Hydro mechanical numerical modelling of geotechnical problems using local second gradient models

Abstract

The paper presents some applications of a local second gradient theory used to describe the mechanical behavior of a continua. This theory has been developed in order to avoid some well known drawbacks of classical theories, when softening and/or localization occur in a computation. This theory is extended and then applied in a hydromechanical coupled problem, in the case of fully saturated geomaterials. The corresponding finite element method taking into account the geometrical non linearities is detailed. Preliminary results using the finite element code developed in this context are then discussed and allow to study post localization behavior.1 INTRODUCTION This paper is devoted to some preliminary results concerning the use of a local second gradient model in initial boundary value problems in the context of hydromechanical coupled applications. This is mainly a work in progress. We focus on the equations solved and the finite element method used to tackle properly the problem.Soils and rocks are mainly porous materials filled by a fluid. It is very important then to study numerically hydromechanical problems. This has been extensively done in the past and this paper is not intended neither to give new results within this field nor to discuss general equations (general means here taking into account unsaturated conditions). The reader interested by numerical computations of multiphasic materials can read for instance the book of Lewis and Schrefler (Lewis and Schrefler 2000). An other important reference dealing with hyper elasto plastic modelling is the paper written by Borja and Alarcon (Borja and Alarcon 1995).When submitted to large strains, geomaterials exhibit clear localized ruptures, this phenomenon has been extensively studied, especially when the geomaterial is assumed to be a monophasic material. In this case, it is well known that it is necessary to use an enhanced model, in order to properly compute post localized paths. Many enhancements have been proposed and studied in the past. It is not the aim of this paper to compare the advantages and the shortcomings of every class of enhanced models. Readers interested by such a topic can have a look to the references of our paper coauthored with D. Caillerie and C. Tamagnini (Chambon, Caillerie, and Tamagnini 2004).The present paper paper is restricted to the use of a local second gradient model in hydromechanical coupled problems. To our knowledge very few works have been done using an enhanced model in such problems. It is our opinion that the more important works done in this topic has been performed by Ehlers and coworkers. Since years they use Cosserat continuum in coupled problems within a large strain elasto plastic framework (Ehlers and Volk 1998) (Ehlers, Ellsiepen, and Ammann 2001). More recently some work has been carried out by Zhang and Shrefler (Zhang and Schrefler 2004) using a non local elasto plastic second gradient model.Let us first give the main assumptions of this work. We are dealing with quasi static problems (which means that a...