Authors: Valerio, M; Clayton, C; D’Ambra, S; Yan, C

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Valerio, M, Clayton, C, D’Ambra, S & Yan, C 2013, 'An application of a reliability based method to evaluate open pit slope stability', in PM Dight (ed.), Proceedings of the 2013 International Symposium on Slope Stability in Open Pit Mining and Civil Engineering, Australian Centre for Geomechanics, Perth, pp. 457-471,

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The stability of open pit rock slopes is commonly assessed using deterministic methods. A single value for the Factor of Safety of the slope is calculated, and is assumed to represent the overall stability of the slope. A limitation of the deterministic approach is that it does not account for the natural variability of the input parameters or the uncertainty caused by sampling. The uncertainty and variability of input parameters such as frictional strength, cohesive strength, and discontinuity orientations are often accounted for by selecting values that incorporate conservatism based on limited laboratory testing or other data collection methods. The confidence in the Factor of Safety calculated using deterministic analyses remains a matter of engineering and experiential judgment. Reliability based methods, now adopted by many practitioners, overcome some of the limitations of deterministic methods by incorporating the natural variability of key input parameters into the calculation methods. If the natural variability is included, then a range of Factors of Safety can be calculated for the various combinations of the input variables. This range represents the probability density function of the continuous distribution of Factors of Safety, from minimum to maximum values. The cumulative distribution of values can then be used to quantitatively describe the likelihood of achieving a certain Factor of Safety. Understanding the distribution of Factors of Safety, and the reliability of the results, provides a method to make reliability based decisions. This paper presents a feasibility level study undertaken for Diavik Diamond Mines Inc. using point estimation methods in combination with limit equilibrium methods to evaluate the Factor of Safety of a proposed open pit slope. Point estimation involves the use of sample statistics to estimate population parameters. Confidence intervals are constructed that include the value of an unknown variable—in this case Factor of Safety—with high probability. The confidence intervals are developed based on the method of moments from probability theory, which is used to describe random variables of the sample population using the expected value of the random variable and the square of the expected value. A Monte Carlo random sampling method is used to develop a simulated population to approximate a normal distribution, which in this case represents the probability of slope performance defined in terms of the Factor of Safety. This paper describes the process followed to develop the probability density and cumulative distribution functions for the Factor of Safety. The statistical distribution of Factor of Safety is presented and is used to evaluate the pit slope stability in terms of probability of failure and acceptable risk tolerance.

Barton, N.R. and Choubey, V. (1977) The shear strength of rock joints in theory and practice, Journal of Rock Mechanics, Springer, Vol. 10(1−2), pp. 1–54.
Harr, M.E. (1989) Probabilistic estimates for multivariate analyses, Journal of Applied Mathematical Modelling, Elsevier, Vol. 13(5), pp. 313−318.
Hoek, E., Carranza-Torres, C. and Corkum, B. (2002) Hoek-Brown Failure Criterion – 2002 Edition, in Proceedings Mining and Tunnelling Innovation and Opportunity, R. Hammah, W. Bawden, J. Curran and M. Telesnicki, Fifth North American Rock Mechanics Symposium, 7–10 July 2002, Toronto, Canada, University of Toronto Press, Toronto, Vol. 1, pp. 267–273.
Jennings, J.E. (1972) An approach to the stability of rock slopes based on the theory of limiting equilibrium with a material exhibiting anisotropic shear strength, Stability of Rock Slopes, in Proceedings Stability of Rock Slopes, E.J. Cording (ed), 13th US Symposium on Rock Mechanics, 30 August–1 September 1971, Urbana, USA, American Society of Civil Engineers, Reston, pp. 269–302.
Khalokakaie, R., Dowd, P.A. and Fowell, R.J. (2000) Incorporation of slope design into optimal pit design algorithms, Journal of Mining Technology, Maney Publishing, Vol. 109(2), pp. 70–76.
McCracken, G. (1983) Probabilistic Analysis of Slope Stability at a Large Quartzite Quarry, in Proceedings Surface mining and quarrying, Second International Surface Mining and Quarrying Symposium, 4–6 October 1983, Bristol, UK, Institution of Mining and Metallurgy, London, pp. 13–20.
Oracle (2013) Crystal Ball, at .
Palmstrom, A. (1995) Appendix 1, On Joints and Jointing, RMi – a rock mass characterization system for rock engineering purposes, PhD thesis, Oslo University, Norway, 400 p.
Rocscience Inc. (2013) RocData version 4.0, .
Rosenblueth, E. (1975) Point estimates for probability moments, in Proceedings of the National Academy of Sciences of the United States of America, National Academy of Sciences of the United States of America, Vol. 72(10) October 1975, pp. 3812−3814.
Steffen, O.K.H. (1997) Planning open pit mines on a risk basis, Journal of the South African Institute of Mining and Metallurgy, South African Institute of Mining and Metallurgy, Vol. 97, pp. 47‒56.
Terbrugge, P.J., Wesseloo, J., Venter, J. and Steffen, O.K.H. (2006) A risk consequence approach to open pit slope design, Journal of the South African Institute of Mining and Metallurgy, South African Institute of Mining and Metallurgy, Vol. 106(7), pp. 503‒511.
Thornton, S.I. (1995) Slope Reliability, MBTC FR 1014, Civil Engineering Department, University of Arkansas.
United States Geological Survey (2005) MODFLOW-2005, .

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