Abstract
The variation of 2D fundamental frequency of stand-alone structure on rock ({F}_{{02{text{D}}}}^{text{S}} ) and in a basin ({F}_{{02{text{D}}}}^{text{BS}} ) with the polarization of the incident S-wave is presented. This paper also presents the role of city density and polarization of the exciting S-wave in the site–city interaction effects on the response of structures in a city as well as free-field motion. The seismic responses of the various considered basin and site–city models are computed using SH-wave and P-SV-wave finite-difference programs. A considerable decrease in the value of {F}_{{02{text{D}}}}^{text{S}} of stand-alone structure on rock is obtained with the increase in shape ratio for the SV-wave but not for the SH-wave, as compared to the 1D fundamental frequency of structure ( {F}_{{01{text{D}}}}^{text{S}} ). However, a considerable decrease in the value of {F}_{{02{text{D}}}}^{text{BS}} of a stand-alone structure in basin under double resonance condition is obtained for the SH-wave and not for the SV-wave. The spectral amplification factor at the top of a structure at {F}_{{02{text{D}}}}^{text{BS}} of structure is larger for the SV-wave as compared to the SH-wave. A splitting of the bandwidth of the fundamental mode of vibration of structure and very large reduction in spectral amplification factor at {F}_{{02{text{D}}}}^{text{BS}} of structure is obtained due to the site–city interaction effects under double resonance condition for both the S-wave polarizations. Further, an increase in these inferred effects with an increase in city density and number of structures in a city with a constant city density is obtained. This finding raises the question concerning the validity of ground-motion prediction using soil–structure interaction for the design of structures in an urban environment. Further, the decrease in spectral amplification factor at {F}_{{02{text{D}}}}^{text{BS}} of structure due to the site–city interaction effects is larger in the case of SV-wave as compared to SH-wave. Furthermore, a considerable site–city interaction effects on free-field motion is obtained.
Highlights
The explanation of behaviour of buildings during an earthquake is a great challenge for researchers because of the complex soil–structure interaction phenomenon
The past studies have revealed that the kinematic soil–structure interaction largely affects the seismic response of structures (Housner 1954; Wong and Trifunac 1975)
A frequency-dependent damping in the time-domain simulations of responses of basins, structures and site–city models is essential for accurate prediction of fundamental frequency of 2D basin and structure, spectral amplification factors (SAF) and site–city interaction (SCI) effects on the characteristics of free-field ground motion (Narayan and Sahar 2014)
Summary
The explanation of behaviour of buildings during an earthquake is a great challenge for researchers because of the complex soil–structure interaction phenomenon. Paolucci (1999) have simulated the responses of various 2D and 3D basins and have given empirical relations to predict the fundamental frequency of elliptical-shaped closed basins They have reported a considerable difference between the 2D fundamental frequency of a basin for the SH-wave and the SV-wave. The first subsection of this paper presents the variation of 2D fundamental frequency of structure and basin with shape ratio (H/W) and the polarization of the exciting incident S-wave. The effects of site–city interaction on the variation of 2D fundamental frequency of structure and corresponding spectral amplification factor as well as free-field motion due to change of polarization of the incident S-wave and the city density are given. The SH-wave and SV-wave responses of the various considered basins, structures and site–city models are simulated using recently developed fourthorder viscoelastic staggered-grid finite-difference SH-wave (Narayan and Kumar 2013) and P-SV-wave (Narayan and Kumar 2014) programs
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