# Research on the Reasonable Width of Coal Pillar Driving along Goal under Thick Hard Roof
## 4 Results and Discussion
### Numerical Simulation Analysis of Coal Pillar Width
#### 4.2.2 Characteristics of the Displacement Distribution along Goal  
Through the statistical analysis of the vertical displacement and horizontal displacement data of the roadway, the maximum values of the roof subsidence and floor heave, as well as the maximum values of the coal pillar and solid coal slope moving close to the roadway were obtained, the amount of movement of the coal pillar towards the roadway is called displacement of coal pillar, and the amount of movement of the solid coal side towards the roadway is called displacement of solid coal slope, and the deformation of the roadway perimeter rock under different widths of coal pillars is shown as follows:  
It can be analyzed according to the Figure 10 and Table 6:  
Figure 10: Deformation of roadway under different widths of coal pillars.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Width of Coal** & \multicolumn{2}{c}{**Peak Vertical Stress/MPa**} & \multicolumn{2}{c}{**Stress Concentration Factor**} \\
**Pillar/m** & **Coal Pillar** & **Solid Coal Slope** & **Coal Pillar** & **Solid Coal Slope** \\ \hline
7 & 23.04 & 18.74 & 3.69 & 3.00 \\
8 & 20.05 & 17.14 & 3.21 & 2.74 \\
9 & 19.98 & 16.10 & 3.20 & 2.58 \\
10 & 19.34 & 16.07 & 3.09 & 2.57 \\
11 & 19.20 & 15.65 & 3.07 & 2.50 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Peak vertical stress and stress concentration factor for different coal pillar widths.  
(1) Under the condition of different coal pillar widths, the deformation of the roadway shows obvious asymmetry, in which the value of roof subsidence is much larger than the value of floor heave, and the deformation at the coal pillar is larger than that the solid coal slope; the proportion of roof subsidence in roof and floor approach under different coal pillar widths (7 m to 11 m) is 69.5%, 69.4%, 67.5%, 67.8%, and 66.9%, with the increase of coal pillar width, the proportion of roof subsidence in roof and floor approach decrease little, and the change of subsidence under each coal pillar width after 8 m is very small. The proportion of the approach of two sides under different coal pillar widths (7 m to 11 m) is 70.7%, 66.5%, 64.4%, 65.2%, and 65%, and the proportion decreases with the increase of the width of the coal pillar, which indicates that the deformation of the roadway is mainly reflected in the roof and coal pillar;  
(2) An 8 m and 9 m wide coal pillar is an important turning point, compared with the displacement situation when the width of a coal pillar is 7 m and 8 m, the roof and floor of the roadway under 8 m are reduced by 26.14 mm, the two sides are reduced by 48.45 mm, and the deformation of the roadway surrounding rock and the trend of change is larger; after the coal pillar is above 9 m, the deformation of the roadway surrounding rock gradually tends to be stable and the trend of change is relatively smooth, when the width is 9 m, compared with 10 m, the roof and floor are reduced by only 7.67 mm and the two sides are reduced by 23.27 mm. It can be seen that when the width of the coal pillar is 8 m or 9 m, it is more favorable to the stability control of the roadway peripheral rock displacement.  
In summary, in addition to ensuring the use of the roadway, the coal pillar needs to have a certain elastic area to facilitate the anchor solid body in the anchor cable for force. It should be avoided waste of resources caused by the width of the coal pillar. Therefore, after comprehensively analyzing the stress distribution and displacement distribution characteristics of the roadway along goat, the width of the coal pillar is selected to be 8.0 m.