## 2 Tunnel Description and Geological Conditions
### Establishment of the DEM-Based Computational Model
#### 3.3.1 Change Rule of Displacement Field  
A scenario with a tunnel depth of 400 m, a fault dip angle of 50\({}^{\circ}\), and a water pressure of 2 MPa was selected for analysis. Figure 4 illustrates the process of tunnel face excavation crossing the water-rich fault fracture zone until the occurrence of water innyth damage, where the numbers in different colors indicate the displacements and h is the distance between the tunnel face and the fault. The displacement nephgrams in Figure 4 indicated the displacement conditions when the model was in equilibrium after each excavation, and the displacement nephgram after the 5 th excavation was the displacement condition when the face was obviously destabilized and damaged. Figure 4a-d confirmed that the maximum transverse extrusion displacements of the water-resistant rock mass at the face after the first, second, third, and fourth excavation steps were 0.84 mm, 3.45 mm, 5.63 mm, and 7.54 mm, respectively, which were increased by 2.61 mm, 2.18 mm, and 1.91 mm, respectively. This indicated that with the tunnel advancing towards the fault, the maximum transverse extrusion displacement of the water-resistant rock mass at the face increased \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Volumetric Weight** & **Bulk Modulus** & **Shear Modulus** & **Poisson’s** & **Cohesion \(c\)** & **Internal Friction** \\  & **\(\gamma\) (kN/m\({}^{3}\))** & **K (GPa)** & **G (GPa)** & **Ratio \(\
u\)** & **Angle \(\varphi\) (\({}^{\circ}\))** \\ \hline Rock mass & 2000 & 1.44 & 19.4 & 0.25 & 0.35 & 28.6 \\ Fault fracture zone & 1800 & 0.48 & 6.4 & 0.25 & 0.12 & 28.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mechanical parameters of the rock masses of the Xianglushan tunnel. Figure 3: Tunnel fault system and its simplified numerical calculation model: (**a**) Tunnel–Fault System; (**b**) Simplified numerical calculation model. continuously under the joint influence of excavation disturbance and fault water pressure. Meanwhile, after the excavation was completed, the displacement of the lower part of the face on the axial longitudinal section of the tunnel was significantly larger than that of the upper part, indicating that the fault dip angle had a significant influence on the tunnel excavation. Figure 4d-f demonstrated that when the 4 th excavation of the tunnel was advanced to x = 4 m, the water inrush damage did not occur yet. When the face was excavated to x = 5 m, the maximum transverse extrusion displacement reached 1.59 m. The water-resistant rock mass could not maintain stability, and its displacement changed abruptly. The fissures inside the rock mass were continuously generated and expanded to form a seepage channel. Finally, the water-resistant rock mass at the face collapsed and damaged under the joint action of excavation and fault water pressure, resulting in a water inrush disaster. Figure 4f revealed that there were obvious displacement changes in the blocks at the face, and it was expected that a large number of blocks would enter the tunnel if the calculation was continued. It was therefore concluded that under this scenario, the minimum safety thickness of the water-resistant rock mass at the face of the tunnel crossing the water-rich fault was about 5-6 m.  
When the tunnel was excavated towards the water-rich fault, three monitoring sections were arranged at 3 m (x = 7 m), 4 m (x = 6 m), and 5 m (x = 5 m) away from the fault in the water-resistant rock mass at the face, and eight monitoring points were set on  
Figure 4: Evolution process of displacement field (unit: m): (**a**) First excavation (\(h\) = 14 m); (**b**) Second excavation (\(h\) = 10 m); (**c**) Third excavation (\(h\) = 8 m); (**d**) Fourth excavation (\(h\) = 6 m); (**e**) Fifth excavation (\(h\) = 5 m); (**f**) Local failure at \(h\) = 5 m.  
each monitoring section.