**4. Numerical Simulation of Dynamic Movement of Overlying Strata**

#### *4.1. Establishment of Rock Strata Movement Numerical Model*

The strike section of the panel is selected as the calculation object in the numerical model. The dimensions of the model are 350 × 1000 m, the mining distance is 440 m, and the coal pillars of the numerical model are 275 m and 285 m, which can ensure that the left and right boundaries of the model are outside of the range of the influence angle of strata movement and avoid the influence of boundary conditions on the movement caused by the excavation. As for the boundary conditions of the model, the left and right sides of the model have roller constraints, the bottom has full constraints, and the top has free boundary conditions. The input parameters of the numerical model rock mass are repeatedly checked by adjusting the geological strength index (GSI) [32–34], in order that the numerical model can truly reflect the strata movement. These parameters are obtained by the inversion method. The physical and mechanical parameters of coal and rock mass and the parameters related to Hoek-Brown strength criterion are shown in Table 1.


**Table 1.** Mechanical property parameter of rock and coal in numerical model.

#### *4.2. Verification of the Numerical Model of Strata Movement*

The rationality of the numerical model directly determines the accuracy of the numerical simulation analysis. In this paper, the accuracy of the numerical model is assessed through the comparative analysis of the survey data of the surface movement survey line, the theoretical calculation value of the abutment pressure, and the theoretical calculation value of the stress-recovery distance in the goaf with the numerical simulation.

(1) The uniaxial compressive strength of intact rock sample σci is 25 MPa, the GSI is 30, and the coal mechanical parameters are obtained by Willson's theoretical formula [35].

As shown in Figure 6, the peak abutment pressure of the coal seam is 17.50 MPa, the stress concentration factor *K* is 2.49, the distance between the peak abutment pressure and the coal wall is 16.21 m, and the influence distance before the peak abutment pressure is 65.86 m. According to the numerical simulation, the abutment pressure peak value is located 15 m near the front of the coal wall, and its peak value is 18.52 MPa. The errors of peak stress value and peak position are 5.51% and 8.06%, respectively. Moreover, according to the fact that the ground pressure of the headentry and tailentry of the panel is apparent in the area of 14~17 m, the correctness of the numerical model for the calculation value of abutment pressure is verified.

**Figure 6.** The distribution of abutment pressure ahead of the working face.

(2) According to the numerical model stress monitoring in the goaf, it is found that the stress in the goaf at 101.5 m behind the coal wall reaches the original rock stress, and the corresponding stress-recovery distance in the goaf is 101.5 m (i.e., 0.6 times the mining depth), conforming to the laws of domestic and foreign experience, which is the mining depth of 0.3~0.4 times the stress-recovery distance in the goaf.

(3) The parameters of the surface probability integral method are obtained based on research on the strike survey line over the panel: The subsidence coefficient *q* = 0.80, the tangent of influence angle tan *β* = 1.88, and the offset of inflection point is 0.15 *H*, where H is the average depth of coal seam.

The subsidence data of the surface are extracted with the mining distance of 440 m, and the numerical model subsidence curve is obtained and used for comparison with the data calculated by the probability integral method. The subsidence curves of the measured data and numerical model are shown in Figure 7. It can be surveyed that the subsidence coefficient *q* is 0.80 with supercritical mining. The maximum subsidence obtained by the numerical model is 5.78 m, i.e., the subsidence coefficient is 0.77, and thus the error rate is 3.66%. It can be considered that the measured results and the numerical model results are consistent in terms of accuracy and distribution law. This shows that the numerical model can accurately inverse the rock strata movement and can be used as an effective means to study the law of overlying strata and surface movement [36].

**Figure 7.** Contrast subsidence curves between the survey data and the numerical model.
