To avoid the deficiency of a single failure criterion and deterministic thresholds of limit states in seismic fragility analysis of underground structures, a method of fuzzy seismic fragility analysis of underground structures considering multiple failure criteria is proposed by combining fuzzy-random theory and copula theory. In this method, probabilistic seismic demand and capacity analyses based on different failure criteria are first performed. Then, the fuzziness of the limit states of different failure criteria is characterized by using membership functions, and the fuzzy seismic fragility of underground structures considering a single failure criterion with different membership functions is further calculated. On this basis, the copula function and the combination of membership functions are optimized to characterize the correlation between multiple failure criteria and establish fuzzy seismic fragility curves considering multiple failure criteria. Taking the Daikai subway station as the background, the effects of different failure criteria and the fuzziness of limit states on the seismic fragility are discussed, and the optimal combination of membership functions that characterizes the fuzziness of limit states under the failure criteria of deformation and strength is also presented. The results show that the failure criteria and fuzziness of limit states have significant effects on the seismic fragility of underground structures, and the combination of trigonometric membership functions is the optimal combination that characterizes the fuzziness of multiple failure criteria. Moreover, the fuzzy seismic fragility of underground structures considering multiple failure criteria is more sensitive to the fuzziness of limit states under frequent earthquakes and basic earthquakes, while the multiple failure criteria and the correlation between different failure criteria have more significant effects on the fuzzy seismic fragility considering multiple failure criteria under rare earthquakes and extremely rare earthquakes.

针对地下结构地震易损性分析中单一破坏准则和极限状态确定性阈值的不足，结合模糊随机理论和Copula理论，提出一种考虑多种破坏准则的地下结构模糊地震易损性分析方法。在该方法中，首先执行基于不同失效准则的概率地震需求和能力分析。然后，利用隶属函数表征不同破坏准则极限状态的模糊性，并进一步计算考虑不同隶属函数的单一破坏准则的地下结构的模糊地震易损性。在此基础上，优化Copula函数和隶属函数组合，刻画多失效准则之间的相关性，建立考虑多失效准则的模糊地震易损性曲线。以大开地铁车站为背景，讨论了不同破坏准则和极限状态模糊性对地震易损性的影响，并在变形和强度破坏准则下，表征极限状态模糊性的隶属函数的优化组合还提出了。结果表明，破坏准则和极限状态的模糊性对地下结构的地震易损性有显着影响，三角隶属函数组合是表征多种破坏准则模糊性的最优组合。此外，考虑多重破坏准则的地下结构的模糊地震易损性对频繁地震和基本地震下极限状态的模糊性更加敏感，而多重破坏准则以及不同破坏准则之间的相关性对模糊地震易损性的影响更加显着。考虑罕见地震和极其罕见地震下的多种破坏标准。