Mining of Mineral Deposits

ISSN 2415-3443 (Online)

ISSN 2415-3435 (Print)

Flag Counter

Application of the deterministic block theory to the slope stability design of an open-pit mine in Morocco

Youssef Zerradi1, Mohamed Souissi1, Abdelkader Larabi1

1Mohammadia School of Engineers, Mohammed V University in Rabat, Rabat, Morocco


Min. miner. depos. 2023, 17(2):53-60


https://doi.org/10.33271/mining17.02.053

Full text (PDF)


      ABSTRACT

      Purpose. Discontinuities in rock masses are natural fractures that delimit various block shapes and sizes, which can fall, slide or topple from the excavation and collapse under their own weight inducing probably severe damage. Thus, it is essential to carry out a block analysis before beginning any surface or underground excavation project. This paper proposes a methodology based on key block theory analysis to select the suitable slope of different discontinuous rock masses of an open-pit mine in Morocco.

      Methods. At first, the main discontinuities of each bench are determined and projected onto a stereonet with a maximum dip angle of the excavation plane. Then, it is possible to identify the removable blocks by using the theorem of removability according to block theory. After that, a limit equilibrium analysis is performed to determine the failure mode and the friction angle required to stabilize the blocks. When the selected dip angle of the slope plane is found to be unsuitable, it is changed and reduced by one degree, and the same approach is repeated until the maximum safe slope dip angle is obtained.

      Findings. The results of the proposed methodology based on key block theory analysis have shown that the maximum safe slope angles of the studied benches are in the range of 63-73°. When compared to the slope angles used in the mine, which are between 58-78°, the results of this study are close to in-situ conditions.

      Originality. In this research, the maximum safe slope angle of fractured rock masses was optimized by eliminating slope angles inducing unstable blocks (key blocks) and by using the stereographic projection method of key block theory.

      Practical implications. Using this methodology, stability of rock slopes in civil or mining-engineering projects can be designed or assessed when geotechnical data are very limited.

      Keywords: key block theory, slope stability, limit equilibrium analysis, discontinuous rock masses, stereographic projectio


      REFERENCES

  1. Lilly, P.A. (2002). Open pit mine slope engineering: A 2002 perspective. 150 years of Mining, Proceedings of the AusIMM Annual Conference.
  2. Goodman, R.E., & Shi, G.H. (1985). Block theory and its application to rock engineering. New Jersey, United States: Prentice-Hall, 335 p.
  3. Goodman, R.E. (1995). Block theory and its application. Geotecnique, 45(3), 383-423. https://doi.org/10.1680/geot.1995.45.3.383
  4. Warburton, P.M. (1981). Vector stability analysis of an arbitrary polyhedral rock block with any number of free faces. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 18(5), 415-427. https://doi.org/10.1016/0148-9062(81)90005-X
  5. Delport, J.L., & Martin, D.H. (1986). A multiplier method for identifying keyblocks in excavations through jointed rock. SIAM Journal on Algebraic Discrete Methods, 7(2), 321-330. https://doi.org/10.1137/0607035
  6. Heliot, D. (1988). Generating a blocky rock mass. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 25(3), 127-138. https://doi.org/10.1016/0148-9062(88)92295-4
  7. Lin, D., & Fairhurst, C. (1988). Static analysis of the stability of three-dimensional blocky systems around excavations in rock. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 25(3), 139-147. https://doi.org/10.1016/0148-9062(88)92296-6
  8. Mauldon, M., & Goodman, R.E. (1996). Vector analysis of keyblock rotations. Journal of Geotechnical Engineering, 122(12), 976-987. https://doi.org/10.1061/(ASCE)0733-9410(1996)122:12(976)
  9. Tonon, F. (1998). Generalization of Mauldon’s and Goodman’s vector analysis of keyblock rotations. Journal of Geotechnical and Geoenvironmental Engineering, 124(10), 913-922. https://doi.org/10.1061/(ASCE)1090-0241(1998)124:10(913)
  10. Azarafza, M., Akgün, H., Ghazifard, A., & Asghari-Kaljahi, E. (2020). Key-block based analytical stability method for discontinuous rock slope subjected to toppling failure. Computers and Geotechnics, (124), 103620. https://doi.org/10.1016/j.compgeo.2020.103620
  11. Lu, J. (2002). Systematic identification of polyhedral rock blocks with arbitrary joints and faults. Computers and Geotechnics, 29(1), 49-72. https://doi.org/10.1016/S0266-352X(01)00018-0
  12. González-Palacio, C., Menéndez-Díaz, A., Álvarez-Vigil, A.E., & González-Nicieza, C. (2005). Identification of non-pyramidal key blocks in jointed rock masses for tunnel excavation. Computers and Geotechnics, 32(3), 179-200. https://doi.org/10.1016/j.compgeo.2005.01.004
  13. Menéndez-Díaz, A., González-Palacio, C., Álvarez-Vigil, A.E., González-Nicieza, C., & Ramírez-Oyanguren, P. (2009). Analysis of tetrahedral and pentahedral key blocks in underground excavations. Computers and Geotechnics, 36(6), 1009-1023. https://doi.org/10.1016/j.compgeo.2009.03.013
  14. Elmouttie, M., Poropat, G., & Krähenbühl, G. (2010). Polyhedral modelling of rock mass structure. International Journal of Rock Mechanics and Mining Sciences, 47(4), 544-552. https://doi.org/10.1016/j.ijrmms.2010.03.002
  15. Fu, G.Y., & Ma, G.W. (2014). Extended key block analysis for sup-port design of blocky rock mass. Tunnelling and Underground Space Technology, (41), 1-13. https://doi.org/10.1016/j.tust.2013.11.003
  16. Li, J., Xue, J., Xiao, J., & Wang, Y. (2012). Block theory on the com-plex combinations of free planes. Computers and Geotechnics, (40), 127-134. https://doi.org/10.1016/j.compgeo.2011.10.006
  17. Yarahmadi Bafghi, A.R., & Verdel, T. (2003). The key‐group method. International Journal for Numerical and Ananalytical Methods in Geomechanics, 27(6), 495-511. https://doi.org/10.1002/nag.283
  18. Noroozi, M., Jalali, S.E., & Yarahmadi‐Bafghi, A.R. (2012). 3D key‐group method for slope stability analysis. International Journal for Numerical and Analytical Methods in Geomechanics, 36(16), 1780-1792. https://doi.org/10.1002/nag.1074
  19. Sun, G., Zheng, H., & Huang, Y. (2015). Stability analysis of statically indeterminate blocks in key block theory and application to rock slope in Jinping-I Hydropower Station. Engineering Geology, (186), 57-67. https://doi.org/10.1016/j.enggeo.2014.09.012
  20. Zheng, Y., Xia, L., & Yu, Q. (2015). Analysis of removability and stability of rock blocks by considering the rock bridge effect. Canadian Geotechnical Journal, 53(3), 384-395. https://doi.org/10.1139/cgj-2014-0503
  21. Zhang, L., Sherizadeh, T., Zhang, Y., Sunkpal, M., Liu, H., & Yu, Q. (2020). Stability analysis of three-dimensional rock blocks based on general block method. Computers and Geotechnics, (124), 103621. https://doi.org/10.1016/j.compgeo.2020.103621
  22. Zhu, H., Azarafza, M., & Akgün, H. (2022). Deep learning-based key-block classification framework for discontinuous rock slopes. Journal of Rock Mechanics and Geotechnical Engineering, 14(4), 1131-1139. https://doi.org/10.1016/j.jrmge.2022.06.007
  23. Chan, L.Y., & Goodman, R.E. (1983). Prediction of support requirements for hard rock excavations using keyblock theory and joint statistics. In 24th US Symposium on Rock Mechanics.
  24. Hoerger, S.F., & Young, D.S. (1990). Probabilistic prediction of keyblock occurrences. In 31st US Symposium on Rock Mechanics.
  25. Tyler, D.B., Trueman, R., & Pine, R.J. (1991). A probabilistic method for predicting the formation of key blocks. Mining Science and Technology, 13(2), 145-156. https://doi.org/10.1016/0167-9031(91)91310-E
  26. Mauldon, M. (1990). Probability aspects of the removability and rotatability of tetrahedral blocks. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 27(4), 303-307. https://doi.org/10.1016/0148-9062(90)90532-7
  27. Hatzor, Y. (1993). The block failure likelihood: A contribution to rock engineering in blocky rock masses. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 30(7), 1591-1597. https://doi.org/10.1016/0148-9062(93)90162-7
  28. Mauldon, M. (1995). Keyblock probabilities and size distributions: A first model for impersistent 2-D fractures. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 32(6), 575-583. https://doi.org/10.1016/0148-9062(95)00009-6
  29. Stone, C.A., Kuszmaul, J.S., Boontun, A., & Young, D. (1996). Comparison of an analytical and a numerical approach to probabilistic keyblock analysis. In 2nd North American Rock Mechanics Symposium.
  30. Chen, G., Jia, Z., & Ke, J. (1997). Probabilistic analysis of underground excavation stability. International Journal of Rock Mechanics and Mining Sciences, 34(3-4), 51-e1. https://doi.org/10.1016/S1365-1609(97)00167-6
  31. Esterhuizen, G.S., & Streuders, S. (1998). Rockfall hazard evaluation using probabilistic keyblock analysis. Journal of the Southern African Institute of Mining and Metallurgy, 98(2), 59-63.
  32. Yarahmadi Bafghi, A.R., & Verdel, T. (2004). The probabilistic key‐group method. International Journal for Numerical and Analytical Methods in Geomechanics, 28(9), 899-917. https://doi.org/10.1002/nag.339
  33. Chen, G. (2012). Probabilistic key block analysis of a mine ventilation shaft stability – A case study. Geomechanics and Geoengineering, 7(4), 255-262. https://doi.org/10.1080/17486025.2011.592609
  34. Zheng, J., Kulatilake, P.H., Shu, B., Sherizadeh, T., & Deng, J. (2014). Probabilistic block theory analysis for a rock slope at an open pit mine in USA. Computers and Geotechnics, (61), 254-265. https://doi.org/10.1016/j.compgeo.2014.06.002
  35. Zheng, J., Kulatilake, P.H.S.W., & Deng, J. (2015). Development of a probabilistic block theory analysis procedure and its application to a rock slope at a hydropower station in China. Engineering Geology, (188), 110-125. https://doi.org/10.1016/j.enggeo.2015.01.010
  36. Hoerger, S.F., & Young, D.S. (2020). Probabilistic analysis of keyblock failures. Mechanics of Jointed and Faulted Rock, 503-508. https://doi.org/10.1201/9781003078975-70
  37. Yeung, M.R., Jiang, Q.H., & Sun, N. (2003). Validation of block theory and three-dimensional discontinuous deformation analysis as wedge stability analysis methods. International Journal of Rock Mechanics and Mining Sciences, 40(2), 265-275. https://doi.org/10.1016/S1365-1609(02)00137-5
  38. Hatzor, Y. (1992). Validation of block theory using field case histories. Berkeley, United States: University of California.
  39. Chan, L.Y. (1987). Application of block theory and simulation techniques to optimum design of rock excavations. Berkeley, United States: University of California, 372 p. https://doi.org/10.1142/0351
  40. Huang, T.K., Chen, J.C., & Chang, C.C. (2003). Stability analysis of rock slopes using block theory. Journal of the Chinese institute of Engineers, 26(3), 353-359. https://doi.org/10.1080/02533839.2003.9670787
  41. Kulatilake, P.H., Wang, L., Tang, H., & Liang, Y. (2011). Evaluation of rock slope stability for Yujian River dam site by kinematic and block theory analyses. Computers and Geotechnics, 38(6), 846-860. https://doi.org/10.1016/j.compgeo.2011.05.004
  42. Zerradi, Y., Lahmili, A., & Souissi, M. (2020). Stability of a rock mass using the key block theory: a case study. E3S Web of Conferences, (150), 03024. https://doi.org/10.1051/e3sconf/202015003024
  43. Nakai, T., Ryu, M., Ohnishi, Y., Nishiyama, S., & Tatebe, T. (2021). Support design of river crossing tunnel using keyblock concept and its validation by monitoring of the countermeasure by digital photogrammetry at Suzuka tunnel. Development and Application of Discontinuous Modelling for Rock Engineering, 175-181. https://doi.org/10.1201/9781003211389-26
  44. Wittke, W. (1965). Methods to analyze the stability of rock slopes with and without additional loading. Rock Mechanics and Engineering Geology, (II), 52-79.
  45. Londe, P. (1965). Une méthode d’analyse à trois dimensions de la stabilité d’une rive rocheuse. Ann Ponts Chaussees, 135(1), 37-60.
  46. John, K.W. (1968). Graphical stability analysis of slopes in jointed rock. Journal of the Soil Mechanics and Foundations Division, 94(2), 497-526. https://doi.org/10.1061/JSFEAQ.0001108
  47. Goodman, R.E. (1976). Methods of geological engineering in discontinuous rocks. Saint Paul, United States: West Group, 484 p.
  48. 石根华. (1982). A geometric method for stability analysis of discontinuous rocks. Science in China, (A).
  49. Hoek, E., & Bray, J.D. (1981). Rock slope engineering. London, United Kingdom: CRC Press, 364 p. https://doi.org/10.1201/9781482267099
  50. Asladay, A., Barodi, E., Maacha, L., & Zinbi, Y. (1998). Les mineralisations cupriferes du Maroc. Chronique de la Recherche Miniere, (531-532), 29-44.
  51. Verhaert, M., Madi, A., El Basbas, A., Elharkaty, M., Oummouch, A., Oumohou, L., & Yans, J. (2020). Genesis of As-Pb-rich supergene mineralization: The Tazalaght and Agoujgal Cu Deposits (Moroccan Anti-Atlas Copperbelt). Economic Geology, 115(8), 1725-1748. https://doi.org/10.5382/econgeo.4779
  52. Massacrier, P. (1980). Les boutonnières précambriennes d’Aït Abdel-lah-Alma et leur couverture adoudounienne (Protérozoïque supérieur et terminal de l’Anti-Atlas occidental, Maroc). Étude cartographique, lithostratigraphique et structurale. étude cartographique, lithostratigraphique et structurale. Aix Marseille, (I), 118.
  53. Asladay, A., Barodi, E.B., Watanabe, Y., Mouttaqi, A., & Annich, M. (2002). Gisement de Tazalaght. Méthodes et techniques d’exploration minière et principaux gisements au Maroc. Bureau de Recherche Pétrolière et Minière, 215-219.
  54. El Basbas, A., Aissa, M., Ouguir, H., Mahdoudi, M., Madi, O., Baoutoul, H., & Ibouh, H. (2011). La mine de Tazalarht (Anti-Atlas occidental). Les nouveaux guides géologiques et miniers du Maroc: Notes et Mémoires du Service Géologique du Maroc. Les Principales Mines du Maroc, (9), 145-149.
  55. Лицензия Creative Commons