## 3 Fracture and Damage Analysis of Model Experiments  
### Directional Fracture Analysis  
Binarization is performed on each layer of the PMMA plates of the layered rock mass specimen after blasting to obtain the crack distribution state of each layer of the specimen, as shown in Figure 5. It can be seen in the figure that most of the PMMA plates have formed long directional cracks along the slit direction, indicating that the slit charge can still exert a good directional fracture effect in the layered rock mass. There continue to be obvious differences in the failure morphology and crack distribution of different layers. The cracks at the end layers (the 12 th and 13 th layers) are short and randomly distributed, and the directional fracture effect is relatively poor. Although the PMMA plates on the first and fourteenth layers are not charged with explosives, they were still damaged under the blasting load of adjacent layers. In particular, the first layer forms long directional cracks along the slit direction.  
The propagation length of the directional crack is an important index used to evaluate the blasting effect of the slit charge. The lengths of the directional cracks in each layer in Figure 5 are measured, and the statistical data shown in Table 1 are obtained. There are also some differences in the propagation lengths of the two directional cracks at the same layer. Therefore, the average length of the two directional cracks is taken for further analysis.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Layer Number** & **1 st** & **2 nd** & **3 rd** & **4 th** & **5 th** & **6 th** & **7 th** \\ \hline Length 1/mm & 37 & 57 & 51 & 47 & 40 & 38 & 35 \\ Length 2/mm & 27 & 53 & 52 & 49 & 39 & 44 & 42 \\ Average length/mm & 32 & 55 & 52 & 48 & 40 & 41 & 39 \\
**Layer number** & **8 th** & **9 th** & **10 th** & **11 th** & **12 th** & **13 th** & **14 th** \\ Length 1/mm & 34 & 34 & 24 & 24 & 19 & 10 & 6 \\ Length 2/mm & 40 & 38 & 30 & 23 & 16 & 6 & 0 \\ Average length/mm & 37 & 36 & 27 & 24 & 18 & 8 & 3 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The lengths of the directional cracks in each layer of the specimen.  
Figure 4: Slit tube after blasting and the corresponding layer number.  
Figure 5: Crack distribution state of each layer of the specimen after blasting.  
Figure 6 shows the changing curve of the average length of directional cracks with the layer number (detonation direction) in the model experiment. The average length of the directional cracks in the second layer (initiation position) is the largest, which is \(55\,\mathrm{mm}\). Except for the first and fourteenth layers, the average length of the directional cracks gradually decreases along the detonation direction. In the unlayered rock mass, when the slit charge is detonated from one end, the previous research results show that the length of the directional crack increases first and then decreases along the detonation direction [21]. It can be seen that the changing law of the directional crack length along the detonation direction in the layered rock mass is significantly different from that in the unlayered rock mass. The distribution law of the directional crack length in the layered rock mass along the detonation direction shows that in engineering practice, the directional fracture effect of the layered rock mass can be improved by detonating both ends of the slit charge at the same time.