Semi-analytical and numerical methods for computing transient waves in 2D acoustic / poroelastic stratified media

Wave propagation in a stratified fluid / porous medium is studied here using analytical and numerical methods. The semi-analytical method is based on an exact stiffness matrix method coupled with a matrix conditioning procedure, preventing the occurrence of poorly conditioned numerical systems. Special attention is paid to calculating the Fourier integrals. The numerical method is based on a high order finite-difference time-domain scheme. Mesh refinement is applied near the interfaces to discretize the slow compressional diffusive wave predicted by Biot's theory. Lastly, an immersed interface method is used to discretize the boundary conditions. The numerical benchmarks are based on realistic soil parameters and on various degrees of hydraulic contact at the fluid / porous boundary. The time evolution of the acoustic pressure and the porous velocity is plotted in the case of one and four interfaces. The excellent level of agreement found to exist between the two approaches confirms the validity of both methods, which cross-checks them and provides useful tools for future researches.Comment: Wave Motion (2012) XX

Ground vibration due to a high-speed moving harmonic rectangular load on a poroviscoelastic half-space

AbstractThe transmission of vibrations in the ground, due to a high-speed moving vertical harmonic rectangular load, is investigated theoretically. The problem is three-dimensional and the interior of the ground is modelled as a totally or partially saturated porous viscoelastic half-space, using the complete Biot theory. The solutions in the transformed domain are obtained using a double Fourier transform on the surface spatial variables. A modified hysteretic damping model defined in the wavenumber domain is used, first presented by Lefeuve-Mesgouez et al. [Lefeuve-Mesgouez, G., Le Houédec, D., Peplow, A.T., 2000. Vibration in the vicinity of a high-speed moving harmonic strip load. Journal of Sound and Vibration 231(5) 1289–1309]. Numerical results for the displacements of the solid and fluid phases, over the surface of the ground and in depth, are presented for loads moving with speeds up to and beyond the Rayleigh wave speed of the medium

Simulation numérique d'un dispositif de retenue d'enfant

International audienceThe present paper deals with the use of numerical methods in the design project of a child restraint system (CRS). First, the experimental dynamic test of child restraint systems is presented as imposed by the European reglamentation R44/03. Then, a first numerical simulation of the CRS is performed using both an elastostatic mode! and an elastodynamic approach. In order to improve the mode!, we focus on the modelling of the material behaviour (polypropylene). The constitutive equation of glassy polymer developed by Boyce, Parks and Argon is chosen. This mode! superimposes an isotropie resistance that simulates defaults in the molecular chains during shear and an entropie resistance due to the chain alignment induced by deformation. A comparison between explicit and implicit integration methods is performed. This study, which aim is the limitation of CPU time during finite elements analysis, will pave the way for the implementation of the constitutive equation in a commercial code.Le présent article s'intéresse à l'utilisation de la simulation numérique dans la boucle de conception d'un dispositif de retenue d'enfant (DRE). L'essai dynamique expérimental d'homologation de DRE imposé par le règlement européen R44/03 est tout d'abord présenté. Une première simulation numérique de DRE est ensuite réalisée dans un cas élastostatique, puis avec un modèle élastodynamique. Afin d'améliorer le modèle, l'accent est mis sur une modélisation fiable du comportement du matériau utilisé (polypropylène). Le choix se porte sur le modèle de comportement de polymère vitreux développé par Boyce, Parks et Argon. Ce modèle superpose une résistance isotrope simulant l'inclusion de défauts dans les chaînes moléculaires lors du cisaillement et une résistance entropique due à l'alignement de ces chaînes sous l'effet de la déformation, et simulée par un modèle moléculaire. Une comparaison entre intégration explicite et intégration implicite de cette loi de comportement est réalisée, dans le but de limiter les temps de calcul en vue d'une implantation de la loi dans un code de calcul commercial

Dynamic response of a circular tunnel with imperfect surface interaction embedded in an elastic medium

The research work proposed here is part of a global project that aims at better characterizing a specific underground environment in the LSBB (Low Noise Inter-disciplinary Underground Science and Technology), situated in Rustrel, Vaucluse, France. The experimental environment under study is characterized by a system of galleries, several ones with a concrete layer. The first step of the methodology deals with setting up a forward problem to apprehend the geometry of the LSBB. \\In this paper, the 2D transient response of imperfect bonded circular lined pipeline lying in an elastic, homogeneous and infinite medium is studied. At first, the problem is solved in the frequency domain by using the wave function expansion method and imperfect interaction surface between elastic medium and tunnel is modeled as a linear spring. Wave propagation fields in tunnel and soil are expressed in terms of infinite series and stresses and displacements are given based on those series. By implying boundary conditions a linear equations system is obtained and the results of these equations lead to displacement and stress responses of the rock and tunnel.To solve the transient problem, the Laplace transform with respect to time is used which leads to system of linear equations in the Laplace domain. Durbin's numerical Laplace transform inversion method is employed to obtain dynamic responses. To exhibit a behavior of the responses, influences of the different parameters such as wall thickness of the tunnel is investigated. Hoop stresses and the displacements of the tunnel and rock are obtained due to acting load on the inner surface of the tunnel for selected parameters. In order to check the validity of the present work, we pay attention on the convergence of the results and also excellent agreement with previous result is achieved

Contribution to the modeling and the mechanical characterization of the subsoil in the LSBB environment

The present research work aims at better characterizing the specific underground environment of the LSBB (Low Noise Inter-Disciplinary Underground Science and Technology, Rustrel, France) using mechanical wave propagation information. The LSBB experimental environment is characterized by a system of cylindrical galleries, some of them presenting a concrete layer. In the global project, three steps are considered : firstly the construction of an efficient forward mechanical wave propagation model to calculate the displacement vector and stress tensor components; secondly a sensitivity analysis to extract the pertinent parameters in the configurations and models under study (viscoelastic or poroviscoelastic media with potential anisotropy); and lastly an inversion strategy to recover some of the pertinent parameters. In this proposal, the first step, under progress, is described. The work carried out is in the continuity of the work presented by Yi et al. (2016) [1] who studied the harmonic response of a cylindrical elastic tunnel, impacted by a plane compressional wave, embedded in an infinite elastic ground. The interface between the rock mass and the linen is an imperfect contact modeled with two spring parameters, Achenbach and Zhu (1989) [2]. We choose a semi-analytical approach to calculate the two-dimensional displacement and stress fields in order to get a fast tool, from the numerical point of view. The main steps of the theoretical approach are : use of the Helmholtz decomposition, solving the wave equation based on the separation method and the expansion in Bessel function series in the harmonic domain. The harmonic results are validated by comparison with Yi et al. (2016) [1] and new ones are presented. Moreover, the transient regime case obtained with the use of a Fourier transform on the time variable, is under progress

Biot-JKD model: simulation of 1D transient poroelastic waves with fractional derivatives

A time-domain numerical modeling of Biot poroelastic waves is presented. The viscous dissipation occurring in the pores is described using the dynamic permeability model developed by Johnson-Koplik-Dashen (JKD). Some of the coefficients in the Biot-JKD model are proportional to the square root of the frequency: in the time-domain, these coefficients introduce order 1/2 shifted fractional derivatives involving a convolution product. Based on a diffusive representation, the convolution kernel is replaced by a finite number of memory variables that satisfy local-in-time ordinary differential equations. Thanks to the dispersion relation, the coefficients in the diffusive representation are obtained by performing an optimization procedure in the frequency range of interest. A splitting strategy is then applied numerically: the propagative part of Biot-JKD equations is discretized using a fourth-order ADER scheme on a Cartesian grid, whereas the diffusive part is solved exactly. Comparisons with analytical solutions show the efficiency and the accuracy of this approach.Comment: arXiv admin note: substantial text overlap with arXiv:1210.036

Railway-induced ground vibrations – a review of vehicle effects

This paper is a review of the effect of vehicle characteristics on ground- and track borne-vibrations from railways. It combines traditional theory with modern thinking and uses a range of numerical analysis and experimental results to provide a broad analysis of the subject area. First, the effect of different train types on vibration propagation is investigated. Then, despite not being the focus of this work, numerical approaches to vibration propagation modelling within the track and soil are briefly touched upon. Next an in-depth discussion is presented related to the evolution of numerical models, with analysis of the suitability of various modelling approaches for analysing vehicle effects. The differences between quasi-static and dynamic characteristics are also discussed with insights into defects such as wheel/rail irregularities. Additionally, as an appendix, a modest database of train types are presented along with detailed information related to their physical attributes. It is hoped that this information may provide assistance to future researchers attempting to simulate railway vehicle vibrations. It is concluded that train type and the contact conditions at the wheel/rail interface can be influential in the generation of vibration. Therefore, where possible, when using numerical approach, the vehicle should be modelled in detail. Additionally, it was found that there are a wide variety of modelling approaches capable of simulating train types effects. If non-linear behaviour needs to be included in the model, then time domain simulations are preferable, however if the system can be assumed linear then frequency domain simulations are suitable due to their reduced computational demand