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11 8,000,000 7,000,000 6,000,000 Maximum Modulus, psi 5,000,000 AASHTO TP62 4,000,000 Reduced Set 3,000,000 2,000,000 1,000,000 0 ALF1 ALF2 ALF3 ALF4 ALF5 ALF7 ALF8 ALF9 ALF10 ALF11 ALF12 MN16 MN17 MN18 MN20 MN22 WSTR2 WSTR4 WSTR7 WSTR15 WSTR23 WSTR24 Section Figure 6. Comparison of limiting maximum moduli. temperatures (9). This coupled with potential friction in the 2.5 Abbreviated Dynamic Modulus linearly variable differential transformer (LVDT) guide rod Master Curve Testing used included in the AASHTO TP62 recommended instru- Conditions mentation is the most likely cause of the high variability in the low temperature measurements. This probably also The previous section showed that reasonable dynamic explains the unrealistically high moduli measured for four modulus master curves can be obtained using an estimated of the ALF mixtures. limiting maximum modulus and data collected at tempera- The limiting maximum modulus also affects the limiting tures of 40, 70, 100, and 130F and frequencies of 25, 10, 5, minimum modulus because of the symmetry inherent to the 1.0, 0.5, and 0.1 Hz. However, these temperatures and load- MEPDG dynamic modulus master curve. Figure 7 compares ing rates are not optimal for use with the estimated limiting limiting minimum modulus values from the two data sets maximum modulus approach. This section presents an for individual mixtures. As shown the largest differences analysis of the temperatures and loading rates that should be between the two occur for the same mixtures that have used in combination with an estimated limiting maximum the largest differences in the limiting maximum modulus. modulus to develop dynamic modulus master curves. Table 4 summarizes limiting minimum modulus values The optimum approach for fitting the S shaped sigmoidal averaged over similar mixtures. The two data sets produce function is to obtain data defining the limiting maximum reasonably similar average limiting minimum modulus modulus, the limiting minimum modulus, and the slope over values. The limiting minimum modulus represents the stiff- the middle portion of this range on a log scale. Unfortunately, ness of the aggregate structure in the absence of binder. Both the limiting moduli cannot be obtained directly by testing as procedures provide the same rankings for the mixtures com- these would require tests at extremely low and high tempera- pared in this evaluation. tures. Therefore, the approach taken in AASHTO TP62 is to collect data over a wide temperature range and essentially Table 2. Limiting maximum modulus values averaged over mixture type. Table 3. Dynamic modulus variability reported by Pellinen (9). Limiting Maximum Modulus, psi Mixture Number AASHTO TP62 Reduced Set Pooled Between Specimen Coefficient of Variation, % MNRoad 5 3,109,668 3,206,382 Temperature, F 12.5 mm Mixtures 19.0 mm Mixtures ALF 19 mm 9 3,867,636 3,077,348 15.8 16.7 25.4 ALF 25 mm 2 4,735,721 3,324,313 40.0 12.8 19.0 WesTrack 19 mm Fine 3 2,985,757 3,187,770 70.0 14.2 9.4 WesTrack 19 mm Coarse 3 2,934,664 3,345,151 100.0 14.5 20.3 All Mixtures 22 3,526,808 3,180,702 130.0 28.1 22.7

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12 35,000 30,000 Minimum Modulus, psi 25,000 20,000 AASHTO TP62 Reduced Set 15,000 10,000 5,000 0 F1 F2 F3 F4 AL 8 AL 9 AL 0 AL 1 M 2 M 6 M 8 20 W 22 ST 3 24 W R2 W R4 AL 5 ST 5 17 ST 7 F7 F F F1 F1 F1 1 1 W R2 F W R1 W R N N N N R AL AL AL AL AL AL N ST ST ST M M Section Figure 7. Comparison of limiting minimum moduli. extrapolate these data to define the limiting maximum and program is to increase temperature; however, for the glued minimum moduli. As shown in this evaluation, the AASHTO gage point instrumentation used in the dynamic modulus test, TP62 approach is sensitive to the quality of the data at the the maximum testing temperature appears to be approxi- lowest temperature, which is often variable, and potentially in- mately 104F. Above this temperature, the gage points may accurate due to testing difficulties. For the same intermediate- loosen, particularly when the gage points are attached to the and high-temperature data, high-limiting maximum moduli matrix of fine aggregate and binder. Higher temperatures may result in lower limiting minimum moduli while low-limiting be possible when stiff modified binders are used or the gage maximum moduli result in higher limiting minimum moduli points are attached to the coarse aggregate, but this can not be due to the symmetry of the MEPDG master curve equation. assured in most mixtures. Figure 8 presents experimentally In the alternate approach developed in Phase IV of NCHRP determined shift factors for the mixtures included in this eval- Project 9-29, a reasonable, rational estimate of the limiting uation. As shown, the shift factors for the maximum recom- maximum modulus is provided by the Hirsch model. This mended testing temperature of 104F range from about 10-1.8 eliminates the need for testing at low temperatures, and the to 10-2.5. From Equation 2, this results in a loading frequency potential inaccuracies caused by these difficult testing condi- of approximately 0.03 to 0.06 Hz at 104 F to obtain reduced tions. To provide an accurate estimate of the limiting mini- frequencies ranging from 10-3 to 10-4 Hz. Thus, the use of a mum modulus, data should be collected to the slowest reduced loading rate of 0.01 Hz at 104F will provide somewhat lower frequency possible. From Equation 2, the reduced frequency is reduced frequencies than obtained with 0.1 Hz at 130F as a function of both temperature and frequency of loading. High specified in AASHTO TP62. temperature, slow frequency dynamic modulus tests result in Because the shift factor relationship is not linear, a mini- the lowest reduced frequency values. The AASHTO TP62 test- mum of three temperatures spaced as widely as possible ing conditions yielded minimum reduced frequencies for the should be used in the testing program. This will provide a rea- mixtures studied ranging from 10-3 to 10-4 Hz. The most sonable estimate of the coefficient, c, in the shift factor rela- efficient way to decrease the reduced frequency in the testing tionship, Equation 3. A low testing temperature of 40F would allow reasonable priced environmental chambers to be Table 4. Limiting minimum modulus values averaged used, and will eliminate the icing problems that occur when over mixture type. testing at temperatures below freezing. The recommended testing temperatures for the abbrevi- Limiting Minimum Modulus, psi Mixture Number ated dynamic modulus master curve testing are 40, 70, and AASHTO TP62 Reduced Set MNRoad 5 4,383 3,873 104F. Based on the performance of typical LVDT deforma- ALF 19 mm 9 11,247 11,044 tion systems, the maximum frequency of loading should be ALF 25 mm 2 14,092 13,426 WesTrack 19 mm Fine 3 16,589 14,077 limited to 10 Hz. Using loading frequencies of 10, 1, 0.1, and WesTrack 19 mm Coarse 3 19,101 15,569 0.01 Hz at each of the temperatures results in well spaced Overall 22 11,745 10,662 data in reduced frequency with a minimum of overlap. This

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13 6 5 4 3 2 Log Shift Factor 1 0 -1 -2 -3 -4 -5 -6 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 Temperature, F Figure 8. Shift factors as a function of temperature for the mixtures in Table 2. is shown in Figure 9, based on the average shift factors at with a small overlap of the high and low temperature data 40 and 104F shown in Figure 8. The recommended testing with the reference temperature data. temperatures and frequencies for the abbreviated dynamic The SPT software applies 20 cycles at each loading frequency. modulus master curve testing result in data over the range of The first 10 cycles are used to adjust the load to produce strains reduced frequency at 70F from approximately 10-4 to 105 within the specified 75 to 125 strain range. The data from the 1.0E+05 1.0E+04 1.0E+03 1.0E+02 Reduced Frequency, Hz 1.0E+01 1.0E+00 1.0E-01 1.0E-02 1.0E-03 1.0E-04 1.0E-05 1.0E-06 1.0E-07 30 40 50 60 70 80 90 100 110 Temperature, F Figure 9. Approximate reduced frequencies for abbreviated dynamic modulus master curve testing sequence.