Fuzzy risk-based technique for the design of an ogee spillway in a diversion dam based on hydrological return period discharge and the resistance-load theory

Abstract

This paper provides a Fuzzy methodology based on calculating the hydrological return period discharge and the resistance-load theory for designing an ogee spillway in a diversion dam. Hence, the uncertainties of rainfall intensity, catchment runoff coefficient, and spillway discharge coefficient are endowed with triangular Fuzzy numbers (TFNs), describing possible values the uncertain parameters may have. To do so, the rational formula and, later, the spillway discharge equation are analyzed here to obtain the Fuzzy products of the peak runoff and spillway discharge capacity. On the basis that both must match, the risk is calculated using the difference between the obtained Fuzzy product quantities with three Fuzzy arithmetic operations. It is observed that the standard approximation closely tracks the result of the alpha-cut (exact) method, providing a time-saving tool for Fuzzy calculations. Since the return period (T) and risk of failure are related quantities, the spillway dimensions are calculated for several recurrence intervals, assuming risk equal to 1/T. Then, the Fuzzy approach is compared with the conventional return-period approach for the design of an ogee crest in three experimental catchments in Iran with adequate historical data. The result indicates that the Fuzzy technique outperforms the conventional return-period approach for designing an ogee spillway, obtaining an average 29% larger spillway dimension in all case studies. Beyond that, the Fuzzy procedure is applied to another catchment with short rainfall-runoff data, which is impossible to implement the conventional return-period method for the hydrologic design of an ogee spillway.