Geomechanics and Engineering

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

A complement to Hoek-Brown failure criterion for strength prediction in anisotropic rock

  • Received : 2010.11.28
  • Accepted : 2011.02.14
  • Published : 2011.03.25
⟨ Previous Next ⟩

Abstract

In this paper, a complement to the Hoek-Brown criterion is proposed in order to derive the strength of anisotropic rock from strength of the corresponding truly intact rock. The complement is a decay function, which unlike other modifications or suggestions made in the past, is multiplied to the function of the original Hoek-Brown failure criterion for intact rock. This results in a combined and extended form of the criterion which describes the strength of anisotropic rock as a varying fraction of the corresponding truly intact rock strength. Statistical procedures and in particular regression analyses were conducted into data obtained in experiments conducted in the current research program and those collected from the literature in order to define the Hoek-Brown's criterion complement. The complement function was best described by a simple polynomial including only three constants to be empirically evaluated. Further investigations also showed that these constants can be related to the other readily available parameters of rock material which further facilitate determining the constants. A great and prime advantage of the proposed complement is that it is mathematically simple including the least possible number of empirical constants which are easily estimated with minimum experimental effort. Moreover, proposed concept does not suggests any change to the original Hoek-Brown criterion itself or its constants and serves whenever anisotropy does exist in the rock. This further implies on the possibility of using any other failure criterion for intact rock in conjunction with the compliment to reach the strength of anisotropic rock.

Keywords

References

  1. Asadi, M., Eftekhari, M. and Bagheripour, M.H. (2010), "Evaluating the strength of intact rock through Genetic Programming", J. Appl. Soft Comput. (in press)
  2. Attewell, B. and Sandford, M.R. (1974), "Intrinsic shear strength of a brittle anisotropic rock. I. Experimental and mechanical interpretation. II. Textural data acquisition and processing. III. Textural interpretation of failure", Int. J. Rock Mech. Min. Sci., 11, 423-430, 431-438, 439-451. https://doi.org/10.1016/0148-9062(74)90453-7
  3. Bagheripour, M.H. and Mostyn, G.R. (1996), "Prediction of strength of jointed rock-theory and ractice", Proc. ISRM Int. Symp. on Prediction and Performance in Rock Mechanics and Rock Engineering, Eurock 96, Sept. 2-5, Torino, Italy, 231-238.
  4. 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, 27-29 Oct., 2009, Tehran University, Iran.
  5. Bagheripour, M.H. and Asadi, M. (2006), "Anisotropy index and determining the strength of intact rock", Geomech. Strength Mater. J., 23(107), 28-36.
  6. Bagheripour, M.H. and Pashnehsaz, H. (2006), "The impact of discountinuity dip on the compressive strength of rock", Proc. 3rd Rock Mechanics Conf., Amirkabir University of Technology, 16-18 Oct., 2006, Tehran , Iran.
  7. Bagheripour, M.H., Marandi, S.M. and Moradi, A.R. (2003), "Evaluation of the compressive strength of jointed rock using decay functions", Proc. 3rd Geology and Environmental Engineering Conf., 11-12 Sept. 2003, Hamedan, Iran.
  8. Benz, T., Schwab, R., Kauther, R.A. and Vermeer, P.A. (2008), "A Hoek and Brown criterion with intrinsic material factorization", Int. J. Rock Mech. Min. Sci., 45, 210-222. https://doi.org/10.1016/j.ijrmms.2007.05.003
  9. Borecki, M. and Kwasniewski, M.A. (1981), "Experimental and analytical studies on compressive strength of anisotropic rocks", Proc. 7th Scientific Session of the Int. Bureau of Rock Mechanics, Katowice, 23-49.
  10. Brown, E.T., Richards, L.R. and Barr, M.V. (1977), "Shear strength characteristics of Delabole slates", Proc. Con. in Rock Engineering, Newcastle Upon Tyne, 33-51.
  11. Colak, K. and Unlu, T. (2004), "Effect of transverse anisotropy on the Hoek-Brown strength parameter "mi" for intact rocks", Int. J. Rock Mech. Min. Sci., 41, 1045-1052. https://doi.org/10.1016/j.ijrmms.2004.04.004
  12. Dehler, W. and Labuz, J.F. (2007), "Stress path testing of an anisotropic sandstone", J. Geotech. Geoenviron. Eng., 133(1), 116-119. https://doi.org/10.1061/(ASCE)1090-0241(2007)133:1(116)
  13. Donath, F.A. (1964), "Strength variation and deformational behaviour of anisotropic rocks", In: State of Stress in the Earth's Crust, New York, Elsevier, 281-298.
  14. Duveau, G. and Shao, J.F. (1998), "A modified single discontinuity theory for the failure of highly stratified rocks", Int. J. Rock Mech. Min. Sci., 35(6), 807-813. https://doi.org/10.1016/S0148-9062(98)00013-8
  15. Hoek, E. and Brown, E.T. (1980a), "Underground excavations in rock", Inst. Min. Metall, London.
  16. Hoek, E. and Brown, E.T. (1980b), "Empirical strength criterion for rock masses", J. Geotech. Eng. Div. - ASCE, 106(GT9), 1013-1035.
  17. Hoek, E. (1983), "Strength of jointed rock masses", Geotechnique, 33, 187-223. https://doi.org/10.1680/geot.1983.33.3.187
  18. Hoek, E., Wood, D. and Shah, S. (1992), "A modified Hoek-Brown failure criterion for jointed rock masses", Eurock 92 Proc., ISRM Int. Symp. on Rock Mech.
  19. Hoek, E. (1994), "Strength of rock and rock masses", ISRM News J., 2(2), 4-26.
  20. Hoek, E. and Brown, E.T. (1997), "Practical estimates of rock mass strength", Int. J. Rock Mech. Min. Sci., 34(8), 1165-1186. https://doi.org/10.1016/S1365-1609(97)80069-X
  21. Hoek, E., Carranza-Torres, C. and Corkum, B. (2002), "Hoek-Brown failure criterion-2002 edition", Proc of the NARMS-TAC joint conference, Toronto, 267-273.
  22. Horino, F.G. and Ellickson, M.L. (1970), "A method of estimating the strength of rock containing planes of weakness", US Bureau of Mines, Report of Investigation 7449.
  23. Jaeger, J.C. (1960), "Shear fracture of anisotropic rocks", Geol. Mag., 97, 65-72. https://doi.org/10.1017/S0016756800061100
  24. Jaeger, J.C. and Cook, N.G.W. (1979), Fundamental of rock mechanics, (3rd ed.), London Chapman and Hall.
  25. Kwasniewski, M.A. (1993), "Mechanical behaviour of anisotropic rocks", In Hudson JA, Editor., Comprehensive rock engineering, Fundamentals. Oxford, Pergamon Press, 1, 285-312.
  26. Mclamor, R. and Gray, K.E. (1967), "The mechanical behaviour of anisotropic sedimentary rocks", J. Eng. Industry - T. ASME, 80, 62-73.
  27. Merifield, R., Lyamin, A.V. and Sloan, S.W. (2006), "Limit analysis solution for the bearing capacity rock masses using the generalized Hoek and Brwon criterion", Int. J. Rock Mech. Min. Sci., 43, 920-937. https://doi.org/10.1016/j.ijrmms.2006.02.001
  28. Mostyn, G.R. and Bagheripour, M.H. (1995), "A new model material to simulate rock", Proc. 2nd Int. Conf. on Mech. Jointed and Faulted Rock (MJFR-1), 10-14 April, Viena, Austria.
  29. Nasseri, M.H.B., Rao, K.S. and Ramamurthy, T. (2003), "Anisotropic strength and deformation behaviour of Himalayan schists", Int. J. Rock Mech. Min. Sci., 40, 3-23. https://doi.org/10.1016/S1365-1609(02)00103-X
  30. Niandou, H., Shao, J.F., Henry, J.P. and Fourmaintraux, D. (1997), "Laboratory investigation of the mechanical behaviour of Tournemire shale", Int. J. Rock Mech. Min. Sci., 34, 3-16. https://doi.org/10.1016/S1365-1609(97)80029-9
  31. Ramamurthy, T. and Arora, V.K. (1994), "Strength predictions for jointed rocks in confined and unconfined states", Int. J. Rock. Mech. Min. Sci.Geomech. Abs., 31(1), 9-22. https://doi.org/10.1016/0148-9062(94)92311-6
  32. Ramamurty, T. (1993), "Strength and modulus responses of anisotropic rocks", In: Hudson J.A Editor. Comprehensive Rock Engineering Oxford, Pergamon Press, 312-329.
  33. Saroglou, H. and Tsiambaos, G. (2008), "A modified Hoek-Brown failure criterion for anisotropic intact rock", Int. J. Rock Mech. Min. Sci., 45, 223-234. https://doi.org/10.1016/j.ijrmms.2007.05.004
  34. Sheorey, P.R. (1997), Empirical rock failure criteria, Rotterdom, A.A. Balkema (Pub.).
  35. Sing, J., Ramamurthy, T. and Rao, G. (1989), "Strength anisotropies in rocks", Indian Geotech. J., 19(2), 147- 166.
  36. Tien, Y.M. and Kuo, M.C. (2001), "A failure criterion for transversely isotropic rocks", Int. J. Rock Mech. Min. Sci., 38, 399-412. https://doi.org/10.1016/S1365-1609(01)00007-7
  37. Tien, Y.M. and Tsao, P.F. (2000), "Preparation and mechanical properties of artificial transversely isotropic rock", Int. J. Rock Mech. Min. Sci., 37, 1001-1012. https://doi.org/10.1016/S1365-1609(00)00024-1
  38. Wu, Y.F. and Zhou, Y.W. (2010), "Unified strength model based on Hoek and Brown failure criterion for circular and square columns confined by FRP", J. Compos. Constr., 14(2), 175-184. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000062

Cited by

  1. Optimized Mamdani fuzzy models for predicting the strength of intact rocks and anisotropic rock masses vol.8, pp.2, 2016, https://doi.org/10.1016/j.jrmge.2015.11.005
  2. Relationship of box counting of fractured rock mass with Hoek-Brown parameters using particle flow simulation vol.9, pp.5, 2015, https://doi.org/10.12989/gae.2015.9.5.619
  3. Influence of water content and anisotropy on the strength and deformability of low porosity meta-sedimentary rocks under triaxial compression vol.126, 2012, https://doi.org/10.1016/j.enggeo.2011.12.009
  4. Estimating model parameters of rockfill materials based on genetic algorithm and strain measurements vol.10, pp.1, 2016, https://doi.org/10.12989/gae.2016.10.1.037
  5. Finite element model updating effect on the structural behavior of long span concrete highway bridges vol.14, pp.6, 2014, https://doi.org/10.12989/cac.2014.14.6.745
  6. Failure criteria of concrete- A review vol.14, pp.5, 2014, https://doi.org/10.12989/cac.2014.14.5.503
  7. A simplified approach to directly consider intact rock anisotropy in Hoek–Brown failure criterion vol.6, pp.5, 2014, https://doi.org/10.1016/j.jrmge.2014.06.003
  8. Dog bone shaped specimen testing method to evaluate tensile strength of rock materials vol.12, pp.6, 2011, https://doi.org/10.12989/gae.2017.12.6.883
  9. Experimental study of crack propagation of rock-like specimens containing conjugate fractures vol.17, pp.4, 2011, https://doi.org/10.12989/gae.2019.17.4.323
  10. A Case Study on the Optimal Design of the Horizontal Wellbore Trajectory for Hydraulic Fracturing in Nong’an Oil Shale vol.13, pp.1, 2011, https://doi.org/10.3390/en13010286
  11. Anisotropic modeling of layered rocks incorporating planes of weakness and volumetric stress vol.8, pp.3, 2020, https://doi.org/10.1002/ese3.551
  12. Ground support performance in deep underground mine with large anisotropic deformation using calibrated numerical simulation (case of mine-H) vol.21, pp.6, 2011, https://doi.org/10.12989/gae.2020.21.6.551
  13. Coupled Plasticity and Damage Constitutive Model Considering Residual Shear Strength for Shales vol.20, pp.8, 2011, https://doi.org/10.1061/(asce)gm.1943-5622.0001721
  14. A-BQ, a classification system for anisotropic rock mass based on China National Standard vol.27, pp.10, 2020, https://doi.org/10.1007/s11771-020-4531-7
  15. Quantitative risk assessment for wellbore stability analysis using different failure criteria vol.24, pp.3, 2011, https://doi.org/10.12989/gae.2021.24.3.281
  16. Anisotropic deformability and strength of slate from NW-Spain vol.148, pp.None, 2011, https://doi.org/10.1016/j.ijrmms.2021.104923
  17. Bayesian inference of rock strength anisotropy: Uncertainty analysis of the Hoek-Brown failure criterion vol.148, pp.None, 2011, https://doi.org/10.1016/j.ijrmms.2021.104952