# Developing a Micro-Scale Model of Soil Freezing

## Main Article Content

## Abstract

In this contribution, we analyze thermal and mechanical effects related to the soil freezing at micro-scale. A simple 2D mechanical model of the phase transition in a pore is presented. This model is based on the Navier equations and on the continuity equation and serves mainly for a verification of the dynamics of the mechanical reaction. A basic qualitative computational study of this model is presented. Further, this model is generalized by supplementing it with a heat balance law and considering pore structure geometry onto the thermo-mechanical model describing the mutual interaction of all pore components. For this model, some basic qualitative studies, which indicate non-trivial progress of the interaction, are presented as well.

## Article Details

How to Cite

Žák, A., Beneš, M., & Illangasekare, T.
(2016).
Developing a Micro-Scale Model of Soil Freezing.

*Proceedings Of The Conference Algoritmy,*, 234-243. Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/view/412/329
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Articles

## References

[1] R. R. Gilpin, A Model for the Prediction of Ice Lensing and Frost Heave in Soils, Water Resources Research, 16/5 (1980), pp. 918–930.

[2] A. C. Fowler, Secondary Frost Heave in Freezing Soils, SIAM J. APPL. Math., 49/4 (1989), pp. 991–1008.

[3] J. Hartikainen and M. Mikkola, Thermomechanical Model of Freezing Soil by Use of the Theory of Mixtures, in Proc. of the 6th Finnish Mechanics Days, (1997), pp. 1–6.

[4] R. L. Michalowski, A Constitutive Model of Saturated Soils for Frost Heave Simulations, Cold Region Science and Technology, 22/1 (1993), pp. 47–63.

[5] R. D. Miller, Frost Heaving in Non-Colloidal Soils, in Proc. 3rd Int. Conference on Per- mafrost, (1978), pp. 707–713.

[6] A. W. Rempel, J. S. Wettlaufer, and M. G. Worster, Interfacial premelting and the thermomolecular force: thermodynamic buoyancy, Physical Review Letters, 87 (2001).

[7] A. Mikelić and M.F. Wheeler, On the interface law between a deformable porous medium containing a viscous fluid and an elastic body, Math. Models Methods Appl. Sci., 22 (2012).

[8] https://www.comsol.com/

[9] A. Žák, M. Beneš, and T. H. Illangasekare, Analysis of Model of Soil Freezing and Thawing, IAENG International Journal of Appl. Mathematics, 43/3 (2013), pp. 127–134.

[2] A. C. Fowler, Secondary Frost Heave in Freezing Soils, SIAM J. APPL. Math., 49/4 (1989), pp. 991–1008.

[3] J. Hartikainen and M. Mikkola, Thermomechanical Model of Freezing Soil by Use of the Theory of Mixtures, in Proc. of the 6th Finnish Mechanics Days, (1997), pp. 1–6.

[4] R. L. Michalowski, A Constitutive Model of Saturated Soils for Frost Heave Simulations, Cold Region Science and Technology, 22/1 (1993), pp. 47–63.

[5] R. D. Miller, Frost Heaving in Non-Colloidal Soils, in Proc. 3rd Int. Conference on Per- mafrost, (1978), pp. 707–713.

[6] A. W. Rempel, J. S. Wettlaufer, and M. G. Worster, Interfacial premelting and the thermomolecular force: thermodynamic buoyancy, Physical Review Letters, 87 (2001).

[7] A. Mikelić and M.F. Wheeler, On the interface law between a deformable porous medium containing a viscous fluid and an elastic body, Math. Models Methods Appl. Sci., 22 (2012).

[8] https://www.comsol.com/

[9] A. Žák, M. Beneš, and T. H. Illangasekare, Analysis of Model of Soil Freezing and Thawing, IAENG International Journal of Appl. Mathematics, 43/3 (2013), pp. 127–134.