## 2 Materials and Methods
### Numerical Simulation
#### 2.2.2 Numerical Model, Boundary Conditions, and Material Properties  
Based on the basic situation of the selected research scope of the tunnel, the numerical calculation model was established using FLAC3D 5.0 finite difference software. According to the Saint-Venant principle, to reduce the boundary effect of the model, the distance between the model's boundary and the excavation boundary should be 3 to 5 times the tunnel span. Therefore, in this study, the distance between the left and right boundaries of the model and the tunnel side boundary is 4 times the tunnel span. The distance between the lower boundary and the bottom surface of the tunnel is 4 times the tunnel span. The upper boundary is taken to the surface, and the front and rear boundaries are 3.5 times the tunnel span. The left and right sides of the model's boundary are subjected to horizontal constraints, the bottom is subjected to vertical constraints, and the top is the free surface. Figure 3 shows the numerical calculation model. The LDP curve is the deformation curve  
Figure 1: Schematic diagram of the convergence-constraint method.  
of the tunnel in the open hole state, so the numerical simulation does not set the support and only follows the excavation sequence of the construction method, the footage of tunnel excavation is 1m. The rock mass adopts the Mohr-Coulomb yield criterion, the vertical stress is simulated by the self-weight stress field, and the lateral stress coefficient is set to 0.5.  
The water content greatly affects the mechanical properties of the surrounding rock of the Xigeda stratum. Based on the engineering site survey data and the current research results [30], the physical and mechanical parameters of the surrounding rock of the Xigeda stratum under different water content conditions are determined, as shown in Table 1.  
Considering the complexity of the engineering site and the limitations of numerical simulation, the numerical simulation is simplified as follows:  
1. The surrounding rock in the model is a continuous and homogeneous ideal body, and the surrounding rock adopts the Mohr-Coulomb model constitutive relation.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Water Content\%** & **Density/g.cm\({}^{-3}\)** & **Elastic Modulus/MPa** & **Poisson Ratio** & **Cohesion/kPa** & **Friction Angle/\({}^{c}\)** \\ \hline
0 & 1.95 & 193.89 & 0.4 & 343.4 & 44.5 \\
5 & 1.95 & 189.54 & 0.4 & 322.8 & 40.7 \\
10 & 1.95 & 184.80 & 0.4 & 302.1 & 36.8 \\
15 & 1.95 & 180.06 & 0.4 & 281.4 & 33.0 \\
20 & 1.95 & 175.35 & 0.4 & 260.7 & 29.1 \\
25 & 1.95 & 121.65 & 0.4 & 196.3 & 24.8 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Physical and mechanical parameters of surrounding rock under different water contents.  
Figure 3: Schematic diagram of tunnel model.  
Figure 2: Exposure of excavation face. (**a**) Overall condition of the excavation surface; (**b**) local conditions of the excavation surface.  
2. The initial in situ rock and soil mass stress only considers the gravity stress and does not consider the effect of tectonic stress and groundwater seepage.
3. Assuming the surface of the study area is horizontal.