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Abstract In traditional finite element failure analyses of geotechnical structures, the micro grain rotations cannot be modelled and numerical solutions are mesh dependent. In this study, a user element including rotational degree of freedom has been developed based on micropolar theory (Cosserat theory), then an enhanced non-associated sand model is calibrated with laboratory data and used to model the plane strain tests. The simulated results demonstrate the polarized model is able to model reasonably the sand behavior as well as the grain rotations in the localized region. What’s more, with this enhanced model, the mesh independent numerical solutions in terms of mechanical responses, shear bands thickness and orientations have been obtained. Article highlights In failure analysis of geostructures, significant rotations of soil grains have been observed to occur in the strain localized regions, but the current commercial Finite Element tools cannot model the micro rotations. Therefore, a user defined element must be developed to include the rotational degree of freedom. The micropolar approach is proven to be effective to model the grain rations in present paper. More suitable than other classical soil or sand constitutive models, the selected non-associated sand model in present paper is capable of describing well the contraction and shear dilatancy behaviors of sand. Then the model has been enhanced by means of micropolar technique, in this way, the reasonable strain localization phenomena in laboratory tests could be predicted well. There are always the mesh dependent problems for traditional simulations of the strain localization phenomena in finite element analysis. It can be found in present paper that the mesh independent numerical solutions are obtained by means of micropolar technique. Furthermore, the micropolar approach can obviously improve convergence difficulties in finite element analyses.

It is well known that the compressibility of crushable granular materials increases with the moisture content, due to the decrease of particle strength in a humid environment. An existing approach to take into account the effect of grain breakage in constitutive modeling consists in linking the evolution of the grain size distribution to the plastic work. But how the material humidity can affect this relationship is not clear, and experimental evidence is quite scarce. Based on compression tests on dry and saturated crushable sand recently reported by the present authors, a new non-linear relationship is proposed between the amount of particle breakage and the plastic work. The expression contains two parameters: (1) a material constant dependent on the grain characteristics and (2) a constant depending on the wetting condition (in this study, dry or saturated). A key finding is that the relationship does not depend on the stress path and, for a given wetting condition, only one set of parameters is necessary to reproduce the results of isotropic, oedometric, and triaxial compression tests. The relationship has been introduced into an elastoplastic constitutive model based on the critical state concept with a double yield surface for plastic sliding and compression. The breakage ratio is introduced into the expression of the elastic stiffness, the critical state line and the hardening compression pressure. Incremental stress-strain computations with the model allow the plastic work to be calculated and, therefore, the evolution of particle crushing can be predicted through the proposed non-linear relationship and reintroduced into the constitutive equations. Accurate predictions of the experimental results in terms of both stress-strain relationships and breakage ratio were obtained. Keywords: Grain crushing, Wetting, Constitutive modeling

International audience; We revisit the Critical State (CS) in a dynamic perspective at a mesoscopic scale to enrich the classical view of the critical state as a steady state. The dynamics of meso-structures has been characterized by recording generating and vanishing processes in discrete element simulations. Our results suggest that mesostructures have a short but regular lifespan at critical state along a biaxial compression loading path.

International audience; The aim of this paper is to offer a fresh perspective on the classic concept of critical state (CS) in granular materials by suggesting that CS can be defined through the use of a single proportional strain test. In classic conventional testing, CS manifests itself under constant lateral stress and controlled strain in one given direction whenever continuous shearing is applied without change being induced to material volume. However, a comparison between proportional strain tests and biaxial tests simulated with DEM has clearly shown that the CS line (CSL) characterized by stresses, void ratio and fabric indexes can act as an attractor. The mechanical responses and fabric metrics evolve along dilatant proportional strain loading paths according to similar values after the strain level has become large enough to wipe out the material memory in the homogeneous domains considered in this analysis, i.e., the shear band area in dense samples and the whole area in loose samples. This suggests that the micro-structure of a granular material subjected to any dilatant proportional strain loading paths evolves while preserving its ability to withstand shearing without volume change at any time. Therefore, the CS concept can be generalized to a wide class of loading paths which shows that CS acts as a general attractor irrespective of the loading path considered.

The effect of water on the hydromechanical behavior of unsaturated granular materials has been studied with a micromechanical model based on thermodynamic principles. A general framework based on the theory of thermodynamics with internal variables for constructing thermodynamically consistent multiscale constitutive relations for unsaturated granular materials has been developed. Within this framework, the microscopic total Helmholtz free energy has been separated between a mechanical and a hydraulic part, each of which is a function of either the elastic displacement or the capillary bridge volume and the distance between particles at the microscale. The inter-particle dissipation of energy, assumed to be frictional in origin, is a function of the incremental plastic displacements at the microscale. Both the microscale Helmholtz free energy and the dissipative energy have been volumetrically averaged to obtain the homogenized energy functions at the macroscale. In accordance with the suggested multiscale thermomechanical framework, a micromechanical model has been constructed to describe the behavior of partially saturated granular soils. This model has considered the deformation of soil skeleton by applying a Coulomb-type criterion at the inter-particle contacts. The hydraulic potential is made to be dependent on the size of the particles and is derived through use of the expression for the water retention curve by assuming that liquid bridges are isotropically distributed within the specimen. The performance of the suggested model has been demonstrated through numerical simulations of the behavior of sand under various degrees of saturation and a wide range of mechanical loadings.

International audience; Grain breakage during compression and shearing is one important mechanism responsible for irrecoverable changes of the mechanical properties of granular materials. Here we present results of triaxial tests on limestone fragments under some monotonic and cyclic stress paths and we investigate the relationships between the progression of grain breakage, the plastic work and the evolution of the critical state line. Using the plastic work concept, we propose a method for determining grain shape and grain breakage indices, and we show how grain breakage influences the critical stress state, and hence the mechanical behaviour. The validity of the relationships is then verified on different granular assemblies (granite fragments and quartz sands), although further tests remain necessary to validate them under more generic stress paths.

The aim of this paper is to answer the question: how to construct a thermodynamically consistent micromechanical model and to analyze the existing micromechanical models from an energy perspective. For this purpose, we extended the framework of thermodynamics to micromechanical models by considering the energy stored and dissipated at the inter-particle contacts. In the suggested framework, the Helmholtz free energy and the dissipation energy at the macro scale are equaled to the volumetric average of the Helmholtz free energy and the dissipation energy at the micro scale. Consequently, the elasto-plastic formulation at inter-particle contacts can be obtained from the expressions of the micro free energy and the micro dissipation potentials. A thermodynamically consistent micromechanical model has been constructed on the basis of the static hypothesis. An isotropic compression and several triaxial tests were simulated with the model to analyze the energy conservation and dissipation under loading. Free energy and dissipation energy were computed at both micro and macro scales, and the orientation of the failure plane was explained by the evolution of the local dissipation energy. The maximum micro dissipation energy agreed with the static hypothesis for which, when one direction reaches the limit state, the rupture at the macro scale is obtained. The model has been implemented into a finite element code, and with this code a biaxial compression test was performed. Strain localization appeared, and the orientations of the shear band displayed by either the accumulated deviatoric plastic shear strain or the dissipative energy were consistent.

In this chapter, a newly constructed constitutive model is presented for modeling the time-dependent behavior of granular materials. The model consists of dividing the stress tensor into an inviscid stress using a hypoplastic formulation and a viscous stress with a high-order term representing the strain acceleration. Then, different laboratory tests on granular soils are simulated to evaluate the model performance, i.e., a series of constant strain rate triaxial tests and a stepwise strain rate triaxial test on Toyoura sand, a stepwise strain rate triaxial test on Chiba gravelly soil, and creep tests under different stress levels on Toyoura sand. Comparisons between the experimental and numerical results show the capability of the model in describing the strain rate and acceleration effects, as well as the creep behavior of granular materials. Moreover, the coupling between the inviscid stress and viscous stress enables the evolution of the strain rate increase in the creep tests. Consequently, the three stages of creep, namely, primary, secondary, and tertiary creep, can be well described. Finally, the model, named HYPOSAND, is presented in the ErosLab platform as a practical exercise.

This chapter presents the multiscale modeling methodology for soils from micro to macro. First, the multiscale feature of soils within the general framework of the multiscale approach to granular materials is presented. Then, the fundamentals of micromechanics are presented in more detail, including interparticle contact laws, definitions of the strain tensor, effective stress tensor and fabric tensor, averaging and localization operators, and homogenization integration. As an example, the micromechanics-based Chang–Hicher (CH) model is presented with experimental validation. Some possible developments of models based on the CH model are presented considering the capillary force, the chemical force in grouted sand, the surface energy force, and the mechanical force in clayey materials. Finally, the MicroSoil model in the ErosLab platform is presented for a practical exercise.

It is still an open problem to develop a model with a uniform theoretical treatment under various loading conditions. This paper aims to formulate such a model for describing both monotonic...

International audience; In geotechnical and particularly in dam engineering, observations in the field and, in some cases, dramatic failures of structures have often incited research and increased knowledge. For instance, the first rockfill dams were elevated without any prior knowledge of the mechanical capacities of the rockfill mass. As natural and local resources are usually preferred for economic and environmental issues, their non-optimal properties can lead to potential severe damage to the hydraulic structure. Similarly, a basic principle of construction of rockfill dams or embankments consists in sluicing rockfill after deposition and before compaction: this recommendation has been adopted for a long time. However, the beneficial effects of such a practice have been understood only in light of recent studies on unsaturated soil and multi-scale analyses.

Micromechanics-based model have proved to be efficient in describing the mechanical behaviour of granular soils with few physical meaning parameters. Among these models, a family of micromechanical models was constructed based on the static approach that is a bridge connecting micro forces and macro stress. This paper presents the application of a static hypothesis based CH micromechanical model to solve boundary value problems (BVPs) using an implicit integration method. The model was first calibrated by results of elementary tests of Hostun sand and then was implemented into a finite element code. Two typical boundary value problems: a biaxial test and a square footing were numerically analysed to demonstrate how the micromechanical model can be applied to multiscale modelling of geotechnical structures.

A microstructural model to consider the mechanical behavior of granular materials has been enhanced to incorporate the evolution of the critical state when significantly high grain breakage occurs during loading. The influence of grain size on grain strength is highlighted and its impact on the properties of granular assemblies is shown through the results of oedometer test simulations.

Straining depicts the geometrical retention of fine particles within materials'pore network. Whether or not fines can be retained depends on (1) the structure of materials'pore network as well as (2) fines'size distribution, manner of deposition, and retained amount. In this paper, the main results of straining tests are presented for randomly packed beads filters. The experimental program included a series of tests performed in both dry and water-saturated filters. The tests provided information on the dynamics of fines in the filters'pore network and changes of filters'efficiency. For instance, data supported the existence of four distinct stages: the filling of accessible cavities, the formation then clogging of the preferential pathways, the transfer of fines toward the lateral unobstructed capillaries, and eventual formation of a surface cake. The postulated mechanisms inherent to every single stage are discussed in terms of retention rate, straining length, lateral transfer, andprogressive obstruction of constrictions. Additionally, the straining mechanisms were also probed in hydrodynamic conditions at increasingwater flows.

International audience; Presented here is a numerical method able to predict the mechanical behaviour of granular materials subjected to particle removal. The purpose of this study is to improve understanding of the mechanical behaviour of soils subjected to internal erosion in hydraulic works. The approach is based on a homogenisation technique for deriving the stress–strain relationship of a granular assembly from forces and displacements at the particle level. The soil's local behaviour is assumed to follow a Hertz–Mindlin elastic law and a Mohr–Coulomb plastic law. Sliding resistance on each plane is made to depend on the actual void ratio of the granular assembly. The solid fraction removal is modelled by progressively increasing the granular assembly void ratio, which provokes a decrease of the sliding resistance of each interparticle contact, leading to macroscopic deformations of the soil specimen. At elevated stress levels, large deformations can develop and lead to soil failure. Numerical simulations also demonstrate that a type of failure called diffuse failure can occur in eroded soil masses whenever an increase in pore pressure is generated within the soil. These numerical results appear to be coherent with observations made on embankment dams that have suffered internal erosion and, in particular, with the description of their modes of failure.

International audience; A novel approach has been developed to predict the mechanical behavior of very coarse granular materials with a constitutive model, which considers both grain breakage and size effect. The behavior of granular assemblies is significantly influenced by particle breakage. A critical-state double-yield-surface model incorporating the change in the critical-state line and in elastic stiffness caused by grain breakage during loading has been adopted. The amount of grain breakage was estimated by extending the size effect theory on individual grains to granular assemblies. The results from earlier studies on granular materials with parallel gradations have been usefully exploited to calibrate and to validate the model. Comparisons between experiments and simulations suggest that this approach can predict the mechanical behavior of very coarse granular materials from test results performed on a finer fraction with a homothetic gradation.

SUMMARY Internal erosion (IE) affects the stability of natural and reinforced materials by causing instability within their granular structure. The dislodgement and transport of eroded particles affect both the particulate concentration of eroding fluid and the pore network of eroded material. In this study, we examined these modifications using a transport model with a finite element code. First, IE tests on chemically reinforced sand columns were performed to obtain information about eroded material loss of mass, particulate concentration of effluent, porosity and permeability modifications, and existing IE stages. Second, based on experimental results, a mathematical one-dimensional model has been formulated to monitor the evolution and spatial distribution of erodible solids, fluidized particles, porosity, permeability, and seepage stresses. The model consists of a set of coupled nonlinear differential equations solved in sequence. It provides valuable information about the extent and the dynamics of structural changes, which can be used to estimate an IE time for the hydraulic work to reach failure. Copyright © 2011 John Wiley & Sons, Ltd.

Instability of granular material may lead to catastrophic events such as the gross collapse of earth structures, and thus it is an important topic in geotechnical engineering. In this paper, we adopt the micromechanics approach for constitutive modeling, in which the soil is considered an assembly of particles, and the stress-strain relationship for the assembly is determined by integrating the behavior of the interparticle contacts in all orientations. Although analyses regarding material instability have been extensively studied for a soil element at the constitutive level, it has not been considered at the interparticle contact level. Through an eigenvalue analysis, two modes of instability are identified at the local contact level: the singularity of tangential stiffness matrix and the loss of positiveness of second-order work. The constitutive model is applied to simulate drained and undrained triaxial tests on Toyoura sand of various densities under various confining pressures. The predictions are compared with experimentally measured instability at the assembly level. The modes of stability at the interparticle contact level and their relations to the overall instability of the assembly are also analyzed.

International audience; A multi-scale approach is proposed as an attempt to assess internal erosion induced effects on the mechanical properties of a granular medium. When submitted to internal flow, some particles tend to be removed from the initial granular material, leading to drastic changes in the microstructure. The medium is changing during its lifetime and this cannot be ignored in attempts to model its mechanical behavior. In this first analysis, the degradation of a granular assembly is simulated through the progressive removal of its finest particles for both isotropic and anisotropic stress states. A discrete element model as well as an analytical micromechanical model are used to compare induced deformations and properties changes along the erosion process. The shear strength and flow properties appear to be strongly modified by this extraction phase: both models highlight a change from a dilatant to a contractant behavior with the degradation as well as strong dependency of the overall stability on the mobilized friction level. In particular, results show how failure is triggered when particle removal occurs for mobilized frictions greater than the one reached at the critical state.; Une approche multi-échelle est proposée dans le but d'étudier les effets de l'érosion interne sur les propriétés mécaniques d'un milieu granulaire. Dans cette première analyse, la dégradation d'un assemblage granulaire est simulée par la suppression progressive de ses particules les plus fines pour différents états de contrainte, isotropes et anisotropes. Un modèle aux élements discrets ainsi qu'un modèle micromécanique analytique sont utilisés dans le but de comparer les déformations et les modifications induites sur le milieu. La resistance au cisaillement et les propriétés d'écoulement du matériau semblent être significativement modifiées par un tel processus d'extraction : les deux modèles sont unanimes pour mettre en évidence le passage d'un comportement dilatant à un comportement contractant du matériau avec sa dégradation, ainsi q'une dépendance critique de sa stabilité globale selon le niveau du frottement mobilisé auquel l'extraction de ses particules solides est réalisée. En particulier, les resultats montrent une tendance à l'effondrement lorsque l'extraction intervient pour des frottements mobilisés supérieurs à celui atteint à l'état critique.

International audience; Clay material can be considered as a collection of clusters, which interact with each other mainly through mechanical forces. From this point of view, clay is modeled by analogy to granular material in this paper. An elastoplastic stress-strain relationship for clay is derived by using the granular mechanics approach developed in previous studies for sand. However, unlike sand, clay deformation is generated not only by the mobilizing but also by compressing clusters. Thus, in addition to the Mohr-Coulomb's plastic shear sliding and a dilatancy type flow rule, a plastic normal deformation has been modeled for two clusters in compression. The overall stress-strain relationship can then be obtained from the mobilization and compressing of clusters through a static hypothesis of the macro-micro relations. The predictions are compared with the experimental results for clay under both drained and undrained triaxial loading conditions. Three different types of clay, including remolded and natural clay, have been selected to evaluate the model's performance. The comparisons verify that this model is capable of accurately reproducing the overall behavior of clay, which accounts for the influence of key parameters such as void ratio and mean stress. A section of this paper is devoted to show the model's capability of considering the influence of inherent anisotropy on the stress-strain response under undrained triaxial loading conditions.

This paper presents a micromechanical study of unsaturated granular media in the pendular regime, based upon numerical experiments using the discrete element method, compared to a microstructural elastoplastic model. Water effects are taken into account by adding capillary menisci at contacts and their consequences in terms of force and water volume are studied. Simulations of triaxial compression tests are used to investigate both macro and micro-effects of a partial saturation. The results provided by the two methods appear to be in good agreement, reproducing the major trends of a partially saturated granular assembly, such as the increase in the shear strength and the hardening with suction. Moreover, a capillary stress tensor is exhibited from capillary forces by using homogenisation techniques. Both macroscopic and microscopic considerations emphasize an induced anisotropy of the capillary stress tensor in relation with the pore fluid distribution inside the material. In so far as the tensorial nature of this fluid fabric implies shear effects on the solid phase associated with suction, a comparison has been made with the standard equivalent pore pressure assumption. It is shown that water effects induce microstrural phenomena that cannot be considered at the macro level, particularly when dealing with material history. Thus, the study points out that unsaturated soil stress definitions should include, besides the macroscopic stresses such as the total stress, the microscopic interparticle stresses such as the ones resulting from capillary forces, in order to interpret more precisely the implications of the pore fluid on the mechanical behaviour of granular materials., 39 pages

Studies in the past have tried to reproduce the mechanical behaviour of granular materials by proposing constitutive relations based on a common assumption that model parameters and parameters describing the properties, including gradation of individual grains are inevitably linked. However successful these models have proved to be, they cannot account for the changes in granular assembly behaviour if the grains start to break during mechanical loading. This paper proposes to analyse the relation between grading change and the mechanical behaviour of granular assembly. A way to model the influence of grain breakage is to use a critical state-based model. The influence of the amount of grain breakage during loading, depending on the individual grain strength and size distribution, can be introduced into constitutive relations by means of a new parameter that controls the evolution of critical state with changes in grain size distribution. Experimental data from a calcareous sand, a quartz sand, and a rockfill material were compared with numerical results and good-quality simulations were obtained. The main consequences of grain breakage are increased compressibility and a gradual dilatancy disappearance in the granular material. The critical state concept is also enriched by considering its overall relation to the evolution of the granular material. Copyright © 2009 John Wiley & Sons, Ltd.

International audience; The homogenization technique is used to obtain an elastoplastic stress-strain relationship for dry, saturated and unsaturated granular materials. Deformation of a representative volume of material is generated by mobilizing particle contacts in all orientations. In this way, the stress-strain relationship can be derived as an average of the mobilization behavior of these local contact planes. The local behavior is assumed to follow a Hertz-Mindlin's elastic law and a Mohr-Coulomb's plastic law. For the non-saturated state, capillary forces at the grain contacts are added to the contact forces created by an external load. They are calculated as a function of the degree of saturation, depending on the grain size distribution and on the void ratio of the granular assembly. Numerical simulations show that the model is capable of reproducing the major trends of a partially saturated granular assembly under various stress and water content conditions. The model predictions are compared to experimental results on saturated and unsaturated samples of silty sands under undrained triaxial loading condition. This comparison shows that the model is able to account for the influence of capillary forces on the stress-strain response of the granular materials and therefore, to reproduce the overall mechanical behavior of unsaturated granular materials.

International audience; It has been widely shown that particle crushing increases the compressibility of granular materials. For a particular crushable material and given test conditions, an empirical relation can be established between the breakage ratio and the plastic work. Along these lines, constitutive models have been developed based on the effect of grading evolution during crushing. In parallel, due to corrosive attacks of the humid environment at the tip of microcracks within solid grains, the mechanical behavior of crushable granular materials depends also on the water content: the higher the material humidity, the higher the particle crushing. However, the experimental data on the relation between loading–wetting conditions and the breakage ratio are still quite scarce. In this paper, we present experimental results on crushable sand to study the effect of flooding under isotropic, oedometric, and triaxial stress paths. The main objective of this study is to obtain a consistent framework for the effect of water based on the breakage ratio. Our results have shown that, for a given initial density and stress path, the dry material after flooding reaches the equivalent behavior of the initially wetted material in terms of compression curve, particle crushing, and creep compressibility index, regardless of the point of flooding. Moreover, the relation between the breakage ratio and the final void ratio is unique and depends neither on the stress path, the water content, the point of flooding, nor the loading condition (time of creep or relaxation), but exclusively on the initial density and on intrinsic parameters. These findings could improve the prediction of the effect of water and time on the mechanical response of crushable granular materials through constitutive models based on grading evolution.; Il est reconnu que la rupture des grains augmente la compressibilité des matériaux granulaires. Pour des conditions d'essai données, une relation empirique peut être établie entre le taux de rupture des grains et le travail plastique. Ainsi, des modèles constitutifs ont été développés sur la base de l'évolution de la granulométrie liée a ` cette rupture des grains. Parallèle-ment, du fait des attaques corrosives de l'environnement humide en pointe des micro-fissures dans les grains solides, le comportement mécanique des matériaux granulaires broyables dépend également de la teneur en eau: plus l'humidité du matériau est élevée, plus la rupture semble favorisée. Toutefois, les données expérimentales sur la relation entre les conditions de chargement, les conditions hydriques et le taux de rupture sont encore très rares. Dans cet article, on présente des résultats expérimentaux sur un sable affecté par la rupture des grains pour étudier l'effet de l'imbibition sur des chemins de contraintes isotropes, eudiométriques, et triaxiales. L'objectif principal de cette étude est d'obtenir un schéma de comportement cohérent décrivant l'effet de l'eau sur le taux de rupture des grains. Les résultats montrent que, pour une densité initiale et un chemin de contraintes donné, après l'imbibition d'un échantillon sec, il suit un comportement identique à celui d'un échantillon saturé dès le début du chargement en termes de compressibilité, ruptures des grains et d'indice de compressibilité au fluage, quel que soit le point d'imbibition. Par ailleurs, la relation entre le taux de rupture et l'indice des vides final est unique et ne dépend pas du chemin de contraintes, ni de la teneur en eau, ni du point initial de l'imbibition, ni des conditions de chargement (temps de fluage ou de relaxation), mais uniquement de la densité initiale et de paramètres intrinsèques. Ces résultats pourraient améliorer la prédiction de l'effet de l'eau et du temps sur la réponse mécanique des matériaux granulaires broyables à l'aide des modèles constitutifs basés sur la granulométrie.

International audience; This paper discusses the notion of failure in a granular assembly by examining the key microstructural mechanisms which are most likely to trigger the nucleation and propagation of instabilities within a granular material. For this purpose, the key variable to predict the occurrence of failure, known as second-order work, is expressed from variables on the grain scale. The local behaviour incidents (where contacts may open or slide), compared to the global response of the assembly, are analysed by two approaches. First, numerical computations made by a discrete element model confirm the microscopic definition of the second-order work. Secondly, a micromechanical model, based on a homogenization procedure, relating the macroscopic behaviour to microscopic ingredients, namely contact planes, points to a close link between the occurrence of failure on the macroscopic scale as well as on the contact planes.

International audience; The aim of this paper is to investigate the effect of soil grading on the stress-strain and the critical-state behavior of granular materials from idealized spheres to natural soils as well as from discrete to continuous modeling. The three-dimensional discrete-element method has been applied to study the mechanical behavior of idealized granular materials. The results confirm that the critical-state line (CSL) shifts down-ward as grading broadens with an increase of the coefficient of uniformity Cu. An exponential relationship between the critical-state parameters and the coefficient of uniformity Cu can then be established. Furthermore, experimental investigations on an artificial material (glass beads) and a natural material (Hostun sand) were carried out. The experimental results confirm the grading dependency of the critical-state behavior, and a similar relationship between CSL and Cu, for both glass beads and natural sand, extending previous literature results for high Cu values up to 20. Moreover, the experimental results show that the CSL tends to stabilize when the coefficient of uniformity Cu becomes higher than 10. Based on all test results, a simple elastoplastic model accounting for the influence of the grain size distribution (GSD) on the mechanical behavior of granular materials has been developed within the framework of critical-state soil mechanics. Comparisons between experimental results and simulations show that the model can accurately reproduce the mechanical behavior of granular materials with different GSDs.

International audience; Testing the mechanical response of coarse granular materials requires very large and expensive laboratory equipments. During the 1960s, pioneering experimental programs were carried out on several rockfill dam materials, and those results are still a reference for engineers and researchers. However, only few experimental works have been reported to this day, and due to the scarcity of empirical data, the role of the size effect caused by grain crushing is not well known. To improve understanding of this rarely studied issue and the influence of individual particle strength, this paper analyzes the size effect on rock aggregate crushing strength and its connection with the shear envelope of rockfills. The suitability of the 4-parameter Weibull equation to describe size effects on the crushing strength reported in the literature is discussed. Furthermore, a Weibull statistical analysis was carried out for a wide number of experimental results on rock aggregates, where it has been observed that strength decreases with particle size. In parallel, the results of large triaxial tests on homothetic scaled rockfill samples of 250 and 1,000 mm in diameter reveal that the coarser the material, the higher the amount of grain breakage and the lower the shear strength. The impact of size effects obtained from the experiments is analyzed and discussed in terms of the factor of safety of rockfill slope stability. Furthermore, the results are compared with the only existing theoretical method that links the rock aggregate with the strength of the granular assembly. Good agreement between the empirical results and this theoretical method has been confirmed.

International audience; This paper aims at investigating the influence of grading on the undrained behavior of granular materials. Series of undrained triaxial tests were carried out with two different materials, glass balls and Hostun sand. For each material, samples with different gradings and similar relative densities were prepared. Experimental results show that the undrained shear strength decreases when the coefficient of uniformity Cu=d60/d10Cu=d60/d10 increases from 1.1 to 20. The conditions of instability for the selected granular materials were also analyzed, based on the sign of the second-order work during undrained triaxial loading. The results demonstrate a significant influence of the grading: increasing the coefficient of uniformity heightens the potential of static liquefaction and the materials become more unstable. Furthermore, numerical tests using the three-dimensional discrete element method (DEM) were conducted on assemblies of spheres. The DEM inter-particle parameters were derived from the experimental test results on glass balls. The DEM simulations showed similar behaviors compared to experimental results and confirmed the influence of the grain size distribution on the stress–strain relationship and instability phenomena.; Cet article vise à étudier l'influence de l'étalement granulométrique sur le comportement non drainé des matériaux granulaires. Des séries d'essais triaxiaux non drainés ont été réalisés sur deux matériaux différents, des billes de verre et du sable Hostun. Pour chaque matériau, des échantillons de différentes granulométries et de densités relatives similaires ont été préparés. Les résultats expérimentaux montrent que la résistance au cisaillement diminue lorsque le coefficient d'uniformité Cu=d60/d10Cu=d60/d10 augmente de 1,1 à 20. Les conditions d'instabilité pour les matériaux granulaires sélectionnés ont également été analysées, sur la base du signe du travail du second ordre au cours d'un chargement triaxial non drainé. Les résultats montrent une influence significative de l'étalement granulométrique : l'augmentation du coefficient d'uniformité accroît le potentiel de liquéfaction statique et les matériaux deviennent plus instables. En outre, des essais numériques en utilisant la méthode des éléments discrets en trois dimensions (DEM) ont été effectués sur des assemblages de sphères. Les paramètres inter-particules DEM ont été calculés à partir des résultats d'essais expérimentaux sur des billes de verre. Les simulations DEM ont montré des comportements similaires comparés aux résultats expérimentaux et confirment l'influence de l'étalement granulométrique sur la relation contrainte–déformation et les phénomènes d'instabilité.

The mechanical behaviour of granular materials depends on the properties of the grains and on the arrangement of the grain assembly. Using a methodology for connecting the discontinuous medium and the supposedly continuous medium, the authors present at first a set of correlations and standard behaviours for granular media made of elastic grains without “glue”, inside this scheme it is then possible to enlight the influence of grain breakage during loading. It appears that the most significant parameter, for a given mineralogy of the grains, is the grain size distribution. Its effects are particularly noticeable on the volume change amplitudes during isotropic and deviatoric loadings.

International audience; Depending on stress state and loading conditions, instability in loose sand can develop at a shear stress level much lower than the Mohr-Coulomb failure criterion. This type of failure mode, very different from strain-softening in dense sand, can lead to catastrophic collapse of earth structures. An appropriate constitutive model is therefore needed that can capture the correct failure modes and accurately predict the stress-strain response for both dense and loose sands. In this paper, a micromechanical approach developed earlier for the modelling of granular material behaviour is adopted. The constitutive model is utilised to simulate undrained triaxial, constant-q and proportional strain tests on loose sand, and numerical results are compared with experimental results. The model is capable of accurately reproducing the macroscopic experimental tests, and is also able to provide microstructural information. This enables the observation of instability at the particle scale, and provides a better understanding of the linkage between particle-scale instability and instability at the assembly level.

We present a method to predict how grain size distribution (gsd) evolves during confined comminution. We describe particle breakage as a probabilistic phenomenon considering the single particle strength and the pdf of interparticle contact forces from DEM simulations. Our results show a good agreement with published experimental data.

International audience; In this paper, we present a method to take into account the existence of inner forces between grains and their influence upon the mechanical behavior of granular assemblies. Two examples were retained. The first one concerns unsaturated granular materials for which we have considered capillary forces depending on the degree of saturation. The second one concerns extraterrestrials soils for which surface energy forces, such as Van der Waals forces, cannot be neglected due to tiny atmospheric pressure.

This paper aims to investigate the influence of grain size distribution (GSD) on the critical state of Hostun sand. Drained triaxial tests were conducted on saturated specimens with different GSD (Cu=1.4, 5, 10, 20) under different confining pressures (100, 200, 400 kPa). The experimental results highlight that the critical state of the tested sand predominantly depends on its GSD.

International audience; The shear strength of coarse granular materials, widely used in civil works such as rockfill in dam construction, is seldom measured because of severe practical experimental limitations. This paper presents an original method for evaluating the shear strength of such materials, based on size effects in granular materials affected by grain breakage according to fracture mechanics. Through a general size effect relation operating on shear strength envelopes, this method makes it possible to determine the shear strength of a coarse-grained granular material from the measured properties of a finer-grained granular material made of the same mineral. In the paper, the method is explicitly proved, taking into account the statistical distribution of breakage resistances of particles with different sizes, within materials that can be considered as physically similar, particularly having parallel grain size distributions and the same compactness. A wide set of independent experimental results is shown to validate the method consistently.

International audience; A particle breakage has a significant impact on the mechanical behavior of granular materials. In this paper, we present an elasto-plastic model with two yield surfaces to which the influence of particle breakage has been introduced. The main feature of this model is to incorporate the change in the critical state line (CSL) consequent to the grain breakage induced by isotropic and deviatoric stresses during loading. For this purpose we propose a breakage function which connects the evolution of the CSL to the energy consumed. Results from earlier studies on drained and undrained compression and extension triaxial tests were used to calibrate and validate the model. Comparison between earlier results and our simulations indicates that the model can reproduce with good accuracy the mechanical behavior of crushable granular materials and predict the evolution of the grain size distribution during loading.

International audience; Natural soils or coarse granular materials containing large particles such as rockfill or ballast are often an issue for geotechnical projects. However, since it is usually complicated or impossible to set up a big enough experimental apparatus to test these materials, their mechanical behavior remains poorly known.To circumvent this difficulty, we have developed a set of triaxial cells of various sizes to study the experimental behavior of granular soils containing particle sizes of up to 160 mm. This paper presents the first results of a two-part experimental study. The first part consists of triaxial tests on sand samples of different sizes in order to examine specimen scale effects. Pre-peak behavior is not affected by the specimen size, whereas post-peak behavior depends on the test conditions that control the development of strain localizations. In the second part, we present drained triaxial compression tests on large samples of calcareous rockfill materials that have parallel grain size distributions.The results show a nonstandard evolution of the friction angle in relationship to grain size if compared to similar studies on coarse granular materials. Although grain crushing occurs during compression, the strain-stress curves of the different materials with different grain sizes do remain close. We explain this phenomenon by the strength evolution of the individual grains with respect to their sizes

Under certain loading conditions, loose sand can develop instability at a shear stress level much lower than the critical state failure line. To analyze these types of problems, we have adopted the micromechanics model developed by Chang and Hicher for modelling granular material behaviour. The stress-strain relationship for a granular assembly is determined by integrating the behaviour of the inter-particle contacts in all orientations. The constitutive model is applied to simulate undrained triaxial, constant-q and proportional strain tests on loose Hostun sand. Experimental results are used to evaluate how well the model can capture the modes of instability at the assembly level. The notion of control variables is discussed according to these different loading conditions.

International audience; An elasto-plastic model with two yield surfaces has been developed for the simulation of granular materials with consideration of grain ruptures. Grain breakage is induced by deviatoric as well as isotropic stresses. One yield function is based on a Mohr-Coulomb criterion with a hyperbolic hardening function of the plastic deviatoric strain. A second yield function is introduced to describe the plastic behaviour under compression, in which a hardening function of the plastic volumetric strain is introduced. The main assumption of this model is that, upon loading, the position of the critical state changes as a consequence of grain breakage. The effect of the grain size distribution is introduced in the relationship between the void ratio at critical state and the mean effective stress. Triaxial and oedometer tests have been performed on crushable granular materials. Comparison of experimental results and numerical simulations shows that the new model can reproduce with good accuracy the behaviour of granular materials subjected to grain ruptures during mechanical loading.

Because of the lack of experimental devices for testing granular materials with large particles, the mechanical behavior of rockfill is not very well known. This lack of knowledge can lead to improper design of rockfill dams, and as a consequence, to severe accidents including dam failures. A method has been developed by Frossard (2005) for evaluating the shear strength of rockfill based on the estimation of size effect in granular materials, affected by grain breakage. Comparison between experimental results and numerical predictions shows that this method can estimate with good accuracy the strength of granular materials made of large particles.

Granular materials with large particles have been widely used to construct embankments or rockfills dams. However, due to limitations in the size of experimental set-ups, their behavior remains relatively less investigated than the behavior of sands for instance. A new large triaxial apparatus, with a maximum specimen diameter of 1000mm, has been designed to study the behavior of such coarse granular materials. This device is described in this paper. The results of a triaxial test on calcareous particles with a maximum particle size of 160 mm are presented. Special attention has been paid on grain crushing under shear loading.

International audience; Under certain loading conditions, instability in loose sand can develop at a shear stress level much lower than the critical state failure line. To analyse these types of problems, we adopt the micromechanical approach developed earlier for the modelling of granular material behaviour. The stress-strain relationship for a granular assembly is determined by integrating the behaviour of the inter-particle contacts in all orientations. The constitutive model is applied to simulate undrained triaxial and constant-q tests on loose sand. Numerical simulations are compared to experimental results in order to evaluate the model's ability to predict the different modes of instability of the granular assembly. With the model we have also analysed instability at inter-particle level to observe how it is connected to instability at the assembly level.; Dans certaines conditions de chargement, des ruptures par instabilité peuvent prendre naissance dans les sables lâches pour des niveaux de contraintes très nettement inférieurs à ceux correspondant à la plasticité parfaite. Pour analyser ce type de problèmes, nous adoptons une approche d'homogénéisation développée précédemment pour la modélisation du comportement des matériaux granulaires. La relation contrainte-déformation macroscopique est obtenue en intégrant le comportement défini au niveau du contact inter-granulaire. Le modèle est utilisé pour simuler des essais non drainés et des essais à déviateur constant sur un sable lâche. Les résultats de la simulation à l'échelle macroscopique sont comparés à des résultats expérimentaux de façon à apprécier la capacité du modèle à prédire la naissance de l'instabilité sur ces chemins particuliers. Une analyse à l'échelle des différents plans de contact inter-granulaire a également été entreprise afin de relier les conditions d'instabilité aux différentes échelles.

The approach of micromechanical modeling has been used in developing stress‐strain models for granular materials. This approach takes into account of the behavior at grain level and predicts the stress‐strain behavior of the granular assembly. Although the developed stress‐strain models may be in different form, the issues encountered during the process of modeling are expected to be similar. Most issues are connected to two general questions: (1) How to reduce the errors caused by macro‐to‐micro hypotheses and other simplified assumptions? and (2) For the local behavior at the grain level, how to include the correct physics to establish a suitable yet simple inter‐particle model? These issues will be discussed and suitability of the approach will be evaluated in the presentation.

In this paper we study the influence of internal erosion on the development of instability in soil masses. A constitutive modeling method for granular materials based on particle level interactions has been developed using an homogenization technique. In the model, a simple elastic‐plastic behavior is assumed on each contact plane. A numerical analysis of the condition of instability expressed by the vanishing of the second‐order work is performed in the context of soil subjected to internal erosion. Special attention is given to constant deviatoric stress paths, which are representative of a change in hydraulic conditions within a soil element. Numerical results show that instability condition can be reached along such stress path when the soil undergoes internal erosion.