On the Efficiency and Accuracy of the FORM Algorithm Applied to Nonlinear Models for Geotechnical Design

Reliability is frequently measured as a probability of failure related to a reliability index. Many approximate methods have been developed so far for the assessment of this index, and among these methods, the first order reliability method known as FORM is considered to be one of the most efficient computational methods. In fact, over the past three decades contributions from numerous studies have made it a worldwide used technique in structural reliability. As this approach is only an approximation, the divergence from other methodologies of reference may be important in nonlinear problems, and convergence difficulties have been further identified. In this paper two matrix methodologies for implementation of the FORM algorithm are discussed in the light of efficiency and accuracy, considered the errors caused by transformations into equivalent normal random variables. Particularly, the influence of skewed distributions of nonnormal random variables in the performance of the FORM algorithm is focused. The results obtained from two nonlinear models for geotechnical design with correlated nonnormal random variables show that whenever the performance function is efficiently expressed by suitable transformations in the standard normal space instead of the original space, the accuracy of the FORM algorithm may be improved, particularly in the presence of important nonlinear behaviour of highly skewed output functions if considered skewed distributions of nonnormal random variables.