## 3 Results and Discussion
### Water Pressure  
Under train-induced vibrations, the surrounding water pressure of super-large-diameter twin tunnels exerts varying influences on adjacent tunnel liners and surroundings. This section investigates the static-dynamic responses of liners and surroundings under different water pressures (\(P_{1}=74.6\) kPa, \(P_{2}=149\) kPa, \(P_{3}=223\) kPa). Figure 12a compares the maximum \(D_{\text{R}}\) values under different water pressures (C\({}_{1}\)-C\({}_{3}\) conditions). The \(D_{\text{R}}\) of liners and surroundings at C\({}_{2}\) condition is slightly smaller than at C\({}_{1}\) condition, while \(D_{\text{R}}\) at C\({}_{3}\) condition exceeds that at C\({}_{2}\) condition. This suggests that moderate water pressure (\(P_{2}=149\) kPa) can mitigate train-induced vibrations in adjacent tunnels, whereas excessive water pressure (\(P_{3}=223\) kPa) possibly amplifies displacements. Figure 12b compares the maximum \(V_{\text{R}}\) values. Across all monitoring points (0-315\({}^{\circ}\)), \(V_{\text{R}}\) initially increases and then decreases, peaking at 180\({}^{\circ}\) and 225\({}^{\circ}\). The higher \(V_{\text{R}}\) in the central tunnel region (90-270\({}^{\circ}\)) correlates with proximity to the vibration source. From 0\({}^{\circ}\) to 180\({}^{\circ}\), the liner \(V_{\text{R}}\) exceeds the surroundings \(V_{\text{R}}\), while the reverse occurs from 180 to 315\({}^{\circ}\), indicating that the distance to the vibration source significantly influences velocity distributions. As shown in Figure 12a, b, the \(D_{\text{R}}\) and \(V_{\text{R}}\) of liners and surroundings remain similar for most monitoring points under C\({}_{1}\)-C\({}_{3}\) conditions, with only minor variations observed at specific points such as 180\({}^{\circ}\) and 225\({}^{\circ}\). The maximum displacement occurs at 180\({}^{\circ}\), while peak velocity appears at 225\({}^{\circ}\), indicating a spatial shift between the locations. Both displacement and velocity patterns are closely tied to proximity to the vibration source. Moderate water pressure (\(P_{2}=149\) kPa) effectively reduces the static-dynamic responses of adjacent tunnel liners and surroundings under train-induced vibrations. Figure 13a compares the average coordination of the surroundings. The results show significantly lower coordination under the C\({}_{1}\) condition compared to the C\({}_{2}\) and C\({}_{3}\) conditions. This demonstrates that increasing water pressure from 74.6 kPa to 149 kPa substantially enhances surroundings stability, particularly in the central tunnel region, where coordination at 180\({}^{\circ}\) increases by up to 9.81%. Under the C\({}_{3}\) condition, coordination improvements over the C\({}_{2}\) condition are marginal, indicating comparable stability levels between these two pressure conditions. The coordination variation rate is defined as in Equation (13), and its change rate of the surroundings is shown in Figure 13b. Under the C\({}_{3}\) condition, the variation rate reaches its maximum at 180\({}^{\circ}\), indicating significant instability in this region. The higher variation rate at the C\({}_{3}\) condition reflects reduced stability in the tunnel and surroundings  
Figure 12: Comparison of maximum \(D_{\text{R}}\) and \(V_{\text{R}}\) at characteristic points of liners and surroundings under C\({}_{1}\)–C\({}_{3}\) conditions: (**a**) \(D_{\text{R}}\); (**b**) \(V_{\text{R}}\). due to excessive water pressure, which increases stress in the twin tunnel structure and compromises stability. \[\text{A}=\frac{M1-M2}{M1}\times 100\% \tag{13}\]  
where \(M_{1}\) is the maximum coordination, and \(M_{2}\) is the minimum coordination. As shown in Figure 13a,b, the C\({}_{2}\) condition exhibits the highest stability among the three conditions. The central region of the twin tunnels (particularly at 180\({}^{\circ}\)) experiences the greatest impact. Optimal water pressure (\(P_{2}\) = 149 kPa) effectively enhances the stability of super-large-diameter tunnels.