Probabilistic modelling of auto-correlation characteristics of heterogeneous slopes

Spatial variability of soil materials has long been recognised as an important factor influencing the reliability of geo-structures. This study stochastically investigates the influence of spatial variability of shear strength on the stability of heterogeneous slopes, focusing on the auto-correlation function, auto-correlation distance and cross-correlation between soil parameters. The finite element method is merged with the random field theory to probabilistically evaluate factor of safety and probability of failure via Monte-Carlo simulations. The simulation procedure is explained in detail with suggestions on improving efficiency of the Monte-Carlo process. A simple procedure to create cross-correlation between random variables, which allows direct comparison of the influence of each strength variable, is discussed. The results show that the auto-correlation distance and cross-correlation can significantly influence slope stability, while the choice of auto-correlation function only has a minor effect. An equation relating the probability of failure with the auto-correlation distance is suggested in light of the analyses performed in this work and other results from the literature.