# Dynamic Response Analysis of Parallel Twin Tunnels Under Different Train Loads
## 4 Results and Discussion
### Surrounding Soil Response
#### 4.2.2 Surroundings  
Analyzing the response of the surroundings to train loads is crucial for understanding their support role for tunnel liners, making such disturbances a key observational parameter. Figure 15 illustrates the maximum \(D_{\rm R}\) of the T2 surroundings under different conditions. Specifically, Figure 15a shows that the variation pattern of soil1 \(D_{\rm R}\) in T2 is similar to that of the surface. Figures 10b and 15a reveal that under the same conditions, the \(D_{\rm R}\) values at four points in the T2 surroundings correspond to those in tunnel liners, ranked from highest  
Figure 14: Comparison of surface \(V_{\rm V}\) under different conditions: (**a**) Comparison of maximum and minimum \(V_{\rm V}\) difference under three conditions; (**b**) The \(V_{\rm V}\) time–history curve of P\({}_{42}\) point under three conditions. to lowest: 180\({}^{\circ}\), 90\({}^{\circ}\), 270\({}^{\circ}\), and 0\({}^{\circ}\). The \(D_{\rm R}\) is highest at 180\({}^{\circ}\) and lowest at 0\({}^{\circ}\), indicating that propagation distance is a decisive factor. Additionally, the \(D_{\rm R}\) at 90\({}^{\circ}\) slightly exceeds that at 270\({}^{\circ}\), suggesting that depth affects the displacement response; deeper rock layers, characterized by higher initial stress, exhibit greater stability and smaller displacements under equivalent loads. The soil \(D_{\rm R}\) values at 90\({}^{\circ}\) and 180\({}^{\circ}\) slightly exceed those in tunnel liners, while at 0\({}^{\circ}\) and 270\({}^{\circ}\), they are marginally lower. This discrepancy indicates uneven compressive forces in T2's lower-right and upper-left regions under train loads, potentially leading to rock fracturing and void formation. Figure 15b-d compare the maximum \(D_{\rm R}\) across four layers of surroundings on the T2 right side (0\({}^{\circ}\), 90\({}^{\circ}\), and 270\({}^{\circ}\)). The data indicate that as the distance from the vibration source increases, the \(D_{\rm R}\) gradually decreases. Specifically, the \(D_{\rm R}\) reduction rate increases with distance at 0\({}^{\circ}\) and 90\({}^{\circ}\), while it exhibits a slight decrease at 270\({}^{\circ}\). The \(D_{\rm R}\) reaches its peak at 90\({}^{\circ}\), followed by 0\({}^{\circ}\), and is lowest at 270\({}^{\circ}\). This pattern highlights the tunnel crown as the most vulnerable area under vibration loads, a conclusion substantiated by extensive studies [27; 28; 29]. By contrast, the \(D_{\rm R}\) at the tunnel invert (270\({}^{\circ}\)) is relatively small and rapidly attenuates with depth, indicating that it is the safest region. The comparison between Figures 10 and 15 shows that the surroundings and tunnel structure exhibit similar displacement patterns, with a significant abrupt change observed under the A\({}_{7}\) condition. However, the maximum \(D_{\rm R}\) of T2 liners occurs at 180\({}^{\circ}\) (closest to T1), while the surroundings' maximum \(D_{\rm R}\) is at the crown of T2. This difference can be attributed to the granular nature of the surrounding soil, where particle displacement under train vibrations reduces porosity at the crown, causing larger displacements. By contrast, T2 liners, being a tightly bonded monolithic structure, experience minimal changes in porosity, resulting in greater displacement responses closer to the vibration source. Figure 16 compares the maximum \(V_{\rm R}\) of the T2 surroundings under different conditions. As depicted in Figure 16a, the \(V_{\rm R}\) variation patterns under all conditions resemble those of \(D_{\rm R}\). Notably, the soil \(V_{\rm R}\) values at 0\({}^{\circ}\), 90\({}^{\circ}\), and 180\({}^{\circ}\) in the T2 surroundings are similar. Under the same condition, the \(V_{\rm R}\) values at the four monitoring points in the T2 surroundings follow the order of 180\({}^{\circ}\), 90\({}^{\circ}\), 0\({}^{\circ}\), and 270\({}^{\circ}\).