Effective poroelastic properties of transversely isotropic rock-like composites with arbitrarily oriented ellipsoidal inclusions
Résumé
The present work is devoted to the determination of the macroscopic poroelastic properties of transversely isotropic geomaterials or rock-like composites with arbitrarily oriented ellipsoïdal inhomogeneities. The key problem to solve is to separate respective effects of matrix anisotropy and of inhomogeneities' orientation distribution and shape. Based on a numerical integration of the exact Green function provided by Pan and Chou [Pan, Y.C., Chou, T.W., 1976. Point force solution for an infinite transversely isotropic solid. Journal of Applied Mechanics 43, 608–612] for the transversely isotropic media, the Hill tensor Click to view the MathML source is obtained for an arbitrarily oriented oblate spheroidal inclusion. The integrate of the Hill tensor is performed in an intermediate system coordinate attached to the inhomogeneity and with one axis equal to the symmetry axis of the transversely isotropic matrix. This choice of system coordinate allows to simplify numerical calculations and to gain accuracy because partial integrate can be performed analytically. The obtained Hill tensor is next used to study the effect of matrix anisotropy, pores systems and microstructure-related parameters on the overall effective poroelastic properties in transversely isotropic rocks. As an example, a two step-homogenization scheme is presented to test the ability of the proposed model in the evaluation of effective Biot tensor and Biot modulus and stiffness tensor. With the help of an orientation distribution function (ODF) the anisotropy due to the pore systems is also accounted. Numerical applications are finally carried out for anisotropic porous rocks both composed of a matrix with solid minerals constituents and a pore space.