Multiscale Approach to Micro-Poro-Mechanical Modelling of Unsaturated Shales

  • Richard WanEmail author
  • Mahdad Eghbalian
Conference paper
Part of the Springer Series in Geomechanics and Geoengineering book series (SSGG)


The paper outlines the multiscale mathematical formulation of clay-rich shales as a swelling capillary porous medium with a resolution as fine as the nanoscale. The starting point is the description of the physicochemical interactions between elementary crystalline units–the so-called clay sheets or platelets. By way of homogenization, the clay platelet physics is upscaled to represent a system of randomly dispersed shale particles at the microscale with the void spaces partially saturated with a liquid, i.e. water. The end result is the constitutive description of clay shales enriched with microstructural details down to the clay platelet level that can readily describe swelling or shrinkage in terms of physicochemical loading.


Matric Suction Uniform Strain Shale Sample Clay Platelet Clay Shale 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



Financial support for this research was provided by the Natural Sciences and Engineering Research Council of Canada (NSERC) and Foundation CMG.


  1. Budiansky B (1965) On the elastic moduli of some heterogeneous materials. J Mech Phys Solids 13:223–227CrossRefGoogle Scholar
  2. Cariou S, Dormieux L, Skoczylas F (2013) An original constitutive law for Callovo-Oxfordian argillite, a two-scale double-porosity material. Appl Clay Sci 80–81:18–30CrossRefGoogle Scholar
  3. Chateau X, Dormieux L (2002) Micromechanics of saturated and unsaturated porous media. Int J Numer Anal Methods Geomech 26(8):831–844CrossRefzbMATHGoogle Scholar
  4. Dormieux L, Kondo D, Ulm F-J (2006a) Microporomechanics. Wiley, Chichester. doi: 10.1002/0470032006
  5. Dormieux L, Lemarchand E, Coussy O (2003) Macroscopic and micromechanical approaches to the modelling of the osmotic swelling in clays. Transp Porous Media 50(1–2):75–91CrossRefGoogle Scholar
  6. Dormieux L, Lemarchand E, Sanahuja J (2006b) Comportement macroscopique des mat´eriaux poreux `a microstructure en feuillets. Comptes Rendus - Mec 334(5):304–310CrossRefzbMATHGoogle Scholar
  7. Hill R (1965) A self-consistent mechanics of composite materials. J Mech Phys Solids 13:213–222CrossRefGoogle Scholar
  8. Huyghe J, Janssen J (1997) Quadriphasic mechanics of swelling incompressible porous media. Int J Eng Sci 35(8):793–802. doi: 10.1016/S0020-7225(96)00119-X CrossRefzbMATHGoogle Scholar
  9. Levin V (1967) Thermal expansion coefficient of heterogeneous materials. Mekhanika Tverd Tela 2:83–94Google Scholar
  10. Mainka J, Murad AM, Moyne C, Lima AS (2013) A modified form of Terzaghi’s effective stress principle of unsaturated expansive clays derived from micromechanical analysis. In: Hellmich C, Pichler B, Adam D (eds) Fifth Biot Conf Poromechanics. American Society of Civil Engineers, Vienna, Austria, pp 1425–1434CrossRefGoogle Scholar
  11. Moyne C, Murad M (2003) Macroscopic behavior of swelling porous media derived from micromechanical analysis. Transp Porous Media 50(1–2):127–151MathSciNetCrossRefGoogle Scholar
  12. Moyne C, Murad MA (2006a) A two-scale model for coupled electro-chemo-mechanical phenomena and Onsager’s reciprocity relations in expansive clays: I Homogenization Analysis. Transp Porous Media 62(1):333–380Google Scholar
  13. Moyne C, Murad MA (2006b) A two-scale model for coupled electro-chemo-mechanical phenomena and Onsager’s reciprocity relations in expansive clays: II computational validation. Transp Porous Media 63(1):13–56Google Scholar
  14. Mura T (1987) Micromechanics of defects in solids. Mechanics of elastic and inelastic solids. vol 3, 2nd edn. Springer, Dordrecht. doi: 10.1007/978-94-009-3489-4
  15. Pichler B, Dormieux L (2009) Cracking risk of partially saturated porous media-part I: microporoelasticity model. Int J Numer Anal Methods Geomech 34:135–157zbMATHGoogle Scholar
  16. Sposito G (1972) Thermodynamics of swelling clay-water systems. Soil Sci 114(4)Google Scholar
  17. Sridharan A, Rao GV (1973) Mechanisms controlling volume change of saturated clays and the role of the effective stress concept. Geotechnique 23(3):359–382. doi: 10.1680/geot.1973.23.3.359 CrossRefGoogle Scholar
  18. Tanaka K, Mori T (1972) Note on volume integrals of the elastic field around an ellipsoidal inclusion. J Elasticity 2:199–200CrossRefGoogle Scholar
  19. 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
  20. Wan RG, Eghbalian M (2016) Micromechanics approach to swelling behaviour of capillary-porous media with coupled physics. Submitted to Transport Porous MedGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Civil EngineeringUniversity of CalgaryCalgaryCanada

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