Efficient seismic fragility analysis of structures from dynamic reliability perspective

Abstract

Seismic fragility analysis of structures quantitatively describes the relationship between the failure probabilities of structures and ground motion Intensity Measures (IMs). Generally, two steps are involved: (1). calculating the failure probabilities of the structure under consideration at a set of IM levels; (2). regressing the IM levels and the corresponding failure probabilities to obtain a bunch of fragility curves. In this paper, a new method is proposed for seismic fragility analysis of structures from a dynamic reliability perspective, where efficiency and accuracy are emphasized. First, the dynamic reliability of structures under fully non-stationary ground motions is presented, where the Fractional Exponential Moments-based Maximum Entropy Method (FEM-MEM) is applied to derive the extreme value distribution with high efficiency. In this method, only a total of 89 samples of fully non-stationary ground motions generated by the spectral representation method and consistent with the design response spectrum that are sufficient in the FEM-MEM for efficient dynamic reliability computations are required. Then, a four-parameter distribution model, which exhibits high flexibility, is used to recover the fragility curves. A two-step strategy is developed for parameter estimation based on four failure probabilities at four different IM levels. In addition, a strategy for selecting a small number of IM levels for all damage states is also suggested, which improves the computational efficiency. Two numerical examples, including a seven-story nonlinear shear frame structure and a five-story three-span frame structure designed according to Chinese codes, are investigated to verify the effectiveness of the proposed method, where the results obtained from the traditional lognormal distribution are also compared.