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Double-scale modelling of the hydro-mechanical behaviour of clay rocks
van den Eijnden, Abraham Pieter; Bésuelle, Pierre; Chambon, René
2012
 

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Keywords :
static condensation
Abstract :
[en] The work to be presented concerns the modelling of hydro-mechanical behaviour of clayey rocks as encountered in the field of underground nuclear waste storage. For the modelling a two scale finite element (FE2) approach is envisioned, containing a macro-scale model of a poro mechanical continuous medium and a micro-scale model of a representative elementary volume (REV) containing a (discontinuous) microstructure of solid grains and pore space. The difference with classical finite element modelling is the absence of a direct constitutive relation on the macro scale. Instead, for each integration point on the macro level, a REV is modelled on the micro level to numerically derive this relation to be used on the macro level. In this way the constitutive behaviour at the macro-scale is dictated by the global response of the REV that serves as its (numerical) constitutive relation. This constitutive relation can be found by homogenization of the REV. In continuation of the work of Frey [1], [2], a finite element model is developed to model the constitutive relation for the macro level by means of a REV with a microstructure. The microstructure contains elastic, impermeable grains with interface elements to model the intergranular contacts. These interface elements are used for both fluid flow and intergranular cohesive and frictional forces. The hydraulic and mechanical part are coupled by the connectivity of the interfaces itself depending on an equivalent opening between the opposite sides of the interface elements (the grain boundaries). The representation of an actual opening by these interface elements allows deformation and damage to concentrate in the interfaces. Intergranular cohesive forces are modelled by damage laws for normal and tangential displacements of opposite interface sides. By defining different grain geometries and arrangements, different macroscopic responses can be obtained. In this way, complex macroscopic constitutive behaviour can be modelled with very simple interface damage models at the micro level. However, the use of the FE2 method is computationally expensive. The derivation of the consistent tangent stiffness matrix of the global response of the REV is part of this computational expense. In order to overcome a significant part of this computational expense of the method, the idea is to use analytical homogenization to derive the tangent stiffness matrix from the REV instead of more straightforward numerical homogenization. A particular challenge in the application of analytical condensation is to overcome the discontinuous nature of the interface elements that are caused by cohesive forces over the interface opening. Once this is obtained, condensation of the finite element system of equations and the application of the boundary conditions can lead to an analytic solution for the consistent tangent stiffness matrix at the macro scale. For a continuous, solid phase media this condensation method for homogenization is described in [3]. It is the goal to add the coupling with the fluid phase and the cohesive forces to this method of analytic homogenization. In addition to the homogenization, the more straightforward approach to reduce calculation time by parallelization is foreseen. References: [1] Frey, J. (2010), Modélisation multi-échelle de l’endommagement hydroméchanique des roches argileuses, PhD Thesis, INP Grenoble, Université de Grenoble [2] Frey, J; Chambon, R; Dascalu C; (2012), A two scale poromechanical model for cohesive rocks accepted for publication, Acta Geotechnica [3] Kouznetsova, V; Brekelmans, W.A.M; Braaijens, F.P.T (2001) An approach to micro-macro modeling of heterogeneous materials, Computational Geomechanics 27, 37-48
Disciplines :
Civil engineering
Author, co-author :
van den Eijnden, Abraham Pieter ;  Université de Liège - ULiège > Doct. sc. ingé. (architecture, génie civ. & géol.)
Bésuelle, Pierre;  3SR Grenoble
Chambon, René;  3SR-Grenoble
Language :
English
Title :
Double-scale modelling of the hydro-mechanical behaviour of clay rocks
Publication date :
02 October 2012
Event name :
ALERT Workshop 2012
Event organizer :
ALERT Geomaterials
Event place :
Aussois, France
Event date :
1-3 October 2012
Audience :
International
Available on ORBi :
since 25 September 2013

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