## 4 Analysis of Response Model Results  
### Model Validity Testing  
As discussed above, this study selects the borehole enlargement radius \(R_{\text{well}}\), total area of the smash zone \(A_{\text{crush}}\), shape factor of the smash zone \(\zeta_{\text{crush}}\), total length of fractures \(L_{\text{frac}}\), and shape factor of the fracture zone \(\zeta_{\text{frac}}\) as response targets. These response targets are defined as \(F_{1}\), \(F_{2}\), \(F_{3}\), \(F_{4}\), and \(F_{5}\), respectively, to quantify the interactive effects of vertical in situ stress \(E_{1}\), stress difference \(E_{2}\), and explosive load \(E_{3}\) on the plastic deformation around the borehole, the smash zone, and the fracture zone. A statistical analysis of the three response variables and five response targets yields the results shown in Table 7.  
To systematically quantify the control mechanisms of the selected response indicators \(F_{1}\) to \(F_{5}\) under the influence of three response variables \(E_{1}\) to \(E_{3}\) and their interactions, \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**No.** & \(E_{1}\)**/MPa** & \(E_{2}\)**/MPa** & \(E_{3}\)**/MPa** & \(F_{1}\)**/mm** & \(F_{2}\) & \(F_{3}\)**/mm\({}^{2}\)** & \(F_{4}\) & \(F_{5}\)**/mm** \\ \hline
1 & 5 & 5 & 150 & \(1.17\times 10^{3}\) & 1.00 & 2.64 \(\times\) 10\({}^{3}\) & 1.02 & 12.47 \\
2 & 5 & 5 & 270 & \(8.55\times 10^{3}\) & 1.03 & 1.80 \(\times\) 10\({}^{3}\) & 1.04 & 11.63 \\
3 & 15 & 5 & 150 & \(1.09\times 10^{3}\) & 1.57 & 2.29 \(\times\) 10\({}^{3}\) & 1.16 & 12.09 \\
4 & 15 & 5 & 270 & \(4.44\times 10^{3}\) & 1.10 & 1.17 \(\times\) 10\({}^{3}\) & 1.10 & 11.28 \\
5 & 10 & 0 & 150 & \(1.08\times 10^{3}\) & 1.06 & 1.82 \(\times\) 10\({}^{3}\) & 1.09 & 10.68 \\
6 & 10 & 0 & 270 & \(8.19\times 10^{3}\) & 1.21 & \(1.38\times 10^{3}\) & 1.09 & 9.81 \\
7 & 10 & 10 & 150 & \(1.71\times 10^{3}\) & 1.15 & \(2.65\times 10^{3}\) & 1.28 & 13.40 \\
8 & 10 & 10 & 270 & \(7.24\times 10^{3}\) & 1.42 & \(1.89\times 10^{3}\) & 1.01 & 12.71 \\
9 & 5 & 0 & 210 & \(1.40\times 10^{3}\) & 1.00 & \(1.70\times 10^{3}\) & 1.00 & 10.37 \\
10 & 15 & 0 & 210 & \(5.94\times 10^{3}\) & 1.72 & \(1.29\times 10^{3}\) & 1.14 & 9.81 \\
11 & 5 & 10 & 210 & \(1.73\times 10^{3}\) & 1.00 & \(2.87\times 10^{3}\) & 1.01 & 13.57 \\
12 & 15 & 10 & 210 & \(1.10\times 10^{3}\) & 1.33 & \(2.38\times 10^{3}\) & 1.06 & 12.86 \\
13 & 10 & 5 & 210 & \(9.63\times 10^{3}\) & 1.20 & \(1.81\times 10^{3}\) & 1.05 & 11.84 \\
14 & 10 & 5 & 210 & \(9.66\times 10^{3}\) & 1.20 & \(1.82\times 10^{3}\) & 1.04 & 11.73 \\
15 & 10 & 5 & 210 & \(9.61\times 10^{3}\) & 1.20 & \(1.80\times 10^{3}\) & 1.07 & 11.96 \\ \hline \end{tabular}
\end{table} 
Table 7: Response factors and response variables under different simulation conditions. Figure 8: v-m stress–time curves at different test points. multiple regression fitting was performed for each response indicator, with the regression models summarized in Table 8.  
Significance testing and a correlation analysis are primary methods for assessing the reliability of regression models. According to the ANOVA table shown in Table 9, the regression equations for response indicators \(F_{1}\), \(F_{2}\), and \(F_{4}\) have \(p\)-values less than 0.05, with \(F_{1}\) and \(F_{2}\) having \(p\)-values below 0.0001, indicating highly significant regression results. Analyzing the F-values reveals that the L-CO\({}_{2}\) phase transition explosive load has the greatest impact on the borehole diameter and the area of the smash zone, followed by in situ stress, while the influence of stress difference on both the borehole diameter and smash zone area is minimal. The regression model for borehole diameter has an \(F\)-value of 686.92, significantly higher than the \(F\)-values for in situ stress and stress difference, confirming that the plastic deformation in the near-borehole region is primarily controlled by explosive load.