## 3 Finite Element Simulation
### Finite Element Simulation Results
#### 3.3.2 Changes in Soil Stresses  
To have a more detailed understanding of the stress trends in the soil after the excavation surface is destabilized, soil stress points are selected in numerical simulation conditions 1-4 along the transverse and longitudinal stress paths in different cross-sections in front of the excavation surface (\(Z=-0.30\) m, \(-0.22\) m, \(-0.04\) m). Soil stresses at different setback stages are analyzed. The stress paths, soil vertical stresses, and average horizontal stress changes are shown in Figures 12 and 13. As shown in the figure, \(Z=-0.30\) m marks the center of the excavation face of the new tunnel, \(Z=-0.22\) m marks the location between the two tunnels, and \(Z=-0.04\) m marks the location above the existing tunnels. The vertical stress and average horizontal stress of the soil body are \(\sigma_{zz}\) and \((\sigma_{xx}+\sigma_{yy})/2\), respectively. As shown in Figure 12, when the excavation surface retreat distance is 3 mm, the soil body in front of the excavation undergoes stress unloading. The vertical stress of the soil body on both sides of the stress path at the center of the excavation surface (\(Z=-0.30\) m) is significantly reduced for all horizontal spacing. The minimum vertical stress varies in the range of 51.02-53.87% as opposed to the initial stress state, wherein the area of the soil body with reduced vertical stress in each condition at this stage develops at a distance of  
Figure 12: Vertical stress change of soil mass (different horizontal spacings). 0.42 \(D\)-0.5 \(D\) from the center of the excavation surface. As the distance of the soil body from the excavation surface increases, the vertical stress of the soil body gradually increases until it becomes stable. This might be because this area is located at the boundary of the soil arch, which is subjected to the transmission of the soil pressure at the far end. A comparison of the vertical stresses in the two directions of the stress paths reveals that the transverse stress path has higher vertical stresses than the longitudinal direction. This is because the soil in this region is adjacent to the new tunnel, and following destabilization, the soil in front of the excavation is driven into the tunnel. This leads to the interaction between the soil in this region and the new tunnel, increasing vertical stresses. Comparing the conditions between cases with and without the existing tunnel reveals that the existing tunnel has a greater impact on the soil stresses when \(L\)/\(D\) = 1 and \(L\)/\(D\) = 0, primarily in the soil between the two tunnels. When \(Z\) = \(-\)0.22 m and \(S\) = 0 mm, Figure 12b shows a stress settling in the soil body under the existing tunnels, with an average vertical stress reduction in the longitudinal direction of about 10.8%. Figure 12c shows an overall reduction in initial vertical stress along the transverse axis, wherein the average vertical stresses in the transverse direction are reduced by about 20.8%. This reflects that the existing tunnel balances some of the stresses in the upper soil by self-deformation and isolates the transmission of vertical stresses from the upper soil. \(Z\) = \(-\)0.04 m marks the area above the existing tunnel, where the vertical stresses of the soil body always remain in a relatively stable state. Figure 13 illustrates that the average horizontal stress in the soil body of each path follows a similar trend to that of vertical stress, except for minute differences. The minimum average horizontal stress at \(Z\) = \(-\)0.30 m has a larger shrinkage value, which is concentrated in the range of 89.2-92.5%, whereas at \(Z\) = \(-\)0.22 m, there is no visible change in the average horizontal stress when \(L\)/\(D\) = 0 and \(L\)/\(D\) = 1. Therefore, the presence of existing tunnels has less influence on the average horizontal stress of the soil body.