## 4 Numerical Simulation
### Numerical Modeling  
According to the specific geological conditions of a mine working face (Table 1), the finite element differential simulation software, FLAC3D, was selected to establish a numerical calculation model of the auxiliary transport chute of the working face, and the physical and mechanical parameters of the coal seam and each rock layer at the roof and bottom of the roadway in the model are shown in Table 2.  
To find out the influence of weak interlayer thickness and underlying hard strata thickness on roadway stability, a numerical test method is developed for weak interlayersand underlying hard strata of different thicknesses. Surrounding rock horizontal stress and plastic zone failure are used as the evaluation criteria. Model mesh division: In the process of establishing the numerical calculation model, consider the model boundary effect and calculation speed, based on the characteristics of the FLAC3D 3D model: 1. the larger the model, the denser the meshing, accordingly the longer the calculation time; 2. when simulating the mining of a working face, the model calculation is slow, and it is hard to reach a balance; 3. to highlight the object of our study, the calculation model has to be meshed densely, with 0.25 m as a unit). The final determination of the numerical calculation model side length is x \(\times\) y \(\times\) z = 25 m \(\times\) 20 m \(\times\) 25 m and is combined with the actual rock structure situation for grid division. The model uses the Mohr-Coulomb constitutive model for the simulated coal rock mass, with displacement constraints applied all around the model and at the base, and a free boundary at the roof. Application of vertical load to the model: the vertical load to the model is applied to simulate the state of stress to which the coal rock body would be subjected if undisturbed by excavation, i.e., the original rock stress. The vertical load values are usually obtained using calculations based on the formula (\(p=\gamma h\)), with the seam weight \(\gamma\) taken as 25 KN/m\({}^{3}\) and h is the depth of burial of the coal seam. However, through the above (Figures 3 and 4) analysis, it can be seen that the stress value of the coal rock body around the roadway increases under the influence of the mining-disturbed area of the working face, and the stress value of the coal rock body around the roadway is between 30 MPa-35 MPa, and the closer to the coal pillar area, the higher the stress value. The literature [10] also points out that there are many factors affecting the distribution of the mining superimposed stress field, but for deeply buried and moderately buried mines, due to the small size of the roadway section relative to the spatial dimensions formed by the working face, the stress redistribution caused by the working face at the location of the retrieved roadway can be roughly considered as the stress state around the retrieved roadway before the destruction of the surrounding rock. Therefore, instead of directly simulating the influence of face mining on roadway stability, a representative vertical and horizontal load is given by analyzing the mining stress environment at the roadway around the mining face (Figures 3 and 4). Vertical load (32.5 MPa) and horizontal load (1.5 times the vertical load) are applied to the roof of the model to simulate the influence of working face mining on the roadway. The numerical  
roadway roof stability is numerically simulated under different underlying hard strata thicknesses (1 m, 1.5 m, 2 m), at a constant weak interlayer thickness of 0.6. The horizontal stress nephograms of the roadway surrounding rock are shown in Figure 7.  
From Figure 7a-c, when the underlying hard strata thickness is 1 m, one single stress concentration zone appears above the roadway roof; the stress concentration reaches its maximum of approximately 51.62 MPa, primarily located at 3 m from the roadway roof (key layer 1).