CC BY-NC 3.0 Polska


Azad University
Mining Science 2018;25:125–141
The mi is an important parameter in the use of the Hoek-Brown failure criterion. It can be estimated using a triaxial compressive strength test but in many projects there is no actual test result for the parameter. An estimation of mi comes from a reference table giving a constant value. Elsewhere some empirical equations for the value were suggested in the 1990s. Applying these equations is limited use since they are available for a few rock types and the equations are based on just uniaxial compressive strength tests of rock. In this research rocks were divided into three categories (Igneous, Sedimentary and Metamorphic) and three empirical formulas are suggested for the categories based on uniaxial compressive strength (σci) and tensile strength (σt) of rocks by nonlinear regression. The equations have been obtained by a combination of the two independent parameters and the trial and error method was used to find the equations with the highest correlation coefficient. The data base uses data from many original international research projects and much data from Iranian tunnelling projects. The models have a high level of accuracy and have been used to describe most rock types although the authors know that the technique can be improved using a new and larger collection of data in the future.
Shobeir Arshadnejad   
Azad University, Unit28, No.1, 9th alley, Laleh Blv., Jannat Abad, Tehran, Iran, 1473813146 Tehran, Iran
1. AKAI K., YAMAMOTO K., ARIOKA M., 1970, Experimental research on the structural anisotropy of crystalline schists, 2nd Int. Cong. Rock Mech. (ISRM), Belgrade, Vol. 1, 181–186.
2. ALDRITCH M.J., 1969, Pore pressure effects on Berea sandstone subjected to experimental deformation, Geol. Soc. Amer. Bull., Vol. 80, 1577–1586.
3. ATTEWELL P.B., SANDFORD M.R., 1974, Intrinsic shear strength of a brittle anisotropic rock, Int.
4. J. Rock Mech. Min. Sci. Geomech. Abstr., Vol. 11, 423–430.
5. BALMER G., 1952, A general analytical solution for Mohr’s Envelope, Proc. Am. Soc. for Testing Materials, Vol. 52, 1260–1271.
6. BARAT D., 1995, Personal communication from C.M.R.I., Dhanbad.
7. BETOURNEY M.C., GORSKI B., LABRIE D., JACKSON R., GYENGE M., 1991, New considerations in the determination of Hoek and Brown material constants, 7th Int. Cong. Rock Mech. (ISRM) (Ed. W. Wittke), Aachen, Vol. 1, 195–200.
8. BIENIAWSKI Z.T., 1974, Estimating the strength of rock materials, J.S. Afr. Inst. Min. Metall. (SAIMM), Vol. 74, 312–-320.
9. BODONYI J., 1970, Laboratory tests of certain rocks under axially symmetrical loading conditions, 2nd Int. Cong. Rock Mech., ISRM, Belgrade, Vol. 1, 389–397.
10. BORECKI M., KWASNIEWSKI M., PACHA J., OLEKSY S., BERSZAKIEWICZ Z., GUZIK J., 1982, Triaxial compressive strength of two mineralogic/diagenetic varieties of coal measure. fine-medium grained Pniowek and Anna sandstones tested under confining pressure up to 60 MPa, Prace Instytutu PBKiOP Politechniki Sląskiej, 119/2, Gliwice.
11. BRACE W.F., 1964, Brittle fracture of rocks. State of Stress in the Earth’s Crust, W.R. Judd (Ed.),.
12. Elsevier, New York, 695–798.
13. BROCH E., 1974, The influence of water on some rock properties, Advances in Rock Mechanics. 3rd Int. Cong. Rock Mech., Denver, 2, Part A, 33–38.
14. CAI M., KAISER P.K., UNO H., TASAKA Y., MINAMI M., 2004, Estimation of rock mass strength and deformation modulus of jointed hard rock masses using the GSI system, Int. J. Rock Mech. Min. Sci., Vol. 41, No. 1, 3–19.
15. CAI M., KAISER P.K., TASAKA Y., MINAMI M., 2007, Determination of residual strength parameters of jointed rock masses using the GSI system, Int. J. of Rock Mech. and Min. Sci., Vol. 44, 247–265.
16. CHAN S.S.M., CROCKER T.J., WARDELL G.G., 1972, Engineering properties of rocks and rock masses in the deep mines of the Coeur d’Alene Mining District. Idaho, Trans. Soc. Min. Engrs. of AIME, 252, 353–361.
17. DAYRE M., GIRAUD A., 1986, Mechanical properties of granodiorite from laboratory test, Eng. Geol. Vol. 23, 109–124.
18. DONATH F.A., 1964, Strength variations and deformational behavior in anisotropic rock. State of Stress in the Earth’s Crust, W.R. Judd (Ed.), Elsevier, New York, 281–297.
19. EBERHARDT E., 2012, The Hoek. Brown failure criterion, J. Rock Mech. Rock Eng., Vol. 45, 981–988.
20. ETTEHAD RAH Co., 2008, Geotechnical report of Omidiye-Jayezan tunnel, Iran, 50.
21. ETTEHAD RAH Co., 2015, Geotechnical report of tunnels, No. 1, 2, 3, 4, 9, 10 in Patave-Dehdasht, Iran, 255.
22. EVERLING G., 1960, Rock mechanical investigations and basis for determination of rock pressure according to deformation of drill holes, Gluckauf, Vol. 96, 390–409.
23. FAIRHURST C., 1964, On the validity of the “Brazilian” test for brittle materials, Int. J. Rock Mech. Min. Sci., Vol. 1, 515–546.
24. FRANKLIN J.A., Hoek E., 1970, Developments in triaxial testing technique, Rock Mech., Vol. 2, 223–228.
25. FRANKLIN J.A., 1971, Triaxial Strength of rock material, J. Rock Mech., Vol. 3, 86–89.
26. FAROUGH HOSSEINI S.M., VUTUKURI V.S., 1993, On the accuracy of multifailure triaxial test for the determination of peak and residual strength of rocks, Aust. Conf. Geotech. Instrumentation and Monitoring in Open pit and underground Mining, T. Szwedzicki (Ed.), Kalgoorlie, 223–228.
27. GLUSHKO V.T., KIRNICHANSKIY G.T., 1974, Engineering Geological Prognosticating of stability of the openings in deep coal mines, Nedar, Moscow.
28. GNIRK P.F., CHEATHAM J.B., 1965, An experimental study of single bit tooth penetration into dry rock at confining pressures of 0–5000 psi, J. Soc. Pet. Engrs., Vol. 5, 117–130.
29. GOWD T.N., RUMMEL F., 1980, Effect of confining pressure on the fracture behavior of a porous rock, Int. J. Rock Mech. Min. Sci. Geomech. Abstr., Vol. 17, 225–229.
30. HARELAND G., POLSTON C.E., WHITE W.E., 1993, Normalized rock failure envelope as a function of grain size, Int. J. Rock Mech. Min. Sci. Geomech. Abstr., Vol. 30, 715–717.
31. HOBBS D.W., 1964, The strength and the stress strain characteristics of coal in triaxial compression,.
32. J. Geol., Vol. 72, 214–231.
33. HOBBS D.W., 1970, Behavior of broken rocks under triaxial compression, Int. J. Rock Mech. Min. Sci., Vol. 7, 125–148.
34. HOEK E., BROWN E.T., 1980, Underground excavations in rock, Institution of Min. Metall., London, 527.
35. HOEK E., BROWN E.T., 1980, Empirical strength criterion for rock masses, J. Geotechnical Eng. Divi-sion, BT9, 1013–1035.
36. HOEK E., 1983, Strength of jointed rock masses, 23th Rankine Lecture. Geotechnique, Vol. 33, No. 3, 187–223.
37. HOEK E., BROWN E.T., 1988, The Hoek–Brown failure criterion – a 1988 update, In: J. Curran (Ed.), Proceedings of the 15th Canadian Rock Mech. Sym., University of Toronto, 31–38.
38. HOEK E., WOOD D., SHAH S., 1992, A modified Hoek-Brown criterion for jointed rock masses, In: J.A. Hudson (Ed.), Rock characterization, ISRM Sym. Eurock ’92, Chester, UK, London, 209–213.
39. HOEK E., KAISER P.K., BAWDEN W.F., 1995, Support of underground excavations in hard rock, A.A. BALKEMA, Rotterdam.
40. HOEK E., BROWN E.T., 1997, Practical estimates of rock mass strength, Int. J. of Rock Mech. and Min. Sci., Vol. 34, No. 8, 1165–1186.
41. HOEK E., MARINOS P., BENISSI M., 1998, Applicability of the Geological Strength Index (GSI) Clas-sification for very weak and sheared rock masses. The case of the Athens Schist formation, Bull. Eng. Geol. Env., Vol. 57, No. 2, 51–160.
42. HOEK E., CARRANZA-TORRES C.T., CORKUM B., 2002, Hoek–Brown failure criterion 2002 edition, In: R. Haumah, W. Bawden, J. Curran, M. Telesnicki (Eds.), Proc. Fifth North American Rock Mech. Sym. (NARMS-TAC), University of Toronto Press, Toronto, 267–273.
43. HOEK E., CARTER T.G., DIEDERICHS M.S., 2013, Quantification of the Geological Strength Index Chart, 47th US Rock Mech., Sym., ARMA, American Rock Mechanics Association, San Francisco, USA, paper No. 13-762, 1–8.
44. HOSSEINI S.M.F., 1993, Some aspects of the strength characteristics of intact and jointed rocks, Ph.D. Thesis, University of New South Wales.
45. HOSHINO K., KOIDE H., INAMI K., IWAMURA S., MITSUI S., 1972, Mechanical properties of Japanese tertiary sedimentary rocks under high confining pressures, Rept. Geol. Survey, Japan, No. 244.
46. HOSKINS E.R., 1969, The failure of thick-walled hollow cylinders of isotropic rock, Int. J. Rock Mech. Min. Sci., Vol. 6, 99–125.
47. ILLNITSKAYA E.I., TEDER R.I., VATOLIN E.S., KUNTYSH M.F., 1969, Properties of rocks and methods of their determination, Nedar, Moscow.
48. IRANOSTONE Co., 2012, Geotechnical report of tunnels, No.1 and No. 2 in Gilavand, Iran, 80.
49. JAEGER J.C., 1970, Behavior of closely jointed rock, Rock Mechanics – Theory and Practice, 11th U.S. Symp. Rock Mech., W.H. Somerton (Ed.), SME of AIME, New York, 57–68.
50. JOHNSON B., FRIEDMAN M., HOPKINS T.N., 1987, Strength and micro fracturing of Westerly gran-ite extended wet and dry at temperatures to 800 C and pressures to 200 MPa, 28th US Symp. Rock Mech, I.W. Farmer, J.J.K. Daeman, C.S. Desai, C.E. Glass, S.P. Newman (Eds.), Tucson, 399–412.
51. JOHNSTONE J.W., 1985, Strength of intact geomechanical materials, J. Geotech. Eng., 111, 730–749.
52. KOVARI K., TISA A., 1975, Multiple failure state and strain controlled triaxial tests, Rock Mech., 7,.
53. 17–33.
54. KWASNIEWSKI M.A., 1983, Deformational and strength properties of the three structural varieties of carboniferous sandstones, 5th Int. Cong. Rock Mech. (ISRM), Vol. 1, Balkema, Rotterdam,.
55. A 105–A 115.
56. MCLAMORE R., GRAY K.E., 1967, The mechanical behavior of anisotropic sedimentary rocks, Trans. Amer. Soc. Mech. Engr., Series B, 62–76.
57. MISRA B., 1972, Correlation of rock properties with machine performance, Ph.D. Thesis, Leeds Univer-sity.
58. MOGI K., 1965, Deformation and fracture of rocks under confining pressure, (2): Elasticity and Plasticity of some rocks, Bull., Earthquake Res. Inst., Tokyo Univ., 42, 349–379.
59. MOGI K., 1966, Some precise measurements of fracture strength of rocks under uniform compressive stress, Rock Mech. Eng. Geol., IV, 41–44.
60. MOGI K., 2007, Experimental rock mechanics, Taylor & Francis, London, UK.
61. MURREL S.A.F., 1965, The effect of triaxial stress systems on the strength of rock at atmospheric tem-perature, Geophys. J., 10, 231–281.
62. OUYANG Z., ELSWORTH D., 1991, A phenomenological failure criterion for brittle rock, Rock Mech. Rock Eng., 24, 133–153.
63. PARS Co., 2014, Geotechnical report of trench Km 18+200 Polsefid-Ghaemshahr, Iran, 76.
64. RAHVAR E IRAN Co., 2014, Geotechnical report of tunnel No. 3 and No. 4 Polsefid-Ghaemshahr, Iran, 95.
65. RAMAMURTHY T., RAO G.V., RAO K.S., 1985, A strength criterion for rocks, Indian Geotech. Conf., Roorkee, 1, 59–64.
66. RAMAMURTHY T., 1989, Personal Communication from I.I.T., Delhi.
67. RAMAMURTHY T., 2001, Shear strength response of some geological materials in triaxial compres-sion, Int. J, Rock Mech., Min, 38, 683–697.
68. RAMEZ M.R.H., 1967, Fractures and strength of sandstone under triaxial compression, Int. J. Rock Mech. Min. Sci., 4, 257–268.
69. RAO K.S., RAO G.V., RAMAMURTHY T., 1983, Strength anisotropy of a Vindhyan sandstone, Indian Geotech. Conf., Vol. 1, Madras, VI41–VI48.
70. ROCSCIENCE, 2007, Roclab, 1.031. Edn., Rocscience, Inc., Toronto.
71. RUSSO G., 2009, A new rational method for calculating the GSI, Tunneling and Underground Space Technology, 24, 103–111.
72. SCHWARTZ A.E., 1964, Failure of rock in triaxial shear test, 6th Symp. Rock Mech., Rolla, 109–135.
73. SHEA-ALBIN V.R., HANSEN D.R., GERLICK R.E., 1991, Elastic wave velocity and attenuation as used to define phases of loading and failure in coal, USBM Rept. Inv. 9355, 43.
74. SHEORY P.R., BISWAS A.K., CHOUBEY V.D., 1989, An empirical failure criterion for rocks and jointed rock masses, Eng. Geol., 26, 141–159.
75. SHEORY P.R., 1997, Empirical rock failure criteria", A.A. Balkema.
76. SHIMADA M., CHO A., YUKUTAKE H., 1983, Fracture strength of dry silicate rock at high confining pressure and activity of acoustic emission, Tectonophysics, 96, 159–172.
77. SINGH S.K., 1995, Personal communication from C.M.R.I., Dhanbad.
78. SINGH M., SAHU A.K., SRIVASTAVA R.K., TIWARI R.P., 1992, Evaluation and applicability of strength for rocks: sandstones and quartzites of Mirzarpur region, Asian Regional Sump. Rock Slopes, Oxford and IBH, New Delhi, 117–124.
79. SONMEZ H., ULUSAY R., 2002, A discussion on the Hoek–Brown failure criterion and suggested modifications to the criterion verified by slope stability case studies, Yerbilimleri, 26, 77–99.
80. STOWE R.L., 1969, Strength and deformation properties of granite, basalt, limestone and tuff at various loading rates, U.S. Army Corp. Eng., Waterways Exp. Stn., Vicksburg, Miss., Misc. Paper C-69-1.
81. VUTUKURI V.S., FAROUGH HOSSEINI S.M., 1993, Correlation between the effect of confining pressure on compressive strength in triaxial test and the effect of dia/height ratio on compressive strength in unconfined compression test, 12th Conf. Ground Control in Mining, S.S. Peng (Ed.), Morgantown, 316–321.
82. WANG R., KEMENY J.M., 1995, A new empirical failure criterion for rock under polyaxial compressive stresses, 35th US Symp. Rock Mech., J.J. Daemen, R.A. Schultz (Eds.), A.A. Balkema, Rotterdam, 453–458.
83. WILHELMI B., SOMERTON W.H., 1967, Simultaneous measurement of pore and elastic properties of rocks under triaxial stress conditions, J. Soc. Pet. Engrs., 7, 283–294.
84. YOSHIDA N., MORGENSTEM N.R., CHAN D.H., 1990, A failure criterion for stiff soils and rocks exhibiting softening, Canadian Geotechnical Journal, 27, 2, 195–202.
85. YOU M.Q., SU C.D., CHEN X.L., 2011, Brazilian Splitting strengths of discs and rings of rocks in dry and saturated conditions, Chinese J. Rock Mech. and Eng., 30, 3, 464–472.
86. YUDHBIR, LEMANZA W., PRINZL F., 1983, An empirical failure criterion for rock masses, 5th Int. Cong. Rock Mech. (ISRM), 1, A.A. Balkema, Rotterdam, B1–B8.