Rock Mechanics and Rock Engineering

, Volume 52, Issue 10, pp 3889–3907 | Cite as

Thermo-Hydro-Mechanical Modeling of Artificial Ground Freezing: Application in Mining Engineering

  • H. TounsiEmail author
  • A. Rouabhi
  • M. Tijani
  • F. Guérin
Original Paper


For decades, artificial ground freezing (AGF) has been used as a temporary soil stabilization and waterproofing technique in multiple geotechnical engineering applications. Experience gained from AGF experiments indicates that the pore water expansion during freezing and the resulting pressure have the potential to induce ground movements in adjacent nonfrozen areas. This process was investigated in this paper using a comprehensive set of in situ temperature and displacement monitoring data collected in the Cigar Lake underground mine, Canada. The data set allowed to investigate the mechanical impact of freezing on a mine tunnel and prompted the need to derive a fully coupled thermo-hydro-mechanical model to predict ground temperature and displacements. Thermodynamically consistent, the model developed for this study is based on a macroscopic continuum approach and uses simplifying assumptions to overcome the computational difficulties associated with the modeling of complex mining environments over a long period of time. This model was used to perform three-dimensional finite-element simulations of the ground freezing and excavation activities in the Cigar Lake mine, showing good agreement with field measurements.


Artificial ground freezing In situ measurements THM modeling 3D finite-element simulations 

List of Symbols

\(\rho ^{\!\!\;\alpha }\)

Apparent density of phase \(\alpha\)

\(\rho _{\!\!\;\alpha }\)

Density of phase \(\alpha\)

\(\nu _{\!\!\;\alpha }\)

Specific volume of phase \(\alpha\)

\(C_{p\alpha }\)

Heat capacity at constant pressure of phase \(\alpha\)

\(\rho C_{p}\)

Volumetric heat capacity

\({\varLambda }_{\!\!\;\alpha }\)

Thermal conductivity of phase \(\alpha\)

\(\varDelta h\)

Latent heat of phase change

\(L_ {\lambda \gamma }\)

Latent heat of phase change on the coexistence curve


Thermal conductivity


Intrinsic permeability

\(k_{\text {r}}\)

Relative permeability of phase \(\lambda\)


Filtration velocity of phase \(\lambda\)

\({\varvec{\psi }}\)

Conductive heat flux vector

\(h_{\!\!\;\alpha }\)

Specific enthalpy of phase \(\alpha\)

\(g_{\!\!\;\alpha }\)

Specific Gibbs free energy of phase \(\alpha\)



\(n_{\!\!\;\alpha }\)

Volume fraction of phase \(\alpha\)

\(S_{\lambda }\)

Liquid saturation degree



\(T_ {\lambda \gamma }\)

Temperature at thermodynamic equilibrium between \(\lambda\) and \(\gamma\)


Coexistence temperature at reference pressure


Reference pressure

\(p_{\!\!\;\alpha }\)

Pressure of phase \(\alpha\)

\(p_ {\lambda \gamma }\)

Pressure at thermodynamic equilibrium between \(\lambda\) and \(\gamma\)

\(p_{\text {c}}\)

Capillary pressure


Equivalent pore pressure


Second-order unit tensor

\({\varvec{\sigma }}\)

Stress tensor

\({\varvec{\varepsilon }}\)

Strain tensor


Displacement vector

\(\varepsilon _{\text {v}}\)

Volumetric strain


Drained bulk modulus

\(K_{\!\!\;\sigma }\)

Bulk modulus of solid phase \(\sigma\)


Young’s modulus


Young’s modulus of the material in the nonfrozen state

\(E_{\text {f}}\)

Young’s modulus of the material in the fully frozen state


Poisson coefficient

Subscripts or superscripts (\(\alpha\))


Solid phase


Liquid water





This research was financially supported by Orano. The authors thank the Cameco Corporation for providing information on the use of artificial ground freezing in the Cigar Lake uranium ore deposit and for allowing this paper to be published.


  1. Bishop C, Mainville A, Yesnik L (2016) Cigar Lake Operation—Northern Saskatchewan, Canada (Technical report, Cameco Corporation)Google Scholar
  2. Bittelli M, Flury M, Roth K (2004) Use of dielectric spectroscopy to estimate ice content in frozen porous media. Water Resour Res. CrossRefGoogle Scholar
  3. Black PB, Tice AR (1989) Comparison of soil freezing curve and soil water curve data for windsor sandy loam. Water Resour Res 25(10):2205−2210CrossRefGoogle Scholar
  4. Casini F, Gens Solé A, Olivella Pastallé S, Viggiani G (2016) Artificial ground freezing of a volcanic ash: laboratory tests and modelling. Environ Geotech 3(3):1−14CrossRefGoogle Scholar
  5. Côté J, Konrad JM (2005) A generalized thermal conductivity model for soils and construction materials. Can Geotech J 42(2):443−458CrossRefGoogle Scholar
  6. Coussy O (1991) Mécanique des milieux poreux. Editions Technip, ParisGoogle Scholar
  7. Coussy O (2005) Poromechanics of freezing materials. J Mech Phys Solids 53(8):1689−1718CrossRefGoogle Scholar
  8. Coussy O, Monteiro PJ (2008) Poroelastic model for concrete exposed to freezing temperatures. Cem Concr Res 38(1):40−48CrossRefGoogle Scholar
  9. Darabi A, Ahangari K, Noorzad A, Arab A (2012) Subsidence estimation utilizing various approaches—a case study: Tehran no. 3 subway line. Tunn Undergr Sp Technol 31:117−127CrossRefGoogle Scholar
  10. Fabbri A (2006) Physico-mécanique des matériaux cimentaires soumis au gel-dégel. Ph.D. thesis, Université de Marne la ValléeGoogle Scholar
  11. Fabbri A, Fen-Chong T (2013) Indirect measurement of the ice content curve of partially frozen cement based materials. Cold Reg Sci Technol 90:14−21CrossRefGoogle Scholar
  12. Feistel R, Wagner W (2006) A new equation of state for H2O ice Ih. J Phys Chem Ref Data 35(2):1021−1047CrossRefGoogle Scholar
  13. Ghoreishian Amiri S, Grimstad G, Kadivar M, Nordal S (2016) Constitutive model for rate-independent behavior of saturated frozen soils. Can Geotech J 53(10):1646−1657CrossRefGoogle Scholar
  14. Hu J, Liu Y, Li Y, Yao K (2018) Artificial ground freezing in tunnelling through aquifer soil layers: a case study in Nanjing metro line 2. KSCE J Civ Eng 22(10):4136−4142CrossRefGoogle Scholar
  15. Jefferson C, Thomas D, Gandhi S, Ramaekers P, Delaney G, Brisbin D, Cutts C, Portella P, Olson R et al (2007) Unconformity-associated uranium deposits of the athabasca basin, saskatchewan and alberta. Bull Geol Surv Can 588:23Google Scholar
  16. Kaczowka A (2018) Geometallurgical and geological evaluation of the high-grade polymetallic unconformity-related cigar lake uranium deposit. Master’s thesisGoogle Scholar
  17. Kang Y, Liu Q, Huang S (2013) A fully coupled thermo-hydro-mechanical model for rock mass under freezing/thawing condition. Cold Regions Sci Technol 95:19−26CrossRefGoogle Scholar
  18. Koopmans RWR, Miller R (1966) Soil freezing and soil water characteristic curves. Soil Sci Soc Am J 30(6):680−685CrossRefGoogle Scholar
  19. Lai Y, Pei W, Zhang M, Zhou J (2014) Study on theory model of hydro-thermal-mechanical interaction process in saturated freezing silty soil. Int J Heat Mass Transf 78:805−819CrossRefGoogle Scholar
  20. Li N, Chen F, Su B, Cheng G (2002) Theoretical frame of the saturated freezing soil. Cold Reg Sci Technol 35(2):73−80CrossRefGoogle Scholar
  21. Li S, Feng XT, Li Z, Zhang C, Chen B (2012) Evolution of fractures in the excavation damaged zone of a deeply buried tunnel during tbm construction. Int J Rock Mech Min Sci 55:125−138CrossRefGoogle Scholar
  22. Li S, Zhang M, Pei W, Lai Y (2017) Experimental and numerical simulations on heat-water-mechanics interaction mechanism in a freezing soil. Appl Thermal Eng 132:209−220Google Scholar
  23. Na S, Sun W (2017) Computational thermo-hydro-mechanics for multiphase freezing and thawing porous media in the finite deformation range. Comput Methods Appl Mech Eng 318:667−700CrossRefGoogle Scholar
  24. Neaupane KM, Yamabe T (2001) A fully coupled thermo-hydro-mechanical nonlinear model for a frozen medium. Comput Geotech 28(8):613−637CrossRefGoogle Scholar
  25. Nishimura S, Gens A, Olivella S, Jardine R (2008) THM-coupled finite element analysis of frozen soil: formulation and application. Géotechnique 59(3):159−171CrossRefGoogle Scholar
  26. Pimentel E, Sres A, Anagnostou G (2012) Large-scale laboratory tests on artificial ground freezing under seepage-flow conditions. Géotechnique 62(3):227−241CrossRefGoogle Scholar
  27. Pimentel E, Papakonstantinou S, Anagnostou G (2012) Numerical interpretation of temperature distributions from three ground freezing applications in urban tunnelling. Tunn Undergr Sp Technol 28:57−69CrossRefGoogle Scholar
  28. Rempel A (2007) Formation of ice lenses and frost heave. JGR Earth Surf. CrossRefGoogle Scholar
  29. Rempel AW, Wettlaufer J, Worster MG (2004) Premelting dynamics in a continuum model of frost heave. J Fluid Mech 498:227−244CrossRefGoogle Scholar
  30. Rouabhi A, Jahangir E, Tounsi H (2018) Modeling heat and mass transfer during ground freezing taking into account the salinity of the saturating fluid. Int J Heat Mass Transf 120:523−533CrossRefGoogle Scholar
  31. Rouabhi A, Tijani M (2017) Modélisation thermo-hydraulique de la congélation artificielle des terrains. In: Gasc-Barbier M, Merrien-Soukatchoff V, Berest P (eds) Manuel de mécanique des roches Tome V - Thermomécanique des roches, chapter 9. Presses des Mines, Paris, pp 281–303Google Scholar
  32. Russo G, Corbo A, Cavuoto F, Autuori S (2015) Artificial ground freezing to excavate a tunnel in sandy soil measurements and back analysis. Tunn Undergr Sp Technol 50:226−238CrossRefGoogle Scholar
  33. Spaans EJ, Baker JM (1996) The soil freezing characteristic: its measurement and similarity to the soil moisture characteristic. Soil Sci Soc Am J 60(1):13−19CrossRefGoogle Scholar
  34. Thomas HR, Cleall PJ, Li Y, Harris C, Kern-Luetschg M (2009) Modelling of cryogenic processes in permafrost and seasonally frozen soils. Geotechnique 59(3):173−184CrossRefGoogle Scholar
  35. Tian H, Wei C, Wei H, Zhou J (2014) Freezing and thawing characteristics of frozen soils: bound water content and hysteresis phenomenon. Cold Regions Sci Technol 103:74−81CrossRefGoogle Scholar
  36. Van Genuchten MT (1980) A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci Soc Am J 44(5):892−898CrossRefGoogle Scholar
  37. Vitel M (2015) Modélisation thermo-hydraulique de la congélation artificielle des terrains. Ph.D. thesis, Paris, ENMPGoogle Scholar
  38. Vitel M, Rouabhi A, Tijani M, Guérin F (2016) Modeling heat and mass transfer during ground freezing subjected to high seepage velocities. Comput Geotechn 73:1−15CrossRefGoogle Scholar
  39. Vitel M, Rouabhi A, Tijani M, Guérin F (2016) Thermo-hydraulic modeling of artificial ground freezing: application to an underground mine in fractured sandstone. Comput Geotech 75:80−92CrossRefGoogle Scholar
  40. Wagner W, Pruß A (2002) The iapws formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use. J Phys Chem Ref Data 31(2):387−535CrossRefGoogle Scholar
  41. Wettlaufer J, Worster MG (2006) Premelting dynamics. Annu Rev Fluid Mech 38:427−452CrossRefGoogle Scholar
  42. Yan Q, Xu Y, Yang W, Geng P (2018) Nonlinear transient analysis of temperature fields in an AGF project used for a cross-passage tunnel in the Suzhou metro. KSCE J Civ Eng 22:1473–1483CrossRefGoogle Scholar
  43. Zeng Q (2011) Poromechanical behavior of cement-based materials subjected to freeze-thaw actions with salts: modeling and experiments. Ph.D. thesis, Université Paris-EstGoogle Scholar
  44. Zhang Y, Michalowski RL (2015) Thermal-hydro-mechanical analysis of frost heave and thaw settlement. J Geotech Geoenviron Eng 141(7):04015027CrossRefGoogle Scholar
  45. Zhou J, Li D (2012) Numerical analysis of coupled water, heat and stress in saturated freezing soil. Cold Regions Sci Technol 72:43−49CrossRefGoogle Scholar
  46. Zhou M, Meschke G (2013) A three-phase thermo-hydro-mechanical finite element model for freezing soils. Int J Numer Anal Methods Geomech 37(18):3173−3193CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.MINES ParisTech, PSL Research University, Centre de GéosciencesFontainebleauFrance
  2. 2.ORANOCourbevoieFrance

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