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.

Análise probabilística da contaminação da água subterrânea usando métodos de confiabilidade de primeira e segunda ordem

“…Essa defasagem estimulou estudos na área de modelagem probabilística e estocástica do fluxo de água subterrânea e transporte de contaminantes nas últimas décadas (SITAR et al, 1987;JANG et al, 1994;HAMED, 1996;LI et al, 2005;BAALOUSHA;KÖNGETER, 2006) por meio de diversos métodos, dentre eles a simulação de Monte Carlo (SMC) e métodos de confiabilidade.…”

“…No transporte de contaminantes o evento de falha pode ser definido como a ocorrência de uma concentração observada (Cobservada) acima de uma concentração limite, Cobjetivo, para um tempo máximo pré-estabelecido, tanálise (SITAR et al, 1987;JANG et al, 1994;HAMED, 1996;LI et al, 2005;BAALOUSHA;KÖNGETER, 2006). Assim a função de performance torna-se:…”

Sensitivity-Based Reliability Analysis of MEMS Acceleration Switch

“…However, the accuracy and efficiency of FORM is low when there are large number of random variables involved. For example, Jang et al (1994) found that when the number of random variables are more than 100, MCS was more efficient than FORM.…”

“…Recently, FORM has been used in water resources engineering (Skaggs & Barry, 1997;Jang, Sitar & Kiureghian, 1994) and nuclear engineering (Cizelj, Mavko & Oppermann, 1994). In FOSM, the performance function is linearized about the mean value, which is the reason that method is not accurate and optimal for reliability analysis.…”

Polynomial Response Surfaces for Probabilistic Risk Assessment and Risk Control via Robust Design

“…These secants (polynomials) approximate the model over the entire parameter space in a weighted least-square sense (compare with the best unbiased ensemble linearization approach described by Nowak (2009)). This is more beneficial to computing a tangent or local second derivatives (compare FORM, SORM methods, e.g., Jang et al (1994)) that approximate the model well just around one point in the parameter space.…”