Free-field rotations during earthquakes: Relevance on buildings

Soil rotations around horizontal axes, during an earthquake, are studied through records collected by closely spaced arrays of strong motion accelerometers. The cross power spectrum of accelerations at nearby stations has been generally utilized to describe the spatial distribution of the motion. A number of cross spectra have been obtained during the training of these arrays. To take profit of these elaborations, a mathematical relation is established between the cross power spectrum and the power spectrum of the rotation. Rotation data presented by Liu et al, concerning 52 earthquake records collected at a single station in Taiwan, are compared with rotation data computed according to our procedure. The two series of data are suitably normalized to the peak horizontal acceleration. The data are shown in function of the distance from epicentre. The same ratio, computed according to our procedure, is in good agreement with the average value of these data. Direct measurements and the present approach have lead to evaluations of rotation higher than those predicted by mathematical investigations on the basis of the wave propagation theory, for comparable circumstances. The relevance of this input motion for relatively tall structures is examined, with reference to the structural effects that the horizontal motion concurrently provides. Meaningful will be ranked those effects of the order of magnitude of 20% or higher than those implied by the horizontal excitation. For understanding the relevance on building structures, the procedure has two areas of concern: 1) the coherence implicit in the cross power spectra, which depends on the interpolation process of the original records, collected in the arrays of instruments, and 2) the relative importance of the vertical to the horizontal input motion. As to the second item, the relevance of the rotation component on structures largely depends on the relative importance of the vertical to the horizontal input motion. When the records in an area a few km from the epicenter are considered, the response spectrum of vertical motion is comparable and in some records even higher, than that of horizontal motion, over the entire range of frequencies. This has been observed as well for the 2009 earthquake event of L’Aquila, Italy, and that at the Christchurch (New Zealand) 2011. When the response spectrum of vertical motion is comparable to that of horizontal motion, the effects of rotational motions on most engineering structures can be meaningful.