## 5 Discussion  
This study systematically compared the mechanical properties and failure characteristics of coal under quasi-static and dynamic loading regimes. The variations in cyclic peak stress, strain, and Young's modulus reflected the fundamental differences in coal's mechanical responses to these distinct loading conditions. The AE signal evolution and surface crack patterns further delineated the failure mechanisms: AE localization captured the progressive damage under quasi-static loading, while surface crack networks illustrate the dynamic failure's sudden energy release. The comparative analyses of \(\sigma_{\text{cc}}\) and \(\sigma_{\text{cd}}\) further demonstrated how loading regimes govern internal crack initiation and propagation. The strain rate disparity between quasi-static (\(10^{-5}\)-\(10^{-3}\) s\({}^{-1}\)) and dynamic (\(10^{2}\)-\(10^{3}\) s\({}^{-1}\)) loading spanned multiple orders of magnitude, a critical factor that is often overlooked in single-regime studies [18]. To address this gap, experiments were conducted at strain rates of \(10^{-3}\) s\({}^{-1}\) (quasi-static loading) and \(10^{2}\) s\({}^{-1}\) (dynamic loading). Figure 3 shows the contrasting stress paths: quasi-static loading showed a continuous trajectory, whereas dynamic loading involves intermittent cycles with partial unloading phases. This divergence in stress paths explains why quasi-static unloading minimally affects coal integrity, whereas dynamic cycles represent single-impact events on progressively damaged specimens [44]. Consequently, dynamic loading produced less pronounced peak stress transitions compared to quasi-static  
Figure 11: Crack closure stress under quasi-static and dynamic loading conditions. Figure 12: Crack damage stress under quasi-static and dynamic loading conditions. conditions. For instance, as shown in Figure 7c, a sharp stress drop occurred between N = 16 and N = 17 under quasi-static loading, while dynamic loading (N = 4-6) exhibited gradual stress variations. This stress path dichotomy also governed the Young's modulus evolution. Dynamic loading induced earlier modulus transition points due to the high strain rates suppressing microcrack closure and propagation [45]. Since coal's stiffness is primarily derived from an intact matrix, cumulative damage under dynamic loading progressively reduces the undamaged matrix volume, accelerating modulus degradation. There were significant differences in the failure characteristics between quasi-static and dynamic loading regimes. As shown in Figures 9 and 10, the coal specimens under quasi-static loading failed via oblique shear failure, governed by the coupled effects of confining pressure and axial stress. In contrast, dynamic loading induced composite failure modes: longitudinal splitting fractures and transverse tensile cracks (Figure 13). This duality arose from stress wave interactions within the coal. A portion of the incident compressive stress wave is reflected as a tensile wave at internal boundaries. When the amplitude of the tensile wave exceeds the dynamic tensile strength (\(\sigma_{\text{t}}\)), lateral tensile failure occurs [23], satisfying the criterion in Equation (3). Conversely, axial compressive fractures develop when the incident compressive stress surpasses the dynamic compressive strength (\(\sigma_{\text{c}}\)), as defined by Equation (4). During cyclic dynamic loading, the initial impacts generate stresses below \(\sigma_{\text{c}}\), producing lateral tensile cracks. As N increases and stresses exceed \(\sigma_{\text{c}}\), axial compressive cracks emerge. Consequently, fully failed specimens exhibit hybrid fracture networks: early-stage transverse tensile cracks and late-stage axial compressive fractures (Figure 13).