## 3 Study of the Floor Heave in Gob-Side Entry Retaining  
### Numerical Model  
The geotechnical conditions of the 11-longwall panel of the Pivdennodonbasskaya coal mine were the basis of the numerical model that was realized by ANSYS 17.2 software. The simulation zone is indicated in Figure 4a, and the numerical model is shown in Figure 4b.  
The model was three-dimensional (3D). The size is 250 m along the x direction, 60 m along the y direction, and 25 m along the z direction. Half of the panel width was simulated due to symmetry. The height and width of the gob-side entry were 3.65 m and 5.2 m, respectively. The height and width of the filling wall were 1.3 m and 1.95 m, respectively. The bottom boundary of the model was fixed vertically; displacements of lateral boundaries were constrained in the normal direction. Vertical pressure, which was equivalent to the strata weight at a depth of 900 m (22.5 MPa), was applied to the top boundary.  
To simulate the behavior of rock mass, filling wall material, and gangue in the goal, the Drucker-Prager model was applied. The capability of the Drucker-Prager model to adequately simulate the behavior of pressure-dependent materials (like rocks) has been shown in previous studies [44; 45; 46]. The bilinear isotropic hardening model was used to simulate the behavior of the steel arch frame, rock bolt, and steel pile.  
The surrounding rocks of gob-side entry retaining were failured and discontinuous. Therefore, the mechanical parameters of intact rock (Figure 2a) should have been corrected. The Hoek-Brown Failure Criterion [47] was used to calculate the properties of rock mass in gob-side entry retaining. The Geological Strength Index (GSI), the \"mi\" constant, and the disturbance factor (D) were determined.  
Figure 4: _Cont._The GSI was calculated as RMR89-5 [48]. RMR89 was determined on the basis of geological documentation, results of the uniaxial strength tests, tests of the drill cores, and the observation of exposure of rock mass during gateroad repairs according to the Bieniawski method [49].  
The \"mi\" constant was 8 for mudstones, 17 for coal, and 12 for sandstone. The D parameter corresponded to [PERSON]'s classification categories: \"squeezing problems result in significant floor heave, disturbance can be severe unless a temporary invert is placed\" for mudstone and sandstone; \"mechanical excavation in poor quality rock masses resulting in minimal disturbance to the surrounding rock mass\" for coal seams [47].  
The deformation modulus (E\({}_{\mathrm{rm}}\)), friction angle (\(\varphi\)), and cohesive strength (c) were calculated according to [PERSON] empirical method [48]. The calculation procedure was described in previous studies [18; 50]. The calculated rock mass properties are presented in Table 1. The filling wall body in the case of a longwall retreat with a distance of 100 m was fissured and discontinuous. Therefore, the same method was applied for the filling wall material. The properties of the filling wall are shown in Table 1. To simulate the behavior of the broken gangue in the goaf, Poisson's ratio = 0.45, and E\({}_{\mathrm{rm}}\) = 30 MPa were applied [51]. The properties of the steel arch frame are shown in Table 2.