Seismic Vulnerability of the Highway System

Task B1-3: Fragility Curves for Seismically Retrofitted Bridges and Effect of Retrofit on Transportation Network Performance

Subject Area: Loss Estimation Methodologies 
Research Year 2

Principal Investigator(s) and Institution(s)

M. Shinozuka, University of Southern California


The purpose of this study is to develop fragility curves of Caltrans' bridges strengthened for seismic retrofit following the 1994 Northridge earthquake by means of steel and fiber reinforced composite (FRC) jacketing of bridge columns. Fragility curves in this study are represented by lognormal distribution functions with two parameters (fragility parameters consisting of median and log-standard deviation). The fragility curves for the retrofitted bridges will be obtained making use of the correlational relationship to be developed between the fragility parameters and the hysteretic parameters of bridge columns. A pair of these parameter sets will be developed from the fragility curves empirically derived for the Caltrans' bridges (without retrofit) from the Northridge earthquake damage data and hysteretic parameters, typically represented by hysteretic envelopes, computed for the same bridges. This relationship is assumed to be valid for the retrofitted bridges, for the purpose of developing their fragility curves from the corresponding hysteretic parameters. The fragility curves thus developed will be used to estimate the effect of the bridge retrofit on the seismic performance of Caltrans' transportation networks.


The Northridge earthquake inflicted various levels of damage upon a large number of Caltrans' bridges not retrofitted by column jacketing. Empirical fragility curves of these bridges were derived previously by this investigator in the form of two-parameter lognormal distribution and will be utilized in the analysis to be performed for the purpose of this study.

Three principal assumptions, all practical and reasonable, will be introduced for the tractability of this study as delineated below. First of all, it is assumed that hysteretic parameters of bridge columns, such as hysteretic envelopes which can be evaluated typically by means of the Colx computer code, will control the seismic capacity for bridges. A straightforward extension of this assumption leads to the second assumption that the fragility parameters can also be correlated to the hysteretic parameters. More specifically, this correlational dependence will be established in such a way that the median and log standard deviation of each fragility curve representing a damage state for a population of bridges are given as functions of hysteretic parameters. This correlational dependence will be developed by observing the relationship between the fragility curves empirically derived for Caltrans' bridges from the Northridge earthquake data and the hysteretic parameters computed for their columns not retrofitted. The third assumption contends that the same correlation is valid for the relationship between the fragility curves for the Caltrans' bridges retrofitted by jacketing and the hysteretic parameters of the jacketed columns. The latter will be computed in the same way as for the columns not retrofitted and provide the fragility curves for the retrofitted bridges through the postulated correlation. These fragility curves will be utilized in the transportation network analysis to evaluate the effect of the bridge column retrofit in terms of the enhancement of the network performance. The network performance will be measured in the form of reduction either in the drivers' delay or in the related economic loss, as also studied previously by this investigator.


Technical report and progress reports.

Technical Challenges

To deal with the uncertainty involved in correlational relationship between fragility and hysteretic parameters.


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