Probabilistic Slope Stability Assessment with Adaptive Monte Carlo Importance Sampling

In the Netherlands, levee segments are assigned a maximum allowable annual probability of flooding. One of the failure mechanisms leading to flooding is instability of the inner slope of the levee. The stability of a levee is generally assessed with a Limit Equilibrium Model (LEM), with calculation times ranging from a few to tens of seconds for a single model run. The LEM has to be coupled with a probabilistic method in order to assess whether target failure probabilities are complied with. Crude Monte Carlo Sampling results in unacceptably long calculations times as in practice, times up to an hour are tolerated. The First Order Reliability Method on the other is faster but often not robust enough due to convergence problems for stability analyses. In this paper, we adopt and apply an efficient and robust algorithm, the Adaptive Monte Carlo Importance Sampling. The approach consists of several loops of MC-IS calculations, in which the design point of one loop is the center of the importance distribution of the next loop. The approach is suited for unsupervised execution and parallelization. We develop decision and convergence criteria to guide when to break a loop and start a new loop or stop the calculation. This approach has now been successfully applied in several levee reinforcement projects. We highlight one of these applications for a selected case study and discuss the lessons learned.

Keywords: Reliability, Importance Sampling, Slope Stability, Levees, Application.