Comparison of Risk Calculation Methods for a Culvert

Abstract

A comparative study of eight different risk calculation methods has been performed on the occurrence probability of inad- equate capacity of a culvert to pass floods. The five basic risk calculation methods used in this study are the mean-value first-order second-moment method, advanced first-order second-moment method, point estimate method, Latin hypercube sampling method, and Monte Carlo simulation. Two options each for the point estimation and Monte Carlo methods are also investigated. Building upon the first four basic calculation methods, three additional methods are suggested. They are the first-order second-moment mixed mode method, generalized mixed mode method, and significant component method. Within each of the first four basic methods risks are calculated, whenever possible, using two definitions of failure parameter, i.e., ~1! the performance function Z directly as a function of all the contributing variables; and ~2! separate calculations of loading and resistance ~capacity!. Logic trees are presented to illustrate possible causes of culvert failure, the ways to account for component factors such as those from hydraulics and hydrology and to combine the component risks for total risk. Risk of inadequate flow capacity for a five-foot diameter culvert is evaluated as an example. Three sets of uncertainty data for the random variables are used; the first set data is adopted from a study in the literature, in which uncertainties from loading dominate. The second set of data is hypothetical with resistance uncertainties as the major contribution to failure; whereas in the third set, loading and resistance have about equal contributions of uncertainties. The relative errors of computed risks with respect to Monte Carlo simulation results are compared. The results show that for conditions similar to those tested, most of the methods are computationally simpler than the Monte Carlo simulation, and can be used for risk calculation. Cautions to some of the methods are remarked.