Effect of geometry on in-plane responses of a symmetric canyon subjected by P waves

Abstract

Topographic site effects in anti-plane problems have been studied for four decades cause of the obtained analytical solutions. The authors have developed proposed hybrid methods combining Lamb's series with finite element method (FEM) to resolve the problem of anti-plane scattering; however, it has been difficult to account for site effects in in-plane problems due to mode conversion. In this study, we sought to resolve this issue by developing a novel hybrid method to investigate the site effects of a canyon subjected to longitudinal waves (P waves) as well as horizontal and vertical displacement amplitudes (|ux| and |uz|) near and along canyons of various shapes. A transfinite interpolation function (TFI) was used to obtain the coordinates of nodes and conduct node numbering in the inner finite region within the canyon. Combining hybrid method with TFI function, similar procedures can be used to resolve the scattering problems in both anti-plane and in-plane problems.Canyons are divided into three groups according to shape: 1) smooth shallow, 2) non-smooth, and 3) smooth deep. We also examine the incident angle of P waves (θ), the dimensionless frequencies (η), and the shape of a canyon in terms of their effect on |ux| and |uz|. These factors were shown to generate site effects, including canyon-decay-effect, oblique-effect, shield effect, and SDCP (slope discontinuous points) effect. The site effects induce variations in |ux| and |uz| with constructive interference in the illuminated zone, destructive interference in the shadow zone, and attenuation along the surface of the canyon.