# Dynamic Response Analysis of Parallel Twin Tunnels Under Different Train Loads
## 4 Results and Discussion
### Surrounding Soil Response
#### 4.2.1 Surface  
Train operations can cause ground vibrations, leading to surface subsidence that worsens with increasing train loads. Figure 12 shows the surface settlement curves under various conditions. P\({}_{44}\) is above T1's center, P\({}_{52}\) is between the twin tunnels, and P\({}_{60}\) is above T2's center. Figure 12a shows that the surface settlement is most pronounced above T1, gradually diminishing toward both sides, with a more rapid decrease on the left side. The maximum surface \(D_{\rm V}\) occurs at P\({}_{42}\), slightly to the left of T1's center, attributed to the loading effect of T1 and the reinforcing influence of the twin tunnels. Under the A\({}_{1}\) to A\({}_{8}\) conditions, the maximum \(D_{\rm V}\) values at monitoring point P\({}_{42}\) are \(-4.31\), \(-4.97\), \(-5.63\), \(-6.28\), \(-6.94\), \(-7.59\), \(-6.62\), and \(-8.90\) mm, respectively. Although surface settlement generally increases at higher train loads, a significant drop occurs under the A\({}_{7}\) condition, followed by a rapid increase under the A\({}_{8}\) condition. Figure 12b illustrates the maximum \(D_{\rm V}\) at four characteristic points (P\({}_{42}\), P\({}_{44}\), P\({}_{52}\), and P\({}_{60}\)) under all conditions. The variation patterns at each point are mainly consistent, with the \(D_{\rm V}\) curves for P\({}_{42}\) and P\({}_{44}\) being nearly identical and exhibiting the highest values. P\({}_{52}\) shows intermediate displacement, and P\({}_{60}\) demonstrates the least displacement. This trend suggests that the surface \(D_{\rm V}\) decreases with increasing distance from the vibration source. Figures 11b and 12b show that the \(D_{\rm R}\) of T1 liners is less than the absolute \(D_{\rm V}\) at the surface above T1 (P\({}_{44}\)). Under the A\({}_{1}\) condition, the maximum \(D_{\rm R}\) of T1 liners is 3.72 mm, and the absolute \(D_{\rm V}\) at P\({}_{44}\) is 4.27 mm. Under the A\({}_{8}\) condition, the maximum \(D_{\rm R}\) of T1 liners increases to 7.87 mm, and the absolute \(D_{\rm V}\) at P\({}_{44}\) increases to 8.91 mm. This difference highlights the amplified surface response to train vibrations, emphasizing the need to monitor the impact of subway trains on surface displacement. Figure 12c shows the surface settlement curves under the A\({}_{1}\), A\({}_{4}\), and A\({}_{7}\) conditions. The maximum surface \(D_{\rm V}\) under the A\({}_{7}\) condition is slightly higher than that  
Figure 12: The surface settlement curve under different conditions: (**a**) The maximum \(D_{\rm V}\) of different monitoring points on the surface under different conditions; (**b**) Comparison of the maximum \(D_{\rm V}\) of several characteristic points under different conditions; (**c**) The maximum \(D_{\rm V}\) of different monitoring points on the surface; (**d**) \(D_{\rm V}\) time–history curves at point P\({}_{42}\). under the A\({}_{4}\) condition, with nearly no difference at point P\({}_{60}\) on the right. This suggests that at the A\({}_{7}\) level, the twin-tunnel structure may reach a new \"equilibrium\" to accommodate overloading. Figure 12d presents the time-history curves of surface \(D_{\rm V}\) at point P\({}_{42}\) under these conditions. The label A\({}_{1}\)-P\({}_{42}\) represents the vertical displacement of the point P\({}_{42}\) of the surface under the A\({}_{1}\) condition. Equilibrium is achieved at approximately 1.3 s, with the \(D_{\rm V}\) variation patterns remaining consistent under all conditions and oscillating in response to changes in trainload. Comparing the maximum positive \(D_{\rm V}\) at point P\({}_{42}\), the order is A\({}_{4}\) > A\({}_{1}\) > A\({}_{7}\), while for the maximum absolute negative \(D_{\rm V}\), it is A\({}_{7}\) > A\({}_{4}\) > A\({}_{1}\). These observations demonstrate that as train vibration load increases, the surface initially experiences stronger \(D_{\rm V}\) fluctuations, followed by an overall downward trend.