# Discrete Element Analysis of Indirect Tensile Fatigue Test of Asphal Mixture
## 1 Introduction  
The fatigue failure is one of the most common distresses in asphalt pavements [1]. The fatigue properties of asphalt mixture could be evaluated by an indirect tensile fatigue test [2]. At present, the fatigue test of asphalt mixture is mainly carried out in the laboratory. However, the variability of asphalt mixture is very difficult to control during a laboratory test. Because of its heterogeneity, the fatigue properties are impossible to be fundamentally explored and evaluated by the laboratory test. Therefore, it is necessary to find a way to study the behavior and mechanism of the fatigue failure based on a more non-uniform microstructure [3].  
Numerical simulation analysis is frequently used to study the micromechanical properties of the asphalt mixtures. Recently, some researchers have been trying to use a discrete element method (DEM) to analyze the fatigue properties of asphalt mixtures. [PERSON] et al. analyzed the impacts of different parameters of air voids on the creep behavior of an asphalt mixture by the DEM [4; 5]. [PERSON] et al. conducted a two-point bending beam fatigue simulation test with the trapezoidal samples. The relationship between the fatigue properties of a French high modulus asphalt mixture and the Burger's parameters were investigated by the DEM [6]. [PERSON] et al. analyzed the failure procedure of an asphalt mixtureby the DEM [7]. A local discrete element model was established to discuss the damage and cracks caused by the cyclic fatigue load [8]. [PERSON] analyzed the effect of the aggregate packing on the dynamic modulus of an asphalt mixture by the DEM [9]. These achievements mentioned above demonstrate that the DEM is applicable for the research on fatigue characteristics of pavement asphalt mixes. However, the discrete element models of asphalt mixtures are generated by computer algorithms, which are different from the actual microstructures. The distribution characteristics of cracks and internal forces of asphalt mixtures are also seldom described in the indirect tensile fatigue test.  
Since microstructure images captured by X-ray computed tomography (X-ray CT) can show the internal distribution and composition of the material, CT and the DEM have been widely applied to asphalt mixture together recently. [PERSON] et al. obtained the images of asphalt mixture samples by the optical scanning, and reconstructed two-dimensional discrete element models based on these optical images [10]. Based on many two-dimensional slices of the same sample, the three-dimensional discrete element model of an asphalt mixture was reconstructed [11; 12]. [PERSON] et al. described the microstructure of asphalt mixtures obtained by CT and established a two-dimensional discrete element model to predict the creep compliance of uniaxial loading [13]. [PERSON] investigated the dynamic deformation process of an asphalt mixture based on the image-based discrete element model [14]. [PERSON] believed that image-based discrete element model could provide a potential detailed insight into the failure mechanism of the heterogeneous rocks at the microscopic level [15]. Generally speaking, the asphalt mixture is a non-uniform complex viscoelastic material. It can be simulated more accurately by the DEM with CT image-based microstructural modeling. Therefore, the CT image-based microstructural modeling is feasible to simulate the asphalt mixture.  
Therefore, in this paper, the two-dimensional discrete element model was reconstructed by the Particle Flow Code (PFC) software, based on the CT images. The indirect tensile fatigue simulation test was carried out to analyze the fatigue properties of the asphalt mixtures. The distribution of internal forces, damage to the microstructure, and some other micromechanical responses in the model were investigated. Furthermore, the simulation test was verified by the laboratory fatigue test.