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

  • Neeraj Kumar
  • Jay Prakash NarayanEmail author


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.


3D basin response shape ratio effects site–city interaction fundamental frequency of 3D basin and structure 



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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Earthquake EngineeringIndian Institute of TechnologyRoorkeeIndia

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