A fractal analytical model for coupled thermo-mechanical permeability of porous rocks incorporating cross-coupling effects

Abstract

Permeability evolution in porous rocks under coupled thermo-mechanical conditions is critical for deep underground engineering. Since the existing models treat the thermal and stress effects separately, they failed to capture their competing mechanisms of thermoelastic compaction and thermal cracking. To address this, we propose a novel fractal analytical model that incorporates a cross-coupling term into a fractal-based permeability framework. The model naturally produces a non-monotonic permeability evolution with temperature: initially decreasing due to thermoelastic compression, then rising as thermal cracking dominates and finally declining when stress-induced compaction overcomes thermal expansion. The proposed permeability model is expressed as a function of temperature, stress, and key fractal parameters including fractal dimensions for pore area and tortuosity. The model is validated against experimental data under different temperature-stress paths, demonstrating excellent agreement. Parametric analyses further reveal the roles of the thermo-mechanical loading rate and coupling coefficients in controlling permeability behavior, capturing the transition from thermoelastic reduction to thermal cracking enhancement. The proposed model offers a physically based and computationally efficient tool for evaluating coupled permeability evolution in deep high-temperature rock engineering.