The Alestle - Vol. 57 No. 30 - 01/11/2005

Vol. 57 No. 3

Mechanical characterization of porous sandstones in true triaxial conditions : diffuse and localized deformation, effect of anisotropy

.Ce travail de thèse s'intéresse à la caractérisation de la déformation diffuse et localisée dans les grès isotropes et anisotropes sous contrainte de chargement monotone. En particulier, la cinématique de la localisation émergente et continue est étudiée dans une approche à la fois expérimentale, analytique et numérique, explorant l'effet de différentes sollicitations triaxial vrai dans le plan octaédrique.Plusieurs séries d'essais expérimentaux ont été réalisées en laboratoire, au sein d'une cellule de chargement en triaxial vrai (TTA), permettant la mesure de champs cinématiques à haute résolution spatiale et temporelle à la surface de l'échantillon. D'importants développements apportés au court de ce travail de thèse ont permis l'implémentation de modes de chargement par contrôle des invariants du tenseur de contrainte, tout en mesurant les déformations en temps réel par combinaison de jauges de déformation et mesures par corrélation d'images numériques (DIC). Utilisant cet appareil expérimental, deux campagnes d'essais ont été réalisées, mettant l'emphase sur la caractérisation du comportement mécanique d'un grès des Vosges isotrope largement étudié, ainsi que d'un grès des Vosges anisotrope nouvellement étudié. Ce dernier grès ayant été sélectionné pour sa composition matérielle en plans de litage orienté et organisé en couches de différentes porosités. Les séries d'essais mécaniques sur ces grès fournissent un apport important à la compréhension du caractère émergent et évolutif de la localisation, à différents stades du chargement déviatoire. Le caractère unique ce ces essais permet ainsi une analyse comparative approfondie entre la réponse macroscopique en contrainte-déformation et l'analyse des champs cinématiques par la DIC, et par tomographie à rayons X post-mortem. De plus, explorant des chemins de contrainte encore peu étudiés, l'analyse des essais expérimentaux sur le rôle indépendant de la contrainte moyenne, de l'angle de Lode et de l’orientation des plans de litage apporte une contribution novatrice à l'étude du comportement mécanique des roches poreuses. En particulier, la résistance à la rupture du grès, la manifestation de la localisation , ainsi que la transition du comportement ductile sont étudiées sous différentes conditions de chargement.En ce qui a trait au développement analytique, une analyse en bifurcation est proposée pour un modèle original à trois invariants, validé dans le cas des essais expérimentaux obtenus pour le grès isotrope. La pertinence de ce modèle théorique est démontrée pour la prédiction de l'orientation des bandes de cisaillement et de l'angle de dilatance à la rupture.Parallèlement, un modèle double-échelle basé sur l'homogénéisation numérique est présenté. Dans cette approche combinée, un modèle macroscopique en 2D des éléments finis (FEM) est couplé à un modèle microscopique en 3D des éléments discrets (DEM), sur la base d'un volume élémentaire représentative (VER) et dans la cadre d'un système hiérarchique (FEMxDEM) comportant une régularisation par second gradient. Ce modèle est étendu dans la portée des présents travaux pour l'étude des matériaux granulaire cimentés, par le développement d'une loi frictionnelle-cohésive endommageable au niveau de la DEM. Dans une vaste étude numérique de simulations en conditions de chargement triaxial vrai, ce modèle hiérarchique est utilisé afin d'explorer l'effet de différents arrangements granulaire (DEM), ainsi que différentes distributions hétérogènes à l'échelle macroscopique (FEM). En ce sens, deux types d'anisotropies résultant de l'hétérogénéité, définie à chacune des échelles, sont davantage étudiés. La réponse mécanique et la déformation localisée, émergeant du modèle constitutif à l'échelle du VER, démontrent une bonne concordance des comportements mécaniques complexes par rapport aux résultats de l'étude expérimentale.The objective of this doctoral thesis consists in the characterization of diffuse and localized deformations during monotonic loading of both isotropic and anisotropic porous sandstones. In particular, the kinematics of emerging and persistent strain localization structures are investigated in a combination of complementary experimental, analytical and numerical approaches, exploring the effect of different true triaxial loading paths in the octahedral plane.A series of experimental loading tests have been performed in a laboratory environment comprising a high pressure true triaxial apparatus (TTA), which is designed to provide access to full-field measurements of one of the sample surfaces at high spacial and temporal resolutions. Important developments contributed in this work enabled to extend the capabilities for this apparatus to perform invariant controlled loading paths, while acquiring direct strain measurements from a combination of strain gauges and digital image correlation (DIC). Using this apparatus, two experimental campaigns have been realized, focusing on the mechanical characterization of both a well-studied isotropic Vosges sandstone and a newly studied anisotropic Vosges sandstone. The later sandstone has been selected for the organization of its granular fabric in thin bedding plane layers of variable porosity. The results from these series of mechanical loading experiments contribute an original insight into the emergence and development of localized deformation during different stages of loading. A combined analysis is performed on the evolution of the macroscopic stress-strain responses, full-field measurements of incremental strains through DIC, as well as post-mortem x-ray tomography. Additionally, in this investigation exploring rarely considered loading paths, the independent role of the mean stress, the Lode angle and the orientation of the bedding planes is systematically studied according to their respective influence on the material strength, the manifestation of localized structures and the transition towards a ductile behavior of the material.In terms of analytical development, a bifurcation analysis is proposed for a novel three invariant model, validated with experimental results obtained for the isotropic sandstone. This theoretical model, proved to be successful in predicting both the deformation band inclination and the dilatancy angle of the material at failure.In parallel, a double scale model based on numerical homogenization is presented. In this approach, a macro 2D finite element model (FEM) is coupled to a micro 3D discrete element model (DEM) at the particle scale of a representative elementary volume (REV) in the frame of a hierarchical scheme (FEMxDEM), with second gradient regularization. This model is extended in the scope of this work to the study of cemented granular materials, with the development of a frictional-cohesive damageable contact law, implemented at the DEM level. In an extensive series of true triaxial loading simulations, the hierarchical numerical model is used to explore both the influence of different micro-structural arrangements (DEM) and heterogeneities at the sample scale (FEM). In this respect, two types of anisotropies resulting from heterogeneities defined at each scales are further investigated. The mechanical response and localized deformation, emerging from the micro-scale constitutive model, is shown to display significant correspondence with experimental observations in the studied Vosges sandstones.This combination of advanced experimental, analytical and numerical studies contributes a unique insight into important and open questions regarding the mechanical response and deformation processes of cemented granular material

A true triaxial experimental study on porous Vosges sandstone: from strain localization precursors to failure using full-field measurements

International audienceThis study systematically investigates the effect of deviatoric loading paths on diffuse and localized deformation developing during the mechanical loading of a high porosity (20%) Vosges sandstone (Eastern France). Laboratory scale experiments are performed using a high pressure true triaxial apparatus, designed to provide access to full-field surface kinematics at high spatial and temporal resolutions during the loading phase. The true triaxial experiments, with independent control of the three principal stress, are conducted at two constant mean stresses, in the brittle-ductile transition regime, and at five prescribed Lode angles, from axisymmetric compression (ASC) to axisymmetric extension (ASE). First, the transition from diffuse towards localized deformation is analyzed in different loading increments and shows an intermediate step of early strain localization, characterized by a large number of early deformation bands developing well before the stress peak and with a predominantly dilatant behavior. Secondly, the evolution of the mechanical behavior and localization patterns, such as deformation band angles and localized dilatancy, indicate a transition from the brittle regime to the ductile regime that is not only dependent on an increase in the mean stress, but also on a decrease in the Lode angle. The analysis of fullfield measurements also provides insights into the emergence and evolution of local strains, as deformation structures coalesce or relocate and different failure modes develop depending on the prescribed stress paths

A one parameter damageable contact law for DEM, with application to frictional-cohesive granular materials

A novel type of damageable cohesive law is presented for paired particle interactions in a DEM granular arrangement. It is designed in the spirit of a mixed breakage criterion for solid cohesion interaction, which can be implemented in parallel to a granular-frictional contact law. The evolution of damage at the contact level can be be easily modulated to enable a progressive transition from an initially linear elastic response to a loss of cohesion, by using a single parameter χ*. In a straightforward numerical implementation, the effect of this contact model is presented for a 3D periodic boundary condition DEM code. The results from a series of simulations show that, for a constant peak resistance of the cohesion, a more progressive damage result in an increase of the peak stress in a particle assembly, as well as a continuous transition in the stiffness of the stress-strain response around the peak stress

A one parameter damageable contact law for DEM, with application to frictional-cohesive granular materials

A novel type of damageable cohesive law is presented for paired particle interactions in a DEM granular arrangement. It is designed in the spirit of a mixed breakage criterion for solid cohesion interaction, which can be implemented in parallel to a granular-frictional contact law. The evolution of damage at the contact level can be be easily modulated to enable a progressive transition from an initially linear elastic response to a loss of cohesion, by using a single parameter χ*. In a straightforward numerical implementation, the effect of this contact model is presented for a 3D periodic boundary condition DEM code. The results from a series of simulations show that, for a constant peak resistance of the cohesion, a more progressive damage result in an increase of the peak stress in a particle assembly, as well as a continuous transition in the stiffness of the stress-strain response around the peak stress

A double-scale FEMxDEM model applied to cohesive-frictional granular materials in polyaxial loading conditions

International audienc

A double-scale FEMxDEM model applied to cohesive-frictional granular materials in polyaxial loading conditions

International audienc

3D transcranial Ultrasound Localization Microscopy for discrimination between ischemic and hemorrhagic stroke in early phase

International audienceEarly diagnosis is a critical part of the emergency care of cerebral hemorrhages and ischemia. A rapid and accurate diagnosis of strokes reduces the delays to appropriate treatments and a better functional recovery. Currently, CTscan and MRI are the gold standards with constraints of accessibility, availability, and possibly some contraindications. The development of Ultrasound Localization Microscopy (ULM) has enabled new perspectives to conventional transcranial ultrasound imaging with increased sensitivity, penetration depth, and resolution. The possibility of volumetric imaging has increased the field-of-view and provided a more precise description of the microvascularisation. In this study, rats (n=9) were subjected to thromboembolic ischemic stroke or intracerebral hemorrhages prior to volumetric ULM at the early phases after onsets. Although the volumetric ULM performed in the early phase of ischemic stroke revealed a large hypoperfused area in the cortical area of the occluded artery, it showed a more diffused hypoperfusion in the hemorrhagic model. Respective computations of a Microvascular Diffusion Index highlighted different patterns of perfusion loss during the first 24h of these two strokes' subtypes. Our study provides the first proof that this methodology should allow early discrimination between ischemic and hemorrhagic stroke with a potential toward diagnosis and monitoring in clinic