# Experimental Study on the Dynamic Characteristics of Fractured Coal Under Cumulative Impact
## 3 Results and Analysis
### Dynamic Compressive Strength Analysis  
Dynamic stress-strain curves characterize the deformation and failure processes of fractured coal under dynamic loading conditions. Figure 4 presents these curves for coal samples with varying fracture inclinations subjected to cumulative impacts. Figure 4 demonstrates that the dynamic stress-strain curves of fractured coal samples can be divided into three distinct phases: the elastic stage, yield stage and failure stage. Due to the narrow aperture of prefabricated fractures, rapid compression under impact loading  
Figure 4: Dynamic stress-strain curves of coal samples with different fracture angles under cumulative impact. (**a**) No impact effect; (**b**) Impact effect-1; (**c**) Impact effect-3; (**d**) Impact effect-5. eliminates a discernible compaction phase. The elastic stage exhibits near-linear stress escalation with minimal non-linearity. The yield stage corresponds to microcrack initiation and propagation, while the failure stage is characterized by gradual stress degradation. Under identical impact cycles, intact specimens exhibit the highest elastic modulus (slope), whereas 30\({}^{\circ}\) inclined fractures show the lowest values, indicating severely compromised deformation resistance. Progressive reduction in elastic modulus slope with cumulative impacts reflects accumulated internal damage, directly impairing the coal's load-bearing capacity. The stress-strain curve of 30\({}^{\circ}\) fractured coal samples subjected to five cumulative impacts exhibits a shortened elastic stage with significant slope reduction and a marked decrease in peak strength. This demonstrates that damage accumulation from repeated impacts and fracture dip-angle characteristics critically govern the failure mechanism of fractured coal specimens. Dynamic compressive strength quantifies fracture coal's ability to resist failure under impact loads, with its degradation patterns providing critical insights into mechanical behavior and stability assessment. The dynamic compressive strength data extracted from Figure 4, summarized in Table 1, reveal systematic strength reduction with cumulative impacts. After five impacts, the dynamic strength decreases by approximately 25-40%, demonstrating severe material degradation. Furthermore, under identical impact cycles, coal specimens with 30\({}^{\circ}\) crack dip angle exhibit the lowest dynamic compressive strength values. For instance, after the initial impact, the strength reduction percentages were 5.9%, 11.7%, 8.5% and 7.0% for the corresponding specimens without pre-existing cracks and those with crack dip angles of 30\({}^{\circ}\), 60\({}^{\circ}\) and 90\({}^{\circ}\). The 30\({}^{\circ}\)dip-angle specimens demonstrate the most substantial strength degradation. This indicates that coal specimens containing 30\({}^{\circ}\) cracks possess the highest susceptibility to premature failure. The literature [45] revealed that variations in joint inclination significantly affect the impact resistance of specimens, with the weakest impact resistance observed at a joint inclination of 30\({}^{\circ}\). The conclusions of this study are consistent with those findings, which also validate the reliability of the conclusions drawn in this research. Cumulative impact loading essentially subjects fractured coal specimens to cyclic disturbances, where the number of impacts corresponds to distinct levels of input disturbance energy. Impact cycles were configured as 0, 1, 3 and 5, with corresponding disturbance energies calculated via kinetic energy formulae as 0 J, 0.784 J, 2.352 J and 3.92 J, respectively. A quantitative relationship is established between disturbance energy and dynamic compressive strength to investigate their interdependence. Furthermore, correlative analysis between wave velocity reduction and strength degradation is conducted. Figure 5 illustrates the triaxial relationships among wave velocity, disturbance energy and dynamic compressive strength for 60\({}^{\circ}\) inclined fracture specimens.