1、Standard Practice for Developing Dynamic Modulus Master Curves for Asphalt Mixtures Using the Asphalt Mixture Performance Tester (AMPT) AASHTO Designation: R 84-171 Technical Section: 2d, Proportioning of AsphaltAggregate Mixtures Release: Group 3 (August 2017) American Association of State Highway
2、and Transportation Officials 444 North Capitol Street N.W., Suite 249 Washington, D.C. 20001 TS-2d R 84-1 AASHTO Standard Practice for Developing Dynamic Modulus Master Curves for Asphalt Mixtures Using the Asphalt Mixture Performance Tester (AMPT) AASHTO Designation: R 84-171 Technical Section: 2d,
3、 Proportioning of AsphaltAggregate Mixtures Release: Group 3 (August 2017) 1. SCOPE 1.1. This practice describes testing and analysis for developing a dynamic modulus master curve for asphalt mixtures using the Asphalt Mixture Performance Tester (AMPT). This practice is intended for dense- and gap-g
4、raded mixtures with nominal-maximum aggregate sizes up to 37.5 mm. This practice accounts for the temperature limitations of the AMPT and provides guidance to the user for the selection of appropriate test temperatures. 1.2. This standard may involve hazardous materials, operations, and equipment. T
5、his standard does not purport to address all of the safety concerns associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use. 2. REFERENCED DOCUMENTS 2.1.
6、 AASHTO Publications: R 83, Preparation of Cylindrical Performance Test Specimens Using the Superpave Gyratory Compactor (SGC) T 378, Determining the Dynamic Modulus and Flow Number for Asphalt Mixtures Using the Asphalt Mixture Performance Tester (AMPT) Mechanistic-Empirical Pavement Design Guide (
7、MEPDG) 2.2. Other Publication: Equipment Specification for the Simple Performance Test System, Version 3.0, Prepared for National Cooperative Highway Research Program (NCHRP), October 16, 2007. 3. TERMINOLOGY 3.1. Definitions: 3.1.1. dynamic modulus master curvea composite curve constructed at a ref
8、erence temperature by shifting dynamic modulus data from various temperatures along the log frequency axis. 2017 by the American Association of State Highway and Transportation Officials. All rights reserved. Duplication is a violation of applicable law.TS-2d R 84-2 AASHTO 3.1.2. reduced frequencyth
9、e computed frequency at the reference temperature, equivalent to the actual loading frequency at the test temperature. 3.1.3. reference temperaturethe temperature at which the master curve is constructed. 3.1.4. shift factorshift in frequency associated with a shift from a test temperature to the re
10、ference temperature. 4. SUMMARY OF PRACTICE 4.1. This practice describes the testing required using the AMPT and the analysis needed to develop a dynamic modulus master curve for asphalt mixtures. It involves collecting dynamic modulus test data at specified temperatures and loading rates, then mani
11、pulating the test data to obtain a continuous function describing the dynamic modulus as a function of frequency and temperature. 5. SIGNIFICANCE AND USE 5.1. Dynamic modulus master curves can be used for mixture evaluation and for characterizing the modulus of asphalt mixtures for mechanistic-empir
12、ical pavement design. 6. APPARATUS 6.1. Specimen Fabrication EquipmentFor fabricating dynamic modulus test specimens as described in R 83. 6.2. Dynamic Modulus Test SystemMeeting the requirements of the equipment specification for the Simple Performance Test (SPT) System, Version 3.0. 6.3. Analysis
13、SoftwareCapable of performing numerical optimization of nonlinear equations. Note 1The Solver tool included in Microsoft Excelis capable of performing the numerical optimization required by this practice. 7. HAZARDS 7.1. This practice and associated standards involve the handling of hot asphalt bind
14、er, aggregates, and asphalt mixtures. It also includes the use of sawing and coring machinery and servohydraulic testing equipment. Use standard safety precautions, equipment, and clothing when handling hot materials and operating machinery. 8. STANDARDIZATION 8.1. Items associated with this practic
15、e that require calibration or verification are included in the documents referenced in Section 2. Refer to the pertinent section of the referenced documents for information concerning calibration or verification. 9. DYNAMIC MODULUS TEST DATA 9.1. Test Specimen Fabrication: 2017 by the American Assoc
16、iation of State Highway and Transportation Officials. All rights reserved. Duplication is a violation of applicable law.TS-2d R 84-3 AASHTO 9.1.1. Prepare at least two test specimens at the target air void content 0.5 percent and with the aging condition in accordance with R 83. Note 2The number of
17、specimens to test depends on the desired accuracy of the analysis. Refer to Table 4 in T 378 for guidance on the reproducibility of dynamic modulus and phase angle measurements. 9.1.2. Record the following volumetric properties for each test specimen: Voids in the mineral aggregate (VMA), and Voids
18、filled with asphalt (VFA). 9.2. Testing Conditions: 9.2.1. Measure the dynamic modulus and phase angle of each specimen using the dynamic modulus test system at each of the temperatures and loading frequencies given in Table 1. Begin testing at the lowest temperature and highest frequency. Test all
19、frequencies in descending order before moving to the next highest temperature. Table 1Recommended Testing Temperatures and Loading Frequencies PG 58-XX and Softer PG 64-XX and PG 70-XX PG 76-XX and Stiffer Temperature, C Loading Frequencies, Hz Temperature, C Loading Frequencies, Hz Temperature, C L
20、oading Frequencies, Hz 4 10, 1, 0.1 4 10, 1, 0.1 4 10, 1, 0.1 20 10, 1, 0.1 20 10, 1, 0.1 20 10, 1, 0.1 35 10, 1, 0.1, and 0.01 40 10, 1, 0.1, and 0.01 45 10, 1, 0.1, and 0.01 Note 3The dynamic modulus testing may be performed with or without confinement. The same confining stress conditions must be
21、 used at all temperatures and loading rates. An unconfined dynamic modulus master curve is typically used in mechanistic-empirical pavement analysis methods. 9.2.2. Accept only test data meeting the data quality statistics given in Table 2. Repeat tests as necessary to obtain test data meeting the d
22、ata quality statistics requirements. Table 2Data Quality Statistics Requirements Data Quality Statistic Limit Load standard error 10% Deformation standard error 10% Deformation uniformity 30% Phase uniformity 3 degrees Note 4The data quality statistics in Table 2 are reported by the AMPT software. I
23、f a dynamic modulus test system other than the AMPT is used, refer to the equipment specification for the SPT System, Version 3.0, for algorithms for the computation of dynamic modulus, phase angle, and data quality statistics. 9.3. Dynamic Modulus Data Summary: 9.3.1. Prepare a summary table of the
24、 dynamic modulus data. At each temperature and frequency, compute the following: 1. Average dynamic modulus; 2017 by the American Association of State Highway and Transportation Officials. All rights reserved. Duplication is a violation of applicable law.TS-2d R 84-4 AASHTO 2. Average phase angle; 3
25、 Coefficient of variation of the dynamic modulus; and 4. Standard deviation of the phase angle. Figure 1 presents an example summary data sheet. Conditions Specimen 1 Specimen 2 Specimen 3 Average Modulus, ksi Modulus CV, % Average Phase Angle, degree Std Dev Phase Angle, degree Temperature, C Freq
26、uency, Hz Modulus, ksi Phase Angle, degree Modulus, ksi Phase Angle, degree Modulus, ksi Phase Angle, degree 4 0.1 1170.9 18.8 1214.8 19.6 1443.2 18.5 1276.3 11.5 19.0 0.5 4 1 1660.8 12.0 1743.5 12.5 2027.0 11.6 1810.5 10.6 12.0 0.4 4 10 2107.3 8.1 2245.6 8.4 2596.1 8.2 2316.3 10.9 8.2 0.2 20 0.1 25
27、9.1 33.9 289.9 33.5 315.2 34.6 288.1 9.8 34.0 0.6 20 1 604.1 27.4 657.3 26.8 711.2 27.0 657.5 8.1 27.1 0.3 20 10 1065.1 21.0 1181.5 18.8 1231.4 19.8 1159.3 7.4 19.9 1.1 40 0.01 17.2 18.6 16.5 18.8 18.8 19.2 17.5 6.7 18.9 0.3 40 0.1 26.5 24.8 26.4 26.1 30.6 26.0 27.8 8.6 25.6 0.7 40 1 62.9 31.5 63.9
28、32.1 74.5 32.7 67.1 9.6 32.1 0.6 40 10 180.1 35.2 197.6 35.1 220.6 35.2 199.4 10.2 35.2 0.1 Figure 1Example Dynamic Modulus Summary Sheet 10. DATA ANALYSIS 10.1. Dynamic Modulus Master Curve Equation: 10.1.1. General FormThe general form of the dynamic modulus master curve is a modified version of t
29、he dynamic modulus master curve equation included in the Mechanistic-Empirical Pavement Design Guide (MEPDG). ( ) logMaxlog *1rfEe+= +(1) where: *E = the dynamic modulus, psi; , , and = the fitting parameters; Max = the limiting maximum modulus, psi; and fr= the reduced frequency, Hz. 10.1.2. Reduce
30、d FrequencyThe reduced frequency in Equation 1 is computed using the Arrhenius equation. 11log log19.14714arrEffTT=+(2) where: fr= the reduced frequency at the reference temperature, Hz; f = the loading frequency at the test temperature, Hz; Ea= the activation energy (treated as a fitting parameter)
31、 T = the test temperature, K; and Tr= the reference temperature, K. 10.1.3. Final FormThe final form of the dynamic modulus master curve equation is obtained by substituting Equation 2 into Equation 1. 2017 by the American Association of State Highway and Transportation Officials. All rights reserv
32、ed. Duplication is a violation of applicable law.TS-2d R 84-5 AASHTO ( )11log19.14714Maxlog *1arEfTTEe+ + =+(3) 10.2. Shift FactorsThe shift factors at each temperature are given in Equation 4 as follows: ( )11log19.14714arEaTTT= (4) where: a(T) = the shift factor at temperature T; Ea= the activatio
33、n energy (treated as a fitting parameter); T = the test temperature, K; and Tr= the reference temperature, K. 10.3. Limiting Maximum ModulusThe maximum limiting modulus is estimated from asphalt mixture volumetric properties using the Hirsch model (Christensen et al., 2003) and a limiting binder mod
34、ulus of 1 GPa as provided in Equations 5 and 6. ( )( )max1001* 4, 200, 000 1 435, 0001100 10, 0004, 200, 000 435, 000VMAccPVMA VFA VMAEPVMAVFA= + + (5) where: ( )( )0.580.58435,00020435,000650cVFAVMAPVFAVMA+=+(6) max*E = the limiting maximum asphalt mixture dynamic modulus, psi; VMA = the voids in t
35、he mineral aggregate, percent; and VFA = the voids filled with asphalt, percent. 10.4. Fitting the Dynamic Modulus Master Curve: 10.4.1. Estimate Limiting Maximum Modulus: 10.4.1.1. Using the average VMA and VFA of the specimens tested, compute the limiting maximum modulus using Equations 5 and 6. 1
36、0.4.1.2. Compute the logarithm of the limiting maximum modulus, and designate this value as max. 10.4.2. Select the Reference Temperature: 10.4.2.1. Select the reference temperature for the dynamic modulus master curve; and designate this value as Tr. Usually 20C (293.15K) is used as the reference t
37、emperature. 10.4.3. Perform Numerical Optimization: 10.4.3.1. Substitute “max,” computed in Section 10.4.1.2, and Tr, selected in Section 10.4.2.1, into Equation 3. 2017 by the American Association of State Highway and Transportation Officials. All rights reserved. Duplication is a violation of appl
38、icable law.TS-2d R 84-6 AASHTO 10.4.3.2. Determine the four fitting parameters of Equation 3 (, , , and Ea) using numerical optimization. The optimization can be performed using the Solver function in Microsoft Excel. This calculation is performed by a spreadsheet to compute the sum of the squared e
39、rrors between the logarithm of the average measured dynamic moduli at each temperature/frequency combination and the values predicted by Equation 3. The Solver function is used to minimize the sum of the squared errors by varying the fitting parameters in Equation 3. The following initial estimates
40、are recommended: = 0.5, = 1.0, = 0.5, and Ea= 200 000. 10.4.4. Compute “Goodness of Fit” Statistics: 10.4.4.1. Compute the standard deviation of the logarithm of the average measured dynamic modulus values for each temperature/frequency combination. Designate this value as Sy. 10.4.4.2. Compute the
41、standard error of estimate using Equation 7. ( )0.510 211log * log *6eiiS EE= (7) where: Se= the standard error of estimate; log *iE = the value predicted by Equation 3 after optimization for each temperature/frequency combination; and log *iE = the logarithm of the average measured dynamic modulus
42、for each temperature/frequency combination. 10.4.4.3. Compute the explained variance, R2, using Equation 8. 222819eySRS= (8) where: R2= the explained variance; Se= the standard error of estimate from Equation 7; and Sy= the standard deviation of the logarithm of the average dynamic modulus values. 1
43、0.5. Evaluate Fitted Master Curve: 10.5.1. The ratio of Seto Syshould be less than 0.05. 10.5.2. The explained variance should exceed 0.99. 10.6. Determine AASHTO Mechanistic-Empirical Pavement Design Guide (MEPDG) Inputs: 2017 by the American Association of State Highway and Transportation Official
44、s. All rights reserved. Duplication is a violation of applicable law.TS-2d R 84-7 AASHTO 10.6.1. Substitute the logarithm of the limiting maximum modulus (max) determined in Section 10.4.1.2 and the fitting parameters (, , , and Ea) determined in Section 10.4.3.2 into Equation 3, and compute the dyn
45、amic modulus at the following temperatures and loading frequencies. A total of 30 dynamic modulus values will be calculated. Temperatures, C Frequencies, Hz 10, 4.4, 21.1, 37.8, and 54.4 25, 10, 5, 1, 0.5, and 0.1 (14, 40, 70, 100, and 130) 11. REPORT 11.1. Report the following: 11.1.1. Mixture iden
46、tification; 11.1.2. Measured dynamic modulus and phase angle data for each specimen at each temperature/frequency combination; 11.1.3. Average measured dynamic modulus and phase angle at each temperature/frequency combination; 11.1.4. Coefficient of variation of the measured dynamic modulus data at
47、each temperature/frequency combination; 11.1.5. Standard deviation of the measured phase angle data at each temperature/frequency combination; 11.1.6. VMA and VFA of each specimen tested; 11.1.7. Average VMA and VFA for the specimens tested; 11.1.8. Reference temperature; 11.1.9. Parameters of the f
48、itted master curve (Max, , , , and Ea); 11.1.10. “Goodness of Fit” statistics for the fitted master curve (Se, Sy, Se/Sy, R2); 11.1.11. Plot of the fitted dynamic modulus master curve as a function of reduced frequency showing average measured dynamic modulus data; 11.1.12. Plot of shift factors as
49、a function of temperature; 11.1.13. Plot of average phase angle as a function of reduced frequency; and 11.1.14. Tabulated temperature, frequency, and dynamic modulus for input into MEPDG. 12. KEYWORDS 12.1. Dynamic modulus; master curve; phase angle. 2017 by the American Association of State Highway and Transportation Officials. All rights reserved. Duplication is a violation
