## 3 Numerical Simulation
### Stress Release Hole  
Boring holes in the tunnel wall after excavation, the tangential stress of surrounding rock can be released through the deformation of holes, which is a common method of rock burst control. The effect of this method is closely related to the size, length and longitudinal spacing of boreholes, which will be discussed in the simulation of this section, shown in Figure 5. The stress release rate is used to simulate the three-dimensional space effect of boreholes. In order to analyze the effect of various parameters on rockburst prevention, eight conditions were designed as shown in Table 2.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \begin{tabular}{c} **Density \(\rho\)** \\ **(kg/m\({}^{3}\))** \\ \end{tabular} & \begin{tabular}{c} **Poisson Ratio \(\mu\)** \\ **(kg/m\({}^{3}\))** \\ \end{tabular} & \begin{tabular}{c} **Internal Friction** \\ **Angle \(\varphi\) (\({}^{\circ}\))** \\ \end{tabular} & \begin{tabular}{c} **Cohesion \(C\)** \\ **(MPa)** \\ \end{tabular} & \
\begin{tabular}{c} **Elasticity Modulus** \\ **_E_ **(GPa)** \\ \end{tabular} &
\begin{tabular}{c} **Lateral Pressure** \\ **Coefficient** \\ \end{tabular} \\ \hline
2840 & 0.25 & 45 & 7.5 & 80 & 0.8 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Mechanical parameters of surrounding rock.  
Figure 4: Three-dimensional numerical model.  
Taking the No. 3 condition as an example, the typical displacement distribution of surrounding rock after boring holes is shown in Figure 6. The convergence of holes induced the radial deformation of tunnel turns to tangential deformation around the boreholes. Figure 7 shows the distribution of maximum principal stress in surrounding rock before and after boring holes. After boring holes, the maximum principal stress of tunnel wall was reduced about 12%. That is, the stress of surrounding rock was released after boring, which could reduce the risk of rockburst.  
Figure 8 shows the effect of boreholes diameter on stress release rate. The stress release rate of surrounding rock increased linearly with the diameter of borehole. At the same time, the stress decreased in the range of 2 m around the tunnel wall, but the stress increased in the internal rock mass. It also proved that transferring the stress in the surrounding rock to the internal rock was the mechanism of the boreholes stress release method, and the surface rock wall with relatively low stress acted as a protective barrier.  
Figure 7: The change of maximum principal stress in surrounding rock at different locations: (**a**) Before boring holes; (**b**) after boring holes; (**c**) curves at the vault; (**d**) curves at the spandrel and (**e**) curves at the sidewall.  
As we could see from the Figure 9, the longer the drill hole length, the larger the stress release range, but the stress release rate of the tunnel wall did not increase significantly, which shows that increasing the boreholes length had little effect on rockburst prevention. The smaller the borehole spacing, the greater the stress release rate, which is in accordance with the general experience. However, as the spacing continues to decrease, the growth rate of stress release rate gradually slows down, which needs to be weighed based on the workload of boring.