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32 Extrapolations from 4 Million Cycles 10 million cycles using the single-stage Weibull function, is Measured Fatigue Life, Cycles 1.0E+08 7.75. This indicates that the two predictions are relatively close. 8.0E+07 In summary, the Weibull functions were selected for extrap- olating fatigue tests that did not fail within 50 million cycles or 6.0E+07 when the test was interrupted prior to failure (as occurred with 4.0E+07 Sample 6 of the PG 67-22 mix at optimum asphalt content). Sample 5 Weibull For long-life fatigue tests, at strain levels slightly above the 2.0E+07 endurance limit, the single-stage Weibull function appears 0.0E+00 to provide the most accurate extrapolation of fatigue life. 0.0E+00 2.0E+07 4.0E+07 6.0E+07 8.0E+07 1.0E+08 The three-stage Weibull function, however, provides the best Predicted Fatigue Life, Cycles fit to the stiffness versus loading cycle data. Fatigue extrapo- Exponential Single-Stage Weibull lations from both methods are shown when discussing evi- dence of the endurance limit. Based on the results from this Figure 4.14. Comparison of exponential and single- section, an AASHTO Standard Practice for Predicting the En- stage Weibull extrapolations with measured durance Limit of Hot Mix Asphalt (HMA) for Long-Life Pave- fatigue lives. ment Design was developed and is presented in Appendix A. The draft format includes extrapolation techniques using both the single- and three-stage Weibull functions. equality is underestimated and below the line of equality is overestimated. The error is greater for larger extrapolations (e.g., testing to 10 million cycles for a sample with a fatigue Existence of the Endurance Limit life of 40 million cycles). The extrapolations for the single-stage Samples tested below the fatigue endurance limit are ex- Weibull model are distributed around the line of equality. As pected to have an essentially infinite fatigue life. As noted noted previously, the fatigue life for Sample 5 is significantly previously, testing was only conducted to 50 million cycles. overestimated. However, the single-stage Weibull function Therefore, the failure point of these samples needed to be appears to give the most reasonable extrapolation of fatigue extrapolated. Two techniques were used to extrapolate the test results. stiffness versus loading cycle data, the single- and three-stage When looking at the accuracy of fatigue predictions, it Weibull functions. Additionally, the data were analyzed using should be considered that strain versus fatigue life data typ- the RDEC procedures to determine the plateau value. The fol- ically is looked at on a log-log plot. The log of 26 million, lowing sections present the results from the testing and dis- the measured fatigue life for Sample 2, is 7.41, while the log cuss each of the analyses. Tables 4.3 through 4.6 present the of 56 million, the fatigue life estimated based on the first data collected in Phase I of the study. Table 4.3. Granite 19.0 mm NMAS mix with PG 67-22 at optimum asphalt. Beam Air Initial Micro- Cycles Extrapolated Cycles to 50% PV Cycles to 50% Average ID Voids, Flexural Strain Tested Initial Stiffness Initial Cycles % Stiffness, Single-Stage Three-Stage Stiffness to Failure MPa Weibull Weibull 18 6.6 5,175 800 6,000 NA NA 3.66E-5 6,000 3 6.8 4,686 800 7,130 NA NA 2.06E-5 7,130 6,377 7 7.4 4,522 800 6,000 NA NA 2.63E-5 6,000 10 6.8 5,153 400 246,220 NA NA 6.25E-7 246,220 46 7.0 5,239 400 57,000 NA NA 2.24E-7 267,8081 252,136 1 7.0 5,868 400 242,380 NA NA 3.17E-7 242,380 2 6.6 5,175 200 26,029,000 NA NA 5.33E-94 26,029,000 6 7.2 6,435 200 12,930,000 NA NA 6.19E-94 14,537,1862 20,445,922 21 7.4 6,240 200 20,771,580 NA NA 6.35E-94 20,771,580 5 6.7 4,519 170 34,724,500 NA NA 2.30E-94 34,724,500 69,362,250 23 6.8 5,645 170 60,000,000 1.04E+08 9.16E+07 5.37E-104 1.04E+083 4 6.7 6,602 100 50,000,000 5.49E+09 5.52E+09 9.25E-154 5.49E+093 2.90E+09 13 7.4 5,059 100 50,000,000 3.00E+08 1.04E+11 6.37E-164 3.00E+083 Notes: 1 Failure extrapolated. Testing suspended at 58% of initial stiffness at 57,000 due to computer problem. 2 Software froze, apparently due to error writing to network drive. Sample stiffness 3,439 MPa, at 53.4% of initial stiffness. Result extrapolated using linear regression of latter cycles. 3 Results extrapolated using single-stage Weibull model. 4 Less than 8.57E-9 proposed by Shen and Carpenter (40 ) as indicative of long-life pavement.
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33 Table 4.4. Granite 19.0 mm NMAS mix with PG 76-22 at optimum asphalt. Beam Air Initial Micro- Cycles Extrapolated Cycles to 50% PV Cycles to 50% Average ID Voids, Flexural Strain Tested Initial Stiffness Initial Cycles % Stiffness, Single-Stage Three-Stage Stiffness to Failure MPa Weibull Weibull 4 7.2 3,025 800 42,240 NA NA 4.02E-06 42,240 26,160 7 6.7 5,445 800 10,080 NA NA 1.58E-05 10,080 2 7.1 4,191 400 3,609,470 NA NA 1.66E-08 3,609,470 8 6.6 4,976 400 591,770 NA NA 2.87E-07 591,770 1,664,400 13 7.2 3,675 400 791,960 NA NA 2.15E-07 791,960 1 7.3 4637 250 14,837,450 NA NA 3.30E-08 14,837,450 NA 11 6.8 4148 250 50,000,000 2.91E+09 1.31E+15 2.22E-182 2.91E+091 5 6.7 4,460 200 50,000,000 2.75E+09 1.53E+11 0.00E+002 2.75E+091 2.72E+09 3 7.1 4,062 200 50,000,000 2.68E+09 2.61E+21 0.00E+002 2.68E+091 Notes: 1 Results extrapolated using single-stage Weibull model. 2 Less than 8.57E-9 proposed by Shen and Carpenter (40) as indicative of long-life pavement. Table 4.5. Granite 19.0 mm NMAS mix with PG 67-22 at optimum plus asphalt. Beam Air Initial Micro- Cycles Extrapolated Cycles to 50% PV Cycles to 50% Average ID Voids, Flexural Strain Tested Initial Stiffness Initial Cycles % Stiffness, Single-Stage Three-Stage Stiffness to Failure MPa Weibull Weibull Cox & Sons fixture in Interlaken Load Frame, except as noted 8 3.0 5,054 800 15,464 NA NA 15,464 24,982 14 3.2 5,306 800 34,500 NA NA 34,500 10 3.2 5,896 400 468,343 NA NA 468,343 403,232 15 3.3 6,698 400 338,121 NA NA 338,121 9 3.4 6,094 200 10,000,000 24,944,621 1.14E+08 24,944,6211 42 3.5 6,923 200 38,985,510 NA NA 38,985,510 62,310,044 13 3.8 6,219 200 50,000,000 1.23E+08 9.95E+07 1.23E+081 IPC Global fatigue device 6 4.7 6,862 800 5,570 NA NA 4.17E-05 5,570 5,400 3 4.1 7,472 800 5,230 NA NA 3.99E-05 5,230 7 5.1 7,675 400 131,390 NA NA 1.49E-06 131,390 94,615 4 4.9 7,653 400 57,840 NA NA 6.26E-06 57,840 2 4.7 7,512 200 3,584,740 NA NA 1.58E-07 3,584,740 3,584,740 6a 3.3 8,605 100 15,350,090 5.81E+08 NA4 NA 5.81E+081 5.81E+08 Notes: 1 Results extrapolated using single-stage Weibull model. 2 Testing conducted by Rutgers University on an IPC Global fatigue device. 3 Tested on Asphalt Institute IPC Global fatigue device. 4 No solution. Table 4.6. Granite 19.0 mm NMAS mix with PG 76-22 at optimum plus asphalt. Beam Air Initial Micro- Cycles Extrapolated Cycles to 50% PV Cycles to 50% Average ID Voids, Flexural Strain Tested Initial Stiffness Initial Cycles % Stiffness, Single-Stage Three-Stage Stiffness to Failure MPa Weibull Weibull 8 3.7 3,520 800 252,450 NA NA 2.61E-07 252,4501 5 3.0 5,451 800 32,520 NA NA 3.12E-06 32,520 48,050 14 3.3 5,764 800 63,580 NA NA 1.09E-06 63,580 1 2.8 5,532 400 2,860,000 NA NA 1.17E-08 2,860,000 6,257,500 4 3.0 5,532 400 9,655,000 NA NA 2.05E-093 9,655,000 10 3.6 4,308 300 39,624,000 NA NA 1.71E-093 39,624,000 2 3.5 5,427 300 8,811,8104 4.88E+7 5.63E+09 1.84E-133 4.88E+72 7.57E+07 12 3.5 4,105 300 20,080,7504 1.47E+8 2.46E+10 7.33E-173 1.47E+82 11 4.0 5,162 300 50,000,000 6.75E+7 4.50E+09 1.25E-133 6.75E+72 13 3.1 6,841 200 50,000,000 5.96E+9 6.79E+11 2.22E-183 5.96E+92 1.85E+10 9 3.1 5,609 200 50,000,000 3.10E+10 1.58E+16 0.00E+003 3.10E+102 Notes: 1 Not included in average. 2 Results extrapolated using single-stage Weibull model. 3 Less than 8.57E-9 proposed by Shen and Carpenter (40) as indicative of long-life pavement. 4 Sample did not fail, extrapolated using single-stage Weibull model.
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34 PG 67-22 Mix at Optimum Asphalt Content Figure 4.17 shows a log-log plot of cycles to failure versus strain. For samples that did not fail within 50 million cycles, The results for the PG 67-22 mix tested at optimum asphalt extrapolations are shown using single-stage Weibull, three- content were presented in Table 4.3. The PG 67-22 mix at opti- stage Weibull, and RDEC. The data from 800 through 170 ms mum asphalt content was tested by NCAT. The extrapolations were used to fit the regression line. A fatigue life of 60 million shown in Table 4.3 are based on the single- and three-stage cycles was assigned to Sample 23, tested at 170 ms (the actual Weibull functions, as well as the RDEC. Sample 23, tested at number of cycles tested). Ninety-five percent confidence 170 ms, produced Nf of 1.04E+08 and 9.16E+07 using the limits are shown for the regression line and 95% prediction single- and three-stage Weibull functions, respectively. Sam- intervals are shown from 170 through 50 ms. Although the ples 4 and 13, tested at 100 ms produced extrapolated Nf three-stage Weibull extrapolation of Nf for Samples 23 and 4 using the single-stage Weibull function of 5.49E+09 and fall on the upper prediction limit, the fatigue life estimate at 3.00E+08, respectively. Although both of these numbers rep- 100 ms for Sample 13 indicates a deviation from the log-log resent extraordinarily long fatigue lives, Table 4.3 indicates that Sample 13 would be expected to have a longer fatigue life. regression line, which in turn indicates the existence of an The single-stage Weibull function fits for Samples 4 and 13 endurance limit between 100 and 170 ms. was previously presented in Figure 4.4. As shown in Figure 4.4, Recall that 170 ms was selected to produce a beam fatigue the slope of the data decreases above approximately 1 million life of 50 million cycles, or approximately 500 million load loading cycles, indicating less damage. The best fit line for the repetitions in the field. Based on Sample 23's deviation Weibull function for Sample 13 has a steeper slope, resulting from the prediction limits in Figure 4.17, this strain level in the prediction of a shorter fatigue life. appears to be close to the endurance limit, but slightly high. Tsai et al. (57) developed a three-stage Weibull function to Nf was substituted in the regression as the predictor for strain more accurately model the changes in slope observed in the level and the regression re-run, resulting in Equation 17, as data. As discussed previously, three regions can be observed follows: with the Weibull function. In the third region, damage can = 103.54 × ( N ) -0.170 either increase rapidly--leading to failure--or decrease as (17) observed for Sample 13. The three-stage Weibull results for Sample 13 are shown in Figures 4.15 and 4.16. The three- Ninety-five percent prediction limit, in terms of strain, stage Weibull function resulted in Nf predictions of 5.52E+09 was calculated for N = 50 million cycles. The lower predic- and 1.04E+11 for Samples 4 and 13, respectively. tion limit for Equation 17 at 50 million cycles was 151 ms. 0 -2 Ln (-Ln(Stiffness Ratio)) -4 -6 Raw Data Fit -8 -10 -12 0 2 4 6 8 10 12 14 16 18 20 Ln (Loading Cycles) Figure 4.15. Three-stage Weibull function for Sample 13, PG 67-22 at optimum.
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35 6,000 5,000 Stiffness, MPa 4,000 3,000 Raw Data Fit 2,000 1,000 0 0 10,000,000 20,000,000 30,000,000 40,000,000 50,000,000 60,000,000 Loading Cycles Figure 4.16. Three-stage Weibull fit for Sample 13, PG 67-22 at optimum. By using the lower prediction limit, the strain level resulting pavements. Although all three strain levels appear to provide in 50 million cycles should be below the endurance limit for a long fatigue life, 170 ms appears to be at, or slightly above, the PG 67-22 mix at optimum asphalt content. the endurance limit based on the other analyses. The recom- The RDEC plateau values were calculated for each of the mended plateau value may not define the endurance limit, PG 67-22 at optimum samples. The results are shown in but rather a long fatigue life. Table 4.3. The samples tested at 200, 170, and 100 ms produce Figure 4.18 shows the relationship between cycles to failure plateau values lower than the critical value, 8.57E-9 recom- and plateau value. The relationship for low strain tests devel- mended by Shen and Carpenter (40) as indicative of long-life oped by Shen and Carpenter (40) based on testing 602 beams 1000 R² = 0.99 Sam ple 23 Sa mp le 4 100 Micro-Strain Sa mp le 13 10 1 1 100 10000 1000000 100000000 1E+10 1E+12 1E+14 Cycles to Failure (50% Stiffness) Measured Single-Stage Weibull Function 3-Stage Weibull Function RDEC Confidence Limits Prediction Limits Figure 4.17. Cycles to failure versus strain for PG 67-22 at optimum.
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36 1 0.1 0.01 y = 0.2937x-1.05 0.001 0.0001 R2 = 0.999 1E-05 Plateau Value 1E-06 1E-07 1E-08 1E-09 1E-10 1E-11 1E-12 1E-13 y = 0.2871x -1.0793 1E-14 1E-15 1 100 10000 1000000 10000000 1E+10 1E+12 1E+14 0 Cycles to 50% Initial Stiffness NCAT NCHRP 9-38 Shen and Carpenter Power (NCAT NCHRP 9-38) Power (Shen and Carpenter) Figure 4.18. Cycles to failure versus plateau value. is shown for comparison. The relationships are very similar. Weibull function. Extrapolations were also conducted using This would support Shen and Carpenter's proposal that there the three-stage Weibull function and RDEC. Sample 2 was is one relationship between cycles to failure and plateau value evaluated as a potential outlier using the repeatability data for all mixes, regardless of the manner of testing. developed in Phase II. The acceptable difference between two results is estimated to be 0.69 (on a log basis), while the differ- ence between Sample 2 and Sample 13 is 0.66 on a log basis. PG 76-22 at Optimum Asphalt Content This indicates that Sample 2 is within acceptable variation. The results for the PG 76-22 mix tested at optimum asphalt Sample 2 increased the variability of the data, producing an content were presented in Table 4.4. The PG 76-22 mix at R = 0.92 and resulting in larger prediction and confidence 2 optimum asphalt content was tested by NCAT. The extrap- intervals (Figure 4.19). However, both points at 200 ms and olations shown in Table 4.4 are based on the single-stage one point at 250 ms indicate a deviation from the log-log plot 1000 Sample 11 Sample 5 R² = 0.92 100 Micro-Strain Sample 3 10 1 1.E+00 1.E+02 1.E+04 1.E+06 1.E+08 1.E+10 1.E+12 1.E+14 1.E+16 1.E+18 1.E+20 1.E+22 Cycles to Failure (50% Stiffness) Measured Three-Stage Weibull Single-Stage Weibull 95% Confidence Interval 95% Prediction Interval Figure 4.19. Cycles to failure versus strain for PG 76-22 at optimum.
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37 N f = 2.738 × 105 exp0.077 VFA ( 0 ) (S0)-2.720 of cycles to failure versus strain, indicative of the endurance -3.624 (18) limit. Similar to the PG 67-22 results at optimum, the regres- sion was reversed to solve for the strain level that would produce where, 50 million and 100 million cycles. The lower 95% prediction Nf = fatigue life, interval indicated a strain level of 146 ms to produce 50 mil- VFA = voids filled with asphalt, percent, lion cycles to failure. This strain level is slightly lower than 0 = initial strain, and that determined for the PG 67-22 at optimum even though S 0 = initial loss stiffness, psi. the endurance limit appears to be at a higher value (between 200 and 250 ms). This is due to the increased variability in Table 4.7 shows the predicted fatigue lives using Equa- the testing. tion 18 and the actual and predicted percent difference between One sample at 250 ms and both samples at 200 ms pro- the two sets of beams. The SHRP A-404 surrogate fatigue duced plateau values less than the critical value indicated by equation fairly accurately predicts the percentage reduction Shen and Carpenter to be indicative of long fatigue life. in fatigue life at 800 ms (estimated 70% versus actual 78%). It underestimated the reduction at the lower strain levels. All PG 67-22 at Optimum Plus Asphalt Content of the fatigue lives predicted using the SHRP A-404 surrogate Testing for the PG 67-22 mix at optimum plus asphalt con- model are considerably lower than the measured values. Sen- tent was initially conducted on the Asphalt Institute's Inter- sitivity analyses indicated that most of the effect was due to the laken servo-hydraulic frame using a Cox & Sons fixture. Due increased initial stiffness. For the PG 76-22 mixes, initial stiff- to problems with the Interlaken system, low-strain beams ness increased with the lower air voids determined for the were later tested on IPC Global beam fatigue devices operated optimum plus samples. Comparisons between the asphalt by both the Asphalt Institute and Rutgers University. Due to content and gradation of randomly selected beams indicated concerns about possible differences caused by the various no significant differences. There were also no differences in machines, it was decided to retest the cells using the Asphalt the environmental chamber temperature of measured stiff- Institute's IPC Global beam fatigue device. The initial results ness of a plastic test beam to support the change in initial stiff- from the three machines and the retests using the IPC Global ness. Therefore, it is felt that the difference in initial stiffness machine were presented in Table 4.5. must be attributed to the different binders used to produce The fatigue lives for the retests are significantly shorter the beams. than for the original mix. A number of factors appear to con- Figure 4.20 shows a log-log plot of cycles to failure versus tribute to this difference. The initial stiffness for the original strain. Sample 1 from the first set at 200 ms and Sample 6a set of beams averaged 6,027 MPa; the initial stiffness of the from the second set at 100 ms show deviations indicative of replacement beams averaged 7,435 MPa. The beams were the endurance limit from their respective best-fit lines. Based prepared at air voids contents outside of the tolerance for the on the first data set, the 95% lower prediction interval for a optimum plus target (3.3 ± 0.5%) and used NCAT's lab stock fatigue life of 50 million cycles is 158 ms, which is essentially PG 67-22 binder instead of the dual graded PG 64/67-22 the same as that determined for the PG 67-22 at optimum binder, which was used at the NCAT Test Track. (151 ms). The SHRP A-404 surrogate fatigue model (Equation 18) (18) was used to assess whether the differences in initial stiff- PG 76-22 at Optimum Plus Asphalt Content ness and voids filled with asphalt (VFA) would tend to cause the degree of observed difference in the measured fatigue The results for the PG 76-22 mix tested at optimum plus lives. VFA would be lower due to the higher air voids. asphalt content were presented in Table 4.6. The PG 76-22 Table 4.7. Fatigue life predictions based on SHRP A-404 surrogate model. Binder Micro- Initial VFA Predicted Predicted Measured Strain Stiffness, Nf Percent Percent psi Reduction Reduction First Set 800 751,307 76 1,659 70 78 Second Set 800 1,039,502 72 504 First Set 400 913,317 76 12,027 57 77 Second Set 400 1,111,587 72 5,180 First Set 200 929,996 76 141,164 52 94 Second Set 200 1,089,540 72 67,442
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38 1000 R² = 0.96 R² = 0.98 10 0 Micro-Strain Sample 1, First Set Sample 6a, Second Set 10 1 1 10 10 10 10 1E 0 00 00 00 +1 0 00 00 0 0 00 0 Cycles to Failure (50% Stiffness) First Set Measured Three-Stage Weibull Single-Stage Weibull Figure 4.20. Cycles to failure versus strain for PG 67-22 at optimum plus. mix at optimum asphalt content was tested by NCAT. The Summary of Phase I Observations extrapolations shown in Table 4.6 are based on the single- Regarding Endurance Limit stage Weibull function. Extrapolations also were conducted using the three-stage Weibull function and RDEC. Figure 4.21 Clear indications of the endurance limit were shown for shows the log-log plot of cycles to failure versus strain. Although three of four mixes (not PG 67-22 at optimum plus). The strain a deviation from the regression line is first indicated at 300 ms, level corresponding to the endurance limit appears to be mix particularly for the three-stage Weibull and RDEC extrapola- dependent. Visually, the endurance limit appears to be more tions, it is not clear until 200 ms. The 95% lower confidence sensitive to binder properties than to asphalt content/air void limit for the endurance limit using the methodology described content. An endurance limit (predicted value, not lower pre- in Appendix A is 200 ms. This represents an increase as com- diction interval) of approximately 170 ms was determined for pared to both the PG 76-22 at optimum and PG 67-22 at opti- the PG 67-22 mix at optimum asphalt content. The endurance mum plus mixes. limit for the PG 76-22 mixture appears to be on the order of 1000 R² = 0.93 100 Micro-Strain 10 1 1 100 10000 1000000 100000000 1E+10 1E+12 1E+14 1E+16 Cycles to Failure (50% Stiffness) Measured Three-Stage Weibull Single-Stage Weibull RDEC Figure 4.21. Cycles to failure versus strain for PG 76-22 at optimum plus.
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39 Table 4.8. Granite 19.0 mm NMAS mix with PG 58-28 at optimum asphalt. Sample Air Initial Micro- Cycles Extrapolation Cycles to 50% Cycles to Average Voids, Stiffness, Strain Tested Stiffness 50% Cycles to % MPa Single-Stage Three-Stage Stiffness Failure Weibull Weibull 4 6.8 3,216 800 12,730 NA NA 12,730 10,097 8 7.2 3,014 800 8,730 NA NA 8,730 9 7.0 2,974 800 8,830 NA NA 8,830 2 6.9 3,372 400 166,290 NA NA 166,290 183,793 6 7.4 3,424 400 148,090 NA NA 148,090 7 7.4 3,424 400 237,000 NA NA 237,000 5 7 4,217 76 12,000,000 1.01E+09 1.11E+08 1.01E+091 1.03E+09 15 7 4,332 76 12,000,000 1.57E+09 5.30E+09 1.57E+091 16 7 4,706 76 12,000,000 5.04E+08 4.39E+09 5.04E+081 Note: 1 Extrapolated using single-stage Weibull model. 220 ms, and approximately 300 ms for the PG 76-22 at opti- Phase II Testing to Investigate mum plus. The plateau value criteria determined by Shen and Additional Binder Grades Carpenter (40) appears to be indicative of very long fatigue life, but not necessarily the endurance limit. Testing was conducted in Phase II to evaluate additional The Weibull function appears to be the best technique for binder grades. The 19.0 mm NMAS granite test track mix was extrapolation of low strain stiffness results. One rapid technique replicated using a true grade PG 64-22 and PG 58-28. Three for determining the endurance limit may be to test three repli- beams were tested at 800 ms and three beams were tested at cates at each of two strain levels, nominally 800 and 400 ms 400 ms for each mixture. The fatigue testing was conducted and then fit a log-log relationship between cycles to failure and by NCAT. The endurance limit was estimated using the one- strain. Testing additional samples at normal strain levels would sided 95% lower prediction interval for a strain level corre- potentially reduce the estimate of the standard deviation sponding to 50 million cycles according to the methodology and therefore increase the confidence in the prediction. The described in Appendix A. The lower 95% prediction inter- predicted endurance limit for the PG 76-22 mix at optimum vals were 82 and 75 ms, respectively, for the PG 58-28 and asphalt content would most likely benefit from testing addi- PG 64-22 mixtures. Confirmation tests for the endurance tional samples. The lower 95% prediction limit for a fatigue limit of the mixture using the PG 58-28 binder were carried life of 50 million cycles appears to be reasonably close to the out at 76 ms due to an error in the t-value used in determin- endurance limit. This technique was originally presented in ing the lower prediction limit. The tests should have been the Proposed Standard Practice for Predicting the Endurance carried out at 82 ms. The test data is presented in Tables 4.8 Limit of Hot Mix Asphalt (HMA) for Long-Life Pavements and 4.9 and shown graphically in Figures 4.22 and 4.23. in Appendix A. This technique was used for the testing con- For the PG 58-28 mixture, the single-stage Weibull extrap- ducted in Phase II. Appendix A was later modified in an effort olations for the samples tested at 76 ms indicate fatigue lives to obtain a more accurate estimate of the endurance limit. that are longer than that predicted from the log-log regression, Table 4.9. Granite 19.0 mm NMAS mix with PG 64-22 at optimum asphalt. Sample Air Initial Micro- Cycles Extrapolation Cycles to 50% Cycles to 50% Average Voids, Stiffness, Strain Tested Stiffness Stiffness Cycles to % MPa Single-Stage Three-Stage Failure Weibull Weibull 5 7.5 3,635 800 5,580 NA NA 5,580 5,377 6 7.5 3,736 800 5,060 NA NA 5,060 8 7.5 4,234 800 5,490 NA NA 5,490 2 7.3 4,666 400 98,120 NA NA 98,120 95,377 4 7.5 4,449 400 111,250 NA NA 111,250 9 7.4 4,227 400 76,760 NA NA 76,760 3 6.6 5,190 75 12,000,000 8.18E+10 1.08E+09 8.18E+101 3.95E+10 7 6.7 4,667 75 12,000,000 3.64E+10 3.18E+08 3.64E+101 10 6.7 5,989 75 12,000,000 2.82E+08 2.82E+08 2.82E+081 Note: 1 Extrapolated using single-stage Weibull model.
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40 10000 1000 Micro-Strain 100 R² = 0.98 10 1 1 100 10000 1000000 100000000 1E+10 Cycles to Failure (50% Stiffness) Measured Three-Stage Weibull Single-Stage Weibull Confidence Limits Prediction Limits Figure 4.22. Cycles to failure versus strain for PG 58-28 at optimum asphalt content. but within the prediction limits for the extrapolation. Two of prediction limits for the log-log regression line. This is a clear the three-stage Weibull extrapolations exceed the prediction indication of the endurance limit. limits, but Sample 16 indicates a shorter fatigue life. In general, the predicted endurance limits for the PG 58-28 The single- and three-stage Weibull fatigue life extrapola- and PG 64-22 binders were lower than what might have been tions for the PG 64-22 mixture samples exceeded the fatigue expected based on the Phase I testing. Historically, softer lives estimated from the log-log plot of cycles to failure ver- binders are believed to perform better in constant strain tests sus strain. The extrapolated fatigue lives also exceeded the (see Table 2.1). 10000 1000 Micro-Strain R² = 0.99 100 10 1 1.0E+00 1.0E+01 1.0E+02 1.0E+03 1.0E+04 1.0E+05 1.0E+06 1.0E+07 1.0E+08 1.0E+09 1.0E+10 1.0E+11 Loading Cycles Measured Three-Stage Weibull Single-Stage Weibull Confidence Limit Series5 Prediction Limit Series7 Power (Measured) Figure 4.23. Cycles to failure versus strain for PG 64-22 at optimum asphalt content.