Probabilistic modelling of auto-correlation characteristics of heterogeneous slopes

Abstract

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.

Keywords:

• factor of safety
• slope
• stability
• random field
• spatial variability
• cross-correlation

Acknowledgements

The authors sincerely thank Professor Gordon A. Fenton, Department of Mathematics, Dalhousie University, Canada, and Professor Mike Hicks, Technical University of Delft, The Netherlands, for helpful discussions and suggestions. The Department of Geotechnics, Universitat Politécnica de Catalunya (UPC), Barcelona, Spain is acknowledged for providing Code_Bright and for technical assistance in using the code.

Additional information

Funding

This research was financially supported by the Scottish Funding Council through the Glasgow Research Partnership in Engineering (GRPE).