Abstract 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.

中文翻译：

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非饱和冻土的工作共轭应力和应变变量

摘要 一般而言，寒冷地区建筑物的地基大多位于冻土上，冻土常处于非饱和状态，承受机械载荷和热载荷。热载荷会引起水的迁移和水冰相变，从而导致未冻水和冰之间发生动态相变，影响冻土的饱和度。这些使理解机械和热载荷下冻土的强度和变形特性变得复杂。此外，有必要开发用于实际多年冻土工程的热-水-机械耦合模型。迄今为止，通过具有适当应力和应变变量的非饱和冻土框架来量化这一复杂问题的研究还很有限。本研究基于多相多孔介质理论推导了非饱和冻土的输入功率表达式。功共轭应力和应变变量已根据输入功率的表达式确定。这组变量不仅可以在温度高于冰点时从非饱和冻结状态平滑过渡到不饱和解冻状态，而且可以从不饱和状态平滑过渡到饱和状态。所提出的框架可以一致地应用于具有非饱和冻土、非饱和土壤和饱和土壤的多相土壤。此外，该框架的应用可以进一步扩展到其他多孔介质。此外，此框架中选定的变量已根据已发布的实验结果进行验证。