Estimation of failure probabilities for intersections of non-linear limit states

This paper is concerned with estimating the failure probability associated with the intersection of two or more non-linear limit state functions. Previous work has relied on the use of general non-linear minimization routines to establish the intersection point of the limit states and then to use tangents to bound the region for estimating the failure probability. The present paper outlines two approaches based on successive approximation both to find the intersection point and to estimate the intersection probability. It is shown that the results for selected examples converge to the probabilities estimated using Monte Carlo analysis. Comments about extending the results to using second order or asymptotic probability estimates close the paper.