Vol. 3, No. 4, 2008

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ISSN: 1559-3959
A variational deduction of second gradient poroelasticity II: an application to the consolidation problem

Angela Madeo, Francesco dell’Isola, Nicoletta Ianiro and Giulio Sciarra

Vol. 3 (2008), No. 4, 607–625
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.

Keywords
poromechanics, second gradient materials, consolidation
Milestones
Received: 8 March 2007
Revised: 27 July 2007
Accepted: 25 November 2007
Published: 1 June 2008
Authors
Angela Madeo
Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate
Università di Roma “La Sapienza”
Via Scarpa 16
00161 Rome
Italy
Francesco dell’Isola
Dipartimento di Ingegneria Strutturale e Geotecnica
Università di Roma “La Sapienza”
Via Eudossiana 18
00184 Rome
Italy
Laboratorio di Strutture e Materiali Intelligenti
Palazzo Caetani (Ala Nord)
04012 Cisterna di Latina
Italy
Nicoletta Ianiro
Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate
Università di Roma “La Sapienza”
Via Scarpa 16
00161 Rome
Italy
Giulio Sciarra
Dipartimento di Ingegneria Chimica Materiali Ambiente
Università di Roma “La Sapienza”
Via Eudossiana 18
00184 Rome
Italy