Estimating Failure Probabilities for California Levees

The probability of failure of California Delta levees was estimated using simple statistical procedures, based heavily on empirical data. Forty‐four islands were included in the study, and it was found that the probability of failure was strongly linked to the thickness of peat beneath the levees. When the islands were grouped according to peat thickness, it was found that sufficient historical levee failure data was available to estimate the average probability of failure for all the islands in a given peat thickness group. The relative probabilities of failure for the islands within a group were then estimated using slope stability analysis and simple statistical methods. For each island a Factor of Safety Index (FSI) was computed for ranges in water level outside the levee and a range of values of the strength parameter, $\varphi \prime \text{.}$ The water level was statistically characterized by the Gumbel Distribution and $\varphi \prime$ by a Normal Distribution. The probability that the FSI would fall below some critical value was used to rank the probabilities of failure for islands within a peat thickness group.