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27 3.1 Introduction The equipment effects experiment was designed to inves- tigate differences in dynamic modulus and flow number test data from SPTs built by the three suppliers selected for NCHRP Project 9-29. The experiment was designed as a full factorial where four independent specimens of the dense-graded mix- ture were tested in each device. This experimental design is conveniently analyzed using standard analysis of variance techniques. The basic design for the equipment effects experiment was repeated for selected testing conditions. The testing condi- tions were selected to examine the range of capabilities of the equipment. For the dynamic modulus test, unconfined tests were conducted for 10 combinations of temperature and fre- quency. Confined tests were conducted only at high temper- ature using four frequencies. Table 31 summarizes the testing conditions used in the dynamic modulus test. The responses considered in the analysis of variance were the dynamic mod- ulus and phase angle. Flow number tests were conducted for unconfined and confined conditions. Table 32 summarizes the testing condi- tions used. The responses considered in the analysis were the measured permanent strain for each load cycle, and the flow number for the unconfined tests. Flow did not occur in the confined tests. To minimize variability associated with specimen fabrica- tion and testing, all specimens were fabricated by the same technician, then grouped to obtain the same average air void contents for specimens tested in the three machines. Table 33 and Table 34 summarize the air void contents for the specimens used in the dynamic modulus and flow num- ber testing, respectively. The same experienced technician performed all of the tests. Tests with the IPC equipment were performed at the Turner-Fairbank Highway Research Center. Tests with the ITC and MDTS equipment were performed at AAT. 3.2 Dynamic Modulus Dynamic modulus data were collected with each machine beginning at the lowest temperature and proceeding to the highest. At each temperature, the testing proceeded from the highest frequency to the lowest. At the highest temperature, the unconfined tests were performed before the confined tests. Initial graphical review of the data revealed several problems that required equipment modifications to be made by the manufacturers as discussed below. 3.2.1 Equipment Modifications 3.2.1.1 MDTS Dynamic modulus data initially collected with the MDTS equipment were consistently 30 percent lower than that col- lected with the other machines. Several possible causes were investigated. This investigation led to the conclusion that the lower dynamic moduli were the result of the size of the gauge points used with the MDTS equipment. The gauge points used with this equipment exceed the size given in the specification. Apparently, the dynamic modulus test is sensitive to the size of the glued gauge point, with larger gauge points resulting in shorter effective gauge lengths and lower modulus values. The MDTS gauge points were reduced in size by grinding some of the material from the top and bottom, and the dynamic modulus tests were repeated. The modulus values at low and moderate temperatures improved. However, at high tempera- tures, there was not sufficient contact area to resist the moment caused by the spring force in the LVDT, and the gauge points were pried off of the specimen by the LVDT spring force. Based on these observations, MDTS decided to completely redesign the specimen-mounted LVDT system. The re- designed system uses an LVDT in a holder that is magnetically attached to the gauge points on the specimen. With this sys- tem the moment caused by the LVDT spring force is signifi- cantly reduced. The dynamic modulus tests were repeated C H A P T E R 3 Results and Analysis of Equipment Effects Experiment
using this system and these results were included in the analy- sis presented below. 3.2.1.2 ITC The ITC equipment could not accurately control the loading rate for the 0.01 Hz tests at high temperatures. This problem was traced to the algorithm that ITC used to control sinusoidal loading. The method becomes less accurate as the frequency and amplitude of the sinusoidal loading decrease. Very low load levels are required during dynamic modulus testing at 0.01 Hz at high temperatures. ITC modified the control software to use a different control algorithm for low frequency loading. The high temperature testing was repeated and used in the analysis presented below. 3.2.1.3 IPC Initial graphical analysis of the dynamic modulus data in- cluding the repeated tests with the MDTS and IITC equipment revealed that the high temperature, 0.1 and 0.01 Hz test results from the IPC equipment were much lower than those obtained with the other equipment. Further review of the data showed that the LVDT drift measured at these combinations of tem- perature and frequency was in the opposite direction of the applied load, indicating that the LVDT spring force was push- ing the gauge points apart. The drift computation used in re- ducing the dynamic modulus data is intended to remove the creep caused by the non-zero mean stress that occurs in a compression haversine loading. It should not be used to sub- tract drift caused by the LVDT spring force moving the gauge 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. These data were used in the analysis presented below. 3.2.2 Statistical Analysis The dynamic modulus data from the equipment effects ex- periment is presented in Appendix C. It includes the meas- ured modulus and phase angle as well as the reported data quality statistics for each test. The data were analyzed using analysis of variance, which is a statistical technique for com- paring the mean values from multiple populations. In this 28 Confining Pressure, kPa Temperature, °C Frequency, Hz 0 10 10 0 10 1 0 10 0.1 0 20 10 0 20 1 0 20 0.1 0 35 10 0 35 1 0 35 0.1 0 35 0.01 135 35 10 135 35 1 135 35 0.1 135 35 0.01 Table 31. Testing conditions for the dynamic modulus equipment effects experiment. Confinement, kPa Deviatoric Stress, kPa Temperature, °C 0 140 35 140 965 50 Table 32. Testing conditions for the flow number tests. Machine Specimen Air Voids, % Average Air Voids, % 109 6.0 114 6.1 115 5.9 ITC 118 5.8 6.0 111 6.5 112 6.2 117 5.8 IPC 119 6.2 6.2 110 6.2 113 6.1 116 6.1 MDTS 120 5.9 6.1 Table 33. Air void content for specimens used in the dynamic modulus testing. Test Machine Specimen Air Voids, % Average Air Voids, % 127 6.4 133 6.1 138 6.2 ITC 153 6.2 6.2 125 5.9 131 6.2 147 6.4 IPC 154 5.9 6.1 122 5.9 134 6.2 140 6.1 Unconfined MDTS 148 6.3 6.1 128 6.1 141 6.0 145 6.2 ITC 152 6.1 6.1 129 6.0 131 6.2 149 6.3 IPC 156 6.2 6.2 132 6.2 139 6.2 143 6.4 Confined MDTS 150 6.4 6.3 Table 34. Air void content for specimens used in the flow number testing.
study, it was used to compare the mean values of the dynamic modulus and phase angle data collected with the three SPTs for various combinations of confining pressure, temperature, and loading rate. The analysis of variance test as applied here is summarized below (13): Null Hypothesis, H0: μIPC = μITC = μMDTS Alternative Hypothesis: The mean value from at least one of the machines is different Test Statistic: Rejection Region: Reject H0 if F > Fcr for (k â 1, N â k) degrees of freedom. Where: μIPC = mean for the IPC device μITC = mean for the ITD device μMDTS = mean for the MDTS device F = value of F-statistic F MS MS b w = MSb = mean squares between groups MSw = mean squares within groups k = number of groups (3 for this experiment) N = total number of tests (12 for this experiment) For this experiment, the critical value of the F-statistic for a level of significance of 5 percent is 4.26. Table 35 and Table 36 present the analysis of variance for the dynamic modulus and phase angle for all testing conditions. The data in Table 35 and Table 36 show some significant differences in the dynamic moduli and phase angles measured with the three machines. The Duncan multiple range test was used to determine which values were significantly different (13). This test compares the difference in the mean value between two machines to a critical value based on the mean squares within groups. If the difference exceeds the critical value, it is concluded that there is a significant difference in the property measured by the two machines. Table 37 and Table 38 present the Duncan multiple range tests for all testing conditions. 29 IPC ITC MDTS Analysis of Variance Temp., C Freq., Hz Conf., kPa Avg SSW Avg SSW Avg SSW Grand 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 Table 35. Analysis of variance for dynamic modulus. IPC ITC MDTS Analysis of Variance Tem p., C Freq., Hz Conf., kPa Avg SSW Avg SSW Avg SSW Grand 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 sam e 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 sam e 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 sam e 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 sam e 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 sam e 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 Table 36. Analysis of variance for phase angle.
For the dynamic modulus, there is good agreement be- tween the three machines except for the lower frequency tests at high temperatures. In these tests, the ITC machine yields significantly higher dynamic moduli than the MDTS ma- chine. For the phase angle, the agreement between the three machines is somewhat poorer. The MDTS machine typically yields lower phase angles than the other machines. Table 39 summarizes the variability of the dynamic mod- ulus test data obtained by pooling the standard deviation of the data for each testing condition across all machines. Except for the 0.01 Hz loading at the high temperature, the variability of the test data are reasonably low with the coefficient of variation for the dynamic modulus being approximately 10 percent and the standard deviation of the phase angle being approximately 1 degree. The overall variability obtained by pooling the coefficient of variation for the dynamic modu- lus and the standard deviation for the phase angle over all test conditions were 11.6 percent, and 1.2 degrees, respectively. 30 Duncan Multiple Range Test Temp., C Freq., Hz Conf., kPa Critical IPC- ITC IPC- MDTS ITC- MDTS Conclusion Max 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 Duncan Multiple Range Test Tem p., C Freq., Hz Conf., kPa Critical IPC- ITC IPC- MDTS ITC- MDTS Conclusion Max difference, % 10 10 0 0.78 0.55 0.85 0.30 Sam e 0.8 10 1 0 1.22 -0.12 0.60 0.72 Sa me 0.7 10 0.1 0 2.05 0.03 1.03 1.00 Sam e 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 Sa me -0.3 35 0.1 0 4.06 3.19 -1.08 -4.28 Sam e 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 Table 37. Duncan multiple range test for dynamic modulus. Table 38. Duncan multiple range test for phase angle. Dynam ic Modulus Phase Angle Tem p., C Freq., Hz Conf., kPa Mean COV Mean Standard Deviation 10 10 0 10953 12.9 15.5 0.4 10 1 0 7040 13.6 21.5 0.7 10 0.1 0 3939 15.2 27.6 1.1 20 10 0 6037 10.4 24.6 0.9 20 1 0 3124 10.3 31.1 1.1 20 0.1 0 1375 11.0 34.8 1.3 35 10 0 2019 6.9 34.4 0.7 35 1 0 826 8.7 33.9 1.5 35 0.1 0 345 13.7 29.2 2.2 35 0.01 0 189 20.1 21.3 1.5 35 10 130 2543 7.9 29.2 1.0 35 1 130 1357 7.7 25.4 1.1 35 0.1 130 901 7.5 19.4 1.3 35 0.01 130 736 8.1 13.9 1.4 Overall 11.6 1.2 Table 39. Grand mean and variability of dynamic modulus test data.
These values agree well with those measured in Phase II where the coefficient of variation for the dynamic modulus was approximately 13 percent and the standard deviation of the phase angle was approximately 1.7 degrees (11). Figure 18 and Figure 19 graphically depict the results dis- cussed above. In these figures, the mean for each machine is plotted as a function of the grand mean obtained from the data for all machines. These figures also include 95 percent confidence intervals for the grand mean computed using the overall coefficient of variation for the dynamic modulus data of 11.6 percent and the overall standard deviation for the phase angle of 1.2 degrees. Significant differences occur when the data from a particular machine plot outside the 95 per- cent confidence intervals. For the dynamic modulus this occurs only for the low frequency tests at high temperatures, where the data for the ITC machine are significantly higher and the data for the MDTS machine are significantly lower than the grand average. Phase angles measured in with the MDTS ma- chine tend to be lower than the grand average, while those measured with the IPC Global machine tend to be higher than the grand average. Each machine exhibits a significant difference from the grand average for various combinations of temperature, frequency, and confinement, but there does not appear to be a consistent trend for these departures. 31 100 1000 10000 100 1000 10000 Grand Average Dynamic Modulus, MPa A ve ra ge D yn am ic M od ul us , M Pa IPC ITC MDTS Figure 18. Comparison of mean dynamic moduli from the three machines. 10.0 15.0 20.0 25.0 30.0 35.0 40.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 Grand Average Phase Angle, Degree A ve ra ge P ha se A ng le , D eg re e IPC ITC MDTS Figure 19. Comparison of mean phase angle from the three machines.
3.3 Flow Number Unconfined and confined flow number tests were performed with each machine at a temperature of 50ËC. The unconfined tests used a deviatioric stress of 140 kPa. The confined tests used a confining stress of 140 kPa and a deviatoric stress of 965 kPa. Four specimens were tested in each machine. The tests were continued to 10,000 cycles or a permanent strain of 5 percent. For the confined tests with the ITC machine, the data from one sample was not included in the analysis be- cause a leak developed in the membrane resulting in loss of confining stress and early failure of the specimen. Figure 20 and Figure 21 present repeated load permanent deformation curves based on the average of the data for the samples tested in each machine. The complete database of the permanent deformation responses is presented in Appendix D. 32 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0 500 1000 1500 2000 2500 3000 Load Cycles Pe rm an en t S tra in , % ITC IPC MDTS Figure 20. Average permanent strain response for unconfined repeated load tests. 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0 2000 4000 6000 8000 10000 12000 Load Cycles Pe rm an en t S tra in , % ITC IPC MDTS Figure 21. Average permanent strain response for confined repeated load tests.
The permanent deformation curves in Figure 20 are for un- confined tests; those in Figure 21 are for confined tests. For unconfined tests, flow occurred at approximately 1,000 cycles. Flow did not occur in the confined tests. The sections below discuss the statistical analysis of these data. 3.3.1 Statistical Analysis Analysis of variance as discussed previously in the dy- namic modulus section was used to analyze differences in the permanent deformation response from different machines. The analysis for selected load cycles is presented in Table 40 for the unconfined tests and Table 41 for the confined tests. The data in Table 40 indicate a significant difference in the permanent deformation response between devices early in the tests up to approximately 100 load cycles. Although there is a significant difference and based on the Duncan multiple range test, the permanent deformation from the ITC device is significantly lower than the other two, the difference is only 0.05 percent, which is not significant from an engineering 33 ITC IPC MDTS Grand Pooled Analysis of Variance Cycle Avg SSW Avg SSW Avg SSW Avg COV SSB MS W MSB F Fcr Conclusion 1 0.04 0.0000 0.05 0.0000 0.06 0.0001 0.05 6.02 0.0014 0.0000 0.0007 55.85 4.26 Permanent strains are different 16 0.23 0.0008 0.27 0.0002 0.27 0.0008 0.26 4.67 0.0040 0.0002 0.0020 10.42 4.26 Permanent strains are different 25 0.28 0.0010 0.33 0.0002 0.33 0.0012 0.31 4.54 0.0050 0.0003 0.0025 9.36 4.26 Permanent strains are different 40 0.34 0.0020 0.39 0.0002 0.39 0.0017 0.38 4.77 0.0063 0.0004 0.0031 7.32 4.26 Permanent strains are different 63 0.41 0.0026 0.46 0.0002 0.46 0.0024 0.45 4.68 0.0065 0.0006 0.0033 5.58 4.26 Permanent strains are different 100 0.49 0.0048 0.54 0.0003 0.54 0.0039 0.52 5.23 0.0082 0.0010 0.0041 4.10 4.26 Perm anent strains are the sam e 160 0.58 0.0072 0.64 0.0005 0.63 0.0066 0.62 5.58 0.0088 0.0016 0.0044 2.77 4.26 Perm anent strains are the sam e 250 0.69 0.0130 0.75 0.0007 0.74 0.0105 0.73 6.19 0.0094 0.0027 0.0047 1.75 4.26 Perm anent strains are the sam e 400 0.83 0.0219 0.89 0.0015 0.88 0.0192 0.87 6.88 0.0090 0.0047 0.0045 0.95 4.26 Perm anent strains are the sam e 630 1.01 0.0377 1.07 0.0032 1.06 0.0375 1.05 7.70 0.0080 0.0087 0.0040 0.46 4.26 Perm anent strains are the sam e 1000 1.30 0.0721 1.35 0.0078 1.33 0.0871 1.32 8.91 0.0056 0.0186 0.0028 0.15 4.26 Perm anent strains are the sam e 1600 1.80 0.1451 1.84 0.0225 1.80 0.2871 1.81 10.75 0.0034 0.0505 0.0017 0.03 4.26 Perm anent strains are the sam e 2500 2.91 0.4842 2.89 0.0964 2.83 1.7224 2.88 15.22 0.0152 0.2559 0.0076 0.03 4.26 Perm anent strains are the sam e Table 40. Analysis of variance for unconfined repeated load permanent deformation response. IPC ITC MDTS Grand Pooled Cycle Avg SSW Avg SSW Avg SSW Avg COV SSB MS W MSB F Fcr Conclusion 1 0.14 0.0001 0.13 0.0100 0.14 0.0009 0.13 22.83 0.0002 0.0014 0.0001 0.06 4.46 Perm anent strains are the sam e 16 0.55 0.0032 0.52 0.2046 0.52 0.0229 0.53 26.14 0.0017 0.0288 0.0008 0.03 4.46 Perm anent strains are the sam e 25 0.64 0.0063 0.61 0.2692 0.62 0.0304 0.63 25.58 0.0017 0.0382 0.0009 0.02 4.46 Perm anent strains are the sam e 40 0.74 0.0082 0.72 0.3464 0.73 0.0432 0.73 24.99 0.0009 0.0497 0.0004 0.01 4.46 Perm anent strains are the sam e 63 0.84 0.0133 0.84 0.4260 0.84 0.0602 0.84 24.40 0.0001 0.0624 0.0001 0.00 4.46 Perm anent strains are the sam e 100 0.96 0.0191 0.98 0.5152 0.96 0.0862 0.96 23.69 0.0010 0.0776 0.0005 0.01 4.46 Perm anent strains are the sam e 160 1.09 0.0279 1.13 0.6066 1.09 0.1218 1.10 22.88 0.0046 0.0945 0.0023 0.02 4.46 Perm anent strains are the sam e 250 1.23 0.0394 1.30 0.6931 1.23 0.1735 1.25 22.12 0.0128 0.1133 0.0064 0.06 4.46 Perm anent strains are the sam e 400 1.39 0.0573 1.49 0.7840 1.39 0.2531 1.43 21.37 0.0277 0.1368 0.0139 0.10 4.46 Perm anent strains are the sam e 630 1.57 0.0713 1.71 0.9001 1.56 0.3657 1.61 20.86 0.0544 0.1671 0.0272 0.16 4.46 Perm anent strains are the sam e 1000 1.77 0.0857 1.96 1.0391 1.74 0.4888 1.82 20.31 0.1052 0.2017 0.0526 0.26 4.46 Perm anent strains are the sam e 1600 2.00 0.0963 2.23 1.2087 1.94 0.6473 2.06 19.77 0.1810 0.2440 0.0905 0.37 4.46 Perm anent strains are the sam e 2500 2.26 0.0954 2.51 1.3856 2.16 0.8518 2.31 19.21 0.2682 0.2916 0.1341 0.46 4.46 Perm anent strains are the sam e 4000 2.62 0.0746 2.85 1.5940 2.41 1.1233 2.63 18.45 0.4015 0.3490 0.2007 0.58 4.46 Perm anent strains are the sam e 6300 3.06 0.0966 3.22 1.8747 2.67 1.4255 2.98 17.91 0.6448 0.4246 0.3224 0.76 4.46 Perm anent strains are the sam e 10000 3.50 0.3918 3.62 2.1780 2.96 1.7957 3.36 18.23 0.9769 0.5457 0.4884 0.90 4.46 Perm anent strains are the sam e Analysis of Variance Table 41. Analysis of variance for confined repeated load permanent deformation response.
standpoint. Figure 22 compares to early portion of the perma- nent deformation curves for unconfined tests with the three devices. The data in Table 41 indicate that there is not a significant difference in the permanent deformation response for confined tests using different equipment. However, confined testing has greater variability compared to unconfined testing making significant differences more difficult to detect. Figure 23 is a plot showing the coefficient of variation for confined and uncon- fined tests as a function of axial strain in the specimen. The co- efficient of variation plotted in this figure is a pooled value based on data from the three machines. The coefficient of variation in the unconfined test increases with increasing axial strain, while it decreases with increasing strain in confined tests. Before, the 34 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0 20 40 60 80 100 Load Cycles Pe rm an en t S tra in , % ITC IPC MDTS Figure 22. Comparison of permanent deformation response for the early portion of the unconfined repeated load tests. 0 5 10 15 20 25 30 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Permanent Strain, % Co ef fic ei nt o f V ar ia tio n, % Unconfined Confined Figure 23. Coefficient of variation for unconfined and confined repeated load tests.
flow point, the coefficient of variation in the unconfined test is less than 10 percent. At high strain levels, the coefficient of vari- ation is similar for confined and unconfined tests. An analysis of variance was also conducted on flow num- bers obtained from unconfined repeated load permanent de- formation tests. The flow number of each of these tests was computed using the improved algorithm developed at the Arizona State University (ASU) for detecting the flow num- ber with the Franken model (14). The flow number data are summarized in Table 42. Table 43 presents the results of the analysis of variance for the flow numbers. The conclusion from this analysis is that the flow number is not significantly affected by the type of equipment. Figure 24 presents a bar chart showing these results. Figure 24 includes the mean flow number obtained with each device, and 95 percent confidence intervals based on the pooled standard deviation from the three devices. The pooled coefficient of variation in these tests is 10.8 percent, which is much lower than the value of 35 per- cent obtained for this same mixture in Phase II of the proj- ect (11). The lower variability reported here is the result of the improved flow number algorithm developed at ASU. 3.4 Repeatability The data from the equipment effects experiment can be used to make initial estimates of the repeatability of the dy- namic modulus and flow number tests. These estimates of re- peatability can be useful in early evaluations of the equipment and in the planning of an interlaboratory study where formal statements of both the repeatability, within laboratory preci- sion, and reproducibility, between laboratory precision, of the tests are developed. The term âdifference two standard deviation limitâ or d2s is used to define the repeatability of a test method. For tests conducted within a laboratory, the difference in two meas- urements on the same material should not exceed the d2s 35 Replicate ITC IPC MDTS 1 1027 917 760 2 891 906 961 3 918 893 1164 4 1093 978 1106 Average 982 924 968 Standard Deviation 94.4 37.6 180.0 SSW 26723 4249 97233 Source of Variation Degree of Freedom Sum of Squares Mean Squares F Statistic Conclusion Between 2 12273 6136 0.43< Fcr =4.64 Within 9 128204 14245 Total 11 Not a significant equipment effect Table 42. Flow numbers for unconfined tests. Table 43. Analysis of variance for flow number. 0 200 400 600 800 1000 1200 1400 ITC IPC MDTS Flow Number Figure 24. Bar chart for flow number.
limit 95 percent of the time. The d2s limit is determined using Equation 2. (2) where: d2s = difference two standard deviation limit s = standard deviation of the test When the standard deviation of the test varies with test result, as it does of the dynamic modulus, the coefficient of variation is used in place of the standard deviation in Equation 2. Table 44 summarizes estimates of single laboratory re- peatability for the dynamic modulus and flow number tests. Two properly conducted tests on the same material in the same laboratory should not result in differences in the dy- namic modulus greater than 32 percent or differences in the phase angle greater than 3.3 degrees. The repeatability of the flow number is likely to depend on the magnitude of the flow number and whether the test is confined or uncon- fined. For unconfined flow number tests on materials with a flow number of approximately 1,000, two properly con- ducted tests on the same material in the same laboratory should not result in differences in the flow number of more than 320 cycles. 3.5 Summary The equipment effects experiment provided the opportunity to compare dynamic modulus and repeated load permanent deformation test data collected on the same mixture using equipment from the three manufacturers. The dynamic modulus portion of this testing revealed flaws with each de- vice that were resolved by the respective manufacturer during the experiment. The ITC device required modification of the control software to control low frequency dynamic modulus testing at high temperatures. The IPC device required the addition of springs to the specimen-mounted deformation d s s2 1 960 2= . measuring equipment to counteract the LVDT spring force and minimize unwanted movement of the glued gauge points. Finally the MDTS device required a complete redesign of the specimen-mounted deformation measuring system. Significant equipment effects were detected in the dynamic modulus testing. For low stiffness dynamic modulus measure- ments, below about 500 MPa, the dynamic modulus meas- ured with the MDTS equipment was significantly lower and the dynamic modulus measured with the ITC equipment was significantly higher. The equipment effect was approximately 20 percent while the testing error was only approximately 12 percent. One possible cause for this difference at low stiff- ness levels is calibration of the low range of the load cell. The applied load levels for low stiffness dynamic modulus tests are very low, 0.5 percent or less of the capacity of the load cell of the machine. The manufacturer-supplied load cell calibrations were not verified prior to the equipment effects experiment. The calibration of the temperature sensor and the deformation measuring equipment was verified using independent NIST traceable standards immediately before conducting the equip- ment effects experiment. For various combinations of tem- perature and frequency, significant differences in phase angles were also detected. The trend that was evident in phase angle data was that the IPC equipment produces the highest phase angles and the MDTS equipment produces the lowest phase angles. The difference between these two machines averaged over the range of data collected was 1.5 degrees. The testing error for the phase angle is 1.4 degrees. Significant equipment effects were not detected in the flow number tests. Although there was a statistical difference in the early portion of the permanent deformation in the unconfined tests, its magnitude was not of engineering significance. Variability of the dynamic modulus data collected during this Phase of NCHRP Project 9-29 is similar to that collected during Phase II. The use of the new flow number algorithm developed at ASU appears to reduce variability in the com- puted flow number. This algorithm provides a more precise method for computing the derivative and inflection point in repeated load permanent deformation curves. 36 Test Parameter s CV d2s Dynamic Modulus NA 11.6% 32 % Dynamic Modulus Phase Angle 1.2 degrees NA 3.3 degrees Unconfined Flow Number Flow Number 119 cycles* NA 320 cycles* * For a material with a flow number of 1,000. Table 44. Initial repeatability estimates for the dynamic modulus and flow number.
