## 5 Numerical Model Establishment and Results Analysis
### Analysis of the Surrounding Rock's Existing State  
The existing state of the surrounding rock can be represented by equivalent plastic strain, as shown in Figure 12.  
In Figure 12a, when the full-section excavation face is 4 m away from the junction interface and the TBM face is 16 m away, the disturbance to the surrounding rock at the junction interface is minimal due to the distance between the working face and the junction interface. The equivalent plastic strain for the entire section is 0 (blue area). When the full-section excavation face reaches the junction interface, at which point the TBM face is 12 m away from the junction interface (Figure 12b), the rock mass at the junction interface inside the ventilation tunnel outline loses its constraint from the rock mass at the full-section excavation, leading to a change in the stress state. Plastic strain first appears inside the outline, with a larger plastic strain at the bottom of the pilot tunnel (red area), and the shape of the entire plastic zone is similar to a butterfly. Since the area of the pilot tunnel is smaller than the area of the rock mass within the ventilation tunnel outline, the plastic zone undergoes almost no change during the excavation of the pilot tunnel, and the size and distribution of the equivalent plastic strain are almost the same as in Figure 12b. As the TBM face advances to the junction interface (Figure 12c), the plastic strain of the rock mass inside the ventilation tunnel outline increases, the concentration of plastic strain at the bottom edge of the pilot tunnel deepens, and the plastic zone extends to the outer edge of the side wall. There is little change in the plastic zone beneath the bottom plate. When the excavation is complete (Figure 12d), the plastic zone of the surrounding rock is concentrated from the bottom corner to the upper part of the arch shoulder. The plastic zone is approximately symmetrically distributed on the left and right sides. Due to the overall monoclonal structure of the surrounding rock, the left arch shoulder has a greater depth of plastic zone than the right side. The plastic strain and depth of the plastic zone on the side wall are significantly greater than those on the arch shoulder and bottom corner. The maximum plastic strain is located in the shallow rock mass at the middle of the side wall, and the maximum depth of the plastic zone is 2.2 m. With the application of support for the excavation section (Figure 12e), the plastic strain in the shallow rock mass of the side wall significantly decreases, and the maximum depth of the plastic zone in the side wall also decreases from 2.2 m to 1.9 m. The maximum depth of the plastic zone in the arch shoulder and its upper surrounding rock also decreases from 1.7 m to 1.5 m. The maximum expansion depth of the shoulder and its upper surrounding rock has decreased from 1.7 m to 1.5 m, indicating that the application of support has altered the stress state of the surrounding rock, effectively suppressing its deformation. As the excavation face gradually moves away from the boundary interface (Figure 12f), the disturbance of the surrounding rock at the interface by the construction is minimal. Consequently, the existing state of the surrounding rock at the interface has undergone almost no change.  
Through an analysis of the expansion pattern of the plastic zone, it is recommended to pay attention to monitoring the shoulder and sidewall during construction. When necessary, improvements to the stress state of the surrounding rock can be achieved by increasing the density of anchor rods.