## 3 Results and Analysis
### Model Analysis
Additionally, it can be observed that continuous increases in Young's modulus and Grout-stiffness of the bolts effectively reduce energy dissipation in the surrounding rock. Similarly, increasing the cross-sectional area of the bolt initially  
Figure 7: Energy analysis of parameters design schemes of shotcrete layer. **(a)** Isotropic; **(b)** Poisson’ ratio; **(c)** Thickness. reduces energy dissipation. However, when the cross-sectional area exceeds a threshold value of 0.006079 m\({}^{2}\), the dissipation energy begins to rise instead of further decreasing. This suggests that there is an optimal range for the bolt cross-sectional area in minimizing energy dissipation, beyond which the effect may become counterproductive. The plastic dissipation energy (PDE) distribution for the shotcrete layer parameter design scheme is illustrated in Figure 9. The diagram indicates that the dissipation energy is primarily concentrated near the sidewalls and floor of the roadway. The depth of energy dissipation at the sidewalls extends to approximately 2 m, while at the floor, the dissipation depth reaches nearly twice this value, reflecting a pronounced disparity in energy distribution between these zones. In cases where the shotcrete layer is characterized by low isotropy and minimal thickness, the dissipation energy tends to propagate towards the roof of the roadway. The maximum dissipation energy is observed at the junction between the sidewall and floor, which emerges as the primary zone of energy concentration. As the isotropy and thickness of the shotcrete layer increase, the distribution range of dissipation energy gradually diminishes, indicating an enhancement in the structural ability to contain energy dissipation. Conversely, Poisson's ratio exhibits minimal influence on the spatial distribution range of dissipation energy. Figure 8: \(Cont.\)  
The parameter design scheme for the shotcrete layer and the corresponding elastic strain energy (ESE) distribution cloud diagram are presented in Figure 10. The diagram illustrates that the elastic strain energy is predominantly concentrated within a vertical band extending approximately 1 m from the tunnel section in all directions. As the support parameters increase, the distribution of elastic strain energy exhibits a tendency to shift toward the inner wall of the tunnel. Notably, when the isotropic parameter reaches 100 GPa, a significant change is observed in the distribution pattern of elastic strain energy, suggesting an enhanced capacity of the support structure to constrain energy accumulation. In contrast, variations in Poisson's ratio appear to have a negligible effect on the spatial distribution of elastic strain energy. Analysis of the results reveals that the isotropic properties and thickness of the concrete layer have a significant influence on both elastic strain energy (ESE) and plastic dissipated energy (PDE), whereas the energy distribution shows minimal sensitivity to variations in Poisson's ratio. In contrast, the distribution of energy is notably affected by parameters such as Young's modulus, cross-sectional area, and grout stiffness of the anchor rod. Furthermore, the distribution patterns observed in the cloud maps appear to be correlated with the maximum energy values. Changes in the maximum energy values are accompanied by corresponding alterations in the energy distribution. Notably, the cloud map distribution patterns under different anchor rod parameter design schemes exhibit a high degree of consistency with those observed for different shotcrete layer parameter design schemes. Therefore, detailed descriptions of these similarities are omitted for brevity. Figure 8: Energy analysis of rock bolt parameter design schemes. (**a**) Young; (**b**) Yield-tension; (**c**) Grout-cohesion; (**d**) Grout-stiffness; (**e**) Grout-friction; (**f**) Grout-perimeter; (**g**) Cross-sectional-area; (**h**) Pre-tension force.