Mathematical Model of Freezing in a Porous Medium at Micro-Scale

Abstract

We present a micro-scale model describing the dynamics of pore water phase transition and associated mechanical effects within water-saturated soil subjected to freezing conditions. Since mechanical manifestations in areas subjected to either seasonal soil freezing and thawing or climate change induced thawing of permanently frozen land may have severe impacts on infrastructures present, further research on this topic is timely and warranted.
For better understanding the process of soil freezing and thawing at the field-scale, consequent upscaling may help improve our understanding of the phenomenon at the macro-scale.
In an effort to investigate the effect of the pore water density change during the propagation of the phase transition front within cooled soil material, we have designed a 2D continuum micro-scale model which describes the solid phase in terms of a heat and momentum balance and the fluid phase in terms of a modified heat equation that accounts for the phase transition of the pore water and a momentum conservation equation for Newtonian fluid. This model provides the information on force acting on a single soil grain induced by the gradual phase transition of the surrounding medium within a nontrivial (i.e. curved) pore geometry. Solutions obtained by this model show expected thermal evolution but indicate a non-trivial structural behavior.