## 4 Numerical Results and Discussion
### Stability Analysis of Small Clear-Distance Tunnels under Different Excavation Schemes
#### 4.3.2 Stress Analysis of the Supporting Structure  
Figure 19 shows the distribution of primary lining stress under different footages after the tunnel was penetrated. The maximum stress was distributed in the range of 0-5 m in the left hande of the main tunnel. Under the influence of the overall displacement of the ramp tunnel hance after excavation and support, the horizontal displacement of the main tunnel hance tended to be zero, resulting in a large stress concentration. The stress distribution was consistent in all the footage conditions, but some differences in stress size were observed. The stress of the 4 m footage was the least, followed by that of the 5 m footage. The stress of the 3 m footage was the largest. Therefore, the 4 m footage was beneficial to the stress of the lining. Overall, the footage had little influence on the deformation of the surrounding rocks and the stress and deformation of the lining. Reducing the footage was beneficial to the deformation of the vault and hance, but when the footage was small, the overall force was large, and the construction steps increased, which was not conducive to the economic feasibility of the whole project. Therefore, when the geological conditions are good, large footage can be selected for rapid excavation; meanwhile, when crossing special sections, the footage should be reduced to control the deformation and strengthen the support, thereby preventing damage on the support structure. The excavation effect of small clear-distance tunnels under different excavation schemes, surrounding rock grades, and footage lengths are listed in Table 5. The excavation effect of the double wall heading method in small clear-distance tunnels was better than the other methods, and the same conclusion has been reached by scholars in the study of large section tunnels [35; 36]. The higher of the grade of the surrounding rock, the smaller of the deformation and stress caused by excavation, which has been confirmed in literature [37]. Reducing footage was conducive to controlling the deformation and stress of surrounding rock, but not the smaller the better, which is consistent with the literature [38]. See Table 5.  
Figure 19: Stress distribution of supporting structure in different footage: (**a**) Footage 3 m; (**b**) Footage 4 m; (**c**) Footage 5 m.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Excavation Effect**} & \multicolumn{4}{c}{**Excavation Methods**} & \multicolumn{4}{c}{**Lithology Grades**} & \multicolumn{4}{c}{**Footage Lengths (m)**} \\ \cline{2-10}  & **Full-Section Method** & **Step** & **CD** & **Double Wall Method** & **Hading Method** & **III** & **IV** & **V** & **3** & **4** & **5** \\ \hline \hline \multirow{8}{*}{Displacement} & (1) The influence range of vertical displacement of surrounding rock above the ramp from small to large was the full section, CD, double wall heading and step method. (2) In step and full section methods, the horizontal displacement range of surrounding rock around the tunnel was large. (3) In the CD and double wall heading methods, the overall horizontal displacement was relatively average. (4) In the CD method and double wall heading methods, the overall horizontal displacement of the lining structure was mainly concentrated on the temporary structural deformation. (5) The double wall heading method could maintain the integrity of the primary lining displacement, and the horizontal displacement of the primary lining at the hance was small.