Transport in Porous Media

, Volume 19, Issue 2, pp 93–122 | Cite as

A multi-scale theory of swelling porous media: I. Application to one-dimensional consolidation

  • Márcio A. Murad
  • Lynn S. Bennethum
  • John H. Cushman


A theory is developed which describes flow in multi-scale, saturated swelling media. To upscale information, both the hybrid theory of mixtures and the homogenization technique are employed. In particular, a model is formulated in which vicinal water (water adsorbed to the solid phase) is treated as a separate phase from bulk (non-vicinal) water. A new form of Darcy's law governing the flow of both vicinal and bulk water is derived which involves an interaction potential to account for the swelling nature of the system. The theory is applied to the classical one-dimensional consolidation problem of Terzaghi and to verify Low's empirical, exponential, swelling result for clay at the macroscale.

Key words

Swelling clay soil multi-scale flow hybrid mixture theory homogenization consolidation 


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Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Márcio A. Murad
    • 1
    • 2
  • Lynn S. Bennethum
    • 3
  • John H. Cushman
    • 4
  1. 1.Laboratório National de ComputaÇÃo CientificaLNCC/CNPqRio de JaneiroBrazil
  2. 2.The Center for Applied MathPurdue UniversityWest LafayetteUSA
  3. 3.Department of MathematicsPurdue UniversityWest LafayetteUSA
  4. 4.Department of Mathematics and Department of AgronomyPurdue UniversityWest LafayetteUSA

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