Efficient Probabilistic Algorithm Illustrated for a Rock Slope

A new spreadsheet-based algorithm for the first-order reliability method (FORM) is illustrated for a two-dimensional rock slope of Hong Kong. The new algorithm combines inverse distribution functions and a refined Newton method with the automatic constrained-optimization search of the design point in the original space of the random variables; it obviates the need for computations of equivalent normal means and equivalent normal standard deviations. In the rock slope analysis, the versatile 4-parameter beta distribution is used in lieu of a truncated normal distribution. Probabilities of failure inferred from reliability indices are compared with those from Monte Carlo simulations. The effects of parametric correlations on the required reinforcing force for a target reliability index value are studied. The intuitive perspective of an expanding equivalent dispersion ellipsoid in the original space of the basic random variables is also described as it is the basis from which the new approach evolved.