Viscoelastoplastic and incremental analysis of bridge with functional bearing

The functional bearing is one kind of the seismic isolation merging the advantages of the sliding system and the bearing system and it is widely used in Taiwan. To evaluate the performance of the functional bearing in a bridge effectively, a simple but accurate model is appreciated. The present paper attempts to model a bridge with functional bearing taking into account that the rate-dependent pier with hardening behavior. The proposed model is viscoelastoplastic and contains four phases including a viscoelastic-sticking, a viscoelastic-sliding, a viscoplastic-sticking, and a viscoplastic-sliding phase. The theoretical analysis in the state-space space enables us to obtain an exact solution for each phase. In order to simulate the exact behavior of the bridge system, the phase switching criteria with four conditions are derived and four computing modules for computations in four phases as well as four pull-back modules to direct toward to an exact module are developed. The four-phase model and the exact arrangement of computation qualitatively and quantitatively provide the exact duration of each phase and the proper indices for the plastic degradation of the pier as well as the consumption of the friction interface. One comparison between the simulation and the experimental result of a bridge's shaking table test demonstrates the accuracy of the proposed model and its algorithm for the response of the bridge with functional bearing. Three numerical demonstrations show the performance of the proposed incremental analysis and the capability of the proposed model to distinguish the behavior of the bridge system under the near-fault and the far-fault earthquake. The duration of each of the four phases is accurately determined and the plastic degradation of the pier as well as the consumption of the friction interface are exactly evaluated. The difference of the behavior of the bridge system under the near-fault and the far-fault earthquake is qualitatively and quantitatively recognized.