Instabilité de Rayleigh-Taylor

L’instabilité de Rayleigh–Taylor, nommée en hommage aux physiciens britanniques Lord Rayleigh et G. I. Taylor, est une instabilité de l’interface séparant deux fluides de densités différentes, qui résulte de la poussée du fluide le plus lourd sur le fluide le plus léger (l'accélération dans le cas d'un système dynamique ou la gravité pour un système initialement statique est dirigée vers la phase légère). Ce phénomène est produit par exemple par l'onde de choc à l'origine des nuages interstellaires. Dans ce cas particulier où le choc est à l'origine de la mise en vitesse du système, on parlera d'instabilité de Richtmyer-Meshkov. Il se produit une situation analogue lorsque la gravité affecte deux fluides de densités différentes (le fluide le plus dense se trouvant au-dessus du fluide le moins dense) comme de l'huile minérale à la surface de l'eau. Considérons deux couches de fluides immiscibles superposées dans deux plans parallèles, la plus lourde surplombant

The effects of Prandtl number on the nonlinear dynamics of Kelvin-Helmholtz instability in two dimensions

Jeremy Peter Parker

It is known that the pitchfork bifurcation of Kelvin-Helmholtz instability occurring at minimum gradient Richardson number Ri(m) similar or equal to 1/4 in viscous stratified shear flows can be subcritical or supercritical depending on the value of the Prandtl number, Pr. Here, we study stratified shear flow restricted to two dimensions at finite Reynolds number, continuously forced to have a constant background density gradient and a hyperbolic tangent shear profile, corresponding to the 'Drazin model' base flow. Bifurcation diagrams are produced for fluids with Pr = 0.7 (typical for air), 3 and 7 (typical for water). For Pr = 3 and 7, steady billow-like solutions are found to exist for strongly stable stratification of Ri(m) beyond 1/2. Interestingly, these solutions are not a direct product of a Kelvin-Helmholtz instability, having half the wavelength of the linear instability, and arising through a superharmonic bifurcation. These short-wavelength states can be tracked down to at least Pr approximate to 2.3 and act as instigators of complex dynamics, even in strongly stratified flows. Direct numerical simulations of forced and unforced two-dimensional flows are performed, which support the results of the bifurcation analyses. Perturbations are observed to grow approximately exponentially from random initial conditions where no modal instability is predicted by a linear stability analysis.

2021

Out-of-plane instability of thin reinforced concrete walls under seismic loading

Angelica Rosso

Out of plane instability of reinforced concrete walls is a failure mechanism observed rather recently following the earthquakes in Chile (2010) and New Zealand (2011). Global out of plane instability is a phenomenon that may occur in thin walls, subjected to in plane cyclic loading, which develop large out of plane deformations over the storey height. Past experimental efforts to study this phenomenon focussed on thin members with two layers of longitudinal reinforcement. Hence, also the phenomenological models proposed in literature were mainly based on experimental evidence from double layered members. However, a constructive boom in Latin America, together with an elevated cost of materials, has led over the last fifteen years to the massive construction of reinforced concrete buildings in which the shear walls are very thin and have a single layer of reinforcement. Given the lack of experimental data on single layered members made it questionable whether the mechanism develops as in double layered members, and if the existing models are capable to reproduce the response. In view of the above, the present thesis has the two following goals: (i) Provide new experimental insight on the out of plane instability of members with a single layer of reinforcement; (ii) Develop and validate numerical and mechanical tools to simulate and assess the vulnerability of thin walls to out of plane buckling. The experimental findings obtained from two experimental programs, on thin walls and isolated wall boundary elements respectively, are presented. The importance of the maximum (or critical) tensile strain experienced by the member to trigger instability, which was already identified in the past, is supported by the experimental results. Nevertheless, discrepancies from the usual hypotheses assumed for members with two layers of reinforcement are pinpointed, in particular with respect to the buckling height involved in the deformation, and to the magnitude of the axial force at onset of out of plane instability. Moreover, the crucial role played by the crack pattern is discussed, and an innovative failure criteria based on a three hinge mechanism related to the compressive strains attained in the cracks is identified. Finally, also the adverse effect of an imposed out of plane displacement at the top is also addressed. For a more thorough understanding of the phenomenon, and with the intent of developing simple methods to calculate the critical tensile strain triggering out of plane failure, numerical models are developed and validated against experimental results. The simulations allowed identifying important differences between the isolated boundary element and the wall behaviour, in particular with respect to the vertical displacement profile along the height. On the basis of the numerical findings, an improved boundary element model, rather simple to use for assessment and design, is presented. Finally, building on the experimental and numerical findings, a new mechanical is proposed. The model is in principle developed for members with one layer of reinforcement, but it is shown how it can be extended to double layered members. The mechanical model sets apart from existing ones as it assumes different curvature and vertical displacement profiles along the entire storey height, it accounts for axial forces lower than yielding in compression, and it allows to consider various boundary conditions.

EPFL2018

Experimental tests on the out-of-plane response of RC columns subjected to cyclic tensile-compressive loading

Katrin Beyer, Lisandro Arturo Jimenez Roa, Angelica Rosso, João Saraiva Esteves Pacheco de Almeida

Over the last few years the increasing demand of housing for low income population in Colombia and several neighboring countries, associated to the significant increase of cost of land, has prompted construction companies to build medium to high rise reinforced concrete (RC) wall buildings. Most of these new residential buildings are constructed with walls that have thicknesses as low as 80 mm and are only lightly reinforced. The recent earthquakes in Chile (2010) and New Zealand (2011) have caused significant damage to some of the RC walls, some of which tended to buckle out-of-plane. In Colombia the wall thicknesses are significantly thinner than in Chile or New Zealand and is therefore is to be feared that these buildings may present the same out-of-plane failure mode during a future earthquake. Furthermore, many of the walls have only a single vertical reinforcement layer, which could increase the out-of-plane instability, as it will be shown in this paper. Although recent experimental tests have shown that wall out-of-plane deformations can extend throughout a relatively large part of the wall length, the boundary regions are the critical zones that control the development of associated failure modes. For thin walls behaving predominantly in flexure those boundary regions are subjected to mainly axial strains, and hence testing equivalent RC columns under cyclic axial tension and compression provides direct insights into the influence of the parameters triggering wall instability and possible out-of-plane failure. Within a collaborative project between the École Polytechnique Fédérale de Lausanne (EPFL) in Switzerland and the Universidad del Valle, the EIA University, and the University of Medellin in Colombia, equivalent RC columns with a single vertical reinforcement layer are tested at EPFL in order to investigate the effect of loading history, reinforcement ratio and eccentricity of the longitudinal rebars with regard to the element axis ration the out-of-plane response. The paper presents the details of this recent experimental campaign, describing the geometry and the reinforcement layout of the specimens, the test setup, the extensive instrumentation used, and the results obtained from the first tests. The experimental findings allowed to draw initial conclusions on the development of the out-of-plane instability, on the particularities of single layer reinforcement members and on the development of out-of-plane failures.

2017