## 3 Numerical Modeling
### Modeling Results and Analysis  
Figure 4 shows the distribution of the maximum principal stress. Under the action of the applied confining pressure, the maximum principal stress first started to concentrate at the bottom corner of the side wall of the tunnel, and the stress on the surrounding rock of the tunnel profile also increased immediately. As the loading continued, cracks started to be generated from the tunnel vault and bottom corners of the side wall, forming multiple main cracks that propagated around and bifurcated during the propagation process. The cracks on the vault and bottom developed faster, and those on the side wall developed slower. The tunnel was unstable at this point because the late loading stage caused all the cracks in the surrounding rock of the tunnel profile to be penetrated. Figure 5 shows the distribution of the maximum principal strain, which was constant throughout the loading and failure process of the rock mass. Figure 6 shows the changes in the elastic modulus of the rock, with the red color indicating the failure area. It can be seen that the distribution of the failure is consistent with that of the maximum principal stress. In practical engineering, the ground stress field cannot be directly observed, but rock fracture will occur, so the acoustic emission phenomenon can be monitored to understand the failure of the surrounding rock. Figure 7 shows the spatial distribution of the acoustic emission phenomenon during the failure process of rock. The center of the sphere in the \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Elastic** & **Uniaxial Compressive** & **Poisson’s Ratio** & **Internal Friction** & **Residual Strength** & **Coefficient of** & **Coefficient of** \\
**Modulus (GPa)** & **Strength (MPa)** & & **Angle (°)** & & **Confining Pressure** & **Homogeneity** \\ \hline
10 & 35 & 0.25 & 30 & 0.1 & 2 & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mechanical parameters of the rock mass. Figure 4: Distribution of the maximum principal stress. Figure 5: Distribution of the maximum principal strain. Figure 6: Distribution of the elastic modulus. figure represents the location of the acoustic emission, and the radius of the sphere indicates the relative magnitude of the energy released from the acoustic emission. In Figure 7, the red sphere and blue sphere represent the acoustic emission events generated from the failure of elements satisfying the tensile criteria or shear criteria, respectively. As can be seen from the figure, in the initial loading stage, a large number of red spheres started to concentrate at the tunnel vault and bottom corners of the side wall, indicating that the rock damage gradually propagated at this moment. As the loading proceeded, the red spheres on both sides of the tunnel also started to increase, and there were red spheres of larger radius gathering at the tunnel vault and corners of the side wall continuously, indicating that the rock fracture intensified and the energy released increased at this time. Meanwhile, blue spheres began to appear at the tunnel vault and bottom, indicating that shear failure occurred locally, but this area was dominated by tensile failure. In the late loading stage, the red spheres kept expanding inward and the blue spheres kept increasing, indicating that the damage to the side wall kept intensifying and that more and more energy was released by micro-fractures. Especially, acoustic emissions were mainly concentrated at the tunnel vault and corners of the side wall. The damage distribution of the vault and the corners of the side walls are influenced by the in situ stress and weak structures. Moreover, the distribution of the initial in situ stress field in the tunnel surrounding rock will influence the damage range and degree. Inevitably, the increase of lateral pressure coefficients will expand the damage range and degree.