Scattering and diffraction of plane SH-waves by periodically distributed canyons

A new method is presented to study the scattering and diffraction of plane SH-waves by periodically distributed canyons in a layered half-space. This method uses the indirect boundary element method combined with Green’s functions of uniformly distributed loads acting on periodically distributed inclined lines. The periodicity feature of the canyons is exploited to limit the discretization effort to a single canyon, which avoids errors induced by the truncation of the infinite boundary, and the computational complexity and the demand on memory can be significantly reduced. Furthermore, the total wave fields are decomposed into the free field and scattered field in the process of calculation, which means that the method has definite physical meaning. The implementation of the method is described in detail and its accuracy is verified. Parametric studies are performed in the frequency domain by taking periodically distributed canyons of semi-circular and semi-elliptic cross-sections as examples. Numerical results show that the dynamic responses of periodically distributed canyons can be quite different from those for a single canyon and significant dynamic interactions exist between the canyons.