Evaluation of Rock Slope Stability Conditions Through Discriminant Analysis

  • Allan Erlikhman Medeiros Santos
  • Milene Sabino Lana
  • Ivo Eyer Cabral
  • Tiago Martins Pereira
  • Masoud Zare Naghadehi
  • Denise de Fátima Santos da Silva
  • Tatiana Barreto dos Santos
Original Paper


A methodology to predict the stability status of mine rock slopes is proposed. Two techniques of multivariate statistics are used: principal component analysis and discriminant analysis. Firstly, principal component analysis was applied in order to change the original qualitative variables into quantitative ones, as well as to reduce data dimensionality. Then, a boosting procedure was used to optimize the resulting function by the application of discriminant analysis in the principal components. In this research two analyses were performed. In the first analysis two conditions of slope stability were considered: stable and unstable. In the second analysis three conditions of slope stability were considered: stable, overall failure and failure in set of benches. A comprehensive geotechnical database consisting of 18 variables measured in 84 pit-walls all over the world was used to validate the methodology. The discriminant function was validated by two different procedures, internal and external validations. Internal validation presented an overall probability of success of 94.73% in the first analysis and 68.42% in the second analysis. In the second analysis the main source of errors was due to failure in set of benches. In external validation, the discriminant function was able to classify all slopes correctly, in analysis with two conditions of slope stability. In the external validation in the analysis with three conditions of slope stability, the discriminant function was able to classify six slopes correctly of a total of nine slopes. The proposed methodology provides a powerful tool for rock slope hazard assessment in open-pit mines.


Multivariate statistics Rock slope stability Principal component analysis Boosting technique Discriminant analysis 



The authors wish to thank CNPq (National Counsel of Technological and Scientific Development) and Fapemig (Foundation for Research Support of Minas Gerais) for supporting this work.


  1. Adhikari SP, Yoo HJ, Kim H (2011) Boosting-based on-road obstacle sensing using discriminative weak classifiers. Sensors 12:4372–4384CrossRefGoogle Scholar
  2. Ahmed B, Dewan A (2017) Application of bivariate and multivariate statistical techniques in landslide susceptibility modeling in Chittagong City corporation, Bangladesh. Remote Sens 304:1–32Google Scholar
  3. Anderson TW (1984) An introduction to multivariate statistics, 3rd edn. Wiley, New YorkGoogle Scholar
  4. Cattell RB (1966) The screen test for the number of factors. Multivar Behav Res 1:140–161Google Scholar
  5. Efron B, Tibshirani R (1993) An introduction to the bootstrap, 1st edn. Chapman and Hall, LondonCrossRefGoogle Scholar
  6. Erener A, Sivas AA, Selcuk-Kestel AS, Düzgün HS (2017) Analysis of training sample selection strategies for regression-based quantitative landslide susceptibility mapping methods. Comput Geosci 104:62–74CrossRefGoogle Scholar
  7. Fisher RA (1936) The use of multiple measurements in taxonomic problems. Ann Eugen 7:179–188CrossRefGoogle Scholar
  8. Hottelling H (1933) Analysis of a complex of statistical variables into principal component. J Educ Psychol 24:417–441 and 498–520Google Scholar
  9. Hudson JA (1992) Rock engineering systems, theory and practice, 1st edn. Ellis Horwood, ChichesterGoogle Scholar
  10. Johnson RA, Wichern DW (1998) Applied multivariate statistical analysis, 6th edn. Prentice Hall, Upper Saddle RiverGoogle Scholar
  11. Kaiser HF (1958) The varimax criterion for analytic rotation in factor analysis. Psychometrika 23:187–200CrossRefGoogle Scholar
  12. Kulatilake PHSW, Hudaverdi T, Wu Q (2012) New prediction models for mean particle size in rock blast fragmentation. Geotech Geol Eng 30:665–684CrossRefGoogle Scholar
  13. Lin YK (2011) Spare routing problem with p minimal paths for time-based stochastic flow networks. Appl Math Model 35:1427–1438CrossRefGoogle Scholar
  14. Massumi A, Gholami F (2016) The influence of seismic intensity parameters on structural damage of RC buildings using principal component analysis. Appl Math Model 40:2161–2176CrossRefGoogle Scholar
  15. Nickson SD (1992) Cable support guidelines for underground hard rock mine operations. Master thesis, University of British ColumbiaGoogle Scholar
  16. Okada K, Flores A, Linguraru MG (2010) Boosting weighted linear discriminant analysis. Int J Adv Stat IT&C Econ Life Sci 2:1–10Google Scholar
  17. Pearson K (1901) On lines and planes of closest fit to systems of points in space. Philos Mag 6:559–572CrossRefGoogle Scholar
  18. R Development Core Team (2006) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna. ISBN 3-900051-07-0. Accessed 2016
  19. Read J, Stacey P (2009) Guidelines for open pit slope design. CSIRO Publishing, MelbourneGoogle Scholar
  20. Schapire RE (1990) The strength of weak learnability. Mach Learn 5:197–227Google Scholar
  21. Skurichina M, Duin RPW (2000) Boosting in linear discriminant analysis. In: First international workshop on multiple classifier systems, CagliariGoogle Scholar
  22. Wu X, Wu B, Sun J, Qiu S, Li X (2015) A hybrid fuzzy K-harmonic means clustering algorithm. Appl Math Model 39:3398–3409CrossRefGoogle Scholar
  23. Wyllie DC, Mah CW (2004) Rock slope engineering, civil and mining, 4th edn. Spon Press, Taylor & Francis Group, LondonGoogle Scholar
  24. Yilmaz Is-ık (2009) Landslide susceptibility mapping using frequency ratio, logistic regression, artificial neural networks and their comparison: case study from Kat landslides (Tokat-Turkey). Comput Geosci 35:1125–1138CrossRefGoogle Scholar
  25. Zare Naghadehi M, Jimenez R, Khalokakaie R, Jalali SME (2013) A new open-pit mine slope instability index defined using the improved rock engineering systems approach. Int J Rock Mech Min Sci 61:1–14Google Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Allan Erlikhman Medeiros Santos
    • 1
  • Milene Sabino Lana
    • 1
  • Ivo Eyer Cabral
    • 1
  • Tiago Martins Pereira
    • 2
  • Masoud Zare Naghadehi
    • 3
  • Denise de Fátima Santos da Silva
    • 4
  • Tatiana Barreto dos Santos
    • 1
  1. 1.Graduate Program in Mineral Engineering – PPGEMFederal University of Ouro Preto – UFOPOuro PrêtoBrazil
  2. 2.Department of StatisticsFederal University of Ouro Preto – UFOPOuro PrêtoBrazil
  3. 3.Department of Mining EngineeringHamedan University of TechnologyHamedanIran
  4. 4.Graduate Geotechnical Center School of Mines, Geotechnical NucleusFederal University of Ouro Preto – UFOPOuro PrêtoBrazil

Personalised recommendations