## 3 Dynamic Response Behavior of Cracks and Explosive Holes under Dynamic Impact
### Research on the Influence of Waves Generated by Cracks on the Initiation of Explosive Holes  
In the above research, it can be found that compared to existing cracks, the characteristics of the newly generated main cracks around the blast hole are quite obvious and have certain characteristics due to the reflection and diffraction effects of the corresponding stress waves of the pre-existing cracks. Firstly, by simulating the crack-free model, it can be found that the crack propagation around the blast hole has a high degree of symmetry, and after extending to a certain extent, there will be many bifurcations at the end, as shown in Figure 12.  
By comparing the simulation of the crack-containing model with the crack-free blast hole model, it can be found that in the crack-containing model, there is a narrow and less branched characteristic crack in the upper and lower positions of the blast hole that are approximately parallel to the crack, as shown in Figure 13. However, in the simulation, the generation and propagation behavior of new cracks are only affected by the diffraction of the tip and the reflection of the wave. In this process, the reflection wave plays a major  
Figure 11: Crack propagation state generated at 60–90\({}^{\circ}\). Figure 12: Model without cracks. role. Therefore, it can be considered that the interference of the reflection wave causes the generated cracks to become more narrow. In this study, the characteristic cracks with narrower and fewer branches are also known as the main cracks in the blast hole that are induced by the reflection wave (hereinafter referred to as the main cracks). By comparing the length of the cracks around the blast hole near the end of the crack propagation in the 45\({}^{\circ}\) to 90\({}^{\circ}\) simulation experiment, it can be observed that the main crack has a longer propagation distance compared to the other cracks, indicating that the main crack may be the main cause of instability. In conventional underground engineering, cracks with a longer or faster growth rate will obviously be more easily connected with the surrounding free surface or other cracks, which will lead to local crushing and instability. At the same time, the data image of the main crack propagation length changing with time at the same angle is shown in Figure 14.  
The study of the stress wave propagation in the first part found that at around 30 \(\upmu\)s, the length of the main crack is similar to that of the surrounding crack, and even shows an approximate length in various angles of the model. Therefore, it can be considered that the process before 30 \(\upmu\)s did not promote the propagation of cracks around the borehole, and the generation of cracks was caused by the stress wave of the initial load. In the 45\({}^{\circ}\) model, the propagation speed of the main crack can be roughly calculated to be about 0.7 mm/\(\upmu\)s from 0-30 \(\upmu\)s, and the reflection wave begins to affect the main crack after 30 \(\upmu\)s. At 30-40 \(\upmu\)s, the average propagation speed of the crack is about 1.1 mm/\(\upmu\)s, while at 40-50 \(\upmu\)s, the propagation speed decreases to about 1 mm/\(\upmu\)s, and even to about 0.89 mm/\(\upmu\)s at 50-60 \(\upmu\)s. This phenomenon indicates that in the 45\({}^{\circ}\) state, the reflected wave has a significant promoting effect on the main crack, resulting in a faster propagation rate compared to the initial stress wave load. Moreover, by calculating the main crack propagation rates at different stages of 30-60 \(\upmu\)s in Figure 14b-d, it can be found that after being affected by the reflected waves, the average propagation rate of the cracks is the highest during the period of 30-40 \(\upmu\)s, and then gradually decreases at 40 \(\upmu\)s. This phenomenon is common. This indicates that cracks with an inclination angle greater than 45\({}^{\circ}\) around them will significantly promote the propagation behavior of cracks that are approximately parallel to the blast hole and cracks.