Interval risk analysis for gravity dam instability

Fuzziness and randomness are two inseparable uncertainty attributes of most factors influencing stability of gravity dam. Moreover, there is a fuzzy transition from stability status into failure status. Risk analysis and fuzzy mathematics are conducted to evaluate the stability problems of gravity dams, where the process of stability failure is studied as a fuzzy event. Membership functions are used to describe the extent of stability failure risk for gravity dams. The fuzziness of both the design parameters and failure criterion are accordingly eliminated through a transformation by use of the concept of the Level Set. Corresponding analysis procedures are then provided to calculate the fuzzy risk and its probability of the stability failure for gravity dams. Based on a real dam section, a detailed example is further provided to illustrate the proposed risk analysis approach. The results show that it is feasible to apply the present method to analyze the fuzzy risk of stability failure for gravity dams. The modeling approach is sound and the findings do improve the current understanding of this important problem. The conventional risk is a determinate value but the proposed fuzzy risk is an interval value. The obtained conclusions can reflect more reasonably the actual dam engineering.