## 4 Stress Distribution Law in Island Working Face
### Numerical Simulation Results Analysis
#### 4.2.5 The Stress Distribution Influenced by Coal Pillar Width  
When considering different coal pillar widths, we conducted simulations and analyzed the feature distribution of the stress on the island working face, as shown in Figure 16a. Figure 15: (**a**) Stress distribution features of island working face under different coal seam thicknesses; (**b**) the stress variation law and plastic zone evolution characteristics of coal pillar under different coal seam thicknesses; (**c**) fitting curve of peak stress of entity coal and coal seam thickness. The simulation results indicate that as the width of the coal pillar increases, the plastic zone range proportion of the surrounding coal pillar in the roadway decreases. This suggests that the bearing capacity of the coal pillars increases with wider widths, allowing them to effectively disperse and withstand higher levels of stress. Additionally, the peak stress of the coal pillar increases gradually, while the peak stress of the entity coal decreases gradually. Figure 16b shows in detail the variation law of the coal pillar stress and the evolution characteristics of the plastic zone under different coal pillar width conditions. It can be clearly seen from the figure that when the width of the coal pillars is 10 m, 20 m, 30 m, and 40 m, respectively, the total number of grids in the plastic zone proportion of the coal pillars shows a decreasing trend, which is 94.38%, 84.38%, 56.25%, and 37.66%, respectively. At the same time, the peak stress of the corresponding coal pillar gradually increases from 6.5 Mpa to 34.3 Mpa, showing the characteristics of increasing stress. It is particularly noteworthy that under the condition that the width of the coal pillar is 10 m, the coal pillar has been completely destroyed, and the plastic zone is almost all over the whole coal pillar. However, although the coal pillar has suffered such serious damage, it can still withstand a stress of up to 6.5 Mpa. When the coal pillar width is 30 m and 40 m, the plastic zone of the coal pillar accounts for 18.59% of the gap, but the stress is relatively close, only 0.8 Mpa. This shows that a too-small coal pillar width will lead to instability and failure of the coal pillar, but it can still bear some stress. With the increase of coal pillar width, the smaller the coal pillar damage is, the more complete the coal pillar is, but the peak stress difference is not large. The variation law of peak stress of entity coal under different coal pillar width conditions is shown in Figure 16c. The peak stress of the entity coal decreases with the increase of coal pillar width, and the specific values are 38.5 Mpa, 34 Mpa, 32.2 Mpa, and 29.5 Mpa, respectively. An increase of the width of the coal pillar can indeed effectively improve the bearing capacity of the coal pillar so that it can withstand greater stress. Therefore, with the increase of the coal pillar width, the stress of the entity coal is relatively small. However, when the coal pillar width continues to increase, there is not a significant change in the peak stress experienced by the coal pillar. This shows that when designing the island working face, it is very important to select a reasonable coal pillar width, which can effectively prevent stress concentration and avoid excessive waste of coal. By scientifically optimizing the width of coal pillars, we can ensure the safety of mining and achieve efficient use of resources. To analyze the peak stress of the entity coal, the SPSS statistical software (27.0) of IBM (Armonk, NY, USA) was used to analyze and fit the peak stress of the entity coal and several key influencing factors, including the length of the gob, the length of the working face, the thickness of the coal seam, the width of the coal pillar, and the buried depth.