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The accuracy of seismic demand models in seismic vulnerability analysis of structures or components mainly depends on the seismic intensity measures (IMs) and engineering demand parameters (EDPs). This paper proposes a novel method to obtain the optimal seismic demand model for the seismic vulnerability analysis of bridges. The method obtains the IM-EDP combination by matching all IMs and EDPs within a wide range one by one, considering the contribution of multiple IM parameters to the seismic response of the structure and avoiding the blindness of EDP selection. The IM is determined by calculating Pearson correlation coefficient and partial correlation coefficient, controlling the correlation between EDP and IM (or IMs) to a minimum to reduce the multicollinearity within the vector IMs and avoid ill-conditioned models. The optimal seismic demand model is obtained by inspecting the scatter plot and residual plot of suboptimal seismic demand models determined from all combinations by guaranteeing efficiency and sufficiency. The efficiency of seismic demand models is guaranteed by controlling the root mean square error (RMSE) and the coefficient of determination (R2). The sufficiency of models is guaranteed by controlling the slope of fitted line. A continuous rigid frame bridge with double thin-walled piers is used as a case study and a dynamic time-history analysis is performed to obtain the seismic vulnerability of bridge with the proposed method. The results show that the proposed method is feasible and ideally suited for optimizing seismic demand model. [ABSTRACT FROM AUTHOR]

Accurate prediction of barge impact force contributes greatly to the research of the soundness of the bridge under barge impact. Toward this end, the calculation method of barge impact force caused by ship-bridge collision is investigated in this study. Firstly, a comparative analysis for different energy conversion relationships is conducted via the high-precision finite element method (HPFEM) and the coupled vessel impact analysis (CVIA). A construction method of nonlinear spring stiffness (NSS) is proposed therefrom. Secondly, a high-precision finite element model is developed to simulate the barge-bridge collision under different barge masses and impact velocities. NSS under each condition is obtained, and the influences of barge mass and impact velocity on NSS are further discussed. An NSS model considering the effects of impact mass and impact velocity is proposed. Lastly, based on the NSS model, a prediction method of barge impact force is introduced. The results show that the impact mass has little influence on the peak value of NSS; however, the impact mass and impact velocity have a great influence on the tail of the NSS curve. According to the characteristics of NSS, four key control points can be extracted and NSS is simplified into a polyline model. The NSS model of the barge is obtained by nonlinear response surface fitting. The impact force can be predicted by combining the simplified NSS model and the proposed method in this study. The proposed method in this paper does not consider the pier stiffness; hence, it can be combined with NSS to quickly estimate the impact force, which can provide a design basis for the impact force in ship-bridge collision design. The rigid wall and a continuous rigid frame bridge impacted by the barge are studied; the results show that the proposed method can reasonably estimate the impact force. [ABSTRACT FROM AUTHOR]

Piers and bearings influence each other in earthquakes, and the failure of any component will affect the whole function of bridges. Thus, it is critical to consider the correlations between multiple components in the seismic vulnerability analysis of the overall bridge system. In this paper, a method of overall seismic vulnerability analysis with nested copula model was proposed to model the correlations between multiple components. The components were combined according to their types to construct the hierarchical structure of the system. The correlation of components was modeled with copula functions, and the nested copula model of the system was eventually developed. Maximum likelihood estimation and goodness-of-fit test were used to select and optimize the copula functions. The overall seismic vulnerability of the multispan bridge system was established using the nested copula model. A four-span continuous rigid frame bridge was used to illustrate the application of the proposed method. The results show that the nested copula model accurately simulated the correlations between multiple components, which would eliminate the overestimation or underestimation by the first-order boundary method. [ABSTRACT FROM AUTHOR]