Macroelement modeling of shallow foundations

The paper presents a new macroelement model for shallow foundations. The model is defined through a non-linear constitutive law written in terms of some generalized force and displacement parameters. The linear part of this constitutive law comes from the dynamic impedances of the foundation. The non-linear part comprises two mechanisms. One is due to the irreversible elastoplastic soil behavior: it is described with a bounding surface hypoplastic model, adapted for the description of the cyclic soil response. An original feature of the formulation is that the bounding surface is considered independently of the surface of ultimate loads of the system. The second mechanism is the detachment that can take place at the soil-footing interface (foundation uplift). It is totally reversible and non-dissipative and can thus be described by a phenomenological non-linear elastic model. The macroelement is qualitatively validated by application to soil-structure interaction analyses of simple real structures

Rupture sismique des fondations par perte de capacité portante: Le cas des semelles circulaires

International audienceWithin the context of earthquake-resistant design of shallow foundations, the present study is concerned with the determination of the seismic bearing capacity of a circular footing resting on the surface of a heterogene-ous purely cohesive semi-infinite soil layer. In the first part of the paper, a database, containing case histories of civil engineering structures that sustained a foundation seismic bearing capacity failure, is briefly pre-sented, aiming at a better understanding of the studied phenomenon and offering a number of case studies useful for validation of theoretical computations. In the second part of the paper, the aforementioned problem is addressed using the kinematic approach of the Yield Design theory, thus establishing optimal upper bounds for the ultimate seismic loads supported by the soil-footing system. The results lead to the establishment of some very simple guidelines that extend the existing formulae for the seismic bearing capacity contained in the European norms (proposed for strip footings on homogeneous soils) to the case of circular footings and to that of heterogeneous cohesive soils

Solid behavior of anisotropic rigid frictionless bead assemblies

We investigate the structure and mechanical behavior of assemblies of frictionless, nearly rigid equal-sized beads, in the quasistatic limit, by numerical simulation. Three different loading paths are explored: triaxial compression, triaxial extension and simple shear. Generalizing recent results [1], we show that the material, despite rather strong finite sample size effects, is able to sustain a finite deviator stress in the macroscopic limit, along all three paths, without dilatancy. The shape of the yield surface is adequately described by a Lade-Duncan (rather than Mohr-Coulomb) criterion. While scalar state variables keep the same values as in isotropic systems, fabric and force anisotropies are each characterized by one parameter and are in one-to-one correspondence with principal stress ratio along all three loading paths.The anisotropy of the pair correlation function extends to a distance between bead surfaces on the order of 10% of the diameter. The tensor of elastic moduli is shown to possess a nearly singular, uniaxial structure related to stress anisotropy. Possible stress-strain relations in monotonic loading paths are also discussed

Internal states of model isotropic granular packings. III. Elastic properties

In this third and final paper of a series, elastic properties of numerically simulated isotropic packings of spherical beads assembled by different procedures and subjected to a varying confining pressure P are investigated. In addition P, which determines the stiffness of contacts by Hertz's law, elastic moduli are chiefly sensitive to the coordination number, the possible values of which are not necessarily correlated with the density. Comparisons of numerical and experimental results for glass beads in the 10kPa-10MPa range reveal similar differences between dry samples compacted by vibrations and lubricated packings. The greater stiffness of the latter, in spite of their lower density, can hence be attributed to a larger coordination number. Voigt and Reuss bounds bracket bulk modulus B accurately, but simple estimation schemes fail for shear modulus G, especially in poorly coordinated configurations under low P. Tenuous, fragile networks respond differently to changes in load direction, as compared to load intensity. The shear modulus, in poorly coordinated packings, tends to vary proportionally to the degree of force indeterminacy per unit volume. The elastic range extends to small strain intervals, in agreement with experimental observations. The origins of nonelastic response are discussed. We conclude that elastic moduli provide access to mechanically important information about coordination numbers, which escape direct measurement techniques, and indicate further perspectives.Comment: Published in Physical Review E 25 page

Internal states of model isotropic granular packings. I. Assembling process, geometry and contact networks

This is the first paper of a series of three, reporting on numerical simulation studies of geometric and mechanical properties of static assemblies of spherical beads under an isotropic pressure. Frictionless systems assemble in the unique random close packing (RCP) state in the low pressure limit if the compression process is fast enough, slower processes inducing traces of crystallization, and exhibit specific properties directly related to isostaticity of the force-carrying structure. The different structures of frictional packings assembled by various methods cannot be classified by the sole density. While lubricated systems approach RCP densities and coordination number z^*~=6 on the backbone in the rigid limit, an idealized "vibration" procedure results in equally dense configurations with z^*~=4.5. Near neighbor correlations on various scales are computed and compared to available laboratory data, although z^* values remain experimentally inaccessible. Low coordination packings have many rattlers (more than 10% of the grains carry no force), which should be accounted for on studying position correlations, and a small proportion of harmless "floppy modes" associated with divalent grains. Frictional packings, however slowly assembled under low pressure, retain a finite level of force indeterminacy, except in the limit of infinite friction.Comment: 29 pages. Published in Physical Review

De l'Elasto-plasticité au Calcul à la rupture (264 pages)

Cet ouvrage est une introduction à l'élasto-plasticité et au calcul à la rupture pour leurs applications à l'analyse du comportement des systèmes mécaniques, des structures et des ouvrages. Le comportement élasto-plastique y est d'abord présenté pour le milieu continu tridimensionnel dans le contexte de la transformation infinitésimale et de la règle d'écoulement plastique " associée ". Ce modèle est ensuite étendu aux milieux continus généralisés. En se plaçant dans le cadre d'hypothèses des petites perturbations, le comportement global d'un système constitué d'un tel matériau élasto-plastique soumis à un processus de chargement quasi-statique, exprimé en fonction des paramètres de chargement, répond au modèle élasto-plastique. L'écrouissage du système est dû à la fois à l'écrouissage propre du matériau et aux contraintes et déformations résiduelles engendrées par l'incompatibilité géométrique des déformations plastiques. (Afin de conserver à l'ouvrage la concision d'une introduction, on s'est ici abstenu de tout développement relatif aux méthodes employées dans les logiciels de résolution ou aux théorèmes d'adaptation). En l'absence d'écrouissage propre du matériau constitutif on met en évidence les chargements limites de ruine plastique du système. La théorie du calcul à la rupture élargit ce point de vue en considérant un système dont le matériau constitutif a des capacités de résistance limitées physiquement ou réglementairement. Les chargements extrêmes sont définis par la compatibilité de l'équilibre du système et de la résistance du matériau. Des théorèmes variationnels permettent de les déterminer. Cette théorie générale montre l'unité, souvent occultée par leurs présentations disjointes, des diverses méthodes mises en œuvre dans la pratique pour les milieux continus tridimensionnels ou bidimensionnels, pour les poutres, les plaques, etc. exposées dans de nombreux traités classiques. La pertinence pratique de l'approche par le calcul à la rupture du point de vue des applications dépend du phénomène physique qui limite la résistance ; cela est notamment pris en compte dans l'approche réglementaire de la sécurité aux états limites ultimes dont la théorie du calcul à la rupture constitue le socle fondamental

Action d'une conduite circulaire sur un sol cohérent

No abstract provide