## 4 Numerical Simulation Calculation  
### Numerical Simulation Analysis of Coal Column Stability in a Weakly Cemented Environment  
1. Numerical model establishment and roadway excavation design  
To verify whether it is feasible in working area 130,205 to leave a 5 m wide coal column in the ventilation return lane, a numerical model is created with the help of FLAC3D, and the deformation, stress distribution, and plastic zone range of the weakly cemented surrounding rock of the 5 m wide coal column are analyzed. In this way, the 5 m wide coal column is further justified.  
To analyze the geological conditions of working surface 130,205 in the Yangchangwan Coal Mine, four sets of numerical models of the ventilation return lane were first constructed. The four groups of models uniformly maintained a burial depth of 650 m, with the same support conditions, but the width of the coal column was 3 m, 5 m, 8 m, and 10 m in turn. After the model balance, the ventilation return lane was excavated, and the stability of the 3 m, 5 m, 8 m, and 10 m width coal pillars was analyzed from the vertical stress distribution, the plastic zone range, and the deformation of the weak cement surrounding rock.  
Support scheme  
The working surface roadway support conditions were as follows: a number of sets of rebar anchor rod supported the top, with an anchor rod combined with two sections of resin cartridges; the ends were supported by multiple sets of threaded steel rock bolts. The rock anchor rod used was model 20#-M22-2300 mm-BHRB500, with mesh specifications of 6000 \(\times\) 1000 mm, a steel strand anchor cable anchor, and 300 \(\times\) 300 \(\times\) 16 mm arch plates, filled with four sections of \(\Phi 23\times 700\) mm resin powder roll (including two with ultrafast roll and two with fast roll).  
Simulation scenario  
The model is based on the actual mining conditions. The burial depth is 650 m; 100 m is taken along the direction of the working surface tendency, 200 m is taken along the direction of the working surface, the inclination angle is 5\({}^{\circ}\), and the coal seam endowment and rock formation structure are established according to the actual geological conditions. The size of the final numerical calculation model is 400 m \(\times\) 100 m \(\times\) 215 m, and the entire model is divided into 122,039 units and 132,902 nodes, as shown in Figure 6.  
Both the X and Y boundaries of the model apply horizontal displacement constraints, and the bottom boundary of the model applies vertical (Z-direction) displacement constraints. The upper part of the model is a free boundary, the stress boundary condition is applied, the self-weight of the upper rock layer is simulated, and the simulation calculates the application of vertical stress \(\sigma_{x}\) = 13.75. The Mohr-Coulomb criterion was selected for the model failure criterion, the stress softening model for coal seam selection, and the Mohr-Coulomb criterion was also selected for other stratigraphic failure criteria. The weak cement formation in the simulation scheme is taken from borehole number 1711 at the coal mine site, and the physical and mechanical parameters of the related rock formation are shown in Table 2.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Numbering**} & **Rock Name** & **Thickness** & \multirow{2}{*}{**Depth [m]**} & **Compressive Strength** & **Tensile Strength** & **Elastic Modulus** & **Poisson’s Ratio** & **Cohesion** & **Unit Weight** \\  & & & & **[MPa]** & **[MPa]** & **[MPa]** & **[GPa]** & **[MPa]** & **[MPa]** & **[kg/m3]** \\ \hline M10 & Silstone & 14.68 & 474.90 & 42.2 & 4.22 & 13.6 & 0.24 & 4.66 & 2.35 \\ M9 & Medium & 22.40 &