## 4 Numerical Simulation
### Numerical Analysis of Charge Structure
#### 4.1.3 Numerical Results  
Numerical simulation analysis was conducted on the damage evolution process and dynamic damage characteristics of coal and rock bench blasting under different interval lengths of borehole charges to effectively control the damaging effect of bench blasting on coal seams. The damage evolution process of coal-rock mixed blasting under different charge structures is depicted in Figure 9.  
Figure 9 illustrates the damage evolution of coal-rock mixed blasting under varying filling lengths. Under the intense effect of explosive detonation pressure, the cavity volume around the borehole increases, forming a compressive damage zone. As the propagation distance increases, the tangential tensile stress caused by radial compression leads to tensile failure in the rock mass, forming a fracture zone. Transmission and reflection effects occur when the blast stress wave reaches the coal-rock interface. The transmitted stress wave further enhances the damage to the coal-rock mass, while the reflected stress wave induces tensile stress in the coal-rock mass, causing tensile failure and forming a tensile damage zone. Significant differences can be observed in the blasting damage effects on coal and rock under varying stemming or decoupling lengths. (1) Damage effect of rock blasting  
A study on the blasting damage characteristics of different decoupling lengths at the bottom of rock benches was conducted to determine the reasonable range of decoupling \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \(\rho_{0}\) & \(D\) & **PCJ** & **BETA** & **\(K\)** & **\(G\)** & **SIGY** & \(A\) & \(B\) & \(R_{1}\) & \(R_{2}\) & \(\omega\) & \(E_{\rm g}\) & \(V_{0}\) \\ (kg/m\({}^{3}\)) & **(m/s)** & **(GPa)** & & & & **(Pa)** & **(GPa)** & **(GPa)** & & & & **(J/m\({}^{3}\))** & \\ \hline
1100 & 4200 & 5.15 & 0 & 0 & 0 & 0 & 49.46 & 1.89 & 3.9077 & 1.118 & 0.33 & \(2.668\times 10^{9}\) & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Explosive material parameters and *EOS_JWL parameters. Figure 9: Damage evolution of coal and rock mixed blasting with different fill lengths. lengths. The blasting damage contour maps and damage curves under different charge structures were extracted from the simulation results, as shown in Figures 10 and 11. Figure 10 indicates that when the interval length at the bottom of the rock is 1 m, as illustrated in Figure 10, the charge position in the rock is close to the coal-rock interface, resulting in strong reflection stress. This causes significant reflection tensile failure near the interface, leading to extensive tensile damage and full rock mass fracturing. Simultaneously, the transmitted stress wave also causes significant damage to the bottom of the coal seam. Figure 10 presents the blasting damage when the spacing length at the bottom of the rock is 1.5 m. Its stress wave effects are similar to those of Scheme 1; however, due to the increased stemming length, the duration of the blast stress wave in the rock mass increases, leading to a decrease in the tensile stress intensity near the interface, though the damage to the coal-rock mass remains severe. When the interval length is 2.0 m, as shown in Figure 12, the tensile damage to the rock is significantly mitigated, and the damage to the coal seam is effectively reduced. Figure 10 shows the condition when the interval length is 2.5 m, where the tensile failure of the rock mass near the interface further decreases, though  
Figure 11: Rock damage curves at each measuring point. Figure 10: Coal and rock mixed blasting damage with different charge structures (1). the crack connectivity remains adequate. When the interval length increases to 3.5 m, as depicted in Figure 10d, the damage range of the rock mass near the interface does not propagate effectively. Figure 11 illustrates the blasting damage curves of the rock at each measurement point under varying stemming lengths of charge structures.