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

Yonghui Zhang and Fangtao Li

PLOS ONE, 2026, vol. 21, issue 9, 1-14

Abstract: 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.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:plo:pone00:0358254

DOI: 10.1371/journal.pone.0358254

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