Evaluation of the Stress State in Two Adjacent Backfilled Stopes Within an Elasto-Plastic Rock Mass

  • Nooshin Falaknaz
  • Michel Aubertin
  • Li Li
Original paper


Backfill is used in the mining industry to improve the stability of underground openings and reduce the environmental impact due to the surface disposal of mine wastes. A critical issue for the design of backfilled stopes is the determination of the stress state in the backfill and surrounding rock mass. In recent years, much work has been conducted to assess the stresses in isolated backfilled stopes. Recent work performed by the authors indicates that the stress distribution in a backfilled stope may also be affected by the excavation of an adjacent opening. So far however, simulations of neighbouring stopes have been based on an elastic behavior for the rock mass, which may not reflect its actual response (especially under large stresses). This paper presents key results obtained from numerical simulations of two backfilled stopes excavated in sequence in an elasto-plastic rock mass. The simulations results illustrate the effects of the non-linear rock mass response and of other characteristics including stopes geometry (size and spacing) and depth, natural stress state, and backfill properties. These results indicate that, although arching effects tend to develop in all narrow stopes, the stress distribution in adjacent openings can be quite different for elastic or elasto-plastic rock mass behavior. The results presented here also illustrate the similarities and differences between the behavior of a single backfilled stope and of two adjacent stopes, depending on the rock mass properties and overall characteristics of the system.


Adjacent stopes Mine backfill Rock mass Stresses Numerical modelling Elastic Elasto-plastic behavior 

List of symbols


Stope width (m)


Cohesion of backfill (kPa)


Cohesion of rock (kPa)


Distance between stopes (or pillar width) (m)


Backfill modulus (MPa)


Rock mass elastic modulus (GPa)


Rock mass deformation modulus (GPa)


Depth (m) in the backfill


Stope height (m)


Earth pressure coefficient in the backfill (-)


Rankine’s active earth pressure coefficient


Earth pressure coefficient at rest


Earth pressure coefficient for the natural stresses in the rock mass


Depth at the base of the stope (m)


Maximum difference between the horizontal displacements (cm)


Maximum difference between the horizontal stresses (kPa)


Maximum difference between the vertical stresses (kPa)


Unit weight of backfill (kN/m3)


Unit weight of rock (kN/m3)


Unit weight of rock mass (kN/m3)


Horizontal displacement of rock walls (m)


Horizontal strain of backfill (%)


Poisson’s ratio of rock mass


Backfill Poisson’s ratio


Horizontal stress at backfill and in situ horizontal stress (kPa)


Vertical stress at backfill and in situ vertical stress (kPa)


Internal friction angle (°) of backfill


Internal friction angle (°) of rock mass


Dilatancy angle of backfill (°)



The authors acknowledge the financial support from NSERC and from the partners of the Industrial NSERC Polytechnique-UQAT Chair on Environment and Mine Wastes Management (2006–2012) and of the Research Institute on Mines and the Environment (RIME UQAT-Polytechnique;


  1. Arjang B (1996) In situ ground stresses in the Abitibi Mining District. CIM Bull 89(996):65–71Google Scholar
  2. Askew J, McCarthy PL, Fitzgerald DJ (1978) Backfill research for pillar extraction at ZC/NBHC. Mining with backfill: 12th Canadian Rock Mechanics Symposium, 23–25 May 1978, CIM, Sudbury, pp 100–110Google Scholar
  3. Aubertin M, Li L, Arnold S, Belem T, Bussiere B, Benzaazoua M, Simon R (2003) Interaction between backfill and rock mass in narrow Stopes. In: Culligan PJ, Einstein HH, Whittle AJ (eds) Proceedings of Soil and Rock America 2003, Verlag Glückauf Essen VGE, Essen, Germany, 1, pp 1157–1164Google Scholar
  4. Belem T, Benzaazoua M, Bussière B (2000) Mechanical behaviour of cemented paste backfill. In: Proceedings of 53th Canadian Geotechnical Conference, CGS, Richmond, 1, pp 373–380Google Scholar
  5. Benzaazoua M, Fall M, Belem T (2004) A contribution to understanding the hardening process of cemented pastefill. Miner Eng 17(2):141–152CrossRefGoogle Scholar
  6. Bieniawski ZT (1989) Engineering Rock Mass Classifications. Wiley, New York 215 ppGoogle Scholar
  7. Boumiz A, Vernet C, Tenoudjit FC (1996) Mechanical properties of cement pastes and mortars at early ages—evolution with time and degree of hydration. Adv Cem Based Mater 3:94–106Google Scholar
  8. Bowles JE (1988) Foundation analysis and design. McGraw-Hill, New YorkGoogle Scholar
  9. Brady BHG, Brown ET (2004) Rock mechanics for underground mining, 3rd edn. Kluwer, Dordrecht 628 pGoogle Scholar
  10. El Mkadmi N, Aubertin M, Li L (2014) Effect of drainage and sequential filling on the behavior of backfill in mine stopes. Can Geotech J 51(1):1–15CrossRefGoogle Scholar
  11. Falaknaz N (2014) Analysis of mine backfill behaviour in multiple stopes. PhD Thesis, Ecole Polytechnique, MontrealGoogle Scholar
  12. Falaknaz N, Aubertin M, Li L (2013) Numerical investigation of the stress state in adjacent backfilled mine stopes. In: Proceedings of Canadian Geotechnical Conference, GeoMontreal, MontrealGoogle Scholar
  13. Falaknaz N, Aubertin M, Li L (2014) A numerical modelling study to assess the stress distribution in two nearby backfilled openings created in sequence. In: Proceedings of Canadian Geotechnical Conference, GeoRegina, ReginaGoogle Scholar
  14. Grice T (1998) Underground mining with backfill. Mine tailings disposal-2nd Annual Summit, BrisbaneGoogle Scholar
  15. Hambley DF (2011) Backfill mining. In: Darling P (ed) SME mining engineering handbook, vol 1. Littleton, SME, pp 1375–1384Google Scholar
  16. Hamrin H (2001) Underground mining methods and applications. In: Hustrulid WA, Bullock RL (eds) Underground mining methods: engineering fundamentals and international case studies. SME, Littleton, pp 3–14Google Scholar
  17. Handy RL (1985) The arch in soil arching. J Geotech Eng ASCE 111(3):302–318CrossRefGoogle Scholar
  18. Harrop-Williams K (1989) Arch in soil arching. J Geotech Eng ASCE 115(3):415–419CrossRefGoogle Scholar
  19. Hassani F, Archibald J (1998) Mine backfill. Canadian Institute of Mine, Metallurgy and Petroleum, MontrealGoogle Scholar
  20. Hoek E (2007) Practical rock engineering. Hoek’s corner (rock science). Accessed 15 Apr 2014
  21. Hoek E, Kaiser PK, Bawden WF (1995) Support of underground excavations in hard rock. Balkema, Rotterdam, p 215Google Scholar
  22. Hoek E, Carranza-Torres CT, Corkum B (2002) Hoek-Brown failure criterion 2002 edition. In: Proceedings of 5th North American Rock Mechanics Symposium, Toronto. 1, pp 267–273Google Scholar
  23. Hustrulid W, Qianyuan Y, Krauland N (1989) Modeling of cut and- fill mining systems—Näsliden revisited. In: Hassani FP, Scoble MJ, Yu TR (eds) Innovation in mining backfill technology. Balkema, Rotterdam, pp 147–164Google Scholar
  24. Itasca (2002) FLAC version 5.0. users manuals. ITASCA Consulting Group, MinneapolisGoogle Scholar
  25. Itasca (2014) FLAC3D version 5.0. users manuals. ITASCA Consulting Group, MinnesotaGoogle Scholar
  26. Kaiser PK, Kim, BH (2008) Rock mechanics advances of underground construction and mining. Keynote lecture, Korea Rock Mechanics Symposium, South Korea, pp 1–16Google Scholar
  27. Knutsson S (1981) Stresses in the hydraulic backfill from analytical calculations and in situ measurements. In: Proceedings of Conference on Application of Rock Mechanical to Cut and Fill Mining, Institution of Mining and Metallurgy, London, pp 261–268Google Scholar
  28. Li L, Aubertin M (2008) An improved analytical solution to estimate the stress state in subvertical backfilled Stopes. Can Geotech J 45(10):1487–1496CrossRefGoogle Scholar
  29. Li L, Aubertin M (2009a) Influence of water pressure on the stress state in stopes with cohesionless backfill. Geotech Geol Eng 27(1):1–11CrossRefGoogle Scholar
  30. Li L, Aubertin M (2009b) Numerical investigation of the stress state in inclined backfilled stopes. Int J Geomech 9(2):52–62CrossRefGoogle Scholar
  31. Li L, Aubertin M, Simon R, Bussiere B, and Belem T (2003) Modelling arching effects in narrow backfilled stopes with FLAC. In: Brummer R, Andrieux P, Detournay C, Hart R (eds) Proceedings of the 3rd international FLAC symposium, A.A.Balkema, Rotterdam, pp 211–219Google Scholar
  32. Li L, Aubertin M, Belem T (2005) Formulation of a three dimensional analytical solution to evaluate stress in backfilled vertical narrow openings. Can Geotech J 42(6):1705–1717CrossRefGoogle Scholar
  33. Li L, Aubertin M, Shirazi A, Belem T, Simon R (2007) Stress distribution in inclined backfilled stopes. MINEFILL 2007, Canadian Institute of Mining, Metallurgy and Petroleum, MontrealGoogle Scholar
  34. Li L, Aubertin M, Shirazi A (2010) Implementation and application of a new elasto-plastic model based on a multiaxial criterion to assess the stress state near underground openings. ASCE Int J Geomech 10(1):13–21CrossRefGoogle Scholar
  35. McCarthy DF (1988) Essentials of soil mechanics and foundations: basic geotechnics, 4th edn. Prentice Hall, New JerseyGoogle Scholar
  36. Mitchell RJ (1992) Centrifuge model studies of fill pressures on temporary bulkheads. CIM Bull 85(960):48–54Google Scholar
  37. Ouellet J, Bidwell TJ, Servant S (1998) Physical and mechanical characterisation of paste backfill by laboratory and in situ testing. In: Proceedings of Minefill’98, Brisbane, April 1998, pp 249–254Google Scholar
  38. Pierce ME (1997) Laboratory and numerical analysis of the strength and deformation behaviour of paste backfill. Master’s Thesis, Department of mining engineering, Queen’s University, KingstonGoogle Scholar
  39. Pirapakaran K (2008) Load-deformation characteristics of mine fills with particular reference to arching and stress developments. Ph.D. Thesis, James Cook University, AustraliaGoogle Scholar
  40. Pirapakaran K, Sivakugan N (2006) Numerical and experimental studies of arching effects within mine fill stopes. In: Ng CWW, Zhang LM, Wang YH (eds) Proceedings of the 6th International Conference on Physical Modelling in Geotechnics, Vol 2. Taylor & Francis, Hong Kong, pp 1519–1525Google Scholar
  41. Potvin Y, Thomas E, Fourie A (2005) Handbook on mine fill. Australian Centre for Geomechanics, The University of Western Australia, NedlandsGoogle Scholar
  42. Singh S, Shukla S, Sivakugan N (2011) Arching in inclined and vertical mine stopes. Geotech Geol Eng J 29(5):685–693. doi: 10.1007/s10706-011-9410-4 CrossRefGoogle Scholar
  43. Sivakugan N, Widisinghe S, Wang V (2013) A note on vertical stress determination within the backfilled mine stopes. J. Geomech, Int. doi: 10.1061/(ASCE)GM.1943-5622.0000367 Google Scholar
  44. Thompson B, Bawden W, Grabinsky M (2012) In situ measurements of cemented paste backfill at the Cayeli Mine. Can Geotech J 49(7):755–772CrossRefGoogle Scholar
  45. Veenstra R (2013) A design procedure for determining the in situ stresses of early age cemented paste backfill. PhD Thesis, University of TorontoGoogle Scholar
  46. Winch C (1999) Geotechnical characteristics and stability of paste backfill at BHP Cannington Mine. B. E. Hons Thesis, James Cook University, TownsvilleGoogle Scholar
  47. Wood D (1990) Soil behavior and critical state soil mechanics. Cambridge University Press, ISBN 0-521-33782-8Google Scholar
  48. Yilmaz E, Benzaazoua M, Belem T, Bussiere B (2009) Effect of curing pressure on compressive strength development of cemented paste backfill. Miner Eng 22:772–785CrossRefGoogle Scholar
  49. Zoback ML (1992) First and second order patterns of tectonic stress: the world stress map project. J Geophys Res, 97(11):703–711,728Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Civil, Geological and Mining EngineeringPolytechnique MontrealMontrealCanada

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