Study on the Fracture Behaviors of Porous Media Based on the Fractal Geometry Theory and Phase Field Fracture Method

This paper proposes an approach for investigating the fracture mechanical behavior of fractal porous media by integrating fractal geometry theory with the phase field fracture method. Based on fractal geometry theory, multiple Sierpinski carpet fractal porous media models were constructed by adjusting geometric scales and iteration times. Different loading angles were applied to simulate and analyze the effects of porosity and fractal dimension on the fracture mechanical behavior of the models. The results indicate that: (1) When the fractal dimension is fixed, the fracture resistance of fractal porous media decreases with increasing porosity; (2) When the porosity is fixed, the fracture resistance decreases with increasing fractal dimension; (3) The influence of porosity on fracture resistance is more pronounced than that of the fractal dimension. The findings of this paper offer a novel approach to mitigating engineering fractures in structures featuring fractal porous media.