Application of the endurance time method to the seismic analysis and damage evaluation of a continuous rigid-frame bridge

The endurance time method (ETM) is a novel dynamic analysis method in which artificially intensified accelerograms characterized by the increase in seismic intensity with time are used as loading inputs. In this method, various dynamic responses, i.e., ranging from elastic to failure, under seismic excitations of different intensity levels are estimated with a reduced dynamic calculation effort. Based on these merits, this study investigated the accuracy and effectiveness of ETM in predicting the seismic responses and damage to continuous rigid-frame bridges considering the real internal force state (called element initial strain state) of the completed bridge. In detail, first, a typical irregular continuous rigid-frame bridge was selected as the target of the analysis, and its finite element model considering the real construction process was established by MIDAS/Civil. Then, the real internal force state considering the 10-year concrete shrinkage and creep was determined through construction phase analysis, and a dynamic analysis model considering the real internal force state was built via OpenSees utilizing the equivalent load method. Subsequently, the incremental dynamic analysis results under natural ground motions were obtained and compared with the results of the ETM, and the applicability of the ETM to obtain seismic responses rapidly and accurately was verified. Finally, the seismic responses of pier displacement, girder displacement, and pounding force were analyzed using the ETM, and the damage to piers was evaluated using the displacement ductility factor and Park–Ang damage index. The results indicate that ETM can predict the time when a continuous rigid-frame bridge reaches a certain damage status under the real internal force state of the completed bridge. Moreover, the damage to the main-bridge pier is smaller than that of the approach-bridge pier when the endurance time is short. However, when the endurance time is long, the opposite is true.