## 2 Engineering Conditions  
In the Dongtan Coal Mine, the 3 rd coal seam in Mining District 4 is subdivided into two distinct layers: the 3 upper and 3 lower coal seams. The depth of the 3 lower coal seam varies from 605.31 m to 700.31 m, with an average depth exceeding 650 m. A siltstone interlayer, ranging in thickness from 2.35 m to 6.05 m (with an average thickness of 4 m), separates the two coal seams. This study focuses on the 43 lower01 and 43 lower02 working faces, as well as the overlying 43 upper01 and 43 upper02 working faces. The 43 lower02 working face is bordered by the mined-out areas of the 43 lower04 (north) and 43 lower03 working faces on either side, with the 43 upper01 and 43 upper02 longwall mining faces above and their associated mined-out areas. The design length of the working face is 300 m, and the advance length exceeds 1500 m. The layout of the working faces and the surrounding strata conditions are shown in Figure 1, while the physical and mechanical parameters of the adjacent rock layers are provided in Table 1. In-situ stress measurement results for the 3 lower coal seam, as supplied by the mine, are presented in Table 2.  
the model would require a significantly large overall size, a high number of particles, and substantial computational resources. As a result, simulations for deep mining faces using PFC2D are relatively scarce. Therefore, it is essential to simplify the numerical model within reasonable bounds. The approach for model simplification is outlined as follows:  
1. Reduction in the number of strata in the vertical direction: In the simulation process, the strata directly related to the immediate roof and the coal seam play an important role. Therefore, only the portions directly related to these strata are selected. To eliminate the influence of other strata and ensure the accuracy of the model, the remaining overlying strata are replaced by a single flexible cluster with equivalent weight, based on the results of the in-situ stress test. For this study, only the layers from the 3 upper coal seam to the second thick hard roof, and from the 3 lower coal seam to the first thick hard floor, are retained. This results in a total of nine layers of rock, with a height of 94.66 m.
2. Reduction in the lateral dimensions of the working face: A stress model for the main roof is developed, and the breakage length of the roof strata is determined through limit analysis. Based on these results, the width of the working face is reduced, which in turn minimizes the overall model length. 3. Adjustment of particle size: Given that the study focuses on the macro-scale structural evolution and its impact, the size of the particles is increased accordingly. Based on the limit analysis of a simply supported beam [33], the minimum working face length required to induce failure in the critical strata is determined. \[L_{B}=2h\sqrt{\frac{2\sigma_{t}}{3q}} \tag{1}\]  
The parameter \(L_{B}\) represents the ultimate breakage length, or minimum breakage length, of the critical layer (m); h is the thickness of the critical layer (m); \(\sigma_{t}\) is the tensile strength (MPa); and q denotes the self-load of the strata (kN). All these parameters can be obtained directly or indirectly from Table 1.  
Based on the calculations, the theoretical breakage length of the first fine sandstone layer, under the influence of its self-weight, is determined to be 99.7 m, while the theoretical breakage length of the fourth fine sandstone layer is 90.01 m.  
The theoretical results indicate that the breakage length of the two thick hard roof layers above the 3 rd coal seam does not exceed 100 m under their respective gravitational forces. Moreover, the 3 upper coal seam is essentially in a mined-out state, where the impact of the remaining coal pillars is negligible. Consequently, the length of the working face can be reduced to 200 m, and the lateral extent of the model can be reduced to 675 m.  
The corrected parameters are assigned to each layer in the model.