Fuzzy seismic fragility analysis of gravity dams considering spatial variability of material parameters

Due to the heterogeneity of massive concrete and unevenness of pouring process, concrete strengths in gravity dams show obvious spatial variability. In addition, since the evolution of damage states for gravity dams is a gradually transitional process, the threshold between adjacent damage states is ambiguous. A mathematical model for describing the fuzziness of damage states threshold is presented. And a methodology for fuzzy seismic fragility analysis of gravity dams considering spatial variability of material parameters is proposed by combining nonlinear dynamic analysis of dam-reservoir-foundation system, Hariri-Ardebili's damage quantification method and an approach for simulation of random field of material parameters. The seismic fragility of gravity dams was investigated to illustrate the proposed methodology. It is found that the spatial variability of concrete tensile strength leads the seismic damage of the dam to be spatially varying as well. The damage of dam body intensifies and the probability of exceeding for each damage state increases. The fuzzy seismic fragility curves are insensitive to the types of membership function (linear, mountain and polynomial). Due to the influence of frequency distribution of damage index, the effects of variation in the size of the fuzzy interval of threshold on seismic fragility curves are different. The probability of exceeding of each damage state for gravity dams obviously increases when the spatial variability of tensile strength and fuzziness of damage states threshold are considered simultaneously.