## 2 Project Profile
### Material Parameter Selection and Scheme Setting  
The model first determines the excavation face dimensions based on the tunnel size at the construction site. In Midas GTX NS, a model with dimensions of 120 m, 60 m, and 100 m in the x, y, and z directions, respectively, is created and meshed. The model is then imported into FLAC\({}^{\text{3D}}\) (Version 6.0) software, where the rock mass parameters are assigned using command scripts. The rock mass uses the Mohr-Coulomb criterion, with the following parameters: Young's modulus \(E=2\) GPa, Poisson's ratio \(\mu=0.3\), bulk modulus = 1.67 GPa, shear modulus = 0.77 GPa, friction = 30\({}^{\circ}\), cohesion = 0.2 MPa, and density = 2250 kg/m\({}^{3}\). Considering the actual excavation conditions of the Huaying  
Figure 2: Position relationship between tunnel and goaf. Mountain High-Speed Rail Tunnel, the tunnel excavation employs full-face excavation using cyclic mechanical methods. The advance per cycle is 2 m, and the total length of tunnel excavation is 40 m. The FISH language is used to set up excavation command scripts. During tunnel excavation, void commands are used to remove elements to simulate the excavation of rock. Immediately after excavation, the initial support measures are implemented. The initial support thickness is 23 cm. The initial support is made of concrete material, simulated using shell elements. The shell elements are set as isotropic, with a Young's modulus \(E\) = 25 GPa, Poisson's ratio = 0.22, density = 2500 kg/m\({}^{3}\). Based on geological survey data and on-site material, the numerical model parameters of the Huaying Mountain High-Speed Rail Tunnel are shown in Table 1. To conduct accurate numerical simulation studies, the goaf in Huaying Mountain was simplified into a cylindrical shape, neglecting the influence of roof collapse in the goaf on the tunnel floor. The center cross-section of the goaf is located 20 m from the entrance of the excavation section, with a longitudinal length of 80 m and a circular cavity with a diameter of \(D\). The goaf is inclined horizontally to the tunnel at an angle \(\theta\), with a distance \(H\) between the goaf and the tunnel. The interior of the goaf cavity is unfilled. The spatial relationship between the goaf and the tunnel is depicted in Figure 2.  
To analyze the impact patterns of different distances, scales, and angles of the goaf relative to the tunnel on the stability of surrounding rock, simulation scenarios were designed, as outlined in Table 2. Situation I maintains a constant scale and angle of the goaf, examining different distances (\(H\) values of 5 m, 10 m, 15 m, and 20 m), evaluating the displacement, stress, and initial support axial forces of the surrounding rock. Situation II maintains constant distance and angle, investigating different scales of the goaf (\(D\) values of 5 m, 7.5 m, 10 m, and 12.5 m), analyzing the displacement, stress, and initial support axial forces of the surrounding rock. Situation III maintains constant distance and scale of the goaf, exploring different angles (\(\theta\) values of 15\({}^{\circ}\), 30\({}^{\circ}\), 45\({}^{\circ}\), and 60\({}^{\circ}\)), examining the displacement, stress, and initial support axial forces of the surrounding rock. The numerical modeling analysis focuses on the excavation section at 20 m, as depicted in Figure 2. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Name** & \(\rho\)**/(kg.m\({}^{-3}\))** & \(E\)**/GPa** & \(\mu\) & \(c\)**/MPa** & \(\varphi\)**/(\({}^{\circ}\)) & \(K\) \\ \hline IV Surrounding Rock & 2250 & 2 & 0.3 & 0.2 & 30 & 0.5 \\ Initial Support & 2500 & 25 & 0.22 & - & - & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mechanical parameters of surrounding rock and initial support.