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A two-scale model for fluid flow in an unsaturated porous medium with cohesive cracks. (English) Zbl 1154.76053
Summary: We develop a two-scale model 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 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 finite element shape functions, the position and direction of fractures are independent of the underlying discretization. The resulting discrete equations are nonlinear due to the cohesive crack model and the nonlinearity of coupling terms. A consistent linearization is given for use within a Newton-Raphson iterative procedure. Finally, examples are given to show the versatility and efficiency of the approach. The calculations indicate that the evolving cohesive cracks can have a significant influence on the fluid flow and vice versa.

##### MSC:
 76S05 Flows in porous media; filtration; seepage 76M10 Finite element methods applied to problems in fluid mechanics 74R99 Fracture and damage
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