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The influence of lateral heterogeneities on alluvial deposits is a topic of particular interest in the field of urban planning and engineering design of structures and infrastructures. This work focuses on the effects of such heterogeneities on the shear strains produced within the recent alluvial deposits of the Tiber River in the historical center of Rome in case of the worst expected earthquake scenario. To this aim, a 3D engineering-geology model of the subsoil is used to derive four geological sections across the Tiber River valley as well as 48 soil columns to perform numerical simulations. Various models are considered: a viscoelastic equivalent linear rheology in a ID finite-difference model for one-component horizontal input, a nonlinear elastoplastic model in a ID finite-element scheme for three-component input, and a nonlinear viscoelasto- plastic rheology in a 2D finite-difference model under one-component horizontal input. After comparing these different simulations, results have shown that lateral heterogeneities play a key role with respect to the expected shear strains within multilayered soils. To this aim, some specific indexes are introduced to estimate the maximum shear strain (MSS) concentration within the soil layers as well as to highlight their effect due to the stratigraphic position of the layers, within the soil column, independently from its depth. A final differential index leads to the evaluation of the lateral heterogeneity effect on the estimated MSS, demonstrating their prevalent role with respect to the bedrock shape (i.e., the angle of inclination of the buried valley slopes). From these results, an MSS zoning map is obtained for the historical center of Rome, showing that the local seismic response should be modeled by assuming ID or 2D conditions depending on the location considered. [ABSTRACT FROM AUTHOR]

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, and so on. All these methods have various advantages and drawbacks to analyze the propagation of seismic waves. In surficial soil layers, seismic waves may be strongly amplified because of 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. Two-dimensional/three dimensional (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 explicitly accounted for in the boundary element method. Various absorbing layer methods (e.g., F-PML, M-PML, CALM) 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 may involve nonlinear effects in surficial soil layers. To model strong ground motion, it is thus necessary to consider the nonlinear dynamic behavior 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. [ABSTRACT FROM AUTHOR]

The 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 method (FMM) reduces the complexity of a 3-D elastodynamic BEM to per GMRES iteration and demonstrated its effectiveness on 3-D canyon configurations. In this paper, 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 FM 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. [ABSTRACT FROM AUTHOR]

Seismic surface waves are well-adapted to study the elastic parameters, and hence the mechanical properties, of soils. The aim herein is to evaluate whether Rayleigh waves in heterogeneous soils may be used to estimate average elastic parameters and to determine how these parameters are influenced by heterogeneities. The heterogeneous medium, underlain by a homogeneous half-space, is consid-ered as a homogeneous matrix with one or several types of randomly distributed inclusions (with a normal distribution) in the matrix. Seismic waves generated by surface loads and propagating in this medium were calculated using the finite element method (FEM) and then compared with single- and multiple-scattering homogenization methods. For the FEM calculation, special care was taken to reduce numerical dispersion through the use of elements smaller than 1/20 of the dominant wavelength. The group and phase velocity dispersion curves were measured and inverted in order to obtain the effective shear wave velocity of the heterogeneous medium. The results show a clear dependence of the wave velocity with respect to the nature, concentration, and size of the inclusions. The dependence with respect to the nature and concentration of inclusions coincides with that obtained from a multiple-scattering homogenization method up to an inclusion concentration of approximately 50%. [ABSTRACT FROM AUTHOR]