Analytical Method to Evaluate the Stress State Within Vertical Backfill

  • Qizhi ChenEmail author
  • Changjie Xu
  • Luju Liang
  • Xiaozhen Fan
Conference paper
Part of the Sustainable Civil Infrastructures book series (SUCI)


In mining industry, voids created during ore removal are generally backfilled with mill tailings that are left over from processing of mineral ore. Evaluating the stress state in backfill is a critical step for design of backfilled stopes. An analytical method to evaluate the stress is proposed in this paper. Nonuniform distribution of vertical stress is considered in this method. The trajectory of minor principle stress in the fill from the centreline to the wall is assumed as circular-arc. The stress state within vertical backfill can be obtained through the equilibrium consideration of differential flat element. Several examples carried out by analytical and numerical modeling are then presented and compared with existing analytical solutions. The proposed analytical method is also used to evaluate an in situ project from literature. The results by presented analytical method are in good agreement with numerical results and in situ data from literature. So the proposed analytical method can be used to evaluate the stress state in backfilled stopes.



The authors acknowledge the financial supports from the National Key Basic Research Program of China (973 Program) (No. 2015CB057801), National Natural Science Foundation of China (NSFC Grant No. 51278449, NSFC Grant No. 51238009 and NSFC Grant No. 51338009).


  1. ABAQUS User’s Manual, Version 6.1, Hibbitt, Karlsson and Sorenson Inc. (2000) Google Scholar
  2. Goodey, R.J., Brown, C.J., Rotter, J.M.: Predicted patterns of filling pressures in thin-walled square silos. Eng. Struct. 28(1), 109–119 (2006)CrossRefGoogle Scholar
  3. Hasan, A., Karrech, A., Chareyre, B.: Evaluating force distributions within virtual uncemented mine backfill using discrete element method. Int. J. Geomech. 17(7), 06016042 (2016)CrossRefGoogle Scholar
  4. Janssen, H.A.: Versuche über getreidedruck in silozellen. Zeitschr. d. Vereines deutscher Ingenieure 39(35), 1045–1049 (1895)Google Scholar
  5. Knutsson, S.: Stresses in the hydraulic backfill from analytical calculations and in-situ measurements. In: Conference on the Application of Rock Mechanics to Cut and Fill Mining: 01/06/1980-03/06/1980, pp. 261–268. The Institution of Mining and Metallurgy (1981)Google Scholar
  6. Krynine, D.P.: Discussion on ‘Stability and stiffness of cellular cofferdams’ by Karl Terzaghi. Trans. Am. Soc. Civ. Eng. 110(1), 1175–1178 (1945)Google Scholar
  7. Li, L., Aubertin, M., Simon, R., Bussière, B., Belem, T.: Modeling arching effects in narrow backfilled stopes with FLAC. In: Proceedings of the 3rd International Symposium on FLAC & FLAC 3D Numerical Modelling in Geomechanics, Ontario, Canada, pp. 211–219 (2003)Google Scholar
  8. Marston, A.: The theory of external loads on closed conduits in the light of the latest experiments. In: Highway Research Board Proceedings, vol. 9. (1930)Google Scholar
  9. Paik, K.H., Salgado, R.: Estimation of active earth pressure against rigid retaining walls considering arching effects. Géotechnique 53(7), 643–653 (2003)CrossRefGoogle Scholar
  10. Pirapakaran, K., Sivakugan, N.: Arching within hydraulic fill stopes. Geotech. Geol. Eng. 25(1), 25–35 (2007)CrossRefGoogle Scholar
  11. Pirapakaran, K.: Load-deformation characteristics of minefills with particular reference to arching and stress developments. Doctoral dissertation, James Cook University (2008)Google Scholar
  12. Ting, C.H., Sivakugan, N., Read, W., Shukla, S.K.: Analytical method to determine vertical stresses within a granular material contained in right vertical prisms. Int. J. Geomech. 12(1), 74–79 (2010)CrossRefGoogle Scholar
  13. Widisinghe, S., Sivakugan, N.: Vertical stress isobars for trenches and mine stopes containing granular backfills. Int. J. Geomech. 14(2), 313–318 (2014)CrossRefGoogle Scholar
  14. Widisinghe, S., Sivakugan, N.: Vertical stress isobars for silos and square backfilled mine stopes. Int. J. Geomech. 16(2), 06015003 (2015)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • Qizhi Chen
    • 1
    Email author
  • Changjie Xu
    • 1
    • 2
  • Luju Liang
    • 1
  • Xiaozhen Fan
    • 1
  1. 1.Research Center of Coastal and Urban Geotechnical EngineeringZhejiang UniversityHangzhouChina
  2. 2.College of Civil Engineering and ArchitectureEast China Jiaotong UniversityNanchangChina

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