## 5 Numerical Model Establishment and Results Analysis
### Ventilation Tunnel Stress Analysis  
As is well known, stress is a key factor affecting rock mass deformation. Referring to the results in Section 5.2, the stress variation pattern during the construction steps of the analysis section (S20-S25) was analyzed to reflect the mechanical state of the rock mass during construction. Since the maximum principal stress can comprehensively consider the distribution of vertical stress, horizontal stress, and shear stress in the surrounding rock, this section analyzed the stress state of the surrounding rock near the ventilation tunnel using the maximum principal stress. Figure 11 shows the contour plots of the maximum principal stress during the construction stages of S20-S25. Figure 11: Contour of maximum principal stress: (**a**) S20, (**b**) S21, (**c**) S24, and (**d**) S25. From Figure 11a, it can be seen that when the full-section excavation face is 4 m away from the junction interface and the TBM face is 16 m away, the overall rock mass surrounding the ventilation tunnel is under compression and the stress distribution is relatively uniform. The stress exhibits a \"butterfly-shaped\" symmetric distribution, with only a slight stress concentration above the outline of the pilot tunnel. The maximum principal stress value is around \(-1.25\) MPa. Figure 11b shows that when the full-section excavation face advances to the junction interface, at which point the TBM face is 12 m away from the junction interface, the rock mass inside the ventilation tunnel outline changes from three-dimensional stress to two-dimensional stress. The rock mass experiences unloading effects and deforms toward the full-section excavation segment, causing tensile stress in the upper rock mass within the outline. The maximum tensile stress is 0.19 MPa. Additionally, stress concentration occurs at the junction interface, especially at the arch shoulder and bottom corner (blue area), where the maximum compressive stress is about 1.27 MPa. The stress distribution exhibits a \"crescent moon\" shape. This is mainly because, after the completion of the full-section excavation, the upper rock mass inside the outline transfers load forward, and the force flow intersects with the force flow transmitted downward by the rock mass at the arch shoulder, resulting in stress concentration in this part. The load at the arch shoulder is transmitted through the side wall, causing the side wall to move closer, while the rock mass inside the ventilation tunnel restrains the deformation of the side wall, subjecting it to a certain compression effect. The bottom corner is affected by the transmission of load and compression from the working face after the completion of the full-section excavation, leading to stress concentration in this part. In the subsequent construction process, due to the smaller size of the pilot tunnel compared to the overall size of the ventilation tunnel outline, the excavation of the pilot tunnel has a relatively small impact on the stress distribution and magnitude in the surrounding rock. The stress distribution in Figure 11c is similar to that in Figure 11b. In Figure 11c, when the TBM face advances to the junction interface, the tensile stress in the rock mass inside the ventilation tunnel outline further increases, with the maximum tensile stress reaching 0.35 MPa, appearing near the top of the TBM pilot tunnel. The arch shoulder and arch top are affected by the excavation of the pilot tunnel, resulting in tensile stress in the rock mass. The concentration of compressive stress is alleviated to a certain extent, and the maximum compressive stress decreases to 1.2 MPa. Figure 11d shows that as the excavation begins, the shallow rock mass near the ventilation tunnel outline is in a loose state. The range of loosening is greater on the left arch shoulder than on the right, and the loosening range of the roof and bottom is significantly greater than that of the side wall.