## 3 Numerical Simulation
### Simulation Results  
The detonation time was set using the keyword * INITIAL_DETONATION, with the shallow hole detonation being first and the deep hole detonation second, with a delay interval of 250 ms. Coupled charges were used, with a cut-off calculation time of 1000 ms. The shallow hole detonation section at 50 cm in the negative z-axis direction and the deep hole detonation section at 200 cm in the negative z-axis direction were analyzed using the initial free surface of each blast hole in the model as the XOY plane. The combined effects of the long and short holes at different times are illustrated in Figures 3-6. As shown in Figures 3 and 4, the propagation of stress waves in the rock mass during the combined long and short hole cutting blasting process is illustrated. Following a detonation of the shallow hole after 70 ms, the blast stress wave propagates radially from the center of the explosive; at this point, the stress waves from each hole have not yet come into contact. After 110 ms, the vertical stress wave makes initial contact and superimposition occurs. At 150 ms, the stress wave in the central shallow hole contacts and superimposes with the stress waves on either side. At 200 ms, the stress wave propagates to the empty hole of the deep hole without charge, resulting in stress reflection and the superposition of the stress wave, and continues to propagate outward. Subsequently, following a period of 250 ms after the detonation of the shallow hole, the detonation of the deep hole commences. During this phase, stress diffusion occurs in the short holes at this depth. The attenuation rate of stress waves in deep holes was observed to be less than that of shallow hole detonations. At 310 ms, the stress wave generated by the deep hole causes stress concentration and reflection at the shallow hole position, resulting in the reflected wave meeting the incident wave at the centerline of the borehole. At 370 ms, the stress wave in the deep hole continues to diffuse, leading to stress concentration in the middle part of the rock mass at the shallow hole position. The stress fields of all holes are initially combined into a single entity. At 450 ms, the stress waves emanating from the three deep holes converge and superimpose in the upper part of the model, resulting in the formation and radial propagation of the stress field. As shown in Figures 5 and 6, the damage to the rock mass that occurs during the excavation and blasting process of the combined long and short hole cutting process is presented. Following the detonation of the shallow holes for approximately 110 ms, the damage zones of the two shallow holes in the vertical direction are connected, with the rock crushing zone of each hole measuring approximately three times the crushed range. After 170 ms, the damage range of each hole continues to expand, with the damage areas \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Density/kg/m3** & **Initial Internal Energy/MPa** & **C4** & **C5** & **V0** \\ \hline
1.29 & 0.25 & 0.4 & 0.4 & 1.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Main parameter values of air model. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Density/kg/m3**} & **Explosion** & **Explosion** & **A/GPa** & **B/GPa** & **R1** & **R2** & **\(\mathbf{\omega}\)** & **E0/GPa** \\  & **Velocity/m/s** & **Pressure/GPa** & **A/GPa** & **B/GPa** & **R1** & **R2** & **\(\mathbf{\omega}\)** & **E0/GPa** \\ \hline
1500 & 7000 & 22 & 625 & 23.3 & 5.2 & 1.6 & 0.25 & 8.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Main parameter values of explosive model. of the five holes being preliminarily connected. At 200 ms, rock damage occurs near the empty hole wall of the deep hole without charge due to the stress concentration effect. At 240 ms, the shallow hole blasting funnel is basically formed.