# Numerical Study on the Pressure Relief Characteristics of a Large-Diameter Borehole
## 3 Materials and Methods  
### Build Numerical Model  
FLAC3D software can effectively simulate the stress and plasticity characteristics of materials such as rock and soil. Therefore, FLAC3D numerical simulation software was selected by the authors of this paper for simulating the influences of different drilling parameters on the pressure relief effect to achieve good simulation results.  
After the excavation of the upper section of the W1123 working face in the B2 coal seam of Kuangou coal mine, the internal stress of the roadway side was redistributed, the peak value of the lateral abutment pressure of the roadway was increased, and the peak value of the stress was close to the coal wall; thus, it was easy to accumulate high energy and impact. Therefore, we obtained the established numerical model as shown in Figure 3, the model being 40 m in length, 12 m in width, and 32 m in height.  
The vertical buried depth of the W1123 working face in the B2 coal seam is \(H\) = 400 m, and the vertical stress s basically equal to the weight of overlying strata. After measuring the average bulk density of rock mass \(\gamma\) = 2500 kg/m\({}^{3}\), taking into account the mining influence and tectonic influence, the stress concentration coefficient was identified as 1.3, and the vertical stress on the B2 coal seam was \(\sigma_{\rm z}\) = 1.3\(\gamma H\), calculated to obtain \(\sigma_{\rm z}\) = 13 MPa, and the lateral pressure coefficient was \(\lambda\) = 0.8, calculated to obtain \(\sigma_{\rm x}\) = \(\sigma_{\rm y}\) = 0.8 \(\sigma_{\rm z}\) = 10.4 MPa. The material parameters are shown in Table 1.  
Because coal is an elastic-plastic material, the Mohr-Coulomb criterion for the ideal elastoplastic body is used to judge the deformation and failure of rock.  
\[f_{\rm s}=\sigma_{1}-\sigma_{3}\frac{1+\sin\varphi}{1-\sin\varphi}-2c\sqrt{ \frac{1+\sin\varphi}{1-\sin\varphi}} \tag{1}\]  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Name**} & **Density** & **Modulus of** & **Shear** & **Bulk** & **Poisson’s** & **Cohesive** & **Internal** & **Tensile** \\  & **(kg/m\({}^{3}\))** & **Elasticity** & **Modulus** & **Modulus** & **Ratio** & **Force (MPa)** & **Article** & **Article (\({}^{\circ}\))** & **Strength** \\  & **(GPa)** & **(GPa)** & **(GPa)** & **(GPa)** & **Ratio** & **Angle (\({}^{\circ}\))** & **(MPa)** \\ \hline Sandy & 2467 & 21.26 & 8.50 & 14.17 & 0.25 & 16.22 & 31.74 & 2.33 \\ conglomerate & 2597 & 9.80 & 3.83 & 7.10 & 0.28 & 4.39 & 30.41 & 2.28 \\ b2 coal & 1640 & 4.93 & 1.91 & 3.91 & 0.29 & 4.90 & 31.26 & 2.21 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Physical and mechanical parameters of the roof and coal seam.  
Figure 3: Numerical calculation model.  
In this formula, \(\sigma_{1}\) and \(\sigma_{3}\) are the maximum and minimum principal stress, respectively, \(c\) is the adhesive force, and \(\varphi\) is the friction angle. When \(f_{5}>0\), the material will undergo shear failure and strain softening. Under normal stress conditions, the tensile strength of the rock mass is very low; thus, one can judge whether the rock mass has tensile failure according to the tensile strength criterion (\(\sigma_{3}\geq\sigma_{\rm T}\)).