Generation of Fourier amplitude spectra and power spectral density functions compatible with orientation-independent design spectra for bidirectional seismic analyses of nuclear facilities

While matching input motions to a design response spectrum (DRS) is standard practice, the US-NRC Standard Review Plan (SRP) 3.7.1 also mandates a minimum power spectral density (PSD) check to prevent power deficiencies that can lead to unconservative in-structure response spectra (ISRS). However, existing methodologies for constructing the required target PSD functions are designed for single-component analysis and do not accommodate the modern orientation-independent spectra (e.g., RotDnn) toward which bidirectional analysis is moving. This article addresses this gap by introducing an iterative algorithm to generate duration-dependent, orientation-independent PSD and Fourier Amplitude Spectra (FAS) functions compatible with any target RotDnn spectrum. The algorithm iteratively adjusts the target FAS of two orthogonal components until their combined RotDnn response spectrum provides a close match to the target DRS, from which a large set of synthetic motions is generated to define the final orientation-independent target spectra. The accuracy and robustness of the proposed methodology is demonstrated by successfully reproducing the FASRotD100 and PSDRotD100 from a benchmark dataset of 50 historical earthquake records, providing an essential tool for reliable seismic assessments consistent with modern hazard definitions.