## 4 Numerical Results and Discussion
### Stability Analysis of Small Clear-Distance Tunnels under Different Excavation Schemes
#### 4.1.3 Stress Analysis of the Supporting Structure  
Given that the primary lining was mainly a concrete material, which has high compressive capacity but low tensile capacity, the main tensile parts can be determined by the overall stress distribution on the supporting structure. Figure 11 presents the maximum principal stress distribution of the main line tunnel and ramp support structure after the tunnel was penetrated using the different excavation schemes. Positive values in the figure indicate tension, and negative values indicate compression.  
Figure 11 reveals that tensile state distribution existed around the arch in the step and full section methods without temporary support. In the full section method, the main tunnel and ramp were almost distributed in length, which was not conducive to the bearing performance of the primary lining structure. Figure 11 also shows that tension stress existed around the vault without temporary support, such as in the step and full section methods. In the full section method, the main line tunnel and ramp were almost distributed throughout the length, which was not conducive to the pressure bearing performance of the primary lining structure. Local tensile stress was observed in the CD method, but almost no tensile stress was observed in the double wall heading method. In the full section and step methods, the maximum principal stress was distributed in the inverted arch. Meanwhile, the inverted arch of the CD and double wall heading methods could effectively bear the load transmitted from the upper lining to the lower part without a large maximum principal stress. The distribution range and value of the principal stress of the ramp invert were smaller than those of the main line tunnel, which was highly obvious in the step and full section methods. The reason was that after the excavation of the main line, the stress  
Figure 11: Maximum principal stress of lining structure (unit: Pa): (**a**) Step method; (**b**) Full section method; (**c**) CD method; (**d**) Double wall heading method.  
was first released on the lining of the main line tunnel. However, if the main line tunnel was equipped with temporary support, the disadvantageous stress position of the main tunnel could be effectively adjusted, as shown in Figure 11c,d.  
Generally, the four excavation schemes had little influence on the vertical deformation of the vault. The CD method had the smallest vertical displacement, and the double wall heading method effectively controlled the horizontal displacement of the hance, which was similar to the research conclusions of scholars in large section tunnels [35; 36]. The overall stress of the lining was reasonable in the CD and double wall heading methods with temporary support, but a large range of tensile stress was observed in the full-section and step methods.  
Analysis of the Construction Behaviour of the Small Clear-Distance Tunnel under Different Lithology Grades  
Grades III-V surrounding rocks were distributed in the range of ZK2+780-ZK3+120 of the main line tunnel. Therefore, a simulation of small clear-distance tunnel construction with grades III-V surrounding rocks was conducted to determine the possible dangerous parts in advance. The other condition parameters in the model remained constant, and the grid division was the same. The tunnel was 110 m long, and the step method was adopted. The main line tunnel was excavated first, followed by the ramp. The staggering distance between the main line and the ramp was 25 m, and the staggering distance between the bench face and the tunnel face was 25 m. The section 20 m away from the main line tunnel portal was selected as the target section for analysis. The parameters of three types of the surrounding rock are shown in Table 3.