Characteristics of Moduli Decay for the Asphalt Mixture under Different Loading Conditions
In order to explore the moduli decay patterns of asphalt mixtures under different loading conditions, the nonlinear fatigue damage model was implemented in order to simulate the moduli decay patterns. Then, the direct tensile, indirect tensile, and uniaxial compression fatigue tests were employed under four kinds of stress levels with four parallel tests. The specimens of AC-13C Styrene-butadiene-styrene (SBS) modified mixtures were manufactured. Based on the test results, the decay patterns of
... e decay patterns of the moduli during fatigue tests under different stress states were revealed, and the parameters of the damage model under different test conditions were obtained. By changing the values of the model parameters under a certain loading condition, fatigue curves were obtained. Then, the fatigue properties of asphalt mixtures under different stress states could be compared and analyzed directly. The result indicated that the evolution curves of fatigue damage for the direct tensile test, the indirect tensile test, and the uniaxial compression test all experienced three stages, which indicates that the fatigue damage characteristic of asphalt mixtures is non-linear. The decay patterns of the direct tensile moduli and the tensile moduli measured by the indirect tensile test are similar. The decay patterns of the uniaxial compression and the compression moduli measured by indirect tensile test are similar. The decay patterns of tensile and compressive moduli are obviously different. At the same cycle ratio state, the position of the decay curve for the compression moduli is higher than that of the tensile moduli. It indicates that the tensile failure is the main reason of the fatigue damage for asphalt mixture. The new analysis method of fatigue damage was proposed, which provides a possibility to compare the fatigue results that were obtained from different loading conditions and different specimen sizes. traffic and environmental conditions have been conducted [12, 13] . In order to ensure the durability and usability of asphalt pavement, many researchers have been conducting the works of evaluation of fatigue characteristics via varied fatigue test methods in different specimen's size and different stress levels. Xie Jun suggested that the direct tension strength got larger at higher strain loading rate  . Hyung Suk Lee conducted an indirect tensile test and determined the fundamental viscoelastic material property, which means that the strength of asphalt mixture were related to the temperature and loading time  . Waleed A. Zeiada employed the uniaxial compression test and observed that the fatigue endurance limit value increases by the increasing of temperature, asphalt content, and rest periods, whereas it decreased when the volume of air voids increases  . Different test methods produce different results. So far, three traditional test methods have been employed extensively: the direct tensile test, the indirect tensile test, and the uniaxial compression test. The direct tensile test refers to the test of a material under the action of a uniaxial tensile load. Under the assumption of homogeneity, the stress level or the stress ratio is same on each cross-section of the specimen during the test process, so the fracture position will appear at the weakest cross-section. The failure will occur for the accumulation of the micro-cracks  . The indirect tensile test (IDT, also called splitting test) is in a two-dimensional stress state. The lateral direction lies in the tension state, while the longitudinal direction lies in the compression one. It can simulate the stress state of asphalt pavement under traffic loads. The tensile stress near the crack area of the IDT specimen is uniform relatively  . The uniaxial compression test is also a one-dimensional stress test method. During the process of the uniaxial compression test, the stress level and the stress ratio are same on each cross-section of the specimen. The stress state on each cross-section is the one-dimensional compression stress state  . Fatigue test results of asphalt mixtures are sensitive to different test conditions. Different test methods will have the different loading conditions, which will lead to the different stress states for the specimen of asphalt mixtures. For each test method, the test results of fatigue are not correlated and are inconsistent with others. Moreover, the difference of fatigue test results is still relatively large. Therefore, even to the same material, the fatigue properties from the different test methods cannot be compared. So far, it cannot form a unified evaluation and comparison method among different fatigue test results of asphalt mixtures. Furthermore, the fatigue tests of asphalt mixtures are sensitive to the test types and size of the specimens [19, 20] . The main purpose of this paper is to reveal the decay patterns of different modulus for asphalt mixture in fatigue test, which can be employed to improve the design accuracy of asphalt pavement.