# Peridynamics for Fracture Analysis of Reflective Cracks in Semi-Rigid Base Asphalt Pavement
## 4 Pavement Simulation Model
### Influence of Asphalt Surface Thickness  
Several solutions are proposed to retard the reflective cracking problem. Simply increasing the asphalt overlay thickness could be considered the most common retardation treatment. This section will explore the reflective crack propagation under asphalt surfaces of different thicknesses to evaluate the retardation effect of increasing asphalt surface thickness on reflective cracks.  
A more refined model is needed to better observe the propagation of reflective cracks. This means that the spacing of PD points needs to be reduced, and at the same time, more PD points are needed, which will greatly increase the calculation time. To make the calculation model more refined without slowing down the calculation efficiency, it is necessary to optimize the road surface model. Generally, when studying the behavior of reflective crack propagation, only the process of crack propagation upward to the asphalt surface is considered, assuming that the base is not cracked. Therefore, this section only considers the interaction between the asphalt surface and semi-rigid base as the main factor, while the influence of the plain base and soil base as the secondary factor will not be considered.  
The double-layer pavement structure model shown in Figure 10 was established. The length of the model was 1 m, and the thickness of the semi-rigid base was 15 cm. The bottom of the model was fixed, and both ends were free. The asymmetrical load was selected as the loading mode, and the load was 10 MPa. The PD point discrete spacing is \(\Delta=1\) cm, and the horizon \(\delta=3.0\Delta\). This paper used 3 cm as the gradient of asphalt surface thickness to explore the propagation of reflective cracks on the road surface under different thicknesses of 6-15 cm, and there were four working conditions in total. To better observe the crack propagation trajectory, only the damage cloud map of the crack growth area was selected for display, which is the same as in Section 4.5. Numerical simulation results of the reflective crack propagation of asphalt pavement with different thicknesses under asymmetrical loading are shown in Figure 12.  
Figure 12: Crack propagation of asphalt pavement with different thicknesses.  
The expansion behavior of reflective cracks in asphalt overlays of different thicknesses is analyzed in Table 4.  
According to the above simulation results, with the increase in asphalt overlay thickness, the time of initial crack initiation is delayed, and the crack propagation speed slows down. In the numerical simulation example of the asphalt overlay with a thickness of 15 cm, the cracks do not penetrate the asphalt overlay when the structure reaches stability. All the above results indicate that increasing the thickness of the overlay has a certain inhibitory effect on the reflective crack propagation. However, increasing the thickness of the asphalt surface means a huge increase in cost, which is not wise. In addition, cracks in the semi-rigid base initially extend horizontally along the interface of adjacent layers, so maintaining a good bond between the semi-rigid base and asphalt surface will also help to slow down the expansion of reflective cracks.