The role of strong motion rotations in the response of structures near earthquake faults: Fid-Bau Portal

The role of strong motion rotations in the response of structures near earthquake faults

Trifunac, Mihailo D.

AbstractEarly studies of earthquake strong motion assumed linear materials and small deformations. It was observed that under favorable conditions (long waves), the accompanying rotational motions are usually small, and so their effects could be neglected. In 1932, when Biot opted for the vibrational method of solution of the dynamic response problems [Trifunac MD. 75th anniversary of the response spectrum method—a historical review. Soil Dyn Earthquake Eng 2008 [in press].] in his formulation of the response spectrum concept, his choice of the discrete mathematical models of buildings further led to the conditions that did not explicitly require consideration of the rotations [Trifunac MD. Buildings as sources of rotational waves, Chapter I.5. In: Teisseyre R, Nagahama H, Majewski E, editors. Physics of asymmetric continua: extreme and fracture processes. Heidelberg, Germany: Springer; 2008 [in press].]. The engineering profession was not prepared in the 1930s and 1940s for Biot's new theory and first had to learn the basic dynamics of structures before it could question the wisdom and consequences of the vibrational versus the wave-propagation approaches to the solution. Also, there were too many other concerns, often caused by the modeling simplifications, that pushed the studies of the rotational motion further down to the low levels of priority. Even today, 40 years after the arrival of digital computers and the emergence of powerful numerical computational capabilities, which uncovered unexpectedly large families of chaotic solutions accompanying large deformations, as well as nonlinear response [Trifunac MD. Nonlinear problems in earthquake engineering. In: Springer's encyclopedia of complexity and system science, 2008 [in press] [94].], most researchers continue to ignore the role of rotations. Had Biot chosen the wave-propagation approach for the solution of the earthquake engineering problems in 1932, the “progress” might have been faster. The wave representation can be differentiated with respect to a space coordinate, giving the rotations at a point directly. In contrast, the lumped-mass models in the vibrational approach do not make this possible, and the closest one can come to considering rotations is in terms of average, per-floor rotation, or drift.This paper reviews some elementary aspects of ground motion near faults and the resulting structural deformations in order to illustrate the role of the strong-motion rotations. We show rough estimates of how large such rotations can be, and we suggest how the profession might begin to study and interpret their consequences. Whether the aim is to understand why micro-tremors in metropolitan areas abound with high-frequency Rayleigh waves, why buildings rock and occasionally overturn during strong earthquake shaking, or why columns fail, we must consider the rotational components of ground and structural motions. Only then will we be able to understand and control the response to strong earthquake excitation.