# Numerical Analysis of Cyclic Impact Damage Evolution of Rock Materials under Confining Pressure
## 3 Results and Analysis
### Numerical Simulation of Rock Fracture  
When the amplitude of half-sine incident stress waves is 180 MPa, the rock fracture process after cyclic impacts under 0 MPa confining pressure and 2 MPa confining pressure  
Figure 4: Stress balance under 180 MPa half-sine incident stress wave. (**a**) 2 MPa confining pressure (b) 4 MPa confining pressure.  
Figure 5: Dynamic stress-strain curves of rock specimens after cyclic impacts at 180 MPa half-sine incident stress wave. (**a**) 0 MPa confining pressure, (**b**) 2 MPa confining pressure.  
are illustrated in Figures 6 and 7, respectively. In numerical simulation, the crack generation and propagation result in the failure of elements.  
As shown in Figure 6, the rock failure process exhibits a fracture surface approximately along the axial direction without the end effect. At the initial stage of the fracture process, a crack first appears on the periphery of the rock specimen, as shown in Figure 6b. Under the impact loads, the rock specimen experiences axial compression and radial tension. When the transverse tensile strain exceeds the criterion, short cracks generate in the middle of the outer side of the rock specimen, as depicted in Figure 6c. As the transverse tension deformation continues, the short cracks extend parallel to the length of the rock specimen until penetrating the entire specimen. Eventually, strip-shaped blocks are observed at the periphery of the rock specimen, as depicted in Figure 6d. Under cyclic impacts, the fracture of the rock specimen extends from the periphery toward the interior.  
Figure 6: Rock fracture process after cyclic impacts under 180 MPa half-sine incident stress wave and 0 MPa confining pressure. (**a**) Intact state before impact, (**b**) Broken state after the 1 st impact, (**c**) Broken state after the 2 nd impact, (**d**) Broken state after the 3 rd impact.  
Figure 7: Rock fracture process after cyclic impacts under 180 MPa half-sine incident stress wave and 2 MPa confining pressure. (**a**) Intact state before impact, (**b**) Broken state after the 1 st impact, (**c**) Broken state after the 2 nd impact, (**d**) Broken state after the 3 rd impact, (**e**) Broken state after the 4 th impact, (**f**) Broken state after the 5 th impact, (**g**) Broken state after the 6 th impact, (**h**) Broken state after the 7 th impact.  
As illustrated in Figure 7, the fracture on the rock specimen increases with the number of cyclic impacts. In the early stage of the fracture process, a crack also first generates on the periphery of the rock specimen, as shown in Figure 7b. Due to the constraint effect of confining pressure on crack propagation, the number of cyclic impacts before macroscopic fracture in Figure 7 is much larger than that in Figure 6, and the number of cracks in Figure 7b is much less than that in Figure 6b. The damage to the rock specimen accumulates with the crack propagation after each impact. With the number of cyclic impacts increasing, the cracks extend from the periphery towards the interior, as illustrated in Figure 7c-g. Finally, strip-shaped blocks are also observed at the periphery of the rock specimen, as depicted in Figure 7h.