Probability-based residual displacement estimation of unbonded laminated rubber bearing supported highway bridges retrofitted with Transverse Steel Damper

Abstract

Predicting the post-earthquake residual displacement of isolated bridges is crucial in deciding their operational and recovery strategies after a seismic event. This study proposes a probability-based approach to estimate the residual displacement of a trilinear hysteretic system representing the unbonded laminated rubber bearing (ULRB) supported highway bridge retrofitted with transverse steel dampers (TSDs), considering the uncertainty of structural parameters and the variability of ground motions. To this end, this study systematically derives the quasi-static residual displacement of a trilinear hysteretic system, and presents the statistical distribution model for the related structural parameters, especially for the pier height and the TSD model parameters. After that, the dynamic residual displacement property of the ULRB supported highway bridge retrofitted with TSDs is investigated considering the uncertainty of various parameters, including model parameters of TSD and ULRB, the mass of superstructure, the height of piers, as well as the ground motions with and without pulse. The maximum possible residual displacement of the trilinear hysteretic system is then related to its quasi-static residual displacement and peak displacement demand. Finally, an innovative probability-based approach is developed in this study to estimate the conditional probability of the dynamic residual displacement of the trilinear system exceeding a threshold at the given ground motion intensity, and this innovative approach is further validated by comparing it with the incremental dynamic analysis (IDA) method. Results show that the dynamic residual displacement of the TSD retrofitted ULRB supported highway bridge system is random, and the ratio between the dynamic residual displacement and the maximum possible residual displacement approximately satisfies a uniform distribution bounded by zero and one. The probability-based approach can obtain a close result with the IDA method and significantly reduce computational efforts. This research represents a first step toward developing a rapid post-earthquake assessment approach for seismically isolated bridges and the seismic design of these bridges considering the residual displacement.