Abstract

The most commonly used intensity measure of ground motion in earthquake engineering is the 5% damped spectral ordinate, which varies in different directions. Several different measures have been proposed over the years to combine the intensity of the two horizontal recorded ground motions to derive ground-motion models as well as for design purposes. This study provides the relation to seven previously used measures of horizontal ground motion with respect to a recently proposed orientation-independent measure of horizontal ground-motion intensity referred to as MaxRotD50. This new measure of horizontal intensity is defined as the median value of the maximum spectral ordinate of two orthogonal directions computed for all possible nonredundant orientations. The relations are computed using 5065 pairs of horizontal ground motions taken from the database of ground motions recorded in shallow crustal earthquakes in active tectonic regions developed as part of the Pacific Earthquake Engineering Research Center's Next Generation Attenuation-West2 project. Empirically derived period-dependent relations are presented for three quantities that permit transforming any of the seven other definitions of horizontal ground-motion intensity to MaxRotD50, namely, (1) geometric mean of the ratio of MaxRotD50 to any of the seven other measures of intensities, (2) standard deviation of the natural logarithm of the ratio of MaxRotD50 to any of the seven other measures of intensities, and (3) the correlation between the natural logarithm of the ratio of MaxRotD50 to the other measures of intensities and the natural logarithm of the other measure of intensity. In addition, the influence of site class at the recording station, earthquake magnitude, and distance to the horizontal projection of the rupture is examined on the geometric mean of the ratio of MaxRotD50 to the median intensity of all nonredundant orientations (i.e., RotD50), showing negligible influence of site class and only a relatively small influence of magnitude and distance.