Seismic Vulnerability of the Highway System

Task D2-2: Theoretical Formulation for Highly Damped Bridge Systems
Subject Area: Earthquake Protective Systems

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 of the bridge system. It is generally believed that, concurrent with an increase in energy dissipation capability, 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; e.g., due to the effects of geometry or 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, as will be addressed under this task.

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 models, 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 2-year task will consist of three subtasks, as follows:

Subtask 1 - Numerical studies will be performed to examine quantitatively the cross/orthogonal effects on several common types of highway bridges. This examination will initially focus on three kinds of protective systems: base isolation for short-span bridges, passive fluid dampers for long-span bridges, and variable passive fluid devices on critical bridges for fail-safe protections.

Subtask 2 - Experimental studies and verifications will be performed, based on the numerical simulations and generally damped MDOF model bridges. This task will be done by using a 3-directional shaking table with large velocity and displacement testing capacity. The main effort will be limited to the base-isolation type of protective systems.

Subtask 3 - More accurate yet not too complicated mathematical models will be established. With the help of this formulation, one should be able to model most common types of bridges. In addition, quantitative results on both cross/orthogonal effects and more accurate response computations will be obtained. It is important that the corresponding computation should not be too complex for bridge engineers to apply, nor too complicated resulting in increased cost of design.

These three subtasks will be accomplished by:

establishing accurate and applicable dynamic models for bridges with highly damped earthquake protective systems by: (a) comparing dynamic responses of isolated bridges based on conventional SDOF (including proportionally damped MDOF) models with generally damped MDOF models based on theoretical formulations and numerical simulations; and (b) experimentally verifying the numerical results by using 3-D shaking tables in a cooperative project with the Taiwan Earthquake Engineering Research Center; and quantifying cross (orthogonal) effects for typical highway bridges by: (a) establishing engineering definitions of the cross (orthogonal) effects; (b) quantifying the effects caused by damping; and (c) quantifying the effects caused by stiffness.

Anticipated Start Date and Duration
January 1, 1999 - 24 months