1、Standard Practice for Developing Dynamic Modulus Master Curves for Asphalt Mixtures Using the Asphalt Mixture Performance Tester (AMPT) AASHTO Designation: PP 61-13 (2015)1,2American Association of State Highway and Transportation Officials 444 North Capitol Street N.W., Suite 249 Washington, D.C. 2
2、0001 TS-2d PP 61-1 AASHTO Standard Practice for Developing Dynamic Modulus Master Curves for Asphalt Mixtures Using the Asphalt Mixture Performance Tester (AMPT) AASHTO Designation: PP 61-13 (2015)1,21. SCOPE 1.1. This practice describes testing and analysis for developing a dynamic modulus master c
3、urve for asphalt mixtures using the Asphalt Mixture Performance Tester (AMPT). This practice is intended for dense- and gap-graded 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
4、 selection of appropriate test temperatures. 1.2. This standard may involve hazardous materials, operations, and equipment. This 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 saf
5、ety and health practices and determine the applicability of regulatory limitations prior to use. 2. REFERENCED DOCUMENTS 2.1. AASHTO Standards: PP 60, Preparation of Cylindrical Performance Test Specimens Using the Superpave Gyratory Compactor (SGC) TP 79, Determining the Dynamic Modulus and Flow Nu
6、mber for Asphalt Mixtures Using the Asphalt Mixture Performance Tester (AMPT) Mechanistic-Empirical Pavement Design Guide (MEPDG) 2.2. Other Publication: Equipment Specification for the Simple Performance Test System, Version 3.0, Prepared for National Cooperative Highway Research Program (NCHRP), O
7、ctober 16, 2007. 3. TERMINOLOGY 3.1. Definitions: 3.1.1. dynamic modulus master curvea composite curve constructed at a reference temperature by shifting dynamic modulus data from various temperatures along the log frequency axis. 3.1.2. reduced frequencythe computed frequency at the reference tempe
8、rature, equivalent to the actual loading frequency at the test temperature. 3.1.3. reference temperaturethe temperature at which the master curve is constructed. 2015 by the American Association of State Highway and Transportation Officials.All rights reserved. Duplication is a violation of applicab
9、le law.TS-2d PP 61-2 AASHTO 3.1.4. shift factorshift in frequency associated with a shift from a test temperature to the reference 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 fo
10、r asphalt mixtures. It involves collecting dynamic modulus test data at specified temperatures and loading rates, then manipulating 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 ma
11、ster curves can be used for mixture evaluation and for characterizing the modulus of asphalt mixtures for mechanistic-empirical pavement design. 6. APPARATUS 6.1. Specimen Fabrication EquipmentFor fabricating dynamic modulus test specimens as described in PP 60. 6.2. Dynamic Modulus Test SystemMeeti
12、ng the requirements of the equipment specification for the Simple Performance Test (SPT) System, Version 3.0. 6.3. Analysis SoftwareCapable of performing numerical optimization of nonlinear equations. Note 1The Solver tool included in Microsoft Excelis capable of performing the numerical optimizatio
13、n required by this practice. 7. HAZARDS 7.1. This practice and associated standards involve the handling of hot asphalt binder, aggregates, and asphalt mixtures. It also includes the use of sawing and coring machinery and servohydraulic testing equipment. Use standard safety precautions, equipment,
14、and clothing when handling hot materials and operating machinery. 8. STANDARDIZATION 8.1. Items associated with this practice 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 con
15、cerning calibration or verification. 9. DYNAMIC MODULUS TEST DATA 9.1. Test Specimen Fabrication: 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 PP 60. Note 2The number of specimens to test depends on the desired
16、accuracy of the analysis. Refer to Table 4 in TP 79 for guidance on the reproducibility of dynamic modulus and phase angle measurements. 2015 by the American Association of State Highway and Transportation Officials.All rights reserved. Duplication is a violation of applicable law.TS-2d PP 61-3 AASH
17、TO 9.1.2. Record the following volumetric properties for each test specimen: Voids in the mineral aggregate (VMA), and Voids 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 te
18、mperatures and loading frequencies given in Table 1. Begin testing at the lowest temperature and highest frequency. Test all 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
19、 PG 70-XX PG 76-XX and Stiffer Temperature, C Loading Frequencies, Hz Temperature, C Loading Frequencies, Hz Temperature, C Loading 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
20、 Note 3The dynamic modulus testing may be performed with or without confinement. The same confining stress conditions must be 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 onl
21、y test data meeting the data quality statistics given in Table 2. Repeat tests as necessary to obtain test data meeting the data quality statistics requirements. Table 2Data Quality Statistics Requirements Data Quality Statistic Limit Load standard error 10% Deformation standard error 10% Deformatio
22、n uniformity 30% Phase uniformity 3 degrees Note 4The data quality statistics in Table 2 are reported by the AMPT software. If 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 dynami
23、c modulus, phase angle, and data quality statistics. 9.3. Dynamic Modulus Data Summary: 9.3.1. Prepare a summary table of the dynamic modulus data. At each temperature and frequency, compute the following: 1. Average dynamic modulus; 2. Average phase angle; 3. Coefficient of variation of the dynamic
24、 modulus; and 4. Standard deviation of the phase angle. Figure 1 presents an example summary data sheet. 2015 by the American Association of State Highway and Transportation Officials.All rights reserved. Duplication is a violation of applicable law.TS-2d PP 61-4 AASHTO Conditions Specimen 1 Specime
25、n 2 Specimen 3 Average Modulus, ksi Modulus CV, % Average Phase Angle, degree Std Dev Phase Angle, degree Temperature, C Frequency, 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
26、 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 0.1 259.1 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 0.0
27、1 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 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 Modul
28、us Master Curve Equation: 10.1.1. General FormThe general form of the dynamic modulus master curve is a modified version of the dynamic modulus master curve equation included in the Mechanistic-Empirical Pavement Design Guide (MEPDG). ( )logMaxlog *1rfEe+= +(1) where: *E = the dynamic modulus, psi;
29、, , and = the fitting parameters; Max = the limiting maximum modulus, psi; and fr= the reduced frequency, Hz. 10.1.2. Reduced FrequencyThe reduced frequency in Equation 1 is computed using the Arrhenius equation. 11log log19.14714arrEffTT=+(2) where: fr= the reduced frequency at the reference temper
30、ature, Hz; f = the loading frequency at the test temperature, Hz; Ea= the activation energy (treated as a fitting parameter); 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 E
31、quation 2 into Equation 1. ( )11log19.14714Maxlog *1arEfTTEe+ + =+(3) 2015 by the American Association of State Highway and Transportation Officials.All rights reserved. Duplication is a violation of applicable law.TS-2d PP 61-5 AASHTO 10.2. Shift FactorsThe shift factors at each temperature are giv
32、en in Equation 4 as follows: ( )11log19.14714arEaTTT= (4) where: a(T) = the shift factor at temperature T; Ea= the activation 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 esti
33、mated from asphalt mixture volumetric properties using the Hirsch model (Christensen et al., 2003) and a limiting binder modulus 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
34、,00020435,000650cVFAVMAPVFAVMA+=+(6) max*E = the limiting maximum asphalt mixture dynamic modulus, psi; VMA = the voids in the 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
35、.1.1. Using the average VMA and VFA of the specimens tested, compute the limiting maximum modulus using Equations 5 and 6. 10.4.1.2. 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 temper
36、ature for the dynamic modulus master curve; and designate this value as Tr. Usually 20C (293.15K) is used as the reference temperature. 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. 10.4.3.2. D
37、etermine the four fitting parameters of Equation 3 (, , , and Ea) using numerical optimization. The optimization can be performed using the Solver function in Microsoft Excel. 2015 by the American Association of State Highway and Transportation Officials.All rights reserved. Duplication is a violati
38、on of applicable law.TS-2d PP 61-6 AASHTO This calculation is performed by a spreadsheet to compute the sum of the squared errors 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
39、 to minimize the sum of the squared errors by varying the fitting parameters in Equation 3. The following initial estimates 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 me
40、asured dynamic modulus values for each temperature/frequency combination. Designate this value as Sy. 10.4.4.2. Compute the 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 o
41、ptimization for each temperature/frequency combination; and log *iE = the logarithm of the average measured dynamic modulus 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
42、 error of estimate from Equation 7; and Sy= the standard deviation of the logarithm of the average dynamic modulus values. 10.5. 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-E
43、mpirical Pavement Design Guide (MEPDG) Inputs: 2015 by the American Association of State Highway and Transportation Officials.All rights reserved. Duplication is a violation of applicable law.TS-2d PP 61-7 AASHTO 10.6.1. Substitute the logarithm of the limiting maximum modulus (max) determined in Se
44、ction 10.4.1.2 and the fitting parameters (, , , and Ea) determined in Section 10.4.3.2 into Equation 3, and compute the dynamic 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
45、, 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 identification; 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 phas
46、e angle at each temperature/frequency combination; 11.1.4. Coefficient of variation of the measured dynamic modulus data at 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 speci
47、men tested; 11.1.7. Average VMA and VFA for the specimens tested; 11.1.8. Reference temperature; 11.1.9. Parameters of the fitted 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 maste
48、r curve as a function of reduced frequency showing average measured dynamic modulus data; 11.1.12. Plot of shift factors as 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
49、 into MEPDG. 12. KEYWORDS 12.1. Dynamic modulus; master curve; phase angle. 2015 by the American Association of State Highway and Transportation Officials.All rights reserved. Duplication is a violation of applicable law.TS-2d PP 61-8 AASHTO 13. REFERENCES 13.1. Applied Research Associates, Inc., ERES Consultants Division, Guide for Mechanistic-Empirical Design of New and Rehabi
