## 3 Results and Discussion
### Inner Walls
#### 3.1.2 Liner  
As shown in Figure 8, the maximum resultant displacements (\(D_{\rm R}\)) and velocities (\(V_{\rm R}\)) values at four monitoring points (0\({}^{\circ}\), 90\({}^{\circ}\), 180\({}^{\circ}\), and 270\({}^{\circ}\)) of the Tunnel 2 liner vary significantly across the A1-A5 conditions. \(D_{\rm R}\) and \(V_{\rm R}\) are calculated by Equations (11) and (12).  
\[D_{R}=\sqrt{D_{h}^{2}+D_{\rm v}^{2}} \tag{11}\]  
\[V_{R}=\sqrt{V_{h}^{2}+V_{\rm v}^{2}} \tag{12}\]  
where \(D_{\rm H}\) is the maximum horizontal displacement; \(D_{\rm V}\) is the maximum vertical displacement; \(V_{\rm H}\) is the maximum horizontal velocity; and \(V_{\rm V}\) is the maximum vertical velocity.  
As shown in Figure 8a, the maximum \(D_{\rm R}\) values at the 0\({}^{\circ}\), 90\({}^{\circ}\), 180\({}^{\circ}\), and 270\({}^{\circ}\) monitoring points of the Tunnel 2 liner vary significantly under A1-A5 conditions. \(D_{\rm R}\) magnitudes follow the order 180\({}^{\circ}\) \(>\) 90\({}^{\circ}\) \(>\) 270\({}^{\circ}\) \(>\) 0\({}^{\circ}\) across all conditions, reflecting distinct vibration impacts at each angle. The largest \(D_{\rm R}\) consistently occurs at 180\({}^{\circ}\) (closest to T1), while the smallest \(D_{\rm R}\) is observed at 0\({}^{\circ}\) (farthest from T1). \(D_{\rm R}\) attenuates progressively from the vibration source (180\({}^{\circ}\)) toward the opposite side (0\({}^{\circ}\)), demonstrating a clear distance-dependent decay pattern. Notably, \(D_{\rm R}\) at 270\({}^{\circ}\) is slightly smaller than at 90\({}^{\circ}\), indicating that deeper burial depth enhances structural restraint from the surroundings, thereby improving the liner's resistance to disturbances and reducing displacements. This highlights two key factors influencing \(D_{\rm R}\): (1) proximity to the vibration source and (2) burial depth, with deeper sections benefiting from stronger soil support to mitigate displacement.  
Figure 8: Comparison of maximum \(D_{\rm R}\) and \(V_{\rm R}\) at four monitoring points of Tunnel 2 liners under A1–A5 conditions: (**a**) \(D_{\rm R}\); (**b**) \(V_{\rm R}\).  
The maximum \(V_{\rm R}\) values of the Tunnel 2 liner are shown in Figure 8b. Under conditions with internal walls, the \(V_{\rm R}\) trends align with the \(D_{\rm R}\) patterns in Figure 8a, following the order \(180^{\circ}>90^{\circ}>270^{\circ}>0^{\circ}\), further confirming that \(V_{\rm R}\) increases with proximity to the vibration source (T1). However, under the NW condition, the \(V_{\rm R}\) ranking shifts to \(180^{\circ}>270^{\circ}>0^{\circ}>90^{\circ}\). This anomaly likely stems from the reduced structural stability of the liner without internal walls, making it more susceptible to vibrations from T1 and resulting in markedly different velocity patterns compared to wall-equipped conditions.  
Under train-induced vibrations, both \(D_{\rm R}\) and \(V_{\rm R}\) at the four monitoring points of Tunnel 2 liner correlate strongly with distance from the vibration source and burial depth. The NW condition exhibits distinct \(D_{\rm R}\) and \(V_{\rm R}\) patterns (e.g., reversed ranking at \(270^{\circ}\) and \(0^{\circ}\)) and significantly higher magnitudes compared to other conditions, emphasizing the critical role of internal walls in stabilizing dynamic responses.