A FEM for three-field u–p–η poroelasticity with nonreciprocal interactions

Abstract

The de la Cruz and Spanos (dCS) theory of poroelasticity is a pore-scale volume averaged formulation and differs from the widely used Biot (BT) theory. A novel Finite Element Method (FEM) is developed for dCS theory to enable the study of nonreciprocal solid–fluid interactions, which are omitted from BT model. Solid deformations are quasi-static and pore fluid flow is transient; dynamic effects are neglected. The form of the dCS theory chosen includes BT theory as a special case. The governing equations are written in terms of three fields: solid displacement u, fluid pressure p, and porosity η. Fully implicit time integration and a mixed-element formulation are employed to ensure stability. The convergence rate of the FEM dCS model is shown to be optimal in a one-dimensional consolidation problem. Examples of a footing and subsurface injection problems in two dimensions further attest the robustness of the implementation and are shown to reproduce BT model results as a special case. The effect of nonreciprocal solid–fluid interactions is studied in all examples and shows a wide range of importance depending on the properties of the porous media (e.g., permeability) and problem-specific constraints. The developed FEM provides a tool to enable further comparisons between dCS and BT theories and validation in practical applications.