Numerical analysis of seismic wave amplification in Nice (France) and comparisons with experiments

The analysis of site effects is very important since the amplification of seismic motion in some specific areas can be very strong. In this paper, the site considered is located in the centre of Nice on the French Riviera. Site effects are investigated considering a numerical approach (Boundary Element Method) and are compared to experimental results (weak motion and microtremors). The investigation of seismic site effects through numerical approaches is interesting because it shows the dependency of the amplification level on such parameters as wave velocity in surface soil layers, velocity contrast with deep layers, seismic wave type, incidence and damping. In this specific area of Nice, a one-dimensional (1D) analytical analysis of amplification does not give a satisfactory estimation of the maximum reached levels. A boundary element model is then proposed considering different wave types (SH, P, SV) as the seismic loading. The alluvial basin is successively assumed as an isotropic linear elastic medium and an isotropic linear viscoelastic solid (standard solid). The thickness of the surface layer, its mechanical properties, its general shape as well as the seismic wave type involved have a great influence on the maximum amplification and the frequency for which it occurs. For real earthquakes, the numerical results are in very good agreement with experimental measurements for each motion component. Two-dimensional basin effects are found to be very strong and are well reproduced numerically

Wave propagation through soils in centrifuge testing.

International audienceWave propagation phenomena in soils can be experimentally simulated using centrifuge scale models. An original excitation device (drop-ball arrangement) is proposed to generate short wave trains. Wave reflections on model boundaries are taken into account and removed by homomorphic filtering. Propagation is investigated through dispersion laws. For drop-ball experiments, spherical wave field analysis assuming linear viscoelasticity leads to a complete analytical description of wave propagation. Damping phenomena are examined and evaluated using this description

A Fast Multipole Method formulation for 3D elastodynamics in the frequency domain

The solution of the elastodynamic equations using boundary element methods (BEMs) gives rise to fully-populated matrix equations. Earlier investigations on the Helmholtz and Maxwell equations have established that the Fast Multipole (FM) method reduces the complexity of a BEM solution to N \mbox{log}_{2}N per GMRES teration. The present Note address the extension of the FM-BEM strategy to 3D elastodynamics in the frequency domain. Its efficiency and accuracy are demonstrated on numerical examples involving up to $N=O(10^{6})$ nodal unknowns

3D Hopkinson bar: new experiments for dynamic testing on soils.

International audienceThe direct analysis of the dynamic response of materials is possible using Split Hopkinson pressure bar method. For soils, it has to be adapted since the specimen has generally poor mechanical properties. An original experimental arrangement called "Three-Dimensional Split Hopkinson Pressure Bar" (3D SHPB) is proposed. It allows the measurement of the complete three-dimensional dynamic response of soils. Different types of confinement systems are used. The results on different loading paths are compared with other works on sand and clay. The analysis at grain-size level gives further elements on the comminution process

Sollicitations sismiques dues aux exploitations minières : amplification des ondes en surface (et vibrations des structures)

National audienceL'objectif de ce travail est d'analyser l'impact des secousses induites par les exploitations minières sur les structures situées en surface. Du fait des conditions géologiques locales, le mouvement créé par les secousses peut parfois être amplifié de façon importante en surface (effet de site). A partir d'une modélisation numérique du problème, l'amplification du mouvement est analysée pour différentes formes de remplissages sédimentaires et des contrastes de propriétés entre couches variables. Les valeurs de fréquences fondamentales (i.e amplification maximale) sont comparées à des résultats antérieurs

Modeling seismic wave propagation and amplification in 1D/2D/3D linear and nonlinear unbounded media

To analyze seismic wave propagation in geological structures, it is possible to consider various numerical approaches: the finite difference method, the spectral element method, the boundary element method, the finite element method, the finite volume method, etc. All these methods have various advantages and drawbacks. The amplification of seismic waves in surface soil layers is mainly due to the velocity contrast between these layers and, possibly, to topographic effects around crests and hills. The influence of the geometry of alluvial basins on the amplification process is also know to be large. Nevertheless, strong heterogeneities and complex geometries are not easy to take into account with all numerical methods. 2D/3D models are needed in many situations and the efficiency/accuracy of the numerical methods in such cases is in question. Furthermore, the radiation conditions at infinity are not easy to handle with finite differences or finite/spectral elements whereas it is explicitely accounted in the Boundary Element Method. Various absorbing layer methods (e.g. F-PML, M-PML) were recently proposed to attenuate the spurious wave reflections especially in some difficult cases such as shallow numerical models or grazing incidences. Finally, strong earthquakes involve nonlinear effects in surficial soil layers. To model strong ground motion, it is thus necessary to consider the nonlinear dynamic behaviour of soils and simultaneously investigate seismic wave propagation in complex 2D/3D geological structures! Recent advances in numerical formulations and constitutive models in such complex situations are presented and discussed in this paper. A crucial issue is the availability of the field/laboratory data to feed and validate such models.Comment: of International Journal Geomechanics (2010) 1-1

Effet de la pression interstitielle sur la réponse sismique des sols : modélisation numérique 1D-3 Composantes

International audienceDuring strong quakes, the propagation of seismic waves in soil layers involves nonlinearities changing with the excitation level. A nonlinear hysteretic law is necessary to describe the variations of the stiffness and the energy dissipation during the seismic shaking. Furthermore, the influence of the pore pressure (cyclic mobility and liquefaction) cannot be neglected for saturated soils under strong quakes. Starting from a FEM formulation describing 1D propagation and three-dimensional loading ("1D-3 components approach"), the influence of the water is accounted for through a relation between the pore pressure and the work of the shear stress initially proposed by Iai. This model describes the variations of the pore pressure from the three-dimensional stress state of the soil. It has been validated through comparisons to laboratory tests (cyclic triaxial tests on saturated sands) and an analysis under three-dimensional excitations (seismic loading polarized along the 3 directions of space). The results involving 3 simultaneous excitation components and a single component in 3 separated analyses show the influence of the loading path on the seismic response and the pore pressure build-up

A new fast multi-domain BEM to model seismic wave propagation and amplification in 3D geological structures

International audienceThe analysis of seismic wave propagation and amplification in complex geological structures raises the need for efficient and accurate numerical methods. The solution of the elastodynamic equations using traditional boundary element methods (BEMs) is greatly hindered by the fully-populated nature of the matrix equations arising from the discretization. In a previous study limited to homogeneous media, the present authors have established that the Fast Multipole (FM) method reduces the complexity of a 3-D elastodynamic BEM to $N \log N$ per GMRES iteration and demonstrated its effectiveness on 3-D canyon configurations. In this article, the frequency-domain FM-BEM methodology is extented to 3-D elastic wave propagation in piecewise-homogeneous domains in the form of a FM-accelerated multi-region BE-BE coupling approach. This new method considerably enhances the capability of the BEM for studying the propagation of seismic waves in 3-D alluvial basins of arbitrary geometry embedded in semi-infinite media. Several fully 3-D examples (oblique SV-waves) representative of such configurations validate and demonstrate the capabilities of the multi-domain fast multipole approach. They include comparisons with available (low-frequency) results for various types of incident wavefields, and time-domain results obtained by means of Fourier synthesis