## 2 Engineering Background and Numerical Simulation Scheme
### Numerical Simulation Scheme and Simulation Steps  
The purpose of the stope stability analysis is to optimize the structural parameters of the tall, collapse-prone slopes located north of the 60 line in the Dongguashan deposit. Based on the profile of the stope at the 60 line, which mainly includes stopes 60-2# to 60-28#,this study uses the 61 line profile as a reference to establish a stope model that closely aligns with the actual conditions for the theoretical and numerical simulation analyses. Given that the Dongguashan ore body is buried at a considerable depth and that the structural stress in the mining area is complex due to factors such as folding structures, an analysis of the original rock stress testing was conducted prior to the numerical simulation. The results of the original rock stress testing are presented in Table 1.  
The rock mass in the Dongguashan mining section is layered, and, to simplify the model, the average mechanical parameters based on the properties of the layered surrounding rock were calculated for the simulation data. Given the significant differences between the engineering mechanical properties of the in situ rock mass and the results from laboratory tests, it was necessary to apply a reduction process to the laboratory test results before utilizing them in the numerical simulation. This study is based on engineering geological surveys and the RQD values of the ore body and roof rock. A specific reduction method was employed to calculate the reduced mechanical parameters of the rock mass. According to the geological variations of the rock mass at the 60 line of Dongguashan and field investigations, combined with rock classification standards, the average joint spacing was determined to be between 0.6 and 2 m. The [PERSON] method was used for the reduction, resulting in a reduction factor of 0.1 for the shear strength parameters (cohesion c and internal friction angle \(\varphi\)). The deformation parameters of the rock mass include the elastic modulus and Poisson's ratio, with the Poisson's ratio being used directly from the test values without reduction. For the compressive and tensile strength of the rock mass, the literature recommends using a cracking coefficient for reduction. This study did not conduct elastic wave testing, so the cracking reduction coefficient was chosen based on empirical values. Given that the integrity of the rock mass north of the 60 line in Dongguashan differs significantly from earlier assessments, with some areas being more fractured and forming blocky rock masses, a reduction coefficient of 0.45 was selected for the blocky and fractured rock masses. After reducing the physical parameters, it was necessary to calculate the bulk modulus and shear modulus. In FLAC3D, the deformation parameters no longer use the elastic modulus E and Poisson's ratio \(\upsilon\) but instead utilize the bulk modulus K and the shear modulus G, which represent the material's resistance to volumetric deformation and shear deformation, respectively. In practical applications, the deformation parameters typically provided are E and \(\upsilon\), which can be converted to K and G using the formulas \(\mathrm{K}=\mathrm{E}/3(1-2\upsilon)\) and \(\mathrm{G}=\mathrm{E}/2(1+\upsilon)\). The slope in the Dongguashan mining section consists of three extraction steps, with different fill material proportions used after each step. Based on the actual filling conditions of the first and second steps, combined with the data on the filling material's mechanical parameters from domestic and international sources, the parameters for the fill material selected for the numerical simulation were determined. The final physical and mechanical parameters for the numerical simulation are presented in Table 2.