## 1 Introduction  
With the development of the social economy, the demand for mineral resources is increasing [1]. Tailings is the byproduct generated from the extraction and beneficiation of ore, and consists of waste rock, slag, wastewater, and chemical wastes. The compounds are acidic or alkaline, with elevated levels of dangerous heavy metals that can cause serious environmental damage if not managed correctly [2]. To prevent pollution, tailings is typically deposited into tailing ponds. A tailings pond is a containment area for storing industrial wastes, such as tailings, produced by metal and non-metal mining [3]. It is created by constructing dams at the river closure of a valley or by enclosing it on all sides. The tailings pond is a geotechnical engineering structure with internal water forces that create a complex multi-field coupling effect, making it more susceptible to deterioration compared to other forms of water-storage dams. According to statistics, tailings dams have a roughly tenfold higher failure rate than water-storage dams due to factors such foundation settlement, dam seepage, earthquakes, and extreme weather [2, 4]. Several significant failures of tailings dams have been documented worldwide in recent decades, resulting in several adverse effects on the surrounding environment and adjoining residential communities [5, 6, 7, 8, 9, 10, 11, 12]. The 2019 rupture of the Brumadinho tailings dam in Brazil caused 259 deaths. It had a significant environmental impact by increasing heavy metal levels in the Paraopepa River, posing a health risk to communities nearby [13]. Tailing ponds, as substantial geotechnical structures, are recognized as a significant hazard for nearby communities [14]. Comprehensive safety monitoring, timely analysis, and early warning are crucial for enhancing tailings pond safety management and preventing dam-failure accidents. Engineers have become increasingly concerned about monitoring the safety of tailing ponds in recent years. The safety monitoring elements of tailing ponds primarily consist of displacement, the infiltration line, the water level in the reservoir area, and the length of the dry beach [15]. The length of the dry beach is a crucial factor that impacts safe operation and directly affects the position of the infiltration line and the flood control capacity of tailing ponds. An insufficient length of dry beach can pose a serious threat to the safety of tailing dams. In history, there have been many collapse accidents associated with tailing ponds due to dry beach length, such as the 2008 Xiangfen tailings dam failure in Shanxi Province, China. Tailing ponds consist of tailings stacking facilities, drainage equipment, discharge spigot, sewage treatment station, safety-monitoring equipment, and other auxiliary facilities [16]. The mineral processing plant mixes tailings with water to form a slurry, which is discharged into the tailings pond for storage through the discharge spigot. After the slurry is discharged into the tailings pond, due to gravity settlement, a dry beach area and water area will be formed [17]. The length of dry beach refers to the distance from the drainage faucet to the waterline, which is closely related to dam safety [18]. The discharge of tailings with high water content into the pond and the influence of rainfall and other factors cause the fluctuation of dry beach length. Therefore, it is necessary to monitor the length of dry beaches. Figure 1 depicts the dry beach area and water area of the tailings pond. The method of monitoring the length of dry beaches is crucial for tailings pond safety. However, the soft sedimentary surface of beaches make it challenging to manually determine the boundary between the dry beach and water areas. [PERSON] et al. [19] proposed a slope projection technique for determining the length of a dry beach.