A simple TD-BEM model for heterogeneous orthotropic hill-shaped topographies

Abstract A simple numerical model named DASBEM was successfully developed to analyze the seismic heterogeneous orthotropic hill-shaped topographies by a time-domain boundary element method (TD-BEM) based on half-space Green’s functions. The model was elaborated only by discretizing the hill surface and its interface with the underlying half-space through the use of image source theory and the substructure approach. To improve the model at the corners, the double node procedure was applied to the extreme nodes of the quadratic elements. An attenuation ratio is implemented in the boundary equations using a decremental exponential function. After presenting the technique, a validation example is presented alongside the literature to measure the convergence with an isotropic response. Next, a sample Gaussian-shaped hill model is prepared under propagating obliquely incident SH-waves as a common sample topography and the surface response is obtained by considering some significant parameters as well as the shape ratio, isotropy factor, frequency content, and angle of the incident wave. The ground surface response is sensitized in two time and frequency domains. The results showed that the amplitude of the response was not only dependent on the impedance ratio but also the orthotropy ratio, which was always effective in orienting the wave-front to amplify the ground movement. Graphical Abstract