## 3 Numerical Model and Calculation Scheme
### PFC Simulation Results Analysis
#### 3.3.2 Analysis of Overlying Strata Displacement Field Evolution  
In order to quantitatively analyze the subsidence law of roof strata, the subsidence data of rock strata are recorded. At the height of 40 m, 50 m, 57 m, 65 m, 76 m, and 85 m, respectively, set up six layers of monitoring points; each layer set up 14 measuring balls, namely from 0 to 150 m, every 10 m to establish a measuring ball, in order to analyze the movement of different heights of rock subsidence law. The Figure 19 is a schematic diagram of the measurement ball monitoring points set up inside the model. The following figures are the vertical movement displacement curve and subsidence cloud diagram of the roof strata when the working face advances at different distances. When the advancing distance of the working face is small, the height of the roof breaking and caving is relatively slow, so the following diagram begins to analyze when the basic roof of the working face advances 20 m.  
Figure 18: _Cont._  
Figure 18: Failure modes of overburden rock with different advancing distances. (**a**) Working face advance 10 m; (**b**)Working face advance 20 m; (**c**) Working face advance 30 m; (**d**) Working face advance 40 m; (**e**) Working face advance 50 m; (**f**) Working face advance 60 m; (**g**) Working face advance 70 m; (**h**) Working face advance 80 m; (**i**) Working face advance 90 m.  
Figure 20a-c show the movement displacement curve and sinking displacement nephogram of overlying strata when the working face advances 20 m, 30 m, and 40 m. It can be seen from the diagram that with the advancement of the working face, the original rock stress is gradually destroyed, and the stress field is redistributed, which is manifested by the regular movement and collapse of the roof strata. Due to the low strength of the immediate roof, it collapses with mining and fills the goaf, forming a 'U' shape. The subsidence of the main roof and its overlying strata is gradually small and basically unaffected by mining. Figure 20d show the movement deformation curve and subsidence displacement cloud diagram of overlying strata when the working face advances 50 m. It can be seen from the figure with the advance of the working face the amount of roof subsidence increased significantly. At 50 m above the goaf from the roof of the coal seam, the maximum vertical deformation reached about 0.9 m. It can be seen that the main roof above the working face broke and sank, and the shape of the 'U' curve formed was more obvious. The maximum subsidence occurred in the middle of the goaf, and the subsidence gradually decreased at a distance of 58 m from the roof of the coal seam. Figure 20e-h is the movement deformation curve and subsidence displacement diagram of overlying strata when the working face advances 50 m to 90 m. It can be found from the figure that as the working face continues to advance, the roof subsidence increases slowly, and the maximum vertical deformation is 4.45 m. The subsidence at 85 m from the roof of the coal seam is small which is basically not affected by mining. As the goaf is slowly compacted, the subsidence of the rock stratum is not increasing. Moreover, when the coal seam is mined, the overlying roof breaks and falls. With the gradual increase of the mining distance, the fracture of the rock stratum develops step by step. The movement and deformation of the overlying rock stratum are similar. The fractured rock mass fills the goaf, and the more it goes to the upper part of the coal seam, the smaller the subsidence is. The subsidence curve of each rock stratum shows an asymmetric shape. At the same time, the subsidence of each rock stratum is always smaller than the thickness of the coal seam mined from the working face due to the existence of bulking characteristics of rock mass failure.