Micromechanical assessment of unsaturation freezing impact on compressive fracture in brittle rocks

Micro-macro compressive fracturing of brittle rocks under subzero and unsaturated conditions is not well quantified, particularly the coupled effects of ambient temperature T a and degree of saturation S r on wing-crack propagation and peak compressive strength. This study develops a unified micro-macro compression fracture model for unsaturated freezing brittle rocks by integrating the compression wing-crack framework, fracture criterion, crack-strain damage relation, and coupled T a and S r formulations for six governing quantities. These include three key mechanical parameters—fracture toughness ( K IC ), friction coefficient ( μ ), and initial damage ( D 0 )—and three crack-surface stresses—effective frost heave stress ( P f i ), effective cohesive stress ( P c i ), and skeleton contractile stress ( P t )—all parameterized as functions of T a and S r based on experimental evidence. The proposed model quantifies the evolution of stress intensity factor ( K I ), stress-strain response, crack initiation stress ( σ 1c ), and peak compressive strength ( σ 1p ) under unsaturated freezing. A pore-structure-controlled three-stage mechanism is further identified, with S r ≈60% and S r ≈90% separating skeleton-contraction strengthening, cohesive-stress strengthening, and frost-heave-induced offset, respectively. Model predictions agree well with independent published subzero uniaxial-compression data across rock types and varying saturation levels, capturing peak stress and key stress-strain features. The findings inform stability assessment and design of cold-region rock engineering.