# Stability Analysis of the Longitudinal Slope Linear Shield Tunnel Excavation Face
## 3 Results and Discussion
### Results and Discussion of Transparent Soil Experiment  
Longitudinal section displacement contour maps for slopes of \(i=-15\%\), \(0\%\), and \(15\%\) with a setback of \(S=3\) were obtained from the transparent soil experiment and are presented in Figure 6a-c. Figure 6d-f present the displacement contour maps of the soil in front of the excavation face for three slope conditions at \(S=6\) mm. Furthermore, Figure 6g-i present the displacement contour maps of the soil in front of the excavation face for three slope conditions when \(S=9\) mm.  
By analyzing the shape, direction, and extent of the displacement of the destabilized soil in front of the excavation face, it can be concluded that the destabilization process follows a consistent pattern under different slope conditions. As the inner tube retreats, the localized soil in front of and above the excavation face displaces inward. First, the localized soil in front of and above the longitudinal section of the shield tunnel is displaced inward, forming a 'bull's-horn' instability pattern. This is consistent with the logarithmic helix instability model proposed by [PERSON] et al. (2013).  
As the setback \(S\) increases, the instability region of the excavation face gradually expands. As shown in Figure 6d-f, when \(S=6\) mm, the destabilization region of the soil maintains its shape, while the instability range in front of and above the excavation face expands. The destabilization process of the shield tunnel excavation face is essentially driven by the reduction in support force, which leads to the loosening of the soil in front of the tunnel. This, in turn, induces the upward soil to move inward toward the tunnel, continuously expanding and evolving.  
As shown in Figure 6g-i, when \(S=9\) mm, the destabilization region extends to the ground surface, while the development rate of the destabilized soil in front of the excavation decreases. At this stage, the destabilization process is primarily characterized by a vertically upward extension of the failure zone. The destabilized zone undergoes slight horizontal expansion, but its overall shape predominantly exhibits vertical growth. Under the condition of slope \(i=-15\%\), the destabilized soil is more prone to forward sliding, exhibiting a clockwise sliding trend. In contrast, excavation at \(i=15\%\) leads to a further expansion of the destabilization region. Compared to other longitudinal slope conditions with the same setback (\(S\)), the displacement range of the soil in front of and above the excavation face increases significantly.  
To facilitate a more rigorous analysis of the factors affecting excavation face stability, the evaluation method of maximum destabilization width \(B\)(KalFigure 6: Displacement nephogram diagram of face instability process in the longitudinal section. (**a**) \(S=3\)mm \(i=-15\%\); (**b**) \(S=3\)mm \(i=0\%\); (**c**) \(S=3\)mm \(i=15\%\); (**d**) \(S=6\)mm \(i=-15\%\); (**e**) \(S=6\)mm \(i=0\%\); (**f**) \(S=6\)mm \(i=15\%\); (**g**) \(S=9\)mm \(i=-15\%\); (**h**) \(S=9\)mm \(i=0\%\); (**i**) \(S=9\)mm \(i=15\%\).