Rock Failure Criteria and Mechanisms of Failure for Excavation Stability Design: A Chronological Evolution
Keywords:
Rock, Rock mass, Rock failure mechanism, Failure Criteria, Strength
Abstract
Failure of rock, when it does occur, follows definite mechanical laws and that its probability, can, at least in some instances, be predicted sufficiently in advance of actual occurrence so as to prevent any great danger to the miner. The article chronologically describes rock failure criteria of some practical and most frequently featured strength criteria for predicting failure mechanism of rocks from rock sample or models (lab scale) to total structure or rock mass breakdown (field scale). A cross section range of criteria, from the typical and indispensable to state of the art ones, categorised under isotropic or anisotropic, stress, strain and energy related failure criteria that are predominantly derived on the basis of Coulomb, von Mises and Griffith theories of failure are reviewed. More attention and discussion has been given to most practical criteria like the Mohr-Coulomb and Hoek-Brown. Evolution of mechanisms of rock failure over time by various authors. The paper demonstrates progression of rock failure criteria, and that current theories hinge on classical onesReferences
1. Al-Ajmi, A.M. and Zimmerman, R.W, (2005), Relation between the Mogi and the Coulomb failure criteria. International Journal of Rock Mechanics and Mining Sciences, 42(3), pp.431-439.
2. Al-Ajmi, A.M. and Zimmerman, R.W, (2006), Stability analysis of vertical boreholes using the Mogi–Coulomb failure criterion. International Journal of Rock Mechanics and Mining Sciences, 43(8), pp.1200-1211.
3. Al-Ajmi, A.M. and Zimmerman, R.W, (2007), July. The Mogi-Coulomb true-triaxial failure criterion and some implications for rock engineering. In Proc., 11th Int. Society for Rock Mechanics Congress, Taylor & Francis, London(pp. 475-486).
4. Bagheripour, M.H. and Mostyn, G. (1996), January. Prediction of the Strength of Jointed Rock-Theory and Practice. In ISRM International Symposium-EUROCK 96. International Society for Rock Mechanics.
5. Bagheripour, M. H. and Hakimipour, R. (2009), “Evaluating the efficiency of the Hoek-Brown failure criterion in predicting strength of rock mass for dam foundations and tunnels”, Proc. 1st National Conference on Engineering and Infrastructure Managements.
6. Bagheripour, M.H., Rahgozar, R., Pashnesaz, H. and Malekinejad, M. (2011), A complement to Hoek-Brown failure criterion for strength prediction in anisotropic rock. Geomechanics and Engineering, Vol. 3, No. 1 (2011) 61-81.
7. Benz, T., Schwab, R., Kauther, R.A. and Vermeer, P.A. (2008), A Hoek–Brown criterion with intrinsic material strength factorization. International Journal of Rock Mechanics and Mining Sciences,45(2), pp.210-222.
8. Brady, B.H.G. and Brown, E.T. (1985), Rock Mechanics for underground mining. Publisher: Kluwer Academic Publishers New York, Boston, Dordrecht, London, Moscow, 2005 Springer Science + Business Media, Inc., p 227.
9. Chen, W., Konietzky, H., Tan, X. and Frühwirt, T. (2016), Pre-failure damage analysis for brittle rocks under triaxial compression. Computers and Geotechnics, 74, pp.45-55.
10. Drucker, D.C. and Prager, W. (1952), Soil mechanics and plastic analysis or limit design. Brown University 10(2), pp.157-165.
11. Ewy, R.T. (1999), Wellbore-stability predictions by use of a modified Lade criterion. SPE Drilling and Completion, 14(02), pp.85-91.
12. Griffith, A.A. and Eng, M. (1921), VI. The phenomena of rupture and flow in solids. Phil. Trans. R. Soc. London. A, 221(582-593), pp.163-198.
13. Griffith, A. (1924), “The theory of rupture.” In: Proc., Ist., Int., Congr., Appl., Mech. Biereno, C.B. Burgers, J.M(eds). Delft: Tech. Boekhandel en Drukkerij. J. Waltman Jr., pp. 54-63.
14. Hao, T.S. and Liang, W.G. (2016), A new improved failure criterion for salt rock based on energy method. Rock Mechanics and Rock Engineering, 49(5), pp.1721-1731.
15. Hoek, E. and Martin, C.D. (2014), Fracture initiation and propagation in intact rock–a review. Journal of Rock Mechanics and Geotechnical Engineering, 6(4), pp.287-300.
16. Hoek, E., Carranza-Torres, C. and Corkum, B. (2002), Hoek-Brown failure criterion-2002 edition. Proceedings of NARMS-Tac, 1, 267-273.
17. Hoek, E., Wood, D. and Shah, S. (1992), A modified Hoek–Brown failure criterion for jointed rock masses. In Rock Characterization: ISRM Symposium, Eurock’92, Chester, UK, 14–17 Thomas Telford Publishing (pp. 209-214).
18. Hoek, E. and Brown, E.T. (1997), Practical estimates of rock mass strength. International journal of rock mechanics and mining sciences, 34(8), pp.1165-1186.
19. Hoek, E. and Brown, E.T. (1980), Empirical strength criterion for rock masses. J. Geotechnical Engineering Div. Res. 106: 1013–1035.
20. Ismael, M. (2015), January. Extension and modification of Hoek and Brown failure criterion to incorporate anisotropy. In ISRM Regional Symposium-EUROCK 2015. International Society for Rock Mechanics and Rock Engineering.
21. Jaeger, J. C. and Cook, N. G. W. (1976), Fundamentals of rock mechanics, John Wiley and Sons, Inc.
22. Kwaśniewski, M. (2013), Recent advances in studies of the strength of rocks under true triaxial compression conditions/postępy w badaniachnadwytrzymałościąskał warunkachprawdziwegotrójosiowegościskania. Archives of Mining Sciences, 58(4).
23. Kwasniewski, M. and Takahashi, M. (2010), Strain-based failure criteria for rocks: state of the art and recent advances. Rock Mechanics in Civil and Environmental Engineering.
24. Lade, P. V. (1977), Elasto-plastic stress-strain theory for cohesionless soil with curved yield surfaces. International Journal of Solids and Structures, 13(11) pp 1019-1035.
25. Labuz, J.F. and Zang, A. (2012), Mohr–Coulomb Failure Criterion. Springer-Verlag 975-979.Li, C. and Nordlund, E. (1993), Deformation of brittle rocks under compression-with particular reference to microcracks. Mechanics of materials, 15(3), pp.223-239.
26. Lubarda, V.A. (2000), Deformation theory of plasticity revisited. Proc. Mont. Acad. Sci. Arts, 13, pp.117-143.
27. Mises, R.V. (1986), The mechanics of solids in the plastically-deformable state. Göttin Nachr Math Phys., 1, 582-592.
28. Mogi, K. (1971), Effect of the triaxial stress system on the failure of dolomite and limestone. Tectonophysics, 11(2), pp.111-127.
29. Mogi, K. (2007), Experimental rock mechanics (Vol. 3). CRC Press, pp51-56.
30. Mogi, K. (1971), Fracture and flow of rocks under high triaxial compression. Journal of Geophysical Research, 76(5).
31. Murrell, S.A.F. (1964), The theory of the propagation of elliptical Griffith cracks under various conditions of plane strain or plane stress: Parts II and III. British Journal of Applied Physics, 15(10), p.1211.
32. Rahimi, R. (2014), The effect of using different rock failure criteria in wellbore stability analysis. Missouri University of Science and Technology, pp4-17.
33. Rice, J.R. (2010), Solid mechanics. Cambridge: Harvard University, 31-32.
34. Sandhu, R. S. (1972), A survey of failure theories of isotropic and anisotropic materials. Air Force Flight, Dynamics Laboratory Wright-Patterson Air Force Base, Ohio.
35. Saroglou, H. and Tsiambaos, G. (2008), A modified Hoek–Brown failure criterion for anisotropic intact rock. International Journal of Rock Mechanics and Mining Sciences, 45(2), pp.223-234.
36. Stacey, T.R. and Page, C.H. (1986), Practical handbook for underground rock mechanics. Trans Tech Publications, Clausthal-Zellerfeld.
37. Stassi-D’Alia, F. (1967), Flow and fracture of materials according to a new limiting condition of yelding. Meccanica, 2(3), pp.178-195.
38. Walsh, J.B. and Brace, W.F. (1964), A fracture criterion for brittle anisotropic rock. Journal of Geophysical Research, 69(16).
39. Wu, Y.F. and Zhou, Y.W. (2010), Unified strength model based on Hoek-Brown failure criterion for circular and square concrete columns confined by FRP. Journal of Composites for Construction, 14(2), pp.175-184.
40. Xie, H., Li, L., Peng, R. and Ju, Y. (2009). Energy analysis and criteria for structural failure of rocks. Journal of Rock Mechanics and Geotechnical Engineering, 1(1): 11–20.
41. Wiebols, G.A. and Cook, N.G.W. (1968), An energy criterion for the strength of rock in polyaxial compression. Int J Rock Mech Min 5(6): 529–549. doi:10.1016 / 0148-9062(68)90040-5.
42. Zhang, L. (2008), A generalised three-dimensional Hoek–Brown strength criterion. Rock mechanics and rock engineering, 41(6), pp.893-915.
2. Al-Ajmi, A.M. and Zimmerman, R.W, (2006), Stability analysis of vertical boreholes using the Mogi–Coulomb failure criterion. International Journal of Rock Mechanics and Mining Sciences, 43(8), pp.1200-1211.
3. Al-Ajmi, A.M. and Zimmerman, R.W, (2007), July. The Mogi-Coulomb true-triaxial failure criterion and some implications for rock engineering. In Proc., 11th Int. Society for Rock Mechanics Congress, Taylor & Francis, London(pp. 475-486).
4. Bagheripour, M.H. and Mostyn, G. (1996), January. Prediction of the Strength of Jointed Rock-Theory and Practice. In ISRM International Symposium-EUROCK 96. International Society for Rock Mechanics.
5. Bagheripour, M. H. and Hakimipour, R. (2009), “Evaluating the efficiency of the Hoek-Brown failure criterion in predicting strength of rock mass for dam foundations and tunnels”, Proc. 1st National Conference on Engineering and Infrastructure Managements.
6. Bagheripour, M.H., Rahgozar, R., Pashnesaz, H. and Malekinejad, M. (2011), A complement to Hoek-Brown failure criterion for strength prediction in anisotropic rock. Geomechanics and Engineering, Vol. 3, No. 1 (2011) 61-81.
7. Benz, T., Schwab, R., Kauther, R.A. and Vermeer, P.A. (2008), A Hoek–Brown criterion with intrinsic material strength factorization. International Journal of Rock Mechanics and Mining Sciences,45(2), pp.210-222.
8. Brady, B.H.G. and Brown, E.T. (1985), Rock Mechanics for underground mining. Publisher: Kluwer Academic Publishers New York, Boston, Dordrecht, London, Moscow, 2005 Springer Science + Business Media, Inc., p 227.
9. Chen, W., Konietzky, H., Tan, X. and Frühwirt, T. (2016), Pre-failure damage analysis for brittle rocks under triaxial compression. Computers and Geotechnics, 74, pp.45-55.
10. Drucker, D.C. and Prager, W. (1952), Soil mechanics and plastic analysis or limit design. Brown University 10(2), pp.157-165.
11. Ewy, R.T. (1999), Wellbore-stability predictions by use of a modified Lade criterion. SPE Drilling and Completion, 14(02), pp.85-91.
12. Griffith, A.A. and Eng, M. (1921), VI. The phenomena of rupture and flow in solids. Phil. Trans. R. Soc. London. A, 221(582-593), pp.163-198.
13. Griffith, A. (1924), “The theory of rupture.” In: Proc., Ist., Int., Congr., Appl., Mech. Biereno, C.B. Burgers, J.M(eds). Delft: Tech. Boekhandel en Drukkerij. J. Waltman Jr., pp. 54-63.
14. Hao, T.S. and Liang, W.G. (2016), A new improved failure criterion for salt rock based on energy method. Rock Mechanics and Rock Engineering, 49(5), pp.1721-1731.
15. Hoek, E. and Martin, C.D. (2014), Fracture initiation and propagation in intact rock–a review. Journal of Rock Mechanics and Geotechnical Engineering, 6(4), pp.287-300.
16. Hoek, E., Carranza-Torres, C. and Corkum, B. (2002), Hoek-Brown failure criterion-2002 edition. Proceedings of NARMS-Tac, 1, 267-273.
17. Hoek, E., Wood, D. and Shah, S. (1992), A modified Hoek–Brown failure criterion for jointed rock masses. In Rock Characterization: ISRM Symposium, Eurock’92, Chester, UK, 14–17 Thomas Telford Publishing (pp. 209-214).
18. Hoek, E. and Brown, E.T. (1997), Practical estimates of rock mass strength. International journal of rock mechanics and mining sciences, 34(8), pp.1165-1186.
19. Hoek, E. and Brown, E.T. (1980), Empirical strength criterion for rock masses. J. Geotechnical Engineering Div. Res. 106: 1013–1035.
20. Ismael, M. (2015), January. Extension and modification of Hoek and Brown failure criterion to incorporate anisotropy. In ISRM Regional Symposium-EUROCK 2015. International Society for Rock Mechanics and Rock Engineering.
21. Jaeger, J. C. and Cook, N. G. W. (1976), Fundamentals of rock mechanics, John Wiley and Sons, Inc.
22. Kwaśniewski, M. (2013), Recent advances in studies of the strength of rocks under true triaxial compression conditions/postępy w badaniachnadwytrzymałościąskał warunkachprawdziwegotrójosiowegościskania. Archives of Mining Sciences, 58(4).
23. Kwasniewski, M. and Takahashi, M. (2010), Strain-based failure criteria for rocks: state of the art and recent advances. Rock Mechanics in Civil and Environmental Engineering.
24. Lade, P. V. (1977), Elasto-plastic stress-strain theory for cohesionless soil with curved yield surfaces. International Journal of Solids and Structures, 13(11) pp 1019-1035.
25. Labuz, J.F. and Zang, A. (2012), Mohr–Coulomb Failure Criterion. Springer-Verlag 975-979.Li, C. and Nordlund, E. (1993), Deformation of brittle rocks under compression-with particular reference to microcracks. Mechanics of materials, 15(3), pp.223-239.
26. Lubarda, V.A. (2000), Deformation theory of plasticity revisited. Proc. Mont. Acad. Sci. Arts, 13, pp.117-143.
27. Mises, R.V. (1986), The mechanics of solids in the plastically-deformable state. Göttin Nachr Math Phys., 1, 582-592.
28. Mogi, K. (1971), Effect of the triaxial stress system on the failure of dolomite and limestone. Tectonophysics, 11(2), pp.111-127.
29. Mogi, K. (2007), Experimental rock mechanics (Vol. 3). CRC Press, pp51-56.
30. Mogi, K. (1971), Fracture and flow of rocks under high triaxial compression. Journal of Geophysical Research, 76(5).
31. Murrell, S.A.F. (1964), The theory of the propagation of elliptical Griffith cracks under various conditions of plane strain or plane stress: Parts II and III. British Journal of Applied Physics, 15(10), p.1211.
32. Rahimi, R. (2014), The effect of using different rock failure criteria in wellbore stability analysis. Missouri University of Science and Technology, pp4-17.
33. Rice, J.R. (2010), Solid mechanics. Cambridge: Harvard University, 31-32.
34. Sandhu, R. S. (1972), A survey of failure theories of isotropic and anisotropic materials. Air Force Flight, Dynamics Laboratory Wright-Patterson Air Force Base, Ohio.
35. Saroglou, H. and Tsiambaos, G. (2008), A modified Hoek–Brown failure criterion for anisotropic intact rock. International Journal of Rock Mechanics and Mining Sciences, 45(2), pp.223-234.
36. Stacey, T.R. and Page, C.H. (1986), Practical handbook for underground rock mechanics. Trans Tech Publications, Clausthal-Zellerfeld.
37. Stassi-D’Alia, F. (1967), Flow and fracture of materials according to a new limiting condition of yelding. Meccanica, 2(3), pp.178-195.
38. Walsh, J.B. and Brace, W.F. (1964), A fracture criterion for brittle anisotropic rock. Journal of Geophysical Research, 69(16).
39. Wu, Y.F. and Zhou, Y.W. (2010), Unified strength model based on Hoek-Brown failure criterion for circular and square concrete columns confined by FRP. Journal of Composites for Construction, 14(2), pp.175-184.
40. Xie, H., Li, L., Peng, R. and Ju, Y. (2009). Energy analysis and criteria for structural failure of rocks. Journal of Rock Mechanics and Geotechnical Engineering, 1(1): 11–20.
41. Wiebols, G.A. and Cook, N.G.W. (1968), An energy criterion for the strength of rock in polyaxial compression. Int J Rock Mech Min 5(6): 529–549. doi:10.1016 / 0148-9062(68)90040-5.
42. Zhang, L. (2008), A generalised three-dimensional Hoek–Brown strength criterion. Rock mechanics and rock engineering, 41(6), pp.893-915.
Published
2021-01-28
How to Cite
[1]
M. Gama and P. Chileshe, “Rock Failure Criteria and Mechanisms of Failure for Excavation Stability Design: A Chronological Evolution”, Journal of Natural and Applied Sciences, vol. 3, no. 1, pp. 18-35, Jan. 2021.
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