Pierre Bésuelle

Failure Mode and Spatial Distribution of Damage in Rothbach Sandstone in the Brittle-ductile Transition

To elucidate the spatial complexity of damage and evolution of localized failure in the transitional regime from brittle faulting to cataclastic ductile flow in a porous sandstone, we performed a series of triaxial compression experiments on Rothbach sandstone (20% porosity). Quantitative microstructural analysis and X-ray computed tomography (CT) imaging were conducted on deformed samples. Localized failure was observed in samples at effective pressures ranging from 5 MPa to 130 MPa. In the brittle faulting regime, dilating shear bands were observed. The CT images and stereological measurements reveal the geometric complexity and spatial heterogeneity of damage in the failed samples. In the transitional regime (at effective pressures between 45 MPa and 130 MPa), compacting shear bands at high angles and compaction bands perpendicular to the maximum compression direction were observed. The laboratory results suggest that these complex localized features can be pervasive in sandstone formations, not just limited to the very porous aeolian sandstone in which they were first documented. The microstructural observations are in qualitative agreement with theoretical predictions of bifurcation analyses, except for the occurrence of compaction bands in the sample deformed at effective pressure of 130 MPa. The bifurcation analysis with the constitutive model used in this paper is nonadequate to predict compaction band formation, may be due to the neglect of bedding anisotropy of the rock and multiple yield mechanisms in the constitutive model.

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.

Water Retention Behaviour Explored by X-Ray CT Analysis

This study aims to experimentally characterise the link between partial water saturation and suction in a sand sample at the micro scale. The paper presents the first results of an experimental study in which high resolution (7.5μm/px) X-ray tomography has been performed on a small (10×10mm) cylindrical sample of Hostun HN31 sand at several different levels of imposed suction. A specialised cell allowing X-ray scanning as well as fine control of suction (imposed both by negative water pressure as well as by positive air pressure) has been developed for this study and is described herein. The 3D images resulting from X-ray tomography are treated in order to define each voxel in the image as either air, water or grain. From these “trinarised” 3D images, local and global values of porosity and degree of saturation are then measured. This method enables the study of water retention behaviour of sand at the grain scale, all the while allowing characterisation of water retention in the sample as a whole.

Local Second Gradient Models and Damage Mechanics: 1D Post-Localization Studies in Concrete Specimens

Continuum damage mechanics is often used as a framework for describing the variations of the elastic properties of due to micro-structural degradations. Experimentally, concrete specimens exhibit a network of microscopic cracks that nucleate sub-parallel to the axis of loading. Due to the presence of heterogeneities in the material (aggregates surrounded by a cement matrix), tensile transverse strains generate a self-equilibrated stress field orthogonal to the loading direction, a pure mode I (extension) is thus considered to describe the behaviour even in compression. This rupture mode must be reproduced numerically. This is the reason why the failure criterion of the chosen constitutive law is expressed in terms of the principal extensions and that a tension test is modelled at the end of this paper. The influence of micro-cracking due to the external loads is introduced via damage variables, ranging from 0 for the undamaged material to 1 for a completely damaged material.

Investigation of microstructures in naturally and experimentally deformed reference clay rocks using innovative methods in scanning electron microscopy

The application of ion-beam milling techniques to clays allows investigation of the porosity at nm resolution using scanning electron microscopy (SEM). Imaging of pores by SEM of surfaces prepared by broad ion beam (BIB) gives both qualitative and quantitative insights into the porosity and mineral fabrics in 2D representative cross-sections. The combination of cryogenic techniques with ion-beam milling preparation (BIB and FIB, focused ion beam) allows the study of pore fluids in preserved clay-rich samples. Characterization of the pore network is achieved, first, using X-ray computed tomography to provide insights into the largest pore bodies only, which are generally not connected at the resolution achieved. Secondly, access to 3D pore connectivity is achieved by FIB-SEM tomography and the results are compared with 2D porosity analysis (BIBSEM) and correlated with bulk porosity measurements (e.g. mercury injection porosimetry, MIP). Effective pore connectivity was investigated with an analog of MIP based on Wood’s metal (WM), which is solid at room temperature and allows microstructural investigation of WM-filled pores with BIB-SEM after injection. Combination of these microstructural investigations at scales of ,1 mm with conventional stressstrain data, and strain localization characterized by strain-fields measurement (DIC – digital image correlation) on the same sample offers a unique opportunity to answer the fundamental questions: (1) when, (2) where, and (3) how the sample was deformed in the laboratory. All the methods above were combined to study the microstructures in naturally and experimentally deformed argillites. Preliminary results are promising and leading toward better understanding of the deformation behavior displayed by argillites in the transition between rocks and soils.

Application of X-ray Tomography to the Characterisation of Grain-Scale Mechanisms in Sand

X-ray micro-tomography allows 3D imaging at sufficiently high spatial resolution to distinguish all the individual sand grains in a small sample (10mm diameter), as well as the distribution of air and/or water at this scale. Since this imaging technique is completely non-destructive, an imaged sample can be made to evolve by controlling some relevant variable (e.g., imposed deformation, suction), and can subsequently be re-imaged. This allows processes to be followed in 4 dimensions (3D + relevant variable). This paper shows the application of this technique and philosophy to the study of two different phenomena: localised deformation resulting from imposed triaxial compression, and the water retention behaviour of sand. The experimental techniques and setups for these two studies are detailed, and the fundamental steps of image treatment are outlined. Some key results are given to demonstrate the power of this “full-field” characterisation approach, such as rotations and displacements for each of the 50,000 grains of a sample in which a shear band occurs as well as the evolution of local measurements of porosity and degree of saturation in a sand where suction is being varied.

Localisation Precursors in Geomaterials

Strain localisation in soils and rocks has been studied extensively for the last 40 years or so. On the experimental side, a large number of these studies have been devoted to the experimental observation of localised deformation in laboratory element tests like biaxial (plane strain) and triaxial tests. 2D and 3D imaging techniques and image analysis methods have been used to characterize the onset and subsequent development of strain localisation. In the recent years, these techniques and methods have improved dramatically, allowing considerably more accurate measurement of displacement and strain field in the laboratory specimens. It is time to have a second look, with these new glasses, at some decades-old results, to assess what can be confirmed and what should be reconsidered.

Microstructural Effects on Strain Localization in a Multiscale Model for Hydro-Mechanical Coupling

The formulation and implementation of a double-scale finite element model for hydro-mechanical coupling in the framework of the finite element squared method has allowed studying macroscale boundary value problems in a poromechanical continuum. The macroscale constitutive relations are directly derived from the micromechanical interaction between fluid and solid microstructure, captured in representative elementary volumes. The application of this model in the simulation of a biaxial test and a gallery excavation problem is presented here to give examples of the model in strain localization problems. While using simple micromechanical models, the results demonstrate the ability of the model to provide complex macroscale material behaviour, that controls the initiation and development of the strain localization.

A FE² model for Hydro-mechanical coupling

A new approach is investigated for the modelling of the hydro-mechanical behaviour of Callovo-Oxfordian claystone, a potential host rock for radioactive waste repositories in France. This approach is a double-scale finite element method with a micro and a macro scale. At the micro level a representative elementary volume (REV) is used to model the material behaviour. The global response of this REV serves as an implicit constitutive law for the macro scale. On the macro scale, a poro-mechanical continuum is defined with fully coupled hydro-mechanical behaviour; the microscale contains a model that takes into account the material micro structure and fluid/solid interaction to provide the material responses and associated stiffness matrices. Computational homogenization is used to retrieve these stiffness matrices from the micro level. This double scale approach is applied in the simulation of a biaxial deformation test and the response at the macro level is related to the micro-mechanical behaviour.

Characterizing in the Laboratory Permeability Changes Induced by Deviatoric Stress in Clayey Rocks

Abstract Hydromechanical coupling is a major issue when dealing with fracturation problems in stiff overconsolidated clays in civil, environmental and geology engineering. Clays and clayey rocks are mainly characterized by a strong hydromechanical coupling and very low permeability leading to numerous difficulties when trying to study them experimentally. For that purpose, experimental set up and special procedures to investigate the evolution of such material permeability with stress-strain behaviour in specimens undergoing triaxial tests up to failure are presented. The experimental device is composed of a high pressure triaxial cell (confining pressure, pore pressure up to 60 MPa, deviatoric stress up to 270 MPa) in order to perform permeability measurement under triaxial compression using the pulse decay method. In order to characterize precisely the strains during a triaxial path, we use a local strain measurement device composed of 7 LVDTs. It allows us to measure strains in 4 radial directions (90° from each other) and in 3 axial directions (120° from each other) in order to detect a possible loss of homogeneity in the strain field e.g. strain localization in shear bands.