A VARIATIONAL DEDUCTION OF SECOND GRADIENT POROELASTICITY II: AN APPLICATION TO THE CONSOLIDATION PROBLEM

Angela Madeo (1) , Francesco Dell'Isola (2, 3) , Nicoletta Ianiro (1) , Giulio Sciarra (4)

1 MeMoMat - Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate
2 Dipartimento di Ingegneria Strutturale e Geotecnica
3 Laboratorio Strutture e Materiali Intelligenti - Fondazione Tullio Levi-Civita
4 Dipartimento Ingegneria Chimica Materiali Ambiente

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.

Domains: Mechanics [physics.med-ph]

Angela Madeo, Francesco Dell'Isola, Nicoletta Ianiro, Giulio Sciarra. A VARIATIONAL DEDUCTION OF SECOND GRADIENT POROELASTICITY II: AN APPLICATION TO THE CONSOLIDATION PROBLEM. Journal of Mechanics of Materials and Structures, 2008, pp.20. ⟨hal-00499567⟩