## 4 Discussion  
### Porous Rock Crack Propagation Modes  
Based on the improved SPH method, this paper simulated the rock crack propagation process under different pore properties. The crack propagation modes in different calculation schemes showed significant differences and regularities. For Scheme A, that is, the case of different pore percentages, when the pore percentage was 1% (A1), the crack propagation mainly originated from the local stress concentration areas in the model, which were mostly at the edges of pores or the weak areas of the rock matrix. Due to the small number of pores, the crack was hardly affected by the pores in the initial stage of propagation and basically extended linearly along the direction of the maximum principal stress. Only when encountering a small number of pores did it deflect briefly at a small angle and then quickly resume the original direction. As the pore percentage increased to 2% (A2), the number of pores increased, and the crack initiation points also increased and were scattered near multiple pores. At this time, the crack propagation was no longer a simple straight line. Instead, it was frequently attracted or blocked by adjacent pores, resulting in frequent branching and coalescence, forming a complex secondary crack network that intertwined with the main crack. The failure mode changed from a relatively simple local fracture to a complex mode with an increased number of local fracture areas. When the pore percentage further increased to 3% (A3), the internal structure of the rock became porous due to a large number of pores. Under low stress, a large number of microcracks were generated around the pores and expanded and connected rapidly. The crack propagation path presented a disordered network structure, and the pores became the key nodes. The cracks shuttled, branched, and coalesced among the pores, and the rock was almost completely fragmented when it failed, running through the entire model. This indicated that the increase in pore percentage greatly changed the path morphology and failure degree of crack propagation. When the pore percentage reached 4% (A4), the mechanical properties of the rock deteriorated severely. The model was initially filled with a large number of microcracks, which expanded in all directions under the guidance of the pores without a clear main crack direction, forming an extremely complex fragmentation mode and completely losing the bearing capacity. This further highlighted the strong influence of a high pore percentage on crack propagation, changing it from a relatively orderly propagation to a disorderly overall fragmentation propagation. In Scheme B, different pore sizes had different influences on the crack propagation mode. When the pore size was small (B1, (\(d_{\text{min}}\), \(d_{\text{max}}\)) = (0.0005, 0.001) m), the pores were densely distributed in the model. After the crack initiated, due to the existence of many small pores, the propagation process was frequently blocked and interfered with, constantly branching and turning and forming a complex crack network. The interaction between holes and cracks was strong, promoting the generation of new microcracks, guiding the crack propagation, and resulting in a local fragmentation and crack interlaced failure mode when the rock failed. As the pore size increased to (B2, \((d_{\text{min}},d_{\text{max}})\) = (0.001, 0.002) m), the number of pores decreased, and the stress concentration areas were concentrated around the larger pores. The frequency of the crack being disturbed by the pores decreased. However, when it met a pore, it would deflect significantly at the pore surface and might even extend along the pore surface to form a connection between the secondary crack and the main crack. The failure mode was slightly simpler than that of B1 but still had a certain complexity, indicating that the increase in pore size changed the interaction mode between the crack and the pore and the complexity of the propagation path.