Precise seismic fragility analysis holds significant importance in the evaluation of seismic resilience for underground structures. However, the conventional seismic fragility analysis of underground structures usually ignores the hybrid epistemic uncertainties caused by the limited samples of both seismic demand and thresholds and deterministic boundaries between different limit states, which can inevitably cause errors in the seismic resilience evaluation of underground structures. Thus, focusing on the quantification of epistemic uncertainties, this paper aims to propose an approach to seismic fragility evaluation of underground structures considering hybrid epistemic uncertainties of both seismic demand and capacity. In this approach, the analytical formulation of seismic fragility considering the fuzziness of limit states is firstly derived via adopting the entropy equivalence method. Then, the non-parametric Bootstrap method and maximum entropy principle, as well as the Copula theory are combined to establish a probability model characterizing the statistical uncertainties of both seismic demand and capacity. On this basis, the variability of failure probability of underground structures is quantified, and the envelope fuzzy seismic fragility is obtained. Moreover, the influences of the coupling effect of statistical uncertainty and fuzziness on the seismic fragility of underground structures are also analyzed in this paper. The results show that the seismic fragility of underground structures based on limited samples of both seismic demand and thresholds and deterministic boundaries between different limit states has significant variability, and the variability degree of fragility is various under different ground motion intensities. Besides, the envelope fuzzy seismic fragility curves can effectively reflect the coupling effect of statistical uncertainty and fuzziness and adequately characterize the variability of estimated seismic fragility, which can provide a more accurate basis for seismic resilience evaluation of underground structures.

中文翻译：

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一种考虑地震需求和容量的混合认识不确定性的地下结构地震脆性评价的新方法


精确的地震脆性分析在评估地下结构的抗震能力中具有重要意义。然而，常规的地下结构地震脆性分析往往忽略了地震需求和阈值样本有限以及不同极限状态之间的确定性边界所引起的混合认识不确定性，这不可避免地导致地下结构的抗震韧性评价出现误差。因此，本文着眼于认识不确定性的量化，旨在提出一种考虑地震需求和容量的混合认识不确定性的地下结构地震脆性评估方法。该方法首先采用熵等效法推导了考虑极限态模糊性的地震脆性解析公式。然后，将非参数 Bootstrap 方法和最大熵原理以及 Copula 理论相结合，建立了表征地震需求和容量统计不确定性的概率模型。在此基础上，量化了地下结构破坏概率的变异性，得到了包络模糊地震脆性。此外，本文还分析了统计不确定性和模糊性耦合效应对地下结构地震脆性的影响。结果表明：基于地震需量和阈值的有限样本以及不同极限状态之间的确定性边界的地下结构地震脆性具有显著的可变性，在不同地震动强度下脆性的可变程度是不同的。 此外，包络模糊地震脆性曲线能有效反映统计不确定性和模糊性的耦合效应，并充分表征了估计地震脆性的变化性，可为地下结构的地震韧性评价提供更准确的依据。