The Hoeke-Brown failure criterion and GSI-2018 edition
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摘要
The Hoeke Brown criterion was introduced in 1980 to provide input for the design of underground excavations in rock. The criterion now incorporates both intact rock and discontinuities, such as joints,characterized by the geological strength index(GSI), into a system designed to estimate the mechanical behaviour of typical rock masses encountered in tunnels, slopes and foundations. The strength and deformation properties of intact rock, derived from laboratory tests, are reduced based on the properties of discontinuities in the rock mass. The nonlinear Hoeke Brown criterion for rock masses is widely accepted and has been applied in many projects around the world. While, in general, it has been found to provide satisfactory estimates, there are several questions on the limits of its applicability and on the inaccuracies related to the quality of the input data. This paper introduces relatively few fundamental changes, but it does discuss many of the issues of utilization and presents case histories to demonstrate practical applications of the criterion and the GSI system.
The Hoeke Brown criterion was introduced in 1980 to provide input for the design of underground excavations in rock. The criterion now incorporates both intact rock and discontinuities, such as joints,characterized by the geological strength index(GSI), into a system designed to estimate the mechanical behaviour of typical rock masses encountered in tunnels, slopes and foundations. The strength and deformation properties of intact rock, derived from laboratory tests, are reduced based on the properties of discontinuities in the rock mass. The nonlinear Hoeke Brown criterion for rock masses is widely accepted and has been applied in many projects around the world. While, in general, it has been found to provide satisfactory estimates, there are several questions on the limits of its applicability and on the inaccuracies related to the quality of the input data. This paper introduces relatively few fundamental changes, but it does discuss many of the issues of utilization and presents case histories to demonstrate practical applications of the criterion and the GSI system.
The Hoeke Brown criterion was introduced in 1980 to provide input for the design of underground excavations in rock. The criterion now incorporates both intact rock and discontinuities, such as joints,characterized by the geological strength index(GSI), into a system designed to estimate the mechanical behaviour of typical rock masses encountered in tunnels, slopes and foundations. The strength and deformation properties of intact rock, derived from laboratory tests, are reduced based on the properties of discontinuities in the rock mass. The nonlinear Hoeke Brown criterion for rock masses is widely accepted and has been applied in many projects around the world. While, in general, it has been found to provide satisfactory estimates, there are several questions on the limits of its applicability and on the inaccuracies related to the quality of the input data. This paper introduces relatively few fundamental changes, but it does discuss many of the issues of utilization and presents case histories to demonstrate practical applications of the criterion and the GSI system.
引文
Aydan O,Dalgic S.Prediction of deformation behaviour of 3-lane Bolu tunnels through squeezing rocks of North Anatolian fault zone(NAFZ).In:Proceedings of the regional symposium on sedimentary rock engineering.Taipei,China;1998.p.228e33.
Andriev GE.Brittle failure of rock materials.Rotterdam:A.A.Balkema;1995.
Barton N.Some new Q value correlations to assist in site characterization and tunnel design.International Journal of Rock Mechanics and Mining Sciences2002;39(2):185e216.
Bewick RP,Amann F,Kaiser PK,Martin CD.Interpretation of UCS test results for engineering design.In:Proceedings of the 13th international congress on rock mechanics:ISRM congress 2015 e advances in applied&theoretical rock mechanics.Montréal,Canada:International Society for Rock Mechanics;2015.paper 521.
Bewick RP,Kaiser PK,Amann F.Strength of massive to moderately jointed hard rock masses.Journal of Rock Mechanics and Geotechnical Engineering 2019;11(3):562e75.
Bieniawski ZT.Determining rock mass deformability e experience from case histories.International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts 1978;15(5):237e47.
Bobich JK.Experimental analysis of the extension to shear fracture transition in Berea sandstone.MS Thesis.Texas A&M University;2005.
Bowcock JB,Boyd LM,Hoek E,Sharp JC.Drakensberg pumped storage scheme:rock engineering aspects.In:Bieniawski ZT,editor.Exploration in rock engineering.Proceedings of the symposium on exploration for rock engineering.Rotterdam:A.A.Balkema;1976.p.121e39.
Bozorgzadeh N,Escobar MD,Harrison JP.Comprehensive statistical analysis of intact rock strength for reliability-based design.International Journal of Rock Mechanics and Mining Sciences 2018;106:374e87.
Brace WF.Brittle fracture of rocks.In:Judd WR,editor.State of stress in the Earth’s crust.New York:Elsevier;1964.p.111e74.
Brown ET.Strength of models of rock with intermittent joints.Journal of the Soil Mechanics and Foundations Division 1970;96(SM6):1935e49.
Brown ET,Hoek E.Discussion on paper 20431 by R.Ucar entitled“Determination of shear failure envelope in rock masses”.Journal of Geotechnical Engineering1988;114(3):37le73.
Cai M,Kaiser PK,Uno H,Tasaka Y,Minami M.Estimation of rock mass deformation modulus and strength of jointed hard rock masses using the GSI system.International Journal of Rock Mechanics and Mining Sciences 2004;41(1):3e19.
Contreras LF,Brown ET.Bayesian inference of geotechnical parameters for slope reliability analysis.In:Slope stability 2018 e XIV international congress on energy and mineral resources.Seville,Spain:Asociación Nacional de Ingenieros de Minas;2018.p.1998e2026.
Contreras LF,Brown ET,Ruest M.Bayesian data analysis to quantify the uncertainty of intact rock strength.Journal of Rock Mechanics and Geotechnical Engineering 2018;10(1):11e31.
Cook NGW.The failure of rock.International Journal of Rock Mechanics and Mining Sciences 1965;2(4):389e403.
Day JJ,Hutchinson DJ,Diederichs MS.A critical look at geotechnical classification for rock strength estimation.In:Proceedings of the 46th US rock mechanics/geomechanics symposium.Chicago,USA:American Rock Mechanics Association(ARMA);2012.paper 12-563.
Deere DU.Geological considerations.In:Stagg KG,Zienkiewicz OC,editors.Rock mechanics in engineering practice.London:Wiley;1968.p.1e20.
Endersbee LA,Hofto EO.Civil engineering design and studies in rock mechanics for Poatina underground power,Tasmania.Journal of the Institution of Engineers1963;35:187e206.
Fairhurst C.On the validity of the“Brazilian”test for brittle materials.International Journal of Rock Mechanics and Mining Sciences 1964;1(4):535e46.
Flores G,Catalan A.A transition from a large open pit to a novel“macroblock variant”block caving geometry at Chuquicamata Mine,Codelco Chile.Journal of Rock Mechanics and Geotechnical Engineering 2019;11(3):549e61.
Franklin JA,Hoek E.Developments in triaxial testing technique.Rock Mechanics1970;2(2):223e8.
Gerogiannopoulos NG,Brown ET.The critical state concept applied to rock.International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts 1978;15(1):1e10.
Griffith AA.The phenomena of rupture and flow in solids.Philosophical Transactions of the Royal Society of London(Series A)1921;221(2):163e98.
Griffith AA.Theory of rupture.In:Proceedings of the 1st international congress on applied mechanics.Delft,The Netherlands;1924.p.55e63.
Hoek E.Fracture of anisotropic rock.Journal of the South African Institute of Mining and Metallurgy 1964;64(10):501e18.
Hoek E.Rock fracture under static stress conditions.CSIR report MEG.1965.p.383.Pretoria,South Africa.
Hoek E,Brown ET.Underground excavations in rock.London:Institution of Mining and Metallurgy;1980a.
Hoek E,Brown ET.Empirical strength criterion for rock masses.Journal of the Geotechnical Engineering Division 1980b;106(GT9):1013e35.
Hoek E.Strength of jointed rock masses.Géotechnique 1983;33(3):187e223.
Hoek E.Strength of rock and rock masses.ISRM News Journal 1994;2(2):4e16.
Hoek E,Kaiser PK,Bawden WF.Support of underground excavations in hard rock.Rotterdam:A.A.Balkema;1995.
Hoek E,Brown ET.Practical estimates of rock mass strength.International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts 1997;34(8):1165e86.
Hoek E,Marinos P,Benissi M.Applicability of the Geological Strength Index(GSI)classification for very weak and sheared rock masses.The case of the Athens schist formation.Bulletin of Engineering Geology and the Environment1998;57(2):151e60.
Hoek E,Marinos PG.Predicting tunnel squeezing problems in weak heterogeneous rock masses.Tunnels and Tunnelling International 2000;132(11):45e51.
Hoek E,Carranza-Torres C,Corkum B.Hoek-Brown criterion e 2002 edition.In:Hammah R,Bawden W,Curran J,Telesnicki M,editors.Mining and tunnelling innovation and opportunity,proceedings of the 5th North American rock mechanics symposium and 17th tunnelling association of Canada conference.Toronto,Canada.Toronto:University of Toronto;2002.p.267e73.
Hoek E,Marinos P,Marinos V.Characterization and engineering properties of tectonically undisturbed but lithologically varied sedimentary rock masses.International Journal of Rock Mechanics and Mining Sciences 2005;42(2):277e85.
Hoek E,Diederichs MS.Empirical estimation of rock mass modulus.International Journal of Rock Mechanics and Mining Sciences 2006;43(2):203e15.
Hoek E,Martin CD.Fracture initiation and propagation in intact rock e a review.Journal of Rock Mechanics and Geotechnical Engineering 2014;6(4):278e300.
Jaeger JC,Cook NGW.Fundamentals of rock mechanics.3rd ed.London:Chapman and Hall;1969.
Kaiser PK,Amann F,Bewick RP.Overcoming challenges of rock mass characterisation for underground construction in deep mines.In:Proceedings of the 13th international congress on rock mechanics:ISRM congress 2015 e advances in applied&theoretical rock mechanics.Montréal,Canada:International Society for Rock Mechanics;2015.Paper 241.
Kaiser PK,Kim B,Bewick RP,Valley B.Rock mass strength at depth and implications for pillar design.In:Van Sint Jan M,Potvin Y,editors.Deep mining 2010,proceedings of the fifth international seminar on deep and high stress mining,santiago,Chile.Perth,Australia:Australian Centre for Geomechanics;2010.p.463e76.
Kalamaris GS,Bieniawski ZT.A rock mass strength concept for coal incorporating the effect of time.In:Fuji T,editor.Proceedings of the 8th congress on rock mechanics,ISRM.Tokyo,Japan.Rotterdam:A.A.Balkema;1995.p.295e302.
Kellaway M,Taylor D,Keyter GJ.The use of geotechnical instrumentation to monitor ground displacement during excavation of the Ingula power cavern,for model verification and design verification purposes.In:Proceedings of South African tunnelling 2012 e lessons learned on major projects,ladysmith.South Africa.Johannesburg:Southern African Institute of Mining and Metallurgy;2010.p.1e23.
Keyter GJ,Ridgeway M,Varley PM.Rock engineering aspects of the Ingula powerhouse caverns.In:Proceedings of the 6th international symposium on ground support in mining and civil engineering construction,Cape Town,South Africa.Johannesburg.Southern African Institute of Mining and Metallurgy;2008.p.409e45.
Kovari K,Tisa A.Multiple failure state and strain controlled triaxial tests.Rock Mechanics 1974;7(1):17e33.
Kruschke JK.Doing Bayesian data analysis:a tutorial with R,JAGS and Stan.2nd ed.Amsterdam,New York:Academic Press;2015.
Langford JC,Diederichs MS.Quantifying uncertainty in Hoek-Brown intact strength envelopes.International Journal of Rock Mechanics and Mining Sciences2015;74:91e104.
Lau JSO,Gorski B.Uniaxial and triaxial compression tests on URL rock samples from boreholes 207-045-GC3 and 209-069-PH3.Divisional Report(Mining Research Laboratories(Canada)),MRL 92-025(TR).Ottawa:Mining Research Laboratories;1992.
Marinos P,Hoek E.GSI e a geologically friendly tool for rock mass strength.In:Proceedings GeoEng 2000,International conference on geotechnical and geological engineering.Melbourne,Australia,Lancaster,PA:Technomic Publishing Co.;2000.p.1422e40.
Marinos P,Hoek E.Estimating the geotechnical properties of heterogeneous rock masses such as flysch.Bulletin of Engineering Geology and the Environment2001;60(2):85e92.
Marinos V,Marinos P,Hoek E.The geological strength index:applications and limitations.Bulletin of Engineering Geology and the Environment 2005;64(1):55e65.
Marinos V.A revised geotechnical classification GSI system for tectonically disturbed rock masses,such as flysch.Bulletin of Engineering Geology and the Environment 2017;19:1e14.https://doi.org/10.1007/s10064-017-1151-z.
Marinos V,Carter TG.Maintaining geological reality in application of GSI for design of engineering structures in rock.Journal of Engineering Geology 2018;239:282e97.
McClintock FA,Walsh JB.Friction on Griffith cracks in rocks under pressure.In:Proceedings of the 4th US National congress of applied mechanics.Berkeley,USA.New York:American Society of Mechanical Engineers;1962.p.1015e21.
Mogi K.Pressure dependence of rock strength and transition from brittle fracture to ductile flow.Bulletin Earthquake Research Institute 1966;44:215e32.
Murrell SAF.The strength of coal under triaxial compression.In:Walton WH,editor.Mechanical properties of non-metallic brittle materials.London:Butterworths Scientific Publications;1958.p.123e45.
Olavarría S,Adriasola P,Karzulovic A.Transition from open pit to underground mining at Chuquicamata,Antofagasta,Chile.In:Proceedings of the international symposium on stability of rock slopes in open pit mining and civil engineering.Cape Town:South Africa.Johannesburg:Institute of Mining and Metallurgy;2006.p.421e34.
Perras MA,Diederichs MS.A review of the tensile strength of rock:concepts and testing.Geotechnical and Geological Engineering 2014;32(2):525e46.
Ramamurthy T.Strength,modulus responses of anisotropic rocks.In:Hudson JA,editor.Compressive rock engineering,vol.1.Oxford:Pergamon;1993.p.313e29.
Ramsey JM,Chester FM.Hybrid fracture and the transition from extension fracture to shear fracture.Nature 2004;428:63e6.
Read SAL,Richards LR,Perrin ND.Applicability of the Hoek-Brown failure criterion to New Zealand greywacke rocks.In:Vouille G,Berest P,editors.Proceedings of the 9th international congress on rock mechanics.Paris,France.Lisse:A.A.Balkema;1999.p.655e60.
Ros M,Eichinger A.Experimental study of theories of rupture.Non-metallic materials,No.28.Eidgenoss,Materialprufungsanstalt,E.T.H Zurich;1928(in German).
Rosengren KJ,Jaeger JC.The mechanical properties of an interlocked low-porosity aggregate.Géotechnique 1968;18(3):317e26.
Rose ND,Scholz M,Burden J,King M,Maggs C,Havaej M.Quantifying transitional rock mass disturbance in open pit slopes related to mining excavation.In:Slope stability 2018 e XIV International congress on energy and mineral Resources.Seville,Spain:Asociación Nacional de Ingenieros de Minas;2018.p.1273e88.
Sakurai S.Back analysis in rock engineering.ISRM Book Series,.London:Taylor&Francis Group;2017.
Schwartz AE.Failure of rock in the triaxial shear test.In:Proceedings of the 6th rock mechanics symposium.Rolla,USA:University of Missouri;1964.p.109e51.
Serafim JL,Pereira JP.Consideration of the geomechanical classification of Bieniawski.In:Proceedings of the international symposium on engineering geology and underground construction.Lisbon,Portugal.Lisbon:SPG/LNEC;1983.p.33e44.
Sheorey PR.Empirical rock failure criteria.Rotterdam:A.A.Balkema;1997.
Stephens RE,Banks DC.Moduli for deformation studies of the foundation and abutments of the Portugues Dam-Puerto Rico.In:Khair AW,editor.Rock mechanics as a guide for efficient utilization of Natural resources,proceedings of the 30th US symposium on rock mechanics.Morgantown,USA.Rotterdam:A.A.Balkema;1989.p.31e8.
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Vlachopoulos N,Diederichs MS,Marinos V,Marinos P.Tunnel behaviour associated with the weak Alpine rock masses of the Driskos Twin Tunnel system,Egnatia Odos Highway.Canadian Geotechnical Journal 2012;50(1):91e120.
Von Kármán T.Festigkeitsversuche unter allseitigem Druck.Zeitschrift Verein Deutscher Ingenieure 1911;55:1749e57(in German).
Walton S,Hasan O,Morgan K,Brown MR.Modified cuckoo search:a new gradient free optimization algorithm.Chaos,Solutions and Fractals 2011;44(9):710e8.
Zuo JP,Li HT,Xie HP,Ju Y,Peng SP.A nonlinear strength criterion for rocklike materials based on fracture mechanics.International Journal of Rock Mechanics and Mining Sciences 2008;45(4):594e9.
Zuo JP,Liu H,Li H.A theoretical derivation of the Hoek-Brown failure criterion for rock materials.Journal of Rock Mechanics and Geotechnical Engineering2015;7(4):361e6.
Andriev GE.Brittle failure of rock materials.Rotterdam:A.A.Balkema;1995.
Barton N.Some new Q value correlations to assist in site characterization and tunnel design.International Journal of Rock Mechanics and Mining Sciences2002;39(2):185e216.
Bewick RP,Amann F,Kaiser PK,Martin CD.Interpretation of UCS test results for engineering design.In:Proceedings of the 13th international congress on rock mechanics:ISRM congress 2015 e advances in applied&theoretical rock mechanics.Montréal,Canada:International Society for Rock Mechanics;2015.paper 521.
Bewick RP,Kaiser PK,Amann F.Strength of massive to moderately jointed hard rock masses.Journal of Rock Mechanics and Geotechnical Engineering 2019;11(3):562e75.
Bieniawski ZT.Determining rock mass deformability e experience from case histories.International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts 1978;15(5):237e47.
Bobich JK.Experimental analysis of the extension to shear fracture transition in Berea sandstone.MS Thesis.Texas A&M University;2005.
Bowcock JB,Boyd LM,Hoek E,Sharp JC.Drakensberg pumped storage scheme:rock engineering aspects.In:Bieniawski ZT,editor.Exploration in rock engineering.Proceedings of the symposium on exploration for rock engineering.Rotterdam:A.A.Balkema;1976.p.121e39.
Bozorgzadeh N,Escobar MD,Harrison JP.Comprehensive statistical analysis of intact rock strength for reliability-based design.International Journal of Rock Mechanics and Mining Sciences 2018;106:374e87.
Brace WF.Brittle fracture of rocks.In:Judd WR,editor.State of stress in the Earth’s crust.New York:Elsevier;1964.p.111e74.
Brown ET.Strength of models of rock with intermittent joints.Journal of the Soil Mechanics and Foundations Division 1970;96(SM6):1935e49.
Brown ET,Hoek E.Discussion on paper 20431 by R.Ucar entitled“Determination of shear failure envelope in rock masses”.Journal of Geotechnical Engineering1988;114(3):37le73.
Cai M,Kaiser PK,Uno H,Tasaka Y,Minami M.Estimation of rock mass deformation modulus and strength of jointed hard rock masses using the GSI system.International Journal of Rock Mechanics and Mining Sciences 2004;41(1):3e19.
Contreras LF,Brown ET.Bayesian inference of geotechnical parameters for slope reliability analysis.In:Slope stability 2018 e XIV international congress on energy and mineral resources.Seville,Spain:Asociación Nacional de Ingenieros de Minas;2018.p.1998e2026.
Contreras LF,Brown ET,Ruest M.Bayesian data analysis to quantify the uncertainty of intact rock strength.Journal of Rock Mechanics and Geotechnical Engineering 2018;10(1):11e31.
Cook NGW.The failure of rock.International Journal of Rock Mechanics and Mining Sciences 1965;2(4):389e403.
Day JJ,Hutchinson DJ,Diederichs MS.A critical look at geotechnical classification for rock strength estimation.In:Proceedings of the 46th US rock mechanics/geomechanics symposium.Chicago,USA:American Rock Mechanics Association(ARMA);2012.paper 12-563.
Deere DU.Geological considerations.In:Stagg KG,Zienkiewicz OC,editors.Rock mechanics in engineering practice.London:Wiley;1968.p.1e20.
Endersbee LA,Hofto EO.Civil engineering design and studies in rock mechanics for Poatina underground power,Tasmania.Journal of the Institution of Engineers1963;35:187e206.
Fairhurst C.On the validity of the“Brazilian”test for brittle materials.International Journal of Rock Mechanics and Mining Sciences 1964;1(4):535e46.
Flores G,Catalan A.A transition from a large open pit to a novel“macroblock variant”block caving geometry at Chuquicamata Mine,Codelco Chile.Journal of Rock Mechanics and Geotechnical Engineering 2019;11(3):549e61.
Franklin JA,Hoek E.Developments in triaxial testing technique.Rock Mechanics1970;2(2):223e8.
Gerogiannopoulos NG,Brown ET.The critical state concept applied to rock.International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts 1978;15(1):1e10.
Griffith AA.The phenomena of rupture and flow in solids.Philosophical Transactions of the Royal Society of London(Series A)1921;221(2):163e98.
Griffith AA.Theory of rupture.In:Proceedings of the 1st international congress on applied mechanics.Delft,The Netherlands;1924.p.55e63.
Hoek E.Fracture of anisotropic rock.Journal of the South African Institute of Mining and Metallurgy 1964;64(10):501e18.
Hoek E.Rock fracture under static stress conditions.CSIR report MEG.1965.p.383.Pretoria,South Africa.
Hoek E,Brown ET.Underground excavations in rock.London:Institution of Mining and Metallurgy;1980a.
Hoek E,Brown ET.Empirical strength criterion for rock masses.Journal of the Geotechnical Engineering Division 1980b;106(GT9):1013e35.
Hoek E.Strength of jointed rock masses.Géotechnique 1983;33(3):187e223.
Hoek E.Strength of rock and rock masses.ISRM News Journal 1994;2(2):4e16.
Hoek E,Kaiser PK,Bawden WF.Support of underground excavations in hard rock.Rotterdam:A.A.Balkema;1995.
Hoek E,Brown ET.Practical estimates of rock mass strength.International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts 1997;34(8):1165e86.
Hoek E,Marinos P,Benissi M.Applicability of the Geological Strength Index(GSI)classification for very weak and sheared rock masses.The case of the Athens schist formation.Bulletin of Engineering Geology and the Environment1998;57(2):151e60.
Hoek E,Marinos PG.Predicting tunnel squeezing problems in weak heterogeneous rock masses.Tunnels and Tunnelling International 2000;132(11):45e51.
Hoek E,Carranza-Torres C,Corkum B.Hoek-Brown criterion e 2002 edition.In:Hammah R,Bawden W,Curran J,Telesnicki M,editors.Mining and tunnelling innovation and opportunity,proceedings of the 5th North American rock mechanics symposium and 17th tunnelling association of Canada conference.Toronto,Canada.Toronto:University of Toronto;2002.p.267e73.
Hoek E,Marinos P,Marinos V.Characterization and engineering properties of tectonically undisturbed but lithologically varied sedimentary rock masses.International Journal of Rock Mechanics and Mining Sciences 2005;42(2):277e85.
Hoek E,Diederichs MS.Empirical estimation of rock mass modulus.International Journal of Rock Mechanics and Mining Sciences 2006;43(2):203e15.
Hoek E,Martin CD.Fracture initiation and propagation in intact rock e a review.Journal of Rock Mechanics and Geotechnical Engineering 2014;6(4):278e300.
Jaeger JC,Cook NGW.Fundamentals of rock mechanics.3rd ed.London:Chapman and Hall;1969.
Kaiser PK,Amann F,Bewick RP.Overcoming challenges of rock mass characterisation for underground construction in deep mines.In:Proceedings of the 13th international congress on rock mechanics:ISRM congress 2015 e advances in applied&theoretical rock mechanics.Montréal,Canada:International Society for Rock Mechanics;2015.Paper 241.
Kaiser PK,Kim B,Bewick RP,Valley B.Rock mass strength at depth and implications for pillar design.In:Van Sint Jan M,Potvin Y,editors.Deep mining 2010,proceedings of the fifth international seminar on deep and high stress mining,santiago,Chile.Perth,Australia:Australian Centre for Geomechanics;2010.p.463e76.
Kalamaris GS,Bieniawski ZT.A rock mass strength concept for coal incorporating the effect of time.In:Fuji T,editor.Proceedings of the 8th congress on rock mechanics,ISRM.Tokyo,Japan.Rotterdam:A.A.Balkema;1995.p.295e302.
Kellaway M,Taylor D,Keyter GJ.The use of geotechnical instrumentation to monitor ground displacement during excavation of the Ingula power cavern,for model verification and design verification purposes.In:Proceedings of South African tunnelling 2012 e lessons learned on major projects,ladysmith.South Africa.Johannesburg:Southern African Institute of Mining and Metallurgy;2010.p.1e23.
Keyter GJ,Ridgeway M,Varley PM.Rock engineering aspects of the Ingula powerhouse caverns.In:Proceedings of the 6th international symposium on ground support in mining and civil engineering construction,Cape Town,South Africa.Johannesburg.Southern African Institute of Mining and Metallurgy;2008.p.409e45.
Kovari K,Tisa A.Multiple failure state and strain controlled triaxial tests.Rock Mechanics 1974;7(1):17e33.
Kruschke JK.Doing Bayesian data analysis:a tutorial with R,JAGS and Stan.2nd ed.Amsterdam,New York:Academic Press;2015.
Langford JC,Diederichs MS.Quantifying uncertainty in Hoek-Brown intact strength envelopes.International Journal of Rock Mechanics and Mining Sciences2015;74:91e104.
Lau JSO,Gorski B.Uniaxial and triaxial compression tests on URL rock samples from boreholes 207-045-GC3 and 209-069-PH3.Divisional Report(Mining Research Laboratories(Canada)),MRL 92-025(TR).Ottawa:Mining Research Laboratories;1992.
Marinos P,Hoek E.GSI e a geologically friendly tool for rock mass strength.In:Proceedings GeoEng 2000,International conference on geotechnical and geological engineering.Melbourne,Australia,Lancaster,PA:Technomic Publishing Co.;2000.p.1422e40.
Marinos P,Hoek E.Estimating the geotechnical properties of heterogeneous rock masses such as flysch.Bulletin of Engineering Geology and the Environment2001;60(2):85e92.
Marinos V,Marinos P,Hoek E.The geological strength index:applications and limitations.Bulletin of Engineering Geology and the Environment 2005;64(1):55e65.
Marinos V.A revised geotechnical classification GSI system for tectonically disturbed rock masses,such as flysch.Bulletin of Engineering Geology and the Environment 2017;19:1e14.https://doi.org/10.1007/s10064-017-1151-z.
Marinos V,Carter TG.Maintaining geological reality in application of GSI for design of engineering structures in rock.Journal of Engineering Geology 2018;239:282e97.
McClintock FA,Walsh JB.Friction on Griffith cracks in rocks under pressure.In:Proceedings of the 4th US National congress of applied mechanics.Berkeley,USA.New York:American Society of Mechanical Engineers;1962.p.1015e21.
Mogi K.Pressure dependence of rock strength and transition from brittle fracture to ductile flow.Bulletin Earthquake Research Institute 1966;44:215e32.
Murrell SAF.The strength of coal under triaxial compression.In:Walton WH,editor.Mechanical properties of non-metallic brittle materials.London:Butterworths Scientific Publications;1958.p.123e45.
Olavarría S,Adriasola P,Karzulovic A.Transition from open pit to underground mining at Chuquicamata,Antofagasta,Chile.In:Proceedings of the international symposium on stability of rock slopes in open pit mining and civil engineering.Cape Town:South Africa.Johannesburg:Institute of Mining and Metallurgy;2006.p.421e34.
Perras MA,Diederichs MS.A review of the tensile strength of rock:concepts and testing.Geotechnical and Geological Engineering 2014;32(2):525e46.
Ramamurthy T.Strength,modulus responses of anisotropic rocks.In:Hudson JA,editor.Compressive rock engineering,vol.1.Oxford:Pergamon;1993.p.313e29.
Ramsey JM,Chester FM.Hybrid fracture and the transition from extension fracture to shear fracture.Nature 2004;428:63e6.
Read SAL,Richards LR,Perrin ND.Applicability of the Hoek-Brown failure criterion to New Zealand greywacke rocks.In:Vouille G,Berest P,editors.Proceedings of the 9th international congress on rock mechanics.Paris,France.Lisse:A.A.Balkema;1999.p.655e60.
Ros M,Eichinger A.Experimental study of theories of rupture.Non-metallic materials,No.28.Eidgenoss,Materialprufungsanstalt,E.T.H Zurich;1928(in German).
Rosengren KJ,Jaeger JC.The mechanical properties of an interlocked low-porosity aggregate.Géotechnique 1968;18(3):317e26.
Rose ND,Scholz M,Burden J,King M,Maggs C,Havaej M.Quantifying transitional rock mass disturbance in open pit slopes related to mining excavation.In:Slope stability 2018 e XIV International congress on energy and mineral Resources.Seville,Spain:Asociación Nacional de Ingenieros de Minas;2018.p.1273e88.
Sakurai S.Back analysis in rock engineering.ISRM Book Series,.London:Taylor&Francis Group;2017.
Schwartz AE.Failure of rock in the triaxial shear test.In:Proceedings of the 6th rock mechanics symposium.Rolla,USA:University of Missouri;1964.p.109e51.
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