An algorithm in generalized coordinate system and its application to reliability analysis of seismic slope stability of high rockfill dams

Abstract

This paper introduced generalized coordinate system into reliability analysis involving correlated random variables. Correlation between two random variables is reflected by rotation of the corresponding coordinate axes and correlation coefficient between the two variables is identical to cosine of angle between the axes. The equivalent matrix formulation for the Hasofer–Lind reliability index represents the shortest distance from the failure surface to the origin in the generalized coordinate system of standardized normal variables. A simple optimization algorithm for reliability computing was established based on the perspective of reliability index and the gradient of limit state function in generalized coordinate system. Based on the algorithm and the Ordinary method of slices, a probabilistic approach for evaluating the seismic slope stability of high rockfill dams was developed and was applied to the slope reliability analysis of an actual high rockfill dam under seismic loading. The results of the slope reliability analysis are discussed and conclusions are presented in this paper.