Damping-dependent correlations between horizontal-horizontal, horizontal-vertical, and vertical-vertical pairs of spectral accelerations

Correlation coefficients for 5%-damped spectral accelerations (SAs) of horizontal ground-motion components have been extensively studied and applied in probabilistic seismic analysis using vector-valued intensity measures (IMs). Such correlations are, however, not sufficient for structures with different damping ratios under multidirectional earthquake shakings. This paper presents a comprehensive study on the correlations between horizontal-horizontal (H-H), horizontal-vertical (H-V), and vertical-vertical (V-V) pairs of SAs for different damping ratios based on the NGA-West2 ground motion database. The correlations of SAs with peak ground acceleration (PGA) and peak ground velocity (PGV) are also investigated. The uncertainty in correlations is measured by integrating the bootstrap method into the logic-tree framework. Comparative results indicate that the correlation coefficients generally increase for IMs of larger damping ratios. The relative difference between the damping-dependent and conventional 5%-damped correlation coefficients can be notable, reaching 100% and 35% in the SA-SA and SA-PGV (or PGA) pairs, respectively. Based on the empirical correlation results, an artificial neural network is utilized to develop parametric models of the correlations and the executive files for implementing these models are provided. The ANN-aided damping-dependent correlation models developed can be considered as a generalization of the conventional 5%-damped correlation models, and may serve as useful tool in applications such as ground-motion selection and vector-valued probabilistic seismic risk assessment for structure systems.