## 4 Discussion  
To briefly explain the mechanism of delay time on blasting fragmentation, the stress wave was analyzed in a two-dimensional horizontal plane. The propagation of the P-wave generated from borehole-A is shown in Figure 19. The solid line represents the front of the P-wave and the dashed line represents the tail of the P-wave.  
Figure 19: P-wave propagation at two intersections of a bench blasting model with three kinds of delays: (**a**) the bottom intersection of the bench slope; (**b**) the top intersection of charge column.  
Figure 18: Particle size at 50% mass passing vs. delay time.  
Stress waves propagate in the specimen after the detonation of borehole-A. The P-wave in both intersections has not reached the free surface at 13.69 \(\upmu\)s. If the borehole-B is detonated at this time, the P-wave of borehole-A and borehole-B will superpose between the two holes. Similarly, if the delay time between boreholes is 27.36 \(\upmu\)s, the P-wave from borehole-A will propagate to the center of borehole-B. It can be seen from Figure 18b that the P-wave from borehole-B will interact with the tensile wave formed by the P-wave from borehole-A reflected at the free surface. When the delay time increases to 54.72 \(\upmu\)s, the superposition of the stress waves between the two holes is relatively weak compared to the above two short delay times. The above three cases represent the stress wave propagation in the DT1-DT3 experiments. The same method of stress wave analysis can be used in the remaining experiments.  
In the first three experiments, the particle size gradually coarsened with the weakened stress wave superposition. This weakening did not consistently increase the particle size of fragments. In the experiment of DT4 (60 \(\upmu\)s), the fragment size was significantly reduced in the coarse zone, and fragmentation was improved. When the delay time was increased to 90 \(\upmu\)s, the maximum \(x_{100}\) was obtained. In the experiments of DT5-DT8, the stress wave interaction disappeared, but the particle size decreased with the increase in delay time. DT1, with P-wave superposition between the blast holes, did not achieve the smallest particle size of \(x_{50}\). The \(x_{50}\) of DT7 improved by 19% compared to that of DT1. Although there was no superposition of stress waves, the DT7 specimen achieved the best fragment size distribution. This suggests that as the delay time increased, there were factors other than stress wave interaction that improved rock fragmentation. In particular, the improvement in the coarse zone was significant when a longer delay time was used.  
As the above description, stress wave superposition is not the only important factor in affecting the fragment size distribution in multi-hole bench blasting. During rock blasting, the crack velocity is slower than the P-wave velocity. [PERSON] et al. [52] studied the crack velocity of granite and measured the coefficient between crack velocity and P-wave velocity as 0.33. When the delay time increases, the crack formed by the first blast hole obtains enough time to extend and is influenced by the stress wave from the neighboring blast hole during blasting. The full-field strains, progressive breakage processes, and post-blast patterns with fragments backfilled showed that with the increase in delay time, vertical cracks gradually dominated in rock fragmentation. For the column charge in the borehole, the vertical crack extension of the bench slope seemed more favorable to rock fragmentation. In particular, for the radial cracks extending from the blast hole to the free surface, the increase in delay time made the extension distance gradually increase. This crack extension provides new boundary conditions for the neighboring borehole. Thus, the crack propagation needs to be considered in addition to stress distribution to determine the optimal delay time in multi-hole bench blasting.