A Critical-State Thermo-Elasto-Viscoplastic Model for Frozen Soils under Freeze–Thaw Cycles

Abstract This paper presents a critical-state thermo-elasto-viscoplastic constitutive model by integrating thermoelasticity and thermo-viscoplasticity and employing two independent stress variables: solid-phase stress and cryogenic suction. The model effectively captures the time-, temperature-, and rate-dependent behavior of frozen soils, such as creep and cyclic freeze–thaw deformations. During freeze–thaw cycles, soils tend to approach a specific residual state for each stress level, called an ultimate freeze–thaw line (UFTL). The distance between the current state of the soil and the UFTL represents the potential for volumetric deformation reduction due to cyclic freeze–thaw processes. Additionally, an empirical relationship is proposed to describe the plastic volume change as a function of the number of freeze–thaw cycles. Comparisons with experimental data from the literature validate the model’s ability to predict the complex mechanical responses of saturated frozen soils under varying thermal and mechanical conditions.