## 3 Materials and Methods
### Numerical Model  
Figure 6a shows a schematic representation of the geomechanical conditions after the excavation of the 817 longwall. The numerical model, which was used in this study (Figure 6b), was based on this scheme. The coal-bearing strata are Permian multi-strength rock mass represented mainly by sandstone, mudstones, and limestones. For the numerical simulation in this study, the lithological column was simplified. The rock strata were combined into groups. Each rock strata group had a thickness of 125 m. The choice of such thickness was determined by the distance from the number 8 coal seam to the aquifer. The Cenozoic strata, which cover the Permian, were also divided into 125 m groups. The rock properties in each group were calculated as a weighted average and were specified during model calibration. The calibration procedure is given below. The aquifers are divided into the Quaternary loose-layer pore aquifer group, the Permian main coal-bearing sandstone fracture aquifer sections, and the Taiyuan Group and Ordovician limestone karst fracture aquifer sections [25]. Number 8 coal seam belongs to the Permian coal-bearing strata. The Permian strata contain three groups of the fractured sandstone aquifers. The main recharge water source for mine water is the Cenozoic bottom aquifer, which covers the Permian coal-bearing strata. This aquifer directly overlays the coal-bearing strata, with a thickness ranging from 0 to 20.65 m, averaging 6.53 m. The floor depth ranges from 425.40 to 516.60 m, with an average of 487.57 m. The aquifer thickness varies greatly and consists of silty yellow, deep yellow, and variegated fine to medium sand, gravel, claystone, and silty gravel (Figure 6a). The right boundary of the model was positioned at a distance exceeding 40% of the length of the 817 longwall goat along the dip direction. The lateral boundaries did not affect the stress-strain state near the longwall panel. Thus, the boundary conditions in the model were satisfied. The finite element method in the Ansys Mechanical 17.2 software for three-dimensional solid modeling was used for numerical simulation. The numerical model's dimensions were set to 1000 m in width, 814 m in height, and 200 m in length (Figure 6b). The model width was pre-optimized by testing the sensitivity of the model by the stress factor. The horizontal displacements of the lateral boundaries of the model were constrained in a normal direction, while the bottom boundary was fixed vertically. The upper boundary of the model was not fixed. Vertical gravity was the only applied force in the model. A meshing of the prismatic elements was used in the model. The numerical model was automatically divided into finite elements by the built-in meshing module. The optimal shape and size of the finite elements were selected based on its geometry. After  
Figure 6: Principal scheme of the model after the excavation of 817 longwall (**a**), numerical model in Ansys software (**b**). mesh generation, the model was checked for geometric errors (such as zero-length elements, degenerate elements, and duplicate node numbers). Subsequently, a manual mesh optimization was performed. An orthotropic model was used to simulate the behavior of the rock mass. The behavior of anisotropic material, such as sedimentary rocks, is accurately simulated by this model [26; 27; 28]. The variation in the physical and mechanical properties of rock mass along and across the bedding planes was determined by the calibration of the numerical model, as described in the study of [29]. Since the model represented a scenario after excavation of the number 815 longwall and the number 817 longwall, a fractured zone and caved zone were simulated in goaf, according to three-zone theory [9; 10; 11; 12]. The height of caved zone was equivalent to eight coal seam thicknesses, and the height of fractured zone was equivalent to twenty seam thicknesses.