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8 where For the comparison, the database of dynamic modulus meas- ) urements assembled for NCHRP Project 9-19 was used (9). Pc = ( 435,000(VFA ) 0.58 20 + VMA (11) This database includes test data from replicate samples tested at temperatures of 15.8, 40, 70, 100, and 130F and frequen- 650 + ( 435,000(VFA) 0.58 VMA ) cies of 25, 10, 5, 1.0, 0.5, and 0.1 Hz. Table 1 summarizes pertinent properties of the mixtures included in the evalua- E * max = limiting maximum mixture dynamic modulus; tion. The mixtures include 5 mixtures from the MNRoad VMA = voids in mineral aggregates, %; and project, 11 mixtures from the FHWA Pavement Testing VFA = voids filled with asphalt, %. Facility, and 6 mixtures from the WesTrack project. This combination of mixtures includes a range of nominal maxi- Figure 2 presents limiting maximum moduli computed mum aggregate sizes, binders, and volumetric properties. using Equation 10 for VMA ranging from 10 to 20 percent, For each mixture included in Table 1, master curves were and VFA ranging from 55 to 85 percent. For this wide range developed using the MEPDG master curve. Data from all of volumetric properties, the limiting maximum modulus temperatures were used to develop the AASHTO TP62 mas- varies from about 3,000,000 to 3,800,000 psi. These limiting ter curves, while the reduced data set excluded the data at maximum modulus values appear very rational. For condi- 15.8F and included an estimate of the limiting maximum tions with low VMA and high VFA, the limiting maximum modulus from the Hirsch model. The master curves then modulus approaches 4,000,000 psi, which is often assumed were compared graphically. The rationality of the master for the modulus of portland cement concrete. curve parameters also was considered. Figure 3 and Figure 4 present examples of the master curves generated. Figure 3 is for Lane 2 at the FHWA Pave- 2.4 Comparison of Master Curves ment Testing Facility and is an example of the worst agree- Using Complete and Reduced ment between the two methods. The limiting maximum Data Sets modulus from the reduced data set at 3,236,868 psi is much This section presents comparisons of master curves fitted lower than the 6,714,030 psi limiting maximum modulus to actual laboratory test data using the complete AASHTO from the AASHTO TP62 data set. The difference in the lim- TP62 data and a reduced data set where test data at the low- iting maximum modulus also affects the limiting minimum est temperature are eliminated and replaced with an estimate modulus because the sigmoidal master curve is symmetrical. of the limiting maximum modulus from the Hirsch model. The limiting minimum modulus from the reduced data set is 4,000,000 3,900,000 3,800,000 Limiting Dynamic Modulus, psi 3,700,000 3,600,000 VFA = 55% 3,500,000 VFA = 70% VFA = 85% 3,400,000 3,300,000 3,200,000 3,100,000 3,000,000 9 11 13 15 17 19 21 VMA, % Figure 2. Limiting maximum dynamic modulus values from the Hirsch model.

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9 Table 1. Properties of mixtures used in the master curve comparison study. Description Mix Volumetric Properties AASHTO T240 Residue Binder Properties Project Project ID Binder Mix Type AC, % Va, % VMA, % VFA, % A VTS 70 RTFOT , cP MNRoad Cell 16 AC-20 Fine 9.5 mm 5.08 8.2 18.0 54.4 10.7826 -3.6065 1.22E+09 MNRoad Cell 17 AC-20 Fine 9.5 mm 5.45 7.7 18.2 57.6 10.7826 -3.6065 1.22E+09 MNRoad Cell 18 AC-20 Fine 9.5 mm 5.83 5.6 17.1 67.2 10.7826 -3.6065 1.22E+09 MNRoad Cell 20 120/150 Pen Fine 9.5 mm 6.06 6.3 18.3 65.6 10.8101 -3.6254 3.96E+08 MNRoad Cell 22 120/150 Pen Fine 9.5 mm 5.35 6.5 16.9 61.5 10.8101 -3.6254 3.96E+08 ALF Lane 1 AC-5 Fine 19 mm 4.75 6.1 16.9 63.9 10.6766 -3.5740 5.35E+08 ALF Lane 2 AC-20 Fine 19 mm 4.85 6.5 17.3 62.5 10.6569 -3.5594 1.38E+09 ALF Lane 3 AC-5 Fine 19 mm 4.75 7.7 18.3 57.9 10.6766 -3.5740 5.35E+08 ALF Lane 4 AC-20 Fine 19 mm 4.9 9.7 20.3 52.1 10.6569 -3.5594 1.38E+09 ALF Lane 5 AC-10 Fine 19 mm 4.8 8.6 19.0 54.7 10.7805 -3.6116 5.72E+08 ALF Lane 7 Styrelf Fine 19 mm 4.9 11.9 22.1 46.2 8.9064 -2.9089 4.02E+09 ALF Lane 8 Novophalt Fine 19 mm 4.7 11.9 21.6 45.0 8.8136 -2.8817 1.58E+09 ALF Lane 9 AC-5 Fine 19 mm 4.9 7.7 18.4 58.1 10.6766 -3.5740 5.35E+08 ALF Lane 10 AC-20 Fine 19 mm 4.9 9.3 19.8 53.0 10.6569 -3.5594 1.38E+09 ALF Lane 11 AC-5 Fine 37.5 mm 4.05 6 14.2 57.9 10.6766 -3.5740 5.35E+08 ALF Lane 12 AC-20 Fine 37.5 mm 4.05 7.4 15.5 52.3 10.6569 -3.5594 1.38E+09 WesTrack Sec 2 PG 64-22 Fine 19 mm 5.02 10.4 17.3 39.9 11.0757 -3.7119 1.63E+09 WesTrack Sec 4 PG 64-22 Fine 19 mm 5.24 6.6 14.3 53.8 11.0757 -3.7119 1.63E+09 WesTrack Sec 7 PG 64-22 Coarse 19 mm 6.28 6.9 15.9 56.6 11.0757 -3.7119 1.63E+09 WesTrack Sec 15 PG 64-22 Fine 19 mm 5.55 8.7 16.9 48.4 11.0757 -3.7119 1.63E+09 WesTrack Sec 23 PG 64-22 Coarse 19 mm 5.78 4.9 13.0 62.3 11.0757 -3.7119 1.63E+09 WesTrack Sec 24 PG 64-22 Coarse 19 mm 5.91 7.2 15.4 53.2 11.0757 -3.7119 1.63E+09 higher, 16,826 psi compared to 2,222 psi for the AASHTO case, the two approaches yield essentially the same master TP62 data set. Both approaches fit the measured data well curves. over the temperature range from 40 to 130F and the shift fac- To compare master curves for all of the mixtures, dynamic tors for the two approaches are essentially the same. moduli were calculated for temperatures ranging from -30 to Figure 4 is for Cell 17 at the MNRoad project, and is an 150F using loading rates of 25, 10, 1, 0.1, and 0.01 Hz. The example of best agreement between the two methods. In this results are shown in Figure 5. As shown, the two approaches 10,000,000 1,000,000 15.8 F 40 F E* , psi 70 F 100,000 100 F 130 F 6 AASHTO TP62 AASHTO TP62 4 Log Shift Factor REDUCED SET REDUCED SET 2 0 10,000 -2 -4 -6 0 50 100 150 Temperature, F 1,000 1.0E-07 1.0E-05 1.0E-03 1.0E-01 1.0E+01 1.0E+03 1.0E+05 1.0E+07 Reduced Frequency, Hz Figure 3. Comparison of fitted master curves for Lane 2 from the FHWA Pavement Testing Facility

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10 10,000,000 1,000,000 15.8 F 40 F E* , psi 70 F 100,000 100 F 130 F 6 AASHTO TP62 AASHTO TP62 4 Log Shift Factor REDUCED SET REDUCED SET 2 0 10,000 -2 -4 -6 0 50 100 150 Temperature, F 1,000 1.0E-07 1.0E-05 1.0E-03 1.0E-01 1.0E+01 1.0E+03 1.0E+05 1.0E+07 Reduced Frequency, Hz Figure 4. Comparison of fitted master curves for Cell 17 from the MNRoad. yield the same moduli over the range of the measured data, As shown, the two data sets produce reasonably similar but sometimes yield differences at high and low moduli pri- average limiting maximum modulus values except for the marily due to differences caused by the maximum limiting ALF mixtures, which had four unrealistically high values modulus. in the AASHTO TP62 data set. The quality of the data for Figure 6 compares limiting maximum moduli from the the low temperature test condition has a major impact on two data sets. As shown, the AASHTO TP62 data set yields the limiting maximum modulus in the MEPDG master unrealistically high moduli in four cases, ALF 2, ALF 3, ALF curve equation. Pellinen reported significantly greater vari- 10, and ALF 11. It also yields unrealistically low values in ability for data collected at 15.8 F and 130F as summarized two cases, ALF 8 and WSTR 2. Table 2 summarizes limiting Table 3 (9). As reported by Pellinen, strain levels for the maximum modulus values averaged over similar mixtures. 15.8F data were significantly lower than those at other 10,000,000 E* From Reduced Data Set, psi 1,000,000 100,000 10,000 1,000 1,000 10,000 100,000 1,000,000 10,000,000 E* From AASHTO TP 62 Data Set, psi Figure 5. Comparison of dynamic moduli computed from master curves.