Dynamic Reliability-based Theory And Application For The Seismic Performance Probabilistic Analysis Of High-Pier Bridges

Due to the excellent spanning ability and topography adaptability,high-pier and long-span continuous rigid frame bridges(CRFB)have become one of the most common birdges of highway and railway to cross a river and valley in western regions of China.As is well known,western regions of China are typical earthquake prone areaes.Earthquake has become the most important factor threatening high-pier CRFB.Due to uncertainties of ground motions and bridge structure itself,as well as the nonlinearity of bridge structure when subjected to disastrous earthquake events,the existing methods can not accurately evaluate the seismic performance of the bridge from the perspective of probability.It is required to estatblish a set of bridge seismic reliability analysis method that keeps the tradeoff of the accuracy and efficiency,and can consider the influence of multiple complex factors such as bridge structure nonlinearity,bridge structure and ground motion uncertainties.The method can evaluate the seismic performance of high-pier CRFB from the perspective of probability,so as to provide guidance for the seismic design and reinforcement decision-making of bridge structures.It has very significant theoretical significance and engineering application value.This study is committed to establishing an efficient numerical method for seismic reliability analysis of complex-nonlinear bridge structures under non-stationary random earthquake excitaitons.Based on this,the seismic reliability analysis of high-pier and long-span CRFB is carried out.The effects of seismic and structural uncertainties on the seismic performance of high-pier and long-span CRFB are also studied in detail.The main research work and results of this study are as follows:1.A fourth-order moment method for the first-passage seismic reliability evaluation of strongly nonlinear structures under small failure probability level is proposed.In the proposed method,a flexible four-parameter distribution,namely the shifted generalized lognormal distribution,is introuced to estimate the extreme value distribution(EVD)of structural nonlinear seismic response under random earthquakes.Then,the solution of structural first-passage probability under stochastic earthquakes is transformed into the calculation of fourth-order extreme moment of structural nonlinear seismic response.To deal with the problem that the the high-order central moments,i.e.skewness and kurtosis,of the the extreme value of seismic response of strongly nonlinear structures is difficult to be evaluated,a partial stratified sampling method based on number-theory method and minimum distance maximization criterion is proposed.The first four-order central moments of the extreme value of structural nonlinear seismic response can be efficient calculated by the proposed method.Finally,numerical examples are provided and the accuracy,efficiency and stability of the proposed method are verified by comparing with the existing partial stratified sampling methods.2.A fractional moment method using the Box-Cox transformation(BCT)and the maximum entropy principle is proposed for the EVD and first-passage seismic reliability evaluation of nonlinear structures under stochastic ground motions.This method normalizes the extreme value samples of structural nonlinear seismic response by using the BCT.Then,the EVD of structural nonlinear seismic response under random earthquake is constructed by the maximum entropy principle(MEP)constrainted with fractional moments,which encapsulate information regarding numerous integer moments.An unbiased likelihood function is introduced into the MEP,so as to the iterative solution of the maximum entropy distribution model of random variables is transformed into the solution of linear equations.The method overcomes the drawback of the of the existing maximum entropy distribution model solution that is greatly affected by the initial value and is not easy to converge.Finally,a nonlinear single-degree of freedom hysteretic system and a two-span T-shaped rigid frame bridge are taken as examples to verify the proposed method.The results show that the proposed method can significantly improve the insufficient accuracy of the existing maximum entropy method in estimating the seismic reliability of structures at the level of small failure probability.3.Carried out the siemsic reliability analysis of high-pier and long-span CRFB under the response spectrum compatibled fully non-stationary ground motions.A typical high-pier and long-span CRFB is taken as a numerical example.The nonlinear dynamic analysis model of the bridge that consider the nonlinear behaviors such as the yield of pier,the failure of bearing,the abutment-soil-structure dynamic interation,and the collision between main beam and abutment,is established in Open Sees platform.The design response spectrum of ground motion is transformed into a compatible time-frequency evolution power spectrum.The seismic reliability of the CRFB under fully non-stationary earthquake is evaluated by the proposed fractional moment method.The effects of bridge structure uncertainty,seismic uncertainty and abutment-soil-structure dynamic interation on the seismic reliability of irregular high-pier and long-span CRFB are discussed.4.The pounding probability analysis method of irregular high-pier and long-span CRFB under spatially varing ground motions is established.The random function-based spectral representation method is introduced into the dimensionality reduction simulation of spatially correlated fully non-stationary ground motion.High-dimensional random variables in the spatially correlated ground motion simulation are reduced to three elementary random variables based on this framework.Then,the fractional moment method for structural seismic reliability analysis proposed in this paper is extended to estimate the demand of required separation distance of high-pier bridges under spatially variable ground motions to avoid seismic pounding.Therefore,the pounding probability analysis method of high-pier bridges considering the spatial variability of ground motion is established.The accuracy and efficiency of the proposed method are verified via Monte Carlo Simulation.The influence of the site effect of ground motion on the pounding probability of high-pier bridges is studied in detail.Meawhile,the required separation distance of expansion joint of CRFB corresponding to different exceedance probabilities under the uniform/spatially variable site conditions are estimated by the proposed method.