A Study On Seismic Fragility Analysis Of Bridge System Considering Dependence Among Components

The seismic demand of bridge structure is related to the amplitude, spectrum and duration characteristics of the ground motion, due to its complexity and randomness. It is difficult to describe the seismic characteristics by adopting a single seismic intensity measure. In addition, the bridge is in compound random vibration in respond to earthquake due to the influence of the random parameters in the structure. Therefore, the probability analysis method is more appropriate to be used in the seismic analysis of bridge structures.As an important part of full probability analysis, seismic fragility analysis is a key component of the performance-based earthquake engineering. However, the dependences among the seismic demands of components in the system influence the accuracy of the traditional fragility analysis. Therefore, it is necessary to accurately describe the dependences among seismic demands of each component in the seismic fragility analysis of bridge structure.The seismic performance of bridge structure will be reduced with service time due to the aging of materials. Moreover, component seismic demands also change with service time,which leads to the variation of their dependences among each other. Therefore,the changes in the seismic fragility of bridge system are becoming more complicated with time.In view of the above problems, the dissertation studies the following aspects:(1) The importance analysis method is introduced to sort the importance of stochastic parameters in structural seismic demand analysis and fragility analysis to overcome the limitation of local sensitivity analysis method. Variance-based importance and moment-independent importance measurements are solved with Monte-Carlo numerical method and kernel density estimation based integral method respectively. The influence of stochastic parameters on structural seismic demand and fragility is analyzed for small and medium span concrete bridge, and the stochastic parameters with significant influence on structural seismic demand and fragility are selected. Thus the number of samples for bridge seismic demand analysis and fragility analysis can be reduced, which will significantly improve the computational efficiency of structural seismic fragility analysis.(2) Distance analysis, rank correlation analysis and Pearson correlation analysis methods are presented to evaluate the applicability and composability of the ground motion intensity measures from the perspective of similarity, concordance and correlation,considering the diversity of ground motion intensity measurements. These methods are not limited to linear correlation analysis and have a wider range of application. A certain number of bridge analysis samples are developed by Latin hypercube sampling method based on parameters of uncertainty which significantly affect the structure obtained from the importance analysis. Ground motion-bridge samples are derived from randomly combining the bridge analysis samples with the seismic records obtained by interval grouping method.Combined with the probabilistic seismic demand analysis, a canonical correlation analysis method is proposed to analyze the overall correlation between ground motion intensity measures and component seismic demand parameters. The canonical correlation relationship between ground motion intensity measures and component seismic demand parameters is established, and the ground motion intensity measure parameters which are suitable for the seismic demand analysis of small and medium span concrete bridge are selected. Finally,these parameters are tested according to the evaluation criteria of efficiency, proficiency and sufficiency.(3) The Copula function is introduced to separate the correlation between component seismic demands and the marginal distribution function of each component, based on incremental dynamic analysis of small and medium span concrete bridge, thus simplifying the modeling of multivariate joint distribution function. The non-parametric kernel density method is employed to estimate the marginal distribution function and the related parameters in the Copula function. Then, the appropriate Copula function model is selected by the non-parametric kernel density and the minimum distance fitting method. Based on the seismic fragility of a single component, a bridge system fragility analysis method is proposed to consider the relationship of component seismic demands. Due to the limitation of single Copula function, a hybrid Copula function is constructed by Bayesian weighted average method to describe the upper and lower tail non-linear dependence structure among component seismic demands. The correlation parameters in mixed Copula function are estimated based on the rule of minimum of sum square variation. Finally, the Copula function method is verified by the comparison of system fragility curves obtained by Copula function, first order boundary method and Monte-Carlo method. The influence of dependence among component seismic demands on the seismic fragility of bridge system is discussed.(4) The degradation models of steel bar, concrete and rubber material is established based on Fick's second law and the aging law of rubber material. The time-varying characteristics of steel bar, concrete and rubber material are investigated. Ground motion-bridge samples obtained by Latin hypercube sampling and interval grouping method are then updated. The time evolution of component seismic demands and the time-varying fragility of single component are analyzed by incremental dynamic analysis method. The hybrid Copula function is introduced to describe the dependence structures among component seismic demands at different service time points. The time-varying characteristics of the dependence structures among component seismic demands are evaluated. Based on the time-varying fragility of the components and the time-varying dependence structures among them, an approach to develop the time-varying seismic fragility of bridge system is proposed. Regression analysis of the time-varying seismic fragility of the bridge system is performed by least square method based on the logarithmic normal distribution function and the time-varying law of the bridge system seismic fragility is also investigated, thereby the problem of excessive computation caused by Monte-Carlo method is avoided.