Computational Mechanics

, Volume 42, Issue 2, pp 227–238 | Cite as

A two-scale model for fluid flow in an unsaturated porous medium with cohesive cracks

  • Julien Réthoré
  • René de BorstEmail author
  • Marie-Angèle Abellan
Open Access
Original Paper


A two-scale model is developed for fluid flow in a deforming, unsaturated and progressively fracturing porous medium. At the microscale, the flow in the cohesive crack is modelled using Darcy’s relation for fluid flow in a porous medium, taking into account changes in the permeability due to the progressive damage evolution inside the cohesive zone. From the micromechanics of the flow in the cavity, identities are derived that couple the local momentum and the mass balances to the governing equations for an unsaturated porous medium, which are assumed to hold on the macroscopic scale. The finite element equations are derived for this two-scale approach and integrated over time. By exploiting the partition-of-unity property of the finite element shape functions, the position and direction of the fractures are independent from the underlying discretization. The resulting discrete equations are nonlinear due to the cohesive crack model and the nonlinearity of the coupling terms. A consistent linearization is given for use within a Newton–Raphson iterative procedure. Finally, examples are given to show the versatility and the efficiency of the approach. The calculations indicate that the evolving cohesive cracks can have a significant influence on the fluid flow and vice versa.


Fracture Unsaturated porous medium Multiscale method Multiphase medium Fluid flow Cohesive crack 


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Copyright information

© Springer Verlag 2007

Authors and Affiliations

  • Julien Réthoré
    • 1
  • René de Borst
    • 1
    Email author
  • Marie-Angèle Abellan
    • 2
  1. 1.Faculty of Aerospace EngineeringDelft University of TechnologyDelftNetherlands
  2. 2.LTDS-ENISE-UMR CNRSSaint-EtienneFrance

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