A unified water/ice kinematics approach for phase-field thermo-hydro-mechanical modeling of frost action in porous media

Abstract

This research work introduces a novel phase-field thermo-hydro-mechanical (P-THM) modeling approach that allows to deeply understand and model the freezing–thawing cyclic process in a fluid-saturated porous medium. In this, a biphasic macroscopic, non-isothermal porous media model, augmented by the phase-field method (PFM), is applied to account for the temperature development, the interstitial pore-fluid flow, and the volumetric deformations due to ice formation (phase change). Utilizing the theory of porous media (TPM) in the continuum mechanical formulation provides a well-founded basis for the description of deformable, fluid-saturated, non-isothermal porous solid materials. Of particular importance in the underlying work is the unified kinematics treatment of the ice and water constituents as a single pore-fluid, where the PFM is employed for the description of the phase transition between both constituents. The PFM is a diffuse-interface approach that relies on the specification of the free energy density function as the main driving force in the phase transition. It employs a scalar-valued, phase-field variable to indicate the state of the pore-fluid, i.e., a solid (ice) or a liquid (water). A significant virtue of using the PFM approach is its viability in the implementation within standard finite element frameworks, as no need to explicitly track the moving boundaries (interfaces) of the phase-change constituent. The numerical examples and comparisons presented at the end of the manuscript demonstrate the ability, reliability and usefulness of the proposed modeling framework in describing the freezing–thawing process in a saturated porous solid under thermal loading within an elastic deformation limit.