###### Abstract  
This study conducts a simulation analysis of the stability of tall and collapse-prone stopes at the Dongguanshan copper mine, using the FLAC3D-3.0 software to investigate the stress distribution and deformation behavior of geological materials under different working conditions, providing an effective means of addressing complex mechanical issues inotechnical engineering. In this paper, the stability of the tall stopes in the Dongguanshan mining area was analyzed through numerical simulations using the FLAC3D finite difference method. First, a three-dimensional numerical model of the tall stopes was established based on the actual conditions of the mining area, simulating the mining conditions and environment. Next, the stress distribution, displacement variation, and potential instability zones under different mining schemes were studied, with a comparative analysis conducted between traditional mining methods and optimized schemes to clarify their respective advantages and disadvantages. Finally, based on the simulation results, the most suitable mining scheme for the area was identified, aimed at reducing the risk of stope collapse and improving the overall stability and safety of the mine. The findings provide technical support for the design and support of tall stopes in deep deposits and offer important reference points for mine safety management. t +
Footnote †: journal: applied sciences  
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instability of block structures, providing a theoretical foundation for studying structural instability in slopes [12]. Fracture mechanics has been widely applied in instability studies of underground slopes, especially in analyzing fracture propagation within rock masses and its impact on stability [13]. In addition, models based on elastic theory [14], plastic theory [15], and energy theory [16] have also been used. Traditional methods of stop stability analysis primarily rely on theoretical models, but these approaches often struggle to accurately reflect real-world conditions when dealing with complex rock masses and uneven stress distributions. In recent years, the development of numerical simulation technologies has provided new avenues for analyzing the stability of underground slopes [17; 18; 19; 20]. Numerical simulations can accurately replicate the complex stress-strain states and failure processes of rock masses, offering critical insights for engineering design and risk assessment. Various numerical methods have been applied in underground stop studies [21], including the finite element method (FEM) [22], discrete element method (DEM) [23], and finite difference method (FDM) [24], yielding numerous research findings. The finite element method (FEM) is currently one of the most commonly used numerical simulation techniques, typically suitable for handling deformation characteristics and stability under complex geometries and boundary conditions. It can provide high-accuracy results, especially excelling in static and quasi-static analyses. [PERSON] et al. [25] conducted a numerical simulation study using PLAXIS2D finite element analysis software to investigate the structural parameter scheme of the mining area and the waste rock filling scheme. By analyzing the displacement variation, surrounding rock stress distribution, and plastic zone, they determined the optimal structural parameters for the mining area. However, its computational cost is relatively high, and it requires significant computational resources. The discrete element method (DEM) is widely used to simulate the movement and interaction of particles or blocks within fractured rock masses [26]. The DEM can capture local failure processes, such as crack propagation and block sliding within the rock mass, which is particularly important for studying instability in complex underground mining areas. However, this method may not perform as well as finite difference methods when dealing with the stability analysis of continuous media.