## 4 Analysis of the Influence of Overlying Strata Movement on the Stability of Coal
### Deformation Evolution of Coal  
Figure 9 shows the displacement contour map of coal along goaf in the x-direction at the time of marking points 1 and 2. The analysis area is shown in the orange area in Figure 2b, with the x-axis to the right and the y-axis to the bottom, as positive. In the horizontal direction, coal moved away from the direction of the goaf, and the isolines on the left side were dense and small in magnitude, while the displacement on the right side was uniform but large in magnitude. The isolines in the upper left corner were dense and had a certain torsion angle, which was due to the bending moment effect on the lower coal seam caused by the rotation of the overlying strata. The horizontal distribution of the isolines at the upper boundary position of the coal seam indicated that there was an interlayer slip between the coal seam and the direct roof.  
Figure 10 shows the displacement contour map of coal along goaf in the y-direction at the time of marking points 1 and 2. In the vertical direction, coal moved downward as a whole due to compression. In the area near the goaf, the vertical displacement isoline of the coal was densely distributed, and the magnitude difference was obvious, while in the  
Figure 9: x-Direction displacement contour map of coal at different times (unit: cm). (**a**,**b**) show the displacement contour map of coal along goaf in the x-direction at the time of marking points 1 and 2.  
area far from the goat, the vertical displacement of the coal was close. This showed that the coal next to the goat entered a plastic state, which made the displacement occur more easily. With the subsidence of the overlying strata, the displacement isoline extended to an area far away from the goat, which indicated that the plastic area of the coal was expanding.  
In order to analyze the evolution process of the deformation field of the coal along goat in detail, a shear strain nephogram of the coal at different times was extracted and analyzed. As shown in Figure 11, at the time of marking point 1, a shear strain concentration zone appeared at the upper boundary of the coal, and the shear strain reached the maximum at x = 5 m. At the time of marking point 2, the shear strain variable value of the upper boundary further increased, and the x-range continuously extended, indicating that there was an obvious shear force between the coal and the direct roof. In addition, a new shear strain concentration area appeared at x = 10 m inside the coal. Combined with the y-direction displacement contour map of coal in Figure 10, it was found that this area was just at the boundary of whether the vertical deformation of coal was obvious or not. It can be seen that under the action of shear force, the micro-cracks in the coal at the boundary of the plastic zone were constantly expanding, and macro-cracks were gradually formed.  
The research showed that the vertical movement of the overlying strata along the goat in the first stage caused the vertical stress concentration of the coal, while the horizontal movement in the second stage exerted an obvious shearing effect on the coal. Under these two effects, the strength of the coal and rock masses along goat approaches the strength limit, deformation localization occurred, and the micro-cracks were further concentrated and merged in the area to form macro-cracks. When the macro-cracks expand and an  
Figure 10: y-Direction displacement contour map of coal at different times (unit: cm). (**a,b**) show the displacement contour map of coal along goat in the y-direction at the time of marking points 1 and 2.  
unstable expansion occurs, the sudden release of elastic energy will lead to dynamic disasters, such as rock burst.