Surface motion of an arbitrary number of semi-circular viscoelastic alluvial valleys for incident planeSHwaves

Abstract

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.

Coupled-mode separation of multiply scattered wavefield components in two-dimensional waveguides

“…The development in [46, Sec. V] concerns a 3D point source (or line source), while SH papers such as [27,41] typically prescribe an incident plane wave. Generation of a plane wave by an royalsocietypublishing.org/journal/rsos R. Soc.…”

“…The amplitude results are given relative to the incident-wave amplitude, and the star symbols indicate corresponding results from Zhang et al [41] and Ba & Liang [56]. The Zhang et al [41] and Ba & Liang [56] results are often somewhat different for the 90° angle. At each x , the two star symbols in ( c ) are, therefore, connected by a vertical line segment for visual clarity.…”

Effect of a symmetric V‐shaped canyon on the seismic response of an adjacent building under oblique incident SH waves

“…25 In fact, in the research field of topographic effect and the associated wave scattering problem, much progress has been made recently. [26][27][28] Particularly, a more realistic V-shaped canyon model has been proposed by Tsaur and Chang. 29 Based on a series of studies on the topographic effect of V-shaped canyons, [30][31][32] it is concluded that this type of canyon has a stronger impact on ground motions in comparison to the semicircular one.…”

“…Previous studies about the dynamic canyon‐soil‐structure interaction all adopted the semicircular canyon model proposed by Trifunac 25 . In fact, in the research field of topographic effect and the associated wave scattering problem, much progress has been made recently 26–28 . Particularly, a more realistic V‐shaped canyon model has been proposed by Tsaur and Chang 29 .…”

Effect of a V‐shaped canyon on the seismic response of a bridge under oblique incident SH waves

“…As an analytical method, the wave function expansion has unique scientific value in dealing with the propagation and scattering of seismic waves in canyon sites. Based on this method, analytical solutions to the wave propagation in and around canyons with various geometry and materials have been proposed 24–29 . The analytical study of seismic response of bridges using the wave function expansion method began with the simply supported bridge model proposed by Abdel‐Ghaffar and Trifunac, 30 which is composed of two rigid semi‐circular foundation‐abutment systems and an elastic shear beam supported by them.…”