Implementation and validation of a simple probabilistic tool for finite element codes

Both a circular slip surface stability calculation (Bishop or Fellenius) and a FEM calculation
(c-phi reduction) produce a safety factor but not a probability of failure or reliability index. The mayor problem with the probabilistical calculations is that variable soil parameters create a correlated and therefore also variable failure mechanism. The question is how much the value of the calculated probability of failure is influenced by this correlation. The Monte-Carlo method leads, because of the many slip surface calculations, to the most accurate calculation of the probability of safety. The disadvantage of this method is that it is far too time consuming for daily FEM calculations. The idea is therefore to replace the Monte-Carlo approach by another approach with only a limited amount of calculations. In this paper several methods are discussed and validated. An indication is given about the error, the number of necessary stability calculations and the optimal estimation points for an additional stability calculation. In this way a minimum number of FEM calculations is needed to obtain a certain desired accuracy.