Incorporation of Cost-Benefit Analysis Considering Epistemic Uncertainty for Calculating the Optimal Design Flood

Design flood via flood frequency analysis provides basic information for designing hydraulic structures. Quantification of uncertainty in flood frequency analysis has become an important issue during the past three decades. However, few studies have considered practical procedures for selecting a single design flood in the uncertainty range. Cost-benefit analysis can be incorporated to select a single design flood by calculating the optimal value in the total expected cost function. In particular, in this study, the relationship between conventional flood frequency analysis and cost-benefit analysis is addressed. Additionally, the parameter uncertainty is quantified by the Metropolis-Hastings algorithm to find the optimal design floods considering parameter uncertainty. The annual maximum (AM) series and partial duration (PD) series were used to identify the effect of various types of data. The optimal design floods obtained by the cost-benefit analysis considering parameter uncertainty were systematically larger than the design flood obtained by the conventional flood frequency analysis. Regarding the types of data, the generalized Pareto distribution (GPD) had the largest values in all return periods, while the Gumbel distribution had the smallest values in all cases.

     

Probability of pipe breakage regarding transient flow in a small pipe network

A reliability model was developed for the calculations of the probability of pipe breakage associated with transient effect. The statistical distribution for the maximum pressure wave heights was determined from the results of 168 transient analyses. It was found that the statistical distribution for internal pressure among the random variables of reliability function is well matched with the Gumbel distribution. The probability of pipe breakage in a small pipe network was calculated according to pipe diameter, thickness, allowable stress, and internal pressure. From the results, it was found that transient effect significantly increases the probability of pipe breakage. Using the present reliability model, it could be possible to find a pipe that contains the high probability of pipe breakage in a water distribution system. If the reliability model developed in the present study is applied for the design, a safe design will be accomplished. Furthermore, it can be effectively used for the management and maintenance of a water distribution system.