1、Proposed Standard Practice for Developing Dynamic Modulus Master Curves for Asphalt Mixtures Using the Indirect Tension Testing Method AASHTO Designation: PP 96-18 Technical Section: 2d, Bituminous Materials Release: Group 3 (August) American Association of State Highway and Transportation Officials
2、 444 North Capitol Street N.W., Suite 249 Washington, D.C. 20001 TS 2d PP 96-1 AASHTO Proposed Standard Practice for Developing Dynamic Modulus Master Curves for Asphalt Mixtures Using the Indirect Tension Testing Method AASHTO Designation: PP 96-18 Technical Section: 2d, Bituminous Materials Releas
3、e: Group 3 (August) 1. SCOPE 1.1. This practice describes testing and analysis for developing a dynamic modulus master curve for asphalt concrete using a servo-hydraulic closed loop testing machine. This practice is intended for dense- and gap- graded mixtures with nominal maximum aggregate sizes up
4、 to 25 mm. 1.2. This standard may involve hazardous materials, operations, and equipment. This standard does not purport to address all of the safety problems associated with its use. It is the responsibility of the user of this procedure to establish appropriate safety and health practices and to d
5、etermine the applicability of regulatory limitations prior to its use. 2. REFERENCED DOCUMENTS 2.1. AASHTO Standards: PP 95, Preparation of Indirect Tension Performance Test Specimens TP 131, Determining the Dynamic Modulus of Asphalt Mixtures Using the Indirect Tension Test 2.2. Other Publications:
6、 Equipment Specification for the Simple Performance Test System, Version 3.0, Prepared for National Cooperative Highway Research Program (NCHRP), October 16, 2007. Kim, Y.R., Y. Seo, M. King, and M. Momen. Dynamic Modulus Testing of Asphalt Concrete in Indirect Tension Mode. In Transportation Resear
7、ch Record: Journal of the Transportation Research Board, No. 1891, TRB, National Research Council, Washington, D.C., 2004. Applied Research Associates, Inc., ERES Consultants Division Guide for Mechanistic-Empirical Design of New and Rehabilitated Pavement Structures, Final Report Prepared for the N
8、ational Cooperative Highway Research Program, March, 2004. 3. TERMINOLOGY 3.1. Dynamic Modulus Master Curvea composite curve constructed at a reference temperature by shifting dynamic modulus data from various temperatures along the log frequency axis. 3.2. Indirect Tension (IDT)a method of loading
9、a material by applying a compressive force on a cylindrical specimen in one direction, which results in a tensile strain in the perpendicular direction due to the Poissons effect. 2018 by the American Association of State Highway and Transportation Officials. All rights reserved. Duplication is a vi
10、olation of applicable law.TS 2d PP 96-2 AASHTO 3.3. Reduced Frequencythe computed frequency at the reference temperature equivalent to the actual loading frequency at the test temperature. 3.4. Reference Temperaturethe temperature at which the master curve is constructed. 3.5. Shift Factorshift in f
11、requency associated with a shift from a test temperature to the reference temperature. 4. SUMMARY OF PRACTICE 4.1. This practice describes the testing and analysis needed to develop a dynamic modulus master curve for asphalt mixtures from indirect tension specimens, specifically from field cores. It
12、 involves collecting dynamic modulus test data at specified temperatures and loading frequencies, determining time-temperature shift factors from individual temperature data, and finally fitting the test data to obtain a continuous function describing the dynamic modulus as a function of reduced fre
13、quency. 5. SIGNIFICANCE AND USE 5.1. Dynamic modulus master curves can be used for mixture evaluation and for characterizing the modulus of asphalt concrete for mechanistic-empirical pavement design. 6. APPARATUS 6.1. Specimen Fabrication Equipmentequipment for fabricating dynamic modulus test speci
14、mens as described in AASHTO PP 95, Preparation of Indirect Tension Performance Test Specimens. 6.2. Dynamic Modulus Test Systema dynamic test system meeting the requirements of Equipment Specification for the Simple Performance Test System, Version 3.0. 6.3. Specimen Deformation Measurement DevicesT
15、he specimen deformation measurement devices shall consist of four displacement transducers with a range of at least 0.25 mm, and a minimum resolution throughout the range of 0.10 m. 6.4. Analysis Softwaresoftware capable of performing numerical optimization of non-linear equations. Note 1The Solver
16、Tool included in Microsoft Excel is capable of performing the numerical optimization required by this practice. 7. HAZARDS 7.1. This practice and associated standards involve handling of hot asphalt binder, aggregates, and asphalt mixtures. It also includes the use of sawing and coring machinery and
17、 servo-hydraulic testing equipment. Use standard safety precautions, equipment, and clothing when handling hot materials and operating machinery. 8. STANDARDIZATION 8.1. Items associated with this practice that require calibration are included in the documents referenced in Section 2. Refer to the p
18、ertinent section of the referenced documents for information concerning calibration. 2018 by the American Association of State Highway and Transportation Officials. All rights reserved. Duplication is a violation of applicable law.TS 2d PP 96-3 AASHTO 9. DYNAMIC MODULUS TEST DATA 9.1. Test Specimen
19、Fabrication 9.1.1. Prepare at least three test specimens to the target air void content and aging condition in accordance with AASHTO PP 95, Preparation of Indirect Tension Performance Test Specimens. Note 2A reasonable air void tolerance for test specimen fabrication is 0.5 %. 9.1.2. Record the fol
20、lowing volumetric properties for each test specimen: Voids in the mineral aggregate (VMA) Voids filled with asphalt concrete (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 (1.0C) and
21、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 Test Type Test Temperatures (C) Loading History
22、 Frequency (Hz) |E*| -10, 10, 35 Sinusoidal 25, 10, 5, 1, 0.5, 0.1, 0.05, 0.01 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 data quality statistics requirements. Table 2Data Quality Statistics Requirement
23、s Data Quality Statistic Limit Load standard error 5 % Deformation standard error 10 % Deformation uniformity 30 % Phase uniformity 3 degrees Phase angle TBD Note 3Refer to Equipment Specification for the Simple Performance Test System, Version 3.0 for algorithms for data quality statistics. Refer t
24、o AASHTO TP 131, Determining the Dynamic Modulus of Asphalt Concrete Using the Indirect Tension Test for computation of dynamic modulus and phase angle. 9.3. Dynamic Modulus Data Summary 9.3.1. Prepare a summary table of the dynamic modulus data. At each temperature and frequency, compute: 1. Averag
25、e dynamic modulus 2. Average phase angle 3. Poissons ratio 4. Dynamic modulus coefficient of variation 5. Standard deviation of phase angle 2018 by the American Association of State Highway and Transportation Officials. All rights reserved. Duplication is a violation of applicable law.TS 2d PP 96-4
26、AASHTO 10. DATA ANALYSIS 10.1. Dynamic Modulus Master Curve Equation 10.1.1. General Form. The general form of the dynamic modulus master curve is the sigmoidal function included in the Mechanistic-Empirical Pavement Design Guide (MEPDG) (Applied Research Associates, Inc., 2004) (1) where: |E*| = pr
27、edicted dynamic modulus, MPa or psi; fr= reduced frequency at the reference temperature, Hz; and , , , and = fitting parameters 10.1.2. Reduced Frequency. The reduce frequency in Equation 1 is computed using time-temperature shift factors. Several time-temperature shift functions are available in th
28、e literature. This practice presents two shift factor equations: shift factors from the Pavement ME program and second order polynomial. 10.1.2.1. Pavement ME Shift Factors (2) where: f = loading frequency at the test temperature; = viscosity of the binder at the test temperature, cP; TR= reference
29、temperature, R (F+459.67); RT = viscosity of the binder at the reference temperature, cP; and c = fitting coefficient. The viscosities in Equation 2 are determined using Equation 3. (3) where: A and VTS = parameters of the binder viscosity-temperature susceptibility relationship. 10.1.2.2. Second Or
30、der Polynomial (4) where: T = test temperature, C; TR= reference temperature, C; and a1, a2= fitting coefficients. 10.1.3. Final Form. The final form of the dynamic modulus master curve equation is obtained by substituting the selected shift factor relationship into Equation 1. 10.1.3.1. Pavement ME
31、 Shift Factors log( )log(| *|)1rfEe+= +log log (log log )RrTf fc =+ )log(10logRTVTSA+=212log log ( ) ( )r RRf faTTaTT= + + 2018 by the American Association of State Highway and Transportation Officials. All rights reserved. Duplication is a violation of applicable law.TS 2d PP 96-5 AASHTO (5) 10.1.3
32、.2. Second Order Polynomial Shift Factors (6) 10.2. Fitting the Dynamic Modulus Master Curve 10.2.1. Step 1. Select the Reference Temperature 10.2.1.1. Select the reference temperature for the dynamic modulus master curve and designate this as TR. Usually 20C (293.15K) is used as the reference tempe
33、rature. 10.2.2. Step 2. Perform Numerical Optimization 10.2.2.1. Determine the fitting parameters of Equation 5 or 6 using numerical optimization. The optimization can be performed using the Solver function in Microsoft EXCEL. This is done by setting up a spreadsheet to compute the sum of the square
34、d errors in Equation (1)(7) between the logarithm of the average measured dynamic moduli at each temperature/frequency combination and the values predicted by Equation 5 or 6. The Solver function is used to minimize the sum of the squared errors by varying the fitting parameters. Recommended initial
35、 estimates for a reference temperature of 20C are listed in Table 3. ( )0.521log * log *niiSum Squared Error E E= (7) where: log *Ei= value predicted by Equation 5 or 6 after optimization for each temperature/frequency combination and log *Ei= logarithm of the average measured dynamic modulus for ea
36、ch temperature/frequency combination. Table 3Recommended Initial Estimates for 20C Reference Temperature Pavement ME Shift Factors Polynomial Shift Factors Fitting Parameters Initial Estimates MPa (ksi) Fitting Parameters Initial Estimates MPa (ksi) 2.0 (0.5) 2.0 (0.5) 2.5 (3.0) 2.5 (3.0) -1.5 (-1.0
37、) -1.5 (-1.0) -0.5 (-0.5) -0.5 (-0.5) c 1.0 (1.0) a1 0.1 (0.1) a2 0.0001 (0.0001) ( log )( log )log 10 10log *1A VTS TA VTS TRfcEe+ = +212log()()log *1RRfaTTaTTEe+ + + = + 2018 by the American Association of State Highway and Transportation Officials. All rights reserved. Duplication is a violation
38、of applicable law.TS 2d PP 96-6 AASHTO 10.2.3. Step 3. Compute Goodness of Fit Statistics 10.2.3.1. Compute the standard deviation of the logarithm of the average measured dynamic modulus values for each temperature/frequency combination. Designate this value as Sy. 10.2.3.2. Compute the standard er
39、ror of estimate using Equation 7. (8) where: Se= standard error of estimate; n = number of temperature/frequency combinations used in the testing; and p = number of fitting parameters. 10.2.3.3. Compute the explained variance, R2, using Equation 8. (9) where: R2= explained variance. 10.3. Evaluate F
40、itted Master Curve 10.3.1. The ratio of Se to Syshould be less than 0.05. 10.3.2. The explained variance should exceed 0.99. 11. REPORT 11.1. Mixture identification 11.2. Measured dynamic modulus and phase angle data for each specimen at each temperature/frequency combination 11.3. Average measured
41、dynamic modulus and phase angle at each temperature/frequency combination. 11.4. Coefficient of variation of the measured dynamic modulus data at each temperature/frequency combination. 11.5. Standard deviation of the measured phase angle data at each temperature/frequency combination. 11.6. Air voi
42、ds, binder content, VMA and VFA of each specimen tested. 11.7. Average air voids, average binder content, average VMA, and average VFA for the specimens tested. 11.8. Reference temperature. 11.9. Parameters of the fitted master curve. 11.10. Goodness of fit statistics for the fitted master curve (Se
43、, Sy, Se/Sy, R2). ( )5.012*log*log)1(1= niieEEpnS222)1()1(1yeSnSpnR= 2018 by the American Association of State Highway and Transportation Officials. All rights reserved. Duplication is a violation of applicable law.TS 2d PP 96-7 AASHTO 11.11. Plot of the fitted dynamic modulus master curve as a func
44、tion of reduced frequency showing average measured dynamic modulus data. 11.12. Plot of shift factors as a function of temperature. 11.13. Plot of average phase angle as a function of reduced frequency. 12. KEYWORDS 12.1. Asphalt mixture; dynamic modulus; indirect tension; master curve; phase angle. 2018 by the American Association of State Highway and Transportation Officials. All rights reserved. Duplication is a violation of applicable law.
