PART 05 - Rock Foundations and Slopes

7/31/2019 PART 05 - Rock Foundations and Slopes

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RockMechanicsMcaniquedesroches

CourseLectures

Part5 RockFoundationsandSlopes(a)

ProfessorZHAOJian

EPFLENACLMR

RockMechanicsandTunnelEngineering

Introduction

Rockfoundations(ofbuildings,bridges,anddams)

Rockslopes(andembankments)

Rocktunnels(caverns,mines,andhydropowers)


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Foundationengineeringinvolvesthedesignandanalysisoftype,loadcarryingandsettlementof

Introduction

TypesofRockFoundations

Introduction

adequaterocksurface. Foundationissupportedbybearingoftherock.

Socketed piles: Socketed orsinked intounderlyingadequaterock.Foundationis

su ortedb sidewallshearresistanceandendbearing.


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TypesofRockFoundations

Introduction

onadequaterocksurfacetosupportthegravityloadandwaterpressure.Foundationissupportedbybearingandslidingresistanceoftherock.

Tensionfoundations: Steelboltandcableanchoredintorocktosupporttension(uplift)loads. Foundationis

supportedbyshearresistanceoftheanchorandtherockmass.

FailureofRockFoundations

FailuresofRockFoundation

mass

Forheavilyfracturedandweakrockmassmayleadstogeneralwedgefailureoffoundation.

Foropenjoints,failureisbycompression.


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Oftenforarigidlayeroverlyingsoftmaterial.

(d)Breakingofpinnacles



(e)Collapseofshallowcaveandcavities.

(f)Slopefailurebyfoundationloadingor

byblocksliding.


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settlementofpiles.

(h)Creepfailurewhenathighstresslevel. Creepmayalsooccurduetodegradationofrocksub ectedtoweatherin .



massfailureatdamtoeunderhighwaterpressure.

(j)Failureofanchorgroutorrockmassaroundanchorbylarge

tensileload.


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InfluenceofGeologicalFeaturesonFoundationFailures

Features EffectonFoundation

Rocktype Strengthanddeformationcharacteristic bearingcapacityandsettlement.

Creeprock creepandtimedependentfailure.Stratigraph Layeredstructure punchingorshearingofrigidlayerofrockabovesoft

layer.

Fold Rocksurfaceinclinedduetofolding bearingsurfacemaybeinclined.

Rockhead contour drasticchangeofrocksurfaceandrocktype.

Fault Daylightingfault slopefailurewithfoundation.

Faultingofrockstructure drasticchangeofrocktype.

Faultwithinfill displacementduetocompressionofinfillmaterial.

Joint Openjoints failurebycompression.

Closelyspacedjoints generalwedgefailure.

Intersectingjointsets formingwedgeblockandshearalongthejoints.

Daylightingjoint slidingofrockblock.

Weathering Weatheredcavities punchingorshearofthinlayerofroofrock.

Weatheringofrock maycausecreepfailure.

Karst Karstic surface piletipbendinganddamage,failureofpinnacles.

Solutioncavities punchingorshearofthinlayerofroofrock.

InSituRockMassCompressiveStrength

RockFoundationDesignParameters

1 = 3 +(mb 3 ci +s ci2)a

mb =mi exp[(GSI100)/28]

Forrockmassesofreasonablequality,i.e.GSI>25,

, .

Forpoorrockmasses,i.e.,GSI


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Graniterockmass,GSI=75, ci=150MPa,a=0.5.mi forgraniteis32,

3 (MPa) 1 (MPa)

0 37

0.2 43

0.4 47

51

b i .

s=exp[(GSI 100)/9]=0.062

1 = 3 +(1956 3 +1395)0.5

cm =37MPa, tm =0.7MPa

.

0.8 55

1.0 59

1.2 63

1.5 67

2.0 75

0.7( tm)0

Siltstonerockmass,GSI=20, ci=65MPa,s=0.3 (MPa) 1 (MPa)

0 0.8

0.2 1.8

i

mb =mi exp[(GSI 100)/28]=0.40

GSI


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RockMassCohesionandFrictionfromRMR


strengthcriteria.

RMR c(MPa) (degree)< 20

0.4 >

45

c=4.5 =50

InSituRockMassDeformationModulus


Em =25logQ forQ>1

Em =10(Q ci/100)1/3

Em =2RMR 100 forRMR>50

Em =10(RMR10)/40 for20


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SurfaceFootingonUniformRockMass

1

BearingCapacityofFootFoundations

Maximumsupportisthestrength( 1)oftherockmassunderfootingintriaxial compression(red),whoseconfiningstress

3

1

equalstotheuniaxialstrength cmoftheadjacentrockmass(green).

cm3

Uniaxial

Triaxial


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Uniaxialstrengthoftherockmass(green): Uniaxial


cm = s

ci

Triaxial strengthoftherockmass(red):

1 = cm+(mb cm ci+s ci2)

cm

1

riaxial

cm

3 = cm3 = cm

1 = s

ci+(mbs

ci2+s ci

2)T

1

Allowablebearingcapacityofsurfacefooting


qa =Cf1 1 /FS

Cf1 istheshapecorrectionfactor,giveninChartF1. FSisfactorofsafety,23,typically3.

Foundation sha e C C B

ChartF1

Strip (L/B > 6) 1.0 1.0

Rectangular (L/B = 2) 1.12 0.9

Rectangular (L/B = 5) 1.05 0.95

Square 1.25 0.85

Circular 1.2 0.7

L


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RecessedFooting 1


1

massunderfoundationisintriaxial compression(red),whoseconfiningstress( 3)equalstothetriaxial strength( 1)oftheadjacentrock

1 3 isthesurchargepressure

3 =qs

,confiningstressisthe

surcharge

pressure

( 3).

33

Triaxial

Triaxial

1

Surchargepressure 3 =qs =unitweighttimetherecessdepth. Uniaxial

3 =qs


Triaxial strengthofmass(green):

1 =qs+(mbqs ci+s ci2)1/2

Triaxial strengthofmass(red):

1=

1+(m

b 1 ci+s

ci

2)1/2

1

1

riaxial

=

Allowablebearingcapacity

qa =Cf1 1 /FS (Cf1 inChartF1)

T3 1

1


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BearingCapacityofWeak/PoorRock(BellSolution)


a f1 c f2 q

istherockunitweight,crockmasscohesion,Cf2inChartF1.

Nc =2N (N +1), N =N (N 2 1), Nq =N

2

= 2 +

Nc,N ,Nq canalsobefoundchart.

BearingCapacityofWeakandPoorRockMass


large(>>weightofrockmass),theequationcanbesimplified:

qa =(Cf1cNc)/FS


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BearingCapacityofFootingonSlope

Chart F2


qa =(Cf1cNcq+Cf2B N q) /FS

istherockunitweight,crockmasscohesion,Cf2 inChartF1.

Ncq andN q arebearing

(USNavyDept,1982)

capac y ac ors, n ar .

StabilityNumber

N0 = H/c

StressDistributionbelowFootFoundation

SettlementofFootFoundations


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Distributionofverticalstressduetoaloadedcircularfootingonelasticmaterial:(a)alongverticallines;(b)alonghorizontallines.

(Winterkorn &Fang

1975)


(Winterkorn &Fang1975)

Stresscontoursforfootingsonelasticmaterial:(a)verticalnormalstressesbelowcirculararea;(b)radialstressesbelowlineload.


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(Winterkorn &Fang1975)

Verticalnormalstressbelowcircularareaoftwolayerselasticmaterials.

Radialstresscontourunderlineloadsontransverselyisotropicrock.

FootingonHomogeneousandIsotropicRockMass


=CdqD(12)/E

qistheuniformlydistributedbearingpressure,Dcharacteristicdimensionoftheloadedarea( forcircleandBfor

rectan le , andEPoissonsratioand

E,

D

Youngsmodulus.

Cd istheshapeandrigidityfactor,giveninChartF3.


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Cd forsettlementcalculations(Winterkorn &Fang1975)Shape Centre Corner MiddleofBside Middle ofLside Average

ChartF3

. . . . .

Circle(rigid) 0.79 0.79 0.79 0.79 0.79Square 1.12 0.56 0.76 0.76 0.95

Square(rigid) 0.99 0.99 0.99 0.99 0.99Rectangle (L/B=1.5) 1.36 0.67 0.89 0.97 1.15

Rectangle (L/B=2) 1.52 0.76 0.98 1.12 1.30

Rectan le L B=3 1.78 0.88 1.11 1.35 1.52. . . . .

Rectangle (L/B=5) 2.10 1.05 1.27 1.68 1.83

Rectangle (L/B=10) 2.53 1.26 1.49 2.12 2.25

Rectangle (L/B=100) 4.00 2.00 2.20 3.60 3.70

Rectangle (L/B=1000) 5.47 2.75 2.94 5.03 5.15

FootingonCompressibleLayeroverRigidBase


=CdqD(12)/E

qthebearingpressure,Ddimensionoftheloadedarea, andEPoissonsratioandYoungsmodulusofthe

compressiblelayer.

E,D

Cd istheshapefactor,giveninChartF4.


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Cd forsettlementofcentreonelasticlayeroverrigidbase(Winterkorn &Fang1975)

H/D Circle Rectangle

ChartF4

D ia me te r D L /B =1 L/ B=1.5 L/B=2 L/B=3 L/B=5 L/B=10 L/B=

0.1 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09

0.25 0.24 0.24 0.23 0.23 0.23 0.23 0.23 0.23

0.5 0.48 0.48 0.47 0.47 0.47 0.47 0.47 0.47

1.0 0.70 0.75 0.81 0.83 0.83 0.83 0.83 0.83

1.5 0.80 0.86 0.97 1.03 1.07 1.08 1.08 1.08

2.5 0.88 0.97 1.12 1.22 1.33 1.39 1.40 1.40

3.5 0.91 1.01 1.19 1.31 1.45 1.56 1.59 1.60

5.0 0.94 1.05 1.24 1.38 1.55 1.72 1.82 1.83

1.00 1.12 1.36 1.52 1.78 2.10 2.53

FootingwithCompressibleLayerbetweenStiffLayers


=CdqD(12)/E

E=(E1H1+E2H2)/(H1+H2)

Cd isgiveninChartF5.ItisthesameasChartF4,byreplacingH

E1

E2

H1

H2

1 2 .


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Cd forsettlementofelasticlayerbetweenstifflayers(Winterkorn &Fang1975)

(H1+H2)/Circle Rectangle

ChartF5

D Di am et er D L /B =1 L /B =1.5 L/B=2 L/B=3 L/B=5 L/B=10 L/B=

0.1 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09

0.25 0.24 0.24 0.23 0.23 0.23 0.23 0.23 0.23

0.5 0.48 0.48 0.47 0.47 0.47 0.47 0.47 0.47

1.0 0.70 0.75 0.81 0.83 0.83 0.83 0.83 0.83

1.5 0.80 0.86 0.97 1.03 1.07 1.08 1.08 1.08

2.5 0.88 0.97 1.12 1.22 1.33 1.39 1.40 1.40

3.5 0.91 1.01 1.19 1.31 1.45 1.56 1.59 1.60

5.0 0.94 1.05 1.24 1.38 1.55 1.72 1.82 1.83

1.00 1.12 1.36 1.52 1.78 2.10 2.53

FootingonStiffLayeroverCompressibleFormation


(i)Calculatesettlementasifallcompressiblebelow,withshapefactorCd fromChartF4.

=CdqD(1 22)/E2

E1

E2, 2

H D

, thecorrectionfactorafromChartF6,calculateactualsettlement

=a


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Correctionfactora forsettlementelasticlayerbelowstifflayer(Winterkorn &Fang1975)

H/D E1/E2

ChartF6

1 2 5 10 100

0 1.0 1.000 1.000 1.000 1.000

0.1 1.0 0.972 0.943 0.923 0.760

0.25 1.0 0.885 0.779 0.699 0.431

0.5 1.0 0.747 0.566 0.463 0.228

1.0 1.0 0.627 0.399 0.287 0.121

2.5 1.0 0.550 0.274 0.175 0.058

5.0 1.0 0.525 0.238 0.136 0.036

1.0 0.500 0.200 0.100 0.010

StressesbelowEccentricallyLoadedFooting


(i)ForeccentricdistanceeB/6,

q1 =(4/3Q)/(B 2e) Pressuredistributionq1

e


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SettlementofFoundationwithComplexFormationsandLoads


Stressdistributionandsettlementoffoundationsoncomplexformationand/orwithcomplexloadscanbecalculatedbynumericalmodelling,e.g.,FEM.

RockSocketed PileFoundations

(1)Pileinrockat

sidesandbase,

su ortedb

(2)Pileinrockat

sideswithloose

cuttin orweak

(3)Pileinsoilat

sidesandbaseon

oodrock,sidebothsidefriction

andendbearing.

UsuallyQs>Qb

seamatbase,

supportedbyside

frictiononly.

Qb=0

frictionissmall,

supportedmainly

byendbearing.

Qb>>Qs


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SideFrictionandEndBearingofPileFoundation


and/orsidefriction.

SideFriction:needtoestimaterockconcreteshearresistance.

EndBearing:userockmassstrengthtoestimate.

Settlement:needtoconsiderdisplacementsofbothrockmassandconcrete.

SideFrictionofPileFoundation


Qs = s DL/FS

s issidewallshearresistance,Dpilediameter,Lsocketlength

= a s m s

m(s) isrockmassuniaxial compressivestrength,Rissocketwallroughnesscoefficient,0.3forundulating>10mm,0.25forundulating


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EndBearingofPileFoundation


Qb = D2 1m(b) /FS

1m(b) triaxial compressivestrengthofrockmassbelowpile,Dpilediameter.

HoekBrowncriterion.

SettlementofFrictionPileQ

Ec


m(s)

Qappliedload,Dpilediameter,Em(s) surroundingrockmassmodulus.

Iisthesettlementinfluence

D

Em(s)

R=Ec/Em(s)

ChartP1

, .

(Pell&Turner1979)


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SettlementofEndBearingPile2 2 2


c d m(b)

Qappliedload,Dpilediameter,Ldepthtopileend,Ec ofconcrete,

andEm(b) ofrockmass.Cdshapefactor(ChartF4).

,RF

Deformationofpile Deformationofrockmassbelowpile

ReductionfactorRFisgivenin

ChartP2.(Pell&Turner1979)

Reduc

tion

factor

Q

L

D

Em(b)

Ec ChartP2

SettlementofSideFrictionandEndBearingPile


m(s)

Qistheappliedload,Dpilediameter,Em(s) socketrockmassmodulus,IthesettlementinfluencefactorgiveninChartP3.

UseChartP3toestimatepercentageofloadcarried

yen ear ng. ec en ear ngan s e r c onthatdonotexceedtheallowablecapacities.


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I II

ChartP3

ChartP3

ChartP3

Influencefactorandendbearingratiosforsocketpilefoundations.

QbQ (%)Qb

Q (%)

b

Q (%)

L/B

L/B

L/B(Rowe&Armitage 1987)

FoundationforGravityDams

DamFoundations

rock.Thefoundationmustbestrongenoughtocarrytheweightofthedam,andthewaterpressuresactingonthedam.

Footingbearingisusuallynotacommonproblem.Themostcommondamfoundationfailureistheslidingmovementunderhighwaterpressure.


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SlidingResistancealongtheSurface

DamFoundations

FS=totalresistance/slidingload

FS=[cA +( V u)tan ]/ H

c=cohesion, =frictionangle

ii Oninclinedsurface

A, base area

,pressure

, we g

u, water uplift

Toresultresistanceandslidingforcesalongtheslidingplane.

FS=totalresistance/slidingload Inclined base

RecessedDamFooting

DamFoundations

rockmassstrengthattoe)/slidingload

(i)Slidingresistance=cA +( V u)tan

c=cohesion, =frictionangle

cm

cm ci

s=exp[(GSI100)/9](forgenerallygoodrockmass)

ci =uniaxial compressivestrengthofrockmaterial

(iii)Slidingload(horizontalwater)= H


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DamStabilityandDisplacement

DamFoundations

geometry,loadingandrockmass,numericalmodellingareusuallyused. Numericalmodellingcanalsoincludethefoundationreinforcement.

TensionFoundationswithAnchors

TensionFoundations

rockmassandgrouted,toprovidetensileloadsupportstructures.E.g.,anchorroofprotectingrockfallonslope,tiedownstopreventdamoverturning,rockanchorto

bridge.


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LoadBearingCapacityofAnchor

TensionFoundations

throughthesteelgroutandgroutrocktothesurroundingrockmass,throughshearresistancebetweenthosematerials. Theoverallloadis

Rockmass

,canbefailedbythepulloutoftheconeblock.

byanchor

DesignPrincipleofAnchorFoundation

TensionFoundations

sufficientsizetocarrythedesignedload(checkwithsteelproductsspecifications).

(ii)Bondlengthofanchorsocket:Estimatingtherequiredbondlengthbasedonbondstrengths

betweensteelgroutrock.(iii)Rockmassstrength:Estimatingsizeofmobilisedrockmassandstrengthoftherockmass,includingtheweight.


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AnchorBonding

TensionFoundations

,bonding(bytests).Theanchorbondingisgovernedbygroutrockbonding.Allowableloadcapacityofanchorduetobondingisdefinedas:

Qa = DLb ult = DLbc/20

s ee e c v e ame ero e ore o e, b eng o egroutedanchorbond. ult istheultimategroutbondstrength(failuretestsorgroutproductsspecifications),or

1/10 c(ofrockorgrout,lowerone).

LocationofRockMassFailure

TensionFoundations

Forcompetentrockmass,thepotentialfailureisinitiatedatthebaseoftheanchor.

Forpoor/weakrockmass,thepotentialfailureisinitiatedatthemidpointofthebondedsection.


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UpliftCapacityofRockAnchor

TensionFoundations

theweightofthecone(Wc)andtherockstrengthalongtheconesurface(Fr).

Wc = r L3tan2

30forpoorrock,

r

L tm

Q

r = tm cos

Upliftcapacity

Q=(fr +Wccos )/FS

45forgoodrockQ

LoadBearingCapacityofRockMasses

TensionFoundations

Theloadbearingcapacityoftheanchortensionfoundationdependsonrockfracturesystems. Thesizeanddimensionoftheconeisinfluencedbythe

.strengthoftherockmassgreatlyreducedbytheexistenceofthefractures.


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SteeplyInclinedUpliftofAnchor

TensionFoundations

,lowerpartoftheconeisundershearresistance,whileotherpartistensilefailure.

Fromcompetentrockmassenerall >> .

tm

OtherConditionsofAnchor

TensionFoundations

tm

,directionoftheconeweightneedtobeanalysed,andthelowerhalfoftheconeisundershearresistance.

Withgroundwater,thebuoyant

Q

Q

effectsneedtobeconsidered.Theconeshouldtaketheeffectiveweight.

r

GW


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Rock MechanicsMcanique des roches

Course Lectures

Part 5 Rock Foundations and Rock Slopes (b)

Professor ZHAO Jian

EPFLENACLMR

RockMechanicsandTunnelEngineering

Introduction

Slopeengineeringinvolvesthedesignandanalysis

ofslopeexcavation,supportandconstruction.


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Slopescanbedividedintonaturalslopesandexcavatedslopes.

Introduction

FailureofRockSlopes

Introduction

(a)CircularFailure

Usuallyoccursinwasterock,heavilyfracturedrockandweakrockwithnoidentifiablestructuralpattern.

(b)PlaneFailure

Occursinrockswithplanediscontinuities,e.g.,beddingplanes.


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FailureofRockSlopes

Introduction

(c)WedgeFailure

Occursinrockswithintersectingdiscontinuitiesformingwedges.

Occursinrockswithcolumnar

orblockstructuresseparatedbysteeplydippingjoints.

CircularFailure

AnalysisofCircularFailure

fracturedorcrushedthatnostructuralpatternexists. Thefailuresurfaceisfreetofindalineofleastresistancethroughtheslope. Theslideiscontrolledby

, . .,andfriction( ).


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Useclassicalsoilmechanicanalysismethods,e.g.,limitequilibriummethods(e.g.,Jambus andBisho s slice methods .


Note:Theequilibriumcannotbesatisfiedwithoutanyassumptions. Pleaserefertothesoilmechanicstextbookforfurtherinformation.

Itisaniterativemethodwhichmeansthatanumberoffailureplanehavetobechosenandthe


equilibriumcalculated.Thelowestfactorofsafety(FOS)istheonefortheslope.

cand arecohesionandfrictionangleoftherockmass.


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Nowadays,analysisaregenerallydonebynumericalmodellingwithcommercialsoftware.Chartsexist


butrelyonmanyassumptions:

a) Rockmassishomogenous;

b) Rockmassshearstrengthischaracterizedbycohesionandfrictionangle;

c) Failureoccursoncircularslidesurface;

d) Averticaltensioncrackoccursintheuppersurfaceorinthefaceoftheslope;

e) Fullysaturatedordryrockmass.

Circularfailure,fully

drained,rockmass

unitweight18.9

kN/m3.

Chartsexistfor

othergroundwater

conditions.


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PlaneFailureTherockmassiscutby

AnalysisofPlaneFailure

a) Theslidingplaneareparallelornearparallel(within20 )totheslopeplane.

" "

Day l ighting

discontinuitiesthatparalleltotheslope.Rockblocksslidealongtheplanes.

es ngp ane ay g n es ope ace, .e., pangleofslidingplanefrictionangleofslidingplane.

d) Lateralresistancetoslidingisnegligible.

HemisphericalProjectionMethod


slidingplanemusthavethesamegeneraldirection( 20 ). Theslidingplanehasasmallerdipangle(red)thanslopedip(blue),butgreaterthanfrictionangle

.


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Whenjointdipangleisgreaterthanslope,joint

N

Slope ,nopotentialslidingplaneexist.

Joint


Whenjointdip


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AnalyticalMethod


resolvingallforcesactingontheslopeintocomponentsparallelandnormaltotheslidingplane.


Tensioncrackfilledwithwater,rockmassimpermeable

H =slopeheight; z =tensioncrackdepth;b=distancebetweencrackandslopecrest; U=waterforcesactingontheslidingplane; W=slidingblockweight; V=waterforcesintensioncrack.


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Criticaltensioncrackdepthandlocation


Groundwaterplaysanimportantroleforslopestability. Pleaserefertotheliteratureformoredetail.

WedgeFailure

AnalysisofWedgeFailure

wedgethatare"daylighting"intheslopeface,i.e.,plungeofthelineofintersectionofthejoint(sliding)planesfrictionangleoftheslidingplanes.

Daylighting


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WedgeFailureAnalysisbyProjectionMethod


,analysiscanbecarriedoutusingprojectionmethod. Thefailureofwedge/blockisalongtheexistingjointsandiscontrolledbytheorientationofthosejointsandfrictionangle. Orientationsand

byprojectionandanalysiscanbeperformed.


NWedgefailureby

slidin alon both

Friction

plane(lineof

intersection

Lineofintersection

Directionofsliding


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NWedgehaspotentialtoslidealon theline

Friction

ofintersection,but

heldbyfriction.

Lineofintersection

Directionofpossiblesliding


NWedgefailureby

slidin alon lane1.

Friction

Lineofintersection

isnotdaylighted.

Joint1isdaylighting.

Directionofsliding


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NLineofintersectionandboth lanesare

Friction

notdaylighted,no

failurebysliding. Lineofintersection

WedgeFailureAnalysisbyAnalyticalMethod


,analysiscanbecarriedoutusinganalyticalmethodsimilartotheplanefailure,butwithmorecomplicatedforceequations. Suchanalysisisonlycarriedoutwhenaspecificwedgeisidentified.

Numericalmethodsareoftenemployedtoanalysewedgestability.


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Assumptions:(i)slidingisresistedonlybyfriction;(ii)frictionanglesforbothplanesarethesame


WedgefactorKmaybeestimatedwiththechartbelow.



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Twodifferentfrictionanglesshouldbeusedforeachslidingplane.


ThedimensionlessfactorsAandBarefoundtodependuponthedipsanddipdirectionsofthetwoplanes.Theymaybefoundinaseriesofcharts.

Thefollowingchartisforadifferenceindipsof10.



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ThisFOSformulationisoversimplistic,includingthefrictiononly.Cohesionsand shouldbeincorporated


intheFOSformulationandthuswillbemorecomplex.

Theformulationissocomplexthatitwillnotbepresentedhereinthislecture.

TopplingFailure

AnalysisofTopplingFailure

dippingdiscontinuities.Rockblockwidth/height


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Determiningrockslopetopplingorsliding

4


a ure

W sin1

2

3

idth/HeightRatio,

b/h

=

Toppling only

b / h > t an

WW cos

0

0 10 20 30 40 50 60 70 80

Base plane angl e , degree

W

Sliding & Toppling>

b / h < t a n

slideplaneangle,noslide;b/h>tan ,gravitycentrallineinside,notoppling;


> ,slideplaneangle>frictionangle,slide;b/h>tan ,gravitycentrallineinside,notoppling;SlidingOnly

slideplaneangle,noslide;

b/h ,slideplaneangle>frictionangle,slide;b/h


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ConditionstoToppling


(b)Aprimarysetofjointsdipsteeplyintothefacecreatingcolumns.

(c)Asecondarysetofjointswidelyspreadandorthogonaltotheprimaryset.

e oc may opp e ecauseo a ossoequilibriumofarockblockorbyflexuralfailureofa

column.

Theprimejointsetdipssteeplyandinoppositedirectiontotheslope


Joint

poles


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TopplingFailureAnalysisbyAnalyticalMethod


Theblockcannotslideif


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LimitEquilibriumAnalysis


Forcesonbase:normalandshear(Rn ,Sn)Interfaceforces:(Pn ,Qn,Pn1,Qn1)



Pointsofapplication:(Mn ,Ln)


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.

(ii) Checktopplingbyblockshapetest.

(iii) Forthefirsttopplingblock,lateralforcestopreventtopplingPn1,tandslidingPn1,sarecalculatedas:



Slidingwilloccurif

(v)Checkthatslidingdoesnotoccur


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EstimatingSlopeFailurebyRockMassRating

AnalysisbyRockMassRating

quality. RMRsystemprovidesqualityratingfortherockmassoftheslope.

However,adjustmentforjointorientationmustbeappliedwithrespecttotheorientationofslope.


Adjustment ofRMRwithConstruction

,mayrepresentdifferentquality(ordegreeofdifficultforconstruction)inrelationtoaproject.

StableslopeUnstableslope


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(a)BasicRMRrating

RockMassRating(RMR)rockmassclassificationsystem

Basic RMRratingisthesumofratingsoffiverockparameters:(i)rockmaterialstrength,(ii)RQD,

(iii)jointspacing,(iv)jointconditionand,(v)groundwatercondition.

RMRratings >81 61 80 41 60 21 40


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RMR(slope) adjustments for sliding failure


AdjustmentVery

favourableFavourable Fair Unfavourable

Veryunfavourable

Jointdipdirection slopedipdirection

< 30or>30

30~ 2030~20

20~ 1020~10

10~ 510~5

5~5

A 0.15 0.40 0.70 0.85 1.00

Joint dipangle 45

B 0.15 0.40 0.70 0.85 1.00

Jointdipangleslopedipangle

>10 10~0 0 0~ 10 < 10

C 0 6 25 50 60

Slopeformation Naturalslope PresplittingSmoothblasting

Blasting/ripping

Deficientblasting

D +15 +10 +8 0 8

Jointdipdirection Slopedipdirection

Jointplaneparalleltotheslopeface(0)leadsto


highpotentialofplaneandblocksliding.

Jointdip

Slidingfailureoccurswhenjointhassteepdipangle(>frictionangle).

Joint di Slo e diJointdip


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Slope rock mass quality based on RMR(slope)


RMR(Slope) SlopeRock Slope SlopeFailure SupportRating MassQuality Stability Mode Requirements

>81 VerygoodCompletely

stableNone None

61~80 Good Stable Someblocks Spot

41~60 Fair PartiallystableSomejointsor

Systematic

21~40 Poor UnstablePlanarorlarge

wedgesImportant/Corrective


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SmoothBlasting

RockSlopeExcavationandSupport

drilledalongthefinalslopeface,withholespacing60~100cm.

Chargesarelight.

mainblast.

PreSplittingBlasting


face,withholespacing50~80cm.

Chargesareverylight.

Chargesaredecoupledfromholewalls,leaving

Rowisfiredbeforethemainblast.


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SlopeSupportandProtection


Nonesupport/reinforcementScaling

Protection:ToeditchingFences(attoeoronslope)Nets(overtheslopeface)

Reinforcement:Bolts

Anchors

SlopeSupportandProtection


ShotcreteDentalconcreteRibsand/orbeamsToewalls

Drainage:SurfaceDeep

Reexcavation:MethodOrientation


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Rockboltsarethemostcommonrockslope


suppor me o .

Boltlength:Normally3~4m;1~2minsolidrockafterunstablejoint(>slopeheight/10)

Bolt diameter:normally20~25mm

Boltstrength:120~150kN

Resin ExpansionshellSteelbolt

Blockyhardrock(averagejointspacing>1m):Systematicbolting3~4mspacing.

~


. Systematicbolting1~3mspacing(3xthetypicaljointspacing).

Veryfracturedhardrock(averagejointspacing


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1. Preliminarycollectionofgeologicaldatafromairphotos,surfacemappingandboreholecores.

2. Preliminaryanalysisofgeologicaldatatoestablishmajorgeologicalpatterns. Examinationofthesepatternsinrelationtoproposedslopestoassessprobabilityof

slidesdeveloping.

3. Slopesinwhichnounfavourablediscontinuitiesexistorslopesinwhichfailurewouldnotmatteridentified. Nofurtherstabilityanalysisofthoseslopesrequired. Slope

anglesdetermined

from

operational

considerations.

4. Slopesinwhichunfavourablediscontinuitiesexistidentifiedandthoseslopesinwhich failure would be critical at any stage of the excavation operation marked for

anal

ysis

detailedstudy.

5. Detailedgeologicalinvestigationofcriticalslopeareasonbasisofsurfacemappinganddrillcorelogging. Specialdrillinginthevicinitymayberequired.

6. Sheartestingofdiscontinuitysurfaces,particularlyifclaycoveredorslickensided.

7. Installationofpiezometers indrillholestoestablishgroundwaterflowpattersandpressuresandtomonitorchangesingroundwaterlevelsduringexcavation.

8. Reanalysecriticalslopeareasonbasisofdetailedinformationfromsteps5,6and7,usinglimitedequilibriumtechniquesfircircular,planeorwedgeslides. Examinepossibilityofothertypesoffailureinducedbyweathering,toppingordamageduetoblasting.

k

slope

stability

9. Examineslopesinwhichriskoffailureishighintermsofslopedesign. Optionsare:a) Flattenslopes;b) Stabiliseslopesbydrainage,and/orrockbolts;c) Acceptriskoffailureandimplementmonitoringprogrammeforfailureprediction.

10. Stabilisationofslopesbydrainageorreinforcementfeasibleifcostsavingresultingfromsteepeningofslopesexceedscostofdesigningandconstructionstabilisationsystem. Additionalfieldmeasurementsrequiredtoestablishdrainagecharacteristicsofrockmass.

11. Acceptingriskoffailureonbasisofabilitytopredictandtoaccommodateslopewithoutendangeringmanandequipment. Mostreliablepredictionmethodbaseduponmeasurementofslopedisplacement.

Roc

Largescalerocksliding


downofthewedgeformedbytwointersectingdiscontinuities.


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ExampleAroadrunningeastwestistocutthrougharockhillof

RockSlopeAnalysisExample

blockyrock.Theestimatedrockmassqualityisgoodwith

RMRat65. Therockmasshas3jointsets(025/10,165/46,

220/75). Estimatedaveragejointfrictionangleis40.Slopes

aretobecutatanangleof60onbothsidesoftheroad.

J1

AnalysisPlotjoints(J1,J2,J3),

slopes(Ssfacing

south,Sn facing

north).

Sn

Ss

Note ntersect onso

J1,J2andJ3.I(23)

daylightsonSs,I(12)

andI(13)daylighton

Sn,butaresub

horizontal,Sn stable.

DrawfrictioncircleF.

J3NoteI(23)andJ2in

theareaofSsandF,

i.e.,daylightand

steeper,plane/wedge

sliding,Ssnotstable.


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J1

RedesignPossibleredesign:

70

angle.Sn notsuffer

fromsliding.Steep

an lesavesexcavation

RedesignSs

RedesignSs

J3volume.

AnalysisbyRMR(Slope)


D(smoothbasting)=+8

Adjustment=9 +8= 1

RMR(s)=65 1=64(good)

Sn slopegenerallystable.

J1 J2 J3

25 165 80

A 0.4 0.15 0.15

10 46 75

B 0.15 1.0 1.0

50 14 15

C 60 60 0

A*B*C 4 9 0


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AnalysisbyRMR(Slope)


D(smoothbasting)=+8

Adjustment=42 +8= 34

RMR(s)=65 34=31(poor)

Ssslopeunstableandtobe

J1 J2 J3

155 15 40

A 0.15 0.7 0.15

10 46 75

B 0.15 1.0 1.0

50 14 15

redesignedorheavily

supported.

C 60 60 0

A*B*C 1 42 0

Documents

PART 05 - Rock Foundations and Slopes