## 3 Analysis of Numerical Simulation Results
### Crack Propagation Process
#### 3.2.2 Influence of Different Pore Sizes on Rock Failure Modes  
The tensile stress direction is perpendicular to the upper and lower sides of the model. Figure 5 shows the uniaxial tensile crack propagation process of the rock model under different pore percentages in Scheme B. In Scheme B1 (\((d_{\rm min}\), \(d_{\rm max}\)) = (0.0005, 0.001) m), since the pore size is small, the pores are relatively densely distributed in the model. As the tensile stress increases, cracks initiate in the stress concentration areas. These areas are often located at the periphery of pores or the inhomogeneous areas of the rock matrix. Due to the large number of pores and small size, the crack propagation process is frequently disturbed by the pores, resulting in continuous branching and turning of the cracks. When the crack approaches a pore, it will change the propagation direction due to the stress concentration at the edge of the pore, forming a relatively complex crack network. At this time, the interaction between holes and cracks is strong. The pores act as stress concentration points to continuously promote the generation of new microcracks and guide the crack propagation around them, resulting in local fragmentation and a crack-interlaced failure mode when the rock fails. For Scheme B2 (\((d_{\rm min}\), \(d_{\rm max}\)) = (0.001, 0.002) m), the pore size increases, and the number decreases. During the loading process, the stress concentration areas are mainly distributed around the larger pores. After the crack initiates, when it propagates to the surroundings, compared with Scheme B1, the frequency of being disturbed by the pores decreases. However, due to the increase in pore size, when the crack meets a pore, it will deflect significantly at the pore surface and may even extend along the pore surface for a certain distance before continuing to extend outward, forming a situation where the secondary crack is connected to the main crack. In this case, the interaction between holesand cracks is manifested as a significant change in the crack propagation path. When the rock fails, the fragmentation area is relatively concentrated near the pores, and the failure mode is slightly simpler than that of Scheme B1 but still has a certain complexity. Under the condition of Scheme B3 (\((d_{\min}\), \(d_{\max})\) = (0.0015, 0.003) m), the pores further increase in size and decrease in number. During loading, the stress concentration phenomenon mainly appears at a few large pores. After the crack initiates, the number of times affected by the pores during the propagation process is significantly reduced, and the crack propagation path is relatively straight. However, when encountering a pore, there will still be obvious deflection and branching. At this time, the interaction between holes and cracks is mainly reflected in the control of the crack propagation direction at key nodes; that is, the pores become important turning points of the crack propagation path, resulting in a local  
Figure 5: Uniaxial tensile crack propagation process of the rock model under different pore sizes. (**a**) (\(d_{\min}\), \(d_{\max}\)) = (0.0005, 0.001) m; (**b**) (\(d_{\min}\), \(d_{\max}\)) = (0.001, 0.002) m; (**c**) (\(d_{\min}\), \(d_{\max}\)) = (0.0015, 0.003) m; (**d**) (\(d_{\min}\), \(d_{\max}\)) = (0.002, 0.004) m.  
large block fracture when the rock fails. The failure range is relatively reduced compared with Scheme B1 and B2, but the failure degree is still relatively serious. In Scheme B4 ((\(d_{\text{min}}\), \(d_{\text{max}}\)) = (0.002, 0.004) m), the pore size is the largest, and the number is the least. At the beginning of loading, after the crack initiates in the relatively weak part of the rock matrix and due to the large pore spacing, the crack is basically not disturbed by other pores during the propagation process and mainly develops along the direction of the maximum principal stress. The propagation path is relatively single and straight.