Seismic Pounding Analysis Of Bridge Based On Precise Pounding Algorithm

The investigation of earthquake damage shows that the collision phenomenon of bridge structure in earthquake and the structural damage caused by collision are very common.In order to get the reasonable analysis results,the adjacent beam collision effect is one of the factors that must be considered in the seismic response analysis of bridge structures.Collision is a typical state nonlinear problem.Due to the limitation of the algorithm,the accuracy of the traditional implicit or explicit integration method only have two or three order.In the case of bridge seismic pounding analysis,a very small time step is set in order to improve the convergence of the pounding analysis.However,It also makes the time consuming much longer.The precise integration method is an explicit recursive method,which has high accuracy independent of the time step and unconditional stability.In this paper,the method is introduced into the seismic pounding analysis of bridge,and a precise pounding algorithm is developed to analyze the multi point seismic collision of the elastic and plastic structures as well as the practical application is carried out.The main research work is as follows:1.The seismic responses of structures are divided into two states: separation and collision,and total dynamic equilibrium equations and incremental dynamic equilibrium equations are established respectively.The precise integration method for total dynamic equilibrium equation,incremental dynamic equilibrium equation and collision dynamic equation is derived.In view of the characteristics of elastoplastic collision,time history analysis is implemented by means of a combination of total equations’ precise integration method and incremental equations’ precise integration method.And further more,the transformation of elastic-plastic state and separation-collision state is solved.A precise pounding algorithm is designed by setting different time step size to seperation stage and collision stage.And then the calculation program is coded in the Matlab software.2.Based on the precise pounding algorithm,A multipoint collision response spectrum program has been coded.A SDOF model with two sides pounding is defined,and the concept of pounding force spectrum and pounding times spectrum is proposed.According to the principle of wave selection based on displacement spectrum,14 waves of I~III site were selected.The pounding force spectrum and pounding times spectrum considering two sides pounding of I~III site were carried out.The influence rule of change parameters,such as the stiffness of the contact element,the coefficient of the collision recovery,the gap of the expansion joint,the damping ratio of the bridge,the period ratio of the main span and approach span,the yield displacement of the bridge pier to the pounding force spectrum and pounding times spectrum are studied.And the study indicate the direction for structural pounding control.3.In order to improve the shortcomings of multiplied caculation and storage caused by "increasing dimension and decreasing order" method,the newmark precise integration method and Wilson-θ precise integration method are researched furtherly.In addition,a series solution of nonhomogeneous term is given for the sake of avoid system matrix inversion.For the time-varying stiffness problem,a total iteration method and incremental iteration method are proposed.The feasibility of the proposed algorithms are verified by examples.It is found that the accuracy of Newmark precise integration method and Wilson-θ precise integration method are sensitive to time step size,and the accuracy of Wilson-θ precise integration method is the worst.4.Based on the FEM of beam structures,the precise pounding algorithm is further applied to the seismic pounding analysis of complex bridge structures.Therefore,the 3-D contact-friction element model is improved,and handling principles of nonlinear effects caused by material,bearing,damper,pounding etc.are discussed in this paper.5.A space rigid frame model is suggested for equivalent the space flexibility of pile-group foundation.Firstly,the flexibility of pile-group foundation should be caculate with “m”method.And then the formulas to caculate geometrical parameters include height of the rigid frame,length and width of the column section,distance between the columns are deduced.These parameters can confirm a rigid frame exclusively.6.Based on the precise pounding algorithm of beam structures,the case study of longitudinal and lateral seismic pounding analysis of urban bridges are carried out.In the case of ramp bridge widening retrofit,the influence of collision and lateral connection on bridge’s displacement and internal force response is discussed.In another case,which is the reconstruction of multi span continuous beam bridge,the influence of different bearing type on the seismic response of bridge structures is studied.The research results have some reference meaning for the lateral widening of ramp bridge and the pounding control of multi span long bridge.