SciELO - Scientific Electronic Library Online

vol.111 número5Meeting the milestones: Are South African small- to medium-scale mines up to the task? índice de autoresíndice de assuntospesquisa de artigos
Home Pagelista alfabética de periódicos  

Serviços Personalizados



Links relacionados

  • Em processo de indexaçãoCitado por Google
  • Em processo de indexaçãoSimilares em Google


Journal of the Southern African Institute of Mining and Metallurgy

versão On-line ISSN 2411-9717
versão impressa ISSN 0038-223X

J. S. Afr. Inst. Min. Metall. vol.111 no.5 Johannesburg Mai. 2011




Analysis of the radial and tangential stress distribution between two neighbouring circular holes under internal pressure by numerical modelling



Sh. ArshadnejadI; K. GoshtasbiII

IDepartment of Mining Engineering, Mahallat Branch, Islamic Azad University, Mahallat, Iran
IIDepartment of Mining Engineering, Tarbiat Modares University, Tehran, Iran




Stress analysis in a rock medium is essential to determine the stress concentration between two consecutive circular holes and prediction of fracture behaviour. When two consecutive circular holes in a hard rock medium such as granite are loaded internally by the pressure of non-explosive expansion material (NEEM), stress concentration occurs between the holes which then causes the rock to fracture. In this work, finite element (FE) analysis using Phase2 code was employed to study the stress concentration between two consecutive circular holes under internal pressure induced by NEEM. Effects of different hole diameters and spacings, rock properties and NEEM pressures have been analysed. The data gained from the numerical analysis and analytical solutions were then used to develop two models. These models were then modified by using the FE data and polynomial regression analysis. The developed analytical models showed to be in a very good agreement with the FE analysis. Hence, the developed models can be used with confidence to determine stress distribution and concentration factors around two consecutive circular holes in a hard and brittle rock which are loaded internally by the pressure induced from the NEEM.

Keywords: Finite element method, non-explosive, quarry mining, stress concentration



“Full text available only in PDF format”




1. ARSHADNEJAD, SH., A model for analysis of rock fracture in granite due to non-explosive expansion material. PhD Thesis, Azad University, Tehran, Iran, 2010, 173 p.         [ Links ]

2. ZHANGZHE, J., HONG, L., and WEN, ZH. Splitting mechanism of rock and concrete under expansive pressure, Conference of Demolition and Reuse of Concrete and Masonry, vol. 1, Demolition method and practice (RILEM), Y. Kasai, (ed.) Nihon University, Japan, 1988, pp. 141-148.         [ Links ]

3. GOTO, K., KOJIMA, K., and WATABE, K. The mechanism of expansive pressure and blow-out of static demolition agent, Conference of Demolition and Reuse of Concrete and Masonry, vol. 1, Demolition method and practice (RILEM), Y. Kasai, (ed.) Nihon University, Japan, 1988, pp. 116-125.         [ Links ]

4. JANA, S. Non-explosive expanding agent-an aid for reducing environmental pollution in mines, Indian Mining and Engineering Journal, 1991, pp. 31-35.         [ Links ]

5. HAYASHI, H., SOEDA, K., HIDA, T., and KANBAYASHI, M. Non-explosive demolition agent in Japan, Conference of Demolition and Reuse of Concrete (RILEM), Erik K. (ed.) Lauritzen, London,1994, pp. 231-241.         [ Links ]

6. HOEK, E. and BIENIAWSKI, Z.T. Brittle rock fracture propagation in rock under compression, Int. J. Fracture Mechanics, vol. 1, no. 3, 1965, pp. 137-155.         [ Links ]

7. LAJTAI, E.Z. Effect of tensile stress gradient on brittle fracture initiation, Int. J. Rock Mech. & Min. Sci., vol. 9, 1972, pp. 569-578.         [ Links ]

8. LAWN, B.R. and WILSHAW, T.R. Fracture of brittle solids, Cambridge University Press, Cambridge, UK, 1975.         [ Links ]

9. INGRAFFEA, A.R. and SCHMIDT, R.A. Experimental verification of a fracture mechanics model for tensile strength prediction of Indiana limestone, Proceeding of 19th US Symp. on rock Mechanics, 1978, pp. 247-253.         [ Links ]

10. FOWELL, R.J. Suggested method for determining mode I fracture toughness using cracked chevron notched Brazilian disc (CCNBD) specimens, ISRM Commission on Testing Methods, Int. J. Rock Mech. Min. Sci., vol. 32, no. 1, 1995, pp. 57-64.         [ Links ]

11. EBERHARDT, E., STIMPSON, B., and STEAD, D. The influence of mineralogy on the initiation of microfractures in granite, Proceeding of 9th International Congress on Rock Mechanics, Paris. G. Vouille and P. Berest, (eds.) A.A. Balkema, Rotterdam, 1999, pp. 1007-1010.         [ Links ]

12. OREKHOV, B.G. and ZERTSALOV, M.G. Fracture Mechanics of Engineering Structures and Rocks, A. A. Balkema, 2001.         [ Links ]

13. YAGIZ, S. Assessment of brittleness using rock strength and density with punch penetration test, Journal of Tunnelling and Underground Space Technology, vol. 24, 2009, pp. 66-74.         [ Links ]

14. HOEK, E. and BIENIAWSKI, Z.T. Application of the photoelastic coating technique to the study of the stress redistribution associated with plastic flow around notches, S. Afr. Mech. Eng. vol. 12, no. 8, 1963, pp. 22-226.         [ Links ]

15. JOUSSINEAU, GH. D., PETIT, J. P., and GAUTHIER, B. D. M. Photoelastic and numerical investigation of stress distributions around fault models under biaxial compressive loading conditions, Journal of Tectonophysics, vol. 363, 2003, pp. 19-43.         [ Links ]

16. NESETOVA, V. and LAJTAI, E. Z. Fracture from compressive stress concentrations around elastic flaws, Int. J. Rock Mech. & Min. Sci., vol. 10, 1973, pp. 265-284.         [ Links ]

17. CHONG, K.P., HARKINS, J.S., KURUPPU, D.M., and LESKINEN, A.I.L. Strain rate dependent mechanical properties of western oil shale, Proceeding of 28th US Symp. on Rock Mechanics, 1987, pp. 157-164.         [ Links ]

18. BAZANT, Z.P. Crack band model for fracture and geomaterials, Numerical methods in geomechanics proc., Edmonton, 1982, pp. 1137-1152.         [ Links ]

19. YAN, X. Rectangular tensile sheet with single edge crack or edge halfcircular-hole crack, Journal of Engineering Failure Analysis, vol. 14, 2007, pp. 1406-1410.         [ Links ]

20. KIRSCH, G. Die theorie der elastizitat und die bedurfnisse der festigkeitslehre, Veit. Ver. Deut. Ing., vol. 42, 1898, pp. 797-807.         [ Links ]

21. TIMOSHENKO, S.P. and GOODIER, J.N. Theory of Elasticity, McGraw-Hill, New York, 1951.         [ Links ]

22. HOEK, E. and BROWN, E.T. Underground excavations in rock, The institution of mining and metallurgy, London, 1980.         [ Links ]

23. GOODMAN, R.E. Introduction to rock mechanics, 2nd edition, John Wiley and Sons, New York, 1989.         [ Links ]

24. SHIGLEY, J.E. Machine Design, McGraw-Hill, 1956.         [ Links ]

25. HERTZBERG, R.W. Deformation and fracture mechanics of Engineering materials, John Wiley & Jons, Inc., 1996.         [ Links ]

26. HOWLAND, R.C.J. On the stress in the neighborhood of a circular hole in a strip under tension, Trans. Roy. Soc., London, A., vol. 229, 1929.         [ Links ]

27. FORCHT, M.M. Factors of stress concentration photoelastically determined, Trans. ASME, Ap. M., vol. 57, 1935, pp. A-67.         [ Links ]

28. LIPSON, CH. and JUVINALL, R. Handbook of stress and strength design and material applications, The Macmillan Company, New York, 1963.         [ Links ]

29. OBERT, L. and DUVALL, W.I. Rock mechanics and the design of structures in rock, John Wiley & Sons, New York, 1967.         [ Links ]

30. SCHULZ, K.J. On the state of stress in perforated strips and plates, Proceeding of Neth. Roy. Acad. Sci., vols. 45 to 48, 1942.         [ Links ]

31. PETERSON, R.E. Stress concentration design factors, John Wiley & Sons, Inc., New York, 1974.         [ Links ]

32. ROCSCIENCE, Inc., Phase2 Verification manual, Version 2.1, 1999.         [ Links ]

33. ROCSCIENCE, Inc., Phase2 model program reference manual, 2001.         [ Links ]

34. ZIENKIEWICZ, O.C. The finite element method in engineering science, Second edition, McGraw-Hill, London, 1971.         [ Links ]

35. CHATFIELD, CH. Statistics for technology, 3th edition, Chapman & Hall, 1983.         [ Links ]

36. MONTGOMERY, D.C., RUNGER, G.C., and HUBELE, N.F. Engineering statistics, Second edition, John Wiley & Sons, Inc., 2001.         [ Links ]

Creative Commons License Todo o conteúdo deste periódico, exceto onde está identificado, está licenciado sob uma Licença Creative Commons