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20 Comparison of Endurance Limits of Beam and Uniaxial Fatigue Tests The beam fatigue model was developed using three bind- ers (PG 58-28, PG 64-22, PG 76-16), while the uniaxial test model was developed using one binder only (PG 64-22). Since the beam and uniaxial fatigue tests produce different types of stresses, they produce different endurance limit val- ues as shown in Tables 4 and 5. In order to have a fair comparison between the endur- ance limits of beam and uniaxial fatigue tests, only the beam fatigue data of the PG 64-22 mixture were used to develop a new beam fatigue model to predict the SR in the form of Equation 2. The model was then used to estimate the endur- ance limit values at different temperatures when the SR-et relationships reach an SR value of 1.0. The results of the beam fatigue model were compared with the results of the uniaxial fatigue model in the same form (Equation 2). The results showed that the endurance limit values of the two tests exhibit simi- lar trends. The endurance limits obtained from the uniaxial fatigue model are about 10% less than those obtained from the beam fatigue model when the same binder was used. This comparison showed that, regardless of the fatigue test type, the asphalt mixtures are prone to heal in a similar fashion if allowed to rest. Figure 24 includes a direct comparison of the endurance limit values obtained from the beam fatigue model and the uniaxial fatigue model using the same binder. These values were estimated for all mixtures at a 5s rest period, 20,000 loading cycles, and three temperatures (40, 70, and 100°F). It is clear that there is a good correlation between the endur- ance limit values from both models when the same binder is used. It must be recognized that simplifying the models by replac- ing the binder grade, binder content, air voids, and tempera- ture with the stiffness of the material may produce a certain level of inaccuracy. For example, mixtures with high binder content and low air voids showed similar stiffness to those that have low binder content and high air voids, even though their endurance limits are different. This stiffness effect became more apparent in the uniaxial PSR model since it covered a narrow range of stiffness (one binder grade only), while the beam fatigue model covered a wide range of stiffness (three binder grades), which reduced the impact of the stiffness effect. This observation may explain the difference between the endurance limits obtained from the two stiffness-based models as shown in Figures 12 and 22 (Tables 4 and 5). As indicated earlier, the uniaxial test is more time con- suming than the beam fatigue test and requires an enormous attention to details. Uniaxial specimens have to be carefully glued to the loading platens and properly aligned in the load- ing machine in order to avoid improper or premature failure. In addition, the beam fatigue test is more established with a larger database available in the literature than the uniax- ial test. Finally, it is most important to understand that all pavement fatigue cracking subsystems in mechanistic design procedures for asphalt concrete are based upon tensile strain generated in the pavement by a repetitive flexing of the layer. As a consequence, it is suggested that the future endurance limit studies utilize beam fatigue tests. Incorporating the Endurance Limit in Fatigue Relationships The fatigue relationships shown in the literature are typi- cally parallel straight lines for different Eo values on a log-log graph as shown in Figure 25. These lines show that when the applied strain decreases, the number of load applications to failure (Nf) increases following a log-log relationship, with- out consideration of an endurance limit. The endurance limit obtained from the beam fatigue model developed in this study (Equation 3) can be easily and directly incorporated in the fatigue relationships for a specific rest period as demon- strated in Figure 25. This means that if the applied strain is above the endurance limit, damage will accumulate and the asphalt layer will last up to a certain value of Nf. However, if C H A P T E R 4 Recommended Fatigue Test and Endurance Limit Implementation
21 expected load spacing (rest period) of the design truck den- sity in the total traffic stream. Figure 25 also shows that when the material stiffness increases, Nf decreases if the strain is above the endurance limit. It also shows that when the material stiffness increases, the endurance limit decreases. The figure demonstrates the endurance limit concept for a specific rest period that cor- responds to a specific AADTT in the field. If the rest period increases, complete healing will occur at larger strains and the endurance limit values will increase. Incorporating the Endurance Limit in the Pavement ME Design The current AASHTOWare Pavement ME Design does provide the effect of an endurance limit to be incorporated into the analysis. The designer is required to input a single value of endurance limit. As shown earlier, the endurance limit values vary depending on the material stiffness and the rest period between loading cycles. The incorporation of the beam fatigue endurance limit, developed from this project, into the ME Design will require additional software code to calculate the endurance limit value for the rest period associated with the typical design truck traffic spectra on the facility within the models developed in this project. However, this task of revising the software should be a relatively simple endeavor to accomplish. At the same time, the critical strain value of the HMA layer (or sublayer) can be calculated using the Jacob Uzan Layered Elastic Analysis (JULEA) multilayer elastic computer pro- gram already incorporated in the ME Design software. If the critical strain calculated from the JULEA program is less than the fatigue endurance limit, the average axle is not counted in the analysis for this period, which means that there is no fatigue damage during this time period. However, if the critical strain is greater than the fatigue endurance limit, the average axle is counted as causing cumulative fatigue damage during this period. the strain is below the endurance limit value and is applied at a certain rate (for a specific rest period), complete healing will occur and damage will not accumulate. This concept has a significant implication on extending pavement life, where the layer thicknesses and material properties can be controlled so that the strain does not exceed the endurance limit for the y = 0.8978x -1.8906 R2 = 0.9758 10 100 1000 000100101 Un iax ial F at igu e EL , μ ε Beam Fatigue EL, με Figure 24. Comparison of endurance limit values obtained from uniaxial fatigue and beam fatigue models (PG 64-22, RP îµ 5s, N îµ 20,000 cycles). Endurance Limits at a Specific Rest Period Increasing Stiffness Typical Fatigue Lines In iti al S tra in Number of Loading Cycles to Failure, Nf Figure 25. Incorporating endurance limits in fatigue relationships.
