Adaptation of Finite Element Models for Probabilistic Design

Both a circular slip surface stability calculation (Bishop or Fellenius) and a Finite
Element Method calculation (c-phi reduction) produce a safety factor but not a probability of
failure or reliability index. A Monte-Carlo method leads, because of the many slip surface
calculations, to the most accurate calculation of the probability of safety, but this method is far too time consuming for daily FEM calculations. The idea is therefore to replace the Monte-Carlo
approach by a First Order Reliability Method (FORM), based on a limited number of FEM
calculations. A possible problem with this FORM is, that variable soil parameters create a
correlated and therefore variable failure mechanism. However, FORM gives an indication of this
non-linear behaviour and in most cases an accurate probability of failure of the structure can be
calculated. This article gives a complete example of the calculation of the probability of failure of a dyke ring along a river, based on a limited number of Phi-C reduction calculations with Plaxis. The input data for this calculation is based on a limited number of given soil test data.