## 3 Methodology  
### Simulation of Explosive Detonation  
The model has dimensions of 4 m \(\times\) 2 m, with a blast hole (70 mm in diameter) positioned at its center. The blast hole features a coupled charge structure, with an explosive length of 1.0 m and a plugging length of 0.3 m. To minimize the influence of reflected stress waves on the simulation results, non-reflecting boundary conditions were applied to the lateral and bottom surfaces, while the top surface was treated as a free boundary. The front and rear surfaces were defined as symmetric boundaries. To analyze the blasting load along the blast hole wall during detonation, five measurement points (L\({}_{1}\)-L\({}_{5}\)) were spaced at 0.2 m intervals from the detonation point. Furthermore, the rock and fluid elements were spatially overlapped during modeling to ensure effective fluid-solid coupling. The model was finely discretized with a minimum mesh size of 5 mm \(\times\) 5 mm, resulting in 998,382 elements and 1,504,380 nodes. The two-dimensional plane strain configuration is shown in Figure 1.  
The relationship between the pressure, volume, and energy of the detonation products during the calculation process is modeled using the Jones-Wilkins-Lee (JWL) equation of state [32], as shown in Equation (1). \[P_{\text{d}}=A_{1}(1-\frac{\omega}{R_{1}V})e^{-R_{1}V}+B_{1}(1-\frac{\omega}{R _{2}V})e^{-R_{2}V}+\frac{\omega E_{0}}{V} \tag{1}\]  
where \(P_{\text{d}}\) represents the pressure of the detonation products and \(A_{1}\), \(B_{1}\), \(R_{1}\), and \(R_{2}\) are constants determined by the properties of the explosive. \(V\) is the relative volume of the detonation products, and \(E_{0}\) is the internal energy of the initial volume. The detailed parameters of the explosive are provided in Table 2. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Nunenoidal Simulation Methods** & **Software** & **Advances** & **Diameterations** & **Jose-Solar** \\ \hline \multirow{3}{*}{Finite element method} & LS-DYNA & These methods result in simulating strong waves, liquids, & & \\  & ANSYS & vibration, and damage resulting from explosions, & & \\  & SDC & Thesss are capable of simulating phenomena such as & & \\  & SDC & Thesss are capable of simulating phenomena such as & & \\  & TPC & non-segregation and exploits during blasting & & \\  & CDEM & Thesss methods effectively simulate the rock failure process & & \\  & CDEM & There methods effectively simulate the rock failure process & & \\  & CDEM & under the influence of explosive detonation. & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Advantages and disadvantages of common numerical simulation methods for rock blasting. Figure 1: Two-dimensional plane strain model. The RHT material model [33] is chosen as the constitutive model for rock. Compared to the HJC model, the RHT model is capable of describing the entire material behavior process, from elasticity to failure. It is widely used to simulate the dynamic response, damage, and fracture characteristics of concrete and rock under impact loads [34]. The failure equation is given by Equation (2):  
\[\left\{ \begin{array}{l}\sigma_{eq}^{*}(p,\theta,\varepsilon)=Y^{*}{}_{TXC}(p )R_{3}(\theta)F_{rate}(\varepsilon)\\ Y^{*}{}_{TXC}(p)=A(p^{*}-p_{spall}^{*}F_{rate}(\varepsilon))N\\ p_{spall}^{*}=p_{spall}/f_{\varepsilon}\end{array} \right. \tag{2}\]  
where \(\sigma^{*}\)eq represents the equivalent stress intensity on the failure surface; \(p\), \(\theta\), and \(\varepsilon\) denote pressure, Lode angle, and strain rate, respectively; \(R_{3}(\theta)\) is the angular even function on the deviatoric plane; \(F_{\text{rate}}(\varepsilon)\) is the strain rate strengthening factor; \(Y^{*}{}_{TXC}(p)\) is the equivalent stress intensity on the compression meridian; \(p^{*}\) is the normalized static pressure;\(f_{\text{c}}\) is the uniaxial compressive strength; \(p_{\text{spall}}\) is the spalling strength; and \(p^{*}_{\text{spall}}\) is the normalized spalling strength. \(A\) and \(N\) are material constants.