## 1 Introduction
Below this critical value, the strength of the coal sample increases with the loading rate; above this value, the strength actually decreases. Both the peak strength and fragmentation degree of coal depend on the strain loading rate [19; 24], while the strength and failure mechanisms of coal are influenced by the strain rate and microstructure [25]. [PERSON] et al. [26] proposed a method for assessing coal sample impact that takes loading rate into account. [PERSON] et al. [27] addressed the initial damage of coal and examined the effect of loading rate on the creep mechanical behavior of initially damaged coal samples. The coal pillar is influenced not only by the mining water immersion and variable loading rate environment but also by the structure and properties of the coal itself, both of which are important factors affecting its stability. Due to geological sedimentation, coal bodies exhibit significant heterogeneity and anisotropy. [PERSON] et al. [28] demonstrated that the peak strength and axial peak strain of coal show a \"V\"-shaped trend, initially decreasing and then increasing with the dip angle of the bedding plane, reaching a maximum at a dip angle of 0\({}^{\circ}\) and a minimum at 60\({}^{\circ}\). [PERSON] et al. [29] reported that the mechanical properties of coal depend on both the loading type of the coal sample and environmental factors. [PERSON] et al. [30] found that the fractal crack propagation rate of coal samples with a bedding angle of 0\({}^{\circ}\) was the lowest. [PERSON] et al. [31] studied the energy evolution characteristics during the coal failure process through uniaxial and triaxial compression tests, establishing a brittle evaluation index for coal samples that considers the effect of bedding. [PERSON] et al. [32] introduced the bedding ratio index to quantitatively analyze the impact of bedding on the strength, deformation, and permeability characteristics of coal samples under triaxial stress conditions. However, long-term immersion in mine water causes complex changes in the matrix, bedding planes, and structure of coal pillars, which undeniably affects their mechanical properties and failure modes. However, under long-term immersion in mine water and the disturbances caused by mining, when the stress concentration at the crack tip exceeds the coal fracture pressure, the crack will propagate and penetrate until a macroscopic crack is formed. The capacity of cracked materials to resist fracture is a significant topic in fracture mechanics. Current research primarily focuses on the effects of pure water immersion on the permeability, tensile strength, and compressive strength of coal pillars, while there is a lack of studies addressing the influence of coal crack propagation and fracture toughness. Additionally, the long-term effects of mine water are often overlooked; however, mine water contains more complex ionic components than pure water, and these effects cannot be ignored. Moreover, the ability of coal pillars to resist fracture instability is an evolving process influenced by variable loading rates. Existing research does not adequately consider the fracture characteristics of coal under varying loading rates affected by mine water immersion. Therefore, it is essential to investigate the fracture mechanics characteristics of coal, taking into account the combined effects of mine water immersion, different loading rates, and bedding directions, to provide a reference for the stability analysis of coal pillar dam bodies.