Risk assessment in hydraulic engineering projects: uncertainties and reliability

Abstract

This article presents the procedure and application of several methods of risk and reliability analysis to a simple problem, such as the discharge capacity of a sewer. The analysis considers that the three variables of roughness, diameter, and slope have normal probability distributions and are applied for comparing direct integration methods; the Monte Carlo Method; Mellin Transform, with first-order variance estimation; Rosenblueth's and Harr's Point Estimation Method; the First Order Second Moment Method (MFOSM); and two versions of the Advanced First Order Second Moment Method (AFOSM): Hasofer-Lind's and Tang's. The result of the probability of failure obtained with the direct integration method is taken as true (which is not possible in complex analyses, especially when uncertainties are significant) and results are compared. Most methods can be applied, and it is possible to obtain reliable estimations when the methods come close to linear behaviors, but when the variables are not linear or when uncertainties increase significantly, the accuracy of some methods deteriorates rapidly. Such is the case of the MFOSM method. For methods with samples with sizeable variables, the Monte Carlo method is the most commonly applied, but the reliability of the method converges when there is a large number of simulations, and the final result of the probability of failure is strictly unknown; another important limitation is that the number of variables may cause the problem not to have a practical solution. Methods where point estimation is used (Rosenblueth and Harr) may be very attractive from a computational perspective in as much as the number of variables increases and may seem to be good to use, since they offer similar results to those obtained with the Monte Carlo method and the direct integration method. However, if uncertainties are significant, there may be meaningful differences. The MFOSM method is applicable only in very simple cases where the behavior function is clearly defined and there is variable linearity; however, it rapidly looses accuracy in complex problems. The MFOSM method is quite applicable and can take into account uncertainties in case the analyst decides to make correlations of the variables that intervene in the problem and that most of the times are associated with uncertainties. This seems to be a great advantage over the other methods, since it is possible to involve variables that are many times ignored or undervalued because they cannot be analyzed. The Hasofer Method seems to be quite appropriate for simple problems; however, the Tang Method is quite attractive for analyzing the failure limit state of the problem studied.