## 4 Analysis of the Influence of Overlying Strata Movement on the Stability of Coal  
### Overlying Strata Movement Characteristics  
By calculating the subsidence curve of overlying strata in the goaf and the displacement vector of overlying strata along the goaf, the temporal and spatial evolution characteristics of the overlying strata movement were analyzed in-depth. Figure 4: Stress curves of coal along the goaf. Figure 5 shows the experimental model diagram of the working face after mining. Due to the movement of overlying strata caused by excavation, a caving zone and a fracture zone appeared in the overlying strata in the goaf, and the height of the two zones was 87 m, forming a \"hinged rock beam\" structure as a whole. With the subsidence of the overlying strata, the deformed strata in the upper part of goaf the were gradually compacted, forming a trapezoidal distribution compaction area. In the fracture zone, cracks were distributed vertically or obliquely in the rock, and there was a crack at the left end of the fracture zone that ran through the whole overlying rock, and the crack opening was obvious. There were unexploited coal seams on both sides of the goaf, and the overlying strata were divided into two areas, namely, the overlying strata in the goaf and the overlying strata in the coal seam area along the goaf. Figure 6 shows the subsidence curves of the overlying strata in the goaf. It can be seen that the overlying strata in the goaf formed a \"hinged rock beam\" structure after mining, and the fracture occurred at the end of the fracture zone. The subsidence of the overlying strata in the middle of the goaf was the largest, and the largest displacement was about 12 m. Under the combined action of the overburden and weight of the strata, the overburden strata in the goaf bent and sunk, leading to a large number of inclined fissures between the strata as well as the fracture of some strata. Figure 7 shows the vector displacement of the overlying strata along goaf. The red dotted areas in Figure 2a are the specific analysis areas. It can be seen from Figure 7 that at the time of marking point 1, the displacement of the strata above the coal along the goaf was mainly vertical, while at the time of marking point 2, the proportion of horizontal displacement obviously increased. Therefore, the movement of strata above the coal along the goaf can be divided into two stages  
Table 2 shows a comparative analysis of the u field (displacement in x-direction) and the v field (displacement in y-direction) of the overlying strata along the goaf at different times. Among them, the data in rows 1-5 represent the displacement calculation results of 5 characteristic points along the horizontal axis at different times, with the y-coordinate unchanged. From the data of rows 1-5, it can be found that in terms of horizontal displacement, the rock layer as a whole moved towards the goaf, and the farther away from the goaf, the greater the horizontal displacement. The horizontal displacement at marking point 2 was much greater than that at marking point 1. In terms of vertical displacement, the closer to the goaf, the greater the vertical displacement. The data in rows 6-12 represent the displacement calculation results of 7 characteristic points along the vertical axis at different times, with the x-coordinate unchanged. From the data of rows 6-12, it can be obtained that in terms of horizontal displacement, the overall direction  
Figure 6: Subsidence curves of overlying strata in the goaf. Figure 7: Vector displacement of the overlying strata along the goaf. (**a**) shows the time of marking point 1 and (**b**) shows the time of the corresponding marking point 2.  
was towards the goaf, the value increased with the increase of height, and the horizontal displacement at the time of marking point 2 was also much larger than that at the time of marking point 1. As for the vertical displacement, with the increase of the height, the vertical displacement value at y = 10-30 m was close at two moments.