A Macro–Microscopic Coupled Mixed Finite-Element Model for One-Dimensional Nonlinear Consolidation

The purpose of this research is to develop a numerical model for one-dimensional consolidation of saturated poroelastic media with compressible components while accounting for porosity-dependent compressibility and permeability. In contrast to the previous numerical methods that were established based on Biot’s model, the current model provides a more comprehensive consideration incorporating both macroscopic and microscopic effects. Specifically, the displacement of the solid skeleton, the volumetric strain of solid constituent, and the fluid pressure are fully coupled in the present numerical model. In the present paper, a numerical implementation for the macro–microscopic coupled one-dimensional consolidation model is first provided. Subsequently, the numerical model is extended to incorporate the effects of porosity on the compressibility and permeability by employing a piecewise linear method. Finally, two examples are provided to verify the proposed model and illustrate its application. Based on the proposed numerical model, the influences of compressibility of the solid and fluid constituents on the settlement are studied and discussed.