# Numerical Analysis of Cyclic Impact Damage Evolution of Rock Materials under Confining Pressure
## 2 Numerical Modeling and Verification
### Cyclic Impact Simulation of Rock Materials under Confining Pressure  
As illustrated in Figure 2, cyclic impact tests for rock material under confining pressure are implemented by applying static circumferential confining pressure on rock specimens before impact load. In Figure 2, \(P_{c}\) and \(P_{d}\) represent the static circumferential confining pressure and dynamic impact load.  
LS-DYNA offers two methods to apply static circumferential confining pressure on rock specimens before cyclic impact, namely the dyain file method and the dynamic relaxation method [34]. But the dyain file method cannot inherit the damage of rock specimens in cyclic impact simulations. Therefore, the dynamic relaxation method is employed for a full restart analysis to apply static circumferential confining pressure on rock specimens. The convergence of dynamic relaxation can be assessed through the deformation movement energy. When the dynamic relaxation process ends, the prestressed state is transferred to the initial conditions for transient analysis, allowing for a full restart. The key steps of cyclic impact simulation of rock materials under confining pressure are listed as follows.  
1. [label=(0)]
2. Segment setting. The lateral surface of the cylindrical rock specimen and the end surface of the transmission bar are defined as different groups by using the keyword SEGMENT_SET.  
\begin{table}
\begin{tabular}{c c c c c} \hline \(\rho\)/(g\(\cdot\)cm\({}^{-3}\)) & \(E\)/GPa & \(\mu\) & \(f_{c}\)/MPa & \(G\)/GPa & \(K\)/GPa \\ \hline
2.42 & 12.9 & 0.25 & 88.1 & 5.16 & 8.6 \\ \hline \end{tabular}
\end{table}
Table 1: Physical and static mechanical parameters of steel pressure bar.  
\begin{table}
\begin{tabular}{c c c c c} \hline \(\rho\)/(g\(\cdot\)cm\({}^{-3}\)) & \(E\)/GPa & \(\mu\) & \(f_{c}\)/MPa & \(G\)/GPa & \(K\)/GPa \\ \hline
2.42 & 12.9 & 0.25 & 88.1 & 5.16 & 8.6 \\ \hline \end{tabular}
\end{table}
Table 2: Physical and static mechanical parameters of rock material.  
Figure 2: Force diagram of rock specimen under combined confining pressure and impact load. (**a**) Combined confining pressure and impact load, (**b**) Static circumferential confining pressure.  
2. Boundary setting. Firstly, constrain all translation and rotation of the incident bar and transmission bar except the horizontal motion by using the keyword SPC_SET. Secondly, set the non-reflective boundary at the end surface of the transmission bar by using the keyword NON_REFLECTING.
3. Confining pressure applying. Firstly, define a preload curve according to static circumferential confining pressure by using the keyword DEFINE_CURVE. Secondly, apply the preload curve on the lateral surface of the cylindrical rock specimen by using the keyword LODING_SEGMENT_SET. Thirdly, run the dynamic relaxation analysis by keyword CONTROL_DYNAMIC_RELAXATION to make the static circumferential confining pressure maintain the designed value before impact load.
4. Cyclic impacts realization. Cyclic impact simulation is realized by using a full restart analysis.  
Cyclic impact simulations are conducted on rock specimens under confining pressures of 0 MPa, 2 MPa, and 4 MPa, respectively. The amplitude of half-sine incident stress for cyclic impact simulations is 170 MPa, 180 MPa, and 190 MPa under 0 MPa confining pressure, while it is only 180 MPa under 2 MPa and 4 MPa confining pressure. The objective is to investigate the effect of the amplitude of incident stress waves and confining pressure on the damage degree and damage evolution of rock materials.