Theoretical relationship between the horizontal-to-vertical response and Fourier spectral ratios of ground motions

IF 4.2 2区工程技术 Q1 ENGINEERING, GEOLOGICAL

Soil Dynamics and Earthquake Engineering Pub Date : 2024-10-07 DOI:10.1016/j.soildyn.2024.109010

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引用次数: 0

Abstract

Similar to the horizontal-to-vertical Fourier spectral ratio (HVF) of ground motions, the horizontal-to-vertical response spectral ratio (HVR) is a valuable tool for evaluating site effects. Although these two spectral ratios often exhibit similar behaviours, each possesses its own set of properties, prompting increased attention to their relationship. Previously, the relationship between HVF and HVR has been statistically investigated to explore which is more reasonable for predominant period estimation. However, the theoretical link between them remains unexplored. To clarify their theoretical relationship, in this study, an expression relating HVR to HVF based on random vibration theory was derived. The accuracy of the derived expression was confirmed through a comparison with the results obtained via direct numerical integration using real seismic records. Subsequently, based on the derived expression, the theoretical relationship between HVF and HVR was systematically explored. HVR was found to be the result of smoothing the square of the HVF, and the spectral window for this smoothing operation was determined using the Fourier amplitude spectrum of the vertical ground motion and the oscillator transfer function.

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地动水平-垂直响应与傅里叶频谱比之间的理论关系

与地震动的水平-垂直傅立叶频谱比（HVF）类似，水平-垂直响应频谱比（HVR）也是评估场地效应的重要工具。虽然这两个频谱比经常表现出相似的行为，但各自都有自己的特性，这促使人们更加关注它们之间的关系。在此之前，曾对 HVF 和 HVR 之间的关系进行过统计调查，以探索哪一个在主要周期估算中更合理。然而，它们之间的理论联系仍未得到探讨。为了阐明它们之间的理论关系，本研究基于随机振动理论推导出了 HVR 与 HVF 的相关表达式。通过与使用真实地震记录进行直接数值积分得到的结果进行比较，确认了推导表达式的准确性。随后，根据推导出的表达式，系统地探讨了 HVF 和 HVR 之间的理论关系。研究发现 HVR 是平滑 HVF 平方的结果，并利用垂直地面运动的傅里叶振幅谱和振荡器传递函数确定了平滑操作的频谱窗口。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Soil Dynamics and Earthquake Engineering 工程技术-地球科学综合

CiteScore

7.50

自引率

15.00%

发文量

446

审稿时长

8 months

期刊介绍： The journal aims to encourage and enhance the role of mechanics and other disciplines as they relate to earthquake engineering by providing opportunities for the publication of the work of applied mathematicians, engineers and other applied scientists involved in solving problems closely related to the field of earthquake engineering and geotechnical earthquake engineering. Emphasis is placed on new concepts and techniques, but case histories will also be published if they enhance the presentation and understanding of new technical concepts.