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Modelling Geomechanical Heterogeneity of Rock Masses Using Direct and Indirect Geostatistical Conditional Simulation Methods

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Abstract

An accurate characterization and modelling of rock mass geomechanical heterogeneity can lead to more efficient mine planning and design. Using deterministic approaches and random field methods for modelling rock mass heterogeneity is known to be limited in simulating the spatial variation and spatial pattern of the geomechanical properties. Although the applications of geostatistical techniques have demonstrated improvements in modelling the heterogeneity of geomechanical properties, geostatistical estimation methods such as Kriging result in estimates of geomechanical variables that are not fully representative of field observations. This paper reports on the development of 3D models for spatial variability of rock mass geomechanical properties using geostatistical conditional simulation method based on sequential Gaussian simulation. A methodology to simulate the heterogeneity of rock mass quality based on the rock mass rating is proposed and applied to a large open-pit mine in Canada. Using geomechanical core logging data collected from the mine site, a direct and an indirect approach were used to model the spatial variability of rock mass quality. The results of the two modelling approaches were validated against collected field data. The study aims to quantify the risks of pit slope failure and provides a measure of uncertainties in spatial variability of rock mass properties in different areas of the pit.

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References

  • Allan FC, Yacoub TE, Curran JH (2012) On using spatial methods for heterogeneous slope stability analysis. In: Proceedings of 46th US rock mechanics/geomechanics symposium. 24–27 June 2012, Chicago, IL, USA

  • Atilla Oztürk C, Nasuf E (2002) Geostatistical assessment of rock zones for tunnelling. Tunn Undergr Space Technol 17:275–285

    Article  Google Scholar 

  • Ayalew L, Reik G, Busch W (2002) Characterizing weathered rock masses-a geostatistical approach. Int J Rock Mech Min Sci 39(1):105–114

    Article  Google Scholar 

  • Baker JW, Seifried A, Andrade JE, Chen Q (2011) Characterization of random fields at multiple scales: an efficient conditional simulation procedure and applications in geomechanics. In: Proceedings of 11th international conference on applications of statistics and probability in soil and structural engineering (ICASP11). 1–4 Aug 2011, Zurich, Switzerland

  • Barnett RM, Manchuk JM, Deutsch CV (2014) Projection pursuit multivariate transform. Math Geosci 46:337–359

    Article  Google Scholar 

  • Barton N, Lien R, Lunde J (1974) Engineering classification of rock masses for the design of tunnel support. Rock Mech 6(4):189–236

    Article  Google Scholar 

  • Bieniawski ZT (1976) Rock mass classification in rock engineering. In: Proceedings of the symposium on exploration for rock engineering. 1–5 Nov 1976, Johannesburg, South Africa, pp 97–106

  • Bieniawski ZT (1989) Engineering rock mass classifications. Wiley, New York, p 251

    Google Scholar 

  • Bye AR (2011) Case studies demonstrating value from geometallurgy initiatives. In: First AusIMM international geometallurgy conference (GeoMet 2011), 5–7 Sept 2011, Brisbane, Australia

  • Chiles JP, Delfiner P (1999) Geostatistics: modeling spatial uncertainty, 2nd edn. Wiley, Hoboken, p 734

    Book  Google Scholar 

  • Coli N, Berry P, Boldini D, Bruno R (2012) The contribution of geostatistics to the characterisation of some bimrock properties. Eng Geol 137–138:53–63

    Article  Google Scholar 

  • Demsar U, Harris P, Brunsdon C, Fotheringham AS, Mcloone S (2013) Principal component analysis on spatial data: an overview. Ann Assoc Am Geogr 103:106–128

    Article  Google Scholar 

  • Deutsch CV (2002) Geostatistical reservoir modeling. Oxford University Press, Oxford

    Google Scholar 

  • Doostmohammadi M, Jafari A, Asghari O (2015) Geostatistical modeling of uniaxial compressive strength along the axis of the Behesht-Abad tunnel in Central Iran. Bull Eng Geol Environ 74(3):789–802

    Article  Google Scholar 

  • Dunham S, Vann J (2007) Geometallurgy, geostatistics and project value—does your block model tell you what you need to know? In: Project evaluation conference, 19–20 June 2007, Melbourne, Australia, pp 189–196

  • Egaña M, Ortiz JM (2013) Assessment of RMR and its uncertainty by using geostatistical simulation in a mining project. J GeoEng 8(3):83–90

    Google Scholar 

  • Eivazy H, Esmaieli K, Jean R, Albor F (2015) Application of 3D geotechnical block models in design of open pit mine—a case study at mont-wright open pit mine. In: Proceeding of 37th international symposium on the application of computers and operations research in mineral industry (APCOM 2015), 23–27 May 2015, Fairbank, USA

  • Eivazy H, Esmaieli K, Jean R (2016) Challenges in modelling geomechanical heterogeneity of rock masses using geostatistical approaches. In: Proceedings of 24th world mining congress, 18–21 Oct 2016, Rio de Janeiro, Brazil

  • Ellefmo SL, Eidsvik J (2009) Local and spatial joint frequency uncertainty and its application to rock mass characterisation. Rock Mech Rock Eng 42:667–688

    Article  Google Scholar 

  • Exadaktylos G, Stavropoulou M (2008) A specific upscaling theory of rock mass parameters exhibiting spatial variability: analytical relations and computational scheme. Int J Rock Mech Min Sci 45:1102–1125

    Article  Google Scholar 

  • Ferrari F, Apuani T, Giani GP (2014) Rock mass rating spatial estimation by geostatistical analysis. Int J Rock Mech Min Sci 70:162–176

    Google Scholar 

  • Goovaerts P (1993) Spatial orthogonality of the principal components computed from coregionalized variables. Math Geol 25:281–302

    Article  Google Scholar 

  • Griffiths DV, Fenton GA (2004) Probabilistic slope stability analysis by finite elements. J Geotech Geoenviron Eng 130:507–518

    Article  Google Scholar 

  • Griffiths D, Huang J, Fenton G (2009) Influence of spatial variability on slope reliability using 2-D random fields. J Geotech Geoenviron Eng 135:1367–1378

    Article  Google Scholar 

  • Hack R, Orlic B, Ozmutlu S, Zhu S, Rengers N (2006) Three and more dimensional modelling in geo-engineering. Bull Eng Geol Environ 65:143–153

    Article  Google Scholar 

  • Isaaks EH, Srivastava RM (1989) An introduction to applied geostatistics, 1st edn. Oxford University Press, New York

    Google Scholar 

  • Journel AG, Huijbregts CJ (1978) Mining geostatistics. The Blackburn Press, Caldwell, p 600

    Google Scholar 

  • La Pointe PR (1980) Analysis of the spatial variation in rock mass properties through geostatistics. In: Proceedings of 21st US rock mechanics symposium, 28–30 May 1980, University of Missouri, Rolla, pp 570–580

  • Leuangthong O, Deutsch CV (2003) Stepwise conditional transformation for simulation of multiple variables. Math Geol 35(2):155–173

    Article  Google Scholar 

  • Manchuk JG, Leuangthong O, Deutsch CV (2009) The proportional effect. Math Geosci 41:799–816

    Article  Google Scholar 

  • MAPTEK (2014) Vulcan-V.9 software

  • Marchesi VR, Da fontoura SAB, Rubio NPR (2009) How 3D modeling can improve quality and reliability of geotechnical projects. In: EUROCK symposium, 29–31 Oct 2009, Cavtat, Croatia

  • Marinoni O (2003) Improving geological models using a combined ordinary–indicator kriging approach. Eng Geol 69:37–45

    Article  Google Scholar 

  • Mayer JM, Stead D (2017) A comparison of traditional, step-path, and geostatistical techniques in the stability analysis of a large open pit. Rock Mech Rock Eng 2017(50):927–949

    Article  Google Scholar 

  • Mueller UA, Ferreira J (2012) The U-WEDGE transformation method for multivariate geostatistical simulation. Math Geosci 44:427–448

    Article  Google Scholar 

  • Ozturk CA, Simdi E (2014) Geostatistical investigation of geotechnical and constructional properties in Kadikoy-Kartal subway, Turkey. Tunn Undergr Space Technol 41:35–45

    Article  Google Scholar 

  • Savard P, Jean R (2012) Report of the mineral reserves and resources. ArcelorMittal mines Canada, Internal Report

  • Srivastava RM (2013) Geostatistics: a toolkit for data analysis, spatial prediction and risk management in the coal industry. Int J Coal Geol 112:2–13

    Article  Google Scholar 

  • Stavropoulou M, Exadaktylos G, Saratsis G (2007) A combined three-dimensional geological-geostatistical-numerical model of underground excavations in rock. Rock Mech Rock Eng 40:213–243

    Article  Google Scholar 

  • Switzer P, Green A (1984) Min/max autocorrelation factors for multivariate spatial imaging. Technical Report no. 6, Department of Statistics, Stanford University

  • Syrjänen P, Lovén P (2003) 3D modeling of rock mass quality. In: Proceedings of 10th International Society for Rock Mechanics (ISRM) Congress, 8–12 September, Sandton, South Africa

  • Vatcher J, Mckinnon SD, Sjöberg J (2016) Developing 3-D mine-scale geomechanical models in complex geological environments, as applied to the Kiirunavaara Mine. Eng Geol 203:140–150

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to acknowledge ArcelorMittal Mines Canada and the Natural Science and Engineering Research Council of Canada (NSERC) for their financial support. The authors also appreciate access to the Vulcan software provided by Maptek. The technical input of Mr. Mohan Srivastava is also greatly appreciated.

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Authors and Affiliations

  1. Lassonde Institute of Mining, University of Toronto, 170 College St., Toronto, ON, M5S 3E3, Canada

    Hesameddin Eivazy & Kamran Esmaieli

  2. ArcelorMittal Mines Canada, Montreal, QC, Canada

    Raynald Jean

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  1. Hesameddin Eivazy
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  2. Kamran Esmaieli
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  3. Raynald Jean
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Correspondence to Kamran Esmaieli.

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Eivazy, H., Esmaieli, K. & Jean, R. Modelling Geomechanical Heterogeneity of Rock Masses Using Direct and Indirect Geostatistical Conditional Simulation Methods. Rock Mech Rock Eng 50, 3175–3195 (2017). https://doi.org/10.1007/s00603-017-1293-0

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  • DOI: https://doi.org/10.1007/s00603-017-1293-0

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