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Material Modelling of Porous Media for Wave Propagation Problems
Author(s) -
Schanz M.
Publication year - 2003
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200310186
Subject(s) - biot number , poromechanics , mathematical analysis , laplace transform , porous medium , compressibility , mathematics , constitutive equation , mechanics , mixture theory , differential equation , porosity , physics , thermodynamics , finite element method , geology , geotechnical engineering , statistics , mixture model
Under the assumption of a linear geometry description and linear constitutive equations, the governing equations are derived for two poroelastic theories, Biot's theory and Theory of Porous Media (TPM), using solid displacements and pore pressure as unknowns. In both theories, this is only possible in the Laplace domain. Comparing the sets of differential equations of Biot's theory and of TPM, they show different constant coefficients but the same structure of coupled differential equations. Identifying these coefficients with the material data and correlating them leads to the known problem with Biot's ‘apparent mass density’. Further, in trying to find a correlation between Biot's stress coefficient to parameters used in TPM yet unsolved inconsistencies are found. For studying the numerical effect of these differences, wave propagation results of a one‐dimensional poroelastic column are analysed. Differences between both theories are resolved only for compressible constituents.