# Characteristics of Moduli Decay for the Asphalt Mixture under Different Loading Conditions
## 1 Introduction  
Fatigue cracking is one of the most common distresses in asphalt pavement [1; 2; 3]. Fatigue cracking of asphalt pavement is an important consideration in asphalt mixture design and the structural design of flexible pavements [4; 5]. Fatigue life design and maintenance strategies employ a challenging task due to the inherent nonlinear viscoelastic properties of asphalt mixtures and the complex cracking behavior observed in the field [6; 7; 8; 9; 10]. The damage appeared and accumulated gradually during the service life of asphalt pavement [11]. Under the action of cyclical traffic loads, the damage will increase and the pavement would suffer from the fatigue failure. Therefore, the service life of asphalt pavement would be decreased. More and more studies of fatigue performance for asphalt mixtures under thetraffic 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.  
[PERSON] suggested that the direct tension strength got larger at higher strain loading rate [14]. [PERSON] 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 [15]. [PERSON] 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 [16]. 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 [14]. 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 [17]. 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 [18].  
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.