Numerical Simulation of Crack Propagation in Rocks with Random Pores Based on Improved Smoothed Particle Hydrodynamics Method

This study aims to explore the influence of random pore characteristics inside rock mass on the fracture mechanical properties of rock under tensile stress. By means of numerical simulation based on the improved smoothed particle hydrodynamics (SPH) method, a specific kernel function approximate integral interpolation form and discrete particle superposition expression form are constructed to handle physical processes. The maximum tensile stress criterion and fracture marker ω are introduced to improve the traditional smooth kernel function for dealing with crack propagation. Meanwhile, the center and radius information of circular pores are generated using random numbers to create a rock model with random pores. The research results show that in terms of crack propagation morphology, as the pore percentage increases, the crack gradually changes from a straight propagation slightly disturbed by pores to an overall fragmentation propagation with frequent branching and coalescence; when 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 key nodes of large pores. In terms of the stress–strain law, the increase in pore percentage leads to a decrease in the elastic modulus and peak strength of the rock and a weakened post-peak ductility; when the pore size increases, 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. The conclusion indicates that the pore percentage and size have a significant and complex influence on the mechanical properties of the rock.