Estimating Stable Mean Responses for Linear Structural Systems by Using a Limited Number of Acceleration Time Histories

Abstract

Abstract For seismic analyses of linear structural systems including soil-structure systems, the current practice (e.g., the U.S. Nuclear Regulatory Commission (NRC) Standard Review Plan (SRP) (NUREG-0800 [1], “Standard Review Plan for the Review of Safety Analysis Reports for Nuclear Power Plants: LWR Edition”) and American Society of Civil Engineers (ASCE)/Structural Engineering Institute (SEI) Standard 4-16 [2], “Seismic Analysis of Safety-Related Nuclear Structures”) allows for estimating mean seismic responses by using as few as four or five input time histories. This paper examined whether this practice can achieve a stable mean response by explicitly considering the uncertainty in the Fourier phase spectra of the input time histories and exploring how this uncertainty can affect the coefficient of variation (CV) of the in-structure response spectra (ISRS). ISRS are the response spectra of the seismic response time history at a location in the structure subjected to an input seismic time history. We found that the maximum CVISRS across all frequencies is around 40% purely due to the uncertainty in the Fourier phase spectra for a typical range of design earthquakes for U.S. nuclear power plants. To estimate a mean ISRS within ±10% of the true mean ISRS, our analyses showed that this level of CVISRS may require a minimum of 16 input time histories for a confidence level (CL) of 68% and 61 for a CL of 95% for soil-structure systems of low fundamental frequencies. For stiffer systems (for example, with a fundamental frequency of 5 hertz (Hz)), the maximum CVISRS is about 30%, and thus, the minimum required number of input time histories may be reduced to 9 for a CL of 68% and 35 for a CL of 95%. In summary, the four or five time histories in the current practice may not be sufficient for estimating stable mean responses, especially for soil-structure systems with very low frequencies.