## 3 Results
### Fragment Size Distribution  
To further study the effect of delay timing on rock fragmentation, the fragments of each bench specimen were screened through a set of 16 standard sieves. The mesh sizes of the standard sieves ranged from 0.048 to 35 mm. The coarse fragments with particle sizes larger than 35 mm were weighed individually. The connected scatterplots of the fragment size distribution for all bench specimens are shown in Figure 13.  
Figure 12: Blast excavation weights of all bench specimens. Figure 13: Fragment size distribution for all bench specimens. Due to the wide size range of fragments, the size distributions of measured data were constructed using the extended Swebrec function, which is considered one of the best-fitting distribution functions to describe rock fragmentation data [48; 49; 50]. The extended Swebrec function is a five-parameter distribution whose cumulative distribution, \(P(x)\), is as follows [50]:  
\[P(x)=\frac{1}{1+a\cdot\left[\ln(x_{\max}/x)/\ln(x_{\max}/x_{50})\right]^{b}+(1- a)\cdot\left[\left(\frac{x_{\max}}{x}-1\right)/\left(\frac{x_{\max}}{x_{50}}-1 \right)\right]^{c}} \tag{1}\]  
The five fitting parameters include the maximum size \(x_{\max}\), the median size \(x_{50}\), the partition coefficient \(a\), the shape parameter \(b\), and the shape parameter \(c\). Given the wide variation in fragment sizes and accumulated mass passing values, as well as the tendency of an ordinary least squares scheme to match the coarse zone and ignore the fine zone, a weighted least squares scheme was used to fit the curves. In this study, the curves fitted by the extended Swebrec function were made with \(1/P^{2}\) weighting to make the fitted curves more accurate. The corresponding parameters of fitted curves are shown in Table 3.  
Figure 14 shows the sieving data for the fragments and the constructed sieving curves. The accumulated mass passing is generally divided into four zones, including mass passing less than 2% (very fine zone), mass passing from 2 to 20% (fine zone), mass passing from 20 to 80% (central zone), and mass passing more than 80% (coarse zone) [51]. A larger particle size represents a coarser fragment at the same mass passing. In the range of the four zones, mass passings of 1%, 10%, 50%, and 100% were selected as the parameters for comparison and analysis. The particle sizes of each bench specimen at the selected four percentages are given in Table 4.  
The fitted curves of the first three experiments are shown in Figure 15. By combining Table 3 and Figure 15, the fitted curves move downward in the range of 1-20% mass passing, indicating that the particle sizes become larger with increasing delay time in this range. However, the fitted curve of BS2 is located above the fitted curve of BS1 in the range of 20-100% mass passing, which indicates that the fragmentation of BS2 was better than that of BS1 in this range. Additionally, the difference in particle size between BS1 and BS2 becomes significant in the coarse zone. Taking 100% passing as an example, the \(x_{100}\) of BS1 was 195.4 mm, while the \(x_{100}\) of BS2 was 166.3 mm, with the difference between the \(x_{100}\) values reaching 29.1 mm. When the inter-hole delay was increased to 100 us, the particle size produced by BS3 was larger than BS2 in the range of 1-100% passing, which indicated that further increases in inter-hole delay in the range of 50-100 us were not effectively improved rock fragmentation. The maximum particle size of BS3 reached 237.1 mm, which is 1.4 times larger than that of BS2. The variation in the fragmentation of BS1-BS3 shows that when the inter-hole delay was in the range of 0-100 us, the delays had less effect on the particle size at 1-50% mass passing. For example, the median sizes of BS1, BS2, and BS3 were 122.1 mm, 121.3 mm, and 128.4 mm, respectively, with insignificant differences. In the blasting experiments of BS1-BS3, the effect of delay time on fragmentation was mainly observed in 50-100% mass passing, especially in the coarse zone.