## 2 Numerical Simulation Method
### Model Parameter Assignment and Simulation Plan  
#### 2.3.1 Parameter Assignment for Numerical Model  
The L-CO\({}_{2}\) blasting device can generate different explosion pressures by controlling the filling amount and the rupture pressure of the pressure-shearing plate. This study selects three common explosion pressures on the market, 150 MPa, 210 MPa, and 270 MPa, for a process parameter optimization analysis. Based on surveys conducted by our research team with multiple manufacturers and suppliers of L-CO\({}_{2}\) blasting devices, these three explosion pressure levels are the most common on the market and can accommodate the majority of L-CO\({}_{2}\) blasting pipe models. Through extensive trial calculations, EOS state parameters that match the model dimensions are determined, as shown in Table 1, along with the material model parameters for L-CO\({}_{2}\) listed in Table 2.  
The parameters of the RHT constitutive model are complex and require the clarification of the 34 undetermined parameters in the model based on the elastic limit surface equation, failure surface equation, linear strengthening segment equation, and damage softening phase equation of the RHT model. Previous research indicates that the undetermined parameters mainly fall into four categories: fixed parameters, experimental test parameters, numerical calculation parameters, and parameters that cannot be directly determined [24]. This study references the RHT constitutive parameters obtained from the #2 coal seam of the Baijiao Coal Mine in Yibin, Sichuan Province, as shown in Table 3 [25]. The gas content of the coal seam in the Baijiao Coal Mine ranges from 12.10 to 18.86 m\({}^{3}\)/t, and the coal seam permeability coefficient is between 0 and 0.29 m\({}^{2}\)/(MPa\({}^{2}\)-d), classifying it as a low-permeability coal seam group. Therefore, applying L-CO\({}_{2}\) phase transition blasting for permeability enhancement in the #2 coal seam of this mine is of practical significance. Additionally, the detailed RHT constitutive parameters of this coal seam ensure the reliability of the research results.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline Characteristic parameters & C0 & C3/Bar & C6/Bar & \(E_{\mathrm{m}}\)/J & V \\ \hline Value & 0 & 0.2950 & 0.2950 & 2.60 \(\times\) 10\({}^{3}\) & 1.0 \\ \hline \multicolumn{5}{c}{Blast load = 210 MPa} \\ \hline Characteristic parameters & C0 & C3/Bar & C6/Bar & \(E_{\mathrm{m}}\)/J & V \\ Value & 0 & 0.2950 & 0.2950 & 4.80 \(\times\) 10\({}^{3}\) & 1.0 \\ \hline \multicolumn{5}{c}{Blast load = 270 MPa} \\ \hline Characteristic parameters & C0 & C3/Bar & C6/Bar & \(E_{\mathrm{m}}\)/J & V \\ Value & 0 & 0.2950 & 0.2950 & 3.70 \(\times\) 10\({}^{3}\) & 1.0 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameter value table for *EOS_LINEAR_POLYNOMIAL equation of state.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline Characteristic Parameters & \(\rho_{0}\)/(kg\(\cdot\)m\({}^{-3}\)) & \(d\)/(m\(\cdot\)s\({}^{-1}\)) & \(P_{\mathrm{G}}\)/MPa \\ \hline Value & 915 & 4000 & 270 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Parameter value table for *MAT_HIGH_EXPLOSIVE_BURN energetic material.