Yield design formulation for porous media subjected to flow, using approximate pressure field. Calcul à la rupture en présence d'un écoulement : formulation cinématique avec un champ de pression approché

International audienceYield design formulation for porous media subjected to flow, using approximate pressure field. We attempt here to use the kinematic method of yield design in the case of a porous medium subjected to flow (with or without free surface), without looking for the exact solution of the pressure field. The method proposed here is based on the use of approximate pressure fields. In this paper, we show how, under different conditions concerning the yield criterion and the velocity field, the use of such approximate fields allows to obtain a necessary condition for stability without having to find the real pressure field. Nous cherchons ici à utiliser la méthode cinématique du calcul à la rupture dans le cas d'un milieu poreux soumis à un écoulement avec ou sans surface libre sans connaître la solution exacte du champ de pression. La méthode proposée ici repose sur l'utilisation de champs de pression approchés par défaut. Nous montrerons comment sous certaines conditions portant sur le critère de résistance et sur le champ de vitesse utilisé, l'utilisation de tels champs de pression approchés permet d'obtenir une condition nécessaire de stabilité sans avoir à déterminer exactement l'écoulement

Yield design for porous media subjected to unconfined flow: construction of approximate pressure fields.––– Calcul à la rupture en présence d'un écoulement à surface libre : construction de champs de pression approchés

International audienceWe consider the stability of a porous medium submitted to a steady-state flow with free-boundary. Assuming some hypotheses, it is possible to implement the kinematic method by using an approximate pressure field bounding the true pressure field from below. We are interested in finding such approximate pressure fields and in proving that they bound the true pressure field from below without knowing the true pressure field. We use fields which are solutions of a problem with relaxed conditions with regard to the real problem. Under a uniqueness condition of the solution of a weak formulation of the problem, such fields are lower bounds for the true pressure field. Finally, we give the example of a vertical dam

Variational Formulation and Upper Bounds for Degenerate Scales in Plane Elasticity

International audienceDegenerate scales appear when certain plane boundary value problems solved using Boundary Integral Equations do not have a unique solution. The main contribution of this paper is to prove four inequalities that constrain the degenerate scales for plane elasticity. These results are based on a new variational formulation. It is shown that the degenerate scales depend only on Poisson’s ratio. The bounds on the degenerate scales for plane elasticity in a given boundary are obtained mainly from the degenerate scales obtained from the Laplace equation for the same boundary, which are well documented

Annular shear of cohesionless granular materials: from inertial to quasistatic regime

Using discrete simulations, we investigate the behavior of a model granular material within an annular shear cell. Specifically, two-dimensional assemblies of disks are placed between two circular walls, the inner one rotating with prescribed angular velocity, while the outer one may expand or shrink and maintains a constant radial pressure. Focusing on steady state flows, we delineate in parameter space the range of applicability of the recently introduced constitutive laws for sheared granular materials (based on the inertial number). We discuss the two origins of the stronger strain rates observed near the inner boundary, the vicinity of the wall and the heteregeneous stress field in a Couette cell. Above a certain velocity, an inertial region develops near the inner wall, to which the known constitutive laws apply, with suitable corrections due to wall slip, for small enough stress gradients. Away from the inner wall, slow, apparently unbounded creep takes place in the nominally solid material, although its density and shear to normal stress ratio are on the jammed side of the critical values. In addition to rheological characterizations, our simulations provide microscopic information on the contact network and velocity fluctuations that is potentially useful to assess theoretical approaches

Limit design of axisymmetric shells with application to cellular cofferdams

This paper is devoted to the limit design of cellular cofferdams that are regarded as mixed structures where the backfill is modeled as a three-dimensional continuum, while the surrounding sheet pile wall is treated as a cylindrical shell. Dealing with this structure from a static point of view, it turns out that the problem under consideration requires the calculation of the ultimate load value of a circular cylindrical shell subjected to a linearly varying pressure distribution representing the thrust of the backfill material. Extending the results of previous works, a complete solution to this problem is developed for different boundary conditions. The corresponding results are discussed, notably the influence of the shell relative thickness. They are applied to the design of a single cellular cofferdam whose stability under gravity forces is examined, with the strength of the granular backfill material being described by a Mohr-Coulomb criterion

Modélisation d'échantillons numériques de sol armé sous sollicitations dynamiques

On effectue une étude paramétrique portant un remblai simplifié de sol renforcé par la méthode des éléments finis, en deux dimensions, soumis à une impulsion à son sommet et sous hypothèses de comportement élastique linéaire. On fait varier la façon de modéliser le renforcement (discret/homogénéisé) ainsi que la direction de chargement. Les réponses en déplacements et contraintes pour les différents modèles sont analysées. Les résultats indiquent que les barres du renforcement améliorent globalement la rigidité du massif sans modifier radicalement sa réponse à une impulsion. Par ailleurs, l'utilisation du modèle homogénéisé pour ce type d'ouvrages, considérée comme acceptable en statique, semble aussi justifiée en dynamique. Enfin, des différences entre les temps d'évolution des contraintes, notamment au niveau des barres, sont mis en évidence

Exact degenerate scales in plane elasticity using complex variable methods

International audienceA recent work has shown that using conformal mapping can lead to exact values of the degenerate scales in plane elasticity. We elaborate on this work by introducing some algebraic tools when this conformal mapping is a rational fraction transforming the outside of the unit circle into the outside of the considered domain. Using these tools, new cases are solved including shortened hypotrochoid, arc of circle, new approximates of equilateral triangle and square or symmetric Joukowski profiles. Another method makes it possible to obtain the degenerate scales for plane elasticity from the degenerate scale for Laplace's equation for some multiply connected sets: the cases of segments on a line or of arcs of circle with a n-fold symmetry. In these last cases, the exact values of the degenerate scales are obtained when the degenerate scale for the Laplace problem is known