## 4 Analysis of Response Model Results
### Univariate Analysis  
Based on the results of the ANOVA and error analysis, the impact relationships of response variables \(E_{1}\) to \(E_{3}\) on response targets \(F_{1}\) to \(F_{5}\) were determined, along with the significance of the models. The data indicate that the regression results for \(F_{3}\) and \(F_{5}\) are not significant. Therefore, we first analyze the univariate effects of \(E_{1}\) to \(E_{3}\) on \(F_{1}\), \(F_{2}\), and \(F_{4}\). To intuitively present the influence trend of a single factor on the response variables, the other two response variables were set to their middle values, with vertical in situ stress at 10 MPa, stress difference at 5 MPa, and explosive load at 210 MPa. As shown in Figure 9a,b, the borehole radius and smash zone area show a consistent response to the three response variables, decreasing linearly with increasing vertical in situ stress and stress difference, while increasing linearly with increasing explosive load. Notably, the borehole radius is influenced far less by in situ stress compared to explosive load, indicating that the primary controlling factor for plastic deformation around the borehole is the explosive load. The smash zone area is mainly controlled by the same factors, as the radial compressive stress in the near-borehole region increases with distance from the borehole center, while the change in circumferential compressive stress is relatively minor. During the propagation of explosive load within the coal body, attenuation occurs, with the most rapid decay happening in the near-borehole area. Both factors act together in this region, resulting in the formation of a compressive-shear smash zone.  
From Figure 9c, it can be observed that greater in situ stress correlates with a smaller total fracture length, showing an approximately negative exponential relationship, indicating that increased in situ stress significantly suppresses the propagation of explosive fractures. As stress difference increases, the total fracture length continues to decrease, though the influence is the smallest among the three response variables. Conversely, with increasing explosive load, the total fracture length significantly increases, although its impact is lower than that of in situ stress on total fracture length. These results demonstrate that the formation of explosive fractures is mainly controlled by in situ stress. This is due to the significant attenuation of shock waves in the far field, while the stress field generated by in situ stress within the coal body remains relatively stable. When the shock wave attenuates to a certain degree, in situ stress becomes dominant in the propagation of explosive fractures. Figure 9d indicates that the shape factor of the fracture zone is primarily controlled by stress difference, while the influences of in situ stress and explosive load are negligible. As the stress difference increases from 0 to 10 MPa, the shape of the fracture zone changes from circular to elliptical, with the ratio of the ellipse's long to short axes increasing alongside the stress difference.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Statistical Items** & \(F_{1}\) & \(F_{2}\) & \(F_{3}\) & \(F_{4}\) & \(F_{5}\) \\ \hline \(R^{2}\) & 0.986 & 0.907 & 0.688 & 0.966 & 0.550 \\ \(R^{2}_{A}\) & 0.982 & 0.881 & 0.454 & 0.905 & 0.428 \\ \(R^{2}_{P}\) & 0.972 & 0.818 & 0.552 & 0.858 & 0.037 \\ \(C_{V}/\%\) & 45.634 & 18.600 & 5.612 & 14.994 & 5.296 \\ \(P_{A}\) & 1.365 & 8.985 & 4.949 & 15.407 & 13.461 \\ \hline \hline \end{tabular}
\end{table}
Table 10: Error analysis.