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Probabilistic Methods for Slope Analysis and Design

William Gibson
Thursday, September 1, 2011
First presented: 
Australian Geomechanics, Vol 46, No 3, September 2011
Published paper
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 analysis 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.

Feature Author

William Gibson

William Gibson has over 30 years’ experience in geotechnical, mining and civil engineering projects as well as in development of computer programs.  His expertise in open pit mining includes slope stability analysis for Chuquicamata, Esperanza and Pelamberes (Chile), Olympic Dam (Australia) and Oyu Tolgoi (Mongolia).  He has expertise in the analysis of interaction between open pit and underground mining operations.  William’s experience in underground mine design includes analysis of block caving mines, mining sequence, open stoping, stability of pillars and interaction of block caving operations with mine facilities.  William is experienced in the analysis of static and seismic conditions, having undertaken seismic risk assessments in parts of South and Central America and Canada.  His computer programming experience includes finite elements and discontinuous deformation analysis programs; and programs for rock fall 3D analysis (RFall_3D), probabilistic wedge stability analysis (MWedge_P), rock mass strength assessment and gravity flow analysis (MFlow) and generation of artificial earthquakes for dynamic analysis (Crono). 

Principal Consultant (Geotechnical Engineering)
MSc (Geotechnical Engineering)
SRK Perth
SRK North America