Fuzzy seismic fragility analysis of underground structures considering multiple failure criteria

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.