Report No.: CCEER-98-3
Title: Extraction of Nonlinear Hysteretic Properties of Seismically Isolated Bridges from Quick-Release Field Tests
Authors: Qingbin Chen, Bruce Douglas, E. Maragakis, and Ian. G. Buckle
Date: June 1998
A Report to the:
National Center for Earthquake Engineering Research, State University of New York at Buffalo
Department of Civil Engineering/258
University of Nevada, Reno
Reno, NV 89557
A time domain system identification method is used to identify the hysteretic properties of lead-rubber bearings installed in seismically isolated bridge systems. The longitudinal or transverse motion of the superstructure is idealized as a single degree of freedom (SDOF) system. The total damping effect has been divided into two parts. The most significant component of damping, which is caused by hysteretic behavior, is described directly by the nonlinear models. The viscous damping component, which is assumed to be proportional to the velocity of the mass, is described by the damping ratio.
Two theoretical models are used for modeling the force-displacement characteristics of the rubber-lead bearings. These are the Generalized Ramberg-Osgood model and the bilinear model. The Generalized Ramberg-Osgood model has been found to be more consistent with the hysteresis characteristics of the lead-rubber bearings obtained from the laboratory tests. On the other hand, the bilinear model, with its simplicity and the clear physical meaning of its parameters, is a useful equivalent model for analysis and design purposes.
A step-by-step integration method is used for computing the displacement and velocity time histories of the nonlinear SDOF system numerically. The displacement and acceleration time histories of the superstructure observed during quick release tests are compared with theoretical ones in order to identify the important characteristics of the lead-rubber bearings from field experiments. The parameters to be identified include the four parameters used for describing the Generalized Ramberg-Osgood model or the three parameters defining the bilinear model as well as the viscous damping ratio. The parameters are obtained from the field data by minimizing an objective function which is defined as the sum of the squares of the difference between the numerical time histories and the observed ones. A direct search algorithm proposed by Hooke and Jeeves (Hooke and Jeeves, 1961) is used for the optimization process.
Time histories recorded from field quick-release tests on two bridges are used for the examples presented herein. Hysteresis curves for the isolators obtained from the laboratory tests conducted before they were installed in the bridge were compared with those obtained from the generalized Ramberg-Osgood models and the bilinear models obtained using the optimization method, and they agree well. Thus, this shows that this simple efficient quick-release test can be used to identify the essential in-situ hysteretic characteristics of lead-rubber isolation bearings.
Due to the high flexibility of the isolators and high stiffness of the superstructure and the columns, the fundamental mode is usually well separated from the higher modes. The displacement time histories are generally dominated by the motion of the fundamental mode and is thus ideal for identifying the hysteretic properties of the isolators. The acceleration time histories can be dominated by the motion of the higher modes thus they can not always be used directly for this purpose. This characteristic of the seismically isolated bridge is the essential basis for a SDOF identification method.
Finally, the dynamic behavior of the bilinear model for the quick release response was studied analytically. A closed form solution for the response of a bilinear SDOF oscillator to quick release excitation was obtained. This solution was helpful to better understand the behavior of the bilinear model. Also, it was used to check the computer codes. Based on the principle of conservation of energy, the condition for producing zero permanent displacement for quick release test was obtained in closed form for the zero damped case (Summary by authors).