## 1 Introduction  
In recent years, the depletion of shallow coal resources, coupled with intensified deep coal mining in China, has posed significant challenges in preventing and controlling mining disasters, especially in isolated working faces and residual coal pillars [1, 2]. An isolated working face refers to a mining area surrounded by goals (mined-out areas) or unmined coal pillars on two, three, or even four sides, depending on the mining layout [3]. These isolated working faces present unique geological and operational challenges, making them highly susceptible to coal burst accidents, which increase the risk to workers and equipment [4, 5, 6]. As coal mining technology in China continues to advance, the depth and intensity of mining operations have also increased. This has led to a rise in the number of coal mines experiencing coal bursts, from 32 in 1985 to 177 in 2017, and the number decreased in 2021 to approximately 150. (Figure 1) [7]. These incidents significantly threaten worker safety and operational stability. For instance, the Zhaolou Coal Mine in Shandong Provinceexperienced a rockburst on 29 July 2015, resulting in multiple injuries and significant economic losses. Another rockburst in the same year at Gucheng Coal Mine caused both fatalities and damage to mining equipment [8,9]. The increasing frequency of these events has garnered attention from government authorities, industry practitioners, and researchers, making the development of predictive methods and control measures for coal bursts an urgent priority [10]. Such coal burst accidents pose severe threats to the life safety of underground workers and the operational safety and economic benefits of coal mines. Predicting the pre-mining coal bursts of isolated working faces and implementing targeted control measures are crucial to addressing these problems [11]. In addition to China, countries like Kazakhstan and Ukraine also face similar challenges in managing coal bursts. Research in Kazakhstan emphasizes the role of rock mass stiffness and energy accumulation in mitigating dynamic energy release during mining. Yielding support systems such as D-bolts have been effective in absorbing energy and reducing rock mass deformation, similar to the issues in isolated working faces in China. In Ukraine, numerical simulations have been used to study the effects of mining depth and rock strength on coal burst risks, providing insights for managing these risks in deep mining operations [12,13]. These international studies show that coal bursts are a global issue, with many co-producing countries adopting similar strategies to manage energy accumulation and ensure operational stability. By incorporating these global perspectives, our study gains a broader context for understanding coal burst risks and developing more widely applicable preventive measures. The unique geological conditions of isolated working faces make them more prone to coal burst accidents, threatening the safety and stability of mining operations. Investigating the mechanisms of coal bursts, particularly the energy balance and support system selection, is one of the key solutions to this problem. Coal burst accidents are typically caused by the sudden release of elastic energy accumulated in coal seams and surrounding rocks during mining activities. When this energy exceeds the bearing capacity of the surrounding rock,  
Figure 1: Growth trend of the number of coal mines with rockburst in China from 1985 to 2021.  
a coal burst occurs. Selecting an appropriate support system to regulate energy release has gradually become one of the critical aspects of ensuring coal mine safety. [PERSON] et al. [14] pointed out that the occurrence of coal bursts is closely related to differences in rock mass stiffness and energy accumulation. Yielding support systems, such as D-bolts and Roofex, are highly effective in absorbing energy, mitigating dynamic energy release, and reducing rock mass deformation during coal bursts.