## 4 Numerical Results and Discussion
### Stability Analysis of Small Clear-Distance Tunnels under Different Excavation Schemes
#### 4.3.1 Deformation Analysis of the Surrounding Rocks and Lining  
Figure 16 shows the vertical displacement curves of the surface, main line, and ramp vault with different footage lengths at the target section. The vault displacement of the main tunnel was greater than that of the ramp, and the ground settlement was the smallest. The final displacement curves were very close; that is, the final deformation was almost the same under the different footage lengths. In the process of tunnel excavation, the smaller the footage was, the smaller the vertical displacement was. When the footage was 3 m, the displacement curve floated above the curves of 4 and 5 m, and the difference between 4 and 5 m in terms of vertical displacement was small. Specifically, when crossing the section with poor geological and design conditions, the smaller the footage was, the better the settlement control effect was.  
To analyze the influence of footage on different sections of the tunnel within a range of 48 m from the tunnel portal, a section of every 6 m was selected for analysis. Figure 17 presents the vertical displacement of the main line tunnel and ramp vault at different distances from the tunnel portal under different footages after the tunnel was penetrated. With the increase in the distance from the portal, the vertical displacement of the main line tunnel and ramp vault decreased. Most of the displacement curve data points with a footage of 3 m were above the curves with footages of 4 and 5 m; that is, the displacement of the vault at the section with a footage of 3 m was smaller than that with footage of 4 and 5 m. This result indicated that reducing the footage length helped control the vertical displacement.  
Figure 15: Maximum principal stress distribution of main line tunnel and ramp support structures: (a) Grade III rock mass; (b) Grade IV rock mass; (c) Grade V rock mass.  
To analyze the characteristics of the horizontal displacement of the tunnel arch waist at different excavation footages, the horizontal displacement of the monitoring point shown in Figure 9 was selected for analysis. Figure 18 shows the variation curve of the horizontal displacement at the main line and ramp hance at different footages. The horizontal displacement of the main line tunnel hance tended to be close to zero after penetration, whereas the ramp tunnel had a tendency to move toward the tunnel because the ramp tunnel was constructed at an \(8^{\circ}\) inclination, and the redistribution generated by the excavation was offset to the main line tunnel, which had a certain bias effect on the ramp. A small footage had a positive effect on the horizontal displacement of the hance, but it exerted an obvious effect on the deformation of the arch.  
Figure 16: The vertical displacement curves of the surface, main line and ramp vault with different footage: (**a**) Surface; (**b**) Main line tunnel; (**c**) Ramp.  
Figure 17: The vertical displacement of the main line tunnel and ramp vault at different distances from the tunnel portal: (**a**) Main line tunnel; (**b**) Ramp.