Joughin, WC 2017, 'Dealing with uncertainty and risk in the design of deep and high stress mining excavations', in J Wesseloo (ed.), Deep Mining 2017: Proceedings of the Eighth International Conference on Deep and High Stress Mining
, Australian Centre for Geomechanics, Perth, pp. 489-507, https://doi.org/10.36487/ACG_rep/1704_33.3_Joughin
A method for risk-based design under high stress conditions is described in this paper. Probabilistic methods of analysis are applied to stress modelling to determine the probability of exceeding a given depth of failure. Suggestions are provided for dealing with geotechnical uncertainty. The understanding of aleatory variability can be improved by collecting more data and improving the quality of data through training and quality control. Stress and model uncertainty remain a challenge in geotechnical engineering. Some degree of subjective engineering judgement will therefore always be required in geotechnical design.
An economic risk model is used to determine the frequency and severity of the consequences of stress damage. The cost of rehabilitation of tunnels and the financial losses due to lost production are assessed using the model. A typical risk matrix is used to evaluate the level of risk. Different types of excavations have different risk profiles based on the potential impact on production. The design engineer can use the model to determine design criteria for stress damage. The risk can be mitigated through improved support or by changing the mining layout. These measures both have financial implications and the economic risk model is useful for decision making.
A brief discussion on risk-based design criteria for rockbursts is also included.
Keywords: risk-based design, probabilistic design, uncertainty
Abdellah, W, Mitri, HS & Thibodeau, D 2014, ‘Risk indexing tool for mine planning’, Journal of the Southern African institute of Mining and Metallurgy, vol. 114, pp. 435–443.
Baecher, GB & Christian, JT 2003, Reliability and Statistics in Geotechnical Engineering, John Wiley & Sons, Ltd.
Bradley, N 2007, The Response Surface Methodology, Master’s thesis, Indiana University South Bend.
Brown, ET 2012, ‘Risk assessment and management in underground rock engineering—an overview’, Journal of Rock Mechanics and Geotechnical Engineering, vol. 4, no. 3, pp. 193–204, viewed 30 January 2017,
Chiwaye, HT & Stacey, TR 2010, ‘A comparison of limit equilibrium and numerical modelling approaches to risk analysis for open pit mining’, Journal of the Southern African institute of Mining and Metallurgy, vol. 110, no. 10, pp. 571–580.
Christian, JT & Baecher, GB 1999, ‘Point-estimate method as numerical quadrature’, Journal of Geotechnical and Geoenvironmental Engineering, vol. 125, pp. 779–786, viewed 30 January 2017,
Christian, JT & Baecher, GB 2002, ‘The point estimate method with large numbers of variables’, International Journal for Numerical and Analytical Methods in Geomechanics, vol. 26, pp. 1,515–1,529, viewed 30 January 2017,
Contreras, LF 2015 ‘An economic risk evaluation approach for pit slope optimization’, Journal of the Southern African Institute of Mining and Metallurgy, vol. 115, no. 7, pp. 607–622.
Hadjigeorgiou, J & Harrison, JP 2011, ‘Uncertainty and sources of error in rock engineering’, in Y Zhou (ed.), ISRM 12th International Congress on Rock Mechanics, International Society for Rock Mechanics, Lisboa, pp. 2,063–2,067, viewed 30 January 2017,
Harr, ME 1996, Reliability-based Design in Civil Engineering, Dover Publications Inc., New York.
Harris, P & Wesseloo, J 2015, mXrap, Australian Centre for Geomechanics, Perth, www.mxrap.com
Hoek, E, Carranza-Torres, C & Corkum, B 2002, ‘Hoek-Brown failure criterion – 2002 edition’, in R Hammah (ed.), Proceedings of the 5th North American Rock Mechanics Symposium and the 17th Tunnelling Association of Canada Conference, University of Toronto, Toronto, pp. 267–273.
Hoek, E, Carter, TG & Diederichs, MS 2013, ‘Quantification of the geological strength index chart’, Proceedings of the 47th US Rock Mechanics/Geomechanics Symposium, American Rock Mechanics Association, Alexandria, ARMA 13-672.
Joughin, WC, Swart, A & Wesseloo, J 2000, ‘Risk based chromitite pillar design - Part II, non-linear modelling’, Proceedings of the South African National Institute of Rock Engineers Symposium, South African National Institute of Rock Engineering, Rustenburg, pp. 8.
Joughin, WC, Muaku, JJM & Wessleoo, J 2016, ‘A risk-based approach to ground support design’, in E Nordlund, TH Jones & A Eitzenberger (eds), Proceedings of the Eighth International Symposium on Ground Support in Mining and Underground Construction, Luleå University of Technology, Luleå, Sweden, pp. 1–20.
Joughin, WC, Jager, A, Nezomba, E & Rwodzi, L 2012 ‘A risk evaluation model for support design in Bushveld Complex underground mines: Part I – Description of the model’, Journal of The Southern African Institute of Mining and Metallurgy, vol. 112, no. 2, pp. 83–94.
Kaiser, PK, McCreath, DR & Tannant, D 1995, Rockburst Support Handbook, Geomechanics Research Centre, Laurentian University, Sudbury, Ontario.
Kroese, D & Rubinstein, R 2012, ‘Monte Carlo methods’, Wiley Interdisciplinary Reviews: Computational Statistics, vol. 4, no. 1, pp. 48–58.
Langford, J & Diederichs, M 2015, ‘Reliable support design for excavations in brittle rock using a global response surface method’, Rock Mechanics and Rock Engineering, vol. 48, pp. 669–689.
Linkov, AM 2005 ‘Numerical modeling of seismic and aseismic events in geomechanics’, Journal of Mining Science, vol. 41, no. 1, pp. 14–26.
Lü, Q, Chan, C & Low, B 2012, ‘Probabilistic evaluation of ground-support interaction for deep rock excavation using artificial neural network and uniform design’, Tunnelling and Underground Space Technology, vol. 32, pp. 1–18.
Lü, Q & Low, BK 2011a ‘Probabilistic analysis of underground rock excavations using response surface method and SORM’, Computers and Geotechnics, vol. 38, no. 8, pp. 1,008–1,021, viewed 30 January 2017,
Lü, Q & Low, BK 2011b ‘Probabilistic analysis of underground rock excavations using response surface method and SORM’, Computers and Geotechnics, vol. 38, no. 8, pp. 1,008–1,021, viewed 30 January 2017,
Malovichko, DA & Basson, G 2014 ‘Simulation of mining-induced seismicity using Salamon-Linkov method’, in M Hudyma & Y Potvin (eds), Proceedings of the Seventh International Seminar on Deep and High Stress Mining, 16–18 September 2014, Sudbury, Australian Centre for Geomechanics, Perth, pp. 667–680.
Marinos, P & Hoek, E 2000, ‘GSI: A geologically friendly tool for rock mass strength estimation’, Proceedings of GeoEng2000: An International Conference on Geotechnical and Geological Engineering, Technomic Publishing Co., Lancaster, pp. 1422–1442.
Marinos, V, Marinos, P & Hoek, E 2005, ‘The geological strength index: Applications and limitations’, Bulletin of Engineering Geology and the Environment, vol. 64, no. 1, pp. 55–65.
Rosenblueth, E 1975, ‘Point estimates for probability moments’, Proc. Nt. Acad. Sci. USA Vol. 72, No 10. pp 3812-3814.
Rosenblueth, E 1981, ‘Two-point estimates in probabilities’, Applied Mathematical Modelling, vol. 5, no. 5, pp. 329–335, viewed 30 January 2017,
Ryder, JA & Jager, AJ 2002, A Textbook on Rock Mechanics for Tabular Hard Rock Mines, The Safety in Mines Research Advisory Committee (SIMRAC), Braamfontein.
Salamon, M 1993, ‘Keynote address: Some applications of geomechanical modelling in rockburst and related research’, in RP Young (ed.), Proceedings of the 3rd International Symposium on Rockbursts and Seismicity in Mines, AA Balkema, Rotterdam, pp. 297–309.
Steffen, OKH, Contreras, LF, Terbrugge, PJ & Venter, J 2008, 'A Risk Evaluation Approach for Pit Slope Design', in The 42nd U.S. Rock Mechanics Symposium, USRMS, 29 June-2 July 2008, San Francisco, California, American Rock Mechanics Association.
Tapia, A, Contreras, LF, Jefferies, M & Steffen, O 2007, ‘Risk evaluation of slope failure at the Chuquicamata mine’, in Y Potvin (ed.), Proceedings of the 2007 International Symposium on Rock Slope Stability in Open Pit Mining and Civil Engineering, 12–14 September 2007, Perth, pp. 477–495, viewed 30 January 2017,
Terbrugge, PJ, Wesseloo, J, Venter, J & Steffen, OKH 2006 ‘A risk consequence approach to open pit slope design’, Journal of the Southern African Institute of Mining and Metallurgy, vol. 106, no. 7, pp. 503–511.
Valley, B, Kaiser, P & Duff, D 2010, ‘Consideration of uncertainty in modelling the behaviour of underground excavations’, in M Van Sint Jan & Y Potvin (eds), Proceedings of the Fifth International Seminar on Deep and High Stress Mining, Australian Centre for Geomechanics, Perth, pp.423–435.
Vick, S, 2002 Degrees of Belief - Subjective Probability and Engineering Judgment, American Society of Civil Engineers Press, Reston, Virginia.
Wesseloo, J 2016, ‘The use of elastic superposition as part of a multi-tiered probabilistic ground support design approach’, in E Nordlund, TH Jones & A Eitzenberger (eds), Proceedings of the Eighth International Symposium on Ground Support in Mining and Underground Construction, Luleå University of Technology, pp. 1–9.
Wesseloo, J, 2013, ‘Towards real-time probabilistic hazard assessment of the current hazard state for mines’, Proceedings of the Eighth International Symposium on Rockbursts and Seismicity in Mines, Geophysical Survey of Russian Academy of Sciences, Obninsk, Mining Institute of the Ural Branch of the Russian Academy of Sciences, A Malovichko and D Malovichko (eds), Perm, pp. 307–312.
Wesseloo, J & Read, J 2009, ‘Acceptance Criteria’, in P Stacey & J Read (eds), Guidelines for Open Pit slope Design, Commonwealth Scientific and Industrial Research Organisation Publishing, Collingwood, pp. 221–236.
Wiles, T 2016, Map3D Fault Slip, Map3D International Ltd, www.map3d.com