## 3 Analysis of Numerical Simulation Results
### Crack Propagation Process  
#### 3.2.1 Influence of Different Pore Percentages on Rock Failure Modes  
The tensile stress direction is perpendicular to the upper and lower sides of the model. Figure 4 shows the uniaxial tensile crack propagation process of the rock model under different pore percentages in Scheme A. In the figure, red represents cracks, white represents the generated random pores, and blue represents the rock matrix. In Scheme A1 (\(P_{\text{por}}\) = 1%), during the initial loading stage, the stress in the rock model is evenly distributed, and the randomly distributed few pores have little influence on the overall stress field. As the tensile stress gradually increases, cracks first initiate in the stress concentration areas in the model. These areas are usually located at the edges of pores or local weak areas of the rock matrix. Due to the low porosity, the interaction between pores is relatively weak, and the crack propagation path is relatively straight, mainly developing along the direction of the maximum principal stress. During the crack propagation process, when encountering pores, the crack will deflect briefly, but due to the limited number of pores, the crack will quickly resume its original direction and continue to propagate until the model finally fails. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Scheme** & **Details** & **Scheme** & **Details** \\ \hline A1 & \(P_{\text{por}}\) = 1\% & B1 & (\(d_{\text{min}}\), \(d_{\text{max}}\)) = (0.0005, 0.001) m \\ A2 & \(P_{\text{por}}\) = 2\% & B2 & (\(d_{\text{min}}\), \(d_{\text{max}}\)) = (0.001, 0.002) m \\ A3 & \(P_{\text{por}}\) = 3\% & B3 & (\(d_{\text{min}}\), \(d_{\text{max}}\)) = (0.0015, 0.003) m \\ A4 & \(P_{\text{por}}\) = 4\% & B4 & (\(d_{\text{min}}\), \(d_{\text{max}}\)) = (0.002, 0.004) m \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Numerical simulation calculation scheme. Figure 3: Model size and particle partitioning. For Scheme A2 (\(P_{\text{por}}=2\%\)), the number of pores in the model increases. During the loading process, the influence of pores on the internal stress distribution of the rock is more significant. The crack initiation points increase and are scattered near multiple pores. The crack propagation presents a more complex form. When the crack propagates to the surroundings, it is more likely to be attracted or blocked by adjacent pores, resulting in frequent branching and coalescence of cracks and the formation of multiple interlaced secondary cracks. These secondary cracks interact with the main crack and jointly affect the failure mode of the rock. When the rock fails, the local fracture area increases compared with Scheme A1, the failure mode is more complex, and the integrity is significantly reduced. Figure 4: Uniaxial tensile crack propagation process of the rock model under different pore percentages. (**a**) \(P_{\text{por}}=1\%\); (**b**) \(P_{\text{por}}=2\%\); (**c**) \(P_{\text{por}}=3\%\); (**d**) \(P_{\text{por}}=4\%\). Under the condition of Scheme A3 (\(P_{\rm por}\) = 3%), the higher pore percentage makes the internal structure of the rock more porous. Under a relatively small tensile stress, a large number of microcracks will be generated around the pores. These microcracks will expand and connect rapidly. As the stress further increases, the crack propagation presents a disordered network structure. The pores become the key nodes of crack propagation. The cracks shuttle, branch, and coalesce among the pores, forming a complex crack network system. When the rock fails, it is no longer a simple local fracture but a large-area fragmentation, almost running through the entire model. The failure degree is much higher than that of the previous two schemes. In Scheme A4 (\(P_{\rm por}\) = 4%), the pores occupy a large proportion of the rock. The mechanical properties of the rock decline significantly. At the beginning of loading, a large number of microcracks are distributed inside the model. These cracks expand and interweave rapidly under the guidance of the pores.