Seismic Vulnerability of the Highway System

Task D1-3: Displacement Estimates for Isolated Bridges

Subject Area: Seismic Response Modification Devices
Research Year 3

Principal Investigator and Institution

Andrew Whittaker, University at Buffalo


Equation 3a in Section 7 of the AASHTO Guide Specification for Seismic Isolation Design is widely used for the design of seismic isolation systems in bridges and buildings. The design spectrum upon which the equation is based assumes unidirectional seismic excitation only. Bi-directional seismic input will both increase the maximum displacement in the isolation system and modify the unidirectional properties of the isolators (e.g., Qd). Assuming that damping is correctly accounted for through the displacement-reduction factor, B, a correction factor that accounts for the effect of bi-directional seismic excitation is needed if the AASHTO equation is to be used for analysis and design of seismically isolated structures.


This research will build on work started by the PI with funding from Caltrans, while he was at the University of California, Berkeley. Five large sets of earthquake histories, four of which are binned by magnitude and distance, will be used for the analysis: (1) near-field, (2) large magnitude short distance, (3) large magnitude long distance, (4) small magnitude short distance, and (5) small magnitude long distance, where large magnitude is greater than 6.5, and short distance is less than 30 km. Earthquake histories will be extracted from the ground motion data base at Previous studies conducted under the direction of the PI have shown that the sets of binned earthquake histories will produce, on average, a spectrum that matches well the shape of the assumed AASHTO spectrum.

This research will characterize the force-displacement response of seismic isolators using the AASHTO approach, namely, Qd and Kd. Substantial variations in Qd (from 0.03W to 0.12W) and Kd (producing effective periods from 1.0 second to 4.0 seconds) will be considered to ensure that the resulting conclusions will be broadly applicable in the United States. Using a Matlab model of a rigid superstructure supported by four seismic isolators, the simplest possible seismic isolation system, displacements of the isolation system will be calculated using unidirectional and bi-directional seismic input for each of the earthquake-history pairs in each of the five bins. The resulting data will be statistically sorted and interpreted to provide a factor, say K, greater than unity, to correct unidirectional displacements for the effect of bi-directional seismic excitation.

A second subtask will be to check the accuracy of the AASHTO equation for predicting displacements of isolated bridges under uni-directional excitation. It is known that the equation provides a good median estimate of the displacement of a 5-percent damped oscillator and that the values of the displacement-reduction factor, B, are substantially conservative (small). The resulting displacement of an isolation system with significant damping, calculated using the AASHTO formula, is therefore conservative (large) but not necessarily accurate. Assuming that the use of the improved values of B produce good estimates of the unidirectional displacement, a change to the AASHTO equation will be proposed; namely


which may vary as a function of ground motion type (one of the five bins), Qd, and Kd. A useful byproduct of this analytical study will be information that will be used to propose substantial revisions to the AASHTO requirements for prototype testing of seismic isolators, which are based in large part on theTask D1-3 (continued)testing requirements for building isolators. Information on the total energy dissipated by the isolation system, measured as a percentage of the energy dissipated in one fully-reversed cycle of loading to the maximum displacement, will be used as the basis for the proposed changes to Sections 13.2 (b) parts 3, 4, and 6 of the AASHTO Guide Specifications.


  • Correction factors to Equation 3a of the AASHTO Guide Specification for Seismic Isolation Design for bi-directional seismic excitation as a function of ground motion type which, if used with improved values of the displacement reduction factor, B, will better predict the maximum displacement of an isolator in a bridge.

Technical Challenges

The major technical challenges for this task include the statistical interpretation of the response-history data to establish correction factors for bi-directional excitation; and modification of the AASHTO design equation to correct for the assumed spectral shape in the constant-velocity range, bi-directional excitation, and improved estimates of the damping factor, B.

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