Modelling Porous and Deformable Media with Several Scales ofHeterogeneity

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This study proposes to develop a theory of heterogeneous poroelastic media whose material properties are characterized by several distinct length scales (e.g. grains, layers, global). The modern mathematical techniques of homogenization theory, so far developed for composite media will be extended. The constitutive coefficients for quasi static thermal consolidation, and dynamic poroelasticity will be studied. Explicit calculations for a simple but versatile 3-D micro structure (Wigner-Seitz polyhedron) will be performed. The transversely isotropic macroscale equations will be solved for several physical problems such as the rising geothermal plume, the submerged point sink, etc., and seismic wave propagation.