Freezing Deformation of Saturation-Dependent Porous Media Considering Interface Energy and Microstructure Effects: from Thermodynamics-Based Macroscopic Constitutive Relation to Micromechanical Upscaling Model

This work provides a theoretical framework originated from thermodynamics and micromechanics theories to quantitatively determine the dependence of the freezing deformation of saturation-dependent porous media on the interface energy and microstructures. In the thermodynamics theory, the macroscopic constitutive model including the interface energy and three loading cases (i.e., elasticity, pore pressure, and thermal stress) is derived. Subsequently, in the micromechanics theory, an upscaling model for the macroscopic constitutive relation is obtained, incorporating microstructure information under three loading cases provided by the thermodynamics-based model. The constitutive form of the latter micromechanical upscaling model is the same as the former thermodynamics-based model. Importantly, the proposed upscaling model not only gives a powerful physical understanding of the freezing deformation affected by interface energy, microstructure characteristics of porous media, and environmental conditions, but also provides the microstructure-dependent thermo-poro-elastic properties as the freezing deformation capacity of porous media. Comparisons against experimental measurements of porous materials suggest the reliability of the present theoretical framework in estimating the freezing deformation of saturated and unsaturated porous media. The proposed model highlights the effects of pore configurations, such as pore size distribution (PSD) and porosity, on the freezing deformation of saturation-dependent porous media. The results elucidate that the interface energy reduces the pressure acting on the pore wall, which is more significant under unsaturated conditions. Furthermore, the effect of interface energy on freezing deformation strongly depends on PSD and saturation degrees of porous media. These results can provide guidance for evaluating infrastructure durability and designing frost-resistant porous materials.