Effective porothermoelastic properties of transversely isotropic rock-like composites

The present work is devoted to the determination of the overall porothermoelastic properties of transversely isotropic rock-like composites with transversely isotropic matrix and randomly oriented ellipsoidal inhomogeneities and/or pores. By using the solution of a single ellipsoidal inhomogeneity arbitrarily oriented in a transversely isotropic matrix presented by Giraud et al. [A. Giraud, Q.V. Huynh, D. Hoxha, D. Kondo, Effective poroelastic properties of transversely isotropic rocks-like composites with arbitrarily oriented ellipsoidal inclusions, Mechanics of Materials 39 (11) (2007) 1006–1024], it is possible to observe the effect of the shape and orientation distribution of inhomogeneities on the effective porothermoelastic properties. Based on recent works on porous rock-like composites such as shales or argillites, an application of the developed solution to a two-level microporomechanics model is presented. The microporosity is homogenized at the first level, and multiple solid mineral phase inclusions are added at the second level. The overall porothermoelastic coefficients are estimated in the particular context of heterogeneous solid matrix. The present model generalizes to transversely isotropic media a recently developed two-level model in the simpler case of isotropic media (see Giraud et al. [A. Giraud, D. Hoxha, D.P. Do, V. Magnenet, Effect of pore shape on effective thermoporoelastic properties of isotropic rocks, International Journal of Solids and Structures 45 (2008) 1–23]). Numerical results are presented for data representative of transversely isotropic rock-like composites.