# Numerical Analysis of Cyclic Impact Damage Evolution of Rock Materials under Confining Pressure
## 3 Results and Analysis
### Damage Evolution Analysis  
Rock is a typical brittle material in nature, characterized by numerous microcracks in it. When subjected to an external load or energy, rock experiences closure of original fissures, initiation and propagation of new cracks, and eventual coalescence of these cracks. This process significantly impacts the macroscopic behavior of rock. By incorporating the volume of the rock specimen after cyclic impacts into Equation (4), the damage of the rock specimen under various impact conditions is obtained. The calculated results are presented in Table 3, and the trends of damage evolution are depicted in Figure 8. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(P_{max}\)/MPa & \(P_{c}\)/MPa & \(n\) & \(V_{i}\)/(10\({}^{-6}\) m\({}^{3}\)) & \(D\) \\ \hline \multirow{6}{*}{170} & \multirow{6}{*}{0} & 1 & 47.024 & 0.041 \\  & & 2 & 46.730 & 0.047 \\  & & 3 & 46.632 & 0.049 \\ \cline{1-1}  & & 4 & 45.455 & 0.073 \\ \cline{1-1}  & & 5 & 44.426 & 0.094 \\ \cline{1-1}  & & 6 & 40.552 & 0.173 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Damage of rock specimen after cyclic impacts. As illustrated in Figure 8, the cumulative damage of the rock specimen under confining pressure progressively increases with the number of cyclic impacts, exhibiting three distinct evolutionary stages: rapid rising, steady development, and sharp rising. In the numerical simulation, as there are no pre-existing cracks in the rock specimen, the initial impact generates the cracks in the rock specimen, and the subsequent impacts lead to the propagation of the previously generated cracks. As the constraint effect of confining pressure, damage accumulates at a low speed after each impact. Once the damage reaches a specific level, the damage accelerates to form a macroscopic fracture due to the rapid propagation of cracks. Both confining pressure and amplitude of incident stress waves significantly affect the damage evolution and the number of cyclic impacts. As seen from Figure 8a, under 0 MPa confining pressure, the damage of the rock specimen at 190 MPa incident stress wave is more severe than that at 170 MPa. The high incident stress wave leads to many cracks generated after the first impact and a small number of cyclic impacts. The higher the  
Figure 8: The trend of cyclic impact damage evolution. (**a**) Damage evolution under 0 confining pressure, (**b**) Damage evolution under 180 MPa half-sine incident stress wave. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(P_{max}\)/MPa & \(P_{c}\)/MPa & \(n\) & \(V_{i}\)/(10\({}^{-6}\) m\({}^{3}\)) & \(D\) \\ \hline \multirow{8}{*}{180} & & 1 & 45.556 & 0.071 \\  & 0 & 2 & 43.73 & 0.108 \\  & & 3 & 33.736 & 0.312 \\ \cline{2-5}  & & 1 & 47.851 & 0.024 \\  & & 2 & 47.417 & 0.033 \\  & & 3 & 47.221 & 0.037 \\  & 2 & 4 & 46.730 & 0.047 \\  & & 5 & 45.848 & 0.065 \\  & & 6 & 43.445 & 0.114 \\  & & 7 & 39.571 & 0.193 \\ \hline \multirow{8}{*}{180} & & 1 & 48.937 & 0.002 \\  & & 2 & 48.839 & 0.004 \\  & & 3 & 48.741 & 0.006 \\  & & 4 & 48.643 & 0.008 \\  & & 5 & 48.250 & 0.016 \\  & 4 & 6 & 47.858 & 0.024 \\  & & 7 & 46.927 & 0.043 \\  & & 8 & 46.338 & 0.055 \\  & & 9 & 45.014 & 0.082 \\  & & 10 & 42.857 & 0.126 \\  & & 11 & 32.804 & 0.331 \\ \hline \multirow{2}{*}{190} & \multirow{2}{*}{0} & 1 & 42.611 & 0.131 \\  & & 2 & 22.066 & 0.550 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: _Cont._amplitude of the incident stress wave, the greater the damage after each impact and the smaller the number of cyclic impacts before macroscopic fracture. As seen from Figure 8b, under the same number of cyclic impacts, the damage of the rock specimen under 4 MPa confining pressure is significantly less than that under 0 MPa confining pressure. Due to the existence of confining pressure, the development of transverse cracks in the rock specimen is constrained; namely, the confining pressure has a significant constraint effect on the propagation of cracks in the rock specimen.