Seismic resilient design of rocking tall bridge piers using inerter-based systems

Seismic resilient design of tall bridge piers with rocking foundation by using inerter-based systems is investigated in this work. A simplified model is developed in OpenSees to simulate the rocking bridge pier equipped with a tuned viscous mass damper (TVMD) system, wherein nonlinearity of the pier response is incorporated through a distributed-plasticity fiber-based section approach; the rocking behavior is simulated through elastic-no-tension spring elements located at the foundation interface of the pier as per FEMA 356 recommendations; an equivalent model comprising a rotational mass linked with the two terminals of the TVMD through appropriate constraint conditions is utilized for modeling the inerter-based system. Optimal design parameters of the TVMD are determined through an extensive parametric analysis, aiming to minimize the tilt angle of the bridge pier. The effectiveness of the selected design parameters of the TVMD on the seismic mitigation performance of rocking tall piers is then investigated numerically. Besides, guidelines are proposed for the design of TVMD parameters in engineering practice based on these analytical results. Nonlinear time-history analysis is conducted under both far-field and near-fault motions, followed by seismic fragility analysis for the overturning damage state, assuming the peak ground acceleration as intensity measure and the dimensionless tilt angle as the engineering demand parameter. The parametric analysis results show that the TVMD is less efficient for near-fault motions, due to reduced energy dissipation capacity caused by pulse-type feature. Additionally, the optimal parameters obtained from parametric analysis could be generalized to a higher number of seismic excitations, achieving a similar seismic performance, which indicates robustness of the TVMD. The TVMD is found able to reduce the tilt angle at the rocking interface especially during strong earthquake events, consequently increasing the overturning sta- bility of rocking foundations adopted for tall bridge piers.