Analysis of Uniaxial Fatigue Mechanical Properties and Constitutive Modeling for Freeze–Thaw Cycled Red Sandstone with Double Fissures

Abstract

This study addresses the challenge of the mechanical behavior of fractured rock masses in cold regions under freeze–thaw-fatigue coupling. Uniaxial step-incremental cyclic loading tests were conducted on double-cracked red sandstone subjected to different numbers of freeze–thaw cycles to reveal the damage evolution laws. Based on the variable-order fractional derivative theory, the traditional Nishihara model was improved by replacing the Abel dashpot in the viscoplastic component with a variable-order fractional dashpot, thereby establishing a fatigue deformation constitutive model that accounts for freeze–thaw damage. The novelty of the model lies in coupling the variable-order fractional viscoplastic element with stepwise cyclic loading equivalence, fatigue-threshold-controlled deformation, and freeze–thaw damage degradation, rather than merely replacing the dashpot in the classical Nishihara framework. The experimental results indicate that freeze–thaw cycles accelerate macroscopic damage of the rock mass. As the number of freeze–thaw cycles increases, the crack initiation stress, dilatancy stress, and peak stress decrease in a stepwise manner. The rock specimens exhibit significant softening characteristics, accompanied by intensified dilatancy, propagation of secondary cracks at the tips of pre-existing flaws, and a transition of the failure mode towards shear failure. By analyzing the mean stress versus axial deformation curves of the last two stages of cyclic loading, the fatigue threshold stress ratio of freeze–thaw damaged double-cracked sandstone was determined, confirming that freeze–thaw damage reduces the fatigue strength of the rock mass.