A ground motion model for orientation-independent inelastic spectral displacements from shallow crustal earthquakes

The peak inelastic displacement of a single-degree-of-freedom (SDOF) system is an efficient ground motion (GM) intensity measure (IM) for estimating seismic demands in structures and infrastructures. Most ground motion models (GMMs) that predict this IM are developed to estimate the arbitrary or geometric mean of the horizontal GM components obtained from the two as-recorded orientations. In this study, the median and maximum directional inelastic spectral displacements, denoted as Sdi,RotD50 and Sdi,RotD100, respectively, were considered as IMs to develop GMMs. These orientation-independent measures of horizontal motion were calculated by rotating the GMs through all non-redundant rotation angles and have the advantage of removing the sensor orientation as a contributor to overall uncertainty. To do this, several SDOF systems were considered using a subset of the NGA-West2 database to fit GMMs for these IMs. A set of functional forms was developed using a mixed-effects regression approach. The predictor variables were the elastic period, T, the strength ratio, R, and a set of seismological GM causal parameters (i.e. magnitude, distance, soil condition, and so on). Comparison with existing GMMs that consider either inelastic spectral displacement or directionality is provided to highlight key differences and developments. In addition, the response directionality, defined as the ratio Sdi,RotD100/Sdi,RotD50, was observed to be notably impacted by the strength ratio and elastic period, which has not been discussed in the literature to date. Overall, this GMM has the advantage of quantifying ground motion intensity via an efficient IM in Sdi, which can better highlight some fundamental issues surrounding the directionality of GMs and allow for more informative risk estimates.