Modal Superposition Method for the Analysis of Seismic-Wave Amplification

Seismic site effects involve both wave propagation phenomena and vibratory resonance processes. In this article, modal approaches are then considered to investigate site effects in alluvial basins through the latter aspect. Some simplified modal methods are briefly recalled first. For a shallow alluvial site in Nice, France, standard eigenmode estimation is then proposed to make a qualitative analysis and preliminary comparisons with other numerical results obtained by the boundary element method (BEM). The influence of the bedrock on these results is discussed. One considers afterward the modal superposition method to analyze site effects from a quantitative point of view (effective modal mass). For a translational excitation (assumption of rigid base motion) and a frequency range acceptable for such vibratory investigations, a strong amplification appears around 1.6 and 1.8 Hz, giving a very high value of the cumulated effective modal mass (80%). These results are shown to be in good agreement with experimental ones and other numerical ones (BEM). The modal superposition method, accounting for the seismic excitation, then appears as an efficient tool, not only for the vibratory characterization, but also for simplified analyses of site effects in alluvial basins.