A Variational Deduction of Second Gradient Poroelasticity II: An Application to the Consolidation Problem

TL;DR

This paper applies a second gradient poromechanics model to the classical consolidation problem, incorporating boundary layer effects and initial stresses, and compares numerical solutions with traditional Terzaghi results.

Contribution

It extends the second gradient poroelasticity model to the consolidation problem, including boundary effects and stability analysis, providing a more detailed understanding of boundary layer phenomena.

Findings

Boundary layer effects are captured near surfaces and walls.

Numerical solutions align with classical Terzaghi solutions.

Stability analysis accounts for initial stresses.

Abstract

The second gradient model of poromechanics, introduced in Part I, is here linearized in the neighborhood of a prestressed reference configuration to be applied to the one-dimensional consolidation problem originally considered by Terzaghi and Biot. Second gradient models allow for the description of boundary layer effects both in the vicinity of the external surface and the impermeable wall. The formulated differential problem involves linear pencils of ordinary differential operators on a finite interval, with boundary conditions depending on the spectral parameter. Taking into account the dependence of the differential problem on initial stresses a linear stability analysis is carried out. Finally,numerical solutions are compared with the corresponding classical Terzaghi solutions.