## 5 Numerical Model Establishment and Results Analysis  
### Numerical Model Establishment  
According to the actual excavation conditions on-site, excavation was conducted simultaneously from the left and right boundaries toward the dividing interface. The left side of the dividing interface was excavated using the full-section method (labeled as 1 in Figure 6a), while the right side of the dividing interface initially used a TBM to create a pilot tunnel (labeled as 2 in Figure 6a). When the working faces of both methods reached the junction interface, the right side of the dividing interface started reverse excavation (labeled as 3 in Figure 6a) toward the right boundary of the model. This adjustment was made to ensure that the dimensions of the ventilation shaft met the design requirements. The relative positions of the pilot tunnel and the ventilation shaft are illustrated in Figure 6b.  
Midas GTS NX was used in this study to simulate the excavation process of the ventilation shaft, and the numerical model is shown in Figure 7. To mitigate the boundary effects, [26; 27], the width of the model on both the left and right sides was set to 100 m. The longitudinal length of the model was 178 m. The minimum distance from the bottom edge of the ventilation shaft to the model bottom was 50 m, and the model's upper surface was set to the terrain surface. The cross-section of the ventilation shaft was taken according to the actual dimensions, with a width of 7.9 m and a height of 7.0 m. The boundary conditions of the model were as follows: the bottom was fixed, constraining the normal deformation of the model's sides, and the top was a free surface. The cross-section at 80 m along the model's length (the junction of full-section excavation and TBM pilot tunnel excavation) was set as the analysis section to study the mechanical behavior of the surrounding rock at the junction.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Materials/Location** & **Density/g\_cm\_3** & \(E_{\text{m}}\)/GPa & \(\mu\) & \(\phi\)/\({}^{\circ}\) & _c_/MPa \\ \hline Shale & 2.65 & 0.8 & 0.35 & 27 & 0.4 \\ Muddy limestone & 2.69 & 6 & 0.25 & 42 & 1.2 \\ Leopard skin limestone & 2.69 & 9 & 0.25 & 48 & 1.5 \\ Shotcrete & 2.5 & 23 & 0.2 & - & - \\ Equivalent concrete & 2.5 & 30.97 & 0.2 & - & - \\ Anchor bolt & 7.85 & 200 & 0.3 & - & - \\ L1 & 2.44 & 0.6 & 0.31 & 23 & 0.29 \\ L2 & 2.4 & 0.5 & 0.32 & 22 & 0.38 \\ L3 & 2.34 & 0.4 & 0.33 & 21 & 0.52 \\ L4 & 2.32 & 0.4 & 0.33 & 21 & 0.56 \\ R1 & 2.43 & 0.6 & 0.31 & 23 & 0.31 \\ R2 & 2.38 & 0.5 & 0.32 & 22 & 0.43 \\ R3 & 2.32 & 0.4 & 0.33 & 21 & 0.56 \\ R4 & 2.30 & 0.4 & 0.33 & 20 & 0.61 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Mechanical parameters of the surrounding and supporting structures.  
The surrounding rock was simulated using solid elements following the Mohr-Coulomb criterion, and shotcrete was simulated using plate elements. The concrete thickness for the full-section excavation was 100 mm, and for the TBM pilot tunnel excavation it was 200 mm. I18 Steel arches with a spacing of 750 mm were installed in this section, and the flexural stiffness of the steel arches was converted to the concrete [28]. The anchor bolts were simulated using embedded truss elements. The specifications of the anchor bolts in the fully excavated section were \(\Phi\)22 mm \(\times\) 3000 mm, with a spacing of 2000 mm \(\times\) 2000 mm between the arch and the sidewall. In the TBM-driven tunnel section, the anchor bolts had specifications of \(\Phi\)25 mm \(\times\) 4000 mm, with a spacing of 1250 mm \(\times\) 1250 mm between the arch and the sidewall. The mechanical parameters of the surrounding rock and support are provided in Table 4, and Figure 8 illustrates the schematic diagram of the modified rock mass parameters.  
Figure 6: Schematic diagram of the construction process and pilot tunnel: (**a**) schematic diagram of the construction process, and (**b**) schematic diagram of the pilot tunnel.  
Figure 7: Mesh partition for computational model.