## 3 Methodology
### Simulation of Explosive Detonation
In the early stages of detonation, the explosive reaction is incomplete, resulting in a lower detonation velocity and, consequently, a reduced blasting load. As the reaction progresses, the detonation velocity increases, causing the blasting load to rise until the system stabilizes at a steady detonation state, where the blasting load reaches its maximum value. Furthermore, the theoretical peak value of the blasting load during detonation can be calculated using the formula below. Based on the Chapman-Jouguet (C-J) theory of detonation waves in condensed explosives [37], the peak blasting load, \(P_{\text{b}}\), is expressed as follows:  
The peak blasting load, \(P_{\text{b}}\), under the coupled charge condition, is  
Figure 3: Load curve of blast hole wall. Figure 2: Detonation process in a coupled charge. \[P_{\rm b}=\frac{\rho_{0}D^{2}}{2(\gamma+1)} \tag{4}\]  
The peak blasting load, \(P_{\rm b}\), under the uncoupled charge condition, is  
\[P_{\rm b}=\frac{\rho_{0}D^{2}}{2(\gamma+1)}\Big{(}\frac{a}{b}\Big{)}^{2\gamma} \tag{5}\]  
Here, \(\rho_{0}\) represents the density of the explosive; \(D\) is the detonation velocity of the explosive; \(\gamma\) is the isentropic adiabatic index. When the pressure in the hole exceeds the critical pressure of the explosive, \(\gamma=3\); when the pressure in the hole is below the critical pressure, \(\gamma=4/3\); \(a\) is the diameter of the charge; \(b\) is the diameter of the blast hole. According to previous studies [38], the blasting load increases when the detonation of the explosive transitions from the detonation products to the rock medium. In the case of one-dimensional explosive detonation flow, the detonation wave is initiated at the detonation position. Upon reaching the interface with the rock medium, reflection occurs due to differences in material wave impedance, resulting in a superposition effect. This phenomenon causes a sudden pressure increase, leading to a pressure multiplication effect [39]. In this numerical simulation, the peak load was determined to be 3.5 GPa. The incident pressure, calculated using the formula, was 3.168 GPa, yielding a pressure increase factor of 1.1. The detonation characteristics of explosives are influenced by their charge structure. For example, the blasting effect of explosives varies with different uncoupling coefficients and charging media [39]. Furthermore, variations in initiation positions and charge structures can optimize the blasting effect under different conditions. To further investigate the detonation characteristics of explosives, the detonation processes of explosives with various charge structures were examined. Figure 4 illustrates the detonation wave propagation process under two-point initiation. Similar to bottom initiation, the detonation wave is triggered at the initiation positions and propagates through the explosive material. Following detonation, the two detonation waves travel in opposite directions and collide at \(t=90\)\(\upmu\)s. At the moment of collision, an angle exists between the two detonation waves. After the collision, the detonation waves reflect off one another, and the angle between them transitions from inclined to horizontal due to their interaction [40]. Figure 5 illustrates the blasting load curve on the hole wall under two-position detonation. As shown in the figure, the blasting loads at measuring points L\({}_{1}\) and L\({}_{5}\) are identical, as are the loads at L\({}_{2}\) and L\({}_{4}\). Similar to the detonation process of bottom-initiated explosives, the blasting load starts relatively low at the initiation of detonation and gradu  
Figure 4: Two-point detonation initiation process. ally increases as the detonation reaction progresses. Upon collision of the two opposing detonation waves, the blasting load experiences a sudden, sharp increase. Compared to coupled charges, uncoupled charges can effectively reduce the peak load on the blast hole wall, enhance the utilization of explosive energy, and improve the overall blasting effect [39].