A slope may have many possible slip surfaces. As sliding along any slip surface can cause slope failure, the system failure probability of a slope is different from the probability of failure along an individual slip surface. In this paper, we first suggest an efficient method for evaluating the system failure probability of a slope that considers a large number of possible slip surfaces. To obtain more insights into the system failure probability of a slope, we also propose a method to identify a few representative slip surfaces most important for system reliability analysis among a large number of potential slip surfaces and to calculate the system failure probability based on these representative slip surfaces. An equation for estimating the bounds of system failure probability based on the failure probability of the most critical slip surface is also suggested. The system failure probability is governed by only a few representative slip surfaces. For a homogenous slope, the failure probability of the most critical slip surface is a good approximation of the system failure probability. For a slope in layered soils, the system failure probability can be significantly larger than the failure probability of the most critical slip surface.
Reliability analysis of slopes considering spatial variability of soil properties based on efficiently identified representative slip surfaces
