A Physics-Based Study on the Correlation Between Fourier Amplitude Spectra and Deformations of a Caisson-Type Quay Wall: To Illustrate the Utility of PSHA Based on Fourier Spectra for Assigning Seismic Actions for Geotechnical Structures

Abstract Consideration of ground deformations caused by earthquakes is essential in assessing seismic risk to geotechnical structures. In this process, seismic actions are generally determined based on seismic hazard analysis. This raises the question of whether the analysis should be based on Fourier spectrum or response spectrum. Modern Probabilistic Seismic Hazard Analysis (PSHA) is often based on response spectrum. However, the Japanese design standards for port structures uses PSHA based on Fourier spectrum. This choice partly came from the fact that the deformation of port structures is a complex phenomenon influenced by various factors including soil–structure interaction and liquefaction, and cannot be well represented by the response of a single degree of freedom system. However, there has not been sufficient study on the advantage of Fourier spectrum-based analyses in assessing the deformation of geotechnical structures. In this study, physics-based nonlinear finite-element seismic response analyses of a caisson-type quay wall were conducted for a variety of input ground motions to evaluate the deformation of the system. A well-calibrated finite-element model that can reproduce actual damage experienced during the 1995 Kobe earthquake was used. The input ground motions were systematically selected from strong-motion records observed between 1996 and 2024 in Japan. Based on the results, the correlations between the residual horizontal displacements and the integrated values of the Fourier and response spectra were investigated. The results clearly indicated that the integrated values of the velocity Fourier spectra show the highest correlation. This clearly shows the advantage of assigning the seismic actions on caisson-type quay walls as a representative geotechnical structure in terms of Fourier spectra rather than response spectra in assessing the deformation of those structures. Furthermore, based on the approach by Luco and Cornell (2007), it was shown that the integrated values of Fourier spectra show better sufficiency compared to those of response spectra.