## 3 Simulation of BBT
### Numerical Simulation Results  
Under the condition of single-hole ordinary blasting, the effective stress propagation process in the rock is shown in Figure 6. At t = 4.48 \(\times\) 10\({}^{-6}\) s, the stress wave is transmitted to the rock at the blasthole wall. At this time, the pressure is greater than the compressive strength of the rock, and the rock at the blasthole wall is initially damaged. When t = 4.5 \(\times\) 10\({}^{-6}\) s\(\sim\)10.48 \(\times\) 10\({}^{-6}\) s, under the action of the explosive stress wave, the damage range of the rock is increasing, and the maximum effective stress also increases. At t = 24.99 \(\times\) 10\({}^{-6}\) s, the rock at the blasthole was completely crushed, the stress wave gradually expanded outward, and the rock damage range continued to increase. The effective stress at the edge of the \"circle\" of the stress wave far exceeds the compressive strength of the rock. Therefore, it can be determined that the rock in the \"circle\" is damaged, and an explosion cavity is formed. When t = 24.99 \(\times\) 10\({}^{-6}\) s\(\sim\)34.45 \(\times\) 10\({}^{-6}\) s, the size of the \"circle\" increases continuously, and the explosion stress wave spreads out uniformly in a circular shape. At t = 34.45 \(\times\) 10\({}^{-6}\) s, the shock wave attenuates, and the impact on the rock is reduced. It can be seen that in ordinary blasting, the explosion stress wave always spreads outwards uniformly, and the effective stress at the same position from the center of the blast hole is basically the same. Under the condition of energy-gathering blasting, the effective stress distribution of the surrounding rock is shown in Figure 7. After the explosive is detonated, the effect force is developed first, and the blasthole wall is initially damaged in the energy-gathering direction. Between t = 4.49 \(\times\) 10\({}^{-6}\) s and t = 11.46 \(\times\) 10\({}^{-6}\) s, the stress wave gradually propagates outward, and the effective stress range increases in the direction of gathering energy. Under the action of the explosive stress wave, the rock is damaged under pressure. Under the action of the explosive stress wave, the rock is destroyed under pressure in the energy-gathering direction. A t = 17.98 \(\times\) 10\({}^{-6}\) s, the stress wave continues to expand outward in a \"circular arc\" shape. Under the action of the explosive stress wave, the rock within the \"circular arc\" reaches a yielding state. At this time, the effective stress attenuates in the rock. The form of failure changes from compression to tensile failure. After t = 21.97 \(\times\) 10\({}^{-6}\) s, the stress concentration range of the blasthole wall increased, and the rock broke along the energy-gathering direction. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameter** & \(RO\)**/(g\(\cdot\)cm\({}^{-3}\))** & \(A\) & \(B\) & \(N\) & \(C\) \\ \hline Value & 2.7 & 0.79 & 1.6 & 0.61 & 0.007 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Rock parameters. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Parameter** & \(C_{0}\) & \(C_{1}\) & \(C_{2}\) & \(C_{3}\) & \(C_{4}\) & \(C_{5}\) & \(C_{6}\) & \(E_{0}\) \\ \hline Value & 0 & 0 & 0 & 0 & 0.4 & 0.4 & 0 & \(2.5\times 10^{-6}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Air parameters. As shown in Figure 8a, in the ordinary blasting, measuring points 1, 2, 3, and 4 are arranged in the horizontal direction 1, 3, 5, and 10 cm from the center of the blashhole wall. In addition, 5, 6, 7, and 8 measuring points are arranged at the same distance in the vertical direction to monitor pressure changes at each point. Figure 6: Effective stress distribution of ordinary blasting. **(a)** The effective stress at t = 4.48 \(\times\) 10\({}^{-6}\) s; **(b)** the effective stress at t = 10.48 \(\times\) 10\({}^{-6}\) s; **(c)** the effective stress at t = 24.99 \(\times\) 10\({}^{-6}\) s; **(d)** the effective stress at t = 34.45 \(\times\) 10\({}^{-6}\) s.  
Figure 7: Effective stress distribution of energy-gathering blasting.