## 2 Stability Classification of Goafs Based on CMS Measurement and Numerical Simulation
### Numerical Simulation Analysis of Goaf Stability  
According to the basic 3D model obtained by 3 DMine, the data files of the basic model are operated and converted to obtain a mesh model that can be numerically simulated using FLAC3D. The model is assigned values with the mechanical parameters obtained onsite for simulation calculation. The surrounding rock of Shirengou iron ore body is simple, and the top and bottom of the goat areas are biotite hornblende plagioclase gneiss and hornblende plagioclase gneiss. The specific physical and mechanical parameters of the rocks in the numerical simulation are shown in Table 2.  
Elastic models are constructed in FLAC3D to simulate the displacement, stress, and distribution of the plastic zone of each goat under various conditions. Goaf CSJ-2# is selected as an example in Table 2. Numerical simulation diagrams of the displacement, plastic zone, and the minimum and maximum principal stress of goat CSJ-2# are presented in Figures 3-6. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \multirow{2}{*}{**Rock Name**} & \multirow{2}{*}{\begin{tabular}{c} **Bulk Density** \\ **g/cm3** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Compressive** \\ **Strength MPa** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Tensile** \\ **Strength MPa** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Cohesion C** \\ **MPa** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Angle of** \\ **Internal** \\ **Friction \(\varphi\)** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Modulus of** \\ **Elasticity 104** \\ **MPa** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Poisson’s** \\ **Ratio** \\ \end{tabular} } \\ \hline M\({}_{1}\) orebody & 3.58 & 99.44 & 11.95 & 2.183 & 48.36 & 8.03 & 0.21 \\ M\({}_{2}\) orebody & 3.46 & 130.77 & 10.52 & 2.367 & 53.33 & 7.59 & 0.20 \\ Biotite & & & & & & \\ hornblende & 2.74 & 141.58 & 14.37 & 2.754 & 55.08 & 6.98 & 0.26 \\ plagioclase & & & & & & & \\ gneiss & & & & & & & \\ \hline \end{tabular}
\end{table} 
Table 2: Experimental data table of physical and mechanical parameters of surrounding rock. Figure 2: Three-dimensional solid model of goat areas. Figure 4: CSI-2\(\#\) goat plastic zone distribution. Figure 5: Minimum principal stress in goat CSJ-2\(\#\). Figure 6: Maximum principal stress in goat CSJ-2\(\#\). Figure 3 is the goaf displacement cloud map, which shows that the maximum displacement is in the middle part of the goaf on the upper wall, with a size of 4.2 cm. Figure 4 shows the layout of plastic differentiation in the goaf. A plastic zone exists in the surrounding rock of the goaf and at the bottom of the goaf upper wall. Figures 5 and 6 show the cloud map of the maximum and minimum principal stresses of the goaf. The minimum principal stress at the roof position of goaf CSJ-2# is 0.25 MPa, which is the tensile stress. The maximum principal stress is 7.74 MPa in the lower part of the left goaf wall, and the maximum principal stress of the roof is 7.00 MPa. According to the numerical simulation analysis results of the goaf areas in Shirengou, the maximum displacement of the goaf roof, the maximum lateral displacement of the goaf side wall or pillar, and the minimum principal stress of the goaf roof are measured, and the final statistical results are shown in Figure 7.  
According to the analysis in Figure 7, the displacement of the goaf roof and side wall in the slope area of the measure well is large because the goaf distribution in this area is very dense, forming a group effect, and they influence each other to increase their respective displacements. In addition, the roof displacement of goaf with a larger span is larger. Moreover, the goaf roof tensile stress is concentrated in the slope of the measure well, which indicates that the goaf group effect has a major influence on goaf stability. The lateral displacement of the goaf side wall and pillar is small, which suggests that the pillar or side wall is stable.