Microstructure‐based effective stress for unsaturated frozen soils

Abstract Current knowledge on unsaturated soils suggests that the effective stress should be related to soil microstructures, by which the immobile water attached to the soil solid in micropores and the free water mainly governed by capillary effects in relatively large pores can be distinguished. Paying attention to this knowledge, the micro‐ and macroscopic degrees of saturation to separate micro‐ and macropores occupied by the equivalent water (ice and liquid water) are used and the microstructurally based effective stress for unsaturated frozen soils is proposed using the first law of thermodynamics and the mixture theory. The formulated effective stress considers morphological and mechanical differences of ice in two porosity scales, and can reduce to familiar forms under various assumptions for both frozen–unfrozen and saturated–unsaturated states. Regarding the mixture of microscopic ice and soil particles as the solid skeleton, the elastic bulk modulus of the solid matrix for frozen soils in the regime of compressible solids has also been derived. In addition, other emerging energy‐conjugate pairs have been identified and the second law of thermodynamics is employed to obtain the dissipation inequality in the regime of inelastic deformation for unsaturated frozen soils. The theoretical work presented in this paper could provide an important insight into mechanical constitutive study for unsaturated (saturated) frozen soils in cold regions engineering.