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Generalized Biot's theory and Mandel's problem of multiple‐porosity and multiple‐permeability poroelasticity
Author(s) -
Mehrabian Amin,
Abousleiman Younane N.
Publication year - 2014
Publication title -
journal of geophysical research: solid earth
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.983
H-Index - 232
eISSN - 2169-9356
pISSN - 2169-9313
DOI - 10.1002/2013jb010602
Subject(s) - biot number , poromechanics , porosity , consolidation (business) , permeability (electromagnetism) , porous medium , slab , constitutive equation , materials science , mathematical analysis , mathematics , mechanics , finite element method , geotechnical engineering , physics , geology , thermodynamics , structural engineering , engineering , chemistry , biochemistry , accounting , membrane , business
This paper finds in Biot's theory of poroelasticity a complete and consistent extension to the general case of multiple‐porosity and multiple‐permeability, fluid‐saturated, and linearly elastic media. The constitutive stress‐strain relations for a medium identified with this extension are presented, and the coefficient matrix of mechanical properties associated with these relations is derived from the corresponding intrinsic properties of its single‐porosity constituents. The closed form analytical solution to Mandel's problem is upgraded to the case being considered in this study. This problem addresses the transient consolidation of a porous elastic slab of rectangular geometry, when confined from the top and bottom. A numerical example solution for shale with laboratory setup of Mandel's problem is provided. Results are compared for the cases of single‐, double‐, and triple‐porosity solutions.