## 4 Safety Analysis of Waterproof Coal Pillar Width in the Working Faces
### Numerical Simulation of the Developmental Height of the Water-Conducting Fracture Zone
#### 4.3.3 Numerical Simulation Results  
An analysis was performed on the development height of the water conducting fracture zone and to determine whether the fracture zone above the coal pillar was connected in the 2303 and 2305 work faces. Therefore, the cross-section was obtained when the working face advanced 200 m to analyze the vertical stress distribution of the overlying rock above the face and the development of the plastic zone.  
The analysis of the vertical stress distribution of overlying rock is shown in Figures 9-11.  
The vertical stress showed the same change in law under three kinds of coal pillar widths. After the coal seam is at the end of the mining stages, the roof strata above the working face goal ruptures gradually under the mine pressure, and when the roof rock layer is not enough to support the pressure of the overlying rock, the roof rock layer will collapse, and the overlying rock stress in the goal will be released to form a low-pressure area.  
The vertical stress of the overlying rock above the goal is symmetrically distributed and forms an arch. The vertical stress is mainly concentrated on both sides of the goaf, the side of the coal pillar, and the side of the coal seam.  
When the widths of the coal pillar are 52 m, 54 m, and 60 m, the peak stresses in the coal pillar near the 2303 mining goal are 61.1 MPa, 61.4 MPa, and 61.5 MPa, respectively, with an increase in the width of the coal pillar. The peak stress is stabilized at about 61 MPa; the peak stresses in the coal pillar at the side of the mining hollow area near the 2305 working face are 59.5 MPa, 59.3 MPa, and 57.1 MPa.  
Figure 8: Initial computational model.  
* 2. The analysis of the plastic zone distribution of the overlying rock is shown in Figures 12-14.  
Figure 11: Vertical stress distribution of overburden rock at 60 m width of the coal pillar (Unit: Pa).  
Figure 9: Vertical stress distribution of overburden rock at 52 m width of the coal pillar (Unit: Pa).  
Figure 14: Plastic zone distribution of overburden rock at 60 m width of coal the pillar.  
Figure 12: Plastic zone distribution of overburden rock at 52 m width of the coal pillar.  
Figure 13: Plastic zone distribution of overburden rock at 54 m width of the coal pillar.  
After the mining stabilization of the 2303 and 2305 working faces, the damage mode of the overlying rock on the roof plate in the goat is shear damage and tensile damage, and the development stops when the range of the plastic zone reaches a certain distance on both sides of the goat.  
Under three kinds of coal pillar widths, the maximum development height of the plastic damage zone in the 2303 workforce is 95 m after the stabilization of the mining area, and the maximum development height of the plastic damage zone in the 2305 workforce is 135 m, which is due to the different development heights of the water-conducting fracture zone caused by different mining heights of the two working faces.  
In the transverse direction of the plastic damage range of the overlying rock above the goat, when the widths of the coal pillar are 52 m, 54 m, and 60 m, there are 6 m, 9 m, and 15 m of elastic state rock above the coal pillar, respectively; thus, the plastic zone above the goat of the two adjacent working faces of 2303 and 2305 has not been connected, which can effectively prevent the accumulation of water in the 2303 goat.  
In summary, through the analysis of overburden stress and plastic zone after the mining of the 2303 and 2305 working faces, the development heights of the water-conducting fracture zone after work face mining were 95 m and 135 m respectively, and there were elastic zones of 6 m, 9 m, and 15 m above the middle coal pillar of the two goat zones. Therefore, it can be seen from the numerical simulation that the Cuijiagou Coal Mine can meet the safety production of the working face by retaining 52 m, 54 m, and 60 m coal pillars.