## 2 Project Overview  
The Prang Copper Mine is in northeastern Shangri-la County, Diqing Tibetan Autonomous Prefecture, northwest Yunnan Province, China. The geographical location of the Prang copper mine is shown in Figure 1. Within the mining area, the geological formations are relatively homogeneous, comprising blocky rock types with a predominance of hard rock and the development of localized fracture zones. This mine uses the natural caving mining method. The Prong Copper Deposit is located within a complex porphyry body, with the ore-containing rock center composed of finely veined impregnated ore and vein-like ore bodies at the periphery. The scale of the ore body is classified as super large, and its morphology is straightforward. The primary elements within the ore body are copper, accompanied by precious metals such as tungsten, cobalt, palladium, and gold. The exposed geological formations in the mining area include the Triassic Tumugou Formation, Prang-type intermediate acid porphyry (mica) rock, and a small number of fourth-series strata. The Tumugou Formation is constructed of volcanic clastic rocks and is divided into three lithological segments based on rock-type combinations. The first lithological segment comprises schistose slate and metamorphic sandstone, interbedded with layers of gray limestone, and schistose slate containing gleaming threads, with a thickness exceeding 400 m. The first layer of the second lithological segment consists of gray to dark gray slate, interbedded with metamorphic sandstone and volcanic angular breccia, with a thickness exceeding 1000 m. The second lithological segment's second layer consists of gray to dark gray slate and acceptable sandy schistose slate, with a thickness exceeding 1000 m. The third lithological segment comprises good sandy schistose slate and crystalline gray limestone with a thickness exceeding 271.4 m. The upper portion of the ore body is covered by Quaternary glacial deposits, with an average thickness of approximately 16.84 m (reaching a maximum of 85.73 m) and a total volume of around 48.47 million cubic meters. While the copper ore body is substantial, it possesses a relatively lower average ore grade and features fault development.  
Since the commencement of copper mining operations in 2017, ongoing mining activities have led to surface subsidence. During this period, the relevant authorities implemented various measures to address issues in the subsidence area. Presently, the morphology of the study area, as shown in Figure 2, exhibits a circular subsidence crater with a diameter of approximately 400 m. The bottom of the hole is about 3853 m, and a large drainage channel runs along the southern side. Notably, a substantial crack has emerged on  
Figure 1: Location of the study area.  
the western slope of the drainage channel, demonstrating a tendency for outward extension and elongation. It is speculated that the formation of this crack is related to the presence of weak planes in the slope and new mining activities in the southern part of the initial mining area.  
The positional relationship between underground mining and surface subsidence is depicted in Figure 3. Based on this hypothesis, the present study constructed a three-dimensional geological model of the subsidence area and employed three-dimensional numerical simulation methods to analyze and predict the patterns of crack formation and development. This research endeavor will provide valuable insights for future mining and engineering activities.