Research on a Microplastic Stochastic Coupled Damage Evolution Model for Freeze–Thaw Rocks

Natural rock contains irregular and randomly distributed micropores and microcracks. Under the action of freeze–thaw cycles, the pore water in these microdefects generates a frost heave force during the water–ice phase transition, leading to pore expansion and damage and the formation of cracks in the rock. This study establishes a microplastic freeze–thaw damage model based on the Clausius–Duhem inequality and an orthogonal rule based on irreversible thermodynamics. We determine the fatigue life that conforms to the characteristics of microplastic damage and the model parameters that satisfy the microplastic fatigue equation. To characterize the heterogeneity of rock materials at the mesoscopic scale and the randomness of initial microdefect distribution, a statistical damage model that conforms to strain-softening characteristics and model parameters that reflect the correlation between the microelement strength and the stress state of rocks are proposed based on the damage variable defined by the defect density ratio and probability density distribution under microelement. A direct correlation between axial strain and stress state is achieved. Based on the damage range and nonnegativity of individual damage variables and considering the increased damage caused by micropore expansion and stress changes, a freeze–thaw stress coupling model is derived to estimate fatigue life and characterize the strength of rock microelements. The damage variables and value range under the coupling state are also estimated. The fatigue, statistical, and freeze–thaw stress coupling damage models of freeze–thawed rocks are verified. The coupled damage evolution model is a power function that directly reflects the axial strain of the stress–strain state and the number of freeze–thaw cycles as independent variables. The model expresses the damage evolution of rocks in the initial compaction, postcompaction, and rapid damage stages. Furthermore, it describes the stochasticity, accumulation process, and regional sensitivity of microelement damage failure, revealing the correlation between the number of freeze–thaw cycles and material brittleness.