## 4 Numerical Simulation Analysis of Knife Handle Working Face
### Materials and Methods  
#### 4.1.1 Building the Numerical Model  
The FLAC\({}^{\text{3D}}\) 5.0 numerical simulation analysis software has the characteristics of continuity, which is suitable for the analysis of stress and elastic energy change characteristics in mine production and is widely used in mine mining. Through the analysis of finite element numerical simulation software, in order to fully understand the stress distribution and energy evolution characteristics of the surrounding rock in the knife handle working face, this section is based on the geological conditions of Kuangou Coal Mine and the mining layout of the working face, and builds a numerical analysis model based on the comprehensive histogram of the borehole for research.  
The 1010206 working face of Kuangou Coal Mine was selected as the research object. The physical and mechanical parameters of the coal and rock mass used in FLAC\({}^{\text{3D}}\) are shown in Table 1. In the process of simulation, additional parameters should be added to the simulated rock strata in the numerical model according to the parameters of each rock stratum in Table 1, so as to realize the reproduction of the field geological conditions [29; 30; 31; 32]. The borehole comprehensive histogram is shown in Figure 4.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**Serial number** & **Rock Character** & **Density kg/m\({}^{\text{5}}\)** & **Cohesion MPa** & **Internal Friction Angle** & **Tensile Strength** & **Modulus of Elasticity** \\ \hline
1 & Coarse grained sandstone & 2618 & 6.38 & 28.86 & 3.17 & 10.33 \\
2 & Sandy mudstone & 2517 & 4.48 & 30.41 & 5.37 & 4.33 \\
3 & Mudstone & 2543 & 3.47 & 21.32 & 3.55 & 7.57 \\
4 & Fine-grained sandstone & 2635 & 6.49 & 35.39 & 5.04 & 13.70 \\
5 & B4-1 coal seam & 1304 & 2.81 & 37.49 & 2.02 & 7.49 \\
6 & B2 coal seam & 1640 & 2.95 & 28.50 & 2.15 & 4.32 \\ \hline \end{tabular}
\end{table}
Table 1: Physical and mechanical parameters of numerical simulation.  
Figure 4: Borehole comprehensive histogram.  
The designed numerical model is 600 m long, 460 m wide, and 250 m high, as shown in Figure 5. The strata designed by numerical simulation are 16 layers; the coal seams are the B2 coal seam and B4-1 coal seam; the average dip angle is 14\({}^{\circ}\). The simulated thickness of the B2 coal seam is 9.5 m and of the B4-1 coal seam is 3 m; the designed initial gravity acceleration is 9.8 m/s\({}^{2}\). The Mohr-Coulomb model is adopted in the model. The initial gradient stress is applied to the top of the model. In the horizontal direction, except for the undefined boundary at the top of the model, the allowable deformation of the other five boundary surfaces is 0.2 m, and the bottom and lateral displacement of the model are limited.  
The horizontal stress applied to both sides of the model is 13.8 MPa. Since the model is not simulated to the surface, the top of the model is 310 m away from the surface. According to the Kinnick theory [33], the vertical stress applied to the top of the model is calculated as:  
\[\sigma_{z}=\gamma\cdot H=2500\ \mathrm{kg/m^{3}\times 310\ m}=7.75\ \mathrm{MPa} \tag{13}\]  
A vertical load of 7.75 MPa is applied to the top of the model.