## 3 Results and Discussion
### Inner Walls
#### 3.1.3 Surroundings  
The surroundings play a critical role in supporting tunnel structures to maintain stability under dynamic loads. Analyzing the dynamic characteristics of the surroundings provides essential insights to complement the dynamic behavior of Tunnel 2 liners. Figure 9 shows the \(D_{\rm R}\) and \(V_{\rm R}\) of Tunnel 2 surroundings under A\({}_{1}\)-A\({}_{5}\) conditions. Figure 9a compares the maximum \(D_{\rm R}\) values of the T2 surroundings. The \(D_{\rm R}\) magnitudes at four monitoring points follow the order \(180^{\circ}>90^{\circ}>270^{\circ}>0^{\circ}\), consistent with the trends observed in Figure 8a. This confirms that the \(D_{\rm R}\) of surroundings is similarly influenced by propagation distance from the vibration source and burial depth. Figures 8a and 9a reveal minimal differences in \(D_{\rm R}\) between Tunnel 2 liners and surroundings across A\({}_{1}\)-A\({}_{5}\) conditions. Notably, the \(D_{\rm R}\) values at four angles (\(0^{\circ}\), \(90^{\circ}\), \(180^{\circ}\), \(270^{\circ}\)) are identical for both liners and surroundings under W2 and NW conditions, indicating that the displacement patterns of tunnel structures and surroundings are closely aligned under metro train-induced vibrations, signifying a structurally safe state. Comparing T2 and NW conditions, the differences of \(D_{\rm R}\) in surroundings at \(180^{\circ}\) and \(0^{\circ}\) are 0.65 mm and 0.71 mm under the T2 condition are increased by 48.15% and 151.06% when compared to the NW condition. These results demonstrate that internal walls significantly reduce \(D_{\rm R}\) in surroundings, with effectiveness varying by proximity to the vibration source. Figure 9b compares the maximum \(V_{\rm R}\) values of the Tunnel 2 surroundings under A\({}_{1}\)-A\({}_{5}\) conditions. Similar to the \(D_{\rm R}\) trends in Figure 9a and the liner \(V_{\rm R}\) patterns in Figure 8b, the \(V_{\rm R}\) magnitudes under A\({}_{1}\)-A\({}_{5}\) conditions follow \(180^{\circ}>90^{\circ}>270^{\circ}>0^{\circ}\) which is consistence with the \(D_{\rm R}\) trends in Figure 9a and the liner \(V_{\rm R}\) patterns in Figure 8b, confirming that \(V_{\rm R}\) increases with proximity to the vibration source, consistent with findings from liner analysis. Under the NW condition, the \(V_{\rm R}\) ranking shifts to \(180^{\circ}>0^{\circ}>270^{\circ}>90^{\circ}\), deviating from the established patterns observed in wall-equipped conditions. This indicates that the vibration transmission law identified in Figure 8b does not apply to NW condition. Compared to the most stable condition T2, the \(V_{\rm R}\) differences in surroundings at \(180^{\circ}\) and \(0^{\circ}\) under NW condition are 11.79 mm/s and 15.03 mm/s, increased by 93.57% and 230.30% when compared to the value in the most stable condition T2. This indicates that the absence of internal walls (NW) leads to significantly amplified and complex dynamic responses in both liners and surroundings under dynamic loads, further proving the critical role of internal walls in stabilizing the surroundings. As shown in Figure 9a, b, the \(D_{\rm R}\) and \(V_{\rm R}\) patterns in the surroundings at four monitoring points align closely with those of the liners, governed by their position, proximity to the vibration source, and burial depth. Additionally, the T2 condition exhibits the highest stability, and the internal walls significantly reduce the \(D_{\rm R}\) and \(V_{\rm R}\) of the surroundings when comparing T2 and NW conditions. Notably, wall2 contributes most prominently to maintaining the stability of the surroundings. Figure 10 shows the coordination of the surroundings at various angles of Tunnel 2 under T2 and NW conditions. Coordination is defined as the average number of particles in contact with a central particle within a measurement circle, which can reflect structural stability. A higher coordination means greater stability.