An indirect boundary element method applied to simulate the seismic response of alluvial valleys for incident P, S and Rayleigh waves

Abstract

SUMMARYA boundary integral formulation is presented and applied to model the ground motion on alluvial valleys under incident P, S and Rayleigh waves. It is based on integral representations for the diffracted and the refracted elastic waves using single-layer boundary sources. This approach is called indirect BEM in the literature as the sources' strengths should be obtained as an intermediate step. Boundary conditions lead to a system of integral equations for boundary sources. A discretization scheme based on the numerical and analytical integration of exact Green's functions for displacements and tractions is used. Various examples are given for two-dimensional problems of diffraction of elastic waves by soft elastic inclusion models of alluvial deposits in an elastic half-space. Results are displayed in both frequency and time domains. These results show the significant influence of locally generated surface waves in seismic response and suggest approximations of practical interest. For shallow alluvial valleys the response and its resonant frequencies are controlled by a coupling mechanism that involves both the simple one-dimensional shear beam model and the propagation of surface waves.

Geotechnical Site Characterisation in the Umbria-Marche Area and Evaluation of Earthquake Site-Response

“…This result confirms what many authors have already proved; that is 2-D effects play a fundamental role in the determination of amplitude and phase of TF at deep alluvial sites (AKI and LERNER, 1970;BARD and BUCHON, 1985;SANCHEZ-SESMA et al, 1993;KAWASE, 2002). These authors have demonstrated theoretically that surface waves are generated at the lateral boundary between soft sediments and rock, and these cause an increase in wave amplitudes, both in the horizontal and vertical components.…”

“…A bi-dimensional method (SANCHEZ-SESMA et al, 1993) was also applied to simulate the seismic response of two sites located on large alluvial valleys. The results of the 2-D model indicates that even a very simple model is able to simulate successfully the interaction between seismic waves and sediments of complex sedimentary structures.…”

Seismic Hazard and Ground Motion Characterization at the Itoiz Dam (Northern Spain)

“…This problem can be estimated with the knowledge of the geometry of the irregular topography, their elastic properties, and the application of numerical methods for wave propagation modeling in topographical structures such as boundary elements (see, e.g., SÁNCHEZ-SESMA et al 1993;LUZÓN et al 1997) or finite difference methods (see, e.g., PEREZ-RUIZ et al 2005) among others. Moreover, the influence of strong motion rotations (TRIFUNAC 2009;GODINHO et al 2009) produced by possible near earthquakes on the response of the surface topography should be evaluated as well.…”

Elastic wave propagation in an irregularly layered medium

“…Along the segments, the force density variation is prescribed and Gaussian integration (or analytical integration, where the Green function is singular) is performed. More details about the discretization procedure can be found in Sánchez-Sesma et al [28] and in Sánchez-Sesma and Campillo [25]. The results we present are obtained choosing the segment size minor than one sixth of the wavelength, f is assumed constant on each segment and three Gaussian points are used.…”