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Seismic waves may be strongly amplified in deep alluvial basins due to thevelocity contrast (or velocity gradient) between the various layers as well asthe basin edge effects. In this work, the seismic ground motion in a deepalpine valley (Grenoble basin, French Alps) is investigated through various'classical' Boundary Element models. This deep valley has a peculiar geometry("Y"-shaped) and involves a strong velocity gradient between surface geologicalstructures. In the framework of a numerical benchmark [21-23], a representativecross section of the valley has been proposed to investigate 2D site effectsthrough various numerical methods. The 'classical' Boundary Element Method isconsidered herein to model the strong velocity gradient with a 2D piecewisehomogeneous medium. For a large incidence angle, the transfer functionsestimated from plane SH waves are close to the one computed with shallow SHpoint sources. The fundamental frequency is estimated at 0.33 Hz (SH wave) andthe agreement with previous experimental results (spectral ratios) is good.Comparisons between 1D and 2D amplification are then performed: the values ofthe fundamental frequency and the corresponding amplitude are larger in 2D.Converting frequency domain results into the time domain, we underline surfacewaves generated at the valley edges and the directivity effect for theamplified wave-field. In the time domain for plane SV-wave, we also computedthe ground motion for a strong seismic event (M=6): time duration and peakground velocity are found to be 3 times larger than for the input signal. Such2D models involving basin effects are then capable to recover the highamplification level measured in the field. Nevertheless, to deal with complex3D basins as also proposed in the "ESG" benchmark [21-23], the capabilities ofthe classical Boundary Element Method are limited. As shown recently[43,47,52], such improvements as the fast multipole formulation (FM-BEM) may bea promising alternative for future 3D simulations.

Site effects in an alpine valley with strong velocity gradient: interest and limitations of the 'classical' BEM