Accumulative Residual Deformations And Influencing Factors Of High-speed Railway Bridge Piers Subjected To Multiple Earthquakes

In recent years,with the rapid development of high-speed railway in our country,the construction regions of high-speed railway is gradually transformed to the midwest,resulting that more high-speed railway bridges were located in the seismic active field.When subjected to multiple earthquakes,the bridges may experience accumulative residual deformations,adversely affecting the geometry of track and operation of high-speed vehicles.In this paper,a nonlinear finite element model with fiber elements is developed based on the flexibility method in OpenSees,taking into account the bending deformations and bond-slip behaviors of reinforcement.The developed model is implemented to analyze the accumulated residual deformations of round-ended piers in a simply supported bridge under different seismic sequences.The factors influencing the accumulated residual deformations are investigated.The main contents and conclusions are summarized below.(1)Based on the analysis of the characteristics of ground motions and the accumulated damage of structures under multiple earthquakes,the limit values of residual deformations specified in domestic and foreign related codes.A review of the computing method,the influencing factors and measures of residual deformations after ground motions are presented.Research achievements and drawbacks of the existing studies on accumulated structural damage are reviewed.(2)The overall framework and the main functions details of OpenSees program are introduced.And the computational principles and applicable conditions of stiffness-based beam-column element,flexibility-based beam-column element and flexibility-based plastic hinge beam-column element are also analyzed.Besides,on the basis of mastering the different properties of concrete constitutive relations of ConceteOl,Concrete04 and ConcreteO1 WithSITC,the steel constitutive relations of Stee102 and the Bond_SP01 constitutive relations between concrete and steel Bond_SP01,the selection principles of these constitutive relations in OpenSees program are determined.Thus,a nonlinear numerical analysis model based on flexibility-based beam-column element is proposed to calculate the residual deformations and cumulative damage effect of bridge pier.(3)Based on a quasi-static test and the shake table tests under single earthquake and multiple earthquakes,the comparison of the hysteretic curves,skeleton curves,equivalent stiffnesses,residual deformations and maximum deformations are calculated using the testing data and nonlinear numerical analysis model.The results calculated by nonlinear numerical analysis model agree well with the experimental results.That validates the effectiveness and reliability of the numerical model based on flexibility-based beam-column element under quasi-static analysis and dynamic analysis.Then,the nonlinear fiber element model of pier with 32m height of high-speed railway bridge with Concrete04 and Steel02 constitutive relations is established to calculate the accumulated residual deformations.(4)Mainshock-aftershock seismic sequences are formed using real seismic ground motions following the Gutenberg-Richter rule and the Joyner-Boore empirical formula.Repeated seismic sequences are formed by single ground motion.On the basis of the nonlinear numerical model of bridge pier,the elastic-plastic time-history analyses of the high-speed railway bridge pier under the above two seismic sequences and single earthquakes are conducted.The time history curves of the top displacements of pier under multiple earthquakes are obtained.Then,the residual deformation after earthquake is extracted and the accumulated residual deformations curves are drawn.The values of accumulated residual deformations computed under multiple earthquakes and the sum values computed under single earthquake are compared.The results show that accumulated residual deformations of pier increase with the number of earthquakes under mainshock-aftershock seismic sequences.Structural damage under mainshock-aftershock seismic sequences is more serious than that under the main shock.The cumulative effects of residual deformation under aftershock cannot be ignored.Under repeated seismic sequences,the accumulated residual deformations of piers increase nonlinearly with the number of earthquakes.After the accumulated residual deformations of piers reaching the inflection point at 30～60 mm,the accumulative rate increase suddenly and the pier may failure at any time.The swarm type of earthquake is more dangerous to structures.(5)The residual deformation ratios,N10andN17.5(the number of ground motions when the residual deformation ratio reaches 10‰ and 17.5‰)are used as the indexes to evaluate the cumulative residual deformations.Under repeated seismic sequences,the accumulated residual deformations of piers are affected by the peak ground acceleration,longitudinal reinforcement ratio,and axial compression ratio.The results show that the indexes decrease with the ground acceleration and axial compression ratio,and increase with the longitudinal reinforcement ratio.Suggestions are proposed for seismic designs and health monitoring.