Direct Method of Generating Floor Response Spectra
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Floor Response Spectra (FRS), also called In-structure Response Spectra (IRS) in some standards and literature, are extensively used as seismic input in safety assessment for Systems, Structures, and Components (SSCs) in nuclear power plants. Efficient and accurate determination of FRS is crucial in Seismic Probabilistic Risk Analysis (SPRA) and design of nuclear power facilities. Time history method has been commonly used for generating FRS in practice. However, it has been demonstrated that time history analyses produce large variability in the resultant FRS, especially at FRS peaks, which are of main interest to engineers. Therefore, results from only a single, or a few, time history analysis cannot yield reliable FRS; a large number of time history analyses are needed to achieve sufficient accuracy in FRS. Nevertheless, this procedure is time-consuming and cumbersome from a practical point of view. The purpose of this study is to develop a method of generating FRS that overcomes the deficiencies of the time history method and preserves the advantages of conventional response spectrum analysis for structures. A direct spectra-to-spectra method is analytically developed for the generation of FRS without introducing spectrum-compatible time histories as intermediate seismic input or performing time history analyses. Only the information required in a conventional response spectrum analysis for structural responses, including prescribed GRS and basic modal information of the structure (modal frequencies, mode shapes, and participation factors) is needed. The concept of t-response spectrum is proposed to determine the responses in the tuning case when the secondary system is resonant with the supporting structure. Furthermore, a new modal combination rule (called FRS-CQC), which fully considers the correlation between the responses of the secondary system and the supporting structure, and the correlation between modal responses of the structure, is derived based on random vibration theory. A scaling method, based on the proposed direct spectra-to-spectra method, is further developed for generating FRS in a situation when the modal information of structure is not available. A system identification technique is carried out to recover the modal information of equivalent significant modes of the structure from existing GRS-I and FRS-I. Scaling factors are then determined in terms of the equivalent modal information along with the GRS-I and GRS-II. The proposed scaling method can scale FRS to various damping ratios when the interpolation method recommended in standards are not applicable, and can also consider the large variations in the spectral shapes between GRS-I and GRS-II. The proposed direct spectra-to-spectra method is further extended to generate FRS considering the effect of soil-structure interaction in conjunction with the substructure method. A methodology is presented to develop a vector of modification factors for the tri-directional Foundation Input Response Spectra (FIRS) obtained from a free-field site response analysis using the properties of the structure and underlying soil. The modified response spectra, called Foundation Level Input Response Spectra (FLIRS), are then used as input in the direct method to a fixed-base model for generating FRS. The proposed methods are both efficient and accurate, giving a complete probabilistic description of FRS peaks, and accurate FRS comparable to those obtained from time history analysis using a large number of spectrum-compatible time histories.