## 4 Numerical Results and Discussion
### Stability Analysis of Small Clear-Distance Tunnels under Different Excavation Schemes
#### 4.2.1 Deformation Analysis of the Surrounding Rocks and Lining  
Figure 12 shows the vertical displacement curves of the ground, main line, and ramp vault with different grades of surrounding rocks in the target section as the construction progressed. The surface settlement revealed that the worse the rock mass quality was and the lower the grade was, the greater the surface settlement was. The final surface settlement of grades III, IV, and V was 1.71, 2.70, and 4.73 cm, respectively, and the ratio was basically stable at 1.5-1.7. Meanwhile, the ratio of elastic modulus in the lithologic parameters was constant at 2, and the elastic modulus was the controlling value of surface settlement; the two showed a positive correlation. The vertical displacement of the vault of the main line and ramp lining had a falling section at the same construction step, which corresponded to the vault settlement caused by the excavation of the tunnel face. Table 4 shows the relationship among the surface, main line, and ramp vault displacements under different lithology grades. With the deterioration of lithology quality, the displacement of the surface and vault increased. The difference between the mean values of surface and vault settlement increased with the deterioration of the lithologic grade. Surface settlement accounted for about 8% of the vertical displacement of the vault. The proportion increased with the deterioration of the lithologic grade. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Materials** & **Density (kg/m\({}^{3}\))** & **Elastic Modulus (GPa)** & **Poisson’s Ratio** & **Cohesion (MPa)** & **Friction Angle (\({}^{\circ}\))** \\ \hline Grade III rock mass & 2200 & 6 & 0.25 & 2.1 & 50 \\ Grade IV rock mass & 1900 & 3 & 0.30 & 1.4 & 30 \\ Grade V rock mass & 1600 & 1.5 & 0.35 & 0.7 & 10 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameters of three types of the surrounding rock. Figure 13 shows the horizontal displacement distribution of the surrounding rocks and lining after tunnel penetration. The large horizontal displacement in the surrounding rocks of grades III and IV was mainly distributed from the hance to the arch foot at both ends of the tunnel, and the displacement of the surrounding rocks was driven by the horizontal deformation at both ends of the tunnel. Comparison of the horizontal displacements of the surrounding rocks in grades III and IV revealed that the horizontal displacements of the grade IV surrounding rocks had a wide distribution range, whereas in the grade V surrounding rocks, although the overall displacement was relatively uniform, the absolute value of the displacement was the largest. The horizontal displacement of the lining indicates that the maximum horizontal displacement on the lining was at the hance. Therefore, the displacement of the hance needed to be analyzed further. The hance monitoring point in Figure 9 was selected to analyze the horizontal displacement at the target section with the construction process. The horizontal displacement of the main line and ramp hance monitoring points under different lithological grades are shown in Figure 14.  
Figure 14a indicates that the deformation curve of the hance of the main line tunnel initially declined and then rose; afterwards, it became stable. The reason was that after the excavation of the upper half step, the section did not form a closed loop, and the lower half step bulged and squeezed the hance to move to the side of the surrounding rocks. After the excavation of the lower half step, the hance moved to the free face in the tunnel, the displacement curve rose, and a closed-loop stable structure was formed. Afterwards, the displacement curve gradually flattened. Under grades III and IV lithologic conditions, the horizontal displacement of the hance was well controlled, and the horizontal displacement of the hance tended to be close to 0. Under the grade V lithologic condition, residual