System reliability of slope stability

In stability problems, the failure probability associated with the critical slip surface is known to be smaller than that for the system that comprises all potential slip surfaces. The difference depends on the correlation between the failure probabilities of the different slip surfaces. Calculations of the upper bound of the probability of system failure were made for the Congress Street cut, in Chicago. The computed upper bound of the probability of system failure is about twice the failure probability for the critical slip surface. The failure probabilities for the slip surfaces that pass through the two clay layers near the bottom of the cut have about the same value. Because of the assumption that the strengths of these layers are statistically independent, the safety factor of a slip surface that passes through the upper clay layer but not the lower one is poorly correlated with that of a slip surface that passes through both layers. This leads to a large difference between the failure probability o...