Statistical damage model of rock considering pore water pressure and multifractal characteristics

A statistical damage model incorporating multifractal characteristics is proposed for micro-fractured rocks subjected to pore water pressure. Based on the assumption that microelement strength follows a Weibull distribution, the unified strength theory is adopted as the statistical variable, and a relative fractal dimension λ is introduced to quantitatively characterize the heterogeneity and anisotropy of the material, thereby establishing a statistical damage model for the rock, which is finally validated through experiments. The results show that: (1) The model predictions agree well with test curves, effectively reflecting the mechanical responses under varying pore water pressures; (2) Increasing pore water pressure accelerates damage evolution, lowers the critical damage threshold, and promotes rock failure; (3) A larger relative fractal dimension λ reduces microelement strength concentration, brittleness, damage threshold, and overall strength, making the rock more prone to instability. This study provides a reference for safety analysis of rock engineering under stress‑seepage coupling conditions.