A MATHEMATICAL MODEL OF FREEZING OF UNSATURATED SOILS IN THE PRESENCE OF CAPILLARY PRESSURE
https://doi.org/10.25587/SVFU.2017.2.9249
Abstract
A mathematical model of freezing of soils saturated with a heterogeneous mixture of water and air in the presence of capillary pressure is proposed. The derivation of the diffusion equation for the redistribution of moisture from the laws of conservation of mass and momentum is given. This allows us to define the diffusion coefficient through the parameters of the porous medium and fluids. Balance relations through the water crystallization front is derived. A self-similar solution of the problem in the linear approximation is obtained. It is shown that the growth of capillary forces reduces the amount of ice formed, and a more intensive freezing regime leads to an increase in the saturation with ice.
Supporting agencies: The work was supported by the grant from the Russian Foundation for Basic Research (project code 16–01–00363).
About the Author
G. G. Tsypkin
Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences
Russian Federation
Russian Federation
Georgii G. Tsypkin
Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, pr. Vernadskogo 101-1, Moscow 119526, Russia
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Review
For citations:
Tsypkin G.G. A MATHEMATICAL MODEL OF FREEZING OF UNSATURATED SOILS IN THE PRESENCE OF CAPILLARY PRESSURE. Mathematical notes of NEFU. 2017;24(2):94-105. (In Russ.) https://doi.org/10.25587/SVFU.2017.2.9249
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