# Dynamic Response Analysis of Parallel Twin Tunnels Under Different Train Loads
## 4 Results and Discussion
### Surrounding Soil Response
#### 4.2.2 Surroundings
This indicates that while the \(V_{\rm R}\) magnitude in the T2 surroundings is mainly influenced by distance from the vibration source, the liner depth has a more pronounced impact on \(V_{\rm R}\) compared to \(D_{\rm R}\). Figures 10d and 16a show that the \(V_{\rm R}\) of T2 liners remains relatively stable when  
Figure 15: The maximum value of the \(D_{\rm R}\) of the surroundings of T2 under different conditions: (**a**) soil1; (**b**) 0\({}^{\circ}\); (**c**) 90\({}^{\circ}\); (**d**) 270\({}^{\circ}\). propagating to the surroundings, except at 270\({}^{\circ}\), where the \(V_{\rm R}\) slightly attenuates due to burial depth effects. The maximum \(V_{\rm R}\) of the surrounding layers on the T2 right side (0\({}^{\circ}\), 90\({}^{\circ}\), and 270\({}^{\circ}\)) under different conditions is illustrated in Figure 16b-d. As depicted in Figure 16b, under the same condition, the maximum \(V_{\rm R}\) values across the four layers at 0\({}^{\circ}\) follow the order: soil2 \(>\) soil1 \(>\) soil3 \(>\) soil4. This observation, along with the uneven displacement between T2 liners and the surroundings in Figure 15, explains why the \(D_{\rm R}\) of the T2 right-side surroundings initially increases and then decreases with distance from the tunnel. Figure 16c,d show that the \(V_{\rm R}\) values in the surroundings above T2 (90\({}^{\circ}\)) follow the order: soil4 \(>\) soil3 \(>\) soil2 \(>\) soil1. Conversely, the pattern below T2 (270\({}^{\circ}\)) is inverted, with the soil1 \(V_{\rm R}\) being lower beneath T2 compared to above it. This suggests that greater burial depth increases the earth pressure on the T2 surroundings, leading to reduced \(V_{\rm R}\). Figure 17 shows the rate of porosity variations (\(R_{\rm P}\)) in the T2 surroundings under eight conditions. As the train load increases, the adjacent tunnel surroundings reorganize to accommodate the additional stress, leading to significant changes in soil porosity, with the \(R_{\rm P}\) in the T2 surroundings increasing accordingly. Notably, the \(R_{\rm P}\) decreases under the A\({}_{7}\) condition before rapidly increasing again. As shown in Figure 17a, the \(R_{\rm P}\) values in T2 soil1 follow the order: 90\({}^{\circ}\) \(>\) 270\({}^{\circ}\) \(>\) 180\({}^{\circ}\) \(>\) 0\({}^{\circ}\). The maximum \(R_{\rm P}\) occurs at the T2 crown (90\({}^{\circ}\)), validating the conclusion from Figure 15 that train vibrations displace the surrounding particles downward, causing significant porosity changes above the tunnel. Meanwhile, the \(R_{\rm P}\) value on the T2 left side (180\({}^{\circ}\)) is higher than that on the right (0\({}^{\circ}\)) due to its greater distance from the vibration source. After the A\({}_{4}\) condition, the \(R_{\rm P}\) curve for the T2 left side (180\({}^{\circ}\)) diverges, reaching 0.46% under the A\({}_{6}\) condition, surpassing the crown \(R_{\rm P}\). This indicates destabilization of the soil between the twin tunnels as the load increases, especially after the A\({}_{5}\) condition. Figure 17b-d illustrate the \(R_{\rm P}\) in the T2 surrounding layers (0\({}^{\circ}\), 90\({}^{\circ}\), and 270\({}^{\circ}\)). Under all conditions, the \(R_{\rm P}\) on the right side of T2 is highest in soil4 and lowest in soil3. Following the A\({}_{4}\) condition, the \(R_{\rm P}\) in soil2 exceeds that in soil1, supporting the conclusion from Figure 15a that the T2 lower-right corner experiences uneven compressive stress under train loads. Furthermore, the \(R_{\rm P}\) above T2 is significantly higher than that below, with soil4 below T2 exhibiting nearly constant \(R_{\rm P}\) values under all conditions. This suggests that the influence of train load on soil structure diminishes with increasing depth. Figure 17 shows that the \(R_{\text{P}}\) of the tunnel surroundings is influenced by train load, tunnel structural configuration, and burial depth. Notably, the region between dual tunnels experiences the most significant combined effects, leading to the highest value of \(R_{\text{P}}\).