Summary In this paper, a multiscale finite element framework is developed based on the first‐order homogenization method for fully coupled saturated porous media using an extension of the Hill‐Mandel theory in the presence of microdynamic effects. The multiscale method is employed for the consolidation problem of a 2‐dimensional saturated soil medium generated from the periodic arrangement of circular particles embedded in a square matrix, which is compared with the direct numerical simulation method. The effects of various issues, including the boundary conditions, size effects, particle arrangements, and the integral domain constraints for the microscale boundary value problem, are numerically investigated to illustrate the performance of a representative volume element in the proposed computational homogenization method of fully coupled saturated porous media. This study is aimed to clarify the effect of scale separation and size dependence, and to introduce characteristics of a proper representative volume element in multiscale modeling of saturated porous media.

Summary In this paper, a multiscale homogenization approach is developed for fully coupled saturated porous media to represent the idealized sugar cube model, which is generally employed in fractured porous media on the basis of dual porosity models. In this manner, an extended version of the Hill‐Mandel theory that incorporates the microdynamic effects into the multiscale analysis is presented, and the concept of the deformable dual porosity model is demonstrated. Numerical simulations are performed employing the multiscale analysis and dual porosity model, and the results are compared with the direct numerical simulation through 2 numerical examples. Finally, a combined multiscale‐dual porosity technique is introduced by employing a bridge between these 2 techniques as an alternative approach that reduces the computational cost of numerical simulation in modeling of heterogeneous deformable porous media.

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σ 1 , σ 2 and σ 3 denotes principal stresses. In standard triaxial test, q = σ 1 − σ 3. The plot represents a useful two-dimensional graphical illustration of the admissible stress space and the stress regime applied to rocks.

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