# Dynamic Response Analysis of Parallel Twin Tunnels Under Different Train Loads
## 4 Results and Discussion
### Twin-Tunnel Structure Response
#### 4.1.2 Liners
As illustrated in Figure 11a, the \(D_{\rm R}\) values at different angular positions of T1 liners are highly consistent under the same conditions, indicating that the vibration source dominates displacement patterns. Figure 11b reveals the variation patterns of \(D_{\rm R}\) at four critical positions (0\({}^{\circ}\), 90\({}^{\circ}\), 180\({}^{\circ}\), and 270\({}^{\circ}\)) under different conditions, following the order: 180\({}^{\circ}>270^{\circ}>90^{\circ}>0^{\circ}\). The higher \(D_{\rm R}\) value at 180\({}^{\circ}\) compared to that at 270\({}^{\circ}\) (the position closest to the vibration source) can be explained by: (1) the downward loading direction at 270\({}^{\circ}\) potentially constrains the liner's \(D_{\rm R}\); and (2) greater geostatic pressure at 270\({}^{\circ}\) due to increased burial depth. As evidenced by Figure 11c,d, the \(V_{\rm R}\) values at various angular positions of T1 liners remain relatively consistent under identical conditions, with the maximum \(V_{\rm R}\) following the order: 270\({}^{\circ}>180^{\circ}>0^{\circ}>90^{\circ}\). This pattern differs from the \(V_{\rm R}\) characteristics, suggesting that velocity measurements are more sensitive to train vibrations and positively correlate with proximity to the vibration source. Furthermore, the twin-tunnel structure influences the \(V_{\rm R}\) distribution, resulting in a higher \(V_{\rm R}\) value at 180\({}^{\circ}\) compared to that at 0\({}^{\circ}\). Figures 10 and 11 reveal that the maximum \(D_{\rm R}\) at the 180\({}^{\circ}\) position of T2 liners is 72% to 76% of that in T1, while the maximum \(V_{\rm R}\) varies from 88% to 93%, highlighting significant static and dynamic responses in adjacent tunnel liners induced by train operations. These results demonstrate that metro train vibrations significantly affect closely spaced adjacent  
tunnels. Increasing load exacerbates displacement differentials more in adjacent tunnels than in the operating tunnel. Therefore, both the operating tunnel and the static and dynamic responses of adjacent tunnel structures need to be monitored, with particular emphasis on liner displacements to prevent cracks caused by overloading. Under the A\({}_{7}\) condition, T1 and T2 show significant decreases in displacement and velocity responses. Since T1 exhibits stronger static and dynamic responses than T2 under all conditions, the similar patterns observed under the A\({}_{7}\) condition likely stem from a shared underlying cause. Additionally, T2's transitional behavior is probably influenced by T1's structural responses. This mutation phenomenon is a unique finding of this study and is rarely reported in the existing literature. It is found that the overload value set in the existing literature is mainly divided into the following three cases:  
1. It does not reach the value under the A\({}_{7}\) condition (121.6 kN). 2. It exceeds the value under the A\({}_{7}\) condition (121.6 kN), for example, [PERSON] et al. [1] studied the railway tunnel under 300 kN load and [PERSON] et al. [3] studied the train axle load between 27 and 30 t.
3. The load setting spacing between conditions is too large, for example, [PERSON] et al. [14] studied the load response to the surface when the axle loads were 10 t, 14 t, and 18 t.  
The structure's static and dynamic responses to train loading may stem from two factors: (1) the increase in subway train load significantly enhances the vibration effect, which amplifies the dynamic response of the structure; and (2) the downward force of subway train loading on T1 sleepers exerts a pressure effect, partially suppressing vibrations in both the T1 sleeper and liner, thereby reducing the vibration of the T2 structure. Under the A\({}_{1}\)-A\({}_{6}\) conditions, the dynamic amplification effect outweighs the pressure effect, leading to a progressive increase in T2's dynamic response with increased loading.