Multidimensional seismic fragility analysis of subway station structures using the adaptive bandwidth kernel density estimation and Copula function

• A framework of multidimensional seismic fragility analysis for subway stations is proposed. • The correlation between different seismic demands is considered in this analysis. • The Copula theory and adaptive bandwidth kernel density estimation are combined to formulate a bivariate seismic fragility function. • An optimal Copula function is employed with respect to the squared Euclidean distance. Structural damages during an earthquake are typically controlled by seismic demands, which are represented by the combination of amplitude of ground motion and cyclic load effects. Since traditional methods normally assume the lognormal distributions of seismic demands and resistance parameters, uncertainties are inevitably induced in the seismic fragility analysis. In this paper, the Copula function and adaptive bandwidth kernel density estimation method (ABKDE) are used to establish a novel multidimensional seismic fragility analysis framework. Based on the results of incremental dynamic analysis for subway station structures, ABKDE is adopted to establish single-parameter seismic fragility curves for both the maximum inter-story drift ratio (MIDR) and cumulated dissipated hysteretic energy (CDHE), respectively. Subsequently, the Copula function is used to formulate a bivariate seismic fragility function considering the correlations among seismic demand measures and establish the corresponding fragility curves. Finally, comparative analyses are conducted to evaluate seismic fragility curves using Copula-based dual and single-parameter damage models as well as the traditional damage models. It is found that the seismic fragility analysis method using the Copula function has the ability to gain a comprehensive consideration of the MIDR and CDHE during the damage process of subway station structures. Moreover, this newly developed seismic fragility analysis framework can capture the influence of the correlation between deformation and energy under various peak ground accelerations on structural damage. Thus, this framework can provide a scientific basis for predicting structural damage in subway stations subjected to varying intensities of ground motion while considering multiple damage indicators.