Construction of rational models for topographic effects and size-conditioned-response-spectra

Abstract

We used the decay-with-distance effect of diffracted waves generated from the interaction of a plane wave with a geometric singularity, to establish the connection between the spectral response of a topographic profile and the minimum required size of a model to capture the response up to a prescribed target period. To study the behaviour of the diffraction sources we conducted parametric analysis over a symmetrical trapezoidal canyon subjected to vertically incident SV and SH waves. The analysis identified the frequency above which, the amplitude of the transfer function of the diffracted part of the field decays below a prescribed tolerance. This distance-cut off frequency relation was then used to propose a simple expression to find the size of a topographic profile in terms of a prescribed value of the target period. We refer to the resulting response spectra capturing the model ground motions as size-dependent-response-spectra. The reduced models, tailored to match a target structural period, were then tested in a scenario corresponding to a modified cross section of the Aburrá Valley in Medellin Colombia where we computed ratios of response spectra between the response with the reduced model and that obtained considering the full regional scenario at several receivers for this profile. The results at all the explored receivers exhibit the prescribed accuracy even for larger values of the structural period showing that the proposed approach can be effectively used in the study of the aggravation introduced by the presence of topography on the local site response.