A comparison among different methods in the evaluation of torsional ground motion

Rotational motions (torsional and rocking) induced by seismic waves have been essentially ignored for a long time, first because rotational effects were thought to be small for man-made structures, and second because sensitive measuring devices were not available until quite recently. The benefits of the determination of rotational motion in seismology and engineering are still under investigation. In seismology, rotational motions can provide accurate data for arrival times of SH waves and, in the near-source distance range, rotational motions might provide more detailed information on the rupture processes of earthquakes. Rotational motions could also be used to better estimate the static displacement from seismic recordings, identifying translational signals caused by rotation. In engineering, the dynamic response estimation of structures subjected to earthquake-induced base excitations is often simplified by ignoring the rotational components. This has been a widely accepted practice in the engineering community, mainly caused by the lack of recorded strong motion accelerograms for these motions. Many structural failures and the damage caused by earthquakes can be linked to differential and rotational ground motions. The torsional responses of tall buildings in Los Angeles during the San Fernando earthquake in 1971 could be ascribed to torsional excitation, while rotational and longitudinal differential motions may have caused the collapse of bridges during the San Fernando (1971), Miyagi-ken-Oki (1978) and Northridge (1994) earthquakes. Several studies have shown the importance of torsional components in seismic analysis and design of structures. The seismic design codes also prescribe ‘Accidental Eccentricity’ in design force calculations to account for unknown torsional inputs and unpredictable eccentricities. Since then, many researchers have studied the dynamic and accidental eccentricities of structures. For the first time, Newmark (1969) established a simple relationship between the translational and torsional components of the ground motion. He presented a deterministic procedure for estimating the increase in the displacement of symmetric-plan buildings caused by rotational ground motions at the base due to the horizontal propagation of plane waves with a constant velocity and further explored in the other studies. Three main approaches have been developed to incorporate rotational motions in engineering applications: one is a numerical simulation of the field of radiation from the source mechanism. It requires an appropriate model of the faulting mechanism, without considering the effects of path and local site conditions. The second approach is based on a theoretical formulation of the spatial distribution of ground motion. In this method, some information on the source, path and local layering are required. All of these studies are based on assumed models for ground motion and none of them has the benefit of being tested against field measurements. The third approach is the application of recorded strong motion data from seismic arrays. In this paper, data were collected from the Chiba dense array, which consists of 44 accelerometers with inter-station spacing in the range of 5 to 300 meters, located 30 Km east of Tokyo, that are employed to estimate the torsional ground motion. This provides a unique opportunity to examine accuracy in the estimation of torsional motion. To this end, three methods, namely, time derivation, finite difference and geodetic methods were employed. The geodetic method could be used as the criterion for accuracy of torsional motion, since it has second order accuracy for an array with regular accelerogram patterns. The results showed that the peak torsional ground motion as computed by the time derivation method is larger than those computed by the geodetic method. Peak torsional ground motion values estimated by the finite difference method show smaller values than those computed by time derivation for long separation distances (>20). However, they showed close values for short separation distances. Finally, the effects of peak ground acceleration and magnitude of earthquake on the torsional motions have been investigated. The results reveal that there is a linear relationship between peak horizontal ground acceleration and peak torsional acceleration.