## 4 Simulation Results and Analysis
### Influence of Angle  
In Figures 13-15, it is observed that the horizontal displacement of the surrounding rock decreases while the vertical displacement increases with different angles. When the  
Figure 11: Surrounding rock stress of tunnel under different scales of goals. Figure 12: The maximum axial force of initial support of tunnel under different scales of goals (Units: m). Figure 10: Displacement of tunnel hence and vault under different scales of goals. angles are 15\({}^{\circ}\), 30\({}^{\circ}\), 45\({}^{\circ}\), and 60\({}^{\circ}\), respectively, the horizontal displacements of the left arch foot of the surrounding rock are 9.15 mm, 9.52 mm, 9.89 mm, and 11.2 mm, and the vertical displacements of the vault are 12.62 mm, 11.96 mm, 10.59 mm, and 9.56 mm. Compared to 15\({}^{\circ}\), the horizontal displacements of the left arch foot increased by 4.1%, 8.1%, and 18.3%, respectively, while the displacements of the vault decreased by 5.2%, 16.1%, and 24.2%. As the angle increases, the horizontal displacement of the surrounding rock gradually increases, while the vertical displacement decreases. Due to the tendency of the surrounding rock around the tunnel to displace toward the goal, the proportion of vertical displacement in the total displacement gradually increases. Consequently, the overall displacement shifts toward being predominantly vertical with the increasing angle of the goat, resulting in a gradual reduction in vertical displacement. This phenomenon is similar to the research results of [PERSON] [41]. The smaller the dip angle, the greater the vault settlement. The larger the dip angle, the greater the horizontal convergence of the two sides of the tunnel. Figure 16 shows the surrounding rock stress of the tunnel under different angles of goafs. In Figure 16, it is evident that the horizontal stresses at the foot and crown of the tunnel arch are significantly influenced by the angle of the goat. As the angle increases, the horizontal stress at the foot increases continuously, while the vertical stress decreases. When the angle is 60\({}^{\circ}\), the horizontal stress at the right foot is 2.43 MPa. Compared to the angle of 15\({}^{\circ}\), the horizontal displacement at the right crown increases by 13.9%. At the angle of 60\({}^{\circ}\), the vertical stress at the shoulder is 1.97 MPa. Compared to the angle of 15\({}^{\circ}\), the vertical displacement at the crown decreases by 10.7%. Therefore, with the increasing angle, the stress concentration at the right crown becomes more pronounced, leading to increased depression, while the collapse deformation at the crown diminishes continuously. Figure 17 shows the maximum axial force of the initial support of the tunnel under different angles of goafs. In Figure 17, it can be observed that the magnitude of the initial support axial forces increases as the tunnel advances continuously toward the adjacent goat. At the arch section of the tunnel near the goat, the initial support bears significantly higher positive axial forces compared to locations further from the goat. This indicates that the initial support of the surrounding tunnel rock near the goat effectively provides excellent support, thereby controlling rock deformation and improving the stress conditions of the tunnel support structure. With the increasing angle, the maximum axial force of the initial support shows an increasing trend. For angles of 15\({}^{\circ}\), 30\({}^{\circ}\), 45\({}^{\circ}\), and 60\({}^{\circ}\), respectively, the maximum initial support axial forces are 4564 kN, 4432 kN, 4338 kN, and 4231 kN. As the angle increases, the structural bearing capacity of the initial support becomes stronger. Figure 13: _Cont._  
Figure 14: Vertical displacement of tunnel surrounding rock under different angles of go afs (Units: m). Figure 13: Horizontal displacement of surrounding rock of tunnel under different angles of goafs (Units: m). Figure 16: Surrounding rock stress of tunnel under different angles of goafs.