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«THÈSE Pour obtenir le grade de DOCTEUR DE L’UNIVERSITÉ GRENOBLE ALPES Spécialité : mécanique, matériaux, génie mécanique, génie civil ...»

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THÈSE

Pour obtenir le grade de

DOCTEUR DE L’UNIVERSITÉ GRENOBLE ALPES

Spécialité : mécanique, matériaux, génie mécanique, génie

civil

Arrêté ministériel : 7 août 2006

Présentée par

Huaxiang ZHU

Thèse dirigée par François NICOT et

codirigée par Félix DARVE

préparée au sein du IRSTEA-Grenoble

dans l'École Doctorale Ingénierie, Matériaux, Energétique,

Environnement, Procédés, Production (I-MEP2)

Prise en compte d'une échelle intermédiaire dans la modélisation micro-structurelle des sols granulaires Thèse soutenue publiquement le 11 Décembre 2015,

devant le jury composé de :

Professor, Bernard CAMBOU Professor, École Centrale de Lyon, Rapporteur Professor, Niels KRUYT Professor, University of Twente, Rapporteur Professor, Jean LERBET Professor, Université Evry Val d'Essonne, Président Professor, Francesco FROIIO Professor, École Centrale de Lyon, Examinateur Professor, Félix DARVE Professor, INP-Grenoble, Co-directeur de thèse Professor, François NICOT Professor, IRSTEA-Grenoble, Directeur de thèse Including a meso-structure in multi-scale modeling of granular soils Huaxiang ZHU Grenoble 2015 Including a meso-structure in multi-scale modeling of granular soils Huaxiang ZHU Huaxiang ZHU Irstea de Grenoble Unité de Recherche Erosion Torrentielle Neige et Avalanches Domaine Universitaire, BP 76 F38402 – Saint Martin d’Hères Cedex – France huaxiang.zhu@irstea.fr Abstract Granular materials exhibit a wide spectrum of constitutive features under various loading paths. Developing constitutive models which succeed to characterize these features has been challenging scientists for decades. A promising direction of achieving this can be the multi-scale approach. Through this approach the constitutive model is formulated by relating material’s macroscopic properties to their corresponding microstructure properties.

A comprehensive investigation has been carried out on the basis of numerical biaxial tests using a 2D discrete element method (DEM), in order to ascertain the micro-structure characteristics of the granular material, the way they evolve along the loading path and roles they play in the macroscopic behaviors. In a meso-scale, intermediate between the single contact scale and the macro-scale, the force transmission network (force-chains) and area element enclosed by contacts branches (meso-loops) are highlighted in terms of their significant influences on material’s macro-scale behavior. Meso-loops herein are tessellated from the whole area of the granular assembly by the contact network, and are subsequently categorized according to their side number.

The development of meso-loops is observed to be intimately related to material’s volumetric evolution, especially to the plastic part. Then, the interaction between forcechains and meso-loops and the significance of this interaction to the global volumetric behavior and the macroscopic strength are revealed. Meso-loops with 3 sides (L3 ) appear to be indispensable for the force-chain stability, meanwhile, meso-loops with more than or equal to 6 sides (L6+ ) contribute much to the volume expansion and accelerate the buckling of the force-chain they confine. Otherwise, in the critical state, an identical vi meso-structure is found in the failure area of both localized and diffuse failure mode. To this extent, L3 and L6+ are enormously important for the granular material to transmit forces and to perform the volumetric variation.

A constitutive model has been developed by modifying the H-directional model (Nicot and Darve, 2011b). In this model, the individual hexagons, the representatives of L6+, construct the fabric as distributing along different directions in the space. A homogenization approach is then used to relate macroscopic properties to local ones.

This model is then validated in different loading paths, and eventually proved satisfying.

Keywords:

Failure, instability, micro-structure, constitutive modeling, multi-scale, DEM Résumé Les matériaux granulaires exhibe un spectre très large de propriétés constitutives, le long de chemins de chargement très divers. Développer des modèles constitutifs permettant de reproduire ces caractéristiques a demeuré un réel challenge scientifique au cours des dernières décennies. A cet égard, les approches multi-échelles constituent aujourd’hui une voie très prometteuse. Elles permettent de relier les propriétés macroscopiques à celles observées à l’échelle microscopique.

Une investigation a été menée sur la base de simulations numériques discrètes (DEM) d’essais biaxiaux, afin d’identifier les caractéristiques micro-structurelles du matériau granulaire, la manière dont elles évoluent au cours d’un chemin de chargement, et le rôle qu’elles jouent dans l’émergence du comportement macroscopique. A l’échelle mésoscopique, le réseau de transmission de force (chaines de force) et les cellules définies par les vecteurs branches (meso-cycles) apparaissent jouer un rôle de première importance.

Les meso-cycles, construits à partir du réseau de contact de l’assemblage, peuvent être caractérisés en fonction du nombre de cotés qu’ils contiennent (topologie). Leur influence sur le comportement volumique de l’échantillon est en effet étroitement liée à ce nombre de contact. En outre, leur interaction avec les chaines de force est également fortement dépendante de leur topologie. Ainsi, les cycles contenant 3 cotés (L3 ) participent activement à la stabilisation des chaines de force, alors que les cycles contenants au moins 6 cotés (L6+ ) contribuent essentiellement au comportement dilatant de l’échantillon et à l’effondrement des chaines de force. Enfin, l’existence d’une méso-structure unique à l’état critique, au sein de la bande de cisaillement (rupture localisée) ou au sein de l’échantillon (rupture diffuse), est clairement démontrée.





viii Sur la base de ces résultats, un modèle constitutif a été développé à partir du modèle H-directionnel (Nicot and Darve, 2011b). La structure du matériau granulaire est décrite par un assemblage d’hexagones (modélisant les cycles L6 ), orientés dans toutes les directions de l’espace. A partir d’opérations d’homogénéisation, les contraintes et les déformations incrémentales peuvent être reliées à l’échelle de l’assemblage, donnant lieu à un modèle de comportement dont la performance a pu être testée le long de chemins de chargements variés.

Mots clés:

Rupture, Instabilité, micro-structure, modélisation constitutive, Multi-échelle, DEM Contents

–  –  –

General Introduction

1.1 Background: micro-structure of the soil and multi-scale approach A vast majority of human activities, so far, are limited on the ground by the gravity, and a vast majority of artificial structures are established with contacting to the earth. The soil, covering an enormous proportion of the land surface on the earth, considered to be the “skin of the earth”, is a kind of important material we should deal with in engineering practices of various types, such as civil engineering, environmental engineering, mining engineering, shore engineering and etc.

Being a big material class, the soil contains numerous members, classified according to different criteria, such as the class of the parent material, the grain size distribution and the consolidation history. Otherwise, as composed of gas, fluid and solid to be a three phases system, the soil behaves sensitively to the initial states of three phases, and the way three phases evolve along the loading path. The combination of these factors gives rise to a wide variation of the mechanical properties of the soil, among not only different kinds of soil but also different initial states and various applied loading paths. Up to date, the knowledge on the soil is limited and insufficient, especially when compared with the increasing need of human constructions and activities. Understanding soil’s features in different conditions and circumstances and developing models to simulate its behaviors, therefore, appear to be the fundamental topics for scientists and engineers in the geomechanics community.

2 1. General Introduction

The soil, consisting of soil grains, is basically a member of the granular material, which is a more general family involving the snow, the coal, different kinds of powder and etc.

The constituents of granular materials, as what its name indicates, are discrete grains varying in size and shape. The granular system is simply governed by the frictional nature (with or without a cohesion) on the contact points and the given boundary conditions. However, when it assembles a great number of grains together into a complex system, a series of complex behaviors may consequently emerge, e.g. a highly incrementally non-linear constitutive behavior (Darve, 1990; Darve et al., 1995b), the existence of the non-associate flow rule, and the existence of a bifurcation domain within the plastic limit (Darve et al., 2004; Nicot et al., 2009). Besides, considering the importance of the granular material in application to diverse industries (Rhodes, 1990), such as civil engineering, pharmaceutical industry and agriculture, it has evoked great interest in the mechanics community in last decades. In this thesis, the soil, or called granular soil, is investigated and discussed in the general framework of granular materials.

Benefiting from the advancing of the measurement technique toward the microscopy, plentiful new techniques are introduced to observe the micro-structure of granular materials, such as electron microscope, photoelastic material and X-ray. Researchers are gradually capable of clarifying microscopic essences beneath macroscopic behaviors of the granular material. In dedications to this way, numerous features in the microscale are successively discovered, the fundamental roles played by different kinds of micro-structures in the material’s mechanical behavior are successively recognized.

The material fabric and its decisive influence on the macroscopic mechanical properties have been a popular topic since the pioneering work of Oda (1972a,b,c). Considered as the core of stress-strain relation, the material fabric exists to be the bridge between the stress and strain. Furthermore, two kinds of self-organization of grains (or contacts), the force-chain and the loop, are observed to be prevalent micro-scale structures in granular materials and highlighted to be significant features with mechanical meanings. Forcechains are quasi-linear chains formed by grains transmitting forces of magnitude larger than the average value. It is the strong phase of the force network, as between these chains are regions of the low force carriage, in which grains are shielded by their neighbors vaulting or arching above (Kondic et al., 2012). The force-chain system, contributing most in sustaining external loading, is largely responsible of the force transmission in the specimen. The massive buckling of force-chains betoken a global loss of the material’s sustainability against external loading, i.e. the instability of the material. Loops are the

1.2 Constitutive modeling for granular material: knowledge and problems 3 elementary cells of the granular assembly enclosed inside by contact branches. Since the whole area of the granular assembly can be seamlessly tessellated into loops, they are elementary entities of the material’s volume, therefore, strongly relating to the global volumetric behavior.

Another important work in the geomechanics is to develop constitutive models, which try to give mathematical relations for simulating the behavior of the material as close to the reality as possible. Last decades have seen many phenomenological models, which build constitutive relations by means of mathematically characterizing the different observed phenomena. This kind of model normally has to involve an exceeding number of parameters, whereas most of these parameters lack the physical background.

With the advances in micro-scale investigations, more and more macroscopic phenomena are attributed to the microscopic characteristics of the material. Many researchers then turn to make the attempt of embedding the discovered micro-physics into the constitutive relation. This naturally requires the technique for changing scales between micro and macro, giving birth to the multi-scale approach. To this approach, problems of the constitutive modeling turn from how to properly formulate observed macroscopic phenomena to how to exactly characterize the basic micro-physics underlying the macroscopic phenomena and to sophisticatedly link them to macroscopic properties. This, reversely, brings forward a higher demand on investigating the micro-structure of the granular soil. Along the reasoning line of this approach, investigations and discussions in this thesis unfold.

1.2 Constitutive modeling for granular material: knowledge and problems 1.2.1 micro-structure investigation The way and tool employed for implementing the experiment and measuring results may vary from one research to another, whereas all independent information in a granular assembly is no more than the static properties on contacts, i.e. the contact force, and kinematic properties on particles, i.e. the particles’ position and velocity. Various analyses are then made on the basis of this information.

4 1. General Introduction

1.2.1.1 Material fabric and its evolution

In the granular material subjected to the quasi-static loading, two fabric systems are significant to the mechanical behavior: the material fabric and the force fabric. The material fabric refers to the contact network composed of all contact branches, while the force fabric is the network through which forces pass the material. In practice, the material fabric is the basis of the force fabric and, reversely, the force fabric can reconstruct the material fabric. The evolution and interaction of these two fabrics are essential microscopic ingredients of the granular assembly.



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