Jacques Desrues

Strain localization measurements in undrained plane-strain biaxial tests on Hostun RF sand

Results from a series of biaxial undrained tests on a fine, angular, quartz sand (Hostun FR) are presented. Both dilative and contractive specimens were tested. Strain localization in the specimen was recorded using a false relief stereophotogrammetric method, which allows a full-field measurement of the incremental strain within a specimen throughout the test. Incremental strain maps are obtained at different states on the stress–strain response. It is shown that shear banding can take place in both contractive and dilative specimens, but for the latter the onset of localization is delayed until cavitation takes place in the pore-fluid. It is concluded that in dilative granular media, non-drainage can preclude localization as long as cavitation in the pore-fluid does not relax the isochoric constraint. Copyright

Advances in X-ray Tomography for Geomaterials

A thorough quantitative analysis of strain localization of axisymmetric triaxial sand specimens is presented. Computed tomography technique was used to acquire detailed 3-D images of a series of Ottawa sand specimens subjected to Conventional Triaxial Compression (CTC) conditions at very low effective stresses in microgravity and terrestrial laboratories. Analysis tools were developed to track the onset, propagation, thickness and inclination angle of shear bands, and calculate the variation of void ratio within and outside shear bands. It has been found that shear bands initiate in the post-peak strength regime in CTC specimens, where a rather complex pattern of shear bands develops such that behavior is highly influenced by large-scale kinematics of the specimen. Four main deformation patterns were identified and their contribution to the overall volume change of the specimens was quantified.

Localization criteria for non‐linear constitutive equations of geomaterials

This paper is devoted to two specific aspects of shear band analysis for geomaterials, which are basically, non-standard materials. Problems arising from incremental non-linearity (multilinear or thoroughly non-linear models) and consequences of discontinuities of the constitutive equations with respect to loading parameters, are especially investigated. Copyright

Shear band analysis and shear moduli calibration

Strain localization is a well known phenomenon, generally associated with plastic deformation and rupture in solids, especially in geomaterials. In this process, deformation is observed to concentrate in narrow zones called shear bands. This phenomenon has been studied extensively in the last 20 years by different researchers, experimentally, theoretically and numerically. A criterion for the onset of localization can be predicted solely on the basis of the constitutive law of the material, using the so-called shear band analysis. This criterion gives the critical orientation, and the critical stress state and strain for a given loading history. An important point, already stressed by Vardoulakis in 1980, is that in particular, out-of-axes shear moduli play a central role in the criterion. These are the moduli involved in the response to a deviatoric stress increment with principal axes oriented at 45° from total stress principal axes. Out-of-axes shear moduli are difficult parameters to calibrate; common tests, with fixed principal stress and strain directions, do not provide any information on these moduli, as long as they remain homogeneous. Still, real civil engineering and environmental problems are definitely not simple axisymmetric triaxial tests; practical modeling involves complex stress paths, and need complex parameters to be calibrated. Only special tests, like compression–torsion on hollow cylinder tests, or even more complex tests can be used for shear moduli calibration. However, shear band initiation in homogeneous, fixed-axes tests does activate out-of-axes shear. Hence, it is natural that shear band analysis makes shear moduli enter into the analysis. Then, a typical inverse analysis approach can be used here: experimental observation of strain localization in triaxial tests can be used together with a proper shear band analysis for the model considered, in order to determine out-of-axes shear moduli. This approach has been used for a stiff marl in the framework of a calibration study on a set of triaxial tests. The steps of the method are presented, and the bifurcation surface in the stress space is exhibited.

FEM × DEM modelling of cohesive granular materials: Numerical homogenisation and multi-scale simulations

The article presents a multi-scale modelling approach of cohesive granular materials, its numerical implementation and its results. At microscopic level, Discrete Element Method (DEM) is used to model dense grains packing. At the macroscopic level, the numerical solution is obtained by a Finite Element Method (FEM). In order to bridge the micro- and macro-scales, the concept of Representative Elementary Volume (REV) is applied, in which the average REV stress and the consistent tangent operators are obtained in each macroscopic integration point as the results of DEM’s simulation. In this way, the numerical constitutive law is determined through the detailed modelling of the microstructure, taking into account the nature of granular materials. We first elaborate the principle of the computation homogenisation (FEM × DEM), then demonstrate the features of our multiscale computation in terms of a biaxial compression test. Macroscopic strain location is observed and discussed.

An Internal Instrumentation for Axial and Radial Strain Measurements in Triaxial Tests

A measuring device for axial and radial displacements in triaxial tests on soft rock specimens is described. Developed to optimize the detection of strain localization, the transducers have a linear response and a working range of a few percent. After a presentation of the manufacture and properties, detection of strain localization in the specimen during the compression test is discussed.

Limitations du choix de l'angle de frottement pour le critère de plasticité de Drucker-Prager

ABSTRACT Drucker-Prager model is available in most finite element codes used in civil engineering field, especially those devoted more specifically to geotechnical applications. Indeed, this model is a simple first idealization of the behaviour of frictional-cohesive materials, like soils, rocks, and other granular materials. However, this model must be used with care with respect to the choice of the friction angle. The paper presents a discussion of the validity domain for this parameter, in the context of both purely frictional and cohesive-frictional materials.

Hydro-mechanical coupling and strain localization in saturated porous media

ABSTRACT Experimental studies of Strain Localization in soils and rocks have been performed extensively for the last 20 years. A part of these studies have been devoted to the response of specimens submitted to tests in undrained situation. It was shown that shear banding can take place in both contractive and dilative specimens, with some special features due to the coupling between the granular skeleton and the pore fluid. In the present paper, the relevance of the bifurcation criterion in shear band mode in the case of hydro-mechanical coupling is assessed by numerical study of the response of the constitutive model CLoE-the Hypoplastic model developed in L3S-Grenoble- in two kinds of numerical integration: local, i.e. at the material point level and global, i.e. in boundary value problems analyzed by finite elements.

A DEM—FEM two scale approach of the behaviour of granular materials

We study the macroscopic behaviour of granular material, as a consequence of the interactions of individual grains at the micro scale. A two‐scale approach of computational homogenization is considered. On the micro‐level, we consider granular structures modelled using the Discrete Element Method (DEM). Grain interactions are modelled by normal and tangential contact laws with friction (Coulomb’s criterion). On the macro‐level, we use a Finite Element Formulation (FEM). The upscaling technique consists in using the response of the DEM model at each Gauss point of the FEM discretisation to derive numerically the constitutive response. In this process, a tangent operator is generated together with the stress increment corresponding to the strain increment in the Gauss point. In order to get more insight on the consistency of the resulting constitutive response, we compute the determinant of the acoustic tensor associated with the tangent operator. This quantity is known to be an indicator of a possible loss...

FEM × DEM Multi-scale Analysis of Boundary Value Problems Involving Strain Localization

The paper presents a FEM × DEM multiscale modeling analysis of boundary value problems involving strain localization in cohesive granular materials. At the microscopic level, a discrete element method (DEM) is used to model the granular structure. At the macroscopic level, the numerical solution of the boundary value problem (BVP) is obtained via a finite element method (FEM) formulation. In order to bridge the gap between micro- and macro-scale, the concept of representative volume element (REV) is applied: the average REV stress and the consistent tangent operators are obtained in each macroscopic integration point as the results of DEM simulation. The numerical constitutive law is determined through the DEM modeling of the microstructure to take into account the discrete nature of granular materials. The computational homogenization method is described and illustrated in the case of a hollow cylinder made of cohesive-frictional granular material, submitted to different internal and external pressures. Strain localization is observed to occur at the macro scale in this simulation.