Lyman, G, Poropat, GV & Elmouttie, M 2008, 'Uncertainty in Rock Mass Jointing Characterisation', in Y Potvin, J Carter, A Dyskin & R Jeffrey (eds), Proceedings of the First Southern Hemisphere International Rock Mechanics Symposium
, Australian Centre for Geomechanics, Perth, pp. 419-432.
The analysis of jointing in a rock mass is a critical step in any rock engineering project as the extent of fracturing in the rock mass is the dominant factor controlling the rock mass strength. Uncertainties in the characterisation of a rock mass are very rarely considered.
Historically, the assessment of jointing has been a largely empirical process and a project may proceed when in the opinion of the geotechnical staff 'enough' data has been collected. For example, the number of fractures in a length of core is used to calculate the RQD or the fracture frequency, but the direction of the core axis may be ignored even though it is known that the fracture frequency is a function of direction when the jointing is not isotropic and thus the fracture frequency may be incorrectly assessed.
The orientation distribution of joint sets in a rock mass can be analysed quite easily as conventional scanline mapping of the rock mass provides a reasonably precise estimate of the dip and dip direction of every joint logged. However, to make a three-dimensional estimate of the extent of fracturing in a rock mass, it is necessary to determine joint persistence in three dimensions. To do this requires the assumption of a model of the geometry of the joints and flat disks are usually chosen as this is the simplest possible two-dimensional shape, requiring the least amount of information to describe the joints.
The estimation of the size distribution of the joints in a joint set is a statistical estimation process that is in principle well defined, once a model for the joints has been adopted. If the estimation process has a sound mathematical basis, it is possible to estimate the uncertainty in the parameters. These estimates of the uncertainties in the nature of the joints can be propagated through to arrive at a range of values for the rock mass indices of interest rather than a single value of unknown reliability. Once these ranges are known, an objective decision can be made regarding the state of knowledge of the rock mass.
This paper introduces the new paradigm of quantification of uncertainty in the assessment of the extent of fracturing in jointed rock masses and provides some examples of how estimates of rock mass indices are affected by the quantity of data available for analysis.
ASPRS (2004) Manual of Photogrammetry 5th Edition.
Dershowitz, W.S. and Einstein, H.H. (1988) Characterizing Rock Joint Geometry with Joint System Models, Rock Mechanics and Rock Engineering 1988, 21, pp. 21–51.
Fisher, R. (1953) Dispersion on a sphere, Proceedings Roy Soc London, A217, pp. 295–305.
Fisher, N., Lewis, T. and Embleton, B.J.J. (1993) Statistical Analysis of Spherical Data, Cambridge University Press.
Kemeny, J., Mofya, E., Holmlund, J. and Ahlgren, S. (2002) Digital Imaging For Rock Mass Characterization, Proceedings 2nd Annual Conference on the Application of Geophysical and NDT Methodologies To Transportation Facilities and Infrastructure (Geophysics 2002), Los Angeles, April, 2002.
Kulatilake, P.H.S.W, Wu, T.H. and Wathugala, D.N. (1990) Probabilistic modelling of joint orientation, International Journal for Numerical and Analytical methods in Geomechanics, Vol. 14, Issue 5, pp. 325–350 (Note: This paper was republished on-line in 2005).
Lin, D., Fairhurst, C. and Starfield, A.M. (1987) Geometrical identification of three dimensional rock block systems using topological techniques, Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 1987, 24 No 6, pp. 331–338.
Lyman, G.J. (2003) Rock fracture mean trace length estimation and confidence interval calculation using maximum likelihood methods, International Journal of Rock Mechanics and Mining Sciences, Vol. 40 (6), pp. 825–832
Meyers, A.G. and Priest, S.D. (2000) Generating Discontinuity Orientation Data for Use in Probabilistic Models for Modelling Excavations in Rock, Proceedings Geo Eng 2000, November 2000.
Mikhail, E.M. (1983) Observation and Least Squares, Univ Press of America.
Potsch, M., Pishinger, G. and Schubert, W. (2007) Dealing with uncertain parameters in rock slope stability analysis, Slope Stability 2007 – Proceedings 2007 International Symposium on Rock Slope Stability and Open Pit Mining and Civil Engineering, Y. Potvin (editor), Australian Centre for Geomechanics, Perth, pp. 129–141.
Priest, S.D. (1993) Discontinuity Analysis for Rock Engineering, Chapman and Hall.
Vose, D. (2000) Risk Analysis: A Quantitative Guide (2nd Edition), Wiley.
Webster, R. and Oliver, M.A. (2007) Geostatistics for Environmental Scientists, Wiley.