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Quantification of Fundamental Frequencies of 3D Basins and Structures and Site–City Interaction Effects on Responses of Structures

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Abstract

Large-scale commercialization in Indian metrocities has made realtors develop new construction sites by filling land depressions with loose soil, which may behave as small three-dimensional (3D) basins. This study presents the development of empirical relations to predict the fundamental frequency of basins (\(F_{{03{\text{D}}}}^{\text{B}}\)) and structures (\(F_{{03{\text{D}}}}^{\text{S}}\)) on rock for different shape ratios to study the effects of site–city interactions (SCIs) on the response of structures under a double resonance condition. The S-wave responses of the various considered basins, structures, and site–city models are simulated using the finite-difference method. Analysis of the simulation results reveals that the \(F_{{03{\text{D}}}}^{\text{B}}\) of the basin and the \(F_{{03{\text{D}}}}^{\text{S}}\) of the structure depend strongly on the shape ratio, on average matching with those obtained using the SV-wave response of the section of the respective basin/structure. However, the spectral amplification factor (SAF) obtained at \(F_{{03{\text{D}}}}^{\text{B}}\)/\(F_{{03{\text{D}}}}^{\text{S}}\) for the basin/structure is much larger than that obtained using the SV-wave response of a section of the respective basin/structure. Empirical relations are developed to predict the \(F_{{03{\text{D}}}}^{\text{B}}\) of basins and \(F_{{03{\text{D}}}}^{\text{S}}\) of structures in terms of the shape ratio and one-dimensional (1D) fundamental frequency of the respective model. Analysis of 3D SCI effects reveals a reduction of the SAF at the fundamental frequency of the structure in the basin (\(F_{{03{\text{D}}}}^{\text{SB}}\)) with an increase of the number of structures as compared with that at the fundamental frequency (\(F_{{03{\text{D}}}}^{\text{SB}}\)) of a standalone structure in the basin, being on the order of about 60 % in the case of a city with 25 structures. This finding indicates the need for 3D SCI studies in urban environments for cost-effective earthquake engineering.

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  1. Department of Earthquake Engineering, Indian Institute of Technology, Roorkee, India

    Neeraj Kumar & Jay Prakash Narayan

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Kumar, N., Narayan, J.P. Quantification of Fundamental Frequencies of 3D Basins and Structures and Site–City Interaction Effects on Responses of Structures. Pure Appl. Geophys. 176, 4477–4502 (2019). https://doi.org/10.1007/s00024-019-02158-8

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  • DOI: https://doi.org/10.1007/s00024-019-02158-8

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