## 1 Introduction  
As the depth of coal resource extraction has increased, the complex geological environment and high-intensity mining disturbances in deep underground operations have significantly elevated the risks of dynamic hazards such as rock burst and roof collapses [1, 2, 3, 4, 5, 6]. Influenced by advancing working faces, roof fracturing, and blasting activities, deep coal-rock masses undergo continuous loading-unloading effects [7, 8], leading to cumulative internal damage and mechanical property degradation of the coal, which serves as a critical trigger for dynamic hazards [9; 10; 11]. Consequently, elucidating the mechanical responses and failure characteristics of coal rock under cyclic loading-unloading conditions is of paramount theoretical significance for stability control in deep mining goats and hazard prevention. Cyclic loading-unloading under varying conditions exerts markedly distinct influences on the mechanical properties and failure behaviors of coal [12; 13; 14; 15]. The current research is predominantly focused on coal mechanics under quasi-static cyclic loading, encompassing uniaxial, biaxial, and true triaxial servo-controlled experiments [16; 17; 18]. However, the strain rate is typically under 0 s\({}^{-1}\) in those studies. But in deep mining, dynamic disturbances like blasting or roof impacts can cause instantaneous strain rates of up to 10\({}^{3}\) s\({}^{-1}\). The strain rates from different disturbances vary widely in magnitude. As a result, the mechanical properties and failure characteristics of coal and rock masses show remarkable differences under different strain rates [19; 20; 21; 22]. Studies have revealed that coal rock under quasi-static loading exhibits progressive damage evolution, whereas dynamic impact loads trigger instantaneous energy accumulation and crack propagation through stress wave transmission, resulting in a transition from simple splitting to pulverizing failure mode [21; 22]. For instance, SHPB experiments have demonstrated that increased dynamic loading rates substantially enhance energy dissipation rates in coal and induce brittle fractures dominated by axial tensile stresses [23; 24]. Furthermore, the fatigue damage characteristics of coal rock under cyclic dynamic loads (e.g., frequency dependence) fundamentally differ from those under quasi-static loading: low-frequency cycles amplify internal crack network propagation through prolonged energy accumulation, while high-frequency disturbances accelerate localized stress concentration via stress wave superposition [25]. Although current studies have explored coal-rock mechanics under quasi-static and dynamic loading conditions, most studies have focused on a single loading condition. In practice, coal and rock may experience both quasi-static and dynamic loading. Yet, few studies have compared the mechanical properties under these two conditions. Moreover, for deep mining \"three-high\" environments (high geostress, gas pressure, and temperature), the situation becomes even more complicated [26; 27]. Thus, a comparative investigation of the mechanical behaviors and failure characteristics under quasi-static and dynamic loading is imperative, especially a comparative study of the crack characteristic stress and failure modes under the two conditions. This study investigated coal specimens through quasi-static cyclic loading-unloading experiments under different confining pressures and SHPB dynamic impact tests, systematically analyzing the influence of cyclic loading and unloading cycles on the mechanical properties of coal under these two loading conditions. By contrasting the failure characteristics under quasi-static loading (characterized by AE signals) with those under dynamic loading (evaluated through crack distribution patterns), combined with crack characteristic stress analysis, the failure mechanisms of coal rock under both loading conditions were comprehensively elucidated.