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1 SUMMARY Validating the Fatigue Endurance Limit for Hot Mix Asphalt Hot-mix asphalt (HMA) pavements have been designed primarily to resist rutting of the subgrade and bottom-up fatigue cracking. In classical pavement design, as design load applications increase, pavement thickness also must increase. There is a growing belief that bottom-up fatigue cracking does not occur for thick pavements. The concept of the HMA fatigue endurance limit--a level of strain below which there is no cumulative damage over an indefinite number of load cycles--is proposed to explain this occurrence. Therefore, addi- tional pavement thickness, greater than that required to keep strain levels at the bottom of the HMA layer below the endurance limit, would not provide additional life. This concept has significant design and economic implications. Research in the 1970s observed that the log-log relationship between strain and bending cycles for a number of HMA mixes converged below 70 micro-strain (ms) at a high number of loading cycles. Field studies in the United Kingdom recommended an HMA thickness range between 7.9 in. and 15.4 in. for a long-life pavement depending on such factors as binder stiffness. The stiffness of thick pavements was observed to increase with time, most likely due to binder aging. Other studies have documented the absence of bottom-up fatigue cracking in thick pavements and the common occurrence of top-down cracking. In theory, samples tested at a strain level below the endurance limit should last for an indefinite or infinite number of loading cycles. It is impossible to test samples to an infinite number of cycles. Therefore, a practical definition of the endurance limit, or a laboratory life representative of the endurance limit was needed. A capacity analysis indicated that at minimum safe spacing, a lane carrying 100% trucks 24 hours a day, 7 days a week for 40 years could carry a maximum of 329,376,000 trucks that would produce 1,317,504,000 axle rep- etitions (neglecting the steer axle). However, a more likely traffic stream would produce a maximum of approximately 500 million axle load repetitions. Studies have indicated that a shift factor, ranging from 4 to 100, must be applied to relate laboratory and field fatigue performance. There are many reasons that probably lead to the need for a shift factor with two primary factors being rest periods and healing. A shift factor of 10 was recommended in the Strategic Highway Research Program (SHRP) by Leahy et al. (46). Considering this shift factor, laboratory testing to 50 million cycles would equate to approximately 500 million loading cycles in the field or approximately the maximum prob- able loading in a 40-year period. This was considered a practical target for evaluating param- eters indicating an endurance limit. An experimental plan was developed using a single aggregate gradation, two levels of binder content (optimum and optimum plus 0.7%), and two binder grades (PG 67-22 and PG 76-22). The aggregates, gradations, optimum binder content, and binder grades/sources matched those used in the base layers of the 2003 National Center for Asphalt Technology (NCAT) Test Track structural sections. Using the same mixtures as the NCAT Test Track

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2 allowed calibration of the fatigue shift factor. Samples at optimum asphalt content were compacted to 7 0.5% air voids while samples at optimum plus asphalt content were com- pacted to 3.3 0.5% air voids. Beam fatigue and uniaxial tension testing were performed on the four mixtures. In Phase II, beam fatigue tests were performed on two additional mixes at optimum asphalt content using a PG 58-28 and PG 64-22. Beam fatigue testing was conducted according to AASHTO T321. At least two replicates were tested at 800, 400, 200, or 100 ms until the fatigue lives of two replicates at a given strain level exceeded 50 million cycles. The time to test a single sample to 50 million load cycles is approximately 50 days. At this point, a log-log regression was performed between strain and fatigue life using all of the data for which samples failed in less than 50 million cycles. The strain level that corresponded to a fatigue life of 50 million cycles was predicted. Two addi- tional beams were tested at this strain level. A number of extrapolation techniques were considered to predict the number of cycles to failure (Nf) for beams that are not tested to failure, including the exponential model described in AASHTO T321, a logarithmic regression, ratio of dissipated energy change, and single- and three-stage Weibull models. The extrapolations were evaluated using samples that had long fatigue lives--in excess of 12 million cycles--but failed before 50 million cycles. The logarithmic regression and ratio of dissipated energy change consistently overestimated Nf, often by several orders of magnitude. The exponential model consistently underestimated Nf if the entire loading history to failure was not used in the calculation. This suggested the exponential model was not a good technique for extrapolation from a number of load- ing cycles less than Nf. Extrapolations using the single-stage Weibull model were gener- ally distributed around the line of equality and provided the best prediction. In one case, the three-stage Weibull model provided a more accurate prediction of Nf and it always provided a better fit to the stiffness versus loading cycle data. For each mixture, log-log regression plots were created using the data for samples that failed in less than 50 million cycles. Prediction limits were determined for lower strain levels. The extrapolated Nf for samples that did not fail within 50 million cycles indicated fatigue lives that were longer than those indicated by the prediction limits from the regression of sam- ples tested at "normal" strain levels. This deviation indicates the existence of an endurance limit for HMA. A standard practice was developed to predict the endurance limit based on tests con- ducted at normal strain levels (above the endurance limit) based on statistical prediction limits. The estimate of the endurance limit is the one-sided, 95% confidence lower predic- tion limit for the strain level that produces a fatigue life of 50 million cycles. Confirmation tests at the predicted strain level are recommended. The predicted endurance limits deter- mined using this methodology ranged from 75 to 200 ms. Stiffer binders tended to produce higher endurance limits. Optimum plus binder content combined with lower sample air voids produced a slight increase in the endurance limit. A mini round-robin was conducted to assess the variability of beam fatigue tests at normal strain levels and extrapolations at low strain levels. Nf varies significantly depending on the strain level at which the samples are tested. The log base 10 transformation of Nf was used in the round robin analyses to produce a relatively constant variability across the range of strain levels evaluated. On a log basis for normal strain fatigue tests, the repeatability (within-lab) standard deviation was determined to be 0.248 and the reproducibility (between-lab) stan- dard deviation was determined to be 0.318. This results in within- and between-lab coeffi- cients of variation of 5.4% and 6.8%, respectively. The single-stage Weibull extrapolations had the lowest variability within and between labs. Uniaxial tension tests were performed on cylindrical samples cored and sawed from speci- mens compacted in the Superpave gyratory compactor. Testing included complex modulus, monotonic, and fatigue tests in uniaxial tension. Analysis of these data was done using vis- coelastic and continuum damage mechanics principles to identify the fatigue endurance limit

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3 of the PG 67-22 optimum, PG 67-22 optimum plus, PG 76-22 optimum, and PG 76-22 opti- mum plus mixtures. Frequency sweeps at various temperatures were run to measure the complex dynamic modulus of each mix. The dynamic modulus and phase angle master curves were constructed from these data and the relaxation master curve obtained through linear viscoelastic conversion. The damage characteristic curve of each mix was obtained by running uniaxial monotonic tests to failure or by running constant amplitude fatigue tests to failure. The characteristic damage curve was used to predict the number of cycles to fail- ure at different strain amplitudes to determine the fatigue endurance limit of the mixture. The estimated endurance limits from this method varied depending on whether the gener- alized power law or exponential model was used to fit the data in the characteristic curve. The estimated endurance limits for the generalized power law ranged from 164 to 261 ms, while those for the exponential model ranged from 47 to 96 ms. The relative rankings of the binders evaluated in Phase I appeared to be reversed from the beam fatigue tests. A second methodology was employed where fatigue tests with increasing strain amplitude were run in uniaxial tension to directly identify the fatigue endurance limit of the mixtures. The stress versus strain loading history forms a hysteresis loop, the area of which is the dis- sipated energy per cycle. The use of pseudo strain instead of engineering strain in constitu- tive analysis removes the hysteretic effect of viscoelasticity. If the induced strain levels are low enough not to induce damage (e.g., below the endurance limit) then the hysteresis loop collapses since the dissipated energy is only due to the viscoelastic response of the material. The estimated endurance limit using this methodology ranged from 115 to 250 ms. However, differences were observed between the strain applied through the cross head and the induced strain measured on the samples. These differences made it difficult to precisely increment the induced strain in order to accurately determine the endurance limit. Analyses were performed of LTPP data for indications of the endurance limit. A 1995 survivability analysis of data from the general pavement studies (GPS) experiments known as GPS-1 and GPS-2 indicated an endurance limit of approximately 65 ms. However, when the analysis was updated, and LTPP special pavement studies (SPS) data were added from SPS-1, no endurance limit was indicated. During the period between the original and updated analyses, LTPP changed the definition of longitudinal cracking in the wheel path. This may have resulted in cracks previously identified as top-down cracking to be reclassi- fied as bottom-up fatigue cracks. Forensic investigations on the thicker pavements in the study, exhibiting cracking, are required to identify the type of cracking. Still, separation was indicated between the survivability of pavements with tensile strains at the bottom of the HMA layer less than 150 ms and those equal to or greater than 150 ms. This may indi- cate that neglecting top-down cracking, the endurance limit may be less than 150 ms. Addi- tional cracking data were presented, which demonstrates the improved fatigue performance of mixes containing polymer modified binders, similar to that indicated in the beam fatigue testing program. Analyses were conducted on data from the structural sections of the 2003 NCAT Test Track to estimate the shift factor between laboratory and field performance. Three of the eight structural sections exhibited fatigue cracking in excess of 40% of the wheel-path area or approximately 20% of the total lane area during the test track loading cycle (application of 10 million equivalent single-axle loads [ESALs]). Forensic investigations indicated that the cracking in one of these sections resulted from debonding of the HMA layers. A fourth section had limited cracking and cumulative damage was estimated at 0.7 at the end of the loading cycles. All of the structural sections were instrumented to measure strain at the bottom of the HMA layer. The measured strain data, pavement temperatures, and axle repetitions were used with the fatigue transfer functions developed as part of the beam fatigue testing to calculate incremental damage on an hourly basis. Shift factors between 4.2 and 75.8 were calculated between laboratory and field performance. The shift factor of 4.2 was determined

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4 for a polymer modified section with a total asphalt thickness of only 4.8 in. Similar calcula- tions were performed with PerRoad and the Mechanistic-Empirical Pavement Design Guide (MEPDG). The shift factors determined using PerRoad ranged from 6.7 to 45.0. Damage in the MEPDG was calculated using the nationally calibrated fatigue model, not the transfer function developed as part of the beam fatigue testing. Shift factors for two sections ana- lyzed with the MEPDG ranged from 0.7 to 1.0. The predicted cracking based on 90% reli- ability was much higher. Overall, it was concluded that the assumption of a shift factor of 10 between laboratory and field performance was reasonable. Analyses were conducted using the MEPDG and PerRoad to determine their sensitivity to the measured fatigue endurance limit. Analyses were conducted with both the NCAT Test Track traffic (very limited range of axle weights) and the MEPDG default truck traffic clas- sification No. 1 for principal arterials. The perpetual pavement thickness determined with both programs was sensitive to the measured endurance, a 50 ms change in the endurance limit resulted in approximately a 7- to 8-in. change in pavement thickness for the MEPDG or a 4-in. change in pavement thickness for PerRoad. Using the endurance limits predicted from beam fatigue tests conducted as part of the study and the default traffic classification, the perpetual pavement thickness determined with Per- Road was approximately the same as the 20- and 40-year conventional (no endurance limit) MEPDG or 1993 AASHTO Pavement Design Guide pavement thicknesses. The MEPDG perpetual thickness was approximately 50% thicker. The overall conclusions at the end of a 20- or 40-year period were significantly different. With the conventional designs, the pave- ments would have failed in bottom-up fatigue with cracking over 20% of the lane area at 90% reliability while no cracking would be expected if the endurance limit was considered. The implementation of the endurance limit as a single value for a given mix appears rea- sonable for M-E design programs that use equivalent temperature concepts, such as PerRoad. For the MEPDG, however, temperature as a function of depth is calculated on an hourly basis throughout the design life or analysis period. This can result in higher peak temperatures, with corresponding higher strains at the bottom of the asphalt layer, than equivalent temper- ature methods. Research conducted outside this study indicates that the endurance limit based on lab- oratory testing varies as a function of temperature. One interpretation of this may be that a mix's ability to heal and therefore its fatigue "capacity" are greater at higher temperatures. A field study of data from the NCAT Test Track indicates pavements can withstand a distri- bution of strains without incurring cumulative damage. Both of these concepts have merit and both are recommended for future research aimed at better implementing the endurance limit in the MEPDG.