Reliability analysis of contaminant transport in saturated porous media

Abstract

An approach to probabilistic modeling of contaminant transport based on the first‐ and second‐order reliability methods (FORM and SORM) is presented. FORM and SORM were initially developed for structural reliability applications to estimate the occurrence of low‐probability events. They can be readily used with both analytical and numerical models and do not require restrictive assumptions about the problem geometry or about the properties of the media. Sensitivity information is obtained as an integral part of these analyses and is used to identify the variables or parameters which have a major influence on the estimate of probability. Example reliability analyses of one‐ and two‐dimensional transport are used to illustrate the approach, and the accuracy of the reliability methods is evaluated in comparison with Monte Carlo simulations. The results show that FORM increasingly overestimates the probability of exceedance as the spatial variability of the domain increases. SORM, on the other hand, accounts for the nonlinearity of the limit state surface and gives results consistent with Monte Carlo simulation over a range of coefficient of variation of K from 0.1 to 0.7. In addition, the FORM/SORM analyses are shown to provide a computational advantage over the Monte Carlo simulation for low‐probability events, because the computational effort is independent of the probability and the results also include sensitivity information. Finally, an example application of system reliability using FORM and SORM shows that problems with multiple limit state surfaces can be readily analyzed and the computational effort is proportional to the number and complexity of the limit state functions.