Influence of the spatial correlation structure of an elastic random medium on its scattering properties

International audienceIn the weakly heterogeneous regime of elastic wave propagation through a random medium, transport and diffusion models for the energy densities can be set up. In the isotropic case, the scattering cross sections are explicitly known as a function of the wave number and the correlations of the Lamé parameters and density. In this paper, we discuss the precise influence of the correlation structure on the scattering cross sections, mean free paths and diffusion parameter, and separate that influence from that of the correlation length and variance. We also analyze the convergence rates towards the low-and high-frequency ranges. For all analyses, we consider five different correlation structures, that allow us to explore a wide range of behaviors. We identify that the controlling factors for the low-frequency behavior are the value of the Power Spectral Density Function (PSDF) and its first non-vanishing derivative at the origin. In the high frequency range, the controlling factor is the third moment of the PSDF (which may be unbounded)

Nonlinear Dynamic Soil-Structure Interaction in Earthquake Engineering

Ce travail détaille une approche de calcul pour la résolution de problèmes dynamiques qui combinent des discrétisations en temps et dans le domaine de Laplace reposant sur une technique de sous-structuration. En particulier, la méthode développée cherche à remplir le besoin industriel de réaliser des calculs dynamiques tridimensionnels pour le risque sismique en prenant en compte des effets non-linéaires d'interaction sol-structure (ISS). Deux sous-domaines sont considérés dans ce problème. D'une part, le domaine de sol linéaire et non-borné qui est modélisé par une impédance de bord discrétisée dans le domaine de Laplace au moyen d'une méthode d'éléments de frontière ; et, de l'autre part, la superstructure qui fait référence pas seulement à la structure et sa fondation mais aussi, éventuellement, à une partie du sol présentant un comportement non-linéaire. Ce dernier sous-domaine est formulé dans le domaine temporel et discrétisé avec la méthode des éléments finis (FE). Dans ce cadre, les forces liées à l'ISS s'écrivent sous la forme d'une intégrale de convolution en temps dont le noyau est la transformée de Laplace inverse de la matrice d'impédance de sol. Pour pouvoir évaluer cette convolution dans le domaine temporel à partir d'une impédance de sol définie dans le domaine de Laplace, une approche basée sur des Quadratures de Convolution (QC) est présentée : la méthode hybride Laplace-Temps (L-T). La stabilité numérique de son couplage avec un schéma d'intégration de type Newmark est ensuite étudiée sur plusieurs modèles d'ISS en dynamique linéaire et non-linéaire. Finalement, la méthode L-T est testée sur un modèle numérique plus complexe, proche d'une application sismique de caractère industriel, et des résultats satisfaisants sont obtenus par rapport aux solutions de référence.The present work addresses a computational methodology to solve dynamic problems coupling time and Laplace domain discretizations within a domain decomposition approach. In particular, the proposed methodology aims at meeting the industrial need of performing more accurate seismic risk assessments by accounting for three-dimensional dynamic soil-structure interaction (DSSI) in nonlinear analysis. Two subdomains are considered in this problem. On the one hand, the linear and unbounded domain of soil which is modelled by an impedance operator computed in the Laplace domain using a Boundary Element (BE) method; and, on the other hand, the superstructure which refers not only to the structure and its foundations but also to a region of soil that possibly exhibits nonlinear behaviour. The latter subdomain is formulated in the time domain and discretized using a Finite Element (FE) method. In this framework, the DSSI forces are expressed as a time convolution integral whose kernel is the inverse Laplace transform of the soil impedance matrix. In order to evaluate this convolution in the time domain by means of the soil impedance matrix (available in the Laplace domain), a Convolution Quadrature-based approach called the Hybrid Laplace-Time domain Approach (HLTA), is thus introduced. Its numerical stability when coupled to Newmark time integration schemes is subsequently investigated through several numerical examples of DSSI applications in linear and nonlinear analyses. The HLTA is finally tested on a more complex numerical model, closer to that of an industrial seismic application, and good results are obtained when compared to the reference solutions.CHATENAY MALABRY-Ecole centrale (920192301) / SudocSudocFranceF

Numerical analysis of local geology effects on ground motion prediction

It is well known that to better characterize the seismic phenomenon several parameters such as site effects have to be considered. Indeed, during the wave propagation process, the soil near the surface can have an effect of amplification or de-amplification on the ground motion. This may be related to soil type (soft), geology or soil heterogeneity among others. This work aims to study numerically the effect of local geology on ground motion prediction at a regional scale. The studied site is located at Kefalonia Island (Greece). This site is well characterized and instrumented by several sensors placed in such a way that allow to measure the effect of spatial variability on the recorded signals.The present work places itself within the framework of the French research project SINAPS (Séismes et Installations Nucléaires, Améliorer et Préserver la Sûreté) managed by the National Research Agency under the program Future Investments (SINAPS@ reference No.ANR-11-RSNR-0022). This project has been initiated by the members of the institute SEISM (https://www.institut-seism.fr/en/) after the nuclear disaster of Fukushima (Japan, 2011). It aims to enhance the scientific background in the area of the nuclear safety and radiation protection. The project contains different work packages. Our present work is part of the work package "Non-Linear Sites Effects and Soil-Structure Interaction"

Wavelet approach to vibratory analysis of surface due to a load moving in the layer

This article is available open access through the publisher’s website at the link below. Copyright @ 2007 Elsevier B.V.The paper analyses theoretically the surface vibration induced by a point load moving uniformly along a infinitely long beam embedded in a two-dimensional viscoelastic layer. The beam is placed parallel to the traction-free surface and the layer under the beam is assumed to be a half space. The response due to a harmonically varying load is investigated for different load frequencies. The influence of the layer damping and moving load speed on the level of vibrations at the surface is analysed and analytical closed form solutions in the integral form for the displacement amplitude and the amplitude spectra are derived. Approximate displacement values depending on Young’s modulus and mass density of layers are obtained. The mathematical model is described by the Euler–Bernoulli beam equation, Navier’s elastodynamic equation of motion for the elastic medium and appropriate boundary and continuity conditions. A special approximation method based on the wavelet theory is used for calculation of the displacements at the surface

Numerical modelling of ground borne vibrations from underground railway traffic

International audienceVibrations due to the passage of trains in tunnels propagate through the soil and produce vibrations and re-radiated noise in adjacent structures. Within the frame of the EC-Growth project CONVURT ("The control of vibration from underground railway traffic"), an efficient and modular numerical prediction tool is being developed to predict vibration and re-radiated noise in adjacent buildings from excitation due to metro trains in tunnels for both new-build and existing situations. The model will be validated by means of in situ experiments at the site of Cité Universitaire in Paris and at Regent's Park in London. The development of a coupled periodic finite element-boundary element method and the results obtained from the in-situ experiments conducted in Paris are described in the present paper

Seismic motion in urban sites consisting of blocks in welded contact with a soft layer overlying a hard half space: I. Finite set of blocks

We address the problem of the response to a seismic wave of an urban site consisting of $N$ non-identical, non-equispaced blocks overlying a soft layer underlain by a hard substratum. The results of a theoretical analysis, appealing to a space-frequency mode-matching (MM) technique, are compared to those obtained by a space-time finite element (FE) technique. The two methods are shown to give rise to the same prediction of the seismic response for N=1 and N=2 blocks. The mechanism of the interaction between blocks and the ground, as well as that of the mutual interaction between blocks, are studied. It is shown that the presence of a small number of blocks modifies the seismic disturbance in a manner which evokes qualitatively, but not quantitatively, what was observed during the 1985 Michoacan earthquake in Mexico City. Disturbances at a much greater level, induced by a large number of blocks (in fact, a periodic set) are studied in the companion paper.Comment: submitted to Geophys.J.Int

The effect of tunnel construction on future underground railway vibrations

This paper investigates the effect of initial tunnel construction on the future ground vibration levels generated during underground railway line operation. This is important because tunnel construction results in soil disturbance, thus inducing high soil strain levels near the tunnel lining. The resulting soil stiffness degradation impacts the future generation of ground-borne traffic vibration and it's propagation to the foundations of nearby buildings, however has never been investigated. Therefore, to address this, this work develops a novel hybrid modelling approach, consisting of a construction simulation model and an elastodynamics model. First the convergence-confinement method is used to determine the stress state induced during tunnel construction using a tunnel boring machine (TBM). Next a 2.5D FEM-PML model consisting of vehicle-track-tunnel-soil is used to predict the vibration fields induced by underground trains. To link the approaches, the soil stiffness degradation contours computed from the tunnelling simulation act as inputs for the 2.5D underground railway model. This facilitates the assessment of the effect of tunnel construction on vibration levels. It is found that railway ground-borne vibration levels are underestimated if construction effects are ignored, with discrepancies of up to 10 dB found at higher frequencies. Therefore, when estimating future vibration levels during the underground railway design stage (e.g. for subway, metro, high-speed lines … etc), tunnel construction should be considered as an operational source of uncertainty

Comment penser l'erreur en régie d'art contemporain ?

Le présent article souhaite entamer une réflexion sur un cadre théorique pour traiter durablement de l'erreur en régie d'art contemporain. En tenant compte d’une part de la reconnaissance récente de l’activité en France et des spécificités de l’art contemporain d’autre part, nous nous interrogerons sur la manière dont le traitement de l’erreur participe à la construction d’un modèle professionnel.<br>The present article intends to engage a reflection on a theoretical frame to deal durably with the error in the registrar's and art preparator's practices in contemporary art. By taking into account on one hand the recent recognition of the activity in France and on the other hand the specificities of the contemporary art, we will examine the way in which the treatment of the error can partake in the construction of a professional model