Rational Polynomial Technique in lope‐Reliability Analysis

Abstract

This paper is concerned with the application of a numerical technique, known as the rational polynomial approximation, to the first‐order second‐moment method for calculating statistical moments of a performance function in reliability analysis. The approach is used for slope reliability analysis within the framework of limit equilibrium considering two recognized methods of analysis (i.e. the 1965 generalized procedure of slices of Morgenstein and Price and the 1979 Sarma method). It is shown that the rational polynomial technique works well for the first‐order second‐moment method of slope reliability analysis based on two rigorous methods of limit equilibrium involving nonexplicit performance functions. The calculation can always be made with confidence whether the performance function is explicit or inexplicit, linear or nonlinear. Two illustrative examples are presented in this paper: one for a homogeneous slope and the other for a slope in layered soil. The results for the reliability index are compared with two other methods, the point‐estimate method and Monte Carlo simulation method. In the past, such comparisons have generally been made only for slope‐stability models involving explicit performance functions.