In cold locales, the thermal conductivity of soil porous media varies according to their composition and the phase state of the substance contained within the pore space. During the winter, water and other media in the soil pore space freeze-thaw, resulting in their phase state, composition, distribution, and significant thermal conductivity changes. There are some shortcomings in the current research regarding the thermal conductivity change pattern of unsaturated ice-containing soils. In this paper, the representative elementary volume (REV) selection method is given for unsaturated ice-containing soil with porosity as a representative state variable. Under the condition of freeze-thaw, two thermal conductivity REV analysis models for unsaturated ice-containing soil are established: a simplified volume-weighted average REV model and a fine volume-weighted average REV model; accordingly, a macroscopic thermal conductivity analysis model is given. The computational analysis is carried out with an actual unsaturated ice-containing soil example. The influence of the application of frozen soil in China is examined for its effect on the variation law of the thermal conductivity of porous medium. The variation characteristics of thermal conductivity of permafrost soil with related parameters (porosity, water ratio, moisture percentage, ice content, and tortuosity) are discussed. The model built in this paper provides novel concepts and methods for analyzing the thermal conductivity characteristics of unsaturated soil, as well as enhancing and advancing the analysis.

The relationship between the stress-strain characteristics of ice-containing unsaturated soil and its various physical properties has important implications for the design and construction of transportation and building projects. The study also reveals the varying phases of the substance that can be deposited within the pore space. During winter, the freezing-thawing cycles affect the various media that can be deposited within the soil pore space, such as water and other water. The presence of water and others in the soil’s pores can cause a freeze-thawing phenomenon and a significant change in the material’s elastic modulus. This paper presents a method that uses the representative elementary volume (REV) model to perform a representative state variable analysis on an unsaturated ice-containing soil with porosity. The three stress-strain REV models that were developed for the study were designed to analyze the properties of an unsaturated ice-containing soil under freezing-thawing conditions. Then a comprehensive analysis of the soil’s various components was performed. The effects of frozen soil on the change law of the relationship between different porous medium are studied. The study also explores the effects of the presence of porosity on the variation law of the frozen soil relationship between the stress-strain. The paper presents the study of the variation characteristics of the elastic modulus of permafrost soil. It also explores the various factors (porosity, moisture content, ice percentage, and tortuosity) that influence the stress-strain characteristics of unsaturated soil.

In cold regions, the pore space’s composition and phase state can affect the elastic modulus of the media. During the winter, the freezing conditions in the soil results in the release of water from the pore space, which results in significant changes in the media’s distribution and composition. There are a few weaknesses in the current research with respect to the elastic modulus change example of frozen soil. This paper presents that the Representative Macroscopic Volume (RMV) choice strategy is provided for frozen soil with porosity as a typical condition variable. Under the state of freezing, a “three-box” analytical model for stress-strain calculation of frozen soil porous media is established, namely, the black-box model, the gray-box model, and the white-box model. The relevant equations for calculating elastic modulus are presented based on the proposed “three-box” model and the analysis of the stress conduction process. Results show that the discrepancy between the computed and experimental values of the white-box model is slight, and the elastic modulus of frozen soil calculated by the model established in this paper is consistent with the actual state. It can be deduced that the model established in this paper has practicality and the conclusions of the study are of guiding significance for the application of frozen soil.