Stochastic evaluation of heterogeneous slope stability

The influence of heterogeneity of undrained shear strength is investigated for simple slope stability problems, by linking finite elements and random field theory within a Monte Carlo framework. In particular, simple probabilistic and stochastic approaches are compared for various slope geometries. It is shown that simple probabilistic models give problem-independent solutions and, for practical levels of reliability, may give over-conservative estimates of structural response. In contrast, the consideration of spatial variability (in stochastic models) leads to problem dependent solutions and economy of design. It is shown that anisotropy of the heterogeneity is an important component of a stochastic analysis, and that it takes on an increased importance for flatter slopes, due to the greater tendency for failure mechanisms to develop along semi-continuous weak zones. However, for many cases, it may he reasonable to assume an infinite scale of fluctuation in the horizontal direction. Stochastic analysis leads to reliability, rather than a single factor of safety. Significantly, it can be used to determine reliability-based characteristic values in line with modern design codes such as Eurocode 7.