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:

• Define Decision Variable pertinent to bridge function state and repair time after an earthquake.
• Develop bridge fragility curves using bridge function Decision Variables for simple, yet common, bridge systems and sub-assemblies.
• Develop bridge post-earthquake aftershock (and traffic load, if time permits) fragility curves for collapse limit state.

This project feeds fragility function data to the testbed projects. Thus, it is vertically linked to PEER bridge testbed projects: Humboldt Bay Bridge, I-880 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 I-880 Transportation Testbed, this project contributes by developing the methodology for evaluating post-earthquake 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.

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 first-shock earthquakes are grouped into bins characterized by magnitude and distance. Each earthquake is applied to a bridge to induce first-shock 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 (IM-EDP relation). This process is repeated for each first-shock 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 IM-EDP probabilistic seismic demand models for the virgin bridge and the bridge damaged in a first shock.

In Year 5 we have investigated a large number of ground motion IMs and bridge EDPs and identified a small number of optimal IM-EDP pairs. The primary IMs is the spectral acceleration at the fundamental period of the bridge (a period-dependent IM) and Arias Intensity (a period-independent IM). The primary EDPs are drift and curvature. Local EDPs, such as strain, did not produce optimal IM-EDP pairs.

Optimal IM-EDP 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 EDP-DM model developed by Eberhard at UW, and customary ground motion IM attenuation curves, we developed bridge EDP-hazard and DM-hazard curves, as well as customary fragility curves. Samples are shown below.

Larger View

A major project on the development of a risk-based 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 performance-based methodology and developed using sophisticated non-linear 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 post-earthquake operational state, repair time and cost, and aftershock collapse risk.

The first objective in Year 7 is to complete the aftershock and truck loading runs, render the results, and present the post-aftershock IM-EDP 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:

1. Hold a meeting of 10-12 PEER researcher involved in PEER bridge, in development of experimental databases, in development of bridge component fragility functions, and in validation of OpenSees deterioration elements. The objective of this meeting is to select a set of Decision Variables for further investigation.
2. Hold a meeting between PEER researchers and Caltrans engineers to present the set of Decision Variables and the DV-DM relations. Augment using Caltrans’ feedback.
3. Take part in the Tri-Center Bridge/Network Performance Workshop.

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.

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.

The milestones of this project are:

1. Propose a straw-man version of bridge post-earthquake operational state and bridge repair time/cost Decision Variables
2. Produce a document that clearly defines damage states that are relevant to the performance of bridges. This document will also classify bridge components according to the availability of fragility information and according to the perceived importance for bridge system fragility.
3. Parameterize the selected Decision Variables in terms of Damage Measures available form analytical or experimental databases. Develop the relevant DV-DM relations.
4. Use the PEER experimental database, and other sources to relate selected Damage Measures to Engineering Demand Parameters computed in Project 312 for simple bridge types. Develop the relevant DM-EDP relations.
5. Use the PEER total probability integral to integrate the components and produce fragility functions for the selected Decision Variables.
6. Perform post-earthquake collapse likelihood studies for simple bridge types using OpenSees deteriorating elements. Develop collapse fragility function for aftershocks (and if time permits) typical traffic loads.

Deliverables of this project are:

1. A document that defines a set of Decision Variables relevant of post-earthquake operation and performance of bridges. The definitions will include continuous or discrete ranges of such Decision Variables and their parameterization in terms of relevant Damage Measures.
2. A document that defines the approach to fragility function integration within the PEER total probability integral framework.
3. A document that transfers the compute fragility functions to PEER bridge testbed researchers.
4. A final report for the project that integrates the three documents and provides the background data necessary for interpreting the presented results.