## 3 Finite Element Simulation
### Finite Element Simulation Results  
#### 3.3.1 Comparison of Experimental Results with Finite Element Simulation Results  
The support pressure ratio curves obtained from numerical simulation schemes 1-4 and the corresponding model tests are shown in Figure 10a. As can be seen from the diagram, the support pressure ratio curves under each existing tunnel condition are similar to the results obtained when there is no existing tunnel. The changing trend of the support pressure ratio can still be divided into two phases, as mentioned in Section 2.5.1. The maximum discrepancy between the values of the ultimate support pressure ratios obtained from the numerical simulation and the model test is about 5.5%, which initially verifies the reliability of the numerical model. Figure 10b shows the support pressure ratio curves after reducing the vertical distance and diameter ratio of the two tunnels in the numerical simulation. Compared to the numerical simulation conditions of _h/D_ = 1 and _d/D_ = 1, the reduction of the vertical distance of the two tunnels (_h/D_ = 0.75 and _d/D_ = 1) lowers the ultimate support pressure at _L/D_ = 1 and _L/D_ = 0 by about 2.9% and 2.2%. This phenomenon can be attributed to the fact that the decrease in the vertical distance between the two tunnels allows for a larger area of the upper soil layer to be supported by the existing tunnels, thereby isolating the stress transfer from the upper soil to the lower soil to a greater extent. The existing tunnel further hinders the development of the soil arch zone, and the reduction of the lower soil arch zone enables the soil within the range to reattain a stable state after a shorter backward displacement. The reduction of the tunnel diameter ratio (_h/D_ = 1, _d/D_ = 0.5) increases the ultimate support pressure at _L/D_ = 1 and _L/D_ = 0 by about 8.3% and 2.6%, respectively. The decrease in the tunnel diameter of the existing tunnel weakens its interaction with the surrounding soil and reduces the area of soil that can be confined. Therefore, the stress transfer from the soil above the existing tunnel is more direct. After the destabilization of the excavation surface, the soil arch area develops to the ground surface more obviously, so it needs a larger ultimate support force to make the excavation surface reach a stable state again. Figure 10: Support pressure ratio (test and simulation): **(a)** Different horizontal spacing; **(b)** Different vertical spacing and tunnel diameter ratio. As shown in Figure 11, the soil destabilization deformation maps (\(S=3\) mm) obtained from the test for each working condition are processed to produce the corresponding displacement contour maps, which are then compared to the results of numerical simulation schemes 1-10. The soil damage patterns derived from the numerical simulation of conditions 1-4 are consistent with the model test results. The main source of discrepancy between the two is the variation in the extent of the soil deformation area. Specifically, the error range of the farthest distance from the excavation surface in the horizontal direction is about 2.4-9%, while the error range of the maximum height extending upward from the excavation surface axis in the vertical direction is about 2.4-13.3%. These findings further confirm that the soil deformation pattern is consistent with the model test results. In addition, compared to \(h/D=1\), the soil destabilization area under different horizontal spacing conditions reduces when \(h/D=0.75\). When \(L/D=1\), the maximum height of the destabilization area extending from the central axis of the excavation surface to the ground surface is reduced by about 10%, and the whole damage mode is reflected as the extension of the gap between the two tunnels. When \(L/D=0\), the farthest distance of influence in the horizontal direction is reduced by about 2.3%, while the maximum height of extension in the vertical direction is reduced by about 30%.