Work conjugate stress and strain variables for unsaturated frozen soils

In general, most of the foundations of structures in the cold regions rest on frozen soils which are often under unsaturated state and subject to mechanical and thermal loads. The thermal loads will induce water migration and water-ice phase change, as a result, the dynamic phase transition between unfrozen water and ice occurs and degree of saturation in frozen soils is affected. These complicate the understanding of the strength and deformation characteristics of frozen soils under mechanical and thermal loads. Furthermore, it leads to a necessity to develop a coupling thermo-hydro-mechanical model for practical permafrost engineering. Up to date, there are limited studies to quantify this complicated problem by a framework with proper stress and strain variables for unsaturated frozen soils. This study derives the expression of input work rate for unsaturated frozen soils based on the multiphase porous media theory. Work conjugate stress and strain variables have been determined based on the expression of input work rate. This set of variables not only can smoothly transit from unsaturated frozen state to unsaturated unfrozen state when temperature is above freezing point, but also can smoothly transit from unsaturated state to saturate state. The proposed framework can be consistently applied to multi-phase soils with unsaturated frozen soils, unsaturated soils and saturated soils. Moreover, the application of the framework can be further extended to other porous mediums. Additionally, the selected variables in this framework are validated against published experimental results. This framework can subsequently be used to establish the coupled thermo-hydro-mechanical models for unsaturated and saturated frozen soils.