| China is situated between two major seismic zones,and seismicity often occurs.As an important national infrastructure and transportation hub,the bridge structure is prone to damage under earthquake,which has a great impact on transportation.Therefore,seismic risk assessment of bridge structures is more important.As an important part of seismic risk assessment,seismic vulnerability analysis has been studied extensively at home and abroad,but there are still some shortcomings.As a new analytical tool,Copula theory not only simplifies the construction process of the joint distribution function but also considers the non-linear correlation among variables,which provides a convenient and accurate way for bridge vulnerability model.In this paper,the seismic vulnerability model of bridges is studied based on Copula theory.The main research contents are as follows:(1)Taking a three-span simple-supported small box girder bridge as a reference bridge,the distribution function of bridge material parameters and structural parameters is determined,and750 bridge samples are obtained by Latin hypercube sampling method.In order to fully consider the uncertainties of earthquake ground motion,750 seismic waves are randomly selected from the seismic database,and then modified,truncated and filtered.The processed seismic waves are matched with the bridge samples one by one for non-linear dynamic time history analysis.According to the seismic damage of bridges in the past,piers,abutments,and supports are considered as vulnerable components of bridges under seismic action.Referring to previous research,the damage index and damage limit state value of bridge vulnerable components are determined.(2)In order to fully consider the uncertainty of seismic capacity of bridge components and the correlation between seismic intensity index and seismic demand of components,the corresponding function is defined according to reliability theory.By using Copula function and maximum likelihood estimation method,the joint probability distribution function of component function value and the ground motion intensity index is established.The best Copula function is selected to describe the relevant structures under different damage states through the goodness of fit test values of AIC,BIC and OLS criteria.Based on the existing joint distribution function,the damage level of bridge components and systems under different earthquake intensity is calculated.In order to facilitate the comparison and analysis with traditional methods,the least square method is used to estimate the parameters of the vulnerability frequency points,and the relevant parameters of the bridge vulnerability function are obtained under the condition of lognormal distribution.(3)The seismic vulnerability analysis method based on probabilistic seismic demand model and the estimation method based on the maximum likelihood principle is used to analyze the vulnerability of bridge components and systems respectively.The seismic vulnerability of bridges based on Copula function and the calculation results of traditional methods are compared.By the comparison of the results from different calculation methods,it is found that the Copula function can gives a better describe of the non-linear correlation between seismic demand and seismic intensity index.Furthermore,due to the edge distribution function and correlation can be constructed separately,the construction of a joint distribution function model is simpler and the damage state of bridge structure can be evaluated more accurately. |
