In order to directly reflect the response relationship between mining and surface subsidence, taking the advancing distance of working face as the time axis, the whole process change of 38 surface monitoring points from K1 to K38 is analyzed. The surface subsidence curve is shown in Fig. 2.

Figure 2 shows that the subsidence curve of the working face is L-shaped, and the surface subsidence change is mainly concentrated within the advancing distance of 400 m. After that, the surface subsidence no longer increases with the change of mining size. The subsidence values of the surface in different areas of the mining surface are different. The maximum subsidence is the K19 curve. The measuring point is located within the goaf, 80 m away from the open-off cut, the subsidence is 6.20 m, and the subsidence coefficient is 0.72. The K15 curve is located directly above the cutting eye, and its subsidence is 1.85 m, which is about 0.3 of the maximum subsidence value, less than half of the maximum subsidence value. The surface subsidence outside the open-off cut decreases with the increase of distance. The maximum subsidence of 80 m (K11) outside the open-off cut is 0.09 m, which means that the surface subsidence is less than 10 cm, indicating that the mining influence is not obvious. In order to vividly express the relationship between the progress degree of the advance, the ratio of the advance distance to the buried depth of 210 m and the face length of 299.2 m is used, that is, 400 m/210 m ≈ 1.9,400 m /299.2 m ≈ 1.34. It can be judged that the 12401 working face has reached the full mining state when the advance degree (ratio) is 1.34 ~ 1.9.

## 3.1 Mining subsidence and residual subsidence

The stability of surface subsidence requires a long process, especially the residual subsidence usually reaches the final stable state after N ( buried depth /100m ) years after mining. In order to visually display the ratio relationship between mining subsidence and residual subsidence, the subsidence at two time nodes of 300 m advance on May 30, 2018 (advance degree 1.4 ) and after stopping mining on August 12, 2019 (advance degree 25) was selected for comparison, and the ratio analysis of surface subsidence in the range of 200 m before and after cutting was carried out, as shown in Fig. 3.

When the advancing distance of 12401 working face is 300 m, the surface subsidence in the range of -80 m ~ 100 m on the surface nearby open-off cut occupies more than 95% of the final subsidence value. With the increase of the distance from the open-off cut, the proportion of mining subsidence decreases, but still occupies more than 80%. It can be seen that the surface of the open-off cut has basically reached the state of full mining when fully mined, and the proportion of mining subsidence accounts for 80% ~ 95%. The maximum subsidence threshold boundary can be set to 0.9, that is, the subsidence reaches 90% of the maximum subsidence value as full mining or full subsidence.

Generally speaking, the surface of mining boundary is characterized by S-shaped subsidence curve, which is mainly manifested as discontinuous deformation zone and uniform subsidence zone (Liu et al 2019). The inflection point controls the basic form of subsidence curve. The discontinuous deformation zone has the greatest influence on surface vegetation. In order to identify the boundary of discontinuous and continuous subsidence, the second derivative of S-shaped curve is equal to 0, that is, the inflection point position represents the boundary of discontinuous deformation of surface.

## 3.2 Trajectory analysis of advancing direction inflection point

The surface subsidence has reached the full mining state when the advance distance is 300 m. In order to fully express the change of the whole process, the curve shape dynamic change characteristics of the interval process from the working face open-off cut to the advance of 800 m (advance degree 3.8 ) are selected, and the inflection point trajectory is shown in Fig. 4.

In Fig. 4, B is the length of the working face, M is the mining height, H is the buried depth, and h is the thickness of the loose layer.

When the open-off cut (10m) is equivalent to the advance distance of 10m, the position of the inflection point is approximately equal to zero, indicating that the surface has almost no effect. With the increase of mining distance, the surface appearance began to appear, and the inflection point quickly shifted outside the mining boundary. When the advancing distance was 80 m, the position of the inflection point reached the peak, which was 60 m outside the open-off cut, indicating that the surface subsidence curve within the advancing distance of 0–80 m was basically a monotonically increasing state, and the shape did not change significantly. With the further increase of the advance distance, the inflection point begins to gradually shift from the outside of the cut to the inside of the cut, indicating that the discontinuous deformation of the surface has occurred after the advance distance of 80, and the shape of the subsidence curve has also changed. The inflection point position is zero when the advance distance is 100 m, and then finally stabilizes in the range of 25m ~ 28m in the goaf. The trajectory path of the inflection point can be simplified as 0m→-60m→0m→25m→28m.

Therefore, it can be judged that the main influence boundary of the 12401 working face to the surface is 60 m outside the open-off cut and 28 m inside the open-off cut.