Project Title/ID Number  Bridge Fragility and Post Earthquake Capacity—3182002 
Start/End Dates  10/1/02—9/30/03 
Project Leader  Bozidar Stojadinovic (UCB/Faculty) 
Team Members  Kevin Mackie (UCB/Grad Student) & Kyunghoo Lee (UCB/Grad Student) 
Project goals and objectives  
The goal of this project is to develop fragility functions for bridges to be used in PEER testbed projects. Fragility functions express the probability that a certain level of a decision variable related to bridge function is exceeded in a given seismic hazard environment. The objectives of the proposed project are:


Role of this project in supporting PEER’s vision  
This project feeds fragility function data to the testbed projects. Thus, it is vertically linked to PEER bridge testbed projects: Humboldt Bay Bridge, I880 Bridge, and Bay Area Highway Network. Work on this project depends on the results of several PEER projects. In particular, it is horizontally linked to bridge component database projects (Eberhardt and Seible), OpenSees deteriorating element development and validation projects (Mahin, Moehle, Lehman), and fragility research (Project 304). As a part of the I880 Transportation Testbed, this project contributes by developing the methodology for evaluating postearthquake operation state and repair effort of simple and common bridges. As a part of the Highway Network Testbed, this project provides the fragility curve data necessary to evaluate the operational state of a typical bridge after an earthquake. Such information will be used in the Highway Network Testbed to evaluate the state of the entire regional transportation network after an earthquake. 

Methodology employed  
Development of bridge fragility curves was conducted using the PEER framing integral and the probabilistic seismic demand analysis method. Using this method, a number of firstshock earthquakes are grouped into bins characterized by magnitude and distance. Each earthquake is applied to a bridge to induce firstshock damage: this damage state is saved. A number of aftershocks is grouped into a separate bin. The damaged bridge is subjected to this bin of aftershock ground motions to obtain an aftershock probabilistic seismic demand model (IMEDP relation). This process is repeated for each firstshock earthquake. Furthermore, the bridge damaged in the first shock is subjected to a strategically distributed traffic load which is increased until the bridge collapses. Lastly, a total of 108 bridges, varied by their design parameters, are analyzed. Thus the number of analyses is quite large. The effect of aftershocks and traffic load on the bridge is evaluated by identifying the difference in IMEDP probabilistic seismic demand models for the virgin bridge and the bridge damaged in a first shock. 

Brief description of past year’s accomplishments and more detail on expected Year 6 accomplishments  
In Year 5 we have investigated a large number of ground motion IMs and bridge EDPs and identified a small number of optimal IMEDP pairs. The primary IMs is the spectral acceleration at the fundamental period of the bridge (a perioddependent IM) and Arias Intensity (a periodindependent IM). The primary EDPs are drift and curvature. Local EDPs, such as strain, did not produce optimal IMEDP pairs. Optimal IMEDP pairs, identified to be sufficient, efficient and robust, are used to establish probabilistic seismic demand models in the PEER framing equation. Using the PEER framing equation, the work on EDPDM model developed by Eberhard at UW, and customary ground motion IM attenuation curves, we developed bridge EDPhazard and DMhazard curves, as well as customary fragility curves. Samples are shown below. 

Other similar work being conducted within and outside PEER and how this project differs  
A major project on the development of a riskbased methodology for assessing seismic performance of highway systems, conducted in cooperation between MCEER and USC, is similar to this project. The differences are: (1) the fragility curves developed in this project will be based on PEER probabilistic performancebased methodology and developed using sophisticated nonlinear bridge computer models, while the USC/MCEER project uses simplified bridge models or empirical fragility curves; (2) USC/MCEER project has a significantly wider aim, while this project is focused on rational evaluation of bridge postearthquake operational state, repair time and cost, and aftershock collapse risk. 

Plans for Year 7 if this project is expected to be continued  
The first objective in Year 7 is to complete the aftershock and truck loading runs, render the results, and present the postaftershock IMEDP relation and traffic load fragility curves for the damaged bridges. The second objective for Year 7 is to defined bridge DVs, as specified in the project milestones. Three meetings will be organized:
A major step towards defining bridge DVs is collection of data and processing of typical repair costs for bridge elements, given a damage state. Laura Lowes is working on a similar task for buildings. An attempt to extend a similar cost study from bridge elements to bridges systems will be made. 

Describe any instances where you are aware that your results have been used in industry  
To date, we are not aware that the results of this project have been used in bridge design practice. However, there is a keen interest, expressed by Caltrans’ Tom Harrington, in the evaluation of the effect of aftershocks on a damaged bridge. 

Expected milestones  
The milestones of this project are:


Deliverables  
Deliverables of this project are:
