A Seismic Demand Model for Bridges Based on IM and EDP Parameter Matching and Bidirectional Optimization

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.

Fragility Analyses of Bridge Structures Using the Logarithmic Piecewise Function-Based Probabilistic Seismic Demand Model

Seismic fragility analysis is an efficient method to evaluate the structural failure probability during earthquake events. Among the existing fragility analysis methods, the probabilistic seismic demand model (PSDM) and the joint probabilistic seismic demand model (JPSDM) are generally used to compute the component and system fragility, respectively. However, the statistical significance behind the parameters related to the current PSDM and JPSDM are not comparable. Aside from that, when calculating the system fragility, the Monte Carlo sampling (MCS) method is time-consuming. To solve the two flaws, in this paper, the logarithm piecewise functions were used to generate the PSDM and the JPSDM, and the MCS was replaced by the univariate conditioning approximation (UCA) method. The concepts and application procedures of the proposed fragility analysis methods were elaborated first. Then, the UCA method was illustrated in detail. Finally, fragility curves of a steel arch truss case study bridge were generated by the proposed method. The research results indicate the following: (1) the proposed methods unify the data sources and statistical significance of the parameters used in the PSDM and the JPSDM; (2) the logarithmic piecewise function-based PSDM sensitively reflects the changing trend of the component’s demand with the fluctuation of the seismic intensity measure; (3) under transverse seismic waves, major injuries happen on the side bearings of the bridge, while slight damage may occur on each pier, and as the seismic intensity measure increases, the side bearings are more likely to be damaged; (4) for the severe damage and the absolute damage of the studied bridge, the system fragility curves are closer to the upper failure bounds; and (5) compared with the MSC method, the accuracy of the UCA method can be guaranteed with less calculation time.

Seismic Response Analysis and Evaluation of Laminated Rubber Bearing Supported Bridge Based on the Artificial Neural Network

Laminated rubber bearings are commonly adopted in small-to-medium span highway bridges in earthquake-prone areas. The accurate establishment of the mechanical model of laminated rubber bearings is one of most critical steps for the bridge seismic response analysis. A new constitutive model of bearing based on the artificial neural network (ANN) technique is established through the static cyclic test of laminated rubber bearings, considering the bearing initial stiffness, friction coefficient, and other parameters such as the bearing sectional area, height, loading velocity, vertical load, and aging time. Combined with the ANN method, the ANN-based bridge seismic demand model is built and applied to the rapid evaluation of the bridge seismic damage. The importance of the bearing affecting design factors in the bridge seismic demands are ranked. The results demonstrated that the dimensions of the bearing and vertical load are the main factors affecting the bearings constitutive model. Based on the partial dependency analysis with the ANN-based bridge seismic demand model, it is concluded that the height of bearing is the key design parameter which affects the bridge seismic response the most. The ANN seismic demands model can fit the complex function relationship between various factors and bridge seismic response with high precision, so as to achieve the rapid evaluation of bridge seismic damage.