## 3 Results and Analysis
### Model Analysis  
Figure 7 illustrates the energy analysis results under different parameter design schemes for the shotcrete layer. As shown in Figure 6(a), with the exception of an isotropic modulus of 1 GPa, the maximum plastic dissipated energy (PDE) of the surrounding rock initially decreases and then increases as the isotropic modulus of the shotcrete layer increases, while the elastic strain energy (ESE) exhibits a gradual increase. When the isotropic modulus is 1 GPa, the structural stiffness of the shotcrete layer is insufficient to provide reliable support for the roadway. This inadequacy leads to damage and energy dissipation in the surrounding rock, resulting in increased stress concentration and significant energy accumulation. At an isotropic modulus of 100 GPa, the shotcrete layer exhibits high structural stiffness, which limits the deformation of the surrounding rock. As a result, elastic strain energy accumulates within the surrounding rock due to the inability to dissipate energy through displacement, reaching approximately 185 kJ. This accumulation, often accompanied by stress concentration, may lead to damage in the rock mass, with PDE values exceeding 22 kJ. In contrast, a moderate isotropic modulus (e.g., 25 GPa) effectively facilitates the release of accumulated ESE in the surrounding rock, thereby reducing the extent of \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Variable**} & \multirow{2}{*}{**Young’s**} & \multirow{2}{*}{**Yo**ung’s**} & \multirow{2}{*}{**Yield-**} & \multirow{2}{*}{**Grout-**} & \multirow{2}{*}{**Grout-**} & \multirow{2}{*}{**Grout-**} & \multirow{2}{*}{**Friction**} & \multirow{2}{*}{**Ferimeter**} & \multirow{2}{*}{**Cros-**} & \multirow{2}{*}{**Pre-**} \\  & & & & & & & & & & \\ \hline Young & 0 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ Yield-tension & 1 & 0 & 1 & 1 & 1 & 1 & 1 & 1 \\ Grout-cohesion & 1 & 1 & 0 & 1 & 1 & 1 & 1 & 1 \\ Grout-stiffness & 1 & 1 & 1 & 0 & 1 & 1 & 1 & 0.001 \\ Grout-friction & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 \\ Grout-perimeter & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 1 \\ Cross-sectional-area & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 1 \\ Pre-tensioning Force & 1 & 1 & 1 & 0.001 & 1 & 1 & 1 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Kendall correlation \(p\)-value table (B). Figure 6: Kendall correlation coefficient. damage and achieving significant displacement control. As depicted in Figure 7b, Poisson's ratio has a comparatively weaker influence on the energy evolution characteristics (EEC) of the surrounding rock than isotropic modulus and thickness. The PDE increases with higher Poisson's ratio, whereas ESE decreases correspondingly. Figure 7c illustrates that the thickness of the shotcrete layer also affects the energy dynamics. Specifically, as thickness increases, PDE initially decreases, then increases, while ESE follows a trend of increasing, subsequently decreasing, and eventually stabilizing. At a thickness of 0.01 m, the shotcrete layer's structural stiffness is notably insufficient, failing to provide stable roadway support. Under such conditions, the surrounding rock is prone to destructive deformation and energy dissipation, further exacerbating stress concentration and significantly increasing the accumulated energy. The energy analysis results under different bolt parameter design schemes are presented in Figure 8. Compared to the shotcrete layer, the influence of bolt parameters on the plastic dissipated energy (PDE) of the surrounding rock is relatively minor. Most bolt parameters exhibit a slight increasing trend in PDE as their values increase, but the overall variation remains insignificant. For elastic strain energy (ESE), the Yield-tension and Pre-tension force parameters of the bolt have minimal impact. However, as the Grout-cohesion, Grout-friction, and Grout-perimeter parameters increase, ESE shows a slight decrease before stabilizing.