Seismic response of multi-layered basins with velocity gradients upon incidence of plane shear waves

Abstract

A boundary integral scheme based on boundary-integral discrete-wave-number approach has been developed to compute the seismic response of two-dimensional irregular-shaped basins with horizontal soil layers. Each layer exhibits a linear gradient of shear wave velocity with depth. The approach combines the boundary-integral representation of the seismic wave field outside the basin with plane wave representation of the seismic wave field inside the basin. The propagation throughout the layers is performed by matrix propagators in which the effect of the vertical variation of the velocity is incorporated by using confluent hyper-geometric functions of the Whittaker type. Our method is tested against other well-accepted solutions for the case of a circular basin with excellent agreement. Test of the ground response for a semi-circular basin with radius a shows that stable solutions are obtained if the chosen model parameters satisfy following conditions: (1) the distance from the sources to the interface is greater than 0.1a; (2) the distance between the sources is smaller than a quarter of the incident wavelength; and (3) the discrete wave-number step is smaller than 2π/4a. The computation of ground response of basins with a sharp interface and several horizontal deposits leads to the following main results: (1) the amplification of a basin with velocity gradients is larger than that of a basin with homogeneous layers; (2) the frequencies of the second- and third-order harmonics for a basin with velocity gradients are lower than those of a basin with homogeneous layers; and (3) the response amplitude of the basin with velocity gradients attenuates more slowly in time domain than when layers are homogeneous. Since these results have been obtained for realistic values of basin geometrical and mechanical consideration, they should find some interest in earthquake engineering or seismic microzonation studies.