Considerations for Effectively Using Probability of Failure as a Means of Slope Design Appraisal for Homogeneous and Heterogeneous Rock Masses
Probability of failure (PF) often appears alongside factor of safety (FS) in design acceptance criteria for rock slope, underground excavation and open pit mine designs. However, the design acceptance criteria generally provide no guidance relating to how PF should be calculated for homogeneous and heterogeneous rock masses, or what qualifies a ‘reasonable’ PF assessment for a given slope design. Observational and kinematic methods were widely used in the 1990s until advances in computing permitted the routine use of numerical modelling. In the 2000s and early 2010s, PF in numerical models was generally calculated using the point estimate method. More recently, some limit equilibrium analysis software offer statistical parameter inputs along with Monte-Carlo or Latin-Hypercube sampling methods to automatically calculate PF. Factors including rock type and density, weathering and alteration, intact rock strength, rock mass quality and shear strength, the location and orientation of geologic structure, shear strength of geologic structure and groundwater pore pressure influence the stability of rock slopes. Significant engineering and geological judgment, interpretation and data interpolation is usually applied in determining these factors and amalgamating them into a geotechnical model which can then be analysed. Most factors are estimated ‘approximately’ or with allowances for some variability rather than ‘exactly’. When it comes to numerical modelling, some of these factors are then treated deterministically (i.e. as exact values), while others have probabilistic inputs based on the user’s discretion and understanding of the problem being analysed. This paper discusses the importance of understanding the key aspects of slope design for homogeneous and heterogeneous rock masses and how they can be translated into reasonable PF assessments where the data permits. A case study from a large open pit gold mine in a complex geological setting in Western Australia is presented to illustrate how PF can be calculated using different methods and obtain markedly different results. Ultimately sound engineering judgement and logic is often required to decipher the true meaning and significance (if any) of some PF results.
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 N. Bar & N. Barton, “The Q-slope method for rock slope engineering”, Int. J. Rock Mechanics & Rock Engineering, Springer-Verlag, Austria, 2017.
 N. Bar, T. M. Johnson & G. Weekes, “Using directional shear stress models to predict slope stability in highly anisotropic rock masses”, Rock Mechanics & Rock Engineering: From the Past to the Future, Taylor & Francis Group, London, 2016, pp. 595-600.
 N. Barton, “Review of a new shear-strength criterion for rock joints”, Engineering Geology Journal vol. 7, Elsevier, Amsterdam, 1973, pp. 287-322.
 N. Barton & V. Choubey, “The shear strength of rock joints in theory and practice”, J. Rock Mechanics vol. 10, Springer-Verlag, 1977, pp.1-54.
 N. Barton & S. Bandis, “Effects of block size on the shear behavior of jointed rock”, J. Rock Mechanics vol. 23, 1982, pp. 739-760.
 Z. T. Bieniawski, “Engineering rock mass classifications: a complete manual for engineers and geologists in mining, civil and petroleum engineering”. Wiley, New York, 1989, pp. 40-47.
 M. E. Harr, “Reliability-based Design in Civil Engineering”, Dover Publications, New York, 1987.
 E. Hoek & E. T. Brown, “Empirical strength criterion for rock masses”, J. Geotech. Engng. Div. ASCE 106(GT9), 1980, pp. 1013-1035.
 E. Hoek, C. Carranza-Torres & B. Corkum, “The Hoek-Brown failure criterion – 2002 edition”, Proc. 5th North American Rock Mechanics Symp. And 17th Tunneling Assoc. of Canada Conf, NARMS-TAC, Toronto, 2002, pp. 267-271.
 E. Hoek, P. K. Kaiser & W. F. Bawden, “Support of Underground Excavations in Hard Rock”, Taylor & Francis, New York, 1995.
 C. W. Mah & D. C. Wyllie, “Rock Slope Engineering, Civil and Mining”, 4th Edition, Spon Press, London, 2005.
 J. Read & P. Stacey, ”Guidelines for Open Pit Slope Design”, CSIRO Publishing, Melbourne, 2009.
 E. Rosenbleuth, “Point Estimates for Probability Moments”, Proc. Nat. Acad. Sci. USA vol. 72 no. 10, 1975.
 C. A. Coulomb, “Essai sur une application des regles des maximis et minimis a quelquels problemesde statique relatifs, a la architecture”, Mem. Acad. Roy. Div. Sav., vol. 7, 1776, pp. 343–387.
 N. Barton & E. Quadros, “Anisotropy is Everywhere, to See, to Measure, to Model”, Int. J. Rock Mechanics & Rock Engineering, Springer-Verlag, Austria, 2014.