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28 Table 31. Testing conditions for the dynamic Table 33. Air void content for modulus equipment effects experiment. specimens used in the dynamic modulus testing. Confining Pressure, kPa Temperature, C Frequency, Hz 0 10 10 Air Voids, Average Air 0 10 1 Machine Specimen % Voids, % 0 10 0.1 ITC 109 6.0 0 20 10 114 6.1 6.0 0 20 1 115 5.9 0 20 0.1 118 5.8 0 35 10 IPC 111 6.5 0 35 1 112 6.2 6.2 0 35 0.1 117 5.8 0 35 0.01 119 6.2 135 35 10 MDTS 110 6.2 135 35 1 113 6.1 6.1 135 35 0.1 116 6.1 135 35 0.01 120 5.9 using this system and these results were included in the analy- tract drift caused by the LVDT spring force moving the gauge sis presented below. points apart. IPC designed a set of springs to counter the LVDT spring force. The high temperature tests were repeated with substantial improvement of the data at low frequency. 3.2.1.2 ITC These data were used in the analysis presented below. The ITC equipment could not accurately control the loading rate for the 0.01 Hz tests at high temperatures. This 3.2.2 Statistical Analysis problem was traced to the algorithm that ITC used to control sinusoidal loading. The method becomes less accurate as the The dynamic modulus data from the equipment effects ex- frequency and amplitude of the sinusoidal loading decrease. periment is presented in Appendix C. It includes the meas- Very low load levels are required during dynamic modulus ured modulus and phase angle as well as the reported data testing at 0.01 Hz at high temperatures. ITC modified the quality statistics for each test. The data were analyzed using control software to use a different control algorithm for low analysis of variance, which is a statistical technique for com- frequency loading. The high temperature testing was repeated paring the mean values from multiple populations. In this and used in the analysis presented below. Table 34. Air void content for specimens used in the flow number testing. 3.2.1.3 IPC Air Voids, Average Air Initial graphical analysis of the dynamic modulus data in- Test Machine Specimen % Voids, % cluding the repeated tests with the MDTS and IITC equipment ITC 127 6.4 133 6.1 6.2 revealed that the high temperature, 0.1 and 0.01 Hz test results 138 6.2 from the IPC equipment were much lower than those obtained 153 6.2 IPC 125 5.9 with the other equipment. Further review of the data showed Unconfined 131 6.2 6.1 that the LVDT drift measured at these combinations of tem- 147 6.4 perature and frequency was in the opposite direction of the 154 5.9 MDTS 122 5.9 applied load, indicating that the LVDT spring force was push- 134 6.2 6.1 ing the gauge points apart. The drift computation used in re- 140 6.1 148 6.3 ducing the dynamic modulus data is intended to remove the ITC 128 6.1 creep caused by the non-zero mean stress that occurs in a 141 6.0 6.1 compression haversine loading. It should not be used to sub- 145 6.2 152 6.1 IPC 129 6.0 Confined 131 6.2 6.2 Table 32. Testing conditions for the flow 149 6.3 number tests. 156 6.2 MDTS 132 6.2 Confinement, kPa Deviatoric Stress, kPa Temperature, C 139 6.2 6.3 0 140 35 143 6.4 140 965 50 150 6.4

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29 Table 35. Analysis of variance for dynamic modulus. Temp., Freq., Conf., IPC ITC MDTS Grand Analysis of Variance C Hz kPa Avg SSW Avg SSW Avg SSW Avg SSB MSW MSB F Fcr Conclusion 10 10 0 10687 1486055 10923 2609222 11248 13952430 10953 636155 2005301 318078 0.16 4.26 Moduli are the same 10 1 0 6795 742675 7006 869039 7318 6635076 7040 555795 916310 277898 0.30 4.26 Moduli are the same 10 0.1 0 3735 255849 3881 209442 4201 2770140 3939 456021 359492 228010 0.63 4.26 Moduli are the same 20 10 0 5723 483349 6192 142035 6194 2895315 6037 588841 391189 294421 0.75 4.26 Moduli are the same 20 1 0 3012 243403 3105 34839 3372 694325 3124 456959 103198 228480 2.21 4.26 Moduli are the same 20 0.1 0 1324 34612 1391 11249 1486 151007 1375 116224 22802 58112 2.55 4.26 Moduli are the same 35 10 0 2119 60941 1988 51075 1951 64987 2019 62052 19667 31026 1.58 4.26 Moduli are the same 35 1 0 906 11472 827 5720 745 29547 826 51642 5193 25821 4.97 4.26 Moduli are different 35 0.1 0 357 2906 397 289 281 16994 345 28190 2243 14095 6.28 4.26 Moduli are different 35 0.01 0 175 1348 245 967 148 10691 189 19831 1445 9916 6.86 4.26 Moduli are different 35 10 130 2365 37498 2556 46045 2709 281680 2543 237422 40580 118711 2.93 4.26 Moduli are the same 35 1 130 1272 6355 1396 8784 1403 82317 1357 43051 10828 21525 1.99 4.26 Moduli are the same 35 0.1 130 833 1773 946 3075 926 36549 901 29147 4600 14574 3.17 4.26 Moduli are the same 35 0.01 130 682 590 759 2478 769 29276 736 18183 3594 9092 2.53 4.26 Moduli are the same study, it was used to compare the mean values of the dynamic MSb = mean squares between groups modulus and phase angle data collected with the three SPTs MSw = mean squares within groups for various combinations of confining pressure, temperature, k = number of groups (3 for this experiment) and loading rate. The analysis of variance test as applied here N = total number of tests (12 for this experiment) is summarized below (13): For this experiment, the critical value of the F-statistic for a Null Hypothesis, H0: IPC = ITC = MDTS level of significance of 5 percent is 4.26. Table 35 and Table 36 Alternative Hypothesis: The mean value from at least one present the analysis of variance for the dynamic modulus and of the machines is different phase angle for all testing conditions. MSb The data in Table 35 and Table 36 show some significant Test Statistic: F = MSw differences in the dynamic moduli and phase angles measured Rejection Region: Reject H0 if F > Fcr for (k - 1, N - k) with the three machines. The Duncan multiple range test was degrees of freedom. used to determine which values were significantly different (13). This test compares the difference in the mean value between Where: two machines to a critical value based on the mean squares IPC = mean for the IPC device within groups. If the difference exceeds the critical value, it is ITC = mean for the ITD device concluded that there is a significant difference in the property MDTS = mean for the MDTS device measured by the two machines. Table 37 and Table 38 present F = value of F-statistic the Duncan multiple range tests for all testing conditions. Table 36. Analysis of variance for phase angle. Temp., Freq., Conf., IPC ITC MDTS Grand Analysis of Variance C Hz kPa Avg SSW Avg SSW Avg SSW Avg SSB MSW MSB F Fcr Conclusion 10 10 0 16.0 0.34 15.4 0.15 15.1 1.11 15.5 1.49 0.18 0.74 4.18 4.26 Phase angles are the same 10 1 0 21.6 1.04 21.7 0.71 21.0 2.20 21.5 1.19 0.44 0.60 1.36 4.26 Phase angles are the same 10 0.1 0 27.9 2.65 27.9 1.82 26.9 6.64 27.6 2.74 1.24 1.37 1.11 4.26 Phase angles are the same 20 10 0 25.0 2.29 25.7 0.36 23.2 4.10 24.6 12.41 0.75 6.20 8.26 4.26 Phase angles are different 20 1 0 32.2 4.70 32.4 1.51 29.1 6.78 31.1 24.58 1.27 12.29 9.67 4.26 Phase angles are different 20 0.1 0 35.3 3.06 35.6 5.15 33.1 7.60 34.8 17.12 1.62 8.56 5.28 4.26 Phase angles are different 35 10 0 34.7 1.63 35.2 1.03 33.4 2.32 34.4 6.98 0.55 3.49 6.31 4.26 Phase angles are different 35 1 0 33.5 1.66 33.8 4.06 34.5 13.57 33.9 1.92 2.14 0.96 0.45 4.26 Phase angles are the same 35 0.1 0 29.9 3.66 26.7 4.29 31.0 35.43 29.2 39.52 4.82 19.76 4.10 4.26 Phase angles are the same 35 0.01 0 22.9 4.27 18.1 1.23 22.8 13.64 21.3 60.20 2.13 30.10 14.15 4.26 Phase angles are different 35 10 130 30.9 0.79 29.2 0.64 27.5 7.42 29.2 23.17 0.98 11.59 11.79 4.26 Phase angles are different 35 1 130 26.8 3.53 25.2 0.95 24.3 6.72 25.4 13.32 1.24 6.66 5.35 4.26 Phase angles are different 35 0.1 130 21.4 7.25 19.3 0.94 17.5 7.39 19.4 29.88 1.73 14.94 8.62 4.26 Phase angles are different 35 0.01 130 15.5 4.73 13.3 0.98 12.8 11.72 13.9 17.27 1.94 8.63 4.46 4.26 Phase angles are different

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30 Table 37. Duncan multiple range test for dynamic modulus. Temp., Freq., Conf., Duncan Multiple Range Test C Hz kPa Critical IPC- IPC- ITC- Conclusion Max ITC MDTS MDTS difference, % 10 10 0 2616 -236 -562 -326 Same 5.1 10 1 0 1769 -212 -524 -312 Same 7.4 10 0.1 0 1108 -147 -467 -320 Same 11.9 20 10 0 1156 -469 -471 -2 Same 7.8 20 1 0 594 -210 -477 -267 Same 15.3 20 0.1 0 279 -144 -239 -95 Same 17.4 35 10 0 259 131 168 37 Same 8.3 35 1 0 133 78 161 82 MDTS < IPC 19.5 35 0.1 0 88 -40 77 117 MDTS < ITC 33.9 35 0.01 0 70 -70 26 96 MDTS < ITC 50.9 35 10 130 372 -191 -344 -152 Same 13.5 35 1 130 192 -123 -130 -7 Same 9.6 35 0.1 130 125 -113 -93 20 Same 10.3 35 0.01 130 111 -77 -87 -10 Same 11.8 Table 38. Duncan multiple range test for phase angle. Temp., Freq., Conf., Duncan Multiple Range Test C Hz kPa Critical IPC- IPC- ITC- Max ITC MDTS MDTS Conclusion difference, % 10 10 0 0.78 0.55 0.85 0.30 Same 0.8 10 1 0 1.22 -0.12 0.60 0.72 Same 0.7 10 0.1 0 2.05 0.03 1.03 1.00 Same 1.0 20 10 0 1.60 -0.69 1.73 2.42 MDTS< IPC and ITC 2.4 20 1 0 2.08 -0.66 2.66 3.31 MDTS< IPC and ITC 3.3 20 0.1 0 2.35 0.16 2.61 2.45 MDTS< IPC and ITC 2.6 35 10 0 1.37 -0.54 1.28 1.82 MDTS< ITC 1.8 35 1 0 2.71 -0.26 -0.95 -0.69 Same -0.3 35 0.1 0 4.06 3.19 -1.08 -4.28 Same 3.2 35 0.01 0 2.69 4.78 0.06 -4.72 ITC < IPC and MDTS 4.8 35 10 130 1.83 1.78 3.40 1.62 MDTS < IPC 3.4 35 1 130 2.06 1.61 2.55 0.95 MDTS < IPC 2.6 35 0.1 130 2.43 2.05 3.86 1.81 MDTS < IPC 3.9 35 0.01 130 2.57 2.26 2.76 0.49 MDTS < IPC 2.8 For the dynamic modulus, there is good agreement be- Table 39. Grand mean and variability tween the three machines except for the lower frequency tests of dynamic modulus test data. at high temperatures. In these tests, the ITC machine yields significantly higher dynamic moduli than the MDTS ma- Temp., Freq., Conf., Dynamic Modulus Phase Angle C Hz kPa Mean COV Mean Standard chine. For the phase angle, the agreement between the three Deviation machines is somewhat poorer. The MDTS machine typically 10 10 0 10953 12.9 15.5 0.4 yields lower phase angles than the other machines. 10 1 0 7040 13.6 21.5 0.7 Table 39 summarizes the variability of the dynamic mod- 10 0.1 0 3939 15.2 27.6 1.1 20 10 0 6037 10.4 24.6 0.9 ulus test data obtained by pooling the standard deviation of 20 1 0 3124 10.3 31.1 1.1 the data for each testing condition across all machines. Except 20 0.1 0 1375 11.0 34.8 1.3 for the 0.01 Hz loading at the high temperature, the variability 35 10 0 2019 6.9 34.4 0.7 of the test data are reasonably low with the coefficient of 35 1 0 826 8.7 33.9 1.5 variation for the dynamic modulus being approximately 35 0.1 0 345 13.7 29.2 2.2 35 0.01 0 189 20.1 21.3 1.5 10 percent and the standard deviation of the phase angle 35 10 130 2543 7.9 29.2 1.0 being approximately 1 degree. The overall variability obtained 35 1 130 1357 7.7 25.4 1.1 by pooling the coefficient of variation for the dynamic modu- 35 0.1 130 901 7.5 19.4 1.3 lus and the standard deviation for the phase angle over all test 35 0.01 130 736 8.1 13.9 1.4 conditions were 11.6 percent, and 1.2 degrees, respectively. Overall 11.6 1.2

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31 10000 Average Dynamic Modulus, MPa IPC 1000 ITC MDTS 100 100 1000 10000 Grand Average Dynamic Modulus, MPa Figure 18. Comparison of mean dynamic moduli from the three machines. These values agree well with those measured in Phase II where the data from a particular machine plot outside the 95 per- the coefficient of variation for the dynamic modulus was cent confidence intervals. For the dynamic modulus this occurs approximately 13 percent and the standard deviation of the only for the low frequency tests at high temperatures, where phase angle was approximately 1.7 degrees (11). the data for the ITC machine are significantly higher and the Figure 18 and Figure 19 graphically depict the results dis- data for the MDTS machine are significantly lower than the cussed above. In these figures, the mean for each machine is grand average. Phase angles measured in with the MDTS ma- plotted as a function of the grand mean obtained from the chine tend to be lower than the grand average, while those data for all machines. These figures also include 95 percent measured with the IPC Global machine tend to be higher confidence intervals for the grand mean computed using the than the grand average. Each machine exhibits a significant overall coefficient of variation for the dynamic modulus data difference from the grand average for various combinations of 11.6 percent and the overall standard deviation for the of temperature, frequency, and confinement, but there does phase angle of 1.2 degrees. Significant differences occur when not appear to be a consistent trend for these departures. 40.0 35.0 Average Phase Angle, Degree 30.0 IPC 25.0 ITC MDTS 20.0 15.0 10.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 Grand Average Phase Angle, Degree Figure 19. Comparison of mean phase angle from the three machines.