Computational modeling and numerical analysis of dynamics of sustainable mining of mineral complexes

  • 53 Accesses


Understanding the sustainable mining dynamics prevents economic uncertainties, operational errors and severe environmental degradation during mining. The mine dynamics vary depending on multiple factors that can affect overall efficiency. A computational model would help in assessing mining operations. This paper proposes a set of novel computational normed linear vector space models to determine various aspects of mining operations and the estimation of mineral associations in an ore complex by employing matrix algebra. The proposed computational models consider that, distribution of minerals and mine operations can be formulated based on multidimensional vector space, which is computable in nature. Analysis of range of influence interaction matrix (RIIM) basing on a 3-mineral model is carried out to assess the mining dynamics. In addition to RIIM, the cause–effect (C–E) interaction model is employed to assess the interaction intensity and dominance of minerals in an ore deposit in terms of availability as well as extraction. The C–E interrelationships between minerals are evaluated basing on the generic coding method. The transformations of structural domains resulting in multidimensional space are further assessed to envision C–E variations between Cu–Ni–Pb as a mineral complex. The projection analysis based on nonlinear regression and numerical evaluations of computational models provide an insight of the life time of a mine. The proposed computational approaches can be applied in combination on n-mineral models to aid in decision making during all stages of sustainable mining.

This is a preview of subscription content, log in to check access.

Access options

Buy single article

Instant unlimited access to the full article PDF.

US$ 39.95

Price includes VAT for USA

Subscribe to journal

Immediate online access to all issues from 2019. Subscription will auto renew annually.

US$ 199

This is the net price. Taxes to be calculated in checkout.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7.
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15.
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23


  1. African Rainbow Minerals. Mineral resources and mineral reserves 2018, 2018 Integrated Annual Report, 56

  2. Aker ŞL, Aghaei I (2019) Comparison of business environments in oil-rich MENA countries: a clustering analysis of economic diversification and performance. Emerg Mark Financ Trade 55(12):2871–2885.

  3. Australian Centre for Sustainable Mining Practices (2011) A guide to leading practice sustainable development in mining Department of resources, energy and tourism, Australian government. Australian Centre for Sustainable Mining Practices, Sydney, p 201

  4. Beale CO (1985) Copper in South Africa-Part I. SAIMM 85(3):73–80

  5. Berger BR, Ayuso RA, Wynn JC, Seal RR (2008) Preliminary model of porphyry copper deposits. US Geol Surv Open File Rep 1321:55

  6. Böyükata M, Belchior JC (2008) Structural and energetic analysis of copper clusters: MD study of Cun (n = 2–45). J Braz Chem Soc 19(5):884–893.

  7. British Geological Survey report. Minerals, UK: Centre for sustainable mineral development. Nickel: definition, mineralogy and deposits, September 2008, 23.

  8. British Geological Survey, Minerals, UK: Centre for sustainable mineral development. World mineral statistics data, statistics and commodities.

  9. Cramer G (1750) Introduction à l'analyse des lignes courbes algébriques, University of Lausanne. chez les frères Cramer et C. Philibert, pp. 656–659.

  10. Dubiński J (2013) Sustainable development of mining mineral resources. J Sustain Min 12(1):1–45

  11. Evans DM, Hunt JP, John S (2016) An overview of nickel mineralisation in Africa with emphasis on the Mesoproterozoic East African Nickel Belt (EANB). Episodes 39(2):319–333.

  12. Fontan D, Murgese D (2011) Debris-flow hazard assessment related to geomorphological and geological setting and to shallow-landslides occurrence. In Proceedings of the Second World Landslide Forum, 2011 3–7 October, Rome, Italy, 12

  13. Friedrich WR, Roland WS (2018) What is the optimal and sustainable lifetime of a mine? Sustainability 10(2):22.

  14. Gandhi SM, Sarkar BC (2016) Essentials of mineral exploration and evaluation. Elsevier, 1st Edition, 406.

  15. Göknur G, Gordon KS (2016) Statmod: probability calculations for the inverse gaussian distribution. R Found R J 8(1):339–351.

  16. Götz DA, Shayeghi A, Johnston RL, Schwerdtfegerc P, Schäfera R (2016) Structural evolution and metallicity of lead clusters. Royal Soc Chem Nanoscale 8:11153–11160.

  17. Hao L, Zhang Z, Yang X (2019) Mine tailing extraction indexes and model using remote-sensing images in southeast Hubei Province. Environ Earth Sci 78:493

  18. Hudson JA, Harrison JP (1992) A new approach to studying complete rock engineering problems. Geol Soc Lond Eng Geol Hydrogeol 25:93–105.

  19. Hyseni S, Durmishaj B, Fetahaj B, Shala F, Berisha A, Large D (2010) Trepça Ore Belt and Stan Terg mine—geological overview and interpretation, Kosovo (SE Europe). Geologija 53(1):87–92.

  20. Jones RT, Mackey PJ (2015) An overview of copper smelting in southern Africa. Copper Cobalt Africa. Incorporating the 8th Southern African Base Metals Conference Livingstone, Zambia, pp. 499–504.

  21. Kolodziejczyk J, Prsek J, Qela H, Asllani B (2012) New survey of lead and zinc ore mineralization in Republic of Kosovo. Geol Geophys Environ 38(3):295–306.

  22. Li WC, Deng G, Cao W, Xu C, Chen J, Lee ML (2019) Discrete element modeling of the Hongshiyan landslide triggered by the 2014 Ms 65 Ludian earthquake in Yunnan China. Environ Earth Sci 78:20

  23. Liberti L, Lavor C, Maculan N, Mucherino A (2012) Euclidean distance geometry and applications. SIAM Rev 56(1):64.

  24. Masoud Z, Jimenez N, KhaloKakaie R, EsmaeilJalali SM (2013) A new open-pit mine slope instability index defined using the improved rock engineering systems approach. Rock Mech Min Sci 61:1–14

  25. Maulida AZ, Jaharadak AA, Abdul AK (2019) Analysis of factors affecting stock prices in mining sector: evidence from Indonesia Stock Exchange. Manag Sci Lett 9(10):1701–1710.

  26. Mavroulidou M, Hughes SJ, Hellawell EE (2007) Developing the interaction matrix technique as a tool assessing the impact of traffic on air quality. Environ Manag 84(4):513–522.

  27. Mookherjee A, Philip R (1979) Distribution of copper, cobalt and nickel in ores and host-rocks, Ingladhal, Karnataka, India. Mineral Depos 14(1):33–55

  28. National Minerals Information Center, Africa and the Middle East. Country: South Africa, United States Geological Society.

  29. Nurcihan C, Sener C (2008) An application of the interaction matrices method for slope failure susceptibility zoning: Dogankent settlement area (Giresun, NE Turkey). Eng Geol Environ 67(3):375–385

  30. Palabora Mining Company. Limpopo province (Location: Phalaborwa), South Africa.

  31. Segal N, Malherbe S (2000) A perspective on the South African mining industry in the 21st Century. An independent report prepared for the Chamber of Mines of South Africa by the Graduate School of Business of the University of Cape Town in association with Genesis Analytics. The bulk of the work was completed in February 2000, p. 49.

  32. Shengo ML, Kime M-B, Mambwe MP, Nyembo TK (2019) A review of the beneficiation of copper-cobalt-bearing minerals in the Democratic Republic of Congo. J Sustain Min 18(4):226–246.

  33. Simon CD, Mark AN, Alwyn EA (2002) Errors and uncertainty in mineral resource and ore reserve estimation: the importance of getting it right. Can Inst Min Metall Pet Explor Min Geol 11(1–4):77–98.

  34. Singh R, Goel R (1999) Rock mass classification: a practical approach in civil engineering, 1st edn. Elsevier, Amsterdam, p 267

  35. Sinha PK (2014) Location of Lead–Zinc ore deposits in India and its salient features. Ministry of Mines (Geological Survey of India), Government of India.

  36. Snodgaass AA (1986) Lead in South Africa. SAIMM 86(4):97–111

  37. Ueki K, Iwamori H (2017) Geochemical differentiation processes for arc magma of the Sengan volcanic cluster, Northeastern Japan, constrained from principal component analysis. Lithos 290–291:60–75.

  38. Usaini S, Muhammad L (2014) On the rhotrix Eigen values and Eigen vectors. Afr Math Union 25:223–235.

  39. Verhaert M, Bernard A, Saddiqi O, Dekoninck A, Essalhi M, Yans J (2018) Mineralogy and genesis of the polymetallic and polyphased low grade Fe–Mn–Cu Ore of Jbel Rhals deposit (Eastern High Atlas, Morocco). J Miner 8(2):23.

  40. Vitaly AS, Kungurova VE (2010) Irarsite discovery in copper–nickel ores of shanuch deposit (Kamchatka). New Data Miner 45:23–27

  41. Vollmer FW (1990) An application of eigenvalue methods to structural domain analysis. Geol Soc Am Bull 102(6):786–791.

  42. Whittle D (1999) Factors that influence mine design and project value. In Strategic Mine Planning–A Financial Perspective conference, Melbourne Australia 26–27 August 1999, 27

  43. Xue C, Chi G, Zhao X, Wu G, Zhao Z, Dong L (2016) Multiple and prolonged porphyry Cu–Au mineralization and alteration events in the Halasu deposit, Chinese Altai, Xinjiang, Northwestern China. Geosci Front 7(5):799–809.

  44. Yongue-Fouateu R, Ghogomu RT, Penaye J, Ekodeck GE, Stendal H, Colin F (2006) Nickel and cobalt distribution in the laterites of the Lomie region, south-east Cameroon. Afr Earth Sci 45(1):33–47.

  45. Zeraoulia R, Salas AH, Ocampo DL (2018) A new special function and its application in probability. Int J Math Math Sci 10:12.

Download references

Author information

Correspondence to Susmit Bagchi.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Sembatya, E.N., Bagchi, S. Computational modeling and numerical analysis of dynamics of sustainable mining of mineral complexes. Environ Earth Sci 79, 64 (2020) doi:10.1007/s12665-019-8794-y

Download citation


  • Computational model
  • Range of influence matrix
  • Eigen value
  • Nonlinear regression
  • Cause–effect analysis
  • 3-mineral model