## 2 Model Test
### Test Results
#### 2.5.2 Soil Deformation Patterns  
During the test, the computer controls the synchronized movement of the laser and the industrial camera, and 11 photographs are taken for every 1 mm of retreat of the excavated surface [26]. Figure 7 shows the cloud map of the soil deformation area after the excavation surface is destabilized. It is obtained by processing the photos taken at different moments in the test through particle image velocimetry. The test results show that the soil destabilization zone of each case essentially enters a state of equilibrium when the excavation surface setback distance \(S=3\) mm or so. Accordingly, the soil destabilization and deformation region when \(S=1\) mm, 2 mm, and 3 mm are selected for further analysis.  
Under typical working conditions without the existing tunnel, the soil body ahead of the excavation undergoes stress release when the excavation face recedes by 1 mm. This eliminates the original stress state; however, due to the small distance of destabilization, no significant deformation of the soil body ahead of the excavation occurs. As the excavation face recedes, the soil body's destabilization area expands gradually and extends to the surface. When the excavation face recedes by 3 mm, the damage mode of the soil body mainly consists of the logarithmic spiral body and the silo body above the excavation face. This finding is consistent with the conclusions of [PERSON] [34] and [PERSON] [35]. The existing tunnel has the greatest influence on the soil damage pattern when the excavation face is approaching it (\(L/D=1\)). The damage form of the soil above the excavation face, in this case, is reflected as the extension of the soil along the outer contour of the existing tunnel to the surface, and the existing tunnel restricts the formation of the upper silo. When \(L/D=0\), the area of the upper silo in the destabilization region becomes narrower and the deformation trend of the soil body is reflected as a progression towards the surface along the side of the existing tunnel. When the excavation has already passed through the existing tunnel (\(L/D=-1\)), the existing tunnel has little effect on the soil in the destabilization zone.  
The 11 photographs taken at different moments of instability of the excavation surface are reconstructed using the 3D reconstruction program developed by [PERSON] [26], from which the 3D displacement field of the soil instability region can then be obtained. Figure 8 shows the three-dimensional displacement field of the soil destabilization region at \(S=3\) mm. It can be observed that the damaged area along the negative \(Z\)-axis of the 3D damage  
Figure 7: Soil instability deformation area (for different horizontal spacings).  
body model for each condition gradually decreases. This is because, as one moves farther away from the center section of the new tunnel along the \(Z\)-axis, the diameter of the corresponding section of the new tunnel becomes smaller, resulting in less influx of soil after destabilization, and the deformation area of the soil body is gradually reduced. This demonstrates that the stability problem of the excavated surface under the presence of an existing tunnel is a three-dimensional problem.