# Stability Assessment of Gob Side Entry at the Steeply Inclined Mining Face
## 2 Materials and Methods
### Numerical Simulation  
Numerical simulation is utilized to assess the stress and deformation characteristics of the support system. The initial design of coal pillar are 3 m, 4 m, 5 m, and 6 m in width. The stability of the roadway will be quantitatively assessed using Flac3D to ascertain the optimal pillar width. Flac3D Version 6.0 is a three-dimensional numerical simulation software,  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Point** & **Elevation/m** & **Location** & **Direction/\({}^{\circ}\)** & **Dipl/\({}^{\circ}\)** \\ \hline
1\# & \(-650\) & Air tunnel for the \(-650\) m phase & 120 & 4.5 \\
2\# & \(-650\) & Air tunnel for the \(-650\) m phase & 113 & 5 \\
3\# & 920 & Belt tunnel for the third mining area & 16 & 4 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Drilling parameters of in situ stress measurement.  
suitable for the analysis of the mechanical behavior of rocks and structures. It is based on the finite difference method and is suitable to simulate the stress and deformation of complex geological bodies. The Flac3D is particularly suitable for the analysis of surrounding rock stability and supporting structure. The size of this model is 708,060 m, as shown in Figure 2. The numerical model consists of 138,710 grid points, 799,586 zones, and 28 zone groups. The grid near the roadway and the coal post was 0.4 m. The size of the model boundary grid was 2.0 m. The model top was subjected to a gravitational load of 22 MPa, with fixed normal displacement at other boundaries. The studied roadway was close to the ground stress measurement point of #3, so the initial ground stress was set according to its value. Three main stress vectors are included in the stress solution calculation results. During the numerical simulation process, the numerical value and direction of the maximum, intermediate, or minimum stress was separately set by the \"zone initialize stress-principle\" keyword.  
In the roadway support simulation, the Mohr-Coulomb criterion can be used to analyze the stress mechanism of supporting structures such as anchors and shotcrete. The M-C criterion has the advantages of a strong foundation and easily accessible parameters in the roadway stability simulation. One can conduct a sensitivity analysis by adjusting cohesion and friction to assess their effects on the extent of the plastic zone and the supporting effect. By adjusting the length, diameter, row distance, and other parameters of the bolt, the control function of the roof and roadway deformation is quantitatively evaluated so as to provide data support for the support design. As illustrated in Figure 3, from point A to B,  
\[f^{s}=-\sigma_{1}+\sigma_{3}\frac{1+\sin\varphi}{1-\sin\varphi}-2c\sqrt{\frac{ 1+\sin\varphi}{1-\sin\varphi}} \tag{1}\]  
and from B to C by a tension failure,  
\[f^{t}=\sigma_{3}-\sigma^{t} \tag{2}\]  
where \(\sigma_{1}\) and \(\sigma_{3}\) are the maximum and minimum principle stresses, respectively, MPa; \(\sigma^{t}\) is the tensile strength, MPa; \(c\) is cohesion, MPa; and \(\phi\) is friction, \({}^{\circ}\).  
Figure 2: Numerical model. (**a**) Top view. (**b**) Front view. (**c**) Perspective view.