## 4 Numerical Simulation
### Casting Blasting Simulation
#### 4.2.2 Blast Effect Analysis  
(1) Rock Throw Law and Coal-Rock Fragmentation Effect Analysis  
The numerical simulation of the cast blasting of the rock bench and loosening blasting of the coal seam with different charge structures extracted the equivalent strain cloud maps of the rock mass at 0.2, 0.4, 0.6, and 0.8 s during the blasting process, as shown in Figure 15.  
Figure 15.-d present the effects of coal-rock blasting under varying charge structures. The analysis begins with the ejection blasting effect of the rock bench. First, the cast blasting effect of the rock bench was analyzed. Under the action of detonation pressure and explosive gases, the rock mass surrounding the borehole was damaged and gradually moved toward the free face. Simultaneously, due to the reflection of the shock waves at the free face and the tensile effect, the rock mass near the free face was thrown. As the explosives detonated hole by hole based on the delay time, the explosive energy acted on the rock mass, causing more rock mass to be thrown, as shown in Figure 15. However, \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Scheme**} & \multirow{2}{*}{**Type**} & \(H\) & \(D\) & \(L\) & \(\theta\) & \(a\) & \(b\) & \(q\) & \(L_{\text{F}}\) (m) & \(L_{\text{F}}\) & \(L_{\text{P}^{*}}\) & \(W\) & **Charge** \\  & & **(m)** & **(mm)** & **(m)** & **(\({}^{\circ}\))** & **(m)** & **(m)** & **(kg\(\cdot\)m\({}^{\circ}\))** & **Up** & **Down** & **(m)** & **(m)** & **(m)** & **Form** \\ \hline  & Rock & 14 & 170 & 14.9 & 70 & 6.0 & 4.5 & 0.57 & 4.5 & 2 & 8.4 & 0 & 4.0 & coupled \\ S-1 & Coal & 6 & 170 & 6.4 & 70 & 6.0 & 4.5 & 0.18 & 2.0 & 0.8 & 0.715 & 2.17 & 4.0 & interval \\ S-2 & Coal & 6 & 170 & 6.4 & 70 & 6.0 & 4.5 & 0.18 & 2.5 & 0.8 & 0.715 & 1.67 & 4.0 & interval \\ S-3 & Coal & 6 & 170 & 6.4 & 70 & 6.0 & 4.5 & 0.18 & 3.0 & 0.8 & 0.715 & 1.17 & 4.0 & interval \\ S-4 & Coal & 6 & 170 & 6.4 & 70 & 6.0 & 4.5 & 0.18 & 3.5 & 0.8 & 0.715 & 0.67 & 4.0 & interval \\ \hline  & & & & & & & & & & & & & & \\ \end{tabular} Note: \(H\): bench height, m; \(D\): borehole diameter, mm; \(\theta\): borehole inclination angle, \({}^{\circ}\); \(a\): hole spacing, m; \(b\): row spacing, m; \(q\): specific charge, kg\(\cdot\)m\({}^{\circ}\); \(L_{\text{F}}\): fill length or interval length, m; \(L_{\text{E}}\): charge length, m; \(W\): resistance line, m.  
\end{table} 
Table 7: Model blasting parameters. Figure 14: SPH-FEM numerical calculation model. the front-row damaged rock fragments obstructed the movement space of the rear-row rock mass, causing the rear-row damaged rock fragments to be thrown more upward, failing to achieve effective casting. The casting volume of the rock bench was approximately 37%, concentrated within 37.75 m, the maximum casting distance was 50.37 m, and the pile height was about 4 m, demonstrating a good casting effect. When the stemming length in the loosening blasting of the coal seam was 2.0 m, as shown in Figure 15i, the coal at the seam interface experienced blasting stress, causing a bulging phenomenon and significant interaction between coal and rock. Simultaneously, the upper rock body near the coal layer's free face sustained significant damage and throwing. When the stemming length increased to 2.5 m (Figure 15j), the bulging phenomenon at the seam interface was effectively alleviated, and no casting phenomenon occurred. When the stemming length reached 3.0 m (Figure 15k), the bulging phenomenon at the coal-rock interface was not apparent. At the free surface of the coal bench, due to the concentration of explosives in the middle of the borehole, the coal was severely broken in the middle of the coal bench, resulting in coal bulging at the free surface, but no casting phenomenon occurred. Similarly, when the stemming length was 3.5 m (Figure 15l), there was no significant bulging phenomenon at the coal seam interface, and the coal in the middle and lower part of the coal bench's free surface was cast.