Mathematical Model of Freezing in a Porous Medium at Micro-Scale (Communications in Computational Physics, 2018)
We present a micro-scale model describing the dynamics of pore water phasetransition and associated mechanical effects within water-saturated soil subjected tofreezing conditions. Since mechanical manifestations in areas subjected to either seasonal soil freezing and thawing or climate change induced thawing of permanentlyfrozen land may have severe impacts on infrastructures present, further research onthis 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 themacro-scale.In an effort to investigate the effect of the pore water density change during thepropagation of the phase transition front within cooled soil material, we have designeda 2D continuum micro-scale model which describes the solid phase in terms of a heatand momentum balance and the fluid phase in terms of a modified heat equation thataccounts for the phase transition of the pore water and a momentum conservationequation for Newtonian fluid. This model provides the information on force acting ona single soil grain induced by the gradual phase transition of the surrounding mediumwithin a nontrivial (i.e. curved) pore geometry. Solutions obtained by this model showexpected thermal evolution but indicate a non-trivial structural behavior.
Keywords: Freezing; mechanics; phase-transition; soil; micro-scale.