Influence of heterogeneity on the reliability and failure of a long 3D slope

The influence of heterogeneity of undrained shear strength on the performance of a long slope cut in clay is investigated. Random field theory is used to model the heterogeneity and finite elements are used to compute the slope response. These have been used within a Monte Carlo simulation to compute reliability as a function of global factor of safety. It is shown that three failure modes are possible, depending on the ratio of the horizontal scale of fluctuation to the slope size, as characterised by its height and length. For very small values of this ratio, the slope fails along its entire length and the result is similar to a conventional 2D analysis based on the mean strength. For intermediate values, discrete failures are likely and reliability is a function of slope length. For large values of the ratio, the variability takes on a layered appearance and the result is equivalent to a 2D stochastic analysis. The validity of the boundary conditions is examined by analysing slopes of different length. It is shown that simple probability theory may be linked with stochastic analysis and finite elements to give efficient solutions for some large 3D problems.