## 5 Conclusions  
This study developed a numerical simulation system for rocks with random pores based on the improved SPH method. By introducing the maximum tensile stress criterion and the fracture marker \(\omega\), the traditional smooth kernel function was improved, and the SPH control equations considering the failure characteristics of particles were obtained, enabling the accurate simulation of particle behavior during crack propagation. Meanwhile, a random pore generation algorithm was developed to create a rock model with random pores. The research found that pore percentage and pore size have significant impacts on crack propagation morphology, the stress-strain law, and the mechanical properties of rocks. As the pore percentage increases, the crack propagation changes from a straight-line propagation slightly disturbed by pores to a complex network-like propagation with frequent branching and coalescence, eventually leading to overall fragmentation. The elastic modulus and peak strength of the rock decrease, and the post-peak ductility weakens. As the pore size increases, the crack propagation changes from a complex network-like shape frequently disturbed by small pores to a relatively simple through fracture controlled by the key nodes of large pores. The elastic modulus first decreases and then increases, the peak strength changes similarly, and the post-peak characteristics change from complex fluctuations to a stable transition. However, this study has certain limitations. Firstly, the research is based on a two-dimensional model, while rock structures in actual engineering are three-dimensional. The two-dimensional model cannot fully reflect the complex geometric shapes and mechanical properties of crack propagation paths and pore distributions in three-dimensional space. Secondly, although the randomness of pores is considered in the simulation process, other characteristics of rock materials, such as the distribution of mineral components and the complexity of the cementation between particles, have not been fully considered, which may affect the agreement between the simulation results and the actual situation. In addition, in terms of computational efficiency, the current simulation method has certain limitations when dealing with large-scale models. The calculation time is relatively long, making it difficult to meet the requirements of rapid analysis in practical engineering. In response to the above-mentioned deficiencies, future research will focus on developing a high-performance, three-dimensional parallel SPH program. During the development process, the particle search algorithm will be optimized to improve computational efficiency and cope with the significant increase in the number of particles and computational complexity in three-dimensional models. By combining geological survey data and rock microstructure analysis, a more realistic rock model will be constructed, fully considering the influences of different mineral compositions, particle size distributions, and cementation conditions on crack propagation. Multi-scale modeling techniques will be introduced to link the microscopic pore structure with the macroscopic crack propagation behavior and deeply explore the failure mechanism of rocks under different loading conditions and environmental factors. This will provide more reliable stability assessment and disaster prediction methods for rock engineering, such as underground mining, slope stability analysis, and the design of hydraulic engineering foundations, and promote the development of rock mechanics in engineering practice. Conceptualization, W.S. ; Methodology, X.R. and H.X. ; Software, W.S. ; Validation, J.Z. ; Investigation, W.S., X.R. and J.Z. ; Resources, X.R. ; Writing--original draft, W.S. ; Supervision, X.R. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. The original contributions presented in this study are included in the article.