The National Academies Press

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From page 20... ... However, if the test was terminated prior to reaching 50% of initial stiffness, either due to an equipment problem or to reaching 50 million cycles, an extrapolation procedure was used to estimate the number of loading cycles, Nf, corresponding to 50% of initial stiffness. Ideally, a method of extrapolation would be identified that could be used to shorten the beam fatigue testing procedure used to determine the endurance limit. Read the entire page →
From page 21... ... The goal of this additional point was to help define the transition from "normal" strain test to tests below the apparent fatigue endurance limit or "low" strain tests. For the PG 67-22 mix at optimum asphalt content, the data from 800 through 200 ms were used to estimate the strain level that would result in a fatigue life of 50 million cycles. Read the entire page →
From page 22... ... 0 10,000,000 20,000,000 30,000,000 40,000,000 50,000,000 Fatigue Life Extrapolation Using Natural Logarithm of Loading Cycles versus Stiffness A logarithmic model (Equation 3) using the natural logarithm of loading cycles versus stiffness was evaluated as one alternative to the exponential model. Read the entire page →
From page 23... ... Logarithmic Model Starting at 1 million Cyles Logarithmic Model using All Data particularly at low strain levels. In Figure 4.3, logarithmic models were ﬁt to the data from Sample 6 of the PG 67-22 mix at optimum asphalt content, which was tested at 200 ms. Read the entire page →
From page 24... ... Fatigue Life Extrapolation Using Three-Stage Weibull Function In the previous section, the Weibull survivor function was presented as a method for modeling the fatigue life of beam fatigue tests. In later sections, it will be demonstrated that the single-stage Weibull function generally provides a good estimate of a sample's fatigue life and is reproducible when calculated by different laboratories. Read the entire page →
From page 25... ... ) Ln (Loading Cycles) Read the entire page →
From page 26... ... The complete calculation procedure is described in Appendix A, Proposed Standard Practice for Predicting the Endurance Limit of Hot Mix Asphalt (HMA) for Long-Life Pavement Design. Read the entire page →
From page 27... ... Typical RDEC versus loading cycles plot and the indication of PV. 0 0.002 0.004 0.006 10 510 1,010 1,510 2,010 2,510 3,010 3,510 4,010 R D EC Number of Load Cycles I III PV II Read the entire page →
From page 28... ... Loading cycles 800 microstrains Figure 4.10. Dissipated energy versus loading cycle for raw data and various power models. Read the entire page →
From page 29... ... Thus, a model would be ﬁt to the stiffness versus loading cycle data and the number of cycles required to reach 50% of the initial stiffness would be extrapolated. A significant deviation from a log-log plot of strain versus cycles to failure would indicate the strain level corresponding to the endurance limit (this will be shown later in the section on Existence of 29 Figure 4.11. Read the entire page →
From page 30... ... 0 10 20 30 40 50 60 70 80 90 100 110 120 0 10,000,000 20,000,000 30,000,000 40,000,000 50,000,000 60,000,000 Pr ed ic te d Pe rc en t o f A ct ua l S tif fn es s at 5 0 M ill io n Cy cl es Number of Cycles Used for Model Exponential Model Logarithmic Model Power Model Weibull Function the Endurance Limit) Read the entire page →
From page 31... ... The shape of the model will also have an effect. Logarithmic and power models can produce very flat slopes at high numbers of loading cycles that result in overestimation of the fatigue life (particularly if some of the initial cycles are not eliminated to better match the slope of stiffness versus loading cycles at a high number of loading cycles) Read the entire page →
From page 32... ... . For long-life fatigue tests, at strain levels slightly above the endurance limit, the single-stage Weibull function appears to provide the most accurate extrapolation of fatigue life. Read the entire page →
From page 33... ... Extrapolated Cycles to 50% Initial Stiffness Beam ID Air Voids, % Initial Flexural Stiffness, MPa MicroStrain Cycles Tested Single-Stage Weibull Three-Stage Weibull PV Cycles to 50% Initial Stiffness Average Cycles to Failure Cox & Sons fixture in Interlaken Load Frame, except as noted 8 3.0 5,054 800 15,464 NA NA 15,464 14 3.2 5,306 800 34,500 NA NA 34,500 24,982 10 3.2 5,896 400 468,343 NA NA 468,343 15 3.3 6,698 400 338,121 NA NA 338,121 403,232 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 13 3.8 6,219 200 50,000,000 1.23E+08 9.95E+07 1.23E+081 62,310,044 IPC Global fatigue device 6 4.7 6,862 800 5,570 NA NA 4.17E-05 5,570 3 4.1 7,472 800 5,230 NA NA 3.99E-05 5,230 5,400 7 5.1 7,675 400 131,390 NA NA 1.49E-06 131,390 4 4.9 7,653 400 57,840 NA NA 6.26E-06 57,840 94,615 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 Table 4.5. Granite 19.0 mm NMAS mix with PG 67-22 at optimum plus asphalt. Read the entire page →
From page 34... ... Although the three-stage Weibull extrapolation of Nf for Samples 23 and 4 fall on the upper prediction limit, the fatigue life estimate at 100 ms for Sample 13 indicates a deviation from the log-log regression line, which in turn indicates the existence of an endurance limit between 100 and 170 ms. Recall that 170 ms was selected to produce a beam fatigue life of 50 million cycles, or approximately 500 million load repetitions in the field. Read the entire page →
From page 35... ... Measured Single-Stage Weibull Function 3-Stage Weibull Function RDEC Confidence Limits Prediction Limits Sa mp le 13 Sa mp le 4 Sam pl e 23 By using the lower prediction limit, the strain level resulting in 50 million cycles should be below the endurance limit for the PG 67-22 mix at optimum asphalt content. The RDEC plateau values were calculated for each of the PG 67-22 at optimum samples. Read the entire page →
From page 36... ... PG 76-22 at Optimum Asphalt Content The results for the PG 76-22 mix tested at optimum asphalt content were presented in Table 4.4. The PG 76-22 mix at optimum asphalt content was tested by NCAT. Read the entire page →
From page 37... ... The lower 95% prediction interval indicated a strain level of 146 ms to produce 50 million cycles to failure. This strain level is slightly lower than that determined for the PG 67-22 at optimum even though the endurance limit appears to be at a higher value (between 200 and 250 ms) Read the entire page →
From page 38... ... Visually, the endurance limit appears to be more sensitive to binder properties than to asphalt content/air void content. An endurance limit (predicted value, not lower prediction interval) Read the entire page →
From page 39... ... The predicted endurance limit for the PG 76-22 mix at optimum asphalt content would most likely beneﬁt from testing additional samples. The lower 95% prediction limit for a fatigue life of 50 million cycles appears to be reasonably close to the endurance limit. Read the entire page →
From page 40... ... The single- and three-stage Weibull fatigue life extrapolations for the PG 64-22 mixture samples exceeded the fatigue lives estimated from the log-log plot of cycles to failure versus strain. The extrapolated fatigue lives also exceeded the prediction limits for the log-log regression line. Read the entire page →
From page 41... ... The average estimated endurance limits were 151, 175, and 188 ms, respectively, for the PG 67-22 at optimum, PG 67-22 at optimum plus, and PG 76-22 at optimum asphalt content mixes. The strain levels used for the beams tested to evaluate the low strain extrapolations were 130 and 220 ms, respectively, for the PG 67-22 and PG 76-22 mixes at optimum asphalt content. Read the entire page →
From page 42... ... . Strain was calculated at 98% of the peak stress, and the results are shown in Figure 4.24 versus the predicted and 95% lower conﬁdence limits for the endurance limit determined from the beam fatigue tests. Read the entire page →
From page 43... ... y = 0.047x R² = 0.650 y = 0.031x R² = 0.400 0 50 100 150 200 250 300 350 0 1000 2000 3000 4000 5000 6000 En du ra nc e Li m it, M ic ro -S tr ai n Tensile Strain at Failure, Micro-Strain Predicted Endurance Limit 95% Lower Confidence Endurance Limit Linear (Predicted Endurance Limit) Linear (95% Lower Confidence Endurance Limit) Read the entire page →

From page 20...

... However, if the test was terminated prior to reaching 50% of initial stiffness, either due to an equipment problem or to reaching 50 million cycles, an extrapolation procedure was used to estimate the number of loading cycles, Nf, corresponding to 50% of initial stiffness. Ideally, a method of extrapolation would be identified that could be used to shorten the beam fatigue testing procedure used to determine the endurance limit.