Construction of rational models for topographic effects and size-conditioned-response-spectra. Issue 140 (January 2021) - Vergara, Juan; Sierra, César; Sáenz, Mario; Jaramillo, Juan; Gomez, Juan
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. Highlights: There is a direct connection between the spectral response at a site and the geometric features of the topographic profile around the site. The topographic response at a site depends upon the distance between geometric singularities existing in the surface topography and the site. Simplified and size-delimited computational models can be used effectively to find the spectral response at a site considering topographic effects using information easily available for the consulting engineer. Topographic aggravation factors for site response analysis available in code provisions are valid only over a finite period range.