Sciences in Cold and Arid Regions ›› 2017, Vol. 9 ›› Issue (4): 363-377.doi: 10.3724/SP.J.1226.2017.00363

• ARTICLES • Previous Articles    

Numerical simulation of artificial ground freezing in a fluid-saturated rock mass with account for filtration and mechanical processes

Ivan A. Panteleev1, Anastasiia A. Kostina1, Oleg A. Plekhov1, Lev Yu. Levin2   

  1. 1. Institute of Continuous Media Mechanics, Ural Branch of Russian Academy of Sciences, Perm 614013, Russia;
    2. Mining Institute, Ural Branch of Russian Academy of Sciences, Perm 614007, Russia
  • Received:2017-03-05 Revised:2017-04-05 Published:2018-11-23
  • Contact: Dr. habil. Oleg A. Plekhov, Deputy Director of Institute of Continuous Media Mechanics, Ural Branch of Russian Academy of Science, Academika Koroleva st, 1, Perm 614013, Russia. Tel: +7-342-2378321; E-mail:
  • Supported by:
    This work was supported by the Russian Science Foundation (Grant No. 17-11-01204).

Abstract: This study is devoted to the numerical simulation of the artificial ground freezing process in a fluid-saturated rock mass of the potassium salt deposit. A coupled model of nonstationary thermal conductivity, filtration and thermo-poroelasticity, which takes into account dependence of the physical properties on temperature and pressure, is proposed on the basis of the accepted hypotheses. The considered area is a cylinder with a depth of 256 meters and diameter of 26.5 meters and includes 13 layers with different thermophysical and filtration properties. Numerical simulation was carried out by the finite-element method. It has been shown that substantial ice wall formation occurs non-uniformly along the layers. This can be connected with geometry of the freezing wells and with difference in physical properties. The average width of the ice wall in each layer was calculated. It was demonstrated that two toroidal convective cells induced by thermogravitational convection were created from the very beginning of the freezing process. The effect of the constant seepage flow on the ice wall formation was investigated. It was shown that the presence of the slow flow lead to the delay in ice wall closure. In case of the flow with a velocity of more than 30 mm per day, closure of the ice wall was not observed at all in the foreseeable time.

Key words: artificial ground freezing, numerical simulation, thermogravitational convection, thermo-poroelasiticity

Coussy O, 2004. Poromechanics. Chichester: Wiley, pp. 298.
Coussy O, Monteiro P, 2007. Unsaturated poroelasticity for crystallization in pores. Computers and Geotechnics, 34(4): 279–290. DOI: 10.1016/j.compgeo.2007.02.007.
Coussy O, Monteiro P, 2008. Poroelastic model for concrete exposed to freezing temperature. Cement and Concrete Research, 38(1): 40–48. DOI: 10.1016/j.cemconres.2007.06.006.
Guymon GL, Luthin JN, 1974. A coupled heat and moisture transport model for arctic soils. Water Resources Research, 10(5): 995–1001. DOI: 10.1029/WR010i005p00995.
Hansson K, Šimůnek J, Mizoguchi M, et al., 2004. Water flow and heat transport in frozen soil: numerical solution and freeze-thaw applications. Vadose Zone Journal, 3(2): 693–704. DOI: 10.2113/3.2.693.
Harlan RL, 1973. Analysis of coupled heat-fluid transport in partially frozen soil. Water Resources Research, 9(5): 1314–1323. DOI: 10.1029/WR009i005p01314.
Jame YW, Norum DI, 1980. Heat and mass transfer in a freezing unsaturated porous medium. Water Resources Research, 16(4): 811–819. DOI: 10.1029/WR016i004p00811.
Konrad JM, 1994. Sixteenth Canadian geotechnical colloquium: frost heave in soils: concepts and engineering. Canadian Geotechnical Journal, 31(2): 223–245. DOI: 10.1139/t94-028.
Konrad JM, Morgenstern NR, 1981. The segregation potential of a freezing soil. Canadian Geotechnical Journal, 18(4): 482–491. DOI: 10.1139/t81-059.
Kruschwitz J, Bluhm J, 2005. Modeling of ice formation in porous solids with regard to the description of frost damage. Computational Materials Science, 32(3–4): 407–417. DOI: 10.1016/j.commatsci.2004.09.025.
Mikkola M, Hartikainen J, 2001. Mathematical model of soil freezing and its numerical implementation. International Journal for Numerical Methods in Engineering, 52(5–6): 543–557. DOI: 10.1002/nme.300.
Miller RD, 1978. Frost heaving in non-colloidal soils. In: Proceedings of the Third International Permafrost Conference. Edmonton, Canada, pp. 708–713.
Nishimura S, Gens A, Olivella S, et al., 2009. THM-coupled finite element analysis of frozen soil: formulation and application. Géotechnique, 59(3): 159–171. DOI: 10.1680/geot.2009.59.3.159.
Nixon JF, 1992. Discrete ice lens theory for frost heave beneath pipelines. Canadian Geotechnical Journal, 29(3): 487–497. DOI: 10.1139/t92-053.
Noborio K, McInnes KJ, Heilman JL, 1996a. Two-dimensional model for water, heat, and solute transport in furrow-irrigated soil: I. Theory. Soil Science Society of America Journal, 60(4): 1001–1009. DOI: 10.2136/sssaj1996.03615995006000040007x.
Noborio K, McInnes KJ, Heilman JL, 1996b. Two-dimensional model for water, heat, and solute transport in furrow-irrigated soil: Ⅱ. Field evaluation. Soil Science Society of America Journal, 60(4): 1010–1021. DOI: 10.2136/sssaj1996.03615995006000040008x.
O'Neill K, Miller RD, 1985. Exploration of a rigid ice model of frost heave. Water Resources Research, 21(3): 281–296. DOI: 10.1029/WR021i003p00281.
Rempel AW, Wettlaufer JS, Worster MG, 2004. Premelting dynamics in a continuum model of frost heave. Journal of Fluid Mechanics, 498: 227–244. DOI: 10.1017/S0022112003006761.
Sheng DC, Axelsson K, Knutsson S, 1995. Frost heave due to ice lens formation in freezing soils 1: Theory and verification. Hydrology Research, 26(2): 125–146.
Zhou MM, Meschke G, 2013. A three-phase thermo-hydro-mechanical finite element model for freezing soils. International Journal for Numerical and Analytical Methods in Geomechanics, 37(18): 3173–3193. DOI: 10.1002/nag.2184.
No related articles found!
Full text



No Suggested Reading articles found!