Skip to main content
SpringerLink
Log in

Micromechanical approach to unsaturated water flow in structured geomaterials by two-scale computations

  • Research Paper
  • Published:
Acta Geotechnica Aims and scope Submit manuscript

Abstract

This article presents a micromechanical approach to the problem of unsaturated water flow in heterogeneous porous media in transient conditions. The numerical formulation is based on the two-scale model obtained previously by periodic homogenization. It allows for a coupled solution of the non-linear flow equations at macroscopic and microscopic scales and takes into account the macroscopic anisotropy of the medium and the local non-equilibrium of the capillary pressure. The model was applied to simulate two-dimensional water infiltration at constant flux into an initially dry medium containing inclusions of square and rectangular shapes. The numerical results showed the influence of the inclusion–matrix conductivity ratio and the local geometry on the macroscopic behavior. The influence of the conductivity ratio manifested itself by the acceleration or retardation of the onset of the macroscopic water flux at the outlet, while the local geometry (anisotropy) significantly affected the macroscopic spatial distribution of the water flux. Such type of approach can be extended to simulate coupled phenomena (for example hydro-mechanical problems) with evolving local geometry.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  1. Arbogast T (1997) Computational aspects of dual-porosity models. In: Hornung U (ed) Homogenization and porous media. Springer, New York, pp 203–223

    Google Scholar 

  2. Arbogast T (2002) Implementation of a locally conservative numerical subgrid upscaling scheme for two-phase Darcy flow. Comput Geosci 6:453–481

    Article  MATH  MathSciNet  Google Scholar 

  3. Carsel R, Parrish R (1988) Developing of joint probability distributions of soil water retention characteristics. Water Resour Res 24:755–769

    Article  Google Scholar 

  4. Celia MA, Bouloutas ET, Zarba RL (1990) A general mass-conservative numerical solution for the unsaturated flow equation. Water Resour Res 26:1483–1496

    Google Scholar 

  5. Chen Y, Durlofsky LJ, Gerritsen M, Wen XH (2003) A coupled local-global upscaling approach for simulating flow in highly heterogeneous formations. Adv Water Resour 26:1041–1060

    Article  Google Scholar 

  6. Desbarats AJ (1990) Macrodispersion in sand-shales sequences. Water Resour Res 26:153–163

    Article  Google Scholar 

  7. Durlofsky LJ, Efendiev Y, Ginting V (2007) An adaptive local-global multiscale finite volume element method for two-phase flow simulations. Adv Water Resour 30:576–588

    Article  Google Scholar 

  8. Gens A (2003) The role of geotechnical engineering in nuclear energy utilisation (special lecture). Proc 13th Eur Conf Soil Mech Geotech Engng Prague 3:25–67

    Google Scholar 

  9. Gerke H (2006) Preferential flow descriptions for structured soils. J Plant Nutr Soil Sci 169:382–400

    Article  Google Scholar 

  10. Hou T, Wu XH (1997) A multiscale finite element method for elliptic problems in composite materials and porous media. J Comput Phys 134:169–189

    Article  MATH  MathSciNet  Google Scholar 

  11. Lai C-H, Liu C-W (2001) Accuracy examination of the multiple interacting continua approximation. Proc Natl Sci Counc Repub China A 25:35–39

    Google Scholar 

  12. Lewandowska J, Auriault J-L (2004) Modeling of unsaturated water flow in soils with highly permeable inclusions. Comptes Rendus Mécanique 332:91–96

    Article  MATH  Google Scholar 

  13. Lewandowska J, Laurent J-P (2001) Homogenization modeling and parametric study of moisture transfer in an unsaturated heterogeneous porous medium. Transp Porous Media 45:321–345

    Article  MathSciNet  Google Scholar 

  14. Lewandowska J, Szymkiewicz A, Burzyński K, Vauclin M (2004) Modeling of unsaturated water flow in double porosity soils by the homogenization approach. Adv Water Resour 27:283–296

    Article  Google Scholar 

  15. Lewandowska J, Szymkiewicz A, Boutin C (2005) Modelling of unsaturated hydraulic conductivity of double-porosity soils. Actes de 17ème Congrès Français de Mécanique, CD ROM support (Troyes, 29 August–2 September 2005)

  16. Lunati I, Jenny P (2006) Multiscale finite-volume method for compressible multiphase flow in porous media. J Comput Phys 216:616–636

    Article  MATH  MathSciNet  Google Scholar 

  17. Pruess K, Narasimhan T (1985) A practical method for modeling fluid and heat flow in fractured porous media. Soc Pet Eng J 25:14–26

    Google Scholar 

  18. Ritzi RW, Dominic DF, Slesers AJ, Greer CB, Reboulet EC, Telford JA, Masters RW, Klohe CA, Bogle JL, Means BP (2000) Comparing statistical models of physical heterogeneity in buried-valley aquifers. Water Resour Res 36:3179–3192

    Google Scholar 

  19. Roels S, Carmeliet J, Hens H (2003) Modelling unsaturated moisture transport in heterogeneous limestone. Transp Porous Media 52:333–350

    Article  Google Scholar 

  20. Szymkiewicz A (2005) Calculating effective conductivity of heterogeneous soils by homogenization. Arch Hydro-Eng Environ Mech 52:111–130

    Google Scholar 

  21. Szymkiewicz A, Lewandowska J (2006) Unified macroscopic model for unsaturated water flow in soils of bimodal porosity. Hydrol Sci J 51:1106–1124

    Article  Google Scholar 

  22. Szymkiewicz A, Lewandowska J, Angulo-Jaramillo R, Butlańska J (2007) Two-scale modeling of unsaturated water flow in the double-porosity medium under axi-symmetrical conditions. Can Geotech J (in press)

  23. van Genuchten MTh (1980) A closed form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci Soc Am J 44:892–898

    Article  Google Scholar 

  24. Yue X, E W (2005) Numerical methods for multiscale transport equations and application to two-phase porous media flow. J Comput Phys 210:656–675

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Hydroengineering of the Polish Academy of Sciences, 80328, Gdansk, Poland

    Adam Szymkiewicz

  2. Laboratoire Sols, Solides, Structures – Risques (3S-R), 38041, Grenoble, France

    Jolanta Lewandowska

Authors
  1. Adam Szymkiewicz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jolanta Lewandowska
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jolanta Lewandowska.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Szymkiewicz, A., Lewandowska, J. Micromechanical approach to unsaturated water flow in structured geomaterials by two-scale computations. Acta Geotech. 3, 37–47 (2008). https://doi.org/10.1007/s11440-007-0049-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11440-007-0049-5

Keywords

Search

Navigation