Surface motion of an arbitrary number of semi-circular viscoelastic alluvial valleys for incident plane SH waves

SUMMARY A semi-analytical treatment of the seismic response of an arbitrary number of semi-circular viscoelastic alluvial valleys (including an infinite number of periodically distributed ones) in an elastic half-space under obliquely incident plane SH waves is presented. In terms of a radial wave function expansion and a region matching approach, a rigorous solution is derived for general computation for the anti-plane shear wave scattering problem. Upon confirmation of its accuracy with past solutions for single and twin elastic alluvial valleys, the proposed solution is used to present a comprehensive set of numerical examples to illustrate the sensitivity of the ground motion to the size, distribution, modulus, damping, and number of multiple alluvial valleys and frequency and direction of incident waves. It is found that the magnitudes of ground motions of a central alluvial valley are intensified and reduced by the surrounding valleys for vertical and grazing wave incidences, respectively. In addition, the duration of ground motions of the central alluvial valley tends to be prolonged due to the incoming secondary waves generated by surrounding valleys.