ABSTRACT
A micro-structure model of dual porosity type for flow and deformation in deformable porous media that incorporates intra-grain delayed flow during secondary consolidation is proposed. The model is derived within the framework of the homogenization technique and is resultant from scaling up the constitutive relations on the finer scales. In particular, from upscaling the poroelastic equations for the grains (matrix blocks) coupled with the Stokesian bulk-water movement in the system of larger fissures. In the homogenized dual porosity model with microstructure the macroscopic porous medium is represented as two porous distinct structures coexisting at each macroscopic point: one representing the matrix blocks (or grains) and the other the bulk water. In this picture, the macroscopic flow is that of the bulk water and matrix blocks act as sources/sinks of mass and momentum to the macroscale bulk phase. In the case of deformable porous media under consolidation processes, this source/sink transfer function governs the creep constitutive equations of the macroscale effective stress tensor as it accounts for secondary deformation of the skeleton arising from the delayed drainage of the fluid within the blocks. The governing equations of dual porosity type are discretized by the finite element method. Numerical simulations of creep during secondary consolidation are presented to illustrate the performance of the proposed approach
