Seismic design optimization of two-defense-line restraining system for unbonded laminated rubber bearing supported highway bridges accounting for maximum credible earthquakes

The sliding of girder or bearing of the unbonded laminated rubber bearing (ULRB) supported highway bridge can protect its substructure from earthquake-induced damage but could cause a considerable girder displacement even unseating. This study develops a two-defense-line restraining system, consisting of a transverse steel damper (TSD) and sliding-shear-failure-dominated shear key, to reduce the girder's peak displacement and unseating risk. A practical trilinear mechanical model is proposed to describe the force-displacement behavior of the shear key and validated by comparing it with a series of test data available in the literature. Furthermore, a systematic and user-friendly seismic design optimization methodology for the ULRB-supported bridge with the two-defenseline restraining system is proposed in this study, considering different intensity levels of ground motions, especially for a maximum credible earthquake with a return period of 10000 years. The performance requirements for the ULRB-supported bridge equipped with the two-defense-line restraining system associated with different ground motion intensity levels are specified. After that, a response surface method (RSM) combined with the weighted sum method (WSM) is proposed in this study to optimize the mechanical parameters of the two-defense-line restraining system, realizing an optimal performance of different structural components and balancing the displacement demand of the girder and the force demand of substructure. Finally, this seismic design optimization methodology is implemented through a case study and proved to be feasible.