## 3 Research Framework
### Data Source: Field Measurements and Numerical Simulations  
The data for this paper are sourced from the goat detection and stability research project conducted by Mengzi Mining Co., Ltd. at the Bainiuchang silver-Polymetallic Mine. As shown in Figure 2, the project is located in Bainiuchangcun, Mengzi County, with geographical coordinates of 103 deg43' E longitude and 23 deg27' N latitude. The deposit is situated in the southeastern region of Yunnan Province within the Xilong polymetallic mineralization belt, and it is the largest silver deposit in China, possessing strong representativeness and research value. The mining area extends 50 km from east to west and 4 km from north to south, covering approximately 200 m\({}^{2}\), and is divided into five mining sections: Baiyang, Duimenshan, Chuanxindong, Awei, and Miwei.  
The data collection period was from April to July 2024. During this time frame, all parameter indicators in the mining sections remained stable, with no occurrences of events such as microseisms or rock bursts. We conducted subsidence area detection and surveys in mining sections using methods including three-dimensional laser scanning, UAV photogrammetry, geophysical surveys, and data analysis. These methods were employed to determine the distribution, quantity, size, collapse conditions, and water accumulation of the subsidence areas in each section. The basic characteristic data include 24 fundamental features such as ore body length, thickness, ore body dip angle, exposed area, volume, roof height, key characteristics, exposure time, surface elevation, burial depth, etc. It is worth mentioning that all the data used in this study were repeatedly measured and cross-verified multiple times, and were also checked by several experts. The data quality is sufficient to support subsequent statistical analysis.  
Based on the actual geological occurrence environment and mechanical parameters, we conducted numerical simulation of the Baiyang mine section (195 goals) and Duimenshan mine section (167 goals) by using FLAC3D software, and obtained the stress distribution results, as shown in Figure 3. The rocks in the mine area and its vicinity are mainly dolomite and siltstone. The rock strength parameters used in this simulation calculation come from the research results of the rock mechanics test, as shown in Table 1. According to the calculation results of the numerical simulation of the goat, the stress concentration phenomenon appears in the roof and surrounding rock of each empty area, and the stress mutation will appear at the corner of the roof and wall top in the empty area. After the excavation of the empty area, the tensile stress of the roof exceeds the ultimate tensile strength of the ore body by 1.1 MPa, indicating that most of the roof of the goat area can maintain the stability. The reason is that the mined-out areas were formed a long time  
Figure 2: Study area.  
ago, and the stress release of the surrounding rock has essentially been completed. Taking into account factors such as data quality and representativeness, we used data from 167 monitoring sites in the Duimenshan mining section for subsequent modeling.  
Specifically, the Duimenshan section contains 167 goafs. The ore body exhibits gently to steeply dipping layered or quasi-layered formations, with a thickness ranging from 0.5 m to 23 m, averaging 4.2 m. The length of the goaf in this section varies from a maximum of 155 m to a minimum of 7 m, with an average of 39 m. The width ranges from a maximum of 99 m to a minimum of 3 m, with an average of 21 m, and the height varies from a maximum of 14 m to a minimum of 2.5 m, with an average of 5.5 m.