From mixture theory to biot’s approach for porous media.pdf

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From mixture theory to biot’s approach for porous media.pdf

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From mixture theory to biot’s approach for porous media

Int[ J[ Solids Structures Vol[ 24\ Nos 23D24\ pp[ 3508D3524\ 0887 T 0887 Elsevier Science Ltd[ All rights reserved\ Pergamon Printed in Great Britain 9919D6572:87:,*see front matter PII ] S9919D657287#99976D9 FROM MIXTURE THEORY TO BIOT|S APPROACH FOR POROUS MEDIA OLIVIER COUSSY$ Laboratoire Central des Ponts et Chaussees\ Paris\ France LUC DORMIEUX Laboratoire de Mecanique des Solides\ ENPC!CERCSO\ Marne!la!Vallee\ France EMMANUEL DETOURNAY University of Minnesota\ Minneapolis\ U[S[A[ Received 14 February 0887 ^ in revised form 2 March 0887# Abstract*Two apparently di}erent approaches are used in dealing with the mechanics of a deform! able porous medium ] mixture theories on the one hand\ and purely macroscale theories\ which are mainly associated with the work of Biot\ on the other hand[ In the mixture theories\ the porous medium is represented by spatially superposed interacting media\ while macroscale theories assume that standard concepts of continuum mechanics are still relevant at the macro!level[ The aim of this paper is two!fold[ First\ it is shown that the macroscale _eld equations derived from mixture theories can be reformulated in terms of the measurable quantities involved in the macroscale theories[ Second\ it is demonstrated how these _eld equations\ including the fundamental inequality obtained from the second law\ entail the existence of a macroscale C!potential upon which a thermo! dynamically consistent formulation of the constitutive equations can be _rmly founded[ T 0887 Elsevier Science Ltd[ All rights reserved[ 0[ INTRODUCTION Two apparently di}erent approaches are used in dealing with the mechanics of a deformable porous medium ] mixture theories on the one hand\ and purely macroscale theories\ which are mainly associated with the work of Biot\ on the other hand[ In the mixture theories\ the porous medium is represented by spatially superposed interacting media\ while macroscale theories assume that standard concepts of continuum mechani