A new nonlinear viscoelastic–plastic constitutive model of sandstone subjected to freeze‒thaw cycles under cyclic loading

Abstract

To study the mechanical characteristics and patterns of damage of sandstone subjected to freeze‒thaw (F–T) cycles, a damage constitutive model describing the mechanical behavior of rock subjected to F–T cycles under uniaxial/triaxial cyclic loads was proposed. Initially, on the basis of fractional calculus and viscoelastic mechanics theory, cyclic loads were decomposed into a static load and a time-varying load with a zero equilibrium stress value. Second, to incorporate the impacts of F‒T cycles and stress on sandstone damage, F‒T damage was considered throughout the entire cyclic loading process. When the stress state of a rock sample reached the yield limit, the synergistic effect of damage due to stress was considered. On the basis of the use of nuclear magnetic resonance (NMR) spectroscopy to analyze the characteristics of porosity distribution of rock samples exposed to varying numbers of F‒T cycles, a compliance reduction term representing F‒T damage progression was introduced to adjust the time-varying load. Consequently, a fractional damage constitutive model of a rock mass under coupled F–T and stress was formulated. The theoretical fitting outcomes of this model were compared with experimental and simulated results, validating the patterns of influence of F–T damage and stress on rock performance. This comparison reflects the entire stress‒strain process of rocks subjected to F‒T cycles under cyclic loads and proves the rationality of the established model.