Finite element analyses of slope stability problems using non-associated plasticity

In daily engineering practice the factor of safety in slope stability analysis is still often determined by means of simple limit equilibrium methods such as the methods of slices. However, since displacement based finite element analysis is routinely applied for assessing displacements and stresses for working load conditions, this calculation technique is also increasingly being used to compute ultimate limit states and consequently factors of safety. This is usually done by so-called strength reduction technique. This paper compares the performance of strength reduction finite element analysis with finite element limit analysis, where the latter approach provides rigorous upper and lower bounds on the factor of safety. The main focus of the paper is related to non-associated plasticity. The results indicate that the flow rule may have a larger influence on the factor of safety as commonly assumed. It is shown that displacement based finite element analysis using a strength reduction technique suffers from numerical instabilities when using non-associated plasticity especially when dealing with materials with high friction angles but moderate dilatancy angles. Finite element limit analyses on the other hand are restricted to associated flow rules. Suggestions to overcome this problem have been proposed but it turns out that these result in conservative values of the FoS for slope stability problems and therefore an improvement of this approach is presented in this paper. Another outcome of the performed studies is that the numerical instabilities of displacement based finite element analysis, when modelling non-associated material behaviour, can be avoided by using this modified procedure.