading and proceeded to the lowest. The specimen was placed in freezer overnight at -10 o C to ensure temperature equilibrium. On the morning of testing, the specimen was placed in the environmental chamber at -10 o C and allowed to equilibrate for 1 hour. Latex sheet was placed between the specimen and steel plates at the top and bottom. Testing continued with different numbers of cycles for each frequency as shown in Table 2. The data acquisition system was set up to record the last six cycles at each frequency. The report for the data analysis explains in detail how the raw force and displacement data is manipulated to obtain the dynamic modulus and phase angle for each specimen. After the entire cycle of testing was complete at -10 o C, the environmental chamber was set to the next temperature. After 2 hours conditioning, the step were repeated until completion of the entire sequence of temperatures and frequencies. The protocol requires 200 cycles of load conditioning, but does not state whether this is at the contact load of five percent of test load or at the 25 Hz test load. Table 2 suggests dynamic stress levels for this test. If at any time during the conditioning loading process the unrecoverable axial strain in the sample exceeds 1500 micro-strain, the sample is to be discarded. The strain level range should be from 50 to 150 micro-strain. Experience with the * E test procedure and the HMA mixes being tested is required in order to select the proper stress level that complies with the sample strain limitation. Table 2. Test Sequence and Stress Level Frequency, Hz Number of Cycles Temperature, o C Stress Level, kpa
9 25 103-10 1400-2800 10 106 5 700 1400 1 56 21 350 700 0.1 6 40 140 250 0.05 6 55 35 75 Test Results and Discussions Dynamic modulus tests for the combination of 13mm, 19mm, and 25mm of aggregate with PG 58-22 and PG 64-16 have been conducted at different air voids, temperatures and loading frequency. Table 3 shows the typical test results. Master Curve A master curve of an asphaltic mix allows comparison of visco-elastic materials when testing has been conducted using different loading times or frequencies and test temperatures. A master curve can be constructed utilizing the time temperature superposition principle, which describes visco-elastic behavior of asphalt binders and mixtures. For the construction of master curve, shift factor should be defined. The shifting equation available are the empirical William- Landel-Ferry(WLF) equation, Arrhenius equation, Log-linear method, Experimental method, the Viscosity Temperature Susceptibility(VTS) method(pellinen et al., 2002). Among them, the experimental method was adopted in this research. In the Experimental approach, all shift factor are solved simultaneously with the coefficients of the sigmoidal fitting function using non-linear least squares fitting (Solver Function in EXCEL) without assuming any functional form for the relationship of a(t) versus temperature. Table 3. Dynamic Modulus and Phase Angle for Each Mixture Temp.( o C) Frequency 13mm + PG 58-22 13mm + PG 64-16
10-10 o C 5 o C 21 o C 40 o C 55 o C 2% 4% 6% 2% 4% 6% E* E* E* E* E* E* 0.05 8732 10.72 8299 10.75 7641 9.64 9035 8.85 8253 7.90 7299 9.30 0.1 8876 9.60 8635 10.21 7803 9.49 9291 7.67 12769 7.71 7547 8.29 1 9901 6.65 9372 6.31 8741 6.91 10068 5.52 14170 5.81 8528 4.90 10 10263 4.44 10031 4.50 9271 4.27 11050 3.47 15863 3.82 8784 4.75 25 10025 3.94 9983 1.79 8972 5.88 10275 3.55 15445 5.03 8931 3.12 0.05 5666 15.78 5298 15.91 4780 16.68 5536 15.01 5050 15.72 4485 15.55 0.1 6028 12.66 5680 14.01 5257 15.21 5689 13.63 5413 13.95 6975 14.35 1 7047 8.62 7113 10.30 6350 8.72 7028 9.32 6701 8.36 8480 9.02 10 8045 6.55 7787 7.65 7291 7.16 8226 6.04 7496 6.79 10127 7.16 25 7823 4.15 7536 4.35 7359 5.68 7683 5.31 7734 6.04 9983 4.88 0.05 2706 26.50 2351 26.44 2173 27.02 2426 25.61 2293 25.58 1982 27.05 0.1 3140 24.11 2669 24.96 2474 25.38 4141 24.00 2545 24.36 2254 24.45 1 4463 14.78 4004 16.69 3679 16.29 4253 16.14 3869 15.24 3372 16.60 10 5613 11.85 5241 10.37 5084 11.92 5937 10.01 4923 11.10 4475 11.86 25 6286 12.06 5575 10.56 5820 11.91 5961 8.04 5337 11.74 4968 13.23 0.05 940 18.35 881 19.37 841 21.23 855 18.19 770 20.90 738 23.27 0.1 1036 19.32 975 19.79 910 20.55 856 19.94 870 21.53 825 22.34 1 1564 20.81 1453 19.52 1306 18.05 1401 18.86 1327 19.45 1279 18.25 10 2482 21.28 2267 17.52 2030 21.15 2340 19.83 3087 20.00 1967 16.98 25 2670 19.80 2443 14.12 2312 16.52 2807 17.47 3895 17.85 2190 17.57 0.05 394 12.43 379 14.46 367 12.26 341 9.91 324 13.05 317 13.78 0.1 410 13.25 402 14.64 393 13.58 357 12.27 342 14.27 327 14.52 1 525 15.69 540 16.73 495 16.27 469 15.94 468 18.35 694 18.15 10 846 22.19 818 22.88 714 20.45 726 20.99 727 19.16 712 22.25 25 1087 16.06 1004 27.23 853 20.13 891 21.77 933 22.79 908 23.51 The activation energy from Arrhenius equation is shown below : a(t) = horizontal shift E a = apparent activation energy R = universal gas constant, 8.314J/ o K-mol T = temperature, o K, and T o = reference temperature, o K E a 1 1 Loga( T ) = 2.303R T To The calculated activation energy and the horizontal shift factor are shown in Table 4. Table 5 showed the sigmoidal model coefficients for dynamic modulus master curve, like α, δ, β, and γ for each mixture with different air voids. Fig. 2 shows the master curve for 25mm asphalt mixtures.
11 Table 4. Activation Energy and Horizontal Shift Factor Aggregate Binder Air Shift Factor Activation Energy (kj/mol) Void -10 o C 5 o C 21 o C 40 o C 55 o C -10 o C 5 o C 21 o C 40 o C 55 o C Surface PG 2-5.064-2.248 0 2.696 5.142 268.0 220.1 250.3 279.6 Course 58-22 4-5.462-2.460 0 2.549 4.945 261.1 240.9 236.7 268.8 13mm 6-4.756-2.173 0 2.535 5.114 227.3 212.8 235.4 278.0 PG 2-5.670-2.213 0 2.443 5.030 271.1 207.9 226.9 273.4 64-16 4-5.247-2.281 0 2.508 4.863 250.9 223.4 232.9 264.6 Surface Course 19mm Base Course 25mm PG 58-22 PG 64-16 PG 58-22 PG 64-16 6-5.360-2.226 0 2.413 4.698 256.3 218.0 224.0 255.4 2-4.828-1.837 0 2.858 5.417 230.8 179.9 265.3 294.5 4-5.669-2.171 0 2.854 5.468 271.0 212.6 264.1 297.3 6-5.444-2.256 0 2.725 5.795 260.3 220.9 253.0 315.0 2-4.663-2.190 0 2.848 5.247 223.0 214.4 264.4 285.2 4-4.567-2.183 0 2.816 5.162 218.3 213.7 261.4 280.6 6-4.356-2.190 0 2.884 5.497 208.3 214.5 267.8 298.8 2-7.317-2.427 0 2.565 4.677 352.0 237.0 238.0 254.0 4-5.385-2.530 0 2.667 5.030 257.0 247.0 248.0 273.0 6-5.779-2.483 0 2.506 4.894 276.0 243.0 232.0 266.0 2-6.697-2.775 0 3.694 6.248 320.0 272.0 343.0 340.0 4-4.701-4.782 0 2.426 4.418 225.0 468.0 225.0 240.0 6-5.291-2.443 0 3.535 6.398 253.0 240.0 328.0 348.0 Table 5. The Sigmoidal Function Coefficients for Dynamic Modulus Master Curve Aggregate Binder Air(%) α δ β γ Surface PG 2.24 1.8229 2.2058-1.2977 0.4124 Course 58-22 4.06 1.8424 2.1916-1.1292 0.3965 13mm 6.25 1.6642 2.3381-1.0264 0.4446 PG 2.08 1.7985 2.2402-1.1768 0.4509 64-16 4.21 1.9996 2.0538-1.1384 0.3889 Surface Course 19mm Base Course 25mm PG 58-22 PG 64-16 PG 58-22 PG 64-16 6.24 1.9384 2.0503-1.1321 0.3952 2.45 1.7534 2.2318-1.1718 0.4258 4.48 1.8475 2.1144-1.0756 0.3719 6.38 1.8595 2.1770-0.9385 0.3846 1.93 1.8402 2.1748-1.2462 0.4309 4.16 1.8260 2.1417-1.2340 0.4209 5.93 1.9571 2.0751-1.0143 0.3696 1.80 1.5802 2.3252-1.5748 0.3750 3.62 2.0821 1.8339-1.2936 0.4466 5.61 1.7214 2.2183-1.2001 0.3617 1.87 2.2342 1.7180-1.3268 0.5535 3.78 2.3748 1.4294-1.2290 0.6103 5.92 2.2933 1.6715-1.1964 0.5964
12 Fig. 2 Master Curve for 25mm + PG 58-22 Mixtures The complex plane, called as Cole and Cole plane, is plotted by the storage modulus(e 1 ) to the real axis and the loss modulus(e 2 ) to the imaginary axis. The plotted values form a unique curve, which is independent of frequency or temperature. This allows assessment of the quality of the test data but mainly at intermediate and low temperature. To assess the quality of data at high temperatures, the Black space provides a better way of inspecting the data. In the Black space, the modulus values are plotted in log space and phase angle in arithmetic space. It allows one to estimate the pure elastic component of the complex modulus at very low temperature. Fig. 3 and Fig. 4 show one of the complex plane and the black space. In case of complex plane, the reliability of test data has the range of about 74% to 85%. In case of Black space, the reliability of test data has the range of about 80% to 88%.
13 Fig. 3 Complex Plane for 19mm-PG58-22, 4% Air Void Fig. 4 Black Space for 19mm-PG58-22, 4% Air Void Predictive Equations The dynamic modulus predictive equation developed through research by Witczak and colleagues at the University of Maryland over the last 30 years is one of the most comprehensive mixture stiffness models available to the profession today. This model has the capability to
14 predict the dynamic modulus of asphalt mixtures over a range of temperature, rates of loading, and aging conditions from information that is readily available from material specifications or volumetric design of the mixture. The initial set of predictive equations for the dynamic modulus of asphalt mixtures were developed by Shook and Kallas (1969) of the Asphalt Institute. Fonseca and Witczak(1996) expanded the model to include the effects of mixture aging revised (Andrei et al., 1999) to incorporate the effect of modified binders to the model. Equation presents the current form of the predictive equation. It is based on over 2800 dynamic modulus measurements from about 200 different asphalt mixtures tested in the laboratories of the Asphalt Institute, the University of Maryland, and the Federal Highway Administration. log E * 0.802208V V eff = 1.249937 + 0.029232( P + V a eff 200 3.871977 0.0021( P + 1+ e ) 0.001767( P 200 ) 2 4) + 0.003958( P38) 0.000017( P38) ( 0.603313 0.313351log( f ) 0.393532logη) 2 0.00284( P ) 0.086097( V ) 4 a + 0.00547( P 34 ) where: E* = dynamic modulus, 10 5 psi; = bitumen viscosity, 10 6 poise; f V a = load frequency, Hz; = air voids in the mix, % by volume; V eff = effective bitumen content, by volume; P 34 = cumulative % retained on 19mm sieve P 38 = cumulative % retained on 9.5mm sieve P 4 = cumulative % retained on 4.76mm sieve
15 P 200 = % passing 0.075mm sieve Table 6 shows the binder input data for the equation. The A and VTS parameters are the intercept and slope of the temperature susceptibility line of the binder and are needed in the Witczak et al. equation. Table 4 shows the aggregate gradation of the mixtures that are needed in the Witczak et al equation. Gradation is given in the form of percent retaining for 19.0mm(3/4in), 9.5mm(3/8in), and 4.75mm(No. 4) sieves as the predictive equation is expecting. Sieve size of 0.074mm (No. 200) is given in percent passing. Fig. 5 represents the comparison of predicted dynamic modulus using Witczak equation and measured dynamic modulus at each test temperature. Judging from the results, the predicted dynamic modulus is a little higher than the measured values at high temperature and lower than the values at low temperature. This is the reason why the gradation and shape of aggregate and the properties of asphalt binder is different from the specification of USA. AC G b Specific Gravity Table 6. Binder Data for the Predictive Equations A (RTFO aged) VTS (RTFO aged) T 800 ( ) T 1 ( ) Pen(T 1 ) 0.1mm PG58-22 1.032 10.807-3.6244 45 25 58 PG64-16 1.034 10.833-3.6317 47 25 47 Table 7. Input Aggregate Gradation for Witczak et al. Equation P 34 P 38 Gradation % retained % retained % retained % retained DGM-13mm 0 13.7 16.5 7 2.648 DGM-19mm 2.5 12.6 14.9 5 2.648 BGM-25mm 13 35.0 51.0 4.0 2.621 P 4 P 200 G sb
16 The Witczak equation should be modified and simplified in using Korean Pavement Design Guide, even though only limited test results for dynamic modulus existed. In order to modify and simplify the predictive equation, the parameters for Witczak equation have been investigated and eliminated based on statistical approach(brigison & Roque, 2005). D is the minimum value for dynamic modulus and a function of P 200, P 4, V a, and V V eff eff + V a. A is the maximum value and a function of gradation of aggregate, like P 4, P 34 and P 38. B is a function of viscosity of asphalt binder and loading frequency. Based on the regression analysis of test results, the modified predictive equation has been suggested : * 0.828V eff log E = 1.25 + 0.016( P200 ) 0.0031( P4 ) 0.0823( Va ) V + V eff a 3.851 0.0021( P4 ) + 0.00361( P38) + 0.00611( P + ( 0.65 0.241log( f ) 0.191log( η) 1+ e ) 34 ) Based on the predictive equation, all the dynamic modulus for predicted and measured values are plotted, as shown in Fig. 6. Even though the data is scattered, the plotted values showed 2482.3 MPa of standard deviation. The plotted values showed slightly underestimated at all the test temperature.
17 Fig. 5 Comparison of Measured and Predicted Dynamic Modulus by Witczak Fig. 6 Comparison of Measured and Predicted Dynamic Modulus by Modified Equation Sensitivity Analysis The basic relationship between predictive equation and its parameters has been carried out. Fig. 7 shows the change of loading frequency, such as 1, 4, 16, and 25 Hz, with the change of
18 asphalt binder viscosity. At low temperature, dynamic modulus is not affected very much due to the change of loading frequency and binder viscosity. Fig. 8 represents the effects on the change of test temperature for dynamic modulus. Test temperature is one of the big factors to change dynamic modulus. Dynamic modulus increases as test temperature decreases. Shift factor for developing the master curve has been calculated. It is 2.20 for shift from 0.1 Hz to 16 Hz at reference temperature, 21 o. Below is based on the viscosity of asphalt binder. Both values are very closed. α = 1.037(10 ( A+ VTS log(70+ 459.6) ( A+ VTS log(40+ 459.6) ) 10 ) = 2.11 Fig. 9 is showed the effect on the change of air void. As shown in Fig. 9, dynamic modulus increases as air void decreases. Judging from the results, the effect of air void change is a big factor for dynamic modulus of asphalt mixtures. Fig. 10 is represented the effect of maximum aggregate size. As can be seen, the effect of aggregate size is not more significant than the change of other factors, such as air void and test temperature. Fig. 7 Viscosity and Predicted Dynamic Modulus
19 Fig. 8 Loading Frequency and Dynamic Modulus Fig. 9 Air Void and Dynamic Modulus Fig. 10 Maximum Aggregate Size and Dynamic Modulus
20 Summary and Conclusion This paper involved the dynamic modulus of hot mix asphalt with granite aggregate, which is highly common in Korea. The master curve for each mixtures was fitting sigmoidal function through the compressive dynamic modulus test using non-linear least square regression. The reduced time was determined by Experimental shifting method. The experimental shifting method included solving all shift factors simultaneously with the coefficients of the sigmoidal function, without assuming any functional form for relationship of a(t) versus temperature. The following conclusion can be drawn from the tests : Under a constant load frequency, the dynamic modulus decreases with the increase in test temperature for the same mixture, while the phase angle increases with the increase in test temperature from -10 to 21. However, at 40 and 55 the phase angle decreases with the increase in test temperature. Under a constant test temperature, the dynamic modulus increases with the increase of test frequency and the phase angle generally shows the opposite trend. The softest asphalt (PG 58-22) had the lowest dynamic modulus. The mixtures with stiffer asphalt (PG 64-16) had higher dynamic modulus values. Also, the activation energy, shift factor, and the coefficient of sigmoidal function were determined for the use of Korean Design Guide, which is under developing. The complex plane, called as Cole and Cole plane, allows assessment of the quality of the test data but mainly at intermediate and low temperature. To assess the quality of data at high temperatures, the Black space provides a better way of inspecting the data. In case of complex plane, the reliability of test data has the range of about 74% to 85%. In case of Black space, the reliability of test data has the range of about 80% to 88%.
21 Dynamic modulus was predicted by Witczak equation. Judging from the calculated values, the predicted dynamic modulus is lower than the measured values at high temperature and higher than the values at lower temperature. References Andrei, D., Witczak, M. W., & Mirza, M. W., Development of Revised Predictive Model for the Dynamic Complex Modulus of Asphalt Mixtures, NCHRP 1-37A, Interim Team Technical Report, Dept. of Civil Eng., Univ. of Maryland of College Park, MD, 1999. AASHTO 2002 Design Guide Draft - 2.4, Modulus of Elasticity for Major Material Groups, NCHRP Project 1-37A. Brigison, B. and Roque, R. (2005), "Evaluation of the Gradation Effect on the Dyanmic Modulus", TRB 1929, pp. 193-199 Fonseca, O. A. and Witczak, M. W., "A Prediction Methodology for the Dynamic Modulus of In-Place Aged Asphalt Mixtures", Proceedings of Association of Asphalt Paving Technologists, Volume 65, 1996. Mohammad, L., Wu, Z., Myers, L., Cooper, S. & Abadie, C. (2005), "A Practical Load at the Simple Performance Tests : Louisiana's Experiences", AAPT, pp. 557-600
22 Pellinen, T. K., "Investigation of the Use of Dynamic Modulus as an Indicator of Hot Mix Asphalt Performance", Dissertation, Arizona State University, May 2001, 803 pages. Pellinen, T. K., Witczak, M. W., & Bonaqusit, R., "Master Curve Construction Using Sigmoidal Fitting Function with Non-linear Least Squares Optimization Technique", Proceedings of the 15th ASCE Engineering Mechanics Division Conference, Columbia University, June 2-5, 2002, New York. Pellinen, T. K. and Witczak, M. W., Stress Dependent Master Curve Construction for Dynamic (Complex) Modulus, Proceeding of the Association of Asphalt Paving Technologists, 2002a, Vol. 71, 281-309. Pellinen, T. K., and M. W. Witczak, "Use of Stiffness of Hot-Mix Asphalt as a Simple Performance Test", Transportation Research Board (TRB) 2002 Annual Meeting, Washington, D.C. Shook, J. F. and Kallas, B. F., Factors Influencing Dynamic Modulus of Asphalt Concrete, Proceedings of the Association of Asphalt Paving Technologists, 1969, Vol. 38 Williams, M. L., Landel, R. F., and Ferry, J. D., "The Temperature Dependence of Relaxation Mechanism in Amorphous Polymers and Other Glass-Liquids," J. of Am. Chem. Soc., Vol. 77, 1955, p. 370.