SpringerLink
Log in

Integrating Mathews Stability Chart into the Stope Layout Determination Algorithm

  • Published:
Mining, Metallurgy & Exploration Aims and scope Submit manuscript

Abstract

Stope layout optimization is an important feature of underground mining that maximizes the economic value of the project while taking mining limits into account. The large number of parameters and constraints makes it difficult to obtain the optimum condition. Several algorithms have been created to address these problems using a variety of methods. However, the circulating method has not explicitly included stope dimension stability analysis, resulting in a solution that is not stability-proven, which can result in a suboptimal solution. This study integrates the Mathews stability graph into the stope optimization algorithm so that the optimized stope layout considers stability conditions directly through an assessment of the available geomechanical data within the block model. The proposed algorithm is validated through a case study of a synthetic block model created by considering variations in grade and the geomechanical conditions of the rock. Furthermore, several scenarios are created to compare the performance of the algorithm that applies variations in stope sizes with the common case study of stope sizes that remain fixed. A more detailed assessment is also conducted on each final stope layout wall to ensure the successful application of stability analysis in the proposed algorithm through back analysis on the Mathews stability graph. The optimization results show that all walls in the final stope layout fall into the stable condition. Also, the proposed algorithm is also capable of maintaining the project’s economic value. Ultimately, the proposed algorithm can be deemed applicable and suitable for use in the initial stages of mining as a comprehensive assessment of the optimal stope layout, taking into account the stability conditions of the stope.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Data Availability

The data that support the finding of this study are available from the corresponding author upon reasonable request.

References

  1. Mawdesley C, Trueman R, Whiten WJ (2001) Extending the Mathews stability graph for open–stope design. Min Technol 110:27–39. https://doi.org/10.1179/mnt.2001.110.1.27

    Article  Google Scholar 

  2. Lu A, Yin C, Zhang N (2019) Analytic stress solutions for a lined circular tunnel under frictional slip contact conditions. Eur J Mech A Solids 75:10–20. https://doi.org/10.1016/J.EUROMECHSOL.2019.01.008

    Article  MathSciNet  Google Scholar 

  3. Vitali OPM, Celestino TB, Bobet A (2019) Shallow tunnels misaligned with geostatic principal stress directions: analytical solution and 3d face effects. Tunn Undergr Space Technol 89:268–283. https://doi.org/10.1016/J.TUST.2019.04.006

    Article  Google Scholar 

  4. Napa-García GF, Câmara TR, and Navarro Torres VF (2019) Optimization of room-and-pillar dimensions using automated numerical models. Int J Min Sci Technol 29: https://doi.org/10.1016/J.IJMST.2019.02.003.

  5. Abdellah WR, Ahmed HM, Hefni MA (2019) Numerical modelling of staged stope extraction in a tabular steeply dip** deposit. Geomech Geoeng 14:41–51. https://doi.org/10.1080/17486025.2018.1508856

    Article  Google Scholar 

  6. Mensah T (2023) A binary integer linear programming model for optimizing a binary integer linear programming model for optimizing underground stope layout underground stope layout. https://scholarsmine.mst.edu/masters_theses/8176

  7. Lowson AR, Bieniawski ZT (2013) Critical assessment of RMR based tunnel design practices: a practical engineer’s approach. SME 

  8. Kang Z et al (2019) Optimization calculation of stope structure parameters based on Mathews stabilization graph method. J Vibroeng 21:1227–1239

    Article  Google Scholar 

  9. Wang D et al (2021) Stope stability assessment by the Mathews-Potvin method: a case-study of open sto** in salt rock mass under conditions of secondary stress field. IOP Publishing. https://doi.org/10.1088/1755-1315/684/1/012011

    Article  Google Scholar 

  10. Liu H, Zhao Y, Zhang P, Liu F, Yang T (2021) Stope structure evaluation based on the damage model driven by microseismic data and Mathews stability diagram method in **adian gold mine. Geomat Nat Haz Risk 12:1616–1637. https://doi.org/10.1080/19475705.2021.1941308

    Article  Google Scholar 

  11. Janiszewski M, Pontow S, Rinne M (2021) Industry survey on the current state of stope design methods in the underground mining sector. Energies (Basel) 15:240. https://doi.org/10.3390/en15010240

    Article  Google Scholar 

  12. Nikbin V, Ataee-pour M, Shahriar K, Pourrahimian Y, MirHassani SA (2018) Stope boundary optimization: a mathematical model and efficient heuristics. Resour Policy 62:515–526. https://doi.org/10.1016/J.RESOURPOL.2018.10.007

    Article  Google Scholar 

  13. Basiri Z (2018) Stopes layout and production scheduling optimization in sublevel sto** mining. Dissertation, University of Alberta

    Google Scholar 

  14. Nelis G, Gamache M, Marcotte D, Bai X (2016) Stope optimization with vertical convexity constraints. Optim Eng 17:813–832. https://doi.org/10.1007/s11081-016-9321-6

    Article  Google Scholar 

  15. Wilson B (2020) Heuristic stochastic stope layout optimization. University of Alberta, Thesis

    Google Scholar 

  16. Furtado e Faria M, Dimitrakopoulos R, and Lopes Pinto CL (2022) Integrated stochastic optimization of stope design and long-term underground mine production scheduling. Resources Policy 78: https://doi.org/10.1016/j.resourpol.2022.102918.

  17. Furtado e Faria MA, Dimitrakopoulos R, Pinto C (2022) Stochastic stope design optimisation under grade uncertainty and dynamic development costs. Int J Min Reclam Environ 36:81–103. https://doi.org/10.1080/17480930.2021.1968707

    Article  Google Scholar 

  18. Sari YA, Kumral M (2021) Sublevel stope layout planning through a greedy heuristic approach based on dynamic programming. J Oper Res Soc 72:554–563. https://doi.org/10.1080/01605682.2019.1700179

    Article  Google Scholar 

  19. Tolouei K, Moosavi E, Tabrizi AHB, Afzal P, Bazzazi AA (2021) An optimisation approach for uncertainty-based long-term production scheduling in open-pit mines using meta-heuristic algorithms. Int J Min Reclam Environ 35:115–140. https://doi.org/10.1080/17480930.2020.1773119

    Article  Google Scholar 

  20. Lamghari A, Dimitrakopoulos R (2020) Hyper-heuristic approaches for strategic mine planning under uncertainty. Comput Oper Res 115:104590. https://doi.org/10.1016/j.cor.2018.11.010

    Article  Google Scholar 

  21. Ovanic J, Young DS (1995) Economic optimisation of stope geometry using separable programming with special branch and bound techniques. McGill University

    Google Scholar 

  22. Riddle JM (1977) Dynamic programming solution of a block-caving mine layout. 767–780. https://www.onemine.org/documents/a-dynamic-programming-solution-of-a-block-caving-mine-layout Accessed: Jan. 26, 2023

  23. Deraisme J, De Fouquet C, Fraisse H (1984) Geostatistical orebody model computer optimization of profits from different underground mining methods. 583–590

  24. Cheimanoff NM, Deliac EP, Mallet JL (1989) GEOCAD: an alternative cad and artificial intelligence tool that helps moving from geological resources to mineable reserves. Publ by Soc of Mining Engineers of AIME

  25. Alford C (1995) Optimisation in underground mine design.

  26. Cawrse I (2001) Multiple pass floating stope process.

  27. Ataee-Pour M (2004) Optimisation of stope limits using a heuristic approach. Inst Mining Metall Trans Sect A: Min Technol 113: https://doi.org/10.1179/037178404225004959.

  28. Topal E, Sens J (2010) A new algorithm for stope boundary optimization. J Coal Sci Eng 16:113–119. https://doi.org/10.1007/s12404-010-0201-y

    Article  Google Scholar 

  29. Sandanayake DSS, Topal E, Ali Asad MW (2015) A heuristic approach to optimal design of an underground mine stope layout. Appl Soft Comput 30:595–603. https://doi.org/10.1016/J.ASOC.2015.01.060

    Article  Google Scholar 

  30. Bai X, Marcotte D, Simon R (2013) Underground stope optimization with network flow method. Comput Geosci 52:361–371. https://doi.org/10.1016/j.cageo.2012.10.019

    Article  Google Scholar 

  31. Sandanayake DSS, Topal E, Asad MWA (2015) Designing an optimal stope layout for underground mining based on a heuristic algorithm. Int J Min Sci Technol 25:767–772. https://doi.org/10.1016/j.ijmst.2015.07.011

    Article  Google Scholar 

  32. Sandanayake DSS (2014) Stope boundary optimisation in underground mining based on a heuristic approach. Dissertation, Curtin University

    Google Scholar 

  33. Sari YA, Kumral M (2019) A planning approach for polymetallic mines using a sublevel sto** technique with pillars and ultimate stope limits. Eng Optim 52:932–944. https://doi.org/10.1080/0305215X.2019.1624739

    Article  MathSciNet  Google Scholar 

  34. Sari YA, Kumral M (2021) Clustering-based iterative approach to stope layout optimization for sublevel sto**. J South Afr Inst Min Metall 121:97–106. https://doi.org/10.17159/2411-9717/1237/2021

    Article  Google Scholar 

  35. Kumral M, Sari YA (2020) Underground mine planning for stope-based methods. AIP Publishing LLC 10(1063/5):0006787

    Google Scholar 

  36. Villalba Matamoros ME, Kumral M (2017) Heuristic stope layout optimisation accounting for variable stope dimensions and dilution management. Int J Min Miner Eng 8:1–18. https://doi.org/10.1504/IJMME.2017.082680

    Article  Google Scholar 

  37. Hou J, Xu C, Dowd PA, Li G (2019) Integrated optimisation of stope boundary and access layout for underground mining operations. Min Technol 128:193–205. https://doi.org/10.1080/25726668.2019.1603920

    Article  Google Scholar 

  38. V Nikbin E Mardaneh M Waqar A Asad E Topal 2021 Pattern search method for accelerating stope boundary optimization problem in underground mining operations https://doi.org/10.1080/0305215X.2021.1932869

  39. Esmaeili A, Hamidi JK, Mousavi A (2023) Determination of sublevel sto** layout using a network flow algorithm and the MRMR classification system. Resour Policy 80:103265. https://doi.org/10.1016/J.RESOURPOL.2022.103265

    Article  Google Scholar 

  40. Laubscher DH (1990) A geomechanics classification system for the rating of rock mass in mine design. J South Afr Inst Min Metall 90:257–273

    Google Scholar 

  41. Potvin Y, Hadjigeorgiou J (2001) The stability graph method. Underground Mining Methods 66:513–520

    Google Scholar 

  42. Mathews, K. E. Hoek, D. C. Wyllie, and S. B. V. Stewart (1980) Prediction of stable excavation spans for mining at depths below 1000 metres in hard rock. https://www.scirp.org/(S(i43dyn45teexjx455qlt3d2q))/reference/ReferencesPapers.aspx?ReferenceID=1053122 Accessed: Mar. 02, 2020

  43. Potvin Y (1988) Empirical open stope design in Canada. University of British Columbia

    Google Scholar 

  44. Nickson SD (1992) Cable support guidelines for hard rock mine operations. University of British Columbia

    Google Scholar 

  45. Nhleko A, Tholana T, Neingo P (2018) A review of underground stope boundary optimization algorithms. Resour Policy 56:59–69. https://doi.org/10.1016/J.RESOURPOL.2017.12.004

    Article  Google Scholar 

  46. Prasetyo E (2010) Fractal model and classical block model in ore reserve estimation: a comparison. Riset Geologi Dan Pertambangan 20:119–130

    Article  Google Scholar 

  47. Purwanto SH, Sasaoka T, Wattimena RK, Matsui K, Matsui K (2013) Influence of stope design on stability of hanging wall decline in Cibaliung underground gold mine. Int J Geosci 04:1–8. https://doi.org/10.4236/ijg.2013.410A001

    Article  Google Scholar 

  48. Budi S, Wattimena RK, Ardianto A, Matsui K (2009) Determination of stope geometry in jointed rock mass at Pongkor underground gold mine. Int J JCRM 5:63–68. https://doi.org/10.11187/ijjcrm.5.63

    Article  Google Scholar 

Download references

Funding

The authors express great appreciation to Institut Teknologi Bandung through the Riset Unggulan ITB 2022 for funding this study.

Author information

Authors and Affiliations

  1. Graduate Program of Mining Engineering, Faculty of Mining and Petroleum Engineering, Institut Teknologi Bandung, Jawa Barat, Bandung, 40132, Indonesia

    Danu Putra

  2. Department of Mining Engineering, Faculty of Mining and Petroleum Engineering, Institut Teknologi Bandung, Jawa Barat, Bandung, 40132, Indonesia

    Tri Karian, Budi Sulistianto & Mohammad Nur Heriawan

  3. Mining Engineering Department, Faculty of Earth and Energy Technology, Universitas Trisakti, Jakarta Barat, Jakarta, Indonesia

    Danu Putra

Authors
  1. Danu Putra
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tri Karian
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Budi Sulistianto
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Mohammad Nur Heriawan
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Conceptualization, software, investigation, visualization, writing—review and editing, and project administration: Danu Putra; methodology, validation, formal analysis, and writing—review and editing: Tri Karian; validation, resources, writing—review and editing, supervision, and funding acquisition: Budi Sulistianto; supervision, resources, validation, and writing—review and editing: Mohamad Nur Heriawan.

Corresponding author

Correspondence to Tri Karian.

Ethics declarations

Competing Interests

The authors declare no competing interests.

Additional information

Publisher's Note

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

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Putra, D., Karian, T., Sulistianto, B. et al. Integrating Mathews Stability Chart into the Stope Layout Determination Algorithm. Mining, Metallurgy & Exploration 41, 1351–1364 (2024). https://doi.org/10.1007/s42461-024-00993-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s42461-024-00993-5

Keywords

Search

Navigation