Seismic Vulnerability of the Highway System

Task  D1-2: Theoretical Formulation for Highly Damped Bridge Systems

Subject Area: : Earthquake Protective Systems 
Research Year 2

Principal Investigator(s) and Institution(s)

Zach Liang and George C. Lee, University at Buffalo


The application of earthquake protective systems for bridges currently consists of the addition of devices such as dampers and base isolators which can significantly increase the overall damping or reduce the vibration of the bridge system. It is generally believed that, concurrent with an increase in damping, structural responses will be reduced. This may not always be true however. In some cases, high damping will also cause higher damping proportionality, which in turn results in a higher chance of energy transfer among vibration modes, thereby magnifying responses. The phenomenon of modal cross-effect can be further magnified when a bridge is irregularly shaped; causing skewness in the distribution of mass, damping and stiffness. These kinds of cross-effects can sometimes be large under multiple directional ground motions. In order to quantify the magnitude of cross-effects, the bridge/device system (highly damped) should be modeled as a multi-degree-of-freedom (MDOF) system. In current bridge design, this possible problem is recognized and the designers are suggested to use more rigorous analysis (such as the time-history analysis). However, no further guidelines are given on how to proceed with a very difficult nonlinear structural dynamics problem.

Several earthquake engineering researchers and practitioners have suggested that the dynamic behavior of bridges with high damping may significantly differ from that with low damping. However, the differences have not been quantified in the open literature. The objective of this task is therefore to review and address these issues on the basis of three-dimensional nonlinear time history analyses validated by a large-scale model test.


The use of seismic protective systems is a relatively new approach in bridge design, and can be cost-effective in many situations. At the same time, it also brings in uncertainties in structural response reductions. Although cross/orthogonal effects have been observed in real cases, they need to be properly quantified based on appropriate models.

Conventionally, to quantify the dynamic behavior of a bridge, a single-degree-of-freedom (SDOF) model is often used. The more sophisticated MDOF method employs proportionally damped assumption, which can be modally decoupled into SDOF modes. Mathematically speaking, by using these models, cross effects among modes cannot be described, nor can orthogonal effects among perpendicular directions be quantified.

This Research Year 2 study is divided into three subtasks, as follows:

Subtask 1, Numerical Studies: During Year 1of this task, the PI's examined the theory presently being used for analyzing and conducting experiments for earthquake protective systems. Much of this effort focused on analytical formulation about the cross/orthogonal effects on curved and skewed bridges. A manuscript on theoretical consideration of cross effects is under preparation by Liang and Lee.

Subtask 2, Experimental Studies: Based on the theory examined under Subtask 1, numerical simulations for selected unconventional bridges were carried out and developed during Year 1. Preliminary results show that in many cases the cross effects can be very large. These results will be verified by conducting experimental testing of a large scale model on a 3-directional shaking table with large velocity and displacement capacities. The PI's have been collaborating with Taiwan's National Center for Research on Earthquake Engineering (NCREE) to conduct the testing at their laboratory. NCREE has agreed to conduct the testing including the fabrication of the test model at their cost and MCEER will provide the bearings and other EPS systems to be developed by Task D2-2 and D2-3.

Subtask 3, More Accurate Models: Based on the work in the previous subtask, more accurate, yet not too complicated mathematical models will be established and provided so engineers should be able to model the most common types of unconventional (skewed, curved, long span, etc.) bridges. In addition, quantitative results on both cross/orthogonal effects and more accurate response computations will be obtained. It is recognized that the computations should not be too complex, possibly resulting in increased costs of bridge design or difficulties for bridge engineers to apply.

During the execution this task the dynamic response of isolated bridges based on models with a SDOF (including proportionally damped MDOF) are being compared to the responses obtained from generally damped MDOF models. Furthermore, engineering definitions of the cross/orthogonal effects are being developed.


The product of this task will be a report summarizing the theoretical, numerical, and experimental results resulting from the analysis of cross effects. The report will address suitable modeling procedures and formulate a strategic plan for the potential development of "intelligent" bearing systems in future project tasks. A journal paper on cross effects will be prepared.

Technical Challenges

The major challenges are those typically associated with conducting fundamental research. If the experimental results, do not agree with the mathematical models, it may be difficult to determine where the differences are being generated. Also, the final design of the physical bridge model has to be sufficiently adaptable to allow the future testing of a variety of passive and semi-active devices to be installed in a realistic manner. An additional challenge is to work with the schedule of NCREE shaking table and technical support staff in order to carry out the experiments.


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