In order to characterize the ability of tension and compression deformation of asphalt mixture more truly and to improve the test efficiency and scientificity of the tension and compression moduli, the synchronous test method based on the indirect tension test was proposed. The analytical algorithms of the tension and compression resilient moduli of the indirect tension test were derived by integrating the functions of the horizontal and vertical radial strain at the center of a specimen, which was based on Hooke’s law in the two-dimensional stress state and the principle of calculus. The direct tension, unconfined compression, and indirect tension moduli tests were conducted in both dynamic and static loading states, and the test results were compared in different loading states. The research results indicated that the synchronous testing method based on the indirect tension test is effective, and there is a significant difference between the tension and compression moduli of asphalt mixture, and the dynamic resilient modulus from the indirect tension test increases by a power function with the increase of loading frequencies.

The applicability of the Sigmoidal Function to describe the fatigue law of asphalt mixtures at broad stress ratio conditions was examined. This application aimed to avoid the inaccessibility of the segment function. It also sought to address the inadequacy of traditional $S-N$ fatigue equation in analyzing the fatigue characteristics of asphalt mixtures at broad stress ratio conditions. The asphalt mixture gradation and the optimum asphalt aggregate ratio were determined with raw material testing and mixture proportion design. Fatigue tests of the asphalt mixtures were performed at broad stress ratio conditions with Material Test System $-810$, and results were fitted by the Sigmoidal Function. An improved $S-N$ fatigue model was established with the Sigmoidal Function at broad stress ratio conditions. This improved model, as well as conventional models, can predict the fatigue life of asphalt mixtures. The estimated results were then compared. The improved $S-N$ fatigue model based on the Sigmoidal Function can simulate the fatigue law of asphalt mixtures at broad stress ratio conditions. Therefore, the advantages of the new model were confirmed. The model parameters exhibit clear physical meanings whose values can be obtained easily.

Asphalt mixture is a kind of simple thermal rheological material. The main mechanics behavior character of viscoelastic material is its time dependence, which lies in the existence of the interior timepiece or the characteristic time influenting by many factors. The free volume theory of material viscosity is usually used to study the characteristic time. Based on this theory, this paper deduced the time-temperature equivalent relation of Williams-Landel-Ferry (WLF) equation. Aging influences the viscosity as well. Through the creep test, this paper deduced the time-temperature, time-aging, temperature-aging equivalent equation. The equivalent principle also can be used in asphalt, modified asphalt and modified asphalt mixture.