## 4 Simulation Results and Analysis
### Influence of Scale  
According to the situations shown in Table 2, numerical simulations were conducted to investigate the effects of different scales of goals. The horizontal and vertical displacements of the surrounding rock at the 20 m section under different scales of goals are illustrated  
Figure 5: Displacement of tunnel hance and vault under different distances of goals. Figure 6: Surrounding rock stress of tunnel under different distances of goals. Figure 7: The maximum axial force of initial support of tunnel under different distances of goals (Units: m). in Figures 8-10, respectively. In Figures 8-10, it can be observed that as the scale of the goaf increases, both the horizontal and vertical displacements of the surrounding rock increase. When the diameter is 5 m, 7.5 m, 10 m, and 12.5 m, respectively, the horizontal displacements of the left hande of the surrounding rock are 8.32 mm, 8.84 mm, 9.52 mm, and 10.62 mm, while the vertical displacements of the vault are 10.65 mm, 11.26 mm, 11.97 mm, and 13.37 mm. Compared to a goaf diameter of 5 m, the shoulder displacements increased by 5.8%, 14.4%, and 27.6%, respectively, and the crown displacements increased by 5.7%, 12.4%, and 20.3%. As the scale of the goaf increases, both the horizontal and vertical displacements of the surrounding rock continuously increase, leading to a decrease in the stability of the surrounding rock. When the diameter of the goaf cavity increases from 10 m to 12.5 m, the changes in horizontal displacement at the hance and vertical displacement at the vault of the surrounding rock become most pronounced. Consequently, the collapse deformation of the tunnel vault increases with the increasing scale of the goaf, and larger goal scales also result in a larger collapse zone. Figure 11 shows the surrounding rock stress of the tunnel under different scales of gosf. It shows that the horizontal stress in the left abutment of the surrounding rock is 2.01 MPa, 2.13 MPa, 2.25 MPa, and 2.36 MPa, respectively, when the diameter is 5 m, 7.5 m, 10 m, and 12.5 m. The vertical stress at the left abutment of the surrounding rock is 1.59 MPa, 1.65 MPa, 1.79 MPa, and 1.88 MPa, respectively. Compared to a diameter of 5 m, the horizontal stress at the left abutment decreased by 5.9%, 11.9%, and 17.4%, while the vertical stress at the crown decreased by 3.8%, 12.5%, and 18.2%, respectively. As the scale increases, the horizontal stress at the tunnel shoulders increases continuously, with the concentration of vertical stress at the tunnel foot becoming more pronounced. Larger goats result in more severe settlement of the lower tunnel structure, with settlement increasing uniformly with the scale of the goaf, thereby enlarging the area of settlement under the tunnel. Figure 12 shows the maximum axial force of the initial support of the tunnel under different scales of goats. In Figure 12, it is evident that the initial support forces at the crown and foot of the initial support are relatively minor, with some anchor rods even experiencing negative axial forces, indicating compression. However, the initial support axial forces at the crown of the goaf are mostly positive, effectively controlling the convergence of the crown and allowing the support system to perform optimally. With the increase in the goaf scale, the maximum initial support axial force shows an increasing trend. For goaf diameters of 5 m, 7.5 m, 10 m, and 12.5 m, the maximum initial support axial forces are 4123 kN, 4256 kN, 4432 kN, and 4659 kN, respectively. As the goaf scale increases, the initial support axial forces notably increase, leading to a greater degree of depression and collapse range. In particular, the initial support axial force reaches its maximum at the front end of the tunnel, necessitating reinforced support measures to prevent collapse at the tunnel entrance. Figure 8: _Cont._  
Figure 8: Horizontal displacement of surrounding rock of tunnel under different scales of goals (Units: m).