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

By J. Réthoré, R. de Borst, Marie-Angèle Abellan. 2008

158 citations recorded by the source corpus.

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.

Subfields: Civil and Structural Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/6c077c31d465d8a4d791d9741e0d6294c49397d8

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In Civil and Structural Engineering

In Mechanics of Materials

Citations in the corpus

Hydro‐mechanical modeling of cohesive crack propagation in multiphase porous media using the extended finite element method (2013, methodology): “in [7] and [8], respectively, using the extended finite element method, which is now extended to three-phase porous media.”