## 1 Introduction  
Mining resource development brings significant benefits to humanity. However, it inevitably raises a range of safety and environmental issues. Surface subsidence is an essential problem in mining activities, especially in mines using the natural fallout method. Surface subsidence caused by underground mining activities threatens the safety of people and property in the mining area and may lead to secondary geological hazards and damage to the ecological environment. Mining-induced subsidence has been a problem at several mines around the world [1], such as the Ordzhonikidze iron ore mine in Ukraine, where the use of pillar mining in a chamber resulted in the formation of large underground voids, which triggered widespread subsidence and led to a severe mine collapse [2]. The Sechahun Anomaly No.12 in Yazd Province, Iran, also experienced significant subsidence when using the segmented collapse method. In addition, the SLC mining method also led to ground subsidence problems in the western part of the Chengchao iron ore mine [3]. These cases show the severe impact of mining-induced surface subsidence on the mine site and the surrounding environment. Scholars have employed various methods, including theoretical analysis, physical modeling, field monitoring, and numerical simulation when studying surface subsidence caused by mining activities ([PERSON] et al. [4]). In academic research, [PERSON] et al. [5] utilized limit equilibrium analysis to predict the failure of overlying strata in a mine. In constructing physical models, [PERSON] et al. [6] established a physical model simulating surface and rock mass deformation and monitored surface and surrounding rock displacements with precision. [PERSON] et al. [7] conducted biological model experiments to investigate surface displacement and deformation induced by mining collapses beneath thick loess layers. Physical model experiments can simulate real-world scenarios, provide visual results, and validate numerical models, but they are costly, time-consuming, and subject to scale and parameter limitations. Field monitoring technology offers a direct and effective means of studying surface deformation and rock movement. Field monitoring data can accurately reflect the displacement patterns on the mining surface, guiding mining activities and support design. [PERSON] et al. [8] employed deep borehole extensometers to monitor deformations in the northeastern rock strata of the Jinshandian iron mine, investigating the mechanism of deep rock mass-induced seismic events. [PERSON] et al. [9] effectively monitored surface deformations and ground fissures induced by mining activities. Based on monitoring results, they discussed the lag and displacement change patterns resulting from mining activity. Other scholars have also conducted research on mining-induced disasters [10; 11; 12; 13; 14]. In recent years, with the innovation and advancement of computer technology, the modeling and numerical analysis of complex geological formations have become feasible. As a result, the significance of numerical simulations has progressively gained prominence in addressing complex underground engineering and resource development issues, enhancing engineering safety and efficiency, and optimizing production processes. Standard numerical simulation methods include the Finite Difference Method (FDM, represented by software such as FLAC), the Discrete Element Method (DEM, represented by software like 3 DEC), and the Finite Element Analysis (FEA, represented by software such as ABAQUS). Among these, FLAC3D, which employs finite difference principles, demonstrates excellent stability and efficiency and is competitive for numerical simulations of large-scale geological formations. Many scholars have conducted relevant research using FLAC3D. For instance, [PERSON] et al. [15] employed FLAC3D to perform numerical simulations of the Jindar coal mine.