Reliability-Based Underseepage Analysis in Levees Using a Response Surface–Monte Carlo Simulation Method

Present methods for assessing the potential for unsatisfactory levee performance because of underseepage consist of deterministic seepage analyses and simplified reliability methods. Deterministic methods consist of calculating factors of safety based on the ratio of the critical gradients of the soil and hydraulic exit gradients without taking into account high levels of uncertainty in soil properties and subsurface geometry that are inherent to many levee analyses. The most common simplified reliability approaches currently being used to analyze levees against underseepage apply the first-order second-moment Taylor series method, using the U.S. Army Corps of Engineers blanket theory equations as the performance functions. In many cases, these methods do not realistically reflect the geometry of the levee’s foundation soils and the uncertainty associated with their performance. This study proposes a new application for the response surface method that allows modeling the initiation of erosion process with more accurate failure mechanisms and more complex subsurface geometry. The response surface–Monte Carlo (RSMC) simulation method uses finite-element analyses to develop a series of equations that define the relationship between the variables and the factor of safety ($F$). Using these equations, probability density functions (PDF) for variables, and the computer program @Risk, a Monte Carlo simulation is performed to calculate the conditional probability of unsatisfactory performance because of underseepage for a given river flood level. Two examples are presented to illustrate the proposed procedure. Multiple regression analyses are performed to assess the relative effect that changes in the input variables have on the $F$ for the various analyses. The results suggest that uncertainty in the levee geometry has the greatest effect on the variation of the $F$ for the cases studied.