## 2 Numerical Simulation Method
### Model Parameter Assignment and Simulation Plan
#### 2.3.2 Numerical Simulation Model and Plan  
Figure 3 presents the numerical model for simulating L-CO\({}_{2}\) phase transition blasting of coal. This model can apply confining pressures in the x and y directions and simulate \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter Category** & **Parameter** & **Parameter Value** & **Parameter** & **Parameter Value** \\ \hline \multirow{8}{*}{Fixed parameters} & Failure compression strain rate, \(\hat{\varepsilon}_{\mathrm{c}}/\mathrm{s}^{-1}\) & 3.0 \(\times\) 10\({}^{25}\) & Failure tensile strain rate, \(\hat{\varepsilon}_{\mathrm{t}}/\mathrm{s}^{-1}\) & 3.0 \(\times\) 10\({}^{25}\) \\ \cline{2-5}  & Reference compression strain rate, \(\hat{\varepsilon}_{0}^{c}/\mathrm{s}^{-1}\) & 3.0 \(\times\) 10\({}^{-5}\) & Failure tensile strain rate, \(\hat{\varepsilon}_{0}^{c}/\mathrm{s}^{-1}\) & 3.0 \(\times\) 10\({}^{-6}\) \\ \cline{2-5}  & Damage factor, D\({}_{2}\) & 1.0 & Factor related to the & 0.0105 \\ \cline{2-5}  & Tensile yield surface parameters, \(G_{t}^{*}\) & 0.7 & EOS polynomial parameter, T\({}_{2}\)/GPa & 0.0 \\ \hline \multirow{4}{*}{Experimental testing parameters} & UCS,\(f_{\mathrm{c}}\)/MPa & 21.1 & [PERSON]’s ratio, v & 0.27 \\ \cline{2-5}  & Elastic modulus, \(E\)/GPa & 8.38 & Longitudinal wave velocity, \(c_{0}/(\mathrm{m}\cdot\mathrm{s}^{-1})\) & 1525 \\ \cline{2-5}  & Density, \(\rho_{0}/(\mathrm{kg}\cdot\mathrm{m}^{-3})\) & 1397 & Initial porosity, \(\alpha_{0}\) & 11.8 \\ \hline \multirow{8}{*}{Calculation parameters} & Elastic shear modulus, G/GPa & \multirow{2}{*}{E/(2 (1 + v)), 3.30} & Pore collapse pressure, \(p_{\mathrm{cl}}\)/MPa & \multirow{2}{*}{\(2f_{\mathrm{c}}/3\), 14.1} \\ \cline{2-5}  & Compression strain rate index, \(\beta_{\mathrm{c}}\) & 4/(20 + 3\(f_{\mathrm{c}}\)), 48.02 \(\times\) 10\({}^{-3}\) & Tensile strain rate index, \(\beta_{\mathrm{t}}\) & 2/(20 + \(f_{\mathrm{c}}\)), 48.66 \(\times\) 10\({}^{-3}\) \\ \cline{2-5}  & Hugoniot polynomial parameter, A1/GPa & \multirow{2}{*}{2s \(-\) 1, 2} & Hugoniot polynomial parameter, A2/GPa & A1 (2s \(-\) 1), 0.464 \\ \cline{2-5}  & Hugoniot polynomial parameter, A3/GPa & \multirow{2}{*}{A1(3s\({}^{2}\) - 4s + 1), 0.011} & EOS polynomial parameter, T\({}_{1}\) & A1, 0.454 \\ \cline{2-5}  & EOS polynomial parameter, B\({}_{0}\) & 2s \(-\) 1, 2 & EOS polynomial parameter, B\({}_{1}\) & 2s \(-\) 1, 2 \\ \hline \multirow{8}{*}{Orthogonal experiment-determined parameters} & Residual surface parameters, A\({}_{\mathrm{f}}\) & 1.6 & Residual surface parameters, N\({}_{\mathrm{f}}\) & 0.61 \\ \cline{2-5}  & Relative shear strength, \(f_{s}^{*}\) & 0.18 & Relative tensile strength, \(f_{t}^{*}\) & 0.1 \\ \cline{2-5}  & Rhode angle correlation factor, Q\({}_{0}\) & 0.61 & Compression yield surface parameters, \(G_{c}^{*}\) & 0.35 \\ \cline{2-5}  & Shear modulus reduction factor, XI & 0.45 & Damage factor, \(D_{1}\) & 0.035 \\ \cline{2-5}  & Minimum-damage residual strain, \(\hat{\varepsilon}_{p}^{m}\) & 0.005 & Residual surface parameters, A\({}_{\mathrm{f}}\) & 1.25 \\ \cline{2-5}  & Residual surface parameters, N\({}_{\mathrm{f}}\) & 0.45 & Pore compaction pressure, \(P_{comp}/\mathrm{GPa}\) & 0.55 \\ \hline \multirow{2}{*}{Porosity index, \(n\)} & \multirow{2}{*}{2.0} & Related material parameter, \(s\) & 1.50 \\ \cline{2-5}  & & & & \\ \end{tabular}
\end{table} 
Table 3: RHT constitutive parameters for the #2 coal seam of the Baijiao Coal Mine in Yibin, Sichuan Province. the phase transition fracturing process of L-CO\({}_{2}\) within the borehole. Given that the axial length of the wellbore is much greater than its diameter, the model is simplified to a quasi-two-dimensional model aligned with the vertical axis of the wellbore. The model consists of a coal layer measuring 10,000 mm \(\times\) 10,000 mm \(\times\) 10 mm. A borehole with a diameter of \(\varphi\)100 mm is prefabricated at the center, referencing the actual drilling size of \(\varphi\)94 mm commonly used in coalbed methane drilling.