# Discrete Element Analysis of Indirect Tensile Fatigue Test of Asphal Mixture
## 3 Results and Discussions
### Experimental Test Validation in the Laboratory
#### 3.2.1 Characteristics of the Crack  
The samples were loaded at several stages. At each stage, the vertical deformation was controlled at 1.5 mm. After each loading stage, the sample was taken out for CT scanning. During the laboratory test, the samples were broken after three loading stages. The CT images at each stage were scanned and analyzed. The distribution and development characteristics of the crack from both simulation test and laboratory test were compared. The contact condition of the model and CT images at these three loading stages: no crack, crack developing, and crack interconnected are shown in Figure 12, respectively. In Figure 12, the CT images of the sample, acquired during the loading stages, are not perfect circles. Some part of the image on the right was missing because one X-ray tube of the CT was damaged. Since the cracks mainly distribute in the middle part of the section, the deficiency of the image can be ignored. According to the development and distribution characteristics of the crack at the three loading stages, the analysis is as follows:1. At the first stage, when the vertical deformation of the sample is 1.5 mm, there is no crack in the CT image, as in Figure 11(a). The stress is stable and there is no crack under the corresponding contact conditions in Figure 11(b). It can be seen that the contacts among particles are intact. From the displacement of the particles in Figure 9(c), it can be found that nearly all the particles move downwards under the load, which is in accordant with that in the laboratory test, for the sample is elastically compressed.  
Figure 12: Cracks in the simulation test and laboratory test.  
2. The fatigue loading stop after the top wall has moved downwards at the second 1.5 mm. In Figure 12c, the cracks have extended to the middle of the section, and the length is about 50 mm. Most of the cracks distribute near the loading axis of the section. From Figure 12d, it can be found that the contacts within the asphalt mortar, which is near the top wall or the loading axis, are completely damaged. According to Figure 12c,d, the length and distribution of the cracks are consistent.
3. After loading continually for a while, the cracks continue developing downwards until the main crack is interconnected. That is, the sample is damaged. In Figure 12e, as compared with the former stage, the sample breaks and has lots of small discontinuous cracks. It may result from that that there are only a few aggregates in the top of the model, and the model cannot bear the load after the cracks are interconnected. A few small cracks develop towards two sides of the model, which may be caused by the small cracks near the top wall, because the small cracks will develop outwards under the tensile stress. From Figure 12e,f, it can be found that the shape, length and distribution of the cracks from the simulation test are consistent with those from the laboratory test.
4. From Figure 12a-f, it can be found that the development and distribution characteristics of the cracks of the sample in each loading stage are in accordance with those of the discrete element model. As far as the characteristics of the crack are concerned, the indirect tensile fatigue simulation test matches the indirect tensile fatigue laboratory test very well.