## 5 Stability Analysis on the Stope Below the Goal
### Numerical Modeling  
Numerical simulation has become an indispensable research tool in the field of geotechnical engineering, successfully solving important scientific and technological problems. In this study, the stress, displacement, and failure of surrounding rock during the mining of the ore body were explored with the aid of FLAC3D 6.0. FLAC3D 6.0, an analysis program based on the three-dimensional explicit finite difference method, has become one of the most important pieces of numerical simulation software in geotechnical analysis. The ore body model was built by stretching the ore body cross-sectional shape (Figure 1) along the strike for 60 m. Given that the ore occurrence changes insignificantly along the strike, the elevation changes in the ore body, the roof, and the floor in the stretching direction were not considered. Meanwhile, to reduce the influence of the mining-induced boundary effect, 20 m was added on both sides beyond the range of mining activities, and the finalized numerical model size was 179 m \(\times\) 60 m \(\times\) 80 m (Figure 15). The  
Figure 14: Mechanical tests on the GCB at the optimal ratio. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**UCS/MPa** & **Elastic Modulus/GPa** & **Poisson’ Ratio** & **Cohesion/MPa** & **Internal Frictional Angle/\({}^{\circ}\)** & **Tensile Strength/MPa** \\ \hline
1.09 & 0.081 & 0.25 & 0.21 & 36 & 0.198 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Mechanical parameters of the GCB at the optimal ratio. Mohr-Coulomb model was chosen as the constitutive model of the ore-rock body for this numerical simulation. The instability criterion used in the Mohr-Coulomb model includes the tensile intercept. As shown in Figure 16, the segment from Point A to Point B is defined based on the Mohr-Coulomb instability strength \(f^{s}=0\), and that from Point B to Point C is defined based on the tensile instability criterion \(f^{t}=0\) from. In addition, by introducing the function \(h(\sigma_{1},\sigma_{3})=0\), the Mohr-Coulomb model is defined as the diagonal line between \(f^{s}=0\) and \(f^{t}=0\) on the \((\sigma_{1},\sigma_{3})\) plane. If the stress point is located within Domain 1, the point is in a shear yield state, and if the stress point falls within Domain 2, the point is in a tensile yield state. Based on the experimental results and existing studies [33; 34], the mechanical parameters of the ore-rock body and the GCB in this simulation were determined (Table 6). \[f^{s}=\sigma_{1}-\sigma_{3}\frac{1+\sin(\varphi)}{1-\sin(\varphi)}+2c\sqrt{ \frac{1+\sin(\varphi)}{1-\sin(\varphi)}}\]  
\[f^{t}=\sigma_{3}-\sigma^{t}\]  
\[h=\sigma_{3}-\sigma t+\alpha^{\rm P}(\sigma_{1}-\sigma^{\rm P})\]  
where \(\varphi\) is the internal friction angle; \(C\) is the cohesion; \(\sigma^{t}\) is the tensile strength; \(\alpha^{\rm P}\) and \(\sigma^{\rm P}\) are constants. Figure 16: Mohr–Coulomb model. Figure 15: Numerical simulation model. The boundary conditions of the numerical model are as follows: (I) horizontal displacement constraints in the Y-direction are set on the front and rear sides of the model boundary; (II) horizontal displacement constraints in the X-direction are set on the left and right sides of the model; (III) complete displacement constraints the X-, Y-, and Z-directions are set at the bottom of the model; and (IV) in view of the actual mining geologic conditions, a vertical stress with a magnitude of 3.4 MPa is applied at the top of the model. To accurately reflect the actual engineering situation, the numerical simulation was conducted in close combination with the specific engineering background. Firstly, the ore body extracted above the 459 m level was assigned to the null model to simulate the goaf formed by open-stope mining. Subsequently, according to the theoretically calculated width of the GCB (29 m), the part of the goaf above the 459 m level was filled with slurry.