Risk Analysis of Instability Failure of Earth–Rock Dams Based on the Fuzzy Set Theory

Determining the anti-sliding instability risk of earth–rock dams involves the analysis of complex uncertain factors, which are mostly regarded as random variables in traditional analysis methods. In fact, fuzziness and randomness are two inseparable uncertainty factors influencing the stability of earth–rock dams. Most previous research only focused on the randomness or the fuzziness of individual variables. Moreover, dam systems present a fuzzy transition from a stable state into a failure state. Therefore, both fuzziness and randomness of the influencing factors should be considered in the same framework, where the instability of an earth–rock dam is regarded as a mixed process. In this paper, a fuzzy risk model of instability of earth–rock dams is established by considering the randomness and fuzziness of parameters and the failure criteria comprehensively. We obtained the probability threshold of instability risk of earth–rock dams by Monte-Carlo simulation after the fuzzy parameters were transformed into interval numbers by cut set levels. By applying the proposed model to the instability analysis of the Longxingsi Reservoir, the calculation results showed that the lower limits of risk probability under different cut set levels exceeded the instability risk standard of grade C for earth–rock dams. Compared with the traditional risk determination value, the risk interval obtained with the proposed methods reflects different degrees of dam instability risk and can provide reference for dam structure safety assessment and management.