A Simple Multi-Directional Absorbing Layer Method to Simulate Elastic Wave Propagation in Unbounded Domains

The numerical analysis of elastic wave propagation in unbounded media may be difficult due to spurious waves reflected at the model artificial boundaries. This point is critical for the analysis of wave propagation in heterogeneous or layered solids. Various techniques such as Absorbing Boundary Conditions, infinite elements or Absorbing Boundary Layers (e.g. Perfectly Matched Layers) lead to an important reduction of such spurious reflections. In this paper, a simple absorbing layer method is proposed: it is based on a Rayleigh/Caughey damping formulation which is often already available in existing Finite Element softwares. The principle of the Caughey Absorbing Layer Method is first presented (including a rheological interpretation). The efficiency of the method is then shown through 1D Finite Element simulations considering homogeneous and heterogeneous damping in the absorbing layer. 2D models are considered afterwards to assess the efficiency of the absorbing layer method for various wave types and incidences. A comparison with the PML method is first performed for pure P-waves and the method is shown to be reliable in a more complex 2D case involving various wave types and incidences. It may thus be used for various types of problems involving elastic waves (e.g. machine vibrations, seismic waves, etc)

Modelling strong seismic ground motion: three-dimensional loading path versus wavefield polarization

Seismic waves due to strong earthquakes propagating in surficial soil layers may both reduce soil stiffness and increase the energy dissipation into the soil. To investigate seismic wave amplification in such cases, past studies have been devoted to one-directional shear wave propagation in a soil column (1D-propagation) considering one motion component only (1C-polarization). Three independent purely 1C computations may be performed ('1D-1C' approach) and directly superimposed in the case of weak motions (linear behaviour). This research aims at studying local site effects by considering seismic wave propagation in a 1-D soil profile accounting for the influence of the 3-D loading path and non-linear hysteretic behaviour of the soil. In the proposed '1D-3C' approach, the three components (3C-polarization) of the incident wave are simultaneously propagated into a horizontal multilayered soil. A 3-D non-linear constitutive relation for the soil is implemented in the framework of the Finite Element Method in the time domain. The complex rheology of soils is modelled by mean of a multisurface cyclic plasticity model of the Masing-Prandtl-Ishlinskii-Iwan type. The great advantage of this choice is that the only data needed to describe the model is the modulus reduction curve. A parametric study is carried out to characterize the changes in the seismic motion of the surficial layers due to both incident wavefield properties and soil non-linearities. The numerical simulations show a seismic response depending on several parameters such as polarization of seismic waves, material elastic and dynamic properties, as well as on the impedance contrast between layers and frequency content and oscillatory character of the input motion. The 3-D loading path due to the 3C-polarization leads to multi-axial stress interaction that reduces soil strength and increases non-linear effects. The non-linear behaviour of the soil may have beneficial or detrimental effects on the seismic response at the free surface, depending on the energy dissipation rate. Free surface time histories, stress-strain hysteresis loops and in-depth profiles of octahedral stress and strain are estimated for each soil column. The combination of three separate 1D-1C non-linear analyses is compared to the proposed 1D-3C approach, evidencing the influence of the 3C-polarization and the 3-D loading path on strong seismic motions

A Simple and Efficient Regularization Method for 3D BEM: Application to Frequency-Domain Elastodynamics

An efficient and easy-to-implement method is proposed to regularize integral equations in the 3D boundary element method (BEM). The method takes advantage of an assumed three-noded triangle discretization of the boundary surfaces. The method is based on the derivation of analytical expressions of singular integrals. To demonstrate the accuracy of the method, three elastodynamic problems are numerically worked out in the frequency domain: a cavity under harmonic pressure, diffraction of a plane wave by a spherical cavity, and amplification of seismic waves in a semispherical alluvial basin (the second one is also investigated in the time domain). The numerical results are compared to semi-analytical solutions; a close agreement is found for all problems, showing the accuracy of the proposed method

Identification of Different Seismic Waves Generated by Foundation Vibration in the Centrifuge: Travel Time, Spectral and Numerical Investigations

For the analysis of footings under dynamic loading scaled modeling in the centrifuge assumes that the soil behaves like at prototype scale. This paper demonstrates that for a container filled with dry sand, wave velocities can be described by a model based on the relation between the shear modulus and the depth dependent stress level proposed by Iwasaki and Tatsuoka. A preliminary estimation of the shear wave velocities and of the Poisson’s ratio confirms by dynamical measurements the currently use value of 0.25. A FEM modeling also helps to strengthen the validity of the model proposed, providing another insight in the propagation of waves in a soil with a velocity gradient

Interaction Site-Ville : Approches expérimentales et numériques

À l’échelle d’une ville, les structures de surface telles que les bâtiments peuvent modifier le mouvement sismique en 'champ libre' et agir comme des sources sismiques secondaires. Des observations ont en particulier été réalisées sur des données réelles. Elles montrent que cet effet peut être significatif. La conséquence directe de cette 'interaction site-ville' est la pollution du mouvement sismique en milieu urbain par un champ d’onde secondaire. Des modélisations en centrifugeuse et numériques tendent à confirmer que ce phénomène n’est pas anecdotique. En particulier, ces résultats montrent qu’entre deux bâtiments proches des interactions existent, modifiant le mouvement du sol mais aussi la réponse des structures impliquées. À l’échelle d’une ville, ce phénomène sera d’autant plus marqué lorsqu’un fort couplage existe entre la réponse du sol et la réponse du milieu urbain

Strong Ground Motion in the 2011 Tohoku Earthquake: a 1Directional - 3Component Modeling

Local wave amplification due to strong seismic motions in surficial multilayered soil is influenced by several parameters such as the wavefield polarization and the dynamic properties and impedance contrast between soil layers. The present research aims at investigating seismic motion amplification in the 2011 Tohoku earthquake through a one-directional three-component (1D-3C) wave propagation model. A 3D nonlinear constitutive relation for dry soils under cyclic loading is implemented in a quadratic line finite element model. The soil rheology is modeled by mean of a multi-surface cyclic plasticity model of the Masing-Prandtl-Ishlinskii-Iwan (MPII) type. Its major advantage is that the rheology is characterized by few commonly measured parameters. Ground motions are computed at the surface of soil profiles in the Tohoku area (Japan) by propagating 3C signals recorded at rock outcrops, during the 2011 Tohoku earthquake. Computed surface ground motions are compared to the Tohoku earthquake records at alluvial sites and the reliability of the 1D-3C model is corroborated. The 1D-3C approach is compared with the combination of three separate one-directional analyses of one motion component propagated independently (1D-1C approach). The 3D loading path due to the 3C-polarization leads to multiaxial stress interaction that reduces soil strength and increases nonlinear effects. Time histories and spectral amplitudes, for the Tohoku earthquake, are numerically reproduced. The 1D-3C approach allows the evaluation of various parameters of the 3C motion and 3D stress and strain evolution all over the soil profile.Comment: Bulletin of the Seismological Society of America 103, 2B (2013) 1394-1410. arXiv admin note: substantial text overlap with arXiv:1308.194

Méthode multipôle rapide multi-niveaux en visco-élastodynamique 3D

National audienceSee http://hal.archives-ouvertes.fr/docs/00/59/28/83/ANNEX/r_4VPCS0OY.pd