## 4 Numerical Simulation Analysis
### Analysis of Rock Damage Law  
Blasting operations for rock excavation, while enhancing the efficiency and quality of construction, inevitably cause some degree of damage to the retained rock mass due to explosive detonation. Pre-splitting blasting technology can significantly reduce the damage caused to the retained rock mass during detonation in the main blasting zone, yet the damage caused by pre-splitting blasting itself cannot be overlooked. The damage to the rock mass observed on its surface does not reveal the specific depth of the damage, and thus it is often neglected. However, the damaged rock mass, when subjected to excavation disturbances from other areas, vibrations from passing trucks, rainfall, and other factors, can become increasingly unstable. This instability may lead to phenomena such as collapses and landslides, which can affect the progress of construction and pose threats to the safety of construction personnel. Figure 8: Numerical simulation model of pre-splitting blasting. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Model Dimension/m**} & \multicolumn{1}{c}{**Number of**} & \multicolumn{1}{c}{**Pre-Split Hole**} & \multicolumn{1}{c}{**Pre-Split Hole**} & \multicolumn{1}{c}{**Pre-Split Hole**} & \multicolumn{1}{c}{**Pre-Spliting**} & \multicolumn{1}{c}{**Cartridge**} & \multicolumn{1}{c}{**Charged**} & \multicolumn{1}{c}{**Filling**} \\ \hline
**L** & **W** & **H** & **Pre-Split Holes** & **Diameter/mm** & **Depth/m** & **Hole Spacing/m** & **Diameter/mm** & **Length/m** & **Length/m** \\ \hline
6.4 & 4 & 5 & 3 & 120 & 5 & 1.2 & 32 & 4 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Parameters of hole-by-hole pre-splitting blasting model. To investigate the damage depth under various conditions in this study, cross-sectional views of the damaged areas are taken, and the depth of the damaged regions is measured. Measurements are conducted at three vertical depths: 2 m, 2.5 m, and 3 m. Multiple measurements are performed, with three data points collected for each depth (at the same measurement locations across all models). Ultimately, the average of the nine data points is taken, and half of this average is used for comparison. The process of measuring the damage depth is illustrated in Figure 9. Side views of the damage cloud diagrams constructed for the four models are shown in Figure 10, and a summary of the damage depth measurement data is presented in Table 9.  
When measuring the damage caused to the rock mass after blasting and only varying the inter-hole delay time, it is found that, within the same region, the depth of the damage caused to the rock mass is greatest when the inter-hole delay time is 0 ms, and smallest when the inter-hole delay time is 18 ms; this is shown in Table 9. This indicates that the rock damage is not necessarily reduced with longer delay times. The reason for this is that simultaneous detonation during pre-splitting blasting results in the strongest superposition of explosive stresses. Sequential hole pre-splitting blasting can effectively reduce the superposition of explosive stresses, thereby decreasing the intensity of the stress. However,  
Figure 10: Side view of damage cloud image of model. Figure 9: Damage depth measurement process. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Number** & **Inter-Hole Delay Time (ms)** & **Damage Depth (cm)** \\ \hline
1 & 0 & 32.56 \\
2 & 12 & 32.48 \\
3 & 18 & 30.61 \\
4 & 24 & 31.59 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Summary of damage depth measurement data. the free-face effect of the free surfaces created by the previously detonated holes on the subsequently detonated holes cannot be ignored. The fragmented rock area created by the first detonated hole essentially provides a new free surface for the subsequently detonated holes, which enhances the blasting effect after the detonation of the latter. Therefore, when using sequential hole pre-splitting blasting technology, it is particularly important to select an appropriate inter-hole delay time.