Direct Method of Generating Floor Response Spectra for Structures under Earthquake Excitations at Multiple Supports

Abstract

Floor Response Spectra (FRS) are commonly used as seismic input in the safety assessment for secondary systems in the nuclear power industry. Efficient and accurate determination of FRS is crucial in the design of nuclear power facilities. It has been demonstrated that time history analysis can lead to large variabilities in the generation of FRS, especially at FRS peaks. Therefore, FRS from only a single or a small set of time history analyses is not reliable, while a large number of time history analyses are needed to achieve sufficiently accurate FRS. However, this procedure is time-consuming and computational expensive in practice. Although some direct methods have been developed for the accurate generation of FRS, such as the method proposed by Jiang et al. (2015), they do not focus on structures under earthquake excitations from multiple supports.

The purpose of this study is to develop a method of generating FRS for multiply supported structures which can overcome the deficiencies of the time history method. A direct spectra-to-spectra method is analytically developed for generating FRS of structures with earthquake excitations from multiple supports without performing any time history analyses. Only ground response spectra (GRS), "t-response spectra (tRS)", and basic modal information of primary and secondary structures, including natural frequencies, modal damping ratios, modal participation factors, and mode shapes, which can be readily obtained from modal analyses, are needed. A new combination rule for generating FRS of multi-supported structures, called FRSMS-CQC, is developed based on random vibration theory. FRSMS-CQC fully accounts for the correlations between various components affecting FRS: the correlation between the responses of oscillators excited by any two vibration modes, the correlation between the response of an oscillator excited by a vibration mode and the response of an oscillator mounted directly on a support, and the correlation between the responses of oscillators mounted on different supports.

Practical methods are developed for determining the seismic response of multiply supported secondary structures as well as Tertiary Response Spectra (TRS) using FRS as input. The formulations in two special cases, i.e., the seismic input are fully correlated or independent, which have wide applications in practice are derived explicitly. Two assumptions on the correlation of FRS in the seismic evaluation of secondary systems, i.e., FRS in the same direction at different nodes of the same primary structure can be considered as fully-correlated, while they can be treated as independent if the nodes are located at different primary structures, are proposed for the practical evaluation of multi-supported secondary systems. It is demonstrated that the proposed methods can generate accurate seismic responses of secondary systems as well as TRS efficiently. The proposed direct spectra-to-spectra method for multi-supported structures is further extended to generate FRS considering the effect of soil-structure interaction (SSI) in incorporation with the substructure method, which allows the superstructure and the surrounding soil can be analyzed individually. Based on the soil stiffness and structural modal information, FLIRS transfer matrix and modification factor are derived to convert Foundation Input Response Spectra (FIRS) into Foundation Level Input Response Spectra (FLIRS), which is then used as the seismic input to the decoupled model to generate FRS using the proposed direct spectra-to-spectra method.

The methods developed in this thesis are efficient and accurate for the generation of seismic responses, FRS, and TRS comparing to the benchmarks obtained from time history analyses using a large number of spectrum-compatible time histories.