# Dynamic Response Analysis of Parallel Twin Tunnels Under Different Train Loads
## 4 Results and Discussion
### Surrounding Soil Response
#### 4.2.1 Surface
Figure 12 shows that both proximity to the vibration source and the magnitude of the vibrational load influence surface \(D_{\rm V}\). The surface \(D_{\rm V}\) increases with higher train vibration loads, and excessive overloading can exacerbate surface settlement, which should be avoided. Under the A\({}_{7}\) condition, a comparable change in surface settlement was observed, aligning with the dynamic response of the T2 structure. This phenomenon suggests that under these conditions, the static pressure effect of the train load predominates over its dynamic effect, resulting in simultaneous reductions in both the static and dynamic responses of the tunnel structure and the surface. Figure 13 compares the peak-to-peak \(V_{\rm V}\) at four characteristic points (P\({}_{42}\), P\({}_{44}\), P\({}_{52}\), and P\({}_{60}\)). The data indicate that train load significantly influences the surface \(V_{\rm V}\), with the maximum \(V_{\rm V}\) exceeding 40 mm/s under different conditions, surpassing even the \(V_{\rm V}\) of T1 sleepers. This further confirms the surface amplification effect [25; 26]. Figures 12b and 13 illustrate the variation patterns of \(D_{\rm V}\) and \(V_{\rm V}\) at each point, which are consistent with increasing load. However, the differences in the maximum \(V_{\rm V}\) among points P\({}_{44}\), P\({}_{52}\), and P\({}_{60}\) are more uniform than those in the \(D_{\rm V}\), probability due to a more sensitive and faster propagation of velocity changes. The comparison of surface \(V_{\rm V}\) under three conditions is depicted in Figure 14. The \(V_{\rm V}\) values under the A\({}_{4}\) and A\({}_{7}\) conditions significantly exceed that under the A\({}_{1}\) condition, as illustrated in Figure 14a. At point P\({}_{34}\), the differences between the maximum and minimum \(V_{\rm V}\) are 66.57, 96.04, and 95.22 mm/s under the A\({}_{1}\), A\({}_{4}\), and A\({}_{7}\) conditions, respectively; at point P\({}_{42}\), these differences are 64.64, 95.35, and 98.08 mm/s, respectively. This indicates that the maximum \(V_{\rm V}\) shifts from point P\({}_{34}\) to P\({}_{42}\) as the train vibration load increases. Under the A\({}_{1}\) to A\({}_{6}\) conditions, the maximum \(V_{\rm V}\) occurs at P\({}_{34}\), but under the A\({}_{7}\) condition, the maximum shifts to P\({}_{42}\), suggesting structural reorganization under higher loads, reducing tunnel displacements and velocities. Notably, the maximum \(V_{\rm V}\) remains at P\({}_{42}\) under the As condition. Figure 13: Comparison of the maximum \(V_{\rm V}\) (the difference between the maximum and minimum values) of several characteristic points under different conditions. Figure 14b shows the time-history curves of \(V_{\rm V}\) at point P\({}_{42}\) under three conditions for comparison with surface \(D_{\rm V}\). Equilibrium is achieved approximately at 1.5 s. Before 2.8 s, the \(V_{\rm V}\) under the A\({}_{4}\) conditions exceeds that under the A\({}_{7}\) condition; after 2.8 s, the \(V_{\rm V}\) under the A\({}_{4}\) condition drops below that under the A\({}_{7}\) condition. This shift suggests that the T1 structure may have reorganized or been damaged under the A\({}_{7}\) condition. Figures 12d and 14b reveal that the variation patterns of \(D_{\rm V}\) and \(V_{\rm V}\) at point P\({}_{42}\) are similar under the three conditions, oscillating with train vibration load change. When \(D_{\rm V}\) is negative, \(V_{\rm V}\) also exhibits a negative value. In contrast to the relatively smooth \(D_{\rm V}\) time-history curves, the \(V_{\rm V}\) curves show more peaks and sensitive variations, indicating a more intense response. Figures 12-14 show that the dynamic response of surface soil under various conditions is consistent with that of the tunnel structure. Under train vibration loads, the surface \(D_{\rm V}\) and \(V_{\rm V}\) align in the same direction. As the load increases, the overall dynamic response shifts downward.