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Coupled HM analysis using zero-thickness interface elements with double nodes. I: Theoretical model. (English) Zbl 1273.74546
Summary: In recent years, the authors have proposed a new double-node zero-thickness interface element for diffusion analysis via the finite element method (FEM) [Int. J. Numer. Anal. Methods Geomech. 28, No. 9, 947–962 (2004; Zbl 1075.76580)]. In the present paper, that formulation is combined with an existing mechanical formulation in order to obtain a fully coupled hydro-mechanical (or HM) model applicable to fractured/fracturing geomaterials. Each element (continuum or interface) is formulated in terms of the displacements ($$u$$) and the fluid pressure ($$p$$) at the nodes. After assembly, a particular expression of the traditional ’$$u-p$$’ system of coupled equations is obtained, which is highly non-linear due to the strong dependence between the permeability and the aperture of discontinuities. The formulation is valid for both pre-existing and developing discontinuities by using the appropriate constitutive model that relates effective stresses to relative displacements in the interface. The system of coupled equations is solved following two different numerical approaches: staggered and fully coupled. In the latter, the Newton-Raphson method is used, and it is shown that the Jacobian matrix becomes non-symmetric due to the dependence of the discontinuity permeability on the aperture. In part II [ibid. 32, No. 18, 2103–2123 (2008; Zbl 1273.74547)], the formulation proposed is verified and illustrated with some application examples.

##### MSC:
 74S05 Finite element methods applied to problems in solid mechanics 74L10 Soil and rock mechanics 74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
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