###### Abstract
The finite difference method (FDM) is another commonly used numerical simulation technique, especially suitable for simulating deformation and fluid flow problems in continuous media [27; 28]. This method can effectively address nonlinear problems, performing particularly well in the dynamic analysis of stress and deformation changes. Moreover, the FDM is relatively straightforward to implement computationally, making it especially suitable for simulating the stability of rock masses in deep, high-stress environments. At the same time, FLAC3D, a commercial software based on the FDM, is commonly used for stope stability studies [29; 30]. [PERSON] et al. [31] used the FLAC3D finite difference analysis software to simulate the original in situ stress distribution of a test step, analyzing the effects of rectangular, elliptical, and butterfly-arched stope cross sections on stope stability, ultimately identifying the optimal stope shape. [PERSON] et al. [32] conducted a series of numerical analyses using FLAC to study the stability of open-pit stops. In addition, [PERSON] et al. [33] introduced the combined/hybrid finite-discrete element method (FDEM) and validated its application for slope stability analysis. The study primarily focused on the contact interactions of discrete bodies and the transition between continuum and discontinuum. With the improvements in computational power, three-dimensional numerical simulation techniques have become increasingly widespread in the stability analysis of underground slopes [34; 35]. Three-dimensional models can more accurately describe the geometric shapes of stopes and the distribution of stress fields, overcoming the limitations of two-dimensional simulations. [PERSON] et al. [36] addressed the stability issues of caving method slopes by using three-dimensional finite element methods to conduct numerical simulations of various stope structural parameters. They primarily analyzed the displacement of the roof and the principal stresses during the excavation and ore recovery processes, concluding that larger structural parameters result in greater stability for the stope compared to smaller parameters. By establishing a three-dimensional model and integratingthe mechanical properties of the rock mass with the mining conditions, it is possible to more precisely simulate the stress changes, deformation patterns, and potential failure modes of the stope. This is especially important in the complex working environments of underground mines, where numerical simulations can comprehensively consider multiple factors, providing scientific foundations to guide engineering design and construction. This study focuses on a copper mine in Anhui, systematically analyzing the stability of tall, collapse-prone slopes in underground mines using the FLAC3D finite difference method. By establishing a numerical model of the underground slope and integrating actual working conditions, this study simulates the stress distribution, deformation characteristics, and potential instability zones under various conditions. The findings not only provide technical support for stope design and support systems but also serve as an important reference material for mine safety management.