# Experimental Study on the Dynamic Characteristics of Fractured Coal Under Cumulative Impact
## 3 Results and Analysis  
### Wave Velocity Analysis  
Generally, wave propagation velocity in solid materials increases with higher density and elastic modulus. Ultrasonic wave velocity measurement serves as an effective method for evaluating damage evolution in solids, as increased porosity and crack density significantly alter wave propagation characteristics. Cumulative impacts induce progressive damage in fractured coal samples, with wave velocity measurements providing a quantifiable indicator of damage severity under varying impact cycles. Figure 3 illustrates the wave velocity variations of coal samples with different fracture inclinations under cumulative impacts.  
Figure 3 demonstrates that the wave velocity of coal samples decreases progressively with cumulative impacts under identical fracture inclination. For 30\({}^{\circ}\) inclined fractures, the initial wave velocity of 1626 m/s respectively declines to 1575 m/s, 1327 m/s and 1145 m/s after 1, 3 and 5 impacts. This reduction is attributed to microcrack propagation and porosity enhancement induced by cyclic impacts. Post-impact observations reveal secondary cracks around the prefabricated fractures and micro-debris detachment, indicating cumulative damage mechanisms. Prefabricated fractures reduce the initial wave velocity compared to intact specimens, with 90\({}^{\circ}\) inclined fractures exhibiting minimal reduction, which is parallel to wave direction, while 30\({}^{\circ}\) inclined fractures show the highest attenuation. The 90\({}^{\circ}\) aligned fractures minimally obstruct longitudinal wave propagation, whereas inclined fractures induce multi-path reflections and energy dissipation, elongating wave trajectories.  
Furthermore, linear regression analysis reveals a well-defined linear correlation between cumulative impact cycles and wave velocity reduction across coal samples with varying fracture inclinations. The absolute slopes of fitting curves vary with fracture inclination: 100.6, 70.3 and 65.5 for 30\({}^{\circ}\), 60\({}^{\circ}\) and 90\({}^{\circ}\) fractures, respectively, reflecting differential damage sensitivities. Under cumulative impact loading, the wave velocity decreases most rapidly when the crack inclination angle is 30\({}^{\circ}\). This phenomenon primarily occurs because pre-existing cracks with a 30\({}^{\circ}\) inclination angle readily generate wing cracks and secondary cracks at their tips. The resulting complex crack network impedes wave propagation and  
Figure 3: The variation diagram of wave velocity of coal with different fracture angles under cumulative impact.  
introduces intricate wave path trajectories. Consequently, a significant acceleration in wave velocity attenuation is observed. The wave velocity of fractured coal specimens exhibits dip-angle dependency under cumulative impact loading. The slope of the fitted curve characterizes the sensitivity of crack dip angles to cumulative impact loading. A larger absolute slope value indicates higher sensitivity of the corresponding crack dip angle to cumulative impact loading. This demonstrates that crack dip-angle characteristics significantly influence wave velocity variations under cumulative impact loading.