## 3 Results and Discussion
### Inner Walls
#### 3.1.1 Sleeper  
The horizontal displacement and velocity patterns of adjacent tunnel structures and surroundings are similar to their vertical counterparts, though the vertical displacement and vertical velocity (\(D_{\rm V}\) and \(V_{\rm V}\)) values consistently exceed horizontal measurements based on previous comparative studies [17]. Therefore, this study emphasizes the vertical responses of Tunnel 2 structures and surroundings. Figure 6 illustrates the time-history curves of vertical displacement (\(D_{\rm V}\)) and velocity (\(V_{\rm V}\)) at the mid-point S\({}_{3}\) of Tunnel 2 sleepers under conditions A\({}_{1}\)-A\({}_{5}\). S\({}_{1}\) and S\({}_{5}\) are the left and right endpoints, and S\({}_{2}\) and S\({}_{4}\) are the points of application of the train load. As train-induced vibrations propagate, the \(D_{\rm V}\) and \(V_{\rm V}\) values at S\({}_{3}\) exhibit oscillatory behavior under A\({}_{1}\)-A\({}_{5}\) conditions, with the NW condition demonstrating significantly greater \(D_{\rm V}\) and \(V_{\rm V}\) compared to other conditions. Figure 5: Schematic diagram of water pressure calculation for C\({}_{2}\) condition in the third set of models. The \(D_{\rm V}\) of point S\({}_{3}\) in T2 sleepers is shown in Figure 6a. The minimum and maximum values were \(-\)1.52 mm and 0.79 mm, respectively. The absolute values of negative \(D_{\rm V}\) for S\({}_{3}\) were significantly larger than the positive values, indicating that the sleepers in adjacent tunnels primarily experience downward pressure under train loads. The differences between maximum and minimum \(D_{\rm V}\) values under the five conditions were 1.19 mm (T2), 1.31 mm (W234), 1.3 mm (W12), 1.34 mm (W2), and 2.31 mm (NW). The NW condition exhibited the largest amplitude, with a 94.12% increase compared to T2. At 2.13 s, the \(D_{\rm V}\) reached \(-\)1.52 mm, showing distinct behavior from other conditions. The \(D_{\rm V}\) trends for W234, W12, W2, and T2 were similar, with nearly overlapping curves. Compared to T2, the amplitude increases for these conditions were 10.08%, 9.24%, and 12.61%, respectively. The absence of wall2 in NW led to its significantly higher \(D_{\rm V}\), confirming that wall2 plays a critical role in mitigating train-induced vibrations and maintaining tunnel stability. The \(V_{\rm V}\) of point S\({}_{3}\) in T2 sleepers is shown in Figure 6b. Under T2, W234, W12, and W2, the \(V_{\rm V}\) curves overlapped, with maximum positive and negative peaks at 7.78 mm/s and \(-\)9.39 mm/s, respectively. In contrast, the NW condition showed an outstanding \(V_{\rm V}\) trend, peaking at \(-\)21.35 mm/s (\(t\) = 2.05 s) and 20.87 mm/s (\(t\) = 2.22 s), followed by gradual stabilization. The differences between maximum and minimum \(V_{\rm V}\) values at A\({}_{1}\)-A\({}_{5}\) conditions are 16.17 mm/s (T2), 16.99 mm/s (W234), 16.81 mm/s (W12), 16.95 mm/s (W2), and 42.35 mm/s (NW). Compared to T2, the increases were 5.07%, 3.96%, 4.82%, and 161.90%, respectively. This indicates that the internal walls of super-large tunnels significantly reduce the \(V_{\rm V}\) of adjacent tunnel sleepers, with wall2 playing a decisive role in mitigating the dynamic response of Tunnel 2 sleepers. As shown in Figure 6a,b, the \(V_{\rm V}\) curves largely overlap under A\({}_{1}\)-A\({}_{4}\) conditions, while \(D_{\rm V}\) exhibits some differences. This indicates that inner walls exert a greater influence on \(D_{\rm V}\) than on \(V_{\rm V}\). Adjacent tunnel sleepers oscillate vertically under these vibrations because metro train-induced vibrations induce pronounced dynamic disturbances in closely spaced tunnels. Internal walls in super-large-diameter tunnels markedly reduce the static-dynamic responses of sleepers, with wall2 playing a decisive role. Notably, the NW condition exhibits the most severe sleeper disturbances, significantly exceeding other conditions.