# Research on Hard Rock Pillar Stability Prediction Based on SABO-LSSVM Model
## 1 Introduction  
In conventional open stope mining methods, certain ore bodies are left as supporting pillars to maintain the stability of underground mining workings without the presence of additional support or auxiliary structures [1; 2]. The strength of the mine pillars, hanging wall, and footwall are critical factors that determine the ability of the void area to withstand disturbances and prevent collapse. Unstable mine pillars can lead to mining safety accidents, such as collapse of the void area and interlocking failure of multiple pillars [3]. For instance, the large-scale instability event of the Lewiston-Stockton coal seam (1986) resulted in the collapse of the void area, spreading to a distance of 100 m within 8 h after the accident. This led to more than 0.5 m of subsidence in the unstable region and triggered numerous instances of tilting and instability of mine pillars [4]. As mining operations continue to extend deeper underground, in situ stress increases rapidly with depth, posing significant challenges and higher strength requirements for supporting mine pillars [5; 6]. Consequently, analysis of mine pillar stability has become an inevitable research problem in underground mining. Early research on mine pillar stability primarily focused on analyzing it from the perspective of rock mechanics. Researchers have continuously developed and optimized empirical formulas for estimating pillar strength to explore the key indicators affecting pillar stability and their functional relationships [7; 8]. An earlier estimation formula for pillar strength was developed by [PERSON] and [PERSON]. They constructed a power function formula based on the pillar width, height, and unit volume strength of the pillars using a collection of coal mine pillar cases, and used it to estimate pillar strength [9]. For a long time afterward, numerous scholars built upon their research and developed various empirical formulas, adhering to the viewpoint that pillar strength is linearly related to material strength while considering negligible effects of size when the volume of the rockmass increases [10; 11]. Currently, the widely accepted and applied pillar strength formula is the Lunder-Pakalnis pillar strength formula [12]. This formula, which is based on a large amount of field data, comprehensively considers various factors that influence pillar stability. It is widely applicable to different types of rocks and mining conditions and provides valuable references for pillar design. With the advancement of research and interdisciplinary development, an increasing number of new methods are being applied to analyze mine pillar stability. Currently, research methods for mine pillar stability analysis mainly include the safety factor method [13], reliability analysis method, statistical learning theory, and numerical simulation methods [2; 14]. The safety factor method evaluates the stability of mine pillars by calculating the ratio between the theoretical strength of the pillars and actual working loads. [PERSON] et al. [15] developed a method for estimating pillar strength and selecting design safety factors based on observations of stable and failed pillars supplemented with numerical models. [PERSON] et al. [16] proposed a new calculation method, called the point safety factor calculation method, which considers the multidirectional stress state and ultimate strength values at each point, allowing for an even distribution of the point safety factor within the pillar. Thus, the average overall point safety factor can be used to evaluate the overall safety factor of the pillar. The safety factor method is simple and easy to use; however, it does not consider the characteristics of rock mass engineering randomness and heterogeneity, resulting in issues of insufficient accuracy and subjectivity.