Numerical simulation of freeze/thaw front propagation in a sample of porous media
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Published
Sep 21, 2024
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Abstract
The freezing of water in porous media depends on various characteristics such as pore size, distribution of grains or boundary conditions. In this contribution we describe a numerical model of freeze/thaw process of a soil sample on the centimeter scale (laboratory sample of repacked sand with relatively low porosity and water) using the finite element method. The model is based on the Štefan problem with a modified latent heat release depending on the water content and is treated in axial symmetry the sample domain. We investigate the sensitivity of this model on initial conditions, material properties and boundary conditions. This contributes to a more profound understanding of freeze/thaw processes observed under laboratory conditions.
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Jex, M., Beneš, M., Sněhota, M., Sobotková, M., & Jeřábek, J.
(2024).
Numerical simulation of freeze/thaw front propagation in a sample of porous media.
Proceedings Of The Conference Algoritmy, , 139 - 148.
Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/view/2163/1035
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References
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[24] Michalowski R.L., and Zhu M., Frost heave modelling using porosity rate function, The International Journal for Numerical and Analytical Methods in Geomechanics, Volume 30, pp. 703-722, 2006.
[25] Liu Z., Muldrew K., Wan R.G., and Elliott J.A., Measurement of freezing point depression of water in glass capillaries and the associated ice front shape, Physical review. E, Statistical, nonlinear, and soft matter physics, Volume 67(6 Pt 1), 061602, 2003.
[26] Wodecki A., Strachota P., Oberhuber T., Škardová K., Balázsová M., and Bohatý M., Numerical optimization of the Dirichlet boundary condition in the phase field model with an application to pure substance solidification, Computers & Mathematics with Applications, Volume 145, pp. 90-105, 2023.
[27] Wodecki A., Balázsová M., Strachota P., and Oberhuber T., Existence of optimal control for Dirichlet boundary optimization in a phase field problem, Journal of Dynamical and Control Systems, Volume 29, pp. 1425-1447, 2023.
[2] Guymon G.L., Berg R.L., and Hromadka T.V., Mathematical model of frost heave and thaw settlement in pavements, CRREL report ; 93-2, Hanover, 1993.
[3] Nikolaev P., Jivkov A.P., Margetts L., and Sedighi M., Non-local modelling of freezing and thawing of unsaturated soils, Advances in Water Resources, Volume 184, 104614, 2024.
[4] Lu B.Q., et al., Cooling and wetting of soil decelerated ground freezing-thawing processes of the active layer in Xing’an permafrost regions in Northeast China, Advances in Climate Change Research, Volume 14, pp. 126-135, 2023.
[5] Furuzumi M., et al., Thermal and freezing strains on a face of wet sandstone samples under a subzero temperature cycle, Journal of Thermal Stresses, Volume 27, pp. 331–344, 2004.
[6] Gens A., Soil-environment interactions in geotechnical engineering, Géotechnique, Volume 60(1), pp. 3–74, 2010.
[7] Li J., et al., Modeling permafrost thaw and ecosystem carbon cycle under annual and seasonal warming at an arctic tundra site in Alaska, Journal of Geophysical Research: Biogeosciences, Volume 119, Issue 6, pp. 1129–1146, 2014.
[8] Coussy O., Poromechanics of freezing materials, Journal of the Mechanics and Physics of Solids, Volume 53, pp. 1689–1718, 2005.
[9] Nishimura S., Gens A., Olivella S., and Jardine R.J., THM-coupled finite element analysis of frozen soil: formulation and application, Géotechnique, Volume 59, Issue 3, pp. 159–171, 2009.
[10] Mikkola M., and Hartikainen J., Mathematical model of soil freezing and its numerical implementation, International Journal for Numerical Methods in Engineering, Volume 52, pp. 543–557, 2001.
[11] Lei D., Yang Y., Cai C., Chen Y., and Wang S., The Modelling of freezing process in saturated soil based on the thermal-hydro-mechanical multi-physics field coupling theory, Water, Volume 12, 2684, 2020.
[12] Sweidan A.H., Heider Y., and Markert B, A unified water/ice kinematics approach for phase-field thermo-hydro-mechanical modeling of frost action in porous media, Computer Methods in Applied Mechanics and Engineering, Volume 372, 113358, 2020.
[13] Sweidan A.H., Niggemann K., Heider Y., Ziegler M., and Markert B., Experimental study and numerical modeling of the thermo-hydro-mechanical processes in soil freezing with different frost penetration directions, Acta Geotechnica, Volume 17, pp. 231–255, 2022.
[14] Suh H.S., and Sun W.C., Multi-phase-field microporomechanics model for simulating icelens growth in frozen soil, International Journal for Numerical and Analytical Methods in Geomechanics, Volume 46, Issue 12, pp. 2307–2336, 2022.
[15] Gerber D., Wilen L.A., Dufresne E.R., and Style R.W., Polycrystallinity enhances stress buildup around ice, Physical Review Letters, Volume 131, 208201, 2023.
[16] Žák A., Beneš M., and Illangasekare T.H. and Trautz A.C., Mathematical model of freezing in a porous medium at micro-scale, Communications in Computational Physics, Volume 24, Issue 2, pp. 557–575, https://doi.org/10.4208/cicp.OA-2017-0082, 2018.
[17] Žák A., and Beneš M., Micro-scale model of thermomechanics in solidifying saturated porous media, Acta Physica Polonica A., Volume 134, Issue 3, pp. 678-682, https://doi.org/10.12693/APhysPolA.134.678, 2018.
[18] Žák A., Beneš M., and Illangasekare T.H., Pore-scale model of freezing inception in a porous medium, Computer Methods in Applied Mechanics and Engineering, Volume 414, 116166, https://doi.org/10.1016/j.cma.2023.116166, 2023.
[19] Žák A., Beneš M., and Illangasekare T. H., Analysis of model of soil freezing and thawing, IAENG International Journal of Applied Mathematics, Volume 43, Issue 3, pp. 127–134, September 2013.
[20] Nicolsky D. J., Romanovsky V. E., and Panteleev G. G., Estimation of soil thermal properties using in-situ temperature measurements in the active layer and permafrost, Cold Regions Science and Technology, Volume 55, pp. 120–129, 2009.
[21] Sklenář J., Magnetic resonance imaging of freezing and thawing of water in porous media, Master Thesis, Czech Technical University in Prague, Faculty of Civil Engineering, 2022.
[22] Gurtin M.E., On the two-phase Stefan problem with interfacial energy and entropy, Archive for Rational Mechanics and Analysis, Volume 96, pp. 199-241, 1986.
[23] Schmidt A., Computation of three dimensional dendrites with finite elements, Journal of Computational Physics, Volume 125, pp. 293-312, 1996.
[24] Michalowski R.L., and Zhu M., Frost heave modelling using porosity rate function, The International Journal for Numerical and Analytical Methods in Geomechanics, Volume 30, pp. 703-722, 2006.
[25] Liu Z., Muldrew K., Wan R.G., and Elliott J.A., Measurement of freezing point depression of water in glass capillaries and the associated ice front shape, Physical review. E, Statistical, nonlinear, and soft matter physics, Volume 67(6 Pt 1), 061602, 2003.
[26] Wodecki A., Strachota P., Oberhuber T., Škardová K., Balázsová M., and Bohatý M., Numerical optimization of the Dirichlet boundary condition in the phase field model with an application to pure substance solidification, Computers & Mathematics with Applications, Volume 145, pp. 90-105, 2023.
[27] Wodecki A., Balázsová M., Strachota P., and Oberhuber T., Existence of optimal control for Dirichlet boundary optimization in a phase field problem, Journal of Dynamical and Control Systems, Volume 29, pp. 1425-1447, 2023.