8/12/2019 GSI and Hoek-Brown Procedure

1/5

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.

8/12/2019 GSI and Hoek-Brown Procedure

2/5

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(

8/12/2019 GSI and Hoek-Brown Procedure

3/5

Figure2.GeologicalStrengthIndex(GSI)lookupchartforjointedrockmasses(afterMarinos&Hoek2000).

8/12/2019 GSI and Hoek-Brown Procedure

4/5

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

8/12/2019 GSI and Hoek-Brown Procedure

5/5

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.