Engineers Australia

Probabilistic methods for slope analysis and design

William Gibson


Probabilistic methods combined with risk assessment are a better way to assess slope design in open pit mines compared to deterministic methods. These methods are suitable for use on evaluation of risk or when there is uncertainty in the input parameters.

Probabilistic analyses require more computer power than deterministic analysis. In many case a probabilistic analysis requires ten to thousands more computer resources than an equivalent deterministic analysis. Methods like Monte Carlo simulation (MC) may require thousands of analyses depending on the number of variables considered in the model. Other methods like First Order Second Moment (FOSM) or Point Estimate Method (PEM) and may require tens to hundreds of analyses.

Monte Carlo simulation is applied routinely today on simple analyses like wedge stability or limit equilibrium analysis; current computers can carry thousand of analyses in a relatively short period of time. This is not the case when more complex models are built like 3D models at mine scale including complex mining sequences, or dynamic analysis of a 3D model. Large scale models can run for hours even in fast computers. Where the Monte Carlo method is not an option other alternative methods should be used.

This paper compares four different methods and presents the equations required to use a Modified Point Estimate Method (mPEM) presented by Harr (1989). The methods are compared using simple examples in the paper. Recommended probabilities of failure for open pit design are also presented.