Quantification of site–city interaction effects on the response of structure under double resonance condition

Abstract

This paper presents the site–city interaction (SCI) effects on the response of closely spaced structures under double resonance condition (⁠|$F_{02{\rm{D}}}^{\rm{S}} = F_{02{\rm{D}}}^{\rm{B}}$|⁠), where |$F_{02{\rm{D}}}^{\rm{S}}$| and |$F_{02{\rm{D}}}^{\rm{B}}$| are fundamental frequencies of 2-D structure and 2-D basin, respectively. This paper also presents the development of empirical relations to predict the |$F_{02{\rm{D}}}^{\rm{B}}$| of elliptical and trapezoidal basins for both the polarizations of the S wave. Simulated results revealed that |$F_{02{\rm{D}}}^{\rm{B}}$| of a 2-D basin very much depends on its geometry, shape ratio and polarization of the incident S wave. The obtained spectral amplification factor (SAF) at |$F_{02{\rm{D}}}^{\rm{S}}$| of a standalone structure in a 2-D basin is greater than that in the 1-D case under double resonance condition. A considerable reduction of the fundamental resonance frequency of structures due to the SCI effects is observed for both the polarizations of the S wave. The SAFs at |$F_{02{\rm{D}}}^{\rm{S}}$| of closely spaced structures due to SCI effects is larger in the case of SV than SH waves. A splitting of the fundamental-mode frequency bandwidth along with the drastic decrease of SAF due to the SCI effects is obtained. The findings of this paper raise the question concerning the validity of the predicted response of standalone structure based on soil–structure interaction for the design of structures in a 2-D small basin, in an urban environment.