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8/12/2019 GSI and Hoek-Brown Procedure
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Review:GSIandHoekBrownProcedure
The presence of geological structures within a rock mass (joints, shears, etc.), requires that
consideration be given to the combined influence of intact rock blocks and discontinuities when
calculatingtherockmass'responsetotunnelling.This is incontrasttomosttestingcarriedoutduring
geotechnicalinvestigations,
which
is
usually
restricted
to
laboratory
testing
of
intact
rock
samples.
In
situ tests are often prohibitively expensive and associated with their own issues of reliability,
repeatability and scale.Thishas led to thedevelopmentofanumberof systems that link rockmass
propertiestoobservationsoftherockmasscharacteristics.Amongthese,theGeologicalStrengthIndex
(GSI) coupled with the HoekBrown failure criterion has become one of the industry standards for
estimatingrockmasspropertiesoninternationaltunnellingprojects.
The HoekBrown failure criterion is an empirical formulation for estimating the confinement
strengthrelationshipofarockmass.It'snonlinearformdistinguishesitfromthelinearMohrCoulomb
failurecriterion(Fig.1a).Thecriterionwasoriginallyconceivedbasedonexperienceswithbrittlefailure
inhard rock anddeveloped to assume that rockmass failurewas controlledbyjointingbutwithno
preferred failure directions (Hoek & Brown 1980); i.e. the rock mass responds as an equivalent
continuum.Later
revisions
saw
the
Hoek
Brown
failure
criterion
coupled
with
Bieniawski's
Rock
Mass
Rating(RMR)systemasameanstoscalelaboratoryintactrockpropertiestothoseforthejointedrock
mass(Hoek&Brown1988),andimprovementstobetteraccountforpoorerqualityrockmasses(Hoek
etal.1992).Furtherexperiencewith the latter found that itwasdifficult toapplyRMR toverypoor
quality rock masses. This led to the introduction of the Geological Strength Index (GSI) as a
characterization system based more heavily on fundamental geological observations and less on
'numbers' (Hoeketal.1995).Themostuptodateversion,Hoeketal. (2002), representsamajor re
examination of the entire HoekBrown criterion and includes new derivations for the relationships
betweenthedifferentinputparametersandGSI.
ThegeneralizedformofthenonlinearHoekBrownfailurecriterionis:
(1)where and are the major and minor effective principal stresses at failure, is the uniaxialcompressivestrengthoftheintactrock,and,sandaarematerialconstantsfortherockmass.TheseconstantsaredeterminedfortherockmassusingGSIasperHoeketal.(2002):
(2) (3)
/
/
(4)
Fromabove, isacurvefittingparameterderivedfromtriaxialtestingof intactrock.Theparameter isthereforeareducedvalueofthe intactrockvalue,whichaccountsforthestrengthreducingeffectsoftherockmassconditionsdefinedbyGSI.Strengthreductionfortheparameterssandafollow
accordingly(Fig.1b).D isadisturbancefactorthatcanaccountforblastdamageandstressrelaxation,
withvaluesrangingfrom0forundisturbedconditionsto1forverydisturbedrockmasses.
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Figure1.a)ComparisonoflinearMohrCoulombandnonlinearHoekBrownfailureenvelopesplottedagainsttriaxialtestdataforintactrock;b)ScalingofHoekBrownfailureenvelopeforintactrocktothatforrockmassstrength.
GSIisestimatedinthefieldfromthechartofMarinosetal.(2005);seeFigure2.Intheabsenceof
GSIvaluesorasasecondarycheck,GSIcanbeconvertedfromRMR89values(Bieniawski1989),aswas
thepracticeinearlyapplicationsoftheGSIsystemusingtherelationship:
5 (for >23) (5)where is amodified version of RMR89 inwhich the groundwater rating is set to 15 and theadjustmentforjointorientation issettozero.Theseadjustmentsavoiddoublecountingtheeffectsof
groundwater(aneffectivestressparameterinthenumericalanalysis)andjointorientation(treatedasa
specific input for structural analysis) when deriving rock mass properties to be used in numerical
analyses.Forverypoorqualityrockmasses(
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Figure2.GeologicalStrengthIndex(GSI)lookupchartforjointedrockmasses(afterMarinos&Hoek2000).
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A further consideration is thatmost geotechnical design calculations arewritten for theMohr
Coulomb failure criterion, it is often necessary to calculate equivalent rockmass friction angles and
cohesive strengths from the HoekBrown parameters. Moreover, most practitioners have more
experience,andthereforeanintuitivefeelingforthephysicalmeaningsofcohesionandfriction,which
isnotthecasefor,sanda.Intermsofequivalencies,theparameter isrelatedtothefrictionalstrengthoftherockmass,ands,whichisameasureofhowfracturedtherockmassis,isrelatedtothe
rock mass cohesion. These are only descriptive relationships, however. Where MohrCoulomb
parametersarerequired,thefittingofthelinearMohrCoulombenvelopetothenonlinearHoekBrown
enveloperesultsinthefollowingequationsforfrictionandcohesivestrength: (7)
(8)
where
/.Notethatthevalueof
representstheupperlimitofconfiningstressover
which
the
relationship
between
the
Hoek
Brown
and
Mohr
Coulomb
failure
envelopes
is
considered.
Fordeeptunnels, canbecalculatedfromtheempiricalrelationship(Hoeketal.2002): 0.47 . (9)where istheunitweightoftherockmass,Histhedepthofthetunnelbelowsurface,and isthe"global"rockmassstrengthforthestressrange givenby: (10)Incaseswherethehorizontalstressishigherthantheverticalstress,thehorizontalstressvalueshould
beusedinplaceof
inEqn.(9).
These procedures form the basis for the Rocscience software package ROCLAB, which can be
downloadedforfreefrom: http://www.rocscience.com/products/RocLab.asp.
Incarryingoutthesecalculations,itmustbeemphasizedthatthequantitativeconversionofHoek
BrowntoMohrCoulombparameters isdonebyfittinganaverage linearrelationshiptothenonlinear
HoekBrownenvelope forarangeofminorprincipalstressvaluesdefinedbyt
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Figure3.FittingoflinearMohrCoulombfailureenvelopesalongtwodifferentstressrangesofanonlinearHoekBrownfailureenvelope.Notethechangeincohesionandfrictionanglevaluesforthetwodifferent stressrangesspecified.
References
Barton,
N.,
Lien,
R.
&
Lunde,
J.
(1974).
Engineering
classification
of
rock
masses
for
the
design
of
tunnel
support. RockMechanics6(4):189236.Bieniawski, Z.T. (1989).EngineeringRockMassClassifications:ACompleteManualforEngineers and
GeologistsinMining,Civil,andPetroleumEngineering.NewYork:Wiley,272pp.Hoek,E.(2007).PracticalRockEngineering.Toronto:Rocscience,ebook.Hoek, E.& Brown, E.T. (1980). Underground Excavations in Rock. London: Institution ofMining and
Metallurgy,527pp.
Hoek,E.&Brown,E.T. (1988).TheHoekBrown failurecriterion a1988update. In J.H.Curran (ed.),
Proc.15thCanadianRockMech.Symp.,Toronto.Toronto:UniversityofToronto,pp.3138.Hoek, E., Kaiser, P.K. & Bawden, W.F. (1995). Support of Underground Excavations in Hard Rock.
Rotterdam:Balkema,215pp.
Hoek,E.,Wood,D.&Shah,S. (1992).AmodifiedHoekBrown criterion forjointed rockmasses. In J.
Hudson(ed.),
Rock Characterization: ISRM Symp, Eurock 92, Chester, UK. London: Thomas
Telford,pp.209213.
Marinos, P.&Hoek, E. (2000).GSI:A geologically friendly tool for rockmass strengthestimation. In
GeoEng2000,Melbourne.Lancaster:TechnomicPublishingCompany,CDROM.Marinos,V,Marinos,P.&Hoek,E. (2005).Thegeologicalstrength index:applicationsand limitations.
BulletinofEngineeringGeologyandtheEnvironment64(1):5565.Rocscience(2007).RocLab,version1.031.Toronto:Rocscience,Inc.
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