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.