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## Material Information- Title:
- COMPLEX MODULUS FROM INDIRECT TENSION TESTING
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- 2008
## Subjects- Subjects / Keywords:
- Asphalt ( jstor )
Data analysis ( jstor ) Data smoothing ( jstor ) Datasets ( jstor ) Dynamic modulus ( jstor ) Phase angle ( jstor ) Poisson ratio ( jstor ) Sine function ( jstor ) Specimens ( jstor ) Test data ( jstor )
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PAGE 1 COMPLEX MODULUS FROM INDIRECT TENSION TESTING By JAE SEUNG KIM 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 2002 PAGE 2 ii ACKNOWLEDGMENTS I would like to thank my adviser, Dr. Reynaldo Roque. He always listened and respected my opinion. All tasks were accomplished under his support and guidance. I would like to offer heartfelt gratefulness and respect to him. I will never forget his help. I also would like to thank the other members of my committee, Dr. Bjorn Birgisson and Dr. Mang Tia. I appreciate their advice. I would like to thank Booil Kim, whose advice and knowledge helped me to complete my task. I would like to thank D. J. Swan for generous help. I also would like to thank Sungho Kim and Hong J. Kim for their friendship and encouragement. I wish to thank everyone in the Materials Group at University of Florida. Finally, I would like to thank my parents. They always gave me endless trust, encouragement, and support. PAGE 3 iii TABLE OF CONTENTS page ACKNOWLEDGMENTS...................................................................................................ii LIST OF TABLES.............................................................................................................vi LIST OF FIGURES...........................................................................................................vii ABSTRACT....................................................................................................................... ix CHAPTERS 1 INTRODUCTION...........................................................................................................1 1.1 Background...............................................................................................................1 1.2 Objectives................................................................................................................. .2 1.3 Scope...................................................................................................................... ...2 1.4 Approach................................................................................................................... 3 2 LITERATURE REVIEW................................................................................................4 2.1 Indirect Tensile Test..................................................................................................4 2.2 Superpave IDT..........................................................................................................4 2.3 Complex Modulus using Superpave IDT..................................................................5 2.4 Review for Complex Modulus from Past Study.......................................................5 2.4.1 Concept of Dynamic Modulus........................................................................5 2.4.2 RILEM Report for Bituminous Binders and Mixes........................................6 2.4.3 WitczakÂ’s Predictive Equation of Dynamic Modulus.....................................8 2.4.4 Hollow Cylinder Tensile Tester......................................................................8 3 MATERIAL AND METHODS....................................................................................10 3.1 Specimen Preparation..............................................................................................10 3.2 Equipment...............................................................................................................11 3.3 Test Procedure.........................................................................................................12 PAGE 4 iv 4 DEVELOPMENT AND EVALUATION OF ANALYTICAL METHOD..................13 4.1 Introduction.............................................................................................................13 4.2 Conventional Analysis Method...............................................................................14 4.2.1 Regression Method........................................................................................14 4.2.2 Assessment of Regression Method................................................................15 4.3 Examination of Alternatives....................................................................................17 4.4 Development of Functions to Determine Properties from Complex Modulus Test Using Gaussian Kernel Window Smoothing..........................................................18 4.4.1 Basic Concept of Gaussian Kernel Window Smoothing...............................18 4.4.2 Development of a Function to Find Coefficient Â“aÂ”.....................................20 4.4.3 Development of a Function to Find Maximum or Minimum Points.............22 4.4.4 Development of a Function to Determine Phase Angle and Magnitude between Rising Deformation Curve and Level Loading Curve....................25 4.4.5 Flow Diagram of Developed Functions Using Gaussian Kernel Window Smoothing.....................................................................................................27 4.5 Comparison between Conventional Regression and Peak Smoothing....................27 4.5.1 Comparison of Results from Computer-Simulated Data...............................28 4.5.2 Preparation of Methodology for Comparing Analysis Results by Both Methods from Real Data................................................................................30 4.5.3 Comparison of Results from Real Data.........................................................31 4.6 Summary of Results................................................................................................37 5 SOFTWARE DEVELOPMENT...................................................................................39 5.1 Data Initialization....................................................................................................39 5.2 Intermediate Calculation.........................................................................................40 5.3 Final Calculation of Dynamic Properties................................................................40 5.3.1 Normalization Factors...................................................................................41 5.3.2 Trimmed Mean Deformation and Trimmed Mean Phase Angle...................42 5.3.3 PoissonÂ’s Ratio Calculated for Data Set........................................................43 5.3.4 Average PoissonÂ’s Ratio...............................................................................44 5.3.5 Correction Factors.........................................................................................44 5.3.6 Horizontal and Vertical Moduli of E*, EÂ’ and EÂ”.........................................44 5.4 Output of Program...................................................................................................45 6 EVALUATION OF COMPLEX MODULUS DATA ANALYSIS PROGRAM........46 6.1 Evaluation of Test Results.......................................................................................46 6.2 Evaluation of Data Reduction.................................................................................48 6.3 Comparison between Normalized Dynamic Moduli...............................................49 7 CLOSURE..................................................................................................................... 52 7.1 Summary of Findings..............................................................................................52 7.2 Conclusions.............................................................................................................52 7.3 Recommendations...................................................................................................53 PAGE 5 v APPENDIX A COMPARISION OF DATA ANALYSIS RESULTS BETWEEN TWO METHODS........................................................................................................54 B OUTPUT OF 0.333 Hz.................................................................................................67 C OUTPUT OF 1 Hz........................................................................................................71 D OUTPUT OF 4 Hz.......................................................................................................75 E OUTPUT OF 8 Hz........................................................................................................79 F DATA ANALYSIS RESULTS OF HORIZONTAL DYNAMIC PROPERTIES.......83 LIST OF REFERENCES..................................................................................................94 BIOGRAPHICAL SKETCH............................................................................................96 PAGE 6 vi LIST OF TABLES Table page 3-1. Mix design after wagoner (2001)..................................................................................11 3-2. Test parameters of Superpave IDT...............................................................................12 4-1. Analysis results of both methods for computer-simulated data....................................30 PAGE 7 vii LIST OF FIGURES Figure page 2-1. Dynamic modulus versus frequency after RILEM Report (1998) ............................... 7 2-2. Dynamic modulus versus temperature after RILEM Report (1998)............................. 7 2-3. Dynamic modulus versus phase angle after RILEM Report (1998)............................. 8 4-1. Deformation curve from actual data.............................................................................13 4-2. Process of conventional regression method..................................................................14 4-3. Typical loading signal at high frequency......................................................................15 4-4. Non-symmetric sinusoidal curve simulation.................................................................16 4-5. Basic concept of gaussian kernel window smoothing...................................................19 4-6. Concept of number of band widths...............................................................................20 4-7. Seven types of irregular data.........................................................................................21 4-8. Determination of maximum or minimum Point...........................................................23 4-9. Function to find maximum or minimum peak point.....................................................24 4-10. Non-linear deformation problem................................................................................26 4-11. Flow diagram of new developed method....................................................................28 4-12. Generating computer-simulated data..........................................................................29 4-13. Problems associated with non-uniform loading or non-homogeneous material properties...................................................................................................................31 4-14. Comparison of E* from both methods at 0.333 Hz....................................................32 4-15. Comparison of E* from both methods at 0.5 Hz........................................................33 4-16. Comparison of E* from both methods at 1 Hz...........................................................33 PAGE 8 viii 4-17. Comparison of E* from both methods at 4 Hz...........................................................34 4-18. Comparison of E* from both methods at 8 Hz...........................................................34 4-19. Comparison of phase angle from both methods at 0.333 Hz......................................35 4-20. Comparison of phase angle from both methods at 0.5 Hz..........................................35 4-21. Comparison of phase angle from both methods at 1 Hz.............................................36 4-22. Comparison of phase angle from both methods at 4 Hz.............................................36 4-23. Comparison of phase angle from both methods at 8 Hz.............................................37 4-24. Comparison of phase angle from both methods at all frequencies.............................38 4-25. Comparison of dynamic modulus from both methods at all frequencies....................38 6-1. Horizontal phase angle..................................................................................................4 7 6-2. Horizontal E*............................................................................................................ ....47 6-3. Horizontal EÂ’............................................................................................................ .....48 6-4. Horizontal EÂ”............................................................................................................ ....48 6-5. Normalized dynamic modulus......................................................................................51 PAGE 9 ix 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 COMPLEX MODULUS FROM INDRECT TENSION TESTING By Jae S. Kim May 2002 Chair: Dr. Reynaldo Roque Cochair: Dr. Bjorn Birgisson Department: Civil and Costal Engineering Due to its mechanistic characteristics, the complex modulus is replacing the current resilient modulus as new modulus to characterize asphalt mixture for design of interstate highway and most other high volume facilities. Although it would be of great practical value to obtain the complex modulus from indirect tension testing, the complex modulus has generally been obtained from uniaxial compression or tension tests. There is a clear need to develop and evaluate testing and analysis procedures to determine the complex modulus from indirect tension tests. The Superpave indirect tension test (IDT) was selected for this purpose. This test has been used successfully to measure creep compliance, tensile strength, and resilient modulus. The test and analysis procedures developed for the Superpave IDT were designed to overcome problems typically associated with conventional indirect tension testing systems. PAGE 10 x Data reduction and interpretation procedures were developed and evaluated in this study to obtain complex modulus parameters (i.e., dynamic modulus and phase angle) from the Superpave IDT. It was determined that conventional regression methods can overestimate the true phase angle where asymmetric dynamic loads are applied. Asymmetric loading may sometimes be inevitable at higher loading frequencies, particularly when testing in indirect tension. A procedure that incorporates a gaussian kernel smoothing method was developed to overcome this potential problem. It was shown that complex modulus parameters determined with this method appeared to be accurate and exhibited appropriate trends with respect to loading frequency. In addition, values obtained from limited testing with the Superpave IDT appeared to be reasonable. Automated software was developed from analysis of complex modulus data from Superpave IDT tests. PAGE 11 1 CHAPTER 1 INTRODUCTION 1.1 Background Since the 1960s, many researchers have studied the complex modulus (dynamic modulus and phase angle) of asphalt mixtures. That is because the complex modulus has the potential of providing information and properties that are more suitable for mechanistic analysis and design of pavements. Many states are inclined to implement dynamic modulus for design and specification, but the test needs to be further refined. In NCHRPÂ’s (National Cooperative Highway Research Program) 2002 Guide, the dynamic modulus was adopted as input level 1, which represents a design approach philosophy of the highest practically achievable reliability for asphalt concrete. The Asphalt Institute has adopted the dynamic modulus as the choice test to measure modulus. So, the dynamic modulus is being widely cited for characterizing asphalt concrete mixture in airfield and highway design procedures. Furthermore, AASHTOÂ’s (American Association of State Highway and Transportation Office) upcoming 2002 Guide for design of pavement structures is planning to use the dynamic modulus to characterize mixture for interstate highway and most other high volume facilities. Therefore, it is important to understand all aspects of the complex modulus test, and at the same time, set up the proper testing and analysis methods. The indirect tensile test has been used successfully to measure the resilient modulus of asphalt concrete mixture. The critical stress location by load is generally considered to be at the bottom of the asphalt concrete layer and immediately underneath PAGE 12 2 the load, where the stress state is longitudinal and transverse tension combined with vertical compression. The stress state in the vicinity of the center of the face of an indirect tension specimen is very similar to this stress state. Consequently, the complex modulus obtained by indirect tensile test can be expected to provide reasonable complex modulus as well. 1.2 Objectives The objective of the work was to develop and evaluate analysis and data reduction procedures to obtain complex modulus (dynamic modulus and phase angle) using Superpave IDT. The specific objectives were To establish suitable data acquisition procedures to determine dynamic modulus, phase angle, EÂ’ and EÂ” using the indirect tensile test. To identify appropriate data reduction procedures to determine dynamic modulus, phase angle, EÂ’ and EÂ” using the indirect tensile test. To develop a computer program to determine the dynamic modulus, phase angle, EÂ’, EÂ” and PoissonÂ’s ratio automatically using Superpave IDT data. To conduct an evaluation of the data reduction software using actual test data. 1.3 Scope The complex modulus (dynamic modulus and phase angle) test using the Superpave system was first attempted at University of Florida, so many expected and unexpected problems had to be overcome. Therefore, only a limited amount of reliable laboratory test data was obtained for evaluation. However, this thesis focused on identifying suitable interpretation techniques that could address the numerous problems or sources of error that can occur when obtaining data from this test. Many, if met all of these problems can be simulated with actual data. So, the accuracy of the analysis method was verified with virtual data created to emulate observed and expected problems. In PAGE 13 3 addition, data from Superpave IDT tests performed at multiple frequencies were analyzed to evaluate the method and software developed. 1.4 Approach The steps involved in the research approach may be summarized as follows. Identify problems associated with the determination of complex modulus using Superpave IDT. Identify and evaluate appropriate analysis methods to determine complex modulus. Choose the best analysis method suitable for current Superpave IDT. Develop suitable data reduction and analysis procedures to determine complex modulus form IDT data. PAGE 14 4 CHAPTER 2 LITERATURE REVIEW 2.1 Indirect Tensile Test The indirect tensile test or diametral compression test is conducted by applying compressive loads with a haversine or other suitable waveform. The load is applied vertically along the vertical diametral plane of a cylindrical specimen of asphalt concrete. Roque and Ruth (1987) showed that modulus values determined by indirect tensile test resulted in excellent prediction of strain and deflection measured on full-scale pavements at low in-service temperatures (<30 C (86 F)) when the modulus was used in elastic layer analysis. At present, the Superpave IDT is used for determining the resilient modulus, tensile strength and creep compliance at lower temperature. 2.2 Superpave IDT The Superpave IDT was developed by Roque and Buttlar (1992), and Buttlar and Roque (1994) under the Strategic Highway Research Program. In their paper, they pointed out that accurate properties could not be obtained from the indirect tensile test without measuring accurate PoissonÂ’s ratio. In order to measure accurate PoissonÂ’s ration, Roque and Buttlar suggested two main recommendations. One was to revise the LVDT mounting system and the other was to consider the effect of specimen bulging effect through three dimensional finite element analysis. The testing procedure and analysis equations resulting from their work are being used for the Superpave IDT, which is required for higher level mixture designs in Superpave. Their procedure is listed in AASHTO TP-9, Â“Determining the creep compliance and strength of hot mix asphalt PAGE 15 5 (HMA) using the indirect tensile test deviceÂ”. Besides the creep compliance and strength, the Superpave IDT can be used to determine the resilient modulus of asphalt concrete. The resilient modulus from Superpave IDT results in more accurate and reasonable modulus values for asphalt concrete. Roque et al. (1997) completed the Superpave IDT software based on Roque and Buttlar (1992), and Buttlar and Roque (1994). They developed a trimmed mean approach to determine deformations of both faces, which enhanced accuracy for calculating resilient modulus using Superpave IDT. 2.3 Complex Modulus using Superpave IDT Since the 1960Â’s, the complex modulus has been measured as a fundamental property by asphalt technologists (Papazian, 1962). As we know, bituminous materials display wide variations in properties depending on temperature, loading magnitude, loading time and loading frequency. As mentioned in Chapter 1, because of the relative complexity of the test, the dynamic modulus is generally considered to be more reasonable for evaluation and design of highway or high volume facilities. However, there are no acceptable testing or data interpretation methods to determine the complex modulus using the Superpave IDT. 2.4 Review for Complex Modulus from Past Study 2.4.1 Concept of Dynamic Modulus In order to prevent any confusion, the complex modulus and the dynamic modulus have to be clearly discriminated. After performing the complex or dynamic modulus test, two factors are generally obtained. One is dynamic modulus, which is the ratio between stress and stain amplitudes, and the other is phase angle. The load typically applied in the complex modulus test is used as continuous sinusoidal. The sinusoidal loading function is expressed as = 0eit, in which 0 is stress amplitude and is PAGE 16 6 frequency, which is the same as 2 (where is cycles per second). At the same time, the reaction to the stress was expressed as strain: = 0ei(t-) in which 0 is strain amplitude and is phase angle associated with damping of viscoelastic material. Therefore, the basic modulus equations are as follows: Modulus Loss or Modulus Complex of Parts Imaginary : " Modulus Storage or Modulus Complex of Parts Real : ' Modulus Dynamic : * Angle Phase : Modulus Complex : * : ) sin * " , cos * ' ( " ' * ) sin (cos * * *0 0E E E E where E E E E E i E E i E e E e Ei i 2.4.2 RILEM Report for Bituminous Binders and Mixes RILEM is one of the most active international research related organizations. They have done a lot of tests on Bituminous Binder and Mixture since 1987. Francken (1998) shows the approximate trend of complex modulus test parameters. Figure 2-1 to Figure 2-3 show typical relationships between dynamic modulus, phase angle, frequency and temperature. The examples presented in these figures were used for a standard French semi-granular bituminous mixture (5.4 % binder) in the two-point bending test on trapezoidal specimens in the uniaxial tension-compression test. Their research on complex modulus may be summarized as follows. Dynamic modulus decreases as temperature increases. Dynamic modulus increases as frequency increases. Phase angle decreases as frequency increases (for temperatures below 40 C). Phase angle increases as temperature increases (for temperatures below 40 C). PAGE 17 7 Figure 2-1. Dynamic modulus versus frequency after RILEM Report (1998) Figure 2-2. Dynamic modulus versus temperature after RILEM Report (1998) PAGE 18 8 Figure 2-3. Dynamic modulus versus phase angle after RILEM Report (1998) 2.4.3 WitczakÂ’s Predictive Equation of Dynamic Modulus Witczak has performed a lot of dynamic modulus tests since 1967. He developed several predictive equations based on dynamic modulus test results. An equation developed in 1989 is representative of his work. The dynamic modulus tests (Witczak et al., 1989) were conducted on 149 separate asphalt mixes. The test method was uniaxial test such as triaxial compression without confining stress test as specified by ASTM D3497. Based on the equation (Witczak et al, 1989), the following conclusions can be obtained. Dynamic modulus decreases as temperature increases. Dynamic modulus increases as frequency increases. 2.4.4 Hollow Cylinder Tensile Tester Buttlar et al. (1999) developed a hollow cylinder tensile test for dynamic modulus of asphalt concrete. The basic principle of the test is to apply internal pressure to the inner cavity of a hollow cylinder specimen, which results in circumferential tension. PAGE 19 9 Applied stress is linearly related to applied pressure, and the resulting strain is linearly related to cavity volume change, which can be directly measured using strain gages. The reason for considering their test was to have an alternative to the IDT or direct tension test. Test results were well correlated with WitczakÂ’s predictive equation. PAGE 20 10 CHAPTER 3 MATERIAL AND METHODS The purpose of this work was to identify and overcome problems associated with the performance and interpretation of complex modulus tests performed with the Superpave IDT. This included the identification of a suitable data reduction and analysis method. The work also included development of computer software for automated data reduction and analysis. The system was used to evaluate the results of laboratory tests conducted by Wagoner (2001). The sample and test methods used by Wagoner are summarized below. 3.1 Specimen Preparation The mixture preparation procedure is outlined in AASHTO T-283. First, the aggregates and asphalt binder were heated to 150 C (300 F) for three hours prior to mixing. Once the mixing was completed, the mixture was allowed to cool to room temperature for two hours. After the cooling period, the loose mixture was long term aged for 16 hours at 60 C (140 F). After the mixture was aged for 16 hours, it was reheated to 135 C (275 F) for two hours before compaction. The specimens were then compacted on the Superpave gyratory compactor. The compacted specimen size was 100 mm diameter by 100 mm high. The specimens were then cut by a wet saw for IDT testing. The mixture used in the complex modulus test from Superpave IDT is listed in Table 3-1 PAGE 21 11 Table 3-1. Mix design after wagoner (2001) Material type FDOT code Producer Pit No. Milled Material 29180-3446 Top 5.45" N.B. & S.B. Roadway #7 Stone 52 Martine Maretta Aggregates GA-185 #89 Stone 51 Martine Maretta Aggregates GA-185 Anderson screens 20 Anderson Mining Corp. 29-361 Material 1 2 3 4 Job mix formula Blend 15% 20% 40% 25% Sieve size 1" 100% 100% 100% 100% 100% 3/4" 100% 100% 100% 100% 100% 1/2" 100% 90% 100% 100% 98% 3/8" 100% 48% 99% 100% 89% 4" 84% 3% 29% 87% 47% 10 62% 2% 3% 65% 27% 40 39% 2% 2% 36% 16% 80 25% 1% 2% 19% 10% 200 9.60% 1% 1% 6% 4% SP.GR. 2.62 2.72 2.72 2.36 2.606 Optimum AC= 5.70% AC from milled material= 0.90% Recycling AC= 4.80% Gmm= 2.470 Note: Asphalt cement was AC-30 3.2 Equipment The complex modulus test was conducted using Superpave IDT. The overall testing system includes MTS loading system, measurement, and data acquisition system. A brief description of each component follows: Loads were controlled using a MTS 810 Material Testing System. The data acquisition system used was Labtech Notebook Pro software. The measurements were obtained using extensometers designed by MTS specifically for use with the Superpave IDT. The method used to attach the extensometers to specimen was the same as that specified with Superpave IDT (Roque et al., 1997) a gage length of 1in was used for all specimens. All tests were performed at room temperature, so we did not use the temperature control system specified in Superpave IDT or AASHTO TP-9. PAGE 22 12 3.3 Test Procedure The complex modulus test was performed in load control mode by applying repeated and continuous sinusoidal load at a specified frequency. The load was selected to keep the horizontal strain in the linear viscoelastic range (typically below a horizontal strain of 350 ) during test (Buttlar and Roque, 1994). The tested parameters are listed in Table 3-2. The procedures for indirect tensile complex modulus are summarized in the following steps: 1. Four brass gage points (5/16-inch diameter by 1/8-inch thick) were affixed with epoxy to each specimen face. 2. Extensometers were mounted on the specimen. Horizontal and vertical deformations were measured on each side of the specimen. 3. The test specimen was placed into the load frame. A seating load of 10 to 30 pounds was applied to the test specimen to ensure proper contact of the upper loading head. 4. The specimen was loaded by applying a repeated and continuous sinusoidal load to obtain horizontal strains below 350 . 5. When the applied load was determined, the computer software began recording test data. Table 3-2. Test parameters of Superpave IDT Frequency (Hz) 0.333 0.5 1 4 8 Material SP-2 SP-2 SP-2 SP-2 SP-2 Temperature Room temp. Room temp. Room temp. Room temp. Room temp. Load (lbf) 373.45 398.46 446.91 647.93 645.82 Thickness (in) 2.5 2.5 2.5 2.5 2.5 Diameter (in) 4 4 4 4 4 PAGE 23 13 CHAPTER 4 DEVELOPMENT AND EVALUATION OF ANALYTICAL METHOD 4.1 Introduction As indicated in Chapter 1, analysis of complex modulus data by hand has obvious limitations. Figure 4-1 shows that actual deformation measurements can have significant noise caused by electronic or mechanical vibration, the impact of loading force, or the reaction of the material. It is very hard to choose the maximum or minimum points of the deformation from these irregular curves. Therefore, the analysis is subjective and susceptible to user errors. To solve this problem, we absolutely need to set up a consistent data reduction and analysis procedure. Several methods were considered and evaluated. A summary of each method is presented in the following section. 8hz test (Example) 80 100 120 140 160 180 200 8.999.19.29.3 Time(sec)Deformation(mils) Figure 4-1. Deformation curve from actual data PAGE 24 14 4.2 Conventional Analysis Method 4.2.1 Regression Method One of the most popular methods used to interpret complex modulus data is the regression method. The regression method determines least-fit coefficients for a specified function by minimizing the least square error between the function and the measured data. Zhang et al. (1997) assumed the deformation data to follow a sine function superimposed on a linear function and the load data to follow a sine function. The deformation amplitude and phase angle were obtained as regression coefficients. It is conventional to find a phase angle and E* by the regression method. Figure 4-2 shows the process of finding the angle and amplitude. Figure 4-2. Process of conventional regression method PAGE 25 15 4.2.2 Assessment of Regression Method The merit of the regression method is that it is the most efficient method when an assumed equation and real data are well matched. However, errors increase as discrepancies between the assumed function and the real data increase. The regression method can be of particular concern in a sensitive test such as complex modulus. Figure 4-3 shows the measured loading shape when a testing frequency of 20 Hz was used in the Superpave IDT. In this case, the loading curve is not perfectly sinusoidal and since the deformation curve is determined by a loading curve, then it will also not be sinusoidal. It may be expected that tests performed on asphalt mixtures over a range of temperature, particularly with the Superpave IDT, may not result in perfect sinusoidal curves, especially at higher frequency. One reason is the inertia forces of the loading head increase as the loading frequency increases so, that the loading control system of testing machine may not be able to control the loading curve perfectly. 20Hz (random selection)0 50 100 150 200 250 300 47.984848.0248.0448.06 TimeLoad(lbf) Figure 4-3. Typical loading signal at high frequency PAGE 26 16 If the crooked sinusoidal curve were symmetric, there would be no problem in applying the regression method. However, as shown in Figure 4-3, the signal is not symmetrical. Therefore, the calculated value of phase angle is bigger than that of actual phase angle. This point can be easily made through computer simulation. In fact, a complete series of simulations were conducted to evaluate the effects of these types of errors on determination of complex modulus parameters using different methods. All computer simulations presented herein were performed by Mathcad. The signal in Figure 4-4 was generated by assuming the error in the sine wave was larger at the bottom than at the top of signal. Although it looks like a sine curve, it is not a sine curve. It was made by combining two quadratic functions. Both of the curves have the same function except for the phase angle, which was exactly 20 , so the expected value of the phase angle was also 20 . The table from Figure 4-4 shows the value of the phase angle found using the regression method was 22.05 . Therefore, it appears the regression method can result in significant errors for less than perfect data. Figure 4-4. Non-symmetric sinusoidal curve simulation PAGE 27 17 4.3 Examination of Alternatives To overcome this potential problem, two analysis methods were considered. One is the filtering method and the other is the smoothing method. In case of the filtering method, Fast Fourier Transform was chosen, and in case of the smoothing method, gaussian kernel smoothing method was chosen. The characteristics of both methods are described below. Fast fourier transform . FFT (Fast Fourier Transform) is based on DFT (Discrete Fourier Transform) algorithm. As reduced the number of computations of DFT, the DFT was improved as the FFT, which is much faster than the DFT. The FFT essentially decomposes or separates a waveform or function into sinusoids of different frequency. Consequently, extraneous frequencies of waveform or function can be eliminated using FFT. In spite of a lot of merits, FFT exposed many problems for analyzing complex modulus test data because FFT mainly used for signal analysis, so for complex modulus test, where it can be difficult to control even main the frequency, it resulted much greater problems than the regression method. Also, it is hard to discriminate real noise from the irregular deformation curve. In other words, some of noise may be true response, which should not be filtered. Gaussian kernel window smoothing . Gaussian kernel window smoothing uses local weighted averages of the vertical data to compute. This smoother function is most useful when data lies along a band of relatively constant width. Fortunately, the data from IDT have very constant width, and the result of application of this method showed very good quality. One of the major advantages of this method is that it can be applied to any curve including a curve resulting from an arbitrary function (i.e., having irregular data). However, this method also has problems. This method is not immediately suitable for PAGE 28 18 automated programming because a user has to determine the band width number for analysis. From evaluation of both methods, the gaussian kernel window smoothing method was determined to be a more suitable method to analyze the complex modulus test data. Although it has some problems, those problems can be overcome using programming skills. 4.4 Development of Functions to Determine Properties from Complex Modulus Test Using Gaussian Kernel Window Smoothing The following these steps were used to determine phase angle and dynamic modulus from complex modulus test data. 1. The gaussian kernel window smoothing method was applied to smooth irregular data or noise automatically and effectively from complex modulus test results. 2. Specific functions were developed to identify maximum or minimum data points from each cycle. 3. Specific functions were developed to accurately determine phase angle and amplitude from the maximum or minimum data points. 4.4.1 Basic Concept of Gaussian Kernel Window Smoothing As mentioned, the gaussian kernel window smoothing uses a local weighted average of input n-element vertical data to compute. A smooth function is only available when the horizontal data have a regular number band width. Once the number of band widths is determined, the gaussian kernel window smoothing function finds new vertical data, which depends on the number of band widths. Figure 4-5 shows the basic concept of gaussian kernel window smoothing method. The number of band width is represented by the symbol, b. PAGE 29 19 Figure 4-5. Basic concept of gaussian kernel window smoothing The key input required by the gaussian kernel window smoothing method is the number, Â“a,Â” which dictates how many ranges will be included when computing the gaussian kernel window smoothing function. According to the number, a, the result of gaussian kernel window smoothing will be changed. Figure 4-6 shows the result of using different input numbers. For each set of data, there is an optimal Â“aÂ” that eliminates only noise and has minimal impact on the primary response. Lower or higher Â“aÂ” values result in unsatisfactory smoothing curves. PAGE 30 20 Figure 4-6. Concept of number of band widths 4.4.2 Development of a Function to Find Coefficient Â“aÂ” The main problem associated with the implementation of the gaussina kernel window smoothing method is the proper selection of the coefficient, Â“a.Â” In order to define in order to define the optimal value of, Â“a,Â” the different types of irregular data observed during the complex modulus test must be analyzed. Figure 4-7 shows several types of irregular data observed during the complex modulus test. These seven types of irregular data were obtained from the results of hundreds of actual data sets. PAGE 31 21 Figure 4-7. Seven types of irregular data Special routines were developed to check for the presence of the seven types of irregular data. The idea is that additional smoothing is required as long as irregular data are found. So, the value of Â“aÂ” is increased incrementally until the search routines find no irregular data in the signal. A computer routine was developed to accomplish this in a computationally efficient manner. Rather than checking the entire data set for irregular data at one time, overlapping groups of six data points are checked for irregular data, starting with the first six data points in the data set. Once the optimal value of a PAGE 32 22 determined for these first six points, the check is performed on the subsequent groups of six data points until no irregular data found in the entire data set. For example, data point numbers 1 through 6 are the first group checked, then data points 2 through 7 are the second group checked. This approach minimizes the number of checks that need to be made for irregular data. The steps involved in this automated gaussian kernel window may be summarized as follows: 1. Set a = 1. 2. Special routines check for presence of irregular data among the first of six data points. 3. If irregular data are found, then set a= a+1 and use gaussian kernel window function to smooth the data. 4. Repeat Steps 2 and 3 until no irregular data are found among the first group of six data points. 5. Repeat Steps 2 through 4 for subsequent groups of six data points until the end of the data set is reached. In the case of smoothing the loading curve, the data typically is either type 2 or type 3 because it is generally a smooth curve, and in the case of smoothing the deformation cure, all seven types can be encountered. 4.4.3 Development of a Function to Find Maximum or Minimum Points One of the merits of the gaussian kernel window smoothing is that can be applied to curves which have irregular data. However, function coefficients cannot be obtained directly from the gaussian kernel window smoothing function. It is simply a technique that arranges the irregular data smoothly. Another complexity is that the data acquisition system cannot obtain whole data points, in other words, when the data acquisition system typically record the test data at regular intervals. Consequently, there is generally some PAGE 33 23 difference between actual maximum or minimum data points and maximum or minimum data points obtained by simply smoothing the data. Figure 4-8 illustrates this point. Figure 4-8. Determination of maximum or minimum Point In order to find actual maximum or minimum data points, the regression method was used within a limited range. From the smoothed data, three maximum and minimum data points (see Figure 4-8) can be obtained from every cycle. The curve made up of the three data points is very small so that even if any functions were assumed, the difference in values obtained from any nonlinear functions is almost the same, as long as the assumed function passes through three maximum or minimum points. A quadratic function was assumed because the quadratic function can minimize time of computation. Figure 4-9 shows the procedure to find maximum or minimum point using limited PAGE 34 24 regression method assumed with a quadratic function. To find quadratic function coefficients, simple matrix and differential equation were used. Figure 4-9. Function to find maximum or minimum peak point PAGE 35 25 4.4.4 Development of a Function to Determine Phase Angle and Magnitude between Rising Deformation Curve and Level Loading Curve The phase angle between two level sine curves should be the same at top peak point as at bottom peak point. Also, the magnitude from level sine curve should be the same for the descending direction and rising direction. However, the phase angle between level sine curve and rising sine curve must be different at both top and bottom peak points, and also the magnitude of rising sine curve must be different between descending and rising directions. Figure 4-10 illustrates the problems. To find the correct phase angle between rising sine curve (deformation) and level sine curve (load) and the correct magnitude for the rising sine curve, at least two cycles are necessary. From the two cycles, one bottom phase angle and one top phase angle can be chosen. Also, one descending and rising magnitude can be chosen. Average angle of top and bottom phase angles and average magnitude of descending and rising magnitudes are exactly the same as the phase angle and magnitude from the conventional regression method as long as both curves are perfect sine curves. In summary: To determine phase angle and magnitude accurately, at least two cycles of loading curve and two cycles of deformation curve are necessary. The average of the top and bottom phase angles between loading curve and deformation curve is required to find the correct phase angle. The average magnitude of descending and rising deformation curves is required to find the correct magnitude. The complex modulus test data have many irregular data points or noise, so accurate values of phase angle and magnitude between loading curve and deformation curve cannot be expected with the functions above. The results of data analysis from the complex modulus test data indicated that the phase angle and magnitude between loading curve and deformation curve must be the average of several phase angles and magnitudes PAGE 36 26 from several cycles calculated using the functions above. The key in applying the functions below is the average value from too many cycles cannot be predicted on the change of phase angles and magnitudes and also, it is time consuming for calculation. Figure 4-10. Non-linear deformation problem Therefore, it is proper that five phase angles and magnitudes from 6 cycles calculated using the function below. A simple procedure to use the new function to determine phase angle and magnitude is as follows. To determine more accurate phase angle and magnitude, six cycles of loading curve and six cycles of deformation curve are necessary. 1. The average of five top phase angles and five bottom phase angles between loading curve and deformation curve from the six cycles is required to find accurate phase angle. 2. The average of five descending and rising magnitudes both loading curve and deformation curve from six cycles is required to find accurate magnitude. PAGE 37 27 3. Average of the averaged top and bottom phase angle is final phase angle. 4. Average of the averaged descending and rising magnitude is final magnitude. 4.4.5 Flow Diagram of Developed Functions Using Gaussian Kernel Window Smoothing Based on explanation above, the functions developed using gaussian kernel window smoothing method are described flow on the diagram presented in Figure 4-11. 4.5 Comparison between Conventional Regression and Peak Smoothing The newly developed method was named Â“peak smoothing method.Â” To confirm the accuracy of the peak smoothing method, two sets of data were used; computer simulated test data and real test data. An imaginary function composed of a sine function having a linear slope was used to generate the computer-simulated data. The two methods (conventional regression and peak smoothing) were applied to the same data range to evaluate accuracy and expected trends in both test data sets. In order to obtain the parameters, the following simple equations were used. PAGE 38 28 Figure 4-11. Flow diagram of new developed method 4.5.1 Comparison of Results from Computer-Simulated Data The deformation and load data from the complex modulus test were theoretically composed of sinusoidal curves. In case of the load data, a clean sine function was generated. In case of the deformation data, a sine function having a linear slope was generated. Additionally, the sine function having a linear slope was combined with another function to generate irregular data or noise. As illustrated in Figure 4-12, noise can be generated in either the horizontal or vertical direction. A function was used to generate random numbers. High random number means large noise. Figure 4-12 also shows the equations used to generate imaginary data. The following steps were used. PAGE 39 29 1. An imaginary load function composed of a sine function having constant height was generated. 2. An imaginary deformation function composed of a sine function having a linear slope, constant height, constant phase angle and randomly generated noise was generated. 3. An imaginary deformation curve was generated with a random number equal to zero (i.e., no randomly generated noise) 4. All data generated was analyzed using both methods: conventional regression and peak smoothing. 5. Compare and record the analysis results from both methods. 6. Repeat Steps 3 to 5 for increasing values of random numbers. The results of this effort are presented in Table 4-1. Figure 4-12. Generating computer-simulated data PAGE 40 30 Table 4-1. Analysis results of both methods for computer-simulated data Phase Angle First try Second try Random Number Wishful Answer Smoothing Regression Smoothing Regression 0 30 30 30 -1~1 30 30.047 29.852 29.95 30.124 -2~2 30 31.546 30.3 30.885 29.903 -3~3 30 29.916 30.02 : : -4~4 30 31.338 29.78 : : -5~5 30 31.015 30.095 : : -6~6 30 31.716 29.66 : : -7~7 30 28.035 29.27 : : -8~8 30 30.37 29.91 : : -9~9 30 29.787 29.032 : : Average 30.377 29.7919 Magnitude First try Second try Random Number Wishful Answer Smoothing Regression Smoothing Regression 0 40 40 40 -1~1 40 39.961 40.011 39.772 39.963 -2~2 40 39.717 39.886 39.519 40.154 -3~3 40 40.127 40.371 : : -4~4 40 40.768 39.975 : : -5~5 40 38.717 40.092 : : -6~6 40 40.056 40.287 : : -7~7 40 41.557 40.953 : : -8~8 40 39.23 40.475 : : -9~9 40 39.498 40.015 : : Average 39.9631 40.2065 Both methods showed good results so that the peak smoothing method appears to work well and to be as accurate as the conventional regression method. 4.5.2 Preparation of Methodology for Comparing Analysis Results by Both Methods from Real Data Problems associated with non-uniform loading or non-homogeneous material properties commonly occur in the Superpave IDT test specimens so that the deformation curves from each face are not complete sinusoidal curves having the same magnitudes. Consequently, the analysis results of conventional regression method and peak smoothing method are different because the analysis concepts of the two methods are different. Hence, the properties, phase angle, E*, EÂ’ and EÂ” cannot be compared directly for each PAGE 41 31 face. However, based on computer simulation and literature review, the average of the properties such as phase angle, E*, EÂ’ and EÂ” should be almost same as long as the load is perfectly sinusoidal. In other words, the average of deformations from both faces forms a complete sinusoidal curve when the loading curve was a sinusoidal curve. Figure 4-13 shows the results of computer simulation. Figure 4-13. Problems associated with non-uniform loading or non-homogeneous material properties 4.5.3 Comparison of Results from Real Data As stated earlier, the phase angles determined by the conventional regression method may not be accurate for testing Superpave IDT test results, because of the difficulties in achieving a symmetric loading signal. If the peak smoothing method could solve such a problem, then the Phase angles calculated by the two methods will be PAGE 42 32 different. Superpave IDT tests were performed at five loading frequencies: 0.33 Hz, 0.5 Hz, 1 Hz, 4 Hz, and 8 Hz. Phase angles and dynamic modulus were calculated using the average of the two horizontal deformation measurements. The same ranges were applied to both methods. Figure 4-14 to Figure 4-18 show the result of E* determined by each method and Figure 4-19 to Figure 4-23 show the result of phase angle analyzed by each methods. The results of each point were calculated from 10 cycles. As shown in Figure 4-14 and Figure 4-23, the dynamic moduli were almost the same for both methods at every frequency tested. However, the phase angles were not the same. As the frequency increased, the difference in phase angle between the two methods increased. It appears that the testing machine did not control loading frequency appropriately as the complex modulus test was performed at high frequencies. The testing machine generates an increasingly asymmetrical sinusoidal loading curve as the test frequency was increased. 0.333hz 0 50000 100000 150000 200000 250000 300000 01000200030004000 Time(sec)E*(psi) smoothing regression Figure 4-14. Comparison of E* from both methods at 0.333 Hz PAGE 43 33 0.5hz 0 5 10 15 20 25 30 35 050010001500 Time(sec)Phase angle(degree) smoothing regression Figure 4-15. Comparison of E* from both methods at 0.5 Hz 1hz 0 50000 100000 150000 200000 250000 300000 350000 400000 450000 050010001500 Time(sec)E*(psi) smoothing regression Figure 4-15. Comparison of E* from both methods at 1 Hz PAGE 44 34 4hz 0 100000 200000 300000 400000 500000 600000 700000 050010001500 Time(sec)E*(psi) smoothing regression Figure 4-16. Comparison of E* from both methods at 4 Hz 8hz 0 100000 200000 300000 400000 500000 600000 700000 800000 050100150 Time(sec)E*(psi) smoothing regression Figure 4-17. Comparison of E* from both methods at 8 Hz PAGE 45 35 0.333hz 0 5 10 15 20 25 30 35 01000200030004000 Time(sec)Phase angle(degree) smoothing regression Figure 4-18. Comparison of phase angle from both methods at 0.333 Hz 0.5hz 0 5 10 15 20 25 30 35 050010001500 Time(sec)Phase angle(degree) smoothing regression Figure 4-19. Comparison of phase angle from both methods at 0.5 Hz PAGE 46 36 1hz 0 5 10 15 20 25 30 050010001500 Time(sec)Phase angle(degree) smoothing regression Figure 4-20. Comparison of phase angle from both methods at 1 Hz 4hz 0 5 10 15 20 25 30 050010001500 Time(sec)Phase angle(degree) smoothing regression Figure 4-21. Comparison of phase angle from both methods at 4 Hz PAGE 47 37 8hz 0 5 10 15 20 25 30 050100150 Time(sec)Phase angle(degree) smoothng regression Figure 4-22. Comparison of phase angle from both methods at 8 Hz 4.6 Summary of Results In the end, it appears that the phase angle cannot be accurately determined with the conventional regression method or any kind of regression method when the loading curve gets more crooked as the test frequencies increase. The peak smoothing method is relatively unaffected by mechanical or physical error of the testing machine and it uses almost the same procedure used in hand calculation. So it appears to be the best analysis method for the complex modulus test available at this time for the Superpave IDT. Figure 4-24 and 4-25 show the phase angle and dynamic modulus calculated by conventional regression method and peak smoothing method from horizontal measurements. The values at each frequency presented in Figure 4-24 and 4-25 were calculated by using a median function, which is a very useful function to eliminate error values as long as there is the sufficient number of data points. The median function finds the midpoint value for the data set. The individual values of phase Angle, E*, EÂ’ and EÂ” is presented in Appendix A. PAGE 48 38 Smoothing V.S. Resgression 0 5 10 15 20 25 30 0246810 Frequency (hz)Phas Angle (degree) Smoothing Regression Figure 4-23. Comparison of phase angle from both methods at all frequencies Smoothing V.S. Regession 0 100000 200000 300000 400000 500000 600000 700000 800000 0246810 Frequency (hz)Dynamic modulus (psi) Smoothing Regression Figure 4-24. Comparison of dynamic modulus from both methods at all frequencies PAGE 49 39 CHAPTER 5 SOFTWARE DEVELOPMENT Based on Chapter 4, Roque and Buttlar (1992), and Roque et al (1997), the resilient modulus data analysis program was adopted for use with the complex modulus test. The procedure to find complex modulus was divided into three steps, because the complex modulus test deals with a large amount of data, and the three steps result in greater efficiency. The complex modulus tests from three replicate specimens were for 1000 loading cycles on each specimen. Three data sets are required for analysis. The first step was to organize the raw data for analysis. The second step was to calculate phase lag (time difference between load and strain) and the magnitude of load and deformation. The last step was to determine final phase angle, E*, EÂ’ and EÂ” based on results from the three specimens. 5.1 Data Initialization The complex (dynamic) modulus computer data analysis program (ITLT_dynamic) requires data in an Excel file, which means the original data obtained from data acquisition system must be placed in an Excel file. Also, 1000 cycles loading data were used for each test. The purpose of this step was to change the raw data obtained from the data acquisition system to manageable data. The raw deformation data included initial vibration before loading and were not set to zero. Therefore, the data initialization step accomplishes three things: It eliminates the data obtained prior to loading. It calculates the absolute change in deformations relative to the start of loading. It stars their data in an Excel file. PAGE 50 40 5.2 Intermediate Calculation In this step, the peak smoothing method was used to find basic properties such as phase angle (time difference between peak load and peak strain), magnitude of load and magnitude of deformation. The complex modulus test results vary from cycle to cycle, so to measure the basic properties such as phase angles and the magnitudes, just one or two cycles are not enough. As specified in Chapter 4, six cycles were selected for analysis, from which five values of top phase angles, five values of bottom phase angles, and five values of descending and rising magnitudes are obtained. The complex (dynamic) modulus data analysis program regards the range, six cycles, as one set. Consequently, from the one set, the peak smoothing method is applied to each set. The complex (dynamic) modulus data analysis program requires 1000 cycles for analysis. Among the 1000 cycles of tested data, analyses were performed to obtain parameters every 100 cycles so that a total 10 analyses were performed at each frequency. The intermediate calculation consists of the following steps. 1. Consider six cycles as one data set. 2. Obtain 10 data sets from the 1000 cycles of data obtained (i.e., one data set every 100 cycles). 3. Calculate 5 values of top phase angles, bottom phase angles, descending magnitudes and rising magnitudes of loading curve and deformation curve from each data set. 4. Calculate average values from the five values obtained. 5. Repeat Steps 4 and 5 for each data set. 6. The Intermediate calculation resulted in ten sets of values obtained from cycle number 1 to cycles 900. 5.3 Final Calculation of Dynamic Properties This step requires data results obtained from Step1 (data initialization) and Step 2 (intermediate calculation). In addition, three data sets obtained from three replicate PAGE 51 41 specimens are required for proper interpretation using the Superpave IDT. The horizontal deformation carries the symbol, H, while the vertical deformation carries the symbol, V. The horizontal phase angle carries the symbol, PA_H, while the vertical phase angle carries the symbol, PA_V. 5.3.1 Normalization Factors Since different specimens may have different thickness, diameter, or load, the deformations need to be normalized. Buttlar and Roque (1994) developed the following equations, Equation 5.1, to get normalization factors. i NORM C j ! V j NORM ! V i NORM C j ! H j NORM ! H ) i P AVG P ( ) AVG D i D ( ) AVG t i t ( i NORM C 3 3 1 i i P AVG P 3 3 1 i i D AVG D 3 3 1 i i t AVG t PAGE 52 42 n) deformatio vertical of number the 6, ~ 1 (j specimens replicate for three ns deformatio vertical normalized : j NORM ! V n) deformatio horizontal of number the 6, ~ 1 (j specimen s replicate for three ns deformatio horizontal normalized : j NORM ! H n) deformatio vertical of number the 6, ~ 1 (j specimens replicate for three ns deformatio vertical : j ! V n) deformatio horizontal of number the 6, ~ 1 (j specimens replicate for three ns deformatio horizontal : j ! H specimens replicate three of magnitude load average : AVG P specimens replicate three of diameter average : AVG D specimens replicate three of thickness average : AVG t specimen) replicate of number the 3, ~ 1 (i specimen replicate each of magnitude load : i P specimen) replicate of number the 3, ~ 1 (i specimen replicate each of diameter : i D specimen) replicate of number the 3, ~ 1 (i specimen replicate each of thickness : i t specimens replicate of number the : 3 : Where Equation 5. 1 5.3.2 Trimmed Mean Deformation and Trimmed Mean Phase Angle The six normalized horizontal and vertical deformations, and the six horizontal and vertical phase angles from three replicate specimens are ranked. To get the trimmed mean deformation and the trimmed mean phase angle, the highest and lowest deformation and the highest and lowest phase angle are deleted and then the remaining four deformations and four phase angles are averaged. The equations are as follows. PAGE 53 43 2 3 2 2 6 1 j j ! PA_V k TRIM ! PA_V 2 3 2 2 6 1 j j ! PA_H k TRIM ! PA_H sets) data of number the 10, ~ 1 (k set data each for array angle phase cal mean verti trimmed : k TRIM ! PA_V sets) data of number the 10, ~ 1 (k set data each for array angle phase horizontal mean trimmed : k TRIM ! PA_H : Where Equation 5. 2 2 3 2 2 6 1 j j NORM ! H k TRIM ! H 2 3 2 2 6 1 j j NORM ! H k TRIM ! H sets) data of number the 10, ~ 1 (k set data each for array n deformatio cal mean verti trimmed : k TRIM ! V sets) data of number the 10, ~ 1 (k set data each for array n deformatio horizontal mean trimmed : k TRIM ! H : Where Equation 5. 3 5.3.3 PoissonÂ’s Ratio Calculated for Data Set Equation 5.4 shows equations to find PoissonÂ’s ratio for each data set. 2 ) k TRIM ! V k TRIM ! H ( 2 ) AVG D AVG t ( 0.778 ) k TRIM ! V k TRIM ! H ( 1.480 0.100 k " sets) data of number the 10, ~ 1 (k set data each of n deformatio on based ratio s Poisson' : k " : Where Equation 5. 4 PAGE 54 44 5.3.4 Average PoissonÂ’s Ratio Equation 5.5 shows equations to find average PoissonÂ’s ratio. n deformatio on based ratio s Poisson' average : AVG " : Where 10 10 1 k k " AVG " Equation 5. 5 5.3.5 Correction Factors Buttlar and Roque (1994) developed the following equations, Equation 5.6, to account for three-dimensional stress states in diametrically loaded specimen of finite thickness. 2 AVG AVG 2 AVG AVG AVG AVG AVG AVG SY AVG AVG AVG AVG AVG AVG SX EY EX AVG BY 2 AVG AVG AVG AVG AVG BX) D t ( 0.264 ) D t ( " 0.251 ) D t ( 0.287 " 0.138 0.901 C " ) D t ( 1.4360 " 0.2693 ) D t ( 0.01114 0.9480 C 0.98 C 1.07 C " 0.128 0.994 C ) D t ( 0.089 " 0.081 ) D t ( 0.189 1.030 C Equation 5. 6 5.3.6 Horizontal and Vertical Moduli of E*, EÂ’ and EÂ” The following equations were used to find horizontal and vertical moduli of E*, EÂ’ and EÂ”. PAGE 55 45 ) k TRIM ! PA_V ) k TRIM ! PA_H ) k TRIM ! PA_V ) k TRIM ! PA_Hsin( * E E" sin( * E E" cos( * E E' cos( * E E' )) C t D # P 2 ( " C t D # P 6 ( ) C C GL ! V 1 ( * E )) C t D # P 6 ( " C t D # P 2 ( ) C C GL ! H 1 ( * Ek VERT k VERT k HORI k HORI k VERT k VERT k HORI k HORI SX AVG AVG AVG AVG SY AVG AVG AVG EY BY AVG k TRIM k VERT SY AVG AVG AVG AVG SX AVG AVG AVG EX BX AVG k TRIM k HORI set data each of modulus loss vertical : E" set data each of modulus loss horizontal : E" set data each of modulus storage vertical : E' set data each of modulus storage horizontal : E' set data each of modulus dynamic vertical : * E set data each of modulus dynamic horizontal : * Ek VERT k HORI k VERT k HORI k VERT k HORI: Where Equation 5. 7 5.4 Output of Program The dynamic (complex) modulus computer data analysis program (ITLT_dynamic) was written in Visual Basic Language on the assumption that all input data files and output data files are in Excel. Appendix B through E shows output files. Overall concepts of the complex (dynamic) modulus data analysis program (ITLT_dynamic) were specified in Chapter 4 and 5. PAGE 56 46 CHAPTER 6 EVALUATION OF COMPLEX MODULUS DATA ANALYSIS PROGRAM 6.1 Evaluation of Test Results Figure 6-1 to 6-4 show the results of horizontal phase angle, E*, EÂ’ and EÂ” for four complex modulus tests. These test results were obtained from just one complex modulus test for one specimen, so the one data set was copied three times to perform the analysis. The representative dynamic moduli of each frequency were obtained using median function, which finds the midpoint value for the data set. As presented in Chapter 2 (literature review), certain trends in the dynamic properties such as phase angle, E*, EÂ’ and EÂ” were expected. As the frequency increases, under the assumption that other conditions are same. The dynamic modulus increases. The phase angle decreases. The change in EÂ’ and EÂ” depends on the relative changes in dynamic modulus and the phase angle. The results of the dynamic (complex) modulus computer data analysis program clearly showed that the dynamic modulus and EÂ’ increased as the frequency increased. However, the result of phase angle does not show the trend decreasing successively. It is possible that temperature difference between tests, or insufficient recovery time between tests may account for the relatively high value of phase angle at 8 Hz. The output of the dynamic modulus analysis program is presented in Appendix B thorough Appendix E. The analysis results of horizontal phase angle, E*, EÂ’ and EÂ” for each frequency are PAGE 57 47 presented in Appendix F. Note that the magnitude of vertical properties are unreliable because one of the vertical gages malfunctioned (i.e., only one vertical measurement on one specimen was obtained). PHASE ANGLE0 5 10 15 20 25 0246810 Frequency(hz)Angle(degree) Figure 6-1. Horizontal phase angle E*0 50000 100000 150000 200000 250000 300000 0246810 Frequency(hz)E*(psi) Figure 6-2. Horizontal E* PAGE 58 48 E'0 50000 100000 150000 200000 250000 300000 0246810 Frequency(hz)E'(psi) Figure 6-3. Horizontal EÂ’ E"0 50000 100000 150000 200000 250000 300000 0246810 Frequency(hz)E"(psi) Figure 6-4. Horizontal EÂ” 6.2 Evaluation of Data Reduction The complex modulus data analysis program has an optional function, which allows the user to input PoissonÂ’s ratio manually, so the procedure to calculate PoissonÂ’s ratio is skipped. The complex modulus data from the laboratory tests performed in this investigation had an erroneous set of measurements for one of the vertical gages, so that PAGE 59 49 it was impossible to calculate PoissonÂ’s ratio accurately. Therefore, a PoissonÂ’s ratio of 0.24, which resulted from the resilient modulus test on the same material was used for analysis. The vertical dynamic properties such as phase angle, E*, EÂ’ and EÂ” were calculated using only one vertical measurement 6.3 Comparison between Normalized Dynamic Moduli Because of the limited data obtained (i.e., two horizontal measurements and one vertical measurement), it was impossible to calculate PoissonÂ’s ratio reliably from the test data. For the same reason, it would have been unreasonable to expect the horizontal and vertical dynamic moduli to be equal for the data. However, the relative change in parameters for different frequencies should be the same for the vertical and horizontal deformation data. Therefore, normalized values of dynamic modulus were calculated for comparative purposes. In addition, modulus values were obtained using a predictive equation by Hwang and Witczak (1979), which was developed for the DAMA computer program for the Asphalt Institute. The predictive equation uses regression formulas to determine the dynamic modulus of HMA as follows: logf 0.49825 1.3 $ V 0.483 $ V 0.03476 ) f 0.028829(P 0.553833 $ T $ $ f $ 0.00189 $ 0.000005 $ $ 10 100,000 * E5 b 4 a 0.1703 200 3 $ 0.5 4 2 1.1 2 2 3 1 $5 1 PAGE 60 50 C) (25 F 77 at on penentrati The : F 77 P % in bitumen of volume The : b V % in air void of volume The : a V 200 No. through passing aggregate of by weight percentage The : 200 P F in re temperatu The : T Hz in frequency load The : f 2.1939 ) F 77 (P 29,508.2 % : Where Once again, for comparative purposes, the dynamic modulus obtained from the predictive equation was normalized. The normalized dynamic modulus for each test frequency (0.33, 1, 4, and 8 Hz) was obtained by dividing each dynamic modulus by the dynamic modulus of initial frequency, 0.33 Hz. In summary, the normalized dynamic modulus were obtained as follows: 1. The three sets of dynamic moduli were calculated based on horizontal and vertical dynamic deformation measurements on using the predictive equation. Moduli were obtained for each test frequency. 2. Each dynamic modulus obtained was divided by the dynamic modulus at 0.33 Hz Figure 6-5 shows three sets of normalized dynamic moduli as a function of frequency. The three sets of normalized dynamic moduli exhibited the same trend. Also, the vertical and horizontal values agreed quiet well, while the predictive equation appeared to underestimate the effect of frequency for this particular mixture. The generally good agreement between the vertical and horizontal values, and the reasonable trend obtained with frequency, which was consistent with the trend predicted by a well established predictive equation, indicates that the testing and data reduction program performed well. Unfortunately, one of the gages was broken, so additional tests could not be performed. PAGE 61 51 E* (Dynamic Modulus)0 0.5 1 1.5 2 2.5 3 0123456789Frequency(hz)Normalized Ratio Witzak Horizontal Vertical Figure 6-5. Normalized dynamic modulus PAGE 62 52 CHAPTER 7 CLOSURE 7.1 Summary of Findings The purpose of this study was to find a problem of the complex (dynamic) modulus test using Superpave IDT, to develop suitable interpretation method for data by the complex (dynamic) modulus test, and to develop complex (dynamic) modulus data analysis program (ITLT_dynamic). Findings may be summarized as follows: The load function appears to be more difficult to control when testing using indirect tensile mode of loading The error in the applied loading function results in significant error in calculated parameters, especially phase angle, when conventional data interpretation methods are used (e.g. regression-load approaches). The regression method was shown to overestimate the phase angle in these cases. It was determined that these errors were reduced or eliminated by using the data reduction procedure developed in this thesis, which employs a gaussian kernel window smoothing method to identify load and deformation peaks from which the phase angle and load and deformation amplitudes are determined. Based on limited test data, it appears that complex modulus parameters determined using the Superpave IDT exhibited expected trend and reasonable values. 7.2 Conclusions The data reduction procedure (Â“peak smoothingÂ”) and data reduction computer program (ITLT_dynamic) developed to determine complex modulus based on the measurements and analysis system for Superpave IDT provided reasonable values of dynamic parameters such as phase angle, E*, EÂ’ and EÂ”. The horizontal and vertical PAGE 63 53 normalized dynamic moduli calculated by the data analysis program (ITLT_dynamic) present a good correlated well with each other and the normalized dynamic modulus obtained from predictive equations. 7.3 Recommendations Results of complex modulus data analysis program were obtained from only one test at one temperature and multiple frequencies. Also, the complex modulus test was conducted with incomplete measurements (i.e. one of the vertical measurements was broken). Consequently, using all four measurements (two horizontal and vertical measurements) should be performed to further evaluate dynamic modulus parameters obtained for Superpave IDT. In addition, the use of temperature control systems is highly recommended for further tests. PAGE 64 APPENDIX A COMPARISION OF DATA ANALYSIS RESULTS BETWEEN TWO METHODS PAGE 65 55 0.333hz 0 50000 100000 150000 200000 250000 300000 01000200030004000 Time(sec)E*(psi) smoothing regression Figure A-1. Comparison of E* at 0.333 Hz 0.5hz 0 50000 100000 150000 200000 250000 300000 350000 050010001500 Time(sec)E*(psi) smoothing regression Figure A-2. Comparison of E* at 0.5 Hz PAGE 66 56 1hz 0 50000 100000 150000 200000 250000 300000 350000 400000 450000 050010001500 Time(sec)E*(psi) smoothing regression Figure A-3. Comparison of E* at 1 Hz 4hz 0 100000 200000 300000 400000 500000 600000 700000 050010001500 Time(sec)E*(psi) smoothing regression Figure A-4. Comparison of E* at 4 Hz PAGE 67 57 8hz 0 100000 200000 300000 400000 500000 600000 700000 800000 050100150 Time(sec)E*(psi) smoothing regression Figure A-4. Comparison of E* at 8 Hz 0.333hz 0 5 10 15 20 25 30 35 01000200030004000 Time(sec)Phase angle(degree) smoothing regression Figure A-5. Comparison phase angle of 0.333 Hz PAGE 68 58 0.5hz 0 5 10 15 20 25 30 35 050010001500 Time(sec)Phase angle(degree) smoothing regression Figure A-6. Comparison phase angle of 0.5 Hz 1hz 0 5 10 15 20 25 30 050010001500 Time(sec)Phase angle(degree) smoothing regression Figure A-7. Comparison phase angle of 1 Hz PAGE 69 59 4hz 0 5 10 15 20 25 30 050010001500 Time(sec)Phase angle(degree) smoothing regression Figure A-8. Comparison phase angle of 4 Hz 8hz 0 5 10 15 20 25 30 050100150 Time(sec)Phase angle(degree) smoothng regression Figure A-9. Comparison phase angle of 8 Hz PAGE 70 60 0.333hz0 50000 100000 150000 200000 250000 300000 01000200030004000Time(sec)E'(psi) smoothing regression Figure A-10. Comparison EÂ’ of 0.333 Hz 0.5hz0 50000 100000 150000 200000 250000 300000 350000 050010001500Time(sec)E'(psi) smoothing regression Figure A-11. Comparison EÂ’ of 0.5 Hz PAGE 71 61 1hz0 50000 100000 150000 200000 250000 300000 350000 400000 450000 0500100015002000Time(sec)E'(psi) smoothing regression Figure A-12. Comparison EÂ’ of 1 Hz 4hz0 100000 200000 300000 400000 500000 600000 700000 050010001500Time(sec)E'(psi) smoothing regression Figure A-13. Comparison EÂ’ of 4 Hz PAGE 72 62 8hz0 100000 200000 300000 400000 500000 600000 700000 800000 050100150Time(sec)E'(psi) smoothing regression Figure A-14. Comparison EÂ’ of 8 Hz 0.333hz0 50000 100000 150000 200000 250000 300000 01000200030004000Time(sec)E"(psi) smoothing regression Figure A-15. Comparison EÂ” of 0.333 Hz PAGE 73 63 0.5hz0 50000 100000 150000 200000 250000 300000 350000 050010001500Time(sec)E"(psi)) smoothing regression Figure A-16. Comparison EÂ” of 0.5 Hz 1hz0 50000 100000 150000 200000 250000 300000 350000 400000 450000 0500100015002000Time(sec)E"(psi) smoothing regression Figure A-17. Comparison EÂ” of 1 Hz PAGE 74 64 4hz0 100000 200000 300000 400000 500000 600000 700000 050010001500Time(sec)E"(psi)) smoothing regression Figure A-18. Comparison EÂ” of 4 Hz 8hz0 100000 200000 300000 400000 500000 600000 700000 800000 050100150Time(sec)E"(psi) smoothing regression Figure A-19. Comparison EÂ” of 8 Hz PAGE 75 65 DYNAMIC MODULI0 100000 200000 300000 400000 500000 600000 700000 800000 0123456789Frequency (hz)Dynamic modulus(psi) Smoothing Regression Figure A-20. Comparison of E* PHASE ANGLES0 5 10 15 20 25 30 0123456789Frequency (hz)Phas Angle (degree) Smoothing Regression Figure A-21. Comparison of phase angle PAGE 76 66 E'(STORAGE MODULI)0 100000 200000 300000 400000 500000 600000 700000 800000 0123456789Frequency (hz)E'(psi) Smoothing Regression Figure A-22. Comparison of EÂ’ E"(LOSS MODULI)0 100000 200000 300000 400000 500000 600000 700000 800000 0123456789Frequency (hz)E"(psi) Smoothing Regression Figure A-23. Comparison of EÂ” PAGE 77 APPENDIX B OUTPUT OF 0.333 Hz PAGE 78 68 DYNAMIC MODULUS TEST RESULT FROM THREE SPECIMENS Phase Angle[degree] E*[psi] E'[psi] E''[psi] Poisson's ratio Cycles H V H V H V H V 1~5 30.364 27.5548 92575.2 172487 79876.8 152922 46796 79792.2 0.24 101~5 23.775 21.6684 104228 203220 95383 188860 42019.2 75035.8 0.24 201~5 21.8311 20.8028 104101 205794 96634.8 192378 38712.1 73088.2 0.24 301~5 22.2256 20.1569 100068 205370 92632.7 192792 37851 70768.9 0.24 401~5 24.1689 21.1899 102544 204215 93555.2 190408 41984.3 73815.7 0.24 501~5 20.7882 20.3101 103223 201455 96503.4 188930 36635.4 69925.4 0.24 601~5 21.3216 20.928 102729 199713 95697.6 186537 37352.5 71336.3 0.24 701~5 22.7157 21.5025 97339.8 201193 89789.4 187190 37588.6 73745.8 0.24 801~5 24.6438 22.4952 98997.3 199964 89980.4 184749 41279.4 76507.6 0.24 901~5 23.7858 19.6082 103315 197445 94539.6 185995 41668.9 66260.1 0.24 Cycles NORMALIZED DEFORMATIONS [mils] TRIMED MEAN PHASE ANGLES [degree] 1~5 Face H Face V Face H Face V 1 79.1988 1 393.888 1 29.6481 1 27.5548 3 79.1988 2 393.888 3 29.6481 2 27.5548 5 79.1988 3 393.888 5 29.6481 3 27.5548 2 118.14 4 393.888 2 31.08 4 27.5548 4 118.14 5 393.888 4 31.08 5 27.5548 6 118.14 6 393.888 6 31.08 6 27.5548 101~5 Face H Face V Face H Face V 1 72.6071 1 334.321 2 22.2858 1 21.6684 3 72.6071 2 334.321 4 22.2858 2 21.6684 5 72.6071 3 334.321 6 22.2858 3 21.6684 2 102.669 4 334.321 1 25.2642 4 21.6684 4 102.669 5 334.321 3 25.2642 5 21.6684 6 102.669 6 334.321 5 25.2642 6 21.6684 201~5 Face H Face V Face H Face V 1 71.8551 1 330.14 2 21.6818 1 20.8028 3 71.8551 2 330.14 4 21.6818 2 20.8028 5 71.8551 3 330.14 6 21.6818 3 20.8028 2 103.636 4 330.14 1 21.9804 4 20.8028 4 103.636 5 330.14 3 21.9804 5 20.8028 6 103.636 6 330.14 5 21.9804 6 20.8028 PAGE 79 69 301~5 Face H Face V Face H Face V 1 78.4072 1 330.821 2 20.873 1 20.1569 3 78.4072 2 330.821 4 20.873 2 20.1569 5 78.4072 3 330.821 6 20.873 3 20.1569 2 104.156 4 330.821 1 23.5783 4 20.1569 4 104.156 5 330.821 3 23.5783 5 20.1569 6 104.156 6 330.821 5 23.5783 6 20.1569 401~5 Face H Face V Face H Face V 1 75.0055 1 332.691 1 24.1555 1 21.1899 3 75.0055 2 332.691 3 24.1555 2 21.1899 5 75.0055 3 332.691 5 24.1555 3 21.1899 2 103.149 4 332.691 2 24.1823 4 21.1899 4 103.149 5 332.691 4 24.1823 5 21.1899 6 103.149 6 332.691 6 24.1823 6 21.1899 501~5 Face H Face V Face H Face V 1 76.4736 1 337.249 1 19.6823 1 20.3101 3 76.4736 2 337.249 3 19.6823 2 20.3101 5 76.4736 3 337.249 5 19.6823 3 20.3101 2 100.509 4 337.249 2 21.894 4 20.3101 4 100.509 5 337.249 4 21.894 5 20.3101 6 100.509 6 337.249 6 21.894 6 20.3101 601~5 Face H Face V Face H Face V 1 71.9232 1 340.193 2 20.1508 1 20.928 3 71.9232 2 340.193 4 20.1508 2 20.928 5 71.9232 3 340.193 6 20.1508 3 20.928 2 105.911 4 340.193 1 22.4924 4 20.928 4 105.911 5 340.193 3 22.4924 5 20.928 6 105.911 6 340.193 5 22.4924 6 20.928 701~5 Face H Face V Face H Face V 1 80.2678 1 337.689 1 21.7327 1 21.5025 3 80.2678 2 337.689 3 21.7327 2 21.5025 5 80.2678 3 337.689 5 21.7327 3 21.5025 2 107.412 4 337.689 2 23.6988 4 21.5025 4 107.412 5 337.689 4 23.6988 5 21.5025 6 107.412 6 337.689 6 23.6988 6 21.5025 PAGE 80 70 801~5 Face H Face V Face H Face V 1 78.5587 1 339.765 1 24.0832 1 22.4952 3 78.5587 2 339.765 3 24.0832 2 22.4952 5 78.5587 3 339.765 5 24.0832 3 22.4952 2 105.979 4 339.765 2 25.2043 4 22.4952 4 105.979 5 339.765 4 25.2043 5 22.4952 6 105.979 6 339.765 6 25.2043 6 22.4952 901~5 Face H Face V Face H Face V 1 69.6539 1 344.099 1 22.1524 1 19.6082 3 69.6539 2 344.099 3 22.1524 2 19.6082 5 69.6539 3 344.099 5 22.1524 3 19.6082 2 107.171 4 344.099 2 25.4192 4 19.6082 4 107.171 5 344.099 4 25.4192 5 19.6082 6 107.171 6 344.099 6 25.4192 6 19.6082 (Bold Numbers)-Faces use to calculate Poisson's ratio PROPERTIES OF SPECIMENS Spec.1 Spec.2 Spec.3 Data File Name: V_IDT Third Hz Long_assum.xls V2_IDT Third Hz Long_assum.xls V3_IDT Third Hz Long_assum.xls Diameter [in]: 4 4 4 Thickness [in]: 2.5 2.5 2.5 Temperature [C]: 20 20 20 Frequency [Hz]: 0.333 0.333 0.333 Load [lbf]: 373.344 373.344 373.344 Gage Length [in]: 1 1 1 PAGE 81 APPENDIX C OUTPUT OF 1 Hz PAGE 82 72 DYNAMIC MODULUS TEST RESULT FROM THREE SPECIMENS Phase Angle[degree] E*[psi] E'[psi] E''[psi] Poisson's ratio Cycles H V H V H V H V 1~5 25.4391 28.8943 131733 235047 118961 205787 56586.3 113574 0.24 101~5 24.1309 23.4644 139158 263752 126997 241942 56890.7 105020 0.24 201~5 23.7003 22.6544 142802 269792 130758 248976 57399.6 103916 0.24 301~5 22.396 21.8597 135511 267715 125290 248465 51630.6 99679.5 0.24 401~5 21.3634 21.6068 144457 272100 134532 252981 52623.3 100197 0.24 501~5 19.6066 20.5533 136188 271736 128292 254439 45699.5 95400.6 0.24 601~5 22.2097 20.984 145497 272497 134702 254425 54997.5 97583.1 0.24 701~5 21.0688 20.8762 138770 275437 129493 257355 49886.2 98152.1 0.24 801~5 22.1479 20.6229 138958 270790 128705 253438 52386.8 95376.5 0.24 901~5 21.9418 20.4971 140779 271593 130581 254399 52604 95101.1 0.24 Cycles NORMALIZED DEFORMATIONS [mils] TRIMED MEAN PHASE ANGLES [degree] 1~5 Face H Face V Face H Face V 1 66.5295 1 345.975 1 22.0904 1 28.8943 3 66.5295 2 345.975 3 22.0904 2 28.8943 5 66.5295 3 345.975 5 22.0904 3 28.8943 2 99.4604 4 345.975 2 28.7878 4 28.8943 4 99.4604 5 345.975 4 28.7878 5 28.8943 6 99.4604 6 345.975 6 28.7878 6 28.8943 101~5 Face H Face V Face H Face V 1 67.5789 1 308.322 1 21.7862 1 23.4644 3 67.5789 2 308.322 3 21.7862 2 23.4644 5 67.5789 3 308.322 5 21.7862 3 23.4644 2 89.5552 4 308.322 2 26.4755 4 23.4644 4 89.5552 5 308.322 4 26.4755 5 23.4644 6 89.5552 6 308.322 6 26.4755 6 23.4644 201~5 Face H Face V Face H Face V 1 62.417 1 301.419 1 20.6594 1 22.6544 3 62.417 2 301.419 3 20.6594 2 22.6544 5 62.417 3 301.419 5 20.6594 3 22.6544 2 90.707 4 301.419 2 26.7412 4 22.6544 4 90.707 5 301.419 4 26.7412 5 22.6544 6 90.707 6 301.419 6 26.7412 6 22.6544 PAGE 83 73 301~5 Face H Face V Face H Face V 1 71.9695 1 303.758 1 20.6549 1 21.8597 3 71.9695 2 303.758 3 20.6549 2 21.8597 5 71.9695 3 303.758 5 20.6549 3 21.8597 2 89.3924 4 303.758 2 24.1371 4 21.8597 4 89.3924 5 303.758 4 24.1371 5 21.8597 6 89.3924 6 303.758 6 24.1371 6 21.8597 401~5 Face H Face V Face H Face V 1 62.8974 1 298.862 1 17.8749 1 21.6068 3 62.8974 2 298.862 3 17.8749 2 21.6068 5 62.8974 3 298.862 5 17.8749 3 21.6068 2 88.4717 4 298.862 2 24.8519 4 21.6068 4 88.4717 5 298.862 4 24.8519 5 21.6068 6 88.4717 6 298.862 6 24.8519 6 21.6068 501~5 Face H Face V Face H Face V 1 69.8831 1 299.263 1 17.7429 1 20.5533 3 69.8831 2 299.263 3 17.7429 2 20.5533 5 69.8831 3 299.263 5 17.7429 3 20.5533 2 90.6767 4 299.263 2 21.4704 4 20.5533 4 90.6767 5 299.263 4 21.4704 5 20.5533 6 90.6767 6 299.263 6 21.4704 6 20.5533 601~5 Face H Face V Face H Face V 1 61.3561 1 298.427 1 20.7419 1 20.984 3 61.3561 2 298.427 3 20.7419 2 20.984 5 61.3561 3 298.427 5 20.7419 3 20.984 2 88.9316 4 298.427 2 23.6775 4 20.984 4 88.9316 5 298.427 4 23.6775 5 20.984 6 88.9316 6 298.427 6 23.6775 6 20.984 701~5 Face H Face V Face H Face V 1 66.9797 1 295.242 1 19.6137 1 20.8762 3 66.9797 2 295.242 3 19.6137 2 20.8762 5 66.9797 3 295.242 5 19.6137 3 20.8762 2 90.5932 4 295.242 2 22.5238 4 20.8762 4 90.5932 5 295.242 4 22.5238 5 20.8762 6 90.5932 6 295.242 6 22.5238 6 20.8762 PAGE 84 74 801~5 Face H Face V Face H Face V 1 67.7693 1 300.308 1 21.8575 1 20.6229 3 67.7693 2 300.308 3 21.8575 2 20.6229 5 67.7693 3 300.308 5 21.8575 3 20.6229 2 89.5908 4 300.308 2 22.4382 4 20.6229 4 89.5908 5 300.308 4 22.4382 5 20.6229 6 89.5908 6 300.308 6 22.4382 6 20.6229 901~5 Face H Face V Face H Face V 1 65.1036 1 299.42 1 20.7073 1 20.4971 3 65.1036 2 299.42 3 20.7073 2 20.4971 5 65.1036 3 299.42 5 20.7073 3 20.4971 2 90.2209 4 299.42 2 23.1762 4 20.4971 4 90.2209 5 299.42 4 23.1762 5 20.4971 6 90.2209 6 299.42 6 23.1762 6 20.4971 (Bold Numbers)-Faces use to calculate Poisson's ratio PROPERTIES OF SPECIMENS Spec.1 Spec.2 Spec.3 Data File Name: V_IDT 1Hz Long_assum.xls V2_IDT 1Hz Long_assum.xls V3_IDT 1Hz Long_assum.xls Diameter [in]: 4 4 4 Thickness [in]: 2.5 2.5 2.5 Temperature [C]: 20 20 20 Frequency [Hz]: 1 1 1 Load [lbf]: 446.867 446.867 446.867 Gage Length [in]: 1 1 1 PAGE 85 APPENDIX D OUTPUT OF 4 Hz PAGE 86 76 DYNAMIC MODULUS TEST RESULT FROM THREE SPECIMENS Phase Angle[degree] E*[psi] E'[psi] E''[psi] Poisson's ratio Cycles H V H V H V H V 1~5 18.2371 22.5044 213967 354433 203220 327443 66960.9 135661 0.24 101~5 24.2595 24.1055 208814 370075 190375 337802 85795.6 151145 0.24 201~5 20.154 18.6947 216895 376254 203615 356403 74730.2 120599 0.24 301~5 19.452 20.3373 217940 382694 205500 358838 72577.8 133004 0.24 401~5 19.1557 20.1904 218342 380358 206252 356985 71645.7 131277 0.24 501~5 18.2692 20.0698 219833 380021 208752 356944 68913.9 130410 0.24 601~5 18.8755 20.1305 210300 379939 198991 356729 68034.7 130760 0.24 701~5 18.5564 18.4538 216951 384807 205671 365020 69042 121806 0.24 801~5 18.816 20.655 215256 375422 203753 351291 69426.7 132426 0.24 901~5 20.1012 20.2839 215399 376764 202278 353400 74028.2 130614 0.24 Cycles NORMALIZED DEFORMATIONS [mils] TRIMED MEAN PHASE ANGLES [degree] 1~5 Face H Face V Face H Face V 1 52.5233 1 332.628 1 17.7016 1 22.5044 3 52.5233 2 332.628 3 17.7016 2 22.5044 5 52.5233 3 332.628 5 17.7016 3 22.5044 2 95.6339 4 332.628 2 18.7725 4 22.5044 4 95.6339 5 332.628 4 18.7725 5 22.5044 6 95.6339 6 332.628 6 18.7725 6 22.5044 101~5 Face H Face V Face H Face V 1 54.2229 1 318.569 2 22.6774 1 24.1055 3 54.2229 2 318.569 4 22.6774 2 24.1055 5 54.2229 3 318.569 6 22.6774 3 24.1055 2 97.5904 4 318.569 1 25.8416 4 24.1055 4 97.5904 5 318.569 3 25.8416 5 24.1055 6 97.5904 6 318.569 5 25.8416 6 24.1055 201~5 Face H Face V Face H Face V 1 56.087 1 313.337 1 17.0123 1 18.6947 3 56.087 2 313.337 3 17.0123 2 18.6947 5 56.087 3 313.337 5 17.0123 3 18.6947 2 90.0701 4 313.337 2 23.2957 4 18.6947 4 90.0701 5 313.337 4 23.2957 5 18.6947 6 90.0701 6 313.337 6 23.2957 6 18.6947 PAGE 87 77 301~5 Face H Face V Face H Face V 1 54.5954 1 308.064 1 16.3272 1 20.3373 3 54.5954 2 308.064 3 16.3272 2 20.3373 5 54.5954 3 308.064 5 16.3272 3 20.3373 2 90.8611 4 308.064 2 22.5768 4 20.3373 4 90.8611 5 308.064 4 22.5768 5 20.3373 6 90.8611 6 308.064 6 22.5768 6 20.3373 401~5 Face H Face V Face H Face V 1 53.7778 1 309.956 1 17.1825 1 20.1904 3 53.7778 2 309.956 3 17.1825 2 20.1904 5 53.7778 3 309.956 5 17.1825 3 20.1904 2 91.4112 4 309.956 2 21.1289 4 20.1904 4 91.4112 5 309.956 4 21.1289 5 20.1904 6 91.4112 6 309.956 6 21.1289 6 20.1904 501~5 Face H Face V Face H Face V 1 53.8875 1 310.231 1 14.9768 1 20.0698 3 53.8875 2 310.231 3 14.9768 2 20.0698 5 53.8875 3 310.231 5 14.9768 3 20.0698 2 90.3162 4 310.231 2 21.5617 4 20.0698 4 90.3162 5 310.231 4 21.5617 5 20.0698 6 90.3162 6 310.231 6 21.5617 6 20.0698 601~5 Face H Face V Face H Face V 1 57.9539 1 310.298 2 18.7616 1 20.1305 3 57.9539 2 310.298 4 18.7616 2 20.1305 5 57.9539 3 310.298 6 18.7616 3 20.1305 2 92.7871 4 310.298 1 18.9895 4 20.1305 4 92.7871 5 310.298 3 18.9895 5 20.1305 6 92.7871 6 310.298 5 18.9895 6 20.1305 701~5 Face H Face V Face H Face V 1 58.3296 1 306.373 1 12.4943 1 18.4538 3 58.3296 2 306.373 3 12.4943 2 18.4538 5 58.3296 3 306.373 5 12.4943 3 18.4538 2 87.7903 4 306.373 2 24.6185 4 18.4538 4 87.7903 5 306.373 4 24.6185 5 18.4538 6 87.7903 6 306.373 6 24.6185 6 18.4538 PAGE 88 78 801~5 Face H Face V Face H Face V 1 55.5259 1 314.031 2 18.3082 1 20.655 3 55.5259 2 314.031 4 18.3082 2 20.655 5 55.5259 3 314.031 6 18.3082 3 20.655 2 91.7443 4 314.031 1 19.3239 4 20.655 4 91.7443 5 314.031 3 19.3239 5 20.655 6 91.7443 6 314.031 5 19.3239 6 20.655 901~5 Face H Face V Face H Face V 1 56.5291 1 312.913 1 19.602 1 20.2839 3 56.5291 2 312.913 3 19.602 2 20.2839 5 56.5291 3 312.913 5 19.602 3 20.2839 2 90.6436 4 312.913 2 20.6005 4 20.2839 4 90.6436 5 312.913 4 20.6005 5 20.2839 6 90.6436 6 312.913 6 20.6005 6 20.2839 (Bold Numbers)-Faces use to calculate Poisson's ratio PROPERTIES OF SPECIMENS Spec.1 Spec.2 Spec.3 Data File Name: V_IDT 4Hz Long_assum.xls V2_IDT 4Hz Long_assum.xls V3_IDT 4Hz Long_assum.xls Diameter [in]: 4 4 4 Thickness [in]: 2.5 2.5 2.5 Temperature [C]: 20 20 20 Frequency [Hz]: 4 4 4 Load [lbf]: 647.846 647.846 647.846 Gage Length [in]: 1 1 1 PAGE 89 APPENDIX E OUTPUT OF 8 Hz PAGE 90 80 DYNAMIC MODULUS TEST RESULT FROM THREE SPECIMENS Phase Angle[degree] E*[psi] E'[psi] E''[psi] Poisson's ratio Cycles H V H V H V H V 1~5 26.2248 30.7302 249765 494311 224056 424902 110370 252591 0.24 101~5 23.9302 28.1098 254906 488593 232994 430962 103396 230207 0.24 201~5 23.2162 27.6103 243700 479988 223966 425327 96066.8 222453 0.24 301~5 20.8799 25.7624 256833 474672 239966 427492 91537.9 206312 0.24 401~5 20.8254 25.8325 255771 492801 239061 443556 90932.2 214734 0.24 501~5 22.8848 26.5471 260365 489080 239871 437515 101250 218586 0.24 601~5 20.9062 23.5885 248361 475725 232011 435974 88624.9 190368 0.24 701~5 21.3191 26.7697 243154 474289 226515 423456 88401.4 213622 0.24 801~5 20.1021 24.5931 251171 486087 235870 441992 86325.7 202295 0.24 901~5 20.8576 27.1679 249581 476092 233225 423566 88862.1 217383 0.24 Cycles NORMALIZED DEFORMATIONS [mils] TRIMED MEAN PHASE ANGLES [degree] 1~5 Face H Face V Face H Face V 1 58.3309 1 237.902 1 20.9343 1 30.7302 3 58.3309 2 237.902 3 20.9343 2 30.7302 5 58.3309 3 237.902 5 20.9343 3 30.7302 2 68.2722 4 237.902 2 31.5154 4 30.7302 4 68.2722 5 237.902 4 31.5154 5 30.7302 6 68.2722 6 237.902 6 31.5154 6 30.7302 101~5 Face H Face V Face H Face V 1 54.8364 1 240.686 1 18.6376 1 28.1098 3 54.8364 2 240.686 3 18.6376 2 28.1098 5 54.8364 3 240.686 5 18.6376 3 28.1098 2 69.2135 4 240.686 2 29.2227 4 28.1098 4 69.2135 5 240.686 4 29.2227 5 28.1098 6 69.2135 6 240.686 6 29.2227 6 28.1098 201~5 Face H Face V Face H Face V 1 58.7536 1 245.001 1 16.1263 1 27.6103 3 58.7536 2 245.001 3 16.1263 2 27.6103 5 58.7536 3 245.001 5 16.1263 3 27.6103 2 71.0004 4 245.001 2 30.3061 4 27.6103 4 71.0004 5 245.001 4 30.3061 5 27.6103 6 71.0004 6 245.001 6 30.3061 6 27.6103 PAGE 91 81 301~5 Face H Face V Face H Face V 1 53.9581 1 247.745 1 14.3699 1 25.7624 3 53.9581 2 247.745 3 14.3699 2 25.7624 5 53.9581 3 247.745 5 14.3699 3 25.7624 2 69.1612 4 247.745 2 27.3899 4 25.7624 4 69.1612 5 247.745 4 27.3899 5 25.7624 6 69.1612 6 247.745 6 27.3899 6 25.7624 401~5 Face H Face V Face H Face V 1 52.8266 1 238.631 1 15.3766 1 25.8325 3 52.8266 2 238.631 3 15.3766 2 25.8325 5 52.8266 3 238.631 5 15.3766 3 25.8325 2 70.8037 4 238.631 2 26.2742 4 25.8325 4 70.8037 5 238.631 4 26.2742 5 25.8325 6 70.8037 6 238.631 6 26.2742 6 25.8325 501~5 Face H Face V Face H Face V 1 51.631 1 240.447 1 17.4821 1 26.5471 3 51.631 2 240.447 3 17.4821 2 26.5471 5 51.631 3 240.447 5 17.4821 3 26.5471 2 69.818 4 240.447 2 28.2875 4 26.5471 4 69.818 5 240.447 4 28.2875 5 26.5471 6 69.818 6 240.447 6 28.2875 6 26.5471 601~5 Face H Face V Face H Face V 1 56.602 1 247.197 1 16.6349 1 23.5885 3 56.602 2 247.197 3 16.6349 2 23.5885 5 56.602 3 247.197 5 16.6349 3 23.5885 2 70.7168 4 247.197 2 25.1775 4 23.5885 4 70.7168 5 247.197 4 25.1775 5 23.5885 6 70.7168 6 247.197 6 25.1775 6 23.5885 701~5 Face H Face V Face H Face V 1 57.7575 1 247.945 1 14.0729 1 26.7697 3 57.7575 2 247.945 3 14.0729 2 26.7697 5 57.7575 3 247.945 5 14.0729 3 26.7697 2 72.288 4 247.945 2 28.5653 4 26.7697 4 72.288 5 247.945 4 28.5653 5 26.7697 6 72.288 6 247.945 6 28.5653 6 26.7697 PAGE 92 82 801~5 Face H Face V Face H Face V 1 55.7141 1 241.927 1 15.4327 1 24.5931 3 55.7141 2 241.927 3 15.4327 2 24.5931 5 55.7141 3 241.927 5 15.4327 3 24.5931 2 70.1805 4 241.927 2 24.7714 4 24.5931 4 70.1805 5 241.927 4 24.7714 5 24.5931 6 70.1805 6 241.927 6 24.7714 6 24.5931 901~5 Face H Face V Face H Face V 1 55.427 1 247.006 1 15.7626 1 27.1679 3 55.427 2 247.006 3 15.7626 2 27.1679 5 55.427 3 247.006 5 15.7626 3 27.1679 2 71.2696 4 247.006 2 25.9525 4 27.1679 4 71.2696 5 247.006 4 25.9525 5 27.1679 6 71.2696 6 247.006 6 25.9525 6 27.1679 (Bold Numbers)-Faces use to calculate Poisson's ratio PROPERTIES OF SPECIMENS Spec.1 Spec.2 Spec.3 Data File Name: V_IDT 8Hz Long_assum.xls V2_IDT 8Hz Long_assum.xls V3_IDT 8Hz Long_assum.xls Diameter [in]: 4 4 4 Thickness [in]: 2.5 2.5 2.5 Temperature [C]: 20 20 20 Frequency [Hz]: 8 8 8 Load [lbf]: 646.216 646.216 646.216 Gage Length [in]: 1 1 1 PAGE 93 APPENDIX F DATA ANALYSIS RESULTS OF HORIZONTAL DYNAMIC PROPERTIES PAGE 94 84 0.333hz0 20000 40000 60000 80000 100000 120000 01002003004005006007008009001000CyclesDynamic modulus(psi) Figure F-1. E* at 0.333 Hz 1hz0 20000 40000 60000 80000 100000 120000 140000 160000 01002003004005006007008009001000CyclesDynamic modulus(psi) Figure F-2. E* at 1 Hz PAGE 95 85 4hz0 50000 100000 150000 200000 250000 01002003004005006007008009001000CyclesDynamic modulus(psi) Figure F-3. E* at 4 Hz 8hz0 50000 100000 150000 200000 250000 300000 01002003004005006007008009001000CyclesDynamic modulus(psi) Figure F-4. E* at 8 Hz PAGE 96 86 0.333hz0 5 10 15 20 25 30 35 01002003004005006007008009001000CyclesPhase angle(degree) Figure F-5. Phase angle at 0.333 Hz 1hz0 5 10 15 20 25 30 01002003004005006007008009001000CyclesPhase angle(degree) Figure F-6. Phase angle at 1 Hz PAGE 97 87 4hz0 5 10 15 20 25 30 01002003004005006007008009001000CyclesPhase angle(degree) Figure F-7. Phase angle at 4 Hz 8hz0 5 10 15 20 25 30 01002003004005006007008009001000CyclesPhase angle(degree) Figure F-8. Phase angle at 8 Hz PAGE 98 88 0.333hz0 20000 40000 60000 80000 100000 120000 01002003004005006007008009001000CyclesE'(psi) Figure F-9. EÂ’ at 0.333 Hz 1hz0 20000 40000 60000 80000 100000 120000 140000 160000 01002003004005006007008009001000CyclesE'(psi) Figure F-10. EÂ’ at 1 Hz PAGE 99 89 4hz0 50000 100000 150000 200000 250000 01002003004005006007008009001000CyclesE'(psi) Figure F-10. EÂ’ at 4 Hz 8hz0 50000 100000 150000 200000 250000 300000 01002003004005006007008009001000CyclesE'(psi) Figure F-11. EÂ’ at 8 Hz PAGE 100 90 0.333hz0 20000 40000 60000 80000 100000 120000 01002003004005006007008009001000CyclesE"(psi) Figure F-12. EÂ” at 0.333 Hz 1hz0 20000 40000 60000 80000 100000 120000 140000 160000 01002003004005006007008009001000CyclesE"(psi) Figure F-13. EÂ” at 1 Hz PAGE 101 91 4hz0 50000 100000 150000 200000 250000 01002003004005006007008009001000CyclesE"(psi) Figure F-14. EÂ” at 4 Hz 8hz0 50000 100000 150000 200000 250000 300000 01002003004005006007008009001000CyclesE"(psi) Figure F-15. EÂ” at 8 Hz PAGE 102 92 E*0 50000 100000 150000 200000 250000 300000 0246810 Frequency(hz)E*(psi) Figure F-17. E* PHASE ANGLE0 5 10 15 20 25 0246810 Frequency(hz)Angle(degree) Figure F-16. Phase angle PAGE 103 93 E'0 50000 100000 150000 200000 250000 300000 0246810 Frequency(hz)E'(psi) Figure F-17. EÂ’ E"0 50000 100000 150000 200000 250000 300000 0246810 Frequency(hz)E"(psi) Figure F-18. EÂ” PAGE 104 94 LIST OF REFERENCES AASHTO, 1996. AASHTO provisional standards : TP-9. Washington, DC: American Association of State Highway and Transportation Officials. AASHTO, 1996. AASHTO provisional standards : TP-31. Washington, DC: American Association of State Highway and Transportation Officials AASHTO, 1996. AASHTO provisional standards : TP-283. Washington, DC: American Association of State Highway and Transportation Officials ASTM, 1985. Annual book of ASTM standards : D 3497. Vol. 4.20. Philadelphia, Pa: American Society for Testing and Materials. ASTM, 1985. Annual book of ASTM standards : D 4123. Vol. 4.20. Philadelphia, Pa: American Society for Testing and Materials. Buttlar, W.G., G. G. Al-Khateeb., and D. Bozkurt., 1999. Development of a hollow cylinder tensile tester to obtain mechanical properties of bituminous paving mixtures. Journal of the association of Asphalt Paving Technologists . Vol. 68: pp 369-403. Buttlar, W. G. and R. Roque., 1994. Development and evaluation of the strategic highway research program measurement and analysis system for indirect tensile testing at low temperatures. Transportation Research Record . No. 1454: pp 163-171. Buttlar, W. G. and R. Roque., 1996. Evaluation of empirical and theoretical models to determine asphalt mixture stiffnesses at low temperatures. Journal of the Association of Asphalt Paving Technologists. Vol. 65: pp. 99-141. Fonseca, O. A and M. W. Witczak, 1996. 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Buttlar, B. E. Ruth, M. Tia, S. W. Dickison, and B. Reid, 1997. Evaluation of SHRP indirect tension tester to mitigate cracking in asphalt concrete pavements and overlays . FL-DOT-MO-0510755. Gainesville, Florida: University of Florida. Roque, R, D.R. Hiltunen, and W.G. Buttlar, 1995. Thermal cracking performance and design of mixture using SUPERPAVETM. Journal of the Association of Asphalt Paving Technologists . Vol. 64: pp. 718-735. Roque, R. and B. E. Ruth, 1987. Materials characterization and response of flexible pavements at low temperatures. Proceedings of Association of Asphalt Paving Technologists . Vol. 56: pp. 130-167. Wagoner, M. P., 2001. Investigation moisture sensitive parameters of asphalt concrete. MasterÂ’s thesis. Gainesville, Florida: University of Florida. Witczak, M. W. and O. A Fonseca., 1996. Revised predictive model for dynamic (complex) modulus of asphalt mixture. Transportation Research Record . No. 1540: pp 15-23. Witczak, M. W., R. B. Leahy, Caves, and J. Uzan, 1989. The universal airport pavement design system, report && : asphaltic mixture material characterization. College Park, Maryland: University of Maryland. Zhang. W., A. Drescher and D. Newcomb., 1997. Viscoelastic behavior of asphalt concrete in diametral compression. Journal of Transportation Engineering. Vol. 123: pp 495-502. PAGE 106 96 BIOGRAPHICAL SKETCH Jae Seung Kim was born on March 3, 1974 in Seoul, South Korea. After graduating from Seoul High School, he enrolled in the Department of Civil Engineering at Myong Ji University. In the middle of his studies, he served as a soldier in the Korea military. He received a Bachelor of Engineering degree in February 1999. He spent time working for a construction company during one year after graduation. His academic pursuit led him to attend the University of Florida to pursue a Master of Engineering degree in May 2002. |